LMFDB - Embedded newform 220.2.r.b.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 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("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			171.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	220.171
Dual form			220.2.r.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395472 + 1.35779i) q^{2} +(0.295511 - 0.406737i) q^{3} +(-1.68720 + 1.07394i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.669131 + 0.240391i) q^{6} +(-2.59618 + 1.88624i) q^{7} +(-2.12543 - 1.86616i) q^{8} +(0.848943 + 2.61278i) q^{9} +(-1.41355 - 0.0434654i) q^{10} +(-0.569171 + 3.26742i) q^{11} +(-0.0617787 + 1.00361i) q^{12} +(3.70071 - 1.20243i) q^{13} +(-3.58783 - 2.77912i) q^{14} +(0.295511 + 0.406737i) q^{15} +(1.69332 - 3.62390i) q^{16} +(2.89908 + 0.941970i) q^{17} +(-3.21188 + 2.18597i) q^{18} +(-0.0572103 - 0.0415657i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.61337i q^{21} +(-4.66157 + 0.519356i) q^{22} -5.67459i q^{23} +(-1.38712 + 0.313016i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.09618 + 4.54927i) q^{26} +(2.74803 + 0.892888i) q^{27} +(2.35459 - 5.97060i) q^{28} +(-2.43162 - 3.34684i) q^{29} +(-0.435398 + 0.562096i) q^{30} +(0.894983 - 0.290798i) q^{31} +(5.59017 + 0.866025i) q^{32} +(1.16078 + 1.19706i) q^{33} +(-0.132495 + 4.30888i) q^{34} +(-0.991653 - 3.05199i) q^{35} +(-4.23830 - 3.49658i) q^{36} +(7.15701 - 5.19987i) q^{37} +(0.0338126 - 0.0941179i) q^{38} +(0.604528 - 1.86055i) q^{39} +(2.43162 - 1.44472i) q^{40} +(-4.98410 + 6.86002i) q^{41} +(-2.19062 + 0.638041i) q^{42} -0.496387 q^{43} +(-2.54870 - 6.12406i) q^{44} -2.74724 q^{45} +(7.70491 - 2.24414i) q^{46} +(2.38052 - 3.27651i) q^{47} +(-0.973579 - 1.75964i) q^{48} +(1.01915 - 3.13663i) q^{49} +(0.478148 - 1.33093i) q^{50} +(1.23985 - 0.900801i) q^{51} +(-4.95252 + 6.00308i) q^{52} +(2.43852 + 7.50500i) q^{53} +(-0.125591 + 4.08437i) q^{54} +(-2.93162 - 1.55100i) q^{55} +(9.03802 + 0.835843i) q^{56} +(-0.0338126 + 0.0109864i) q^{57} +(3.58268 - 4.62521i) q^{58} +(8.38521 + 11.5413i) q^{59} +(-0.935398 - 0.368887i) q^{60} +(0.696830 + 0.226414i) q^{61} +(0.748784 + 1.10020i) q^{62} +(-7.13233 - 5.18194i) q^{63} +(1.03487 + 7.93278i) q^{64} +3.89116i q^{65} +(-1.16631 + 2.04951i) q^{66} -0.155688i q^{67} +(-5.90297 + 1.52414i) q^{68} +(-2.30806 - 1.67691i) q^{69} +(3.75181 - 2.55344i) q^{70} +(14.2895 + 4.64294i) q^{71} +(3.07151 - 7.13753i) q^{72} +(-7.84500 - 10.7977i) q^{73} +(9.89074 + 7.66133i) q^{74} +(-0.478148 + 0.155360i) q^{75} +(0.141165 + 0.00868960i) q^{76} +(-4.68546 - 9.55641i) q^{77} +(2.76531 + 0.0850311i) q^{78} +(-3.20955 - 9.87796i) q^{79} +(2.92327 + 2.73029i) q^{80} +(-5.49244 + 3.99049i) q^{81} +(-11.2856 - 4.05443i) q^{82} +(-1.52731 + 4.70059i) q^{83} +(-1.73265 - 2.72208i) q^{84} +(-1.79173 + 2.46611i) q^{85} +(-0.196307 - 0.673990i) q^{86} -2.07985 q^{87} +(7.30727 - 5.88250i) q^{88} +11.9625 q^{89} +(-1.08645 - 3.73018i) q^{90} +(-7.33964 + 10.1021i) q^{91} +(6.09415 + 9.57419i) q^{92} +(0.146200 - 0.449957i) q^{93} +(5.39025 + 1.93649i) q^{94} +(0.0572103 - 0.0415657i) q^{95} +(2.00420 - 2.01781i) q^{96} +(-2.04594 - 6.29675i) q^{97} +(4.66194 + 0.143351i) q^{98} +(-9.02024 + 1.28674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.395472	+	1.35779i	0.279641	+	0.960105i
$2$	0.395472	+	1.35779i	0.279641	+	0.960105i
$3$	0.295511	−	0.406737i	0.170614	−	0.234830i	−0.715144	−	0.698977i	$-0.753639\pi$
$3$	0.295511	−	0.406737i	0.170614	−	0.234830i	0.885758	+	0.464147i	$0.153639\pi$
$4$	−1.68720	+	1.07394i	−0.843602	+	0.536969i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.669131	+	0.240391i	0.273171	+	0.0981391i
$7$	−2.59618	+	1.88624i	−0.981264	+	0.712930i	−0.957991	−	0.286799i	$-0.907409\pi$
$7$	−2.59618	+	1.88624i	−0.981264	+	0.712930i	−0.0232736	+	0.999729i	$0.507409\pi$
$8$	−2.12543	−	1.86616i	−0.751452	−	0.659788i
$9$	0.848943	+	2.61278i	0.282981	+	0.870926i
$10$	−1.41355	−	0.0434654i	−0.447002	−	0.0137450i
$11$	−0.569171	+	3.26742i	−0.171611	+	0.985165i
$11$	−0.569171	+	3.26742i	−0.171611	+	0.985165i
$12$	−0.0617787	+	1.00361i	−0.0178340	+	0.289717i
$13$	3.70071	−	1.20243i	1.02639	−	0.333495i	0.253029	−	0.967459i	$-0.418573\pi$
$13$	3.70071	−	1.20243i	1.02639	−	0.333495i	0.773363	+	0.633964i	$0.218573\pi$
$14$	−3.58783	−	2.77912i	−0.958889	−	0.742752i
$15$	0.295511	+	0.406737i	0.0763007	+	0.105019i
$16$	1.69332	−	3.62390i	0.423330	−	0.905976i
$17$	2.89908	+	0.941970i	0.703131	+	0.228461i	0.638694	−	0.769461i	$-0.279475\pi$
$17$	2.89908	+	0.941970i	0.703131	+	0.228461i	0.0644370	+	0.997922i	$0.479475\pi$
$18$	−3.21188	+	2.18597i	−0.757047	+	0.515238i
$19$	−0.0572103	−	0.0415657i	−0.0131249	−	0.00953583i	0.581203	−	0.813758i	$-0.302582\pi$
$19$	−0.0572103	−	0.0415657i	−0.0131249	−	0.00953583i	−0.594328	+	0.804222i	$0.702582\pi$
$20$	−0.500000	−	1.93649i	−0.111803	−	0.433013i
$21$			1.61337i			0.352065i
$22$	−4.66157	+	0.519356i	−0.993851	+	0.110727i
$23$		−	5.67459i		−	1.18323i	−0.806220	−	0.591616i	$-0.798490\pi$
$23$		−	5.67459i		−	1.18323i	0.806220	−	0.591616i	$-0.201510\pi$
$24$	−1.38712	+	0.313016i	−0.283146	+	0.0638941i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	3.09618	+	4.54927i	0.607211	+	0.892185i
$27$	2.74803	+	0.892888i	0.528858	+	0.171836i
$28$	2.35459	−	5.97060i	0.444976	−	1.12834i
$29$	−2.43162	−	3.34684i	−0.451540	−	0.621492i	0.521187	−	0.853442i	$-0.325489\pi$
$29$	−2.43162	−	3.34684i	−0.451540	−	0.621492i	−0.972728	+	0.231950i	$0.925489\pi$
$30$	−0.435398	+	0.562096i	−0.0794924	+	0.102624i
$31$	0.894983	−	0.290798i	0.160744	−	0.0522288i	−0.227540	−	0.973769i	$-0.573068\pi$
$31$	0.894983	−	0.290798i	0.160744	−	0.0522288i	0.388283	+	0.921540i	$0.373068\pi$
$32$	5.59017	+	0.866025i	0.988212	+	0.153093i
$33$	1.16078	+	1.19706i	0.202067	+	0.208382i
$34$	−0.132495	+	4.30888i	−0.0227226	+	0.738967i
$35$	−0.991653	−	3.05199i	−0.167620	−	0.515881i
$36$	−4.23830	−	3.49658i	−0.706384	−	0.582763i
$37$	7.15701	−	5.19987i	1.17660	−	0.854853i	0.184820	−	0.982772i	$-0.440830\pi$
$37$	7.15701	−	5.19987i	1.17660	−	0.854853i	0.991785	+	0.127919i	$0.0408298\pi$
$38$	0.0338126	−	0.0941179i	0.00548513	−	0.0152679i
$39$	0.604528	−	1.86055i	0.0968020	−	0.297926i
$40$	2.43162	−	1.44472i	0.384473	−	0.228431i
$41$	−4.98410	+	6.86002i	−0.778385	+	1.07136i	0.217073	+	0.976155i	$0.430349\pi$
$41$	−4.98410	+	6.86002i	−0.778385	+	1.07136i	−0.995458	+	0.0951998i	$0.969651\pi$
$42$	−2.19062	+	0.638041i	−0.338020	+	0.0984518i
$43$	−0.496387			−0.0756983			−0.0378491	−	0.999283i	$-0.512051\pi$
$43$	−0.496387			−0.0756983			−0.0378491	+	0.999283i	$0.512051\pi$
$44$	−2.54870	−	6.12406i	−0.384231	−	0.923237i
$45$	−2.74724			−0.409534
$46$	7.70491	−	2.24414i	1.13603	−	0.330880i
$47$	2.38052	−	3.27651i	0.347235	−	0.477928i	−0.599302	−	0.800523i	$-0.704555\pi$
$47$	2.38052	−	3.27651i	0.347235	−	0.477928i	0.946537	+	0.322595i	$0.104555\pi$
$48$	−0.973579	−	1.75964i	−0.140524	−	0.253982i
$49$	1.01915	−	3.13663i	0.145593	−	0.448090i
$50$	0.478148	−	1.33093i	0.0676203	−	0.188222i
$51$	1.23985	−	0.900801i	0.173613	−	0.126137i
$52$	−4.95252	+	6.00308i	−0.686790	+	0.832478i
$53$	2.43852	+	7.50500i	0.334957	+	1.03089i	0.966743	+	0.255749i	$0.0823220\pi$
