Properties

Label 169.3.f.g.80.3
Level 169169
Weight 33
Character 169.80
Analytic conductor 4.6054.605
Analytic rank 00
Dimension 4848
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,3,Mod(19,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 169=132 169 = 13^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 169.f (of order 1212, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.604916467694.60491646769
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 80.3
Character χ\chi == 169.80
Dual form 169.3.f.g.150.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(2.273690.609234i)q2+(2.51175+4.35048i)q3+(1.33442+0.770425i)q4+(1.10964+1.10964i)q5+(3.0604911.4219i)q6+(6.34925+1.70128i)q7+(4.09315+4.09315i)q8+(8.11776+14.0604i)q9+(3.199021.84696i)q10+(0.3010991.12372i)q11+7.74046iq12+15.4727q14+(7.614622.04033i)q15+(9.8945917.1379i)q16+(21.447312.3826i)q17+(27.023427.0234i)q18+(0.174381+0.650797i)q19+(2.33562+0.625828i)q20+(23.349123.3491i)q21+(1.36921+2.37154i)q22+(1.92917+1.11381i)q23+(7.52619+28.0881i)q24+22.5374iq2536.3476q27+(9.783242.62141i)q28+(9.5851616.6020i)q29+(16.0703+9.27818i)q30+(40.7907+40.7907i)q31+(6.06346+22.6291i)q32+(5.644981.51257i)q33+(41.2206+41.2206i)q34+(5.157598.93321i)q35+(21.6649+12.5082i)q36+(1.02942+3.84185i)q371.58595iq389.08389q40+(11.67123.12729i)q41+(38.8636+67.3137i)q42+(43.5991+25.1720i)q43+(1.267531.26753i)q44+(6.5941824.6098i)q45+(5.064911.35714i)q46+(24.309024.3090i)q47+(49.705486.0923i)q48+(5.01666+2.89637i)q49+(13.730551.2431i)q50124.408iq51+65.5668q53+(82.6433+22.1442i)q54+(0.912811+1.58104i)q55+(32.952019.0249i)q56+(2.39328+2.39328i)q57+(11.6792+43.5874i)q58+(71.652119.1991i)q59+(8.589158.58915i)q60+(45.4338+78.6937i)q61+(117.59767.8945i)q62+(27.6211103.083i)q63+24.0109iq6413.7565q66+(91.3047+24.4650i)q67+(19.079733.0470i)q68+(9.691185.59520i)q69+(17.1692+17.1692i)q70+(17.5705+65.5740i)q71+(90.7785+24.3240i)q72+(51.8021+51.8021i)q73+(4.681188.10804i)q74+(98.0483+56.6082i)q75+(0.268695+1.00278i)q76+7.64700iq7749.1050q79+(29.9965+8.03753i)q80+(18.236131.5859i)q81+(24.6315+14.2210i)q82+(70.561870.5618i)q83+(13.168649.1461i)q84+(37.539110.0586i)q85+(83.795583.7955i)q86+(48.151083.4000i)q87+(5.831983.36710i)q88+(21.8165+81.4201i)q89+59.9726iq903.43242q92+(279.91575.0030i)q93+(40.4613+70.0810i)q94+(0.9156540.528653i)q95+(83.2176+83.2176i)q96+(17.512265.3566i)q97+(13.17093.52914i)q98+(13.3556+13.3556i)q99+O(q100)q+(-2.27369 - 0.609234i) q^{2} +(2.51175 + 4.35048i) q^{3} +(1.33442 + 0.770425i) q^{4} +(-1.10964 + 1.10964i) q^{5} +(-3.06049 - 11.4219i) q^{6} +(-6.34925 + 1.70128i) q^{7} +(4.09315 + 4.09315i) q^{8} +(-8.11776 + 14.0604i) q^{9} +(3.19902 - 1.84696i) q^{10} +(0.301099 - 1.12372i) q^{11} +7.74046i q^{12} +15.4727 q^{14} +(-7.61462 - 2.04033i) q^{15} +(-9.89459 - 17.1379i) q^{16} +(-21.4473 - 12.3826i) q^{17} +(27.0234 - 27.0234i) q^{18} +(0.174381 + 0.650797i) q^{19} +(-2.33562 + 0.625828i) q^{20} +(-23.3491 - 23.3491i) q^{21} +(-1.36921 + 2.37154i) q^{22} +(-1.92917 + 1.11381i) q^{23} +(-7.52619 + 28.0881i) q^{24} +22.5374i q^{25} -36.3476 q^{27} +(-9.78324 - 2.62141i) q^{28} +(-9.58516 - 16.6020i) q^{29} +(16.0703 + 9.27818i) q^{30} +(-40.7907 + 40.7907i) q^{31} +(6.06346 + 22.6291i) q^{32} +(5.64498 - 1.51257i) q^{33} +(41.2206 + 41.2206i) q^{34} +(5.15759 - 8.93321i) q^{35} +(-21.6649 + 12.5082i) q^{36} +(-1.02942 + 3.84185i) q^{37} -1.58595i q^{38} -9.08389 q^{40} +(-11.6712 - 3.12729i) q^{41} +(38.8636 + 67.3137i) q^{42} +(43.5991 + 25.1720i) q^{43} +(1.26753 - 1.26753i) q^{44} +(-6.59418 - 24.6098i) q^{45} +(5.06491 - 1.35714i) q^{46} +(-24.3090 - 24.3090i) q^{47} +(49.7054 - 86.0923i) q^{48} +(-5.01666 + 2.89637i) q^{49} +(13.7305 - 51.2431i) q^{50} -124.408i q^{51} +65.5668 q^{53} +(82.6433 + 22.1442i) q^{54} +(0.912811 + 1.58104i) q^{55} +(-32.9520 - 19.0249i) q^{56} +(-2.39328 + 2.39328i) q^{57} +(11.6792 + 43.5874i) q^{58} +(71.6521 - 19.1991i) q^{59} +(-8.58915 - 8.58915i) q^{60} +(-45.4338 + 78.6937i) q^{61} +(117.597 - 67.8945i) q^{62} +(27.6211 - 103.083i) q^{63} +24.0109i q^{64} -13.7565 q^{66} +(91.3047 + 24.4650i) q^{67} +(-19.0797 - 33.0470i) q^{68} +(-9.69118 - 5.59520i) q^{69} +(-17.1692 + 17.1692i) q^{70} +(17.5705 + 65.5740i) q^{71} +(-90.7785 + 24.3240i) q^{72} +(51.8021 + 51.8021i) q^{73} +(4.68118 - 8.10804i) q^{74} +(-98.0483 + 56.6082i) q^{75} +(-0.268695 + 1.00278i) q^{76} +7.64700i q^{77} -49.1050 q^{79} +(29.9965 + 8.03753i) q^{80} +(-18.2361 - 31.5859i) q^{81} +(24.6315 + 14.2210i) q^{82} +(70.5618 - 70.5618i) q^{83} +(-13.1686 - 49.1461i) q^{84} +(37.5391 - 10.0586i) q^{85} +(-83.7955 - 83.7955i) q^{86} +(48.1510 - 83.4000i) q^{87} +(5.83198 - 3.36710i) q^{88} +(-21.8165 + 81.4201i) q^{89} +59.9726i q^{90} -3.43242 q^{92} +(-279.915 - 75.0030i) q^{93} +(40.4613 + 70.0810i) q^{94} +(-0.915654 - 0.528653i) q^{95} +(-83.2176 + 83.2176i) q^{96} +(-17.5122 - 65.3566i) q^{97} +(13.1709 - 3.52914i) q^{98} +(13.3556 + 13.3556i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q12q384q9+376q14188q16+136q22+120q2784q29176q351048q40+368q42+368q4888q53+704q55+8q611480q66+168q68+1132q94+O(q100) 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/169Z)×\left(\mathbb{Z}/169\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(112)e\left(\frac{1}{12}\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 −2.27369 0.609234i −1.13685 0.304617i −0.359164 0.933274i 0.616938π-0.616938\pi
−0.777683 + 0.628657i 0.783605π0.783605\pi
33 2.51175 + 4.35048i 0.837249 + 1.45016i 0.892186 + 0.451669i 0.149171π0.149171\pi
−0.0549364 + 0.998490i 0.517496π0.517496\pi
44 1.33442 + 0.770425i 0.333604 + 0.192606i
55 −1.10964 + 1.10964i −0.221929 + 0.221929i −0.809310 0.587381i 0.800159π-0.800159\pi
0.587381 + 0.809310i 0.300159π0.300159\pi
66 −3.06049 11.4219i −0.510081 1.90365i
77 −6.34925 + 1.70128i −0.907035 + 0.243039i −0.682035 0.731319i 0.738905π-0.738905\pi
−0.225000 + 0.974359i 0.572238π0.572238\pi
88 4.09315 + 4.09315i 0.511644 + 0.511644i
99 −8.11776 + 14.0604i −0.901973 + 1.56226i
1010 3.19902 1.84696i 0.319902 0.184696i
1111 0.301099 1.12372i 0.0273726 0.102156i −0.950888 0.309535i 0.899827π-0.899827\pi
0.978261 + 0.207379i 0.0664933π0.0664933\pi
1212 7.74046i 0.645038i
1313 0 0
1414 15.4727 1.10519
1515 −7.61462 2.04033i −0.507642 0.136022i
1616 −9.89459 17.1379i −0.618412 1.07112i
1717 −21.4473 12.3826i −1.26160 0.728387i −0.288218 0.957565i 0.593063π-0.593063\pi
−0.973385 + 0.229178i 0.926396π0.926396\pi
1818 27.0234 27.0234i 1.50130 1.50130i
1919 0.174381 + 0.650797i 0.00917793 + 0.0342525i 0.970363 0.241652i 0.0776893π-0.0776893\pi
−0.961185 + 0.275905i 0.911023π0.911023\pi
2020 −2.33562 + 0.625828i −0.116781 + 0.0312914i
2121 −23.3491 23.3491i −1.11186 1.11186i
2222 −1.36921 + 2.37154i −0.0622369 + 0.107797i
2323 −1.92917 + 1.11381i −0.0838770 + 0.0484264i −0.541352 0.840796i 0.682087π-0.682087\pi
0.457475 + 0.889223i 0.348754π0.348754\pi
2424 −7.52619 + 28.0881i −0.313591 + 1.17034i
2525 22.5374i 0.901495i
2626 0 0
2727 −36.3476 −1.34621
2828 −9.78324 2.62141i −0.349401 0.0936218i
2929 −9.58516 16.6020i −0.330523 0.572482i 0.652092 0.758140i 0.273892π-0.273892\pi
−0.982614 + 0.185658i 0.940558π0.940558\pi
3030 16.0703 + 9.27818i 0.535676 + 0.309273i
3131 −40.7907 + 40.7907i −1.31583 + 1.31583i −0.398785 + 0.917045i 0.630568π0.630568\pi
−0.917045 + 0.398785i 0.869432π0.869432\pi
3232 6.06346 + 22.6291i 0.189483 + 0.707160i
3333 5.64498 1.51257i 0.171060 0.0458354i
3434 41.2206 + 41.2206i 1.21237 + 1.21237i
3535 5.15759 8.93321i 0.147360 0.255235i
3636 −21.6649 + 12.5082i −0.601803 + 0.347451i
