LMFDB - Embedded newform 552.2.t.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	552.19
Dual form			552.2.t.a.523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40793 - 0.133210i) q^{2} +(0.959493 - 0.281733i) q^{3} +(1.96451 + 0.375100i) q^{4} +(2.14099 + 1.37593i) q^{5} +(-1.38842 + 0.268844i) q^{6} +(0.0311079 + 0.216360i) q^{7} +(-2.71592 - 0.789806i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-1.40793 - 0.133210i) q^{2} +(0.959493 - 0.281733i) q^{3} +(1.96451 + 0.375100i) q^{4} +(2.14099 + 1.37593i) q^{5} +(-1.38842 + 0.268844i) q^{6} +(0.0311079 + 0.216360i) q^{7} +(-2.71592 - 0.789806i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-2.83107 - 2.22241i) q^{10} +(-0.918624 - 0.419522i) q^{11} +(1.99061 - 0.193561i) q^{12} +(4.57257 + 0.657437i) q^{13} +(-0.0149762 - 0.308763i) q^{14} +(2.44191 + 0.717010i) q^{15} +(3.71860 + 1.47378i) q^{16} +(2.49400 - 2.16106i) q^{17} +(-1.25644 + 0.649119i) q^{18} +(0.735339 + 0.637175i) q^{19} +(3.68989 + 3.50612i) q^{20} +(0.0908035 + 0.198832i) q^{21} +(1.23747 + 0.713025i) q^{22} +(-3.97924 + 2.67687i) q^{23} +(-2.82842 + 0.00734944i) q^{24} +(0.613586 + 1.34357i) q^{25} +(-6.35027 - 1.53474i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.0200449 + 0.436710i) q^{28} +(-4.35776 + 3.77602i) q^{29} +(-3.34252 - 1.33478i) q^{30} +(-0.0121013 + 0.0412134i) q^{31} +(-5.03919 - 2.57032i) q^{32} +(-0.999606 - 0.143722i) q^{33} +(-3.79924 + 2.71039i) q^{34} +(-0.231095 + 0.506028i) q^{35} +(1.85545 - 0.746540i) q^{36} +(5.05067 - 3.24587i) q^{37} +(-0.950425 - 0.995050i) q^{38} +(4.57257 - 0.657437i) q^{39} +(-4.72804 - 5.42789i) q^{40} +(0.956371 + 0.614622i) q^{41} +(-0.101358 - 0.292037i) q^{42} +(1.16468 + 3.96653i) q^{43} +(-1.64728 - 1.16873i) q^{44} +2.54500 q^{45} +(5.95906 - 3.23876i) q^{46} +7.88755i q^{47} +(3.98318 + 0.366426i) q^{48} +(6.67061 - 1.95867i) q^{49} +(-0.684907 - 1.97338i) q^{50} +(1.78413 - 2.77616i) q^{51} +(8.73626 + 3.00671i) q^{52} +(-0.00681027 - 0.0473665i) q^{53} +(-1.02267 + 0.976805i) q^{54} +(-1.38953 - 2.16216i) q^{55} +(0.0863960 - 0.612186i) q^{56} +(0.885066 + 0.404196i) q^{57} +(6.63841 - 4.73586i) q^{58} +(1.48915 - 10.3573i) q^{59} +(4.52821 + 2.32454i) q^{60} +(-4.05595 - 1.19094i) q^{61} +(0.0225278 - 0.0564134i) q^{62} +(0.143143 + 0.165196i) q^{63} +(6.75241 + 4.29009i) q^{64} +(8.88526 + 7.69912i) q^{65} +(1.38823 + 0.335507i) q^{66} +(3.56929 - 1.63004i) q^{67} +(5.71009 - 3.30993i) q^{68} +(-3.06389 + 3.68952i) q^{69} +(0.392773 - 0.681666i) q^{70} +(-3.08567 + 1.40918i) q^{71} +(-2.71178 + 0.803909i) q^{72} +(1.99101 - 2.29775i) q^{73} +(-7.54334 + 3.89714i) q^{74} +(0.967258 + 1.11627i) q^{75} +(1.20558 + 1.52756i) q^{76} +(0.0621913 - 0.211804i) q^{77} +(-6.52542 + 0.316509i) q^{78} +(0.547454 - 3.80762i) q^{79} +(5.93368 + 8.27189i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.26462 - 0.992740i) q^{82} +(-6.75806 - 10.5157i) q^{83} +(0.103803 + 0.424668i) q^{84} +(8.31310 - 1.19524i) q^{85} +(-1.11140 - 5.73973i) q^{86} +(-3.11741 + 4.85079i) q^{87} +(2.16357 + 1.86492i) q^{88} +(2.30896 + 7.86360i) q^{89} +(-3.58318 - 0.339020i) q^{90} +1.00977i q^{91} +(-8.82136 + 3.76612i) q^{92} +0.0429533i q^{93} +(1.05070 - 11.1051i) q^{94} +(0.697646 + 2.37596i) q^{95} +(-5.55921 - 1.04650i) q^{96} +(-10.3029 + 16.0316i) q^{97} +(-9.65263 + 1.86907i) q^{98} +(-0.999606 + 0.143722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{15}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40793	−	0.133210i	−0.995554	−	0.0941938i
$2$	−1.40793	−	0.133210i	−0.995554	−	0.0941938i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	1.96451	+	0.375100i	0.982255	+	0.187550i
$5$	2.14099	+	1.37593i	0.957481	+	0.615336i	0.923300	−	0.384080i	$-0.125481\pi$
$5$	2.14099	+	1.37593i	0.957481	+	0.615336i	0.0341814	+	0.999416i	$0.489118\pi$
$6$	−1.38842	+	0.268844i	−0.566822	+	0.109755i
$7$	0.0311079	+	0.216360i	0.0117577	+	0.0817765i	0.994855	−	0.101305i	$-0.0323018\pi$
$7$	0.0311079	+	0.216360i	0.0117577	+	0.0817765i	−0.983098	+	0.183082i	$0.941393\pi$
$8$	−2.71592	−	0.789806i	−0.960222	−	0.279238i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−2.83107	−	2.22241i	−0.895263	−	0.702789i
$11$	−0.918624	−	0.419522i	−0.276976	−	0.126491i	0.272085	−	0.962273i	$-0.412287\pi$
$11$	−0.918624	−	0.419522i	−0.276976	−	0.126491i	−0.549060	+	0.835783i	$0.685014\pi$
$12$	1.99061	−	0.193561i	0.574640	−	0.0558762i
$13$	4.57257	+	0.657437i	1.26820	+	0.182340i	0.743379	−	0.668870i	$-0.233222\pi$
$13$	4.57257	+	0.657437i	1.26820	+	0.182340i	0.524825	+	0.851210i	$0.324131\pi$
$14$	−0.0149762	−	0.308763i	−0.00400257	−	0.0825204i
$15$	2.44191	+	0.717010i	0.630499	+	0.185131i
$16$	3.71860	+	1.47378i	0.929650	+	0.368444i
$17$	2.49400	−	2.16106i	0.604883	−	0.524134i	−0.297695	−	0.954661i	$-0.596218\pi$
$17$	2.49400	−	2.16106i	0.604883	−	0.524134i	0.902578	+	0.430527i	$0.141672\pi$
$18$	−1.25644	+	0.649119i	−0.296146	+	0.152999i
$19$	0.735339	+	0.637175i	0.168698	+	0.146178i	0.735118	−	0.677939i	$-0.237127\pi$
$19$	0.735339	+	0.637175i	0.168698	+	0.146178i	−0.566420	+	0.824117i	$0.691672\pi$
$20$	3.68989	+	3.50612i	0.825085	+	0.783992i
$21$	0.0908035	+	0.198832i	0.0198150	+	0.0433887i
$22$	1.23747	+	0.713025i	0.263829	+	0.152017i
$23$	−3.97924	+	2.67687i	−0.829729	+	0.558166i
$23$	−3.97924	+	2.67687i	−0.829729	+	0.558166i
$24$	−2.82842	+	0.00734944i	−0.577348	+	0.00150020i
$25$	0.613586	+	1.34357i	0.122717	+	0.268713i
$26$	−6.35027	−	1.53474i	−1.24539	−	0.300986i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.0200449	+	0.436710i	−0.00378813	+	0.0825305i
$29$	−4.35776	+	3.77602i	−0.809216	+	0.701190i	−0.957714	−	0.287723i	$-0.907102\pi$
$29$	−4.35776	+	3.77602i	−0.809216	+	0.701190i	0.148497	+	0.988913i	$0.452556\pi$
$30$	−3.34252	−	1.33478i	−0.610258	−	0.243697i
$31$	−0.0121013	+	0.0412134i	−0.00217347	+	0.00740215i	−0.960573	−	0.278029i	$-0.910319\pi$
$31$	−0.0121013	+	0.0412134i	−0.00217347	+	0.00740215i	0.958399	+	0.285432i	$0.0921369\pi$
$32$	−5.03919	−	2.57032i	−0.890812	−	0.454373i
$33$	−0.999606	−	0.143722i	−0.174009	−	0.0250187i
$34$	−3.79924	+	2.71039i	−0.651564	+	0.464827i
$35$	−0.231095	+	0.506028i	−0.0390622	+	0.0855344i
$36$	1.85545	−	0.746540i	0.309241	−	0.124423i
$37$	5.05067	−	3.24587i	0.830324	−	0.533617i	−0.0550566	−	0.998483i	$-0.517534\pi$
$37$	5.05067	−	3.24587i	0.830324	−	0.533617i	0.885381	+	0.464866i	$0.153898\pi$
$38$	−0.950425	−	0.995050i	−0.154179	−	0.161418i
$39$	4.57257	−	0.657437i	0.732198	−	0.105274i
$40$	−4.72804	−	5.42789i	−0.747569	−	0.858224i
$41$	0.956371	+	0.614622i	0.149360	+	0.0959878i	0.613186	−	0.789938i	$-0.289887\pi$
$41$	0.956371	+	0.614622i	0.149360	+	0.0959878i	−0.463826	+	0.885926i	$0.653524\pi$
$42$	−0.101358	−	0.292037i	−0.0156399	−	0.0450622i
$43$	1.16468	+	3.96653i	0.177612	+	0.604891i	0.999385	+	0.0350753i	$0.0111671\pi$
$43$	1.16468	+	3.96653i	0.177612	+	0.604891i	−0.821773	+	0.569815i	$0.807015\pi$
$44$	−1.64728	−	1.16873i	−0.248337	−	0.176193i
$45$	2.54500			0.379387
$46$	5.95906	−	3.23876i	0.878616	−	0.477529i
$47$			7.88755i			1.15052i	0.817972	+	0.575259i	$0.195099\pi$
$47$			7.88755i			1.15052i	−0.817972	+	0.575259i	$0.804901\pi$
$48$	3.98318	+	0.366426i	0.574923	+	0.0528891i
$49$	6.67061	−	1.95867i	0.952944	−	0.279810i
$50$	−0.684907	−	1.97338i	−0.0968605	−	0.279078i
$51$	1.78413	−	2.77616i	0.249828	−	0.388740i
$52$	8.73626	+	3.00671i	1.21150	+	0.416956i
$53$	−0.00681027	−	0.0473665i	−0.000935463	−	0.00650629i	0.989348	−	0.145567i	$-0.0465007\pi$
$53$	−0.00681027	−	0.0473665i	−0.000935463	−	0.00650629i	−0.990284	+	0.139061i	$0.955592\pi$
$54$	−1.02267	+	0.976805i	−0.139168	+	0.132926i
$55$	−1.38953	−	2.16216i	−0.187365	−	0.291545i
$56$	0.0863960	−	0.612186i	0.0115452	−	0.0818068i
$57$	0.885066	+	0.404196i	0.117230	+	0.0535371i
$58$	6.63841	−	4.73586i	0.871666	−	0.621849i
$59$	1.48915	−	10.3573i	0.193871	−	1.34840i	−0.627769	−	0.778399i	$-0.716032\pi$
$59$	1.48915	−	10.3573i	0.193871	−	1.34840i	0.821641	−	0.570006i	$-0.193059\pi$
$60$	4.52821	+	2.32454i	0.584590	+	0.300096i
$61$	−4.05595	−	1.19094i	−0.519311	−	0.152484i	0.0115645	−	0.999933i	$-0.496319\pi$
$61$	−4.05595	−	1.19094i	−0.519311	−	0.152484i	−0.530876	+	0.847450i	$0.678137\pi$
$62$	0.0225278	−	0.0564134i	0.00286104	−	0.00716451i
$63$	0.143143	+	0.165196i	0.0180343	+	0.0208127i
$64$	6.75241	+	4.29009i	0.844052	+	0.536262i
$65$	8.88526	+	7.69912i	1.10208	+	0.954959i
$66$	1.38823	+	0.335507i	0.170879	+	0.0412981i
$67$	3.56929	−	1.63004i	0.436059	−	0.199141i	−0.185276	−	0.982686i	$-0.559318\pi$
$67$	3.56929	−	1.63004i	0.436059	−	0.199141i	0.621335	+	0.783545i	$0.286591\pi$
$68$	5.71009	−	3.30993i	0.692450	−	0.401387i
$69$	−3.06389	+	3.68952i	−0.368849	+	0.444166i
$70$	0.392773	−	0.681666i	0.0469454	−	0.0814747i
$71$	−3.08567	+	1.40918i	−0.366202	+	0.167239i	−0.590013	−	0.807394i	$-0.700877\pi$
$71$	−3.08567	+	1.40918i	−0.366202	+	0.167239i	0.223811	+	0.974633i	$0.428150\pi$
$72$	−2.71178	+	0.803909i	−0.319586	+	0.0947416i
$73$	1.99101	−	2.29775i	0.233030	−	0.268931i	−0.627176	−	0.778878i	$-0.715789\pi$
$73$	1.99101	−	2.29775i	0.233030	−	0.268931i	0.860206	+	0.509946i	$0.170335\pi$
$74$	−7.54334	+	3.89714i	−0.876896	+	0.453033i
$75$	0.967258	+	1.11627i	0.111689	+	0.128896i
$76$	1.20558	+	1.52756i	0.138289	+	0.175223i
$77$	0.0621913	−	0.211804i	0.00708736	−	0.0241373i
