Properties

Label 588.2.n.d.263.6
Level 588588
Weight 22
Character 588.263
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 263.6
Character χ\chi == 588.263
Dual form 588.2.n.d.275.6

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+(0.287629+1.38466i)q2+(1.66143+0.489533i)q3+(1.834540.796533i)q4+(1.085700.626827i)q5+(1.15571+2.15971i)q6+(1.630592.31110i)q8+(2.52072+1.62665i)q9+(0.555662+1.68361i)q10+(2.529144.38059i)q11+(2.658032.22145i)q12+4.41798q13+(2.110660.509947i)q15+(2.73107+2.92254i)q16+(5.069202.92671i)q17+(2.97738+3.02245i)q18+(1.326540.765881i)q19+(2.49104+0.285146i)q20+(5.33816+4.76197i)q22+(0.156785+0.271560i)q23+(3.840473.04151i)q24+(1.71417+2.96904i)q25+(1.27074+6.11738i)q26+(3.39170+3.93654i)q27+5.53862iq29+(0.0990132+3.06922i)q30+(4.242642.44949i)q31+(4.83225+2.94098i)q32+(6.346436.03996i)q33+(5.510536.17729i)q34+(3.328674.99199i)q36+(2.66908+4.62298i)q37+(0.678928+2.05710i)q38+(7.34017+2.16275i)q39+(0.3216663.53125i)q40+1.97938iq41+3.18613iq43+(8.12909+6.02183i)q44+(3.75636+0.185997i)q45+(0.421113+0.138985i)q46+(5.748139.95606i)q47+(3.10681+6.19256i)q48+(3.618053.22752i)q50+(6.989427.34407i)q51+(8.104963.51907i)q52+(11.0767+6.39513i)q53+(6.42631+3.56407i)q546.34133iq55+(2.578890.623072i)q57+(7.669081.59307i)q58+(3.98351+6.89964i)q59+(4.278290.745696i)q60+(0.151445+0.262310i)q61+(4.612005.17005i)q62+(2.682367.53691i)q64+(4.796592.76931i)q65+(6.53785+10.5249i)q66+(9.131225.27191i)q67+(6.96844+9.40695i)q68+(0.127550+0.527930i)q694.53490q71+(7.869603.17322i)q72+(0.707107+1.22474i)q73+(7.16894+2.36605i)q74+(4.30143+4.09371i)q75+(3.04365+0.348402i)q76+(5.10590+9.54154i)q78+(6.000003.46410i)q79+(4.79704+1.46108i)q80+(3.70801+8.20065i)q81+(2.740760.569326i)q826.78340q837.33816q85+(4.411690.916423i)q86+(2.71134+9.20204i)q87+(6.0000012.9880i)q88+(4.15480+2.39878i)q89+(1.33798+5.14777i)q90+(0.07132220.623072i)q92+(5.849756.14657i)q93+(15.43905.09553i)q94+(0.9601501.66303i)q95+(9.46816+2.52070i)q9613.6844q97+(13.50096.92820i)q99+O(q100)q+(-0.287629 + 1.38466i) q^{2} +(1.66143 + 0.489533i) q^{3} +(-1.83454 - 0.796533i) q^{4} +(1.08570 - 0.626827i) q^{5} +(-1.15571 + 2.15971i) q^{6} +(1.63059 - 2.31110i) q^{8} +(2.52072 + 1.62665i) q^{9} +(0.555662 + 1.68361i) q^{10} +(2.52914 - 4.38059i) q^{11} +(-2.65803 - 2.22145i) q^{12} +4.41798 q^{13} +(2.11066 - 0.509947i) q^{15} +(2.73107 + 2.92254i) q^{16} +(-5.06920 - 2.92671i) q^{17} +(-2.97738 + 3.02245i) q^{18} +(1.32654 - 0.765881i) q^{19} +(-2.49104 + 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +(0.156785 + 0.271560i) q^{23} +(3.84047 - 3.04151i) q^{24} +(-1.71417 + 2.96904i) q^{25} +(-1.27074 + 6.11738i) q^{26} +(3.39170 + 3.93654i) q^{27} +5.53862i q^{29} +(0.0990132 + 3.06922i) q^{30} +(-4.24264 - 2.44949i) q^{31} +(-4.83225 + 2.94098i) q^{32} +(6.34643 - 6.03996i) q^{33} +(5.51053 - 6.17729i) q^{34} +(-3.32867 - 4.99199i) q^{36} +(2.66908 + 4.62298i) q^{37} +(0.678928 + 2.05710i) q^{38} +(7.34017 + 2.16275i) q^{39} +(0.321666 - 3.53125i) q^{40} +1.97938i q^{41} +3.18613i q^{43} +(-8.12909 + 6.02183i) q^{44} +(3.75636 + 0.185997i) q^{45} +(-0.421113 + 0.138985i) q^{46} +(-5.74813 - 9.95606i) q^{47} +(3.10681 + 6.19256i) q^{48} +(-3.61805 - 3.22752i) q^{50} +(-6.98942 - 7.34407i) q^{51} +(-8.10496 - 3.51907i) q^{52} +(11.0767 + 6.39513i) q^{53} +(-6.42631 + 3.56407i) q^{54} -6.34133i q^{55} +(2.57889 - 0.623072i) q^{57} +(-7.66908 - 1.59307i) q^{58} +(-3.98351 + 6.89964i) q^{59} +(-4.27829 - 0.745696i) q^{60} +(0.151445 + 0.262310i) q^{61} +(4.61200 - 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} +(4.79659 - 2.76931i) q^{65} +(6.53785 + 10.5249i) q^{66} +(-9.13122 - 5.27191i) q^{67} +(6.96844 + 9.40695i) q^{68} +(0.127550 + 0.527930i) q^{69} -4.53490 q^{71} +(7.86960 - 3.17322i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(-7.16894 + 2.36605i) q^{74} +(-4.30143 + 4.09371i) q^{75} +(-3.04365 + 0.348402i) q^{76} +(-5.10590 + 9.54154i) q^{78} +(6.00000 - 3.46410i) q^{79} +(4.79704 + 1.46108i) q^{80} +(3.70801 + 8.20065i) q^{81} +(-2.74076 - 0.569326i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-4.41169 - 0.916423i) q^{86} +(-2.71134 + 9.20204i) q^{87} +(-6.00000 - 12.9880i) q^{88} +(-4.15480 + 2.39878i) q^{89} +(-1.33798 + 5.14777i) q^{90} +(-0.0713222 - 0.623072i) q^{92} +(-5.84975 - 6.14657i) q^{93} +(15.4390 - 5.09553i) q^{94} +(0.960150 - 1.66303i) q^{95} +(-9.46816 + 2.52070i) q^{96} -13.6844 q^{97} +(13.5009 - 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(23)e\left(\frac{2}{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 −0.287629 + 1.38466i −0.203384 + 0.979099i
33 1.66143 + 0.489533i 0.959228 + 0.282632i
44 −1.83454 0.796533i −0.917270 0.398266i
55 1.08570 0.626827i 0.485538 0.280326i −0.237183 0.971465i 0.576224π-0.576224\pi
0.722722 + 0.691139i 0.242891π0.242891\pi
66 −1.15571 + 2.15971i −0.471817 + 0.881697i
77 0 0
88 1.63059 2.31110i 0.576500 0.817097i
99 2.52072 + 1.62665i 0.840238 + 0.542217i
1010 0.555662 + 1.68361i 0.175716 + 0.532404i
1111 2.52914 4.38059i 0.762563 1.32080i −0.178962 0.983856i 0.557274π-0.557274\pi
0.941525 0.336942i 0.109393π-0.109393\pi
1212 −2.65803 2.22145i −0.767308 0.641278i
1313 4.41798 1.22533 0.612664 0.790344i 0.290098π-0.290098\pi
0.612664 + 0.790344i 0.290098π0.290098\pi
1414 0 0
1515 2.11066 0.509947i 0.544971 0.131668i
1616 2.73107 + 2.92254i 0.682768 + 0.730636i
1717 −5.06920 2.92671i −1.22946 0.709831i −0.262545 0.964920i 0.584562π-0.584562\pi
−0.966918 + 0.255089i 0.917895π0.917895\pi
1818 −2.97738 + 3.02245i −0.701775 + 0.712398i
1919 1.32654 0.765881i 0.304330 0.175705i −0.340056 0.940405i 0.610446π-0.610446\pi
0.644386 + 0.764700i 0.277113π0.277113\pi
2020 −2.49104 + 0.285146i −0.557014 + 0.0637607i
2121 0 0
2222 5.33816 + 4.76197i 1.13810 + 1.01525i
2323 0.156785 + 0.271560i 0.0326920 + 0.0566242i 0.881908 0.471421i 0.156259π-0.156259\pi
−0.849217 + 0.528045i 0.822925π0.822925\pi
2424 3.84047 3.04151i 0.783933 0.620845i
2525 −1.71417 + 2.96904i −0.342835 + 0.593808i
2626 −1.27074 + 6.11738i −0.249212 + 1.19972i
2727 3.39170 + 3.93654i 0.652733 + 0.757588i
2828 0 0
2929 5.53862i 1.02850i 0.857642 + 0.514248i 0.171929π0.171929\pi
−0.857642 + 0.514248i 0.828071π0.828071\pi
3030 0.0990132 + 3.06922i 0.0180773 + 0.560360i
3131 −4.24264 2.44949i −0.762001 0.439941i 0.0680129 0.997684i 0.478334π-0.478334\pi
−0.830014 + 0.557743i 0.811667π0.811667\pi
3232 −4.83225 + 2.94098i −0.854229 + 0.519897i
3333 6.34643 6.03996i 1.10477 1.05142i
3434 5.51053 6.17729i 0.945048 1.05940i
3535 0 0
3636 −3.32867 4.99199i −0.554778 0.831998i
3737 2.66908 + 4.62298i 0.438794 + 0.760013i 0.997597 0.0692872i 0.0220725π-0.0220725\pi
−0.558803 + 0.829301i 0.688739π0.688739\pi
3838 0.678928 + 2.05710i 0.110137 + 0.333705i
3939 7.34017 + 2.16275i 1.17537 + 0.346317i
4040 0.321666 3.53125i 0.0508598 0.558340i
4141 1.97938i 0.309127i 0.987983 + 0.154564i 0.0493971π0.0493971\pi
−0.987983 + 0.154564i 0.950603π0.950603\pi
4242 0 0
4343 3.18613i 0.485881i 0.970041 + 0.242940i 0.0781119π0.0781119\pi
−0.970041 + 0.242940i 0.921888π0.921888\pi
4444 −8.12909 + 6.02183i −1.22551 + 0.907825i
4545 3.75636 + 0.185997i 0.559965 + 0.0277268i
4646 −0.421113 + 0.138985i −0.0620897 + 0.0204922i
4747 −5.74813 9.95606i −0.838451 1.45224i −0.891189 0.453632i 0.850128π-0.850128\pi
0.0527378 0.998608i 0.483205π-0.483205\pi
4848 3.10681 + 6.19256i 0.448429 + 0.893818i
4949 0 0
5050 −3.61805 3.22752i −0.511669 0.456440i
5151 −6.98942 7.34407i −0.978715 1.02838i
