LMFDB - Embedded newform 220.2.r.b.211.1

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			211.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	220.211
Dual form			220.2.r.b.171.1

$q$-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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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	0.885758	−	0.464147i	$-0.153639\pi$
$3$	0.295511	+	0.406737i	0.170614	+	0.234830i	−0.715144	+	0.698977i	$0.753639\pi$
$4$	−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	−0.0232736	−	0.999729i	$-0.507409\pi$
$7$	−2.59618	−	1.88624i	−0.981264	−	0.712930i	−0.957991	+	0.286799i	$0.907409\pi$
$8$	−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	0.773363	−	0.633964i	$-0.218573\pi$
$13$	3.70071	+	1.20243i	1.02639	+	0.333495i	0.253029	+	0.967459i	$0.418573\pi$
$14$	−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	0.0644370	−	0.997922i	$-0.479475\pi$
$17$	2.89908	−	0.941970i	0.703131	−	0.228461i	0.638694	+	0.769461i	$0.279475\pi$
$18$	−3.21188	−	2.18597i	−0.757047	−	0.515238i
$19$	−0.0572103	+	0.0415657i	−0.0131249	+	0.00953583i	−0.594328	−	0.804222i	$-0.702582\pi$
$19$	−0.0572103	+	0.0415657i	−0.0131249	+	0.00953583i	0.581203	+	0.813758i	$0.302582\pi$
$20$	−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	$0.201510\pi$
$23$			5.67459i			1.18323i	−0.806220	+	0.591616i	$0.798490\pi$
$24$	−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	−0.972728	−	0.231950i	$-0.925489\pi$
$29$	−2.43162	+	3.34684i	−0.451540	+	0.621492i	0.521187	+	0.853442i	$0.325489\pi$
$30$	−0.435398	−	0.562096i	−0.0794924	−	0.102624i
$31$	0.894983	+	0.290798i	0.160744	+	0.0522288i	0.388283	−	0.921540i	$-0.373068\pi$
$31$	0.894983	+	0.290798i	0.160744	+	0.0522288i	−0.227540	+	0.973769i	$0.573068\pi$
$32$	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	0.991785	−	0.127919i	$-0.0408298\pi$
$37$	7.15701	+	5.19987i	1.17660	+	0.854853i	0.184820	+	0.982772i	$0.440830\pi$
$38$	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	−0.995458	−	0.0951998i	$-0.969651\pi$
$41$	−4.98410	−	6.86002i	−0.778385	−	1.07136i	0.217073	−	0.976155i	$-0.430349\pi$
$42$	−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	0.946537	−	0.322595i	$-0.104555\pi$
$47$	2.38052	+	3.27651i	0.347235	+	0.477928i	−0.599302	+	0.800523i	$0.704555\pi$
$48$	−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	−0.631786	−	0.775143i	$-0.717678\pi$
$53$	2.43852	−	7.50500i	0.334957	−	1.03089i	0.966743	−	0.255749i	$-0.0823220\pi$
$54$	−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	0.245666	−	0.969355i	$-0.420993\pi$
$59$	8.38521	−	11.5413i	1.09166	−	1.50254i	0.845996	−	0.533189i	$-0.179007\pi$
$60$	−0.935398	+	0.368887i	−0.120759	+	0.0476231i
$61$	0.696830	−	0.226414i	0.0892199	−	0.0289893i	−0.264067	−	0.964504i	$-0.585064\pi$
$61$	0.696830	−	0.226414i	0.0892199	−	0.0289893i	0.353287	+	0.935515i	$0.385064\pi$
$62$	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	$0.00302722\pi$
$67$			0.155688i			0.0190203i	−0.999955	+	0.00951016i	$0.996973\pi$
$68$	−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	0.707972	−	0.706240i	$-0.249610\pi$
$71$	14.2895	−	4.64294i	1.69585	−	0.551016i	0.987879	+	0.155224i	$0.0496101\pi$
$72$	3.07151	+	7.13753i	0.361980	+	0.841166i
$73$	−7.84500	+	10.7977i	−0.918188	+	1.26378i	0.0461045	+	0.998937i	$0.485319\pi$
$73$	−7.84500	+	10.7977i	−0.918188	+	1.26378i	−0.964292	+	0.264840i	$0.914681\pi$
$74$	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	0.591284	+	0.806463i	$0.298621\pi$
$79$	−3.20955	+	9.87796i	−0.361102	+	1.11136i	−0.952386	+	0.304894i	$0.901379\pi$
$80$	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	0.831577	−	0.555409i	$-0.187438\pi$
$83$	−1.52731	−	4.70059i	−0.167644	−	0.515956i	−0.999221	+	0.0394531i	$0.987438\pi$
$84$	−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	0.791857	+	0.610707i	$0.209115\pi$
$97$	−2.04594	+	6.29675i	−0.207734	+	0.639338i	−0.999590	+	0.0286309i	$0.990885\pi$
$98$	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	−0.993185	−	0.116551i	$-0.962816\pi$
$101$	−18.7450	−	6.09061i	−1.86519	−	0.606039i	−0.872010	−	0.489488i	$-0.837184\pi$
$102$	1.71343	−	1.32721i	0.169654	−	0.131414i
$103$	−5.46885	+	7.52722i	−0.538861	+	0.741679i	−0.988448	−	0.151557i	$-0.951571\pi$
$103$	−5.46885	+	7.52722i	−0.538861	+	0.741679i	0.449587	+	0.893237i	$0.351571\pi$
$104$	−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	−0.424303	−	0.905520i	$-0.639481\pi$
$107$	3.16302	−	2.29807i	0.305780	−	0.222162i	0.730084	+	0.683358i	$0.239481\pi$
$108$	−5.59539	−	1.44472i	−0.538417	−	0.139019i
$109$			7.32285i			0.701402i	0.936488	+	0.350701i	$0.114057\pi$
$109$			7.32285i			0.701402i	−0.936488	+	0.350701i	$0.885943\pi$
