Properties

Label 55.3.i.c.6.3
Level 5555
Weight 33
Character 55.6
Analytic conductor 1.4991.499
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,3,Mod(6,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.6");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 55=511 55 = 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 55.i (of order 1010, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.498641453981.49864145398
Analytic rank: 00
Dimension: 1212
Relative dimension: 33 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x122x11+6x10+5x930x8+88x7131x612x5+240x4++1331 x^{12} - 2 x^{11} + 6 x^{10} + 5 x^{9} - 30 x^{8} + 88 x^{7} - 131 x^{6} - 12 x^{5} + 240 x^{4} + \cdots + 1331 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 6.3
Root 1.543290.0151731i1.54329 - 0.0151731i of defining polynomial
Character χ\chi == 55.6
Dual form 55.3.i.c.46.3

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+(1.575800.512008i)q2+(2.41303+1.75317i)q3+(1.01508+0.737497i)q4+(0.6909832.12663i)q5+(4.70008+1.52715i)q6+(1.310031.80310i)q7+(5.11754+7.04369i)q8+(0.03204820.0986342i)q93.70493iq10+(0.94904910.9590i)q113.74236q12+(1.75040+0.568738i)q13+(2.987542.17058i)q14+(5.395693.92020i)q15+(2.90689+8.94649i)q16+(7.97437+2.59103i)q17+(0.1010030.139019i)q18+(15.6197+21.4986i)q19+(0.866979+2.66829i)q206.64762iq21+(7.1066016.7832i)q227.63236q23+(24.6975+8.02472i)q24+(4.045082.93893i)q25+(2.46707+1.79243i)q26+(8.3908425.8243i)q27+(2.65956+0.864143i)q28+(31.8005+43.7696i)q29+(6.495358.94009i)q30+(1.08129+3.32786i)q3119.2397iq32+(16.922828.1082i)q33+13.8926q34+(4.73973+1.54003i)q35+(0.105274+0.0764859i)q36+(37.888127.5273i)q37+(13.6060+41.8749i)q38+(5.220851.69636i)q39+(11.4432+15.7502i)q40+(15.9749+21.9876i)q41+(3.4036410.4753i)q4214.9713iq43+(9.04557+10.4243i)q440.231903q45+(12.0271+3.90783i)q46+(58.0480+42.1743i)q47+(22.6991+16.4919i)q48+(13.606841.8775i)q49+(7.879002.56004i)q50+(14.6999+20.2326i)q51+(1.357341.86822i)q52+(12.177437.4781i)q5344.9902iq54+(23.96145.55420i)q55+19.4046q56+(75.3814+24.4929i)q57+(72.5216+52.6900i)q58+(29.1317+21.1654i)q59+(2.58591+7.95861i)q60+(44.054614.3142i)q61+(3.40779+4.69042i)q62+(0.135863+0.187000i)q63+(21.478566.1039i)q64+4.11543iq65+(12.275452.9574i)q6660.8461q67+(10.0055+3.25097i)q68+(18.417113.3808i)q69+(6.68035+4.85356i)q70+(37.8919+116.619i)q71+(0.858757+0.279027i)q72+(35.124148.3441i)q73+(45.609862.7765i)q74+(4.6084714.1834i)q7533.3422iq76+(18.5169+16.0678i)q779.09555q78+(81.5552+26.4989i)q79+(17.0172+12.3638i)q80+(64.766547.0556i)q81+(13.9155+42.8274i)q82+(43.690214.1958i)q83+(4.90260+6.74785i)q84+(11.020315.1681i)q85+(7.6654523.5918i)q86+161.369iq87+(82.0485+49.3983i)q88+121.940q89+(0.365432+0.118736i)q90+(3.31856+2.41107i)q91+(7.747435.62884i)q92+(3.22512+9.92591i)q93+(113.066+36.7372i)q94+(34.9266+48.0724i)q95+(33.730446.4259i)q96+(10.268531.6031i)q9772.9574iq98+(1.05051+0.444824i)q99+O(q100)q+(1.57580 - 0.512008i) q^{2} +(2.41303 + 1.75317i) q^{3} +(-1.01508 + 0.737497i) q^{4} +(0.690983 - 2.12663i) q^{5} +(4.70008 + 1.52715i) q^{6} +(-1.31003 - 1.80310i) q^{7} +(-5.11754 + 7.04369i) q^{8} +(-0.0320482 - 0.0986342i) q^{9} -3.70493i q^{10} +(-0.949049 - 10.9590i) q^{11} -3.74236 q^{12} +(-1.75040 + 0.568738i) q^{13} +(-2.98754 - 2.17058i) q^{14} +(5.39569 - 3.92020i) q^{15} +(-2.90689 + 8.94649i) q^{16} +(7.97437 + 2.59103i) q^{17} +(-0.101003 - 0.139019i) q^{18} +(-15.6197 + 21.4986i) q^{19} +(0.866979 + 2.66829i) q^{20} -6.64762i q^{21} +(-7.10660 - 16.7832i) q^{22} -7.63236 q^{23} +(-24.6975 + 8.02472i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(-2.46707 + 1.79243i) q^{26} +(8.39084 - 25.8243i) q^{27} +(2.65956 + 0.864143i) q^{28} +(31.8005 + 43.7696i) q^{29} +(6.49535 - 8.94009i) q^{30} +(1.08129 + 3.32786i) q^{31} -19.2397i q^{32} +(16.9228 - 28.1082i) q^{33} +13.8926 q^{34} +(-4.73973 + 1.54003i) q^{35} +(0.105274 + 0.0764859i) q^{36} +(37.8881 - 27.5273i) q^{37} +(-13.6060 + 41.8749i) q^{38} +(-5.22085 - 1.69636i) q^{39} +(11.4432 + 15.7502i) q^{40} +(-15.9749 + 21.9876i) q^{41} +(-3.40364 - 10.4753i) q^{42} -14.9713i q^{43} +(9.04557 + 10.4243i) q^{44} -0.231903 q^{45} +(-12.0271 + 3.90783i) q^{46} +(58.0480 + 42.1743i) q^{47} +(-22.6991 + 16.4919i) q^{48} +(13.6068 - 41.8775i) q^{49} +(-7.87900 - 2.56004i) q^{50} +(14.6999 + 20.2326i) q^{51} +(1.35734 - 1.86822i) q^{52} +(-12.1774 - 37.4781i) q^{53} -44.9902i q^{54} +(-23.9614 - 5.55420i) q^{55} +19.4046 q^{56} +(-75.3814 + 24.4929i) q^{57} +(72.5216 + 52.6900i) q^{58} +(-29.1317 + 21.1654i) q^{59} +(-2.58591 + 7.95861i) q^{60} +(-44.0546 - 14.3142i) q^{61} +(3.40779 + 4.69042i) q^{62} +(-0.135863 + 0.187000i) q^{63} +(-21.4785 - 66.1039i) q^{64} +4.11543i q^{65} +(12.2754 - 52.9574i) q^{66} -60.8461 q^{67} +(-10.0055 + 3.25097i) q^{68} +(-18.4171 - 13.3808i) q^{69} +(-6.68035 + 4.85356i) q^{70} +(-37.8919 + 116.619i) q^{71} +(0.858757 + 0.279027i) q^{72} +(-35.1241 - 48.3441i) q^{73} +(45.6098 - 62.7765i) q^{74} +(-4.60847 - 14.1834i) q^{75} -33.3422i q^{76} +(-18.5169 + 16.0678i) q^{77} -9.09555 q^{78} +(-81.5552 + 26.4989i) q^{79} +(17.0172 + 12.3638i) q^{80} +(64.7665 - 47.0556i) q^{81} +(-13.9155 + 42.8274i) q^{82} +(-43.6902 - 14.1958i) q^{83} +(4.90260 + 6.74785i) q^{84} +(11.0203 - 15.1681i) q^{85} +(-7.66545 - 23.5918i) q^{86} +161.369i q^{87} +(82.0485 + 49.3983i) q^{88} +121.940 q^{89} +(-0.365432 + 0.118736i) q^{90} +(3.31856 + 2.41107i) q^{91} +(7.74743 - 5.62884i) q^{92} +(-3.22512 + 9.92591i) q^{93} +(113.066 + 36.7372i) q^{94} +(34.9266 + 48.0724i) q^{95} +(33.7304 - 46.4259i) q^{96} +(-10.2685 - 31.6031i) q^{97} -72.9574i q^{98} +(-1.05051 + 0.444824i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q5q2+7q3+13q4+15q515q640q715q816q98q11+68q1215q135q14+35q15+77q165q17115q18+15q1920q20++509q99+O(q100) 12 q - 5 q^{2} + 7 q^{3} + 13 q^{4} + 15 q^{5} - 15 q^{6} - 40 q^{7} - 15 q^{8} - 16 q^{9} - 8 q^{11} + 68 q^{12} - 15 q^{13} - 5 q^{14} + 35 q^{15} + 77 q^{16} - 5 q^{17} - 115 q^{18} + 15 q^{19} - 20 q^{20}+ \cdots + 509 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/55Z)×\left(\mathbb{Z}/55\mathbb{Z}\right)^\times.

