Properties

Label 220.2.r.b.211.1
Level 220220
Weight 22
Character 220.211
Analytic conductor 1.7571.757
Analytic rank 00
Dimension 88
Inner twists 22

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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 N == 220=22511 220 = 2^{2} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 220.r (of order 1010, degree 44, 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: 1.756708844471.75670884447
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: Q(ζ15)\Q(\zeta_{15})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x7+x5x4+x3x+1 x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 211.1
Root 0.9781480.207912i-0.978148 - 0.207912i of defining polynomial
Character χ\chi == 220.211
Dual form 220.2.r.b.171.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.3954721.35779i)q2+(0.295511+0.406737i)q3+(1.687201.07394i)q4+(0.3090170.951057i)q5+(0.6691310.240391i)q6+(2.596181.88624i)q7+(2.12543+1.86616i)q8+(0.8489432.61278i)q9+(1.41355+0.0434654i)q10+(0.5691713.26742i)q11+(0.06177871.00361i)q12+(3.70071+1.20243i)q13+(3.58783+2.77912i)q14+(0.2955110.406737i)q15+(1.69332+3.62390i)q16+(2.899080.941970i)q17+(3.211882.18597i)q18+(0.0572103+0.0415657i)q19+(0.500000+1.93649i)q201.61337iq21+(4.661570.519356i)q22+5.67459iq23+(1.387120.313016i)q24+(0.809017+0.587785i)q25+(3.096184.54927i)q26+(2.748030.892888i)q27+(2.35459+5.97060i)q28+(2.43162+3.34684i)q29+(0.4353980.562096i)q30+(0.894983+0.290798i)q31+(5.590170.866025i)q32+(1.160781.19706i)q33+(0.1324954.30888i)q34+(0.991653+3.05199i)q35+(4.23830+3.49658i)q36+(7.15701+5.19987i)q37+(0.0338126+0.0941179i)q38+(0.604528+1.86055i)q39+(2.43162+1.44472i)q40+(4.984106.86002i)q41+(2.190620.638041i)q420.496387q43+(2.54870+6.12406i)q442.74724q45+(7.70491+2.24414i)q46+(2.38052+3.27651i)q47+(0.973579+1.75964i)q48+(1.01915+3.13663i)q49+(0.478148+1.33093i)q50+(1.23985+0.900801i)q51+(4.952526.00308i)q52+(2.438527.50500i)q53+(0.1255914.08437i)q54+(2.93162+1.55100i)q55+(9.038020.835843i)q56+(0.03381260.0109864i)q57+(3.58268+4.62521i)q58+(8.3852111.5413i)q59+(0.935398+0.368887i)q60+(0.6968300.226414i)q61+(0.7487841.10020i)q62+(7.13233+5.18194i)q63+(1.034877.93278i)q643.89116iq65+(1.166312.04951i)q66+0.155688iq67+(5.902971.52414i)q68+(2.30806+1.67691i)q69+(3.75181+2.55344i)q70+(14.28954.64294i)q71+(3.07151+7.13753i)q72+(7.84500+10.7977i)q73+(9.890747.66133i)q74+(0.4781480.155360i)q75+(0.1411650.00868960i)q76+(4.68546+9.55641i)q77+(2.765310.0850311i)q78+(3.20955+9.87796i)q79+(2.923272.73029i)q80+(5.492443.99049i)q81+(11.2856+4.05443i)q82+(1.527314.70059i)q83+(1.73265+2.72208i)q84+(1.791732.46611i)q85+(0.196307+0.673990i)q862.07985q87+(7.30727+5.88250i)q88+11.9625q89+(1.08645+3.73018i)q90+(7.3396410.1021i)q91+(6.094159.57419i)q92+(0.146200+0.449957i)q93+(5.390251.93649i)q94+(0.0572103+0.0415657i)q95+(2.00420+2.01781i)q96+(2.04594+6.29675i)q97+(4.661940.143351i)q98+(9.020241.28674i)q99+O(q100)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})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+5q2+5q3q4+2q5+q63q7+5q8+3q95q10q1110q12+10q13+5q14+5q15+7q165q1710q1811q194q20+6q99+O(q100) 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}) Copy content Toggle raw display

Character values

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

nn 101101 111111 177177
χ(n)\chi(n) e(110)e\left(\frac{1}{10}\right) 1-1 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.395472 1.35779i 0.279641 0.960105i
33 0.295511 + 0.406737i 0.170614 + 0.234830i 0.885758 0.464147i 0.153639π-0.153639\pi
−0.715144 + 0.698977i 0.753639π0.753639\pi
44 −1.68720 1.07394i −0.843602 0.536969i
55 −0.309017 0.951057i −0.138197 0.425325i
66 0.669131 0.240391i 0.273171 0.0981391i
77 −2.59618 1.88624i −0.981264 0.712930i −0.0232736 0.999729i 0.507409π-0.507409\pi
−0.957991 + 0.286799i 0.907409π0.907409\pi
88 −2.12543 + 1.86616i −0.751452 + 0.659788i
99 0.848943 2.61278i 0.282981 0.870926i
1010 −1.41355 + 0.0434654i −0.447002 + 0.0137450i
1111 −0.569171 3.26742i −0.171611 0.985165i
1212 −0.0617787 1.00361i −0.0178340 0.289717i
1313 3.70071 + 1.20243i 1.02639 + 0.333495i 0.773363 0.633964i 0.218573π-0.218573\pi
0.253029 + 0.967459i 0.418573π0.418573\pi
1414 −3.58783 + 2.77912i −0.958889 + 0.742752i
1515 0.295511 0.406737i 0.0763007 0.105019i
1616 1.69332 + 3.62390i 0.423330 + 0.905976i
1717 2.89908 0.941970i 0.703131 0.228461i 0.0644370 0.997922i 0.479475π-0.479475\pi
0.638694 + 0.769461i 0.279475π0.279475\pi
1818 −3.21188 2.18597i −0.757047 0.515238i
1919 −0.0572103 + 0.0415657i −0.0131249 + 0.00953583i −0.594328 0.804222i 0.702582π-0.702582\pi
0.581203 + 0.813758i 0.302582π0.302582\pi
2020 −0.500000 + 1.93649i −0.111803 + 0.433013i
2121 1.61337i 0.352065i
2222 −4.66157 0.519356i −0.993851 0.110727i
2323 5.67459i 1.18323i 0.806220 + 0.591616i 0.201510π0.201510\pi
−0.806220 + 0.591616i 0.798490π0.798490\pi
2424 −1.38712 0.313016i −0.283146 0.0638941i
2525 −0.809017 + 0.587785i −0.161803 + 0.117557i
2626 3.09618 4.54927i 0.607211 0.892185i
2727 2.74803 0.892888i 0.528858 0.171836i
2828 2.35459 + 5.97060i 0.444976 + 1.12834i
2929 −2.43162 + 3.34684i −0.451540 + 0.621492i −0.972728 0.231950i 0.925489π-0.925489\pi
0.521187 + 0.853442i 0.325489π0.325489\pi
3030 −0.435398 0.562096i −0.0794924 0.102624i
3131 0.894983 + 0.290798i 0.160744 + 0.0522288i 0.388283 0.921540i 0.373068π-0.373068\pi
−0.227540 + 0.973769i 0.573068π0.573068\pi
3232 5.59017 0.866025i 0.988212 0.153093i
3333 1.16078 1.19706i 0.202067 0.208382i
3434 −0.132495 4.30888i −0.0227226 0.738967i
3535 −0.991653 + 3.05199i −0.167620 + 0.515881i
3636 −4.23830 + 3.49658i −0.706384 + 0.582763i
3737 7.15701 + 5.19987i 1.17660 + 0.854853i 0.991785 0.127919i 0.0408298π-0.0408298\pi
0.184820 + 0.982772i 0.440830π0.440830\pi
3838 0.0338126 + 0.0941179i 0.00548513 + 0.0152679i
3939 0.604528 + 1.86055i 0.0968020 + 0.297926i
4040 2.43162 + 1.44472i 0.384473 + 0.228431i
4141 −4.98410 6.86002i −0.778385 1.07136i −0.995458 0.0951998i 0.969651π-0.969651\pi
0.217073 0.976155i 0.430349π-0.430349\pi
4242 −2.19062 0.638041i −0.338020 0.0984518i
4343 −0.496387 −0.0756983 −0.0378491 0.999283i 0.512051π-0.512051\pi
−0.0378491 + 0.999283i 0.512051π0.512051\pi
4444 −2.54870 + 6.12406i −0.384231 + 0.923237i
4545 −2.74724 −0.409534
4646 7.70491 + 2.24414i 1.13603 + 0.330880i
4747 2.38052 + 3.27651i 0.347235 + 0.477928i 0.946537 0.322595i 0.104555π-0.104555\pi
−0.599302 + 0.800523i 0.704555π0.704555\pi
4848 −0.973579 + 1.75964i −0.140524 + 0.253982i
4949 1.01915 + 3.13663i 0.145593 + 0.448090i
5050 0.478148 + 1.33093i 0.0676203 + 0.188222i
5151 1.23985 + 0.900801i 0.173613 + 0.126137i
5252 −4.95252 6.00308i −0.686790 0.832478i
5353 2.43852 7.50500i 0.334957 1.03089i −0.631786 0.775143i 0.717678π-0.717678\pi
0.966743 0.255749i 0.0823220π-0.0823220\pi
5454 −0.125591 4.08437i −0.0170908 0.555812i
5555 −2.93162 + 1.55100i −0.395299 + 0.209137i
5656 9.03802 0.835843i 1.20776 0.111694i
5757 −0.0338126 0.0109864i −0.00447859 0.00145518i
5858 3.58268 + 4.62521i 0.470428 + 0.607320i
5959 8.38521 11.5413i 1.09166 1.50254i 0.245666 0.969355i 0.420993π-0.420993\pi
0.845996 0.533189i 0.179007π-0.179007\pi
6060 −0.935398 + 0.368887i −0.120759 + 0.0476231i
6161 0.696830 0.226414i 0.0892199 0.0289893i −0.264067 0.964504i 0.585064π-0.585064\pi
0.353287 + 0.935515i 0.385064π0.385064\pi
6262 0.748784 1.10020i 0.0950956 0.139726i
6363 −7.13233 + 5.18194i −0.898589 + 0.652863i
6464 1.03487 7.93278i 0.129359 0.991598i
6565 3.89116i 0.482639i
6666 −1.16631 2.04951i −0.143562 0.252277i
6767 0.155688i 0.0190203i 0.999955 + 0.00951016i 0.00302722π0.00302722\pi
−0.999955 + 0.00951016i 0.996973π0.996973\pi
6868 −5.90297 1.52414i −0.715840 0.184829i
6969 −2.30806 + 1.67691i −0.277858 + 0.201876i
7070 3.75181 + 2.55344i 0.448427 + 0.305194i
