Properties

Label 588.2.n.d.275.1
Level 588588
Weight 22
Character 588.275
Analytic conductor 4.6954.695
Analytic rank 00
Dimension 2424
Inner twists 88

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")
 
Level: N N == 588=22372 588 = 2^{2} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 588.n (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.695203638854.69520363885
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 275.1
Character χ\chi == 588.275
Dual form 588.2.n.d.263.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.13414+0.844822i)q2+(1.368161.06214i)q3+(0.5725511.91629i)q4+(3.44057+1.98641i)q5+(2.44900+0.0487576i)q6+(0.969574+2.65705i)q8+(0.743736+2.90635i)q9+(5.58025+0.653796i)q10+(1.65172+2.86086i)q11+(2.81871+2.01367i)q120.850601q13+(2.597426.37208i)q15+(3.344372.19435i)q16+(0.4992360.288234i)q17+(3.298852.66788i)q18+(3.110231.79569i)q19+(5.776455.45582i)q20+(4.290211.84921i)q22+(1.98085+3.43094i)q23+(1.495614.66510i)q24+(5.39167+9.33865i)q25+(0.9647010.718606i)q26+(2.069384.76630i)q27+3.37929iq29+(8.32911+5.03249i)q30+(4.242642.44949i)q31+(5.646830.336691i)q32+(0.7788035.66848i)q33+(0.322697+0.748663i)q34+(5.99525+0.238815i)q36+(2.14510+3.71543i)q37+(5.044490.591024i)q38+(1.16376+0.903453i)q39+(1.94212+11.0677i)q405.35550iq41+7.66518iq43+(6.427951.52719i)q44+(3.21433+11.4769i)q45+(0.6519665.56464i)q46+(4.54525+7.87260i)q47+(2.24494+6.55441i)q48+(14.00446.03634i)q50+(0.9891790.135905i)q51+(0.487013+1.63000i)q52+(0.527096+0.304319i)q53+(1.67971+7.15392i)q54+13.1240iq55+(2.34803+5.76029i)q57+(2.854903.83259i)q58+(3.93980+6.82394i)q59+(13.6979+1.32907i)q60+(4.873158.44054i)q61+(2.74237+6.36234i)q62+(6.11985+5.15242i)q64+(2.926551.68964i)q65+(3.90558+7.08680i)q66+(7.833844.52287i)q67+(0.2665031.12171i)q68+(6.354252.59015i)q69+9.15654q71+(7.00121+4.79407i)q72+(0.707107+1.22474i)q73+(0.7060266.02605i)q74+(2.5422318.5035i)q75+(5.22185+4.93200i)q76+(2.083120.0414733i)q78+(6.00000+3.46410i)q79+(7.1476414.1931i)q80+(7.89371+4.32311i)q81+(4.52445+6.07390i)q824.13877q83+2.29021q85+(6.475718.69339i)q86+(3.589264.62341i)q87+(6.00000+7.16253i)q88+(4.98550+2.87838i)q89+(6.0503915.7319i)q90+(5.44055+5.76029i)q92+(8.406311.15496i)q93+(1.4960012.7686i)q94+(7.1339812.3564i)q95+(8.083395.53705i)q9613.5487q97+(7.08622+6.92820i)q99+O(q100)q+(-1.13414 + 0.844822i) q^{2} +(-1.36816 - 1.06214i) q^{3} +(0.572551 - 1.91629i) q^{4} +(3.44057 + 1.98641i) q^{5} +(2.44900 + 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(0.743736 + 2.90635i) q^{9} +(-5.58025 + 0.653796i) q^{10} +(1.65172 + 2.86086i) q^{11} +(-2.81871 + 2.01367i) q^{12} -0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-3.34437 - 2.19435i) q^{16} +(0.499236 - 0.288234i) q^{17} +(-3.29885 - 2.66788i) q^{18} +(-3.11023 - 1.79569i) q^{19} +(5.77645 - 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +(-1.98085 + 3.43094i) q^{23} +(1.49561 - 4.66510i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.964701 - 0.718606i) q^{26} +(2.06938 - 4.76630i) q^{27} +3.37929i q^{29} +(8.32911 + 5.03249i) q^{30} +(4.24264 - 2.44949i) q^{31} +(5.64683 - 0.336691i) q^{32} +(0.778803 - 5.66848i) q^{33} +(-0.322697 + 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(5.04449 - 0.591024i) q^{38} +(1.16376 + 0.903453i) q^{39} +(-1.94212 + 11.0677i) q^{40} -5.35550i q^{41} +7.66518i q^{43} +(6.42795 - 1.52719i) q^{44} +(-3.21433 + 11.4769i) q^{45} +(-0.651966 - 5.56464i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(2.24494 + 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(-0.989179 - 0.135905i) q^{51} +(-0.487013 + 1.63000i) q^{52} +(-0.527096 + 0.304319i) q^{53} +(1.67971 + 7.15392i) q^{54} +13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-2.85490 - 3.83259i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-13.6979 + 1.32907i) q^{60} +(4.87315 - 8.44054i) q^{61} +(-2.74237 + 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +(-2.92655 - 1.68964i) q^{65} +(3.90558 + 7.08680i) q^{66} +(7.83384 - 4.52287i) q^{67} +(-0.266503 - 1.12171i) q^{68} +(6.35425 - 2.59015i) q^{69} +9.15654 q^{71} +(-7.00121 + 4.79407i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.706026 - 6.02605i) q^{74} +(2.54223 - 18.5035i) q^{75} +(-5.22185 + 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-7.14764 - 14.1931i) q^{80} +(-7.89371 + 4.32311i) q^{81} +(4.52445 + 6.07390i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(-6.47571 - 8.69339i) q^{86} +(3.58926 - 4.62341i) q^{87} +(-6.00000 + 7.16253i) q^{88} +(4.98550 + 2.87838i) q^{89} +(-6.05039 - 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(-8.40631 - 1.15496i) q^{93} +(-1.49600 - 12.7686i) q^{94} +(-7.13398 - 12.3564i) q^{95} +(-8.08339 - 5.53705i) q^{96} -13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q12q436q1612q18+12q25+12q30+12q36+96q3996q4612q5124q57120q5884q6048q64+48q6772q7224q78+144q79+24q93+O(q100) 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/588Z)×\left(\mathbb{Z}/588\mathbb{Z}\right)^\times.

nn 197197 295295 493493
χ(n)\chi(n) 1-1 1-1 e(13)e\left(\frac{1}{3}\right)

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 −1.13414 + 0.844822i −0.801959 + 0.597379i
33 −1.36816 1.06214i −0.789909 0.613224i
44 0.572551 1.91629i 0.286276 0.958147i
55 3.44057 + 1.98641i 1.53867 + 0.888351i 0.998917 + 0.0465264i 0.0148152π0.0148152\pi
0.539752 + 0.841824i 0.318518π0.318518\pi
66 2.44900 + 0.0487576i 0.999802 + 0.0199052i
77 0 0
88 0.969574 + 2.65705i 0.342796 + 0.939410i
99 0.743736 + 2.90635i 0.247912 + 0.968783i
1010 −5.58025 + 0.653796i −1.76463 + 0.206748i
1111 1.65172 + 2.86086i 0.498013 + 0.862583i 0.999997 0.00229340i 0.000730012π-0.000730012\pi
−0.501985 + 0.864876i 0.667397π0.667397\pi
1212 −2.81871 + 2.01367i −0.813691 + 0.581298i
1313 −0.850601 −0.235914 −0.117957 0.993019i 0.537635π-0.537635\pi
−0.117957 + 0.993019i 0.537635π0.537635\pi
1414 0 0
1515 −2.59742 6.37208i −0.670650 1.64527i
1616 −3.34437 2.19435i −0.836092 0.548589i
1717 0.499236 0.288234i 0.121082 0.0699070i −0.438236 0.898860i 0.644396π-0.644396\pi
0.559318 + 0.828953i 0.311063π0.311063\pi
1818 −3.29885 2.66788i −0.777546 0.628826i
1919 −3.11023 1.79569i −0.713537 0.411960i 0.0988326 0.995104i 0.468489π-0.468489\pi
−0.812369 + 0.583144i 0.801822π0.801822\pi
2020 5.77645 5.45582i 1.29165 1.21996i
2121 0 0
2222 −4.29021 1.84921i −0.914675 0.394254i
2323 −1.98085 + 3.43094i −0.413037 + 0.715401i −0.995220 0.0976569i 0.968865π-0.968865\pi
0.582183 + 0.813057i 0.302199π0.302199\pi
2424 1.49561 4.66510i 0.305291 0.952259i
2525 5.39167 + 9.33865i 1.07833 + 1.86773i
2626 0.964701 0.718606i 0.189193 0.140930i
2727 2.06938 4.76630i 0.398253 0.917276i
2828 0 0
2929 3.37929i 0.627518i 0.949503 + 0.313759i 0.101588π0.101588\pi
−0.949503 + 0.313759i 0.898412π0.898412\pi
3030 8.32911 + 5.03249i 1.52068 + 0.918802i
3131 4.24264 2.44949i 0.762001 0.439941i −0.0680129 0.997684i 0.521666π-0.521666\pi
0.830014 + 0.557743i 0.188333π0.188333\pi
3232 5.64683 0.336691i 0.998227 0.0595191i
3333 0.778803 5.66848i 0.135572 0.986755i
3434 −0.322697 + 0.748663i −0.0553421 + 0.128395i
3535 0 0
3636 5.99525 + 0.238815i 0.999208 + 0.0398026i
3737 −2.14510 + 3.71543i −0.352653 + 0.610812i −0.986713 0.162471i 0.948054π-0.948054\pi
0.634061 + 0.773283i 0.281387π0.281387\pi
3838 5.04449 0.591024i 0.818324 0.0958767i
3939 1.16376 + 0.903453i 0.186351 + 0.144668i
4040 −1.94212 + 11.0677i −0.307076 + 1.74996i
4141 5.35550i 0.836389i −0.908357 0.418195i 0.862663π-0.862663\pi
0.908357 0.418195i 0.137337π-0.137337\pi