5252 −8.10496 3.51907i −1.12396 0.488007i
5353 11.0767 + 6.39513i 1.52150 + 0.878439i 0.999678 + 0.0253856i 0.00808135π0.00808135\pi
0.521823 + 0.853054i 0.325252π0.325252\pi
5454 −6.42631 + 3.56407i −0.874509 + 0.485008i
5555 6.34133i 0.855064i
5656 0 0
5757 2.57889 0.623072i 0.341582 0.0825279i
5858 −7.66908 1.59307i −1.00700 0.209180i
5959 −3.98351 + 6.89964i −0.518608 + 0.898256i 0.481158 + 0.876634i 0.340216π0.340216\pi
−0.999766 + 0.0216222i 0.993117π0.993117\pi
6060 −4.27829 0.745696i −0.552324 0.0962689i
6161 0.151445 + 0.262310i 0.0193905 + 0.0335853i 0.875558 0.483113i 0.160494π-0.160494\pi
−0.856167 + 0.516699i 0.827161π0.827161\pi
6262 4.61200 5.17005i 0.585725 0.656597i
6363 0 0
6464 −2.68236 7.53691i −0.335295 0.942113i
6565 4.79659 2.76931i 0.594943 0.343491i
6666 6.53785 + 10.5249i 0.804754 + 1.29552i
6767 −9.13122 5.27191i −1.11556 0.644067i −0.175293 0.984516i 0.556087π-0.556087\pi
−0.940263 + 0.340450i 0.889421π0.889421\pi
6868 6.96844 + 9.40695i 0.845047 + 1.14076i
6969 0.127550 + 0.527930i 0.0153553 + 0.0635553i
7070 0 0
7171 −4.53490 −0.538194 −0.269097 0.963113i 0.586725π-0.586725\pi
−0.269097 + 0.963113i 0.586725π0.586725\pi
7272 7.86960 3.17322i 0.927442 0.373968i
7373 −0.707107 + 1.22474i −0.0827606 + 0.143346i −0.904435 0.426612i 0.859707π-0.859707\pi
0.821674 + 0.569958i 0.193040π0.193040\pi
7474 −7.16894 + 2.36605i −0.833372 + 0.275048i
7575 −4.30143 + 4.09371i −0.496686 + 0.472701i
7676 −3.04365 + 0.348402i −0.349130 + 0.0399645i
7777 0 0
7878 −5.10590 + 9.54154i −0.578130 + 1.08037i
7979 6.00000 3.46410i 0.675053 0.389742i −0.122936 0.992415i 0.539231π-0.539231\pi
0.797988 + 0.602673i 0.205898π0.205898\pi
8080 4.79704 + 1.46108i 0.536326 + 0.163354i
8181 3.70801 + 8.20065i 0.412001 + 0.911183i
8282 −2.74076 0.569326i −0.302666 0.0628716i
8383 −6.78340 −0.744575 −0.372287 0.928118i 0.621426π-0.621426\pi
−0.372287 + 0.928118i 0.621426π0.621426\pi
8484 0 0
8585 −7.33816 −0.795935
8686 −4.41169 0.916423i −0.475725 0.0988204i
8787 −2.71134 + 9.20204i −0.290686 + 0.986563i
8888 −6.00000 12.9880i −0.639602 1.38453i
8989 −4.15480 + 2.39878i −0.440408 + 0.254270i −0.703771 0.710427i 0.748502π-0.748502\pi
0.263363 + 0.964697i 0.415168π0.415168\pi
9090 −1.33798 + 5.14777i −0.141035 + 0.542622i
9191 0 0
9292 −0.0713222 0.623072i −0.00743586 0.0649597i
9393 −5.84975 6.14657i −0.606591 0.637370i
9494 15.4390 5.09553i 1.59241 0.525564i
9595 0.960150 1.66303i 0.0985093 0.170623i
9696 −9.46816 + 2.52070i −0.966340 + 0.257268i
9797 −13.6844 −1.38944 −0.694719 0.719281i 0.744471π-0.744471\pi
−0.694719 + 0.719281i 0.744471π0.744471\pi
9898 0 0
9999 13.5009 6.92820i 1.35689 0.696311i
100100 5.50966 4.08142i 0.550966 0.408142i
101101 −3.52631 2.03591i −0.350881 0.202581i 0.314192 0.949359i 0.398266π-0.398266\pi
−0.665073 + 0.746778i 0.731600π0.731600\pi
102102 12.1794 7.56557i 1.20594 0.749103i
103103 11.3239 6.53788i 1.11578 0.644197i 0.175461 0.984486i 0.443859π-0.443859\pi
0.940321 + 0.340290i 0.110525π0.110525\pi
104104 7.20391 10.2104i 0.706402 1.00121i
105105 0 0
106106 −12.0410 + 13.4980i −1.16953 + 1.31104i
107107 1.95388 + 3.38422i 0.188889 + 0.327165i 0.944880 0.327417i 0.106178π-0.106178\pi
−0.755991 + 0.654582i 0.772845π0.772845\pi
108108 −3.08662 9.92335i −0.297010 0.954874i
109109 4.12398 7.14295i 0.395006 0.684170i −0.598096 0.801424i 0.704076π-0.704076\pi
0.993102 + 0.117254i 0.0374092π0.0374092\pi
110110 8.78055 + 1.82395i 0.837193 + 0.173907i
111111 2.17139 + 8.98737i 0.206100 + 0.853044i
112112 0 0
113113 6.72485i 0.632621i 0.948656 + 0.316311i 0.102444π0.102444\pi
−0.948656 + 0.316311i 0.897556π0.897556\pi
114114 0.120978 + 3.75008i 0.0113306 + 0.351227i
115115 0.340442 + 0.196554i 0.0317464 + 0.0183288i
116116 4.41169 10.1608i 0.409615 0.943408i
117117 11.1365 + 7.18651i 1.02957 + 0.664393i
118118 −8.40785 7.50032i −0.774005 0.690460i
119119 0 0
120120 2.26309 5.70947i 0.206591 0.521201i
121121 −7.29306 12.6320i −0.663006 1.14836i
122122 −0.406768 + 0.134251i −0.0368271 + 0.0121545i
123123 −0.968971 + 3.28861i −0.0873692 + 0.296524i
124124 5.83219 + 7.87309i 0.523746 + 0.707024i
125125 10.5662i 0.945073i
126126 0 0
127127 8.50404i 0.754611i 0.926089 + 0.377306i 0.123149π0.123149\pi
−0.926089 + 0.377306i 0.876851π0.876851\pi
128128 11.2075 1.54631i 0.990616 0.136676i
129129 −1.55972 + 5.29354i −0.137325 + 0.466070i
130130 2.45490 + 7.43815i 0.215309 + 0.652369i
131131 −4.20524 7.28368i −0.367413 0.636378i 0.621747 0.783218i 0.286423π-0.286423\pi
−0.989160 + 0.146840i 0.953090π0.953090\pi
132132 −16.4538 + 6.02541i −1.43212 + 0.524445i
133133 0 0
134134 9.92618 11.1272i 0.857491 0.961247i
135135 6.14989 + 2.14788i 0.529298 + 0.184860i
136136 −15.0297 + 6.94318i −1.28879 + 0.595372i
137137 −11.9136 6.87834i −1.01785 0.587657i −0.104370 0.994539i 0.533283π-0.533283\pi
−0.913481 + 0.406882i 0.866616π0.866616\pi
138138 −0.767688 + 0.0247657i −0.0653499 + 0.00210819i
139139 13.1652i 1.11666i −0.829620 0.558328i 0.811443π-0.811443\pi
0.829620 0.558328i 0.188557π-0.188557\pi
140140 0 0
141141 −4.67632 19.3552i −0.393817 1.63000i
142142 1.30437 6.27927i 0.109460 0.526945i
143143 11.1737 19.3534i 0.934389 1.61841i
144144 2.13029 + 11.8094i 0.177524 + 0.984116i
145145 3.47176 + 6.01326i 0.288314 + 0.499374i
146146 −1.49247 1.33137i −0.123517 0.110185i
147147 0 0
148148 −1.21417 10.6071i −0.0998046 0.871894i
149149 9.78354 5.64853i 0.801499 0.462745i −0.0424963 0.999097i 0.513531π-0.513531\pi
0.843995 + 0.536351i 0.180198π0.180198\pi
150150 −4.43116 7.13346i −0.361803 0.582445i
151151 9.61268 + 5.54988i 0.782269 + 0.451643i 0.837234 0.546845i 0.184171π-0.184171\pi
−0.0549650 + 0.998488i 0.517505π0.517505\pi
152152 0.393023 4.31461i 0.0318784 0.349961i
153153 −8.01729 15.6232i −0.648159 1.26306i
154154 0 0
155155 −6.14163 −0.493307
156156 −11.7431 9.81433i −0.940204 0.785776i
157157 7.39785 12.8135i 0.590413 1.02262i −0.403764 0.914863i 0.632298π-0.632298\pi
0.994177 0.107762i 0.0343684π-0.0343684\pi
158158 3.07081 + 9.30431i 0.244301 + 0.740211i
159159 15.2726 + 16.0475i 1.21119 + 1.27265i
160160 −3.40287 + 6.22200i −0.269020 + 0.491892i
161161 0 0
162162 −12.4216 + 2.77557i −0.975933 + 0.218070i
163163 −11.4887 + 6.63300i −0.899864 + 0.519537i −0.877156 0.480205i 0.840562π-0.840562\pi
−0.0227080 + 0.999742i 0.507229π0.507229\pi
164164 1.57664 3.63125i 0.123115 0.283553i
165165 3.10429 10.5357i 0.241668 0.820202i
166166 1.95110 9.39267i 0.151435 0.729012i
167167 −4.78624 −0.370371 −0.185185 0.982704i 0.559289π-0.559289\pi
−0.185185 + 0.982704i 0.559289π0.559289\pi
168168 0 0
169169 6.51854 0.501426
170170 2.11066 10.1608i 0.161881 0.779299i
171171 4.58966 + 0.227258i 0.350980 + 0.0173789i
172172 2.53786 5.84508i 0.193510 0.445684i
173173 −12.4811 + 7.20596i −0.948920 + 0.547859i −0.892745 0.450562i 0.851224π-0.851224\pi
−0.0561749 + 0.998421i 0.517890π0.517890\pi
174174 −11.9618 6.40104i −0.906822 0.485261i
175175 0 0
176176 19.7097 4.57220i 1.48568 0.344643i
177177 −9.99593 + 9.51322i −0.751340 + 0.715058i
178178 −2.12644 6.44293i −0.159383 0.482918i
179179 0.347150 0.601281i 0.0259472 0.0449419i −0.852760 0.522303i 0.825073π-0.825073\pi
0.878707 + 0.477361i 0.158406π0.158406\pi
180180 −6.74304 3.33328i −0.502597 0.248448i
181181 6.31042 0.469050 0.234525 0.972110i 0.424647π-0.424647\pi
0.234525 + 0.972110i 0.424647π0.424647\pi
182182 0 0
183183 0.123206 + 0.509947i 0.00910763 + 0.0376964i
184184 0.883254 + 0.0804567i 0.0651144 + 0.00593134i