7171 14.2895 4.64294i 1.69585 0.551016i 0.707972 0.706240i 0.249610π-0.249610\pi
0.987879 + 0.155224i 0.0496101π0.0496101\pi
7272 3.07151 + 7.13753i 0.361980 + 0.841166i
7373 −7.84500 + 10.7977i −0.918188 + 1.26378i 0.0461045 + 0.998937i 0.485319π0.485319\pi
−0.964292 + 0.264840i 0.914681π0.914681\pi
7474 9.89074 7.66133i 1.14977 0.890612i
7575 −0.478148 0.155360i −0.0552117 0.0179394i
7676 0.141165 0.00868960i 0.0161927 0.000996766i
7777 −4.68546 + 9.55641i −0.533958 + 1.08905i
7878 2.76531 0.0850311i 0.313110 0.00962788i
7979 −3.20955 + 9.87796i −0.361102 + 1.11136i 0.591284 + 0.806463i 0.298621π0.298621\pi
−0.952386 + 0.304894i 0.901379π0.901379\pi
8080 2.92327 2.73029i 0.326832 0.305256i
8181 −5.49244 3.99049i −0.610271 0.443388i
8282 −11.2856 + 4.05443i −1.24628 + 0.447737i
8383 −1.52731 4.70059i −0.167644 0.515956i 0.831577 0.555409i 0.187438π-0.187438\pi
−0.999221 + 0.0394531i 0.987438π0.987438\pi
8484 −1.73265 + 2.72208i −0.189048 + 0.297003i
8585 −1.79173 2.46611i −0.194341 0.267487i
8686 −0.196307 + 0.673990i −0.0211683 + 0.0726783i
8787 −2.07985 −0.222984
8888 7.30727 + 5.88250i 0.778958 + 0.627076i
8989 11.9625 1.26803 0.634014 0.773322i 0.281406π-0.281406\pi
0.634014 + 0.773322i 0.281406π0.281406\pi
9090 −1.08645 + 3.73018i −0.114522 + 0.393196i
9191 −7.33964 10.1021i −0.769403 1.05899i
9292 6.09415 9.57419i 0.635359 0.998178i
9393 0.146200 + 0.449957i 0.0151602 + 0.0466583i
9494 5.39025 1.93649i 0.555962 0.199734i
9595 0.0572103 + 0.0415657i 0.00586966 + 0.00426455i
9696 2.00420 + 2.01781i 0.204553 + 0.205942i
9797 −2.04594 + 6.29675i −0.207734 + 0.639338i 0.791857 + 0.610707i 0.209115π0.209115\pi
−0.999590 + 0.0286309i 0.990885π0.990885\pi
9898 4.66194 0.143351i 0.470927 0.0144806i
9999 −9.02024 1.28674i −0.906569 0.129322i
100100 1.99622 0.122881i 0.199622 0.0122881i
101101 −18.7450 6.09061i −1.86519 0.606039i −0.993185 0.116551i 0.962816π-0.962816\pi
−0.872010 0.489488i 0.837184π-0.837184\pi
102102 1.71343 1.32721i 0.169654 0.131414i
103103 −5.46885 + 7.52722i −0.538861 + 0.741679i −0.988448 0.151557i 0.951571π-0.951571\pi
0.449587 + 0.893237i 0.351571π0.351571\pi
104104 −10.1095 + 4.35045i −0.991320 + 0.426596i
105105 −1.53440 + 0.498558i −0.149742 + 0.0486543i
106106 −9.22587 6.27902i −0.896096 0.609873i
107107 3.16302 2.29807i 0.305780 0.222162i −0.424303 0.905520i 0.639481π-0.639481\pi
0.730084 + 0.683358i 0.239481π0.239481\pi
108108 −5.59539 1.44472i −0.538417 0.139019i
109109 7.32285i 0.701402i 0.936488 + 0.350701i 0.114057π0.114057\pi
−0.936488 + 0.350701i 0.885943π0.885943\pi
110110 0.946568 + 4.59391i 0.0902517 + 0.438012i
111111 4.44764i 0.422151i
112112 2.43938 12.6023i 0.230499 1.19081i
113113 −10.6436 + 7.73303i −1.00127 + 0.727462i −0.962359 0.271781i 0.912387π-0.912387\pi
−0.0389066 + 0.999243i 0.512387π0.512387\pi
114114 −0.0282892 + 0.0415657i −0.00264952 + 0.00389299i
115115 5.39685 1.75354i 0.503259 0.163519i
116116 7.69693 3.03539i 0.714642 0.281829i
117117 6.28339 8.64834i 0.580899 0.799539i
118118 −12.3545 15.9496i −1.13733 1.46828i
119119 −9.30333 3.02283i −0.852835 0.277103i
120120 0.130949 + 1.41596i 0.0119540 + 0.129259i
121121 −10.3521 + 3.71944i −0.941099 + 0.338131i
122122 −0.0318466 1.03569i −0.00288326 0.0937670i
123123 1.31736 4.05443i 0.118783 0.365576i
124124 −1.19772 1.45179i −0.107559 0.130375i
125125 0.809017 + 0.587785i 0.0723607 + 0.0525731i
126126 4.21537 + 11.7335i 0.375535 + 1.04531i
127127 −3.52185 10.8391i −0.312514 0.961819i −0.976766 0.214310i 0.931250π-0.931250\pi
0.664252 0.747509i 0.268750π-0.268750\pi
128128 −10.3618 4.54233i −0.915864 0.401489i
129129 −0.146688 0.201899i −0.0129152 0.0177762i
130130 −5.28339 1.53884i −0.463384 0.134965i
131131 −2.64098 −0.230743 −0.115372 0.993322i 0.536806π-0.536806\pi
−0.115372 + 0.993322i 0.536806π0.536806\pi
132132 −3.24405 + 0.773082i −0.282358 + 0.0672881i
133133 0.226931 0.0196774
134134 0.211392 + 0.0615702i 0.0182615 + 0.00531885i
135135 −1.69837 2.33761i −0.146173 0.201190i
136136 −4.40392 + 7.41225i −0.377633 + 0.635595i
137137 4.87723 + 15.0106i 0.416690 + 1.28244i 0.910730 + 0.413001i 0.135519π0.135519\pi
−0.494040 + 0.869439i 0.664481π0.664481\pi
138138 1.36412 + 3.79704i 0.116121 + 0.323225i
139139 10.4351 + 7.58152i 0.885091 + 0.643056i 0.934593 0.355718i 0.115764π-0.115764\pi
−0.0495025 + 0.998774i 0.515764π0.515764\pi
140140 4.95077 4.08437i 0.418417 0.345192i
141141 −0.629204 + 1.93649i −0.0529886 + 0.163082i
142142 −0.653062 21.2383i −0.0548037 1.78228i
143143 1.82252 12.7762i 0.152407 1.06840i
144144 10.9060 1.34778i 0.908832 0.112315i
145145 3.93444 + 1.27838i 0.326738 + 0.106164i
146146 11.5586 + 14.9221i 0.956596 + 1.23496i
147147 −0.974611 + 1.34144i −0.0803845 + 0.110640i
148148 −6.49100 16.4594i −0.533557 1.35296i
149149 12.2540 3.98156i 1.00388 0.326182i 0.239468 0.970904i 0.423027π-0.423027\pi
0.764417 + 0.644722i 0.223027π0.223027\pi
150150 −0.400040 + 0.587785i −0.0326631 + 0.0479925i
151151 −9.72065 + 7.06247i −0.791055 + 0.574735i −0.908276 0.418370i 0.862601π-0.862601\pi
0.117221 + 0.993106i 0.462601π0.462601\pi
152152 0.0440279 0.195109i 0.00357113 0.0158254i
153153 8.37435i 0.677026i
154154 11.1227 + 10.1412i 0.896290 + 0.817199i
155155 0.941041i 0.0755862i
156156 0.978148 3.78835i 0.0783145 0.303311i
157157 4.93977 3.58895i 0.394236 0.286429i −0.372953 0.927850i 0.621655π-0.621655\pi
0.767189 + 0.641421i 0.221655π0.221655\pi
158158 12.1429 + 8.26435i 0.966041 + 0.657477i
159159 3.77317 1.22598i 0.299232 0.0972263i
160160 −2.55110 5.04895i −0.201682 0.399155i
161161 10.7036 14.7323i 0.843563 1.16106i
162162 −7.59037 + 5.87948i −0.596356 + 0.461935i
163163 22.5515 + 7.32742i 1.76637 + 0.573928i 0.997828 0.0658721i 0.0209829π-0.0209829\pi
0.768541 + 0.639800i 0.220983π0.220983\pi
164164 1.04196 + 16.9269i 0.0813634 + 1.32177i
165165 −1.49718 0.734058i −0.116555 0.0571463i
166166 −6.98643 + 0.214827i −0.542252 + 0.0166738i
167167 −4.45689 + 13.7169i −0.344884 + 1.06144i 0.616762 + 0.787150i 0.288444π0.288444\pi
−0.961646 + 0.274294i 0.911556π0.911556\pi
168168 3.01081 + 3.42909i 0.232289 + 0.264560i
169169 1.73219 + 1.25851i 0.133245 + 0.0968083i
170170 −4.05705 + 1.45753i −0.311161 + 0.111787i
171171 0.0600337 + 0.184765i 0.00459090 + 0.0141293i
172172 0.837506 + 0.533088i 0.0638592 + 0.0406476i
173173 −5.53034 7.61185i −0.420464 0.578719i 0.545268 0.838262i 0.316428π-0.316428\pi
−0.965731 + 0.259543i 0.916428π0.916428\pi
174174 −0.822523 + 2.82401i −0.0623553 + 0.214088i
175175 3.20906 0.242582
176176 10.8770 7.59540i 0.819887 0.572525i
177177 7.17218 0.539094
178178 4.73085 16.2427i 0.354592 1.21744i
179179 −2.33964 3.22024i −0.174873 0.240692i 0.712579 0.701592i 0.247527π-0.247527\pi
−0.887452 + 0.460900i 0.847527π0.847527\pi
180180 4.63515 + 2.95036i 0.345484 + 0.219907i
181181 −0.595756 1.83355i −0.0442822 0.136287i 0.926471 0.376366i 0.122827π-0.122827\pi
−0.970753 + 0.240079i 0.922827π0.922827\pi
182182 −16.6192 + 5.97060i −1.23190 + 0.442570i
183183 0.298012 + 0.216518i 0.0220297 + 0.0160055i
184184 −10.5897 12.0609i −0.780683 0.889142i
185185 2.73373 8.41356i 0.200988 0.618578i
186186 0.668766 0.0205640i 0.0490363 0.00150783i
187187 −4.72789 8.93639i −0.345737 0.653494i
188188 −0.497665 8.08467i −0.0362959 0.589635i
189189 −8.81858 2.86533i −0.641457 0.208422i
190190 0.0790627 0.0612417i 0.00573581 0.00444294i
191191 −10.5199 + 14.4795i −0.761196 + 1.04770i 0.235917 + 0.971773i 0.424191π0.424191\pi
−0.997114 + 0.0759237i 0.975809π0.975809\pi
192192 3.53237 1.92331i 0.254927 0.138803i
193193 6.55977 2.13140i 0.472182 0.153421i −0.0632531 0.997998i 0.520148π-0.520148\pi
0.535435 + 0.844576i 0.320148π0.320148\pi
194194 7.74057 + 5.26815i 0.555741 + 0.378231i
195195 1.58268 1.14988i 0.113338 0.0823447i
196196 1.64902 6.38664i 0.117787 0.456189i
197197 5.15052i 0.366959i −0.983024 0.183480i 0.941264π-0.941264\pi
