Properties

Label 588.2.n.f.263.7
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 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")
 
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);
 
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 = [24,0,0,4,0,-12] 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: no (minimal twist has level 84)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 263.7
Character χ\chi == 588.263
Dual form 588.2.n.f.275.7

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+(0.300756+1.38186i)q2+(0.814407+1.52864i)q3+(1.81909+0.831208i)q4+(0.301907+0.174306i)q5+(1.86743+1.58515i)q6+(1.695722.26374i)q8+(1.67348+2.48987i)q9+(0.3316670.364770i)q10+(1.95188+3.38076i)q11+(2.752102.10379i)q122.93923q13+(0.5123260.319551i)q15+(2.618193.02409i)q16+(3.380761.95188i)q17+(3.943971.56368i)q18+(4.830982.78917i)q19+(0.4043120.568026i)q20+(5.258791.68045i)q22+(1.09094+1.88957i)q23+(2.079454.43575i)q24+(2.43923+4.22488i)q25+(0.8839934.06162i)q26+(5.169010.530383i)q27+9.75220iq29+(0.2874900.804071i)q30+(2.28553+1.31955i)q31+(4.96631+2.70846i)q32+(6.757590.230411i)q33+(1.680455.25879i)q34+(0.9746165.92031i)q36+(0.3195510.553478i)q37+(5.30720+5.83689i)q38+(2.393734.49303i)q39+(0.906533+0.387866i)q407.57031iq412.51757iq43+(0.7405387.77233i)q44+(0.07123611.04341i)q45+(2.28302+2.07583i)q46+(2.18189+3.77914i)q47+(6.75501+1.53943i)q48+(6.571822.10003i)q50+(0.2304116.75759i)q51+(5.346742.44312i)q52+(1.49119+0.860938i)q53+(0.8216977.30238i)q541.36090iq55+(8.19802+5.11331i)q57+(13.4762+2.93304i)q58+(4.123187.14155i)q59+(1.19758+0.155443i)q60+(7.04795+12.2074i)q61+(1.13605+3.55515i)q62+(2.24908+7.67735i)q64+(0.8873750.512326i)q65+(1.713999.40736i)q66+(0.553478+0.319551i)q67+(7.77233+0.740538i)q68+(2.00000+3.20654i)q69+11.9341q71+(8.474190.433786i)q72+(3.93923+6.82295i)q73+(0.6687240.608037i)q74+(8.444850.287941i)q75+(6.46962+9.08930i)q76+(5.488834.65912i)q78+(3.46410+2.00000i)q79+(0.263332+1.36936i)q80+(3.398928.33351i)q81+(10.46112.27682i)q82+8.94358q83+1.36090q85+(3.478940.757175i)q86+(14.9076+7.94226i)q87+(10.96301.31425i)q88+(9.12760+5.26982i)q89+(1.463270.215373i)q90+(3.555152.53050i)q92+(0.155767+4.56840i)q93+(4.56604+4.15167i)q94+(0.972337+1.68414i)q95+(0.0956677+9.79749i)q962.00000q97+(5.1512110.5176i)q99+O(q100)q+(0.300756 + 1.38186i) q^{2} +(0.814407 + 1.52864i) q^{3} +(-1.81909 + 0.831208i) q^{4} +(-0.301907 + 0.174306i) q^{5} +(-1.86743 + 1.58515i) q^{6} +(-1.69572 - 2.26374i) q^{8} +(-1.67348 + 2.48987i) q^{9} +(-0.331667 - 0.364770i) q^{10} +(-1.95188 + 3.38076i) q^{11} +(-2.75210 - 2.10379i) q^{12} -2.93923 q^{13} +(-0.512326 - 0.319551i) q^{15} +(2.61819 - 3.02409i) q^{16} +(-3.38076 - 1.95188i) q^{17} +(-3.94397 - 1.56368i) q^{18} +(4.83098 - 2.78917i) q^{19} +(0.404312 - 0.568026i) q^{20} +(-5.25879 - 1.68045i) q^{22} +(1.09094 + 1.88957i) q^{23} +(2.07945 - 4.43575i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(-0.883993 - 4.06162i) q^{26} +(-5.16901 - 0.530383i) q^{27} +9.75220i q^{29} +(0.287490 - 0.804071i) q^{30} +(2.28553 + 1.31955i) q^{31} +(4.96631 + 2.70846i) q^{32} +(-6.75759 - 0.230411i) q^{33} +(1.68045 - 5.25879i) q^{34} +(0.974616 - 5.92031i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(5.30720 + 5.83689i) q^{38} +(-2.39373 - 4.49303i) q^{39} +(0.906533 + 0.387866i) q^{40} -7.57031i q^{41} -2.51757i q^{43} +(0.740538 - 7.77233i) q^{44} +(0.0712361 - 1.04341i) q^{45} +(-2.28302 + 2.07583i) q^{46} +(2.18189 + 3.77914i) q^{47} +(6.75501 + 1.53943i) q^{48} +(-6.57182 - 2.10003i) q^{50} +(0.230411 - 6.75759i) q^{51} +(5.34674 - 2.44312i) q^{52} +(1.49119 + 0.860938i) q^{53} +(-0.821697 - 7.30238i) q^{54} -1.36090i q^{55} +(8.19802 + 5.11331i) q^{57} +(-13.4762 + 2.93304i) q^{58} +(4.12318 - 7.14155i) q^{59} +(1.19758 + 0.155443i) q^{60} +(7.04795 + 12.2074i) q^{61} +(-1.13605 + 3.55515i) q^{62} +(-2.24908 + 7.67735i) q^{64} +(0.887375 - 0.512326i) q^{65} +(-1.71399 - 9.40736i) q^{66} +(0.553478 + 0.319551i) q^{67} +(7.77233 + 0.740538i) q^{68} +(-2.00000 + 3.20654i) q^{69} +11.9341 q^{71} +(8.47419 - 0.433786i) q^{72} +(-3.93923 + 6.82295i) q^{73} +(0.668724 - 0.608037i) q^{74} +(-8.44485 - 0.287941i) q^{75} +(-6.46962 + 9.08930i) q^{76} +(5.48883 - 4.65912i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(-0.263332 + 1.36936i) q^{80} +(-3.39892 - 8.33351i) q^{81} +(10.4611 - 2.27682i) q^{82} +8.94358 q^{83} +1.36090 q^{85} +(3.47894 - 0.757175i) q^{86} +(-14.9076 + 7.94226i) q^{87} +(10.9630 - 1.31425i) q^{88} +(-9.12760 + 5.26982i) q^{89} +(1.46327 - 0.215373i) q^{90} +(-3.55515 - 2.53050i) q^{92} +(-0.155767 + 4.56840i) q^{93} +(-4.56604 + 4.15167i) q^{94} +(-0.972337 + 1.68414i) q^{95} +(-0.0956677 + 9.79749i) q^{96} -2.00000 q^{97} +(-5.15121 - 10.5176i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+4q412q6+4q94q10+6q124q16+8q1832q222q24+12q2520q30+16q33+64q3440q36+16q3720q4024q45+92q48+48q97+O(q100) 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+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 0.300756 + 1.38186i 0.212667 + 0.977125i
33 0.814407 + 1.52864i 0.470198 + 0.882561i
44 −1.81909 + 0.831208i −0.909546 + 0.415604i
55 −0.301907 + 0.174306i −0.135017 + 0.0779520i −0.565987 0.824414i 0.691505π-0.691505\pi
0.430970 + 0.902366i 0.358171π0.358171\pi
66 −1.86743 + 1.58515i −0.762377 + 0.647134i
77 0 0
88 −1.69572 2.26374i −0.599527 0.800354i
99 −1.67348 + 2.48987i −0.557827 + 0.829957i
1010 −0.331667 0.364770i −0.104882 0.115350i
1111 −1.95188 + 3.38076i −0.588514 + 1.01934i 0.405913 + 0.913912i 0.366954π0.366954\pi
−0.994427 + 0.105425i 0.966380π0.966380\pi
1212 −2.75210 2.10379i −0.794463 0.607313i
1313 −2.93923 −0.815197 −0.407599 0.913161i 0.633634π-0.633634\pi
−0.407599 + 0.913161i 0.633634π0.633634\pi
1414 0 0
1515 −0.512326 0.319551i −0.132282 0.0825077i
1616 2.61819 3.02409i 0.654547 0.756022i
1717 −3.38076 1.95188i −0.819954 0.473401i 0.0304464 0.999536i 0.490307π-0.490307\pi
−0.850401 + 0.526136i 0.823640π0.823640\pi
1818 −3.94397 1.56368i −0.929603 0.368563i
1919 4.83098 2.78917i 1.10830 0.639879i 0.169914 0.985459i 0.445651π-0.445651\pi
0.938389 + 0.345580i 0.112318π0.112318\pi
2020 0.404312 0.568026i 0.0904068 0.127014i
2121 0 0
2222 −5.25879 1.68045i −1.12118 0.358273i
2323 1.09094 + 1.88957i 0.227477 + 0.394003i 0.957060 0.289890i 0.0936189π-0.0936189\pi
−0.729582 + 0.683893i 0.760286π0.760286\pi
2424 2.07945 4.43575i 0.424465 0.905444i
2525 −2.43923 + 4.22488i −0.487847 + 0.844976i
2626 −0.883993 4.06162i −0.173365 0.796549i
2727 −5.16901 0.530383i −0.994777 0.102072i
2828 0 0
2929 9.75220i 1.81094i 0.424412 + 0.905469i 0.360481π0.360481\pi
−0.424412 + 0.905469i 0.639519π0.639519\pi
3030 0.287490 0.804071i 0.0524883 0.146803i
3131 2.28553 + 1.31955i 0.410493 + 0.236998i 0.691002 0.722853i 0.257170π-0.257170\pi
−0.280508 + 0.959852i 0.590503π0.590503\pi
3232 4.96631 + 2.70846i 0.877928 + 0.478793i
3333 −6.75759 0.230411i −1.17635 0.0401094i
3434 1.68045 5.25879i 0.288195 0.901874i
3535 0 0
3636 0.974616 5.92031i 0.162436 0.986719i
3737 −0.319551 0.553478i −0.0525338 0.0909913i 0.838563 0.544805i 0.183396π-0.183396\pi
−0.891096 + 0.453814i 0.850063π0.850063\pi
3838 5.30720 + 5.83689i 0.860941 + 0.946869i
3939 −2.39373 4.49303i −0.383304 0.719461i
4040 0.906533 + 0.387866i 0.143335 + 0.0613270i
4141 7.57031i 1.18228i −0.806567 0.591142i 0.798677π-0.798677\pi
0.806567 0.591142i 0.201323π-0.201323\pi
4242 0 0
4343 2.51757i 0.383926i −0.981402 0.191963i 0.938515π-0.938515\pi
0.981402 0.191963i 0.0614854π-0.0614854\pi
4444 0.740538 7.77233i 0.111640 1.17172i