185185 5.79562 + 3.34610i 0.426103 + 0.246010i
186186 10.1934 6.33196i 0.747419 0.464282i
187187 −25.6414 + 14.8041i −1.87509 + 1.08258i
188188 2.61485 + 22.8434i 0.190707 + 1.66602i
189189 0 0
190190 2.02655 + 1.80781i 0.147022 + 0.131152i
191191 1.95388 + 3.38422i 0.141378 + 0.244873i 0.928016 0.372541i 0.121513π-0.121513\pi
−0.786638 + 0.617415i 0.788180π0.788180\pi
192192 −0.766990 13.8352i −0.0553527 0.998467i
193193 −0.785825 + 1.36109i −0.0565649 + 0.0979733i −0.892921 0.450213i 0.851348π-0.851348\pi
0.836356 + 0.548186i 0.184681π0.184681\pi
194194 3.93602 18.9481i 0.282590 1.36040i
195195 9.32487 2.25294i 0.667768 0.161336i
196196 0 0
197197 1.83285i 0.130585i 0.997866 + 0.0652924i 0.0207980π0.0207980\pi
−0.997866 + 0.0652924i 0.979202π0.979202\pi
198198 5.70992 + 20.6869i 0.405786 + 1.47015i
199199 −3.17910 1.83546i −0.225361 0.130112i 0.383069 0.923720i 0.374867π-0.374867\pi
−0.608430 + 0.793608i 0.708200π0.708200\pi
200200 4.06663 + 8.80291i 0.287554 + 0.622460i
201201 −12.5901 13.2290i −0.888039 0.933099i
202202 3.83331 4.29713i 0.269710 0.302345i
203203 0 0
204204 6.97258 + 19.0403i 0.488178 + 1.33309i
205205 1.24073 + 2.14901i 0.0866563 + 0.150093i
206206 5.79562 + 17.5602i 0.403800 + 1.22348i
207207 −0.0465225 + 0.939560i −0.00323354 + 0.0653039i
208208 12.0658 + 12.9117i 0.836614 + 0.895267i
209209 7.74807i 0.535945i
210210 0 0
211211 14.8763i 1.02413i −0.858948 0.512063i 0.828881π-0.828881\pi
0.858948 0.512063i 0.171119π-0.171119\pi
212212 −15.2267 20.5551i −1.04577 1.41173i
213213 −7.53443 2.21998i −0.516251 0.152111i
214214 −5.24797 + 1.73205i −0.358744 + 0.118401i
215215 1.99715 + 3.45917i 0.136205 + 0.235914i
216216 14.6282 1.41966i 0.995324 0.0965958i
217217 0 0
218218 8.70434 + 7.76481i 0.589533 + 0.525899i
219219 −1.77436 + 1.68868i −0.119900 + 0.114110i
220220 −5.05108 + 11.6334i −0.340543 + 0.784325i
221221 −22.3956 12.9301i −1.50649 0.869775i
222222 −13.0690 + 0.421606i −0.877131 + 0.0282963i
223223 19.4171i 1.30026i 0.759821 + 0.650132i 0.225287π0.225287\pi
−0.759821 + 0.650132i 0.774713π0.774713\pi
224224 0 0
225225 −9.15054 + 4.69573i −0.610036 + 0.313049i
226226 −9.31160 1.93426i −0.619399 0.128665i
227227 5.34136 9.25151i 0.354519 0.614045i −0.632517 0.774547i 0.717978π-0.717978\pi
0.987035 + 0.160502i 0.0513114π0.0513114\pi
228228 −5.22737 0.911118i −0.346191 0.0603403i
229229 −3.75075 6.49650i −0.247857 0.429301i 0.715074 0.699049i 0.246393π-0.246393\pi
−0.962931 + 0.269748i 0.913060π0.913060\pi
230230 −0.370081 + 0.414861i −0.0244024 + 0.0273551i
231231 0 0
232232 12.8003 + 9.03122i 0.840381 + 0.592928i
233233 −2.42423 + 1.39963i −0.158817 + 0.0916930i −0.577302 0.816531i 0.695895π-0.695895\pi
0.418485 + 0.908224i 0.362561π0.362561\pi
234234 −13.1540 + 13.3531i −0.859904 + 0.872921i
235235 −12.4815 7.20617i −0.814201 0.470079i
236236 12.8037 9.48466i 0.833449 0.617399i
237237 11.6644 2.81817i 0.757683 0.183060i
238238 0 0
239239 −20.5467 −1.32905 −0.664527 0.747265i 0.731367π-0.731367\pi
−0.664527 + 0.747265i 0.731367π0.731367\pi
240240 7.25472 + 4.77580i 0.468290 + 0.308277i
241241 −9.02728 + 15.6357i −0.581499 + 1.00718i 0.413804 + 0.910366i 0.364200π0.364200\pi
−0.995302 + 0.0968188i 0.969133π0.969133\pi
242242 19.5886 6.46506i 1.25920 0.415590i
243243 2.14612 + 15.4400i 0.137674 + 0.990478i
244244 −0.0688928 0.601848i −0.00441041 0.0385294i
245245 0 0
246246 −4.27488 2.28759i −0.272556 0.145851i
247247 5.86064 3.38364i 0.372904 0.215296i
248248 −12.5790 + 5.81105i −0.798768 + 0.369002i
249249 −11.2702 3.32070i −0.714217 0.210441i
250250 −14.6306 3.03915i −0.925320 0.192213i
251251 10.4810 0.661555 0.330777 0.943709i 0.392689π-0.392689\pi
0.330777 + 0.943709i 0.392689π0.392689\pi
252252 0 0
253253 1.58612 0.0997188
254254 −11.7752 2.44600i −0.738839 0.153476i
255255 −12.1919 3.59227i −0.763483 0.224957i
256256 −1.08251 + 15.9633i −0.0676566 + 0.997709i
257257 −7.24060 + 4.18036i −0.451656 + 0.260764i −0.708529 0.705681i 0.750641π-0.750641\pi
0.256873 + 0.966445i 0.417308π0.417308\pi
258258 −6.88111 3.68224i −0.428399 0.229246i
259259 0 0
260260 −11.0054 + 1.25977i −0.682524 + 0.0781277i
261261 −9.00941 + 13.9613i −0.557668 + 0.864182i
262262 11.2949 3.72781i 0.697803 0.230305i
263263 −14.6850 + 25.4352i −0.905517 + 1.56840i −0.0852962 + 0.996356i 0.527184π0.527184\pi
−0.820221 + 0.572046i 0.806150π0.806150\pi
264264 −3.61053 24.5159i −0.222212 1.50885i
265265 16.0346 0.984996
266266 0 0
267267 −8.07720 + 1.95149i −0.494317 + 0.119429i
268268 12.5523 + 16.9448i 0.766756 + 1.03507i
269269 17.6649 + 10.1988i 1.07705 + 0.621834i 0.930099 0.367310i 0.119721π-0.119721\pi
0.146950 + 0.989144i 0.453054π0.453054\pi
270270 −4.74296 + 7.89768i −0.288648 + 0.480638i
271271 17.8370 10.2982i 1.08352 0.625572i 0.151678 0.988430i 0.451532π-0.451532\pi
0.931844 + 0.362858i 0.118199π0.118199\pi
272272 −5.29093 22.8080i −0.320810 1.38294i
273273 0 0
274274 12.9508 14.5179i 0.782389 0.877057i
275275 8.67076 + 15.0182i 0.522867 + 0.905632i
276276 0.186517 1.07011i 0.0112270 0.0644128i
277277 1.97345 3.41811i 0.118573 0.205374i −0.800629 0.599160i 0.795501π-0.795501\pi
0.919202 + 0.393786i 0.128835π0.128835\pi
278278 18.2292 + 3.78668i 1.09332 + 0.227110i
279279 −6.71002 13.0758i −0.401719 0.782825i
280280 0 0
281281 1.18623i 0.0707648i 0.999374 + 0.0353824i 0.0112649π0.0112649\pi
−0.999374 + 0.0353824i 0.988735π0.988735\pi
282282 28.1453 0.907971i 1.67603 0.0540689i
283283 23.9744 + 13.8416i 1.42513 + 0.822800i 0.996731 0.0807885i 0.0257438π-0.0257438\pi
0.428401 + 0.903589i 0.359077π0.359077\pi
284284 8.31945 + 3.61220i 0.493669 + 0.214344i
285285 2.40933 2.29298i 0.142716 0.135825i
286286 23.5839 + 21.0383i 1.39454 + 1.24402i
287287 0 0
288288 −16.9647 0.446999i −0.999653 0.0263396i
289289 8.63122 + 14.9497i 0.507719 + 0.879395i
290290 −9.32487 + 3.07760i −0.547575 + 0.180723i
291291 −22.7357 6.69895i −1.33279 0.392700i
292292 2.27276 1.68361i 0.133004 0.0985258i
293293 0.197795i 0.0115553i 0.999983 + 0.00577765i 0.00183909π0.00183909\pi
−0.999983 + 0.00577765i 0.998161π0.998161\pi
294294 0 0
295295 9.98789i 0.581517i
296296 15.0363 + 1.36968i 0.873969 + 0.0796109i
297297 25.8225 4.90159i 1.49837 0.284419i
298298 5.00724 + 15.1715i 0.290061 + 0.878862i
299299 0.692674 + 1.19975i 0.0400584 + 0.0693831i
300300 11.1519 4.08385i 0.643856 0.235781i
301301 0 0
302302 −10.4496 + 11.7139i −0.601304 + 0.674061i
303303 −4.86207 5.10878i −0.279319 0.293492i
304304 5.86120 + 1.78521i 0.336163 + 0.102389i
305305 0.328846 + 0.189859i 0.0188297 + 0.0108713i
306306 23.9388 6.60749i 1.36849 0.377725i
307307 16.6218i 0.948657i 0.880348 + 0.474328i 0.157309π0.157309\pi
−0.880348 + 0.474328i 0.842691π0.842691\pi
308308 0 0
309309 22.0145 5.31881i 1.25236 0.302576i
310310 1.76651 8.50404i 0.100331 0.482997i
311311 −5.37805 + 9.31506i −0.304961 + 0.528209i −0.977253 0.212078i 0.931977π-0.931977\pi
0.672291 + 0.740287i 0.265310π0.265310\pi
312312 16.9671 13.4373i 0.960575 0.760738i
313313 −2.47200 4.28163i −0.139726 0.242012i 0.787667 0.616101i 0.211289π-0.211289\pi
−0.927393 + 0.374089i 0.877955π0.877955\pi
314314 15.6144 + 13.9290i 0.881170 + 0.786058i
315315 0 0
316316 −13.7665 + 1.57583i −0.774427 + 0.0886476i
317317 −18.9960 + 10.9673i −1.06692 + 0.615987i −0.927338 0.374224i 0.877909π-0.877909\pi
−0.139582 + 0.990211i 0.544576π0.544576\pi
318318 −26.6131 + 16.5315i −1.49239 + 0.927041i
319319 24.2624 + 14.0079i 1.35844 + 0.784293i
320320 −7.63656 6.50142i −0.426897 0.363441i