0.983024 0.183480i 0.0587361π-0.0587361\pi
198198 −5.31438 + 11.7388i −0.377676 + 0.834237i
199199 18.1133i 1.28402i 0.766697 + 0.642009i 0.221899π0.221899\pi
−0.766697 + 0.642009i 0.778101π0.778101\pi
200200 0.622602 2.75905i 0.0440246 0.195094i
201201 −0.0633240 + 0.0460076i −0.00446653 + 0.00324513i
202202 −15.6829 + 23.0431i −1.10344 + 1.62131i
203203 12.6259 4.10239i 0.886161 0.287931i
204204 −1.12447 2.85135i −0.0787287 0.199635i
205205 −4.98410 + 6.86002i −0.348104 + 0.479125i
206206 8.05764 + 10.4024i 0.561402 + 0.724767i
207207 14.8264 + 4.81740i 1.03051 + 0.334833i
208208 1.90898 + 15.4471i 0.132364 + 1.07106i
209209 0.168375 + 0.163272i 0.0116468 + 0.0112938i
210210 0.0701256 + 2.28057i 0.00483913 + 0.157374i
211211 −1.09365 + 3.36590i −0.0752897 + 0.231718i −0.981618 0.190856i 0.938874π-0.938874\pi
0.906328 + 0.422574i 0.138874π0.138874\pi
212212 −12.1742 + 10.0437i −0.836127 + 0.689801i
213213 6.11116 + 4.44002i 0.418730 + 0.304225i
214214 −1.86942 5.20354i −0.127791 0.355707i
215215 0.153392 + 0.472092i 0.0104612 + 0.0321964i
216216 −4.17445 + 7.02604i −0.284036 + 0.478061i
217217 −1.77503 2.44311i −0.120497 0.165849i
218218 9.94291 + 2.89598i 0.673419 + 0.196140i
219219 −6.71011 −0.453427
220220 6.61192 + 0.531517i 0.445776 + 0.0358349i
221221 11.8613 0.797879
222222 6.03897 + 1.75891i 0.405309 + 0.118051i
223223 −6.41560 8.83032i −0.429620 0.591322i 0.538246 0.842788i 0.319087π-0.319087\pi
−0.967866 + 0.251466i 0.919087π0.919087\pi
224224 −16.1466 8.29602i −1.07884 0.554301i
225225 0.848943 + 2.61278i 0.0565962 + 0.174185i
226226 6.29061 + 17.5100i 0.418445 + 1.16475i
227227 6.15855 + 4.47445i 0.408757 + 0.296980i 0.773099 0.634286i 0.218706π-0.218706\pi
−0.364341 + 0.931266i 0.618706π0.618706\pi
228228 0.0452501 + 0.0548489i 0.00299676 + 0.00363246i
229229 −2.00680 + 6.17630i −0.132613 + 0.408141i −0.995211 0.0977487i 0.968836π-0.968836\pi
0.862598 + 0.505890i 0.168836π0.168836\pi
230230 −0.246648 8.02128i −0.0162635 0.528908i
231231 −5.27155 + 0.918281i −0.346842 + 0.0604184i
232232 −1.07752 11.6513i −0.0707425 0.764942i
233233 20.0082 + 6.50106i 1.31078 + 0.425899i 0.879320 0.476232i 0.157998π-0.157998\pi
0.431462 + 0.902131i 0.357998π0.357998\pi
234234 −9.25776 11.9517i −0.605198 0.781308i
235235 2.38052 3.27651i 0.155288 0.213736i
236236 −26.5422 + 10.4673i −1.72775 + 0.681361i
237237 −4.96619 + 1.61361i −0.322589 + 0.104815i
238238 −7.78359 + 11.4366i −0.504535 + 0.741321i
239239 11.4476 8.31718i 0.740485 0.537994i −0.152378 0.988322i 0.548693π-0.548693\pi
0.892863 + 0.450329i 0.148693π0.148693\pi
240240 1.97437 + 0.382170i 0.127445 + 0.0246690i
241241 4.74712i 0.305789i 0.988243 + 0.152895i 0.0488595π0.0488595\pi
−0.988243 + 0.152895i 0.951141π0.951141\pi
242242 0.956274 + 15.5269i 0.0614716 + 0.998109i
243243 12.0816i 0.775032i
244244 −1.41885 0.366345i −0.0908324 0.0234528i
245245 2.66818 1.93854i 0.170463 0.123849i
246246 −4.98410 3.39212i −0.317774 0.216274i
247247 −0.261699 + 0.0850311i −0.0166515 + 0.00541040i
248248 −2.44490 + 1.05212i −0.155251 + 0.0668094i
249249 1.46056 2.01029i 0.0925593 0.127397i
250250 1.11803 0.866025i 0.0707107 0.0547723i
251251 12.3766 + 4.02140i 0.781204 + 0.253829i 0.672354 0.740230i 0.265283π-0.265283\pi
0.108850 + 0.994058i 0.465283π0.465283\pi
252252 17.5988 1.08332i 1.10862 0.0682428i
253253 18.5413 3.22981i 1.16568 0.203056i
254254 −16.1101 + 0.495373i −1.01084 + 0.0310825i
255255 0.473579 1.45753i 0.0296567 0.0912739i
256256 −10.2653 + 12.2728i −0.641584 + 0.767053i
257257 −10.5292 7.64990i −0.656792 0.477188i 0.208786 0.977961i 0.433049π-0.433049\pi
−0.865578 + 0.500774i 0.833049π0.833049\pi
258258 −0.332148 + 0.119327i −0.0206786 + 0.00742896i
259259 −8.77270 26.9996i −0.545109 1.67767i
260260 −4.17886 + 6.56518i −0.259162 + 0.407155i
261261 6.68024 + 9.19456i 0.413496 + 0.569129i
262262 −1.04443 + 3.58590i −0.0645252 + 0.221538i
263263 −23.6461 −1.45808 −0.729040 0.684471i 0.760033π-0.760033\pi
−0.729040 + 0.684471i 0.760033π0.760033\pi
264264 −0.233245 + 4.71048i −0.0143552 + 0.289910i
265265 −7.89123 −0.484754
266266 0.0897448 0.308126i 0.00550261 0.0188924i
267267 3.53507 + 4.86561i 0.216343 + 0.297770i
268268 0.167199 0.262678i 0.0102133 0.0160456i
269269 −4.01098 12.3445i −0.244554 0.752660i −0.995709 0.0925345i 0.970503π-0.970503\pi
0.751155 0.660125i 0.229497π-0.229497\pi
270270 −3.84565 + 1.38158i −0.234039 + 0.0840804i
271271 16.9252 + 12.2969i 1.02813 + 0.746981i 0.967934 0.251205i 0.0808270π-0.0808270\pi
0.0601974 + 0.998186i 0.480827π0.480827\pi
272272 8.32268 + 8.91095i 0.504637 + 0.540306i
273273 1.93997 5.97060i 0.117412 0.361357i
274274 22.3101 0.686017i 1.34780 0.0414438i
275275 2.38101 + 2.30885i 0.143580 + 0.139229i
276276 5.69506 0.350569i 0.342803 0.0211018i
277277 13.2733 + 4.31275i 0.797514 + 0.259128i 0.679300 0.733860i 0.262283π-0.262283\pi
0.118213 + 0.992988i 0.462283π0.462283\pi
278278 14.4209 11.1704i 0.864909 0.669955i
279279 1.51958 2.09152i 0.0909749 0.125216i
280280 −3.58783 8.33737i −0.214414 0.498253i
281281 10.5559 3.42982i 0.629712 0.204606i 0.0232643 0.999729i 0.492594π-0.492594\pi
0.606447 + 0.795124i 0.292594π0.292594\pi
282282 2.38052 + 1.62016i 0.141758 + 0.0964789i
283283 10.2954 7.48008i 0.612001 0.444645i −0.238117 0.971236i 0.576530π-0.576530\pi
0.850118 + 0.526592i 0.176530π0.176530\pi
284284 −29.0955 7.51243i −1.72650 0.445781i
285285 0.0355527i 0.00210596i
286286 −16.6266 7.52722i −0.983154 0.445094i
287287 27.2110i 1.60622i
288288 2.48300 15.3411i 0.146312 0.903982i
289289 −6.23590 + 4.53065i −0.366818 + 0.266509i
290290 3.29173 4.83660i 0.193297 0.284015i
291291 −3.16572 + 1.02860i −0.185578 + 0.0602978i
292292 24.8322 9.79292i 1.45319 0.573087i
293293 −17.0950 + 23.5292i −0.998700 + 1.37459i −0.0725812 + 0.997363i 0.523124π0.523124\pi
−0.926119 + 0.377231i 0.876876π0.876876\pi
294294 1.43596 + 1.85382i 0.0837470 + 0.108117i
295295 −13.5676 4.40837i −0.789934 0.256665i
296296 −24.9155 + 2.30420i −1.44818 + 0.133929i
297297 −4.48154 8.47076i −0.260045 0.491523i
298298 −0.560034 18.2130i −0.0324419 1.05505i
299299 −6.82331 + 21.0000i −0.394602 + 1.21446i
300300 0.639886 + 0.775624i 0.0369439 + 0.0447807i
301301 1.28871 + 0.936303i 0.0742800 + 0.0539676i
302302 5.74513 + 15.9916i 0.330595 + 0.920215i
303303 −3.06208 9.42411i −0.175912 0.541401i
304304 −0.247505 0.136941i −0.0141954 0.00785409i
305305 −0.430664 0.592759i −0.0246598 0.0339413i
306306 −11.3706 3.31182i −0.650016 0.189324i
307307 −29.1604 −1.66427 −0.832137 0.554570i 0.812883π-0.812883\pi
−0.832137 + 0.554570i 0.812883π0.812883\pi
308308 18.1683 11.0917i 1.03524 0.632010i
309309 −4.67770 −0.266105
310310 −1.27774 0.372155i −0.0725707 0.0211370i
311311 −6.97622 9.60194i −0.395585 0.544476i 0.564044 0.825745i 0.309245π-0.309245\pi
−0.959629 + 0.281269i 0.909245π0.909245\pi
312312 −4.75697 2.82631i −0.269310 0.160008i
313313 −5.97282 18.3825i −0.337604 1.03904i −0.965425 0.260681i 0.916053π-0.916053\pi
0.627821 0.778358i 0.283947π-0.283947\pi
314314 −2.91952 8.12651i −0.164758 0.458605i
315315 7.13233 + 5.18194i 0.401861 + 0.291969i
316316 16.0235 13.2193i 0.901391 0.743644i
317317 1.99819 6.14980i 0.112230 0.345407i −0.879130 0.476583i 0.841875π-0.841875\pi
0.991359 + 0.131176i 0.0418752π0.0418752\pi
318318 −0.172442 5.60802i −0.00967008 0.314482i
319319 12.3195 + 6.04021i 0.689761 + 0.338187i
320320 −7.86432 + 1.46715i −0.439629 + 0.0820159i
321321 1.86942 + 0.607410i 0.104341 + 0.0339023i
322322 −15.7704 20.3595i −0.878849 1.13459i
323323 −0.126704 + 0.174393i −0.00704999 + 0.00970349i
324324 4.98134 + 12.6313i 0.276741 + 0.701740i
325325 −3.70071 + 1.20243i −0.205278 + 0.0666990i
326326 18.8676 27.7225i 1.04498 1.53541i
327327 −2.97847 + 2.16399i −0.164710 + 0.119669i
328328 23.3952 + 5.27933i 1.29179 + 0.291502i
329329 12.9966i 0.716528i