4242 0 0
4343 7.66518i 1.16893i 0.811419 + 0.584464i 0.198695π0.198695\pi
−0.811419 + 0.584464i 0.801305π0.801305\pi
4444 6.42795 1.52719i 0.969050 0.230233i
4545 −3.21433 + 11.4769i −0.479164 + 1.71087i
4646 −0.651966 5.56464i −0.0961272 0.820461i
4747 −4.54525 + 7.87260i −0.662993 + 1.14834i 0.316833 + 0.948481i 0.397381π0.397381\pi
−0.979825 + 0.199856i 0.935953π0.935953\pi
4848 2.24494 + 6.55441i 0.324029 + 0.946047i
4949 0 0
5050 −14.0044 6.03634i −1.98052 0.853667i
5151 −0.989179 0.135905i −0.138513 0.0190305i
5252 −0.487013 + 1.63000i −0.0675365 + 0.226041i
5353 −0.527096 + 0.304319i −0.0724023 + 0.0418015i −0.535764 0.844368i 0.679976π-0.679976\pi
0.463362 + 0.886169i 0.346643π0.346643\pi
5454 1.67971 + 7.15392i 0.228579 + 0.973525i
5555 13.1240i 1.76964i
5656 0 0
5757 2.34803 + 5.76029i 0.311005 + 0.762969i
5858 −2.85490 3.83259i −0.374866 0.503244i
5959 3.93980 + 6.82394i 0.512919 + 0.888401i 0.999888 + 0.0149820i 0.00476911π0.00476911\pi
−0.486969 + 0.873419i 0.661898π0.661898\pi
6060 −13.6979 + 1.32907i −1.76840 + 0.171582i
6161 4.87315 8.44054i 0.623943 1.08070i −0.364802 0.931085i 0.618863π-0.618863\pi
0.988744 0.149615i 0.0478034π-0.0478034\pi
6262 −2.74237 + 6.36234i −0.348281 + 0.808018i
6363 0 0
6464 −6.11985 + 5.15242i −0.764982 + 0.644052i
6565 −2.92655 1.68964i −0.362994 0.209575i
6666 3.90558 + 7.08680i 0.480744 + 0.872325i
6767 7.83384 4.52287i 0.957056 0.552557i 0.0617904 0.998089i 0.480319π-0.480319\pi
0.895266 + 0.445532i 0.146986π0.146986\pi
6868 −0.266503 1.12171i −0.0323182 0.136027i
6969 6.35425 2.59015i 0.764962 0.311817i
7070 0 0
7171 9.15654 1.08668 0.543341 0.839512i 0.317159π-0.317159\pi
0.543341 + 0.839512i 0.317159π0.317159\pi
7272 −7.00121 + 4.79407i −0.825100 + 0.564986i
7373 0.707107 + 1.22474i 0.0827606 + 0.143346i 0.904435 0.426612i 0.140293π-0.140293\pi
−0.821674 + 0.569958i 0.806960π0.806960\pi
7474 −0.706026 6.02605i −0.0820738 0.700514i
7575 2.54223 18.5035i 0.293551 2.13660i
7676 −5.22185 + 4.93200i −0.598987 + 0.565739i
7777 0 0
7878 −2.08312 0.0414733i −0.235867 0.00469593i
7979 6.00000 + 3.46410i 0.675053 + 0.389742i 0.797988 0.602673i 0.205898π-0.205898\pi
−0.122936 + 0.992415i 0.539231π0.539231\pi
8080 −7.14764 14.1931i −0.799130 1.58684i
8181 −7.89371 + 4.32311i −0.877079 + 0.480346i
8282 4.52445 + 6.07390i 0.499642 + 0.670750i
8383 −4.13877 −0.454289 −0.227144 0.973861i 0.572939π-0.572939\pi
−0.227144 + 0.973861i 0.572939π0.572939\pi
8484 0 0
8585 2.29021 0.248408
8686 −6.47571 8.69339i −0.698294 0.937433i
8787 3.58926 4.62341i 0.384809 0.495682i
8888 −6.00000 + 7.16253i −0.639602 + 0.763528i
8989 4.98550 + 2.87838i 0.528462 + 0.305108i 0.740390 0.672177i 0.234641π-0.234641\pi
−0.211928 + 0.977285i 0.567974π0.567974\pi
9090 −6.05039 15.7319i −0.637768 1.65829i
9191 0 0
9292 5.44055 + 5.76029i 0.567217 + 0.600552i
9393 −8.40631 1.15496i −0.871694 0.119764i
9494 −1.49600 12.7686i −0.154300 1.31698i
9595 −7.13398 12.3564i −0.731931 1.26774i
9696 −8.08339 5.53705i −0.825007 0.565122i
9797 −13.5487 −1.37567 −0.687833 0.725869i 0.741438π-0.741438\pi
−0.687833 + 0.725869i 0.741438π0.741438\pi
9898 0 0
9999 −7.08622 + 6.92820i −0.712192 + 0.696311i
100100 20.9826 4.98517i 2.09826 0.498517i
101101 6.18294 3.56972i 0.615225 0.355200i −0.159782 0.987152i 0.551079π-0.551079\pi
0.775008 + 0.631952i 0.217746π0.217746\pi
102102 1.23668 0.681544i 0.122450 0.0674829i
103103 9.10090 + 5.25441i 0.896738 + 0.517732i 0.876141 0.482056i 0.160110π-0.160110\pi
0.0205978 + 0.999788i 0.493443π0.493443\pi
104104 −0.824720 2.26009i −0.0808705 0.221620i
105105 0 0
106106 0.340706 0.790444i 0.0330923 0.0767747i
107107 −0.616561 + 1.06792i −0.0596052 + 0.103239i −0.894288 0.447491i 0.852318π-0.852318\pi
0.834683 + 0.550731i 0.185651π0.185651\pi
108108 −7.94881 6.69450i −0.764875 0.644179i
109109 1.60147 + 2.77382i 0.153393 + 0.265684i 0.932473 0.361241i 0.117647π-0.117647\pi
−0.779080 + 0.626925i 0.784313π0.784313\pi
110110 −11.0874 14.8845i −1.05715 1.41918i
111111 6.88114 2.80492i 0.653128 0.266231i
112112 0 0
113113 19.9097i 1.87294i −0.350744 0.936471i 0.614071π-0.614071\pi
0.350744 0.936471i 0.385929π-0.385929\pi
114114 −7.52942 4.54931i −0.705195 0.426082i
115115 −13.6305 + 7.86959i −1.27105 + 0.733843i
116116 6.47571 + 1.93482i 0.601255 + 0.179643i
117117 −0.632623 2.47214i −0.0584860 0.228550i
118118 −10.2333 4.41088i −0.942052 0.406054i
119119 0 0
120120 14.4126 13.0797i 1.31568 1.19401i
121121 0.0436371 0.0755817i 0.00396701 0.00687107i
122122 1.60392 + 13.6897i 0.145212 + 1.23941i
123123 −5.68827 + 7.32720i −0.512894 + 0.660671i
124124 −2.26481 9.53261i −0.203386 0.856053i
125125 22.9762i 2.05505i
126126 0 0
127127 16.4426i 1.45904i −0.683957 0.729522i 0.739742π-0.739742\pi
0.683957 0.729522i 0.260258π-0.260258\pi
128128 2.58790 11.0138i 0.228740 0.973488i
129129 8.14146 10.4872i 0.716815 0.923347i
130130 4.74657 0.556119i 0.416302 0.0487749i
131131 1.13845 1.97186i 0.0994670 0.172282i −0.811997 0.583661i 0.801620π-0.801620\pi
0.911464 + 0.411379i 0.134953π0.134953\pi
132132 −10.4166 4.73791i −0.906646 0.412382i
133133 0 0
134134 −5.06366 + 11.7478i −0.437434 + 1.01485i
135135 16.5877 12.2881i 1.42764 1.05759i
136136 1.24990 + 1.04703i 0.107178 + 0.0897822i
137137 −7.97118 + 4.60216i −0.681024 + 0.393189i −0.800241 0.599679i 0.795295π-0.795295\pi
0.119217 + 0.992868i 0.461962π0.461962\pi
138138 −5.01841 + 8.30581i −0.427195 + 0.707037i
139139 11.1056i 0.941960i −0.882144 0.470980i 0.843900π-0.843900\pi
0.882144 0.470980i 0.156100π-0.156100\pi
140140 0 0
141141 14.5804 5.94333i 1.22789 0.500519i
142142 −10.3848 + 7.73565i −0.871474 + 0.649161i
143143 −1.40495 2.43345i −0.117488 0.203496i
144144 3.89023 11.3519i 0.324186 0.945994i
145145 −6.71266 + 11.6267i −0.557456 + 0.965542i
146146 −1.83665 0.791654i −0.152002 0.0655177i
147147 0 0
148148 5.89167 + 6.23792i 0.484292 + 0.512754i
149149 5.81744 + 3.35870i 0.476584 + 0.275156i 0.718992 0.695019i 0.244604π-0.244604\pi
−0.242408 + 0.970174i 0.577937π0.577937\pi
150150 12.7489 + 23.1333i 1.04094 + 1.88882i
151151 11.4426 6.60641i 0.931188 0.537622i 0.0440012 0.999031i 0.485989π-0.485989\pi
0.887187 + 0.461410i 0.152656π0.152656\pi
152152 1.75565 10.0051i 0.142402 0.811522i
153153 1.20901 + 1.23658i 0.0977425 + 0.0999718i
154154 0 0
155155 19.4628 1.56329
156156 2.39759 1.71283i 0.191961 0.137136i
157157 1.19412 + 2.06828i 0.0953011 + 0.165066i 0.909734 0.415191i 0.136285π-0.136285\pi
−0.814433 + 0.580257i 0.802952π0.802952\pi
158158 −9.73140 + 1.14015i −0.774188 + 0.0907057i
159159 1.04438 + 0.143490i 0.0828249 + 0.0113795i
160160 20.0971 + 10.0585i 1.58881 + 0.795196i
161161 0 0
162162 5.30032 11.5718i 0.416433 0.909167i
163163 −15.8412 9.14590i −1.24078 0.716362i −0.271524 0.962432i 0.587528π-0.587528\pi
−0.969252 + 0.246069i 0.920861π0.920861\pi
164164 −10.2627 3.06630i −0.801384 0.239438i
165165 13.9395 17.9558i 1.08519 1.39785i
166166 4.69394 3.49652i 0.364321 0.271383i
167167 −19.3650 −1.49851 −0.749253 0.662284i 0.769587π-0.769587\pi
−0.749253 + 0.662284i 0.769587π0.769587\pi
168168 0 0
169169 −12.2765 −0.944344
170170 −2.59742 + 1.93482i −0.199213 + 0.148394i
171171 2.90572 10.3749i 0.222206 0.793392i
172172 14.6887 + 4.38871i 1.12001 + 0.334636i
173173 −4.83696 2.79262i −0.367748 0.212319i 0.304726 0.952440i 0.401435π-0.401435\pi
−0.672474 + 0.740121i 0.734768π0.734768\pi
174174 −0.164766 + 8.27589i −0.0124909 + 0.627394i
175175 0 0
176176 0.753784 13.1922i 0.0568186 0.994403i
177177 1.85766 13.5209i 0.139630 1.01629i