$53$	2.43852	+	7.50500i	0.334957	+	1.03089i	−0.631786	+	0.775143i	$0.717678\pi$
$54$	−0.125591	+	4.08437i	−0.0170908	+	0.555812i
$55$	−2.93162	−	1.55100i	−0.395299	−	0.209137i
$56$	9.03802	+	0.835843i	1.20776	+	0.111694i
$57$	−0.0338126	+	0.0109864i	−0.00447859	+	0.00145518i
$58$	3.58268	−	4.62521i	0.470428	−	0.607320i
$59$	8.38521	+	11.5413i	1.09166	+	1.50254i	0.845996	+	0.533189i	$0.179007\pi$
$59$	8.38521	+	11.5413i	1.09166	+	1.50254i	0.245666	+	0.969355i	$0.420993\pi$
$60$	−0.935398	−	0.368887i	−0.120759	−	0.0476231i
$61$	0.696830	+	0.226414i	0.0892199	+	0.0289893i	0.353287	−	0.935515i	$-0.385064\pi$
$61$	0.696830	+	0.226414i	0.0892199	+	0.0289893i	−0.264067	+	0.964504i	$0.585064\pi$
$62$	0.748784	+	1.10020i	0.0950956	+	0.139726i
$63$	−7.13233	−	5.18194i	−0.898589	−	0.652863i
$64$	1.03487	+	7.93278i	0.129359	+	0.991598i
$65$			3.89116i			0.482639i
$66$	−1.16631	+	2.04951i	−0.143562	+	0.252277i
$67$		−	0.155688i		−	0.0190203i	−0.999955	−	0.00951016i	$-0.996973\pi$
$67$		−	0.155688i		−	0.0190203i	0.999955	−	0.00951016i	$-0.00302722\pi$
$68$	−5.90297	+	1.52414i	−0.715840	+	0.184829i
$69$	−2.30806	−	1.67691i	−0.277858	−	0.201876i
$70$	3.75181	−	2.55344i	0.448427	−	0.305194i
$71$	14.2895	+	4.64294i	1.69585	+	0.551016i	0.987879	−	0.155224i	$-0.0496101\pi$
$71$	14.2895	+	4.64294i	1.69585	+	0.551016i	0.707972	+	0.706240i	$0.249610\pi$
$72$	3.07151	−	7.13753i	0.361980	−	0.841166i
$73$	−7.84500	−	10.7977i	−0.918188	−	1.26378i	−0.964292	−	0.264840i	$-0.914681\pi$
$73$	−7.84500	−	10.7977i	−0.918188	−	1.26378i	0.0461045	−	0.998937i	$-0.485319\pi$
$74$	9.89074	+	7.66133i	1.14977	+	0.890612i
$75$	−0.478148	+	0.155360i	−0.0552117	+	0.0179394i
$76$	0.141165	+	0.00868960i	0.0161927	+	0.000996766i
$77$	−4.68546	−	9.55641i	−0.533958	−	1.08905i
$78$	2.76531	+	0.0850311i	0.313110	+	0.00962788i
$79$	−3.20955	−	9.87796i	−0.361102	−	1.11136i	−0.952386	−	0.304894i	$-0.901379\pi$
$79$	−3.20955	−	9.87796i	−0.361102	−	1.11136i	0.591284	−	0.806463i	$-0.298621\pi$
$80$	2.92327	+	2.73029i	0.326832	+	0.305256i
$81$	−5.49244	+	3.99049i	−0.610271	+	0.443388i
$82$	−11.2856	−	4.05443i	−1.24628	−	0.447737i
$83$	−1.52731	+	4.70059i	−0.167644	+	0.515956i	−0.999221	−	0.0394531i	$-0.987438\pi$
$83$	−1.52731	+	4.70059i	−0.167644	+	0.515956i	0.831577	+	0.555409i	$0.187438\pi$
$84$	−1.73265	−	2.72208i	−0.189048	−	0.297003i
$85$	−1.79173	+	2.46611i	−0.194341	+	0.267487i
$86$	−0.196307	−	0.673990i	−0.0211683	−	0.0726783i
$87$	−2.07985			−0.222984
$88$	7.30727	−	5.88250i	0.778958	−	0.627076i
$89$	11.9625			1.26803			0.634014	−	0.773322i	$-0.281406\pi$
$89$	11.9625			1.26803			0.634014	+	0.773322i	$0.281406\pi$
$90$	−1.08645	−	3.73018i	−0.114522	−	0.393196i
$91$	−7.33964	+	10.1021i	−0.769403	+	1.05899i
$92$	6.09415	+	9.57419i	0.635359	+	0.998178i
$93$	0.146200	−	0.449957i	0.0151602	−	0.0466583i
$94$	5.39025	+	1.93649i	0.555962	+	0.199734i
$95$	0.0572103	−	0.0415657i	0.00586966	−	0.00426455i
$96$	2.00420	−	2.01781i	0.204553	−	0.205942i
$97$	−2.04594	−	6.29675i	−0.207734	−	0.639338i	−0.999590	−	0.0286309i	$-0.990885\pi$
$97$	−2.04594	−	6.29675i	−0.207734	−	0.639338i	0.791857	−	0.610707i	$-0.209115\pi$
$98$	4.66194	+	0.143351i	0.470927	+	0.0144806i
$99$	−9.02024	+	1.28674i	−0.906569	+	0.129322i
$100$	1.99622	+	0.122881i	0.199622	+	0.0122881i
$101$	−18.7450	+	6.09061i	−1.86519	+	0.606039i	−0.872010	+	0.489488i	$0.837184\pi$
$101$	−18.7450	+	6.09061i	−1.86519	+	0.606039i	−0.993185	+	0.116551i	$0.962816\pi$
$102$	1.71343	+	1.32721i	0.169654	+	0.131414i
$103$	−5.46885	−	7.52722i	−0.538861	−	0.741679i	0.449587	−	0.893237i	$-0.351571\pi$
$103$	−5.46885	−	7.52722i	−0.538861	−	0.741679i	−0.988448	+	0.151557i	$0.951571\pi$
$104$	−10.1095	−	4.35045i	−0.991320	−	0.426596i
$105$	−1.53440	−	0.498558i	−0.149742	−	0.0486543i
$106$	−9.22587	+	6.27902i	−0.896096	+	0.609873i
$107$	3.16302	+	2.29807i	0.305780	+	0.222162i	0.730084	−	0.683358i	$-0.239481\pi$
$107$	3.16302	+	2.29807i	0.305780	+	0.222162i	−0.424303	+	0.905520i	$0.639481\pi$
$108$	−5.59539	+	1.44472i	−0.538417	+	0.139019i
$109$		−	7.32285i		−	0.701402i	−0.936488	−	0.350701i	$-0.885943\pi$
$109$		−	7.32285i		−	0.701402i	0.936488	−	0.350701i	$-0.114057\pi$
$110$	0.946568	−	4.59391i	0.0902517	−	0.438012i
$111$		−	4.44764i		−	0.422151i
$112$	2.43938	+	12.6023i	0.230499	+	1.19081i
$113$	−10.6436	−	7.73303i	−1.00127	−	0.727462i	−0.0389066	−	0.999243i	$-0.512387\pi$
$113$	−10.6436	−	7.73303i	−1.00127	−	0.727462i	−0.962359	+	0.271781i	$0.912387\pi$
$114$	−0.0282892	−	0.0415657i	−0.00264952	−	0.00389299i
$115$	5.39685	+	1.75354i	0.503259	+	0.163519i
$116$	7.69693	+	3.03539i	0.714642	+	0.281829i
$117$	6.28339	+	8.64834i	0.580899	+	0.799539i
$118$	−12.3545	+	15.9496i	−1.13733	+	1.46828i
$119$	−9.30333	+	3.02283i	−0.852835	+	0.277103i
$120$	0.130949	−	1.41596i	0.0119540	−	0.129259i
$121$	−10.3521	−	3.71944i	−0.941099	−	0.338131i
$122$	−0.0318466	+	1.03569i	−0.00288326	+	0.0937670i
$123$	1.31736	+	4.05443i	0.118783	+	0.365576i
$124$	−1.19772	+	1.45179i	−0.107559	+	0.130375i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	4.21537	−	11.7335i	0.375535	−	1.04531i
$127$	−3.52185	+	10.8391i	−0.312514	+	0.961819i	0.664252	+	0.747509i	$0.268750\pi$
$127$	−3.52185	+	10.8391i	−0.312514	+	0.961819i	−0.976766	+	0.214310i	$0.931250\pi$
$128$	−10.3618	+	4.54233i	−0.915864	+	0.401489i
$129$	−0.146688	+	0.201899i	−0.0129152	+	0.0177762i
$130$	−5.28339	+	1.53884i	−0.463384	+	0.134965i
$131$	−2.64098			−0.230743			−0.115372	−	0.993322i	$-0.536806\pi$
$131$	−2.64098			−0.230743			−0.115372	+	0.993322i	$0.536806\pi$
$132$	−3.24405	−	0.773082i	−0.282358	−	0.0672881i
$133$	0.226931			0.0196774
$134$	0.211392	−	0.0615702i	0.0182615	−	0.00531885i
$135$	−1.69837	+	2.33761i	−0.146173	+	0.201190i
$136$	−4.40392	−	7.41225i	−0.377633	−	0.635595i
$137$	4.87723	−	15.0106i	0.416690	−	1.28244i	−0.494040	−	0.869439i	$-0.664481\pi$
$137$	4.87723	−	15.0106i	0.416690	−	1.28244i	0.910730	−	0.413001i	$-0.135519\pi$
$138$	1.36412	−	3.79704i	0.116121	−	0.323225i
$139$	10.4351	−	7.58152i	0.885091	−	0.643056i	−0.0495025	−	0.998774i	$-0.515764\pi$
$139$	10.4351	−	7.58152i	0.885091	−	0.643056i	0.934593	+	0.355718i	$0.115764\pi$
$140$	4.95077	+	4.08437i	0.418417	+	0.345192i
$141$	−0.629204	−	1.93649i	−0.0529886	−	0.163082i
$142$	−0.653062	+	21.2383i	−0.0548037	+	1.78228i
$143$	1.82252	+	12.7762i	0.152407	+	1.06840i
$144$	10.9060	+	1.34778i	0.908832	+	0.112315i
$145$	3.93444	−	1.27838i	0.326738	−	0.106164i
$146$	11.5586	−	14.9221i	0.956596	−	1.23496i
$147$	−0.974611	−	1.34144i	−0.0803845	−	0.110640i
$148$	−6.49100	+	16.4594i	−0.533557	+	1.35296i
$149$	12.2540	+	3.98156i	1.00388	+	0.326182i	0.764417	−	0.644722i	$-0.223027\pi$
$149$	12.2540	+	3.98156i	1.00388	+	0.326182i	0.239468	+	0.970904i	$0.423027\pi$
$150$	−0.400040	−	0.587785i	−0.0326631	−	0.0479925i
$151$	−9.72065	−	7.06247i	−0.791055	−	0.574735i	0.117221	−	0.993106i	$-0.462601\pi$
$151$	−9.72065	−	7.06247i	−0.791055	−	0.574735i	−0.908276	+	0.418370i	$0.862601\pi$
$152$	0.0440279	+	0.195109i	0.00357113	+	0.0158254i
$153$			8.37435i			0.677026i
$154$	11.1227	−	10.1412i	0.896290	−	0.817199i
$155$			0.941041i			0.0755862i
$156$	0.978148	+	3.78835i	0.0783145	+	0.303311i