330330 −1.58879 + 1.74256i −0.0874600 + 0.0959246i
331331 23.7859i 1.30739i −0.756757 0.653697i 0.773217π-0.773217\pi
0.756757 0.653697i 0.226783π-0.226783\pi
332332 −2.47124 + 9.57109i −0.135627 + 0.525282i
333333 19.6620 14.2853i 1.07747 0.782828i
334334 16.8621 + 11.4762i 0.922654 + 0.627948i
335335 0.148068 0.0481102i 0.00808983 0.00262854i
336336 5.84668 2.73194i 0.318963 0.149040i
337337 2.80658 3.86293i 0.152884 0.210427i −0.725704 0.688007i 0.758486π-0.758486\pi
0.878588 + 0.477580i 0.158486π0.158486\pi
338338 2.39382 1.85425i 0.130207 0.100858i
339339 −6.29061 2.04394i −0.341659 0.111012i
340340 0.374574 + 6.08504i 0.0203141 + 0.330008i
341341 0.440761 3.08980i 0.0238685 0.167322i
342342 0.274614 0.00844416i 0.0148494 0.000456608i
343343 −3.67105 + 11.2983i −0.198218 + 0.610053i
344344 1.05503 0.926339i 0.0568836 0.0499448i
345345 2.30806 + 1.67691i 0.124262 + 0.0902815i
346346 −12.5224 + 4.49878i −0.673209 + 0.241856i
347347 −6.31545 19.4370i −0.339031 1.04343i −0.964702 0.263344i 0.915175π-0.915175\pi
0.625671 0.780087i 0.284825π-0.284825\pi
348348 3.50914 + 2.23363i 0.188109 + 0.119735i
349349 1.38082 + 1.90054i 0.0739138 + 0.101734i 0.844373 0.535755i 0.179973π-0.179973\pi
−0.770459 + 0.637489i 0.779973π0.779973\pi
350350 1.26909 4.35724i 0.0678357 0.232904i
351351 11.2433 0.600123
352352 −6.01143 17.7725i −0.320410 0.947279i
353353 −15.3669 −0.817897 −0.408949 0.912557i 0.634104π-0.634104\pi
−0.408949 + 0.912557i 0.634104π0.634104\pi
354354 2.83639 9.73834i 0.150753 0.517587i
355355 −8.83140 12.1554i −0.468722 0.645140i
356356 −20.1833 12.8470i −1.06971 0.680891i
357357 −1.51974 4.67729i −0.0804333 0.247548i
358358 −5.29768 + 1.90324i −0.279991 + 0.100589i
359359 −13.1667 9.56619i −0.694914 0.504884i 0.183358 0.983046i 0.441303π-0.441303\pi
−0.878272 + 0.478162i 0.841303π0.841303\pi
360360 5.83905 5.12680i 0.307745 0.270206i
361361 −5.86978 + 18.0653i −0.308936 + 0.950806i
362362 −2.72519 + 0.0837973i −0.143233 + 0.00440429i
363363 −4.57199 3.11144i −0.239967 0.163308i
364364 1.53440 + 24.9267i 0.0804246 + 1.30651i
365365 12.6935 + 4.12436i 0.664407 + 0.215879i
366366 0.411842 0.319012i 0.0215273 0.0166750i
367367 9.76265 13.4371i 0.509606 0.701413i −0.474246 0.880392i 0.657279π-0.657279\pi
0.983853 + 0.178979i 0.0572794π0.0572794\pi
368368 −20.5641 + 9.60888i −1.07198 + 0.500897i
369369 −22.1549 + 7.19857i −1.15334 + 0.374743i
370370 −10.3428 7.03917i −0.537695 0.365949i
371371 −20.4871 + 14.8847i −1.06363 + 0.772776i
372372 0.236556 0.916178i 0.0122649 0.0475016i
373373 11.8791i 0.615076i 0.951536 + 0.307538i 0.0995051π0.0995051\pi
−0.951536 + 0.307538i 0.900495π0.900495\pi
374374 −14.0035 + 2.88540i −0.724105 + 0.149201i
375375 0.502754i 0.0259621i
376376 −11.1741 2.52153i −0.576261 0.130038i
377377 −13.0231 + 9.46181i −0.670722 + 0.487308i
378378 −7.37802 + 10.8406i −0.379485 + 0.557583i
379379 20.1255 6.53916i 1.03378 0.335894i 0.257494 0.966280i 0.417103π-0.417103\pi
0.776282 + 0.630386i 0.217103π0.217103\pi
380380 −0.0518865 0.131570i −0.00266172 0.00674941i
381381 3.36793 4.63556i 0.172544 0.237487i
382382 15.4998 + 20.0101i 0.793037 + 1.02381i
383383 1.39303 + 0.452624i 0.0711807 + 0.0231280i 0.344391 0.938826i 0.388085π-0.388085\pi
−0.273210 + 0.961954i 0.588085π0.588085\pi
384384 −1.21450 5.55684i −0.0619774 0.283571i
385385 10.5366 + 1.50304i 0.536993 + 0.0766022i
386386 −0.299796 9.74971i −0.0152592 0.496247i
387387 −0.421404 + 1.29695i −0.0214212 + 0.0659276i
388388 10.2142 8.42670i 0.518549 0.427801i
389389 −5.86718 4.26275i −0.297478 0.216130i 0.429027 0.903292i 0.358856π-0.358856\pi
−0.726505 + 0.687161i 0.758856π0.758856\pi
390390 −0.935398 2.60369i −0.0473657 0.131843i
391391 5.34529 + 16.4511i 0.270323 + 0.831968i
392392 −8.01959 4.76477i −0.405051 0.240657i
393393 −0.780439 1.07418i −0.0393680 0.0541853i
394394 −6.99334 2.03688i −0.352319 0.102617i
395395 10.3863 0.522592
396396 13.8371 + 11.8582i 0.695341 + 0.595895i
397397 −37.7420 −1.89422 −0.947108 0.320915i 0.896010π-0.896010\pi
−0.947108 + 0.320915i 0.896010π0.896010\pi
398398 24.5941 + 7.16329i 1.23279 + 0.359063i
399399 0.0670608 + 0.0923012i 0.00335724 + 0.00462084i
400400 −3.50000 1.93649i −0.175000 0.0968246i
401401 10.3234 + 31.7723i 0.515528 + 1.58663i 0.782318 + 0.622879i 0.214037π0.214037\pi
−0.266790 + 0.963755i 0.585963π0.585963\pi
402402 0.0374260 + 0.104176i 0.00186664 + 0.00519581i
403403 2.96241 + 2.15232i 0.147568 + 0.107214i
404404 25.0857 + 30.4070i 1.24806 + 1.51281i
405405 −2.09793 + 6.45675i −0.104247 + 0.320839i
406406 −0.577029 18.7657i −0.0286375 0.931325i
407407 12.9166 26.3446i 0.640252 1.30585i
408408 −4.31624 + 0.399170i −0.213686 + 0.0197618i
409409 −9.88229 3.21095i −0.488648 0.158771i 0.0543221 0.998523i 0.482700π-0.482700\pi
−0.542970 + 0.839752i 0.682700π0.682700\pi
410410 7.34342 + 9.48031i 0.362666 + 0.468199i
411411 −4.66407 + 6.41955i −0.230062 + 0.316653i
412412 17.3108 6.82676i 0.852843 0.336331i
413413 −43.5391 + 14.1467i −2.14242 + 0.696114i
414414 12.4045 18.2261i 0.609646 0.895763i
415415 −3.99856 + 2.90512i −0.196281 + 0.142607i
416416 21.7289 + 3.51690i 1.06535 + 0.172430i
417417 6.48475i 0.317560i
418418 0.288278 0.164049i 0.0141001 0.00802391i
419419 29.4844i 1.44041i 0.693762 + 0.720205i 0.255952π0.255952\pi
−0.693762 + 0.720205i 0.744048π0.744048\pi
420420 3.12427 + 0.806683i 0.152449 + 0.0393621i
421421 −7.51048 + 5.45668i −0.366039 + 0.265943i −0.755566 0.655072i 0.772638π-0.772638\pi
0.389528 + 0.921015i 0.372638π0.372638\pi
422422 4.13769 + 2.81606i 0.201419 + 0.137084i
423423 10.5817 3.43821i 0.514501 0.167171i
424424 8.82266 + 20.5020i 0.428466 + 0.995665i
425425 −1.79173 + 2.46611i −0.0869118 + 0.119624i
426426 8.44542 6.54180i 0.409182 0.316951i
427427 −2.23617 0.726574i −0.108216 0.0351614i
428428 −7.80464 + 0.480427i −0.377251 + 0.0232223i
429429 5.73511 3.03422i 0.276894 0.146493i
430430 0.701665 0.0215756i 0.0338373 0.00104047i
431431 9.30079 28.6249i 0.448003 1.37881i −0.431153 0.902279i 0.641893π-0.641893\pi
0.879157 0.476533i 0.158107π-0.158107\pi
432432 7.88903 + 8.44664i 0.379561 + 0.406389i
433433 7.90428 + 5.74279i 0.379855 + 0.275981i 0.761286 0.648416i 0.224568π-0.224568\pi
−0.381430 + 0.924398i 0.624568π0.624568\pi
434434 −4.01922 + 1.44394i −0.192929 + 0.0693112i
435435 0.642710 + 1.97806i 0.0308156 + 0.0948406i
436436 7.86428 12.3551i 0.376631 0.591704i
437437 −0.235868 0.324645i −0.0112831 0.0155299i
438438 −2.65366 + 9.11095i −0.126797 + 0.435338i
439439 10.3425 0.493622 0.246811 0.969064i 0.420617π-0.420617\pi
0.246811 + 0.969064i 0.420617π0.420617\pi
440440 3.33652 8.76742i 0.159062 0.417970i
441441 9.06052 0.431453
442442 4.69082 16.1052i 0.223119 0.766048i
443443 18.5086 + 25.4750i 0.879372 + 1.21035i 0.976594 + 0.215089i 0.0690042π0.0690042\pi
−0.0972223 + 0.995263i 0.530996π0.530996\pi
444444 4.77648 7.50407i 0.226682 0.356128i
445445 −3.69663 11.3771i −0.175237 0.539324i
446446 −14.5269 + 5.21892i −0.687870 + 0.247123i
447447 5.24064 + 3.80755i 0.247874 + 0.180091i
448448 −17.6498 + 18.6429i −0.833875 + 0.880796i
449449 −0.787165 + 2.42264i −0.0371486 + 0.114332i −0.967911 0.251292i 0.919144π-0.919144\pi
0.930763 + 0.365624i 0.119144π0.119144\pi
450450 3.88335 0.119410i 0.183063 0.00562903i
451451 −19.5778 + 20.1897i −0.921882 + 0.950694i
452452 26.2627 1.61664i 1.23529 0.0760405i
453453 −5.74513 1.86671i −0.269930 0.0877055i
454454 8.51091 6.59252i 0.399437 0.309402i
455455 −7.33964 + 10.1021i −0.344088 + 0.473596i
456456 0.0923686 0.0397491i 0.00432556 0.00186142i
457457 16.2280 5.27279i 0.759113 0.246651i 0.0962151 0.995361i 0.469326π-0.469326\pi
0.662898 + 0.748710i 0.269326π0.269326\pi
458458 7.59251 + 5.16737i 0.354774 + 0.241455i
459459 7.12569 5.17712i 0.332599 0.241647i
460460 −10.9888 2.83729i −0.512355 0.132289i