$110$	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	−0.962359	−	0.271781i	$-0.912387\pi$
$113$	−10.6436	+	7.73303i	−1.00127	+	0.727462i	−0.0389066	+	0.999243i	$0.512387\pi$
$114$	−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	−0.976766	−	0.214310i	$-0.931250\pi$
$127$	−3.52185	−	10.8391i	−0.312514	−	0.961819i	0.664252	−	0.747509i	$-0.268750\pi$
$128$	−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	0.910730	+	0.413001i	$0.135519\pi$
$137$	4.87723	+	15.0106i	0.416690	+	1.28244i	−0.494040	+	0.869439i	$0.664481\pi$
$138$	1.36412	+	3.79704i	0.116121	+	0.323225i
$139$	10.4351	+	7.58152i	0.885091	+	0.643056i	0.934593	−	0.355718i	$-0.115764\pi$
$139$	10.4351	+	7.58152i	0.885091	+	0.643056i	−0.0495025	+	0.998774i	$0.515764\pi$
$140$	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	0.239468	−	0.970904i	$-0.423027\pi$
$149$	12.2540	−	3.98156i	1.00388	−	0.326182i	0.764417	+	0.644722i	$0.223027\pi$
$150$	−0.400040	+	0.587785i	−0.0326631	+	0.0479925i
$151$	−9.72065	+	7.06247i	−0.791055	+	0.574735i	−0.908276	−	0.418370i	$-0.862601\pi$
$151$	−9.72065	+	7.06247i	−0.791055	+	0.574735i	0.117221	+	0.993106i	$0.462601\pi$
$152$	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	−0.372953	−	0.927850i	$-0.621655\pi$
$157$	4.93977	−	3.58895i	0.394236	−	0.286429i	0.767189	+	0.641421i	$0.221655\pi$
$158$	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	0.997828	−	0.0658721i	$-0.0209829\pi$
$163$	22.5515	+	7.32742i	1.76637	+	0.573928i	0.768541	+	0.639800i	$0.220983\pi$
$164$	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	0.616762	+	0.787150i	$0.288444\pi$
$167$	−4.45689	+	13.7169i	−0.344884	+	1.06144i	−0.961646	+	0.274294i	$0.911556\pi$
$168$	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	0.545268	−	0.838262i	$-0.316428\pi$
$173$	−5.53034	−	7.61185i	−0.420464	−	0.578719i	−0.965731	+	0.259543i	$0.916428\pi$
$174$	−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	0.712579	−	0.701592i	$-0.247527\pi$
$179$	−2.33964	−	3.22024i	−0.174873	−	0.240692i	−0.887452	+	0.460900i	$0.847527\pi$
$180$	4.63515	+	2.95036i	0.345484	+	0.219907i
$181$	−0.595756	−	1.83355i	−0.0442822	−	0.136287i	0.926471	−	0.376366i	$-0.122827\pi$
$181$	−0.595756	−	1.83355i	−0.0442822	−	0.136287i	−0.970753	+	0.240079i	$0.922827\pi$
$182$	−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	0.235917	+	0.971773i	$0.424191\pi$
$191$	−10.5199	+	14.4795i	−0.761196	+	1.04770i	−0.997114	+	0.0759237i	$0.975809\pi$
$192$	3.53237	−	1.92331i	0.254927	−	0.138803i
$193$	6.55977	−	2.13140i	0.472182	−	0.153421i	−0.0632531	−	0.997998i	$-0.520148\pi$
$193$	6.55977	−	2.13140i	0.472182	−	0.153421i	0.535435	+	0.844576i	$0.320148\pi$
$194$	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	$-0.941264\pi$
$197$		−	5.15052i		−	0.366959i	0.983024	−	0.183480i	$-0.0587361\pi$
$198$	−5.31438	+	11.7388i	−0.377676	+	0.834237i
$199$			18.1133i			1.28402i	0.766697	+	0.642009i	$0.221899\pi$
$199$			18.1133i			1.28402i	−0.766697	+	0.642009i	$0.778101\pi$
$200$	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	−0.981618	−	0.190856i	$-0.938874\pi$
$211$	−1.09365	+	3.36590i	−0.0752897	+	0.231718i	0.906328	+	0.422574i	$0.138874\pi$
$212$	−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	0.538246	−	0.842788i	$-0.319087\pi$
$223$	−6.41560	−	8.83032i	−0.429620	−	0.591322i	−0.967866	+	0.251466i	$0.919087\pi$
$224$	−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	0.773099	−	0.634286i	$-0.218706\pi$
$227$	6.15855	+	4.47445i	0.408757	+	0.296980i	−0.364341	+	0.931266i	$0.618706\pi$
$228$	0.0452501	+	0.0548489i	0.00299676	+	0.00363246i
$229$	−2.00680	+	6.17630i	−0.132613	+	0.408141i	−0.995211	−	0.0977487i	$-0.968836\pi$
$229$	−2.00680	+	6.17630i	−0.132613	+	0.408141i	0.862598	+	0.505890i	$0.168836\pi$
$230$	−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	0.879320	−	0.476232i	$-0.157998\pi$
$233$	20.0082	+	6.50106i	1.31078	+	0.425899i	0.431462	+	0.902131i	$0.357998\pi$
$234$	−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	−0.152378	−	0.988322i	$-0.548693\pi$
$239$	11.4476	−	8.31718i	0.740485	−	0.537994i	0.892863	+	0.450329i	$0.148693\pi$
$240$	1.97437	+	0.382170i	0.127445	+	0.0246690i
$241$			4.74712i			0.305789i	0.988243	+	0.152895i	$0.0488595\pi$
$241$			4.74712i			0.305789i	−0.988243	+	0.152895i	$0.951141\pi$
$242$	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	0.672354	−	0.740230i	$-0.265283\pi$
$251$	12.3766	+	4.02140i	0.781204	+	0.253829i	0.108850	+	0.994058i	$0.465283\pi$
$252$	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	0.208786	−	0.977961i	$-0.433049\pi$
$257$	−10.5292	−	7.64990i	−0.656792	−	0.477188i	−0.865578	+	0.500774i	$0.833049\pi$