4545 0.0712361 1.04341i 0.0106193 0.155542i
4646 −2.28302 + 2.07583i −0.336613 + 0.306065i
4747 2.18189 + 3.77914i 0.318261 + 0.551244i 0.980125 0.198379i 0.0635678π-0.0635678\pi
−0.661864 + 0.749624i 0.730235π0.730235\pi
4848 6.75501 + 1.53943i 0.975002 + 0.222197i
4949 0 0
5050 −6.57182 2.10003i −0.929396 0.296989i
5151 0.230411 6.75759i 0.0322640 0.946252i
5252 5.34674 2.44312i 0.741459 0.338799i
5353 1.49119 + 0.860938i 0.204830 + 0.118259i 0.598907 0.800819i 0.295602π-0.295602\pi
−0.394076 + 0.919078i 0.628935π0.628935\pi
5454 −0.821697 7.30238i −0.111819 0.993729i
5555 1.36090i 0.183504i
5656 0 0
5757 8.19802 + 5.11331i 1.08585 + 0.677275i
5858 −13.4762 + 2.93304i −1.76951 + 0.385126i
5959 4.12318 7.14155i 0.536792 0.929751i −0.462282 0.886733i 0.652969π-0.652969\pi
0.999074 0.0430181i 0.0136973π-0.0136973\pi
6060 1.19758 + 0.155443i 0.154607 + 0.0200676i
6161 7.04795 + 12.2074i 0.902398 + 1.56300i 0.824372 + 0.566048i 0.191528π0.191528\pi
0.0780257 + 0.996951i 0.475138π0.475138\pi
6262 −1.13605 + 3.55515i −0.144279 + 0.451505i
6363 0 0
6464 −2.24908 + 7.67735i −0.281135 + 0.959668i
6565 0.887375 0.512326i 0.110065 0.0635462i
6666 −1.71399 9.40736i −0.210978 1.15797i
6767 0.553478 + 0.319551i 0.0676181 + 0.0390393i 0.533428 0.845846i 0.320904π-0.320904\pi
−0.465810 + 0.884885i 0.654237π0.654237\pi
6868 7.77233 + 0.740538i 0.942533 + 0.0898034i
6969 −2.00000 + 3.20654i −0.240772 + 0.386022i
7070 0 0
7171 11.9341 1.41632 0.708158 0.706054i 0.249526π-0.249526\pi
0.708158 + 0.706054i 0.249526π0.249526\pi
7272 8.47419 0.433786i 0.998692 0.0511222i
7373 −3.93923 + 6.82295i −0.461053 + 0.798566i −0.999014 0.0444032i 0.985861π-0.985861\pi
0.537961 + 0.842970i 0.319195π0.319195\pi
7474 0.668724 0.608037i 0.0777376 0.0706829i
7575 −8.44485 0.287941i −0.975127 0.0332485i
7676 −6.46962 + 9.08930i −0.742116 + 1.04261i
7777 0 0
7878 5.48883 4.65912i 0.621487 0.527541i
7979 −3.46410 + 2.00000i −0.389742 + 0.225018i −0.682048 0.731307i 0.738911π-0.738911\pi
0.292306 + 0.956325i 0.405577π0.405577\pi
8080 −0.263332 + 1.36936i −0.0294414 + 0.153099i
8181 −3.39892 8.33351i −0.377657 0.925945i
8282 10.4611 2.27682i 1.15524 0.251433i
8383 8.94358 0.981685 0.490843 0.871248i 0.336689π-0.336689\pi
0.490843 + 0.871248i 0.336689π0.336689\pi
8484 0 0
8585 1.36090 0.147610
8686 3.47894 0.757175i 0.375144 0.0816483i
8787 −14.9076 + 7.94226i −1.59826 + 0.851500i
8888 10.9630 1.31425i 1.16866 0.140100i
8989 −9.12760 + 5.26982i −0.967523 + 0.558600i −0.898480 0.439014i 0.855328π-0.855328\pi
−0.0690430 + 0.997614i 0.521995π0.521995\pi
9090 1.46327 0.215373i 0.154242 0.0227023i
9191 0 0
9292 −3.55515 2.53050i −0.370650 0.263823i
9393 −0.155767 + 4.56840i −0.0161523 + 0.473721i
9494 −4.56604 + 4.15167i −0.470951 + 0.428212i
9595 −0.972337 + 1.68414i −0.0997597 + 0.172789i
9696 −0.0956677 + 9.79749i −0.00976404 + 0.999952i
9797 −2.00000 −0.203069 −0.101535 0.994832i 0.532375π-0.532375\pi
−0.101535 + 0.994832i 0.532375π0.532375\pi
9898 0 0
9999 −5.15121 10.5176i −0.517716 1.05706i
100100 0.925439 9.71295i 0.0925439 0.971295i
101101 −2.68047 1.54757i −0.266717 0.153989i 0.360678 0.932690i 0.382545π-0.382545\pi
−0.627395 + 0.778701i 0.715879π0.715879\pi
102102 9.40736 1.71399i 0.931468 0.169710i
103103 −6.26948 + 3.61968i −0.617750 + 0.356658i −0.775992 0.630742i 0.782751π-0.782751\pi
0.158243 + 0.987400i 0.449417π0.449417\pi
104104 4.98412 + 6.65368i 0.488733 + 0.652447i
105105 0 0
106106 −0.741214 + 2.31955i −0.0719931 + 0.225295i
107107 5.50703 + 9.53846i 0.532385 + 0.922118i 0.999285 + 0.0378077i 0.0120374π0.0120374\pi
−0.466900 + 0.884310i 0.654629π0.654629\pi
108108 9.84376 3.33171i 0.947217 0.320594i
109109 −0.699867 + 1.21220i −0.0670351 + 0.116108i −0.897595 0.440821i 0.854687π-0.854687\pi
0.830560 + 0.556929i 0.188021π0.188021\pi
110110 1.88058 0.409299i 0.179306 0.0390251i
111111 0.585825 0.939235i 0.0556040 0.0891482i
112112 0 0
113113 8.83218i 0.830862i −0.909625 0.415431i 0.863631π-0.863631\pi
0.909625 0.415431i 0.136369π-0.136369\pi
114114 −4.60029 + 12.8664i −0.430857 + 1.20505i
115115 −0.658727 0.380316i −0.0614266 0.0354646i
116116 −8.10611 17.7401i −0.752633 1.64713i
117117 4.91876 7.31832i 0.454739 0.676579i
118118 11.1087 + 3.54980i 1.02264 + 0.326786i
119119 0 0
120120 0.145380 + 1.70164i 0.0132713 + 0.155338i
121121 −2.11968 3.67140i −0.192699 0.333764i
122122 −14.7493 + 13.4108i −1.33534 + 1.21415i
123123 11.5723 6.16532i 1.04344 0.555908i
124124 −5.25441 0.500634i −0.471860 0.0449582i
125125 3.44375i 0.308019i
126126 0 0
127127 12.3960i 1.09997i 0.835174 + 0.549985i 0.185367π0.185367\pi
−0.835174 + 0.549985i 0.814633π0.814633\pi
128128 −11.2855 0.798907i −0.997504 0.0706140i
129129 3.84846 2.05033i 0.338838 0.180521i
130130 0.974848 + 1.07215i 0.0854998 + 0.0940334i
131131 0.805238 + 1.39471i 0.0703540 + 0.121857i 0.899056 0.437833i 0.144254π-0.144254\pi
−0.828702 + 0.559689i 0.810920π0.810920\pi
132132 12.4842 5.19782i 1.08661 0.452412i
133133 0 0
134134 −0.275113 + 0.860938i −0.0237662 + 0.0743737i
135135 1.65301 0.740864i 0.142268 0.0637634i
136136 1.31425 + 10.9630i 0.112696 + 0.940071i
137137 −3.77914 2.18189i −0.322874 0.186411i 0.329799 0.944051i 0.393019π-0.393019\pi
−0.652673 + 0.757640i 0.726352π0.726352\pi
138138 −5.03251 1.79934i −0.428396 0.153170i
139139 16.8177i 1.42646i 0.700931 + 0.713230i 0.252768π0.252768\pi
−0.700931 + 0.713230i 0.747232π0.747232\pi
140140 0 0
141141 −4.00000 + 6.41308i −0.336861 + 0.540079i
142142 3.58925 + 16.4913i 0.301203 + 1.38392i
143143 5.73704 9.93684i 0.479755 0.830961i
144144 3.14810 + 11.5797i 0.262341 + 0.964975i
145145 −1.69987 2.94426i −0.141166 0.244507i
146146 −10.6131 3.39144i −0.878350 0.280677i
147147 0 0
148148 1.04135 + 0.741214i 0.0855982 + 0.0609274i
149149 −6.63421 + 3.83026i −0.543496 + 0.313788i −0.746495 0.665391i 0.768265π-0.768265\pi
0.202999 + 0.979179i 0.434931π0.434931\pi
150150 −2.14195 11.7562i −0.174889 0.959892i
151151 10.9458 + 6.31955i 0.890755 + 0.514278i 0.874189 0.485585i 0.161393π-0.161393\pi
0.0165658 + 0.999863i 0.494727π0.494727\pi
152152 −14.5059 6.20646i −1.17659 0.503411i
153153 10.5176 5.15121i 0.850295 0.416451i
154154 0 0
155155 −0.920022 −0.0738980
156156 8.08907 + 6.18355i 0.647644 + 0.495080i
157157 −0.108719 + 0.188307i −0.00867672 + 0.0150285i −0.870331 0.492467i 0.836095π-0.836095\pi
0.861654 + 0.507495i 0.169429π0.169429\pi
158158 −3.80558 4.18540i −0.302755 0.332973i
159159 −0.101630 + 2.98064i −0.00805978 + 0.236381i
160160 −1.97146 + 0.0479539i −0.155858 + 0.00379109i
161161 0 0
162162 10.4935 7.20319i 0.824449 0.565936i
163163 4.53743 2.61968i 0.355399 0.205189i −0.311662 0.950193i 0.600886π-0.600886\pi
0.667060 + 0.745004i 0.267552π0.267552\pi
164164 6.29250 + 13.7711i 0.491362 + 1.07534i
165165 2.08032 1.10833i 0.161953 0.0862830i
166166 2.68984 + 12.3588i 0.208772 + 0.959229i
167167 −11.4741 −0.887891 −0.443945 0.896054i 0.646422π-0.646422\pi
−0.443945 + 0.896054i 0.646422π0.646422\pi
168168 0 0
169169 −4.36090 −0.335454
170170 0.409299 + 1.88058i 0.0313918 + 0.144234i
171171 −1.13989 + 16.6961i −0.0871695 + 1.27679i
172172 2.09263 + 4.57969i 0.159561 + 0.349198i
173173 18.3642 10.6025i 1.39620 0.806097i 0.402208 0.915548i 0.368243π-0.368243\pi
0.993992 + 0.109451i 0.0349094π0.0349094\pi
174174 −15.4587 18.2116i −1.17192 1.38062i
175175 0 0
176176 5.11331 + 14.7541i 0.385430 + 1.11213i
177177 14.2748 + 0.486723i 1.07296 + 0.0365843i
178178 −10.0274 11.0282i −0.751582 0.826595i
179179 −0.906046 + 1.56932i −0.0677211 + 0.117296i −0.897898 0.440204i 0.854906π-0.854906\pi