461461 1.34620i 0.0626990i 0.999508 + 0.0313495i 0.00998049π0.00998049\pi
−0.999508 + 0.0313495i 0.990020π0.990020\pi
462462 −0.837912 + 7.52083i −0.0389832 + 0.349901i
463463 4.36322i 0.202776i −0.994847 0.101388i 0.967672π-0.967672\pi
0.994847 0.101388i 0.0323284π-0.0323284\pi
464464 −16.2461 3.14469i −0.754207 0.145989i
465465 0.382756 0.278088i 0.0177499 0.0128960i
466466 16.7398 24.5960i 0.775455 1.13939i
467467 −17.9687 + 5.83839i −0.831493 + 0.270168i −0.693674 0.720289i 0.744009π-0.744009\pi
−0.137819 + 0.990457i 0.544009π0.544009\pi
468468 −19.8891 + 7.84356i −0.919375 + 0.362568i
469469 0.293664 0.404194i 0.0135602 0.0186640i
470470 −3.50739 4.52802i −0.161784 0.208862i
471471 2.91952 + 0.948608i 0.134524 + 0.0437096i
472472 3.71572 + 40.1783i 0.171030 + 1.84935i
473473 0.282529 + 1.62190i 0.0129907 + 0.0745753i
474474 0.226966 + 7.38119i 0.0104249 + 0.339029i
475475 0.0218524 0.0672548i 0.00100266 0.00308586i
476476 12.4503 + 15.0913i 0.570658 + 0.691710i
477477 −17.5387 12.7426i −0.803044 0.583446i
478478 −6.76580 18.8327i −0.309461 0.861388i
479479 −5.41103 16.6534i −0.247236 0.760915i −0.995261 0.0972438i 0.968997π-0.968997\pi
0.748024 0.663671i 0.231003π-0.231003\pi
480480 1.29972 2.52965i 0.0593236 0.115462i
481481 20.2335 + 27.8490i 0.922568 + 1.26981i
482482 6.44561 + 1.87735i 0.293590 + 0.0855111i
483483 9.15519 0.416575
484484 21.4605 + 4.84204i 0.975479 + 0.220093i
485485 6.62079 0.300635
486486 −16.4043 4.77791i −0.744112 0.216731i
487487 6.32403 + 8.70428i 0.286569 + 0.394429i 0.927896 0.372839i 0.121616π-0.121616\pi
−0.641327 + 0.767268i 0.721616π0.721616\pi
488488 −1.05853 + 1.78162i −0.0479176 + 0.0806503i
489489 3.68389 + 11.3379i 0.166591 + 0.512716i
490490 −1.57695 4.38947i −0.0712395 0.198296i
491491 −18.8359 13.6851i −0.850051 0.617598i 0.0751094 0.997175i 0.476069π-0.476069\pi
−0.925160 + 0.379577i 0.876069π0.876069\pi
492492 −6.57686 + 5.42589i −0.296508 + 0.244618i
493493 −3.89685 + 11.9933i −0.175505 + 0.540150i
494494 0.0119602 + 0.388960i 0.000538115 + 0.0175002i
495495 1.56365 + 8.97639i 0.0702807 + 0.403459i
496496 0.461669 + 3.73575i 0.0207295 + 0.167740i
497497 −45.8558 14.8995i −2.05691 0.668332i
498498 −2.15195 2.77815i −0.0964311 0.124492i
499499 −8.36834 + 11.5180i −0.374618 + 0.515618i −0.954149 0.299333i 0.903236π-0.903236\pi
0.579531 + 0.814951i 0.303236π0.303236\pi
500500 −0.733733 1.86055i −0.0328135 0.0832062i
501501 −6.89622 + 2.24072i −0.308100 + 0.100108i
502502 10.3548 15.2145i 0.462158 0.679057i
503503 −23.5444 + 17.1060i −1.04979 + 0.762718i −0.972173 0.234265i 0.924732π-0.924732\pi
−0.0776187 + 0.996983i 0.524732π0.524732\pi
504504 5.48889 24.3239i 0.244495 1.08347i
505505 19.7096i 0.877067i
506506 2.94713 26.4525i 0.131016 1.17596i
507507 1.07645i 0.0478067i
508508 −5.69848 + 22.0701i −0.252829 + 0.979203i
509509 28.7673 20.9006i 1.27509 0.926404i 0.275693 0.961246i 0.411093π-0.411093\pi
0.999393 + 0.0348414i 0.0110926π0.0110926\pi
510510 −1.79173 1.21943i −0.0793393 0.0539974i
511511 40.7341 13.2353i 1.80197 0.585496i
512512 12.6043 + 18.7918i 0.557038 + 0.830487i
513513 −0.120102 + 0.165306i −0.00530263 + 0.00729845i
514514 −14.5510 + 11.2711i −0.641816 + 0.497148i
515515 8.84878 + 2.87514i 0.389924 + 0.126694i
516516 0.0306661 + 0.498178i 0.00135000 + 0.0219311i
517517 9.35081 9.64306i 0.411248 0.424101i
518518 −40.1292 + 1.23394i −1.76318 + 0.0542163i
519519 1.46174 4.49878i 0.0641634 0.197475i
520520 7.26153 + 8.27037i 0.318439 + 0.362680i
521521 −15.9186 11.5655i −0.697406 0.506695i 0.181680 0.983358i 0.441846π-0.441846\pi
−0.879086 + 0.476662i 0.841846π0.841846\pi
522522 15.1262 5.43420i 0.662054 0.237848i
523523 12.2934 + 37.8352i 0.537554 + 1.65442i 0.738066 + 0.674728i 0.235739π0.235739\pi
−0.200513 + 0.979691i 0.564261π0.564261\pi
524524 4.45587 + 2.83624i 0.194656 + 0.123902i
525525 0.948313 + 1.30524i 0.0413878 + 0.0569654i
526526 −9.35136 + 32.1065i −0.407738 + 1.39991i
527527 2.86856 0.124956
528528 6.30362 + 2.17956i 0.274330 + 0.0948531i
529529 −9.20092 −0.400040
530530 −3.12076 + 10.7147i −0.135557 + 0.465415i
531531 −23.0362 31.7066i −0.999685 1.37595i
532532 −0.382879 0.243710i −0.0165999 0.0105662i
533533 −10.1960 31.3800i −0.441637 1.35922i
534534 8.00451 2.87568i 0.346389 0.124443i
535535 −3.16302 2.29807i −0.136749 0.0993541i
536536 −0.290539 0.330903i −0.0125494 0.0142928i
537537 0.618399 1.90324i 0.0266859 0.0821307i
538538 −18.3476 + 0.564173i −0.791019 + 0.0243232i
539539 9.66862 5.11528i 0.416457 0.220331i
540540 0.355057 + 5.76798i 0.0152792 + 0.248214i
541541 29.0963 + 9.45397i 1.25095 + 0.406458i 0.858261 0.513214i 0.171545π-0.171545\pi
0.392688 + 0.919672i 0.371545π0.371545\pi
542542 23.3900 18.1178i 1.00469 0.778227i
543543 0.569719 0.784151i 0.0244490 0.0336511i
544544 15.3906 7.77645i 0.659867 0.333413i
545545 6.96444 2.26288i 0.298324 0.0969313i
546546 −7.33964 4.99528i −0.314108 0.213778i
547547 6.79763 4.93876i 0.290645 0.211166i −0.432902 0.901441i 0.642510π-0.642510\pi
0.723547 + 0.690275i 0.242510π0.242510\pi
548548 7.89153 30.5638i 0.337109 1.30562i
549549 2.01287i 0.0859074i
550550 4.07656 2.31984i 0.173825 0.0989181i
551551 0.292546i 0.0124629i
552552 1.77624 7.87136i 0.0756016 0.335027i
553553 26.9647 19.5910i 1.14666 0.833095i
554554 11.1050 16.3168i 0.471807 0.693234i
555555 4.22995 1.37440i 0.179552 0.0583398i
556556 −9.46402 23.9982i −0.401364 1.01775i
557557 12.3439 16.9899i 0.523027 0.719885i −0.463021 0.886347i 0.653234π-0.653234\pi
0.986048 + 0.166463i 0.0532345π0.0532345\pi
558558 −2.23890 2.89041i −0.0947804 0.122361i
559559 −1.83698 0.596872i −0.0776961 0.0252450i
560560 −12.7393 + 1.57434i −0.538334 + 0.0665281i
561561 2.23761 4.56381i 0.0944721 0.192684i
562562 −0.482427 15.6891i −0.0203500 0.661805i
563563 1.36983 4.21590i 0.0577313 0.177679i −0.918032 0.396505i 0.870223π-0.870223\pi
0.975764 + 0.218826i 0.0702229π0.0702229\pi
564564 3.14127 2.59153i 0.132271 0.109123i
565565 10.6436 + 7.73303i 0.447780 + 0.325331i
566566 −6.08485 16.9372i −0.255765 0.711926i
567567 6.73237 + 20.7201i 0.282733 + 0.870162i
568568 −21.7068 + 36.5348i −0.910797 + 1.53296i
569569 12.7625 + 17.5661i 0.535033 + 0.736410i 0.987887 0.155175i 0.0495941π-0.0495941\pi
−0.452854 + 0.891585i 0.649594π0.649594\pi
570570 0.0482732 + 0.0140601i 0.00202194 + 0.000588912i
571571 33.8605 1.41702 0.708508 0.705702i 0.249368π-0.249368\pi
0.708508 + 0.705702i 0.249368π0.249368\pi
572572 −16.7958 + 19.5987i −0.702266 + 0.819464i
573573 −8.99809 −0.375901
574574 36.9470 + 10.7612i 1.54214 + 0.449163i
575575 −3.33544 4.59084i −0.139097 0.191451i
576576 −19.8481 9.43837i −0.827003 0.393265i
577577 −8.75266 26.9379i −0.364378 1.12144i −0.950370 0.311123i 0.899295π-0.899295\pi
0.585992 0.810317i 0.300705π-0.300705\pi
578578 3.68556 + 10.2588i 0.153299 + 0.426710i
579579 2.80540 + 2.03825i 0.116589 + 0.0847066i
580580 −5.26531 6.38223i −0.218630 0.265008i
581581 −4.90123 + 15.0844i −0.203337 + 0.625808i
582582 0.144680 + 4.70517i 0.00599719 + 0.195036i
583583 −25.9099 3.69606i −1.07308 0.153075i
584584 −3.47634 37.5898i −0.143852 1.55548i
585585 −10.1667 3.30337i −0.420343 0.136578i
586586 25.1873 + 32.5166i 1.04048 + 1.34325i
587587 15.8943 21.8766i 0.656027 0.902944i −0.343314 0.939221i 0.611550π-0.611550\pi
0.999342 + 0.0362762i 0.0115496π0.0115496\pi
588588 3.08499 1.21661i 0.127223 0.0501720i
589589 −0.0632895 + 0.0205640i −0.00260780 + 0.000847325i
590590 −11.3512 + 16.6786i −0.467323 + 0.686645i
591591 2.09490 1.52204i 0.0861728 0.0626082i
592592 −6.72473 + 34.7413i −0.276385 + 1.42786i
593593 3.03259i 0.124534i −0.998060 0.0622668i 0.980167π-0.980167\pi
0.998060 0.0622668i 0.0198330π-0.0198330\pi
594594 −13.2739 + 2.73506i −0.544633 + 0.112221i
595595 9.78210i 0.401027i
596596 −24.9509 6.44230i −1.02203 0.263887i
597597 −7.36734 + 5.35269i −0.301525 + 0.219071i
