Properties

Label 728.2.z.a.99.18
Level 728728
Weight 22
Character 728.99
Analytic conductor 5.8135.813
Analytic rank 00
Dimension 168168
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [728,2,Mod(99,728)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(728, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("728.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 728=23713 728 = 2^{3} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 728.z (of order 44, degree 22, 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: 5.813109267155.81310926715
Analytic rank: 00
Dimension: 168168
Relative dimension: 8484 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 99.18
Character χ\chi == 728.99
Dual form 728.2.z.a.603.18

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+(1.17472+0.787426i)q2+2.30698q3+(0.7599201.85001i)q4+(0.308723+0.308723i)q5+(2.71005+1.81658i)q6+(0.707107+0.707107i)q7+(0.564051+2.77161i)q8+2.32216q9+(0.1195660.605758i)q10+(3.254573.25457i)q11+(1.753124.26793i)q12+(1.820773.11204i)q13+(1.387440.273856i)q14+(0.712217+0.712217i)q15+(2.845042.81171i)q167.35952iq17+(2.72788+1.82853i)q18+(2.66450+2.66450i)q19+(0.336534+0.805744i)q20+(1.63128+1.63128i)q21+(1.26046+6.38593i)q223.21182q23+(1.30126+6.39406i)q24+4.80938iq25+(0.311607+5.08949i)q261.56377q27+(1.845500.770807i)q28+2.81223iq29+(0.2758351.39747i)q30+(0.4000870.400087i)q31+(5.55614+1.06271i)q32+(7.508227.50822i)q33+(5.79508+8.64536i)q340.436600q35+(1.764654.29600i)q36+(0.845714+0.845714i)q37+(5.228121.03193i)q38+(4.200497.17941i)q39+(1.029800.681525i)q40+(3.82324+3.82324i)q41+(3.200810.631780i)q42+6.36630iq43+(3.547768.49418i)q44+(0.716903+0.716903i)q45+(3.772982.52907i)q46+(2.19728+2.19728i)q47+(6.563466.48657i)q48+1.00000iq49+(3.787035.64966i)q5016.9783iq51+(4.373655.73334i)q5213.2075iq53+(1.836991.23135i)q54+2.00952iq55+(1.56098+2.35867i)q56+(6.14694+6.14694i)q57+(2.214433.30358i)q58+(1.362481.36248i)q59+(0.776378+1.85883i)q60+4.63407iq61+(0.154950+0.785027i)q62+(1.64201+1.64201i)q63+(7.36369+3.12667i)q64+(0.398643+1.52287i)q65+(2.90787+14.7322i)q66+(8.05913+8.05913i)q67+(13.61525.59265i)q687.40961q69+(0.5128810.343790i)q70+(0.561120+0.561120i)q71+(1.30982+6.43612i)q72+(1.08699+1.08699i)q73+(1.659410.327537i)q74+11.0951iq75+(6.954132.90453i)q76+4.60265q77+(0.718871+11.7414i)q788.61872iq79+(1.746370.0102893i)q8010.5741q81+(7.501731.48070i)q82+(3.517633.51763i)q83+(4.257521.77824i)q84+(2.27205+2.27205i)q85+(5.012997.47860i)q86+6.48776iq87+(10.8561+7.18466i)q88+(0.134118+0.134118i)q89+(0.2776501.40667i)q90+(3.488020.913062i)q91+(2.44073+5.94189i)q92+(0.9229920.922992i)q93+(4.311380.850988i)q941.64518q95+(12.8179+2.45165i)q96+(2.97399+2.97399i)q97+(0.7874261.17472i)q98+(7.557617.55761i)q99+O(q100)q+(-1.17472 + 0.787426i) q^{2} +2.30698 q^{3} +(0.759920 - 1.85001i) q^{4} +(-0.308723 + 0.308723i) q^{5} +(-2.71005 + 1.81658i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.564051 + 2.77161i) q^{8} +2.32216 q^{9} +(0.119566 - 0.605758i) q^{10} +(3.25457 - 3.25457i) q^{11} +(1.75312 - 4.26793i) q^{12} +(1.82077 - 3.11204i) q^{13} +(-1.38744 - 0.273856i) q^{14} +(-0.712217 + 0.712217i) q^{15} +(-2.84504 - 2.81171i) q^{16} -7.35952i q^{17} +(-2.72788 + 1.82853i) q^{18} +(2.66450 + 2.66450i) q^{19} +(0.336534 + 0.805744i) q^{20} +(1.63128 + 1.63128i) q^{21} +(-1.26046 + 6.38593i) q^{22} -3.21182 q^{23} +(1.30126 + 6.39406i) q^{24} +4.80938i q^{25} +(0.311607 + 5.08949i) q^{26} -1.56377 q^{27} +(1.84550 - 0.770807i) q^{28} +2.81223i q^{29} +(0.275835 - 1.39747i) q^{30} +(0.400087 - 0.400087i) q^{31} +(5.55614 + 1.06271i) q^{32} +(7.50822 - 7.50822i) q^{33} +(5.79508 + 8.64536i) q^{34} -0.436600 q^{35} +(1.76465 - 4.29600i) q^{36} +(0.845714 + 0.845714i) q^{37} +(-5.22812 - 1.03193i) q^{38} +(4.20049 - 7.17941i) q^{39} +(-1.02980 - 0.681525i) q^{40} +(3.82324 + 3.82324i) q^{41} +(-3.20081 - 0.631780i) q^{42} +6.36630i q^{43} +(-3.54776 - 8.49418i) q^{44} +(-0.716903 + 0.716903i) q^{45} +(3.77298 - 2.52907i) q^{46} +(2.19728 + 2.19728i) q^{47} +(-6.56346 - 6.48657i) q^{48} +1.00000i q^{49} +(-3.78703 - 5.64966i) q^{50} -16.9783i q^{51} +(-4.37365 - 5.73334i) q^{52} -13.2075i q^{53} +(1.83699 - 1.23135i) q^{54} +2.00952i q^{55} +(-1.56098 + 2.35867i) q^{56} +(6.14694 + 6.14694i) q^{57} +(-2.21443 - 3.30358i) q^{58} +(1.36248 - 1.36248i) q^{59} +(0.776378 + 1.85883i) q^{60} +4.63407i q^{61} +(-0.154950 + 0.785027i) q^{62} +(1.64201 + 1.64201i) q^{63} +(-7.36369 + 3.12667i) q^{64} +(0.398643 + 1.52287i) q^{65} +(-2.90787 + 14.7322i) q^{66} +(8.05913 + 8.05913i) q^{67} +(-13.6152 - 5.59265i) q^{68} -7.40961 q^{69} +(0.512881 - 0.343790i) q^{70} +(-0.561120 + 0.561120i) q^{71} +(1.30982 + 6.43612i) q^{72} +(-1.08699 + 1.08699i) q^{73} +(-1.65941 - 0.327537i) q^{74} +11.0951i q^{75} +(6.95413 - 2.90453i) q^{76} +4.60265 q^{77} +(0.718871 + 11.7414i) q^{78} -8.61872i q^{79} +(1.74637 - 0.0102893i) q^{80} -10.5741 q^{81} +(-7.50173 - 1.48070i) q^{82} +(-3.51763 - 3.51763i) q^{83} +(4.25752 - 1.77824i) q^{84} +(2.27205 + 2.27205i) q^{85} +(-5.01299 - 7.47860i) q^{86} +6.48776i q^{87} +(10.8561 + 7.18466i) q^{88} +(-0.134118 + 0.134118i) q^{89} +(0.277650 - 1.40667i) q^{90} +(3.48802 - 0.913062i) q^{91} +(-2.44073 + 5.94189i) q^{92} +(0.922992 - 0.922992i) q^{93} +(-4.31138 - 0.850988i) q^{94} -1.64518 q^{95} +(12.8179 + 2.45165i) q^{96} +(2.97399 + 2.97399i) q^{97} +(-0.787426 - 1.17472i) q^{98} +(7.55761 - 7.55761i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 168q12q612q8+168q916q16+12q1820q20+24q2232q24+44q2620q3416q408q4152q4432q4664q48+72q5056q52+128q99+O(q100) 168 q - 12 q^{6} - 12 q^{8} + 168 q^{9} - 16 q^{16} + 12 q^{18} - 20 q^{20} + 24 q^{22} - 32 q^{24} + 44 q^{26} - 20 q^{34} - 16 q^{40} - 8 q^{41} - 52 q^{44} - 32 q^{46} - 64 q^{48} + 72 q^{50} - 56 q^{52}+ \cdots - 128 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/728Z)×\left(\mathbb{Z}/728\mathbb{Z}\right)^\times.

