Properties

Label 63.3.t.a.40.11
Level 6363
Weight 33
Character 63.40
Analytic conductor 1.7171.717
Analytic rank 00
Dimension 2828
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,3,Mod(40,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.40");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 3 3
Character orbit: [χ][\chi] == 63.t (of order 66, 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: 1.716625665471.71662566547
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 40.11
Character χ\chi == 63.40
Dual form 63.3.t.a.52.11

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.24050q2+(2.954630.519775i)q3+1.01982q4+(1.67528+0.967222i)q5+(6.619831.16455i)q6+(6.98642+0.435817i)q76.67708q8+(8.459673.07148i)q9+(3.75345+2.16706i)q10+(0.1861680.322453i)q11+(3.013190.530076i)q12+(5.01827+2.89730i)q13+(15.6530+0.976446i)q14+(4.44709+3.72855i)q1519.0392q16+(9.965765.75374i)q17+(18.95386.88165i)q18+(18.2323+10.5264i)q19+(1.70848+0.986391i)q20+(20.4158+4.91904i)q21+(0.4171090.722455i)q22+(13.641723.6282i)q23+(19.7283+3.47058i)q24+(10.6290+18.4099i)q25+(11.2434+6.49139i)q26+(23.398713.4722i)q27+(7.12488+0.444454i)q28+(20.140434.8842i)q29+(9.96367+8.35380i)q30+48.8145iq3115.9490q32+(0.3824561.04950i)q33+(22.328212.8912i)q34+(11.28277.48753i)q35+(8.627323.13236i)q36+(14.769125.5809i)q37+(40.8493+23.5844i)q38+(16.3331+5.95208i)q39+(11.18606.45822i)q40+(19.6397+11.3390i)q41+(45.7414+11.0211i)q42+(10.7407+18.6035i)q43+(0.1898580.328844i)q44+(11.2015+13.3280i)q45+(30.564252.9388i)q4653.3035iq47+(56.2539+9.89612i)q48+(48.62016.08960i)q49+(23.8141+41.2473i)q50+(26.454522.1801i)q51+(5.11773+2.95472i)q52+(43.7300+75.7426i)q53+(52.424730.1844i)q54+0.720265iq55+(46.64892.90999i)q56+(59.3409+21.6249i)q57+(45.124578.1579i)q58+9.23111iq59+(4.53522+3.80244i)q6070.5346iq61+109.369iq62+(57.7642+25.1456i)q63+40.4233q6411.2093q65+(0.8568902.35139i)q6675.5440q67+(10.16335.86777i)q68+(52.587662.7219i)q69+(25.278716.7758i)q7097.4729q71+(56.4859+20.5086i)q72+(75.3269+43.4900i)q73+(33.090257.3139i)q74+(21.8356+59.9191i)q75+(18.5936+10.7350i)q76+(1.16012+2.33393i)q77+(36.5942+13.3356i)q7847.1994q79+(31.896018.4152i)q80+(62.132051.9675i)q81+(44.0025+25.4049i)q82+(81.1770+46.8676i)q83+(20.8204+5.01653i)q84+(11.1303+19.2782i)q85+(24.0646+41.6810i)q86+(77.639492.6014i)q87+(1.24306+2.15305i)q88+(25.680314.8266i)q89+(25.0969+29.8612i)q90+(36.322518.0547i)q91+(13.912124.0965i)q92+(25.3726+144.229i)q93119.426iq9440.7255q95+(47.1234+8.28989i)q96+(122.53870.7471i)q97+(108.93313.6437i)q98+(0.5845133.29966i)q99+O(q100)q+2.24050 q^{2} +(2.95463 - 0.519775i) q^{3} +1.01982 q^{4} +(-1.67528 + 0.967222i) q^{5} +(6.61983 - 1.16455i) q^{6} +(-6.98642 + 0.435817i) q^{7} -6.67708 q^{8} +(8.45967 - 3.07148i) q^{9} +(-3.75345 + 2.16706i) q^{10} +(0.186168 - 0.322453i) q^{11} +(3.01319 - 0.530076i) q^{12} +(5.01827 + 2.89730i) q^{13} +(-15.6530 + 0.976446i) q^{14} +(-4.44709 + 3.72855i) q^{15} -19.0392 q^{16} +(9.96576 - 5.75374i) q^{17} +(18.9538 - 6.88165i) q^{18} +(18.2323 + 10.5264i) q^{19} +(-1.70848 + 0.986391i) q^{20} +(-20.4158 + 