598598 25.8152 + 17.5695i 1.05566 + 0.718472i
599599 −31.2756 + 10.1621i −1.27789 + 0.415211i −0.867835 0.496852i 0.834489π-0.834489\pi
−0.410051 + 0.912062i 0.634489π0.634489\pi
600600 1.30619 0.562096i 0.0533251 0.0229475i
601601 25.8004 35.5112i 1.05242 1.44853i 0.165726 0.986172i 0.447003π-0.447003\pi
0.886693 0.462358i 0.152997π-0.152997\pi
602602 1.78095 1.37952i 0.0725862 0.0562251i
603603 0.406778 + 0.132170i 0.0165653 + 0.00538239i
604604 23.9854 1.47646i 0.975951 0.0600762i
605605 6.73637 + 8.69605i 0.273872 + 0.353545i
606606 −14.0070 + 0.430703i −0.568994 + 0.0174961i
607607 −1.04888 + 3.22811i −0.0425726 + 0.131025i −0.970084 0.242771i 0.921944π-0.921944\pi
0.927511 + 0.373795i 0.121944π0.121944\pi
608608 −0.283818 + 0.281905i −0.0115104 + 0.0114328i
609609 5.39968 + 3.92309i 0.218806 + 0.158972i
610610 −0.975159 + 0.350334i −0.0394830 + 0.0141846i
611611 4.86984 + 14.9878i 0.197013 + 0.606343i
612612 −8.99352 + 14.1292i −0.363542 + 0.571140i
613613 −17.4987 24.0849i −0.706765 0.972779i −0.999861 0.0166955i 0.994685π-0.994685\pi
0.293096 0.956083i 0.405315π-0.405315\pi
614614 −11.5321 + 39.5938i −0.465398 + 1.59788i
615615 −4.26308 −0.171904
616616 −7.87522 29.0553i −0.317302 1.17067i
617617 27.3655 1.10169 0.550846 0.834607i 0.314305π-0.314305\pi
0.550846 + 0.834607i 0.314305π0.314305\pi
618618 −1.84990 + 6.35135i −0.0744138 + 0.255489i
619619 7.16184 + 9.85743i 0.287859 + 0.396203i 0.928317 0.371789i 0.121256π-0.121256\pi
−0.640458 + 0.767993i 0.721256π0.721256\pi
620620 −1.01062 + 1.58773i −0.0405874 + 0.0637647i
621621 5.06677 + 15.5939i 0.203323 + 0.625763i
622622 −15.7963 + 5.67497i −0.633376 + 0.227545i
623623 −31.0569 22.5642i −1.24427 0.904015i
624624 −5.71878 + 5.34125i −0.228935 + 0.213821i
625625 0.309017 0.951057i 0.0123607 0.0380423i
626626 −27.3217 + 0.840119i −1.09199 + 0.0335779i
627627 −0.0166520 + 0.116733i −0.000665017 + 0.00466187i
628628 −12.1887 + 0.750295i −0.486382 + 0.0299400i
629629 25.6469 + 8.33318i 1.02261 + 0.332266i
630630 9.85664 7.63492i 0.392698 0.304182i
631631 16.9524 23.3330i 0.674865 0.928873i −0.324993 0.945717i 0.605362π-0.605362\pi
0.999858 + 0.0168439i 0.00536183π0.00536183\pi
632632 −11.6122 26.9844i −0.461910 1.07338i
633633 −1.69222 + 0.549835i −0.0672597 + 0.0218540i
634634 −7.55993 5.14520i −0.300243 0.204342i
635635 −9.22033 + 6.69896i −0.365898 + 0.265840i
636636 −7.68273 1.98367i −0.304640 0.0786578i
637637 12.8332i 0.508471i
638638 13.0734 14.3386i 0.517580 0.567673i
639639 41.2769i 1.63289i
640640 −1.11803 + 11.2583i −0.0441942 + 0.445025i
641641 −5.74895 + 4.17686i −0.227070 + 0.164976i −0.695503 0.718523i 0.744819π-0.744819\pi
0.468434 + 0.883499i 0.344819π0.344819\pi
642642 1.56404 2.29807i 0.0617276 0.0906974i
643643 −27.4095 + 8.90590i −1.08093 + 0.351214i −0.794734 0.606958i 0.792390π-0.792390\pi
−0.286193 + 0.958172i 0.592390π0.592390\pi
644644 −33.8807 + 13.3613i −1.33509 + 0.526510i
645645 −0.146688 + 0.201899i −0.00577583 + 0.00794975i
646646 0.186682 + 0.241005i 0.00734490 + 0.00948222i
647647 −20.3988 6.62796i −0.801959 0.260572i −0.120770 0.992680i 0.538536π-0.538536\pi
−0.681188 + 0.732108i 0.738536π0.738536\pi
648648 19.1207 1.76830i 0.751132 0.0694653i
649649 −42.4828 20.8291i −1.66759 0.817613i
650650 0.169131 + 5.50033i 0.00663385 + 0.215741i
651651 0.469163 1.44394i 0.0183880 0.0565923i
652652 −30.1798 36.5817i −1.18193 1.43265i
653653 24.2792 + 17.6399i 0.950118 + 0.690301i 0.950835 0.309699i 0.100228π-0.100228\pi
−0.000716986 1.00000i 0.500228π0.500228\pi
654654 1.76034 + 4.89994i 0.0688349 + 0.191603i
655655 0.816107 + 2.51172i 0.0318879 + 0.0981410i
656656 16.4204 29.6781i 0.641108 1.15873i
657657 21.5521 + 29.6639i 0.840827 + 1.15730i
658658 −17.6467 5.13980i −0.687942 0.200370i
659659 −25.4932 −0.993075 −0.496537 0.868015i 0.665395π-0.665395\pi
−0.496537 + 0.868015i 0.665395π0.665395\pi
660660 1.73771 + 2.84638i 0.0676403 + 0.110795i
661661 0.531397 0.0206689 0.0103345 0.999947i 0.496710π-0.496710\pi
0.0103345 + 0.999947i 0.496710π0.496710\pi
662662 −32.2964 9.40666i −1.25523 0.365600i
663663 3.50516 + 4.82444i 0.136129 + 0.187366i
664664 12.0182 + 7.14053i 0.466399 + 0.277106i
665665 −0.0701256 0.215824i −0.00271935 0.00836931i
666666 −11.6207 32.3463i −0.450293 1.25340i
667667 −18.9919 13.7984i −0.735370 0.534277i
668668 22.2507 18.3568i 0.860907 0.710245i
669669 1.69573 5.21892i 0.0655607 0.201775i
670670 −0.00676704 0.220072i −0.000261434 0.00850213i
671671 −1.13640 2.14797i −0.0438704 0.0829214i
672672 −1.39722 9.01899i −0.0538988 0.347915i
673673 −8.51337 2.76616i −0.328166 0.106628i 0.140300 0.990109i 0.455193π-0.455193\pi
−0.468466 + 0.883481i 0.655193π0.655193\pi
674674 −4.13513 5.33843i −0.159279 0.205629i
675675 −1.69837 + 2.33761i −0.0653705 + 0.0899747i
676676 −1.57100 3.98362i −0.0604229 0.153216i
677677 −1.77141 + 0.575567i −0.0680809 + 0.0221208i −0.342859 0.939387i 0.611395π-0.611395\pi
0.274779 + 0.961508i 0.411395π0.411395\pi
678678 −5.26301 + 7.73303i −0.202125 + 0.296985i
679679 17.1888 12.4884i 0.659645 0.479260i
680680 8.41036 + 1.89787i 0.322522 + 0.0727798i
681681 3.82716i 0.146657i
682682 −4.02100 1.82039i −0.153972 0.0697063i
683683 18.0214i 0.689571i 0.938681 + 0.344786i 0.112048π0.112048\pi
−0.938681 + 0.344786i 0.887952π0.887952\pi
684684 0.0971366 0.376209i 0.00371411 0.0143847i
685685 12.7688 9.27705i 0.487869 0.354458i
686686 13.8890 + 9.45270i 0.530285 + 0.360906i
687687 −3.10516 + 1.00893i −0.118469 + 0.0384930i
688688 −0.840541 1.79886i −0.0320453 0.0685808i
689689 18.0485 24.8417i 0.687594 0.946392i
690690 3.18966 2.47070i 0.121428 0.0940580i
691691 −35.3967 11.5011i −1.34655 0.437521i −0.455021 0.890481i 0.650368π-0.650368\pi
−0.891531 + 0.452959i 0.850368π0.850368\pi
692692 1.15616 + 18.7820i 0.0439504 + 0.713984i
693693 20.9911 + 20.3549i 0.797386 + 0.773219i
694694 −28.8890 + 0.888312i −1.09661 + 0.0337199i
695695 3.98584 12.2672i 0.151192 0.465320i
696696 4.42057 3.88134i 0.167561 0.147122i
697697 −20.9112 15.1929i −0.792070 0.575473i
698698 3.12662 1.12326i 0.118344 0.0425162i
699699 3.26844 + 10.0592i 0.123624 + 0.380474i
700700 −5.41434 3.44633i −0.204643 0.130259i
701701 22.3855 + 30.8110i 0.845489 + 1.16372i 0.984839 + 0.173473i 0.0554989π0.0554989\pi
−0.139349 + 0.990243i 0.544501π0.544501\pi
702702 4.44640 15.2661i 0.167819 0.576181i
703703 −0.625591 −0.0235946
704704 −26.5088 + 1.13375i −0.999087 + 0.0427298i
705705 2.03615 0.0766858
706706 −6.07717 + 20.8651i −0.228717 + 0.785267i
707707 37.1770 + 51.1698i 1.39819 + 1.92444i
708708 −12.1009 7.70247i −0.454781 0.289477i
709709 −0.133182 0.409893i −0.00500177 0.0153939i 0.948524 0.316704i 0.102576π-0.102576\pi
−0.953526 + 0.301310i 0.902576π0.902576\pi
710710 −19.9971 + 7.18411i −0.750476 + 0.269615i
711711 23.0842 + 16.7717i 0.865726 + 0.628987i
712712 −25.4255 + 22.3241i −0.952861 + 0.836630i
713713 −1.65016 + 5.07866i −0.0617988 + 0.190197i
714714 −6.95180 + 0.213762i −0.260165 + 0.00799985i
715715 −12.7141 + 2.21473i −0.475479 + 0.0828263i
716716 0.489118 + 7.94583i 0.0182792 + 0.296950i
717717 6.76580 + 2.19834i 0.252674 + 0.0820986i
718718 −18.1960 + 14.0945i −0.679068 + 0.526004i
719719 4.70131 6.47080i 0.175329 0.241320i −0.712304 0.701871i 0.752348π-0.752348\pi
0.887633 + 0.460551i 0.152348π0.152348\pi
720720 −4.65195 9.95573i −0.173368 0.371028i
721721 28.3962 9.22650i 1.05753 0.343613i
722722 22.2076 + 15.1143i 0.826483 + 0.562495i
723723 −1.93083 + 1.40283i −0.0718083 + 0.0521718i
724724 −0.963954 + 3.73338i −0.0358251 + 0.138750i
725725 4.13692i 0.153641i
726726 −6.03278 + 4.97734i −0.223898 + 0.184726i
727727 29.1784i 1.08217i −0.840969 0.541084i 0.818014π-0.818014\pi
0.840969 0.541084i 0.181986π-0.181986\pi
728728 34.4521 + 7.77440i 1.27688 + 0.288138i
729729 −11.5633 + 8.40124i −0.428271 + 0.311157i
730730 10.6199 15.6040i 0.393061 0.577532i