$258$	−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	−0.995709	−	0.0925345i	$-0.970503\pi$
$269$	−4.01098	−	12.3445i	−0.244554	−	0.752660i	0.751155	−	0.660125i	$-0.229497\pi$
$270$	−3.84565	+	1.38158i	−0.234039	+	0.0840804i
$271$	16.9252	+	12.2969i	1.02813	+	0.746981i	0.967934	−	0.251205i	$-0.0808270\pi$
$271$	16.9252	+	12.2969i	1.02813	+	0.746981i	0.0601974	+	0.998186i	$0.480827\pi$
$272$	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	0.679300	−	0.733860i	$-0.262283\pi$
$277$	13.2733	+	4.31275i	0.797514	+	0.259128i	0.118213	+	0.992988i	$0.462283\pi$
$278$	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	0.0232643	−	0.999729i	$-0.492594\pi$
$281$	10.5559	−	3.42982i	0.629712	−	0.204606i	0.606447	+	0.795124i	$0.292594\pi$
$282$	2.38052	+	1.62016i	0.141758	+	0.0964789i
$283$	10.2954	−	7.48008i	0.612001	−	0.444645i	−0.238117	−	0.971236i	$-0.576530\pi$
$283$	10.2954	−	7.48008i	0.612001	−	0.444645i	0.850118	+	0.526592i	$0.176530\pi$
$284$	−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	−0.0725812	+	0.997363i	$0.523124\pi$
$293$	−17.0950	+	23.5292i	−0.998700	+	1.37459i	−0.926119	+	0.377231i	$0.876876\pi$
$294$	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	0.564044	−	0.825745i	$-0.309245\pi$
$311$	−6.97622	−	9.60194i	−0.395585	−	0.544476i	−0.959629	+	0.281269i	$0.909245\pi$
$312$	−4.75697	−	2.82631i	−0.269310	−	0.160008i
$313$	−5.97282	−	18.3825i	−0.337604	−	1.03904i	−0.965425	−	0.260681i	$-0.916053\pi$
$313$	−5.97282	−	18.3825i	−0.337604	−	1.03904i	0.627821	−	0.778358i	$-0.283947\pi$
$314$	−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	−0.879130	−	0.476583i	$-0.841875\pi$
$317$	1.99819	−	6.14980i	0.112230	−	0.345407i	0.991359	+	0.131176i	$0.0418752\pi$
$318$	−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	$-0.773217\pi$
$331$		−	23.7859i		−	1.30739i	0.756757	−	0.653697i	$-0.226783\pi$
$332$	−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	−0.725704	−	0.688007i	$-0.758486\pi$
$337$	2.80658	−	3.86293i	0.152884	−	0.210427i	0.878588	+	0.477580i	$0.158486\pi$
$338$	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	−0.964702	−	0.263344i	$-0.915175\pi$
$347$	−6.31545	−	19.4370i	−0.339031	−	1.04343i	0.625671	−	0.780087i	$-0.284825\pi$
$348$	3.50914	+	2.23363i	0.188109	+	0.119735i
$349$	1.38082	+	1.90054i	0.0739138	+	0.101734i	0.844373	−	0.535755i	$-0.179973\pi$
$349$	1.38082	+	1.90054i	0.0739138	+	0.101734i	−0.770459	+	0.637489i	$0.779973\pi$
$350$	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	0.183358	−	0.983046i	$-0.441303\pi$
$359$	−13.1667	−	9.56619i	−0.694914	−	0.504884i	−0.878272	+	0.478162i	$0.841303\pi$
$360$	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	−0.474246	−	0.880392i	$-0.657279\pi$
$367$	9.76265	−	13.4371i	0.509606	−	0.701413i	0.983853	+	0.178979i	$0.0572794\pi$
$368$	−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	$0.0995051\pi$
$373$			11.8791i			0.615076i	−0.951536	+	0.307538i	$0.900495\pi$
$374$	−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	0.257494	−	0.966280i	$-0.417103\pi$
$379$	20.1255	−	6.53916i	1.03378	−	0.335894i	0.776282	+	0.630386i	$0.217103\pi$
$380$	−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	0.344391	−	0.938826i	$-0.388085\pi$
$383$	1.39303	+	0.452624i	0.0711807	+	0.0231280i	−0.273210	+	0.961954i	$0.588085\pi$
$384$	−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	0.429027	−	0.903292i	$-0.358856\pi$
$389$	−5.86718	−	4.26275i	−0.297478	−	0.216130i	−0.726505	+	0.687161i	$0.758856\pi$
$390$	−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	0.782318	+	0.622879i	$0.214037\pi$
$401$	10.3234	+	31.7723i	0.515528	+	1.58663i	−0.266790	+	0.963755i	$0.585963\pi$
$402$	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	0.0543221	−	0.998523i	$-0.482700\pi$
$409$	−9.88229	−	3.21095i	−0.488648	−	0.158771i	−0.542970	+	0.839752i	$0.682700\pi$
$410$	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	$0.255952\pi$
$419$			29.4844i			1.44041i	−0.693762	+	0.720205i	$0.744048\pi$
$420$	3.12427	+	0.806683i	0.152449	+	0.0393621i
$421$	−7.51048	+	5.45668i	−0.366039	+	0.265943i	−0.755566	−	0.655072i	$-0.772638\pi$
$421$	−7.51048	+	5.45668i	−0.366039	+	0.265943i	0.389528	+	0.921015i	$0.372638\pi$
$422$	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	−0.431153	−	0.902279i	$-0.641893\pi$
$431$	9.30079	−	28.6249i	0.448003	−	1.37881i	0.879157	−	0.476533i	$-0.158107\pi$
$432$	7.88903	+	8.44664i	0.379561	+	0.406389i
$433$	7.90428	+	5.74279i	0.379855	+	0.275981i	0.761286	−	0.648416i	$-0.224568\pi$
$433$	7.90428	+	5.74279i	0.379855	+	0.275981i	−0.381430	+	0.924398i	$0.624568\pi$
$434$	−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	0.976594	+	0.215089i	$0.0690042\pi$