0.830177 + 0.557500i 0.188239π0.188239\pi
180180 0.737703 + 1.95726i 0.0549851 + 0.145886i
181181 7.53950 0.560407 0.280203 0.959941i 0.409598π-0.409598\pi
0.280203 + 0.959941i 0.409598π0.409598\pi
182182 0 0
183183 −12.9208 + 20.7156i −0.955136 + 1.53134i
184184 2.42757 5.67380i 0.178963 0.418278i
185185 0.192949 + 0.111399i 0.0141859 + 0.00819023i
186186 −6.35976 + 1.15873i −0.466320 + 0.0849620i
187187 13.1977 7.61968i 0.965110 0.557206i
188188 −7.11030 5.06100i −0.518572 0.369111i
189189 0 0
190190 −2.61968 0.837122i −0.190052 0.0607312i
191191 −0.815830 1.41306i −0.0590314 0.102245i 0.834999 0.550251i 0.185468π-0.185468\pi
−0.894031 + 0.448005i 0.852135π0.852135\pi
192192 −13.5676 + 2.81446i −0.979155 + 0.203116i
193193 7.57834 13.1261i 0.545501 0.944835i −0.453075 0.891473i 0.649673π-0.649673\pi
0.998575 0.0533622i 0.0169938π-0.0169938\pi
194194 −0.601512 2.76373i −0.0431861 0.198424i
195195 1.50585 + 0.939235i 0.107836 + 0.0672600i
196196 0 0
197197 21.2263i 1.51231i −0.654393 0.756155i 0.727076π-0.727076\pi
0.654393 0.756155i 0.272924π-0.272924\pi
198198 12.9846 10.2815i 0.922774 0.730674i
199199 −3.25361 1.87847i −0.230642 0.133161i 0.380226 0.924894i 0.375846π-0.375846\pi
−0.610868 + 0.791732i 0.709179π0.709179\pi
200200 13.7003 1.64240i 0.968758 0.116135i
201201 −0.0377216 + 1.10631i −0.00266067 + 0.0780333i
202202 1.33236 4.16948i 0.0937447 0.293364i
203203 0 0
204204 5.19782 + 12.4842i 0.363920 + 0.874068i
205205 1.31955 + 2.28553i 0.0921614 + 0.159628i
206206 −6.88749 7.57492i −0.479874 0.527769i
207207 −6.53046 0.445852i −0.453898 0.0309888i
208208 −7.69547 + 8.88850i −0.533585 + 0.616307i
209209 21.7765i 1.50631i
210210 0 0
211211 9.83963i 0.677388i −0.940897 0.338694i 0.890015π-0.890015\pi
0.940897 0.338694i 0.109985π-0.109985\pi
212212 −3.42823 0.326637i −0.235452 0.0224335i
213213 9.71921 + 18.2429i 0.665949 + 1.24998i
214214 −11.5246 + 10.4787i −0.787804 + 0.716310i
215215 0.438828 + 0.760072i 0.0299278 + 0.0518365i
216216 7.56454 + 12.6007i 0.514702 + 0.857369i
217217 0 0
218218 −1.88559 0.602542i −0.127708 0.0408093i
219219 −13.6380 0.465009i −0.921570 0.0314224i
220220 1.13119 + 2.47560i 0.0762648 + 0.166905i
221221 9.93684 + 5.73704i 0.668424 + 0.385915i
222222 1.47408 + 0.527049i 0.0989341 + 0.0353732i
223223 22.9136i 1.53441i −0.641403 0.767204i 0.721647π-0.721647\pi
0.641403 0.767204i 0.278353π-0.278353\pi
224224 0 0
225225 −6.43739 13.1436i −0.429159 0.876243i
226226 12.2049 2.65633i 0.811855 0.176697i
227227 6.76508 11.7175i 0.449014 0.777715i −0.549308 0.835620i 0.685109π-0.685109\pi
0.998322 + 0.0579050i 0.0184421π0.0184421\pi
228228 −19.1632 2.48732i −1.26911 0.164727i
229229 −7.34809 12.7273i −0.485575 0.841041i 0.514287 0.857618i 0.328056π-0.328056\pi
−0.999863 + 0.0165769i 0.994723π0.994723\pi
230230 0.327428 1.02465i 0.0215900 0.0675636i
231231 0 0
232232 22.0765 16.5370i 1.44939 1.08571i
233233 14.8869 8.59497i 0.975274 0.563075i 0.0744343 0.997226i 0.476285π-0.476285\pi
0.900840 + 0.434151i 0.142952π0.142952\pi
234234 11.5923 + 4.59602i 0.757810 + 0.300451i
235235 −1.31745 0.760632i −0.0859412 0.0496182i
236236 −1.56432 + 16.4184i −0.101829 + 1.06874i
237237 −5.87847 3.66655i −0.381848 0.238168i
238238 0 0
239239 14.5336 0.940102 0.470051 0.882639i 0.344236π-0.344236\pi
0.470051 + 0.882639i 0.344236π0.344236\pi
240240 −2.30771 + 0.712675i −0.148962 + 0.0460030i
241241 9.39604 16.2744i 0.605252 1.04833i −0.386759 0.922181i 0.626406π-0.626406\pi
0.992012 0.126147i 0.0402611π-0.0402611\pi
242242 4.43586 4.03331i 0.285148 0.259271i
243243 9.97083 11.9826i 0.639629 0.768684i
244244 −22.9678 16.3481i −1.47036 1.04658i
245245 0 0
246246 12.0001 + 14.1371i 0.765096 + 0.901346i
247247 −14.1994 + 8.19802i −0.903485 + 0.521628i
248248 −0.888488 7.41144i −0.0564191 0.470627i
249249 7.28371 + 13.6715i 0.461587 + 0.866397i
250250 4.75879 1.03573i 0.300973 0.0655053i
251251 20.6405 1.30281 0.651407 0.758729i 0.274179π-0.274179\pi
0.651407 + 0.758729i 0.274179π0.274179\pi
252252 0 0
253253 −8.51757 −0.535495
254254 −17.1296 + 3.72819i −1.07481 + 0.233927i
255255 1.10833 + 2.08032i 0.0694060 + 0.130275i
256256 −2.29019 15.8352i −0.143137 0.989703i
257257 4.17752 2.41189i 0.260587 0.150450i −0.364016 0.931393i 0.618594π-0.618594\pi
0.624602 + 0.780943i 0.285261π0.285261\pi
258258 3.99072 + 4.70140i 0.248451 + 0.292696i
259259 0 0
260260 −1.18837 + 1.66956i −0.0736994 + 0.103542i
261261 −24.2817 16.3201i −1.50300 1.01019i
262262 −1.68512 + 1.53220i −0.104107 + 0.0946595i
263263 −7.22891 + 12.5208i −0.445754 + 0.772068i −0.998104 0.0615439i 0.980398π-0.980398\pi
0.552351 + 0.833612i 0.313731π0.313731\pi
264264 10.9374 + 15.6882i 0.673149 + 0.965540i
265265 −0.600267 −0.0368741
266266 0 0
267267 −15.4892 9.66103i −0.947926 0.591246i
268268 −1.27244 0.121237i −0.0777267 0.00740571i
269269 4.08105 + 2.35619i 0.248826 + 0.143660i 0.619226 0.785212i 0.287446π-0.287446\pi
−0.370401 + 0.928872i 0.620780π0.620780\pi
270270 1.52092 + 2.06141i 0.0925605 + 0.125454i
271271 −13.5743 + 7.83712i −0.824580 + 0.476071i −0.851993 0.523553i 0.824606π-0.824606\pi
0.0274135 + 0.999624i 0.491273π0.491273\pi
272272 −14.7541 + 5.11331i −0.894600 + 0.310040i
273273 0 0
274274 1.87847 5.87847i 0.113483 0.355131i
275275 −9.52220 16.4929i −0.574210 0.994561i
276276 0.972882 7.49540i 0.0585606 0.451170i
277277 −8.49815 + 14.7192i −0.510605 + 0.884393i 0.489320 + 0.872104i 0.337245π0.337245\pi
−0.999924 + 0.0122887i 0.996088π0.996088\pi
278278 −23.2398 + 5.05803i −1.39383 + 0.303360i
279279 −7.11030 + 3.48243i −0.425683 + 0.208488i
280280 0 0
281281 5.75822i 0.343507i −0.985140 0.171753i 0.945057π-0.945057\pi
0.985140 0.171753i 0.0549432π-0.0549432\pi
282282 −10.0650 3.59868i −0.599363 0.214298i
283283 4.83098 + 2.78917i 0.287172 + 0.165799i 0.636666 0.771140i 0.280313π-0.280313\pi
−0.349494 + 0.936939i 0.613646π0.613646\pi
284284 −21.7092 + 9.91971i −1.28820 + 0.588626i
285285 −3.36632 0.114780i −0.199404 0.00679899i
286286 15.4568 + 4.93923i 0.913980 + 0.292063i
287287 0 0
288288 −15.0548 + 7.83291i −0.887110 + 0.461558i
289289 −0.880316 1.52475i −0.0517833 0.0896913i
290290 3.55731 3.23449i 0.208893 0.189936i
291291 −1.62881 3.05728i −0.0954828 0.179221i
292292 1.49453 15.6859i 0.0874610 0.917948i
293293 23.7712i 1.38873i 0.719624 + 0.694364i 0.244314π0.244314\pi
−0.719624 + 0.694364i 0.755686π0.755686\pi
294294 0 0
295295 2.87478i 0.167376i
296296 −0.711065 + 1.66192i −0.0413298 + 0.0965974i
297297 11.8824 16.4399i 0.689487 0.953942i
298298 −7.28818 8.01560i −0.422193 0.464331i
299299 −3.20654 5.55389i −0.185439 0.321190i
300300 15.6013 6.49564i 0.900741 0.375026i
301301 0 0
302302 −5.44074 + 17.0262i −0.313080 + 0.979749i
303303 0.182684 5.35783i 0.0104949 0.307799i
304304 4.21373 21.9119i 0.241674 1.25673i
305305 −4.25565 2.45700i −0.243678 0.140687i
306306 10.2815 + 12.9846i 0.587754 + 0.742279i
307307 3.69987i 0.211163i −0.994411 0.105581i 0.966330π-0.966330\pi
0.994411 0.105581i 0.0336703π-0.0336703\pi
308308 0 0
309309 −10.6391 6.63588i −0.605237 0.377502i
310310 −0.276702 1.27134i −0.0157156 0.0722075i
311311 3.79236 6.56857i 0.215045 0.372469i −0.738241 0.674537i 0.764343π-0.764343\pi
0.953287 + 0.302067i 0.0976768π0.0976768\pi
312312 −6.11198 + 13.0377i −0.346023 + 0.738116i
313313 −7.81770 13.5407i −0.441883 0.765363i 0.555946 0.831218i 0.312356π-0.312356\pi
−0.997829 + 0.0658547i 0.979023π0.979023\pi
314314 −0.292912 0.0936004i −0.0165300 0.00528217i
315315 0 0
316316 4.63910 6.51757i 0.260970 0.366642i
317317 12.0318 6.94659i 0.675776 0.390159i −0.122486 0.992470i 0.539087π-0.539087\pi