178178 −8.08598 + 0.947373i −0.606070 + 0.0710086i
179179 9.68969 + 16.7830i 0.724241 + 1.25442i 0.959286 + 0.282438i 0.0911432π0.0911432\pi
−0.235044 + 0.971985i 0.575523π0.575523\pi
180180 20.1527 + 12.7307i 1.50209 + 0.948890i
181181 10.8735 0.808222 0.404111 0.914710i 0.367581π-0.367581\pi
0.404111 + 0.914710i 0.367581π0.367581\pi
182182 0 0
183183 −15.6323 + 6.37208i −1.15557 + 0.471038i
184184 −11.0368 1.93668i −0.813642 0.142774i
185185 −14.7607 + 8.52212i −1.08523 + 0.626559i
186186 10.5097 5.79195i 0.770607 0.424686i
187187 1.64920 + 0.952164i 0.120601 + 0.0696291i
188188 12.4838 + 13.2175i 0.910477 + 0.963986i
189189 0 0
190190 18.5299 + 7.98697i 1.34430 + 0.579436i
191191 −0.616561 + 1.06792i −0.0446128 + 0.0772716i −0.887470 0.460866i 0.847539π-0.847539\pi
0.842857 + 0.538138i 0.180872π0.180872\pi
192192 13.8455 0.549231i 0.999214 0.0396373i
193193 −7.89167 13.6688i −0.568055 0.983900i −0.996758 0.0804546i 0.974363π-0.974363\pi
0.428703 0.903445i 0.358971π-0.358971\pi
194194 15.3662 11.4463i 1.10323 0.821795i
195195 2.20936 + 5.42010i 0.158216 + 0.388141i
196196 0 0
197197 17.3868i 1.23876i 0.785092 + 0.619379i 0.212615π0.212615\pi
−0.785092 + 0.619379i 0.787385π0.787385\pi
198198 2.18367 13.8442i 0.155187 0.983861i
199199 −3.95565 + 2.28380i −0.280409 + 0.161894i −0.633608 0.773654i 0.718427π-0.718427\pi
0.353200 + 0.935548i 0.385094π0.385094\pi
200200 −19.5857 + 23.3805i −1.38491 + 1.65325i
201201 −15.5219 2.13258i −1.09483 0.150421i
202202 −3.99654 + 9.27205i −0.281196 + 0.652379i
203203 0 0
204204 −0.826790 + 1.81775i −0.0578869 + 0.127268i
205205 10.6382 18.4260i 0.743007 1.28693i
206206 −14.7607 + 1.72940i −1.02843 + 0.120493i
207207 −11.4447 3.20534i −0.795464 0.222786i
208208 2.84472 + 1.86652i 0.197246 + 0.129420i
209209 11.8639i 0.820646i
210210 0 0
211211 1.11224i 0.0765696i 0.999267 + 0.0382848i 0.0121894π0.0121894\pi
−0.999267 + 0.0382848i 0.987811π0.987811\pi
212212 0.281376 + 1.18431i 0.0193250 + 0.0813388i
213213 −12.5276 9.72549i −0.858379 0.666379i
214214 −0.202931 1.73205i −0.0138721 0.118401i
215215 −15.2262 + 26.3726i −1.03842 + 1.79859i
216216 14.6707 + 0.877174i 0.998217 + 0.0596841i
217217 0 0
218218 −4.15967 1.79295i −0.281729 0.121434i
219219 0.333408 2.42669i 0.0225296 0.163981i
220220 25.1494 + 7.51416i 1.69558 + 0.506605i
221221 −0.424650 + 0.245172i −0.0285651 + 0.0164920i
222222 −5.43452 + 8.99451i −0.364741 + 0.603672i
223223 23.6328i 1.58257i −0.611447 0.791285i 0.709412π-0.709412\pi
0.611447 0.791285i 0.290588π-0.290588\pi
224224 0 0
225225 −23.1314 + 22.6156i −1.54209 + 1.50770i
226226 16.8201 + 22.5804i 1.11886 + 1.50202i
227227 6.14917 + 10.6507i 0.408135 + 0.706910i 0.994681 0.103006i 0.0328461π-0.0328461\pi
−0.586546 + 0.809916i 0.699513π0.699513\pi
228228 12.3828 1.20146i 0.820070 0.0795688i
229229 −4.51474 + 7.81976i −0.298342 + 0.516744i −0.975757 0.218857i 0.929767π-0.929767\pi
0.677414 + 0.735602i 0.263100π0.263100\pi
230230 8.81054 20.4406i 0.580950 1.34781i
231231 0 0
232232 −8.97895 + 3.27647i −0.589497 + 0.215111i
233233 6.55912 + 3.78691i 0.429703 + 0.248089i 0.699220 0.714907i 0.253531π-0.253531\pi
−0.269517 + 0.962996i 0.586864π0.586864\pi
234234 2.80600 + 2.26930i 0.183434 + 0.148349i
235235 −31.2765 + 18.0575i −2.04025 + 1.17794i
236236 15.3324 3.64277i 0.998055 0.237124i
237237 −4.52963 11.1123i −0.294231 0.721819i
238238 0 0
239239 −9.25206 −0.598466 −0.299233 0.954180i 0.596731π-0.596731\pi
−0.299233 + 0.954180i 0.596731π0.596731\pi
240240 −5.29589 + 27.0103i −0.341848 + 1.74350i
241241 −7.83018 13.5623i −0.504386 0.873623i −0.999987 0.00507224i 0.998385π-0.998385\pi
0.495601 0.868550i 0.334948π-0.334948\pi
242242 0.0143625 + 0.122586i 0.000923254 + 0.00788012i
243243 15.3916 + 2.46947i 0.987372 + 0.158417i
244244 −13.3844 14.1710i −0.856850 0.907207i
245245 0 0
246246 0.261122 13.1157i 0.0166485 0.836223i
247247 2.64557 + 1.52742i 0.168333 + 0.0971873i
248248 10.6220 + 8.89796i 0.674496 + 0.565021i
249249 5.66250 + 4.39593i 0.358847 + 0.278581i
250250 −19.4108 26.0583i −1.22765 1.64807i
251251 −3.08987 −0.195031 −0.0975155 0.995234i 0.531090π-0.531090\pi
−0.0975155 + 0.995234i 0.531090π0.531090\pi
252252 0 0
253253 −13.0873 −0.822790
254254 13.8911 + 18.6482i 0.871603 + 1.17009i
255255 −3.13337 2.43251i −0.196219 0.152330i
256256 6.36962 + 14.6775i 0.398101 + 0.917341i
257257 −6.38190 3.68459i −0.398092 0.229839i 0.287568 0.957760i 0.407153π-0.407153\pi
−0.685660 + 0.727922i 0.740486π0.740486\pi
258258 −0.373736 + 18.7721i −0.0232678 + 1.16870i
259259 0 0
260260 −4.91346 + 4.64072i −0.304720 + 0.287805i
261261 −9.82139 + 2.51330i −0.607929 + 0.155569i
262262 0.374703 + 3.19815i 0.0231492 + 0.197583i
263263 −11.1017 19.2288i −0.684563 1.18570i −0.973574 0.228372i 0.926660π-0.926660\pi
0.289011 0.957326i 0.406673π-0.406673\pi
264264 15.8165 3.42669i 0.973441 0.210898i
265265 −2.41801 −0.148537
266266 0 0
267267 −3.76375 9.23337i −0.230338 0.565073i
268268 −4.18188 17.6015i −0.255449 1.07518i
269269 8.67226 5.00693i 0.528757 0.305278i −0.211753 0.977323i 0.567917π-0.567917\pi
0.740510 + 0.672045i 0.234584π0.234584\pi
270270 −8.43149 + 27.9501i −0.513124 + 1.70099i
271271 −20.4250 11.7924i −1.24073 0.716335i −0.271486 0.962442i 0.587515π-0.587515\pi
−0.969243 + 0.246107i 0.920848π0.920848\pi
272272 −2.30212 0.131539i −0.139586 0.00797574i
273273 0 0
274274 5.15243 11.9537i 0.311270 0.722151i
275275 −17.8111 + 30.8497i −1.07405 + 1.86031i
276276 −1.32535 13.6596i −0.0797767 0.822212i
277277 −14.5299 25.1665i −0.873018 1.51211i −0.858860 0.512211i 0.828826π-0.828826\pi
−0.0141582 0.999900i 0.504507π-0.504507\pi
278278 9.38221 + 12.5953i 0.562708 + 0.755413i
279279 10.2745 + 10.5088i 0.615117 + 0.629146i
280280 0 0
281281 23.2889i 1.38930i −0.719347 0.694651i 0.755559π-0.755559\pi
0.719347 0.694651i 0.244441π-0.244441\pi
282282 −11.5152 + 19.0584i −0.685719 + 1.13491i
283283 15.0916 8.71312i 0.897101 0.517941i 0.0208421 0.999783i 0.493365π-0.493365\pi
0.876258 + 0.481842i 0.160032π0.160032\pi
284284 5.24259 17.5466i 0.311090 1.04120i
285285 −3.36375 + 24.4828i −0.199251 + 1.45024i
286286 3.64925 + 1.57294i 0.215785 + 0.0930100i
287287 0 0
288288 5.17829 + 16.1612i 0.305134 + 0.952310i
289289 −8.33384 + 14.4346i −0.490226 + 0.849096i
290290 −2.20936 18.8573i −0.129738 1.10734i
291291 18.5369 + 14.3906i 1.08665 + 0.843592i
292292 2.75183 0.653796i 0.161038 0.0382605i
293293 1.20747i 0.0705412i 0.999378 + 0.0352706i 0.0112293π0.0112293\pi
−0.999378 + 0.0352706i 0.988771π0.988771\pi
294294 0 0
295295 31.3043i 1.82261i
296296 −11.9519 2.09727i −0.694691 0.121901i
297297 17.0538 1.95238i 0.989561 0.113289i
298298 −9.43531 + 1.10546i −0.546573 + 0.0640377i
299299 1.68492 2.91836i 0.0974412 0.168773i
300300 −34.0025 15.4658i −1.96314 0.892921i
301301 0 0
302302 −7.39632 + 17.1596i −0.425610 + 0.987423i
303303 −12.2508 1.68316i −0.703789 0.0966950i
304304 6.46138 + 12.8304i 0.370586 + 0.735875i
305305 33.5328 19.3602i 1.92008 1.10856i
306306 −2.41588 0.381063i −0.138106 0.0217839i
307307 34.0275i 1.94205i 0.238973 + 0.971026i 0.423189π0.423189\pi
−0.238973 + 0.971026i 0.576811π0.576811\pi
308308 0 0
309309 −6.87062 16.8553i −0.390856 0.958863i
310310 −22.0735 + 16.4426i −1.25369 + 0.933877i
311311 −13.3558 23.1329i −0.757337 1.31175i −0.944204 0.329361i 0.893167π-0.893167\pi
0.186867 0.982385i 0.440167π-0.440167\pi
312312 −1.27217 + 3.96814i −0.0720225 + 0.224651i
313313 −4.66276 + 8.07614i −0.263555 + 0.456490i −0.967184 0.254077i 0.918228π-0.918228\pi