$157$	4.93977	+	3.58895i	0.394236	+	0.286429i	0.767189	−	0.641421i	$-0.221655\pi$
$157$	4.93977	+	3.58895i	0.394236	+	0.286429i	−0.372953	+	0.927850i	$0.621655\pi$
$158$	12.1429	−	8.26435i	0.966041	−	0.657477i
$159$	3.77317	+	1.22598i	0.299232	+	0.0972263i
$160$	−2.55110	+	5.04895i	−0.201682	+	0.399155i
$161$	10.7036	+	14.7323i	0.843563	+	1.16106i
$162$	−7.59037	−	5.87948i	−0.596356	−	0.461935i
$163$	22.5515	−	7.32742i	1.76637	−	0.573928i	0.768541	−	0.639800i	$-0.220983\pi$
$163$	22.5515	−	7.32742i	1.76637	−	0.573928i	0.997828	+	0.0658721i	$0.0209829\pi$
$164$	1.04196	−	16.9269i	0.0813634	−	1.32177i
$165$	−1.49718	+	0.734058i	−0.116555	+	0.0571463i
$166$	−6.98643	−	0.214827i	−0.542252	−	0.0166738i
$167$	−4.45689	−	13.7169i	−0.344884	−	1.06144i	−0.961646	−	0.274294i	$-0.911556\pi$
$167$	−4.45689	−	13.7169i	−0.344884	−	1.06144i	0.616762	−	0.787150i	$-0.288444\pi$
$168$	3.01081	−	3.42909i	0.232289	−	0.264560i
$169$	1.73219	−	1.25851i	0.133245	−	0.0968083i
$170$	−4.05705	−	1.45753i	−0.311161	−	0.111787i
$171$	0.0600337	−	0.184765i	0.00459090	−	0.0141293i
$172$	0.837506	−	0.533088i	0.0638592	−	0.0406476i
$173$	−5.53034	+	7.61185i	−0.420464	+	0.578719i	−0.965731	−	0.259543i	$-0.916428\pi$
$173$	−5.53034	+	7.61185i	−0.420464	+	0.578719i	0.545268	+	0.838262i	$0.316428\pi$
$174$	−0.822523	−	2.82401i	−0.0623553	−	0.214088i
$175$	3.20906			0.242582
$176$	10.8770	+	7.59540i	0.819887	+	0.572525i
$177$	7.17218			0.539094
$178$	4.73085	+	16.2427i	0.354592	+	1.21744i
$179$	−2.33964	+	3.22024i	−0.174873	+	0.240692i	−0.887452	−	0.460900i	$-0.847527\pi$
$179$	−2.33964	+	3.22024i	−0.174873	+	0.240692i	0.712579	+	0.701592i	$0.247527\pi$
$180$	4.63515	−	2.95036i	0.345484	−	0.219907i
$181$	−0.595756	+	1.83355i	−0.0442822	+	0.136287i	−0.970753	−	0.240079i	$-0.922827\pi$
$181$	−0.595756	+	1.83355i	−0.0442822	+	0.136287i	0.926471	+	0.376366i	$0.122827\pi$
$182$	−16.6192	−	5.97060i	−1.23190	−	0.442570i
$183$	0.298012	−	0.216518i	0.0220297	−	0.0160055i
$184$	−10.5897	+	12.0609i	−0.780683	+	0.889142i
$185$	2.73373	+	8.41356i	0.200988	+	0.618578i
$186$	0.668766	+	0.0205640i	0.0490363	+	0.00150783i
$187$	−4.72789	+	8.93639i	−0.345737	+	0.653494i
$188$	−0.497665	+	8.08467i	−0.0362959	+	0.589635i
$189$	−8.81858	+	2.86533i	−0.641457	+	0.208422i
$190$	0.0790627	+	0.0612417i	0.00573581	+	0.00444294i
$191$	−10.5199	−	14.4795i	−0.761196	−	1.04770i	−0.997114	−	0.0759237i	$-0.975809\pi$
$191$	−10.5199	−	14.4795i	−0.761196	−	1.04770i	0.235917	−	0.971773i	$-0.424191\pi$
$192$	3.53237	+	1.92331i	0.254927	+	0.138803i
$193$	6.55977	+	2.13140i	0.472182	+	0.153421i	0.535435	−	0.844576i	$-0.320148\pi$
$193$	6.55977	+	2.13140i	0.472182	+	0.153421i	−0.0632531	+	0.997998i	$0.520148\pi$
$194$	7.74057	−	5.26815i	0.555741	−	0.378231i
$195$	1.58268	+	1.14988i	0.113338	+	0.0823447i
$196$	1.64902	+	6.38664i	0.117787	+	0.456189i
$197$			5.15052i			0.366959i	0.983024	+	0.183480i	$0.0587361\pi$
$197$			5.15052i			0.366959i	−0.983024	+	0.183480i	$0.941264\pi$
$198$	−5.31438	−	11.7388i	−0.377676	−	0.834237i
$199$		−	18.1133i		−	1.28402i	−0.766697	−	0.642009i	$-0.778101\pi$
$199$		−	18.1133i		−	1.28402i	0.766697	−	0.642009i	$-0.221899\pi$
$200$	0.622602	+	2.75905i	0.0440246	+	0.195094i
$201$	−0.0633240	−	0.0460076i	−0.00446653	−	0.00324513i
$202$	−15.6829	−	23.0431i	−1.10344	−	1.62131i
$203$	12.6259	+	4.10239i	0.886161	+	0.287931i
$204$	−1.12447	+	2.85135i	−0.0787287	+	0.199635i
$205$	−4.98410	−	6.86002i	−0.348104	−	0.479125i
$206$	8.05764	−	10.4024i	0.561402	−	0.724767i
$207$	14.8264	−	4.81740i	1.03051	−	0.334833i
$208$	1.90898	−	15.4471i	0.132364	−	1.07106i
$209$	0.168375	−	0.163272i	0.0116468	−	0.0112938i
$210$	0.0701256	−	2.28057i	0.00483913	−	0.157374i
$211$	−1.09365	−	3.36590i	−0.0752897	−	0.231718i	0.906328	−	0.422574i	$-0.138874\pi$
$211$	−1.09365	−	3.36590i	−0.0752897	−	0.231718i	−0.981618	+	0.190856i	$0.938874\pi$
$212$	−12.1742	−	10.0437i	−0.836127	−	0.689801i
$213$	6.11116	−	4.44002i	0.418730	−	0.304225i
$214$	−1.86942	+	5.20354i	−0.127791	+	0.355707i
$215$	0.153392	−	0.472092i	0.0104612	−	0.0321964i
$216$	−4.17445	−	7.02604i	−0.284036	−	0.478061i
$217$	−1.77503	+	2.44311i	−0.120497	+	0.165849i
$218$	9.94291	−	2.89598i	0.673419	−	0.196140i
$219$	−6.71011			−0.453427
$220$	6.61192	−	0.531517i	0.445776	−	0.0358349i
$221$	11.8613			0.797879
$222$	6.03897	−	1.75891i	0.405309	−	0.118051i
$223$	−6.41560	+	8.83032i	−0.429620	+	0.591322i	−0.967866	−	0.251466i	$-0.919087\pi$
$223$	−6.41560	+	8.83032i	−0.429620	+	0.591322i	0.538246	+	0.842788i	$0.319087\pi$
$224$	−16.1466	+	8.29602i	−1.07884	+	0.554301i
$225$	0.848943	−	2.61278i	0.0565962	−	0.174185i
$226$	6.29061	−	17.5100i	0.418445	−	1.16475i
$227$	6.15855	−	4.47445i	0.408757	−	0.296980i	−0.364341	−	0.931266i	$-0.618706\pi$
$227$	6.15855	−	4.47445i	0.408757	−	0.296980i	0.773099	+	0.634286i	$0.218706\pi$
$228$	0.0452501	−	0.0548489i	0.00299676	−	0.00363246i
$229$	−2.00680	−	6.17630i	−0.132613	−	0.408141i	0.862598	−	0.505890i	$-0.168836\pi$
$229$	−2.00680	−	6.17630i	−0.132613	−	0.408141i	−0.995211	+	0.0977487i	$0.968836\pi$
$230$	−0.246648	+	8.02128i	−0.0162635	+	0.528908i
$231$	−5.27155	−	0.918281i	−0.346842	−	0.0604184i
$232$	−1.07752	+	11.6513i	−0.0707425	+	0.764942i
$233$	20.0082	−	6.50106i	1.31078	−	0.425899i	0.431462	−	0.902131i	$-0.357998\pi$
$233$	20.0082	−	6.50106i	1.31078	−	0.425899i	0.879320	+	0.476232i	$0.157998\pi$
$234$	−9.25776	+	11.9517i	−0.605198	+	0.781308i
$235$	2.38052	+	3.27651i	0.155288	+	0.213736i
$236$	−26.5422	−	10.4673i	−1.72775	−	0.681361i
$237$	−4.96619	−	1.61361i	−0.322589	−	0.104815i
$238$	−7.78359	−	11.4366i	−0.504535	−	0.741321i
$239$	11.4476	+	8.31718i	0.740485	+	0.537994i	0.892863	−	0.450329i	$-0.148693\pi$
$239$	11.4476	+	8.31718i	0.740485	+	0.537994i	−0.152378	+	0.988322i	$0.548693\pi$
$240$	1.97437	−	0.382170i	0.127445	−	0.0246690i
$241$		−	4.74712i		−	0.305789i	−0.988243	−	0.152895i	$-0.951141\pi$
$241$		−	4.74712i		−	0.305789i	0.988243	−	0.152895i	$-0.0488595\pi$
$242$	0.956274	−	15.5269i	0.0614716	−	0.998109i
$243$			12.0816i			0.775032i
$244$	−1.41885	+	0.366345i	−0.0908324	+	0.0234528i
$245$	2.66818	+	1.93854i	0.170463	+	0.123849i
$246$	−4.98410	+	3.39212i	−0.317774	+	0.216274i
$247$	−0.261699	−	0.0850311i	−0.0166515	−	0.00541040i
$248$	−2.44490	−	1.05212i	−0.155251	−	0.0668094i
$249$	1.46056	+	2.01029i	0.0925593	+	0.127397i
$250$	1.11803	+	0.866025i	0.0707107	+	0.0547723i
$251$	12.3766	−	4.02140i	0.781204	−	0.253829i	0.108850	−	0.994058i	$-0.465283\pi$
$251$	12.3766	−	4.02140i	0.781204	−	0.253829i	0.672354	+	0.740230i	$0.265283\pi$
$252$	17.5988	+	1.08332i	1.10862	+	0.0682428i
$253$	18.5413	+	3.22981i	1.16568	+	0.203056i
$254$	−16.1101	−	0.495373i	−1.01084	−	0.0310825i
$255$	0.473579	+	1.45753i	0.0296567	+	0.0912739i
$256$	−10.2653	−	12.2728i	−0.641584	−	0.767053i
$257$	−10.5292	+	7.64990i	−0.656792	+	0.477188i	−0.865578	−	0.500774i	$-0.833049\pi$
$257$	−10.5292	+	7.64990i	−0.656792	+	0.477188i	0.208786	+	0.977961i	$0.433049\pi$
$258$	−0.332148	−	0.119327i	−0.0206786	−	0.00742896i
$259$	−8.77270	+	26.9996i	−0.545109	+	1.67767i
$260$	−4.17886	−	6.56518i	−0.259162	−	0.407155i
$261$	6.68024	−	9.19456i	0.413496	−	0.569129i