$78$	−6.52542	+	0.316509i	−0.738859	+	0.0358376i
$79$	0.547454	−	3.80762i	0.0615933	−	0.428391i	−0.935571	−	0.353138i	$-0.885115\pi$
$79$	0.547454	−	3.80762i	0.0615933	−	0.428391i	0.997164	−	0.0752529i	$-0.0239764\pi$
$80$	5.93368	+	8.27189i	0.663406	+	0.924825i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−1.26462	−	0.992740i	−0.139654	−	0.109630i
$83$	−6.75806	−	10.5157i	−0.741793	−	1.15425i	−0.982969	−	0.183771i	$-0.941169\pi$
$83$	−6.75806	−	10.5157i	−0.741793	−	1.15425i	0.241176	−	0.970481i	$-0.422467\pi$
$84$	0.103803	+	0.424668i	0.0113258	+	0.0463351i
$85$	8.31310	−	1.19524i	0.901682	−	0.129642i
$86$	−1.11140	−	5.73973i	−0.119845	−	0.618931i
$87$	−3.11741	+	4.85079i	−0.334222	+	0.520060i
$88$	2.16357	+	1.86492i	0.230637	+	0.198801i
$89$	2.30896	+	7.86360i	0.244749	+	0.833540i	0.986626	+	0.163003i	$0.0521181\pi$
$89$	2.30896	+	7.86360i	0.244749	+	0.833540i	−0.741876	+	0.670537i	$0.766064\pi$
$90$	−3.58318	−	0.339020i	−0.377700	−	0.0357359i
$91$			1.00977i			0.105853i
$92$	−8.82136	+	3.76612i	−0.919690	+	0.392646i
$93$			0.0429533i			0.00445405i
$94$	1.05070	−	11.1051i	0.108372	−	1.14540i
$95$	0.697646	+	2.37596i	0.0715770	+	0.243769i
$96$	−5.55921	−	1.04650i	−0.567385	−	0.106808i
$97$	−10.3029	+	16.0316i	−1.04610	+	1.62776i	−0.310199	+	0.950672i	$0.600396\pi$
$97$	−10.3029	+	16.0316i	−1.04610	+	1.62776i	−0.735900	+	0.677090i	$0.763241\pi$
$98$	−9.65263	+	1.86907i	−0.975063	+	0.188804i
$99$	−0.999606	+	0.143722i	−0.100464	+	0.0144446i
$100$	0.701424	+	2.86960i	0.0701424	+	0.286960i
$101$	−5.45367	−	8.48608i	−0.542661	−	0.844397i	0.456307	−	0.889822i	$-0.349172\pi$
$101$	−5.45367	−	8.48608i	−0.542661	−	0.844397i	−0.998968	+	0.0454258i	$0.985536\pi$
$102$	−2.88174	+	3.67096i	−0.285334	+	0.363480i
$103$	−2.82884	+	6.19430i	−0.278734	+	0.610343i	−0.996281	−	0.0861680i	$-0.972538\pi$
$103$	−2.82884	+	6.19430i	−0.278734	+	0.610343i	0.717546	+	0.696511i	$0.245265\pi$
$104$	−11.8995	−	5.39699i	−1.16684	−	0.529218i
$105$	−0.0791697	+	0.550638i	−0.00772617	+	0.0537367i
$106$	0.00327866	+	0.0675957i	0.000318452	+	0.00656547i
$107$	−0.710963	+	2.42132i	−0.0687314	+	0.234078i	−0.986694	−	0.162590i	$-0.948015\pi$
$107$	−0.710963	+	2.42132i	−0.0687314	+	0.234078i	0.917962	+	0.396668i	$0.129833\pi$
$108$	1.56996	−	1.23904i	0.151070	−	0.119227i
$109$	−5.34910	−	6.17319i	−0.512351	−	0.591284i	0.439348	−	0.898317i	$-0.355209\pi$
$109$	−5.34910	−	6.17319i	−0.512351	−	0.591284i	−0.951699	+	0.307032i	$0.900664\pi$
$110$	1.66834	+	3.22926i	0.159070	+	0.307898i
$111$	3.93161	−	4.53732i	0.373172	−	0.430664i
$112$	−0.203189	+	0.850403i	−0.0191995	+	0.0803555i
$113$	17.4531	−	7.97056i	1.64185	−	0.749807i	0.641991	−	0.766712i	$-0.278108\pi$
$113$	17.4531	−	7.97056i	1.64185	−	0.749807i	0.999857	+	0.0169048i	$0.00538122\pi$
$114$	−1.19226	−	0.686978i	−0.111666	−	0.0643413i
$115$	−12.2027	+	0.255990i	−1.13791	+	0.0238712i
$116$	−9.97726	+	5.78344i	−0.926365	+	0.536979i
$117$	4.20213	−	1.91905i	0.388487	−	0.177416i
$118$	−3.47632	+	14.3839i	−0.320021	+	1.32415i
$119$	0.545150	+	0.472375i	0.0499738	+	0.0433026i
$120$	−6.06574	−	3.87598i	−0.553723	−	0.353827i
$121$	−6.53560	−	7.54248i	−0.594145	−	0.685680i
$122$	5.55184	+	2.21704i	0.502640	+	0.200722i
$123$	1.09079	+	0.320285i	0.0983532	+	0.0288791i
$124$	−0.0392324	+	0.0764249i	−0.00352317	+	0.00686316i
$125$	1.27599	−	8.87468i	0.114128	−	0.793775i
$126$	−0.179529	−	0.251651i	−0.0159937	−	0.0224189i
$127$	−8.40215	−	3.83713i	−0.745570	−	0.340490i	0.00614281	−	0.999981i	$-0.498045\pi$
$127$	−8.40215	−	3.83713i	−0.745570	−	0.340490i	−0.751713	+	0.659491i	$0.770772\pi$
$128$	−8.93541	−	6.93962i	−0.789787	−	0.613382i
$129$	2.23500	+	3.47773i	0.196781	+	0.306197i
$130$	−11.4842	−	12.0234i	−1.00723	−	1.05452i
$131$	−2.21776	−	15.4249i	−0.193767	−	1.34768i	−0.821926	−	0.569594i	$-0.807101\pi$
$131$	−2.21776	−	15.4249i	−0.193767	−	1.34768i	0.628160	−	0.778085i	$-0.283809\pi$
$132$	−1.90983	−	0.657295i	−0.166229	−	0.0572102i
$133$	−0.114984	+	0.178919i	−0.00997042	+	0.0155143i
$134$	−5.24244	+	1.81951i	−0.452878	+	0.157182i
$135$	2.44191	−	0.717010i	0.210166	−	0.0617104i
$136$	−8.48030	+	3.89949i	−0.727180	+	0.334378i
$137$			22.3931i			1.91318i	0.291444	+	0.956588i	$0.405864\pi$
$137$			22.3931i			1.91318i	−0.291444	+	0.956588i	$0.594136\pi$
$138$	4.80522	−	4.78643i	0.409047	−	0.407448i
$139$	−16.9033			−1.43372			−0.716861	−	0.697216i	$-0.754422\pi$
$139$	−16.9033			−1.43372			−0.716861	+	0.697216i	$0.754422\pi$
$140$	−0.643800	+	0.907414i	−0.0544111	+	0.0766904i
$141$	2.22218	+	7.56805i	0.187141	+	0.637345i
$142$	4.53212	−	1.57298i	0.380327	−	0.132001i
$143$	−3.92467	−	2.52223i	−0.328197	−	0.210920i
$144$	3.92507	−	0.770608i	0.327089	−	0.0642174i
$145$	−14.5255	+	2.08845i	−1.20628	+	0.173436i
$146$	−3.10928	+	2.96984i	−0.257326	+	0.245785i
$147$	5.84858	−	3.75865i	0.482383	−	0.310009i
$148$	11.1396	−	4.48203i	0.915670	−	0.368421i
$149$	1.83247	−	4.01256i	0.150122	−	0.328722i	−0.819599	−	0.572938i	$-0.805803\pi$
$149$	1.83247	−	4.01256i	0.150122	−	0.328722i	0.969721	+	0.244217i	$0.0785308\pi$
$150$	−1.21313	−	1.70048i	−0.0990515	−	0.138844i
$151$	−7.94960	−	1.14298i	−0.646929	−	0.0930144i	−0.188963	−	0.981984i	$-0.560513\pi$
$151$	−7.94960	−	1.14298i	−0.646929	−	0.0930144i	−0.457966	+	0.888970i	$0.651422\pi$
$152$	−1.49388	−	2.31129i	−0.121169	−	0.187470i
$153$	0.929726	−	3.16635i	0.0751639	−	0.255985i
$154$	−0.115775	+	0.289920i	−0.00932943	+	0.0233624i
$155$	−0.0826158	+	0.0715870i	−0.00663586	+	0.00575000i
$156$	9.22947	+	0.423631i	0.738949	+	0.0339176i
$157$	−7.46952	+	8.62028i	−0.596132	+	0.687973i	−0.970993	−	0.239108i	$-0.923145\pi$
$157$	−7.46952	+	8.62028i	−0.596132	+	0.687973i	0.374861	+	0.927081i	$0.377691\pi$
$158$	−1.27799	+	5.28793i	−0.101671	+	0.420685i
$159$	−0.0198791	−	0.0435291i	−0.00157651	−	0.00345208i
$160$	−7.25228	−	12.4366i	−0.573343	−	0.983202i
$161$	−0.702954	−	0.777678i	−0.0554005	−	0.0612896i
$162$	−0.706046	+	1.22536i	−0.0554722	+	0.0962731i
$163$	−3.25458	−	7.12653i	−0.254918	−	0.558193i	0.738298	−	0.674475i	$-0.235630\pi$
$163$	−3.25458	−	7.12653i	−0.254918	−	0.558193i	−0.993216	+	0.116282i	$0.962903\pi$
$164$	1.64825	+	1.56617i	0.128707	+	0.122297i
$165$	−1.94240	−	1.68310i	−0.151216	−	0.131029i
$166$	8.11404	+	15.7056i	0.629772	+	1.21899i
$167$	−9.75590	+	8.45353i	−0.754934	+	0.654154i	−0.944797	−	0.327657i	$-0.893741\pi$
$167$	−9.75590	+	8.45353i	−0.754934	+	0.654154i	0.189863	+	0.981811i	$0.439196\pi$
$168$	−0.0895763	−	0.611728i	−0.00691096	−	0.0471959i
$169$	8.00280	+	2.34983i	0.615600	+	0.180757i
$170$	−11.8634	+	0.575425i	−0.909885	+	0.0441331i
$171$	0.963089	+	0.138471i	0.0736493	+	0.0105892i
$172$	0.800178	+	8.22917i	0.0610130	+	0.627468i
$173$	−12.8354	−	5.86172i	−0.975856	−	0.445659i	−0.137333	−	0.990525i	$-0.543853\pi$
$173$	−12.8354	−	5.86172i	−0.975856	−	0.445659i	−0.838523	+	0.544866i	$0.816580\pi$
$174$	5.03526	−	6.41428i	0.381722	−	0.486266i
$175$	−0.271607	+	0.174551i	−0.0205315	+	0.0131948i
$176$	−2.79771	−	2.91388i	−0.210886	−	0.219642i
$177$	−1.48915	−	10.3573i	−0.111932	−	0.778502i
$178$	−2.20334	−	11.3789i	−0.165147	−	0.852888i
$179$	−3.74645	−	2.40770i	−0.280023	−	0.179960i	0.393089	−	0.919500i	$-0.371406\pi$
$179$	−3.74645	−	2.40770i	−0.280023	−	0.179960i	−0.673112	+	0.739541i	$0.735043\pi$
$180$	4.99969	+	0.954631i	0.372655	+	0.0711540i
$181$	−5.39245	+	1.58337i	−0.400818	+	0.117691i	−0.475927	−	0.879485i	$-0.657887\pi$
$181$	−5.39245	+	1.58337i	−0.400818	+	0.117691i	0.0751098	+	0.997175i	$0.476069\pi$
$182$	0.134512	−	1.42169i	0.00997071	−	0.105383i
$183$	−4.22718			−0.312482
$184$	12.9215	−	4.12733i	0.952586	−	0.304271i
$185$	15.2795			1.12337
$186$	0.00572182	−	0.0604751i	0.000419544	−	0.00443425i
$187$	−3.19766	+	0.938916i	−0.233836	+	0.0686604i
$188$	−2.95862	+	15.4952i	−0.215779	+	1.13010i
$189$	0.183885	+	0.118176i	0.0133757	+	0.00859604i
$190$	−0.665731	−	3.43811i	−0.0482972	−	0.249427i
$191$	0.397943	+	2.76775i	0.0287941	+	0.200267i	0.999141	−	0.0414510i	$-0.0131981\pi$
$191$	0.397943	+	2.76775i	0.0287941	+	0.200267i	−0.970346	+	0.241718i	$0.922289\pi$
$192$	7.68755	+	2.21394i	0.554801	+	0.159777i
$193$	−17.9320	+	11.5242i	−1.29077	+	0.829530i	−0.992176	−	0.124849i	$-0.960155\pi$
$193$	−17.9320	+	11.5242i	−1.29077	+	0.829530i	−0.298598	+	0.954379i	$0.596519\pi$
$194$	16.6413	−	21.1988i	1.19477	−	1.52199i
$195$	10.6944	+	4.88399i	0.765845	+	0.349750i
$196$	13.8392	−	1.34568i	0.988512	−	0.0961198i
$197$	24.4512	+	3.51555i	1.74207	+	0.250472i	0.938634	−	0.344915i	$-0.112092\pi$
$197$	24.4512	+	3.51555i	1.74207	+	0.250472i	0.803439	+	0.595387i	$0.203001\pi$
$198$	1.42652	−	0.0691918i	0.101378	−	0.00491725i
$199$	−13.7701	−	4.04325i	−0.976134	−	0.286619i	−0.245506	−	0.969395i	$-0.578954\pi$
$199$	−13.7701	−	4.04325i	−0.976134	−	0.286619i	−0.730627	+	0.682776i	$0.760772\pi$
$200$	−0.605293	−	4.13363i	−0.0428007	−	0.292292i
$201$	2.96548	−	2.56960i	0.209169	−	0.181246i
$202$	6.54794	+	12.6743i	0.460711	+	0.891758i
$203$	−0.952542	−	0.825383i	−0.0668554	−	0.0579305i
$204$	4.54628	−	4.78457i	0.318303	−	0.334987i
$205$	1.20190	+	2.63180i	0.0839446	+	0.183813i
$206$	4.80794	−	8.34429i	0.334985	−	0.581374i
$207$	−1.90033	+	4.40327i	−0.132082	+	0.306048i
$208$	16.0347	+	9.18369i	1.11180	+	0.636774i
$209$	−0.408191	−	0.893815i	−0.0282352	−	0.0618265i