321321 1.58955 + 6.57914i 0.0887202 + 0.367212i
322322 0 0
323323 −8.96603 −0.498883
324324 −0.270403 17.9980i −0.0150224 0.999887i
325325 −7.57319 + 13.1171i −0.420085 + 0.727609i
326326 −5.87994 17.8157i −0.325660 0.986722i
327327 10.3484 9.84870i 0.572269 0.544634i
328328 4.57454 + 3.22756i 0.252587 + 0.178212i
329329 0 0
330330 13.6954 + 7.32873i 0.753908 + 0.403433i
331331 3.24073 1.87104i 0.178127 0.102841i −0.408286 0.912854i 0.633873π-0.633873\pi
0.586412 + 0.810013i 0.300540π0.300540\pi
332332 12.4444 + 5.40320i 0.682976 + 0.296539i
333333 −0.791990 + 15.9949i −0.0434008 + 0.876514i
334334 1.37666 6.62730i 0.0753275 0.362629i
335335 −13.2183 −0.722194
336336 0 0
337337 22.9774 1.25166 0.625829 0.779960i 0.284761π-0.284761\pi
0.625829 + 0.779960i 0.284761π0.284761\pi
338338 −1.87492 + 9.02593i −0.101982 + 0.490946i
339339 −3.29204 + 11.1729i −0.178799 + 0.606828i
340340 13.4621 + 5.84508i 0.730087 + 0.316994i
341341 −21.4604 + 12.3902i −1.16215 + 0.670966i
342342 −1.63479 + 6.28973i −0.0883994 + 0.340110i
343343 0 0
344344 7.36347 + 5.19527i 0.397011 + 0.280110i
345345 0.469402 + 0.493220i 0.0252718 + 0.0265541i
346346 −6.38786 19.3547i −0.343413 1.04051i
347347 −1.06505 + 1.84472i −0.0571750 + 0.0990299i −0.893196 0.449667i 0.851543π-0.851543\pi
0.836021 + 0.548697i 0.184876π0.184876\pi
348348 12.3038 14.7218i 0.659552 0.789174i
349349 −3.55710 −0.190407 −0.0952036 0.995458i 0.530350π-0.530350\pi
−0.0952036 + 0.995458i 0.530350π0.530350\pi
350350 0 0
351351 14.9845 + 17.3916i 0.799811 + 0.928293i
352352 0.661842 + 28.6063i 0.0352763 + 1.52472i
353353 −16.3912 9.46348i −0.872417 0.503690i −0.00426642 0.999991i 0.501358π-0.501358\pi
−0.868151 + 0.496301i 0.834691π0.834691\pi
354354 −10.2974 16.5772i −0.547302 0.881068i
355355 −4.92353 + 2.84260i −0.261314 + 0.150869i
356356 9.53285 1.09121i 0.505240 0.0578342i
357357 0 0
358358 0.732717 + 0.653628i 0.0387253 + 0.0345453i
359359 −0.613000 1.06175i −0.0323529 0.0560369i 0.849396 0.527757i 0.176967π-0.176967\pi
−0.881748 + 0.471720i 0.843633π0.843633\pi
360360 6.55494 8.37804i 0.345476 0.441561i
361361 −8.32685 + 14.4225i −0.438255 + 0.759081i
362362 −1.81506 + 8.73776i −0.0953973 + 0.459246i
363363 −5.93317 24.5573i −0.311411 1.28893i
364364 0 0
365365 1.77294i 0.0927997i
366366 −0.741538 + 0.0239221i −0.0387608 + 0.00125043i
367367 −17.4966 10.1017i −0.913314 0.527302i −0.0318180 0.999494i 0.510130π-0.510130\pi
−0.881496 + 0.472192i 0.843463π0.843463\pi
368368 −0.365454 + 1.19986i −0.0190506 + 0.0625471i
369369 −3.21976 + 4.98945i −0.167614 + 0.259740i
370370 −6.30019 + 7.06250i −0.327531 + 0.367162i
371371 0 0
372372 5.83566 + 15.9357i 0.302565 + 0.826225i
373373 4.09019 + 7.08442i 0.211782 + 0.366817i 0.952272 0.305250i 0.0987400π-0.0987400\pi
−0.740490 + 0.672067i 0.765407π0.765407\pi
374374 −13.1233 39.7626i −0.678592 2.05607i
375375 −5.17252 + 17.5551i −0.267108 + 0.906541i
376376 −32.3823 2.94974i −1.66999 0.152121i
377377 24.4695i 1.26024i
378378 0 0
379379 31.2020i 1.60274i −0.598170 0.801369i 0.704105π-0.704105\pi
0.598170 0.801369i 0.295895π-0.295895\pi
380380 −3.08609 + 2.28610i −0.158313 + 0.117274i
381381 −4.16301 + 14.1289i −0.213277 + 0.723845i
382382 −5.24797 + 1.73205i −0.268509 + 0.0886194i
383383 12.2089 + 21.1465i 0.623848 + 1.08054i 0.988763 + 0.149495i 0.0477647π0.0477647\pi
−0.364915 + 0.931041i 0.618902π0.618902\pi
384384 19.3775 + 2.91737i 0.988856 + 0.148877i
385385 0 0
386386 −1.65861 1.47958i −0.0844212 0.0753089i
387387 −5.18273 + 8.03133i −0.263453 + 0.408255i
388388 25.1045 + 10.9001i 1.27449 + 0.553367i
389389 7.86740 + 4.54225i 0.398893 + 0.230301i 0.686006 0.727596i 0.259362π-0.259362\pi
−0.287113 + 0.957897i 0.592696π0.592696\pi
390390 0.437438 + 13.5597i 0.0221505 + 0.686624i
391391 1.83546i 0.0928230i
392392 0 0
393393 −3.42111 14.1599i −0.172572 0.714275i
394394 −2.53786 0.527179i −0.127855 0.0265589i
395395 4.34279 7.52193i 0.218509 0.378469i
396396 −30.2865 + 1.95613i −1.52196 + 0.0982991i
397397 −11.6405 20.1619i −0.584220 1.01190i −0.994972 0.100151i 0.968067π-0.968067\pi
0.410753 0.911747i 0.365266π-0.365266\pi
398398 3.45588 3.87403i 0.173227 0.194188i
399399 0 0
400400 −13.3587 + 3.09890i −0.667934 + 0.154945i
401401 6.57424 3.79564i 0.328302 0.189545i −0.326785 0.945099i 0.605965π-0.605965\pi
0.655087 + 0.755553i 0.272632π0.272632\pi
402402 21.9388 13.6280i 1.09421 0.679701i
403403 −18.7439 10.8218i −0.933700 0.539072i
404404 4.84748 + 6.54378i 0.241171 + 0.325565i
405405 9.16617 + 6.57914i 0.455470 + 0.326920i
406406 0 0
407407 27.0019 1.33843
408408 −28.3697 + 4.17809i −1.40451 + 0.206846i
409409 3.19509 5.53406i 0.157987 0.273642i −0.776156 0.630541i 0.782833π-0.782833\pi
0.934143 + 0.356900i 0.116166π0.116166\pi
410410 −3.33250 + 1.09987i −0.164580 + 0.0543185i
411411 −16.4265 17.2600i −0.810261 0.851374i
412412 −25.9819 + 2.97411i −1.28003 + 0.146524i
413413 0 0
414414 −1.28759 0.334662i −0.0632814 0.0164477i
415415 −7.36471 + 4.25202i −0.361520 + 0.208723i
416416 −21.3488 + 12.9932i −1.04671 + 0.637044i
417417 6.44479 21.8731i 0.315603 1.07113i
418418 10.7284 + 2.22857i 0.524743 + 0.109003i
419419 −29.1307 −1.42313 −0.711565 0.702620i 0.752013π-0.752013\pi
−0.711565 + 0.702620i 0.752013π0.752013\pi
420420 0 0
421421 −32.0821 −1.56358 −0.781792 0.623539i 0.785694π-0.785694\pi
−0.781792 + 0.623539i 0.785694π0.785694\pi
422422 20.5985 + 4.27885i 1.00272 + 0.208291i
423423 1.70563 34.4466i 0.0829306 1.67485i
424424 32.8413 15.1715i 1.59492 0.736793i
425425 17.3790 10.0338i 0.843006 0.486710i
426426 5.24103 9.79405i 0.253929 0.474523i
427427 0 0
428428 −0.888828 7.76481i −0.0429631 0.375326i
429429 28.0384 26.6844i 1.35371 1.28834i
430430 −5.36420 + 1.77041i −0.258685 + 0.0853769i
431431 9.12282 15.8012i 0.439431 0.761116i −0.558215 0.829696i 0.688514π-0.688514\pi
0.997646 + 0.0685802i 0.0218469π0.0218469\pi
432432 −2.24175 + 20.6634i −0.107856 + 0.994167i
433433 4.84842 0.233000 0.116500 0.993191i 0.462832π-0.462832\pi
0.116500 + 0.993191i 0.462832π0.462832\pi
434434 0 0
435435 2.82440 + 11.6902i 0.135420 + 0.560501i
436436 −13.2552 + 9.81913i −0.634809 + 0.470251i
437437 0.415965 + 0.240157i 0.0198983 + 0.0114883i
438438 −1.82788 2.94259i −0.0873395 0.140603i
439439 −17.5388 + 10.1260i −0.837081 + 0.483289i −0.856271 0.516527i 0.827225π-0.827225\pi
0.0191902 + 0.999816i 0.493891π0.493891\pi
440440 −14.6554 10.3401i −0.698670 0.492945i
441441 0 0
442442 24.3454 27.2912i 1.15799 1.29811i
443443 −11.2335 19.4570i −0.533719 0.924428i −0.999224 0.0393830i 0.987461π-0.987461\pi
0.465505 0.885045i 0.345873π-0.345873\pi
444444 3.17523 18.2173i 0.150690 0.864554i
445445 −3.00724 + 5.20869i −0.142557 + 0.246915i
446446 −26.8860 5.58491i −1.27309 0.264453i
447447 19.0198 4.59528i 0.899607 0.217349i
448448 0 0
449449 29.5660i 1.39531i −0.716435 0.697654i 0.754227π-0.754227\pi
0.716435 0.697654i 0.245773π-0.245773\pi
450450 −3.87002 14.0210i −0.182434 0.660955i
451451 8.67086 + 5.00612i 0.408295 + 0.235729i
452452 5.35657 12.3370i 0.251952 0.580284i
453453 13.2540 + 13.9265i 0.622726 + 0.654323i
454454 11.2738 + 10.0569i 0.529107 + 0.471996i
455455 0 0
456456 2.76513 6.97604i 0.129489 0.326683i
457457 −9.09743 15.7572i −0.425560 0.737091i 0.570913 0.821011i 0.306589π-0.306589\pi
−0.996473 + 0.0839196i 0.973256π0.973256\pi
458458 10.0742 3.32492i 0.470738 0.155363i
459459 −5.67210 29.8817i −0.264751 1.39476i
460460 −0.467993 0.631761i −0.0218203 0.0294560i