$262$	−1.04443	−	3.58590i	−0.0645252	−	0.221538i
$263$	−23.6461			−1.45808			−0.729040	−	0.684471i	$-0.760033\pi$
$263$	−23.6461			−1.45808			−0.729040	+	0.684471i	$0.760033\pi$
$264$	−0.233245	−	4.71048i	−0.0143552	−	0.289910i
$265$	−7.89123			−0.484754
$266$	0.0897448	+	0.308126i	0.00550261	+	0.0188924i
$267$	3.53507	−	4.86561i	0.216343	−	0.297770i
$268$	0.167199	+	0.262678i	0.0102133	+	0.0160456i
$269$	−4.01098	+	12.3445i	−0.244554	+	0.752660i	0.751155	+	0.660125i	$0.229497\pi$
$269$	−4.01098	+	12.3445i	−0.244554	+	0.752660i	−0.995709	+	0.0925345i	$0.970503\pi$
$270$	−3.84565	−	1.38158i	−0.234039	−	0.0840804i
$271$	16.9252	−	12.2969i	1.02813	−	0.746981i	0.0601974	−	0.998186i	$-0.480827\pi$
$271$	16.9252	−	12.2969i	1.02813	−	0.746981i	0.967934	+	0.251205i	$0.0808270\pi$
$272$	8.32268	−	8.91095i	0.504637	−	0.540306i
$273$	1.93997	+	5.97060i	0.117412	+	0.361357i
$274$	22.3101	+	0.686017i	1.34780	+	0.0414438i
$275$	2.38101	−	2.30885i	0.143580	−	0.139229i
$276$	5.69506	+	0.350569i	0.342803	+	0.0211018i
$277$	13.2733	−	4.31275i	0.797514	−	0.259128i	0.118213	−	0.992988i	$-0.462283\pi$
$277$	13.2733	−	4.31275i	0.797514	−	0.259128i	0.679300	+	0.733860i	$0.262283\pi$
$278$	14.4209	+	11.1704i	0.864909	+	0.669955i
$279$	1.51958	+	2.09152i	0.0909749	+	0.125216i
$280$	−3.58783	+	8.33737i	−0.214414	+	0.498253i
$281$	10.5559	+	3.42982i	0.629712	+	0.204606i	0.606447	−	0.795124i	$-0.292594\pi$
$281$	10.5559	+	3.42982i	0.629712	+	0.204606i	0.0232643	+	0.999729i	$0.492594\pi$
$282$	2.38052	−	1.62016i	0.141758	−	0.0964789i
$283$	10.2954	+	7.48008i	0.612001	+	0.444645i	0.850118	−	0.526592i	$-0.176530\pi$
$283$	10.2954	+	7.48008i	0.612001	+	0.444645i	−0.238117	+	0.971236i	$0.576530\pi$
$284$	−29.0955	+	7.51243i	−1.72650	+	0.445781i
$285$		−	0.0355527i		−	0.00210596i
$286$	−16.6266	+	7.52722i	−0.983154	+	0.445094i
$287$		−	27.2110i		−	1.60622i
$288$	2.48300	+	15.3411i	0.146312	+	0.903982i
$289$	−6.23590	−	4.53065i	−0.366818	−	0.266509i
$290$	3.29173	+	4.83660i	0.193297	+	0.284015i
$291$	−3.16572	−	1.02860i	−0.185578	−	0.0602978i
$292$	24.8322	+	9.79292i	1.45319	+	0.573087i
$293$	−17.0950	−	23.5292i	−0.998700	−	1.37459i	−0.926119	−	0.377231i	$-0.876876\pi$
$293$	−17.0950	−	23.5292i	−0.998700	−	1.37459i	−0.0725812	−	0.997363i	$-0.523124\pi$
$294$	1.43596	−	1.85382i	0.0837470	−	0.108117i
$295$	−13.5676	+	4.40837i	−0.789934	+	0.256665i
$296$	−24.9155	−	2.30420i	−1.44818	−	0.133929i
$297$	−4.48154	+	8.47076i	−0.260045	+	0.491523i
$298$	−0.560034	+	18.2130i	−0.0324419	+	1.05505i
$299$	−6.82331	−	21.0000i	−0.394602	−	1.21446i
$300$	0.639886	−	0.775624i	0.0369439	−	0.0447807i
$301$	1.28871	−	0.936303i	0.0742800	−	0.0539676i
$302$	5.74513	−	15.9916i	0.330595	−	0.920215i
$303$	−3.06208	+	9.42411i	−0.175912	+	0.541401i
$304$	−0.247505	+	0.136941i	−0.0141954	+	0.00785409i
$305$	−0.430664	+	0.592759i	−0.0246598	+	0.0339413i
$306$	−11.3706	+	3.31182i	−0.650016	+	0.189324i
$307$	−29.1604			−1.66427			−0.832137	−	0.554570i	$-0.812883\pi$
$307$	−29.1604			−1.66427			−0.832137	+	0.554570i	$0.812883\pi$
$308$	18.1683	+	11.0917i	1.03524	+	0.632010i
$309$	−4.67770			−0.266105
$310$	−1.27774	+	0.372155i	−0.0725707	+	0.0211370i
$311$	−6.97622	+	9.60194i	−0.395585	+	0.544476i	−0.959629	−	0.281269i	$-0.909245\pi$
$311$	−6.97622	+	9.60194i	−0.395585	+	0.544476i	0.564044	+	0.825745i	$0.309245\pi$
$312$	−4.75697	+	2.82631i	−0.269310	+	0.160008i
$313$	−5.97282	+	18.3825i	−0.337604	+	1.03904i	0.627821	+	0.778358i	$0.283947\pi$
$313$	−5.97282	+	18.3825i	−0.337604	+	1.03904i	−0.965425	+	0.260681i	$0.916053\pi$
$314$	−2.91952	+	8.12651i	−0.164758	+	0.458605i
$315$	7.13233	−	5.18194i	0.401861	−	0.291969i
$316$	16.0235	+	13.2193i	0.901391	+	0.743644i
$317$	1.99819	+	6.14980i	0.112230	+	0.345407i	0.991359	−	0.131176i	$-0.0418752\pi$
$317$	1.99819	+	6.14980i	0.112230	+	0.345407i	−0.879130	+	0.476583i	$0.841875\pi$
$318$	−0.172442	+	5.60802i	−0.00967008	+	0.314482i
$319$	12.3195	−	6.04021i	0.689761	−	0.338187i
$320$	−7.86432	−	1.46715i	−0.439629	−	0.0820159i
$321$	1.86942	−	0.607410i	0.104341	−	0.0339023i
$322$	−15.7704	+	20.3595i	−0.878849	+	1.13459i
$323$	−0.126704	−	0.174393i	−0.00704999	−	0.00970349i
$324$	4.98134	−	12.6313i	0.276741	−	0.701740i
$325$	−3.70071	−	1.20243i	−0.205278	−	0.0666990i
$326$	18.8676	+	27.7225i	1.04498	+	1.53541i
$327$	−2.97847	−	2.16399i	−0.164710	−	0.119669i
$328$	23.3952	−	5.27933i	1.29179	−	0.291502i
$329$			12.9966i			0.716528i
$330$	−1.58879	−	1.74256i	−0.0874600	−	0.0959246i
$331$			23.7859i			1.30739i	0.756757	+	0.653697i	$0.226783\pi$
$331$			23.7859i			1.30739i	−0.756757	+	0.653697i	$0.773217\pi$
$332$	−2.47124	−	9.57109i	−0.135627	−	0.525282i
$333$	19.6620	+	14.2853i	1.07747	+	0.782828i
$334$	16.8621	−	11.4762i	0.922654	−	0.627948i
$335$	0.148068	+	0.0481102i	0.00808983	+	0.00262854i
$336$	5.84668	+	2.73194i	0.318963	+	0.149040i
$337$	2.80658	+	3.86293i	0.152884	+	0.210427i	0.878588	−	0.477580i	$-0.158486\pi$
$337$	2.80658	+	3.86293i	0.152884	+	0.210427i	−0.725704	+	0.688007i	$0.758486\pi$
$338$	2.39382	+	1.85425i	0.130207	+	0.100858i
$339$	−6.29061	+	2.04394i	−0.341659	+	0.111012i
$340$	0.374574	−	6.08504i	0.0203141	−	0.330008i
$341$	0.440761	+	3.08980i	0.0238685	+	0.167322i
$342$	0.274614	+	0.00844416i	0.0148494	+	0.000456608i
$343$	−3.67105	−	11.2983i	−0.198218	−	0.610053i
$344$	1.05503	+	0.926339i	0.0568836	+	0.0499448i
$345$	2.30806	−	1.67691i	0.124262	−	0.0902815i
$346$	−12.5224	−	4.49878i	−0.673209	−	0.241856i
$347$	−6.31545	+	19.4370i	−0.339031	+	1.04343i	0.625671	+	0.780087i	$0.284825\pi$
$347$	−6.31545	+	19.4370i	−0.339031	+	1.04343i	−0.964702	+	0.263344i	$0.915175\pi$
$348$	3.50914	−	2.23363i	0.188109	−	0.119735i
$349$	1.38082	−	1.90054i	0.0739138	−	0.101734i	−0.770459	−	0.637489i	$-0.779973\pi$
$349$	1.38082	−	1.90054i	0.0739138	−	0.101734i	0.844373	+	0.535755i	$0.179973\pi$
$350$	1.26909	+	4.35724i	0.0678357	+	0.232904i
$351$	11.2433			0.600123
$352$	−6.01143	+	17.7725i	−0.320410	+	0.947279i
$353$	−15.3669			−0.817897			−0.408949	−	0.912557i	$-0.634104\pi$
$353$	−15.3669			−0.817897			−0.408949	+	0.912557i	$0.634104\pi$
$354$	2.83639	+	9.73834i	0.150753	+	0.517587i
$355$	−8.83140	+	12.1554i	−0.468722	+	0.645140i
$356$	−20.1833	+	12.8470i	−1.06971	+	0.680891i
$357$	−1.51974	+	4.67729i	−0.0804333	+	0.247548i
$358$	−5.29768	−	1.90324i	−0.279991	−	0.100589i
$359$	−13.1667	+	9.56619i	−0.694914	+	0.504884i	−0.878272	−	0.478162i	$-0.841303\pi$
$359$	−13.1667	+	9.56619i	−0.694914	+	0.504884i	0.183358	+	0.983046i	$0.441303\pi$
$360$	5.83905	+	5.12680i	0.307745	+	0.270206i
$361$	−5.86978	−	18.0653i	−0.308936	−	0.950806i
$362$	−2.72519	−	0.0837973i	−0.143233	−	0.00440429i
$363$	−4.57199	+	3.11144i	−0.239967	+	0.163308i
$364$	1.53440	−	24.9267i	0.0804246	−	1.30651i
$365$	12.6935	−	4.12436i	0.664407	−	0.215879i
$366$	0.411842	+	0.319012i	0.0215273	+	0.0166750i
$367$	9.76265	+	13.4371i	0.509606	+	0.701413i	0.983853	−	0.178979i	$-0.0572794\pi$
$367$	9.76265	+	13.4371i	0.509606	+	0.701413i	−0.474246	+	0.880392i	$0.657279\pi$
$368$	−20.5641	−	9.60888i	−1.07198	−	0.500897i
$369$	−22.1549	−	7.19857i	−1.15334	−	0.374743i
$370$	−10.3428	+	7.03917i	−0.537695	+	0.365949i
$371$	−20.4871	−	14.8847i	−1.06363	−	0.772776i