nn 183183 365365 521521 561561
χ(n)\chi(n) 1-1 1-1 11 e(14)e\left(\frac{1}{4}\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 −1.17472 + 0.787426i −0.830650 + 0.556794i
33 2.30698 1.33194 0.665968 0.745981i 0.268019π-0.268019\pi
0.665968 + 0.745981i 0.268019π0.268019\pi
44 0.759920 1.85001i 0.379960 0.925003i
55 −0.308723 + 0.308723i −0.138065 + 0.138065i −0.772762 0.634697i 0.781125π-0.781125\pi
0.634697 + 0.772762i 0.281125π0.281125\pi
66 −2.71005 + 1.81658i −1.10637 + 0.741614i
77 0.707107 + 0.707107i 0.267261 + 0.267261i
88 0.564051 + 2.77161i 0.199422 + 0.979914i
99 2.32216 0.774052
1010 0.119566 0.605758i 0.0378099 0.191558i
1111 3.25457 3.25457i 0.981289 0.981289i −0.0185393 0.999828i 0.505902π-0.505902\pi
0.999828 + 0.0185393i 0.00590158π0.00590158\pi
1212 1.75312 4.26793i 0.506082 1.23204i
1313 1.82077 3.11204i 0.504992 0.863124i
1414 −1.38744 0.273856i −0.370810 0.0731911i
1515 −0.712217 + 0.712217i −0.183894 + 0.183894i
1616 −2.84504 2.81171i −0.711261 0.702928i
1717 7.35952i 1.78495i −0.451101 0.892473i 0.648968π-0.648968\pi
0.451101 0.892473i 0.351032π-0.351032\pi
1818 −2.72788 + 1.82853i −0.642967 + 0.430988i
1919 2.66450 + 2.66450i 0.611277 + 0.611277i 0.943279 0.332002i 0.107724π-0.107724\pi
−0.332002 + 0.943279i 0.607724π0.607724\pi
2020 0.336534 + 0.805744i 0.0752513 + 0.180170i
2121 1.63128 + 1.63128i 0.355975 + 0.355975i
2222 −1.26046 + 6.38593i −0.268732 + 1.36148i
2323 −3.21182 −0.669712 −0.334856 0.942269i 0.608688π-0.608688\pi
−0.334856 + 0.942269i 0.608688π0.608688\pi
2424 1.30126 + 6.39406i 0.265618 + 1.30518i
2525 4.80938i 0.961876i
2626 0.311607 + 5.08949i 0.0611112 + 0.998131i
2727 −1.56377 −0.300948
2828 1.84550 0.770807i 0.348766 0.145669i
2929 2.81223i 0.522219i 0.965309 + 0.261109i 0.0840883π0.0840883\pi
−0.965309 + 0.261109i 0.915912π0.915912\pi
3030 0.275835 1.39747i 0.0503604 0.255142i
3131 0.400087 0.400087i 0.0718577 0.0718577i −0.670265 0.742122i 0.733819π-0.733819\pi
0.742122 + 0.670265i 0.233819π0.233819\pi
3232 5.55614 + 1.06271i 0.982195 + 0.187862i
3333 7.50822 7.50822i 1.30701 1.30701i
3434 5.79508 + 8.64536i 0.993848 + 1.48267i
3535 −0.436600 −0.0737989
3636 1.76465 4.29600i 0.294109 0.716001i
3737 0.845714 + 0.845714i 0.139035 + 0.139035i 0.773199 0.634164i 0.218656π-0.218656\pi
−0.634164 + 0.773199i 0.718656π0.718656\pi
3838 −5.22812 1.03193i −0.848113 0.167402i
3939 4.20049 7.17941i 0.672616 1.14963i
4040 −1.02980 0.681525i −0.162825 0.107759i
4141 3.82324 + 3.82324i 0.597089 + 0.597089i 0.939537 0.342448i 0.111256π-0.111256\pi
−0.342448 + 0.939537i 0.611256π0.611256\pi
4242 −3.20081 0.631780i −0.493895 0.0974858i
4343 6.36630i 0.970852i 0.874278 + 0.485426i 0.161335π0.161335\pi
−0.874278 + 0.485426i 0.838665π0.838665\pi
4444 −3.54776 8.49418i −0.534844 1.28055i
4545 −0.716903 + 0.716903i −0.106870 + 0.106870i
4646 3.77298 2.52907i 0.556296 0.372892i
4747 2.19728 + 2.19728i 0.320507 + 0.320507i 0.848961 0.528455i 0.177228π-0.177228\pi
−0.528455 + 0.848961i 0.677228π0.677228\pi
4848 −6.56346 6.48657i −0.947353 0.936255i
4949 1.00000i 0.142857i
5050 −3.78703 5.64966i −0.535567 0.798983i
5151 16.9783i 2.37743i
5252 −4.37365 5.73334i −0.606516 0.795072i
5353 13.2075i 1.81419i −0.420923 0.907096i 0.638294π-0.638294\pi
0.420923 0.907096i 0.361706π-0.361706\pi
5454 1.83699 1.23135i 0.249982 0.167566i
5555 2.00952i 0.270963i
5656 −1.56098 + 2.35867i −0.208595 + 0.315191i
5757 6.14694 + 6.14694i 0.814182 + 0.814182i
5858 −2.21443 3.30358i −0.290768 0.433781i
5959 1.36248 1.36248i 0.177379 0.177379i −0.612833 0.790212i 0.709970π-0.709970\pi
0.790212 + 0.612833i 0.209970π0.209970\pi
6060 0.776378 + 1.85883i 0.100230 + 0.239974i
6161 4.63407i 0.593332i 0.954981 + 0.296666i 0.0958749π0.0958749\pi
−0.954981 + 0.296666i 0.904125π0.904125\pi
6262 −0.154950 + 0.785027i −0.0196787 + 0.0996985i
6363 1.64201 + 1.64201i 0.206874 + 0.206874i
6464 −7.36369 + 3.12667i −0.920461 + 0.390833i
6565 0.398643 + 1.52287i 0.0494456 + 0.188889i
6666 −2.90787 + 14.7322i −0.357934 + 1.81341i
6767 8.05913 + 8.05913i 0.984580 + 0.984580i 0.999883 0.0153034i 0.00487141π-0.00487141\pi
−0.0153034 + 0.999883i 0.504871π0.504871\pi
6868 −13.6152 5.59265i −1.65108 0.678208i
6969 −7.40961 −0.892013
7070 0.512881 0.343790i 0.0613010 0.0410908i
7171 −0.561120 + 0.561120i −0.0665927 + 0.0665927i −0.739619 0.673026i 0.764994π-0.764994\pi
0.673026 + 0.739619i 0.264994π0.264994\pi
7272 1.30982 + 6.43612i 0.154363 + 0.758504i
7373 −1.08699 + 1.08699i −0.127223 + 0.127223i −0.767851 0.640628i 0.778674π-0.778674\pi
0.640628 + 0.767851i 0.278674π0.278674\pi
7474 −1.65941 0.327537i −0.192903 0.0380754i
7575 11.0951i 1.28116i
7676 6.95413 2.90453i 0.797694 0.333172i
7777 4.60265 0.524521
7878 0.718871 + 11.7414i 0.0813961 + 1.32945i
7979 8.61872i 0.969682i −0.874602 0.484841i 0.838877π-0.838877\pi
0.874602 0.484841i 0.161123π-0.161123\pi
8080 1.74637 0.0102893i 0.195250 0.00115038i
8181 −10.5741 −1.17490
8282 −7.50173 1.48070i −0.828428 0.163516i
8383 −3.51763 3.51763i −0.386110 0.386110i 0.487188 0.873297i 0.338023π-0.338023\pi
−0.873297 + 0.487188i 0.838023π0.838023\pi
8484 4.25752 1.77824i 0.464534 0.194021i
8585 2.27205 + 2.27205i 0.246439 + 0.246439i
8686 −5.01299 7.47860i −0.540565 0.806438i
8787 6.48776i 0.695561i
8888 10.8561 + 7.18466i 1.15727 + 0.765887i
8989 −0.134118 + 0.134118i −0.0142165 + 0.0142165i −0.714179 0.699963i 0.753200π-0.753200\pi
0.699963 + 0.714179i 0.253200π0.253200\pi
9090 0.277650 1.40667i 0.0292669 0.148276i
9191 3.48802 0.913062i 0.365644 0.0957150i
9292 −2.44073 + 5.94189i −0.254464 + 0.619485i
9393 0.922992 0.922992i 0.0957098 0.0957098i
9494 −4.31138 0.850988i −0.444685 0.0877727i
9595 −1.64518 −0.168792
9696 12.8179 + 2.45165i 1.30822 + 0.250220i
9797 2.97399 + 2.97399i 0.301963 + 0.301963i 0.841781 0.539819i 0.181507π-0.181507\pi
−0.539819 + 0.841781i 0.681507π0.681507\pi
9898 −0.787426 1.17472i −0.0795420 0.118664i
9999 7.55761 7.55761i 0.759569 0.759569i
100100 8.89738 + 3.65475i 0.889738 + 0.365475i
101101 −3.97265 −0.395293 −0.197647 0.980273i 0.563330π-0.563330\pi
−0.197647 + 0.980273i 0.563330π0.563330\pi
102102 13.3691 + 19.9447i 1.32374 + 1.97482i
103103 7.85013 0.773496 0.386748 0.922185i 0.373598π-0.373598\pi
0.386748 + 0.922185i 0.373598π0.373598\pi
104104 9.65238 + 3.29113i 0.946494 + 0.322722i
105105 −1.00723 −0.0982953
106106 10.3999 + 15.5151i 1.01013 + 1.50696i
107107 −6.33622 −0.612545 −0.306273 0.951944i 0.599082π-0.599082\pi
−0.306273 + 0.951944i 0.599082π0.599082\pi
108108 −1.18834 + 2.89298i −0.114348 + 0.278378i
109109 −13.4537 + 13.4537i −1.28863 + 1.28863i −0.353009 + 0.935620i 0.614842π0.614842\pi
−0.935620 + 0.353009i 0.885158π0.885158\pi
110110 −1.58235 2.36061i −0.150871 0.225076i
111111 1.95105 + 1.95105i 0.185185 + 0.185185i
112112 −0.0235668 3.99993i −0.00222686 0.377958i
113113 3.45377 0.324903 0.162452 0.986717i 0.448060π-0.448060\pi
0.162452 + 0.986717i 0.448060π0.448060\pi
114114 −12.0612 2.38065i −1.12963 0.222969i
115115 0.991563 0.991563i 0.0924637 0.0924637i
116116 5.20265 + 2.13707i 0.483054 + 0.198422i
117117 4.22812 7.22664i 0.390890 0.668103i
118118 −0.527675 + 2.67338i −0.0485764 + 0.246104i
119119 5.20397 5.20397i 0.477047 0.477047i
120120 −2.37572 1.57226i −0.216872 0.143527i
121121 10.1844i 0.925856i
122122 −3.64899 5.44373i −0.330364 0.492852i
123123 8.82013 + 8.82013i 0.795284 + 0.795284i
124124 −0.436129 1.04420i −0.0391655 0.0937716i
125125 −3.02838 3.02838i −0.270866 0.270866i
126126 −3.22186 0.635937i −0.287026 0.0566537i
127127 17.6002 1.56176 0.780881 0.624680i 0.214770π-0.214770\pi
0.780881 + 0.624680i 0.214770π0.214770\pi
128128 6.18824 9.47131i 0.546968 0.837154i
129129 14.6869i 1.29311i
130130 −1.66744 1.47504i −0.146244 0.129370i
131131 −15.8191 −1.38213 −0.691063 0.722795i 0.742857π-0.742857\pi
−0.691063 + 0.722795i 0.742857π0.742857\pi
132132 −8.18460 19.5959i −0.712378 1.70560i
133133 3.76817i 0.326741i
134134 −15.8132 3.12123i −1.36605 0.269633i
135135 0.482772 0.482772i 0.0415504 0.0415504i
136136 20.3978 4.15115i 1.74909 0.355958i