731731 −1.43907 + 0.467581i −0.0532258 + 0.0172941i
732732 −0.270280 0.685357i −0.00998983 0.0253315i
733733 1.46872 2.02152i 0.0542485 0.0746666i −0.781031 0.624492i 0.785306π-0.785306\pi
0.835279 + 0.549826i 0.185306π0.185306\pi
734734 −14.3840 18.5697i −0.530923 0.685419i
735735 1.57695 + 0.512383i 0.0581668 + 0.0188995i
736736 4.91434 + 31.7219i 0.181145 + 1.16928i
737737 0.508698 0.0886130i 0.0187381 0.00326410i
738738 1.01253 + 32.9286i 0.0372717 + 1.21212i
739739 −0.554914 + 1.70785i −0.0204128 + 0.0628243i −0.960744 0.277436i 0.910515π-0.910515\pi
0.940331 + 0.340261i 0.110515π0.110515\pi
740740 −13.6480 + 11.2595i −0.501711 + 0.413909i
741741 −0.111920 0.0813148i −0.00411149 0.00298718i
742742 12.1083 + 33.7037i 0.444510 + 1.23730i
743743 −6.36470 19.5885i −0.233498 0.718633i −0.997317 0.0732026i 0.976678π-0.976678\pi
0.763819 0.645430i 0.223322π-0.223322\pi
744744 −1.15043 0.683517i −0.0421768 0.0250589i
745745 −7.57337 10.4239i −0.277467 0.381901i
746746 16.1293 + 4.69784i 0.590537 + 0.172000i
747747 −13.5782 −0.496800
748748 −1.62021 + 20.1550i −0.0592408 + 0.736939i
749749 −12.5465 −0.458438
750750 0.682636 + 0.198825i 0.0249263 + 0.00726006i
751751 −8.42266 11.5928i −0.307347 0.423027i 0.627204 0.778855i 0.284199π-0.284199\pi
−0.934552 + 0.355827i 0.884199π0.884199\pi
752752 −7.84277 + 14.1750i −0.285996 + 0.516907i
753753 2.02178 + 6.22239i 0.0736776 + 0.226756i
754754 7.69693 + 21.4245i 0.280306 + 0.780235i
755755 9.72065 + 7.06247i 0.353771 + 0.257030i
756756 11.8016 + 14.3050i 0.429219 + 0.520268i
757757 3.43599 10.5749i 0.124883 0.384351i −0.868997 0.494818i 0.835235π-0.835235\pi
0.993880 + 0.110467i 0.0352347π0.0352347\pi
758758 −0.919778 29.9123i −0.0334078 1.08646i
759759 6.79284 + 6.58697i 0.246564 + 0.239092i
760760 −0.199165 + 0.0184189i −0.00722446 + 0.000668124i
761761 −19.2163 6.24374i −0.696589 0.226336i −0.0607453 0.998153i 0.519348π-0.519348\pi
−0.635844 + 0.771818i 0.719348π0.719348\pi
762762 −4.96221 6.40618i −0.179762 0.232072i
763763 13.8126 19.0114i 0.500050 0.688260i
764764 33.2993 13.1321i 1.20473 0.475101i
765765 −7.96448 + 2.58782i −0.287956 + 0.0935627i
766766 1.16548 1.71245i 0.0421103 0.0618734i
767767 44.9088 32.6282i 1.62156 1.17814i
768768 −8.02534 0.548527i −0.289590 0.0197933i
769769 17.4538i 0.629398i −0.949191 0.314699i 0.898096π-0.898096\pi
0.949191 0.314699i 0.101904π-0.101904\pi
770770 6.20774 13.7121i 0.223711 0.494149i
771771 6.54324i 0.235649i
772772 −13.3567 3.44867i −0.480717 0.124120i
773773 2.37372 1.72461i 0.0853768 0.0620299i −0.544278 0.838905i 0.683196π-0.683196\pi
0.629655 + 0.776875i 0.283196π0.283196\pi
774774 1.59433 + 1.08509i 0.0573072 + 0.0390026i
775775 −0.894983 + 0.290798i −0.0321488 + 0.0104458i
776776 −7.40227 17.2013i −0.265726 0.617492i
777777 8.38929 11.5469i 0.300964 0.414242i
778778 −8.10824 + 6.28061i −0.290694 + 0.225171i
779779 0.570284 + 0.185296i 0.0204325 + 0.00663893i
780780 −3.90520 + 0.240391i −0.139829 + 0.00860737i
781781 −23.3036 44.0472i −0.833869 1.57613i
782782 24.4511 0.751852i 0.874370 0.0268862i
783783 −3.69381 + 11.3684i −0.132006 + 0.406272i
784784 −9.64109 + 9.00462i −0.344325 + 0.321594i
785785 −4.93977 3.58895i −0.176308 0.128095i
786786 −1.76716 + 0.634867i −0.0630325 + 0.0226449i
787787 −1.82997 5.63208i −0.0652316 0.200762i 0.913128 0.407672i 0.133659π-0.133659\pi
−0.978360 + 0.206910i 0.933659π0.933659\pi
788788 −5.53133 + 8.68997i −0.197045 + 0.309567i
789789 −6.98769 9.61773i −0.248768 0.342400i
790790 4.10749 14.1025i 0.146138 0.501743i
791791 42.2190 1.50114
792792 21.5731 14.0984i 0.766568 0.500964i
793793 2.85101 0.101242
794794 −14.9259 + 51.2458i −0.529700 + 1.81865i
795795 −2.33195 3.20965i −0.0827057 0.113835i
796796 19.4525 30.5608i 0.689477 1.08320i
797797 9.45967 + 29.1139i 0.335079 + 1.03127i 0.966683 + 0.255975i 0.0823966π0.0823966\pi
−0.631605 + 0.775291i 0.717603π0.717603\pi
798798 0.151847 0.0545521i 0.00537531 0.00193112i
799799 9.98771 + 7.25650i 0.353340 + 0.256716i
800800 −4.01351 + 3.98645i −0.141899 + 0.140942i
801801 10.1555 31.2555i 0.358828 1.10436i
802802 47.2229 1.45206i 1.66750 0.0512742i
803803 39.7458 + 19.4872i 1.40260 + 0.687688i
804804 0.156250 0.00961821i 0.00551051 0.000339208i
805805 −17.3188 5.62722i −0.610408 0.198333i
806806 4.09395 3.17116i 0.144203 0.111699i
807807 3.83568 5.27937i 0.135022 0.185843i
808808 51.2071 22.0360i 1.80146 0.775225i
809809 1.02262 0.332270i 0.0359534 0.0116820i −0.290985 0.956728i 0.593983π-0.593983\pi
0.326939 + 0.945046i 0.393983π0.393983\pi
810810 7.93727 + 5.40201i 0.278887 + 0.189807i
811811 −37.8442 + 27.4955i −1.32889 + 0.965496i −0.329116 + 0.944289i 0.606751π0.606751\pi
−0.999775 + 0.0212066i 0.993249π0.993249\pi
812812 −25.7081 6.63780i −0.902177 0.232941i
813813 10.5180i 0.368881i
814814 −30.6623 27.9566i −1.07471 0.979879i
815815 23.7120i 0.830597i
816816 −1.16496 + 6.01843i −0.0407818 + 0.210687i
817817 0.0283984 0.0206327i 0.000993536 0.000721846i
818818 −8.26797 + 12.1483i −0.289083 + 0.424754i
819819 −32.6256 + 10.6007i −1.14003 + 0.370419i
820820 15.7764 6.22165i 0.550936 0.217269i
821821 −21.0024 + 28.9073i −0.732989 + 1.00887i 0.266003 + 0.963972i 0.414297π0.414297\pi
−0.998991 + 0.0449002i 0.985703π0.985703\pi
822822 6.87191 + 8.87160i 0.239685 + 0.309432i
823823 −25.9266 8.42406i −0.903744 0.293644i −0.179963 0.983673i 0.557598π-0.557598\pi
−0.723782 + 0.690029i 0.757598π0.757598\pi
824824 −2.42340 26.2043i −0.0844230 0.912870i
825825 −0.235478 + 1.65074i −0.00819828 + 0.0574712i
826826 1.98983 + 64.7117i 0.0692351 + 2.25161i
827827 −2.34368 + 7.21311i −0.0814978 + 0.250825i −0.983500 0.180906i 0.942097π-0.942097\pi
0.902003 + 0.431731i 0.142097π0.142097\pi
828828 −19.8416 24.0506i −0.689545 0.835816i
829829 −13.8143 10.0367i −0.479790 0.348588i 0.321455 0.946925i 0.395828π-0.395828\pi
−0.801244 + 0.598337i 0.795828π0.795828\pi
830830 2.36324 + 6.57811i 0.0820292 + 0.228329i
831831 2.16825 + 6.67319i 0.0752158 + 0.231490i
832832 13.3684 28.1126i 0.463466 0.974628i
833833 5.90922 + 8.13334i 0.204742 + 0.281804i
834834 8.80495 + 2.56453i 0.304890 + 0.0888026i
835835 14.4228 0.499121
836836 −0.108739 0.456298i −0.00376083 0.0157814i
837837 2.71909 0.0939855
838838 40.0338 + 11.6603i 1.38294 + 0.402797i
839839 25.6699 + 35.3316i 0.886224 + 1.21978i 0.974658 + 0.223701i 0.0718138π0.0718138\pi
−0.0884339 + 0.996082i 0.528186π0.528186\pi
840840 2.33087 3.92309i 0.0804226 0.135360i
841841 3.67295 + 11.3042i 0.126653 + 0.389799i
842842 4.43887 + 12.3556i 0.152973 + 0.425804i
843843 4.51442 + 3.27992i 0.155485 + 0.112966i
844844 5.45997 4.50445i 0.187940 0.155050i
845845 0.661637 2.03631i 0.0227610 0.0700511i
846846 −0.483608 15.7275i −0.0166268 0.540723i
847847 33.8916 + 9.87015i 1.16453 + 0.339142i
848848 31.3266 3.87139i 1.07576 0.132944i
849849 6.08485 + 1.97709i 0.208831 + 0.0678534i
850850 2.63989 + 3.40808i 0.0905474 + 0.116896i
851851 −29.5071 + 40.6130i −1.01149 + 1.39220i
852852 −5.54248 14.0542i −0.189882 0.481490i
853853 30.9085 10.0428i 1.05829 0.343858i 0.272371 0.962192i 0.412192π-0.412192\pi
0.785915 + 0.618334i 0.212192π0.212192\pi
854854 −1.87088 + 2.74891i −0.0640201 + 0.0940658i
855855 0.157170 0.114191i 0.00537511 0.00390525i
856856 −2.43419 + 10.7871i −0.0831989 + 0.368695i
857857 13.4666i 0.460010i 0.973190 + 0.230005i 0.0738742π0.0738742\pi
−0.973190 + 0.230005i 0.926126π0.926126\pi
858858 −1.85177 8.98704i −0.0632183 0.306813i
859859 7.48872i 0.255512i −0.991806 0.127756i 0.959223π-0.959223\pi
0.991806 0.127756i 0.0407774π-0.0407774\pi
860860 0.248193 0.961249i 0.00846332 0.0327783i
861861 −11.0677 + 8.04117i −0.377187 + 0.274042i
862862 −35.1885 23.9489i −1.19852 0.815702i
863863 −9.36487 + 3.04283i −0.318784 + 0.103579i −0.464038 0.885815i 0.653600π-0.653600\pi
0.145254 + 0.989394i 0.453600π0.453600\pi