3737 −1.02942 + 3.84185i −0.0278222 + 0.103834i −0.978441 0.206528i 0.933784π-0.933784\pi
0.950618 + 0.310362i 0.100450π0.100450\pi
3838 1.58595i 0.0417356i
3939 0 0
4040 −9.08389 −0.227097
4141 −11.6712 3.12729i −0.284664 0.0762754i 0.113662 0.993519i 0.463742π-0.463742\pi
−0.398326 + 0.917244i 0.630409π0.630409\pi
4242 38.8636 + 67.3137i 0.925323 + 1.60271i
4343 43.5991 + 25.1720i 1.01393 + 0.585395i 0.912341 0.409431i 0.134273π-0.134273\pi
0.101592 + 0.994826i 0.467606π0.467606\pi
4444 1.26753 1.26753i 0.0288075 0.0288075i
4545 −6.59418 24.6098i −0.146537 0.546885i
4646 5.06491 1.35714i 0.110107 0.0295030i
4747 −24.3090 24.3090i −0.517212 0.517212i 0.399515 0.916727i 0.369179π-0.369179\pi
−0.916727 + 0.399515i 0.869179π0.869179\pi
4848 49.7054 86.0923i 1.03553 1.79359i
4949 −5.01666 + 2.89637i −0.102381 + 0.0591096i
5050 13.7305 51.2431i 0.274611 1.02486i
5151 124.408i 2.43937i
5252 0 0
5353 65.5668 1.23711 0.618555 0.785742i 0.287718π-0.287718\pi
0.618555 + 0.785742i 0.287718π0.287718\pi
5454 82.6433 + 22.1442i 1.53043 + 0.410078i
5555 0.912811 + 1.58104i 0.0165966 + 0.0287461i
5656 −32.9520 19.0249i −0.588429 0.339730i
5757 −2.39328 + 2.39328i −0.0419873 + 0.0419873i
5858 11.6792 + 43.5874i 0.201366 + 0.751507i
5959 71.6521 19.1991i 1.21444 0.325409i 0.405938 0.913900i 0.366945π-0.366945\pi
0.808503 + 0.588492i 0.200278π0.200278\pi
6060 −8.58915 8.58915i −0.143152 0.143152i
6161 −45.4338 + 78.6937i −0.744816 + 1.29006i 0.205464 + 0.978665i 0.434130π0.434130\pi
−0.950280 + 0.311395i 0.899204π0.899204\pi
6262 117.597 67.8945i 1.89672 1.09507i
6363 27.6211 103.083i 0.438430 1.63624i
6464 24.0109i 0.375171i
6565 0 0
6666 −13.7565 −0.208431
6767 91.3047 + 24.4650i 1.36276 + 0.365149i 0.864828 0.502069i 0.167428π-0.167428\pi
0.497929 + 0.867218i 0.334094π0.334094\pi
6868 −19.0797 33.0470i −0.280584 0.485985i
6969 −9.69118 5.59520i −0.140452 0.0810899i
7070 −17.1692 + 17.1692i −0.245274 + 0.245274i
7171 17.5705 + 65.5740i 0.247472 + 0.923578i 0.972125 + 0.234464i 0.0753335π0.0753335\pi
−0.724653 + 0.689114i 0.758000π0.758000\pi
7272 −90.7785 + 24.3240i −1.26081 + 0.337834i
7373 51.8021 + 51.8021i 0.709617 + 0.709617i 0.966455 0.256837i 0.0826804π-0.0826804\pi
−0.256837 + 0.966455i 0.582680π0.582680\pi
7474 4.68118 8.10804i 0.0632592 0.109568i
7575 −98.0483 + 56.6082i −1.30731 + 0.754776i
7676 −0.268695 + 1.00278i −0.00353545 + 0.0131945i
7777 7.64700i 0.0993116i
7878 0 0
7979 −49.1050 −0.621582 −0.310791 0.950478i 0.600594π-0.600594\pi
−0.310791 + 0.950478i 0.600594π0.600594\pi
8080 29.9965 + 8.03753i 0.374956 + 0.100469i
8181 −18.2361 31.5859i −0.225138 0.389950i
8282 24.6315 + 14.2210i 0.300384 + 0.173427i
8383 70.5618 70.5618i 0.850142 0.850142i −0.140008 0.990150i 0.544713π-0.544713\pi
0.990150 + 0.140008i 0.0447129π0.0447129\pi
8484 −13.1686 49.1461i −0.156770 0.585072i
8585 37.5391 10.0586i 0.441636 0.118336i
8686 −83.7955 83.7955i −0.974366 0.974366i
8787 48.1510 83.4000i 0.553460 0.958621i
8888 5.83198 3.36710i 0.0662725 0.0382625i
8989 −21.8165 + 81.4201i −0.245129 + 0.914833i 0.728190 + 0.685375i 0.240362π0.240362\pi
−0.973319 + 0.229457i 0.926305π0.926305\pi
9090 59.9726i 0.666362i
9191 0 0
9292 −3.43242 −0.0373089
9393 −279.915 75.0030i −3.00984 0.806484i
9494 40.4613 + 70.0810i 0.430439 + 0.745543i
9595 −0.915654 0.528653i −0.00963846 0.00556477i
9696 −83.2176 + 83.2176i −0.866850 + 0.866850i
9797 −17.5122 65.3566i −0.180539 0.673779i −0.995542 0.0943225i 0.969932π-0.969932\pi
0.815003 0.579457i 0.196735π-0.196735\pi
9898 13.1709 3.52914i 0.134397 0.0360116i
9999 13.3556 + 13.3556i 0.134905 + 0.134905i
100100 −17.3634 + 30.0742i −0.173634 + 0.300742i
101101 −65.4023 + 37.7600i −0.647547 + 0.373862i −0.787516 0.616294i 0.788633π-0.788633\pi
0.139968 + 0.990156i 0.455300π0.455300\pi
102102 −75.7934 + 282.865i −0.743073 + 2.77319i
103103 79.8956i 0.775685i 0.921726 + 0.387843i 0.126780π0.126780\pi
−0.921726 + 0.387843i 0.873220π0.873220\pi
104104 0 0
105105 51.8183 0.493507
106106 −149.079 39.9456i −1.40640 0.376845i
107107 −37.3751 64.7356i −0.349300 0.605005i 0.636825 0.771008i 0.280247π-0.280247\pi
−0.986125 + 0.166003i 0.946914π0.946914\pi
108108 −48.5028 28.0031i −0.449100 0.259288i
109109 −21.0819 + 21.0819i −0.193412 + 0.193412i −0.797169 0.603757i 0.793670π-0.793670\pi
0.603757 + 0.797169i 0.293670π0.293670\pi
110110 −1.11223 4.15091i −0.0101112 0.0377355i
111111 −19.2995 + 5.17130i −0.173870 + 0.0465882i
112112 91.9795 + 91.9795i 0.821246 + 0.821246i
113113 −46.1016 + 79.8504i −0.407979 + 0.706641i −0.994663 0.103175i 0.967100π-0.967100\pi
0.586684 + 0.809816i 0.300433π0.300433\pi
114114 6.89965 3.98351i 0.0605232 0.0349431i
115115 0.904763 3.37662i 0.00786750 0.0293619i
116116 29.5386i 0.254643i
117117 0 0
118118 −174.612 −1.47976
119119 157.240 + 42.1323i 1.32134 + 0.354053i
120120 −22.8164 39.5192i −0.190137 0.329327i
121121 103.617 + 59.8233i 0.856339 + 0.494407i
122122 151.245 151.245i 1.23972 1.23972i
123123 −15.7099 58.6303i −0.127723 0.476669i
124124 −85.8579 + 23.0056i −0.692403 + 0.185529i
125125 −52.7496 52.7496i −0.421996 0.421996i
126126 −125.604 + 217.552i −0.996855 + 1.72660i
127127 4.02217 2.32220i 0.0316706 0.0182850i −0.484081 0.875023i 0.660846π-0.660846\pi
0.515752 + 0.856738i 0.327513π0.327513\pi
128128 38.8821 145.110i 0.303767 1.13367i
129129 252.903i 1.96049i
130130 0 0
131131 58.5190 0.446710 0.223355 0.974737i 0.428299π-0.428299\pi
0.223355 + 0.974737i 0.428299π0.428299\pi
132132 8.69807 + 2.33064i 0.0658945 + 0.0176564i
133133 −2.21437 3.83540i −0.0166494 0.0288376i
134134 −192.694 111.252i −1.43801 0.830238i
135135 40.3329 40.3329i 0.298762 0.298762i
136136 −37.1031 138.471i −0.272817 1.01817i
137137 −159.918 + 42.8498i −1.16728 + 0.312772i −0.789871 0.613274i 0.789852π-0.789852\pi
−0.377411 + 0.926046i 0.623186π0.623186\pi
138138 18.6260 + 18.6260i 0.134971 + 0.134971i
139139 38.3858 66.4861i 0.276156 0.478317i −0.694270 0.719715i 0.744273π-0.744273\pi
0.970426 + 0.241398i 0.0776059π0.0776059\pi
140140 13.7647 7.94708i 0.0983196 0.0567648i
141141 44.6976 166.814i 0.317004 1.18307i
142142 159.800i 1.12535i
143143 0 0
144144 321.288 2.23116
145145 29.0584 + 7.78617i 0.200403 + 0.0536977i
146146 −86.2225 149.342i −0.590565 1.02289i
147147 −25.2012 14.5499i −0.171437 0.0989790i
148148 −4.33354 + 4.33354i −0.0292807 + 0.0292807i
149149 30.9709 + 115.585i 0.207858 + 0.775737i 0.988559 + 0.150833i 0.0481954π0.0481954\pi
−0.780701 + 0.624904i 0.785138π0.785138\pi
150150 257.420 68.9754i 1.71613 0.459836i
151151 −158.935 158.935i −1.05255 1.05255i −0.998541 0.0540078i 0.982800π-0.982800\pi
−0.0540078 0.998541i 0.517200π-0.517200\pi
152152 −1.95005 + 3.37758i −0.0128293 + 0.0222209i
153153 348.207 201.037i 2.27586 1.31397i
154154 4.65881 17.3869i 0.0302520 0.112902i
155155 90.5263i 0.584041i
156156 0 0
157157 121.589 0.774451 0.387225 0.921985i 0.373434π-0.373434\pi
0.387225 + 0.921985i 0.373434π0.373434\pi
158158 111.650 + 29.9165i 0.706644 + 0.189345i
159159 164.687 + 285.247i 1.03577 + 1.79401i
160160 −31.8385 18.3820i −0.198991 0.114887i
161161 10.3539 10.3539i 0.0643098 0.0643098i
162162 22.2202 + 82.9268i 0.137162 + 0.511894i
163163 −143.124 + 38.3498i −0.878059 + 0.235275i −0.669569 0.742750i 0.733521π-0.733521\pi
−0.208489 + 0.978025i 0.566855π0.566855\pi
164164 −13.1649 13.1649i −0.0802738 0.0802738i
165165 −4.58550 + 7.94233i −0.0277909 + 0.0481353i
166166 −203.425 + 117.447i −1.22545 + 0.707513i
167167 8.21496 30.6587i 0.0491914 0.183585i −0.936959 0.349440i 0.886372π-0.886372\pi
0.986150 + 0.165855i 0.0530385π0.0530385\pi
168168 191.143i 1.13775i
169169 0 0
170170 −91.4803 −0.538120