0.703629 + 0.710567i 0.251562π0.251562\pi
314314 −3.10162 1.33690i −0.175035 0.0754455i
315315 0 0
316316 10.0735 9.51439i 0.566681 0.535226i
317317 23.3767 + 13.4966i 1.31297 + 0.758043i 0.982587 0.185805i 0.0594891π-0.0594891\pi
0.330382 + 0.943847i 0.392822π0.392822\pi
318318 −1.30570 + 0.719579i −0.0732200 + 0.0403520i
319319 −9.66769 + 5.58164i −0.541286 + 0.312512i
320320 −31.2906 + 5.57069i −1.74920 + 0.311411i
321321 1.97783 0.806210i 0.110392 0.0449982i
322322 0 0
323323 −2.07032 −0.115196
324324 3.76480 + 17.6019i 0.209156 + 0.977882i
325325 −4.58616 7.94346i −0.254394 0.440624i
326326 25.6928 3.01023i 1.42299 0.166721i
327327 0.755108 5.49601i 0.0417575 0.303930i
328328 14.2299 5.19256i 0.785712 0.286711i
329329 0 0
330330 −0.639895 + 32.1407i −0.0352251 + 1.76929i
331331 12.6382 + 7.29669i 0.694660 + 0.401062i 0.805356 0.592792i 0.201974π-0.201974\pi
−0.110695 + 0.993854i 0.535308π0.535308\pi
332332 −2.36966 + 7.93109i −0.130052 + 0.435275i
333333 −12.3937 3.47112i −0.679171 0.190216i
334334 21.9626 16.3600i 1.20174 0.895177i
335335 35.9372 1.96346
336336 0 0
337337 31.6823 1.72585 0.862924 0.505335i 0.168631π-0.168631\pi
0.862924 + 0.505335i 0.168631π0.168631\pi
338338 13.9233 10.3714i 0.757325 0.564132i
339339 −21.1468 + 27.2396i −1.14853 + 1.47945i
340340 1.31126 4.38871i 0.0711131 0.238011i
341341 14.0153 + 8.09175i 0.758972 + 0.438193i
342342 5.46949 + 14.2215i 0.295756 + 0.769009i
343343 0 0
344344 −20.3668 + 7.43196i −1.09810 + 0.400704i
345345 27.0073 + 3.71059i 1.45403 + 0.199772i
346346 7.84507 0.919147i 0.421753 0.0494136i
347347 −1.07687 1.86519i −0.0578092 0.100128i 0.835673 0.549228i 0.185078π-0.185078\pi
−0.893482 + 0.449100i 0.851745π0.851745\pi
348348 −6.80479 9.52523i −0.364775 0.510606i
349349 33.0517 1.76922 0.884608 0.466335i 0.154426π-0.154426\pi
0.884608 + 0.466335i 0.154426π0.154426\pi
350350 0 0
351351 −1.76022 + 4.05422i −0.0939535 + 0.216398i
352352 10.2902 + 15.5987i 0.548470 + 0.831413i
353353 13.5161 7.80351i 0.719388 0.415339i −0.0951392 0.995464i 0.530330π-0.530330\pi
0.814528 + 0.580125i 0.196996π0.196996\pi
354354 9.31588 + 16.9040i 0.495133 + 0.898435i
355355 31.5037 + 18.1887i 1.67204 + 0.965354i
356356 8.37028 7.90567i 0.443624 0.419000i
357357 0 0
358358 −25.1681 10.8483i −1.33018 0.573348i
359359 16.8237 29.1394i 0.887919 1.53792i 0.0455885 0.998960i 0.485484π-0.485484\pi
0.842331 0.538961i 0.181183π-0.181183\pi
360360 −33.6111 + 2.58701i −1.77146 + 0.136348i
361361 −3.05096 5.28443i −0.160577 0.278128i
362362 −12.3321 + 9.18619i −0.648161 + 0.482815i
363363 −0.139981 + 0.0570595i −0.00734708 + 0.00299485i
364364 0 0
365365 5.61842i 0.294082i
366366 12.3459 20.4333i 0.645331 1.06807i
367367 6.79444 3.92277i 0.354667 0.204767i −0.312072 0.950059i 0.601023π-0.601023\pi
0.666739 + 0.745291i 0.267690π0.267690\pi
368368 14.1534 7.12764i 0.737797 0.371554i
369369 15.5650 3.98308i 0.810279 0.207351i
370370 9.54109 22.1355i 0.496018 1.15077i
371371 0 0
372372 −7.02629 + 15.4477i −0.364296 + 0.800926i
373373 −0.493136 + 0.854137i −0.0255336 + 0.0442256i −0.878510 0.477724i 0.841462π-0.841462\pi
0.852976 + 0.521950i 0.174795π0.174795\pi
374374 −2.67483 + 0.313389i −0.138312 + 0.0162050i
375375 24.4038 31.4352i 1.26021 1.62331i
376376 −25.3249 4.44389i −1.30603 0.229176i
377377 2.87443i 0.148040i
378378 0 0
379379 18.8285i 0.967153i −0.875302 0.483576i 0.839337π-0.839337\pi
0.875302 0.483576i 0.160663π-0.160663\pi
380380 −27.7631 + 6.59612i −1.42422 + 0.338374i
381381 −17.4643 + 22.4961i −0.894721 + 1.15251i
382382 −0.202931 1.73205i −0.0103829 0.0886194i
383383 −1.81144 + 3.13750i −0.0925602 + 0.160319i −0.908588 0.417694i 0.862838π-0.862838\pi
0.816028 + 0.578013i 0.196172π0.196172\pi
384384 −15.2388 + 12.3199i −0.777650 + 0.628697i
385385 0 0
386386 20.4979 + 8.83526i 1.04332 + 0.449703i
387387 −22.2777 + 5.70087i −1.13244 + 0.289792i
388388 −7.75735 + 25.9634i −0.393820 + 1.31809i
389389 −12.6579 + 7.30807i −0.641783 + 0.370534i −0.785301 0.619114i 0.787492π-0.787492\pi
0.143518 + 0.989648i 0.454159π0.454159\pi
390390 −7.08475 4.28064i −0.358750 0.216759i
391391 2.28380i 0.115497i
392392 0 0
393393 −3.65197 + 1.48863i −0.184217 + 0.0750914i
394394 −14.6887 19.7191i −0.740008 0.993432i
395395 13.7623 + 23.8370i 0.692455 + 1.19937i
396396 9.21925 + 17.5460i 0.463285 + 0.881722i
397397 3.04852 5.28019i 0.153001 0.265005i −0.779328 0.626616i 0.784440π-0.784440\pi
0.932329 + 0.361610i 0.117773π0.117773\pi
398398 2.55687 5.93197i 0.128164 0.297343i
399399 0 0
400400 2.46056 43.0631i 0.123028 2.15316i
401401 −6.31340 3.64505i −0.315276 0.182025i 0.334009 0.942570i 0.391598π-0.391598\pi
−0.649285 + 0.760545i 0.724932π0.724932\pi
402402 19.4056 10.6946i 0.967865 0.533397i
403403 −3.60879 + 2.08354i −0.179767 + 0.103788i
404404 −3.30059 13.8922i −0.164210 0.691162i
405405 −35.7463 0.806210i −1.77625 0.0400609i
406406 0 0
407407 −14.1724 −0.702502
408408 −0.597975 2.76007i −0.0296042 0.136644i
409409 10.0950 + 17.4850i 0.499165 + 0.864580i 1.00000 0.000963491i 0.000306689π-0.000306689\pi
−0.500834 + 0.865543i 0.666973π0.666973\pi
410410 3.50140 + 29.8851i 0.172922 + 1.47592i
411411 15.7940 + 2.16997i 0.779060 + 0.107037i
412412 15.2797 14.4316i 0.752778 0.710993i
413413 0 0
414414 15.6879 6.03347i 0.771018 0.296529i
415415 −14.2397 8.22130i −0.699000 0.403568i
416416 −4.80319 + 0.286389i −0.235496 + 0.0140414i
417417 −11.7956 + 15.1942i −0.577633 + 0.744063i
418418 10.0229 + 13.4554i 0.490237 + 0.658124i
419419 −1.32886 −0.0649189 −0.0324594 0.999473i 0.510334π-0.510334\pi
−0.0324594 + 0.999473i 0.510334π0.510334\pi
420420 0 0
421421 −7.31859 −0.356686 −0.178343 0.983968i 0.557074π-0.557074\pi
−0.178343 + 0.983968i 0.557074π0.557074\pi
422422 −0.939643 1.26143i −0.0457411 0.0614057i
423423 −26.2610 7.35493i −1.27685 0.357609i
424424 −1.31965 1.10546i −0.0640879 0.0536860i
425425 5.38343 + 3.10812i 0.261135 + 0.150766i
426426 22.4244 + 0.446451i 1.08647 + 0.0216306i
427427 0 0
428428 1.69343 + 1.79295i 0.0818549 + 0.0866655i
429429 −0.662451 + 4.82161i −0.0319834 + 0.232790i
430430 −5.01146 42.7736i −0.241674 2.06273i
431431 0.0894647 + 0.154957i 0.00430936 + 0.00746403i 0.868172 0.496263i 0.165295π-0.165295\pi
−0.863863 + 0.503727i 0.831962π0.831962\pi
432432 −17.3797 + 11.3993i −0.836183 + 0.548450i
433433 15.2499 0.732866 0.366433 0.930444i 0.380579π-0.380579\pi
0.366433 + 0.930444i 0.380579π0.380579\pi
434434 0 0
435435 21.5331 8.77742i 1.03243 0.420845i
436436 6.23238 1.48073i 0.298477 0.0709139i
437437 12.3218 7.11402i 0.589434 0.340310i
438438 1.67199 + 3.03388i 0.0798909 + 0.144965i
439439 −25.8988 14.9527i −1.23608 0.713654i −0.267793 0.963476i 0.586294π-0.586294\pi
−0.968292 + 0.249823i 0.919628π0.919628\pi
440440 −34.8711 + 12.7247i −1.66242 + 0.606626i
441441 0 0
442442 0.274487 0.636813i 0.0130560 0.0302901i
443443 2.50795 4.34390i 0.119156 0.206385i −0.800277 0.599630i 0.795314π-0.795314\pi
0.919434 + 0.393245i 0.128648π0.128648\pi
444444 −1.43524 14.7922i −0.0681137 0.702009i
445445 11.4353 + 19.8065i 0.542086 + 0.938920i
446446 19.9655 + 26.8029i 0.945395 + 1.26916i
447447 −4.39181 10.7742i −0.207725 0.509601i
448448 0 0
449449 14.4978i 0.684195i 0.939664 + 0.342098i 0.111137π0.111137\pi
−0.939664 + 0.342098i 0.888863π0.888863\pi
450450 7.12811 45.1911i 0.336023 2.13033i
451451 15.3214 8.84580i 0.721455 0.416532i
452452 −38.1528 11.3993i −1.79456 0.536178i
453453 −22.6723 3.11499i −1.06524 0.146355i
454454 −15.9719 6.88441i −0.749600 0.323101i
455455 0 0
456456 −13.0288 + 11.8239i −0.610129 + 0.553704i