137137 −12.2517 + 12.2517i −1.04674 + 1.04674i −0.0478835 + 0.998853i 0.515248π0.515248\pi
−0.998853 + 0.0478835i 0.984752π0.984752\pi
138138 8.70420 5.83452i 0.740951 0.496668i
139139 −20.0418 −1.69993 −0.849963 0.526843i 0.823376π-0.823376\pi
−0.849963 + 0.526843i 0.823376π0.823376\pi
140140 −0.331781 + 0.807712i −0.0280406 + 0.0682641i
141141 5.06909 + 5.06909i 0.426894 + 0.426894i
142142 0.217317 1.10100i 0.0182368 0.0923937i
143143 −4.20251 16.0542i −0.351431 1.34252i
144144 −6.60663 6.52924i −0.550553 0.544103i
145145 −0.868200 0.868200i −0.0721001 0.0721001i
146146 0.420982 2.13283i 0.0348407 0.176515i
147147 2.30698i 0.190277i
148148 2.20725 0.921900i 0.181435 0.0757797i
149149 −11.6375 + 11.6375i −0.953377 + 0.953377i −0.998961 0.0455831i 0.985485π-0.985485\pi
0.0455831 + 0.998961i 0.485485π0.485485\pi
150150 −8.73661 13.0337i −0.713341 1.06419i
151151 −13.2541 13.2541i −1.07860 1.07860i −0.996635 0.0819648i 0.973880π-0.973880\pi
−0.0819648 0.996635i 0.526120π-0.526120\pi
152152 −5.88204 + 8.88786i −0.477096 + 0.720901i
153153 17.0900i 1.38164i
154154 −5.40681 + 3.62425i −0.435694 + 0.292050i
155155 0.247032i 0.0198421i
156156 −10.0899 13.2267i −0.807840 1.05898i
157157 21.0225i 1.67778i 0.544301 + 0.838890i 0.316795π0.316795\pi
−0.544301 + 0.838890i 0.683205π0.683205\pi
158158 6.78661 + 10.1246i 0.539913 + 0.805467i
159159 30.4695i 2.41639i
160160 −2.04339 + 1.38722i −0.161544 + 0.109670i
161161 −2.27110 2.27110i −0.178988 0.178988i
162162 12.4215 8.32629i 0.975927 0.654175i
163163 10.0319 10.0319i 0.785763 0.785763i −0.195034 0.980796i 0.562482π-0.562482\pi
0.980796 + 0.195034i 0.0624817π0.0624817\pi
164164 9.97836 4.16765i 0.779179 0.325439i
165165 4.63592i 0.360906i
166166 6.90209 + 1.36235i 0.535706 + 0.105739i
167167 −9.80242 9.80242i −0.758534 0.758534i 0.217521 0.976056i 0.430203π-0.430203\pi
−0.976056 + 0.217521i 0.930203π0.930203\pi
168168 −3.60116 + 5.44141i −0.277835 + 0.419814i
169169 −6.36957 11.3326i −0.489967 0.871741i
170170 −4.45809 0.879945i −0.341920 0.0674887i
171171 6.18738 + 6.18738i 0.473160 + 0.473160i
172172 11.7777 + 4.83788i 0.898041 + 0.368885i
173173 4.71685 0.358616 0.179308 0.983793i 0.442614π-0.442614\pi
0.179308 + 0.983793i 0.442614π0.442614\pi
174174 −5.10864 7.62129i −0.387285 0.577768i
175175 −3.40075 + 3.40075i −0.257072 + 0.257072i
176176 −18.4103 + 0.108470i −1.38773 + 0.00817623i
177177 3.14321 3.14321i 0.236258 0.236258i
178178 0.0519426 0.263158i 0.00389326 0.0197246i
179179 0.161126i 0.0120431i −0.999982 0.00602155i 0.998083π-0.998083\pi
0.999982 0.00602155i 0.00191673π-0.00191673\pi
180180 0.781485 + 1.87106i 0.0582485 + 0.139461i
181181 −18.7784 −1.39579 −0.697893 0.716202i 0.745879π-0.745879\pi
−0.697893 + 0.716202i 0.745879π0.745879\pi
182182 −3.37847 + 3.81915i −0.250429 + 0.283094i
183183 10.6907i 0.790280i
184184 −1.81163 8.90194i −0.133555 0.656260i
185185 −0.522182 −0.0383916
186186 −0.357466 + 1.81104i −0.0262107 + 0.132792i
187187 −23.9521 23.9521i −1.75155 1.75155i
188188 5.73474 2.39523i 0.418249 0.174690i
189189 −1.10575 1.10575i −0.0804317 0.0804317i
190190 1.93262 1.29546i 0.140207 0.0939824i
191191 7.71346i 0.558127i 0.960273 + 0.279063i 0.0900239π0.0900239\pi
−0.960273 + 0.279063i 0.909976π0.909976\pi
192192 −16.9879 + 7.21316i −1.22600 + 0.520565i
193193 −2.63668 + 2.63668i −0.189792 + 0.189792i −0.795606 0.605814i 0.792848π-0.792848\pi
0.605814 + 0.795606i 0.292848π0.292848\pi
194194 −5.83539 1.15180i −0.418957 0.0826944i
195195 0.919661 + 3.51323i 0.0658583 + 0.251588i
196196 1.85001 + 0.759920i 0.132143 + 0.0542800i
197197 −15.2705 + 15.2705i −1.08798 + 1.08798i −0.0922447 + 0.995736i 0.529404π0.529404\pi
−0.995736 + 0.0922447i 0.970596π0.970596\pi
198198 −2.92700 + 14.8291i −0.208013 + 1.05386i
199199 13.9152 0.986425 0.493213 0.869909i 0.335822π-0.335822\pi
0.493213 + 0.869909i 0.335822π0.335822\pi
200200 −13.3297 + 2.71274i −0.942556 + 0.191820i
201201 18.5923 + 18.5923i 1.31140 + 1.31140i
202202 4.66674 3.12817i 0.328350 0.220097i
203203 −1.98855 + 1.98855i −0.139569 + 0.139569i
204204 −31.4099 12.9021i −2.19913 0.903330i
205205 −2.36064 −0.164874
206206 −9.22168 + 6.18140i −0.642505 + 0.430678i
207207 −7.45836 −0.518392
208208 −13.9303 + 3.73439i −0.965895 + 0.258933i
209209 17.3436 1.19968
210210 1.18321 0.793117i 0.0816490 0.0547303i
211211 1.65051 0.113626 0.0568130 0.998385i 0.481906π-0.481906\pi
0.0568130 + 0.998385i 0.481906π0.481906\pi
212212 −24.4340 10.0367i −1.67813 0.689321i
213213 −1.29449 + 1.29449i −0.0886972 + 0.0886972i
214214 7.44326 4.98930i 0.508811 0.341062i
215215 −1.96542 1.96542i −0.134041 0.134041i
216216 −0.882047 4.33417i −0.0600157 0.294903i
217217 0.565808 0.0384095
218218 5.21049 26.3980i 0.352899 1.78790i
219219 −2.50767 + 2.50767i −0.169452 + 0.169452i
220220 3.71762 + 1.52707i 0.250642 + 0.102955i
221221 −22.9031 13.4000i −1.54063 0.901383i
222222 −3.82823 0.755622i −0.256934 0.0507140i
223223 18.7648 18.7648i 1.25658 1.25658i 0.303871 0.952713i 0.401721π-0.401721\pi
0.952713 0.303871i 0.0982792π-0.0982792\pi
224224 3.17733 + 4.68023i 0.212295 + 0.312711i
225225 11.1681i 0.744542i
226226 −4.05720 + 2.71959i −0.269881 + 0.180904i
227227 15.4040 + 15.4040i 1.02240 + 1.02240i 0.999743 + 0.0226589i 0.00721317π0.00721317\pi
0.0226589 + 0.999743i 0.492787π0.492787\pi
228228 16.0431 6.70069i 1.06248 0.443764i
229229 −10.4687 10.4687i −0.691794 0.691794i 0.270833 0.962626i 0.412701π-0.412701\pi
−0.962626 + 0.270833i 0.912701π0.912701\pi
230230 −0.384023 + 1.94559i −0.0253218 + 0.128288i
231231 10.6182 0.698628
232232 −7.79442 + 1.58624i −0.511729 + 0.104142i
233233 12.2653i 0.803525i −0.915744 0.401762i 0.868398π-0.868398\pi
0.915744 0.401762i 0.131602π-0.131602\pi
234234 0.723600 + 11.8186i 0.0473032 + 0.772606i
235235 −1.35670 −0.0885015
236236 −1.48522 3.55597i −0.0966794 0.231474i
237237 19.8832i 1.29155i
238238 −2.01545 + 10.2109i −0.130642 + 0.661876i
239239 −2.97528 + 2.97528i −0.192455 + 0.192455i −0.796756 0.604301i 0.793452π-0.793452\pi
0.604301 + 0.796756i 0.293452π0.293452\pi
240240 4.02884 0.0237371i 0.260060 0.00153223i
241241 −12.2286 + 12.2286i −0.787716 + 0.787716i −0.981119 0.193403i 0.938047π-0.938047\pi
0.193403 + 0.981119i 0.438047π0.438047\pi
242242 8.01947 + 11.9638i 0.515511 + 0.769062i
243243 −19.7028 −1.26394
244244 8.57306 + 3.52153i 0.548834 + 0.225443i
245245 −0.308723 0.308723i −0.0197236 0.0197236i
246246 −17.3064 3.41596i −1.10341 0.217793i
247247 13.1435 3.44057i 0.836298 0.218918i
248248 1.33456 + 0.883216i 0.0847443 + 0.0560843i
249249 −8.11510 8.11510i −0.514273 0.514273i
250250 5.94211 + 1.17286i 0.375812 + 0.0741784i
251251 18.9930i 1.19883i −0.800439 0.599415i 0.795400π-0.795400\pi
0.800439 0.599415i 0.204600π-0.204600\pi
252252 4.28553 1.78993i 0.269963 0.112755i
253253 −10.4531 + 10.4531i −0.657181 + 0.657181i
254254 −20.6752 + 13.8588i −1.29728 + 0.869580i
255255 5.24158 + 5.24158i 0.328240 + 0.328240i
256256 0.188531 + 15.9989i 0.0117832 + 0.999931i
257257 14.7617i 0.920811i 0.887709 + 0.460406i 0.152296π0.152296\pi
−0.887709 + 0.460406i 0.847704π0.847704\pi
258258 −11.5649 17.2530i −0.719997 1.07412i
259259 1.19602i 0.0743171i
260260 3.12026 + 0.419769i 0.193510 + 0.0260330i
261261 6.53045i 0.404224i
262262 18.5830 12.4564i 1.14806 0.769559i
263263 21.2125i 1.30802i −0.756486 0.654010i 0.773085π-0.773085\pi
0.756486 0.654010i 0.226915π-0.226915\pi
264264 25.0449 + 16.5749i 1.54141 + 1.02011i
265265 4.07746 + 4.07746i 0.250477 + 0.250477i
266266 −2.96715 4.42653i −0.181928 0.271408i
267267 −0.309407 + 0.309407i −0.0189354 + 0.0189354i
268268 21.0337 8.78514i 1.28484 0.536638i
269269 5.87515i 0.358214i −0.983830 0.179107i 0.942679π-0.942679\pi
0.983830 0.179107i 0.0573209π-0.0573209\pi
270270 −0.186973 + 0.947267i −0.0113788 + 0.0576488i
271271 21.5454 + 21.5454i 1.30879 + 1.30879i 0.922291 + 0.386497i 0.126315π0.126315\pi
0.386497 + 0.922291i 0.373685π0.373685\pi
272272 −20.6929 + 20.9382i −1.25469 + 1.26956i
273273 8.04680 2.10642i 0.487015 0.127486i
274274 4.74499 24.0397i 0.286655 1.45229i