$372$	0.236556	+	0.916178i	0.0122649	+	0.0475016i
$373$		−	11.8791i		−	0.615076i	−0.951536	−	0.307538i	$-0.900495\pi$
$373$		−	11.8791i		−	0.615076i	0.951536	−	0.307538i	$-0.0995051\pi$
$374$	−14.0035	−	2.88540i	−0.724105	−	0.149201i
$375$		−	0.502754i		−	0.0259621i
$376$	−11.1741	+	2.52153i	−0.576261	+	0.130038i
$377$	−13.0231	−	9.46181i	−0.670722	−	0.487308i
$378$	−7.37802	−	10.8406i	−0.379485	−	0.557583i
$379$	20.1255	+	6.53916i	1.03378	+	0.335894i	0.776282	−	0.630386i	$-0.217103\pi$
$379$	20.1255	+	6.53916i	1.03378	+	0.335894i	0.257494	+	0.966280i	$0.417103\pi$
$380$	−0.0518865	+	0.131570i	−0.00266172	+	0.00674941i
$381$	3.36793	+	4.63556i	0.172544	+	0.237487i
$382$	15.4998	−	20.0101i	0.793037	−	1.02381i
$383$	1.39303	−	0.452624i	0.0711807	−	0.0231280i	−0.273210	−	0.961954i	$-0.588085\pi$
$383$	1.39303	−	0.452624i	0.0711807	−	0.0231280i	0.344391	+	0.938826i	$0.388085\pi$
$384$	−1.21450	+	5.55684i	−0.0619774	+	0.283571i
$385$	10.5366	−	1.50304i	0.536993	−	0.0766022i
$386$	−0.299796	+	9.74971i	−0.0152592	+	0.496247i
$387$	−0.421404	−	1.29695i	−0.0214212	−	0.0659276i
$388$	10.2142	+	8.42670i	0.518549	+	0.427801i
$389$	−5.86718	+	4.26275i	−0.297478	+	0.216130i	−0.726505	−	0.687161i	$-0.758856\pi$
$389$	−5.86718	+	4.26275i	−0.297478	+	0.216130i	0.429027	+	0.903292i	$0.358856\pi$
$390$	−0.935398	+	2.60369i	−0.0473657	+	0.131843i
$391$	5.34529	−	16.4511i	0.270323	−	0.831968i
$392$	−8.01959	+	4.76477i	−0.405051	+	0.240657i
$393$	−0.780439	+	1.07418i	−0.0393680	+	0.0541853i
$394$	−6.99334	+	2.03688i	−0.352319	+	0.102617i
$395$	10.3863			0.522592
$396$	13.8371	−	11.8582i	0.695341	−	0.595895i
$397$	−37.7420			−1.89422			−0.947108	−	0.320915i	$-0.896010\pi$
$397$	−37.7420			−1.89422			−0.947108	+	0.320915i	$0.896010\pi$
$398$	24.5941	−	7.16329i	1.23279	−	0.359063i
$399$	0.0670608	−	0.0923012i	0.00335724	−	0.00462084i
$400$	−3.50000	+	1.93649i	−0.175000	+	0.0968246i
$401$	10.3234	−	31.7723i	0.515528	−	1.58663i	−0.266790	−	0.963755i	$-0.585963\pi$
$401$	10.3234	−	31.7723i	0.515528	−	1.58663i	0.782318	−	0.622879i	$-0.214037\pi$
$402$	0.0374260	−	0.104176i	0.00186664	−	0.00519581i
$403$	2.96241	−	2.15232i	0.147568	−	0.107214i
$404$	25.0857	−	30.4070i	1.24806	−	1.51281i
$405$	−2.09793	−	6.45675i	−0.104247	−	0.320839i
$406$	−0.577029	+	18.7657i	−0.0286375	+	0.931325i
$407$	12.9166	+	26.3446i	0.640252	+	1.30585i
$408$	−4.31624	−	0.399170i	−0.213686	−	0.0197618i
$409$	−9.88229	+	3.21095i	−0.488648	+	0.158771i	−0.542970	−	0.839752i	$-0.682700\pi$
$409$	−9.88229	+	3.21095i	−0.488648	+	0.158771i	0.0543221	+	0.998523i	$0.482700\pi$
$410$	7.34342	−	9.48031i	0.362666	−	0.468199i
$411$	−4.66407	−	6.41955i	−0.230062	−	0.316653i
$412$	17.3108	+	6.82676i	0.852843	+	0.336331i
$413$	−43.5391	−	14.1467i	−2.14242	−	0.696114i
$414$	12.4045	+	18.2261i	0.609646	+	0.895763i
$415$	−3.99856	−	2.90512i	−0.196281	−	0.142607i
$416$	21.7289	−	3.51690i	1.06535	−	0.172430i
$417$		−	6.48475i		−	0.317560i
$418$	0.288278	+	0.164049i	0.0141001	+	0.00802391i
$419$		−	29.4844i		−	1.44041i	−0.693762	−	0.720205i	$-0.744048\pi$
$419$		−	29.4844i		−	1.44041i	0.693762	−	0.720205i	$-0.255952\pi$
$420$	3.12427	−	0.806683i	0.152449	−	0.0393621i
$421$	−7.51048	−	5.45668i	−0.366039	−	0.265943i	0.389528	−	0.921015i	$-0.372638\pi$
$421$	−7.51048	−	5.45668i	−0.366039	−	0.265943i	−0.755566	+	0.655072i	$0.772638\pi$
$422$	4.13769	−	2.81606i	0.201419	−	0.137084i
$423$	10.5817	+	3.43821i	0.514501	+	0.167171i
$424$	8.82266	−	20.5020i	0.428466	−	0.995665i
$425$	−1.79173	−	2.46611i	−0.0869118	−	0.119624i
$426$	8.44542	+	6.54180i	0.409182	+	0.316951i
$427$	−2.23617	+	0.726574i	−0.108216	+	0.0351614i
$428$	−7.80464	−	0.480427i	−0.377251	−	0.0232223i
$429$	5.73511	+	3.03422i	0.276894	+	0.146493i
$430$	0.701665	+	0.0215756i	0.0338373	+	0.00104047i
$431$	9.30079	+	28.6249i	0.448003	+	1.37881i	0.879157	+	0.476533i	$0.158107\pi$
$431$	9.30079	+	28.6249i	0.448003	+	1.37881i	−0.431153	+	0.902279i	$0.641893\pi$
$432$	7.88903	−	8.44664i	0.379561	−	0.406389i
$433$	7.90428	−	5.74279i	0.379855	−	0.275981i	−0.381430	−	0.924398i	$-0.624568\pi$
$433$	7.90428	−	5.74279i	0.379855	−	0.275981i	0.761286	+	0.648416i	$0.224568\pi$
$434$	−4.01922	−	1.44394i	−0.192929	−	0.0693112i
$435$	0.642710	−	1.97806i	0.0308156	−	0.0948406i
$436$	7.86428	+	12.3551i	0.376631	+	0.591704i
$437$	−0.235868	+	0.324645i	−0.0112831	+	0.0155299i
$438$	−2.65366	−	9.11095i	−0.126797	−	0.435338i
$439$	10.3425			0.493622			0.246811	−	0.969064i	$-0.420617\pi$
$439$	10.3425			0.493622			0.246811	+	0.969064i	$0.420617\pi$
$440$	3.33652	+	8.76742i	0.159062	+	0.417970i
$441$	9.06052			0.431453
$442$	4.69082	+	16.1052i	0.223119	+	0.766048i
$443$	18.5086	−	25.4750i	0.879372	−	1.21035i	−0.0972223	−	0.995263i	$-0.530996\pi$
$443$	18.5086	−	25.4750i	0.879372	−	1.21035i	0.976594	−	0.215089i	$-0.0690042\pi$
$444$	4.77648	+	7.50407i	0.226682	+	0.356128i
$445$	−3.69663	+	11.3771i	−0.175237	+	0.539324i
$446$	−14.5269	−	5.21892i	−0.687870	−	0.247123i
$447$	5.24064	−	3.80755i	0.247874	−	0.180091i
$448$	−17.6498	−	18.6429i	−0.833875	−	0.880796i
$449$	−0.787165	−	2.42264i	−0.0371486	−	0.114332i	0.930763	−	0.365624i	$-0.119144\pi$
$449$	−0.787165	−	2.42264i	−0.0371486	−	0.114332i	−0.967911	+	0.251292i	$0.919144\pi$
$450$	3.88335	+	0.119410i	0.183063	+	0.00562903i
$451$	−19.5778	−	20.1897i	−0.921882	−	0.950694i
$452$	26.2627	+	1.61664i	1.23529	+	0.0760405i
$453$	−5.74513	+	1.86671i	−0.269930	+	0.0877055i
$454$	8.51091	+	6.59252i	0.399437	+	0.309402i
$455$	−7.33964	−	10.1021i	−0.344088	−	0.473596i
$456$	0.0923686	+	0.0397491i	0.00432556	+	0.00186142i
$457$	16.2280	+	5.27279i	0.759113	+	0.246651i	0.662898	−	0.748710i	$-0.269326\pi$
$457$	16.2280	+	5.27279i	0.759113	+	0.246651i	0.0962151	+	0.995361i	$0.469326\pi$
$458$	7.59251	−	5.16737i	0.354774	−	0.241455i
$459$	7.12569	+	5.17712i	0.332599	+	0.241647i
$460$	−10.9888	+	2.83729i	−0.512355	+	0.132289i
$461$		−	1.34620i		−	0.0626990i	−0.999508	−	0.0313495i	$-0.990020\pi$
$461$		−	1.34620i		−	0.0626990i	0.999508	−	0.0313495i	$-0.00998049\pi$
$462$	−0.837912	−	7.52083i	−0.0389832	−	0.349901i
$463$			4.36322i			0.202776i	0.994847	+	0.101388i	$0.0323284\pi$
$463$			4.36322i			0.202776i	−0.994847	+	0.101388i	$0.967672\pi$
$464$	−16.2461	+	3.14469i	−0.754207	+	0.145989i
$465$	0.382756	+	0.278088i	0.0177499	+	0.0128960i
$466$	16.7398	+	24.5960i	0.775455	+	1.13939i
$467$	−17.9687	−	5.83839i	−0.831493	−	0.270168i	−0.137819	−	0.990457i	$-0.544009\pi$
$467$	−17.9687	−	5.83839i	−0.831493	−	0.270168i	−0.693674	+	0.720289i	$0.744009\pi$
$468$	−19.8891	−	7.84356i	−0.919375	−	0.362568i
$469$	0.293664	+	0.404194i	0.0135602	+	0.0186640i
$470$	−3.50739	+	4.52802i	−0.161784	+	0.208862i
$471$	2.91952	−	0.948608i	0.134524	−	0.0437096i
$472$	3.71572	−	40.1783i	0.171030	−	1.84935i
$473$	0.282529	−	1.62190i	0.0129907	−	0.0745753i
$474$	0.226966	−	7.38119i	0.0104249	−	0.339029i
$475$	0.0218524	+	0.0672548i	0.00100266	+	0.00308586i
$476$	12.4503	−	15.0913i	0.570658	−	0.691710i
$477$	−17.5387	+	12.7426i	−0.803044	+	0.583446i
$478$	−6.76580	+	18.8327i	−0.309461	+	0.861388i
$479$	−5.41103	+	16.6534i	−0.247236	+	0.760915i	0.748024	+	0.663671i	$0.231003\pi$
$479$	−5.41103	+	16.6534i	−0.247236	+	0.760915i	−0.995261	+	0.0972438i	$0.968997\pi$