$210$	0.184816	−	0.764711i	0.0127535	−	0.0527700i
$211$	5.09965	−	5.88531i	0.351074	−	0.405161i	−0.552555	−	0.833476i	$-0.686347\pi$
$211$	5.09965	−	5.88531i	0.351074	−	0.405161i	0.903629	+	0.428315i	$0.140893\pi$
$212$	0.00438832	−	0.0956064i	0.000301391	−	0.00656628i
$213$	−2.56367	+	2.22143i	−0.175660	+	0.152210i
$214$	1.32353	−	3.31433i	0.0904745	−	0.226563i
$215$	−2.96411	+	10.0948i	−0.202151	+	0.688462i
$216$	−2.37544	+	1.53534i	−0.161628	+	0.104467i
$217$	−0.00929339	−	0.00133619i	−0.000630876	−	9.07063e-5i
$218$	6.70880	+	9.40395i	0.454378	+	0.636916i
$219$	1.26301	−	2.76561i	0.0853463	−	0.186882i
$220$	−1.91873	−	4.76880i	−0.129361	−	0.321512i
$221$	12.8247	−	8.24196i	0.862685	−	0.554414i
$222$	−6.13984	+	5.86448i	−0.412079	+	0.393598i
$223$	24.9374	−	3.58546i	1.66993	−	0.240100i	0.758537	−	0.651630i	$-0.225915\pi$
$223$	24.9374	−	3.58546i	1.66993	−	0.240100i	0.911396	+	0.411530i	$0.135005\pi$
$224$	0.399357	−	1.17024i	0.0266831	−	0.0781898i
$225$	1.24257	+	0.798550i	0.0828379	+	0.0532367i
$226$	−25.6344	+	8.89703i	−1.70518	+	0.591821i
$227$	1.60629	+	5.47052i	0.106613	+	0.363091i	0.995468	−	0.0950979i	$-0.0303164\pi$
$227$	1.60629	+	5.47052i	0.106613	+	0.363091i	−0.888855	+	0.458189i	$0.848498\pi$
$228$	1.58711	+	1.12603i	0.105109	+	0.0745735i
$229$	−6.67803			−0.441296			−0.220648	−	0.975353i	$-0.570817\pi$
$229$	−6.67803			−0.441296			−0.220648	+	0.975353i	$0.570817\pi$
$230$	17.2146	+	1.26511i	1.13510	+	0.0834190i
$231$		−	0.220746i		−	0.0145240i
$232$	14.8177	−	6.81358i	0.972826	−	0.447334i
$233$	−4.89011	+	1.43586i	−0.320361	+	0.0940666i	−0.437960	−	0.898995i	$-0.644299\pi$
$233$	−4.89011	+	1.43586i	−0.320361	+	0.0940666i	0.117598	+	0.993061i	$0.462481\pi$
$234$	−6.17193	+	2.14211i	−0.403471	+	0.140034i
$235$	−10.8527	+	16.8872i	−0.707954	+	1.10160i
$236$	6.81048	−	19.7884i	0.443324	−	1.28812i
$237$	−0.547454	−	3.80762i	−0.0355609	−	0.247332i
$238$	−0.704606	−	0.737689i	−0.0456728	−	0.0478173i
$239$	−10.8193	−	16.8351i	−0.699841	−	1.08897i	−0.991202	−	0.132361i	$-0.957744\pi$
$239$	−10.8193	−	16.8351i	−0.699841	−	1.08897i	0.291360	−	0.956613i	$-0.405892\pi$
$240$	8.02379	+	6.26511i	0.517933	+	0.404411i
$241$	−6.47580	−	2.95740i	−0.417143	−	0.190503i	0.195776	−	0.980649i	$-0.437277\pi$
$241$	−6.47580	−	2.95740i	−0.417143	−	0.190503i	−0.612919	+	0.790146i	$0.710005\pi$
$242$	8.19690	+	11.4899i	0.526917	+	0.738596i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−7.52124	−	3.86099i	−0.481498	−	0.247175i
$245$	16.9767	+	4.98481i	1.08460	+	0.318468i
$246$	−1.49309	−	0.596241i	−0.0951957	−	0.0380150i
$247$	2.94349	+	3.39697i	0.187290	+	0.216144i
$248$	0.0654168	−	0.102374i	0.00415397	−	0.00650079i
$249$	−9.44693	−	8.18582i	−0.598675	−	0.518755i
$250$	−2.97869	+	12.3249i	−0.188389	+	0.779496i
$251$	−24.6561	+	11.2601i	−1.55628	+	0.710729i	−0.993281	−	0.115728i	$-0.963080\pi$
$251$	−24.6561	+	11.2601i	−1.55628	+	0.710729i	−0.562999	+	0.826458i	$0.690353\pi$
$252$	0.219241	+	0.378221i	0.0138109	+	0.0238257i
$253$	4.77843	−	0.789659i	0.300417	−	0.0496454i
$254$	11.3185	+	6.52165i	0.710183	+	0.409205i
$255$	7.63962	−	3.48890i	0.478412	−	0.218483i
$256$	11.6560	+	10.9608i	0.728498	+	0.685048i
$257$	2.34482	−	2.70606i	0.146266	−	0.168800i	−0.677889	−	0.735164i	$-0.737105\pi$
$257$	2.34482	−	2.70606i	0.146266	−	0.168800i	0.824155	+	0.566364i	$0.191651\pi$
$258$	−2.68345	−	5.19411i	−0.167064	−	0.323371i
$259$	0.859392	+	0.991791i	0.0534000	+	0.0616269i
$260$	14.5672	+	18.4579i	0.903422	+	1.14471i
$261$	−1.62451	+	5.53258i	−0.100555	+	0.342458i
$262$	1.06770	+	22.0125i	0.0659624	+	1.35994i
$263$	2.11308	−	14.6968i	0.130298	−	0.906242i	−0.814867	−	0.579648i	$-0.803190\pi$
$263$	2.11308	−	14.6968i	0.130298	−	0.906242i	0.945165	−	0.326594i	$-0.105901\pi$
$264$	2.60134	+	1.17983i	0.160101	+	0.0726136i
$265$	0.0505923	−	0.110782i	0.00310786	−	0.00680527i
$266$	0.185723	−	0.236588i	0.0113874	−	0.0145061i
$267$	4.43087	+	6.89456i	0.271165	+	0.421940i
$268$	7.62334	−	1.86339i	0.465670	−	0.113825i
$269$	10.8135	−	1.55475i	0.659311	−	0.0947946i	0.195465	−	0.980711i	$-0.437378\pi$
$269$	10.8135	−	1.55475i	0.659311	−	0.0947946i	0.463846	+	0.885916i	$0.346469\pi$
$270$	−3.53355	+	0.684210i	−0.215045	+	0.0416397i
$271$	0.633749	−	0.986133i	0.0384975	−	0.0599033i	−0.821471	−	0.570250i	$-0.806846\pi$
$271$	0.633749	−	0.986133i	0.0384975	−	0.0599033i	0.859969	+	0.510346i	$0.170483\pi$
$272$	12.4591	−	4.36053i	0.755443	−	0.264396i
$273$	0.284486	+	0.968872i	0.0172179	+	0.0586388i
$274$	2.98299	−	31.5279i	0.180209	−	1.90467i
$275$		−	1.49164i		−	0.0899495i
$276$	−7.40299	+	6.09883i	−0.445608	+	0.367107i
$277$		−	18.6989i		−	1.12351i	−0.827303	−	0.561755i	$-0.810126\pi$
$277$		−	18.6989i		−	1.12351i	0.827303	−	0.561755i	$-0.189874\pi$
$278$	23.7986	+	2.25170i	1.42735	+	0.135048i
$279$	0.0121013	+	0.0412134i	0.000724489	+	0.00246738i
$280$	1.02730	−	1.19181i	0.0613929	−	0.0712243i
$281$	3.77690	−	5.87697i	0.225311	−	0.350591i	−0.710132	−	0.704069i	$-0.751365\pi$
$281$	3.77690	−	5.87697i	0.225311	−	0.350591i	0.935443	+	0.353478i	$0.115001\pi$
$282$	−2.12052	−	10.9513i	−0.126275	−	0.652138i
$283$	−9.27412	+	1.33342i	−0.551289	+	0.0792635i	−0.412330	−	0.911035i	$-0.635285\pi$
$283$	−9.27412	+	1.33342i	−0.551289	+	0.0792635i	−0.138960	+	0.990298i	$0.544376\pi$
$284$	−6.59042	+	1.61091i	−0.391069	+	0.0955900i
$285$	1.33877	+	2.08317i	0.0793021	+	0.123396i
$286$	5.18965	+	4.07392i	0.306871	+	0.240896i
$287$	−0.103229	+	0.226040i	−0.00609342	+	0.0133427i
$288$	−5.62886	+	0.562100i	−0.331684	+	0.0331221i
$289$	−0.869517	+	6.04762i	−0.0511480	+	0.355742i
$290$	20.7290	−	1.00544i	1.21725	−	0.0590415i
$291$	−5.36892	+	18.2849i	−0.314732	+	1.07188i
$292$	4.77324	−	3.76712i	0.279333	−	0.220454i
$293$	6.91195	+	7.97682i	0.403801	+	0.466011i	0.920834	−	0.389954i	$-0.127509\pi$
$293$	6.91195	+	7.97682i	0.403801	+	0.466011i	−0.517034	+	0.855965i	$0.672964\pi$
$294$	−8.73506	+	4.51282i	−0.509439	+	0.263193i
$295$	17.4392	−	20.1259i	1.01535	−	1.17178i
$296$	−16.2808	+	4.82646i	−0.946302	+	0.280532i
$297$	−0.918624	+	0.419522i	−0.0533040	+	0.0243431i
$298$	−3.11450	+	5.40528i	−0.180418	+	0.313120i
$299$	−19.9553	+	9.62408i	−1.15404	+	0.556575i
$300$	1.48147	+	2.55575i	0.0855329	+	0.147556i
$301$	−0.821969	+	0.375381i	−0.0473775	+	0.0216366i
$302$	11.0402	+	2.66820i	0.635291	+	0.153538i
$303$	−7.62357	−	6.60586i	−0.437962	−	0.379497i
$304$	1.79538	+	3.45312i	0.102972	+	0.198050i
$305$	−7.04512	−	8.13050i	−0.403402	−	0.465551i
$306$	−1.73078	+	4.33414i	−0.0989418	+	0.247766i
$307$	31.6795	+	9.30195i	1.80805	+	0.530890i	0.998427	−	0.0560660i	$-0.0178557\pi$
$307$	31.6795	+	9.30195i	1.80805	+	0.530890i	0.809619	+	0.586956i	$0.199674\pi$
$308$	0.201623	−	0.392763i	0.0114885	−	0.0223798i
$309$	−0.969118	+	6.74037i	−0.0551312	+	0.383446i
$310$	0.125853	−	0.0897839i	0.00714797	−	0.00509938i
$311$	13.5631	+	6.19408i	0.769096	+	0.351234i	0.761016	−	0.648733i	$-0.224701\pi$
$311$	13.5631	+	6.19408i	0.769096	+	0.351234i	0.00807966	+	0.999967i	$0.497428\pi$
$312$	−12.9380	−	1.82590i	−0.732469	−	0.103371i
$313$	−7.46509	−	11.6159i	−0.421952	−	0.656570i	0.563580	−	0.826062i	$-0.309424\pi$
$313$	−7.46509	−	11.6159i	−0.421952	−	0.656570i	−0.985532	+	0.169492i	$0.945787\pi$
$314$	11.6648	−	11.1417i	0.658285	−	0.628763i
$315$	0.0791697	+	0.550638i	0.00446071	+	0.0310249i
$316$	2.50372	−	7.27477i	0.140845	−	0.409238i
$317$	−5.07627	+	7.89883i	−0.285112	+	0.443643i	−0.954038	−	0.299686i	$-0.903118\pi$
$317$	−5.07627	+	7.89883i	−0.285112	+	0.443643i	0.668926	+	0.743329i	$0.266754\pi$
$318$	0.0221898	+	0.0639339i	0.00124434	+	0.00358523i
$319$	5.58727	−	1.64057i	0.312827	−	0.0918543i
$320$	8.55399	+	18.4759i	0.478183	+	1.03284i
$321$			2.52354i			0.140850i
$322$	0.886112	+	1.18855i	0.0493811	+	0.0662355i
$323$	3.21090			0.178660
$324$	1.15729	−	1.63116i	0.0642939	−	0.0906200i
$325$	1.92236	+	6.54695i	0.106633	+	0.363159i
$326$	3.63288	+	10.4672i	0.201207	+	0.579723i
$327$	−6.87161	−	4.41612i	−0.380001	−	0.244212i
$328$	−2.11199	−	2.42461i	−0.116615	−	0.133877i
$329$	−1.70655	+	0.245365i	−0.0940852	+	0.0135274i
$330$	2.51055	+	2.62842i	0.138201	+	0.144690i
$331$	8.44335	−	5.42621i	0.464088	−	0.298252i	−0.287623	−	0.957744i	$-0.592865\pi$
$331$	8.44335	−	5.42621i	0.464088	−	0.298252i	0.751711	+	0.659492i	$0.229229\pi$
$332$	−9.33182	−	23.1932i	−0.512150	−	1.27289i
$333$	2.49404	−	5.46119i	0.136673	−	0.299271i
$334$	14.8617	−	10.6024i	0.813195	−	0.580136i
$335$	9.88466	+	1.42120i	0.540057	+	0.0776484i
$336$	0.0446283	+	0.873201i	0.00243467	+	0.0476370i
$337$	−1.29835	+	4.42176i	−0.0707254	+	0.240869i	−0.987267	−	0.159070i	$-0.949150\pi$
$337$	−1.29835	+	4.42176i	−0.0707254	+	0.240869i	0.916542	+	0.399939i	$0.130969\pi$
$338$	−10.9543	−	4.37445i	−0.595837	−	0.237939i
$339$	14.5006	−	12.5648i	0.787562	−	0.682426i
$340$	16.7795	+	0.770176i	0.909996	+	0.0417687i
$341$	0.0284065	−	0.0327828i	0.00153830	−	0.00177529i
$342$	−1.33751	−	0.323251i	−0.0723244	−	0.0174794i
$343$	1.26691	+	2.77415i	0.0684068	+	0.149790i
$344$	−0.0303825	−	11.6926i	−0.00163811	−	0.630425i
$345$	−11.6363	+	3.68352i	−0.626478	+	0.198314i
$346$	17.2904	+	9.96268i	0.929539	+	0.535597i
$347$	−1.61909	−	3.54531i	−0.0869172	−	0.190322i	0.861182	−	0.508297i	$-0.169725\pi$
$347$	−1.61909	−	3.54531i	−0.0869172	−	0.190322i	−0.948099	+	0.317975i	$0.896997\pi$
$348$	−7.94373	+	8.36009i	−0.425828	+	0.448148i