457457 9.92844 17.1966i 0.464433 0.804422i −0.534743 0.845015i 0.679591π-0.679591\pi
0.999176 + 0.0405933i 0.0129248π0.0129248\pi
458458 −1.48595 12.6829i −0.0694341 0.592631i
459459 −0.340700 2.97598i −0.0159025 0.138907i
460460 7.27627 + 30.6259i 0.339258 + 1.42794i
461461 17.3910i 0.809978i −0.914322 0.404989i 0.867275π-0.867275\pi
0.914322 0.404989i 0.132725π-0.132725\pi
462462 0 0
463463 15.3304i 0.712462i −0.934398 0.356231i 0.884062π-0.884062\pi
0.934398 0.356231i 0.115938π-0.115938\pi
464464 7.41536 11.3016i 0.344249 0.524663i
465465 −26.6283 20.6721i −1.23486 0.958647i
466466 −10.6382 + 1.24640i −0.492807 + 0.0577384i
467467 10.5410 18.2575i 0.487778 0.844857i −0.512123 0.858912i 0.671141π-0.671141\pi
0.999901 + 0.0140554i 0.00447412π0.00447412\pi
468468 −5.09956 0.203137i −0.235727 0.00938999i
469469 0 0
470470 20.2166 46.9028i 0.932521 2.16346i
471471 0.563040 4.09805i 0.0259435 0.188828i
472472 −14.3116 + 17.0846i −0.658746 + 0.786381i
473473 −21.9290 + 12.6607i −1.00830 + 0.582141i
474474 14.5251 + 8.77615i 0.667161 + 0.403102i
475475 38.7272i 1.77692i
476476 0 0
477477 −1.27648 1.30559i −0.0584459 0.0597790i
478478 10.4931 7.81634i 0.479945 0.357511i
479479 3.79982 + 6.58149i 0.173618 + 0.300716i 0.939682 0.342049i 0.111121π-0.111121\pi
−0.766064 + 0.642764i 0.777787π0.777787\pi
480480 −16.8126 35.1075i −0.767386 1.60243i
481481 1.82463 3.16034i 0.0831958 0.144099i
482482 20.3382 + 8.76642i 0.926381 + 0.399299i
483483 0 0
484484 −0.119852 0.126896i −0.00544784 0.00576800i
485485 −46.6154 26.9134i −2.11670 1.22207i
486486 −19.5425 + 10.2024i −0.886467 + 0.462792i
487487 13.3691 7.71865i 0.605811 0.349765i −0.165513 0.986208i 0.552928π-0.552928\pi
0.771324 + 0.636442i 0.219595π0.219595\pi
488488 27.1518 + 4.76448i 1.22911 + 0.215678i
489489 11.9591 + 29.3386i 0.540809 + 1.32674i
490490 0 0
491491 40.5166 1.82849 0.914243 0.405165i 0.132786π-0.132786\pi
0.914243 + 0.405165i 0.132786π0.132786\pi
492492 10.7842 + 15.0956i 0.486191 + 0.680562i
493493 0.974025 + 1.68706i 0.0438679 + 0.0759814i
494494 −4.29084 + 0.502725i −0.193054 + 0.0226187i
495495 −38.1429 + 9.76079i −1.71440 + 0.438715i
496496 −19.5640 1.11786i −0.878450 0.0501932i
497497 0 0
498498 −10.1359 0.201796i −0.454199 0.00904272i
499499 26.2986 + 15.1835i 1.17729 + 0.679707i 0.955385 0.295362i 0.0954403π-0.0954403\pi
0.221902 + 0.975069i 0.428774π0.428774\pi
500500 44.0292 + 13.1551i 1.96904 + 0.588312i
501501 26.4944 + 20.5682i 1.18368 + 0.918921i
502502 3.50435 2.61039i 0.156407 0.116507i
503503 −13.8974 −0.619652 −0.309826 0.950793i 0.600271π-0.600271\pi
−0.309826 + 0.950793i 0.600271π0.600271\pi
504504 0 0
505505 28.3638 1.26217
506506 14.8428 11.0564i 0.659844 0.491518i
507507 16.7962 + 13.0393i 0.745946 + 0.579095i
508508 −31.5089 9.41423i −1.39798 0.417689i
509509 −25.6830 14.8281i −1.13838 0.657243i −0.192350 0.981326i 0.561611π-0.561611\pi
−0.946029 + 0.324083i 0.894944π0.894944\pi
510510 5.60872 + 0.111665i 0.248358 + 0.00494461i
511511 0 0
512512 −19.6239 11.2651i −0.867262 0.497853i
513513 −14.9951 + 11.1083i −0.662049 + 0.490445i
514514 10.3508 1.21272i 0.456554 0.0534909i
515515 20.8748 + 36.1563i 0.919855 + 1.59324i
516516 −15.4352 21.6059i −0.679496 0.951147i
517517 −30.0299 −1.32071
518518 0 0
519519 3.65161 + 8.95827i 0.160288 + 0.393225i
520520 1.65197 9.41423i 0.0724435 0.412841i
521521 −29.0727 + 16.7851i −1.27370 + 0.735369i −0.975682 0.219192i 0.929658π-0.929658\pi
−0.298015 + 0.954561i 0.596325π0.596325\pi
522522 9.01555 11.1478i 0.394600 0.487924i
523523 8.82946 + 5.09769i 0.386085 + 0.222906i 0.680463 0.732783i 0.261779π-0.261779\pi
−0.294377 + 0.955689i 0.595112π0.595112\pi
524524 −3.12684 3.31060i −0.136596 0.144624i
525525 0 0
526526 28.8358 + 12.4291i 1.25730 + 0.541937i
527527 1.41205 2.44575i 0.0615099 0.106538i
528528 −15.0433 + 17.2485i −0.654674 + 0.750645i
529529 3.65243 + 6.32620i 0.158801 + 0.275052i
530530 2.74237 2.04279i 0.119121 0.0887332i
531531 −16.9026 + 16.5256i −0.733509 + 0.717152i
532532 0 0
533533 4.55539i 0.197316i
534534 12.0692 + 7.29225i 0.522284 + 0.315567i
535535 −4.24264 + 2.44949i −0.183425 + 0.105901i
536536 19.6130 + 16.4297i 0.847152 + 0.709654i
537537 4.56879 33.2537i 0.197158 1.43500i
538538 −5.60560 + 13.0051i −0.241675 + 0.560689i
539539 0 0
540540 −14.0504 38.8225i −0.604633 1.67065i
541541 −5.15243 + 8.92427i −0.221520 + 0.383684i −0.955270 0.295736i 0.904435π-0.904435\pi
0.733750 + 0.679420i 0.237769π0.237769\pi
542542 33.1272 3.88127i 1.42294 0.166715i
543543 −14.8767 11.5492i −0.638422 0.495622i
544544 2.72205 1.79569i 0.116707 0.0769898i
545545 12.7247i 0.545066i
546546 0 0
547547 5.44070i 0.232628i 0.993213 + 0.116314i 0.0371078π0.0371078\pi
−0.993213 + 0.116314i 0.962892π0.962892\pi
548548 4.25519 + 17.9101i 0.181773 + 0.765081i
549549 28.1555 + 7.88552i 1.20165 + 0.336546i
550550 −5.86223 50.0351i −0.249966 2.13350i
551551 6.06817 10.5104i 0.258513 0.447757i
552552 13.0431 + 14.3722i 0.555150 + 0.611723i
553553 0 0
554554 37.7402 + 16.2672i 1.60343 + 0.691128i
555555 29.2467 + 4.01827i 1.24145 + 0.170566i
556556 −21.2815 6.35850i −0.902537 0.269660i
557557 3.84264 2.21855i 0.162818 0.0940030i −0.416377 0.909192i 0.636700π-0.636700\pi
0.579195 + 0.815189i 0.303367π0.303367\pi
558558 −20.5308 3.23837i −0.869137 0.137091i
559559 6.52001i 0.275767i
560560 0 0
561561 −1.24504 3.05438i −0.0525657 0.128956i
562562 19.6750 + 26.4129i 0.829940 + 1.11416i
563563 −19.5639 33.8857i −0.824522 1.42811i −0.902284 0.431141i 0.858111π-0.858111\pi
0.0777627 0.996972i 0.475222π-0.475222\pi
564564 −3.04113 31.3432i −0.128055 1.31979i
565565 39.5488 68.5005i 1.66383 2.88184i
566566 −9.75493 + 22.6316i −0.410030 + 0.951277i
567567 0 0
568568 8.87794 + 24.3294i 0.372510 + 1.02084i
569569 −38.4653 22.2079i −1.61255 0.931005i −0.988777 0.149398i 0.952266π-0.952266\pi
−0.623771 0.781607i 0.714400π-0.714400\pi
570570 −16.8687 30.6088i −0.706551 1.28206i
571571 2.15883 1.24640i 0.0903442 0.0521603i −0.454147 0.890927i 0.650056π-0.650056\pi
0.544491 + 0.838766i 0.316723π0.316723\pi
572572 −5.46762 + 1.29903i −0.228613 + 0.0543152i
573573 1.97783 0.806210i 0.0826249 0.0336799i
574574 0 0
575575 −42.7205 −1.78157
576576 −19.5263 13.9544i −0.813595 0.581432i
577577 18.2933 + 31.6849i 0.761560 + 1.31906i 0.942046 + 0.335482i 0.108899π0.108899\pi
−0.180487 + 0.983577i 0.557767π0.557767\pi
578578 −2.74295 23.4115i −0.114092 0.973791i
579579 −3.72100 + 27.0831i −0.154640 + 1.12554i
580580 18.4368 + 19.5203i 0.765546 + 0.810536i
581581 0 0
582582 −33.1809 0.660605i −1.37539 0.0273830i
583583 −1.74123 1.00530i −0.0721145 0.0416353i
584584 −2.56862 + 3.06630i −0.106290 + 0.126884i
585585 2.73411 9.76222i 0.113042 0.403618i
586586 −1.02010 1.36944i −0.0421398 0.0565711i
587587 −36.8412 −1.52060 −0.760299 0.649573i 0.774948π-0.774948\pi
−0.760299 + 0.649573i 0.774948π0.774948\pi
588588 0 0
589589 −17.5941 −0.724954
590590 −26.4466 35.5035i −1.08879 1.46166i
591591 18.4671 23.7879i 0.759636 0.978505i
592592 15.3270 7.71865i 0.629935 0.317234i
593593 14.9125 + 8.60972i 0.612382 + 0.353559i 0.773897 0.633311i 0.218305π-0.218305\pi
−0.161515 + 0.986870i 0.551638π0.551638\pi
594594 −17.6920 + 16.6217i −0.725911 + 0.681996i
595595 0 0
596596 9.76705 9.22491i 0.400074 0.377867i
597597 7.83768 + 1.07683i 0.320775 + 0.0440719i
598598 0.554563 + 4.73329i 0.0226778 + 0.193558i
599599 −9.51076 16.4731i −0.388599 0.673073i 0.603662 0.797240i 0.293708π-0.293708\pi
−0.992261 + 0.124167i 0.960374π0.960374\pi