171171 −10.5660 2.83116i −0.0617897 0.0165565i
172172 38.7862 + 67.1797i 0.225501 + 0.390580i
173173 −75.3542 43.5058i −0.435574 0.251478i 0.266145 0.963933i 0.414250π-0.414250\pi
−0.701718 + 0.712455i 0.747583π0.747583\pi
174174 −160.291 + 160.291i −0.921211 + 0.921211i
175175 −38.3423 143.095i −0.219099 0.817688i
176176 −22.2374 + 5.95849i −0.126349 + 0.0338551i
177177 263.497 + 263.497i 1.48868 + 1.48868i
178178 99.2079 171.833i 0.557348 0.965354i
179179 −125.261 + 72.3192i −0.699780 + 0.404018i −0.807265 0.590189i 0.799053π-0.799053\pi
0.107486 + 0.994207i 0.465720π0.465720\pi
180180 10.1606 37.9200i 0.0564480 0.210667i
181181 57.4932i 0.317642i −0.987307 0.158821i 0.949231π-0.949231\pi
0.987307 0.158821i 0.0507693π-0.0507693\pi
182182 0 0
183183 −456.473 −2.49439
184184 −12.4554 3.33741i −0.0676923 0.0181381i
185185 −3.12080 5.40538i −0.0168692 0.0292183i
186186 590.746 + 341.068i 3.17606 + 1.83370i
187187 −20.3722 + 20.3722i −0.108942 + 0.108942i
188188 −13.7100 51.1665i −0.0729257 0.272162i
189189 230.780 61.8372i 1.22106 0.327181i
190190 1.75984 + 1.75984i 0.00926233 + 0.00926233i
191191 33.9463 58.7966i 0.177729 0.307836i −0.763373 0.645958i 0.776458π-0.776458\pi
0.941102 + 0.338122i 0.109792π0.109792\pi
192192 −104.459 + 60.3095i −0.544058 + 0.314112i
193193 −55.6354 + 207.634i −0.288266 + 1.07582i 0.658153 + 0.752884i 0.271338π0.271338\pi
−0.946419 + 0.322940i 0.895329π0.895329\pi
194194 159.270i 0.820979i
195195 0 0
196196 −8.92575 −0.0455395
197197 152.818 + 40.9476i 0.775728 + 0.207856i 0.624901 0.780704i 0.285139π-0.285139\pi
0.150828 + 0.988560i 0.451806π0.451806\pi
198198 −22.2299 38.5032i −0.112272 0.194461i
199199 −36.3122 20.9649i −0.182473 0.105351i 0.405981 0.913882i 0.366930π-0.366930\pi
−0.588454 + 0.808530i 0.700263π0.700263\pi
200200 −92.2490 + 92.2490i −0.461245 + 0.461245i
201201 122.900 + 458.669i 0.611442 + 2.28193i
202202 171.710 46.0094i 0.850047 0.227769i
203203 89.1031 + 89.1031i 0.438931 + 0.438931i
204204 95.8468 166.012i 0.469837 0.813782i
205205 16.4211 9.48070i 0.0801027 0.0462473i
206206 48.6751 181.658i 0.236287 0.881835i
207207 36.1665i 0.174717i
208208 0 0
209209 0.783817 0.00375032
210210 −117.819 31.5695i −0.561042 0.150331i
211211 35.3826 + 61.2844i 0.167690 + 0.290447i 0.937607 0.347696i 0.113036π-0.113036\pi
−0.769917 + 0.638144i 0.779703π0.779703\pi
212212 87.4934 + 50.5143i 0.412705 + 0.238275i
213213 −241.146 + 241.146i −1.13214 + 1.13214i
214214 45.5404 + 169.959i 0.212806 + 0.794201i
215215 −76.3114 + 20.4476i −0.354937 + 0.0951050i
216216 −148.776 148.776i −0.688779 0.688779i
217217 189.594 328.386i 0.873705 1.51330i
218218 60.7776 35.0899i 0.278796 0.160963i
219219 −95.2499 + 355.477i −0.434931 + 1.62318i
220220 2.81301i 0.0127864i
221221 0 0
222222 47.0318 0.211855
223223 −147.428 39.5031i −0.661110 0.177144i −0.0873632 0.996177i 0.527844π-0.527844\pi
−0.573747 + 0.819033i 0.694511π0.694511\pi
224224 −76.9968 133.362i −0.343735 0.595367i
225225 −316.884 182.953i −1.40837 0.813124i
226226 153.469 153.469i 0.679065 0.679065i
227227 −18.9293 70.6452i −0.0833891 0.311212i 0.911615 0.411045i 0.134836π-0.134836\pi
−0.995004 + 0.0998323i 0.968169π0.968169\pi
228228 −5.03747 + 1.34979i −0.0220942 + 0.00592011i
229229 −182.706 182.706i −0.797845 0.797845i 0.184911 0.982755i 0.440800π-0.440800\pi
−0.982755 + 0.184911i 0.940800π0.940800\pi
230230 −4.11431 + 7.12619i −0.0178883 + 0.0309834i
231231 −33.2681 + 19.2073i −0.144018 + 0.0831486i
232232 28.7209 107.188i 0.123797 0.462017i
233233 263.622i 1.13142i −0.824603 0.565712i 0.808601π-0.808601\pi
0.824603 0.565712i 0.191399π-0.191399\pi
234234 0 0
235235 53.9486 0.229568
236236 110.405 + 29.5830i 0.467818 + 0.125352i
237237 −123.339 213.630i −0.520419 0.901393i
238238 −331.847 191.592i −1.39432 0.805009i
239239 260.543 260.543i 1.09014 1.09014i 0.0946270 0.995513i 0.469834π-0.469834\pi
0.995513 0.0946270i 0.0301659π-0.0301659\pi
240240 40.3765 + 150.687i 0.168235 + 0.627863i
241241 59.8004 16.0235i 0.248134 0.0664874i −0.132608 0.991169i 0.542335π-0.542335\pi
0.380742 + 0.924681i 0.375668π0.375668\pi
242242 −199.147 199.147i −0.822921 0.822921i
243243 −71.9549 + 124.630i −0.296111 + 0.512879i
244244 −121.255 + 70.0067i −0.496947 + 0.286913i
245245 2.35277 8.78065i 0.00960313 0.0358394i
246246 142.878i 0.580806i
247247 0 0
248248 −333.925 −1.34647
249249 484.211 + 129.744i 1.94462 + 0.521060i
250250 87.7995 + 152.073i 0.351198 + 0.608293i
251251 97.1096 + 56.0663i 0.386891 + 0.223372i 0.680812 0.732458i 0.261627π-0.261627\pi
−0.293921 + 0.955830i 0.594960π0.594960\pi
252252 116.276 116.276i 0.461412 0.461412i
253253 0.670731 + 2.50320i 0.00265111 + 0.00989408i
254254 −10.5599 + 2.82953i −0.0415746 + 0.0111399i
255255 138.048 + 138.048i 0.541365 + 0.541365i
256256 −128.790 + 223.071i −0.503087 + 0.871372i
257257 323.389 186.709i 1.25832 0.726493i 0.285575 0.958356i 0.407815π-0.407815\pi
0.972748 + 0.231863i 0.0744822π0.0744822\pi
258258 154.077 575.023i 0.597198 2.22877i
259259 26.1442i 0.100943i
260260 0 0
261261 311.240 1.19249
262262 −133.054 35.6518i −0.507841 0.136076i
263263 −163.801 283.712i −0.622818 1.07875i −0.988959 0.148192i 0.952655π-0.952655\pi
0.366141 0.930559i 0.380679π-0.380679\pi
264264 29.2969 + 16.9146i 0.110973 + 0.0640704i
265265 −72.7558 + 72.7558i −0.274550 + 0.274550i
266266 2.69814 + 10.0696i 0.0101434 + 0.0378557i
267267 −409.014 + 109.595i −1.53189 + 0.410468i
268268 102.990 + 102.990i 0.384291 + 0.384291i
269269 −137.084 + 237.436i −0.509605 + 0.882661i 0.490333 + 0.871535i 0.336875π0.336875\pi
−0.999938 + 0.0111263i 0.996458π0.996458\pi
270270 −116.277 + 67.1324i −0.430655 + 0.248639i
271271 −58.2447 + 217.372i −0.214925 + 0.802112i 0.771268 + 0.636511i 0.219623π0.219623\pi
−0.986193 + 0.165601i 0.947044π0.947044\pi
272272 490.082i 1.80177i
273273 0 0
274274 389.709 1.42230
275275 25.3256 + 6.78597i 0.0920931 + 0.0246763i
276276 −8.62137 14.9327i −0.0312369 0.0541038i
277277 349.428 + 201.742i 1.26147 + 0.728312i 0.973360 0.229284i 0.0736384π-0.0736384\pi
0.288114 + 0.957596i 0.406972π0.406972\pi
278278 −127.783 + 127.783i −0.459651 + 0.459651i
279279 −242.403 904.661i −0.868829 3.24251i
280280 57.6758 15.4542i 0.205985 0.0551935i
281281 356.187 + 356.187i 1.26757 + 1.26757i 0.947340 + 0.320228i 0.103760π0.103760\pi
0.320228 + 0.947340i 0.396240π0.396240\pi
282282 −203.257 + 352.052i −0.720770 + 1.24841i
283283 302.969 174.919i 1.07056 0.618089i 0.142226 0.989834i 0.454574π-0.454574\pi
0.928335 + 0.371746i 0.121241π0.121241\pi
284284 −27.0735 + 101.040i −0.0953293 + 0.355774i
285285 5.31137i 0.0186364i
286286 0 0
287287 79.4237 0.276738
288288 −367.396 98.4433i −1.27568 0.341817i
289289 162.156 + 280.863i 0.561095 + 0.971845i
290290 −61.3263 35.4067i −0.211470 0.122092i
291291 240.346 240.346i 0.825931 0.825931i
292292 29.2159 + 109.035i 0.100054 + 0.373408i
293293 519.890 139.304i 1.77437 0.475441i 0.784831 0.619710i 0.212750π-0.212750\pi
0.989539 + 0.144269i 0.0460829π0.0460829\pi
294294 48.4355 + 48.4355i 0.164747 + 0.164747i
295295 −58.2041 + 100.812i −0.197302 + 0.341737i
296296 −19.9389 + 11.5117i −0.0673611 + 0.0388909i
297297 −10.9442 + 40.8443i −0.0368492 + 0.137523i
298298 281.673i 0.945211i
299299 0 0
300300 −174.450 −0.581499
301301 −319.646 85.6489i −1.06195 0.284548i
302302 264.541 + 458.198i 0.875962 + 1.51721i
303303 −328.548 189.687i −1.08432 0.626031i
304304 9.42790 9.42790i 0.0310128 0.0310128i
305305 −36.9066 137.737i −0.121005 0.451598i
306306 −914.195 + 244.958i −2.98757 + 0.800516i
307307 −340.580 340.580i −1.10938 1.10938i −0.993232 0.116150i 0.962945π-0.962945\pi