$349$	−22.3063	−	19.3285i	−1.19403	−	1.03463i	−0.998545	−	0.0539238i	$-0.982827\pi$
$349$	−22.3063	−	19.3285i	−1.19403	−	1.03463i	−0.195483	−	0.980707i	$-0.562627\pi$
$350$	0.405654	−	0.209574i	0.0216831	−	0.0112022i
$351$	3.49126	−	3.02519i	0.186350	−	0.161473i
$352$	3.55082	+	4.47521i	0.189259	+	0.238529i
$353$	9.40748	+	2.76228i	0.500709	+	0.147022i	0.522328	−	0.852745i	$-0.325064\pi$
$353$	9.40748	+	2.76228i	0.500709	+	0.147022i	−0.0216184	+	0.999766i	$0.506882\pi$
$354$	0.716922	+	14.7807i	0.0381040	+	0.785584i
$355$	−8.54534	−	1.22863i	−0.453540	−	0.0652092i
$356$	1.58634	+	16.3142i	0.0840760	+	0.864652i
$357$	0.656151	+	0.299654i	0.0347272	+	0.0158594i
$358$	4.95400	+	3.88893i	0.261827	+	0.205536i
$359$	−19.0846	+	12.2649i	−1.00725	+	0.647318i	−0.936679	−	0.350189i	$-0.886117\pi$
$359$	−19.0846	+	12.2649i	−1.00725	+	0.647318i	−0.0705678	+	0.997507i	$0.522481\pi$
$360$	−6.91202	−	2.01006i	−0.364295	−	0.105939i
$361$	−2.56925	−	17.8695i	−0.135224	−	0.940501i
$362$	7.80309	−	1.51093i	0.410121	−	0.0794129i
$363$	−8.39582	−	5.39567i	−0.440666	−	0.283199i
$364$	−0.378766	+	1.98371i	−0.0198528	+	0.103975i
$365$	7.42429	−	2.17997i	0.388605	−	0.114105i
$366$	5.95156	+	0.563104i	0.311093	+	0.0294339i
$367$	26.3587			1.37591			0.687956	−	0.725753i	$-0.258508\pi$
$367$	26.3587			1.37591			0.687956	+	0.725753i	$0.258508\pi$
$368$	−18.7423	+	4.08970i	−0.977011	+	0.213190i
$369$	1.13684			0.0591815
$370$	−21.5124	−	2.03539i	−1.11838	−	0.105815i
$371$	0.0100364	−	0.00294694i	0.000521062	−	0.000152998i
$372$	−0.0161118	+	0.0843822i	−0.000835357	+	0.00437501i
$373$	−11.7497	−	7.55108i	−0.608377	−	0.390980i	0.199871	−	0.979822i	$-0.435948\pi$
$373$	−11.7497	−	7.55108i	−0.608377	−	0.390980i	−0.808248	+	0.588842i	$0.799584\pi$
$374$	4.62713	−	0.895964i	0.239263	−	0.0463292i
$375$	−1.27599	−	8.87468i	−0.0658916	−	0.458286i
$376$	6.22963	−	21.4219i	0.321269	−	1.10475i
$377$	−22.4087	+	14.4012i	−1.15411	+	0.741699i
$378$	−0.243155	−	0.190878i	−0.0125065	−	0.00981773i
$379$	33.6967	+	15.3887i	1.73088	+	0.790467i	0.993347	+	0.115156i	$0.0367369\pi$
$379$	33.6967	+	15.3887i	1.73088	+	0.790467i	0.737534	+	0.675310i	$0.235990\pi$
$380$	0.479309	+	4.92929i	0.0245880	+	0.252867i
$381$	−9.14284	−	1.31454i	−0.468402	−	0.0673461i
$382$	−0.191581	−	3.94980i	−0.00980214	−	0.202089i
$383$	28.9019	+	8.48636i	1.47682	+	0.433633i	0.918309	−	0.395865i	$-0.129555\pi$
$383$	28.9019	+	8.48636i	1.47682	+	0.433633i	0.558509	+	0.829498i	$0.311373\pi$
$384$	−10.5286	−	4.14112i	−0.537285	−	0.211326i
$385$	0.424579	−	0.367900i	0.0216386	−	0.0187499i
$386$	26.7821	−	13.8365i	1.36317	−	0.704259i
$387$	3.12426	+	2.70719i	0.158815	+	0.137614i
$388$	−26.2536	+	27.6296i	−1.33282	+	1.40268i
$389$	−11.9686	−	26.2077i	−0.606834	−	1.32878i	−0.924719	−	0.380651i	$-0.875700\pi$
$389$	−11.9686	−	26.2077i	−0.606834	−	1.32878i	0.317885	−	0.948129i	$-0.397028\pi$
$390$	−14.4064	−	8.30090i	−0.729495	−	0.420332i
$391$	−4.13934	+	15.2755i	−0.209335	+	0.772514i
$392$	−19.6638	+	0.0510949i	−0.993171	+	0.00258068i
$393$	−6.47362	−	14.1753i	−0.326551	−	0.715047i
$394$	−33.9571	−	8.20677i	−1.71073	−	0.413451i
$395$	6.41113	−	7.39884i	0.322579	−	0.372276i
$396$	−2.01765	−	0.0926096i	−0.101391	−	0.00465381i
$397$	−26.6890	+	23.1261i	−1.33948	+	1.16067i	−0.366334	+	0.930484i	$0.619387\pi$
$397$	−26.6890	+	23.1261i	−1.33948	+	1.16067i	−0.973147	+	0.230183i	$0.926067\pi$
$398$	18.8486	+	7.52691i	0.944796	+	0.377290i
$399$	−0.0599194	+	0.204067i	−0.00299972	+	0.0102161i
$400$	0.301567	+	5.90047i	0.0150783	+	0.295024i
$401$	−7.71967	−	1.10992i	−0.385502	−	0.0554268i	−0.0531606	−	0.998586i	$-0.516930\pi$
$401$	−7.71967	−	1.10992i	−0.385502	−	0.0554268i	−0.332341	+	0.943159i	$0.607839\pi$
$402$	−4.51747	+	3.22277i	−0.225311	+	0.160737i
$403$	−0.0824295	+	0.180495i	−0.00410611	+	0.00899112i
$404$	−7.53067	−	18.7167i	−0.374665	−	0.931189i
$405$	2.14099	−	1.37593i	0.106387	−	0.0683707i
$406$	1.23116	+	1.28897i	0.0611014	+	0.0639703i
$407$	−6.00137	+	0.862867i	−0.297477	+	0.0427707i
$408$	−7.03818	+	6.13071i	−0.348442	+	0.303515i
$409$	−11.7106	−	7.52596i	−0.579053	−	0.372135i	0.218087	−	0.975929i	$-0.430018\pi$
$409$	−11.7106	−	7.52596i	−0.579053	−	0.372135i	−0.797140	+	0.603795i	$0.793655\pi$
$410$	−1.34161	−	3.86549i	−0.0662574	−	0.190903i
$411$	6.30888	+	21.4861i	0.311194	+	1.05983i
$412$	−7.88077	+	11.1077i	−0.388258	+	0.547236i
$413$	2.28723			0.112547
$414$	3.26208	−	5.94633i	0.160322	−	0.292246i
$415$		−	31.8128i		−	1.56163i
$416$	−21.3523	−	15.0659i	−1.04688	−	0.738668i
$417$	−16.2186	+	4.76222i	−0.794230	+	0.233207i
$418$	0.455638	+	1.31280i	0.0222860	+	0.0642111i
$419$	9.05384	−	14.0880i	0.442309	−	0.688246i	−0.546496	−	0.837462i	$-0.684039\pi$
$419$	9.05384	−	14.0880i	0.442309	−	0.688246i	0.988805	+	0.149216i	$0.0476749\pi$
$420$	−0.362074	+	1.05204i	−0.0176674	+	0.0513341i
$421$	2.23313	+	15.5317i	0.108836	+	0.756970i	0.969019	+	0.246985i	$0.0794400\pi$
$421$	2.23313	+	15.5317i	0.108836	+	0.756970i	−0.860183	+	0.509985i	$0.829651\pi$
$422$	−7.96391	+	7.60675i	−0.387677	+	0.370291i
$423$	4.26433	+	6.63543i	0.207339	+	0.322626i
$424$	−0.0189142	+	0.134022i	−0.000918553	+	0.00650869i
$425$	4.43381	+	2.02485i	0.215071	+	0.0982197i
$426$	3.90537	−	2.78611i	0.189216	−	0.134987i
$427$	0.131499	−	0.914594i	0.00636367	−	0.0442603i
$428$	−2.30493	+	4.49002i	−0.111413	+	0.217033i
$429$	−4.47629	−	1.31436i	−0.216117	−	0.0634577i
$430$	5.51799	−	13.8179i	0.266101	−	0.666360i
$431$	25.0526	+	28.9122i	1.20674	+	1.39265i	0.897118	+	0.441791i	$0.145657\pi$
$431$	25.0526	+	28.9122i	1.20674	+	1.39265i	0.309621	+	0.950860i	$0.399798\pi$
$432$	3.54897	−	1.84521i	0.170750	−	0.0887778i
$433$	−10.9422	−	9.48146i	−0.525848	−	0.455650i	0.351029	−	0.936365i	$-0.385832\pi$
$433$	−10.9422	−	9.48146i	−0.525848	−	0.455650i	−0.876877	+	0.480715i	$0.840377\pi$
$434$	0.0129064	+	0.00311923i	0.000619527	+	0.000149728i
$435$	−13.3487	+	6.09616i	−0.640023	+	0.292289i
$436$	−8.19280	−	14.1337i	−0.392364	−	0.676883i
$437$	−4.63173	−	0.567067i	−0.221566	−	0.0271265i
$438$	−2.14663	+	3.72552i	−0.102570	+	0.178012i
$439$	−16.9369	+	7.73484i	−0.808355	+	0.369164i	−0.776333	−	0.630324i	$-0.782922\pi$
$439$	−16.9369	+	7.73484i	−0.808355	+	0.369164i	−0.0320229	+	0.999487i	$0.510195\pi$
$440$	2.06618	+	6.96970i	0.0985011	+	0.332268i
$441$	4.55274	−	5.25414i	0.216797	−	0.250197i
$442$	−19.1542	+	9.89568i	−0.911072	+	0.470690i
$443$	−10.4900	−	12.1061i	−0.498394	−	0.575178i	0.449695	−	0.893182i	$-0.351533\pi$
$443$	−10.4900	−	12.1061i	−0.498394	−	0.575178i	−0.948089	+	0.318005i	$0.896987\pi$
$444$	9.42564	−	7.43887i	0.447321	−	0.353033i
$445$	−5.87632	+	20.0129i	−0.278564	+	0.948702i
$446$	−35.5877	+	1.72614i	−1.68512	+	0.0817353i
$447$	0.627778	−	4.36629i	0.0296929	−	0.206518i
$448$	−0.718152	+	1.59441i	−0.0339295	+	0.0753288i
$449$	13.9253	−	30.4921i	0.657174	−	1.43901i	−0.227959	−	0.973671i	$-0.573205\pi$
$449$	13.9253	−	30.4921i	0.657174	−	1.43901i	0.885133	−	0.465339i	$-0.154067\pi$
$450$	−1.64307	−	1.28982i	−0.0774550	−	0.0608028i
$451$	−0.620698	−	0.965825i	−0.0292275	−	0.0454789i
$452$	37.2765	−	9.11159i	1.75334	−	0.428573i
$453$	−7.94960	+	1.14298i	−0.373505	+	0.0537019i
$454$	−1.53281	−	7.91606i	−0.0719382	−	0.371519i
$455$	−1.38938	+	2.16192i	−0.0651352	+	0.101352i
$456$	−2.08453	−	1.79679i	−0.0976170	−	0.0841425i
$457$	4.66733	+	15.8955i	0.218329	+	0.743559i	0.993702	+	0.112056i	$0.0357435\pi$
$457$	4.66733	+	15.8955i	0.218329	+	0.743559i	−0.775373	+	0.631503i	$0.782438\pi$
$458$	9.40216	+	0.889581i	0.439334	+	0.0415674i
$459$		−	3.30003i		−	0.154032i
$460$	−24.0684	−	4.07435i	−1.12219	−	0.189967i
$461$			23.6478i			1.10139i	0.834707	+	0.550695i	$0.185637\pi$
$461$			23.6478i			1.10139i	−0.834707	+	0.550695i	$0.814363\pi$
$462$	−0.0294056	+	0.310794i	−0.00136807	+	0.0144594i
$463$	0.0215611	+	0.0734304i	0.00100203	+	0.00341260i	0.959992	−	0.280026i	$-0.0903430\pi$
$463$	0.0215611	+	0.0734304i	0.00100203	+	0.00341260i	−0.958990	+	0.283438i	$0.908525\pi$
$464$	−21.7698	+	7.61916i	−1.01064	+	0.353710i
$465$	−0.0591009	+	0.0919628i	−0.00274074	+	0.00426467i
$466$	7.07618	−	1.37018i	0.327798	−	0.0634723i
$467$	−4.01262	+	0.576928i	−0.185682	+	0.0266970i	−0.234528	−	0.972109i	$-0.575355\pi$
$467$	−4.01262	+	0.576928i	−0.185682	+	0.0266970i	0.0488465	+	0.998806i	$0.484445\pi$
$468$	8.97496	−	2.19377i	0.414868	−	0.101407i
$469$	0.463709	+	0.721546i	0.0214121	+	0.0333179i
$470$	17.5294	−	22.3302i	0.808571	−	1.03002i
$471$	−4.73833	+	10.3755i	−0.218331	+	0.478078i
$472$	−12.2247	+	26.9534i	−0.562686	+	1.24063i
$473$	0.594144	−	4.13236i	0.0273188	−	0.190006i
$474$	0.263560	+	5.43378i	0.0121057	+	0.249582i
$475$	−0.404893	+	1.37894i	−0.0185778	+	0.0632700i
$476$	0.893765	+	1.13247i	0.0409657	+	0.0519068i
$477$	−0.0313374	−	0.0361653i	−0.00143484	−	0.00165590i
$478$	12.9901	+	25.1439i	0.594155	+	1.15005i
$479$	25.6787	−	29.6348i	1.17329	−	1.35405i	0.250793	−	0.968041i	$-0.419309\pi$
$479$	25.6787	−	29.6348i	1.17329	−	1.35405i	0.922496	−	0.386007i	$-0.126146\pi$
$480$	−10.4623	−	9.88965i	−0.477537	−	0.451399i
$481$	25.2285	−	11.5215i	1.15032	−	0.525334i
$482$	8.72348	+	5.02644i	0.397344	+	0.228948i
$483$	−0.893577	−	0.548131i	−0.0406591	−	0.0249408i
$484$	−10.0101	−	17.2688i	−0.455003	−	0.784945i
$485$	−44.1168	+	20.1475i	−2.00324	+	0.914849i