0.798262 + 0.602311i 0.205753π0.205753\pi
318318 −4.14941 + 0.756009i −0.232687 + 0.0423949i
319319 −32.9698 19.0351i −1.84596 1.06576i
320320 −0.659196 2.70987i −0.0368502 0.151486i
321321 −10.0959 + 16.1865i −0.563499 + 0.903440i
322322 0 0
323323 −21.7765 −1.21168
324324 13.1098 + 12.3342i 0.728323 + 0.685234i
325325 7.16948 12.4179i 0.397691 0.688822i
326326 4.98470 + 5.48222i 0.276077 + 0.303632i
327327 −2.42300 0.0826162i −0.133992 0.00456868i
328328 −17.1373 + 12.8371i −0.946247 + 0.708811i
329329 0 0
330330 2.15722 + 2.54139i 0.118751 + 0.139899i
331331 27.5359 15.8979i 1.51351 0.873827i 0.513638 0.858007i 0.328298π-0.328298\pi
0.999875 0.0158198i 0.00503580π-0.00503580\pi
332332 −16.2692 + 7.43397i −0.892888 + 0.407992i
333333 1.91285 + 0.130595i 0.104824 + 0.00715658i
334334 −3.45090 15.8556i −0.188825 0.867580i
335335 −0.222798 −0.0121728
336336 0 0
337337 −17.1178 −0.932468 −0.466234 0.884661i 0.654390π-0.654390\pi
−0.466234 + 0.884661i 0.654390π0.654390\pi
338338 −1.31157 6.02616i −0.0713399 0.327780i
339339 13.5012 7.19299i 0.733286 0.390670i
340340 −2.47560 + 1.13119i −0.134258 + 0.0613474i
341341 −8.92216 + 5.15121i −0.483162 + 0.278954i
342342 −23.4146 + 3.44630i −1.26612 + 0.186354i
343343 0 0
344344 −5.69914 + 4.26909i −0.307277 + 0.230174i
345345 0.0448946 1.31669i 0.00241704 0.0708881i
346346 20.1744 + 22.1880i 1.08458 + 1.19283i
347347 4.22398 7.31616i 0.226755 0.392752i −0.730089 0.683352i 0.760522π-0.760522\pi
0.956845 + 0.290600i 0.0938549π0.0938549\pi
348348 20.5166 26.8390i 1.09981 1.43872i
349349 17.4956 0.936520 0.468260 0.883591i 0.344881π-0.344881\pi
0.468260 + 0.883591i 0.344881π0.344881\pi
350350 0 0
351351 15.1929 + 1.55892i 0.810939 + 0.0832089i
352352 −18.8503 + 11.5033i −1.00472 + 0.613127i
353353 −7.15990 4.13377i −0.381083 0.220018i 0.297206 0.954813i 0.403945π-0.403945\pi
−0.678289 + 0.734795i 0.737278π0.737278\pi
354354 3.62065 + 19.8722i 0.192436 + 1.05620i
355355 −3.60298 + 2.08018i −0.191226 + 0.110405i
356356 12.2236 17.1732i 0.647850 0.910179i
357357 0 0
358358 −2.44108 0.780049i −0.129015 0.0412269i
359359 12.5650 + 21.7633i 0.663156 + 1.14862i 0.979782 + 0.200070i 0.0641169π0.0641169\pi
−0.316625 + 0.948551i 0.602550π0.602550\pi
360360 −2.48280 + 1.60806i −0.130855 + 0.0847524i
361361 6.05892 10.4944i 0.318890 0.552334i
362362 2.26755 + 10.4186i 0.119180 + 0.547587i
363363 3.88596 6.23025i 0.203960 0.327003i
364364 0 0
365365 2.74653i 0.143760i
366366 −32.5121 11.6245i −1.69944 0.607622i
367367 −18.8041 10.8565i −0.981565 0.566707i −0.0788227 0.996889i 0.525116π-0.525116\pi
−0.902742 + 0.430182i 0.858449π0.858449\pi
368368 8.57052 + 1.64814i 0.446769 + 0.0859152i
369369 18.8491 + 12.6688i 0.981245 + 0.659510i
370370 −0.0959078 + 0.300133i −0.00498601 + 0.0156032i
371371 0 0
372372 −3.51394 8.43982i −0.182189 0.437584i
373373 0.360898 + 0.625094i 0.0186866 + 0.0323662i 0.875217 0.483730i 0.160718π-0.160718\pi
−0.856531 + 0.516096i 0.827385π0.827385\pi
374374 14.4986 + 15.9457i 0.749707 + 0.824534i
375375 5.26426 2.80462i 0.271845 0.144830i
376376 4.85514 11.3476i 0.250385 0.585207i
377377 28.6640i 1.47627i
378378 0 0
379379 18.2745i 0.938699i −0.883013 0.469349i 0.844489π-0.844489\pi
0.883013 0.469349i 0.155511π-0.155511\pi
380380 0.368902 3.87181i 0.0189243 0.198620i
381381 −18.9491 + 10.0954i −0.970791 + 0.517204i
382382 1.70729 1.55235i 0.0873525 0.0794252i
383383 −1.02465 1.77475i −0.0523573 0.0906855i 0.838659 0.544657i 0.183340π-0.183340\pi
−0.891016 + 0.453971i 0.850007π0.850007\pi
384384 −7.96972 17.9021i −0.406703 0.913560i
385385 0 0
386386 20.4177 + 6.52448i 1.03923 + 0.332087i
387387 6.26843 + 4.21311i 0.318642 + 0.214164i
388388 3.63818 1.66242i 0.184701 0.0843964i
389389 9.65328 + 5.57332i 0.489441 + 0.282579i 0.724342 0.689440i 0.242143π-0.242143\pi
−0.234902 + 0.972019i 0.575477π0.575477\pi
390390 −0.845001 + 2.36335i −0.0427883 + 0.119673i
391391 8.51757i 0.430752i
392392 0 0
393393 −1.47622 + 2.36678i −0.0744656 + 0.119389i
394394 29.3318 6.38394i 1.47772 0.321618i
395395 0.697224 1.20763i 0.0350811 0.0607623i
396396 18.1128 + 14.8507i 0.910203 + 0.746275i
397397 −3.98719 6.90601i −0.200111 0.346603i 0.748453 0.663188i 0.230797π-0.230797\pi
−0.948564 + 0.316585i 0.897464π0.897464\pi
398398 1.61725 5.06100i 0.0810652 0.253685i
399399 0 0
400400 6.39002 + 18.4380i 0.319501 + 0.921899i
401401 −18.6004 + 10.7390i −0.928860 + 0.536278i −0.886451 0.462823i 0.846837π-0.846837\pi
−0.0424093 + 0.999100i 0.513503π0.513503\pi
402402 −1.54012 + 0.280605i −0.0768141 + 0.0139953i
403403 −6.71771 3.87847i −0.334633 0.193200i
404404 6.16237 + 0.587144i 0.306589 + 0.0292115i
405405 2.47874 + 1.92349i 0.123169 + 0.0955790i
406406 0 0
407407 2.49490 0.123668
408408 −15.6882 + 10.9374i −0.776680 + 0.541481i
409409 −18.4568 + 31.9681i −0.912630 + 1.58072i −0.102296 + 0.994754i 0.532619π0.532619\pi
−0.810334 + 0.585968i 0.800714π0.800714\pi
410410 −2.76143 + 2.51083i −0.136377 + 0.124001i
411411 0.257562 7.55389i 0.0127046 0.372606i
412412 8.39604 11.7958i 0.413643 0.581136i
413413 0 0
414414 −1.34797 9.15829i −0.0662491 0.450106i
415415 −2.70013 + 1.55892i −0.132544 + 0.0765243i
416416 −14.5971 7.96081i −0.715684 0.390311i
417417 −25.7082 + 13.6965i −1.25894 + 0.670719i
418418 −30.0921 + 6.54942i −1.47186 + 0.320343i
419419 −29.5773 −1.44494 −0.722472 0.691400i 0.756994π-0.756994\pi
−0.722472 + 0.691400i 0.756994π0.756994\pi
420420 0 0
421421 36.8309 1.79503 0.897515 0.440985i 0.145371π-0.145371\pi
0.897515 + 0.440985i 0.145371π0.145371\pi
422422 13.5970 2.95933i 0.661893 0.144058i
423423 −13.0609 0.891703i −0.635044 0.0433561i
424424 −0.579692 4.83558i −0.0281523 0.234836i
425425 16.4929 9.52220i 0.800024 0.461894i
426426 −22.2861 + 18.9173i −1.07977 + 0.916546i
427427 0 0
428428 −17.9462 12.7738i −0.867464 0.617447i
429429 19.8621 + 0.677232i 0.958953 + 0.0326971i
430430 −0.918335 + 0.834996i −0.0442861 + 0.0402671i
431431 −2.33839 + 4.05022i −0.112636 + 0.195092i −0.916832 0.399272i 0.869263π-0.869263\pi
0.804196 + 0.594364i 0.202596π0.202596\pi
432432 −15.1374 + 14.2429i −0.728297 + 0.685262i
433433 −16.5564 −0.795650 −0.397825 0.917461i 0.630235π-0.630235\pi
−0.397825 + 0.917461i 0.630235π0.630235\pi
434434 0 0
435435 3.11632 4.99631i 0.149416 0.239555i
436436 0.265527 2.78685i 0.0127165 0.133466i
437437 10.5407 + 6.08565i 0.504228 + 0.291116i
438438 −3.45913 18.9857i −0.165284 0.907171i
439439 −22.9313 + 13.2394i −1.09445 + 0.631881i −0.934758 0.355286i 0.884383π-0.884383\pi
−0.159692 + 0.987167i 0.551050π0.551050\pi
440440 −3.08073 + 2.30770i −0.146868 + 0.110015i
441441 0 0
442442 −4.93923 + 15.4568i −0.234935 + 0.735205i
443443 2.30049 + 3.98457i 0.109300 + 0.189313i 0.915487 0.402348i 0.131806π-0.131806\pi
−0.806187 + 0.591661i 0.798472π0.798472\pi
444444 −0.284969 + 2.19550i −0.0135240 + 0.104194i
445445 1.83712 3.18199i 0.0870879 0.150841i
446446 31.6635 6.89141i 1.49931 0.326318i
447447 −11.2580 7.02193i −0.532487 0.332126i
448448 0 0
449449 17.0095i 0.802728i 0.915919 + 0.401364i 0.131464π0.131464\pi
−0.915919 + 0.401364i 0.868536π0.868536\pi
450450 16.2266 12.8486i 0.764930 0.605690i
451451 25.5934 + 14.7764i 1.20515 + 0.695791i
452452 7.34138 + 16.0665i 0.345309 + 0.755706i
453453 −0.745995 + 21.8789i −0.0350499 + 1.02796i
454454 18.2266 + 5.82431i 0.855415 + 0.273348i
455455 0 0
456456 −2.32630 27.2290i −0.108939 1.27511i
457457 7.71559 + 13.3638i 0.360920 + 0.625132i 0.988113 0.153732i 0.0491293π-0.0491293\pi
−0.627192 + 0.778864i 0.715796π0.715796\pi
458458 15.3773 13.9819i 0.718536 0.653329i