−0.116150 0.993232i 0.537055π-0.537055\pi
308308 −5.89144 + 10.2043i −0.0191280 + 0.0331307i
309309 −347.584 + 200.678i −1.12487 + 0.649442i
310310 −55.1517 + 205.829i −0.177909 + 0.663965i
311311 100.353i 0.322679i −0.986899 0.161339i 0.948419π-0.948419\pi
0.986899 0.161339i 0.0515814π-0.0515814\pi
312312 0 0
313313 89.9264 0.287305 0.143652 0.989628i 0.454115π-0.454115\pi
0.143652 + 0.989628i 0.454115π0.454115\pi
314314 −276.456 74.0761i −0.880432 0.235911i
315315 83.7361 + 145.035i 0.265829 + 0.460429i
316316 −65.5265 37.8317i −0.207362 0.119721i
317317 −285.497 + 285.497i −0.900622 + 0.900622i −0.995490 0.0948677i 0.969757π-0.969757\pi
0.0948677 + 0.995490i 0.469757π0.469757\pi
318318 −200.666 748.897i −0.631026 2.35502i
319319 −21.5420 + 5.77215i −0.0675297 + 0.0180945i
320320 −26.6436 26.6436i −0.0832612 0.0832612i
321321 187.754 325.199i 0.584902 1.01308i
322322 −29.8495 + 17.2336i −0.0927003 + 0.0535205i
323323 4.31856 16.1171i 0.0133702 0.0498981i
324324 56.1983i 0.173452i
325325 0 0
326326 348.783 1.06989
327327 −144.669 38.7638i −0.442412 0.118544i
328328 −34.9716 60.5725i −0.106621 0.184672i
329329 195.700 + 112.987i 0.594832 + 0.343427i
330330 15.2648 15.2648i 0.0462569 0.0462569i
331331 39.7923 + 148.507i 0.120218 + 0.448661i 0.999624 0.0274116i 0.00872647π-0.00872647\pi
−0.879406 + 0.476073i 0.842060π0.842060\pi
332332 148.521 39.7962i 0.447353 0.119868i
333333 −45.6613 45.6613i −0.137121 0.137121i
334334 −37.3566 + 64.7036i −0.111846 + 0.193723i
335335 −128.463 + 74.1682i −0.383472 + 0.221398i
336336 −169.125 + 631.184i −0.503349 + 1.87852i
337337 366.843i 1.08855i 0.838905 + 0.544277i 0.183196π0.183196\pi
−0.838905 + 0.544277i 0.816804π0.816804\pi
338338 0 0
339339 −463.183 −1.36632
340340 57.8421 + 15.4987i 0.170124 + 0.0455845i
341341 33.5551 + 58.1192i 0.0984021 + 0.170437i
342342 22.2991 + 12.8744i 0.0652020 + 0.0376444i
343343 254.675 254.675i 0.742493 0.742493i
344344 75.4252 + 281.491i 0.219259 + 0.818287i
345345 16.9624 4.54507i 0.0491665 0.0131741i
346346 144.827 + 144.827i 0.418576 + 0.418576i
347347 −200.347 + 347.011i −0.577369 + 1.00003i 0.418411 + 0.908258i 0.362587π0.362587\pi
−0.995780 + 0.0917743i 0.970746π0.970746\pi
348348 128.507 74.1935i 0.369273 0.213200i
349349 116.567 435.035i 0.334004 1.24652i −0.570941 0.820991i 0.693421π-0.693421\pi
0.904945 0.425529i 0.139912π-0.139912\pi
350350 348.715i 0.996327i
351351 0 0
352352 27.2544 0.0774273
353353 −436.385 116.929i −1.23622 0.331244i −0.419220 0.907885i 0.637696π-0.637696\pi
−0.816998 + 0.576641i 0.804363π0.804363\pi
354354 −438.580 759.643i −1.23893 2.14589i
355355 −92.2608 53.2668i −0.259890 0.150047i
356356 −91.8403 + 91.8403i −0.257978 + 0.257978i
357357 211.652 + 789.895i 0.592862 + 2.21259i
358358 328.863 88.1187i 0.918613 0.246142i
359359 167.150 + 167.150i 0.465598 + 0.465598i 0.900485 0.434887i 0.143212π-0.143212\pi
−0.434887 + 0.900485i 0.643212π0.643212\pi
360360 73.7408 127.723i 0.204836 0.354786i
361361 312.242 180.273i 0.864936 0.499371i
362362 −35.0269 + 130.722i −0.0967593 + 0.361111i
363363 601.044i 1.65577i
364364 0 0
365365 −114.964 −0.314969
366366 1037.88 + 278.099i 2.83574 + 0.759834i
367367 −339.395 587.849i −0.924782 1.60177i −0.791912 0.610635i 0.790914π-0.790914\pi
−0.132870 0.991133i 0.542419π-0.542419\pi
368368 38.1767 + 22.0413i 0.103741 + 0.0598949i
369369 138.715 138.715i 0.375921 0.375921i
370370 3.80259 + 14.1915i 0.0102773 + 0.0383553i
371371 −416.300 + 111.547i −1.12210 + 0.300666i
372372 −315.739 315.739i −0.848760 0.848760i
373373 55.5691 96.2484i 0.148979 0.258039i −0.781872 0.623440i 0.785735π-0.785735\pi
0.930850 + 0.365401i 0.119068π0.119068\pi
374374 58.7317 33.9087i 0.157037 0.0906651i
375375 96.9920 361.979i 0.258645 0.965278i
376376 199.001i 0.529257i
377377 0 0
378378 −562.396 −1.48782
379379 333.186 + 89.2768i 0.879118 + 0.235559i 0.670027 0.742337i 0.266283π-0.266283\pi
0.209091 + 0.977896i 0.432949π0.432949\pi
380380 −0.814575 1.41089i −0.00214362 0.00371286i
381381 20.2053 + 11.6656i 0.0530324 + 0.0306183i
382382 −113.004 + 113.004i −0.295823 + 0.295823i
383383 100.507 + 375.095i 0.262419 + 0.979361i 0.963811 + 0.266586i 0.0858956π0.0858956\pi
−0.701392 + 0.712776i 0.747438π0.747438\pi
384384 728.960 195.324i 1.89833 0.508657i
385385 −8.48544 8.48544i −0.0220401 0.0220401i
386386 252.996 438.201i 0.655429 1.13524i
387387 −707.854 + 408.680i −1.82908 + 1.05602i
388388 26.9837 100.705i 0.0695457 0.259548i
389389 391.807i 1.00722i −0.863932 0.503608i 0.832006π-0.832006\pi
0.863932 0.503608i 0.167994π-0.167994\pi
390390 0 0
391391 55.1672 0.141093
392392 −32.3893 8.67868i −0.0826257 0.0221395i
393393 146.985 + 254.586i 0.374008 + 0.647801i
394394 −322.516 186.205i −0.818568 0.472600i
395395 54.4890 54.4890i 0.137947 0.137947i
396396 7.53243 + 28.1114i 0.0190213 + 0.0709884i
397397 −152.232 + 40.7905i −0.383456 + 0.102747i −0.445397 0.895333i 0.646938π-0.646938\pi
0.0619411 + 0.998080i 0.480271π0.480271\pi
398398 69.7904 + 69.7904i 0.175353 + 0.175353i
399399 11.1239 19.2671i 0.0278794 0.0482886i
400400 386.244 222.998i 0.965610 0.557495i
401401 −137.780 + 514.202i −0.343591 + 1.28230i 0.550658 + 0.834731i 0.314377π0.314377\pi
−0.894249 + 0.447569i 0.852290π0.852290\pi
402402 1117.75i 2.78047i
403403 0 0
404404 −116.365 −0.288032
405405 55.2848 + 14.8135i 0.136506 + 0.0365766i
406406 −148.308 256.878i −0.365292 0.632704i
407407 4.00719 + 2.31355i 0.00984568 + 0.00568441i
408408 509.220 509.220i 1.24809 1.24809i
409409 72.0792 + 269.003i 0.176233 + 0.657710i 0.996338 + 0.0854974i 0.0272479π0.0272479\pi
−0.820106 + 0.572212i 0.806085π0.806085\pi
410410 −43.1124 + 11.5519i −0.105152 + 0.0281755i
411411 −588.090 588.090i −1.43088 1.43088i
412412 −61.5536 + 106.614i −0.149402 + 0.258772i
413413 −422.274 + 243.800i −1.02245 + 0.590314i
414414 −22.0338 + 82.2314i −0.0532219 + 0.198627i
415415 156.597i 0.377342i
416416 0 0
417417 385.661 0.924847
418418 −1.78216 0.477528i −0.00426354 0.00114241i
419419 244.472 + 423.438i 0.583465 + 1.01059i 0.995065 + 0.0992269i 0.0316370π0.0316370\pi
−0.411599 + 0.911365i 0.635030π0.635030\pi
420420 69.1471 + 39.9221i 0.164636 + 0.0950526i
421421 −375.601 + 375.601i −0.892163 + 0.892163i −0.994726 0.102563i 0.967296π-0.967296\pi
0.102563 + 0.994726i 0.467296π0.467296\pi
422422 −43.1125 160.898i −0.102162 0.381275i
423423 539.127 144.459i 1.27453 0.341510i
424424 268.375 + 268.375i 0.632960 + 0.632960i
425425 279.071 483.365i 0.656637 1.13733i
426426 695.205 401.377i 1.63194 0.942200i
427427 154.591 576.941i 0.362039 1.35115i
428428 115.179i 0.269110i
429429 0 0
430430 185.966 0.432480
431431 −114.753 30.7479i −0.266247 0.0713407i 0.123226 0.992379i 0.460676π-0.460676\pi
−0.389473 + 0.921038i 0.627343π0.627343\pi
432432 359.644 + 622.922i 0.832510 + 1.44195i
433433 120.208 + 69.4021i 0.277617 + 0.160282i 0.632344 0.774688i 0.282093π-0.282093\pi
−0.354727 + 0.934970i 0.615426π0.615426\pi
434434 −631.143 + 631.143i −1.45425 + 1.45425i
435435 39.1138 + 145.975i 0.0899168 + 0.335574i
436436 −44.3740 + 11.8900i −0.101775 + 0.0272706i
437437 −1.06127 1.06127i −0.00242854 0.00242854i
438438 433.138 750.217i 0.988900 1.71282i
439439 −121.509 + 70.1532i −0.276786 + 0.159802i −0.631967 0.774995i 0.717752π-0.717752\pi
0.355182 + 0.934797i 0.384419π0.384419\pi
440440 −2.73515 + 10.2077i −0.00621624 + 0.0231993i
441441 94.0482i 0.213261i
442442 0 0
443443 390.577 0.881664 0.440832 0.897590i 0.354684π-0.354684\pi
0.440832 + 0.897590i 0.354684π0.354684\pi
444444 −29.7377 7.96819i −0.0669768 0.0179464i
445445 −66.1388 114.556i −0.148627 0.257429i