$443$	18.5086	+	25.4750i	0.879372	+	1.21035i	−0.0972223	+	0.995263i	$0.530996\pi$
$444$	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	−0.967911	−	0.251292i	$-0.919144\pi$
$449$	−0.787165	+	2.42264i	−0.0371486	+	0.114332i	0.930763	+	0.365624i	$0.119144\pi$
$450$	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	0.0962151	−	0.995361i	$-0.469326\pi$
$457$	16.2280	−	5.27279i	0.759113	−	0.246651i	0.662898	+	0.748710i	$0.269326\pi$
$458$	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	$0.00998049\pi$
$461$			1.34620i			0.0626990i	−0.999508	+	0.0313495i	$0.990020\pi$
$462$	−0.837912	+	7.52083i	−0.0389832	+	0.349901i
$463$		−	4.36322i		−	0.202776i	−0.994847	−	0.101388i	$-0.967672\pi$
$463$		−	4.36322i		−	0.202776i	0.994847	−	0.101388i	$-0.0323284\pi$
$464$	−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	−0.693674	−	0.720289i	$-0.744009\pi$
$467$	−17.9687	+	5.83839i	−0.831493	+	0.270168i	−0.137819	+	0.990457i	$0.544009\pi$
$468$	−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	−0.995261	−	0.0972438i	$-0.968997\pi$
$479$	−5.41103	−	16.6534i	−0.247236	−	0.760915i	0.748024	−	0.663671i	$-0.231003\pi$
$480$	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	0.927896	−	0.372839i	$-0.121616\pi$
$487$	6.32403	+	8.70428i	0.286569	+	0.394429i	−0.641327	+	0.767268i	$0.721616\pi$
$488$	−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	0.0751094	−	0.997175i	$-0.476069\pi$
$491$	−18.8359	−	13.6851i	−0.850051	−	0.617598i	−0.925160	+	0.379577i	$0.876069\pi$
$492$	−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	−0.954149	−	0.299333i	$-0.903236\pi$
$499$	−8.36834	+	11.5180i	−0.374618	+	0.515618i	0.579531	+	0.814951i	$0.303236\pi$
$500$	−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	−0.972173	−	0.234265i	$-0.924732\pi$
$503$	−23.5444	+	17.1060i	−1.04979	+	0.762718i	−0.0776187	+	0.996983i	$0.524732\pi$
$504$	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	0.275693	−	0.961246i	$-0.411093\pi$
$509$	28.7673	−	20.9006i	1.27509	−	0.926404i	0.999393	+	0.0348414i	$0.0110926\pi$
$510$	−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	0.181680	−	0.983358i	$-0.441846\pi$
$521$	−15.9186	−	11.5655i	−0.697406	−	0.506695i	−0.879086	+	0.476662i	$0.841846\pi$
$522$	15.1262	−	5.43420i	0.662054	−	0.237848i
$523$	12.2934	+	37.8352i	0.537554	+	1.65442i	0.738066	+	0.674728i	$0.235739\pi$
$523$	12.2934	+	37.8352i	0.537554	+	1.65442i	−0.200513	+	0.979691i	$0.564261\pi$
$524$	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	0.858261	−	0.513214i	$-0.171545\pi$
$541$	29.0963	+	9.45397i	1.25095	+	0.406458i	0.392688	+	0.919672i	$0.371545\pi$
$542$	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	−0.432902	−	0.901441i	$-0.642510\pi$
$547$	6.79763	−	4.93876i	0.290645	−	0.211166i	0.723547	+	0.690275i	$0.242510\pi$
$548$	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	−0.463021	−	0.886347i	$-0.653234\pi$
$557$	12.3439	−	16.9899i	0.523027	−	0.719885i	0.986048	+	0.166463i	$0.0532345\pi$
$558$	−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	−0.918032	−	0.396505i	$-0.870223\pi$
$563$	1.36983	−	4.21590i	0.0577313	−	0.177679i	0.975764	+	0.218826i	$0.0702229\pi$
$564$	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	0.987887	−	0.155175i	$-0.0495941\pi$
$569$	12.7625	+	17.5661i	0.535033	+	0.736410i	−0.452854	+	0.891585i	$0.649594\pi$
$570$	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	−0.950370	−	0.311123i	$-0.899295\pi$
$577$	−8.75266	−	26.9379i	−0.364378	−	1.12144i	0.585992	−	0.810317i	$-0.300705\pi$
$578$	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	−0.343314	−	0.939221i	$-0.611550\pi$
$587$	15.8943	−	21.8766i	0.656027	−	0.902944i	0.999342	+	0.0362762i	$0.0115496\pi$
$588$	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	$-0.980167\pi$
$593$		−	3.03259i		−	0.124534i	0.998060	−	0.0622668i	$-0.0198330\pi$
$594$	−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	−0.867835	−	0.496852i	$-0.834489\pi$
$599$	−31.2756	+	10.1621i	−1.27789	+	0.415211i	−0.410051	+	0.912062i	$0.634489\pi$
$600$	1.30619	−	0.562096i	0.0533251	−	0.0229475i
$601$	25.8004	−	35.5112i	1.05242	−	1.44853i	0.165726	−	0.986172i	$-0.447003\pi$
$601$	25.8004	−	35.5112i	1.05242	−	1.44853i	0.886693	−	0.462358i	$-0.152997\pi$
$602$	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	−0.970084	−	0.242771i	$-0.921944\pi$
$607$	−1.04888	+	3.22811i	−0.0425726	+	0.131025i	0.927511	+	0.373795i	$0.121944\pi$
$608$	−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	−0.999861	−	0.0166955i	$-0.994685\pi$
$613$	−17.4987	−	24.0849i	−0.706765	−	0.972779i	0.293096	−	0.956083i	$-0.405315\pi$
$614$	−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	0.928317	−	0.371789i	$-0.121256\pi$