nn 1212 4646
χ(n)\chi(n) 11 e(910)e\left(\frac{9}{10}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.57580 0.512008i 0.787900 0.256004i 0.112690 0.993630i 0.464053π-0.464053\pi
0.675209 + 0.737626i 0.264053π0.264053\pi
33 2.41303 + 1.75317i 0.804342 + 0.584389i 0.912185 0.409779i 0.134394π-0.134394\pi
−0.107843 + 0.994168i 0.534394π0.534394\pi
44 −1.01508 + 0.737497i −0.253769 + 0.184374i
55 0.690983 2.12663i 0.138197 0.425325i
66 4.70008 + 1.52715i 0.783347 + 0.254525i
77 −1.31003 1.80310i −0.187147 0.257586i 0.705126 0.709082i 0.250890π-0.250890\pi
−0.892273 + 0.451496i 0.850890π0.850890\pi
88 −5.11754 + 7.04369i −0.639693 + 0.880462i
99 −0.0320482 0.0986342i −0.00356091 0.0109594i
1010 3.70493i 0.370493i
1111 −0.949049 10.9590i −0.0862772 0.996271i
1212 −3.74236 −0.311864
1313 −1.75040 + 0.568738i −0.134646 + 0.0437491i −0.375565 0.926796i 0.622551π-0.622551\pi
0.240919 + 0.970545i 0.422551π0.422551\pi
1414 −2.98754 2.17058i −0.213396 0.155041i
1515 5.39569 3.92020i 0.359713 0.261347i
1616 −2.90689 + 8.94649i −0.181681 + 0.559156i
1717 7.97437 + 2.59103i 0.469080 + 0.152413i 0.534013 0.845476i 0.320683π-0.320683\pi
−0.0649328 + 0.997890i 0.520683π0.520683\pi
1818 −0.101003 0.139019i −0.00561128 0.00772326i
1919 −15.6197 + 21.4986i −0.822088 + 1.13151i 0.167257 + 0.985913i 0.446509π0.446509\pi
−0.989344 + 0.145594i 0.953491π0.953491\pi
2020 0.866979 + 2.66829i 0.0433490 + 0.133414i
2121 6.64762i 0.316553i
2222 −7.10660 16.7832i −0.323027 0.762874i
2323 −7.63236 −0.331842 −0.165921 0.986139i 0.553060π-0.553060\pi
−0.165921 + 0.986139i 0.553060π0.553060\pi
2424 −24.6975 + 8.02472i −1.02906 + 0.334363i
2525 −4.04508 2.93893i −0.161803 0.117557i
2626 −2.46707 + 1.79243i −0.0948875 + 0.0689398i
2727 8.39084 25.8243i 0.310772 0.956457i
2828 2.65956 + 0.864143i 0.0949842 + 0.0308623i
2929 31.8005 + 43.7696i 1.09657 + 1.50930i 0.839856 + 0.542809i 0.182639π0.182639\pi
0.256713 + 0.966488i 0.417361π0.417361\pi
3030 6.49535 8.94009i 0.216512 0.298003i
3131 1.08129 + 3.32786i 0.0348803 + 0.107350i 0.966981 0.254849i 0.0820258π-0.0820258\pi
−0.932101 + 0.362200i 0.882026π0.882026\pi
3232 19.2397i 0.601241i
3333 16.9228 28.1082i 0.512813 0.851762i
3434 13.8926 0.408607
3535 −4.73973 + 1.54003i −0.135421 + 0.0440009i
3636 0.105274 + 0.0764859i 0.00292427 + 0.00212461i
3737 37.8881 27.5273i 1.02400 0.743981i 0.0569023 0.998380i 0.481878π-0.481878\pi
0.967099 + 0.254399i 0.0818776π0.0818776\pi
3838 −13.6060 + 41.8749i −0.358052 + 1.10197i
3939 −5.22085 1.69636i −0.133868 0.0434963i
4040 11.4432 + 15.7502i 0.286079 + 0.393754i
4141 −15.9749 + 21.9876i −0.389633 + 0.536283i −0.958104 0.286419i 0.907535π-0.907535\pi
0.568472 + 0.822703i 0.307535π0.307535\pi
4242 −3.40364 10.4753i −0.0810390 0.249412i
4343 14.9713i 0.348171i −0.984731 0.174085i 0.944303π-0.944303\pi
0.984731 0.174085i 0.0556969π-0.0556969\pi
4444 9.04557 + 10.4243i 0.205581 + 0.236916i
4545 −0.231903 −0.00515340
4646 −12.0271 + 3.90783i −0.261458 + 0.0849528i
4747 58.0480 + 42.1743i 1.23506 + 0.897326i 0.997259 0.0739873i 0.0235724π-0.0235724\pi
0.237804 + 0.971313i 0.423572π0.423572\pi
4848 −22.6991 + 16.4919i −0.472898 + 0.343580i
4949 13.6068 41.8775i 0.277691 0.854644i
5050 −7.87900 2.56004i −0.157580 0.0512008i
5151 14.6999 + 20.2326i 0.288232 + 0.396718i
5252 1.35734 1.86822i 0.0261028 0.0359274i
5353 −12.1774 37.4781i −0.229762 0.707134i −0.997773 0.0666977i 0.978754π-0.978754\pi
0.768012 0.640436i 0.221246π-0.221246\pi
5454 44.9902i 0.833151i
5555 −23.9614 5.55420i −0.435663 0.100985i
5656 19.4046 0.346511
5757 −75.3814 + 24.4929i −1.32248 + 0.429700i
5858 72.5216 + 52.6900i 1.25037 + 0.908449i
5959 −29.1317 + 21.1654i −0.493758 + 0.358736i −0.806628 0.591060i 0.798710π-0.798710\pi
0.312870 + 0.949796i 0.398710π0.398710\pi
6060 −2.58591 + 7.95861i −0.0430985 + 0.132643i
6161 −44.0546 14.3142i −0.722207 0.234659i −0.0752273 0.997166i 0.523968π-0.523968\pi
−0.646980 + 0.762507i 0.723968π0.723968\pi
6262 3.40779 + 4.69042i 0.0549643 + 0.0756519i
6363 −0.135863 + 0.187000i −0.00215656 + 0.00296825i
6464 −21.4785 66.1039i −0.335601 1.03287i
6565 4.11543i 0.0633143i
6666 12.2754 52.9574i 0.185991 0.802386i
6767 −60.8461 −0.908151 −0.454075 0.890963i 0.650030π-0.650030\pi
−0.454075 + 0.890963i 0.650030π0.650030\pi
6868 −10.0055 + 3.25097i −0.147139 + 0.0478084i
6969 −18.4171 13.3808i −0.266914 0.193925i
7070 −6.68035 + 4.85356i −0.0954336 + 0.0693365i
7171 −37.8919 + 116.619i −0.533688 + 1.64252i 0.212778 + 0.977101i 0.431749π0.431749\pi
−0.746466 + 0.665423i 0.768251π0.768251\pi
7272 0.858757 + 0.279027i 0.0119272 + 0.00387538i
7373 −35.1241 48.3441i −0.481152 0.662248i 0.497574 0.867422i 0.334224π-0.334224\pi
−0.978726 + 0.205173i 0.934224π0.934224\pi
7474 45.6098 62.7765i 0.616348 0.848331i
7575 −4.60847 14.1834i −0.0614463 0.189112i
7676 33.3422i 0.438713i
7777 −18.5169 + 16.0678i −0.240479 + 0.208673i
7878 −9.09555 −0.116610
7979 −81.5552 + 26.4989i −1.03234 + 0.335429i −0.775717 0.631081i 0.782611π-0.782611\pi
−0.256627 + 0.966510i 0.582611π0.582611\pi
8080 17.0172 + 12.3638i 0.212716 + 0.154547i
8181 64.7665 47.0556i 0.799587 0.580934i
8282 −13.9155 + 42.8274i −0.169701 + 0.522285i
8383 −43.6902 14.1958i −0.526388 0.171034i 0.0337544 0.999430i 0.489254π-0.489254\pi
−0.560142 + 0.828396i 0.689254π0.689254\pi
8484 4.90260 + 6.74785i 0.0583643 + 0.0803315i
8585 11.0203 15.1681i 0.129651 0.178449i
8686 −7.66545 23.5918i −0.0891331 0.274324i
8787 161.369i 1.85481i
8888 82.0485 + 49.3983i 0.932370 + 0.561344i
8989 121.940 1.37011 0.685056 0.728490i 0.259778π-0.259778\pi
0.685056 + 0.728490i 0.259778π0.259778\pi
9090 −0.365432 + 0.118736i −0.00406036 + 0.00131929i
9191 3.31856 + 2.41107i 0.0364677 + 0.0264953i
9292 7.74743 5.62884i 0.0842112 0.0611830i
9393 −3.22512 + 9.92591i −0.0346787 + 0.106730i
9494 113.066 + 36.7372i 1.20282 + 0.390822i
9595 34.9266 + 48.0724i 0.367649 + 0.506025i
9696 33.7304 46.4259i 0.351358 0.483603i
9797 −10.2685 31.6031i −0.105861 0.325805i 0.884071 0.467353i 0.154792π-0.154792\pi
−0.989931 + 0.141547i 0.954792π0.954792\pi
9898 72.9574i 0.744464i
9999 −1.05051 + 0.444824i −0.0106113 + 0.00449317i
100100 6.27352 0.0627352
101101 100.840 32.7650i 0.998420 0.324406i 0.236186 0.971708i 0.424103π-0.424103\pi
0.762234 + 0.647302i 0.224103π0.224103\pi
102102 33.5233 + 24.3561i 0.328660 + 0.238785i
103103 158.992 115.514i 1.54361 1.12150i 0.595591 0.803288i 0.296918π-0.296918\pi
0.948020 0.318211i 0.103082π-0.103082\pi
104104 4.95171 15.2398i 0.0476126 0.146537i
105105 −14.1370 4.59339i −0.134638 0.0437466i
106106 −38.3782 52.8230i −0.362058 0.498330i
107107 −90.2208 + 124.178i −0.843185 + 1.16054i 0.142139 + 0.989847i 0.454602π0.454602\pi
−0.985323 + 0.170697i 0.945398π0.945398\pi
108108 10.5280 + 32.4019i 0.0974816 + 0.300018i
109109 35.9768i 0.330062i −0.986288 0.165031i 0.947228π-0.947228\pi
0.986288 0.165031i 0.0527725π-0.0527725\pi
110110 −40.6022 + 3.51616i −0.369111 + 0.0319651i
111111 139.685 1.25842
112112 19.9395 6.47874i 0.178031 0.0578459i
113113 −107.159 77.8559i −0.948314 0.688990i 0.00209353 0.999998i 0.499334π-0.499334\pi
−0.950407 + 0.311007i 0.899334π0.899334\pi
114114 −106.245 + 77.1918i −0.931977 + 0.677121i
115115 −5.27383 + 16.2312i −0.0458594 + 0.141141i
116116 −64.5599 20.9768i −0.556551 0.180834i
117117 0.112194 + 0.154422i 0.000958923 + 0.00131984i
118118 −35.0689 + 48.2682i −0.297194 + 0.409052i
119119 −5.77476 17.7729i −0.0485274 0.149352i
120120 58.0674i 0.483895i
121121 −119.199 + 20.8012i −0.985112 + 0.171911i
122122 −76.7503 −0.629101
123123 −77.0959 + 25.0500i −0.626796 + 0.203658i
124124 −3.55188 2.58059i −0.0286442 0.0208112i
125125 −9.04508 + 6.57164i −0.0723607 + 0.0525731i
126126 −0.118348 + 0.364237i −0.000939268 + 0.00289077i
127127 −21.4191 6.95949i −0.168654 0.0547991i 0.223473 0.974710i 0.428261π-0.428261\pi
−0.392127 + 0.919911i 0.628261π0.628261\pi
128128 −22.4562 30.9083i −0.175439 0.241471i
129129 26.2473 36.1262i 0.203467 0.280048i
130130 2.10713 + 6.48509i 0.0162087 + 0.0498853i
131131 69.8904i 0.533515i −0.963764 0.266757i 0.914048π-0.914048\pi
0.963764 0.266757i 0.0859522π-0.0859522\pi
132132 3.55168 + 41.0125i 0.0269067 + 0.310701i
133133 59.2264 0.445311
134134 −95.8812 + 31.1537i −0.715532 + 0.232490i
135135 −49.1208 35.6884i −0.363858 0.264358i