446446 311.139 + 179.636i 0.697620 + 0.402771i
447447 −425.058 + 425.058i −0.950913 + 0.950913i
448448 −40.8492 152.451i −0.0911813 0.340293i
449449 −291.660 + 78.1501i −0.649577 + 0.174054i −0.568538 0.822657i 0.692491π-0.692491\pi
−0.0810394 + 0.996711i 0.525824π0.525824\pi
450450 609.036 + 609.036i 1.35341 + 1.35341i
451451 −7.02837 + 12.1735i −0.0155840 + 0.0269922i
452452 −123.038 + 71.0357i −0.272207 + 0.157159i
453453 292.238 1090.65i 0.645116 2.40761i
454454 172.158i 0.379203i
455455 0 0
456456 −19.5921 −0.0429652
457457 294.593 + 78.9361i 0.644625 + 0.172727i 0.566297 0.824201i 0.308375π-0.308375\pi
0.0783273 + 0.996928i 0.475042π0.475042\pi
458458 304.107 + 526.729i 0.663990 + 1.15006i
459459 779.556 + 450.077i 1.69838 + 0.980559i
460460 3.80876 3.80876i 0.00827992 0.00827992i
461461 −209.108 780.401i −0.453596 1.69284i −0.692183 0.721722i 0.743351π-0.743351\pi
0.238587 0.971121i 0.423316π-0.423316\pi
462462 87.3432 23.4035i 0.189054 0.0506570i
463463 411.381 + 411.381i 0.888512 + 0.888512i 0.994380 0.105868i 0.0337620π-0.0337620\pi
−0.105868 + 0.994380i 0.533762π0.533762\pi
464464 −189.682 + 328.540i −0.408798 + 0.708059i
465465 393.832 227.379i 0.846951 0.488988i
466466 −160.608 + 599.395i −0.344651 + 1.28626i
467467 279.834i 0.599215i −0.954062 0.299608i 0.903144π-0.903144\pi
0.954062 0.299608i 0.0968558π-0.0968558\pi
468468 0 0
469469 −621.338 −1.32481
470470 −122.663 32.8673i −0.260984 0.0699305i
471471 305.400 + 528.969i 0.648408 + 1.12308i
472472 371.868 + 214.698i 0.787856 + 0.454869i
473473 41.4138 41.4138i 0.0875555 0.0875555i
474474 150.285 + 560.872i 0.317057 + 1.18327i
475475 −14.6673 + 3.93008i −0.0308785 + 0.00827386i
476476 177.364 + 177.364i 0.372613 + 0.372613i
477477 −532.255 + 921.894i −1.11584 + 1.93269i
478478 −751.128 + 433.664i −1.57140 + 0.907247i
479479 69.2853 258.576i 0.144646 0.539825i −0.855125 0.518422i 0.826520π-0.826520\pi
0.999771 0.0214037i 0.00681354π-0.00681354\pi
480480 184.684i 0.384758i
481481 0 0
482482 −145.730 −0.302344
483483 71.0507 + 19.0380i 0.147103 + 0.0394161i
484484 92.1788 + 159.658i 0.190452 + 0.329873i
485485 91.9548 + 53.0902i 0.189598 + 0.109464i
486486 239.532 239.532i 0.492864 0.492864i
487487 −140.372 523.877i −0.288239 1.07572i −0.946440 0.322881i 0.895349π-0.895349\pi
0.658201 0.752843i 0.271318π-0.271318\pi
488488 −508.073 + 136.138i −1.04113 + 0.278971i
489489 −526.330 526.330i −1.07634 1.07634i
490490 −10.6989 + 18.5311i −0.0218346 + 0.0378186i
491491 20.3866 11.7702i 0.0415205 0.0239719i −0.479096 0.877762i 0.659035π-0.659035\pi
0.520617 + 0.853791i 0.325702π0.325702\pi
492492 24.2067 90.3405i 0.0492005 0.183619i
493493 474.756i 0.962993i
494494 0 0
495495 −29.6399 −0.0598786
496496 1102.68 + 295.461i 2.22314 + 0.595688i
497497 −223.119 386.453i −0.448932 0.777572i
498498 −1021.90 589.996i −2.05201 1.18473i
499499 −105.552 + 105.552i −0.211527 + 0.211527i −0.804916 0.593389i 0.797790π-0.797790\pi
0.593389 + 0.804916i 0.297790π0.297790\pi
500500 −29.7502 111.029i −0.0595005 0.222059i
501501 154.014 41.2678i 0.307412 0.0823709i
502502 −186.640 186.640i −0.371793 0.371793i
503503 328.495 568.970i 0.653071 1.13115i −0.329302 0.944225i 0.606813π-0.606813\pi
0.982374 0.186928i 0.0598532π-0.0598532\pi
504504 534.993 308.878i 1.06149 0.612854i
505505 30.6731 114.473i 0.0607387 0.226680i
506506 6.10015i 0.0120556i
507507 0 0
508508 7.15632 0.0140873
509509 −754.970 202.293i −1.48324 0.397433i −0.575792 0.817596i 0.695306π-0.695306\pi
−0.907449 + 0.420163i 0.861973π0.861973\pi
510510 −229.776 397.983i −0.450540 0.780359i
511511 −417.034 240.775i −0.816113 0.471183i
512512 3.82036 3.82036i 0.00746164 0.00746164i
513513 −6.33831 23.6549i −0.0123554 0.0461109i
514514 −849.037 + 227.499i −1.65182 + 0.442605i
515515 −88.6556 88.6556i −0.172147 0.172147i
516516 −194.843 + 337.477i −0.377602 + 0.654026i
517517 −34.6357 + 19.9970i −0.0669937 + 0.0386788i
518518 −15.9279 + 59.4439i −0.0307489 + 0.114757i
519519 437.102i 0.842201i
520520 0 0
521521 408.859 0.784758 0.392379 0.919804i 0.371652π-0.371652\pi
0.392379 + 0.919804i 0.371652π0.371652\pi
522522 −707.664 189.618i −1.35568 0.363253i
523523 −179.678 311.211i −0.343553 0.595050i 0.641537 0.767092i 0.278297π-0.278297\pi
−0.985090 + 0.172042i 0.944964π0.944964\pi
524524 78.0887 + 45.0845i 0.149024 + 0.0860392i
525525 526.227 526.227i 1.00234 1.00234i
526526 199.586 + 744.867i 0.379442 + 1.41610i
527527 1379.94 369.754i 2.61849 0.701621i
528528 −81.7770 81.7770i −0.154881 0.154881i
529529 −262.019 + 453.830i −0.495310 + 0.857902i
530530 209.750 121.099i 0.395754 0.228489i
531531 −311.707 + 1163.31i −0.587020 + 2.19079i
532532 6.82403i 0.0128271i
533533 0 0
534534 996.741 1.86656
535535 113.306 + 30.3604i 0.211788 + 0.0567484i
536536 273.585 + 473.863i 0.510420 + 0.884073i
537537 −629.246 363.295i −1.17178 0.676528i
538538 456.340 456.340i 0.848216 0.848216i
539539 1.74419 + 6.50939i 0.00323597 + 0.0120768i
540540 84.8943 22.7473i 0.157212 0.0421247i
541541 −62.1232 62.1232i −0.114830 0.114830i 0.647357 0.762187i 0.275874π-0.275874\pi
−0.762187 + 0.647357i 0.775874π0.775874\pi
542542 264.861 458.753i 0.488674 0.846408i
543543 250.123 144.409i 0.460632 0.265946i
544544 150.162 560.414i 0.276034 1.03017i
545545 46.7868i 0.0858473i
546546 0 0
547547 −215.610 −0.394167 −0.197084 0.980387i 0.563147π-0.563147\pi
−0.197084 + 0.980387i 0.563147π0.563147\pi
548548 −246.409 66.0251i −0.449652 0.120484i
549549 −737.641 1277.63i −1.34361 2.32720i
550550 −53.4484 30.8585i −0.0971789 0.0561063i
551551 9.13306 9.13306i 0.0165754 0.0165754i
552552 −16.7655 62.5695i −0.0303722 0.113351i
553553 311.780 83.5411i 0.563797 0.151069i
554554 −671.584 671.584i −1.21225 1.21225i
555555 15.6773 27.1539i 0.0282474 0.0489260i
556556 102.445 59.1467i 0.184254 0.106379i
557557 −235.589 + 879.229i −0.422960 + 1.57851i 0.345377 + 0.938464i 0.387751π0.387751\pi
−0.768338 + 0.640045i 0.778916π0.778916\pi
558558 2204.60i 3.95090i
559559 0 0
560560 −204.129 −0.364516
561561 −139.799 37.4590i −0.249196 0.0667718i
562562 −592.858 1026.86i −1.05491 1.82715i
563563 203.525 + 117.505i 0.361501 + 0.208713i 0.669739 0.742597i 0.266406π-0.266406\pi
−0.308238 + 0.951309i 0.599739π0.599739\pi
564564 188.162 188.162i 0.333621 0.333621i
565565 −37.4491 139.762i −0.0662816 0.247366i
566566 −795.425 + 213.133i −1.40534 + 0.376561i
567567 169.522 + 169.522i 0.298981 + 0.298981i
568568 −196.486 + 340.324i −0.345926 + 0.599161i
569569 −607.150 + 350.538i −1.06705 + 0.616060i −0.927373 0.374137i 0.877939π-0.877939\pi
−0.139674 + 0.990198i 0.544606π0.544606\pi
570570 −3.23587 + 12.0764i −0.00567697 + 0.0211867i
571571 323.381i 0.566341i −0.959070 0.283170i 0.908614π-0.908614\pi
0.959070 0.283170i 0.0913862π-0.0913862\pi
572572 0 0
573573 341.058 0.595214
574574 −180.585 48.3877i −0.314608 0.0842991i
575575 −25.1023 43.4784i −0.0436562 0.0756147i
576576 −337.603 194.915i −0.586116 0.338394i
577577 465.169 465.169i 0.806186 0.806186i −0.177868 0.984054i 0.556920π-0.556920\pi
0.984054 + 0.177868i 0.0569201π0.0569201\pi
578578 −197.583 737.388i −0.341838 1.27576i
579579 −1043.05 + 279.484i −1.80147 + 0.482701i
580580 32.7773 + 32.7773i 0.0565126 + 0.0565126i
581581 −327.969 + 568.059i −0.564491 + 0.977727i
582582 −692.900 + 400.046i −1.19055 + 0.687364i
583583 19.7421 73.6784i 0.0338629 0.126378i
584584 424.068i 0.726143i
585585 0 0
586586 −1266.94 −2.16201
587587 220.274 + 59.0221i 0.375253 + 0.100549i 0.441516 0.897253i 0.354441π-0.354441\pi
−0.0662628 + 0.997802i 0.521108π0.521108\pi
588588 −22.4192 38.8313i −0.0381280 0.0660396i
589589 −33.6596 19.4334i −0.0571470 0.0329939i