$619$	7.16184	+	9.85743i	0.287859	+	0.396203i	−0.640458	+	0.767993i	$0.721256\pi$
$620$	−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	−0.324993	−	0.945717i	$-0.605362\pi$
$631$	16.9524	−	23.3330i	0.674865	−	0.928873i	0.999858	+	0.0168439i	$0.00536183\pi$
$632$	−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	−0.695503	−	0.718523i	$-0.744819\pi$
$641$	−5.74895	+	4.17686i	−0.227070	+	0.164976i	0.468434	+	0.883499i	$0.344819\pi$
$642$	1.56404	−	2.29807i	0.0617276	−	0.0906974i
$643$	−27.4095	+	8.90590i	−1.08093	+	0.351214i	−0.794734	−	0.606958i	$-0.792390\pi$
$643$	−27.4095	+	8.90590i	−1.08093	+	0.351214i	−0.286193	+	0.958172i	$0.592390\pi$
$644$	−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	−0.120770	−	0.992680i	$-0.538536\pi$
$647$	−20.3988	−	6.62796i	−0.801959	−	0.260572i	−0.681188	+	0.732108i	$0.738536\pi$
$648$	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	0.950835	−	0.309699i	$-0.100228\pi$
$653$	24.2792	+	17.6399i	0.950118	+	0.690301i	−0.000716986		1.00000i	$0.500228\pi$
$654$	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	0.140300	−	0.990109i	$-0.455193\pi$
$673$	−8.51337	−	2.76616i	−0.328166	−	0.106628i	−0.468466	+	0.883481i	$0.655193\pi$
$674$	−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	−0.342859	−	0.939387i	$-0.611395\pi$
$677$	−1.77141	+	0.575567i	−0.0680809	+	0.0221208i	0.274779	+	0.961508i	$0.411395\pi$
$678$	−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	$0.112048\pi$
$683$			18.0214i			0.689571i	−0.938681	+	0.344786i	$0.887952\pi$
$684$	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	−0.455021	−	0.890481i	$-0.650368\pi$
$691$	−35.3967	−	11.5011i	−1.34655	−	0.437521i	−0.891531	+	0.452959i	$0.850368\pi$
$692$	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	0.984839	+	0.173473i	$0.0554989\pi$
$701$	22.3855	+	30.8110i	0.845489	+	1.16372i	−0.139349	+	0.990243i	$0.544501\pi$
$702$	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	0.948524	−	0.316704i	$-0.102576\pi$
$709$	−0.133182	−	0.409893i	−0.00500177	−	0.0153939i	−0.953526	+	0.301310i	$0.902576\pi$
$710$	−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	−0.712304	−	0.701871i	$-0.752348\pi$
$719$	4.70131	−	6.47080i	0.175329	−	0.241320i	0.887633	+	0.460551i	$0.152348\pi$
$720$	−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	$-0.818014\pi$
$727$		−	29.1784i		−	1.08217i	0.840969	−	0.541084i	$-0.181986\pi$
$728$	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	−0.781031	−	0.624492i	$-0.785306\pi$
$733$	1.46872	−	2.02152i	0.0542485	−	0.0746666i	0.835279	+	0.549826i	$0.185306\pi$
$734$	−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	−0.960744	−	0.277436i	$-0.910515\pi$
$739$	−0.554914	+	1.70785i	−0.0204128	+	0.0628243i	0.940331	+	0.340261i	$0.110515\pi$
$740$	−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	−0.997317	−	0.0732026i	$-0.976678\pi$
$743$	−6.36470	−	19.5885i	−0.233498	−	0.718633i	0.763819	−	0.645430i	$-0.223322\pi$
$744$	−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	0.627204	−	0.778855i	$-0.284199\pi$
$751$	−8.42266	−	11.5928i	−0.307347	−	0.423027i	−0.934552	+	0.355827i	$0.884199\pi$
$752$	−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	−0.868997	−	0.494818i	$-0.835235\pi$
$757$	3.43599	−	10.5749i	0.124883	−	0.384351i	0.993880	+	0.110467i	$0.0352347\pi$
$758$	−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	−0.0607453	−	0.998153i	$-0.519348\pi$
$761$	−19.2163	−	6.24374i	−0.696589	−	0.226336i	−0.635844	+	0.771818i	$0.719348\pi$
$762$	−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	1.62156	−	1.17814i
$768$	−8.02534	−	0.548527i	−0.289590	−	0.0197933i
$769$		−	17.4538i		−	0.629398i	−0.949191	−	0.314699i	$-0.898096\pi$
$769$		−	17.4538i		−	0.629398i	0.949191	−	0.314699i	$-0.101904\pi$
$770$	6.20774	−	13.7121i	0.223711	−	0.494149i
$771$		−	6.54324i		−	0.235649i
$772$	−13.3567	−	3.44867i	−0.480717	−	0.124120i
$773$	2.37372	−	1.72461i	0.0853768	−	0.0620299i	−0.544278	−	0.838905i	$-0.683196\pi$
$773$	2.37372	−	1.72461i	0.0853768	−	0.0620299i	0.629655	+	0.776875i	$0.283196\pi$
$774$	1.59433	+	1.08509i	0.0573072	+	0.0390026i
$775$	−0.894983	+	0.290798i	−0.0321488	+	0.0104458i
$776$	−7.40227	−	17.2013i	−0.265726	−	0.617492i
$777$	8.38929	−	11.5469i	0.300964	−	0.414242i
$778$	−8.10824	+	6.28061i	−0.290694	+	0.225171i
$779$	0.570284	+	0.185296i	0.0204325	+	0.00663893i
$780$	−3.90520	+	0.240391i	−0.139829	+	0.00860737i
$781$	−23.3036	−	44.0472i	−0.833869	−	1.57613i
$782$	24.4511	−	0.751852i	0.874370	−	0.0268862i
$783$	−3.69381	+	11.3684i	−0.132006	+	0.406272i
$784$	−9.64109	+	9.00462i	−0.344325	+	0.321594i
$785$	−4.93977	−	3.58895i	−0.176308	−	0.128095i