136136 −59.0596 + 42.9093i −0.434262 + 0.315509i
137137 83.0828 255.703i 0.606444 1.86644i 0.119903 0.992786i 0.461742π-0.461742\pi
0.486541 0.873658i 0.338258π-0.338258\pi
138138 −35.8727 11.6557i −0.259947 0.0844619i
139139 −66.4957 91.5235i −0.478386 0.658442i 0.499807 0.866137i 0.333404π-0.333404\pi
−0.978194 + 0.207694i 0.933404π0.933404\pi
140140 3.67542 5.05878i 0.0262530 0.0361342i
141141 66.1327 + 203.535i 0.469026 + 1.44351i
142142 203.169i 1.43077i
143143 7.89400 + 18.6428i 0.0552028 + 0.130369i
144144 0.975591 0.00677493
145145 115.055 37.3837i 0.793484 0.257819i
146146 −80.1011 58.1968i −0.548638 0.398609i
147147 106.252 77.1966i 0.722803 0.525147i
148148 −18.1580 + 55.8846i −0.122689 + 0.377599i
149149 185.247 + 60.1904i 1.24327 + 0.403962i 0.855504 0.517796i 0.173247π-0.173247\pi
0.387764 + 0.921759i 0.373247π0.373247\pi
150150 −14.5240 19.9906i −0.0968270 0.133271i
151151 −82.9127 + 114.120i −0.549091 + 0.755758i −0.989888 0.141848i 0.954696π-0.954696\pi
0.440798 + 0.897606i 0.354696π0.354696\pi
152152 −71.4954 220.040i −0.470365 1.44763i
153153 0.869583i 0.00568355i
154154 −20.9520 + 34.8004i −0.136052 + 0.225977i
155155 7.82428 0.0504792
156156 6.55062 2.12842i 0.0419911 0.0136437i
157157 −39.8372 28.9434i −0.253740 0.184353i 0.453643 0.891184i 0.350124π-0.350124\pi
−0.707383 + 0.706831i 0.750124π0.750124\pi
158158 −114.947 + 83.5138i −0.727512 + 0.528569i
159159 36.3210 111.785i 0.228434 0.703048i
160160 −40.9157 13.2943i −0.255723 0.0830894i
161161 9.99860 + 13.7619i 0.0621031 + 0.0854776i
162162 77.9662 107.311i 0.481273 0.662415i
163163 77.2981 + 237.899i 0.474222 + 1.45950i 0.847005 + 0.531586i 0.178404π0.178404\pi
−0.372783 + 0.927919i 0.621596π0.621596\pi
164164 34.1006i 0.207930i
165165 −48.0822 55.4108i −0.291407 0.335823i
166166 −76.1154 −0.458526
167167 263.329 85.5607i 1.57682 0.512340i 0.615585 0.788071i 0.288920π-0.288920\pi
0.961235 + 0.275731i 0.0889199π0.0889199\pi
168168 46.8238 + 34.0195i 0.278713 + 0.202497i
169169 −133.983 + 97.3447i −0.792801 + 0.576004i
170170 9.59957 29.5444i 0.0564681 0.173791i
171171 2.62108 + 0.851641i 0.0153280 + 0.00498036i
172172 11.0413 + 15.1971i 0.0641937 + 0.0883550i
173173 −1.43083 + 1.96937i −0.00827072 + 0.0113837i −0.813132 0.582079i 0.802239π-0.802239\pi
0.804862 + 0.593463i 0.202239π0.202239\pi
174174 82.6221 + 254.285i 0.474840 + 1.46141i
175175 11.1438i 0.0636787i
176176 100.803 + 23.3659i 0.572746 + 0.132761i
177177 −107.402 −0.606792
178178 192.153 62.4343i 1.07951 0.350754i
179179 −117.428 85.3162i −0.656020 0.476627i 0.209296 0.977852i 0.432883π-0.432883\pi
−0.865317 + 0.501226i 0.832883π0.832883\pi
180180 0.235399 0.171028i 0.00130777 0.000950153i
181181 −49.3147 + 151.775i −0.272457 + 0.838535i 0.717424 + 0.696636i 0.245321π0.245321\pi
−0.989881 + 0.141899i 0.954679π0.954679\pi
182182 6.46387 + 2.10024i 0.0355158 + 0.0115398i
183183 −81.2098 111.776i −0.443769 0.610796i
184184 39.0589 53.7600i 0.212277 0.292174i
185185 −32.3603 99.5947i −0.174920 0.538350i
186186 17.2925i 0.0929706i
187187 20.8270 89.8499i 0.111374 0.480481i
188188 −90.0266 −0.478865
189189 −57.5561 + 18.7011i −0.304529 + 0.0989476i
190190 79.6508 + 57.8697i 0.419215 + 0.304578i
191191 −59.2898 + 43.0766i −0.310418 + 0.225532i −0.732076 0.681223i 0.761448π-0.761448\pi
0.421658 + 0.906755i 0.361448π0.361448\pi
192192 64.0630 197.166i 0.333662 1.02691i
193193 250.612 + 81.4288i 1.29851 + 0.421911i 0.875062 0.484010i 0.160820π-0.160820\pi
0.423446 + 0.905921i 0.360820π0.360820\pi
194194 −32.3621 44.5426i −0.166815 0.229601i
195195 −7.21503 + 9.93064i −0.0370002 + 0.0509263i
196196 17.0726 + 52.5439i 0.0871049 + 0.268081i
197197 219.288i 1.11313i 0.830803 + 0.556567i 0.187882π0.187882\pi
−0.830803 + 0.556567i 0.812118π0.812118\pi
198198 −1.42765 + 1.23883i −0.00721034 + 0.00625670i
199199 −108.109 −0.543261 −0.271630 0.962402i 0.587563π-0.587563\pi
−0.271630 + 0.962402i 0.587563π0.587563\pi
200200 41.4018 13.4523i 0.207009 0.0672613i
201201 −146.823 106.673i −0.730464 0.530713i
202202 142.128 103.262i 0.703605 0.511199i
203203 37.2614 114.679i 0.183554 0.564920i
204204 −29.8430 9.69657i −0.146289 0.0475322i
205205 35.7211 + 49.1658i 0.174249 + 0.239833i
206206 191.395 263.433i 0.929102 1.27880i
207207 0.244603 + 0.752811i 0.00118166 + 0.00363677i
208208 17.3132i 0.0832364i
209209 250.427 + 150.772i 1.19822 + 0.721399i
210210 −24.6290 −0.117281
211211 237.612 77.2048i 1.12612 0.365900i 0.314022 0.949416i 0.398323π-0.398323\pi
0.812102 + 0.583516i 0.198323π0.198323\pi
212212 40.0009 + 29.0624i 0.188684 + 0.137087i
213213 −295.887 + 214.974i −1.38914 + 1.00927i
214214 −78.5895 + 241.874i −0.367241 + 1.13025i
215215 −31.8385 10.3449i −0.148086 0.0481160i
216216 138.958 + 191.260i 0.643325 + 0.885461i
217217 4.58395 6.30927i 0.0211242 0.0290750i
218218 −18.4204 56.6922i −0.0844973 0.260056i
219219 178.234i 0.813854i
220220 28.4189 12.0335i 0.129177 0.0546979i
221221 −15.4319 −0.0698277
222222 220.115 71.5198i 0.991510 0.322161i
223223 −114.964 83.5261i −0.515533 0.374557i 0.299385 0.954132i 0.403218π-0.403218\pi
−0.814919 + 0.579576i 0.803218π0.803218\pi
224224 −34.6911 + 25.2046i −0.154871 + 0.112520i
225225 −0.160241 + 0.493171i −0.000712182 + 0.00219187i
226226 −208.725 67.8188i −0.923561 0.300083i
227227 24.2567 + 33.3864i 0.106858 + 0.147077i 0.859097 0.511814i 0.171026π-0.171026\pi
−0.752239 + 0.658890i 0.771026π0.771026\pi
228228 58.4545 80.4557i 0.256379 0.352876i
229229 110.190 + 339.131i 0.481180 + 1.48092i 0.837438 + 0.546532i 0.184052π0.184052\pi
−0.356258 + 0.934387i 0.615948π0.615948\pi
230230 28.2773i 0.122945i
231231 −72.8512 + 6.30892i −0.315373 + 0.0273113i
232232 −471.040 −2.03035
233233 −181.617 + 59.0111i −0.779474 + 0.253266i −0.671615 0.740900i 0.734399π-0.734399\pi
−0.107858 + 0.994166i 0.534399π0.534399\pi
234234 0.255861 + 0.185894i 0.00109342 + 0.000794417i
235235 129.799 94.3046i 0.552337 0.401296i
236236 13.9615 42.9691i 0.0591589 0.182073i
237237 −243.252 79.0373i −1.02638 0.333491i
238238 −18.1997 25.0498i −0.0764695 0.105251i
239239 −165.024 + 227.136i −0.690476 + 0.950359i −1.00000 0.000532544i 0.999830π-0.999830\pi
0.309523 + 0.950892i 0.399830π0.399830\pi
240240 19.3873 + 59.6681i 0.0807806 + 0.248617i
241241 274.304i 1.13819i −0.822271 0.569096i 0.807293π-0.807293\pi
0.822271 0.569096i 0.192707π-0.192707\pi
242242 −177.183 + 93.8092i −0.732160 + 0.387641i
243243 −5.60007 −0.0230455
244244 55.2755 17.9601i 0.226539 0.0736070i
245245 −79.6558 57.8733i −0.325126 0.236218i
246246 −108.662 + 78.9475i −0.441715 + 0.320925i
247247 15.1135 46.5146i 0.0611883 0.188318i
248248 −28.9740 9.41422i −0.116831 0.0379606i
249249 −80.5380 110.851i −0.323446 0.445185i
250250 −10.8885 + 14.9867i −0.0435540 + 0.0599470i
251251 −37.0091 113.902i −0.147447 0.453794i 0.849871 0.526991i 0.176680π-0.176680\pi
−0.997318 + 0.0731969i 0.976680π0.976680\pi
252252 0.290018i 0.00115086i
253253 7.24348 + 83.6429i 0.0286304 + 0.330604i
254254 −37.3155 −0.146911
255255 53.1846 17.2807i 0.208567 0.0677675i
256256 173.714 + 126.210i 0.678568 + 0.493009i
257257 −29.6399 + 21.5347i −0.115331 + 0.0837925i −0.643955 0.765063i 0.722708π-0.722708\pi
0.528625 + 0.848856i 0.322708π0.322708\pi
258258 22.8635 70.3665i 0.0886181 0.272738i
259259 −99.2689 32.2544i −0.383277 0.124534i
260260 −3.03511 4.17748i −0.0116735 0.0160672i
261261 3.29803 4.53935i 0.0126361 0.0173922i
262262 −35.7845 110.133i −0.136582 0.420356i
263263 26.4631i 0.100620i −0.998734 0.0503101i 0.983979π-0.983979\pi
0.998734 0.0503101i 0.0160210π-0.0160210\pi
264264 111.382 + 263.044i 0.421901 + 0.996379i
265265 −88.1163 −0.332514
266266 93.3289 30.3244i 0.350860 0.114001i
267267 294.244 + 213.781i 1.10204 + 0.800678i
268268 61.7635 44.8738i 0.230461 0.167440i
269269 12.2133 37.5885i 0.0454024 0.139734i −0.925786 0.378049i 0.876595π-0.876595\pi
0.971188 + 0.238315i 0.0765950π0.0765950\pi
270270 −95.6773 31.0874i −0.354360 0.115139i
271271 −244.596 336.658i −0.902568 1.24228i −0.969642 0.244531i 0.921366π-0.921366\pi
0.0670732 0.997748i 0.478634π-0.478634\pi
272272 −46.3612 + 63.8108i −0.170446 + 0.234598i
273273 3.78076 + 11.6360i 0.0138489 + 0.0426226i
274274 445.475i 1.62582i
275275 −28.3687 + 47.1192i −0.103159 + 0.171343i
276276 28.5630 0.103489