459459 16.4399 + 11.8824i 0.767351 + 0.554623i
460460 1.51441 + 0.144291i 0.0706095 + 0.00672759i
461461 33.3764i 1.55449i −0.629196 0.777247i 0.716616π-0.716616\pi
0.629196 0.777247i 0.283384π-0.283384\pi
462462 0 0
463463 26.4787i 1.23057i 0.788304 + 0.615286i 0.210959π0.210959\pi
−0.788304 + 0.615286i 0.789041π0.789041\pi
464464 29.4915 + 25.5331i 1.36911 + 1.18534i
465465 −0.749273 1.40638i −0.0347467 0.0652195i
466466 16.3544 + 17.9867i 0.757603 + 0.833217i
467467 −9.29557 16.1004i −0.430148 0.745038i 0.566738 0.823898i 0.308205π-0.308205\pi
−0.996886 + 0.0788602i 0.974872π0.974872\pi
468468 −2.86462 + 17.4012i −0.132417 + 0.804371i
469469 0 0
470470 0.654857 2.04930i 0.0302063 0.0945274i
471471 −0.376395 0.0128338i −0.0173434 0.000591350i
472472 −23.1584 + 2.77624i −1.06595 + 0.127787i
473473 8.51130 + 4.91400i 0.391350 + 0.225946i
474474 3.29868 9.22598i 0.151514 0.423763i
475475 27.2137i 1.24865i
476476 0 0
477477 −4.63910 + 2.27210i −0.212410 + 0.104032i
478478 4.37108 + 20.0835i 0.199928 + 0.918597i
479479 −20.4388 + 35.4011i −0.933874 + 1.61752i −0.157245 + 0.987560i 0.550261π0.550261\pi
−0.776629 + 0.629958i 0.783072π0.783072\pi
480480 −1.67888 2.97460i −0.0766300 0.135772i
481481 0.939235 + 1.62680i 0.0428254 + 0.0741758i
482482 25.3149 + 8.08941i 1.15306 + 0.368462i
483483 0 0
484484 6.90760 + 4.91671i 0.313982 + 0.223487i
485485 0.603814 0.348612i 0.0274178 0.0158297i
486486 19.5571 + 10.1745i 0.887128 + 0.461524i
487487 18.5599 + 10.7156i 0.841032 + 0.485570i 0.857615 0.514293i 0.171945π-0.171945\pi
−0.0165831 + 0.999862i 0.505279π0.505279\pi
488488 15.6831 36.6551i 0.709941 1.65930i
489489 7.69987 + 4.80260i 0.348200 + 0.217181i
490490 0 0
491491 1.63166 0.0736358 0.0368179 0.999322i 0.488278π-0.488278\pi
0.0368179 + 0.999322i 0.488278π0.488278\pi
492492 −15.9264 + 20.8343i −0.718017 + 0.939281i
493493 19.0351 32.9698i 0.857300 1.48489i
494494 −15.5991 17.1560i −0.701837 0.771885i
495495 3.38846 + 2.27744i 0.152300 + 0.102363i
496496 9.97438 3.45681i 0.447863 0.155215i
497497 0 0
498498 −16.7015 + 14.1769i −0.748414 + 0.635282i
499499 −7.69218 + 4.44108i −0.344349 + 0.198810i −0.662194 0.749333i 0.730374π-0.730374\pi
0.317844 + 0.948143i 0.397041π0.397041\pi
500500 2.86247 + 6.26450i 0.128014 + 0.280157i
501501 −9.34457 17.5397i −0.417485 0.783618i
502502 6.20775 + 28.5223i 0.277065 + 1.27301i
503503 34.8967 1.55597 0.777983 0.628286i 0.216243π-0.216243\pi
0.777983 + 0.628286i 0.216243π0.216243\pi
504504 0 0
505505 1.07900 0.0480150
506506 −2.56171 11.7701i −0.113882 0.523246i
507507 −3.55155 6.66624i −0.157730 0.296058i
508508 −10.3037 22.5495i −0.457152 1.00047i
509509 −20.5865 + 11.8856i −0.912479 + 0.526820i −0.881228 0.472692i 0.843282π-0.843282\pi
−0.0312508 + 0.999512i 0.509949π0.509949\pi
510510 −2.54139 + 2.15722i −0.112535 + 0.0955235i
511511 0 0
512512 21.1934 7.92728i 0.936623 0.350340i
513513 −26.4507 + 11.8550i −1.16783 + 0.523410i
514514 4.58932 + 5.04737i 0.202426 + 0.222630i
515515 1.26186 2.18561i 0.0556044 0.0963097i
516516 −5.29645 + 6.92861i −0.233163 + 0.305015i
517517 −17.0351 −0.749205
518518 0 0
519519 31.1634 + 19.4374i 1.36792 + 0.853207i
520520 −2.66451 1.14003i −0.116847 0.0499936i
521521 4.96256 + 2.86513i 0.217414 + 0.125524i 0.604752 0.796414i 0.293272π-0.293272\pi
−0.387338 + 0.921938i 0.626606π0.626606\pi
522522 15.2493 38.4624i 0.667444 1.68345i
523523 4.17225 2.40885i 0.182440 0.105332i −0.405999 0.913874i 0.633076π-0.633076\pi
0.588439 + 0.808542i 0.299743π0.299743\pi
524524 −2.62410 1.86779i −0.114634 0.0815948i
525525 0 0
526526 −19.4762 6.22364i −0.849204 0.271364i
527527 −5.15121 8.92216i −0.224390 0.388656i
528528 −18.3894 + 19.8323i −0.800297 + 0.863089i
529529 9.11968 15.7958i 0.396508 0.686772i
530530 −0.180534 0.829486i −0.00784189 0.0360306i
531531 10.8815 + 22.2174i 0.472216 + 0.964155i
532532 0 0
533533 22.2509i 0.963795i
534534 8.69174 24.3096i 0.376128 1.05198i
535535 −3.32522 1.91982i −0.143762 0.0830009i
536536 −0.215162 1.79480i −0.00929358 0.0775236i
537537 −3.13681 0.106955i −0.135363 0.00461544i
538538 −2.02854 + 6.34809i −0.0874564 + 0.273685i
539539 0 0
540540 −2.39116 + 2.72169i −0.102899 + 0.117123i
541541 6.01942 + 10.4259i 0.258795 + 0.448246i 0.965919 0.258843i 0.0833413π-0.0833413\pi
−0.707124 + 0.707089i 0.750008π0.750008\pi
542542 −14.9124 16.4008i −0.640542 0.704473i
543543 6.14022 + 11.5252i 0.263502 + 0.494593i
544544 −11.5033 18.8503i −0.493200 0.808200i
545545 0.487964i 0.0209021i
546546 0 0
547547 35.3097i 1.50973i −0.655879 0.754866i 0.727702π-0.727702\pi
0.655879 0.754866i 0.272298π-0.272298\pi
548548 8.68820 + 0.827802i 0.371142 + 0.0353619i
549549 −42.1895 2.88039i −1.80060 0.122932i
550550 19.9271 18.1187i 0.849695 0.772585i
551551 27.2005 + 47.1127i 1.15878 + 2.00707i
552552 10.6502 0.909900i 0.453304 0.0387279i
553553 0 0
554554 −22.8958 7.31638i −0.972751 0.310843i
555555 −0.0131502 + 0.385674i −0.000558194 + 0.0163710i
556556 −13.9790 30.5929i −0.592842 1.29743i
557557 −30.1308 17.3960i −1.27668 0.737093i −0.300445 0.953799i 0.597135π-0.597135\pi
−0.976237 + 0.216706i 0.930469π0.930469\pi
558558 −6.95071 8.77810i −0.294247 0.371607i
559559 7.39973i 0.312975i
560560 0 0
561561 22.3960 + 13.9690i 0.945562 + 0.589771i
562562 7.95707 1.73182i 0.335649 0.0730525i
563563 −6.43088 + 11.1386i −0.271029 + 0.469436i −0.969126 0.246567i 0.920697π-0.920697\pi
0.698096 + 0.716004i 0.254031π0.254031\pi
564564 1.94576 14.9908i 0.0819314 0.631227i
565565 1.53950 + 2.66649i 0.0647673 + 0.112180i
566566 −2.40130 + 7.51461i −0.100934 + 0.315863i
567567 0 0
568568 −20.2369 27.0157i −0.849120 1.13355i
569569 −13.5887 + 7.84543i −0.569667 + 0.328897i −0.757016 0.653396i 0.773344π-0.773344\pi
0.187349 + 0.982293i 0.440010π0.440010\pi
570570 −0.853831 4.68631i −0.0357630 0.196288i
571571 36.4003 + 21.0157i 1.52331 + 0.879481i 0.999620 + 0.0275690i 0.00877659π0.00877659\pi
0.523685 + 0.851912i 0.324557π0.324557\pi
572572 −2.17662 + 22.8447i −0.0910089 + 0.955185i
573573 1.49564 2.39792i 0.0624813 0.100174i
574574 0 0
575575 −10.6443 −0.443897
576576 −15.3518 18.4478i −0.639659 0.768659i
577577 −19.3960 + 33.5949i −0.807468 + 1.39858i 0.107145 + 0.994243i 0.465829π0.465829\pi
−0.914612 + 0.404332i 0.867504π0.867504\pi
578578 1.84224 1.67505i 0.0766270 0.0696731i
579579 26.2369 + 0.894589i 1.09037 + 0.0371778i
580580 5.53950 + 3.94293i 0.230015 + 0.163721i
581581 0 0
582582 3.73487 3.17029i 0.154815 0.131413i
583583 −5.82125 + 3.36090i −0.241091 + 0.139194i
584584 22.1253 2.65239i 0.915550 0.109757i
585585 −0.209380 + 3.06682i −0.00865678 + 0.126797i
586586 −32.8485 + 7.14933i −1.35696 + 0.295336i
587587 7.07471 0.292004 0.146002 0.989284i 0.453359π-0.453359\pi
0.146002 + 0.989284i 0.453359π0.453359\pi
588588 0 0
589589 14.7218 0.606601
590590 −3.97255 + 0.864607i −0.163547 + 0.0355953i
591591 32.4473 17.2868i 1.33471 0.711085i
592592 −2.51041 0.482760i −0.103177 0.0198413i
593593 −15.9258 + 9.19477i −0.653994 + 0.377584i −0.789985 0.613126i 0.789912π-0.789912\pi
0.135991 + 0.990710i 0.456578π0.456578\pi
594594 26.2915 + 11.4754i 1.07875 + 0.470843i
595595 0 0
596596 8.88449 12.4820i 0.363923 0.511283i
597597 0.221745 6.50343i 0.00907542 0.266168i
598598 6.71033 6.10137i 0.274406 0.249503i
599599 18.9258 32.7804i 0.773287 1.33937i −0.162466 0.986714i 0.551945π-0.551945\pi
0.935752 0.352658i 0.114722π-0.114722\pi
600600 13.6683 + 19.6052i 0.558005 + 0.800381i
601601 21.9488 0.895308 0.447654 0.894207i 0.352260π-0.352260\pi
0.447654 + 0.894207i 0.352260π0.352260\pi
602602 0 0