$480$	1.29972	+	2.52965i	0.0593236	+	0.115462i
$481$	20.2335	−	27.8490i	0.922568	−	1.26981i
$482$	6.44561	−	1.87735i	0.293590	−	0.0855111i
$483$	9.15519			0.416575
$484$	21.4605	−	4.84204i	0.975479	−	0.220093i
$485$	6.62079			0.300635
$486$	−16.4043	+	4.77791i	−0.744112	+	0.216731i
$487$	6.32403	−	8.70428i	0.286569	−	0.394429i	−0.641327	−	0.767268i	$-0.721616\pi$
$487$	6.32403	−	8.70428i	0.286569	−	0.394429i	0.927896	+	0.372839i	$0.121616\pi$
$488$	−1.05853	−	1.78162i	−0.0479176	−	0.0806503i
$489$	3.68389	−	11.3379i	0.166591	−	0.512716i
$490$	−1.57695	+	4.38947i	−0.0712395	+	0.198296i
$491$	−18.8359	+	13.6851i	−0.850051	+	0.617598i	−0.925160	−	0.379577i	$-0.876069\pi$
$491$	−18.8359	+	13.6851i	−0.850051	+	0.617598i	0.0751094	+	0.997175i	$0.476069\pi$
$492$	−6.57686	−	5.42589i	−0.296508	−	0.244618i
$493$	−3.89685	−	11.9933i	−0.175505	−	0.540150i
$494$	0.0119602	−	0.388960i	0.000538115	−	0.0175002i
$495$	1.56365	−	8.97639i	0.0702807	−	0.403459i
$496$	0.461669	−	3.73575i	0.0207295	−	0.167740i
$497$	−45.8558	+	14.8995i	−2.05691	+	0.668332i
$498$	−2.15195	+	2.77815i	−0.0964311	+	0.124492i
$499$	−8.36834	−	11.5180i	−0.374618	−	0.515618i	0.579531	−	0.814951i	$-0.303236\pi$
$499$	−8.36834	−	11.5180i	−0.374618	−	0.515618i	−0.954149	+	0.299333i	$0.903236\pi$
$500$	−0.733733	+	1.86055i	−0.0328135	+	0.0832062i
$501$	−6.89622	−	2.24072i	−0.308100	−	0.100108i
$502$	10.3548	+	15.2145i	0.462158	+	0.679057i
$503$	−23.5444	−	17.1060i	−1.04979	−	0.762718i	−0.0776187	−	0.996983i	$-0.524732\pi$
$503$	−23.5444	−	17.1060i	−1.04979	−	0.762718i	−0.972173	+	0.234265i	$0.924732\pi$
$504$	5.48889	+	24.3239i	0.244495	+	1.08347i
$505$		−	19.7096i		−	0.877067i
$506$	2.94713	+	26.4525i	0.131016	+	1.17596i
$507$		−	1.07645i		−	0.0478067i
$508$	−5.69848	−	22.0701i	−0.252829	−	0.979203i
$509$	28.7673	+	20.9006i	1.27509	+	0.926404i	0.999393	−	0.0348414i	$-0.0110926\pi$
$509$	28.7673	+	20.9006i	1.27509	+	0.926404i	0.275693	+	0.961246i	$0.411093\pi$
$510$	−1.79173	+	1.21943i	−0.0793393	+	0.0539974i
$511$	40.7341	+	13.2353i	1.80197	+	0.585496i
$512$	12.6043	−	18.7918i	0.557038	−	0.830487i
$513$	−0.120102	−	0.165306i	−0.00530263	−	0.00729845i
$514$	−14.5510	−	11.2711i	−0.641816	−	0.497148i
$515$	8.84878	−	2.87514i	0.389924	−	0.126694i
$516$	0.0306661	−	0.498178i	0.00135000	−	0.0219311i
$517$	9.35081	+	9.64306i	0.411248	+	0.424101i
$518$	−40.1292	−	1.23394i	−1.76318	−	0.0542163i
$519$	1.46174	+	4.49878i	0.0641634	+	0.197475i
$520$	7.26153	−	8.27037i	0.318439	−	0.362680i
$521$	−15.9186	+	11.5655i	−0.697406	+	0.506695i	−0.879086	−	0.476662i	$-0.841846\pi$
$521$	−15.9186	+	11.5655i	−0.697406	+	0.506695i	0.181680	+	0.983358i	$0.441846\pi$
$522$	15.1262	+	5.43420i	0.662054	+	0.237848i
$523$	12.2934	−	37.8352i	0.537554	−	1.65442i	−0.200513	−	0.979691i	$-0.564261\pi$
$523$	12.2934	−	37.8352i	0.537554	−	1.65442i	0.738066	−	0.674728i	$-0.235739\pi$
$524$	4.45587	−	2.83624i	0.194656	−	0.123902i
$525$	0.948313	−	1.30524i	0.0413878	−	0.0569654i
$526$	−9.35136	−	32.1065i	−0.407738	−	1.39991i
$527$	2.86856			0.124956
$528$	6.30362	−	2.17956i	0.274330	−	0.0948531i
$529$	−9.20092			−0.400040
$530$	−3.12076	−	10.7147i	−0.135557	−	0.465415i
$531$	−23.0362	+	31.7066i	−0.999685	+	1.37595i
$532$	−0.382879	+	0.243710i	−0.0165999	+	0.0105662i
$533$	−10.1960	+	31.3800i	−0.441637	+	1.35922i
$534$	8.00451	+	2.87568i	0.346389	+	0.124443i
$535$	−3.16302	+	2.29807i	−0.136749	+	0.0993541i
$536$	−0.290539	+	0.330903i	−0.0125494	+	0.0142928i
$537$	0.618399	+	1.90324i	0.0266859	+	0.0821307i
$538$	−18.3476	−	0.564173i	−0.791019	−	0.0243232i
$539$	9.66862	+	5.11528i	0.416457	+	0.220331i
$540$	0.355057	−	5.76798i	0.0152792	−	0.248214i
$541$	29.0963	−	9.45397i	1.25095	−	0.406458i	0.392688	−	0.919672i	$-0.371545\pi$
$541$	29.0963	−	9.45397i	1.25095	−	0.406458i	0.858261	+	0.513214i	$0.171545\pi$
$542$	23.3900	+	18.1178i	1.00469	+	0.778227i
$543$	0.569719	+	0.784151i	0.0244490	+	0.0336511i
$544$	15.3906	+	7.77645i	0.659867	+	0.333413i
$545$	6.96444	+	2.26288i	0.298324	+	0.0969313i
$546$	−7.33964	+	4.99528i	−0.314108	+	0.213778i
$547$	6.79763	+	4.93876i	0.290645	+	0.211166i	0.723547	−	0.690275i	$-0.242510\pi$
$547$	6.79763	+	4.93876i	0.290645	+	0.211166i	−0.432902	+	0.901441i	$0.642510\pi$
$548$	7.89153	+	30.5638i	0.337109	+	1.30562i
$549$			2.01287i			0.0859074i
$550$	4.07656	+	2.31984i	0.173825	+	0.0989181i
$551$			0.292546i			0.0124629i
$552$	1.77624	+	7.87136i	0.0756016	+	0.335027i
$553$	26.9647	+	19.5910i	1.14666	+	0.833095i
$554$	11.1050	+	16.3168i	0.471807	+	0.693234i
$555$	4.22995	+	1.37440i	0.179552	+	0.0583398i
$556$	−9.46402	+	23.9982i	−0.401364	+	1.01775i
$557$	12.3439	+	16.9899i	0.523027	+	0.719885i	0.986048	−	0.166463i	$-0.0532345\pi$
$557$	12.3439	+	16.9899i	0.523027	+	0.719885i	−0.463021	+	0.886347i	$0.653234\pi$
$558$	−2.23890	+	2.89041i	−0.0947804	+	0.122361i
$559$	−1.83698	+	0.596872i	−0.0776961	+	0.0252450i
$560$	−12.7393	−	1.57434i	−0.538334	−	0.0665281i
$561$	2.23761	+	4.56381i	0.0944721	+	0.192684i
$562$	−0.482427	+	15.6891i	−0.0203500	+	0.661805i
$563$	1.36983	+	4.21590i	0.0577313	+	0.177679i	0.975764	−	0.218826i	$-0.0702229\pi$
$563$	1.36983	+	4.21590i	0.0577313	+	0.177679i	−0.918032	+	0.396505i	$0.870223\pi$
$564$	3.14127	+	2.59153i	0.132271	+	0.109123i
$565$	10.6436	−	7.73303i	0.447780	−	0.325331i
$566$	−6.08485	+	16.9372i	−0.255765	+	0.711926i
$567$	6.73237	−	20.7201i	0.282733	−	0.870162i
$568$	−21.7068	−	36.5348i	−0.910797	−	1.53296i
$569$	12.7625	−	17.5661i	0.535033	−	0.736410i	−0.452854	−	0.891585i	$-0.649594\pi$
$569$	12.7625	−	17.5661i	0.535033	−	0.736410i	0.987887	+	0.155175i	$0.0495941\pi$
$570$	0.0482732	−	0.0140601i	0.00202194	−	0.000588912i
$571$	33.8605			1.41702			0.708508	−	0.705702i	$-0.249368\pi$
$571$	33.8605			1.41702			0.708508	+	0.705702i	$0.249368\pi$
$572$	−16.7958	−	19.5987i	−0.702266	−	0.819464i
$573$	−8.99809			−0.375901
$574$	36.9470	−	10.7612i	1.54214	−	0.449163i
$575$	−3.33544	+	4.59084i	−0.139097	+	0.191451i
$576$	−19.8481	+	9.43837i	−0.827003	+	0.393265i
$577$	−8.75266	+	26.9379i	−0.364378	+	1.12144i	0.585992	+	0.810317i	$0.300705\pi$
$577$	−8.75266	+	26.9379i	−0.364378	+	1.12144i	−0.950370	+	0.311123i	$0.899295\pi$
$578$	3.68556	−	10.2588i	0.153299	−	0.426710i
$579$	2.80540	−	2.03825i	0.116589	−	0.0847066i
$580$	−5.26531	+	6.38223i	−0.218630	+	0.265008i
$581$	−4.90123	−	15.0844i	−0.203337	−	0.625808i
$582$	0.144680	−	4.70517i	0.00599719	−	0.195036i
$583$	−25.9099	+	3.69606i	−1.07308	+	0.153075i
$584$	−3.47634	+	37.5898i	−0.143852	+	1.55548i
$585$	−10.1667	+	3.30337i	−0.420343	+	0.136578i
$586$	25.1873	−	32.5166i	1.04048	−	1.34325i
$587$	15.8943	+	21.8766i	0.656027	+	0.902944i	0.999342	−	0.0362762i	$-0.0115496\pi$
$587$	15.8943	+	21.8766i	0.656027	+	0.902944i	−0.343314	+	0.939221i	$0.611550\pi$
$588$	3.08499	+	1.21661i	0.127223	+	0.0501720i
$589$	−0.0632895	−	0.0205640i	−0.00260780	−	0.000847325i
$590$	−11.3512	−	16.6786i	−0.467323	−	0.686645i
$591$	2.09490	+	1.52204i	0.0861728	+	0.0626082i
$592$	−6.72473	−	34.7413i	−0.276385	−	1.42786i
$593$			3.03259i			0.124534i	0.998060	+	0.0622668i	$0.0198330\pi$
$593$			3.03259i			0.124534i	−0.998060	+	0.0622668i	$0.980167\pi$