590590 193.757 193.757i 0.328401 0.328401i
591591 205.700 + 767.683i 0.348054 + 1.29896i
592592 76.0271 20.3714i 0.128424 0.0344112i
593593 332.603 + 332.603i 0.560883 + 0.560883i 0.929558 0.368675i 0.120189π-0.120189\pi
−0.368675 + 0.929558i 0.620189π0.620189\pi
594594 49.7675 86.1999i 0.0837837 0.145118i
595595 −221.232 + 127.729i −0.371819 + 0.214670i
596596 −47.7215 + 178.099i −0.0800696 + 0.298824i
597597 210.634i 0.352821i
598598 0 0
599599 −1027.71 −1.71571 −0.857853 0.513895i 0.828202π-0.828202\pi
−0.857853 + 0.513895i 0.828202π0.828202\pi
600600 −633.033 169.621i −1.05506 0.282701i
601601 230.493 + 399.225i 0.383515 + 0.664268i 0.991562 0.129633i 0.0413799π-0.0413799\pi
−0.608047 + 0.793901i 0.708047π0.708047\pi
602602 674.597 + 389.479i 1.12059 + 0.646975i
603603 −1085.18 + 1085.18i −1.79963 + 1.79963i
604604 −89.6377 334.532i −0.148407 0.553862i
605605 −181.361 + 48.5954i −0.299769 + 0.0803230i
606606 631.454 + 631.454i 1.04200 + 1.04200i
607607 −183.169 + 317.257i −0.301761 + 0.522665i −0.976535 0.215360i 0.930908π-0.930908\pi
0.674774 + 0.738024i 0.264241π0.264241\pi
608608 −13.6696 + 7.89216i −0.0224829 + 0.0129805i
609609 −163.836 + 611.445i −0.269025 + 1.00401i
610610 335.657i 0.550258i
611611 0 0
612612 619.537 1.01232
613613 130.022 + 34.8392i 0.212107 + 0.0568339i 0.363308 0.931669i 0.381647π-0.381647\pi
−0.151201 + 0.988503i 0.548314π0.548314\pi
614614 566.882 + 981.868i 0.923260 + 1.59913i
615615 82.4911 + 47.6263i 0.134132 + 0.0774411i
616616 −31.3003 + 31.3003i −0.0508122 + 0.0508122i
617617 −204.976 764.980i −0.332214 1.23984i −0.906858 0.421436i 0.861526π-0.861526\pi
0.574645 0.818403i 0.305140π-0.305140\pi
618618 912.559 244.519i 1.47663 0.395662i
619619 170.666 + 170.666i 0.275713 + 0.275713i 0.831395 0.555682i 0.187543π-0.187543\pi
−0.555682 + 0.831395i 0.687543π0.687543\pi
620620 69.7437 120.800i 0.112490 0.194838i
621621 70.1207 40.4842i 0.112916 0.0651919i
622622 −61.1386 + 228.172i −0.0982935 + 0.366836i
623623 554.072i 0.889361i
624624 0 0
625625 −446.368 −0.714189
626626 −204.465 54.7863i −0.326622 0.0875180i
627627 1.96875 + 3.40998i 0.00313995 + 0.00543856i
628628 162.250 + 93.6750i 0.258360 + 0.149164i
629629 69.6503 69.6503i 0.110732 0.110732i
630630 −102.030 380.781i −0.161952 0.604414i
631631 −76.9356 + 20.6148i −0.121926 + 0.0326701i −0.319266 0.947665i 0.603436π-0.603436\pi
0.197340 + 0.980335i 0.436770π0.436770\pi
632632 −200.994 200.994i −0.318029 0.318029i
633633 −177.744 + 307.862i −0.280796 + 0.486354i
634634 823.068 475.199i 1.29821 0.749525i
635635 −1.88636 + 7.03999i −0.00297064 + 0.0110866i
636636 507.517i 0.797983i
637637 0 0
638638 52.4964 0.0822828
639639 −1064.63 285.266i −1.66608 0.446426i
640640 117.875 + 204.166i 0.184180 + 0.319009i
641641 −449.661 259.612i −0.701500 0.405011i 0.106406 0.994323i 0.466066π-0.466066\pi
−0.807906 + 0.589312i 0.799399π0.799399\pi
642642 −625.017 + 625.017i −0.973546 + 0.973546i
643643 129.563 + 483.537i 0.201498 + 0.752002i 0.990488 + 0.137596i 0.0439376π0.0439376\pi
−0.788990 + 0.614406i 0.789396π0.789396\pi
644644 21.7933 5.83949i 0.0338405 0.00906753i
645645 −280.632 280.632i −0.435088 0.435088i
646646 −19.6382 + 34.0143i −0.0303997 + 0.0526538i
647647 257.204 148.497i 0.397533 0.229516i −0.287886 0.957665i 0.592952π-0.592952\pi
0.685419 + 0.728149i 0.259619π0.259619\pi
648648 54.6427 203.929i 0.0843252 0.314706i
649649 86.2973i 0.132970i
650650 0 0
651651 1904.85 2.92604
652652 −220.532 59.0914i −0.338239 0.0906309i
653653 445.183 + 771.079i 0.681750 + 1.18083i 0.974446 + 0.224620i 0.0721142π0.0721142\pi
−0.292696 + 0.956205i 0.594552π0.594552\pi
654654 305.316 + 176.274i 0.466844 + 0.269532i
655655 −64.9353 + 64.9353i −0.0991378 + 0.0991378i
656656 61.8865 + 230.964i 0.0943392 + 0.352079i
657657 −1148.87 + 307.840i −1.74866 + 0.468553i
658658 −376.126 376.126i −0.571620 0.571620i
659659 321.640 557.097i 0.488073 0.845367i −0.511833 0.859085i 0.671033π-0.671033\pi
0.999906 + 0.0137177i 0.00436660π0.00436660\pi
660660 −12.2379 + 7.06558i −0.0185423 + 0.0107054i
661661 −52.5302 + 196.045i −0.0794708 + 0.296589i −0.994210 0.107456i 0.965729π-0.965729\pi
0.914739 + 0.404045i 0.132396π0.132396\pi
662662 361.902i 0.546680i
663663 0 0
664664 577.641 0.869941
665665 6.71309 + 1.79877i 0.0100949 + 0.00270491i
666666 76.0014 + 131.638i 0.114116 + 0.197655i
667667 36.9828 + 21.3520i 0.0554465 + 0.0320120i
668668 34.5824 34.5824i 0.0517700 0.0517700i
669669 −198.444 740.602i −0.296627 1.10703i
670670 337.272 90.3717i 0.503390 0.134883i
671671 74.7492 + 74.7492i 0.111400 + 0.111400i
672672 386.793 669.945i 0.575585 0.996942i
673673 −236.376 + 136.472i −0.351228 + 0.202781i −0.665226 0.746642i 0.731665π-0.731665\pi
0.313998 + 0.949424i 0.398331π0.398331\pi
674674 223.493 834.088i 0.331592 1.23752i
675675 819.179i 1.21360i
676676 0 0
677677 −413.547 −0.610852 −0.305426 0.952216i 0.598799π-0.598799\pi
−0.305426 + 0.952216i 0.598799π0.598799\pi
678678 1053.14 + 282.187i 1.55330 + 0.416205i
679679 222.379 + 385.172i 0.327510 + 0.567263i
680680 194.824 + 112.482i 0.286506 + 0.165415i
681681 259.795 259.795i 0.381490 0.381490i
682682 −40.8859 152.588i −0.0599499 0.223736i
683683 1155.66 309.658i 1.69203 0.453379i 0.721121 0.692809i 0.243627π-0.243627\pi
0.970914 + 0.239430i 0.0769606π0.0769606\pi
684684 −11.9183 11.9183i −0.0174244 0.0174244i
685685 129.904 225.000i 0.189640 0.328466i
686686 −734.210 + 423.896i −1.07028 + 0.617925i
687687 335.947 1253.77i 0.489006 1.82500i
688688 996.265i 1.44806i
689689 0 0
690690 −41.3364 −0.0599078
691691 816.053 + 218.661i 1.18097 + 0.316441i 0.795313 0.606200i 0.207307π-0.207307\pi
0.385661 + 0.922640i 0.373973π0.373973\pi
692692 −67.0359 116.110i −0.0968727 0.167788i
693693 −107.520 62.0764i −0.155151 0.0895764i
694694 666.939 666.939i 0.961007 0.961007i
695695 31.1813 + 116.370i 0.0448652 + 0.167439i
696696 538.459 144.280i 0.773647 0.207298i
697697 211.591 + 211.591i 0.303574 + 0.303574i
698698 −530.077 + 918.121i −0.759423 + 1.31536i
699699 1146.88 662.152i 1.64074 0.947284i
700700 59.0797 220.489i 0.0843996 0.314984i
701701 765.186i 1.09156i 0.837927 + 0.545782i 0.183767π0.183767\pi
−0.837927 + 0.545782i 0.816233π0.816233\pi
702702 0 0
703703 −2.67978 −0.00381192
704704 26.9815 + 7.22966i 0.0383259 + 0.0102694i
705705 135.505 + 234.702i 0.192206 + 0.332911i
706706 920.969 + 531.721i 1.30449 + 0.753147i
707707 351.015 351.015i 0.496485 0.496485i
708708 148.610 + 554.620i 0.209901 + 0.783361i
709709 −468.858 + 125.630i −0.661295 + 0.177193i −0.573830 0.818974i 0.694543π-0.694543\pi
−0.0874645 + 0.996168i 0.527876π0.527876\pi
710710 177.321 + 177.321i 0.249748 + 0.249748i
711711 398.622 690.434i 0.560650 0.971075i
712712 −422.563 + 243.967i −0.593488 + 0.342650i
713713 33.2592 124.125i 0.0466469 0.174089i
714714 1924.92i 2.69597i
715715 0 0
716716 −222.866 −0.311266
717717 1787.91 + 479.068i 2.49359 + 0.668157i
718718 −278.214 481.881i −0.387484 0.671143i
719719 −732.510 422.915i −1.01879 0.588199i −0.105037 0.994468i 0.533496π-0.533496\pi
−0.913753 + 0.406269i 0.866830π0.866830\pi
720720 −356.515 + 356.515i −0.495159 + 0.495159i
721721 −135.924 507.277i −0.188522 0.703574i
722722 −819.771 + 219.657i −1.13542 + 0.304234i
723723 219.913 + 219.913i 0.304168 + 0.304168i
724724 44.2942 76.7199i 0.0611799 0.105967i
725725 374.165 216.024i 0.516090 0.297965i
726726 366.177 1366.59i 0.504376 1.88236i
727727 1019.65i 1.40255i 0.712892 + 0.701274i 0.247385π0.247385\pi
−0.712892 + 0.701274i 0.752615π0.752615\pi
728728 0 0
729729 −1051.18 −1.44195
730730 261.392 + 70.0398i 0.358072 + 0.0959450i