603603 −1.72188 + 0.843327i −0.0701202 + 0.0343429i
604604 −25.1642 2.39762i −1.02392 0.0975577i
605605 1.27989 + 0.738947i 0.0520351 + 0.0300425i
606606 7.45873 1.35896i 0.302990 0.0552038i
607607 22.4114 12.9392i 0.909651 0.525187i 0.0293323 0.999570i 0.490662π-0.490662\pi
0.880319 + 0.474382i 0.157329π0.157329\pi
608608 31.5465 0.767338i 1.27938 0.0311197i
609609 0 0
610610 2.11533 6.61968i 0.0856470 0.268023i
611611 −6.41308 11.1078i −0.259445 0.449373i
612612 −14.8507 + 18.1128i −0.600304 + 0.732167i
613613 6.45681 11.1835i 0.260788 0.451698i −0.705664 0.708547i 0.749351π-0.749351\pi
0.966452 + 0.256849i 0.0826843π0.0826843\pi
614614 5.11271 1.11276i 0.206332 0.0449073i
615615 −2.41910 + 3.87847i −0.0975475 + 0.156395i
616616 0 0
617617 26.4677i 1.06555i 0.846257 + 0.532775i 0.178851π0.178851\pi
−0.846257 + 0.532775i 0.821149π0.821149\pi
618618 5.97010 16.6976i 0.240153 0.671675i
619619 −29.7384 17.1695i −1.19529 0.690100i −0.235787 0.971805i 0.575767π-0.575767\pi
−0.959501 + 0.281705i 0.909100π0.909100\pi
620620 1.67360 0.764730i 0.0672136 0.0307123i
621621 −4.63691 10.3458i −0.186073 0.415164i
622622 10.2174 + 3.26499i 0.409682 + 0.130914i
623623 0 0
624624 −19.8546 4.52474i −0.794819 0.181135i
625625 −11.5959 20.0847i −0.463836 0.803388i
626626 16.3601 14.8754i 0.653882 0.594542i
627627 −33.2884 + 17.7349i −1.32941 + 0.708265i
628628 0.0412477 0.432916i 0.00164596 0.0172752i
629629 2.49490i 0.0994782i
630630 0 0
631631 27.7569i 1.10499i 0.833517 + 0.552493i 0.186323π0.186323\pi
−0.833517 + 0.552493i 0.813677π0.813677\pi
632632 10.4016 + 4.45040i 0.413755 + 0.177028i
633633 15.0413 8.01347i 0.597836 0.318507i
634634 13.2179 + 14.5371i 0.524949 + 0.577343i
635635 −2.16070 3.74245i −0.0857449 0.148515i
636636 −2.29266 5.50654i −0.0909099 0.218349i
637637 0 0
638638 16.3881 51.2847i 0.648810 2.03038i
639639 −19.9715 + 29.7143i −0.790060 + 1.17548i
640640 3.54641 1.72593i 0.140184 0.0682233i
641641 6.03040 + 3.48165i 0.238186 + 0.137517i 0.614343 0.789039i 0.289421π-0.289421\pi
−0.376156 + 0.926556i 0.622754π0.622754\pi
642642 −25.4039 9.08298i −1.00261 0.358477i
643643 9.74373i 0.384255i −0.981370 0.192128i 0.938461π-0.938461\pi
0.981370 0.192128i 0.0615387π-0.0615387\pi
644644 0 0
645645 −0.804492 + 1.28982i −0.0316768 + 0.0507865i
646646 −6.54942 30.0921i −0.257683 1.18396i
647647 −14.0948 + 24.4129i −0.554123 + 0.959770i 0.443848 + 0.896102i 0.353613π0.353613\pi
−0.997971 + 0.0636677i 0.979720π0.979720\pi
648648 −13.1013 + 21.8256i −0.514669 + 0.857389i
649649 16.0959 + 27.8789i 0.631820 + 1.09434i
650650 19.3161 + 6.17248i 0.757641 + 0.242105i
651651 0 0
652652 −6.07649 + 8.53699i −0.237974 + 0.334334i
653653 9.39867 5.42633i 0.367799 0.212349i −0.304698 0.952449i 0.598555π-0.598555\pi
0.672496 + 0.740101i 0.265222π0.265222\pi
654654 −0.614569 3.37310i −0.0240315 0.131899i
655655 −0.486214 0.280716i −0.0189979 0.0109685i
656656 −22.8933 19.8205i −0.893832 0.773860i
657657 −10.3960 21.2263i −0.405588 0.828116i
658658 0 0
659659 −19.2248 −0.748893 −0.374446 0.927249i 0.622167π-0.622167\pi
−0.374446 + 0.927249i 0.622167π0.622167\pi
660660 −2.86305 + 3.74533i −0.111444 + 0.145787i
661661 1.37371 2.37933i 0.0534311 0.0925454i −0.838073 0.545558i 0.816318π-0.816318\pi
0.891504 + 0.453013i 0.149651π0.149651\pi
662662 30.2503 + 33.2695i 1.17571 + 1.29306i
663663 −0.677232 + 19.8621i −0.0263015 + 0.771382i
664664 −15.1658 20.2460i −0.588547 0.785696i
665665 0 0
666666 0.394837 + 2.68258i 0.0152996 + 0.103948i
667667 −18.4275 + 10.6391i −0.713514 + 0.411948i
668668 20.8724 9.53734i 0.807577 0.369011i
669669 35.0267 18.6610i 1.35421 0.721476i
670670 −0.0670080 0.307877i −0.00258875 0.0118943i
671671 −55.0271 −2.12430
672672 0 0
673673 31.3097 1.20690 0.603449 0.797401i 0.293793π-0.293793\pi
0.603449 + 0.797401i 0.293793π0.293793\pi
674674 −5.14830 23.6545i −0.198305 0.911138i
675675 14.8492 20.5447i 0.571547 0.790767i
676676 7.93287 3.62481i 0.305110 0.139416i
677677 −18.1712 + 10.4911i −0.698376 + 0.403208i −0.806742 0.590903i 0.798771π-0.798771\pi
0.108366 + 0.994111i 0.465438π0.465438\pi
678678 14.0003 + 16.4935i 0.537678 + 0.633429i
679679 0 0
680680 −2.30770 3.08073i −0.0884963 0.118140i
681681 23.4213 + 0.798587i 0.897506 + 0.0306019i
682682 −9.80167 10.7800i −0.375325 0.412786i
683683 7.91172 13.7035i 0.302734 0.524350i −0.674021 0.738713i 0.735434π-0.735434\pi
0.976754 + 0.214363i 0.0687675π0.0687675\pi
684684 −11.8044 31.3193i −0.451353 1.19752i
685685 1.52126 0.0581245
686686 0 0
687687 13.4711 21.5978i 0.513953 0.824006i
688688 −7.61335 6.59147i −0.290256 0.251298i
689689 −4.38295 2.53050i −0.166977 0.0964043i
690690 1.83298 0.333964i 0.0697805 0.0127138i
691691 21.1390 12.2046i 0.804167 0.464286i −0.0407593 0.999169i 0.512978π-0.512978\pi
0.844926 + 0.534883i 0.179644π0.179644\pi
692692 −24.5931 + 34.5514i −0.934891 + 1.31345i
693693 0 0
694694 11.3803 + 3.63659i 0.431991 + 0.138043i
695695 −2.93143 5.07738i −0.111195 0.192596i
696696 43.2584 + 20.2792i 1.63970 + 0.768680i
697697 −14.7764 + 25.5934i −0.559694 + 0.969419i
698698 5.26192 + 24.1766i 0.199167 + 0.915097i
699699 25.2626 + 15.7569i 0.955520 + 0.595982i
700700 0 0
701701 21.4779i 0.811209i 0.914049 + 0.405605i 0.132939π0.132939\pi
−0.914049 + 0.405605i 0.867061π0.867061\pi
702702 2.41516 + 21.4634i 0.0911543 + 0.810085i
703703 −3.08749 1.78256i −0.116447 0.0672306i
704704 −21.5653 22.5889i −0.812774 0.851350i
705705 0.0897892 2.63338i 0.00338166 0.0991787i
706706 3.55892 11.1373i 0.133942 0.419156i
707707 0 0
708708 −26.3718 + 10.9799i −0.991111 + 0.412651i
709709 21.0959 + 36.5392i 0.792273 + 1.37226i 0.924556 + 0.381046i 0.124436π0.124436\pi
−0.132283 + 0.991212i 0.542231π0.542231\pi
710710 −3.95815 4.35320i −0.148547 0.163373i
711711 0.817369 11.9721i 0.0306537 0.448990i
712712 27.4074 + 11.7264i 1.02713 + 0.439466i
713713 5.75822i 0.215647i
714714 0 0
715715 4.00000i 0.149592i
716716 0.343751 3.60784i 0.0128466 0.134831i
717717 11.8363 + 22.2167i 0.442034 + 0.829697i
718718 −26.2948 + 23.9086i −0.981314 + 0.892260i
719719 −9.52940 16.5054i −0.355387 0.615548i 0.631797 0.775134i 0.282317π-0.282317\pi
−0.987184 + 0.159586i 0.948984π0.948984\pi
720720 −2.96884 2.94726i −0.110642 0.109838i
721721 0 0
722722 16.3240 + 5.21635i 0.607517 + 0.194133i
723723 32.5299 + 1.10916i 1.20980 + 0.0412501i
724724 −13.7150 + 6.26689i −0.509716 + 0.232907i
725725 −41.2019 23.7879i −1.53020 0.883461i
726726 9.77808 + 3.49608i 0.362899 + 0.129752i
727727 3.72549i 0.138171i −0.997611 0.0690854i 0.977992π-0.977992\pi
0.997611 0.0690854i 0.0220081π-0.0220081\pi
728728 0 0
729729 26.4374 + 5.48311i 0.979163 + 0.203078i
730730 3.79533 0.826036i 0.140471 0.0305729i
731731 −4.91400 + 8.51130i −0.181751 + 0.314802i
732732 6.28523 48.4235i 0.232309 1.78978i
733733 12.7090 + 22.0126i 0.469417 + 0.813054i 0.999389 0.0349611i 0.0111307π-0.0111307\pi
−0.529972 + 0.848015i 0.677797π0.677797\pi
734734 9.34681 29.2498i 0.344997 1.07963i
735735 0 0
736736 0.300133 + 12.3390i 0.0110631 + 0.454820i
737737 −2.16065 + 1.24745i −0.0795885 + 0.0459504i
738738 −11.8375 + 29.8571i −0.435746 + 1.09906i
739739 −20.1868 11.6548i −0.742582 0.428730i 0.0804256 0.996761i 0.474372π-0.474372\pi
−0.823007 + 0.568031i 0.807705π0.807705\pi
740740 −0.443588 0.0422645i −0.0163066 0.00155368i
741741 −24.0959 15.0292i −0.885185 0.552113i
742742 0 0
743743 33.8576 1.24211 0.621057 0.783765i 0.286703π-0.286703\pi
0.621057 + 0.783765i 0.286703π0.286703\pi
744744 10.6058 7.39411i 0.388829 0.271081i
745745 1.33528 2.31277i 0.0489207 0.0847332i