461461 24.9782i 1.16335i −0.813422 0.581675i 0.802398π-0.802398\pi
0.813422 0.581675i 0.197602π-0.197602\pi
462462 0 0
463463 6.37226i 0.296144i −0.988977 0.148072i 0.952693π-0.952693\pi
0.988977 0.148072i 0.0473068π-0.0473068\pi
464464 −16.1869 + 15.1264i −0.751456 + 0.702224i
465465 −10.2039 3.00653i −0.473195 0.139424i
466466 −1.24073 3.75930i −0.0574757 0.174146i
467467 −13.6785 23.6918i −0.632964 1.09633i −0.986943 0.161072i 0.948505π-0.948505\pi
0.353979 0.935253i 0.384828π-0.384828\pi
468468 −14.7060 22.0545i −0.679785 1.01947i
469469 0 0
470470 13.5681 15.2098i 0.625849 0.701576i
471471 18.5636 17.6672i 0.855367 0.814061i
472472 9.45028 + 20.4568i 0.434984 + 0.941598i
473473 13.9571 + 8.05816i 0.641750 + 0.370515i
474474 0.547187 + 16.9617i 0.0251331 + 0.779078i
475475 5.25141i 0.240951i
476476 0 0
477477 17.5185 + 34.1382i 0.802119 + 1.56308i
478478 5.90981 28.4500i 0.270308 1.30127i
479479 −9.91668 + 17.1762i −0.453105 + 0.784800i −0.998577 0.0533285i 0.983017π-0.983017\pi
0.545472 + 0.838129i 0.316350π0.316350\pi
480480 −8.69951 + 8.67162i −0.397076 + 0.395804i
481481 11.7919 + 20.4242i 0.537666 + 0.931265i
482482 −19.0536 16.9970i −0.867866 0.774190i
483483 0 0
484484 3.31764 + 28.9830i 0.150802 + 1.31741i
485485 −14.8571 + 8.57774i −0.674625 + 0.389495i
486486 −21.9964 1.46936i −0.997776 0.0666513i
487487 35.3792 + 20.4262i 1.60318 + 0.925599i 0.990845 + 0.135003i 0.0431045π0.0431045\pi
0.612339 + 0.790595i 0.290229π0.290229\pi
488488 0.853168 + 0.0777160i 0.0386211 + 0.00351804i
489489 −22.3348 + 5.39619i −1.01001 + 0.244024i
490490 0 0
491491 20.3003 0.916137 0.458069 0.888917i 0.348541π-0.348541\pi
0.458069 + 0.888917i 0.348541π0.348541\pi
492492 4.39710 5.26126i 0.198236 0.237196i
493493 16.2099 28.0764i 0.730058 1.26450i
494494 2.99949 + 9.08821i 0.134954 + 0.408898i
495495 10.3151 15.9847i 0.463631 0.718458i
496496 −4.42821 19.0890i −0.198833 0.857123i
497497 0 0
498498 7.83964 14.6502i 0.351303 0.656489i
499499 −29.6416 + 17.1136i −1.32694 + 0.766110i −0.984825 0.173548i 0.944477π-0.944477\pi
−0.342116 + 0.939658i 0.611144π0.611144\pi
500500 8.41636 19.3842i 0.376391 0.866887i
501501 −7.95202 2.34302i −0.355270 0.104679i
502502 −3.01464 + 14.5126i −0.134550 + 0.647728i
503503 31.1279 1.38792 0.693962 0.720011i 0.255863π-0.255863\pi
0.693962 + 0.720011i 0.255863π0.255863\pi
504504 0 0
505505 −5.10467 −0.227155
506506 −0.456215 + 2.19624i −0.0202812 + 0.0976346i
507507 10.8301 + 3.19104i 0.480982 + 0.141719i
508508 6.77375 15.6010i 0.300536 0.692182i
509509 34.2107 19.7516i 1.51636 0.875474i 0.516549 0.856257i 0.327216π-0.327216\pi
0.999815 0.0192162i 0.00611708π-0.00611708\pi
510510 8.48078 15.8483i 0.375535 0.701773i
511511 0 0
512512 −21.7924 6.09041i −0.963095 0.269161i
513513 7.51416 + 2.62436i 0.331758 + 0.115868i
514514 −3.70576 11.2281i −0.163454 0.495251i
515515 8.19625 14.1963i 0.361170 0.625564i
516516 7.07784 8.46885i 0.311585 0.372820i
517517 −58.1512 −2.55749
518518 0 0
519519 −24.2641 + 5.86232i −1.06507 + 0.257327i
520520 1.42111 15.6010i 0.0623199 0.684149i
521521 −20.8808 12.0555i −0.914803 0.528162i −0.0328296 0.999461i 0.510452π-0.510452\pi
−0.881973 + 0.471299i 0.843785π0.843785\pi
522522 −16.7402 16.4906i −0.732699 0.721773i
523523 −8.02520 + 4.63335i −0.350917 + 0.202602i −0.665089 0.746764i 0.731606π-0.731606\pi
0.314172 + 0.949366i 0.398273π0.398273\pi
524524 1.91298 + 16.7118i 0.0835689 + 0.730059i
525525 0 0
526526 −30.9952 27.6496i −1.35145 1.20558i
527527 14.3379 + 24.8339i 0.624568 + 1.08178i
528528 34.9846 + 2.05215i 1.52251 + 0.0893085i
529529 11.4508 19.8334i 0.497862 0.862323i
530530 −4.61200 + 22.2024i −0.200333 + 0.964409i
531531 −21.2646 + 10.9122i −0.922805 + 0.473551i
532532 0 0
533533 8.74486i 0.378782i
534534 −0.378909 11.7454i −0.0163970 0.508275i
535535 4.24264 + 2.44949i 0.183425 + 0.105901i
536536 −27.0732 + 12.5068i −1.16938 + 0.540213i
537537 0.871113 0.829047i 0.0375913 0.0357760i
538538 −19.2028 + 21.5263i −0.827892 + 0.928066i
539539 0 0
540540 −9.57136 8.83897i −0.411886 0.380369i
541541 −12.9508 22.4315i −0.556800 0.964406i −0.997761 0.0668796i 0.978696π-0.978696\pi
0.440961 0.897526i 0.354638π-0.354638\pi
542542 9.12903 + 27.6602i 0.392125 + 1.18811i
543543 10.4843 + 3.08916i 0.449926 + 0.132568i
544544 33.1030 0.765881i 1.41928 0.0328369i
545545 10.3401i 0.442921i
546546 0 0
547547 32.9387i 1.40836i 0.710022 + 0.704179i 0.248685π0.248685\pi
−0.710022 + 0.704179i 0.751315π0.751315\pi
548548 16.3772 + 22.1082i 0.699600 + 0.944415i
549549 −0.0449378 + 0.907556i −0.00191790 + 0.0387335i
550550 −23.2890 + 7.68635i −0.993046 + 0.327747i
551551 4.24192 + 7.34722i 0.180712 + 0.313002i
552552 1.42808 + 0.566055i 0.0607832 + 0.0240929i
553553 0 0
554554 4.16528 + 3.71569i 0.176966 + 0.157864i
555555 7.99101 + 8.39647i 0.339199 + 0.356410i
556556 −10.4865 + 24.1520i −0.444727 + 1.02427i
557557 25.8991 + 14.9528i 1.09738 + 0.633572i 0.935531 0.353244i 0.114921π-0.114921\pi
0.161847 + 0.986816i 0.448255π0.448255\pi
558558 20.0354 5.53010i 0.848167 0.234108i
559559 14.0763i 0.595363i
560560 0 0
561561 −49.8486 + 12.0437i −2.10461 + 0.508484i
562562 −1.64252 0.341195i −0.0692857 0.0143924i
563563 −15.5531 + 26.9388i −0.655487 + 1.13534i 0.326284 + 0.945272i 0.394203π0.394203\pi
−0.981771 + 0.190065i 0.939130π0.939130\pi
564564 −6.83818 + 39.2328i −0.287939 + 1.65200i
565565 4.21532 + 7.30115i 0.177340 + 0.307162i
566566 −26.0616 + 29.2151i −1.09545 + 1.22800i
567567 0 0
568568 −7.39456 + 10.4806i −0.310269 + 0.439756i
569569 15.3022 8.83472i 0.641501 0.370371i −0.143691 0.989623i 0.545897π-0.545897\pi
0.785193 + 0.619252i 0.212564π0.212564\pi
570570 2.48200 + 3.99562i 0.103960 + 0.167358i
571571 6.51130 + 3.75930i 0.272490 + 0.157322i 0.630018 0.776580i 0.283047π-0.283047\pi
−0.357529 + 0.933902i 0.616381π0.616381\pi
572572 −35.9141 + 26.6043i −1.50165 + 1.11238i
573573 1.58955 + 6.57914i 0.0664045 + 0.274847i
574574 0 0
575575 −1.07503 −0.0448318
576576 5.49846 23.3617i 0.229103 0.973402i
577577 2.13156 3.69196i 0.0887378 0.153698i −0.818240 0.574877i 0.805050π-0.805050\pi
0.906978 + 0.421178i 0.138383π0.138383\pi
578578 −23.1828 + 7.65130i −0.964277 + 0.318252i
579579 −1.97189 + 1.87667i −0.0819491 + 0.0779917i
580580 −1.57932 13.7969i −0.0655776 0.572887i
581581 0 0
582582 15.8152 29.5542i 0.655560 1.22506i
583583 56.0289 32.3483i 2.32048 1.33973i
584584 1.67751 + 3.63125i 0.0694157 + 0.150262i
585585 16.5955 + 0.821731i 0.686141 + 0.0339744i
586586 −0.273878 0.0568914i −0.0113138 0.00235016i
587587 43.2909 1.78681 0.893404 0.449253i 0.148310π-0.148310\pi
0.893404 + 0.449253i 0.148310π0.148310\pi
588588 0 0
589589 −7.50407 −0.309200
590590 −13.8298 2.87280i −0.569363 0.118271i
591591 −0.897238 + 3.04515i −0.0369074 + 0.125261i
592592 −6.22141 + 20.4262i −0.255698 + 0.839511i
593593 −4.99583 + 2.88434i −0.205154 + 0.118446i −0.599057 0.800706i 0.704458π-0.704458\pi
0.393903 + 0.919152i 0.371125π0.371125\pi
594594 −0.640266 + 37.1650i −0.0262704 + 1.52490i
595595 0 0
596596 −22.4475 + 2.56954i −0.919486 + 0.105252i
597597 −4.38335 4.60576i −0.179399 0.188501i
598598 −1.86047 + 0.614033i −0.0760802 + 0.0251097i
599599 17.8985 31.0011i 0.731312 1.26667i −0.225010 0.974356i 0.572242π-0.572242\pi
0.956323 0.292313i 0.0944251π-0.0944251\pi
600600 2.44711 + 16.6162i 0.0999028 + 0.678353i
601601 42.3193 1.72624 0.863121 0.504998i 0.168507π-0.168507\pi
0.863121 + 0.504998i 0.168507π0.168507\pi
602602 0 0
603603 −14.4416 28.1423i −0.588109 1.14604i