275275 15.6525 + 15.6525i 0.943878 + 0.943878i
276276 −5.63072 + 13.7078i −0.338929 + 0.825114i
277277 −7.55761 −0.454092 −0.227046 0.973884i 0.572907π-0.572907\pi
−0.227046 + 0.973884i 0.572907π0.572907\pi
278278 23.5435 15.7815i 1.41204 0.946509i
279279 0.929064 0.929064i 0.0556216 0.0556216i
280280 −0.246265 1.21009i −0.0147171 0.0723165i
281281 16.6452 16.6452i 0.992969 0.992969i −0.00700631 0.999975i 0.502230π-0.502230\pi
0.999975 + 0.00700631i 0.00223020π0.00223020\pi
282282 −9.94627 1.96321i −0.592292 0.116908i
283283 4.26888i 0.253759i −0.991918 0.126879i 0.959504π-0.959504\pi
0.991918 0.126879i 0.0404961π-0.0404961\pi
284284 0.611669 + 1.46448i 0.0362959 + 0.0869010i
285285 −3.79540 −0.224820
286286 17.5782 + 15.5499i 1.03942 + 0.919487i
287287 5.40687i 0.319158i
288288 12.9022 + 2.46777i 0.760271 + 0.145415i
289289 −37.1626 −2.18603
290290 1.70353 + 0.336246i 0.100035 + 0.0197451i
291291 6.86093 + 6.86093i 0.402195 + 0.402195i
292292 1.18491 + 2.83697i 0.0693418 + 0.166021i
293293 20.7876 + 20.7876i 1.21442 + 1.21442i 0.969557 + 0.244867i 0.0787442π0.0787442\pi
0.244867 + 0.969557i 0.421256π0.421256\pi
294294 −1.81658 2.71005i −0.105945 0.158053i
295295 0.841256i 0.0489798i
296296 −1.86697 + 2.82102i −0.108515 + 0.163968i
297297 −5.08940 + 5.08940i −0.295317 + 0.295317i
298298 4.50708 22.8344i 0.261088 1.32276i
299299 −5.84800 + 9.99532i −0.338199 + 0.578044i
300300 20.5261 + 8.43143i 1.18507 + 0.486789i
301301 −4.50165 + 4.50165i −0.259471 + 0.259471i
302302 26.0064 + 5.13318i 1.49650 + 0.295381i
303303 −9.16482 −0.526505
304304 −0.0888037 15.0724i −0.00509324 0.864461i
305305 −1.43064 1.43064i −0.0819184 0.0819184i
306306 13.4571 + 20.0759i 0.769290 + 1.14766i
307307 −13.7067 + 13.7067i −0.782282 + 0.782282i −0.980215 0.197933i 0.936577π-0.936577\pi
0.197933 + 0.980215i 0.436577π0.436577\pi
308308 3.49765 8.51493i 0.199297 0.485183i
309309 18.1101 1.03025
310310 −0.194519 0.290192i −0.0110479 0.0164818i
311311 11.5656 0.655824 0.327912 0.944708i 0.393655π-0.393655\pi
0.327912 + 0.944708i 0.393655π0.393655\pi
312312 22.2678 + 7.59257i 1.26067 + 0.429845i
313313 24.8146 1.40260 0.701302 0.712865i 0.252603π-0.252603\pi
0.701302 + 0.712865i 0.252603π0.252603\pi
314314 −16.5537 24.6955i −0.934178 1.39365i
315315 −1.01385 −0.0571242
316316 −15.9447 6.54954i −0.896959 0.368441i
317317 1.66646 1.66646i 0.0935974 0.0935974i −0.658758 0.752355i 0.728918π-0.728918\pi
0.752355 + 0.658758i 0.228918π0.228918\pi
318318 23.9925 + 35.7930i 1.34543 + 2.00717i
319319 9.15260 + 9.15260i 0.512447 + 0.512447i
320320 1.30807 3.23861i 0.0731231 0.181044i
321321 −14.6175 −0.815871
322322 4.45623 + 0.879578i 0.248336 + 0.0490169i
323323 19.6094 19.6094i 1.09110 1.09110i
324324 −8.03544 + 19.5621i −0.446413 + 1.08678i
325325 14.9670 + 8.75679i 0.830219 + 0.485739i
326326 −3.88528 + 19.6841i −0.215186 + 1.09020i
327327 −31.0374 + 31.0374i −1.71637 + 1.71637i
328328 −8.44003 + 12.7530i −0.466023 + 0.704169i
329329 3.10743i 0.171318i
330330 −3.65044 5.44589i −0.200950 0.299786i
331331 −5.45988 5.45988i −0.300102 0.300102i 0.540952 0.841054i 0.318064π-0.318064\pi
−0.841054 + 0.540952i 0.818064π0.818064\pi
332332 −9.18075 + 3.83452i −0.503859 + 0.210446i
333333 1.96388 + 1.96388i 0.107620 + 0.107620i
334334 19.2338 + 3.79639i 1.05242 + 0.207729i
335335 −4.97607 −0.271872
336336 −0.0543682 9.22776i −0.00296603 0.503416i
337337 9.11530i 0.496542i −0.968691 0.248271i 0.920138π-0.920138\pi
0.968691 0.248271i 0.0798624π-0.0798624\pi
338338 16.4061 + 8.29707i 0.892372 + 0.451301i
339339 7.96778 0.432750
340340 5.92989 2.47673i 0.321593 0.134320i
341341 2.60422i 0.141026i
342342 −12.1405 2.39631i −0.656484 0.129578i
343343 −0.707107 + 0.707107i −0.0381802 + 0.0381802i
344344 −17.6449 + 3.59092i −0.951351 + 0.193609i
345345 2.28752 2.28752i 0.123156 0.123156i
346346 −5.54097 + 3.71417i −0.297884 + 0.199675i
347347 −25.5760 −1.37299 −0.686496 0.727134i 0.740852π-0.740852\pi
−0.686496 + 0.727134i 0.740852π0.740852\pi
348348 12.0024 + 4.93018i 0.643396 + 0.264286i
349349 18.6586 + 18.6586i 0.998772 + 0.998772i 0.999999 0.00122768i 0.000390781π-0.000390781\pi
−0.00122768 + 0.999999i 0.500391π0.500391\pi
350350 1.31708 6.67275i 0.0704008 0.356673i
351351 −2.84727 + 4.86651i −0.151976 + 0.259755i
352352 21.5415 14.6242i 1.14816 0.779471i
353353 −21.4724 21.4724i −1.14286 1.14286i −0.987925 0.154934i 0.950484π-0.950484\pi
−0.154934 0.987925i 0.549516π-0.549516\pi
354354 −1.21734 + 6.16742i −0.0647007 + 0.327795i
355355 0.346461i 0.0183882i
356356 0.146200 + 0.350038i 0.00774858 + 0.0185520i
357357 12.0054 12.0054i 0.635396 0.635396i
358358 0.126875 + 0.189277i 0.00670553 + 0.0100036i
359359 −6.38497 6.38497i −0.336986 0.336986i 0.518246 0.855232i 0.326585π-0.326585\pi
−0.855232 + 0.518246i 0.826585π0.826585\pi
360360 −2.39135 1.58261i −0.126035 0.0834107i
361361 4.80093i 0.252681i
362362 22.0593 14.7866i 1.15941 0.777166i
363363 23.4952i 1.23318i
364364 0.961450 7.14672i 0.0503937 0.374590i
365365 0.671158i 0.0351300i
366366 −8.41815 12.5586i −0.440024 0.656447i
367367 7.32743i 0.382489i −0.981542 0.191244i 0.938748π-0.938748\pi
0.981542 0.191244i 0.0612523π-0.0612523\pi
368368 9.13778 + 9.03073i 0.476339 + 0.470759i
369369 8.87815 + 8.87815i 0.462178 + 0.462178i
370370 0.613416 0.411180i 0.0318900 0.0213762i
371371 9.33913 9.33913i 0.484863 0.484863i
372372 −1.00614 2.40894i −0.0521659 0.124898i
373373 20.8485i 1.07950i 0.841827 + 0.539748i 0.181480π0.181480\pi
−0.841827 + 0.539748i 0.818520π0.818520\pi
374374 46.9974 + 9.27641i 2.43018 + 0.479672i
375375 −6.98641 6.98641i −0.360777 0.360777i
376376 −4.85064 + 7.32940i −0.250153 + 0.377985i
377377 8.75178 + 5.12044i 0.450739 + 0.263716i
378378 2.16965 + 0.428248i 0.111595 + 0.0220267i
379379 −14.8530 14.8530i −0.762949 0.762949i 0.213905 0.976854i 0.431382π-0.431382\pi
−0.976854 + 0.213905i 0.931382π0.931382\pi
380380 −1.25021 + 3.04359i −0.0641342 + 0.156133i
381381 40.6032 2.08017
382382 −6.07378 9.06114i −0.310762 0.463608i
383383 −0.695732 + 0.695732i −0.0355503 + 0.0355503i −0.724658 0.689108i 0.758002π-0.758002\pi
0.689108 + 0.724658i 0.258002π0.258002\pi
384384 14.2761 21.8501i 0.728526 1.11503i
385385 −1.42094 + 1.42094i −0.0724180 + 0.0724180i
386386 1.02116 5.17354i 0.0519758 0.263326i
387387 14.7835i 0.751490i
388388 7.76189 3.24190i 0.394050 0.164583i
389389 34.6577 1.75722 0.878608 0.477543i 0.158473π-0.158473\pi
0.878608 + 0.477543i 0.158473π0.158473\pi
390390 −3.84675 3.40289i −0.194788 0.172312i
391391 23.6375i 1.19540i
392392 −2.77161 + 0.564051i −0.139988 + 0.0284889i
393393 −36.4945 −1.84090
394394 5.91414 29.9630i 0.297950 1.50951i
395395 2.66080 + 2.66080i 0.133879 + 0.133879i
396396 −8.23845 19.7248i −0.413997 0.991209i
397397 15.8377 + 15.8377i 0.794871 + 0.794871i 0.982282 0.187411i 0.0600095π-0.0600095\pi
−0.187411 + 0.982282i 0.560009π0.560009\pi
398398 −16.3465 + 10.9572i −0.819375 + 0.549236i
399399 8.69308i 0.435198i
400400 13.5226 13.6829i 0.676130 0.684145i
401401 4.26188 4.26188i 0.212828 0.212828i −0.592640 0.805468i 0.701914π-0.701914\pi
0.805468 + 0.592640i 0.201914π0.201914\pi
402402 −36.4807 7.20061i −1.81949 0.359134i
403403 −0.516618 1.97355i −0.0257346 0.0983096i
404404 −3.01890 + 7.34942i −0.150196 + 0.365647i
405405 3.26445 3.26445i 0.162212 0.162212i
406406 0.770147 3.90182i 0.0382218 0.193644i
407407 5.50486 0.272866
408408 47.0572 9.57662i 2.32968 0.474113i
409409 4.64032 + 4.64032i 0.229449 + 0.229449i 0.812463 0.583013i 0.198126π-0.198126\pi
−0.583013 + 0.812463i 0.698126π0.698126\pi
410410 2.77308 1.85883i 0.136953 0.0918010i
411411 −28.2645 + 28.2645i −1.39419 + 1.39419i
412412 5.96547 14.5228i 0.293898 0.715486i
413413 1.92683 0.0948133
414414 8.76146 5.87291i 0.430602 0.288638i
415415 2.17194 0.106617
416416 13.4237 15.3560i 0.658149 0.752888i
417417 −46.2361 −2.26419
418418 −20.3738 + 13.6568i −0.996514 + 0.667974i
419419 10.1698 0.496830 0.248415 0.968654i 0.420090π-0.420090\pi
0.248415 + 0.968654i 0.420090π0.420090\pi
420420 −0.765412 + 1.86338i −0.0373483 + 0.0909234i