731731 −623.388 1079.74i −0.852788 1.47707i
732732 −609.125 351.678i −0.832138 0.480435i
733733 −565.267 + 565.267i −0.771170 + 0.771170i −0.978311 0.207141i 0.933584π-0.933584\pi
0.207141 + 0.978311i 0.433584π0.433584\pi
734734 413.542 + 1543.36i 0.563409 + 2.10267i
735735 44.1096 11.8191i 0.0600130 0.0160804i
736736 −36.9019 36.9019i −0.0501385 0.0501385i
737737 54.9834 95.2341i 0.0746044 0.129219i
738738 −399.905 + 230.885i −0.541877 + 0.312853i
739739 72.6381 271.089i 0.0982924 0.366832i −0.899206 0.437526i 0.855855π-0.855855\pi
0.997498 + 0.0706941i 0.0225214π0.0225214\pi
740740 9.61737i 0.0129964i
741741 0 0
742742 1014.50 1.36725
743743 941.890 + 252.379i 1.26768 + 0.339675i 0.829143 0.559036i 0.188829π-0.188829\pi
0.438541 + 0.898711i 0.355495π0.355495\pi
744744 −838.736 1452.73i −1.12733 1.95260i
745745 −162.625 93.8913i −0.218288 0.126029i
746746 −184.985 + 184.985i −0.247969 + 0.247969i
747747 419.321 + 1564.93i 0.561340 + 2.09495i
748748 −42.8803 + 11.4897i −0.0573266 + 0.0153606i
749749 347.437 + 347.437i 0.463867 + 0.463867i
750750 −441.060 + 763.939i −0.588081 + 1.01859i
751751 732.187 422.729i 0.974950 0.562888i 0.0742082 0.997243i 0.476357π-0.476357\pi
0.900742 + 0.434355i 0.143024π0.143024\pi
752752 −176.078 + 657.133i −0.234146 + 0.873847i
753753 563.297i 0.748071i
754754 0 0
755755 352.722 0.467181
756756 355.597 + 95.2819i 0.470366 + 0.126034i
757757 607.165 + 1051.64i 0.802067 + 1.38922i 0.918253 + 0.395994i 0.129600π0.129600\pi
−0.116186 + 0.993227i 0.537067π0.537067\pi
758758 −703.172 405.976i −0.927667 0.535589i
759759 −9.20542 + 9.20542i −0.0121283 + 0.0121283i
760760 −1.58405 5.91177i −0.00208428 0.00777865i
761761 647.756 173.566i 0.851191 0.228076i 0.193254 0.981149i 0.438096π-0.438096\pi
0.657937 + 0.753073i 0.271429π0.271429\pi
762762 −38.8337 38.8337i −0.0509629 0.0509629i
763763 97.9880 169.720i 0.128425 0.222438i
764764 90.5968 52.3061i 0.118582 0.0684635i
765765 −163.306 + 609.466i −0.213472 + 0.796687i
766766 914.084i 1.19332i
767767 0 0
768768 −1293.95 −1.68484
769769 −1053.30 282.232i −1.36971 0.367011i −0.502334 0.864673i 0.667525π-0.667525\pi
−0.867371 + 0.497662i 0.834192π0.834192\pi
770770 14.1237 + 24.4629i 0.0183424 + 0.0317700i
771771 1624.54 + 937.931i 2.10706 + 1.21651i
772772 −234.207 + 234.207i −0.303377 + 0.303377i
773773 −41.9712 156.639i −0.0542965 0.202637i 0.933449 0.358710i 0.116783π-0.116783\pi
−0.987746 + 0.156073i 0.950117π0.950117\pi
774774 1858.43 497.964i 2.40107 0.643364i
775775 −919.316 919.316i −1.18621 1.18621i
776776 195.834 339.195i 0.252364 0.437107i
777777 113.740 65.6677i 0.146383 0.0845144i
778778 −238.702 + 890.849i −0.306815 + 1.14505i
779779 8.14093i 0.0104505i
780780 0 0
781781 78.9770 0.101123
782782 −125.433 33.6098i −0.160401 0.0429792i
783783 348.397 + 603.442i 0.444952 + 0.770679i
784784 99.2756 + 57.3168i 0.126627 + 0.0731082i
785785 −134.920 + 134.920i −0.171873 + 0.171873i
786786 −179.097 668.398i −0.227858 0.850379i
787787 −8.49841 + 2.27714i −0.0107985 + 0.00289345i −0.264214 0.964464i 0.585113π-0.585113\pi
0.253416 + 0.967357i 0.418446π0.418446\pi
788788 172.376 + 172.376i 0.218752 + 0.218752i
789789 822.854 1425.22i 1.04291 1.80637i
790790 −157.088 + 90.6948i −0.198846 + 0.114804i
791791 156.863 585.421i 0.198310 0.740103i
792792 109.333i 0.138047i
793793 0 0
794794 370.980 0.467230
795795 −499.267 133.778i −0.628008 0.168274i
796796 −32.3037 55.9517i −0.0405826 0.0702911i
797797 618.344 + 357.001i 0.775840 + 0.447931i 0.834954 0.550320i 0.185494π-0.185494\pi
−0.0591141 + 0.998251i 0.518828π0.518828\pi
798798 −37.0305 + 37.0305i −0.0464042 + 0.0464042i
799799 220.353 + 822.368i 0.275786 + 1.02925i
800800 −510.001 + 136.654i −0.637502 + 0.170818i
801801 −967.696 967.696i −1.20811 1.20811i
802802 626.540 1085.20i 0.781221 1.35312i
803803 73.8083 42.6132i 0.0919157 0.0530676i
804804 −189.370 + 706.740i −0.235535 + 0.879030i
805805 22.9782i 0.0285444i
806806 0 0
807807 −1377.28 −1.70666
808808 −422.259 113.144i −0.522598 0.140030i
809809 −190.814 330.499i −0.235864 0.408528i 0.723659 0.690157i 0.242459π-0.242459\pi
−0.959523 + 0.281629i 0.909125π0.909125\pi
810810 −116.676 67.3627i −0.144044 0.0831639i
811811 139.562 139.562i 0.172086 0.172086i −0.615809 0.787895i 0.711171π-0.711171\pi
0.787895 + 0.615809i 0.211171π0.211171\pi
812812 50.2533 + 187.548i 0.0618883 + 0.230970i
813813 −1091.97 + 292.592i −1.34314 + 0.359892i
814814 −7.70163 7.70163i −0.00946146 0.00946146i
815815 116.261 201.371i 0.142652 0.247081i
816816 −2132.09 + 1230.96i −2.61286 + 1.50853i
817817 −8.77901 + 32.7637i −0.0107454 + 0.0401025i
818818 655.544i 0.801399i
819819 0 0
820820 29.2167 0.0356301
821821 −732.854 196.368i −0.892635 0.239181i −0.216785 0.976219i 0.569557π-0.569557\pi
−0.675851 + 0.737039i 0.736224π0.736224\pi
822822 978.851 + 1695.42i 1.19082 + 2.06256i
823823 −1372.60 792.473i −1.66781 0.962908i −0.968818 0.247773i 0.920301π-0.920301\pi
−0.698987 0.715134i 0.746366π-0.746366\pi
824824 −327.025 + 327.025i −0.396875 + 0.396875i
825825 34.0893 + 127.223i 0.0413204 + 0.154210i
826826 1108.65 297.062i 1.34219 0.359640i
827827 380.972 + 380.972i 0.460668 + 0.460668i 0.898874 0.438207i 0.144386π-0.144386\pi
−0.438207 + 0.898874i 0.644386π0.644386\pi
828828 27.8635 48.2611i 0.0336516 0.0582863i
829829 −926.803 + 535.090i −1.11798 + 0.645464i −0.940884 0.338730i 0.890003π-0.890003\pi
−0.177093 + 0.984194i 0.556669π0.556669\pi
830830 95.4042 356.053i 0.114945 0.428980i
831831 2026.91i 2.43912i
832832 0 0
833833 143.458 0.172219
834834 −876.876 234.958i −1.05141 0.281724i
835835 24.9045 + 43.1359i 0.0298258 + 0.0516597i
836836 1.04594 + 0.603872i 0.00125112 + 0.000722335i
837837 1482.64 1482.64i 1.77138 1.77138i
838838 −297.882 1111.71i −0.355467 1.32662i
839839 −811.649 + 217.481i −0.967400 + 0.259214i −0.707730 0.706483i 0.750281π-0.750281\pi
−0.259670 + 0.965697i 0.583614π0.583614\pi
840840 212.100 + 212.100i 0.252500 + 0.252500i
841841 236.750 410.062i 0.281510 0.487589i
842842 1082.83 625.172i 1.28602 0.742485i
843843 −654.930 + 2444.23i −0.776904 + 2.89945i
844844 109.038i 0.129192i
845845 0 0
846846 −1313.82 −1.55298
847847 −759.666 203.552i −0.896890 0.240321i
848848 −648.757 1123.68i −0.765043 1.32509i
849849 1521.96 + 878.705i 1.79265 + 1.03499i
850850 −929.004 + 929.004i −1.09295 + 1.09295i
851851 −2.29315 8.55817i −0.00269466 0.0100566i
852852 −507.573 + 136.004i −0.595743 + 0.159629i
853853 500.522 + 500.522i 0.586778 + 0.586778i 0.936757 0.349979i 0.113811π-0.113811\pi
−0.349979 + 0.936757i 0.613811π0.613811\pi
854854 −702.984 + 1217.60i −0.823167 + 1.42577i
855855 14.8661 8.58295i 0.0173873 0.0100385i
856856 111.991 417.955i 0.130830 0.488265i
857857 175.305i 0.204556i 0.994756 + 0.102278i 0.0326132π0.0326132\pi
−0.994756 + 0.102278i 0.967387π0.967387\pi
858858 0 0
859859 1523.72 1.77384 0.886918 0.461928i 0.152842π-0.152842\pi
0.886918 + 0.461928i 0.152842π0.152842\pi
860860 −117.584 31.5067i −0.136726 0.0366357i
861861 199.492 + 345.531i 0.231698 + 0.401314i
862862 242.180 + 139.822i 0.280951 + 0.162207i
863863 −525.826 + 525.826i −0.609300 + 0.609300i −0.942763 0.333463i 0.891783π-0.891783\pi
0.333463 + 0.942763i 0.391783π0.391783\pi
864864 −220.392 822.514i −0.255083 0.951984i
865865 131.892 35.3404i 0.152477 0.0408560i
866866 −231.034 231.034i −0.266783 0.266783i
867867 −814.592 + 1410.91i −0.939552 + 1.62735i
868868 505.994 292.136i 0.582943 0.336562i
869869 −14.7854 + 55.1800i −0.0170143 + 0.0634983i
870870 355.731i 0.408887i
871871 0 0
872872 −172.583 −0.197916
873873 1061.10 + 284.320i 1.21546 + 0.325682i