604604 −13.2142 17.8383i −0.537677 0.725830i
605605 −15.8361 9.14298i −0.643829 0.371715i
606606 8.47236 5.26286i 0.344166 0.213789i
607607 41.0224 23.6843i 1.66505 0.961316i 0.694801 0.719202i 0.255492π-0.255492\pi
0.970248 0.242115i 0.0778411π-0.0778411\pi
608608 −4.15775 + 7.60227i −0.168619 + 0.308313i
609609 0 0
610610 −0.357475 + 0.400729i −0.0144737 + 0.0162250i
611611 −25.3951 43.9857i −1.02738 1.77947i
612612 2.26362 + 35.0475i 0.0915015 + 1.41671i
613613 −1.39456 + 2.41545i −0.0563257 + 0.0975590i −0.892813 0.450427i 0.851272π-0.851272\pi
0.836488 + 0.547986i 0.184605π0.184605\pi
614614 −23.0155 4.78091i −0.928829 0.192942i
615615 1.00938 + 4.17781i 0.0407021 + 0.168465i
616616 0 0
617617 21.6549i 0.871795i 0.899996 + 0.435898i 0.143569π0.143569\pi
−0.899996 + 0.435898i 0.856431π0.856431\pi
618618 1.03272 + 32.0123i 0.0415421 + 1.28772i
619619 −4.88830 2.82226i −0.196477 0.113436i 0.398534 0.917154i 0.369519π-0.369519\pi
−0.595011 + 0.803717i 0.702852π0.702852\pi
620620 11.2671 + 4.89201i 0.452496 + 0.196468i
621621 −0.537240 + 1.53824i −0.0215587 + 0.0617275i
622622 −11.3513 10.1260i −0.455144 0.406017i
623623 0 0
624624 13.7258 + 27.3586i 0.549472 + 1.09522i
625625 −1.94767 3.37346i −0.0779067 0.134938i
626626 6.63959 2.19135i 0.265371 0.0875838i
627627 3.79293 12.8729i 0.151475 0.514094i
628628 −23.7780 + 17.6142i −0.948845 + 0.702881i
629629 31.2464i 1.24588i
630630 0 0
631631 6.37226i 0.253676i −0.991923 0.126838i 0.959517π-0.959517\pi
0.991923 0.126838i 0.0404828π-0.0404828\pi
632632 1.77766 19.5151i 0.0707113 0.776270i
633633 7.28244 24.7160i 0.289451 0.982372i
634634 −9.72219 29.4574i −0.386117 1.16990i
635635 5.33056 + 9.23281i 0.211537 + 0.366393i
636636 −15.2358 41.6048i −0.604137 1.64974i
637637 0 0
638638 −26.3747 + 29.5660i −1.04419 + 1.17053i
639639 −11.4312 7.37670i −0.452211 0.291818i
640640 11.1987 8.70401i 0.442668 0.344056i
641641 14.2860 + 8.24802i 0.564263 + 0.325777i 0.754855 0.655892i 0.227707π-0.227707\pi
−0.190592 + 0.981669i 0.561041π0.561041\pi
642642 −9.56704 + 0.308633i −0.377581 + 0.0121808i
643643 2.36672i 0.0933343i −0.998910 0.0466671i 0.985140π-0.985140\pi
0.998910 0.0466671i 0.0148600π-0.0148600\pi
644644 0 0
645645 1.62476 + 6.72485i 0.0639748 + 0.264791i
646646 2.57889 12.4149i 0.101465 0.488456i
647647 −5.67476 + 9.82897i −0.223098 + 0.386417i −0.955747 0.294190i 0.904950π-0.904950\pi
0.732649 + 0.680606i 0.238284π0.238284\pi
648648 24.9988 + 4.80232i 0.982044 + 0.188653i
649649 20.1497 + 34.9002i 0.790944 + 1.36995i
650650 −15.9845 14.2591i −0.626962 0.559289i
651651 0 0
652652 26.3599 3.01738i 1.03233 0.118170i
653653 38.5978 22.2844i 1.51045 0.872057i 0.510522 0.859865i 0.329452π-0.329452\pi
0.999926 0.0121923i 0.00388102π-0.00388102\pi
654654 10.6605 + 17.1618i 0.416860 + 0.671078i
655655 −9.13122 5.27191i −0.356786 0.205991i
656656 −5.78482 + 5.40582i −0.225859 + 0.211062i
657657 −3.77465 + 1.93702i −0.147263 + 0.0755702i
658658 0 0
659659 −0.590533 −0.0230039 −0.0115019 0.999934i 0.503661π-0.503661\pi
−0.0115019 + 0.999934i 0.503661π0.503661\pi
660660 −14.0870 + 16.8555i −0.548334 + 0.656098i
661661 −21.5502 + 37.3261i −0.838206 + 1.45182i 0.0531863 + 0.998585i 0.483062π0.483062\pi
−0.891393 + 0.453232i 0.850271π0.850271\pi
662662 1.65861 + 5.02546i 0.0644638 + 0.195320i
663663 −30.8791 32.4459i −1.19925 1.26010i
664664 −11.0609 + 15.6771i −0.429248 + 0.608390i
665665 0 0
666666 −21.9196 5.69722i −0.849367 0.220763i
667667 −1.50407 + 0.868374i −0.0582377 + 0.0336236i
668668 8.78055 + 3.81240i 0.339730 + 0.147506i
669669 −9.50530 + 32.2602i −0.367496 + 1.24725i
670670 3.80197 18.3028i 0.146883 0.707099i
671671 1.53210 0.0591459
672672 0 0
673673 15.2706 0.588637 0.294319 0.955707i 0.404907π-0.404907\pi
0.294319 + 0.955707i 0.404907π0.404907\pi
674674 −6.60896 + 31.8158i −0.254567 + 1.22550i
675675 −17.5017 + 3.32216i −0.673641 + 0.127870i
676676 −11.9585 5.19223i −0.459943 0.199701i
677677 35.8437 20.6944i 1.37759 0.795349i 0.385717 0.922617i 0.373954π-0.373954\pi
0.991868 + 0.127268i 0.0406207π0.0406207\pi
678678 −14.5237 7.77198i −0.557780 0.298481i
679679 0 0
680680 −11.9655 + 16.9592i −0.458857 + 0.650356i
681681 13.4032 12.7560i 0.513613 0.488811i
682682 −10.9835 33.2791i −0.420580 1.27432i
683683 −2.26745 + 3.92734i −0.0867615 + 0.150275i −0.906140 0.422977i 0.860985π-0.860985\pi
0.819379 + 0.573252i 0.194318π0.194318\pi
684684 −8.23890 4.07273i −0.315022 0.155725i
685685 −17.2461 −0.658941
686686 0 0
687687 −3.05138 12.6296i −0.116417 0.481850i
688688 −9.31160 + 8.70155i −0.355002 + 0.331744i
689689 48.9366 + 28.2536i 1.86434 + 1.07638i
690690 −0.817953 + 0.508096i −0.0311389 + 0.0193429i
691691 −23.6340 + 13.6451i −0.899079 + 0.519084i −0.876901 0.480670i 0.840393π-0.840393\pi
−0.0221779 + 0.999754i 0.507060π0.507060\pi
692692 28.6369 3.27802i 1.08861 0.124612i
693693 0 0
694694 −2.24797 2.00532i −0.0853316 0.0761211i
695695 −8.25229 14.2934i −0.313027 0.542179i
696696 16.8458 + 21.2709i 0.638537 + 0.806272i
697697 5.79306 10.0339i 0.219428 0.380060i
698698 1.02312 4.92536i 0.0387258 0.186428i
699699 −4.71287 + 1.13865i −0.178257 + 0.0430678i
700700 0 0
701701 9.20431i 0.347642i −0.984777 0.173821i 0.944389π-0.944389\pi
0.984777 0.173821i 0.0556114π-0.0556114\pi
702702 −28.3913 + 15.7460i −1.07156 + 0.594294i
703703 7.08130 + 4.08839i 0.267076 + 0.154197i
704704 −39.8002 7.31156i −1.50003 0.275565i
705705 −17.2094 18.0827i −0.648145 0.681032i
706706 17.8182 19.9742i 0.670598 0.751740i
707707 0 0
708708 25.9155 9.49030i 0.973965 0.356667i
709709 14.8003 + 25.6349i 0.555837 + 0.962738i 0.997838 + 0.0657232i 0.0209354π0.0209354\pi
−0.442001 + 0.897015i 0.645731π0.645731\pi
710710 −2.51987 7.63500i −0.0945691 0.286536i
711711 20.7592 + 1.02790i 0.778530 + 0.0385491i
712712 −1.23097 + 13.5136i −0.0461325 + 0.506443i
713713 1.53617i 0.0575302i
714714 0 0
715715 28.0159i 1.04773i
716716 −1.11580 + 0.826558i −0.0416994 + 0.0308899i
717717 −34.1369 10.0583i −1.27487 0.375633i
718718 1.64647 0.543405i 0.0614457 0.0202797i
719719 −1.35786 2.35188i −0.0506395 0.0877102i 0.839595 0.543214i 0.182793π-0.182793\pi
−0.890234 + 0.455503i 0.849459π0.849459\pi
720720 9.71531 + 11.4861i 0.362068 + 0.428062i
721721 0 0
722722 −17.5752 15.6782i −0.654081 0.583480i
723723 −22.6524 + 21.5585i −0.842453 + 0.801770i
724724 −11.5767 5.02646i −0.430245 0.186807i
725725 −16.4444 9.49416i −0.610729 0.352604i
726726 35.7100 1.15201i 1.32532 0.0427550i
727727 18.9752i 0.703753i −0.936046 0.351876i 0.885544π-0.885544\pi
0.936046 0.351876i 0.114456π-0.114456\pi
728728 0 0
729729 −3.99276 + 26.7031i −0.147880 + 0.989005i
730730 −2.45490 0.509947i −0.0908601 0.0188740i
731731 9.32487 16.1512i 0.344893 0.597372i
732732 0.180164 1.03366i 0.00665905 0.0382050i
733733 −7.65295 13.2553i −0.282668 0.489596i 0.689373 0.724407i 0.257886π-0.257886\pi
−0.972041 + 0.234811i 0.924553π0.924553\pi
734734 19.0198 21.3212i 0.702035 0.786980i
735735 0 0
736736 −1.55628 0.851142i −0.0573652 0.0313735i
737737 −46.1882 + 26.6668i −1.70136 + 0.982283i
738738 −5.98257 5.89337i −0.220222 0.216938i
739739 −23.2697 13.4348i −0.855989 0.494205i 0.00667810 0.999978i 0.497874π-0.497874\pi
−0.862667 + 0.505772i 0.831208π0.831208\pi
740740 −7.96701 10.7550i −0.292873 0.395360i
741741 11.3935 2.75272i 0.418550 0.101124i
742742 0 0
743743 23.4748 0.861208 0.430604 0.902541i 0.358301π-0.358301\pi
0.430604 + 0.902541i 0.358301π0.358301\pi
744744 −23.7439 + 3.49682i −0.870493 + 0.128200i