$786$	−1.76716	+	0.634867i	−0.0630325	+	0.0226449i
$787$	−1.82997	−	5.63208i	−0.0652316	−	0.200762i	0.913128	−	0.407672i	$-0.133659\pi$
$787$	−1.82997	−	5.63208i	−0.0652316	−	0.200762i	−0.978360	+	0.206910i	$0.933659\pi$
$788$	−5.53133	+	8.68997i	−0.197045	+	0.309567i
$789$	−6.98769	−	9.61773i	−0.248768	−	0.342400i
$790$	4.10749	−	14.1025i	0.146138	−	0.501743i
$791$	42.2190			1.50114
$792$	21.5731	−	14.0984i	0.766568	−	0.500964i
$793$	2.85101			0.101242
$794$	−14.9259	+	51.2458i	−0.529700	+	1.81865i
$795$	−2.33195	−	3.20965i	−0.0827057	−	0.113835i
$796$	19.4525	−	30.5608i	0.689477	−	1.08320i
$797$	9.45967	+	29.1139i	0.335079	+	1.03127i	0.966683	+	0.255975i	$0.0823966\pi$
$797$	9.45967	+	29.1139i	0.335079	+	1.03127i	−0.631605	+	0.775291i	$0.717603\pi$
$798$	0.151847	−	0.0545521i	0.00537531	−	0.00193112i
$799$	9.98771	+	7.25650i	0.353340	+	0.256716i
$800$	−4.01351	+	3.98645i	−0.141899	+	0.140942i
$801$	10.1555	−	31.2555i	0.358828	−	1.10436i
$802$	47.2229	−	1.45206i	1.66750	−	0.0512742i
$803$	39.7458	+	19.4872i	1.40260	+	0.687688i
$804$	0.156250	−	0.00961821i	0.00551051	−	0.000339208i
$805$	−17.3188	−	5.62722i	−0.610408	−	0.198333i
$806$	4.09395	−	3.17116i	0.144203	−	0.111699i
$807$	3.83568	−	5.27937i	0.135022	−	0.185843i
$808$	51.2071	−	22.0360i	1.80146	−	0.775225i
$809$	1.02262	−	0.332270i	0.0359534	−	0.0116820i	−0.290985	−	0.956728i	$-0.593983\pi$
$809$	1.02262	−	0.332270i	0.0359534	−	0.0116820i	0.326939	+	0.945046i	$0.393983\pi$
$810$	7.93727	+	5.40201i	0.278887	+	0.189807i
$811$	−37.8442	+	27.4955i	−1.32889	+	0.965496i	−0.329116	+	0.944289i	$0.606751\pi$
$811$	−37.8442	+	27.4955i	−1.32889	+	0.965496i	−0.999775	+	0.0212066i	$0.993249\pi$
$812$	−25.7081	−	6.63780i	−0.902177	−	0.232941i
$813$			10.5180i			0.368881i
$814$	−30.6623	−	27.9566i	−1.07471	−	0.979879i
$815$		−	23.7120i		−	0.830597i
$816$	−1.16496	+	6.01843i	−0.0407818	+	0.210687i
$817$	0.0283984	−	0.0206327i	0.000993536	−	0.000721846i
$818$	−8.26797	+	12.1483i	−0.289083	+	0.424754i
$819$	−32.6256	+	10.6007i	−1.14003	+	0.370419i
$820$	15.7764	−	6.22165i	0.550936	−	0.217269i
$821$	−21.0024	+	28.9073i	−0.732989	+	1.00887i	0.266003	+	0.963972i	$0.414297\pi$
$821$	−21.0024	+	28.9073i	−0.732989	+	1.00887i	−0.998991	+	0.0449002i	$0.985703\pi$
$822$	6.87191	+	8.87160i	0.239685	+	0.309432i
$823$	−25.9266	−	8.42406i	−0.903744	−	0.293644i	−0.179963	−	0.983673i	$-0.557598\pi$
$823$	−25.9266	−	8.42406i	−0.903744	−	0.293644i	−0.723782	+	0.690029i	$0.757598\pi$
$824$	−2.42340	−	26.2043i	−0.0844230	−	0.912870i
$825$	−0.235478	+	1.65074i	−0.00819828	+	0.0574712i
$826$	1.98983	+	64.7117i	0.0692351	+	2.25161i
$827$	−2.34368	+	7.21311i	−0.0814978	+	0.250825i	−0.983500	−	0.180906i	$-0.942097\pi$
$827$	−2.34368	+	7.21311i	−0.0814978	+	0.250825i	0.902003	+	0.431731i	$0.142097\pi$
$828$	−19.8416	−	24.0506i	−0.689545	−	0.835816i
$829$	−13.8143	−	10.0367i	−0.479790	−	0.348588i	0.321455	−	0.946925i	$-0.395828\pi$
$829$	−13.8143	−	10.0367i	−0.479790	−	0.348588i	−0.801244	+	0.598337i	$0.795828\pi$
$830$	2.36324	+	6.57811i	0.0820292	+	0.228329i
$831$	2.16825	+	6.67319i	0.0752158	+	0.231490i
$832$	13.3684	−	28.1126i	0.463466	−	0.974628i
$833$	5.90922	+	8.13334i	0.204742	+	0.281804i
$834$	8.80495	+	2.56453i	0.304890	+	0.0888026i
$835$	14.4228			0.499121
$836$	−0.108739	−	0.456298i	−0.00376083	−	0.0157814i
$837$	2.71909			0.0939855
$838$	40.0338	+	11.6603i	1.38294	+	0.402797i
$839$	25.6699	+	35.3316i	0.886224	+	1.21978i	0.974658	+	0.223701i	$0.0718138\pi$
$839$	25.6699	+	35.3316i	0.886224	+	1.21978i	−0.0884339	+	0.996082i	$0.528186\pi$
$840$	2.33087	−	3.92309i	0.0804226	−	0.135360i
$841$	3.67295	+	11.3042i	0.126653	+	0.389799i
$842$	4.43887	+	12.3556i	0.152973	+	0.425804i
$843$	4.51442	+	3.27992i	0.155485	+	0.112966i
$844$	5.45997	−	4.50445i	0.187940	−	0.155050i
$845$	0.661637	−	2.03631i	0.0227610	−	0.0700511i
$846$	−0.483608	−	15.7275i	−0.0166268	−	0.540723i
$847$	33.8916	+	9.87015i	1.16453	+	0.339142i
$848$	31.3266	−	3.87139i	1.07576	−	0.132944i
$849$	6.08485	+	1.97709i	0.208831	+	0.0678534i
$850$	2.63989	+	3.40808i	0.0905474	+	0.116896i
$851$	−29.5071	+	40.6130i	−1.01149	+	1.39220i
$852$	−5.54248	−	14.0542i	−0.189882	−	0.481490i
$853$	30.9085	−	10.0428i	1.05829	−	0.343858i	0.272371	−	0.962192i	$-0.412192\pi$
$853$	30.9085	−	10.0428i	1.05829	−	0.343858i	0.785915	+	0.618334i	$0.212192\pi$
$854$	−1.87088	+	2.74891i	−0.0640201	+	0.0940658i
$855$	0.157170	−	0.114191i	0.00537511	−	0.00390525i
$856$	−2.43419	+	10.7871i	−0.0831989	+	0.368695i
$857$			13.4666i			0.460010i	0.973190	+	0.230005i	$0.0738742\pi$
$857$			13.4666i			0.460010i	−0.973190	+	0.230005i	$0.926126\pi$
$858$	−1.85177	−	8.98704i	−0.0632183	−	0.306813i