421421 11.3830 11.3830i 0.554774 0.554774i −0.373041 0.927815i 0.621685π-0.621685\pi
0.927815 + 0.373041i 0.121685π0.121685\pi
422422 −1.93889 + 1.29966i −0.0943835 + 0.0632663i
423423 5.10243 + 5.10243i 0.248089 + 0.248089i
424424 36.6062 7.44972i 1.77775 0.361790i
425425 35.3947 1.71690
426426 0.501345 2.53998i 0.0242903 0.123062i
427427 −3.27679 + 3.27679i −0.158575 + 0.158575i
428428 −4.81502 + 11.7220i −0.232743 + 0.566606i
429429 −9.69511 37.0366i −0.468084 1.78815i
430430 3.85644 + 0.761190i 0.185974 + 0.0367078i
431431 −10.0473 + 10.0473i −0.483959 + 0.483959i −0.906393 0.422434i 0.861176π-0.861176\pi
0.422434 + 0.906393i 0.361176π0.361176\pi
432432 4.44899 + 4.39688i 0.214052 + 0.211545i
433433 15.3538i 0.737856i −0.929458 0.368928i 0.879725π-0.879725\pi
0.929458 0.368928i 0.120275π-0.120275\pi
434434 −0.664664 + 0.445532i −0.0319049 + 0.0213862i
435435 −2.00292 2.00292i −0.0960327 0.0960327i
436436 14.6657 + 35.1131i 0.702358 + 1.68161i
437437 −8.55789 8.55789i −0.409379 0.409379i
438438 0.971197 4.92040i 0.0464056 0.235106i
439439 −3.80035 −0.181381 −0.0906905 0.995879i 0.528907π-0.528907\pi
−0.0906905 + 0.995879i 0.528907π0.528907\pi
440440 −5.56961 + 1.13347i −0.265521 + 0.0540361i
441441 2.32216i 0.110579i
442442 37.4562 2.29328i 1.78161 0.109080i
443443 4.80162 0.228132 0.114066 0.993473i 0.463612π-0.463612\pi
0.114066 + 0.993473i 0.463612π0.463612\pi
444444 5.09208 2.12681i 0.241660 0.100934i
445445 0.0828104i 0.00392559i
446446 −7.26744 + 36.8192i −0.344123 + 1.74344i
447447 −26.8474 + 26.8474i −1.26984 + 1.26984i
448448 −7.41780 2.99603i −0.350458 0.141549i
449449 −28.3112 + 28.3112i −1.33609 + 1.33609i −0.436271 + 0.899815i 0.643701π0.643701\pi
−0.899815 + 0.436271i 0.856299π0.856299\pi
450450 −8.79408 13.1194i −0.414557 0.618454i
451451 24.8859 1.17183
452452 2.62459 6.38949i 0.123450 0.300536i
453453 −30.5768 30.5768i −1.43663 1.43663i
454454 −30.2249 5.96585i −1.41853 0.279991i
455455 −0.794949 + 1.35872i −0.0372678 + 0.0636976i
456456 −13.5697 + 20.5041i −0.635462 + 0.960194i
457457 −1.37861 1.37861i −0.0644889 0.0644889i 0.674127 0.738616i 0.264520π-0.264520\pi
−0.738616 + 0.674127i 0.764520π0.764520\pi
458458 20.5412 + 4.05445i 0.959825 + 0.189452i
459459 11.5086i 0.537176i
460460 −1.08089 2.58791i −0.0503967 0.120662i
461461 −14.0302 + 14.0302i −0.653452 + 0.653452i −0.953823 0.300371i 0.902890π-0.902890\pi
0.300371 + 0.953823i 0.402890π0.402890\pi
462462 −12.4734 + 8.36107i −0.580316 + 0.388992i
463463 −17.3484 17.3484i −0.806249 0.806249i 0.177815 0.984064i 0.443097π-0.443097\pi
−0.984064 + 0.177815i 0.943097π0.943097\pi
464464 7.90719 8.00092i 0.367082 0.371433i
465465 0.569897i 0.0264283i
466466 9.65800 + 14.4082i 0.447398 + 0.667448i
467467 4.11535i 0.190436i −0.995456 0.0952178i 0.969645π-0.969645\pi
0.995456 0.0952178i 0.0303547π-0.0303547\pi
468468 −10.1563 13.3137i −0.469475 0.615427i
469469 11.3973i 0.526280i
470470 1.59374 1.06830i 0.0735138 0.0492771i
471471 48.4985i 2.23469i
472472 4.54477 + 3.00775i 0.209190 + 0.138443i
473473 20.7195 + 20.7195i 0.952686 + 0.952686i
474474 15.6566 + 23.3572i 0.719130 + 1.07283i
475475 −12.8146 + 12.8146i −0.587973 + 0.587973i
476476 −5.67277 13.5820i −0.260011 0.622529i
477477 30.6699i 1.40428i
478478 1.15230 5.83792i 0.0527048 0.267020i
479479 1.20602 + 1.20602i 0.0551044 + 0.0551044i 0.734122 0.679018i 0.237594π-0.237594\pi
−0.679018 + 0.734122i 0.737594π0.737594\pi
480480 −4.71405 + 3.20030i −0.215166 + 0.146073i
481481 4.17175 1.09204i 0.190215 0.0497928i
482482 4.73604 23.9943i 0.215721 1.09291i
483483 −5.23939 5.23939i −0.238400 0.238400i
484484 −18.8412 7.73934i −0.856419 0.351788i
485485 −1.83628 −0.0833810
486486 23.1452 15.5145i 1.04989 0.703753i
487487 6.22727 6.22727i 0.282185 0.282185i −0.551795 0.833980i 0.686057π-0.686057\pi
0.833980 + 0.551795i 0.186057π0.186057\pi
488488 −12.8439 + 2.61386i −0.581414 + 0.118324i
489489 23.1435 23.1435i 1.04659 1.04659i
490490 0.605758 + 0.119566i 0.0273654 + 0.00540142i
491491 6.88539i 0.310733i 0.987857 + 0.155367i 0.0496559π0.0496559\pi
−0.987857 + 0.155367i 0.950344π0.950344\pi
492492 23.0199 9.61469i 1.03782 0.433464i
493493 20.6967 0.932132
494494 −12.7306 + 14.3912i −0.572779 + 0.647490i
495495 4.66642i 0.209740i
496496 −2.26319 + 0.0133343i −0.101620 + 0.000598727i
497497 −0.793544 −0.0355953
498498 15.9230 + 3.14290i 0.713526 + 0.140837i
499499 −10.0565 10.0565i −0.450192 0.450192i 0.445226 0.895418i 0.353123π-0.353123\pi
−0.895418 + 0.445226i 0.853123π0.853123\pi
500500 −7.90384 + 3.30119i −0.353471 + 0.147634i
501501 −22.6140 22.6140i −1.01032 1.01032i
502502 14.9556 + 22.3114i 0.667501 + 0.995808i
503503 30.2262i 1.34772i 0.738858 + 0.673861i 0.235365π0.235365\pi
−0.738858 + 0.673861i 0.764635π0.764635\pi
504504 −3.62485 + 5.47721i −0.161464 + 0.243974i
505505 1.22645 1.22645i 0.0545762 0.0545762i
506506 4.04839 20.5105i 0.179973 0.911802i
507507 −14.6945 26.1442i −0.652604 1.16110i
508508 13.3747 32.5604i 0.593407 1.44463i
509509 7.53053 7.53053i 0.333785 0.333785i −0.520237 0.854022i 0.674156π-0.674156\pi
0.854022 + 0.520237i 0.174156π0.174156\pi
510510 −10.2847 2.03002i −0.455415 0.0898906i
511511 −1.53724 −0.0680034
512512 −12.8194 18.6457i −0.566543 0.824032i
513513 −4.16666 4.16666i −0.183962 0.183962i
514514 −11.6238 17.3409i −0.512702 0.764872i
515515 −2.42351 + 2.42351i −0.106793 + 0.106793i
516516 27.1709 + 11.1609i 1.19613 + 0.491331i
517517 14.3024 0.629019
518518 −0.941777 1.40499i −0.0413793 0.0617315i
519519 10.8817 0.477653
520520 −3.99596 + 1.96386i −0.175234 + 0.0861211i
521521 −19.1146 −0.837426 −0.418713 0.908119i 0.637519π-0.637519\pi
−0.418713 + 0.908119i 0.637519π0.637519\pi
522522 −5.14224 7.67143i −0.225070 0.335769i
523523 −33.5877 −1.46869 −0.734344 0.678778i 0.762510π-0.762510\pi
−0.734344 + 0.678778i 0.762510π0.762510\pi
524524 −12.0213 + 29.2655i −0.525152 + 1.27847i
525525 −7.84545 + 7.84545i −0.342404 + 0.342404i
526526 16.7033 + 24.9187i 0.728298 + 1.08651i
527527 −2.94445 2.94445i −0.128262 0.128262i
528528 −42.4722 + 0.250238i −1.84836 + 0.0108902i
529529 −12.6842 −0.551486
530530 −8.00057 1.57916i −0.347522 0.0685945i
531531 3.16389 3.16389i 0.137301 0.137301i
532532 6.97113 + 2.86351i 0.302237 + 0.124149i
533533 18.8593 4.93681i 0.816887 0.213837i
534534 0.119831 0.607101i 0.00518558 0.0262718i
535535 1.95614 1.95614i 0.0845711 0.0845711i
536536 −17.7910 + 26.8826i −0.768456 + 1.16115i
537537 0.371714i 0.0160406i
538538 4.62625 + 6.90164i 0.199452 + 0.297551i
539539 3.25457 + 3.25457i 0.140184 + 0.140184i
540540 −0.526262 1.26000i −0.0226467 0.0542217i
541541 −25.7532 25.7532i −1.10722 1.10722i −0.993515 0.113701i 0.963730π-0.963730\pi
−0.113701 0.993515i 0.536270π-0.536270\pi
542542 −42.2751 8.34433i −1.81587 0.358419i
543543 −43.3214 −1.85910
544544 7.82102 40.8905i 0.335323 1.75317i
545545 8.30692i 0.355829i
546546 −7.79407 + 8.81071i −0.333555 + 0.377063i
547547 45.4367 1.94273 0.971366 0.237589i 0.0763570π-0.0763570\pi
0.971366 + 0.237589i 0.0763570π0.0763570\pi
548548 13.3554 + 31.9761i 0.570516 + 1.36595i
549549 10.7610i 0.459270i
550550 −30.7123 6.06205i −1.30958 0.258487i
551551 −7.49318 + 7.49318i −0.319220 + 0.319220i
552552 −4.17940 20.5366i −0.177887 0.874095i
553553 6.09436 6.09436i 0.259158 0.259158i
554554 8.87805 5.95106i 0.377192 0.252836i
555555 −1.20466 −0.0511351
556556 −15.2302 + 37.0775i −0.645904 + 1.57244i
557557 −16.3395 16.3395i −0.692326 0.692326i 0.270418 0.962743i 0.412838π-0.412838\pi
−0.962743 + 0.270418i 0.912838π0.912838\pi
558558 −0.359818 + 1.82296i −0.0152323 + 0.0771719i
559559 19.8122 + 11.5916i 0.837966 + 0.490272i
560560 1.24215 + 1.22759i 0.0524902 + 0.0518753i
561561 −55.2569 55.2569i −2.33295 2.33295i
562562 −6.44653 + 32.6603i −0.271931 + 1.37769i
563563 0.0579692i 0.00244311i 0.999999 + 0.00122156i 0.000388833π0.000388833\pi
−0.999999 + 0.00122156i 0.999611π0.999611\pi
564564 13.2299 5.52574i 0.557081 0.232676i
565565 −1.06626 + 1.06626i −0.0448578 + 0.0448578i
566566 3.36143 + 5.01473i 0.141291 + 0.210785i