$486$	−0.332223	+	1.37464i	−0.0150699	+	0.0623548i
$487$	−18.2359	−	15.8015i	−0.826347	−	0.716034i	0.135157	−	0.990824i	$-0.456846\pi$
$487$	−18.2359	−	15.8015i	−0.826347	−	0.716034i	−0.961504	+	0.274791i	$0.911391\pi$
$488$	10.0750	+	6.43789i	0.456075	+	0.291430i
$489$	−5.13052	−	5.92094i	−0.232010	−	0.267754i
$490$	−23.2379	−	9.27972i	−1.04978	−	0.419215i
$491$	39.1765	+	11.5033i	1.76801	+	0.519135i	0.993541	−	0.113473i	$-0.0361975\pi$
$491$	39.1765	+	11.5033i	1.76801	+	0.519135i	0.774472	+	0.632608i	$0.218016\pi$
$492$	2.02273	+	1.03836i	0.0911917	+	0.0468128i
$493$	−2.70803	+	18.8348i	−0.121964	+	0.848275i
$494$	−3.69170	−	5.17478i	−0.166098	−	0.232824i
$495$	−2.33790	−	1.06768i	−0.105081	−	0.0479888i
$496$	−0.105739	+	0.135422i	−0.00474784	+	0.00608061i
$497$	−0.400879	−	0.623780i	−0.0179819	−	0.0279804i
$498$	12.2101	+	12.7834i	0.547150	+	0.572840i
$499$	4.25940	+	29.6247i	0.190677	+	1.32619i	0.830222	+	0.557432i	$0.188213\pi$
$499$	4.25940	+	29.6247i	0.190677	+	1.32619i	−0.639546	+	0.768753i	$0.720877\pi$
$500$	5.83558	−	16.9558i	0.260975	−	0.758285i
$501$	−6.97908	+	10.8597i	−0.311802	+	0.485174i
$502$	36.2139	−	12.5689i	1.61631	−	0.560977i
$503$	−23.6489	+	6.94393i	−1.05445	+	0.309615i	−0.762614	−	0.646854i	$-0.776084\pi$
$503$	−23.6489	+	6.94393i	−1.05445	+	0.309615i	−0.291836	+	0.956468i	$0.594266\pi$
$504$	−0.258292	−	0.561713i	−0.0115052	−	0.0250207i
$505$		−	25.6725i		−	1.14241i
$506$	−6.83287	+	0.475246i	−0.303758	+	0.0211272i
$507$	8.34066			0.370422
$508$	−15.0668	−	10.6897i	−0.668481	−	0.474280i
$509$	−4.79783	−	16.3399i	−0.212660	−	0.724254i	−0.994863	−	0.101230i	$-0.967722\pi$
$509$	−4.79783	−	16.3399i	−0.212660	−	0.724254i	0.782203	−	0.623024i	$-0.214096\pi$
$510$	−11.2208	+	3.89444i	−0.496864	+	0.172448i
$511$	0.559077	+	0.359297i	0.0247321	+	0.0158944i
$512$	−14.9507	−	16.9846i	−0.660732	−	0.750622i
$513$	0.963089	−	0.138471i	0.0425214	−	0.00611366i
$514$	−3.66181	+	3.49758i	−0.161515	+	0.154272i
$515$	−14.5795	+	9.36966i	−0.642449	+	0.412877i
$516$	3.08619	+	7.67039i	0.135862	+	0.337670i
$517$	3.30900	−	7.24569i	0.145529	−	0.318665i
$518$	−1.07784	−	1.51085i	−0.0473577	−	0.0663828i
$519$	−13.9669	−	2.00814i	−0.613079	−	0.0881474i
$520$	−18.0508	−	27.9278i	−0.791581	−	1.22472i
$521$	−6.40448	+	21.8117i	−0.280586	+	0.955587i	0.691777	+	0.722111i	$0.256828\pi$
$521$	−6.40448	+	21.8117i	−0.280586	+	0.955587i	−0.972363	+	0.233476i	$0.924990\pi$
$522$	3.02419	−	7.57306i	0.132365	−	0.331464i
$523$	14.7576	−	12.7876i	0.645307	−	0.559161i	−0.269527	−	0.962993i	$-0.586867\pi$
$523$	14.7576	−	12.7876i	0.645307	−	0.559161i	0.914833	+	0.403832i	$0.132322\pi$
$524$	1.42905	−	31.1342i	0.0624285	−	1.36010i
$525$	−0.211428	+	0.244001i	−0.00922748	+	0.0106491i
$526$	−4.93282	+	20.4105i	−0.215081	+	0.889940i
$527$	0.0588839	+	0.128938i	0.00256502	+	0.00561662i
$528$	−3.50532	−	2.00764i	−0.152550	−	0.0873712i
$529$	8.66874	−	21.3038i	0.376902	−	0.926253i
$530$	−0.0859875	+	0.149233i	−0.00373506	+	0.00648227i
$531$	−4.34682	−	9.51821i	−0.188636	−	0.413055i
$532$	−0.293001	+	0.308358i	−0.0127032	+	0.0133690i
$533$	3.96900	+	3.43916i	0.171916	+	0.148966i
$534$	−5.31990	−	10.2973i	−0.230215	−	0.445606i
$535$	−4.85374	+	4.20579i	−0.209845	+	0.181832i
$536$	−10.9813	+	1.60801i	−0.474321	+	0.0694555i
$537$	−4.27302	−	1.25467i	−0.184395	−	0.0541431i
$538$	−15.4317	+	0.748500i	−0.665309	+	0.0322701i
$539$	−6.94948	−	0.999185i	−0.299335	−	0.0430379i
$540$	5.06611	−	0.492613i	0.218011	−	0.0211987i
$541$	−19.0828	−	8.71483i	−0.820434	−	0.374680i	−0.0394430	−	0.999222i	$-0.512558\pi$
$541$	−19.0828	−	8.71483i	−0.820434	−	0.374680i	−0.780991	+	0.624542i	$0.785286\pi$
$542$	−1.02364	+	1.30398i	−0.0439689	+	0.0560108i
$543$	−4.72793	+	3.03846i	−0.202895	+	0.130393i
$544$	−18.1223	+	4.47962i	−0.776989	+	0.192062i
$545$	−2.95849	−	20.5768i	−0.126728	−	0.881412i
$546$	−0.271472	−	1.40200i	−0.0116179	−	0.0599999i
$547$	17.9944	+	11.5643i	0.769387	+	0.494455i	0.865496	−	0.500916i	$-0.167003\pi$
$547$	17.9944	+	11.5643i	0.769387	+	0.494455i	−0.0961092	+	0.995371i	$0.530640\pi$
$548$	−8.39967	+	43.9916i	−0.358816	+	1.87923i
$549$	−4.05595	+	1.19094i	−0.173104	+	0.0508279i
$550$	−0.198702	+	2.10012i	−0.00847269	+	0.0895496i
$551$	−5.61042			−0.239012
$552$	11.2353	−	7.60055i	0.478205	−	0.323501i
$553$	0.840848			0.0357565
$554$	−2.49089	+	26.3267i	−0.105828	+	1.11852i
$555$	14.6606	−	4.30474i	0.622308	−	0.182726i
$556$	−33.2068	−	6.34044i	−1.40828	−	0.268895i
$557$	9.01043	+	5.79065i	0.381784	+	0.245358i	0.717430	−	0.696630i	$-0.245318\pi$
$557$	9.01043	+	5.79065i	0.381784	+	0.245358i	−0.335646	+	0.941988i	$0.608955\pi$
$558$	−0.0115478	−	0.0596374i	−0.000488856	−	0.00252465i
$559$	2.71784	+	18.9030i	0.114952	+	0.799510i
$560$	−1.60512	+	1.54113i	−0.0678288	+	0.0651248i
$561$	−2.80360	+	1.80177i	−0.118368	+	0.0760707i
$562$	−6.10047	+	7.77122i	−0.257333	+	0.327809i
$563$	22.1569	+	10.1187i	0.933804	+	0.426454i	0.823418	−	0.567435i	$-0.192064\pi$
$563$	22.1569	+	10.1187i	0.933804	+	0.426454i	0.110386	+	0.993889i	$0.464791\pi$
$564$	1.52672	+	15.7010i	0.0642865	+	0.661133i
$565$	48.3339	+	6.94937i	2.03342	+	0.292362i
$566$	13.2349	−	0.641946i	0.556304	−	0.0269830i
$567$	0.209731	+	0.0615825i	0.00880787	+	0.00258622i
$568$	9.49341	−	1.39013i	0.398335	−	0.0583287i
$569$	7.18642	−	6.22707i	0.301270	−	0.261052i	−0.491086	−	0.871111i	$-0.663400\pi$
$569$	7.18642	−	6.22707i	0.301270	−	0.261052i	0.792356	+	0.610059i	$0.208854\pi$
$570$	−1.60739	−	3.11129i	−0.0673263	−	0.130318i
$571$	28.0340	+	24.2916i	1.17319	+	1.01657i	0.999495	+	0.0317719i	$0.0101150\pi$
$571$	28.0340	+	24.2916i	1.17319	+	1.01657i	0.173691	+	0.984800i	$0.444430\pi$
$572$	−6.76396	−	6.42709i	−0.282815	−	0.268730i
$573$	1.16159	+	2.54352i	0.0485261	+	0.106257i
$574$	0.175450	−	0.304497i	0.00732313	−	0.0127094i
$575$	−6.03816	−	3.70388i	−0.251809	−	0.154463i
$576$	7.99989	−	0.0415746i	0.333329	−	0.00173227i
$577$	14.0980	+	30.8704i	0.586909	+	1.28515i	0.937292	+	0.348545i	$0.113324\pi$
$577$	14.0980	+	30.8704i	0.586909	+	1.28515i	−0.350383	+	0.936607i	$0.613948\pi$
$578$	2.02982	−	8.39877i	0.0844293	−	0.349343i
$579$	−13.9589	+	16.1094i	−0.580112	+	0.669485i
$580$	−29.3189	−	1.34573i	−1.21740	−	0.0558784i
$581$	2.06496	−	1.78930i	0.0856689	−	0.0742326i
$582$	9.99477	−	25.0285i	0.414297	−	1.03747i
$583$	−0.0136152	+	0.0463690i	−0.000563883	+	0.00192041i
$584$	−7.22219	+	4.66798i	−0.298856	+	0.193163i
$585$	11.6372	+	1.67318i	0.481140	+	0.0691775i
$586$	−8.66892	−	12.1515i	−0.358110	−	0.501974i
$587$	6.58838	−	14.4265i	0.271931	−	0.595447i	−0.723564	−	0.690257i	$-0.757497\pi$
$587$	6.58838	−	14.4265i	0.271931	−	0.595447i	0.995495	+	0.0948106i	$0.0302246\pi$
$588$	12.8995	−	5.19011i	0.531965	−	0.214037i
$589$	−0.0351587	+	0.0225952i	−0.00144869	+	0.000931017i
$590$	−27.2341	+	26.0127i	−1.12121	+	1.07093i
$591$	24.4512	−	3.51555i	1.00579	−	0.144610i
$592$	23.5651	−	4.62653i	0.968519	−	0.190149i
$593$	−8.57144	−	5.50853i	−0.351987	−	0.226208i	0.352684	−	0.935742i	$-0.385269\pi$
$593$	−8.57144	−	5.50853i	−0.351987	−	0.226208i	−0.704671	+	0.709534i	$0.748905\pi$
$594$	1.34924	−	0.468285i	0.0553599	−	0.0192140i
$595$	0.517206	+	1.76144i	0.0212034	+	0.0722121i
$596$	5.10503	−	7.19535i	0.209110	−	0.294733i
$597$	−14.3514			−0.587363
$598$	29.3775	−	10.8918i	1.20134	−	0.445397i
$599$		−	30.3008i		−	1.23806i	−0.785369	−	0.619028i	$-0.787527\pi$
$599$		−	30.3008i		−	1.23806i	0.785369	−	0.619028i	$-0.212473\pi$
$600$	−1.74535	−	3.79566i	−0.0712537	−	0.154957i
$601$	18.3054	−	5.37494i	0.746692	−	0.219248i	0.113816	−	0.993502i	$-0.463693\pi$
$601$	18.3054	−	5.37494i	0.746692	−	0.219248i	0.632876	+	0.774253i	$0.281874\pi$
$602$	1.20728	−	0.419014i	0.0492049	−	0.0170777i
$603$	2.12141	−	3.30098i	0.0863906	−	0.134426i
$604$	−15.1883	−	5.22729i	−0.618005	−	0.212695i
$605$	−3.61472	−	25.1409i	−0.146959	−	1.02212i
$606$	9.85345	+	10.3161i	0.400269	+	0.419063i
$607$	10.6318	+	16.5435i	0.431533	+	0.671478i	0.987120	−	0.159980i	$-0.0511430\pi$
$607$	10.6318	+	16.5435i	0.431533	+	0.671478i	−0.555588	+	0.831458i	$0.687507\pi$
$608$	−2.06777	−	5.10090i	−0.0838591	−	0.206869i
$609$	−1.14649	−	0.523587i	−0.0464583	−	0.0212168i
$610$	8.83594	+	12.3856i	0.357757	+	0.501479i
$611$	−5.18557	+	36.0664i	−0.209786	+	1.45909i
$612$	3.01415	−	5.87160i	0.121840	−	0.237345i
$613$	33.9340	+	9.96392i	1.37058	+	0.402439i	0.882481	−	0.470349i	$-0.155872\pi$
$613$	33.9340	+	9.96392i	1.37058	+	0.402439i	0.488100	+	0.872788i	$0.337690\pi$
$614$	−43.3633	−	17.3165i	−1.75000	−	0.698836i
$615$	1.89468	+	2.18658i	0.0764010	+	0.0881715i
$616$	−0.336191	+	0.526123i	−0.0135455	+	0.0211981i
$617$	32.6173	+	28.2630i	1.31312	+	1.13783i	0.980876	+	0.194635i	$0.0623521\pi$
$617$	32.6173	+	28.2630i	1.31312	+	1.13783i	0.332247	+	0.943193i	$0.392193\pi$
$618$	2.26233	−	9.36084i	0.0910043	−	0.376548i
$619$	42.3886	−	19.3582i	1.70374	−	0.778073i	0.706200	−	0.708012i	$-0.250408\pi$
$619$	42.3886	−	19.3582i	1.70374	−	0.778073i	0.997543	−	0.0700613i	$-0.0223195\pi$
$620$	−0.189152	+	0.109644i	−0.00759652	+	0.00440342i
$621$	−0.582806	+	4.76029i	−0.0233872	+	0.191024i
$622$	−18.2708	−	10.5276i	−0.732592	−	0.422117i
$623$	−1.62954	+	0.744188i	−0.0652863	+	0.0298153i
$624$	17.9725	+	4.29420i	0.719475	+	0.171906i
$625$	19.7791	−	22.8263i	0.791165	−	0.913053i
$626$	8.96293	+	17.3488i	0.358231	+	0.693396i