746746 −0.755252 + 0.686713i −0.0276518 + 0.0251424i
747747 −14.9669 + 22.2684i −0.547611 + 0.814757i
748748 −17.6742 + 24.8309i −0.646234 + 0.907908i
749749 0 0
750750 5.45885 + 6.43098i 0.199329 + 0.234826i
751751 41.7017 24.0765i 1.52172 0.878564i 0.522046 0.852918i 0.325169π-0.325169\pi
0.999671 0.0256461i 0.00816430π-0.00816430\pi
752752 17.1410 + 3.29628i 0.625069 + 0.120203i
753753 16.8097 + 31.5518i 0.612581 + 1.14981i
754754 39.6097 8.62088i 1.44250 0.313954i
755755 −4.40614 −0.160356
756756 0 0
757757 −11.3923 −0.414062 −0.207031 0.978334i 0.566380π-0.566380\pi
−0.207031 + 0.978334i 0.566380π0.566380\pi
758758 25.2529 5.49617i 0.917226 0.199630i
759759 −6.93677 13.0203i −0.251789 0.472607i
760760 5.46127 0.654700i 0.198101 0.0237485i
761761 23.8583 13.7746i 0.864861 0.499328i −0.000776011 1.00000i 0.500247π-0.500247\pi
0.865637 + 0.500672i 0.166914π0.166914\pi
762762 −19.6496 23.1488i −0.711828 0.838592i
763763 0 0
764764 2.65862 + 1.89236i 0.0961853 + 0.0684632i
765765 −2.27744 + 3.38846i −0.0823410 + 0.122510i
766766 2.14429 1.94970i 0.0774764 0.0704454i
767767 −12.1190 + 20.9907i −0.437591 + 0.757930i
768768 22.3412 16.3972i 0.806170 0.591684i
769769 −5.83461 −0.210401 −0.105201 0.994451i 0.533549π-0.533549\pi
−0.105201 + 0.994451i 0.533549π0.533549\pi
770770 0 0
771771 7.08912 + 4.42166i 0.255308 + 0.159242i
772772 −2.87520 + 30.1767i −0.103481 + 1.08608i
773773 −41.1952 23.7841i −1.48169 0.855454i −0.481906 0.876223i 0.660055π-0.660055\pi
−0.999784 + 0.0207689i 0.993389π0.993389\pi
774774 −3.93667 + 9.92923i −0.141501 + 0.356899i
775775 −11.1499 + 6.43739i −0.400516 + 0.231238i
776776 3.39144 + 4.52749i 0.121745 + 0.162527i
777777 0 0
778778 −4.79829 + 15.0157i −0.172027 + 0.538340i
779779 −21.1149 36.5720i −0.756519 1.31033i
780780 −3.51997 0.456882i −0.126035 0.0163590i
781781 −23.2939 + 40.3463i −0.833522 + 1.44370i
782782 11.7701 2.56171i 0.420899 0.0916067i
783783 5.17240 50.4093i 0.184846 1.80148i
784784 0 0
785785 0.0758015i 0.00270547i
786786 −3.71456 1.32811i −0.132494 0.0473723i
787787 42.2774 + 24.4089i 1.50703 + 0.870082i 0.999967 + 0.00817024i 0.00260070π0.00260070\pi
0.507059 + 0.861911i 0.330733π0.330733\pi
788788 17.6435 + 38.6125i 0.628522 + 1.37551i
789789 −25.0271 0.853341i −0.890989 0.0303797i
790790 1.87847 + 0.600267i 0.0668330 + 0.0213565i
791791 0 0
792792 −15.0741 + 29.4959i −0.535634 + 1.04809i
793793 −20.7156 35.8805i −0.735632 1.27415i
794794 8.34399 7.58678i 0.296117 0.269245i
795795 −0.488861 0.917592i −0.0173381 0.0325436i
796796 7.48000 + 0.712686i 0.265122 + 0.0252605i
797797 12.7292i 0.450890i 0.974256 + 0.225445i 0.0723837π0.0723837\pi
−0.974256 + 0.225445i 0.927616π0.927616\pi
798798 0 0
799799 17.0351i 0.602660i
800800 −23.5569 + 14.3755i −0.832863 + 0.508250i
801801 2.15369 31.5455i 0.0760970 1.11461i
802802 −20.4340 22.4734i −0.721548 0.793564i
803803 −15.3778 26.6352i −0.542672 0.939936i
804804 −0.850958 2.04384i −0.0300110 0.0720807i
805805 0 0
806806 3.33912 10.4494i 0.117616 0.368065i
807807 −0.278138 + 8.15735i −0.00979093 + 0.287152i
808808 1.04202 + 8.69214i 0.0366581 + 0.305789i
809809 23.0201 + 13.2906i 0.809342 + 0.467274i 0.846727 0.532027i 0.178570π-0.178570\pi
−0.0373853 + 0.999301i 0.511903π0.511903\pi
810810 −1.91251 + 4.00378i −0.0671986 + 0.140678i
811811 4.13977i 0.145367i 0.997355 + 0.0726835i 0.0231563π0.0231563\pi
−0.997355 + 0.0726835i 0.976844π0.976844\pi
812812 0 0
813813 −23.0351 14.3676i −0.807878 0.503894i
814814 0.750357 + 3.44761i 0.0263000 + 0.120839i
815815 −0.913253 + 1.58180i −0.0319899 + 0.0554081i
816816 −19.8323 18.3894i −0.694268 0.643758i
817817 −7.02193 12.1623i −0.245666 0.425506i
818818 −49.7266 15.8902i −1.73865 0.555587i
819819 0 0
820820 −4.30013 3.06077i −0.150167 0.106887i
821821 −25.5549 + 14.7541i −0.891871 + 0.514922i −0.874554 0.484928i 0.838846π-0.838846\pi
−0.0173172 + 0.999850i 0.505513π0.505513\pi
822822 10.5159 1.91596i 0.366784 0.0668269i
823823 −10.4596 6.03884i −0.364598 0.210501i 0.306498 0.951871i 0.400843π-0.400843\pi
−0.671096 + 0.741371i 0.734176π0.734176\pi
824824 18.8253 + 8.05453i 0.655811 + 0.280593i
825825 17.4568 27.9880i 0.607768 0.974416i
826826 0 0
827827 −11.9341 −0.414989 −0.207494 0.978236i 0.566531π-0.566531\pi
−0.207494 + 0.978236i 0.566531π0.566531\pi
828828 12.2501 4.61712i 0.425720 0.160456i
829829 1.25218 2.16884i 0.0434900 0.0753269i −0.843461 0.537190i 0.819486π-0.819486\pi
0.886951 + 0.461863i 0.152819π0.152819\pi
830830 −2.96629 3.26235i −0.102962 0.113238i
831831 −29.4214 1.00317i −1.02062 0.0347996i
832832 6.61057 22.5655i 0.229180 0.782319i
833833 0 0
834834 −26.6585 31.4059i −0.923110 1.08750i
835835 3.46410 2.00000i 0.119880 0.0692129i
836836 −18.1008 39.6135i −0.626029 1.37006i
837837 −11.1141 8.03298i −0.384158 0.277660i
838838 −8.89555 40.8717i −0.307292 1.41189i
839839 −1.64607 −0.0568288 −0.0284144 0.999596i 0.509046π-0.509046\pi
−0.0284144 + 0.999596i 0.509046π0.509046\pi
840840 0 0
841841 −66.1054 −2.27950
842842 11.0771 + 50.8953i 0.381743 + 1.75397i
843843 8.80225 4.68954i 0.303166 0.161516i
844844 8.17878 + 17.8992i 0.281525 + 0.616116i
845845 1.31658 0.760131i 0.0452919 0.0261493i
846846 −2.69594 18.3166i −0.0926884 0.629737i
847847 0 0
848848 6.50776 2.25539i 0.223477 0.0774503i
849849 −0.329249 + 9.65635i −0.0112998 + 0.331405i
850850 18.1187 + 19.9271i 0.621467 + 0.683494i
851851 0.697224 1.20763i 0.0239005 0.0413969i
852852 −32.8438 25.1069i −1.12521 0.860147i
853853 −15.1311 −0.518077 −0.259039 0.965867i 0.583406π-0.583406\pi
−0.259039 + 0.965867i 0.583406π0.583406\pi
854854 0 0
855855 −2.56610 5.23937i −0.0877587 0.179183i
856856 12.2543 28.6411i 0.418842 0.978931i
857857 42.3681 + 24.4612i 1.44727 + 0.835579i 0.998318 0.0579792i 0.0184657π-0.0184657\pi
0.448947 + 0.893558i 0.351799π0.351799\pi
858858 5.03782 + 27.6504i 0.171988 + 0.943971i
859859 −13.9058 + 8.02854i −0.474461 + 0.273930i −0.718105 0.695935i 0.754990π-0.754990\pi
0.243644 + 0.969865i 0.421657π0.421657\pi
860860 −1.43005 1.01788i −0.0487641 0.0347095i
861861 0 0
862862 −6.30013 2.01321i −0.214583 0.0685703i
863863 7.45171 + 12.9067i 0.253659 + 0.439350i 0.964530 0.263972i 0.0850325π-0.0850325\pi
−0.710871 + 0.703322i 0.751699π0.751699\pi
864864 −24.2344 16.6341i −0.824471 0.565904i
865865 −3.69617 + 6.40196i −0.125674 + 0.217673i
866866 −4.97944 22.8787i −0.169208 0.777449i
867867 1.61386 2.58746i 0.0548096 0.0878746i
868868 0 0
869869 15.6151i 0.529704i
870870 7.84147 + 2.80366i 0.265851 + 0.0950531i
871871 −1.62680 0.939235i −0.0551221 0.0318248i
872872 3.93090 0.471239i 0.133117 0.0159582i
873873 3.34696 4.97974i 0.113278 0.168539i
874874 −5.23937 + 16.3960i −0.177224 + 0.554604i
875875 0 0
876876 25.1953 10.4901i 0.851269 0.354428i
877877 −5.93923 10.2871i −0.200554 0.347369i 0.748153 0.663526i 0.230941π-0.230941\pi
−0.948707 + 0.316157i 0.897607π0.897607\pi
878878 −25.1917 27.7060i −0.850179 0.935033i
879879 −36.3376 + 19.3594i −1.22564 + 0.652977i
880880 −4.11547 3.56309i −0.138733 0.120112i
881881 36.4995i 1.22970i 0.788644 + 0.614850i 0.210783π0.210783\pi
−0.788644 + 0.614850i 0.789217π0.789217\pi
882882 0 0
883883 31.1178i 1.04720i −0.851965 0.523599i 0.824589π-0.824589\pi
0.851965 0.523599i 0.175411π-0.175411\pi
884884 −22.8447 2.17662i −0.768350 0.0732075i
885885 −4.39450 + 2.34124i −0.147720 + 0.0786999i
886886 −4.81424 + 4.37735i −0.161738 + 0.147060i
887887 −28.4624 49.2983i −0.955674 1.65528i −0.732819 0.680424i 0.761796π-0.761796\pi
−0.222855 0.974852i 0.571538π-0.571538\pi
888888 −3.11958 + 0.266521i −0.104686 + 0.00894386i
889889 0 0