600600 51.6296 11.1857i 2.10777 0.456652i
601601 −7.95144 −0.324346 −0.162173 0.986762i 0.551850π-0.551850\pi
−0.162173 + 0.986762i 0.551850π0.551850\pi
602602 0 0
603603 18.9713 + 19.4040i 0.772573 + 0.790194i
604604 −6.10833 25.7100i −0.248544 1.04612i
605605 0.300273 0.173363i 0.0122078 0.00704820i
606606 15.3161 8.44080i 0.622174 0.342884i
607607 −20.5976 11.8920i −0.836030 0.482682i 0.0198827 0.999802i 0.493671π-0.493671\pi
−0.855913 + 0.517120i 0.827004π0.827004\pi
608608 −18.1675 9.09279i −0.736791 0.368761i
609609 0 0
610610 −21.6750 + 50.2864i −0.877596 + 2.03604i
611611 3.86619 6.69644i 0.156409 0.270909i
612612 3.06187 1.60881i 0.123769 0.0650322i
613613 14.8779 + 25.7694i 0.600914 + 1.04081i 0.992683 + 0.120751i 0.0385301π0.0385301\pi
−0.391768 + 0.920064i 0.628137π0.628137\pi
614614 −28.7472 38.5920i −1.16014 1.55745i
615615 −34.1257 + 13.9105i −1.37608 + 0.560924i
616616 0 0
617617 28.7008i 1.15545i 0.816232 + 0.577724i 0.196059π0.196059\pi
−0.816232 + 0.577724i 0.803941π0.803941\pi
618618 22.0320 + 13.3118i 0.886255 + 0.535479i
619619 −19.9082 + 11.4940i −0.800177 + 0.461983i −0.843533 0.537077i 0.819528π-0.819528\pi
0.0433558 + 0.999060i 0.486195π0.486195\pi
620620 11.1434 37.2964i 0.447532 1.49786i
621621 12.2538 + 16.5413i 0.491726 + 0.663779i
622622 34.6905 + 14.9527i 1.39096 + 0.599549i
623623 0 0
624624 −1.90955 5.57518i −0.0764431 0.223186i
625625 −18.6819 + 32.3580i −0.747275 + 1.29432i
626626 −1.53467 13.0987i −0.0613378 0.523529i
627627 −12.6011 + 16.2318i −0.503240 + 0.648236i
628628 4.64712 1.10409i 0.185440 0.0440580i
629629 2.47316i 0.0986115i
630630 0 0
631631 15.3304i 0.610292i −0.952306 0.305146i 0.901295π-0.901295\pi
0.952306 0.305146i 0.0987052π-0.0987052\pi
632632 −3.38685 + 19.3010i −0.134722 + 0.767753i
633633 1.18135 1.52172i 0.0469543 0.0604830i
634634 −37.9147 + 4.44218i −1.50579 + 0.176421i
635635 32.6618 56.5719i 1.29614 2.24499i
636636 0.872931 1.91919i 0.0346140 0.0761008i
637637 0 0
638638 6.24902 14.4978i 0.247401 0.573975i
639639 6.81005 + 26.6121i 0.269401 + 1.05276i
640640 30.7817 32.7529i 1.21675 1.29467i
641641 11.6038 6.69943i 0.458321 0.264612i −0.253017 0.967462i 0.581423π-0.581423\pi
0.711338 + 0.702850i 0.248090π0.248090\pi
642642 −1.56203 + 2.58527i −0.0616484 + 0.102032i
643643 2.68122i 0.105737i 0.998601 + 0.0528684i 0.0168364π0.0168364\pi
−0.998601 + 0.0528684i 0.983164π0.983164\pi
644644 0 0
645645 48.8432 19.9097i 1.92320 0.783942i
646646 2.34803 1.74905i 0.0923822 0.0688155i
647647 9.86799 + 17.0919i 0.387951 + 0.671950i 0.992174 0.124865i 0.0398497π-0.0398497\pi
−0.604223 + 0.796815i 0.706516π0.706516\pi
648648 −19.1403 16.7824i −0.751901 0.659276i
649649 −13.0149 + 22.5425i −0.510880 + 0.884870i
650650 11.9122 + 5.13452i 0.467233 + 0.201392i
651651 0 0
652652 −26.5961 + 25.1198i −1.04158 + 0.983769i
653653 30.5038 + 17.6114i 1.19371 + 0.689186i 0.959145 0.282915i 0.0913015π-0.0913015\pi
0.234561 + 0.972101i 0.424635π0.424635\pi
654654 3.78675 + 6.87118i 0.148074 + 0.268684i
655655 7.83384 4.52287i 0.306094 0.176723i
656656 −11.7519 + 17.9108i −0.458833 + 0.699299i
657657 −3.03363 + 2.96599i −0.118353 + 0.115714i
658658 0 0
659659 −39.7628 −1.54894 −0.774469 0.632612i 0.781983π-0.781983\pi
−0.774469 + 0.632612i 0.781983π0.781983\pi
660660 −26.4275 36.9927i −1.02869 1.43994i
661661 −7.46659 12.9325i −0.290417 0.503017i 0.683492 0.729958i 0.260461π-0.260461\pi
−0.973908 + 0.226942i 0.927127π0.927127\pi
662662 −20.4979 + 2.40159i −0.796675 + 0.0933404i
663663 0.841396 + 0.115601i 0.0326771 + 0.00448957i
664664 −4.01284 10.9969i −0.155728 0.426763i
665665 0 0
666666 16.9887 6.53375i 0.658298 0.253178i
667667 −11.5941 6.69388i −0.448927 0.259188i
668668 −11.0874 + 37.1090i −0.428986 + 1.43579i
669669 −25.1012 + 32.3335i −0.970470 + 1.25009i
670670 −40.7578 + 30.3605i −1.57461 + 1.17293i
671671 32.1963 1.24292
672672 0 0
673673 1.52059 0.0586145 0.0293072 0.999570i 0.490670π-0.490670\pi
0.0293072 + 0.999570i 0.490670π0.490670\pi
674674 −35.9322 + 26.7659i −1.38406 + 1.03099i
675675 55.6683 6.37310i 2.14267 0.245301i
676676 −7.02891 + 23.5253i −0.270343 + 0.904821i
677677 14.2074 + 8.20266i 0.546036 + 0.315254i 0.747522 0.664238i 0.231244π-0.231244\pi
−0.201486 + 0.979491i 0.564577π0.564577\pi
678678 0.970748 48.7588i 0.0372813 1.87257i
679679 0 0
680680 2.22052 + 6.08520i 0.0851532 + 0.233357i
681681 2.89940 21.1031i 0.111105 0.808672i
682682 −22.7314 + 2.66327i −0.870431 + 0.101982i
683683 4.57827 + 7.92980i 0.175183 + 0.303425i 0.940224 0.340555i 0.110615π-0.110615\pi
−0.765042 + 0.643981i 0.777282π0.777282\pi
684684 −18.2178 11.5084i −0.696574 0.440035i
685685 −36.5672 −1.39716
686686 0 0
687687 14.4825 5.90343i 0.552543 0.225230i
688688 16.8201 25.6352i 0.641261 0.977333i
689689 0.448349 0.258854i 0.0170807 0.00986156i
690690 −33.7649 + 18.6081i −1.28541 + 0.708397i
691691 −28.7221 16.5827i −1.09264 0.630836i −0.158362 0.987381i 0.550621π-0.550621\pi
−0.934278 + 0.356545i 0.883955π0.883955\pi
692692 −8.12090 + 7.67013i −0.308710 + 0.291575i
693693 0 0
694694 2.79707 + 1.20562i 0.106175 + 0.0457649i
695695 22.0602 38.2094i 0.836791 1.44937i
696696 15.7647 + 5.05411i 0.597560 + 0.191576i
697697 −1.54364 2.67366i −0.0584694 0.101272i
698698 −37.4853 + 27.9228i −1.41884 + 1.05689i
699699 −4.95173 12.1478i −0.187292 0.459472i
700700 0 0
701701 38.1529i 1.44101i −0.693448 0.720507i 0.743909π-0.743909\pi
0.693448 0.720507i 0.256091π-0.256091\pi
702702 −1.42876 6.08513i −0.0539251 0.229668i
703703 13.3435 7.70390i 0.503261 0.290558i
704704 −24.8487 8.99771i −0.936519 0.339114i
705705 61.9708 + 8.51429i 2.33396 + 0.320667i
706706 −8.73656 + 20.2690i −0.328805 + 0.762833i
707707 0 0
708708 −24.8464 11.3012i −0.933783 0.424725i
709709 −6.97895 + 12.0879i −0.262100 + 0.453970i −0.966800 0.255535i 0.917748π-0.917748\pi
0.704700 + 0.709505i 0.251082π0.251082\pi
710710 −51.0958 + 5.98651i −1.91759 + 0.224670i
711711 −5.60547 + 20.0145i −0.210221 + 0.750601i
712712 −2.81420 + 16.0375i −0.105466 + 0.601032i
713713 19.4083i 0.726848i
714714 0 0
715715 11.1633i 0.417483i
716716 37.7091 8.95915i 1.40925 0.334819i
717717 12.6583 + 9.82694i 0.472733 + 0.366994i
718718 5.53724 + 47.2612i 0.206648 + 1.76377i
719719 −10.0890 + 17.4746i −0.376255 + 0.651693i −0.990514 0.137412i 0.956122π-0.956122\pi
0.614259 + 0.789105i 0.289455π0.289455\pi
720720 35.9342 31.3295i 1.33919 1.16758i
721721 0 0
722722 7.92462 + 3.41576i 0.294924 + 0.127121i
723723 −3.69201 + 26.8721i −0.137307 + 0.999384i
724724 6.22565 20.8369i 0.231374 0.774396i
725725 −31.5580 + 18.2200i −1.17203 + 0.676674i
726726 0.110553 0.182972i 0.00410300 0.00679074i
727727 1.62103i 0.0601206i 0.999548 + 0.0300603i 0.00956993π0.00956993\pi
−0.999548 + 0.0300603i 0.990430π0.990430\pi
728728 0 0
729729 −18.4353 19.7266i −0.682789 0.730615i
730730 −4.74657 6.37208i −0.175678 0.235841i
731731 2.20936 + 3.82673i 0.0817163 + 0.141537i
732732 3.26052 + 33.6043i 0.120512 + 1.24205i
733733 −13.9026 + 24.0801i −0.513505 + 0.889417i 0.486372 + 0.873752i 0.338320π0.338320\pi
−0.999877 + 0.0156654i 0.995013π0.995013\pi
734734 −4.39181 + 10.1891i −0.162105 + 0.376086i
735735 0 0
736736 −10.0304 + 20.0409i −0.369725 + 0.738716i
737737 25.8786 + 14.9410i 0.953252 + 0.550360i
738738 −14.2879 + 17.6670i −0.525943 + 0.650331i
739739 25.1030 14.4932i 0.923429 0.533142i 0.0387013 0.999251i 0.487678π-0.487678\pi
0.884727 + 0.466109i 0.154345π0.154345\pi
740740 7.87961 + 33.1653i 0.289660 + 1.21918i
741741 −1.99724 4.89971i −0.0733704 0.179995i