$594$	−13.2739	−	2.73506i	−0.544633	−	0.112221i
$595$		−	9.78210i		−	0.401027i
$596$	−24.9509	+	6.44230i	−1.02203	+	0.263887i
$597$	−7.36734	−	5.35269i	−0.301525	−	0.219071i
$598$	25.8152	−	17.5695i	1.05566	−	0.718472i
$599$	−31.2756	−	10.1621i	−1.27789	−	0.415211i	−0.410051	−	0.912062i	$-0.634489\pi$
$599$	−31.2756	−	10.1621i	−1.27789	−	0.415211i	−0.867835	+	0.496852i	$0.834489\pi$
$600$	1.30619	+	0.562096i	0.0533251	+	0.0229475i
$601$	25.8004	+	35.5112i	1.05242	+	1.44853i	0.886693	+	0.462358i	$0.152997\pi$
$601$	25.8004	+	35.5112i	1.05242	+	1.44853i	0.165726	+	0.986172i	$0.447003\pi$
$602$	1.78095	+	1.37952i	0.0725862	+	0.0562251i
$603$	0.406778	−	0.132170i	0.0165653	−	0.00538239i
$604$	23.9854	+	1.47646i	0.975951	+	0.0600762i
$605$	6.73637	−	8.69605i	0.273872	−	0.353545i
$606$	−14.0070	−	0.430703i	−0.568994	−	0.0174961i
$607$	−1.04888	−	3.22811i	−0.0425726	−	0.131025i	0.927511	−	0.373795i	$-0.121944\pi$
$607$	−1.04888	−	3.22811i	−0.0425726	−	0.131025i	−0.970084	+	0.242771i	$0.921944\pi$
$608$	−0.283818	−	0.281905i	−0.0115104	−	0.0114328i
$609$	5.39968	−	3.92309i	0.218806	−	0.158972i
$610$	−0.975159	−	0.350334i	−0.0394830	−	0.0141846i
$611$	4.86984	−	14.9878i	0.197013	−	0.606343i
$612$	−8.99352	−	14.1292i	−0.363542	−	0.571140i
$613$	−17.4987	+	24.0849i	−0.706765	+	0.972779i	0.293096	+	0.956083i	$0.405315\pi$
$613$	−17.4987	+	24.0849i	−0.706765	+	0.972779i	−0.999861	+	0.0166955i	$0.994685\pi$
$614$	−11.5321	−	39.5938i	−0.465398	−	1.59788i
$615$	−4.26308			−0.171904
$616$	−7.87522	+	29.0553i	−0.317302	+	1.17067i
$617$	27.3655			1.10169			0.550846	−	0.834607i	$-0.314305\pi$
$617$	27.3655			1.10169			0.550846	+	0.834607i	$0.314305\pi$
$618$	−1.84990	−	6.35135i	−0.0744138	−	0.255489i
$619$	7.16184	−	9.85743i	0.287859	−	0.396203i	−0.640458	−	0.767993i	$-0.721256\pi$
$619$	7.16184	−	9.85743i	0.287859	−	0.396203i	0.928317	+	0.371789i	$0.121256\pi$
$620$	−1.01062	−	1.58773i	−0.0405874	−	0.0637647i
$621$	5.06677	−	15.5939i	0.203323	−	0.625763i
$622$	−15.7963	−	5.67497i	−0.633376	−	0.227545i
$623$	−31.0569	+	22.5642i	−1.24427	+	0.904015i
$624$	−5.71878	−	5.34125i	−0.228935	−	0.213821i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−27.3217	−	0.840119i	−1.09199	−	0.0335779i
$627$	−0.0166520	−	0.116733i	−0.000665017	−	0.00466187i
$628$	−12.1887	−	0.750295i	−0.486382	−	0.0299400i
$629$	25.6469	−	8.33318i	1.02261	−	0.332266i
$630$	9.85664	+	7.63492i	0.392698	+	0.304182i
$631$	16.9524	+	23.3330i	0.674865	+	0.928873i	0.999858	−	0.0168439i	$-0.00536183\pi$
$631$	16.9524	+	23.3330i	0.674865	+	0.928873i	−0.324993	+	0.945717i	$0.605362\pi$
$632$	−11.6122	+	26.9844i	−0.461910	+	1.07338i
$633$	−1.69222	−	0.549835i	−0.0672597	−	0.0218540i
$634$	−7.55993	+	5.14520i	−0.300243	+	0.204342i
$635$	−9.22033	−	6.69896i	−0.365898	−	0.265840i
$636$	−7.68273	+	1.98367i	−0.304640	+	0.0786578i
$637$		−	12.8332i		−	0.508471i
$638$	13.0734	+	14.3386i	0.517580	+	0.567673i
$639$			41.2769i			1.63289i
$640$	−1.11803	−	11.2583i	−0.0441942	−	0.445025i
$641$	−5.74895	−	4.17686i	−0.227070	−	0.164976i	0.468434	−	0.883499i	$-0.344819\pi$
$641$	−5.74895	−	4.17686i	−0.227070	−	0.164976i	−0.695503	+	0.718523i	$0.744819\pi$
$642$	1.56404	+	2.29807i	0.0617276	+	0.0906974i
$643$	−27.4095	−	8.90590i	−1.08093	−	0.351214i	−0.286193	−	0.958172i	$-0.592390\pi$
$643$	−27.4095	−	8.90590i	−1.08093	−	0.351214i	−0.794734	+	0.606958i	$0.792390\pi$
$644$	−33.8807	−	13.3613i	−1.33509	−	0.526510i
$645$	−0.146688	−	0.201899i	−0.00577583	−	0.00794975i
$646$	0.186682	−	0.241005i	0.00734490	−	0.00948222i
$647$	−20.3988	+	6.62796i	−0.801959	+	0.260572i	−0.681188	−	0.732108i	$-0.738536\pi$
$647$	−20.3988	+	6.62796i	−0.801959	+	0.260572i	−0.120770	+	0.992680i	$0.538536\pi$
$648$	19.1207	+	1.76830i	0.751132	+	0.0694653i
$649$	−42.4828	+	20.8291i	−1.66759	+	0.817613i
$650$	0.169131	−	5.50033i	0.00663385	−	0.215741i
$651$	0.469163	+	1.44394i	0.0183880	+	0.0565923i
$652$	−30.1798	+	36.5817i	−1.18193	+	1.43265i
$653$	24.2792	−	17.6399i	0.950118	−	0.690301i	−0.000716986	−	1.00000i	$-0.500228\pi$
$653$	24.2792	−	17.6399i	0.950118	−	0.690301i	0.950835	+	0.309699i	$0.100228\pi$
$654$	1.76034	−	4.89994i	0.0688349	−	0.191603i
$655$	0.816107	−	2.51172i	0.0318879	−	0.0981410i
$656$	16.4204	+	29.6781i	0.641108	+	1.15873i
$657$	21.5521	−	29.6639i	0.840827	−	1.15730i
$658$	−17.6467	+	5.13980i	−0.687942	+	0.200370i
$659$	−25.4932			−0.993075			−0.496537	−	0.868015i	$-0.665395\pi$
$659$	−25.4932			−0.993075			−0.496537	+	0.868015i	$0.665395\pi$
$660$	1.73771	−	2.84638i	0.0676403	−	0.110795i
$661$	0.531397			0.0206689			0.0103345	−	0.999947i	$-0.496710\pi$
$661$	0.531397			0.0206689			0.0103345	+	0.999947i	$0.496710\pi$
$662$	−32.2964	+	9.40666i	−1.25523	+	0.365600i
$663$	3.50516	−	4.82444i	0.136129	−	0.187366i
$664$	12.0182	−	7.14053i	0.466399	−	0.277106i
$665$	−0.0701256	+	0.215824i	−0.00271935	+	0.00836931i
$666$	−11.6207	+	32.3463i	−0.450293	+	1.25340i
$667$	−18.9919	+	13.7984i	−0.735370	+	0.534277i
$668$	22.2507	+	18.3568i	0.860907	+	0.710245i
$669$	1.69573	+	5.21892i	0.0655607	+	0.201775i
$670$	−0.00676704	+	0.220072i	−0.000261434	+	0.00850213i
$671$	−1.13640	+	2.14797i	−0.0438704	+	0.0829214i
$672$	−1.39722	+	9.01899i	−0.0538988	+	0.347915i
$673$	−8.51337	+	2.76616i	−0.328166	+	0.106628i	−0.468466	−	0.883481i	$-0.655193\pi$
$673$	−8.51337	+	2.76616i	−0.328166	+	0.106628i	0.140300	+	0.990109i	$0.455193\pi$
$674$	−4.13513	+	5.33843i	−0.159279	+	0.205629i
$675$	−1.69837	−	2.33761i	−0.0653705	−	0.0899747i
$676$	−1.57100	+	3.98362i	−0.0604229	+	0.153216i
$677$	−1.77141	−	0.575567i	−0.0680809	−	0.0221208i	0.274779	−	0.961508i	$-0.411395\pi$
$677$	−1.77141	−	0.575567i	−0.0680809	−	0.0221208i	−0.342859	+	0.939387i	$0.611395\pi$
$678$	−5.26301	−	7.73303i	−0.202125	−	0.296985i
$679$	17.1888	+	12.4884i	0.659645	+	0.479260i
$680$	8.41036	−	1.89787i	0.322522	−	0.0727798i
$681$		−	3.82716i		−	0.146657i
$682$	−4.02100	+	1.82039i	−0.153972	+	0.0697063i
$683$		−	18.0214i		−	0.689571i	−0.938681	−	0.344786i	$-0.887952\pi$
$683$		−	18.0214i		−	0.689571i	0.938681	−	0.344786i	$-0.112048\pi$
$684$	0.0971366	+	0.376209i	0.00371411	+	0.0143847i
$685$	12.7688	+	9.27705i	0.487869	+	0.354458i
$686$	13.8890	−	9.45270i	0.530285	−	0.360906i
$687$	−3.10516	−	1.00893i	−0.118469	−	0.0384930i
$688$	−0.840541	+	1.79886i	−0.0320453	+	0.0685808i
$689$	18.0485	+	24.8417i	0.687594	+	0.946392i
$690$	3.18966	+	2.47070i	0.121428	+	0.0940580i
$691$	−35.3967	+	11.5011i	−1.34655	+	0.437521i	−0.891531	−	0.452959i	$-0.850368\pi$
$691$	−35.3967	+	11.5011i	−1.34655	+	0.437521i	−0.455021	+	0.890481i	$0.650368\pi$
$692$	1.15616	−	18.7820i	0.0439504	−	0.713984i
$693$	20.9911	−	20.3549i	0.797386	−	0.773219i
$694$	−28.8890	−	0.888312i	−1.09661	−	0.0337199i
$695$	3.98584	+	12.2672i	0.151192	+	0.465320i
$696$	4.42057	+	3.88134i	0.167561	+	0.147122i
$697$	−20.9112	+	15.1929i	−0.792070	+	0.575473i
$698$	3.12662	+	1.12326i	0.118344	+	0.0425162i
$699$	3.26844	−	10.0592i	0.123624	−	0.380474i
$700$	−5.41434	+	3.44633i	−0.204643	+	0.130259i
$701$	22.3855	−	30.8110i	0.845489	−	1.16372i	−0.139349	−	0.990243i	$-0.544501\pi$
$701$	22.3855	−	30.8110i	0.845489	−	1.16372i	0.984839	−	0.173473i	$-0.0554989\pi$