890890 4.94960 + 1.58165i 0.165911 + 0.0530170i
891891 34.8079 + 4.77510i 1.16611 + 0.159972i
892892 19.0460 + 41.6820i 0.637706 + 1.39562i
893893 21.0813 + 12.1713i 0.705459 + 0.407297i
894894 6.31742 17.6690i 0.211286 0.590939i
895895 0.631717i 0.0211160i
896896 0 0
897897 5.87847 9.42477i 0.196276 0.314684i
898898 −23.5048 + 5.11571i −0.784365 + 0.170714i
899899 −12.8685 + 22.2889i −0.429189 + 0.743378i
900900 22.6353 + 18.5587i 0.754510 + 0.618622i
901901 −3.36090 5.82125i −0.111968 0.193934i
902902 −12.7215 + 39.8107i −0.423581 + 1.32555i
903903 0 0
904904 −19.9938 + 14.9769i −0.664984 + 0.498124i
905905 −2.27623 + 1.31418i −0.0756643 + 0.0436848i
906906 −30.4579 + 5.54934i −1.01190 + 0.184364i
907907 5.81050 + 3.35469i 0.192934 + 0.111391i 0.593356 0.804940i 0.297803π-0.297803\pi
−0.400421 + 0.916331i 0.631136π0.631136\pi
908908 −2.56665 + 26.9383i −0.0851773 + 0.893979i
909909 8.33897 4.08419i 0.276586 0.135464i
910910 0 0
911911 −50.1275 −1.66080 −0.830399 0.557169i 0.811888π-0.811888\pi
−0.830399 + 0.557169i 0.811888π0.811888\pi
912912 36.9271 11.4039i 1.22278 0.377621i
913913 −17.4568 + 30.2361i −0.577736 + 1.00067i
914914 −16.1464 + 14.6811i −0.534076 + 0.485609i
915915 0.290038 8.50636i 0.00958836 0.281211i
916916 23.9458 + 17.0443i 0.791193 + 0.563158i
917917 0 0
918918 −11.4754 + 26.2915i −0.378746 + 0.867747i
919919 −14.7529 + 8.51757i −0.486652 + 0.280969i −0.723185 0.690655i 0.757322π-0.757322\pi
0.236532 + 0.971624i 0.423989π0.423989\pi
920920 0.256077 + 2.13610i 0.00844260 + 0.0704250i
921921 5.65577 3.01320i 0.186364 0.0992883i
922922 46.1216 10.0382i 1.51893 0.330589i
923923 −35.0771 −1.15458
924924 0 0
925925 3.11784 0.102514
926926 −36.5900 + 7.96364i −1.20242 + 0.261702i
927927 1.47931 21.6677i 0.0485869 0.711659i
928928 −26.4135 + 48.4324i −0.867065 + 1.58987i
929929 −20.2721 + 11.7041i −0.665105 + 0.383999i −0.794219 0.607631i 0.792120π-0.792120\pi
0.129114 + 0.991630i 0.458787π0.458787\pi
930930 1.71808 1.45837i 0.0563381 0.0478219i
931931 0 0
932932 −19.9365 + 28.0092i −0.653040 + 0.917470i
933933 13.1295 + 0.447672i 0.429841 + 0.0146561i
934934 19.4529 17.6875i 0.636517 0.578753i
935935 −2.65631 + 4.60087i −0.0868707 + 0.150464i
936936 −24.9076 + 1.27500i −0.814131 + 0.0416746i
937937 −48.5929 −1.58746 −0.793730 0.608270i 0.791864π-0.791864\pi
−0.793730 + 0.608270i 0.791864π0.791864\pi
938938 0 0
939939 14.3320 22.9781i 0.467707 0.749861i
940940 3.02881 + 0.288582i 0.0987889 + 0.00941249i
941941 −12.6540 7.30579i −0.412509 0.238162i 0.279358 0.960187i 0.409878π-0.409878\pi
−0.691867 + 0.722025i 0.743212π0.743212\pi
942942 −0.0954686 0.523986i −0.00311054 0.0170724i
943943 14.3046 8.25879i 0.465823 0.268943i
944944 −10.8014 31.1668i −0.351556 1.01439i
945945 0 0
946946 −4.23065 + 13.2394i −0.137550 + 0.430449i
947947 15.7125 + 27.2148i 0.510587 + 0.884362i 0.999925 + 0.0122681i 0.00390516π0.00390516\pi
−0.489338 + 0.872094i 0.662762π0.662762\pi
948948 13.7411 + 1.78356i 0.446291 + 0.0579273i
949949 11.5783 20.0543i 0.375849 0.650989i
950950 −37.6057 + 8.18470i −1.22009 + 0.265547i
951951 20.4177 + 12.7350i 0.662088 + 0.412961i
952952 0 0
953953 14.0113i 0.453872i −0.973910 0.226936i 0.927129π-0.927129\pi
0.973910 0.226936i 0.0728708π-0.0728708\pi
954954 −4.53497 5.72725i −0.146825 0.185427i
955955 0.492609 + 0.284408i 0.0159405 + 0.00920323i
956956 −26.4380 + 12.0805i −0.855065 + 0.390710i
957957 2.24701 65.9014i 0.0726357 2.13029i
958958 −55.0666 17.5966i −1.77912 0.568520i
959959 0 0
960960 3.60556 3.21461i 0.116369 0.103751i
961961 −12.0176 20.8150i −0.387664 0.671453i
962962 −1.96554 + 1.78717i −0.0633715 + 0.0576205i
963963 −32.9655 2.25064i −1.06230 0.0725258i
964964 −3.56483 + 37.4147i −0.114815 + 1.20505i
965965 5.28380i 0.170091i
966966 0 0
967967 35.9876i 1.15728i 0.815582 + 0.578641i 0.196417π0.196417\pi
−0.815582 + 0.578641i 0.803583π0.803583\pi
968968 −4.71672 + 11.0241i −0.151601 + 0.354328i
969969 −17.7349 33.2884i −0.569728 1.06938i
970970 0.663335 + 0.729540i 0.0212984 + 0.0234241i
971971 24.1922 + 41.9022i 0.776365 + 1.34470i 0.934024 + 0.357210i 0.116272π0.116272\pi
−0.157659 + 0.987494i 0.550395π0.550395\pi
972972 −8.17783 + 30.0853i −0.262304 + 0.964985i
973973 0 0
974974 −9.22546 + 28.8701i −0.295603 + 0.925057i
975975 24.8214 + 0.846326i 0.794921 + 0.0271041i
976976 55.3691 + 10.6477i 1.77232 + 0.340824i
977977 −32.6000 18.8216i −1.04296 0.602156i −0.122293 0.992494i 0.539025π-0.539025\pi
−0.920672 + 0.390338i 0.872358π0.872358\pi
978978 −4.32076 + 12.0846i −0.138163 + 0.386422i
979979 41.1443i 1.31498i
980980 0 0
981981 −1.84702 3.77118i −0.0589708 0.120405i
982982 0.490732 + 2.25473i 0.0156599 + 0.0719514i
983983 2.67750 4.63756i 0.0853989 0.147915i −0.820162 0.572131i 0.806117π-0.806117\pi
0.905561 + 0.424216i 0.139450π0.139450\pi
984984 −33.5800 15.7421i −1.07049 0.501838i
985985 3.69987 + 6.40836i 0.117888 + 0.204187i
986986 51.2847 + 16.3881i 1.63324 + 0.521903i
987987 0 0
988988 19.0157 26.7156i 0.604971 0.849936i
989989 4.75713 2.74653i 0.151268 0.0873345i
990990 −2.12801 + 5.36734i −0.0676325 + 0.170585i
991991 −44.1913 25.5139i −1.40378 0.810475i −0.409005 0.912532i 0.634124π-0.634124\pi
−0.994779 + 0.102057i 0.967458π0.967458\pi
992992 7.77669 + 12.7436i 0.246910 + 0.404609i
993993 46.7276 + 29.1452i 1.48286 + 0.924895i
994994 0 0
995995 1.30971 0.0415207
996996 −24.6136 18.8155i −0.779912 0.596190i
997997 26.9653 46.7052i 0.853998 1.47917i −0.0235729 0.999722i 0.507504π-0.507504\pi
0.877571 0.479446i 0.159162π-0.159162\pi
998998 −8.45044 9.29385i −0.267494 0.294192i
999999 1.35821 + 3.03042i 0.0429718 + 0.0958783i
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.f.263.7 24
3.2 odd 2 inner 588.2.n.f.263.6 24
4.3 odd 2 inner 588.2.n.f.263.3 24
7.2 even 3 inner 588.2.n.f.275.10 24
7.3 odd 6 588.2.e.c.491.1 12
7.4 even 3 84.2.e.a.71.1 12
7.5 odd 6 588.2.n.g.275.10 24
7.6 odd 2 588.2.n.g.263.7 24
12.11 even 2 inner 588.2.n.f.263.10 24
21.2 odd 6 inner 588.2.n.f.275.3 24
21.5 even 6 588.2.n.g.275.3 24
21.11 odd 6 84.2.e.a.71.12 yes 12
21.17 even 6 588.2.e.c.491.12 12
21.20 even 2 588.2.n.g.263.6 24
28.3 even 6 588.2.e.c.491.11 12
28.11 odd 6 84.2.e.a.71.11 yes 12
28.19 even 6 588.2.n.g.275.6 24
28.23 odd 6 inner 588.2.n.f.275.6 24
28.27 even 2 588.2.n.g.263.3 24
56.11 odd 6 1344.2.h.h.575.9 12
56.53 even 6 1344.2.h.h.575.4 12
84.11 even 6 84.2.e.a.71.2 yes 12
84.23 even 6 inner 588.2.n.f.275.7 24
84.47 odd 6 588.2.n.g.275.7 24
84.59 odd 6 588.2.e.c.491.2 12
84.83 odd 2 588.2.n.g.263.10 24
168.11 even 6 1344.2.h.h.575.3 12
168.53 odd 6 1344.2.h.h.575.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.e.a.71.1 12 7.4 even 3
84.2.e.a.71.2 yes 12 84.11 even 6
84.2.e.a.71.11 yes 12 28.11 odd 6
84.2.e.a.71.12 yes 12 21.11 odd 6
588.2.e.c.491.1 12 7.3 odd 6
588.2.e.c.491.2 12 84.59 odd 6
588.2.e.c.491.11 12 28.3 even 6
588.2.e.c.491.12 12 21.17 even 6
588.2.n.f.263.3 24 4.3 odd 2 inner
588.2.n.f.263.6 24 3.2 odd 2 inner
588.2.n.f.263.7 24 1.1 even 1 trivial
588.2.n.f.263.10 24 12.11 even 2 inner
588.2.n.f.275.3 24 21.2 odd 6 inner
588.2.n.f.275.6 24 28.23 odd 6 inner
588.2.n.f.275.7 24 84.23 even 6 inner
588.2.n.f.275.10 24 7.2 even 3 inner
588.2.n.g.263.3 24 28.27 even 2
588.2.n.g.263.6 24 21.20 even 2
588.2.n.g.263.7 24 7.6 odd 2
588.2.n.g.263.10 24 84.83 odd 2
588.2.n.g.275.3 24 21.5 even 6
588.2.n.g.275.6 24 28.19 even 6
588.2.n.g.275.7 24 84.47 odd 6
588.2.n.g.275.10 24 7.5 odd 6
1344.2.h.h.575.3 12 168.11 even 6
1344.2.h.h.575.4 12 56.53 even 6
1344.2.h.h.575.9 12 56.11 odd 6
1344.2.h.h.575.10 12 168.53 odd 6