742742 0 0
743743 10.4018 0.381604 0.190802 0.981629i 0.438891π-0.438891\pi
0.190802 + 0.981629i 0.438891π0.438891\pi
744744 −5.08175 23.4558i −0.186306 0.859932i
745745 13.3435 + 23.1117i 0.488870 + 0.846747i
746746 −0.162308 1.38532i −0.00594251 0.0507203i
747747 −3.07815 12.0287i −0.112624 0.440107i
748748 2.76888 2.61518i 0.101240 0.0956205i
749749 0 0
750750 −1.12027 + 56.2688i −0.0409063 + 2.05465i
751751 14.7045 + 8.48962i 0.536573 + 0.309791i 0.743689 0.668526i 0.233074π-0.233074\pi
−0.207116 + 0.978316i 0.566408π0.566408\pi
752752 32.4763 16.3550i 1.18429 0.596406i
753753 4.22745 + 3.28186i 0.154057 + 0.119598i
754754 2.42838 + 3.26000i 0.0884363 + 0.118722i
755755 52.4922 1.91039
756756 0 0
757757 −10.9716 −0.398770 −0.199385 0.979921i 0.563894π-0.563894\pi
−0.199385 + 0.979921i 0.563894π0.563894\pi
758758 15.9067 + 21.3541i 0.577757 + 0.775617i
759759 17.9055 + 13.9005i 0.649929 + 0.504555i
760760 25.9147 30.9358i 0.940026 1.12216i
761761 −10.0723 5.81526i −0.365121 0.210803i 0.306204 0.951966i 0.400941π-0.400941\pi
−0.671325 + 0.741163i 0.734274π0.734274\pi
762762 0.801702 40.2680i 0.0290426 1.45876i
763763 0 0
764764 1.69343 + 1.79295i 0.0612660 + 0.0648666i
765765 1.70331 + 6.65613i 0.0615833 + 0.240653i
766766 −0.596206 5.08871i −0.0215418 0.183863i
767767 −3.35120 5.80445i −0.121005 0.209586i
768768 6.87478 26.8466i 0.248072 0.968742i
769769 0.123424 0.00445080 0.00222540 0.999998i 0.499292π-0.499292\pi
0.00222540 + 0.999998i 0.499292π0.499292\pi
770770 0 0
771771 4.81794 + 11.8196i 0.173514 + 0.425671i
772772 −30.7118 + 7.29669i −1.10534 + 0.262614i
773773 −13.4620 + 7.77229i −0.484194 + 0.279550i −0.722163 0.691723i 0.756852π-0.756852\pi
0.237968 + 0.971273i 0.423519π0.423519\pi
774774 20.4498 25.2863i 0.735053 0.908896i
775775 45.7498 + 26.4137i 1.64338 + 0.948808i
776776 −13.1365 35.9997i −0.471573 1.29231i
777777 0 0
778778 8.18188 18.9821i 0.293334 0.680541i
779779 −9.61685 + 16.6569i −0.344559 + 0.596794i
780780 11.6515 1.13051i 0.417190 0.0404786i
781781 15.1240 + 26.1956i 0.541181 + 0.937353i
782782 −1.92940 2.59015i −0.0689953 0.0926235i
783783 16.1067 + 6.99304i 0.575607 + 0.249911i
784784 0 0
785785 9.48806i 0.338643i
786786 2.88422 4.77358i 0.102877 0.170268i
787787 −36.3048 + 20.9606i −1.29413 + 0.747164i −0.979383 0.202014i 0.935252π-0.935252\pi
−0.314743 + 0.949177i 0.601918π0.601918\pi
788788 33.3182 + 9.95483i 1.18691 + 0.354626i
789789 −5.23459 + 38.0996i −0.186356 + 1.35638i
790790 −35.7463 15.4078i −1.27180 0.548185i
791791 0 0
792792 −25.2792 12.1111i −0.898258 0.430348i
793793 −4.14510 + 7.17953i −0.147197 + 0.254953i
794794 1.00337 + 8.56394i 0.0356083 + 0.303923i
795795 3.30824 + 2.56826i 0.117331 + 0.0910868i
796796 2.11161 + 8.88779i 0.0748442 + 0.315019i
797797 20.7831i 0.736175i −0.929791 0.368088i 0.880013π-0.880013\pi
0.929791 0.368088i 0.119987π-0.119987\pi
798798 0 0
799799 5.24038i 0.185391i
800800 33.5901 + 50.9184i 1.18759 + 1.80024i
801801 −4.65768 + 16.6304i −0.164571 + 0.587605i
802802 10.2397 1.19971i 0.361577 0.0423632i
803803 −2.33589 + 4.04587i −0.0824316 + 0.142776i
804804 −12.9737 + 28.5235i −0.457548 + 1.00595i
805805 0 0
806806 2.33266 5.41181i 0.0821645 0.190623i
807807 −17.1831 2.36082i −0.604874 0.0831048i
808808 15.4797 + 12.9673i 0.544576 + 0.456187i
809809 1.65777 0.957115i 0.0582842 0.0336504i −0.470575 0.882360i 0.655953π-0.655953\pi
0.528859 + 0.848710i 0.322620π0.322620\pi
810810 41.2225 29.2849i 1.44841 1.02897i
811811 4.68171i 0.164397i 0.996616 + 0.0821986i 0.0261942π0.0261942\pi
−0.996616 + 0.0821986i 0.973806π0.973806\pi
812812 0 0
813813 15.4196 + 37.8280i 0.540789 + 1.32668i
814814 16.0735 11.9732i 0.563378 0.419660i
815815 −36.3351 62.9342i −1.27276 2.20449i
816816 3.00996 + 2.62513i 0.105370 + 0.0918978i
817817 13.7643 23.8405i 0.481552 0.834073i
818818 −26.2209 11.3020i −0.916792 0.395166i
819819 0 0
820820 −29.2186 30.9358i −1.02036 1.08033i
821821 1.44771 + 0.835834i 0.0505253 + 0.0291708i 0.525050 0.851071i 0.324047π-0.324047\pi
−0.474525 + 0.880242i 0.657380π0.657380\pi
822822 −19.7458 + 10.8821i −0.688715 + 0.379555i
823823 23.7559 13.7155i 0.828078 0.478091i −0.0251160 0.999685i 0.507996π-0.507996\pi
0.853194 + 0.521593i 0.174662π0.174662\pi
824824 −5.13724 + 29.2761i −0.178964 + 1.01988i
825825 57.1350 23.2896i 1.98918 0.810840i
826826 0 0
827827 −25.9621 −0.902789 −0.451395 0.892324i 0.649073π-0.649073\pi
−0.451395 + 0.892324i 0.649073π0.649073\pi
828828 −12.6951 + 20.0963i −0.441184 + 0.698394i
829829 −14.5674 25.2315i −0.505948 0.876328i −0.999976 0.00688179i 0.997809π-0.997809\pi
0.494028 0.869446i 0.335524π-0.335524\pi
830830 23.0954 2.70591i 0.801652 0.0939234i
831831 −6.85100 + 49.8646i −0.237659 + 1.72979i
832832 5.20555 4.38265i 0.180470 0.151941i
833833 0 0
834834 0.541480 27.1975i 0.0187499 0.941774i
835835 −66.6265 38.4668i −2.30571 1.33120i
836836 −22.7348 6.79272i −0.786300 0.234931i
837837 −2.89536 25.2906i −0.100078 0.874173i
838838 1.50711 1.12265i 0.0520623 0.0387812i
839839 14.3863 0.496671 0.248336 0.968674i 0.420116π-0.420116\pi
0.248336 + 0.968674i 0.420116π0.420116\pi
840840 0 0
841841 17.5804 0.606221
842842 8.30031 6.18290i 0.286048 0.213077i
843843 −24.7360 + 31.8631i −0.851954 + 1.09742i
844844 2.13138 + 0.636813i 0.0733650 + 0.0219200i
845845 −42.2381 24.3862i −1.45303 0.838909i
846846 35.9973 13.8443i 1.23761 0.475978i
847847 0 0
848848 2.43059 + 0.138880i 0.0834668 + 0.00476916i
849849 −29.9022 4.10833i −1.02624 0.140997i
850850 −8.73138 + 1.02299i −0.299484 + 0.0350882i
851851 −8.49827 14.7194i −0.291317 0.504576i
852852 −25.8096 + 18.4383i −0.884223 + 0.631686i
853853 49.4483 1.69308 0.846539 0.532327i 0.178682π-0.178682\pi
0.846539 + 0.532327i 0.178682π0.178682\pi
854854 0 0
855855 30.6062 29.9237i 1.04671 1.02337i
856856 −3.43531 0.602812i −0.117416 0.0206037i
857857 −10.0283 + 5.78983i −0.342560 + 0.197777i −0.661403 0.750030i 0.730039π-0.730039\pi
0.318844 + 0.947807i 0.396705π0.396705\pi
858858 −3.32209 6.02804i −0.113414 0.205794i
859859 6.27765 + 3.62441i 0.214191 + 0.123663i 0.603258 0.797546i 0.293869π-0.293869\pi
−0.389067 + 0.921210i 0.627202π0.627202\pi
860860 41.8198 + 44.2775i 1.42604 + 1.50985i
861861 0 0
862862 −0.232377 0.100162i −0.00791479 0.00341152i
863863 −10.4435 + 18.0886i −0.355500 + 0.615744i −0.987203 0.159466i 0.949023π-0.949023\pi
0.631703 + 0.775210i 0.282356π0.282356\pi
864864 10.0807 27.6112i 0.342952 0.939353i
865865 −11.0946 19.2164i −0.377228 0.653378i
866866 −17.2956 + 12.8835i −0.587728 + 0.437799i
867867 26.7336 10.8973i 0.907920 0.370090i
868868 0 0
869869 22.8869i 0.776385i
870870 −17.0062 + 28.1465i −0.576565 + 0.954255i
871871 −6.66347 + 3.84716i −0.225783 + 0.130356i
872872 −5.81744 + 6.94460i −0.197004 + 0.235174i
873873 −10.0767 39.3774i −0.341044 1.33272i
874874 −7.96462 + 18.4781i −0.269407 + 0.625030i
875875 0 0
876876 −4.45937 2.02831i −0.150668 0.0685304i
877877 28.5877 49.5154i 0.965339 1.67202i 0.256639 0.966507i 0.417385π-0.417385\pi
0.708701 0.705509i 0.249282π-0.249282\pi
878878 42.0053 4.92144i 1.41761 0.166091i
879879 1.28250 1.65202i 0.0432576 0.0557211i
880880 28.7987 43.8915i 0.970804 1.47958i
881881 26.8284i 0.903870i −0.892051 0.451935i 0.850734π-0.850734\pi
0.892051 0.451935i 0.149266π-0.149266\pi
882882 0 0
883883 27.6059i 0.929012i 0.885570 + 0.464506i 0.153768π0.153768\pi
−0.885570 + 0.464506i 0.846232π0.846232\pi
884884 0.226688 + 0.954128i 0.00762433 + 0.0320908i
885885 33.2494 42.8294i 1.11767 1.43969i
886886 0.825451 + 7.04537i 0.0277316 + 0.236694i