745745 7.08130 12.2652i 0.259439 0.449361i
746746 −10.9859 + 3.62582i −0.402224 + 0.132751i
747747 −17.0990 11.0342i −0.625620 0.403721i
748748 58.8321 6.73444i 2.15112 0.246235i
749749 0 0
750750 −22.8200 12.2115i −0.833268 0.445901i
751751 −31.1457 + 17.9820i −1.13652 + 0.656172i −0.945567 0.325427i 0.894492π-0.894492\pi
−0.190955 + 0.981599i 0.561159π0.561159\pi
752752 13.3984 43.9899i 0.488591 1.60415i
753753 17.4135 + 5.13079i 0.634582 + 0.186977i
754754 −33.8818 7.03813i −1.23390 0.256314i
755755 13.9153 0.506429
756756 0 0
757757 23.4202 0.851222 0.425611 0.904906i 0.360059π-0.360059\pi
0.425611 + 0.904906i 0.360059π0.360059\pi
758758 43.2040 + 8.97458i 1.56924 + 0.325972i
759759 2.63524 + 0.776460i 0.0956531 + 0.0281837i
760760 −2.27781 4.93072i −0.0826250 0.178856i
761761 34.9126 20.1568i 1.26558 0.730684i 0.291433 0.956591i 0.405868π-0.405868\pi
0.974149 + 0.225908i 0.0725347π0.0725347\pi
762762 −18.3662 9.82820i −0.665338 0.356038i
763763 0 0
764764 −0.888828 7.76481i −0.0321567 0.280921i
765765 −18.4974 11.9366i −0.668775 0.431570i
766766 −32.7922 + 10.8228i −1.18483 + 0.391045i
767767 −17.5991 + 30.4825i −0.635465 + 1.10066i
768768 −9.61309 + 25.9921i −0.346882 + 0.937909i
769769 20.6279 0.743861 0.371930 0.928261i 0.378696π-0.378696\pi
0.371930 + 0.928261i 0.378696π0.378696\pi
770770 0 0
771771 −14.0762 + 3.40088i −0.506942 + 0.122480i
772772 2.52578 1.87104i 0.0909048 0.0673401i
773773 −20.1789 11.6503i −0.725784 0.419032i 0.0910936 0.995842i 0.470964π-0.470964\pi
−0.816878 + 0.576811i 0.804297π0.804297\pi
774774 −9.62992 9.48633i −0.346140 0.340979i
775775 14.5453 8.39771i 0.522481 0.301655i
776776 −22.3136 + 31.6260i −0.801012 + 1.13531i
777777 0 0
778778 −8.55233 + 9.58716i −0.306616 + 0.343716i
779779 1.51597 + 2.62573i 0.0543152 + 0.0940767i
780780 −18.9014 3.29447i −0.676778 0.117961i
781781 −11.4694 + 19.8655i −0.410407 + 0.710845i
782782 2.54147 + 0.527930i 0.0908829 + 0.0188787i
783783 −21.8030 + 18.7853i −0.779177 + 0.671333i
784784 0 0
785785 18.5487i 0.662032i
786786 20.5906 0.664256i 0.734444 0.0236932i
787787 −2.76123 1.59420i −0.0984271 0.0568269i 0.449978 0.893039i 0.351432π-0.351432\pi
−0.548406 + 0.836212i 0.684765π0.684765\pi
788788 1.45992 3.36243i 0.0520076 0.119782i
789789 −36.8495 + 35.0701i −1.31188 + 1.24853i
790790 9.16617 + 8.17678i 0.326118 + 0.290917i
791791 0 0
792792 6.00271 42.4990i 0.213297 1.51014i
793793 0.669079 + 1.15888i 0.0237597 + 0.0411530i
794794 31.2654 10.3189i 1.10957 0.366205i
795795 26.6404 + 7.84945i 0.944836 + 0.278391i
796796 4.37019 + 5.89948i 0.154897 + 0.209102i
797797 55.9985i 1.98357i 0.127925 + 0.991784i 0.459168π0.459168\pi
−0.127925 + 0.991784i 0.540832π0.540832\pi
798798 0 0
799799 67.2924i 2.38063i
800800 −0.448577 19.3885i −0.0158596 0.685487i
801801 −14.3750 0.711784i −0.507917 0.0251496i
802802 3.36471 + 10.1948i 0.118812 + 0.359991i
803803 3.57674 + 6.19509i 0.126220 + 0.218620i
804804 12.5598 + 34.2975i 0.442950 + 1.20958i
805805 0 0
806806 20.3757 22.8412i 0.717705 0.804546i
807807 24.3564 + 25.5922i 0.857385 + 0.900890i
808808 −10.4552 + 4.82990i −0.367811 + 0.169915i
809809 18.4879 + 10.6740i 0.649999 + 0.375277i 0.788456 0.615091i 0.210881π-0.210881\pi
−0.138457 + 0.990368i 0.544214π0.544214\pi
810810 −11.7463 + 10.7996i −0.412722 + 0.379460i
811811 52.7856i 1.85355i −0.375614 0.926776i 0.622568π-0.622568\pi
0.375614 0.926776i 0.377432π-0.377432\pi
812812 0 0
813813 34.6763 8.37797i 1.21615 0.293828i
814814 −7.76651 + 37.3883i −0.272216 + 1.31046i
815815 −8.31549 + 14.4029i −0.291279 + 0.504510i
816816 2.37474 40.4840i 0.0831326 1.41722i
817817 2.44020 + 4.22654i 0.0853717 + 0.147868i
818818 6.74377 + 6.01585i 0.235790 + 0.210339i
819819 0 0
820820 −0.564413 4.93072i −0.0197101 0.172188i
821821 −5.03883 + 2.90917i −0.175857 + 0.101531i −0.585344 0.810785i 0.699041π-0.699041\pi
0.409488 + 0.912316i 0.365707π0.365707\pi
822822 28.6239 17.7806i 0.998374 0.620170i
823823 −8.78912 5.07440i −0.306369 0.176882i 0.338931 0.940811i 0.389935π-0.389935\pi
−0.645301 + 0.763929i 0.723268π0.723268\pi
824824 3.35501 36.8314i 0.116877 1.28308i
825825 7.05398 + 29.1964i 0.245588 + 1.01649i
826826 0 0
827827 53.0241 1.84383 0.921915 0.387393i 0.126624π-0.126624\pi
0.921915 + 0.387393i 0.126624π0.126624\pi
828828 0.833738 1.68660i 0.0289744 0.0586135i
829829 16.3511 28.3210i 0.567898 0.983628i −0.428876 0.903364i 0.641090π-0.641090\pi
0.996774 0.0802647i 0.0255766π-0.0255766\pi
830830 −3.76928 11.4206i −0.130834 0.396414i
831831 4.95202 4.71289i 0.171784 0.163488i
832832 −11.8506 33.2979i −0.410845 1.15440i
833833 0 0
834834 28.4329 + 15.2151i 0.984552 + 0.526857i
835835 −5.19641 + 3.00015i −0.179829 + 0.103824i
836836 −6.17159 + 14.2141i −0.213449 + 0.491606i
837837 −4.74723 25.0093i −0.164088 0.864447i
838838 8.37884 40.3360i 0.289442 1.39339i
839839 −37.5962 −1.29796 −0.648982 0.760803i 0.724805π-0.724805\pi
−0.648982 + 0.760803i 0.724805π0.724805\pi
840840 0 0
841841 −1.67632 −0.0578040
842842 9.22772 44.4226i 0.318008 1.53090i
843843 −0.580701 + 1.97085i −0.0200004 + 0.0678796i
844844 −11.8495 + 27.2912i −0.407875 + 0.939401i
845845 7.07716 4.08600i 0.243462 0.140563i
846846 47.2061 + 12.2695i 1.62298 + 0.421835i
847847 0 0
848848 11.5612 + 49.8377i 0.397013 + 1.71143i
849849 33.0560 + 34.7332i 1.13448 + 1.19204i
850850 8.89462 + 26.9499i 0.305083 + 0.924375i
851851 −0.836944 + 1.44963i −0.0286901 + 0.0496927i
852852 12.0539 + 10.0741i 0.412960 + 0.345132i
853853 −5.68417 −0.194622 −0.0973112 0.995254i 0.531024π-0.531024\pi
−0.0973112 + 0.995254i 0.531024π0.531024\pi
854854 0 0
855855 5.12543 2.63019i 0.175286 0.0899507i
856856 11.0072 + 1.00266i 0.376220 + 0.0342703i
857857 27.4440 + 15.8448i 0.937471 + 0.541249i 0.889166 0.457584i 0.151285π-0.151285\pi
0.0483040 + 0.998833i 0.484618π0.484618\pi
858858 28.8841 + 46.4987i 0.986086 + 1.58744i
859859 5.22874 3.01882i 0.178402 0.103001i −0.408139 0.912920i 0.633822π-0.633822\pi
0.586542 + 0.809919i 0.300489π0.300489\pi
860860 −0.908514 7.93679i −0.0309801 0.270642i
861861 0 0
862862 19.2552 + 17.1768i 0.655835 + 0.585045i
863863 −20.0569 34.7395i −0.682744 1.18255i −0.974140 0.225944i 0.927453π-0.927453\pi
0.291396 0.956602i 0.405880π-0.405880\pi
864864 −27.9668 9.04742i −0.951451 0.307800i
865865 −9.03379 + 15.6470i −0.307158 + 0.532013i
866866 −1.39454 + 6.71339i −0.0473885 + 0.228130i
867867 7.02181 + 29.0632i 0.238473 + 0.987038i
868868 0 0
869869 35.0447i 1.18881i
870870 −16.9992 + 0.548397i −0.576328 + 0.0185924i
871871 −40.3415 23.2912i −1.36692 0.789192i
872872 −9.78354 21.1781i −0.331312 0.717183i
873873 −34.4944 22.2597i −1.16746 0.753377i
874874 −0.452179 + 0.506892i −0.0152952 + 0.0171459i
875875 0 0
876876 4.60023 1.68461i 0.155427 0.0569177i
877877 21.9436 + 38.0074i 0.740983 + 1.28342i 0.952048 + 0.305948i 0.0989733π0.0989733\pi
−0.211066 + 0.977472i 0.567693π0.567693\pi
878878 −8.97639 27.1977i −0.302939 0.917878i
879879 −0.0968270 + 0.328623i −0.00326590 + 0.0110842i
880880 18.5328 17.3186i 0.624740 0.583810i
881881 1.27293i 0.0428860i 0.999770 + 0.0214430i 0.00682603π0.00682603\pi
−0.999770 + 0.0214430i 0.993174π0.993174\pi
882882 0 0
883883 19.5118i 0.656625i 0.944569 + 0.328312i 0.106480π0.106480\pi
−0.944569 + 0.328312i 0.893520π0.893520\pi
884884 30.7864 + 41.5597i 1.03546 + 1.39780i
885885 −4.88940 + 16.5942i −0.164355 + 0.557808i
886886 30.1722 9.95812i 1.01366 0.334550i
887887 13.4459 + 23.2890i 0.451470 + 0.781969i 0.998478 0.0551585i 0.0175664π-0.0175664\pi