$627$	−0.643474	−	0.742608i	−0.0256979	−	0.0296569i
$628$	−17.9074	+	14.1328i	−0.714583	+	0.563961i
$629$	5.58183	−	19.0100i	0.222562	−	0.757977i
$630$	−0.0381146	−	0.785803i	−0.00151852	−	0.0313071i
$631$	−5.68824	+	39.5626i	−0.226445	+	1.57496i	0.486461	+	0.873702i	$0.338288\pi$
$631$	−5.68824	+	39.5626i	−0.226445	+	1.57496i	−0.712906	+	0.701259i	$0.752622\pi$
$632$	−4.49412	+	9.90881i	−0.178767	+	0.394151i
$633$	3.23499	−	7.08365i	0.128579	−	0.281550i
$634$	8.19922	−	10.4448i	0.325633	−	0.414814i
$635$	−12.7093	−	19.7761i	−0.504353	−	0.784789i
$636$	−0.0227249	−	0.0929700i	−0.000901100	−	0.00368650i
$637$	31.7895	−	4.57065i	1.25955	−	0.181096i
$638$	−8.08500	+	1.56552i	−0.320088	+	0.0619795i
$639$	−1.83397	+	2.85372i	−0.0725509	+	0.112891i
$640$	−9.58221	−	27.1522i	−0.378770	−	1.07329i
$641$	10.3742	+	35.3313i	0.409757	+	1.39550i	0.863490	+	0.504366i	$0.168274\pi$
$641$	10.3742	+	35.3313i	0.409757	+	1.39550i	−0.453733	+	0.891138i	$0.649908\pi$
$642$	0.336161	−	3.55296i	0.0132672	−	0.140224i
$643$		−	23.3596i		−	0.921213i	−0.887605	−	0.460606i	$-0.847632\pi$
$643$		−	23.3596i		−	0.921213i	0.887605	−	0.460606i	$-0.152368\pi$
$644$	−1.08925	−	1.79143i	−0.0429226	−	0.0705924i
$645$			10.5210i			0.414265i
$646$	−4.52072	−	0.427725i	−0.177865	−	0.0168286i
$647$	−0.133461	−	0.454526i	−0.00524689	−	0.0178693i	0.956828	−	0.290655i	$-0.0938732\pi$
$647$	−0.133461	−	0.454526i	−0.00524689	−	0.0178693i	−0.962075	+	0.272786i	$0.912055\pi$
$648$	−1.84667	+	2.14239i	−0.0725439	+	0.0841610i
$649$	−5.71308	+	8.88973i	−0.224258	+	0.348952i
$650$	−1.83442	−	9.47370i	−0.0719518	−	0.371589i
$651$	−0.00929339	+	0.00133619i	−0.000364237	+	5.23693e-5i
$652$	−3.72049	−	15.2209i	−0.145706	−	0.596098i
$653$	−5.13037	−	7.98301i	−0.200767	−	0.312399i	0.726242	−	0.687439i	$-0.241265\pi$
$653$	−5.13037	−	7.98301i	−0.200767	−	0.312399i	−0.927009	+	0.375040i	$0.877629\pi$
$654$	9.08645	+	7.13293i	0.355308	+	0.278920i
$655$	16.4754	−	36.0761i	0.643747	−	1.40961i
$656$	2.65054	+	3.69501i	0.103486	+	0.144266i
$657$	0.432688	−	3.00941i	0.0168808	−	0.117408i
$658$	2.43538	−	0.118126i	0.0949411	−	0.00460503i
$659$	−3.46039	+	11.7850i	−0.134798	+	0.459079i	−0.999031	−	0.0440124i	$-0.985986\pi$
$659$	−3.46039	+	11.7850i	−0.134798	+	0.459079i	0.864233	+	0.503091i	$0.167804\pi$
$660$	−3.18453	−	4.03506i	−0.123958	−	0.157064i
$661$	−3.27074	−	3.77464i	−0.127217	−	0.146817i	0.688567	−	0.725172i	$-0.258240\pi$
$661$	−3.27074	−	3.77464i	−0.127217	−	0.146817i	−0.815785	+	0.578356i	$0.803695\pi$
$662$	−12.6104	+	6.51496i	−0.490118	+	0.253211i
$663$	9.98322	−	11.5212i	0.387716	−	0.447448i
$664$	10.0489	+	33.8974i	0.389974	+	1.31548i
$665$	−0.492362	+	0.224854i	−0.0190930	+	0.00871947i
$666$	−4.23891	+	7.35672i	−0.164255	+	0.285067i
$667$	7.23267	−	26.6909i	0.280050	−	1.03347i
$668$	−22.3365	+	12.9476i	−0.864224	+	0.500958i
$669$	22.9171	−	10.4659i	0.886028	−	0.404635i
$670$	−13.7276	−	3.31768i	−0.530342	−	0.128173i
$671$	3.22627	+	2.79558i	0.124549	+	0.107922i
$672$	0.0534858	−	1.23535i	0.00206326	−	0.0476545i
$673$	−28.4748	−	32.8617i	−1.09762	−	1.26673i	−0.961133	−	0.276085i	$-0.910963\pi$
$673$	−28.4748	−	32.8617i	−1.09762	−	1.26673i	−0.136492	−	0.990641i	$-0.543583\pi$
$674$	2.41700	−	6.05256i	0.0930993	−	0.233136i
$675$	1.41721	+	0.416131i	0.0545485	+	0.0160169i
$676$	14.8402	+	7.61813i	0.570776	+	0.293005i
$677$	−5.99316	+	41.6834i	−0.230336	+	1.60202i	0.466320	+	0.884616i	$0.345580\pi$
$677$	−5.99316	+	41.6834i	−0.230336	+	1.60202i	−0.696656	+	0.717406i	$0.745330\pi$
$678$	−22.0895	+	15.7587i	−0.848340	+	0.605209i
$679$	−3.78910	−	1.73042i	−0.145412	−	0.0664076i
$680$	−23.5217	−	3.31955i	−0.902016	−	0.127299i
$681$	3.08245	+	4.79638i	0.118120	+	0.183798i
$682$	−0.0443613	+	0.0423718i	−0.00169868	+	0.00162250i
$683$	3.22904	+	22.4585i	0.123556	+	0.859351i	0.953476	+	0.301468i	$0.0974768\pi$
$683$	3.22904	+	22.4585i	0.123556	+	0.859351i	−0.829920	+	0.557882i	$0.811614\pi$
$684$	1.84006	+	0.633283i	0.0703564	+	0.0242142i
$685$	−30.8115	+	47.9436i	−1.17725	+	1.83183i
$686$	−1.41417	−	4.07456i	−0.0539933	−	0.155567i
$687$	−6.40752	+	1.88142i	−0.244462	+	0.0717805i
$688$	−1.51480	+	16.4664i	−0.0577513	+	0.627777i
$689$		−	0.221064i		−	0.00842187i
$690$	16.8737	−	3.63606i	0.642372	−	0.138422i
$691$	−28.4746			−1.08322			−0.541612	−	0.840629i	$-0.682186\pi$
$691$	−28.4746			−1.08322			−0.541612	+	0.840629i	$0.682186\pi$
$692$	−23.0165	−	16.3300i	−0.874956	−	0.620772i
$693$	−0.0621913	−	0.211804i	−0.00236245	−	0.00804577i
$694$	1.80728	+	5.20721i	0.0686036	+	0.197663i
$695$	−36.1899	−	23.2579i	−1.37276	−	0.882221i
$696$	12.2978	−	10.7122i	0.466148	−	0.406045i
$697$	3.71342	−	0.533909i	0.140656	−	0.0202232i
$698$	28.8308	+	30.1845i	1.09126	+	1.14250i
$699$	−4.28749	+	2.75540i	−0.162168	+	0.104219i
$700$	−0.599049	+	0.241028i	−0.0226419	+	0.00910999i
$701$	9.13616	−	20.0054i	0.345068	−	0.755593i	−0.654932	−	0.755688i	$-0.727303\pi$
$701$	9.13616	−	20.0054i	0.345068	−	0.755593i	1.00000		9.45055e-5i	$3.00820e-5\pi$
$702$	−5.31842	+	3.79417i	−0.200731	+	0.143202i
$703$	5.78214	+	0.831346i	0.218077	+	0.0313548i
$704$	−4.40314	−	6.77377i	−0.165950	−	0.255296i
$705$	−5.65545	+	19.2607i	−0.212997	+	0.725400i
$706$	−12.8771	−	5.14226i	−0.484635	−	0.193532i
$707$	1.66640	−	1.44394i	0.0626713	−	0.0543050i
$708$	0.959562	−	20.9056i	0.0360626	−	0.785680i
$709$	6.20556	−	7.16160i	0.233055	−	0.268960i	−0.627161	−	0.778890i	$-0.715783\pi$
$709$	6.20556	−	7.16160i	0.233055	−	0.268960i	0.860216	+	0.509930i	$0.170329\pi$
$710$	11.8675	+	2.86815i	0.445381	+	0.107640i
$711$	−1.59801	−	3.49915i	−0.0599300	−	0.131228i
$712$	−0.0602329	−	23.1805i	−0.00225732	−	0.868727i
$713$	−0.0621687	−	0.196392i	−0.00232824	−	0.00735493i
$714$	−0.883895	−	0.509297i	−0.0330790	−	0.0190600i
$715$	−4.93227	−	10.8002i	−0.184456	−	0.403903i
$716$	−6.45682	−	6.13525i	−0.241303	−	0.229285i
$717$	−15.1240	−	13.1050i	−0.564817	−	0.489417i
$718$	28.5035	−	14.7259i	1.06374	−	0.549564i
$719$	−8.65772	+	7.50196i	−0.322878	+	0.279776i	−0.801184	−	0.598417i	$-0.795796\pi$
$719$	−8.65772	+	7.50196i	−0.322878	+	0.279776i	0.478306	+	0.878193i	$0.341251\pi$
$720$	9.46385	+	3.75076i	0.352697	+	0.139783i
$721$	−1.42820	−	0.419357i	−0.0531889	−	0.0156177i
$722$	1.23691	+	25.5012i	0.0460331	+	0.949057i
$723$	−7.04668	−	1.01316i	−0.262069	−	0.0376798i
$724$	−11.1874	+	1.08783i	−0.415778	+	0.0404289i
$725$	−7.74720	−	3.53803i	−0.287724	−	0.131399i
$726$	11.1019	+	8.71511i	0.412031	+	0.323448i
$727$	−34.9877	+	22.4852i	−1.29762	+	0.833931i	−0.992951	−	0.118527i	$-0.962183\pi$
$727$	−34.9877	+	22.4852i	−1.29762	+	0.833931i	−0.304671	+	0.952458i	$0.598546\pi$
$728$	0.797526	−	2.74246i	0.0295583	−	0.101642i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−10.7432	+	2.08024i	−0.397625	+	0.0769932i
$731$	11.4766	+	7.37558i	0.424478	+	0.272796i
$732$	−8.30434	−	1.58562i	−0.306937	−	0.0586061i
$733$	25.9142	−	7.60910i	0.957164	−	0.281049i	0.234397	−	0.972141i	$-0.424688\pi$
$733$	25.9142	−	7.60910i	0.957164	−	0.281049i	0.722767	+	0.691092i	$0.242870\pi$
$734$	−37.1111	−	3.51124i	−1.36979	−	0.129602i
$735$	17.6934			0.652632
$736$	26.9326	−	3.26133i	0.992748	−	0.120214i
$737$	−3.96268			−0.145967
$738$	−1.60059	−	0.151439i	−0.0589184	−	0.00557453i
$739$	10.9014	−	3.20094i	0.401015	−	0.117749i	−0.0750048	−	0.997183i	$-0.523897\pi$
$739$	10.9014	−	3.20094i	0.401015	−	0.117749i	0.476020	+	0.879435i	$0.342079\pi$
$740$	30.0168	+	5.73135i	1.10344	+	0.210689i
$741$	3.78129	+	2.43009i	0.138909	+	0.0892716i
$742$	−0.0145230	+	0.00281213i	−0.000533157	+	0.000103237i
$743$	6.23702	+	43.3794i	0.228814	+	1.59144i	0.703116	+	0.711075i	$0.251791\pi$
$743$	6.23702	+	43.3794i	0.228814	+	1.59144i	−0.474302	+	0.880362i	$0.657300\pi$
$744$	0.0339248	−	0.116658i	0.00124374	−	0.00427688i
$745$	9.44433	−	6.06950i	0.346013	−	0.222369i
$746$	15.5368	+	12.1965i	0.568844	+	0.446547i
$747$	−11.3705	−	5.19272i	−0.416024	−	0.189992i
$748$	−6.63401	+	0.645070i	−0.242564	+	0.0235861i
$749$	−0.545993	−	0.0785020i	−0.0199502	−	0.00286840i
$750$	0.614297	+	12.6649i	0.0224309	+	0.462455i
$751$	−2.78917	−	0.818976i	−0.101778	−	0.0298848i	0.230447	−	0.973085i	$-0.425981\pi$
$751$	−2.78917	−	0.818976i	−0.101778	−	0.0298848i	−0.332225	+	0.943200i	$0.607799\pi$
$752$	−11.6245	+	29.3306i	−0.423901	+	1.06958i
$753$	−20.4850	+	17.7504i	−0.746516	+	0.646860i
$754$	33.4682	−	17.2907i	1.21884	−	0.629692i
$755$	−15.4474	−	13.3852i	−0.562188	−	0.487138i
$756$	0.316917	+	0.301133i	0.0115262	+	0.0109521i
$757$	−6.30523	−	13.8065i	−0.229167	−	0.501807i	0.759761	−	0.650203i	$-0.225316\pi$
$757$	−6.30523	−	13.8065i	−0.229167	−	0.501807i	−0.988928	+	0.148396i	$0.952589\pi$
$758$	−45.3925	−	26.1550i	−1.64873	−	0.949991i
$759$	4.36240	−	2.10391i	0.158345	−	0.0763672i
$760$	−0.0181992	−	7.00393i	−0.000660154	−	0.254059i
$761$	−12.4839	−	27.3358i	−0.452540	−	0.990923i	−0.989125	−	0.147077i	$-0.953013\pi$
$761$	−12.4839	−	27.3358i	−0.452540	−	0.990923i	0.536585	−	0.843846i	$-0.319714\pi$
$762$	12.6973	+	3.06870i	0.459976	+	0.111167i
$763$	1.16923	−	1.34937i	0.0423291	−	0.0488504i
$764$	−0.256421	+	5.58654i	−0.00927699	+	0.202114i
$765$	6.34723	−	5.49990i	0.229484	−	0.198849i
$766$	−39.5613	−	15.7982i	−1.42941	−	0.570812i
$767$	13.6185	−	46.3805i	0.491737	−	1.67470i
$768$	14.2718	+	7.23291i	0.514990	+	0.260995i