864864 14.5887 7.37126i 0.496317 0.250775i
865865 −5.53034 + 7.61185i −0.188037 + 0.258811i
866866 10.9234 8.46126i 0.371194 0.287525i
867867 −3.68556 1.19751i −0.125168 0.0406696i
868868 0.371081 + 6.02830i 0.0125953 + 0.204614i
869869 34.1023 + 4.86469i 1.15684 + 0.165023i
870870 2.93997 0.0904016i 0.0996742 0.00306490i
871871 −0.187205 + 0.576156i −0.00634318 + 0.0195223i
872872 −13.6656 15.5642i −0.462777 0.527069i
873873 14.7151 + 10.6912i 0.498032 + 0.361841i
874874 −0.534080 + 0.191873i −0.0180655 + 0.00649019i
875875 −0.991653 3.05199i −0.0335240 0.103176i
876876 11.3213 + 7.20624i 0.382512 + 0.243476i
877877 −7.33136 10.0908i −0.247562 0.340740i 0.667093 0.744974i 0.267538π-0.267538\pi
−0.914656 + 0.404234i 0.867538π0.867538\pi
878878 4.09018 14.0430i 0.138037 0.473929i
879879 −14.6220 −0.493187
880880 −10.5848 7.99756i −0.356815 0.269598i
881881 −24.2462 −0.816875 −0.408437 0.912786i 0.633926π-0.633926\pi
−0.408437 + 0.912786i 0.633926π0.633926\pi
882882 3.58318 12.3023i 0.120652 0.414240i
883883 11.3687 + 15.6477i 0.382588 + 0.526587i 0.956268 0.292492i 0.0944846π-0.0944846\pi
−0.573680 + 0.819080i 0.694485π0.694485\pi
884884 −20.0125 12.7383i −0.673093 0.428436i
885885 −2.21633 6.82115i −0.0745010 0.229290i
886886 41.9094 15.0563i 1.40797 0.505826i
887887 −36.9618 26.8543i −1.24106 0.901680i −0.243387 0.969929i 0.578259π-0.578259\pi
−0.997668 + 0.0682495i 0.978259π0.978259\pi
888888 −8.30002 9.45312i −0.278530 0.317226i
889889 −11.3018 + 34.7834i −0.379051 + 1.16660i
890890 −16.9096 + 0.519957i −0.566811 + 0.0174290i
891891 −9.91249 + 20.2174i −0.332081 + 0.677308i
892892 1.34123 + 21.7885i 0.0449076 + 0.729533i
893893 −0.272381 0.0885019i −0.00911488 0.00296160i
894894 7.24238 5.60992i 0.242221 0.187624i
895895 −2.33964 + 3.22024i −0.0782056 + 0.107641i
896896 18.3333 + 31.3375i 0.612471 + 1.04691i
897897 −10.5578 + 3.43045i −0.352516 + 0.114539i
898898 2.97815 + 2.02689i 0.0993821 + 0.0676383i
899899 −3.14951 + 2.28825i −0.105042 + 0.0763175i
900900 1.37362 5.32000i 0.0457873 0.177333i
901901 24.0547i 0.801377i
902902 19.6709 + 34.5670i 0.654971 + 1.15096i
903903 0.800854i 0.0266507i
904904 8.19109 36.2987i 0.272432 1.20728i
905905 −1.55971 + 1.13320i −0.0518465 + 0.0376687i
906906 −4.80663 + 7.06247i −0.159690 + 0.234635i
907907 −51.8977 + 16.8626i −1.72323 + 0.559913i −0.992445 0.122691i 0.960847π-0.960847\pi
−0.730789 + 0.682604i 0.760847π0.760847\pi
908908 −5.58546 14.1632i −0.185360 0.470023i
909909 −31.8268 + 43.8059i −1.05563 + 1.45295i
910910 10.8140 + 13.9608i 0.358481 + 0.462797i
911911 19.3513 + 6.28763i 0.641138 + 0.208319i 0.611503 0.791242i 0.290565π-0.290565\pi
0.0296356 + 0.999561i 0.490565π0.490565\pi
912912 −0.0174419 0.141137i −0.000577560 0.00467352i
913913 −14.4895 + 7.66581i −0.479532 + 0.253701i
914914 −0.741655 24.1195i −0.0245318 0.797802i
915915 0.113830 0.350334i 0.00376312 0.0115817i
916916 10.0188 8.26550i 0.331032 0.273100i
917917 6.85646 + 4.98151i 0.226420 + 0.164504i
918918 −4.21145 11.7226i −0.138998 0.386904i
919919 15.1776 + 46.7119i 0.500664 + 1.54088i 0.807941 + 0.589264i 0.200582π0.200582\pi
−0.307277 + 0.951620i 0.599418π0.599418\pi
920920 −8.19821 + 13.7984i −0.270287 + 0.454921i
921921 −8.61724 11.8606i −0.283948 0.390821i
922922 1.82787 + 0.532386i 0.0601976 + 0.0175332i
923923 58.4641 1.92437
924924 9.88036 + 4.11198i 0.325040 + 0.135274i
925925 −8.84655 −0.290873
926926 −5.92435 1.72553i −0.194686 0.0567044i
927927 15.0242 + 20.6791i 0.493460 + 0.679190i
928928 −10.6947 + 20.8152i −0.351071 + 0.683293i
929929 −0.735903 2.26488i −0.0241442 0.0743082i 0.938258 0.345935i 0.112438π-0.112438\pi
−0.962403 + 0.271627i 0.912438π0.912438\pi
930930 −0.226218 0.629679i −0.00741797 0.0206480i
931931 −0.188682 0.137086i −0.00618381 0.00449280i
932932 −26.7762 32.4562i −0.877084 1.06314i
933933 1.84391 5.67497i 0.0603668 0.185790i
934934 0.821210 + 26.7067i 0.0268708 + 0.873870i
935935 −7.03802 + 7.25798i −0.230168 + 0.237361i
936936 2.78434 + 30.1072i 0.0910090 + 0.984086i
937937 18.3283 + 5.95523i 0.598760 + 0.194549i 0.592687 0.805433i 0.298067π-0.298067\pi
0.00607273 + 0.999982i 0.498067π0.498067\pi
938938 −0.432676 0.558583i −0.0141274 0.0182384i
939939 5.71178 7.86159i 0.186397 0.256553i
940940 −7.53519 + 2.97161i −0.245771 + 0.0969232i
941941 −23.6518 + 7.68493i −0.771026 + 0.250521i −0.668004 0.744158i 0.732851π-0.732851\pi
−0.103022 + 0.994679i 0.532851π0.532851\pi
942942 2.44260 3.58895i 0.0795842 0.116934i
943943 38.9278 28.2827i 1.26766 0.921011i
944944 56.0232 + 10.8442i 1.82340 + 0.352948i
945945 9.27240i 0.301631i
946946 2.31394 + 0.257802i 0.0752328 + 0.00838185i
947947 31.5786i 1.02617i 0.858338 + 0.513084i 0.171497π0.171497\pi
−0.858338 + 0.513084i 0.828503π0.828503\pi
948948 10.1119 + 2.61088i 0.328419 + 0.0847974i
949949 −42.0156 + 30.5261i −1.36388 + 0.990920i
950950 −0.0826761 0.0562684i −0.00268237 0.00182559i
951951 3.09184 1.00460i 0.100260 0.0325764i
952952 25.4146 10.9367i 0.823693 0.354461i
953953 −17.7778 + 24.4690i −0.575878 + 0.792628i −0.993236 0.116114i 0.962956π-0.962956\pi
0.417358 + 0.908742i 0.362956π0.362956\pi
954954 −24.2379 + 18.7746i −0.784733 + 0.607851i
955955 17.0216 + 5.53066i 0.550807 + 0.178968i
956956 −28.2466 + 1.73876i −0.913560 + 0.0562357i
957957 1.18379 + 6.79576i 0.0382665 + 0.219676i
958958 −24.7518 + 0.761099i −0.799696 + 0.0245900i
959959 15.6513 48.1698i 0.505407 1.55548i
960960 −2.92074 2.76515i −0.0942664 0.0892448i
961961 −24.3631 17.7008i −0.785906 0.570994i
962962 45.8150 16.4594i 1.47713 0.530673i
963963 −3.31912 10.2152i −0.106957 0.329180i
964964 5.09811 8.00937i 0.164199 0.257964i
965965 −4.05416 5.58007i −0.130508 0.179629i
966966 3.62062 12.4309i 0.116491 0.399956i
967967 −44.0784 −1.41747 −0.708733 0.705477i 0.750733π-0.750733\pi
−0.708733 + 0.705477i 0.750733π0.750733\pi
968968 15.0615 27.2241i 0.484095 0.875015i
969969 −0.108374 −0.00348149
970970 2.61834 8.98967i 0.0840697 0.288641i
971971 −24.5621 33.8068i −0.788235 1.08491i −0.994326 0.106379i 0.966074π-0.966074\pi
0.206091 0.978533i 0.433926π-0.433926\pi
972972 −12.9748 + 20.3841i −0.416168 + 0.653819i
973973 −12.7908 39.3660i −0.410054 1.26202i
974974 14.3196 5.14443i 0.458829 0.164838i
975975 −1.58268 1.14988i −0.0506862 0.0368257i
976976 2.00046 + 2.14185i 0.0640330 + 0.0685590i
977977 −0.985364 + 3.03264i −0.0315246 + 0.0970227i −0.965581 0.260103i 0.916243π-0.916243\pi
0.934056 + 0.357126i 0.116243π0.116243\pi
978978 16.8513 0.518165i 0.538846 0.0165691i
979979 −6.80873 39.0867i −0.217608 1.24922i
980980 −6.58363 + 0.405266i −0.210306 + 0.0129457i
981981 19.1330 + 6.21668i 0.610869 + 0.198483i
982982 −26.0305 + 20.1632i −0.830667 + 0.643432i
983983 7.01991 9.66207i 0.223900 0.308172i −0.682258 0.731112i 0.739002π-0.739002\pi
0.906158 + 0.422940i 0.139002π0.139002\pi
984984 4.76627 + 11.0758i 0.151943 + 0.353084i
985985 −4.89843 + 1.59160i −0.156077 + 0.0507125i
986986 14.7433 + 10.0341i 0.469522 + 0.319551i
987987 5.28621 3.84066i 0.168262 0.122249i
988988 0.532858 + 0.137583i 0.0169525 + 0.00437711i
989989 2.81679i 0.0895687i
990990 12.8065 + 1.42680i 0.407016 + 0.0453465i
991991 42.2327i 1.34156i −0.741654 0.670782i 0.765958π-0.765958\pi
0.741654 0.670782i 0.234042π-0.234042\pi
992992 5.25495 + 0.850530i 0.166845 + 0.0270044i
993993 9.67461 7.02902i 0.307015 0.223059i
994994 −38.3651 + 56.3704i −1.21687 + 1.78796i
995995 17.2268 5.59732i 0.546125 0.177447i
996996 −4.62319 + 1.82322i −0.146491 + 0.0577710i
997997 −32.9568 + 45.3611i −1.04375 + 1.43660i −0.149649 + 0.988739i 0.547814π0.547814\pi
−0.894103 + 0.447862i 0.852186π0.852186\pi
998998 12.3297 + 15.9175i 0.390289 + 0.503860i
999999 24.3106 + 7.89898i 0.769152 + 0.249913i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

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