874874 1.76645 + 3.05957i 0.00202110 + 0.00350066i
875875 424.661 + 245.178i 0.485327 + 0.280204i
876876 −400.972 + 400.972i −0.457730 + 0.457730i
877877 165.712 + 618.447i 0.188954 + 0.705185i 0.993749 + 0.111633i 0.0356082π0.0356082\pi
−0.804796 + 0.593552i 0.797725π0.797725\pi
878878 319.014 85.4795i 0.363342 0.0973571i
879879 1911.87 + 1911.87i 2.17505 + 2.17505i
880880 18.0638 31.2874i 0.0205270 0.0355539i
881881 −964.522 + 556.867i −1.09480 + 0.632085i −0.934851 0.355039i 0.884467π-0.884467\pi
−0.159953 + 0.987125i 0.551134π0.551134\pi
882882 −57.2974 + 213.837i −0.0649630 + 0.242445i
883883 206.038i 0.233338i −0.993171 0.116669i 0.962778π-0.962778\pi
0.993171 0.116669i 0.0372217π-0.0372217\pi
884884 0 0
885885 −584.776 −0.660764
886886 −888.052 237.953i −1.00232 0.268570i
887887 −299.698 519.092i −0.337878 0.585222i 0.646155 0.763206i 0.276376π-0.276376\pi
−0.984033 + 0.177984i 0.943042π0.943042\pi
888888 −100.163 57.8291i −0.112796 0.0651228i
889889 −21.5870 + 21.5870i −0.0242824 + 0.0242824i
890890 80.5881 + 300.759i 0.0905484 + 0.337931i
891891 −40.9845 + 10.9818i −0.0459983 + 0.0123252i
892892 −166.295 166.295i −0.186430 0.186430i
893893 11.5812 20.0592i 0.0129689 0.0224627i
894894 1225.41 707.492i 1.37071 0.791378i
895895 58.7460 219.243i 0.0656380 0.244964i
896896 987.489i 1.10211i
897897 0 0
898898 710.758 0.791489
899899 1068.19 + 286.221i 1.18820 + 0.318377i
900900 −281.903 488.271i −0.313226 0.542523i
901901 −1406.23 811.886i −1.56074 0.901094i
902902 23.3969 23.3969i 0.0259389 0.0259389i
903903 −430.257 1605.74i −0.476475 1.77823i
904904 −515.541 + 138.139i −0.570289 + 0.152808i
905905 63.7970 + 63.7970i 0.0704939 + 0.0704939i
906906 −1328.92 + 2301.75i −1.46680 + 2.54057i
907907 399.745 230.793i 0.440733 0.254457i −0.263176 0.964748i 0.584770π-0.584770\pi
0.703908 + 0.710291i 0.251437π0.251437\pi
908908 29.1673 108.854i 0.0321225 0.119883i
909909 1226.11i 1.34885i
910910 0 0
911911 1377.94 1.51256 0.756281 0.654247i 0.227014π-0.227014\pi
0.756281 + 0.654247i 0.227014π0.227014\pi
912912 64.6964 + 17.3353i 0.0709390 + 0.0190080i
913913 −58.0453 100.537i −0.0635765 0.110118i
914914 −621.725 358.953i −0.680224 0.392728i
915915 506.523 506.523i 0.553577 0.553577i
916916 −103.045 384.568i −0.112494 0.419834i
917917 −371.552 + 99.5570i −0.405182 + 0.108568i
918918 −1498.27 1498.27i −1.63210 1.63210i
919919 58.7147 101.697i 0.0638898 0.110660i −0.832311 0.554309i 0.812983π-0.812983\pi
0.896201 + 0.443648i 0.146316π0.146316\pi
920920 17.5244 10.1177i 0.0190482 0.0109975i
921921 626.234 2337.14i 0.679950 2.53761i
922922 1901.79i 2.06268i
923923 0 0
924924 −59.1912 −0.0640598
925925 −86.5853 23.2005i −0.0936058 0.0250816i
926926 −684.727 1185.98i −0.739446 1.28076i
927927 −1123.36 648.573i −1.21182 0.699647i
928928 317.569 317.569i 0.342208 0.342208i
929929 −147.714 551.276i −0.159003 0.593408i −0.998729 0.0503975i 0.983951π-0.983951\pi
0.839726 0.543010i 0.182715π-0.182715\pi
930930 −1033.98 + 277.055i −1.11181 + 0.297908i
931931 −2.75976 2.75976i −0.00296430 0.00296430i
932932 203.101 351.781i 0.217919 0.377448i
933933 436.584 252.062i 0.467935 0.270163i
934934 −170.484 + 636.256i −0.182531 + 0.681216i
935935 45.2118i 0.0483549i
936936 0 0
937937 −26.9894 −0.0288040 −0.0144020 0.999896i 0.504584π-0.504584\pi
−0.0144020 + 0.999896i 0.504584π0.504584\pi
938938 1412.73 + 378.540i 1.50611 + 0.403561i
939939 225.873 + 391.223i 0.240546 + 0.416638i
940940 71.9898 + 41.5633i 0.0765849 + 0.0442163i
941941 1244.04 1244.04i 1.32204 1.32204i 0.409926 0.912119i 0.365555π-0.365555\pi
0.912119 0.409926i 0.134445π-0.134445\pi
942942 −372.121 1388.77i −0.395033 1.47428i
943943 25.9989 6.96639i 0.0275705 0.00738748i
944944 −1038.00 1038.00i −1.09958 1.09958i
945945 −187.466 + 324.701i −0.198377 + 0.343598i
946946 −119.393 + 68.9315i −0.126208 + 0.0728663i
947947 −19.1413 + 71.4365i −0.0202126 + 0.0754345i −0.975295 0.220904i 0.929099π-0.929099\pi
0.955083 + 0.296339i 0.0957658π0.0957658\pi
948948 380.095i 0.400944i
949949 0 0
950950 35.7432 0.0376245
951951 −1959.15 524.952i −2.06009 0.551999i
952952 471.154 + 816.062i 0.494909 + 0.857208i
953953 334.954 + 193.386i 0.351474 + 0.202923i 0.665334 0.746546i 0.268289π-0.268289\pi
−0.313861 + 0.949469i 0.601622π0.601622\pi
954954 1771.84 1771.84i 1.85727 1.85727i
955955 27.5751 + 102.912i 0.0288744 + 0.107761i
956956 548.402 146.944i 0.573643 0.153707i
957957 −79.2196 79.2196i −0.0827791 0.0827791i
958958 −315.067 + 545.712i −0.328880 + 0.569637i
959959 942.457 544.128i 0.982749 0.567391i
960960 48.9903 182.834i 0.0510316 0.190452i
961961 2366.76i 2.46281i
962962 0 0
963963 1213.61 1.26024
964964 92.1435 + 24.6898i 0.0955845 + 0.0256118i
965965 −168.664 292.135i −0.174782 0.302731i
966966 −149.949 86.5730i −0.155227 0.0896201i
967967 503.064 503.064i 0.520232 0.520232i −0.397409 0.917641i 0.630091π-0.630091\pi
0.917641 + 0.397409i 0.130091π0.130091\pi
968968 179.254 + 668.986i 0.185180 + 0.691102i
969969 80.9642 21.6943i 0.0835544 0.0223883i
970970 −176.733 176.733i −0.182199 0.182199i
971971 −452.612 + 783.946i −0.466129 + 0.807360i −0.999252 0.0386784i 0.987685π-0.987685\pi
0.533122 + 0.846038i 0.321019π0.321019\pi
972972 −192.035 + 110.872i −0.197567 + 0.114066i
973973 −130.609 + 487.441i −0.134234 + 0.500967i
974974 1276.66i 1.31074i
975975 0 0
976976 1798.20 1.84241
977977 797.549 + 213.703i 0.816324 + 0.218733i 0.642739 0.766085i 0.277798π-0.277798\pi
0.173585 + 0.984819i 0.444465π0.444465\pi
978978 876.055 + 1517.37i 0.895762 + 1.55151i
979979 84.9241 + 49.0310i 0.0867458 + 0.0500827i
980980 9.90440 9.90440i 0.0101065 0.0101065i
981981 −125.281 467.557i −0.127708 0.476612i
982982 −53.5236 + 14.3416i −0.0545047 + 0.0146045i
983983 99.0983 + 99.0983i 0.100812 + 0.100812i 0.755714 0.654902i 0.227290π-0.227290\pi
−0.654902 + 0.755714i 0.727290π0.727290\pi
984984 175.680 304.286i 0.178536 0.309234i
985985 −215.011 + 124.137i −0.218286 + 0.126027i
986986 289.238 1079.45i 0.293344 1.09478i
987987 1135.18i 1.15013i
988988 0 0
989989 −112.147 −0.113394
990990 67.3921 + 18.0577i 0.0680728 + 0.0182401i
991991 58.8966 + 102.012i 0.0594315 + 0.102938i 0.894210 0.447647i 0.147738π-0.147738\pi
−0.834779 + 0.550585i 0.814405π0.814405\pi
992992 −1170.39 675.725i −1.17983 0.681175i
993993 −546.127 + 546.127i −0.549977 + 0.549977i
994994 271.864 + 1014.61i 0.273505 + 1.02073i
995995 63.5572 17.0301i 0.0638766 0.0171157i
996996 546.180 + 546.180i 0.548374 + 0.548374i
997997 531.702 920.934i 0.533302 0.923705i −0.465942 0.884815i 0.654284π-0.654284\pi
0.999243 0.0388901i 0.0123822π-0.0123822\pi
998998 304.298 175.687i 0.304908 0.176039i
999999 37.4170 139.642i 0.0374544 0.139782i
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 169.3.f.g.80.3 48
13.2 odd 12 169.3.d.e.99.3 yes 24
13.3 even 3 169.3.d.e.70.10 yes 24
13.4 even 6 inner 169.3.f.g.19.3 48
13.5 odd 4 inner 169.3.f.g.89.3 48
13.6 odd 12 inner 169.3.f.g.150.10 48
13.7 odd 12 inner 169.3.f.g.150.3 48
13.8 odd 4 inner 169.3.f.g.89.10 48
13.9 even 3 inner 169.3.f.g.19.10 48
13.10 even 6 169.3.d.e.70.3 24
13.11 odd 12 169.3.d.e.99.10 yes 24
13.12 even 2 inner 169.3.f.g.80.10 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.3.d.e.70.3 24 13.10 even 6
169.3.d.e.70.10 yes 24 13.3 even 3
169.3.d.e.99.3 yes 24 13.2 odd 12
169.3.d.e.99.10 yes 24 13.11 odd 12
169.3.f.g.19.3 48 13.4 even 6 inner
169.3.f.g.19.10 48 13.9 even 3 inner
169.3.f.g.80.3 48 1.1 even 1 trivial
169.3.f.g.80.10 48 13.12 even 2 inner
169.3.f.g.89.3 48 13.5 odd 4 inner
169.3.f.g.89.10 48 13.8 odd 4 inner
169.3.f.g.150.3 48 13.7 odd 12 inner
169.3.f.g.150.10 48 13.6 odd 12 inner