$702$	4.44640	+	15.2661i	0.167819	+	0.576181i
$703$	−0.625591			−0.0235946
$704$	−26.5088	−	1.13375i	−0.999087	−	0.0427298i
$705$	2.03615			0.0766858
$706$	−6.07717	−	20.8651i	−0.228717	−	0.785267i
$707$	37.1770	−	51.1698i	1.39819	−	1.92444i
$708$	−12.1009	+	7.70247i	−0.454781	+	0.289477i
$709$	−0.133182	+	0.409893i	−0.00500177	+	0.0153939i	−0.953526	−	0.301310i	$-0.902576\pi$
$709$	−0.133182	+	0.409893i	−0.00500177	+	0.0153939i	0.948524	+	0.316704i	$0.102576\pi$
$710$	−19.9971	−	7.18411i	−0.750476	−	0.269615i
$711$	23.0842	−	16.7717i	0.865726	−	0.628987i
$712$	−25.4255	−	22.3241i	−0.952861	−	0.836630i
$713$	−1.65016	−	5.07866i	−0.0617988	−	0.190197i
$714$	−6.95180	−	0.213762i	−0.260165	−	0.00799985i
$715$	−12.7141	−	2.21473i	−0.475479	−	0.0828263i
$716$	0.489118	−	7.94583i	0.0182792	−	0.296950i
$717$	6.76580	−	2.19834i	0.252674	−	0.0820986i
$718$	−18.1960	−	14.0945i	−0.679068	−	0.526004i
$719$	4.70131	+	6.47080i	0.175329	+	0.241320i	0.887633	−	0.460551i	$-0.152348\pi$
$719$	4.70131	+	6.47080i	0.175329	+	0.241320i	−0.712304	+	0.701871i	$0.752348\pi$
$720$	−4.65195	+	9.95573i	−0.173368	+	0.371028i
$721$	28.3962	+	9.22650i	1.05753	+	0.343613i
$722$	22.2076	−	15.1143i	0.826483	−	0.562495i
$723$	−1.93083	−	1.40283i	−0.0718083	−	0.0521718i
$724$	−0.963954	−	3.73338i	−0.0358251	−	0.138750i
$725$			4.13692i			0.153641i
$726$	−6.03278	−	4.97734i	−0.223898	−	0.184726i
$727$			29.1784i			1.08217i	0.840969	+	0.541084i	$0.181986\pi$
$727$			29.1784i			1.08217i	−0.840969	+	0.541084i	$0.818014\pi$
$728$	34.4521	−	7.77440i	1.27688	−	0.288138i
$729$	−11.5633	−	8.40124i	−0.428271	−	0.311157i
$730$	10.6199	+	15.6040i	0.393061	+	0.577532i
$731$	−1.43907	−	0.467581i	−0.0532258	−	0.0172941i
$732$	−0.270280	+	0.685357i	−0.00998983	+	0.0253315i
$733$	1.46872	+	2.02152i	0.0542485	+	0.0746666i	0.835279	−	0.549826i	$-0.185306\pi$
$733$	1.46872	+	2.02152i	0.0542485	+	0.0746666i	−0.781031	+	0.624492i	$0.785306\pi$
$734$	−14.3840	+	18.5697i	−0.530923	+	0.685419i
$735$	1.57695	−	0.512383i	0.0581668	−	0.0188995i
$736$	4.91434	−	31.7219i	0.181145	−	1.16928i
$737$	0.508698	+	0.0886130i	0.0187381	+	0.00326410i
$738$	1.01253	−	32.9286i	0.0372717	−	1.21212i
$739$	−0.554914	−	1.70785i	−0.0204128	−	0.0628243i	0.940331	−	0.340261i	$-0.110515\pi$
$739$	−0.554914	−	1.70785i	−0.0204128	−	0.0628243i	−0.960744	+	0.277436i	$0.910515\pi$
$740$	−13.6480	−	11.2595i	−0.501711	−	0.413909i
$741$	−0.111920	+	0.0813148i	−0.00411149	+	0.00298718i
$742$	12.1083	−	33.7037i	0.444510	−	1.23730i
$743$	−6.36470	+	19.5885i	−0.233498	+	0.718633i	0.763819	+	0.645430i	$0.223322\pi$
$743$	−6.36470	+	19.5885i	−0.233498	+	0.718633i	−0.997317	+	0.0732026i	$0.976678\pi$
$744$	−1.15043	+	0.683517i	−0.0421768	+	0.0250589i
$745$	−7.57337	+	10.4239i	−0.277467	+	0.381901i
$746$	16.1293	−	4.69784i	0.590537	−	0.172000i
$747$	−13.5782			−0.496800
$748$	−1.62021	−	20.1550i	−0.0592408	−	0.736939i
$749$	−12.5465			−0.458438
$750$	0.682636	−	0.198825i	0.0249263	−	0.00726006i
$751$	−8.42266	+	11.5928i	−0.307347	+	0.423027i	−0.934552	−	0.355827i	$-0.884199\pi$
$751$	−8.42266	+	11.5928i	−0.307347	+	0.423027i	0.627204	+	0.778855i	$0.284199\pi$
$752$	−7.84277	−	14.1750i	−0.285996	−	0.516907i
$753$	2.02178	−	6.22239i	0.0736776	−	0.226756i
$754$	7.69693	−	21.4245i	0.280306	−	0.780235i
$755$	9.72065	−	7.06247i	0.353771	−	0.257030i
$756$	11.8016	−	14.3050i	0.429219	−	0.520268i
$757$	3.43599	+	10.5749i	0.124883	+	0.384351i	0.993880	−	0.110467i	$-0.0352347\pi$
$757$	3.43599	+	10.5749i	0.124883	+	0.384351i	−0.868997	+	0.494818i	$0.835235\pi$
$758$	−0.919778	+	29.9123i	−0.0334078	+	1.08646i
$759$	6.79284	−	6.58697i	0.246564	−	0.239092i
$760$	−0.199165	−	0.0184189i	−0.00722446	−	0.000668124i
$761$	−19.2163	+	6.24374i	−0.696589	+	0.226336i	−0.635844	−	0.771818i	$-0.719348\pi$
$761$	−19.2163	+	6.24374i	−0.696589	+	0.226336i	−0.0607453	+	0.998153i	$0.519348\pi$
$762$	−4.96221	+	6.40618i	−0.179762	+	0.232072i
$763$	13.8126	+	19.0114i	0.500050	+	0.688260i
$764$	33.2993	+	13.1321i	1.20473	+	0.475101i
$765$	−7.96448	−	2.58782i	−0.287956	−	0.0935627i
$766$	1.16548	+	1.71245i	0.0421103	+	0.0618734i
$767$	44.9088	+	32.6282i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395472 + 1.35779i) q^{2} +(0.295511 - 0.406737i) q^{3} +(-1.68720 + 1.07394i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.669131 + 0.240391i) q^{6} +(-2.59618 + 1.88624i) q^{7} +(-2.12543 - 1.86616i) q^{8} +(0.848943 + 2.61278i) q^{9} +(-1.41355 - 0.0434654i) q^{10} +(-0.569171 + 3.26742i) q^{11} +(-0.0617787 + 1.00361i) q^{12} +(3.70071 - 1.20243i) q^{13} +(-3.58783 - 2.77912i) q^{14} +(0.295511 + 0.406737i) q^{15} +(1.69332 - 3.62390i) q^{16} +(2.89908 + 0.941970i) q^{17} +(-3.21188 + 2.18597i) q^{18} +(-0.0572103 - 0.0415657i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.61337i q^{21} +(-4.66157 + 0.519356i) q^{22} -5.67459i q^{23} +(-1.38712 + 0.313016i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.09618 + 4.54927i) q^{26} +(2.74803 + 0.892888i) q^{27} +(2.35459 - 5.97060i) q^{28} +(-2.43162 - 3.34684i) q^{29} +(-0.435398 + 0.562096i) q^{30} +(0.894983 - 0.290798i) q^{31} +(5.59017 + 0.866025i) q^{32} +(1.16078 + 1.19706i) q^{33} +(-0.132495 + 4.30888i) q^{34} +(-0.991653 - 3.05199i) q^{35} +(-4.23830 - 3.49658i) q^{36} +(7.15701 - 5.19987i) q^{37} +(0.0338126 - 0.0941179i) q^{38} +(0.604528 - 1.86055i) q^{39} +(2.43162 - 1.44472i) q^{40} +(-4.98410 + 6.86002i) q^{41} +(-2.19062 + 0.638041i) q^{42} -0.496387 q^{43} +(-2.54870 - 6.12406i) q^{44} -2.74724 q^{45} +(7.70491 - 2.24414i) q^{46} +(2.38052 - 3.27651i) q^{47} +(-0.973579 - 1.75964i) q^{48} +(1.01915 - 3.13663i) q^{49} +(0.478148 - 1.33093i) q^{50} +(1.23985 - 0.900801i) q^{51} +(-4.95252 + 6.00308i) q^{52} +(2.43852 + 7.50500i) q^{53} +(-0.125591 + 4.08437i) q^{54} +(-2.93162 - 1.55100i) q^{55} +(9.03802 + 0.835843i) q^{56} +(-0.0338126 + 0.0109864i) q^{57} +(3.58268 - 4.62521i) q^{58} +(8.38521 + 11.5413i) q^{59} +(-0.935398 - 0.368887i) q^{60} +(0.696830 + 0.226414i) q^{61} +(0.748784 + 1.10020i) q^{62} +(-7.13233 - 5.18194i) q^{63} +(1.03487 + 7.93278i) q^{64} +3.89116i q^{65} +(-1.16631 + 2.04951i) q^{66} -0.155688i q^{67} +(-5.90297 + 1.52414i) q^{68} +(-2.30806 - 1.67691i) q^{69} +(3.75181 - 2.55344i) q^{70} +(14.2895 + 4.64294i) q^{71} +(3.07151 - 7.13753i) q^{72} +(-7.84500 - 10.7977i) q^{73} +(9.89074 + 7.66133i) q^{74} +(-0.478148 + 0.155360i) q^{75} +(0.141165 + 0.00868960i) q^{76} +(-4.68546 - 9.55641i) q^{77} +(2.76531 + 0.0850311i) q^{78} +(-3.20955 - 9.87796i) q^{79} +(2.92327 + 2.73029i) q^{80} +(-5.49244 + 3.99049i) q^{81} +(-11.2856 - 4.05443i) q^{82} +(-1.52731 + 4.70059i) q^{83} +(-1.73265 - 2.72208i) q^{84} +(-1.79173 + 2.46611i) q^{85} +(-0.196307 - 0.673990i) q^{86} -2.07985 q^{87} +(7.30727 - 5.88250i) q^{88} +11.9625 q^{89} +(-1.08645 - 3.73018i) q^{90} +(-7.33964 + 10.1021i) q^{91} +(6.09415 + 9.57419i) q^{92} +(0.146200 - 0.449957i) q^{93} +(5.39025 + 1.93649i) q^{94} +(0.0572103 - 0.0415657i) q^{95} +(2.00420 - 2.01781i) q^{96} +(-2.04594 - 6.29675i) q^{97} +(4.66194 + 0.143351i) q^{98} +(-9.02024 + 1.28674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

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