277277 −114.108 + 37.0759i −0.411942 + 0.133848i −0.507654 0.861561i 0.669487π-0.669487\pi
0.0957120 + 0.995409i 0.469487π0.469487\pi
278278 −151.645 110.176i −0.545484 0.396318i
279279 0.293588 0.213304i 0.00105229 0.000764531i
280280 13.4083 41.2664i 0.0478866 0.147380i
281281 406.555 + 132.098i 1.44681 + 0.470098i 0.924014 0.382358i 0.124888π-0.124888\pi
0.522799 + 0.852456i 0.324888π0.324888\pi
282282 208.424 + 286.871i 0.739091 + 1.01727i
283283 119.366 164.293i 0.421787 0.580541i −0.544256 0.838919i 0.683188π-0.683188\pi
0.966044 + 0.258378i 0.0831881π0.0831881\pi
284284 −47.5431 146.323i −0.167405 0.515220i
285285 177.232i 0.621867i
286286 21.9846 + 25.3355i 0.0768693 + 0.0885857i
287287 60.5735 0.211057
288288 −1.89769 + 0.616598i −0.00658921 + 0.00214096i
289289 −176.929 128.546i −0.612211 0.444797i
290290 162.163 117.818i 0.559183 0.406271i
291291 30.6274 94.2615i 0.105249 0.323923i
292292 71.3073 + 23.1691i 0.244203 + 0.0793464i
293293 240.571 + 331.117i 0.821061 + 1.13009i 0.989522 + 0.144385i 0.0461205π0.0461205\pi
−0.168460 + 0.985708i 0.553880π0.553880\pi
294294 127.907 176.048i 0.435056 0.598803i
295295 24.8815 + 76.5773i 0.0843440 + 0.259584i
296296 407.744i 1.37751i
297297 −290.972 67.4465i −0.979703 0.227092i
298298 322.730 1.08299
299299 13.3597 4.34081i 0.0446811 0.0145178i
300300 15.1382 + 10.9985i 0.0504606 + 0.0366618i
301301 −26.9948 + 19.6129i −0.0896838 + 0.0651591i
302302 −72.2236 + 222.281i −0.239151 + 0.736031i
303303 300.773 + 97.7271i 0.992651 + 0.322532i
304304 −146.933 202.235i −0.483331 0.665248i
305305 −60.8820 + 83.7969i −0.199613 + 0.274744i
306306 −0.445233 1.37029i −0.00145501 0.00447806i
307307 548.367i 1.78621i 0.449846 + 0.893106i 0.351479π0.351479\pi
−0.449846 + 0.893106i 0.648521π0.648521\pi
308308 6.94608 29.9662i 0.0225522 0.0972928i
309309 586.168 1.89698
310310 12.3295 4.00610i 0.0397726 0.0129229i
311311 −37.3991 27.1721i −0.120254 0.0873700i 0.526032 0.850465i 0.323679π-0.323679\pi
−0.646287 + 0.763095i 0.723679π0.723679\pi
312312 38.6665 28.0929i 0.123931 0.0900412i
313313 0.359023 1.10496i 0.00114704 0.00353022i −0.950481 0.310782i 0.899409π-0.899409\pi
0.951628 + 0.307251i 0.0994092π0.0994092\pi
314314 −77.5947 25.2120i −0.247117 0.0802931i
315315 0.303799 + 0.418144i 0.000964442 + 0.00132744i
316316 63.2419 87.0451i 0.200133 0.275459i
317317 36.3906 + 111.999i 0.114797 + 0.353308i 0.991905 0.126985i 0.0405301π-0.0405301\pi
−0.877108 + 0.480294i 0.840530π0.840530\pi
318318 194.747i 0.612411i
319319 449.490 390.041i 1.40906 1.22270i
320320 −155.420 −0.485686
321321 −435.410 + 141.473i −1.35642 + 0.440727i
322322 22.8020 + 16.5666i 0.0708137 + 0.0514491i
323323 −180.261 + 130.967i −0.558082 + 0.405470i
324324 −31.0396 + 95.5302i −0.0958014 + 0.294846i
325325 8.75198 + 2.84369i 0.0269292 + 0.00874982i
326326 243.613 + 335.304i 0.747278 + 1.02854i
327327 63.0733 86.8130i 0.192885 0.265483i
328328 −73.1216 225.045i −0.222932 0.686113i
329329 159.916i 0.486066i
330330 −104.139 62.6979i −0.315572 0.189994i
331331 −151.229 −0.456885 −0.228443 0.973557i 0.573363π-0.573363\pi
−0.228443 + 0.973557i 0.573363π0.573363\pi
332332 54.8183 17.8115i 0.165115 0.0536492i
333333 −3.92937 2.85486i −0.0117999 0.00857315i
334334 371.146 269.653i 1.11121 0.807345i
335335 −42.0436 + 129.397i −0.125503 + 0.386260i
336336 59.4729 + 19.3239i 0.177003 + 0.0575117i
337337 −211.142 290.612i −0.626534 0.862351i 0.371274 0.928523i 0.378921π-0.378921\pi
−0.997808 + 0.0661727i 0.978921π0.978921\pi
338338 −161.290 + 221.996i −0.477189 + 0.656794i
339339 −122.084 375.737i −0.360131 1.10837i
340340 23.5243i 0.0691890i
341341 35.4438 15.0081i 0.103941 0.0440121i
342342 4.56635 0.0133519
343343 −197.199 + 64.0737i −0.574923 + 0.186804i
344344 105.454 + 76.6165i 0.306551 + 0.222722i
345345 −41.1819 + 29.9204i −0.119368 + 0.0867257i
346346 −1.24637 + 3.83594i −0.00360223 + 0.0110865i
347347 −73.4954 23.8801i −0.211802 0.0688187i 0.201194 0.979551i 0.435518π-0.435518\pi
−0.412996 + 0.910733i 0.635518π0.635518\pi
348348 −119.009 163.802i −0.341980 0.470695i
349349 −246.959 + 339.910i −0.707619 + 0.973954i 0.292226 + 0.956349i 0.405604π0.405604\pi
−0.999845 + 0.0176044i 0.994396π0.994396\pi
350350 5.70570 + 17.5603i 0.0163020 + 0.0501724i
351351 49.9750i 0.142379i
352352 −210.848 + 18.2594i −0.598999 + 0.0518734i
353353 640.543 1.81457 0.907285 0.420516i 0.138151π-0.138151\pi
0.907285 + 0.420516i 0.138151π0.138151\pi
354354 −169.244 + 54.9908i −0.478091 + 0.155341i
355355 221.823 + 161.164i 0.624853 + 0.453982i
356356 −123.778 + 89.9303i −0.347692 + 0.252613i
357357 17.2242 53.0106i 0.0482470 0.148489i
358358 −228.725 74.3172i −0.638896 0.207590i
359359 −198.623 273.381i −0.553268 0.761508i 0.437183 0.899372i 0.355976π-0.355976\pi
−0.990451 + 0.137865i 0.955976π0.955976\pi
360360 1.18677 1.63345i 0.00329659 0.00453737i
361361 −106.662 328.272i −0.295462 0.909340i
362362 264.416i 0.730432i
363363 −324.097 158.781i −0.892830 0.437414i
364364 −5.14675 −0.0141394
365365 −127.080 + 41.2908i −0.348165 + 0.113126i
366366 −185.200 134.556i −0.506012 0.367639i
367367 381.543 277.207i 1.03963 0.755333i 0.0694140 0.997588i 0.477887π-0.477887\pi
0.970213 + 0.242255i 0.0778871π0.0778871\pi
368368 22.1864 68.2828i 0.0602892 0.185551i
369369 2.68070 + 0.871012i 0.00726477 + 0.00236047i
370370 −101.987 140.372i −0.275639 0.379385i
371371 −51.6240 + 71.0543i −0.139148 + 0.191521i
372372 −4.04657 12.4541i −0.0108779 0.0334787i
373373 50.8370i 0.136292i −0.997675 0.0681461i 0.978292π-0.978292\pi
0.997675 0.0681461i 0.0217084π-0.0217084\pi
374374 −13.1848 152.249i −0.0352534 0.407083i
375375 −33.3472 −0.0889259
376376 −594.126 + 193.043i −1.58012 + 0.513413i
377377 −80.5569 58.5280i −0.213679 0.155247i
378378 −81.1217 + 58.9384i −0.214608 + 0.155922i
379379 −181.638 + 559.025i −0.479256 + 1.47500i 0.360874 + 0.932615i 0.382479π0.382479\pi
−0.840130 + 0.542385i 0.817521π0.817521\pi
380380 −70.9065 23.0389i −0.186596 0.0606287i
381381 −39.4837 54.3447i −0.103632 0.142637i
382382 −71.3733 + 98.2369i −0.186841 + 0.257165i
383383 −10.4312 32.1040i −0.0272356 0.0838226i 0.936515 0.350628i 0.114032π-0.114032\pi
−0.963750 + 0.266806i 0.914032π0.914032\pi
384384 113.952i 0.296750i
385385 21.3754 + 50.4810i 0.0555205 + 0.131120i
386386 436.607 1.13111
387387 −1.47669 + 0.479804i −0.00381573 + 0.00123980i
388388 33.7305 + 24.5066i 0.0869342 + 0.0631614i
389389 −418.883 + 304.337i −1.07682 + 0.782356i −0.977126 0.212662i 0.931787π-0.931787\pi
−0.0996952 + 0.995018i 0.531787π0.531787\pi
390390 −6.28487 + 19.3428i −0.0161151 + 0.0495970i
391391 −60.8632 19.7757i −0.155660 0.0505771i
392392 225.339 + 310.153i 0.574845 + 0.791206i
393393 122.530 168.647i 0.311780 0.429128i
394394 112.277 + 345.553i 0.284967 + 0.877038i
395395 191.748i 0.485437i
396396 0.738297 1.22628i 0.00186439 0.00309667i
397397 86.1063 0.216893 0.108446 0.994102i 0.465412π-0.465412\pi
0.108446 + 0.994102i 0.465412π0.465412\pi
398398 −170.358 + 55.3526i −0.428035 + 0.139077i
399399 142.915 + 103.834i 0.358182 + 0.260235i
400400 38.0517 27.6462i 0.0951293 0.0691155i
401401 49.8340 153.373i 0.124274 0.382477i −0.869494 0.493944i 0.835555π-0.835555\pi
0.993768 + 0.111467i 0.0355548π0.0355548\pi
402402 −285.982 92.9211i −0.711397 0.231147i
403403 −3.78537 5.21011i −0.00939297 0.0129283i
404404 −78.1967 + 107.629i −0.193556 + 0.266407i
405405 −55.3172 170.249i −0.136586 0.420368i
406406 199.789i 0.492091i
407407 −337.629 389.090i −0.829555 0.955995i
408408 −217.739 −0.533675
409409 220.213 71.5515i 0.538418 0.174943i −0.0271696 0.999631i 0.508649π-0.508649\pi
0.565588 + 0.824688i 0.308649π0.308649\pi
410410 81.4625 + 59.1860i 0.198689 + 0.144356i
411411 648.771 471.359i 1.57852 1.14686i
412412 −76.1976 + 234.512i −0.184946 + 0.569204i
413413 76.3268 + 24.8001i 0.184811 + 0.0600486i
414414 0.770891 + 1.06104i 0.00186206 + 0.00256290i
415415 −60.3784 + 83.1037i −0.145490 + 0.200250i
416416 10.9424 + 33.6771i 0.0263037 + 0.0809546i
417417 337.427i 0.809177i
418418 471.819 + 109.366i 1.12875 + 0.261642i
419419 428.346 1.02231 0.511153 0.859490i 0.329219π-0.329219\pi
0.511153 + 0.859490i 0.329219π0.329219\pi
420420 17.7378 5.76335i 0.0422328 0.0137223i
421421 423.964 + 308.028i 1.00704 + 0.731657i 0.963586 0.267398i 0.0861639π-0.0861639\pi