567567 −7.47699 7.47699i −0.314004 0.314004i
568568 −1.87171 1.23871i −0.0785352 0.0519750i
569569 17.8855i 0.749801i 0.927065 + 0.374900i 0.122323π0.122323\pi
−0.927065 + 0.374900i 0.877677π0.877677\pi
570570 4.45852 2.98860i 0.186747 0.125179i
571571 27.9419i 1.16933i −0.811275 0.584665i 0.801226π-0.801226\pi
0.811275 0.584665i 0.198774π-0.198774\pi
572572 −32.8939 4.42522i −1.37536 0.185028i
573573 17.7948i 0.743389i
574574 −4.25751 6.35154i −0.177705 0.265108i
575575 15.4469i 0.644180i
576576 −17.0996 + 7.26061i −0.712485 + 0.302525i
577577 23.2682 + 23.2682i 0.968670 + 0.968670i 0.999524 0.0308540i 0.00982270π-0.00982270\pi
−0.0308540 + 0.999524i 0.509823π0.509823\pi
578578 43.6555 29.2628i 1.81583 1.21717i
579579 −6.08277 + 6.08277i −0.252791 + 0.252791i
580580 −2.26594 + 0.946412i −0.0940880 + 0.0392976i
581581 4.97468i 0.206384i
582582 −13.4621 2.65718i −0.558024 0.110144i
583583 −42.9848 42.9848i −1.78025 1.78025i
584584 −3.62584 2.39960i −0.150038 0.0992962i
585585 0.925712 + 3.53635i 0.0382735 + 0.146210i
586586 −40.7882 8.05084i −1.68495 0.332577i
587587 25.0160 + 25.0160i 1.03252 + 1.03252i 0.999453 + 0.0330681i 0.0105278π0.0105278\pi
0.0330681 + 0.999453i 0.489472π0.489472\pi
588588 4.26793 + 1.75312i 0.176006 + 0.0722975i
589589 2.13206 0.0878499
590590 −0.662427 0.988237i −0.0272717 0.0406851i
591591 −35.2288 + 35.2288i −1.44912 + 1.44912i
592592 −0.0281864 4.78400i −0.00115845 0.196621i
593593 32.7412 32.7412i 1.34452 1.34452i 0.453021 0.891500i 0.350346π-0.350346\pi
0.891500 0.453021i 0.149654π-0.149654\pi
594594 1.97108 9.98612i 0.0808743 0.409736i
595595 3.21317i 0.131727i
596596 12.6858 + 30.3729i 0.519631 + 1.24412i
597597 32.1022 1.31386
598598 −1.00083 16.3465i −0.0409269 0.668460i
599599 4.75407i 0.194246i −0.995272 0.0971230i 0.969036π-0.969036\pi
0.995272 0.0971230i 0.0309640π-0.0309640\pi
600600 −30.7515 + 6.25823i −1.25542 + 0.255491i
601601 19.9892 0.815377 0.407688 0.913121i 0.366335π-0.366335\pi
0.407688 + 0.913121i 0.366335π0.366335\pi
602602 1.74345 8.83289i 0.0710577 0.360002i
603603 18.7146 + 18.7146i 0.762116 + 0.762116i
604604 −34.5921 + 14.4481i −1.40753 + 0.587883i
605605 3.14416 + 3.14416i 0.127828 + 0.127828i
606606 10.7661 7.21662i 0.437342 0.293155i
607607 2.88939i 0.117277i 0.998279 + 0.0586384i 0.0186759π0.0186759\pi
−0.998279 + 0.0586384i 0.981324π0.981324\pi
608608 11.9727 + 17.6359i 0.485558 + 0.715229i
609609 −4.58754 + 4.58754i −0.185897 + 0.185897i
610610 2.80713 + 0.554076i 0.113657 + 0.0224339i
611611 10.8388 2.83727i 0.438490 0.114784i
612612 −31.6165 12.9870i −1.27802 0.524969i
613613 −8.92779 + 8.92779i −0.360590 + 0.360590i −0.864030 0.503440i 0.832068π-0.832068\pi
0.503440 + 0.864030i 0.332068π0.332068\pi
614614 5.30848 26.8945i 0.214233 1.08537i
615615 −5.44595 −0.219602
616616 2.59613 + 12.7568i 0.104601 + 0.513985i
617617 2.43211 + 2.43211i 0.0979131 + 0.0979131i 0.754367 0.656453i 0.227944π-0.227944\pi
−0.656453 + 0.754367i 0.727944π0.727944\pi
618618 −21.2742 + 14.2604i −0.855775 + 0.573636i
619619 −20.5450 + 20.5450i −0.825774 + 0.825774i −0.986929 0.161155i 0.948478π-0.948478\pi
0.161155 + 0.986929i 0.448478π0.448478\pi
620620 0.457010 + 0.187724i 0.0183540 + 0.00753919i
621621 5.02256 0.201548
622622 −13.5863 + 9.10704i −0.544760 + 0.365159i
623623 −0.189671 −0.00759902
624624 −32.1370 + 8.61516i −1.28651 + 0.344882i
625625 −22.1770 −0.887082
626626 −29.1501 + 19.5397i −1.16507 + 0.780961i
627627 40.0112 1.59789
628628 38.8918 + 15.9754i 1.55195 + 0.637490i
629629 6.22405 6.22405i 0.248169 0.248169i
630630 1.19099 0.798335i 0.0474502 0.0318064i
631631 18.4822 + 18.4822i 0.735766 + 0.735766i 0.971756 0.235989i 0.0758330π-0.0758330\pi
−0.235989 + 0.971756i 0.575833π0.575833\pi
632632 23.8878 4.86140i 0.950205 0.193376i
633633 3.80770 0.151343
634634 −0.645403 + 3.26982i −0.0256322 + 0.129861i
635635 −5.43357 + 5.43357i −0.215625 + 0.215625i
636636 −56.3687 23.1544i −2.23517 0.918131i
637637 3.11204 + 1.82077i 0.123303 + 0.0721417i
638638 −17.9587 3.54472i −0.710992 0.140337i
639639 −1.30301 + 1.30301i −0.0515462 + 0.0515462i
640640 1.01356 + 4.83446i 0.0400645 + 0.191099i
641641 47.8020i 1.88807i 0.329851 + 0.944033i 0.393001π0.393001\pi
−0.329851 + 0.944033i 0.606999π0.606999\pi
642642 17.1715 11.5102i 0.677704 0.454272i
643643 17.7744 + 17.7744i 0.700955 + 0.700955i 0.964616 0.263660i 0.0849298π-0.0849298\pi
−0.263660 + 0.964616i 0.584930π0.584930\pi
644644 −5.92741 + 2.47570i −0.233573 + 0.0975561i
645645 −4.53419 4.53419i −0.178534 0.178534i
646646 −7.59455 + 38.4765i −0.298803 + 1.51384i
647647 37.3312 1.46764 0.733820 0.679344i 0.237736π-0.237736\pi
0.733820 + 0.679344i 0.237736π0.237736\pi
648648 −5.96431 29.3072i −0.234300 1.15130i
649649 8.86855i 0.348121i
650650 −24.4773 + 1.49864i −0.960078 + 0.0587814i
651651 1.30531 0.0511590
652652 −10.9357 26.1826i −0.428274 1.02539i
653653 44.9715i 1.75987i −0.475093 0.879936i 0.657586π-0.657586\pi
0.475093 0.879936i 0.342414π-0.342414\pi
654654 12.0205 60.8998i 0.470039 2.38137i
655655 4.88373 4.88373i 0.190823 0.190823i
656656 −0.127423 21.6271i −0.00497502 0.844397i
657657 −2.52416 + 2.52416i −0.0984771 + 0.0984771i
658658 −2.44687 3.65035i −0.0953889 0.142305i
659659 10.4352 0.406496 0.203248 0.979127i 0.434850π-0.434850\pi
0.203248 + 0.979127i 0.434850π0.434850\pi
660660 8.57647 + 3.52293i 0.333839 + 0.137130i
661661 −4.79732 4.79732i −0.186594 0.186594i 0.607628 0.794222i 0.292121π-0.292121\pi
−0.794222 + 0.607628i 0.792121π0.792121\pi
662662 10.7131 + 2.11456i 0.416375 + 0.0821848i
663663 −52.8370 30.9136i −2.05202 1.20058i
664664 7.76539 11.7336i 0.301355 0.455353i
665665 −1.16332 1.16332i −0.0451115 0.0451115i
666666 −3.85341 0.760593i −0.149317 0.0294724i
667667 9.03240i 0.349736i
668668 −25.5836 + 10.6855i −0.989859 + 0.413433i
669669 43.2900 43.2900i 1.67369 1.67369i
670670 5.84548 3.91829i 0.225831 0.151377i
671671 15.0819 + 15.0819i 0.582230 + 0.582230i
672672 7.33005 + 10.7972i 0.282763 + 0.416511i
673673 7.35473i 0.283504i 0.989902 + 0.141752i 0.0452735π0.0452735\pi
−0.989902 + 0.141752i 0.954726π0.954726\pi
674674 7.17763 + 10.7079i 0.276472 + 0.412453i
675675 7.52077i 0.289474i
676676 −25.8058 + 3.17184i −0.992531 + 0.121994i
677677 17.2816i 0.664185i −0.943247 0.332093i 0.892245π-0.892245\pi
0.943247 0.332093i 0.107755π-0.107755\pi
678678 −9.35988 + 6.27403i −0.359464 + 0.240953i
679679 4.20586i 0.161406i
680680 −5.01570 + 7.57881i −0.192343 + 0.290634i
681681 35.5368 + 35.5368i 1.36177 + 1.36177i
682682 2.05063 + 3.05922i 0.0785226 + 0.117144i
683683 17.4628 17.4628i 0.668195 0.668195i −0.289103 0.957298i 0.593357π-0.593357\pi
0.957298 + 0.289103i 0.0933569π0.0933569\pi
684684 16.1486 6.74477i 0.617457 0.257893i
685685 7.56478i 0.289035i
686686 0.273856 1.38744i 0.0104559 0.0529729i
687687 −24.1512 24.1512i −0.921424 0.921424i
688688 17.9002 18.1124i 0.682439 0.690529i
689689 −41.1023 24.0479i −1.56587 0.916152i
690690 −0.885934 + 4.48843i −0.0337269 + 0.170872i
691691 13.0662 + 13.0662i 0.497061 + 0.497061i 0.910522 0.413461i 0.135680π-0.135680\pi
−0.413461 + 0.910522i 0.635680π0.635680\pi
692692 3.58443 8.72620i 0.136260 0.331720i
693693 10.6881 0.406007
694694 30.0446 20.1392i 1.14048 0.764474i
695695 6.18737 6.18737i 0.234700 0.234700i
696696 −17.9816 + 3.65943i −0.681590 + 0.138710i
697697 28.1372 28.1372i 1.06577 1.06577i
698698 −36.6108 7.22630i −1.38574 0.273520i
699699 28.2957i 1.07024i
700700 3.70710 + 8.87569i 0.140115 + 0.335470i
701701 −14.6400 −0.552944 −0.276472 0.961022i 0.589165π-0.589165\pi
−0.276472 + 0.961022i 0.589165π0.589165\pi
702702 −0.487282 7.95879i −0.0183913 0.300385i
703703 4.50680i 0.169977i
704704 −13.7897 + 34.1416i −0.519718 + 1.28676i
705705 −3.12988 −0.117878
706706 42.1318 + 8.31605i 1.58565 + 0.312979i
707707 −2.80909 2.80909i −0.105647 0.105647i
708708 −3.42637 8.20354i −0.128771 0.308308i
709709 7.27499 + 7.27499i 0.273218 + 0.273218i 0.830394 0.557176i 0.188115π-0.188115\pi
−0.557176 + 0.830394i 0.688115π0.688115\pi
710710 0.272813 + 0.406994i 0.0102385 + 0.0152742i