$859$		−	7.48872i		−	0.255512i	−0.991806	−	0.127756i	$-0.959223\pi$
$859$		−	7.48872i		−	0.255512i	0.991806	−	0.127756i	$-0.0407774\pi$
$860$	0.248193	−	0.961249i	0.00846332	−	0.0327783i
$861$	−11.0677	+	8.04117i	−0.377187	+	0.274042i
$862$	−35.1885	−	23.9489i	−1.19852	−	0.815702i
$863$	−9.36487	+	3.04283i	−0.318784	+	0.103579i	−0.464038	−	0.885815i	$-0.653600\pi$
$863$	−9.36487	+	3.04283i	−0.318784	+	0.103579i	0.145254	+	0.989394i	$0.453600\pi$
$864$	14.5887	−	7.37126i	0.496317	−	0.250775i
$865$	−5.53034	+	7.61185i	−0.188037	+	0.258811i
$866$	10.9234	−	8.46126i	0.371194	−	0.287525i
$867$	−3.68556	−	1.19751i	−0.125168	−	0.0406696i
$868$	0.371081	+	6.02830i	0.0125953	+	0.204614i
$869$	34.1023	+	4.86469i	1.15684	+	0.165023i
$870$	2.93997	−	0.0904016i	0.0996742	−	0.00306490i
$871$	−0.187205	+	0.576156i	−0.00634318	+	0.0195223i
$872$	−13.6656	−	15.5642i	−0.462777	−	0.527069i
$873$	14.7151	+	10.6912i	0.498032	+	0.361841i
$874$	−0.534080	+	0.191873i	−0.0180655	+	0.00649019i
$875$	−0.991653	−	3.05199i	−0.0335240	−	0.103176i
$876$	11.3213	+	7.20624i	0.382512	+	0.243476i
$877$	−7.33136	−	10.0908i	−0.247562	−	0.340740i	0.667093	−	0.744974i	$-0.267538\pi$
$877$	−7.33136	−	10.0908i	−0.247562	−	0.340740i	−0.914656	+	0.404234i	$0.867538\pi$
$878$	4.09018	−	14.0430i	0.138037	−	0.473929i
$879$	−14.6220			−0.493187
$880$	−10.5848	−	7.99756i	−0.356815	−	0.269598i
$881$	−24.2462			−0.816875			−0.408437	−	0.912786i	$-0.633926\pi$
$881$	−24.2462			−0.816875			−0.408437	+	0.912786i	$0.633926\pi$
$882$	3.58318	−	12.3023i	0.120652	−	0.414240i
$883$	11.3687	+	15.6477i	0.382588	+	0.526587i	0.956268	−	0.292492i	$-0.0944846\pi$
$883$	11.3687	+	15.6477i	0.382588	+	0.526587i	−0.573680	+	0.819080i	$0.694485\pi$
$884$	−20.0125	−	12.7383i	−0.673093	−	0.428436i
$885$	−2.21633	−	6.82115i	−0.0745010	−	0.229290i
$886$	41.9094	−	15.0563i	1.40797	−	0.505826i
$887$	−36.9618	−	26.8543i	−1.24106	−	0.901680i	−0.243387	−	0.969929i	$-0.578259\pi$
$887$	−36.9618	−	26.8543i	−1.24106	−	0.901680i	−0.997668	+	0.0682495i	$0.978259\pi$
$888$	−8.30002	−	9.45312i	−0.278530	−	0.317226i
$889$	−11.3018	+	34.7834i	−0.379051	+	1.16660i
$890$	−16.9096	+	0.519957i	−0.566811	+	0.0174290i
$891$	−9.91249	+	20.2174i	−0.332081	+	0.677308i
$892$	1.34123	+	21.7885i	0.0449076	+	0.729533i
$893$	−0.272381	−	0.0885019i	−0.00911488	−	0.00296160i
$894$	7.24238	−	5.60992i	0.242221	−	0.187624i
$895$	−2.33964	+	3.22024i	−0.0782056	+	0.107641i
$896$	18.3333	+	31.3375i	0.612471	+	1.04691i
$897$	−10.5578	+	3.43045i	−0.352516	+	0.114539i
$898$	2.97815	+	2.02689i	0.0993821	+	0.0676383i
$899$	−3.14951	+	2.28825i	−0.105042	+	0.0763175i
$900$	1.37362	−	5.32000i	0.0457873	−	0.177333i
$901$		−	24.0547i		−	0.801377i
$902$	19.6709	+	34.5670i	0.654971	+	1.15096i
$903$			0.800854i			0.0266507i
$904$	8.19109	−	36.2987i	0.272432	−	1.20728i
$905$	−1.55971	+	1.13320i	−0.0518465	+	0.0376687i
$906$	−4.80663	+	7.06247i	−0.159690	+	0.234635i
$907$	−51.8977	+	16.8626i	−1.72323	+	0.559913i	−0.992445	−	0.122691i	$-0.960847\pi$
$907$	−51.8977	+	16.8626i	−1.72323	+	0.559913i	−0.730789	+	0.682604i	$0.760847\pi$
$908$	−5.58546	−	14.1632i	−0.185360	−	0.470023i
$909$	−31.8268	+	43.8059i	−1.05563	+	1.45295i
$910$	10.8140	+	13.9608i	0.358481	+	0.462797i
$911$	19.3513	+	6.28763i	0.641138	+	0.208319i	0.611503	−	0.791242i	$-0.290565\pi$
$911$	19.3513	+	6.28763i	0.641138	+	0.208319i	0.0296356	+	0.999561i	$0.490565\pi$
$912$	−0.0174419	−	0.141137i	−0.000577560	−	0.00467352i
$913$	−14.4895	+	7.66581i	−0.479532	+	0.253701i
$914$	−0.741655	−	24.1195i	−0.0245318	−	0.797802i
$915$	0.113830	−	0.350334i	0.00376312	−	0.0115817i
$916$	10.0188	−	8.26550i	0.331032	−	0.273100i
$917$	6.85646	+	4.98151i	0.226420	+	0.164504i
$918$	−4.21145	−	11.7226i	−0.138998	−	0.386904i
$919$	15.1776	+	46.7119i	0.500664	+	1.54088i	0.807941	+	0.589264i	$0.200582\pi$
$919$	15.1776	+	46.7119i	0.500664	+	1.54088i	−0.307277	+	0.951620i	$0.599418\pi$
$920$	−8.19821	+	13.7984i	−0.270287	+	0.454921i
$921$	−8.61724	−	11.8606i	−0.283948	−	0.390821i
$922$	1.82787	+	0.532386i	0.0601976	+	0.0175332i
$923$	58.4641			1.92437
$924$	9.88036	+	4.11198i	0.325040	+	0.135274i
$925$	−8.84655			−0.290873
$926$	−5.92435	−	1.72553i	−0.194686	−	0.0567044i
$927$	15.0242	+	20.6791i	0.493460	+	0.679190i
$928$	−10.6947	+	20.8152i	−0.351071	+	0.683293i
$929$	−0.735903	−	2.26488i	−0.0241442	−	0.0743082i	0.938258	−	0.345935i	$-0.112438\pi$
$929$	−0.735903	−	2.26488i	−0.0241442	−	0.0743082i	−0.962403	+	0.271627i	$0.912438\pi$
$930$	−0.226218	−	0.629679i	−0.00741797	−	0.0206480i
$931$	−0.188682	−	0.137086i	−0.00618381	−	0.00449280i
$932$	−26.7762	−	32.4562i	−0.877084	−	1.06314i
$933$	1.84391	−	5.67497i	0.0603668	−	0.185790i
$934$	0.821210	+	26.7067i	0.0268708	+	0.873870i