0.0434535 + 0.999055i 0.486164π0.486164\pi
422422 334.899 243.319i 0.793600 0.576584i
423423 2.29950 7.07712i 0.00543616 0.0167308i
424424 326.302 + 106.022i 0.769581 + 0.250052i
425425 −24.6421 33.9170i −0.0579815 0.0798047i
426426 −356.190 + 490.253i −0.836126 + 1.15083i
427427 31.9029 + 98.1869i 0.0747140 + 0.229946i
428428 192.588i 0.449972i
429429 −13.6355 + 58.8251i −0.0317844 + 0.137121i
430430 −55.4677 −0.128995
431431 8.66101 2.81413i 0.0200952 0.00652931i −0.298952 0.954268i 0.596637π-0.596637\pi
0.319047 + 0.947739i 0.396637π0.396637\pi
432432 206.646 + 150.137i 0.478347 + 0.347540i
433433 159.214 115.676i 0.367700 0.267150i −0.388556 0.921425i 0.627026π-0.627026\pi
0.756257 + 0.654275i 0.227026π0.227026\pi
434434 3.99299 12.2892i 0.00920044 0.0283160i
435435 343.171 + 111.503i 0.788899 + 0.256329i
436436 26.5328 + 36.5192i 0.0608550 + 0.0837597i
437437 119.215 164.085i 0.272803 0.375481i
438438 −91.2573 280.861i −0.208350 0.641235i
439439 48.0326i 0.109414i 0.998502 + 0.0547069i 0.0174224π0.0174224\pi
−0.998502 + 0.0547069i 0.982578π0.982578\pi
440440 161.746 140.353i 0.367604 0.318985i
441441 −4.56663 −0.0103552
442442 −24.3176 + 7.90127i −0.0550172 + 0.0178762i
443443 102.069 + 74.1577i 0.230405 + 0.167399i 0.696998 0.717073i 0.254519π-0.254519\pi
−0.466593 + 0.884472i 0.654519π0.654519\pi
444444 −141.791 + 103.017i −0.319349 + 0.232020i
445445 84.2584 259.321i 0.189345 0.582743i
446446 −223.926 72.7580i −0.502076 0.163135i
447447 341.482 + 470.010i 0.763942 + 1.05148i
448448 −91.0545 + 125.326i −0.203247 + 0.279745i
449449 −13.6570 42.0320i −0.0304165 0.0936124i 0.934696 0.355449i 0.115672π-0.115672\pi
−0.965112 + 0.261836i 0.915672π0.915672\pi
450450 0.859183i 0.00190930i
451451 256.123 + 154.202i 0.567900 + 0.341911i
452452 166.194 0.367685
453453 −400.141 + 130.014i −0.883314 + 0.287006i
454454 55.3177 + 40.1907i 0.121845 + 0.0885258i
455455 7.42052 5.39133i 0.0163088 0.0118491i
456456 213.247 656.307i 0.467647 1.43927i
457457 −503.324 163.540i −1.10137 0.357855i −0.298738 0.954335i 0.596566π-0.596566\pi
−0.802628 + 0.596480i 0.796566π0.796566\pi
458458 347.275 + 477.983i 0.758243 + 1.04363i
459459 133.823 184.192i 0.291554 0.401289i
460460 −6.61710 20.3653i −0.0143850 0.0442725i
461461 258.714i 0.561202i −0.959825 0.280601i 0.909466π-0.909466\pi
0.959825 0.280601i 0.0905337π-0.0905337\pi
462462 −111.569 + 47.2420i −0.241491 + 0.102255i
463463 −269.759 −0.582633 −0.291317 0.956627i 0.594093π-0.594093\pi
−0.291317 + 0.956627i 0.594093π0.594093\pi
464464 −484.025 + 157.269i −1.04316 + 0.338942i
465465 18.8802 + 13.7173i 0.0406026 + 0.0294995i
466466 −255.978 + 185.979i −0.549310 + 0.399097i
467467 −39.5114 + 121.604i −0.0846070 + 0.260393i −0.984406 0.175911i 0.943713π-0.943713\pi
0.899799 + 0.436304i 0.143713π0.143713\pi
468468 −0.227771 0.0740073i −0.000486691 0.000158135i
469469 79.7101 + 109.712i 0.169958 + 0.233927i
470470 156.253 215.063i 0.332453 0.457582i
471471 −45.3856 139.682i −0.0963600 0.296566i
472472 313.510i 0.664216i
473473 −164.071 + 14.2085i −0.346872 + 0.0300392i
474474 −423.784 −0.894058
475475 126.366 41.0587i 0.266033 0.0864394i
476476 18.9693 + 13.7820i 0.0398514 + 0.0289537i
477477 −3.30636 + 2.40221i −0.00693157 + 0.00503608i
478478 −143.749 + 442.414i −0.300730 + 0.925553i
479479 −478.561 155.494i −0.999084 0.324622i −0.236584 0.971611i 0.576028π-0.576028\pi
−0.762499 + 0.646989i 0.776028π0.776028\pi
480480 −75.4235 103.812i −0.157132 0.216274i
481481 −50.6633 + 69.7320i −0.105329 + 0.144973i
482482 −140.446 432.249i −0.291382 0.896781i
483483 50.7370i 0.105046i
484484 105.655 109.023i 0.218295 0.225255i
485485 −74.3034 −0.153203
486486 −8.82458 + 2.86728i −0.0181576 + 0.00589975i
487487 166.147 + 120.713i 0.341164 + 0.247870i 0.745153 0.666894i 0.232377π-0.232377\pi
−0.403989 + 0.914764i 0.632377π0.632377\pi
488488 326.277 237.054i 0.668599 0.485766i
489489 −230.554 + 709.574i −0.471481 + 1.45107i
490490 −155.153 50.4123i −0.316639 0.102882i
491491 −56.3909 77.6154i −0.114849 0.158076i 0.747722 0.664011i 0.231147π-0.231147\pi
−0.862571 + 0.505935i 0.831147π0.831147\pi
492492 59.7840 82.2856i 0.121512 0.167247i
493493 140.180 + 431.431i 0.284342 + 0.875113i
494494 81.0360i 0.164040i
495495 0.220087 + 2.54142i 0.000444620 + 0.00513418i
496496 −32.9159 −0.0663627
497497 259.915 84.4516i 0.522969 0.169923i
498498 −183.668 133.443i −0.368812 0.267958i
499499 −183.447 + 133.282i −0.367630 + 0.267099i −0.756227 0.654309i 0.772960π-0.772960\pi
0.388598 + 0.921408i 0.372960π0.372960\pi
500500 4.33490 13.3414i 0.00866979 0.0266829i
501501 785.422 + 255.199i 1.56771 + 0.509379i
502502 −116.638 160.538i −0.232346 0.319797i
503503 56.2423 77.4109i 0.111814 0.153898i −0.749442 0.662070i 0.769678π-0.769678\pi
0.861256 + 0.508171i 0.169678π0.169678\pi
504504 −0.621882 1.91396i −0.00123389 0.00379753i
505505 237.090i 0.469485i
506506 54.2401 + 128.096i 0.107194 + 0.253154i
507507 −493.967 −0.974294
508508 26.8746 8.73210i 0.0529028 0.0171892i
509509 80.9705 + 58.8285i 0.159078 + 0.115577i 0.664476 0.747309i 0.268655π-0.268655\pi
−0.505399 + 0.862886i 0.668655π0.668655\pi
510510 74.9603 54.4619i 0.146981 0.106788i
511511 −41.1557 + 126.664i −0.0805396 + 0.247875i
512512 483.698 + 157.163i 0.944723 + 0.306959i
513513 424.126 + 583.759i 0.826756 + 1.13793i
514514 −35.6807 + 49.1102i −0.0694177 + 0.0955452i
515515 −135.795 417.935i −0.263680 0.811524i
516516 56.0282i 0.108582i
517517 407.097 676.172i 0.787422 1.30788i
518518 −172.942 −0.333865
519519 −6.90528 + 2.24366i −0.0133050 + 0.00432305i
520520 −28.9878 21.0609i −0.0557458 0.0405017i
521521 −398.168 + 289.286i −0.764237 + 0.555251i −0.900207 0.435462i 0.856585π-0.856585\pi
0.135970 + 0.990713i 0.456585π0.456585\pi
522522 2.87285 8.84173i 0.00550355 0.0169382i
523523 −423.738 137.681i −0.810206 0.263252i −0.125521 0.992091i 0.540060π-0.540060\pi
−0.684685 + 0.728839i 0.740060π0.740060\pi
524524 51.5440 + 70.9442i 0.0983663 + 0.135390i
525525 −19.5369 + 26.8902i −0.0372131 + 0.0512194i
526526 −13.5493 41.7006i −0.0257592 0.0792787i
527527 29.3393i 0.0556722i
528528 202.277 + 233.107i 0.383100 + 0.441491i
529529 −470.747 −0.889881
530530 −138.854 + 45.1162i −0.261988 + 0.0851250i
531531 3.02126 + 2.19507i 0.00568975 + 0.00413384i
532532 −60.1193 + 43.6792i −0.113006 + 0.0821039i
533533 15.4573 47.5726i 0.0290005 0.0892544i
534534 573.128 + 186.220i 1.07327 + 0.348728i
535535 201.740 + 277.671i 0.377084 + 0.519011i
536536 311.383 428.581i 0.580938 0.799592i
537537 −133.783 411.740i −0.249130 0.766742i
538538 65.4853i 0.121720i
539539 −471.849 109.373i −0.875415 0.202919i
540540 76.1815 0.141077
541541 −102.718 + 33.3750i −0.189866 + 0.0616913i −0.402407 0.915461i 0.631826π-0.631826\pi
0.212541 + 0.977152i 0.431826π0.431826\pi
542542 −557.806 405.270i −1.02916 0.747730i
543543 −385.084 + 279.780i −0.709179 + 0.515249i
544544 49.8506 153.424i 0.0916372 0.282030i
545545 −76.5093 24.8594i −0.140384 0.0456135i
546546 11.9154 + 16.4002i 0.0218231 + 0.0300370i
547547 −18.4002 + 25.3257i −0.0336384 + 0.0462993i −0.825505 0.564395i 0.809110π-0.809110\pi
0.791867 + 0.610694i 0.209110π0.209110\pi
548548 104.244 + 320.831i 0.190227 + 0.585459i
549549 4.80404i 0.00875052i
550550 −20.5779 + 88.7754i −0.0374144 + 0.161410i
551551 −1437.70 −2.60926
552552 188.500 61.2475i 0.341486 0.110956i
553553 154.620 + 112.338i 0.279602 + 0.203142i
554554 −160.828 + 116.848i −0.290303 + 0.210918i
555555 96.5198 297.058i 0.173910 0.535239i
556556 134.997 + 43.8630i 0.242799 + 0.0788903i
557557 75.6402 + 104.110i 0.135799 + 0.186912i 0.871501 0.490394i 0.163147π-0.163147\pi
−0.735701 + 0.677306i 0.763147π0.763147\pi
558558 0.353422 0.486444i 0.000633373 0.000871763i
559559 8.51477 + 26.2058i 0.0152322 + 0.0468797i
560560 46.8806i 0.0837154i
561561 207.778 180.297i 0.370371 0.321385i
562562 708.284 1.26029
563563 281.575 91.4894i 0.500134 0.162503i −0.0480767 0.998844i 0.515309π-0.515309\pi
0.548211 + 0.836340i 0.315309π0.315309\pi
564564 −217.237 157.832i −0.385171 0.279843i
565565 −239.616 + 174.091i −0.424099 + 0.308126i
566566 103.977 320.009i 0.183705 0.565387i
567567 −169.692 55.1363i −0.299280 0.0972421i
568568 −627.517 863.703i −1.10478 1.52060i
569569 355.335 489.077i 0.624491 0.859538i −0.373179 0.927759i 0.621732π-0.621732\pi