711711 20.0140i 0.750585i
712712 −0.447372 0.296073i −0.0167660 0.0110958i
713713 −1.28501 + 1.28501i −0.0481239 + 0.0481239i
714714 −4.64960 + 23.5564i −0.174007 + 0.881577i
715715 6.25370 + 3.65888i 0.233875 + 0.136834i
716716 −0.298084 0.122443i −0.0111399 0.00457590i
717717 −6.86390 + 6.86390i −0.256337 + 0.256337i
718718 12.5282 + 2.47284i 0.467549 + 0.0922856i
719719 22.3752 0.834454 0.417227 0.908802i 0.363002π-0.363002\pi
0.417227 + 0.908802i 0.363002π0.363002\pi
720720 4.05534 0.0238933i 0.151134 0.000890451i
721721 5.55088 + 5.55088i 0.206726 + 0.206726i
722722 3.78038 + 5.63974i 0.140691 + 0.209889i
723723 −28.2112 + 28.2112i −1.04919 + 1.04919i
724724 −14.2701 + 34.7401i −0.530343 + 1.29111i
725725 −13.5251 −0.502310
726726 18.5008 + 27.6003i 0.686628 + 1.02434i
727727 26.5309 0.983976 0.491988 0.870602i 0.336270π-0.336270\pi
0.491988 + 0.870602i 0.336270π0.336270\pi
728728 4.49808 + 9.15245i 0.166710 + 0.339212i
729729 −13.7319 −0.508587
730730 0.528487 + 0.788421i 0.0195602 + 0.0291808i
731731 46.8529 1.73292
732732 19.7779 + 8.12409i 0.731012 + 0.300275i
733733 −1.27103 + 1.27103i −0.0469465 + 0.0469465i −0.730190 0.683244i 0.760569π-0.760569\pi
0.683244 + 0.730190i 0.260569π0.260569\pi
734734 5.76981 + 8.60766i 0.212968 + 0.317714i
735735 −0.712217 0.712217i −0.0262705 0.0262705i
736736 −17.8453 3.41323i −0.657788 0.125813i
737737 52.4580 1.93231
738738 −17.4202 3.43843i −0.641247 0.126570i
739739 3.88679 3.88679i 0.142978 0.142978i −0.631995 0.774973i 0.717764π-0.717764\pi
0.774973 + 0.631995i 0.217764π0.217764\pi
740740 −0.396817 + 0.966040i −0.0145873 + 0.0355123i
741741 30.3217 7.93733i 1.11389 0.291585i
742742 −3.61696 + 18.3247i −0.132783 + 0.672721i
743743 −18.7330 + 18.7330i −0.687245 + 0.687245i −0.961622 0.274377i 0.911528π-0.911528\pi
0.274377 + 0.961622i 0.411528π0.411528\pi
744744 3.07879 + 2.03756i 0.112874 + 0.0747007i
745745 7.18549i 0.263256i
746746 −16.4167 24.4911i −0.601057 0.896683i
747747 −8.16848 8.16848i −0.298869 0.298869i
748748 −62.5131 + 26.1098i −2.28571 + 0.954668i
749749 −4.48038 4.48038i −0.163710 0.163710i
750750 13.7083 + 2.70577i 0.500558 + 0.0988009i
751751 −27.1095 −0.989241 −0.494621 0.869109i 0.664693π-0.664693\pi
−0.494621 + 0.869109i 0.664693π0.664693\pi
752752 −0.0732322 12.4295i −0.00267050 0.453257i
753753 43.8165i 1.59676i
754754 −14.3128 + 0.876311i −0.521242 + 0.0319134i
755755 8.18366 0.297834
756756 −2.88593 + 1.20536i −0.104960 + 0.0438387i
757757 4.80139i 0.174509i −0.996186 0.0872547i 0.972191π-0.972191\pi
0.996186 0.0872547i 0.0278094π-0.0278094\pi
758758 29.1438 + 5.75245i 1.05855 + 0.208938i
759759 −24.1151 + 24.1151i −0.875322 + 0.875322i
760760 −0.927966 4.55981i −0.0336609 0.165402i
761761 8.24646 8.24646i 0.298934 0.298934i −0.541662 0.840596i 0.682205π-0.682205\pi
0.840596 + 0.541662i 0.182205π0.182205\pi
762762 −47.6973 + 31.9720i −1.72789 + 1.15823i
763763 −19.0264 −0.688801
764764 14.2700 + 5.86162i 0.516269 + 0.212066i
765765 5.27606 + 5.27606i 0.190756 + 0.190756i
766766 0.269451 1.36513i 0.00973565 0.0493240i
767767 −1.75932 6.72084i −0.0635254 0.242676i
768768 0.434938 + 36.9091i 0.0156945 + 1.33184i
769769 24.0851 + 24.0851i 0.868530 + 0.868530i 0.992310 0.123780i 0.0395017π-0.0395017\pi
−0.123780 + 0.992310i 0.539502π0.539502\pi
770770 0.550319 2.78809i 0.0198321 0.100476i
771771 34.0550i 1.22646i
772772 2.87421 + 6.88154i 0.103445 + 0.247672i
773773 33.3001 33.3001i 1.19772 1.19772i 0.222874 0.974847i 0.428456π-0.428456\pi
0.974847 0.222874i 0.0715440π-0.0715440\pi
774774 −11.6410 17.3665i −0.418425 0.624225i
775775 1.92417 + 1.92417i 0.0691182 + 0.0691182i
776776 −6.56527 + 9.92024i −0.235679 + 0.356116i
777777 2.75919i 0.0989855i
778778 −40.7130 + 27.2904i −1.45963 + 0.978408i
779779 20.3740i 0.729974i
780780 7.19837 + 0.968399i 0.257743 + 0.0346742i
781781 3.65241i 0.130693i
782782 −18.6128 27.7674i −0.665592 0.992959i
783783 4.39769i 0.157160i
784784 2.81171 2.84504i 0.100418 0.101609i
785785 −6.49013 6.49013i −0.231643 0.231643i
786786 42.8707 28.7367i 1.52915 1.02500i
787787 15.9271 15.9271i 0.567741 0.567741i −0.363754 0.931495i 0.618505π-0.618505\pi
0.931495 + 0.363754i 0.118505π0.118505\pi
788788 16.6462 + 39.8550i 0.592996 + 1.41978i
789789 48.9369i 1.74220i
790790 −5.22086 1.03050i −0.185750 0.0366636i
791791 2.44218 + 2.44218i 0.0868340 + 0.0868340i
792792 25.2097 + 16.6839i 0.895787 + 0.592837i
793793 14.4214 + 8.43760i 0.512120 + 0.299628i
794794 −31.0758 6.13380i −1.10284 0.217680i
795795 9.40662 + 9.40662i 0.333619 + 0.333619i
796796 10.5745 25.7433i 0.374802 0.912446i
797797 28.8545 1.02208 0.511040 0.859557i 0.329260π-0.329260\pi
0.511040 + 0.859557i 0.329260π0.329260\pi
798798 −6.84516 10.2119i −0.242316 0.361498i
799799 16.1709 16.1709i 0.572087 0.572087i
800800 −5.11097 + 26.7216i −0.180700 + 0.944750i
801801 −0.311443 + 0.311443i −0.0110043 + 0.0110043i
802802 −1.65059 + 8.36241i −0.0582842 + 0.295287i
803803 7.07537i 0.249685i
804804 48.5244 20.2671i 1.71132 0.714767i
805805 1.40228 0.0494240
806806 2.16091 + 1.91157i 0.0761147 + 0.0673321i
807807 13.5539i 0.477118i
808808 −2.24078 11.0106i −0.0788303 0.387353i
809809 19.3562 0.680527 0.340264 0.940330i 0.389484π-0.389484\pi
0.340264 + 0.940330i 0.389484π0.389484\pi
810810 −1.26429 + 6.40532i −0.0444227 + 0.225060i
811811 −14.8791 14.8791i −0.522475 0.522475i 0.395843 0.918318i 0.370452π-0.370452\pi
−0.918318 + 0.395843i 0.870452π0.870452\pi
812812 2.16769 + 5.18997i 0.0760709 + 0.182132i
813813 49.7047 + 49.7047i 1.74322 + 1.74322i
814814 −6.46666 + 4.33467i −0.226656 + 0.151930i
815815 6.19418i 0.216973i
816816 −47.7380 + 48.3039i −1.67117 + 1.69097i
817817 −16.9630 + 16.9630i −0.593459 + 0.593459i
818818 −9.10498 1.79715i −0.318348 0.0628360i
819819 8.09974 2.12027i 0.283028 0.0740884i
820820 −1.79390 + 4.36720i −0.0626456 + 0.152509i
821821 −26.3748 + 26.3748i −0.920488 + 0.920488i −0.997064 0.0765758i 0.975601π-0.975601\pi
0.0765758 + 0.997064i 0.475601π0.475601\pi
822822 10.9466 55.4590i 0.381806 1.93436i
823823 −41.5439 −1.44813 −0.724065 0.689731i 0.757729π-0.757729\pi
−0.724065 + 0.689731i 0.757729π0.757729\pi
824824 4.42788 + 21.7575i 0.154252 + 0.757960i
825825 36.1099 + 36.1099i 1.25719 + 1.25719i
826826 −2.26348 + 1.51724i −0.0787567 + 0.0527915i
827827 −3.33553 + 3.33553i −0.115988 + 0.115988i −0.762718 0.646731i 0.776136π-0.776136\pi
0.646731 + 0.762718i 0.276136π0.276136\pi
828828 −5.66776 + 13.7980i −0.196968 + 0.479514i
829829 −50.8931 −1.76759 −0.883796 0.467873i 0.845020π-0.845020\pi
−0.883796 + 0.467873i 0.845020π0.845020\pi
830830 −2.55142 + 1.71025i −0.0885611 + 0.0593635i
831831 −17.4352 −0.604822
832832 −3.67731 + 28.6090i −0.127488 + 0.991840i
833833 7.35952 0.254992
834834 54.3143 36.4075i 1.88075 1.26069i
835835 6.05246 0.209454
836836 13.1797 32.0857i 0.455830 1.10971i
837837 −0.625644 + 0.625644i −0.0216254 + 0.0216254i
838838 −11.9467 + 8.00800i −0.412692 + 0.276632i
839839 22.3335 + 22.3335i 0.771037 + 0.771037i 0.978288 0.207251i 0.0664516π-0.0664516\pi
−0.207251 + 0.978288i 0.566452π0.566452\pi
840840 −0.568128 2.79165i −0.0196023 0.0963209i
841841 21.0913 0.727288
842842 −4.40854 + 22.3351i −0.151928 + 0.769719i
843843 38.4001 38.4001i 1.32257 1.32257i
844844 1.25426 3.05346i 0.0431734 0.105104i
845845 5.46507 + 1.53221i 0.188004 + 0.0527097i
846846 −10.0117 1.97613i −0.344210 0.0679406i
847847 7.20147 7.20147i 0.247445 0.247445i
848848 −37.1358 + 37.5760i −1.27525 + 1.29036i
849849 9.84823i 0.337990i
850850 −41.5788 + 27.8707i −1.42614 + 0.955959i
851851 −2.71628 2.71628i −0.0931130 0.0931130i
852852 1.41111 + 3.37853i 0.0483438 + 0.115747i
853853 10.7946 + 10.7946i 0.369600 + 0.369600i 0.867331 0.497732i 0.165834π-0.165834\pi
−0.497732 + 0.867331i 0.665834π0.665834\pi
854854 1.26907 6.42952i 0.0434267 0.220014i
855855 −3.82037 −0.130654
856856 −3.57395 17.5616i −0.122155 0.600242i
857857 24.6513i 0.842073i −0.907044 0.421036i 0.861666π-0.861666\pi
0.907044 0.421036i 0.138334π-0.138334\pi
858858 40.5526 + 35.8734i 1.38444 + 1.22470i