−0.547007 + 0.837128i 0.684233π0.684233\pi
888888 24.3114 + 9.63641i 0.815836 + 0.323377i
889889 0 0
890890 −6.34727 5.66215i −0.212761 0.189796i
891891 45.3018 + 4.49728i 1.51767 + 0.150665i
892892 15.4664 35.6214i 0.517852 1.19269i
893893 −15.2503 8.80477i −0.510332 0.294640i
894894 0.892237 + 27.6576i 0.0298409 + 0.925010i
895895 0.870412i 0.0290947i
896896 0 0
897897 0.563515 + 2.33238i 0.0188152 + 0.0778760i
898898 40.9388 + 8.50404i 1.36614 + 0.283783i
899899 13.5668 23.4984i 0.452478 0.783715i
900900 20.5273 1.32581i 0.684244 0.0441935i
901901 −37.4334 64.8365i −1.24709 2.16002i
902902 −9.42574 + 10.5662i −0.313843 + 0.351817i
903903 0 0
904904 15.5418 + 10.9655i 0.516913 + 0.364706i
905905 6.85120 3.95554i 0.227742 0.131487i
906906 −23.0956 + 14.3465i −0.767299 + 0.476631i
907907 −16.1538 9.32642i −0.536379 0.309679i 0.207231 0.978292i 0.433555π-0.433555\pi
−0.743610 + 0.668613i 0.766888π0.766888\pi
908908 −17.1681 + 12.7177i −0.569743 + 0.422052i
909909 −5.57709 10.8680i −0.184980 0.360470i
910910 0 0
911911 −8.12909 −0.269329 −0.134664 0.990891i 0.542996π-0.542996\pi
−0.134664 + 0.990891i 0.542996π0.542996\pi
912912 8.86408 + 5.83525i 0.293519 + 0.193225i
913913 −17.1561 + 29.7153i −0.567785 + 0.983433i
914914 24.4350 8.06458i 0.808237 0.266753i
915915 0.453413 + 0.476419i 0.0149894 + 0.0157499i
916916 1.70623 + 14.9057i 0.0563755 + 0.492497i
917917 0 0
918918 43.0072 + 0.740913i 1.41945 + 0.0244538i
919919 15.2109 8.78201i 0.501761 0.289692i −0.227680 0.973736i 0.573114π-0.573114\pi
0.729440 + 0.684044i 0.239781π0.239781\pi
920920 1.00938 0.466296i 0.0332782 0.0153733i
921921 −8.13692 + 27.6160i −0.268121 + 0.909979i
922922 34.5862 + 7.18444i 1.13903 + 0.236607i
923923 −20.0351 −0.659463
924924 0 0
925925 −18.3011 −0.601736
926926 8.82339 + 1.83285i 0.289954 + 0.0602310i
927927 39.1793 + 1.93997i 1.28682 + 0.0637170i
928928 −16.2890 26.7640i −0.534712 0.878571i
929929 −33.7624 + 19.4927i −1.10771 + 0.639535i −0.938235 0.345999i 0.887540π-0.887540\pi
−0.169473 + 0.985535i 0.554207π0.554207\pi
930930 7.09794 13.2641i 0.232751 0.434948i
931931 0 0
932932 5.56221 0.636699i 0.182196 0.0208558i
933933 −13.4953 + 12.8436i −0.441816 + 0.420481i
934934 36.7393 12.1255i 1.20215 0.396759i
935935 −18.5592 + 32.1455i −0.606951 + 1.05127i
936936 34.7677 14.0192i 1.13642 0.458233i
937937 23.7865 0.777072 0.388536 0.921434i 0.372981π-0.372981\pi
0.388536 + 0.921434i 0.372981π0.372981\pi
938938 0 0
939939 −2.01106 8.32376i −0.0656285 0.271636i
940940 17.1578 + 23.1619i 0.559625 + 0.755458i
941941 26.5129 + 15.3073i 0.864297 + 0.499002i 0.865449 0.500997i 0.167033π-0.167033\pi
−0.00115159 + 0.999999i 0.500367π0.500367\pi
942942 19.1235 + 30.7858i 0.623079 + 1.00306i
943943 −0.537520 + 0.310337i −0.0175041 + 0.0101060i
944944 −31.0437 + 7.20143i −1.01039 + 0.234387i
945945 0 0
946946 −15.1722 + 17.0081i −0.493292 + 0.552980i
947947 7.73005 + 13.3888i 0.251193 + 0.435079i 0.963855 0.266429i 0.0858438π-0.0858438\pi
−0.712662 + 0.701508i 0.752510π0.752510\pi
948948 −23.6435 4.12102i −0.767907 0.133844i
949949 −3.12398 + 5.41090i −0.101409 + 0.175645i
950950 −7.27140 1.51046i −0.235915 0.0490057i
951951 −36.9294 + 8.92233i −1.19752 + 0.289326i
952952 0 0
953953 13.4497i 0.435679i −0.975985 0.217839i 0.930099π-0.930099\pi
0.975985 0.217839i 0.0699009π-0.0699009\pi
954954 −52.3085 + 14.4380i −1.69355 + 0.467448i
955955 4.24264 + 2.44949i 0.137289 + 0.0792636i
956956 37.6937 + 16.3661i 1.21910 + 0.529317i
957957 33.4531 + 35.1505i 1.08138 + 1.13625i
958958 −20.9308 18.6715i −0.676243 0.603250i
959959 0 0
960960 −9.50498 14.5400i −0.306772 0.469277i
961961 −3.50000 6.06218i −0.112903 0.195554i
962962 −31.6722 + 10.4532i −1.02115 + 0.337024i
963963 −0.579770 + 11.7089i −0.0186828 + 0.377315i
964964 29.0153 21.4938i 0.934519 0.692269i
965965 1.97031i 0.0634264i
966966 0 0
967967 41.1554i 1.32347i −0.749738 0.661734i 0.769821π-0.769821\pi
0.749738 0.661734i 0.230179π-0.230179\pi
968968 −41.0857 3.74254i −1.32054 0.120290i
969969 −14.8965 4.38917i −0.478543 0.141000i
970970 −7.60389 23.0391i −0.244146 0.739742i
971971 14.4445 + 25.0186i 0.463546 + 0.802886i 0.999135 0.0415934i 0.0132434π-0.0132434\pi
−0.535588 + 0.844479i 0.679910π0.679910\pi
972972 8.36134 30.0348i 0.268190 0.963366i
973973 0 0
974974 −38.4593 + 43.1128i −1.23232 + 1.38142i
975975 −19.0036 + 18.0859i −0.608603 + 0.579213i
976976 −0.353005 + 1.15899i −0.0112994 + 0.0370984i
977977 −40.6932 23.4942i −1.30189 0.751646i −0.321161 0.947024i 0.604073π-0.604073\pi
−0.980728 + 0.195378i 0.937407π0.937407\pi
978978 −1.04774 32.4780i −0.0335032 1.03853i
979979 24.2673i 0.775587i
980980 0 0
981981 22.0145 11.2971i 0.702868 0.360687i
982982 −5.83893 + 28.1088i −0.186328 + 0.896989i
983983 13.6677 23.6731i 0.435931 0.755054i −0.561440 0.827517i 0.689753π-0.689753\pi
0.997371 + 0.0724632i 0.0230860π0.0230860\pi
984984 6.02030 + 7.60175i 0.191920 + 0.242335i
985985 1.14888 + 1.98991i 0.0366063 + 0.0634039i
986986 34.2137 + 30.5207i 1.08959 + 0.971978i
987987 0 0
988988 −13.4468 + 1.53923i −0.427799 + 0.0489696i
989989 −0.865226 + 0.499538i −0.0275126 + 0.0158844i
990990 19.1663 + 18.8805i 0.609146 + 0.600063i
991991 −18.0000 10.3923i −0.571789 0.330122i 0.186075 0.982536i 0.440423π-0.440423\pi
−0.757863 + 0.652413i 0.773757π0.773757\pi
992992 27.7054 0.640999i 0.879647 0.0203517i
993993 6.30019 1.52216i 0.199930 0.0483042i
994994 0 0
995995 −4.60206 −0.145895
996996 18.0305 + 15.0690i 0.571318 + 0.477479i
997997 6.02119 10.4290i 0.190693 0.330290i −0.754787 0.655970i 0.772260π-0.772260\pi
0.945480 + 0.325680i 0.105593π0.105593\pi
998998 −15.1707 45.9658i −0.480219 1.45502i
999999 −9.14586 + 26.1867i −0.289362 + 0.828511i
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.263.6 24
3.2 odd 2 inner 588.2.n.d.263.8 24
4.3 odd 2 588.2.n.h.263.3 24
7.2 even 3 588.2.n.h.275.9 24
7.3 odd 6 588.2.e.f.491.6 yes 24
7.4 even 3 588.2.e.f.491.5 24
7.5 odd 6 588.2.n.h.275.10 24
7.6 odd 2 inner 588.2.n.d.263.5 24
12.11 even 2 588.2.n.h.263.9 24
21.2 odd 6 588.2.n.h.275.3 24
21.5 even 6 588.2.n.h.275.4 24
21.11 odd 6 588.2.e.f.491.20 yes 24
21.17 even 6 588.2.e.f.491.19 yes 24
21.20 even 2 inner 588.2.n.d.263.7 24
28.3 even 6 588.2.e.f.491.17 yes 24
28.11 odd 6 588.2.e.f.491.18 yes 24
28.19 even 6 inner 588.2.n.d.275.7 24
28.23 odd 6 inner 588.2.n.d.275.8 24
28.27 even 2 588.2.n.h.263.4 24
84.11 even 6 588.2.e.f.491.7 yes 24
84.23 even 6 inner 588.2.n.d.275.6 24
84.47 odd 6 inner 588.2.n.d.275.5 24
84.59 odd 6 588.2.e.f.491.8 yes 24
84.83 odd 2 588.2.n.h.263.10 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.f.491.5 24 7.4 even 3
588.2.e.f.491.6 yes 24 7.3 odd 6
588.2.e.f.491.7 yes 24 84.11 even 6
588.2.e.f.491.8 yes 24 84.59 odd 6
588.2.e.f.491.17 yes 24 28.3 even 6
588.2.e.f.491.18 yes 24 28.11 odd 6
588.2.e.f.491.19 yes 24 21.17 even 6
588.2.e.f.491.20 yes 24 21.11 odd 6
588.2.n.d.263.5 24 7.6 odd 2 inner
588.2.n.d.263.6 24 1.1 even 1 trivial
588.2.n.d.263.7 24 21.20 even 2 inner
588.2.n.d.263.8 24 3.2 odd 2 inner
588.2.n.d.275.5 24 84.47 odd 6 inner
588.2.n.d.275.6 24 84.23 even 6 inner
588.2.n.d.275.7 24 28.19 even 6 inner
588.2.n.d.275.8 24 28.23 odd 6 inner
588.2.n.h.263.3 24 4.3 odd 2
588.2.n.h.263.4 24 28.27 even 2
588.2.n.h.263.9 24 12.11 even 2
588.2.n.h.263.10 24 84.83 odd 2
588.2.n.h.275.3 24 21.2 odd 6
588.2.n.h.275.4 24 21.5 even 6
588.2.n.h.275.9 24 7.2 even 3
588.2.n.h.275.10 24 7.5 odd 6