0.997670 + 0.0682211i 0.0217323π0.0217323\pi
570570 90.7443 + 279.282i 0.159201 + 0.489969i
571571 612.659i 1.07296i 0.843914 + 0.536479i 0.180246π0.180246\pi
−0.843914 + 0.536479i 0.819754π0.819754\pi
572572 −21.7620 13.1021i −0.0380455 0.0229057i
573573 −218.588 −0.381481
574574 95.4517 31.0141i 0.166292 0.0540316i
575575 30.8735 + 22.4309i 0.0536931 + 0.0390103i
576576 −5.83176 + 4.23702i −0.0101246 + 0.00735594i
577577 −148.690 + 457.620i −0.257694 + 0.793101i 0.735593 + 0.677424i 0.236904π0.236904\pi
−0.993287 + 0.115677i 0.963096π0.963096\pi
578578 −344.621 111.974i −0.596230 0.193727i
579579 461.976 + 635.855i 0.797885 + 1.09819i
580580 −89.2196 + 122.800i −0.153827 + 0.211724i
581581 31.6390 + 97.3747i 0.0544560 + 0.167598i
582582 164.219i 0.282163i
583583 −399.165 + 169.020i −0.684674 + 0.289914i
584584 520.270 0.890874
585585 0.405922 0.131892i 0.000693884 0.000225456i
586586 548.626 + 398.600i 0.936222 + 0.680205i
587587 −298.317 + 216.740i −0.508206 + 0.369233i −0.812143 0.583459i 0.801699π-0.801699\pi
0.303937 + 0.952692i 0.401699π0.401699\pi
588588 −50.9217 + 156.721i −0.0866016 + 0.266532i
589589 −88.4339 28.7339i −0.150142 0.0487842i
590590 78.4164 + 107.931i 0.132909 + 0.182934i
591591 −384.448 + 529.147i −0.650503 + 0.895341i
592592 136.136 + 418.984i 0.229960 + 0.707744i
593593 881.291i 1.48616i −0.669204 0.743079i 0.733365π-0.733365\pi
0.669204 0.743079i 0.266635π-0.266635\pi
594594 −493.046 + 42.6979i −0.830044 + 0.0718819i
595595 −41.7866 −0.0702295
596596 −232.430 + 75.5211i −0.389984 + 0.126713i
597597 −260.870 189.533i −0.436967 0.317475i
598598 18.8296 13.6805i 0.0314876 0.0228771i
599599 276.534 851.084i 0.461659 1.42084i −0.401477 0.915869i 0.631503π-0.631503\pi
0.863136 0.504972i 0.168497π-0.168497\pi
600600 123.488 + 40.1236i 0.205813 + 0.0668726i
601601 −449.838 619.149i −0.748483 1.03020i −0.998085 0.0618498i 0.980300π-0.980300\pi
0.249603 0.968348i 0.419700π-0.419700\pi
602602 −32.4964 + 44.7275i −0.0539808 + 0.0742982i
603603 1.95001 + 6.00150i 0.00323384 + 0.00995274i
604604 176.988i 0.293026i
605605 −38.1278 + 267.864i −0.0630211 + 0.442751i
606606 523.995 0.864679
607607 1053.73 342.377i 1.73596 0.564048i 0.741672 0.670763i 0.234033π-0.234033\pi
0.994290 + 0.106715i 0.0340332π0.0340332\pi
608608 413.627 + 300.518i 0.680308 + 0.494273i
609609 290.964 211.398i 0.477773 0.347123i
610610 −53.0331 + 163.219i −0.0869396 + 0.267572i
611611 −125.593 40.8077i −0.205553 0.0667883i
612612 0.641314 + 0.882693i 0.00104790 + 0.00144231i
613613 75.0479 103.295i 0.122427 0.168507i −0.743404 0.668842i 0.766790π-0.766790\pi
0.865831 + 0.500336i 0.166790π0.166790\pi
614614 280.769 + 864.117i 0.457278 + 1.40736i
615615 181.263i 0.294737i
616616 −18.4159 212.655i −0.0298960 0.345219i
617617 182.872 0.296389 0.148195 0.988958i 0.452654π-0.452654\pi
0.148195 + 0.988958i 0.452654π0.452654\pi
618618 923.683 300.123i 1.49463 0.485635i
619619 −93.6587 68.0470i −0.151306 0.109931i 0.509556 0.860437i 0.329810π-0.329810\pi
−0.660863 + 0.750507i 0.729810π0.729810\pi
620620 −7.94225 + 5.77038i −0.0128101 + 0.00930706i
621621 −64.0419 + 197.101i −0.103127 + 0.317392i
622622 −72.8458 23.6690i −0.117116 0.0380531i
623623 −159.745 219.870i −0.256412 0.352921i
624624 30.3529 41.7771i 0.0486424 0.0669505i
625625 7.72542 + 23.7764i 0.0123607 + 0.0380423i
626626 1.92501i 0.00307510i
627627 339.958 + 802.858i 0.542197 + 1.28048i
628628 61.7835 0.0983813
629629 373.457 121.344i 0.593732 0.192915i
630630 0.692820 + 0.503363i 0.00109971 + 0.000798989i
631631 675.353 490.673i 1.07029 0.777611i 0.0943258 0.995541i 0.469930π-0.469930\pi
0.975964 + 0.217930i 0.0699305π0.0699305\pi
632632 230.712 710.059i 0.365051 1.12351i
633633 708.717 + 230.276i 1.11962 + 0.363785i
634634 114.689 + 157.855i 0.180897 + 0.248983i
635635 −29.6005 + 40.7415i −0.0466149 + 0.0641599i
636636 45.5721 + 140.257i 0.0716543 + 0.220529i
637637 81.0410i 0.127223i
638638 508.602 844.768i 0.797183 1.32409i
639639 12.7170 0.0199014
640640 −81.2473 + 26.3989i −0.126949 + 0.0412482i
641641 −20.3823 14.8086i −0.0317976 0.0231023i 0.571773 0.820412i 0.306256π-0.306256\pi
−0.603571 + 0.797310i 0.706256π0.706256\pi
642642 −613.684 + 445.867i −0.955893 + 0.694497i
643643 126.790 390.218i 0.197184 0.606871i −0.802760 0.596303i 0.796636π-0.796636\pi
0.999944 0.0105686i 0.00336414π-0.00336414\pi
644644 −20.2987 6.59545i −0.0315197 0.0102414i
645645 −58.6906 80.7807i −0.0909932 0.125241i
646646 −216.998 + 298.672i −0.335911 + 0.462341i
647647 213.067 + 655.754i 0.329316 + 1.01353i 0.969455 + 0.245270i 0.0788767π0.0788767\pi
−0.640139 + 0.768259i 0.721123π0.721123\pi
648648 697.005i 1.07563i
649649 259.599 + 299.167i 0.399999 + 0.460966i
650650 15.2474 0.0234575
651651 22.1224 7.18800i 0.0339822 0.0110415i
652652 −253.913 184.479i −0.389438 0.282943i
653653 291.983 212.138i 0.447140 0.324866i −0.341325 0.939945i 0.610876π-0.610876\pi
0.788466 + 0.615079i 0.210876π0.210876\pi
654654 54.9419 169.094i 0.0840091 0.258553i
655655 −148.631 48.2931i −0.226917 0.0737299i
656656 −150.275 206.835i −0.229077 0.315298i
657657 −3.64272 + 5.01378i −0.00554448 + 0.00763132i
658658 −81.8782 251.995i −0.124435 0.382971i
659659 464.630i 0.705053i 0.935802 + 0.352527i 0.114677π0.114677\pi
−0.935802 + 0.352527i 0.885323π0.885323\pi
660660 89.6724 + 20.7858i 0.135867 + 0.0314937i
661661 103.487 0.156562 0.0782808 0.996931i 0.475057π-0.475057\pi
0.0782808 + 0.996931i 0.475057π0.475057\pi
662662 −238.307 + 77.4305i −0.359980 + 0.116964i
663663 −37.2376 27.0547i −0.0561653 0.0408065i
664664 323.577 235.093i 0.487315 0.354055i
665665 40.9244 125.952i 0.0615405 0.189402i
666666 −7.65362 2.48681i −0.0114919 0.00373395i
667667 −242.713 334.065i −0.363887 0.500848i
668668 −204.198 + 281.055i −0.305686 + 0.420741i
669669 −130.976 403.102i −0.195778 0.602544i
670670 225.430i 0.336463i
671671 −115.059 + 496.379i −0.171474 + 0.739760i
672672 −127.898 −0.190325
673673 −220.508 + 71.6473i −0.327649 + 0.106460i −0.468222 0.883611i 0.655105π-0.655105\pi
0.140573 + 0.990070i 0.455105π0.455105\pi
674674 −481.513 349.840i −0.714412 0.519050i
675675 −109.837 + 79.8016i −0.162722 + 0.118225i
676676 64.2122 197.625i 0.0949884 0.292344i
677677 −201.949 65.6172i −0.298300 0.0969235i 0.156043 0.987750i 0.450126π-0.450126\pi
−0.454343 + 0.890827i 0.650126π0.650126\pi
678678 −384.761 529.578i −0.567494 0.781088i
679679 −43.5316 + 59.9161i −0.0641113 + 0.0882416i
680680 50.4429 + 155.247i 0.0741807 + 0.228305i
681681 123.088i 0.180746i
682682 48.1681 41.7973i 0.0706276 0.0612864i
683683 −537.182 −0.786504 −0.393252 0.919431i 0.628650π-0.628650\pi
−0.393252 + 0.919431i 0.628650π0.628650\pi
684684 −3.28868 + 1.06856i −0.00480802 + 0.00156222i
685685 −486.375 353.372i −0.710037 0.515872i
686686 −277.939 + 201.935i −0.405159 + 0.294365i
687687 −328.660 + 1011.51i −0.478399 + 1.47236i
688688 133.941 + 43.5201i 0.194682 + 0.0632559i
689689 42.6304 + 58.6758i 0.0618729 + 0.0851608i
690690 −49.5749 + 68.2339i −0.0718476 + 0.0988898i
691691 142.052 + 437.192i 0.205575 + 0.632695i 0.999689 + 0.0249265i 0.00793517π0.00793517\pi
−0.794114 + 0.607769i 0.792065π0.792065\pi
692692 3.05430i 0.00441373i
693693 2.17827 + 1.31145i 0.00314324 + 0.00189242i
694694 −128.041 −0.184497
695695 −240.584 + 78.1704i −0.346164 + 0.112475i
696696 −1136.63 825.812i −1.63309 1.18651i
697697 −184.361 + 133.946i −0.264506 + 0.192175i
698698 −215.121 + 662.075i −0.308196 + 0.948531i
699699 −541.704 176.010i −0.774970 0.251803i
700700 −8.21849 11.3118i −0.0117407 0.0161597i
701701 256.752 353.389i 0.366265 0.504121i −0.585616 0.810589i 0.699147π-0.699147\pi
0.951881 + 0.306468i 0.0991472π0.0991472\pi
702702 25.5876 + 78.7506i 0.0364496 + 0.112180i
703703 1244.51i 1.77028i
704704 −704.047 + 298.118i −1.00007 + 0.423463i
705705 478.541 0.678781
706706 1009.37 327.963i 1.42970 0.464537i
707707 −191.182 138.902i −0.270414 0.196467i
708708 109.022 79.2088i 0.153985 0.111877i
709709 401.098 1234.45i 0.565724 1.74112i −0.100067 0.994981i 0.531906π-0.531906\pi
0.665791 0.746138i 0.268094π-0.268094\pi
710710 432.066 + 140.387i 0.608543 + 0.197728i
711711 5.22739 + 7.19489i 0.00735217 + 0.0101194i
712712 −624.033 + 858.908i −0.876451 + 1.20633i
713713 −8.25278 25.3995i −0.0115747 0.0356234i