859859 50.1054 1.70958 0.854788 0.518978i 0.173687π-0.173687\pi
0.854788 + 0.518978i 0.173687π0.173687\pi
860860 −5.12961 + 2.14248i −0.174918 + 0.0730579i
861861 12.4735i 0.425097i
862862 3.89121 19.7141i 0.132535 0.671466i
863863 −1.51329 + 1.51329i −0.0515128 + 0.0515128i −0.732394 0.680881i 0.761597π-0.761597\pi
0.680881 + 0.732394i 0.261597π0.261597\pi
864864 −8.68852 1.66183i −0.295590 0.0565366i
865865 −1.45620 + 1.45620i −0.0495123 + 0.0495123i
866866 12.0900 + 18.0364i 0.410834 + 0.612901i
867867 −85.7333 −2.91166
868868 0.429969 1.04675i 0.0145941 0.0355289i
869869 −28.0502 28.0502i −0.951538 0.951538i
870870 3.93002 + 0.775713i 0.133240 + 0.0262991i
871871 39.7542 10.4065i 1.34702 0.352610i
872872 −44.8770 29.6998i −1.51973 1.00576i
873873 6.90607 + 6.90607i 0.233735 + 0.233735i
874874 16.7918 + 3.31439i 0.567991 + 0.112111i
875875 4.28277i 0.144784i
876876 2.73357 + 6.54483i 0.0923588 + 0.221129i
877877 −15.4722 + 15.4722i −0.522459 + 0.522459i −0.918313 0.395855i 0.870448π-0.870448\pi
0.395855 + 0.918313i 0.370448π0.370448\pi
878878 4.46434 2.99250i 0.150664 0.100992i
879879 47.9565 + 47.9565i 1.61753 + 1.61753i
880880 5.65019 5.71716i 0.190468 0.192726i
881881 15.9804i 0.538393i −0.963085 0.269196i 0.913242π-0.913242\pi
0.963085 0.269196i 0.0867581π-0.0867581\pi
882882 −1.82853 2.72788i −0.0615697 0.0918524i
883883 46.3824i 1.56089i −0.625222 0.780447i 0.714992π-0.714992\pi
0.625222 0.780447i 0.285008π-0.285008\pi
884884 −42.1947 + 32.1879i −1.41916 + 1.08260i
885885 1.94076i 0.0652379i
886886 −5.64055 + 3.78092i −0.189498 + 0.127023i
887887 38.8388i 1.30408i −0.758186 0.652039i 0.773914π-0.773914\pi
0.758186 0.652039i 0.226086π-0.226086\pi
888888 −4.30705 + 6.50803i −0.144535 + 0.218395i
889889 12.4452 + 12.4452i 0.417399 + 0.417399i
890890 0.0652071 + 0.0972788i 0.00218575 + 0.00326079i
891891 −34.4140 + 34.4140i −1.15291 + 1.15291i
892892 −20.4552 48.9747i −0.684892 1.63980i
893893 11.7093i 0.391837i
894894 10.3977 52.6784i 0.347753 1.76183i
895895 0.0497432 + 0.0497432i 0.00166273 + 0.00166273i
896896 11.0730 2.32148i 0.369922 0.0775554i
897897 −13.4912 + 23.0590i −0.450459 + 0.769918i
898898 10.9647 55.5506i 0.365895 1.85375i
899899 1.12514 + 1.12514i 0.0375254 + 0.0375254i
900900 20.6611 + 8.48689i 0.688704 + 0.282896i
901901 −97.2010 −3.23824
902902 −29.2339 + 19.5958i −0.973384 + 0.652470i
903903 −10.3852 + 10.3852i −0.345599 + 0.345599i
904904 1.94810 + 9.57252i 0.0647930 + 0.318377i
905905 5.79732 5.79732i 0.192709 0.192709i
906906 59.9962 + 11.8421i 1.99324 + 0.393429i
907907 47.0520i 1.56234i 0.624320 + 0.781168i 0.285376π0.285376\pi
−0.624320 + 0.781168i 0.714624π0.714624\pi
908908 40.2034 16.7917i 1.33420 0.557253i
909909 −9.22511 −0.305978
910910 −0.136048 2.22207i −0.00450993 0.0736609i
911911 3.60690i 0.119502i −0.998213 0.0597509i 0.980969π-0.980969\pi
0.998213 0.0597509i 0.0190306π-0.0190306\pi
912912 −0.204868 34.7717i −0.00678387 1.15141i
913913 −22.8967 −0.757771
914914 2.70504 + 0.533925i 0.0894747 + 0.0176607i
915915 −3.30047 3.30047i −0.109110 0.109110i
916916 −27.3226 + 11.4118i −0.902765 + 0.377057i
917917 −11.1858 11.1858i −0.369388 0.369388i
918918 −9.06217 13.5194i −0.299096 0.446205i
919919 48.6029i 1.60326i −0.597819 0.801631i 0.703966π-0.703966\pi
0.597819 0.801631i 0.296034π-0.296034\pi
920920 3.30752 + 2.18894i 0.109046 + 0.0721672i
921921 −31.6211 + 31.6211i −1.04195 + 1.04195i
922922 5.43377 27.5293i 0.178952 0.906629i
923923 0.724555 + 2.76790i 0.0238490 + 0.0911066i
924924 8.06901 19.6438i 0.265451 0.646233i
925925 −4.06736 + 4.06736i −0.133734 + 0.133734i
926926 34.0400 + 6.71888i 1.11863 + 0.220796i
927927 18.2292 0.598727
928928 −2.98858 + 15.6251i −0.0981050 + 0.512921i
929929 −3.49837 3.49837i −0.114778 0.114778i 0.647385 0.762163i 0.275863π-0.275863\pi
−0.762163 + 0.647385i 0.775863π0.775863\pi
930930 −0.448752 0.669468i −0.0147152 0.0219527i
931931 −2.66450 + 2.66450i −0.0873253 + 0.0873253i
932932 −22.6908 9.32063i −0.743263 0.305307i
933933 26.6816 0.873515
934934 3.24053 + 4.83437i 0.106033 + 0.158185i
935935 14.7891 0.483655
936936 22.4143 + 7.64252i 0.732636 + 0.249804i
937937 −20.1024 −0.656716 −0.328358 0.944553i 0.606495π-0.606495\pi
−0.328358 + 0.944553i 0.606495π0.606495\pi
938938 −8.97456 13.3886i −0.293030 0.437155i
939939 57.2467 1.86818
940940 −1.03099 + 2.50991i −0.0336270 + 0.0818641i
941941 −22.5373 + 22.5373i −0.734694 + 0.734694i −0.971546 0.236852i 0.923884π-0.923884\pi
0.236852 + 0.971546i 0.423884π0.423884\pi
942942 −38.1890 56.9721i −1.24427 1.85625i
943943 −12.2796 12.2796i −0.399877 0.399877i
944944 −7.70720 + 0.0454094i −0.250848 + 0.00147795i
945945 0.682742 0.0222096
946946 −40.6547 8.02449i −1.32180 0.260899i
947947 5.29700 5.29700i 0.172129 0.172129i −0.615785 0.787914i 0.711161π-0.711161\pi
0.787914 + 0.615785i 0.211161π0.211161\pi
948948 −36.7841 15.1097i −1.19469 0.490739i
949949 1.40359 + 5.36193i 0.0455626 + 0.174055i
950950 4.96297 25.1440i 0.161020 0.815780i
951951 3.84448 3.84448i 0.124666 0.124666i
952952 17.3587 + 11.4881i 0.562599 + 0.372331i
953953 47.5513i 1.54034i 0.637839 + 0.770170i 0.279828π0.279828\pi
−0.637839 + 0.770170i 0.720172π0.720172\pi
954954 24.1503 + 36.0285i 0.781895 + 1.16647i
955955 −2.38132 2.38132i −0.0770578 0.0770578i
956956 3.24330 + 7.76525i 0.104896 + 0.251146i
957957 21.1149 + 21.1149i 0.682547 + 0.682547i
958958 −2.36638 0.467080i −0.0764543 0.0150907i
959959 −17.3266 −0.559504
960960 3.01768 7.47141i 0.0973953 0.241139i
961961 30.6799i 0.989673i
962962 −4.04072 + 4.56778i −0.130278 + 0.147271i
963963 −14.7137 −0.474142
964964 13.3303 + 31.9158i 0.429339 + 1.02794i
965965 1.62801i 0.0524074i
966966 10.2804 + 2.02917i 0.330767 + 0.0652874i
967967 20.3534 20.3534i 0.654521 0.654521i −0.299557 0.954078i 0.596839π-0.596839\pi
0.954078 + 0.299557i 0.0968389π0.0968389\pi
968968 28.2273 5.74453i 0.907258 0.184636i
969969 45.2385 45.2385i 1.45327 1.45327i
970970 2.15711 1.44593i 0.0692605 0.0464261i
971971 −22.5065 −0.722269 −0.361135 0.932514i 0.617610π-0.617610\pi
−0.361135 + 0.932514i 0.617610π0.617610\pi
972972 −14.9726 + 36.4503i −0.480246 + 1.16915i
973973 −14.1717 14.1717i −0.454324 0.454324i
974974 −2.41177 + 12.2188i −0.0772780 + 0.391516i
975975 34.5285 + 20.2017i 1.10580 + 0.646974i
976976 13.0297 13.1841i 0.417070 0.422014i
977977 7.84442 + 7.84442i 0.250965 + 0.250965i 0.821366 0.570401i 0.193212π-0.193212\pi
−0.570401 + 0.821366i 0.693212π0.693212\pi
978978 −8.96327 + 45.4109i −0.286614 + 1.45208i
979979 0.872991i 0.0279009i
980980 −0.805744 + 0.336534i −0.0257385 + 0.0107502i
981981 −31.2416 + 31.2416i −0.997466 + 0.997466i
982982 −5.42173 8.08838i −0.173014 0.258111i
983983 −28.9316 28.9316i −0.922773 0.922773i 0.0744513 0.997225i 0.476279π-0.476279\pi
−0.997225 + 0.0744513i 0.976279π0.976279\pi
984984 −19.4710 + 29.4210i −0.620712 + 0.937907i
985985 9.42873i 0.300424i
986986 −24.3128 + 16.2971i −0.774276 + 0.519006i
987987 7.16877i 0.228184i
988988 3.62290 26.9300i 0.115260 0.856758i
989989 20.4474i 0.650191i
990990 −3.67446 5.48172i −0.116782 0.174220i
991991 25.5515i 0.811672i −0.913946 0.405836i 0.866980π-0.866980\pi
0.913946 0.405836i 0.133020π-0.133020\pi
992992 2.64811 1.79776i 0.0840776 0.0570790i
993993 −12.5958 12.5958i −0.399717 0.399717i
994994 0.932189 0.624857i 0.0295673 0.0198193i
995995 −4.29595 + 4.29595i −0.136191 + 0.136191i
996996 −21.1798 + 8.84615i −0.671108 + 0.280301i
997997 18.0376i 0.571256i 0.958341 + 0.285628i 0.0922022π0.0922022\pi
−0.958341 + 0.285628i 0.907798π0.907798\pi
998998 19.7324 + 3.89480i 0.624617 + 0.123288i
999999 −1.32250 1.32250i −0.0418421 0.0418421i
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 728.2.z.a.99.18 168
8.3 odd 2 inner 728.2.z.a.99.59 yes 168
13.5 odd 4 inner 728.2.z.a.603.59 yes 168
104.83 even 4 inner 728.2.z.a.603.18 yes 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
728.2.z.a.99.18 168 1.1 even 1 trivial
728.2.z.a.99.59 yes 168 8.3 odd 2 inner
728.2.z.a.603.18 yes 168 104.83 even 4 inner
728.2.z.a.603.59 yes 168 13.5 odd 4 inner