$935$	−7.03802	+	7.25798i	−0.230168	+	0.237361i
$936$	2.78434	+	30.1072i	0.0910090	+	0.984086i
$937$	18.3283	+	5.95523i	0.598760	+	0.194549i	0.592687	−	0.805433i	$-0.298067\pi$
$937$	18.3283	+	5.95523i	0.598760	+	0.194549i	0.00607273	+	0.999982i	$0.498067\pi$
$938$	−0.432676	−	0.558583i	−0.0141274	−	0.0182384i
$939$	5.71178	−	7.86159i	0.186397	−	0.256553i
$940$	−7.53519	+	2.97161i	−0.245771	+	0.0969232i
$941$	−23.6518	+	7.68493i	−0.771026	+	0.250521i	−0.668004	−	0.744158i	$-0.732851\pi$
$941$	−23.6518	+	7.68493i	−0.771026	+	0.250521i	−0.103022	+	0.994679i	$0.532851\pi$
$942$	2.44260	−	3.58895i	0.0795842	−	0.116934i
$943$	38.9278	−	28.2827i	1.26766	−	0.921011i
$944$	56.0232	+	10.8442i	1.82340	+	0.352948i
$945$			9.27240i			0.301631i
$946$	2.31394	+	0.257802i	0.0752328	+	0.00838185i
$947$			31.5786i			1.02617i	0.858338	+	0.513084i	$0.171497\pi$
$947$			31.5786i			1.02617i	−0.858338	+	0.513084i	$0.828503\pi$
$948$	10.1119	+	2.61088i	0.328419	+	0.0847974i
$949$	−42.0156	+	30.5261i	−1.36388	+	0.990920i
$950$	−0.0826761	−	0.0562684i	−0.00268237	−	0.00182559i
$951$	3.09184	−	1.00460i	0.100260	−	0.0325764i
$952$	25.4146	−	10.9367i	0.823693	−	0.354461i
$953$	−17.7778	+	24.4690i	−0.575878	+	0.792628i	−0.993236	−	0.116114i	$-0.962956\pi$
$953$	−17.7778	+	24.4690i	−0.575878	+	0.792628i	0.417358	+	0.908742i	$0.362956\pi$
$954$	−24.2379	+	18.7746i	−0.784733	+	0.607851i
$955$	17.0216	+	5.53066i	0.550807	+	0.178968i
$956$	−28.2466	+	1.73876i	−0.913560	+	0.0562357i
$957$	1.18379	+	6.79576i	0.0382665	+	0.219676i
$958$	−24.7518	+	0.761099i	−0.799696	+	0.0245900i
$959$	15.6513	−	48.1698i	0.505407	−	1.55548i
$960$	−2.92074	−	2.76515i	−0.0942664	−	0.0892448i
$961$	−24.3631	−	17.7008i	−0.785906	−	0.570994i
$962$	45.8150	−	16.4594i	1.47713	−	0.530673i
$963$	−3.31912	−	10.2152i	−0.106957	−	0.329180i
$964$	5.09811	−	8.00937i	0.164199	−	0.257964i
$965$	−4.05416	−	5.58007i	−0.130508	−	0.179629i
$966$	3.62062	−	12.4309i	0.116491	−	0.399956i
$967$	−44.0784			−1.41747			−0.708733	−	0.705477i	$-0.750733\pi$
$967$	−44.0784			−1.41747			−0.708733	+	0.705477i	$0.750733\pi$
$968$	15.0615	−	27.2241i	0.484095	−	0.875015i
$969$	−0.108374			−0.00348149
$970$	2.61834	−	8.98967i	0.0840697	−	0.288641i
$971$	−24.5621	−	33.8068i	−0.788235	−	1.08491i	−0.994326	−	0.106379i	$-0.966074\pi$
$971$	−24.5621	−	33.8068i	−0.788235	−	1.08491i	0.206091	−	0.978533i	$-0.433926\pi$
$972$	−12.9748	+	20.3841i	−0.416168	+	0.653819i
$973$	−12.7908	−	39.3660i	−0.410054	−	1.26202i
$974$	14.3196	−	5.14443i	0.458829	−	0.164838i
$975$	−1.58268	−	1.14988i	−0.0506862	−	0.0368257i
$976$	2.00046	+	2.14185i	0.0640330	+	0.0685590i
$977$	−0.985364	+	3.03264i	−0.0315246	+	0.0970227i	−0.965581	−	0.260103i	$-0.916243\pi$
$977$	−0.985364	+	3.03264i	−0.0315246	+	0.0970227i	0.934056	+	0.357126i	$0.116243\pi$
$978$	16.8513	−	0.518165i	0.538846	−	0.0165691i
$979$	−6.80873	−	39.0867i	−0.217608	−	1.24922i
$980$	−6.58363	+	0.405266i	−0.210306	+	0.0129457i
$981$	19.1330	+	6.21668i	0.610869	+	0.198483i
$982$	−26.0305	+	20.1632i	−0.830667	+	0.643432i
$983$	7.01991	−	9.66207i	0.223900	−	0.308172i	−0.682258	−	0.731112i	$-0.739002\pi$
$983$	7.01991	−	9.66207i	0.223900	−	0.308172i	0.906158	+	0.422940i	$0.139002\pi$
$984$	4.76627	+	11.0758i	0.151943	+	0.353084i
$985$	−4.89843	+	1.59160i	−0.156077	+	0.0507125i
$986$	14.7433	+	10.0341i	0.469522	+	0.319551i
$987$	5.28621	−	3.84066i	0.168262	−	0.122249i
$988$	0.532858	+	0.137583i	0.0169525	+	0.00437711i
$989$		−	2.81679i		−	0.0895687i
$990$	12.8065	+	1.42680i	0.407016	+	0.0453465i
$991$		−	42.2327i		−	1.34156i	−0.741654	−	0.670782i	$-0.765958\pi$
$991$		−	42.2327i		−	1.34156i	0.741654	−	0.670782i	$-0.234042\pi$
$992$	5.25495	+	0.850530i	0.166845	+	0.0270044i
$993$	9.67461	−	7.02902i	0.307015	−	0.223059i
$994$	−38.3651	+	56.3704i	−1.21687	+	1.78796i
$995$	17.2268	−	5.59732i	0.546125	−	0.177447i
$996$	−4.62319	+	1.82322i	−0.146491	+	0.0577710i
$997$	−32.9568	+	45.3611i	−1.04375	+	1.43660i	−0.149649	+	0.988739i	$0.547814\pi$
$997$	−32.9568	+	45.3611i	−1.04375	+	1.43660i	−0.894103	+	0.447862i	$0.852186\pi$
$998$	12.3297	+	15.9175i	0.390289	+	0.503860i
$999$	24.3106	+	7.89898i	0.769152	+	0.249913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.b.211.1	yes	8
4.3	odd	2		220.2.r.a.211.1	yes	8
11.6	odd	10		220.2.r.a.171.1	✓	8
44.39	even	10	inner	220.2.r.b.171.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.a.171.1	✓	8	11.6	odd	10
220.2.r.a.211.1	yes	8	4.3	odd	2
220.2.r.b.171.1	yes	8	44.39	even	10	inner
220.2.r.b.211.1	yes	8	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

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Database

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