887887 13.1703 22.8116i 0.442215 0.765939i −0.555639 0.831424i 0.687526π-0.687526\pi
0.997854 + 0.0654853i 0.0208595π0.0208595\pi
888888 14.1246 + 15.5640i 0.473990 + 0.522292i
889889 0 0
890890 −29.7022 12.8026i −0.995622 0.429144i
891891 −25.4060 15.4423i −0.851135 0.517335i
892892 −45.2874 13.5310i −1.51634 0.453051i
893893 28.2736 16.3238i 0.946139 0.546254i
894894 14.0832 + 8.50912i 0.471012 + 0.284588i
895895 76.9909i 2.57352i
896896 0 0
897897 −5.40493 + 2.20318i −0.180465 + 0.0735621i
898898 −12.2481 16.4426i −0.408724 0.548696i
899899 8.27753 + 14.3371i 0.276071 + 0.478169i
900900 30.0942 + 57.2751i 1.00314 + 1.90917i
901901 −0.175430 + 0.303854i −0.00584443 + 0.0101228i
902902 −9.90347 + 22.9762i −0.329749 + 0.765024i
903903 0 0
904904 52.9010 19.3039i 1.75946 0.642038i
905905 37.4111 + 21.5993i 1.24359 + 0.717985i
906906 28.3452 15.6212i 0.941705 0.518980i
907907 9.51618 5.49417i 0.315980 0.182431i −0.333619 0.942708i 0.608270π-0.608270\pi
0.649599 + 0.760277i 0.274937π0.274937\pi
908908 23.9305 5.68556i 0.794163 0.188682i
909909 14.9733 + 15.3148i 0.496634 + 0.507961i
910910 0 0
911911 6.42795 0.212968 0.106484 0.994314i 0.466041π-0.466041\pi
0.106484 + 0.994314i 0.466041π0.466041\pi
912912 4.78742 24.4170i 0.158527 0.808526i
913913 −6.83609 11.8404i −0.226241 0.391862i
914914 3.26779 + 27.8911i 0.108089 + 0.922556i
915915 −66.4414 9.12852i −2.19649 0.301779i
916916 12.4000 + 13.1288i 0.409709 + 0.433787i
917917 0 0
918918 2.90057 + 3.08734i 0.0957331 + 0.101898i
919919 47.7559 + 27.5719i 1.57532 + 0.909512i 0.995499 + 0.0947691i 0.0302113π0.0302113\pi
0.579822 + 0.814743i 0.303122π0.303122\pi
920920 −34.1257 28.5869i −1.12509 0.942481i
921921 36.1418 46.5552i 1.19091 1.53404i
922922 14.6923 + 19.7238i 0.483864 + 0.649569i
923923 −7.78856 −0.256364
924924 0 0
925925 −46.2628 −1.52111
926926 12.9514 + 17.3868i 0.425610 + 0.571365i
927927 −8.50246 + 30.3583i −0.279258 + 0.997096i
928928 1.13777 + 19.0823i 0.0373493 + 0.626406i
929929 −41.5330 23.9791i −1.36265 0.786728i −0.372677 0.927961i 0.621560π-0.621560\pi
−0.989976 + 0.141233i 0.954893π0.954893\pi
930930 47.6645 + 0.948960i 1.56298 + 0.0311176i
931931 0 0
932932 11.0123 10.4010i 0.360719 0.340697i
933933 −6.29739 + 45.8352i −0.206167 + 1.50058i
934934 3.46939 + 29.6118i 0.113522 + 0.968929i
935935 3.78278 + 6.55197i 0.123710 + 0.214272i
936936 5.95523 4.07784i 0.194653 0.133288i
937937 −36.7501 −1.20057 −0.600287 0.799784i 0.704947π-0.704947\pi
−0.600287 + 0.799784i 0.704947π0.704947\pi
938938 0 0
939939 14.9574 6.09698i 0.488115 0.198968i
940940 16.6961 + 70.2738i 0.544566 + 2.29208i
941941 −34.3080 + 19.8077i −1.11841 + 0.645714i −0.940994 0.338422i 0.890107π-0.890107\pi
−0.177415 + 0.984136i 0.556774π0.556774\pi
942942 2.82356 + 5.12344i 0.0919965 + 0.166931i
943943 18.3744 + 10.6085i 0.598353 + 0.345459i
944944 1.79798 31.4671i 0.0585193 1.02417i
945945 0 0
946946 14.1745 32.8852i 0.460854 1.06919i
947947 −5.92594 + 10.2640i −0.192567 + 0.333536i −0.946100 0.323874i 0.895015π-0.895015\pi
0.753533 + 0.657410i 0.228348π0.228348\pi
948948 −23.8878 + 2.31776i −0.775840 + 0.0752773i
949949 −0.601466 1.04177i −0.0195244 0.0338172i
950950 32.7176 + 43.9221i 1.06150 + 1.42502i
951951 −17.6480 43.2948i −0.572275 1.40393i
952952 0 0
953953 39.8193i 1.28987i 0.764236 + 0.644937i 0.223116π0.223116\pi
−0.764236 + 0.644937i 0.776884π0.776884\pi
954954 2.55070 + 0.402328i 0.0825819 + 0.0130259i
955955 −4.24264 + 2.44949i −0.137289 + 0.0792636i
956956 −5.29728 + 17.7297i −0.171326 + 0.573418i
957957 19.1554 + 2.63180i 0.619207 + 0.0850741i
958958 −9.86972 4.25416i −0.318876 0.137446i
959959 0 0
960960 48.7274 + 25.6132i 1.57267 + 0.826664i
961961 −3.50000 + 6.06218i −0.112903 + 0.195554i
962962 0.600546 + 5.12576i 0.0193624 + 0.165261i
963963 −3.56229 0.997694i −0.114793 0.0321502i
964964 −30.4725 + 7.23984i −0.981453 + 0.233179i
965965 62.7045i 2.01853i
966966 0 0
967967 23.4388i 0.753741i −0.926266 0.376871i 0.877000π-0.877000\pi
0.926266 0.376871i 0.123000π-0.123000\pi
968968 0.243134 + 0.0426641i 0.00781462 + 0.00137127i
969969 2.83253 + 2.19896i 0.0909941 + 0.0706408i
970970 75.6054 8.85811i 2.42754 0.284417i
971971 5.55718 9.62532i 0.178338 0.308891i −0.762973 0.646430i 0.776261π-0.776261\pi
0.941312 + 0.337539i 0.109595π0.109595\pi
972972 13.5447 28.0810i 0.434447 0.900697i
973973 0 0
974974 −8.64155 + 20.0485i −0.276893 + 0.642396i
975975 −2.16242 + 15.7391i −0.0692529 + 0.504054i
976976 −34.8191 + 17.5349i −1.11453 + 0.561278i
977977 9.58812 5.53570i 0.306751 0.177103i −0.338721 0.940887i 0.609994π-0.609994\pi
0.645472 + 0.763784i 0.276661π0.276661\pi
978978 −38.3492 23.1707i −1.22627 0.740918i
979979 19.0171i 0.607790i
980980 0 0
981981 −6.87062 + 6.71741i −0.219362 + 0.214470i
982982 −45.9515 + 34.2293i −1.46637 + 1.09230i
983983 15.9716 + 27.6637i 0.509416 + 0.882334i 0.999941 + 0.0109070i 0.00347189π0.00347189\pi
−0.490524 + 0.871427i 0.663195π0.663195\pi
984984 −24.9839 8.00977i −0.796459 0.255342i
985985 −34.5373 + 59.8204i −1.10045 + 1.90604i
986986 −2.52995 1.09049i −0.0805700 0.0347282i
987987 0 0
988988 4.44171 4.19516i 0.141310 0.133466i
989989 −26.2988 15.1836i −0.836252 0.482811i
990990 35.0133 43.2941i 1.11280 1.37598i
991991 −18.0000 + 10.3923i −0.571789 + 0.330122i −0.757863 0.652413i 0.773757π-0.773757\pi
0.186075 + 0.982536i 0.440423π0.440423\pi
992992 23.1327 15.2603i 0.734465 0.484515i
993993 −9.54109 23.4066i −0.302777 0.742785i
994994 0 0
995995 −18.1463 −0.575275
996996 11.6660 8.33413i 0.369650 0.264077i
997997 −20.7685 35.9721i −0.657745 1.13925i −0.981198 0.193003i 0.938177π-0.938177\pi
0.323453 0.946244i 0.395156π-0.395156\pi
998998 −42.6537 + 4.99740i −1.35018 + 0.158190i
999999 13.2698 + 17.9129i 0.419838 + 0.566738i
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 588.2.n.d.275.1 24
3.2 odd 2 inner 588.2.n.d.275.12 24
4.3 odd 2 588.2.n.h.275.8 24
7.2 even 3 588.2.e.f.491.24 yes 24
7.3 odd 6 588.2.n.h.263.6 24
7.4 even 3 588.2.n.h.263.5 24
7.5 odd 6 588.2.e.f.491.23 yes 24
7.6 odd 2 inner 588.2.n.d.275.2 24
12.11 even 2 588.2.n.h.275.5 24
21.2 odd 6 588.2.e.f.491.1 24
21.5 even 6 588.2.e.f.491.2 yes 24
21.11 odd 6 588.2.n.h.263.8 24
21.17 even 6 588.2.n.h.263.7 24
21.20 even 2 inner 588.2.n.d.275.11 24
28.3 even 6 inner 588.2.n.d.263.11 24
28.11 odd 6 inner 588.2.n.d.263.12 24
28.19 even 6 588.2.e.f.491.4 yes 24
28.23 odd 6 588.2.e.f.491.3 yes 24
28.27 even 2 588.2.n.h.275.7 24
84.11 even 6 inner 588.2.n.d.263.1 24
84.23 even 6 588.2.e.f.491.22 yes 24
84.47 odd 6 588.2.e.f.491.21 yes 24
84.59 odd 6 inner 588.2.n.d.263.2 24
84.83 odd 2 588.2.n.h.275.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.f.491.1 24 21.2 odd 6
588.2.e.f.491.2 yes 24 21.5 even 6
588.2.e.f.491.3 yes 24 28.23 odd 6
588.2.e.f.491.4 yes 24 28.19 even 6
588.2.e.f.491.21 yes 24 84.47 odd 6
588.2.e.f.491.22 yes 24 84.23 even 6
588.2.e.f.491.23 yes 24 7.5 odd 6
588.2.e.f.491.24 yes 24 7.2 even 3
588.2.n.d.263.1 24 84.11 even 6 inner
588.2.n.d.263.2 24 84.59 odd 6 inner
588.2.n.d.263.11 24 28.3 even 6 inner
588.2.n.d.263.12 24 28.11 odd 6 inner
588.2.n.d.275.1 24 1.1 even 1 trivial
588.2.n.d.275.2 24 7.6 odd 2 inner
588.2.n.d.275.11 24 21.20 even 2 inner
588.2.n.d.275.12 24 3.2 odd 2 inner
588.2.n.h.263.5 24 7.4 even 3
588.2.n.h.263.6 24 7.3 odd 6
588.2.n.h.263.7 24 21.17 even 6
588.2.n.h.263.8 24 21.11 odd 6
588.2.n.h.275.5 24 12.11 even 2
588.2.n.h.275.6 24 84.83 odd 2
588.2.n.h.275.7 24 28.27 even 2
588.2.n.h.275.8 24 4.3 odd 2