714714 92.3529i 0.129346i
715715 45.1009 3.90574i 0.0630782 0.00546258i
716716 182.118 0.254355
717717 −796.414 + 258.771i −1.11076 + 0.360907i
718718 −452.964 329.097i −0.630869 0.458353i
719719 597.870 434.378i 0.831530 0.604142i −0.0884615 0.996080i 0.528195π-0.528195\pi
0.919992 + 0.391937i 0.128195π0.128195\pi
720720 0.674117 2.07472i 0.000936273 0.00288155i
721721 −416.568 135.351i −0.577764 0.187727i
722722 −336.156 462.678i −0.465589 0.640829i
723723 480.901 661.904i 0.665147 0.915496i
724724 −61.8753 190.433i −0.0854631 0.263028i
725725 270.511i 0.373119i
726726 −592.010 84.2666i −0.815440 0.116070i
727727 721.746 0.992773 0.496386 0.868102i 0.334660π-0.334660\pi
0.496386 + 0.868102i 0.334660π0.334660\pi
728728 −33.9657 + 11.0361i −0.0466562 + 0.0151595i
729729 −596.412 433.319i −0.818123 0.594402i
730730 −179.111 + 130.132i −0.245358 + 0.178263i
731731 38.7912 119.387i 0.0530659 0.163320i
732732 164.868 + 53.5690i 0.225230 + 0.0731817i
733733 −705.403 970.904i −0.962351 1.32456i −0.945818 0.324699i 0.894737π-0.894737\pi
−0.0165330 0.999863i 0.505263π-0.505263\pi
734734 459.303 632.176i 0.625753 0.861275i
735735 −90.7500 279.300i −0.123469 0.380000i
736736 146.844i 0.199517i
737737 57.7459 + 666.811i 0.0783527 + 0.904764i
738738 4.67021 0.00632820
739739 7.68044 2.49552i 0.0103930 0.00337689i −0.303816 0.952731i 0.598261π-0.598261\pi
0.314209 + 0.949354i 0.398261π0.398261\pi
740740 106.299 + 77.2307i 0.143647 + 0.104366i
741741 118.017 85.7445i 0.159267 0.115715i
742742 −44.9687 + 138.399i −0.0606047 + 0.186522i
743743 −246.178 79.9879i −0.331329 0.107655i 0.138628 0.990345i 0.455731π-0.455731\pi
−0.469957 + 0.882689i 0.655731π0.655731\pi
744744 −53.4103 73.5130i −0.0717881 0.0988078i
745745 256.005 352.361i 0.343631 0.472967i
746746 −26.0290 80.1089i −0.0348914 0.107385i
747747 4.76430i 0.00637791i
748748 45.1230 + 106.564i 0.0603249 + 0.142466i
749749 342.097 0.456739
750750 −52.5485 + 17.0740i −0.0700647 + 0.0227654i
751751 381.165 + 276.932i 0.507543 + 0.368751i 0.811891 0.583810i 0.198439π-0.198439\pi
−0.304348 + 0.952561i 0.598439π0.598439\pi
752752 −546.051 + 396.730i −0.726132 + 0.527566i
753753 110.386 339.732i 0.146595 0.451172i
754754 −156.908 50.9826i −0.208101 0.0676162i
755755 185.398 + 255.179i 0.245561 + 0.337985i
756756 44.6318 61.4305i 0.0590368 0.0812572i
757757 268.783 + 827.228i 0.355063 + 1.09277i 0.955973 + 0.293455i 0.0948050π0.0948050\pi
−0.600910 + 0.799317i 0.705195π0.705195\pi
758758 973.911i 1.28484i
759759 −129.161 + 214.532i −0.170173 + 0.282650i
760760 −517.346 −0.680718
761761 614.545 199.678i 0.807549 0.262389i 0.123990 0.992284i 0.460431π-0.460431\pi
0.683559 + 0.729895i 0.260431π0.260431\pi
762762 −90.0433 65.4203i −0.118167 0.0858534i
763763 −64.8698 + 47.1306i −0.0850193 + 0.0617702i
764764 28.4149 87.4521i 0.0371923 0.114466i
765765 −1.84928 0.600867i −0.00241736 0.000785447i
766766 −32.8751 45.2487i −0.0429179 0.0590714i
767767 38.9545 53.6162i 0.0507881 0.0699038i
768768 197.908 + 609.097i 0.257692 + 0.793096i
769769 152.670i 0.198530i 0.995061 + 0.0992650i 0.0316492π0.0316492\pi
−0.995061 + 0.0992650i 0.968351π0.968351\pi
770770 59.5300 + 68.6036i 0.0773117 + 0.0890955i
771771 −109.276 −0.141733
772772 −314.444 + 102.169i −0.407311 + 0.132343i
773773 579.036 + 420.694i 0.749076 + 0.544235i 0.895540 0.444981i 0.146789π-0.146789\pi
−0.146464 + 0.989216i 0.546789π0.546789\pi
774774 −2.08130 + 1.51215i −0.00268901 + 0.00195368i
775775 5.40644 16.6393i 0.00697606 0.0214701i
776776 275.152 + 89.4023i 0.354577 + 0.115209i
777777 −182.991 251.866i −0.235510 0.324151i
778778 −504.253 + 694.045i −0.648141 + 0.892089i
779779 −223.180 686.879i −0.286496 0.881744i
780780 15.4014i 0.0197454i
781781 1313.99 + 304.579i 1.68244 + 0.389986i
782782 −106.034 −0.135593
783783 1397.15 453.963i 1.78436 0.579774i
784784 335.104 + 243.467i 0.427428 + 0.310545i
785785 −89.0786 + 64.7194i −0.113476 + 0.0824451i
786786 106.733 328.491i 0.135793 0.417927i
787787 582.331 + 189.211i 0.739938 + 0.240421i 0.654646 0.755935i 0.272818π-0.272818\pi
0.0852922 + 0.996356i 0.472818π0.472818\pi
788788 −161.724 222.594i −0.205233 0.282479i
789789 46.3943 63.8562i 0.0588014 0.0809331i
790790 98.1764 + 302.156i 0.124274 + 0.382476i
791791 295.213i 0.373214i
792792 2.24285 9.67591i 0.00283188 0.0122171i
793793 85.2541 0.107508
794794 135.686 44.0871i 0.170890 0.0555254i
795795 −212.627 154.482i −0.267455 0.194318i
796796 109.739 79.7299i 0.137863 0.100163i
797797 −35.3761 + 108.877i −0.0443866 + 0.136608i −0.970794 0.239915i 0.922880π-0.922880\pi
0.926407 + 0.376523i 0.122880π0.122880\pi
798798 278.369 + 90.4475i 0.348833 + 0.113343i
799799 353.621 + 486.717i 0.442579 + 0.609158i
800800 −56.5441 + 77.8263i −0.0706801 + 0.0972828i
801801 −3.90795 12.0274i −0.00487884 0.0150155i
802802 267.201i 0.333168i
803803 −496.468 + 430.805i −0.618267 + 0.536494i
804804 227.708 0.283219
805805 36.1753 11.7541i 0.0449382 0.0146013i
806806 −8.63260 6.27195i −0.0107104 0.00778158i
807807 95.3699 69.2903i 0.118178 0.0858615i
808808 −285.268 + 877.966i −0.353055 + 1.08659i
809809 660.065 + 214.468i 0.815902 + 0.265103i 0.687096 0.726567i 0.258885π-0.258885\pi
0.128807 + 0.991670i 0.458885π0.458885\pi
810810 −174.338 239.955i −0.215232 0.296241i
811811 754.445 1038.40i 0.930266 1.28040i −0.0294904 0.999565i 0.509388π-0.509388\pi
0.959756 0.280836i 0.0906116π-0.0906116\pi
812812 46.7521 + 143.888i 0.0575764 + 0.177202i
813813 1241.18i 1.52667i
814814 −731.252 440.259i −0.898344 0.540859i
815815 559.335 0.686300
816816 −223.742 + 72.6981i −0.274193 + 0.0890908i
817817 321.863 + 233.847i 0.393958 + 0.286227i
818818 310.376 225.502i 0.379433 0.275674i
819819 0.131461 0.404594i 0.000160513 0.000494010i
820820 −72.5193 23.5629i −0.0884381 0.0287353i
821821 −208.579 287.084i −0.254054 0.349676i 0.662872 0.748733i 0.269337π-0.269337\pi
−0.916926 + 0.399057i 0.869337π0.869337\pi
822822 780.992 1074.94i 0.950112 1.30772i
823823 −199.071 612.677i −0.241884 0.744444i −0.996133 0.0878551i 0.971999π-0.971999\pi
0.754249 0.656589i 0.228001π-0.228001\pi
824824 1711.04i 2.07651i
825825 −151.062 + 63.9649i −0.183106 + 0.0775332i
826826 132.974 0.160985
827827 −693.571 + 225.355i −0.838660 + 0.272497i −0.696688 0.717374i 0.745344π-0.745344\pi
−0.141971 + 0.989871i 0.545344π0.545344\pi
828828 −0.803487 0.583767i −0.000970395 0.000705033i
829829 −899.621 + 653.613i −1.08519 + 0.788435i −0.978580 0.205866i 0.933999π-0.933999\pi
−0.106608 + 0.994301i 0.533999π0.533999\pi
830830 −52.5944 + 161.869i −0.0633668 + 0.195023i
831831 −340.346 110.585i −0.409562 0.133075i
832832 75.1916 + 103.492i 0.0903745 + 0.124390i
833833 217.012 298.691i 0.260518 0.358573i
834834 −172.765 531.717i −0.207153 0.637550i
835835 619.123i 0.741465i
836836 −365.397 + 31.6434i −0.437078 + 0.0378510i
837837 95.0128 0.113516
838838 674.987 219.317i 0.805474 0.261714i
839839 487.599 + 354.261i 0.581167 + 0.422242i 0.839145 0.543908i 0.183056π-0.183056\pi
−0.257978 + 0.966151i 0.583056π0.583056\pi
840840 104.701 76.0699i 0.124644 0.0905594i
841841 −644.625 + 1983.95i −0.766498 + 2.35904i
842842 825.794 + 268.317i 0.980753 + 0.318666i
843843 749.438 + 1031.51i 0.889013 + 1.22362i
844844 −184.256 + 253.607i −0.218313 + 0.300482i
845845 114.436 + 352.196i 0.135427 + 0.416800i
846846 12.3295i 0.0145739i
847847 193.660 + 187.677i 0.228643 + 0.221578i
848848 370.696 0.437141
849849 576.066 187.175i 0.678523 0.220465i
850850 −56.1969 40.8294i −0.0661139 0.0480346i
851851 −289.175 + 210.098i −0.339806 + 0.246884i
852852 141.805 436.431i 0.166438 0.512243i
853853 −1552.04 504.288i −1.81951 0.591194i −0.999831 0.0183661i 0.994154π-0.994154\pi
−0.819676 0.572828i 0.805846π-0.805846\pi
854854 100.545 + 138.388i 0.117734 + 0.162047i
855855 3.62225 4.98559i 0.00423654 0.00583110i
856856 −412.965 1270.97i −0.482436 1.48478i
857857 1580.81i 1.84459i −0.386486 0.922295i 0.626311π-0.626311\pi
0.386486 0.922295i 0.373689π-0.373689\pi
858858 8.63212 + 99.6780i 0.0100608 + 0.116175i
859859 −1222.90 −1.42364 −0.711819 0.702363i 0.752128π-0.752128\pi
−0.711819 + 0.702363i 0.752128π0.752128\pi
860860 39.9478 12.9798i 0.0464510 0.0150928i
861861 146.165 + 106.195i 0.169762 + 0.123340i
862862 12.2072 8.86902i 0.0141614 0.0102889i