$769$	31.0950	+	4.47079i	1.12131	+	0.161221i	0.677941	−	0.735116i	$-0.262873\pi$
$769$	31.0950	+	4.47079i	1.12131	+	0.161221i	0.443373	+	0.896337i	$0.353782\pi$
$770$	−0.646784	+	0.461418i	−0.0233085	+	0.0166283i
$771$	1.48745	−	3.25706i	0.0535692	−	0.117300i
$772$	−39.5503	+	15.9131i	−1.42345	+	0.572725i
$773$	15.1566	−	9.74054i	0.545144	−	0.350343i	−0.238904	−	0.971043i	$-0.576788\pi$
$773$	15.1566	−	9.74054i	0.545144	−	0.350343i	0.784048	+	0.620700i	$0.213152\pi$
$774$	−4.03810	−	4.22770i	−0.145147	−	0.151962i
$775$	−0.0627981	+	0.00902901i	−0.00225578	+	0.000324332i
$776$	40.6436	−	35.4032i	1.45902	−	1.27090i
$777$	1.10400	+	0.709498i	0.0396058	+	0.0254531i
$778$	13.3598	+	38.4928i	0.478973	+	1.38003i
$779$	0.311635	+	1.06133i	0.0111655	+	0.0380261i
$780$	19.1774	+	13.6061i	0.686659	+	0.487177i
$781$	3.42575			0.122583
$782$	7.86273	−	20.9553i	0.281171	−	0.749361i
$783$			5.76615i			0.206065i
$784$	27.6920	+	2.54748i	0.988998	+	0.0909813i
$785$	−27.8531	+	8.17841i	−0.994120	+	0.291900i
$786$	7.22609	+	20.8201i	0.257746	+	0.742627i
$787$	−12.9713	+	20.1838i	−0.462377	+	0.719473i	−0.991647	−	0.128980i	$-0.958830\pi$
$787$	−12.9713	+	20.1838i	−0.462377	+	0.719473i	0.529270	+	0.848454i	$0.322466\pi$
$788$	46.7159	+	16.0780i	1.66418	+	0.572753i
$789$	−2.11308	−	14.6968i	−0.0752275	−	0.523219i
$790$	−10.0120	+	9.56299i	−0.356211	+	0.340236i
$791$	2.26744	+	3.52821i	0.0806209	+	0.125449i
$792$	2.82836	+	0.399158i	0.100501	+	0.0141835i
$793$	−17.7632	−	8.11217i	−0.630789	−	0.288072i
$794$	40.6567	−	29.0046i	1.44285	−	1.02934i
$795$	0.0173322	−	0.120548i	0.000614708	−	0.00427539i
$796$	−25.5348	−	13.1082i	−0.905057	−	0.464607i
$797$	26.9003	+	7.89863i	0.952857	+	0.279784i	0.720976	−	0.692960i	$-0.243694\pi$
$797$	26.9003	+	7.89863i	0.952857	+	0.279784i	0.231881	+	0.972744i	$0.425512\pi$
$798$	0.111546	−	0.279329i	0.00394868	−	0.00988813i
$799$	17.0455	+	19.6715i	0.603025	+	0.695928i
$800$	0.361419	−	8.34760i	0.0127781	−	0.295132i
$801$	6.19381	+	5.36696i	0.218847	+	0.189632i
$802$	10.7209	+	2.59103i	0.378567	+	0.0914923i
$803$	−2.79294	+	1.27549i	−0.0985609	+	0.0450112i
$804$	6.78956	−	3.93565i	0.239449	−	0.138800i
$805$	−0.434987	−	2.63222i	−0.0153313	−	0.0927736i
$806$	0.140098	−	0.243144i	0.00493476	−	0.00856438i
$807$	9.93746	−	4.53829i	0.349815	−	0.159755i
$808$	8.10937	+	27.3548i	0.285287	+	0.962340i
$809$	−15.9702	+	18.4306i	−0.561481	+	0.647984i	−0.963519	−	0.267639i	$-0.913757\pi$
$809$	−15.9702	+	18.4306i	−0.561481	+	0.647984i	0.402038	+	0.915623i	$0.368302\pi$
$810$	−3.19765	+	1.65201i	−0.112354	+	0.0580457i
$811$	−8.59782	−	9.92241i	−0.301910	−	0.348423i	0.584441	−	0.811436i	$-0.301314\pi$
$811$	−8.59782	−	9.92241i	−0.301910	−	0.348423i	−0.886351	+	0.463013i	$0.846768\pi$
$812$	−1.56168	−	1.97877i	−0.0548042	−	0.0694412i
$813$	0.330252	−	1.12474i	0.0115825	−	0.0394462i
$814$	8.56443	−	0.415409i	0.300183	−	0.0145601i
$815$	2.83760	−	19.7359i	0.0993968	−	0.691320i
$816$	10.7259	−	7.69402i	0.375482	−	0.269345i
$817$	−1.67094	+	3.65885i	−0.0584588	+	0.128007i
$818$	15.4851	+	12.1560i	0.541426	+	0.425023i
$819$	0.545925	+	0.849476i	0.0190762	+	0.0296831i
$820$	1.37396	+	5.62104i	0.0479809	+	0.196295i
$821$	−39.7027	+	5.70839i	−1.38563	+	0.199224i	−0.794459	−	0.607318i	$-0.792245\pi$
$821$	−39.7027	+	5.70839i	−1.38563	+	0.199224i	−0.591176	+	0.806543i	$0.701336\pi$
$822$	−6.02027	−	31.0912i	−0.209981	−	1.08443i
$823$	−12.6717	+	19.7175i	−0.441706	+	0.687308i	−0.988713	−	0.149820i	$-0.952131\pi$
$823$	−12.6717	+	19.7175i	−0.441706	+	0.687308i	0.547007	+	0.837128i	$0.315767\pi$
$824$	12.5752	−	14.5890i	0.438078	−	0.508231i
$825$	−0.420245	−	1.43122i	−0.0146310	−	0.0498288i
$826$	−3.22025	−	0.304682i	−0.112047	−	0.0106013i
$827$		−	52.2927i		−	1.81840i	−0.416363	−	0.909198i	$-0.636696\pi$
$827$		−	52.2927i		−	1.81840i	0.416363	−	0.909198i	$-0.363304\pi$
$828$	−5.38488	+	7.93745i	−0.187137	+	0.275845i
$829$			32.3072i			1.12208i	0.827790	+	0.561038i	$0.189598\pi$
$829$			32.3072i			1.12208i	−0.827790	+	0.561038i	$0.810402\pi$
$830$	−4.23778	+	44.7900i	−0.147096	+	1.55468i
$831$	−5.26810	−	17.9415i	−0.182748	−	0.622384i
$832$	28.0554	+	24.0561i	0.972648	+	0.833994i
$833$	12.4037	−	19.3005i	0.429762	−	0.668722i
$834$	23.4690	−	4.54437i	0.812665	−	0.157359i
$835$	−32.5188	+	4.67550i	−1.12536	+	0.161802i
$836$	−0.466626	−	1.90902i	−0.0161386	−	0.0660249i
$837$	0.0232223	+	0.0361346i	0.000802681	+	0.00124900i
$838$	−14.6238	+	18.6289i	−0.505171	+	0.643523i
$839$	−6.95891	+	15.2379i	−0.240248	+	0.526070i	−0.990896	−	0.134633i	$-0.957014\pi$
$839$	−6.95891	+	15.2379i	−0.240248	+	0.526070i	0.750647	+	0.660703i	$0.229742\pi$
$840$	0.649915	−	1.43296i	0.0224242	−	0.0494417i
$841$	0.604619	−	4.20522i	0.0208489	−	0.145008i
$842$	−1.07509	−	22.1650i	−0.0370501	−	0.763857i
$843$	1.96818	−	6.70299i	0.0677876	−	0.230863i
$844$	12.2259	−	9.64886i	0.420832	−	0.332128i
$845$	13.9007	+	16.0423i	0.478200	+	0.551872i
$846$	−5.11995	−	9.91024i	−0.176028	−	0.340721i
$847$	1.42858	−	1.64867i	0.0490867	−	0.0566491i
$848$	0.0444829	−	0.186174i	0.00152755	−	0.00639323i
$849$	−8.52279	+	3.89223i	−0.292501	+	0.133581i
$850$	−5.97274	−	3.44147i	−0.204863	−	0.118041i
$851$	−11.4091	+	26.4361i	−0.391098	+	0.906216i
$852$	−5.86961	+	3.40239i	−0.201090	+	0.116564i
$853$	21.3245	−	9.73856i	0.730136	−	0.333442i	−0.0154233	−	0.999881i	$-0.504910\pi$
$853$	21.3245	−	9.73856i	0.730136	−	0.333442i	0.745560	+	0.666439i	$0.232182\pi$
$854$	−0.306974	+	1.27016i	−0.0105044	+	0.0434641i
$855$	1.87144	+	1.62161i	0.0640019	+	0.0554580i
$856$	3.84329	−	6.01458i	0.131361	−	0.205574i
$857$	−3.43257	−	3.96140i	−0.117254	−	0.135319i	0.694088	−	0.719891i	$-0.255808\pi$
$857$	−3.43257	−	3.96140i	−0.117254	−	0.135319i	−0.811342	+	0.584572i	$0.801263\pi$
$858$	6.12719	+	2.44680i	0.209179	+	0.0835325i
$859$	−41.0288	−	12.0471i	−1.39988	−	0.411043i	−0.507239	−	0.861805i	$-0.669334\pi$
$859$	−41.0288	−	12.0471i	−1.39988	−	0.411043i	−0.892644	+	0.450763i	$0.851152\pi$
$860$	−9.60960	+	18.7196i	−0.327685	+	0.638332i
$861$	−0.0353647	+	0.245967i	−0.00120523	+	0.00838253i
$862$	−31.4207	−	44.0435i	−1.07019	−	1.50013i
$863$	−0.893377	−	0.407992i	−0.0304109	−	0.0138882i	0.400152	−	0.916449i	$-0.368957\pi$
$863$	−0.893377	−	0.407992i	−0.0304109	−	0.0138882i	−0.430562	+	0.902561i	$0.641685\pi$
$864$	−5.24249	+	2.12516i	−0.178353	+	0.0722995i
$865$	−19.4151	−	30.2105i	−0.660134	−	1.02719i
$866$	14.1428	+	14.8068i	0.480591	+	0.503156i
$867$	0.869517	+	6.04762i	0.0295303	+	0.205388i
$868$	−0.0177558	−	0.00611090i	−0.000602670	−	0.000207418i
$869$	−2.10028	+	3.26811i	−0.0712473	+	0.110863i
$870$	19.6061	−	6.80476i	0.664709	−	0.230703i
$871$	17.3925	−	5.10690i	0.589323	−	0.173041i
$872$	9.65209	+	20.9906i	0.326861	+	0.710832i
$873$			19.0568i			0.644975i
$874$	6.44559	+	1.41538i	0.218025	+	0.0478760i
$875$	1.95982			0.0662540
$876$	3.51857	−	4.95931i	0.118882	−	0.167559i
$877$	4.06843	+	13.8558i	0.137381	+	0.467877i	0.999228	−	0.0392919i	$-0.0125102\pi$
$877$	4.06843	+	13.8558i	0.137381	+	0.467877i	−0.861847	+	0.507169i	$0.830692\pi$
$878$	24.8763	−	8.63390i	0.839534	−	0.291380i
$879$	8.87930	+	5.70638i	0.299491	+	0.192471i
$880$	−1.98059	−	10.0881i	−0.0667656	−	0.340068i
$881$	41.3119	−	5.93975i	1.39183	−	0.200115i	0.594714	−	0.803938i	$-0.297265\pi$
$881$	41.3119	−	5.93975i	1.39183	−	0.200115i	0.797119	+	0.603822i	$0.206356\pi$
$882$	−7.10982	+	6.79097i	−0.239400	+	0.228664i
$883$	3.88201	−	2.49482i	0.130640	−	0.0839573i	−0.473689	−	0.880692i	$-0.657078\pi$
$883$	3.88201	−	2.49482i	0.130640	−	0.0839573i	0.604329	+	0.796735i	$0.293441\pi$
$884$	28.2859	−	11.3809i	0.951357	−	0.382780i
$885$	11.0627	−	24.2239i	0.371868	−	0.814277i
$886$	13.1565	+	18.4418i	0.442000	+	0.619566i
$887$	0.827222	+	0.118937i	0.0277754	+	0.00399350i	0.156189	−	0.987727i	$-0.450079\pi$
$887$	0.827222	+	0.118937i	0.0277754	+	0.00399350i	−0.128413	+	0.991721i	$0.540988\pi$
$888$	−14.2615	+	9.21778i	−0.478586	+	0.309329i
$889$	0.568829	−	1.93726i	0.0190779	−	0.0649735i
$890$	10.9393	−	27.3939i	0.366687	−	0.918245i
$891$	−0.763220	+	0.661334i	−0.0255688	+	0.0221555i
$892$	50.3347	+	2.31035i	1.68533	+	0.0773564i
$893$	−5.02575	+	5.80002i	−0.168180	+	0.194090i
$894$	−1.46550	+	6.06379i	−0.0490136	+	0.202803i
$895$	−4.70830	−	10.3097i	−0.157381	−	0.344617i
$896$	1.22350	−	2.14915i	0.0408741	−	0.0717979i
$897$	−16.4355	+	14.8563i	−0.548766	+	0.496037i
$898$	−23.6676	+	41.0756i	−0.789797	+	1.37071i
$899$	−0.102888	−	0.225293i	−0.00343151	−	0.00751395i
$900$	2.14150	+	2.03485i	0.0713834	+	0.0678282i
$901$	−0.119347	−	0.103414i	−0.00397601	−	0.00344523i
$902$	0.745239	+	1.44249i	0.0248137	+	0.0480297i
$903$	−0.682917	+	0.591751i	−0.0227260	+	0.0196922i
$904$	−53.6963	+	7.86283i	−1.78591	+	0.261514i
$905$	−13.7238	−	4.02967i	−0.456195	−	0.133951i
$906$	11.3447	−	0.550264i	0.376902	−	0.0182813i
$907$	3.13412	+	0.450618i	0.104067	+	0.0149625i	0.194151	−	0.980972i	$-0.437805\pi$
$907$	3.13412	+	0.450618i	0.104067	+	0.0149625i	−0.0900847	+	0.995934i	$0.528714\pi$
$908$	1.10358	+	11.3494i	0.0366236	+	0.376643i
$909$	−9.17584	−	4.19047i	−0.304344	−	0.138989i
$910$	2.24414	−	2.85874i	0.0743924	−	0.0947664i
$911$	−25.2192	+	16.2074i	−0.835550	+	0.536975i	−0.887037	−	0.461699i	$-0.847240\pi$
$911$	−25.2192	+	16.2074i	−0.835550	+	0.536975i	0.0514873	+	0.998674i	$0.483604\pi$
$912$	2.69551	+	2.80743i	0.0892573	+	0.0929633i
$913$	1.79653	+	12.4952i	0.0594566	+	0.413530i
$914$	−4.45382	−	23.0014i	−0.147319	−	0.760818i
$915$	−9.05037	−	5.81632i	−0.299196	−	0.192282i
$916$	−13.1190	−	2.50493i	−0.433466	−	0.0827651i
$917$	3.26834	−	0.959672i	0.107930	−	0.0316911i
$918$	−0.439597	+	4.64620i	−0.0145089	+	0.153347i
$919$	26.4317			0.871900			0.435950	−	0.899971i	$-0.356412\pi$
$919$	26.4317			0.871900			0.435950	+	0.899971i	$0.356412\pi$
$920$	33.3438	+	8.94253i	1.09931	+	0.294827i
$921$	33.0169			1.08795
$922$	3.15013	−	33.2944i	0.103744	−	1.09649i
$923$	−15.0359	+	4.41494i	−0.494913	+	0.145320i
$924$	0.0828018	−	0.433658i	0.00272398	−	0.0142663i
$925$	7.46005	+	4.79428i	0.245285	+	0.157635i
$926$	−0.0205748	−	0.106257i	−0.000676129	−	0.00349181i
$927$	0.969118	+	6.74037i	0.0318300	+	0.221383i
$928$	31.6652	−	7.82725i	1.03946	−	0.256942i
$929$	−32.5412	+	20.9129i	−1.06764	+	0.686131i	−0.951670	−	0.307121i	$-0.900634\pi$
$929$	−32.5412	+	20.9129i	−1.06764	+	0.686131i	−0.115971	+	0.993253i	$0.536998\pi$
$930$	0.0954600	−	0.121604i	0.00313026	−	0.00398755i
$931$	6.15317	+	2.81006i	0.201662	+	0.0920960i
$932$	−10.1453	+	0.986492i	−0.332319	+	0.0323136i
$933$	14.7588	+	2.12200i	0.483182	+	0.0694711i
$934$	5.72632	−	0.277750i	0.187371	−	0.00908825i
$935$	−8.13804	−	2.38955i	−0.266142	−	0.0781465i
$936$	−12.9283	+	1.89311i	−0.422575	+	0.0618783i
$937$	−41.2514	+	35.7445i	−1.34762	+	1.16772i	−0.377252	+	0.926111i	$0.623131\pi$
$937$	−41.2514	+	35.7445i	−1.34762	+	1.16772i	−0.970373	+	0.241613i	$0.922324\pi$
$938$	−0.556751	−	1.07765i	−0.0181786	−	0.0351866i
$939$	−10.4353	−	9.04222i	−0.340542	−	0.295082i
$940$	−27.6547	+	29.1042i	−0.901997	+	0.949274i
$941$	−4.58305	−	10.0355i	−0.149403	−	0.327148i	0.820102	−	0.572217i	$-0.193917\pi$
$941$	−4.58305	−	10.0355i	−0.149403	−	0.327148i	−0.969506	+	0.245069i	$0.921189\pi$
$942$	8.05335	−	13.9767i	0.262392	−	0.455387i
$943$	−5.45089	+	0.114349i	−0.177505	+	0.00372373i
$944$	20.8019	−	36.3200i	0.677044	−	1.18211i
$945$	0.231095	+	0.506028i	0.00751753	+	0.0164611i
$946$	−1.38698	+	5.73891i	−0.0450947	+	0.186588i
$947$	−4.46618	+	5.15425i	−0.145131	+	0.167491i	−0.823661	−	0.567083i	$-0.808072\pi$
$947$	−4.46618	+	5.15425i	−0.145131	+	0.167491i	0.678530	+	0.734573i	$0.262618\pi$
$948$	0.352761	−	7.68547i	0.0114572	−	0.249612i
$949$	10.6147	−	9.19766i	0.344567	−	0.298569i
$950$	0.753747	−	1.88751i	0.0244548	−	0.0612388i
$951$	−2.64529	+	9.00903i	−0.0857794	+	0.292138i
$952$	−1.10750	−	1.71350i	−0.0358942	−	0.0555347i
$953$	−15.2714	−	2.19569i	−0.494689	−	0.0711255i	−0.109544	−	0.993982i	$-0.534939\pi$
$953$	−15.2714	−	2.19569i	−0.494689	−	0.0711255i	−0.385144	+	0.922856i	$0.625848\pi$
$954$	0.0393032	+	0.0550925i	0.00127249	+	0.00178369i
$955$	−2.95625	+	6.47328i	−0.0956619	+	0.209470i
$956$	−14.9397	−	37.1311i	−0.483185	−	1.20091i
$957$	4.89874	−	3.14823i	0.158354	−	0.101768i
$958$	−40.1013	+	38.3029i	−1.29562	+	1.23751i
$959$	−4.84499	+	0.696604i	−0.156453	+	0.0224945i
$960$	13.4128	+	15.3176i	0.432895	+	0.494373i
$961$	26.0773	+	16.7589i	0.841203	+	0.540609i
$962$	−37.0546	+	12.8607i	−1.19469	+	0.414645i
$963$	0.710963	+	2.42132i	0.0229105	+	0.0780259i
$964$	−11.6124	−	8.23891i	−0.374012	−	0.265357i
$965$	−54.2488			−1.74633
$966$	1.18507	+	0.890762i	0.0381291	+	0.0286598i
$967$		−	32.6103i		−	1.04868i	−0.851510	−	0.524338i	$-0.824313\pi$
$967$		−	32.6103i		−	1.04868i	0.851510	−	0.524338i	$-0.175687\pi$
$968$	11.7930	+	25.6466i	0.379043	+	0.824313i
$969$	3.08084	−	0.904616i	0.0989709	−	0.0290605i
$970$	64.7970	−	22.4893i	2.08051	−	0.722089i
$971$	4.25935	−	6.62768i	0.136689	−	0.212693i	−0.766160	−	0.642650i	$-0.777835\pi$
$971$	4.25935	−	6.62768i	0.136689	−	0.212693i	0.902849	+	0.429957i	$0.141471\pi$
$972$	0.650861	−	1.89113i	0.0208764	−	0.0606581i
$973$	−0.525827	−	3.65721i	−0.0168572	−	0.117245i
$974$	23.5699	+	24.6765i	0.755227	+	0.790687i
$975$	3.68898	+	5.74016i	0.118142	+	0.183832i
$976$	−13.3273	−	10.4062i	−0.426596	−	0.333093i
$977$	−27.3311	−	12.4817i	−0.874399	−	0.399325i	−0.0729131	−	0.997338i	$-0.523230\pi$
$977$	−27.3311	−	12.4817i	−0.874399	−	0.399325i	−0.801486	+	0.598014i	$0.795957\pi$
$978$	6.43466	+	9.01968i	0.205758	+	0.288417i
$979$	1.17788	−	8.19235i	0.0376453	−	0.261829i
$980$	31.4811	+	16.1607i	1.00563	+	0.516234i
$981$	−7.83743	−	2.30128i	−0.250230	−	0.0734741i
$982$	−53.6253	−	21.4145i	−1.71125	−	0.683363i
$983$	28.0332	+	32.3521i	0.894121	+	1.03187i	0.999300	+	0.0374173i	$0.0119131\pi$
$983$	28.0332	+	32.3521i	0.894121	+	1.03187i	−0.105179	+	0.994453i	$0.533541\pi$
$984$	−2.70953	−	1.73138i	−0.0863767	−	0.0551943i
$985$	47.5126	+	41.1699i	1.51388	+	1.31178i
$986$	6.32169	−	26.1572i	0.201324	−	0.833016i
$987$	−1.56830	+	0.716217i	−0.0499194	+	0.0227974i
$988$	4.50831	+	7.77748i	0.143429	+	0.247435i
$989$	−15.2524	−	12.6661i	−0.484999	−	0.402759i
$990$	3.14937	+	1.81465i	0.100093	+	0.0576734i
$991$	12.4544	−	5.68771i	0.395625	−	0.180676i	−0.207661	−	0.978201i	$-0.566585\pi$
$991$	12.4544	−	5.68771i	0.395625	−	0.180676i	0.603286	+	0.797525i	$0.293858\pi$
$992$	0.166913	−	0.176578i	0.00529948	−	0.00560635i
$993$	6.57259	−	7.58518i	0.208575	−	0.240708i
$994$	0.481314	+	0.931637i	0.0152664	+	0.0295497i
$995$	−23.9184	−	27.6033i	−0.758263	−	0.875082i
$996$	−15.4881	−	19.6247i	−0.490759	−	0.621831i
$997$	6.59890	−	22.4738i	0.208989	−	0.711752i	−0.786560	−	0.617513i	$-0.788140\pi$
$997$	6.59890	−	22.4738i	0.208989	−	0.711752i	0.995550	−	0.0942386i	$-0.0300417\pi$
$998$	−2.05060	−	42.2768i	−0.0649105	−	1.33825i
$999$	0.854421	−	5.94263i	0.0270327	−	0.188016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.19.1	✓	240
8.3	odd	2	inner	552.2.t.a.19.18	yes	240
23.17	odd	22	inner	552.2.t.a.523.18	yes	240
184.155	even	22	inner	552.2.t.a.523.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.19.1	✓	240	1.1	even	1	trivial
552.2.t.a.19.18	yes	240	8.3	odd	2	inner
552.2.t.a.523.1	yes	240	184.155	even	22	inner
552.2.t.a.523.18	yes	240	23.17	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40793 - 0.133210i) q^{2} +(0.959493 - 0.281733i) q^{3} +(1.96451 + 0.375100i) q^{4} +(2.14099 + 1.37593i) q^{5} +(-1.38842 + 0.268844i) q^{6} +(0.0311079 + 0.216360i) q^{7} +(-2.71592 - 0.789806i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-1.40793 - 0.133210i) q^{2} +(0.959493 - 0.281733i) q^{3} +(1.96451 + 0.375100i) q^{4} +(2.14099 + 1.37593i) q^{5} +(-1.38842 + 0.268844i) q^{6} +(0.0311079 + 0.216360i) q^{7} +(-2.71592 - 0.789806i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-2.83107 - 2.22241i) q^{10} +(-0.918624 - 0.419522i) q^{11} +(1.99061 - 0.193561i) q^{12} +(4.57257 + 0.657437i) q^{13} +(-0.0149762 - 0.308763i) q^{14} +(2.44191 + 0.717010i) q^{15} +(3.71860 + 1.47378i) q^{16} +(2.49400 - 2.16106i) q^{17} +(-1.25644 + 0.649119i) q^{18} +(0.735339 + 0.637175i) q^{19} +(3.68989 + 3.50612i) q^{20} +(0.0908035 + 0.198832i) q^{21} +(1.23747 + 0.713025i) q^{22} +(-3.97924 + 2.67687i) q^{23} +(-2.82842 + 0.00734944i) q^{24} +(0.613586 + 1.34357i) q^{25} +(-6.35027 - 1.53474i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.0200449 + 0.436710i) q^{28} +(-4.35776 + 3.77602i) q^{29} +(-3.34252 - 1.33478i) q^{30} +(-0.0121013 + 0.0412134i) q^{31} +(-5.03919 - 2.57032i) q^{32} +(-0.999606 - 0.143722i) q^{33} +(-3.79924 + 2.71039i) q^{34} +(-0.231095 + 0.506028i) q^{35} +(1.85545 - 0.746540i) q^{36} +(5.05067 - 3.24587i) q^{37} +(-0.950425 - 0.995050i) q^{38} +(4.57257 - 0.657437i) q^{39} +(-4.72804 - 5.42789i) q^{40} +(0.956371 + 0.614622i) q^{41} +(-0.101358 - 0.292037i) q^{42} +(1.16468 + 3.96653i) q^{43} +(-1.64728 - 1.16873i) q^{44} +2.54500 q^{45} +(5.95906 - 3.23876i) q^{46} +7.88755i q^{47} +(3.98318 + 0.366426i) q^{48} +(6.67061 - 1.95867i) q^{49} +(-0.684907 - 1.97338i) q^{50} +(1.78413 - 2.77616i) q^{51} +(8.73626 + 3.00671i) q^{52} +(-0.00681027 - 0.0473665i) q^{53} +(-1.02267 + 0.976805i) q^{54} +(-1.38953 - 2.16216i) q^{55} +(0.0863960 - 0.612186i) q^{56} +(0.885066 + 0.404196i) q^{57} +(6.63841 - 4.73586i) q^{58} +(1.48915 - 10.3573i) q^{59} +(4.52821 + 2.32454i) q^{60} +(-4.05595 - 1.19094i) q^{61} +(0.0225278 - 0.0564134i) q^{62} +(0.143143 + 0.165196i) q^{63} +(6.75241 + 4.29009i) q^{64} +(8.88526 + 7.69912i) q^{65} +(1.38823 + 0.335507i) q^{66} +(3.56929 - 1.63004i) q^{67} +(5.71009 - 3.30993i) q^{68} +(-3.06389 + 3.68952i) q^{69} +(0.392773 - 0.681666i) q^{70} +(-3.08567 + 1.40918i) q^{71} +(-2.71178 + 0.803909i) q^{72} +(1.99101 - 2.29775i) q^{73} +(-7.54334 + 3.89714i) q^{74} +(0.967258 + 1.11627i) q^{75} +(1.20558 + 1.52756i) q^{76} +(0.0621913 - 0.211804i) q^{77} +(-6.52542 + 0.316509i) q^{78} +(0.547454 - 3.80762i) q^{79} +(5.93368 + 8.27189i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.26462 - 0.992740i) q^{82} +(-6.75806 - 10.5157i) q^{83} +(0.103803 + 0.424668i) q^{84} +(8.31310 - 1.19524i) q^{85} +(-1.11140 - 5.73973i) q^{86} +(-3.11741 + 4.85079i) q^{87} +(2.16357 + 1.86492i) q^{88} +(2.30896 + 7.86360i) q^{89} +(-3.58318 - 0.339020i) q^{90} +1.00977i q^{91} +(-8.82136 + 3.76612i) q^{92} +0.0429533i q^{93} +(1.05070 - 11.1051i) q^{94} +(0.697646 + 2.37596i) q^{95} +(-5.55921 - 1.04650i) q^{96} +(-10.3029 + 16.0316i) q^{97} +(-9.65263 + 1.86907i) q^{98} +(-0.999606 + 0.143722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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