863863 361.176 1111.58i 0.418512 1.28805i −0.490560 0.871408i 0.663208π-0.663208\pi
0.909072 0.416640i 0.136792π-0.136792\pi
864864 −496.853 161.437i −0.575061 0.186849i
865865 3.19944 + 4.40365i 0.00369878 + 0.00509093i
866866 191.663 263.801i 0.221320 0.304620i
867867 −201.571 620.371i −0.232492 0.715538i
868868 9.78504i 0.0112731i
869869 367.801 + 868.613i 0.423246 + 0.999555i
870870 597.859 0.687195
871871 106.505 34.6055i 0.122279 0.0397308i
872872 253.410 + 184.113i 0.290607 + 0.211139i
873873 −2.78806 + 2.02565i −0.00319366 + 0.00232033i
874874 103.846 319.604i 0.118817 0.365680i
875875 23.6986 + 7.70015i 0.0270842 + 0.00880017i
876876 131.447 + 180.921i 0.150054 + 0.206531i
877877 320.830 441.585i 0.365827 0.503517i −0.585934 0.810359i 0.699272π-0.699272\pi
0.951761 + 0.306842i 0.0992722π0.0992722\pi
878878 24.5931 + 75.6898i 0.0280104 + 0.0862071i
879879 1220.76i 1.38880i
880880 119.344 198.225i 0.135618 0.225256i
881881 −445.171 −0.505302 −0.252651 0.967557i 0.581302π-0.581302\pi
−0.252651 + 0.967557i 0.581302π0.581302\pi
882882 −7.19609 + 2.33815i −0.00815884 + 0.00265097i
883883 −499.994 363.267i −0.566244 0.411401i 0.267495 0.963559i 0.413804π-0.413804\pi
−0.833739 + 0.552159i 0.813804π0.813804\pi
884884 15.6646 11.3810i 0.0177201 0.0128744i
885885 −74.2131 + 228.404i −0.0838566 + 0.258084i
886886 198.810 + 64.5973i 0.224391 + 0.0729089i
887887 −717.869 988.062i −0.809323 1.11394i −0.991427 0.130658i 0.958291π-0.958291\pi
0.182105 0.983279i 0.441709π-0.441709\pi
888888 −714.843 + 983.897i −0.805004 + 1.10799i
889889 15.5110 + 47.7379i 0.0174477 + 0.0536984i
890890 451.779i 0.507616i
891891 −577.149 665.117i −0.647754 0.746484i
892892 178.297 0.199885
893893 −1813.38 + 589.203i −2.03066 + 0.659802i
894894 778.756 + 565.799i 0.871092 + 0.632885i
895895 −262.576 + 190.773i −0.293381 + 0.213154i
896896 −26.3125 + 80.9815i −0.0293666 + 0.0903812i
897897 39.8474 + 12.9472i 0.0444229 + 0.0144339i
898898 −43.0414 59.2415i −0.0479303 0.0659704i
899899 −111.274 + 153.155i −0.123775 + 0.170362i
900900 −0.201055 0.618784i −0.000223394 0.000687537i
901901 330.416i 0.366721i
902902 482.551 + 111.854i 0.534979 + 0.124007i
903903 −99.5238 −0.110215
904904 1096.79 356.368i 1.21326 0.394212i
905905 288.693 + 209.748i 0.318998 + 0.231766i
906906 −563.974 + 409.751i −0.622488 + 0.452264i
907907 309.050 951.157i 0.340738 1.04868i −0.623088 0.782152i 0.714122π-0.714122\pi
0.963826 0.266532i 0.0858779π-0.0858779\pi
908908 −49.2447 16.0006i −0.0542343 0.0176218i
909909 −6.46351 8.89625i −0.00711057 0.00978686i
910910 8.93285 12.2950i 0.00981632 0.0135110i
911911 390.823 + 1202.83i 0.429004 + 1.32034i 0.899107 + 0.437728i 0.144217π0.144217\pi
−0.470103 + 0.882611i 0.655783π0.655783\pi
912912 745.597i 0.817541i
913913 −114.107 + 492.273i −0.124981 + 0.539182i
914914 −876.872 −0.959378
915915 −293.820 + 95.4678i −0.321115 + 0.104336i
916916 −361.959 262.979i −0.395152 0.287095i
917917 −126.019 + 91.5584i −0.137426 + 0.0998456i
918918 116.571 358.768i 0.126983 0.390815i
919919 −410.290 133.311i −0.446452 0.145061i 0.0771583 0.997019i 0.475415π-0.475415\pi
−0.523611 + 0.851958i 0.675415π0.675415\pi
920920 −87.3384 120.211i −0.0949331 0.130664i
921921 −961.379 + 1323.22i −1.04384 + 1.43673i
922922 −132.464 407.681i −0.143670 0.442171i
923923 225.680i 0.244507i
924924 69.2968 60.1315i 0.0749965 0.0650774i
925925 −234.161 −0.253147
926926 −425.086 + 138.119i −0.459057 + 0.149156i
927927 −16.4891 11.9800i −0.0177876 0.0129234i
928928 842.115 611.832i 0.907451 0.659302i
929929 −394.187 + 1213.18i −0.424313 + 1.30590i 0.479338 + 0.877630i 0.340877π0.340877\pi
−0.903651 + 0.428270i 0.859123π0.859123\pi
930930 36.7747 + 11.9488i 0.0395427 + 0.0128482i
931931 687.776 + 946.642i 0.738749 + 1.01680i
932932 140.835 193.843i 0.151111 0.207986i
933933 −42.6080 131.134i −0.0456677 0.140551i
934934 211.853i 0.226824i
935935 −176.686 106.376i −0.188969 0.113771i
936936 −1.66186 −0.00177549
937937 −802.209 + 260.654i −0.856146 + 0.278179i −0.704018 0.710182i 0.748613π-0.748613\pi
−0.152128 + 0.988361i 0.548613π0.548613\pi
938938 181.780 + 132.071i 0.193796 + 0.140801i
939939 2.80351 2.03687i 0.00298563 0.00216919i
940940 −62.2068 + 191.453i −0.0661775 + 0.203673i
941941 −1486.45 482.975i −1.57964 0.513258i −0.617679 0.786430i 0.711927π-0.711927\pi
−0.961965 + 0.273172i 0.911927π0.911927\pi
942942 −143.037 196.874i −0.151844 0.208995i
943943 121.926 167.817i 0.129296 0.177961i
944944 −104.674 322.153i −0.110883 0.341263i
945945 135.322i 0.143198i
946946 −251.268 + 106.395i −0.265611 + 0.112469i
947947 −986.562 −1.04178 −0.520888 0.853625i 0.674399π-0.674399\pi
−0.520888 + 0.853625i 0.674399π0.674399\pi
948948 305.209 99.1684i 0.321950 0.104608i
949949 88.9762 + 64.6450i 0.0937579 + 0.0681191i
950950 178.105 129.401i 0.187479 0.136211i
951951 −108.541 + 334.055i −0.114134 + 0.351267i
952952 154.739 + 50.2779i 0.162541 + 0.0528129i
953953 995.156 + 1369.71i 1.04424 + 1.43727i 0.893702 + 0.448661i 0.148099π0.148099\pi
0.150533 + 0.988605i 0.451901π0.451901\pi
954954 −3.98020 + 5.47828i −0.00417212 + 0.00574243i
955955 50.6396 + 155.853i 0.0530257 + 0.163196i
956956 352.265i 0.368478i
957957 1768.44 153.147i 1.84790 0.160028i
958958 −833.730 −0.870282
959959 −569.898 + 185.171i −0.594263 + 0.193088i
960960 −375.032 272.476i −0.390658 0.283830i
961961 767.560 557.665i 0.798710 0.580296i
962962 −44.1318 + 135.824i −0.0458751 + 0.141189i
963963 15.1396 + 4.91916i 0.0157213 + 0.00510817i
964964 202.299 + 278.440i 0.209853 + 0.288838i
965965 346.338 476.693i 0.358899 0.493982i
966966 25.9778 + 79.9514i 0.0268921 + 0.0827654i
967967 1364.74i 1.41132i −0.708552 0.705658i 0.750651π-0.750651\pi
0.708552 0.705658i 0.249349π-0.249349\pi
968968 463.487 946.050i 0.478808 0.977324i
969969 −664.580 −0.685841
970970 −117.087 + 38.0439i −0.120708 + 0.0392206i
971971 66.9491 + 48.6413i 0.0689486 + 0.0500941i 0.621726 0.783235i 0.286432π-0.286432\pi
−0.552777 + 0.833329i 0.686432π0.686432\pi
972972 5.68450 4.13003i 0.00584825 0.00424900i
973973 −77.9147 + 239.797i −0.0800767 + 0.246451i
974974 323.620 + 105.151i 0.332259 + 0.107957i
975975 16.1333 + 22.2056i 0.0165470 + 0.0227750i
976976 256.124 352.525i 0.262422 0.361193i
977977 392.445 + 1207.82i 0.401684 + 1.23626i 0.923633 + 0.383279i 0.125205π0.125205\pi
−0.521949 + 0.852977i 0.674795π0.674795\pi
978978 1236.19i 1.26400i
979979 −115.727 1336.34i −0.118209 1.36500i
980980 123.538 0.126059
981981 −3.54854 + 1.15299i −0.00361727 + 0.00117532i
982982 −128.600 93.4336i −0.130958 0.0951463i
983983 303.303 220.362i 0.308548 0.224173i −0.422725 0.906258i 0.638926π-0.638926\pi
0.731273 + 0.682085i 0.238926π0.238926\pi
984984 218.097 671.234i 0.221644 0.682149i
985985 466.343 + 151.524i 0.473444 + 0.153831i
986986 441.792 + 608.075i 0.448065 + 0.616709i
987987 280.359 385.881i 0.284052 0.390964i
988988 18.9630 + 58.3621i 0.0191933 + 0.0590709i
989989 114.267i 0.115538i
990990 1.64804 + 3.89208i 0.00166469 + 0.00393139i
991991 885.269 0.893309 0.446655 0.894707i 0.352615π-0.352615\pi
0.446655 + 0.894707i 0.352615π0.352615\pi
992992 64.0271 20.8037i 0.0645435 0.0209715i
993993 −364.920 265.130i −0.367492 0.266999i
994994 366.335 266.158i 0.368546 0.267764i
995995 −74.7014 + 229.907i −0.0750768 + 0.231063i
996996 163.505 + 53.1259i 0.164161 + 0.0533392i
997997 −43.8072 60.2954i −0.0439390 0.0604769i 0.786482 0.617613i 0.211900π-0.211900\pi
−0.830421 + 0.557136i 0.811900π0.811900\pi
998998 −220.834 + 303.952i −0.221277 + 0.304561i
999999 −392.961 1209.41i −0.393355 1.21062i
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 55.3.i.c.6.3 12
5.2 odd 4 275.3.q.e.149.4 24
5.3 odd 4 275.3.q.e.149.3 24
5.4 even 2 275.3.x.g.226.1 12
11.2 odd 10 inner 55.3.i.c.46.3 yes 12
11.3 even 5 605.3.c.c.241.6 12
11.8 odd 10 605.3.c.c.241.7 12
55.2 even 20 275.3.q.e.24.3 24
55.13 even 20 275.3.q.e.24.4 24
55.24 odd 10 275.3.x.g.101.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.3.i.c.6.3 12 1.1 even 1 trivial
55.3.i.c.46.3 yes 12 11.2 odd 10 inner
275.3.q.e.24.3 24 55.2 even 20
275.3.q.e.24.4 24 55.13 even 20
275.3.q.e.149.3 24 5.3 odd 4
275.3.q.e.149.4 24 5.2 odd 4
275.3.x.g.101.1 12 55.24 odd 10
275.3.x.g.226.1 12 5.4 even 2
605.3.c.c.241.6 12 11.3 even 5
605.3.c.c.241.7 12 11.8 odd 10