4.91904i) q^{21} +(0.417109 - 0.722455i) q^{22} +(-13.6417 - 23.6282i) q^{23} +(-19.7283 + 3.47058i) q^{24} +(-10.6290 + 18.4099i) q^{25} +(11.2434 + 6.49139i) q^{26} +(23.3987 - 13.4722i) q^{27} +(-7.12488 + 0.444454i) q^{28} +(-20.1404 - 34.8842i) q^{29} +(-9.96367 + 8.35380i) q^{30} +48.8145i q^{31} -15.9490 q^{32} +(0.382456 - 1.04950i) q^{33} +(22.3282 - 12.8912i) q^{34} +(11.2827 - 7.48753i) q^{35} +(8.62732 - 3.13236i) q^{36} +(14.7691 - 25.5809i) q^{37} +(40.8493 + 23.5844i) q^{38} +(16.3331 + 5.95208i) q^{39} +(11.1860 - 6.45822i) q^{40} +(19.6397 + 11.3390i) q^{41} +(-45.7414 + 11.0211i) q^{42} +(10.7407 + 18.6035i) q^{43} +(0.189858 - 0.328844i) q^{44} +(-11.2015 + 13.3280i) q^{45} +(-30.5642 - 52.9388i) q^{46} -53.3035i q^{47} +(-56.2539 + 9.89612i) q^{48} +(48.6201 - 6.08960i) q^{49} +(-23.8141 + 41.2473i) q^{50} +(26.4545 - 22.1801i) q^{51} +(5.11773 + 2.95472i) q^{52} +(43.7300 + 75.7426i) q^{53} +(52.4247 - 30.1844i) q^{54} +0.720265i q^{55} +(46.6489 - 2.90999i) q^{56} +(59.3409 + 21.6249i) q^{57} +(-45.1245 - 78.1579i) q^{58} +9.23111i q^{59} +(-4.53522 + 3.80244i) q^{60} -70.5346i q^{61} +109.369i q^{62} +(-57.7642 + 25.1456i) q^{63} +40.4233 q^{64} -11.2093 q^{65} +(0.856890 - 2.35139i) q^{66} -75.5440 q^{67} +(10.1633 - 5.86777i) q^{68} +(-52.5876 - 62.7219i) q^{69} +(25.2787 - 16.7758i) q^{70} -97.4729 q^{71} +(-56.4859 + 20.5086i) q^{72} +(-75.3269 + 43.4900i) q^{73} +(33.0902 - 57.3139i) q^{74} +(-21.8356 + 59.9191i) q^{75} +(18.5936 + 10.7350i) q^{76} +(-1.16012 + 2.33393i) q^{77} +(36.5942 + 13.3356i) q^{78} -47.1994 q^{79} +(31.8960 - 18.4152i) q^{80} +(62.1320 - 51.9675i) q^{81} +(44.0025 + 25.4049i) q^{82} +(-81.1770 + 46.8676i) q^{83} +(-20.8204 + 5.01653i) q^{84} +(-11.1303 + 19.2782i) q^{85} +(24.0646 + 41.6810i) q^{86} +(-77.6394 - 92.6014i) q^{87} +(-1.24306 + 2.15305i) q^{88} +(-25.6803 - 14.8266i) q^{89} +(-25.0969 + 29.8612i) q^{90} +(-36.3225 - 18.0547i) q^{91} +(-13.9121 - 24.0965i) q^{92} +(25.3726 + 144.229i) q^{93} -119.426i q^{94} -40.7255 q^{95} +(-47.1234 + 8.28989i) q^{96} +(122.538 - 70.7471i) q^{97} +(108.933 - 13.6437i) q^{98} +(0.584513 - 3.29966i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q2q23q3+46q43q512q616q815q96q10+7q1130q1215q13+10q1418q15+54q1633q1742q186q19108q20+162q99+O(q100) 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 7 q^{11} - 30 q^{12} - 15 q^{13} + 10 q^{14} - 18 q^{15} + 54 q^{16} - 33 q^{17} - 42 q^{18} - 6 q^{19} - 108 q^{20}+ \cdots - 162 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/63Z)×\left(\mathbb{Z}/63\mathbb{Z}\right)^\times.

nn 1010 2929
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.24050 1.12025 0.560124 0.828409i 0.310754π-0.310754\pi
0.560124 + 0.828409i 0.310754π0.310754\pi
33 2.95463 0.519775i 0.984876 0.173258i
44 1.01982 0.254955
55 −1.67528 + 0.967222i −0.335055 + 0.193444i −0.658083 0.752945i 0.728633π-0.728633\pi
0.323028 + 0.946389i 0.395299π0.395299\pi
66 6.61983 1.16455i 1.10331 0.194092i
77 −6.98642 + 0.435817i −0.998060 + 0.0622596i
88 −6.67708 −0.834635
99 8.45967 3.07148i 0.939963 0.341276i
1010 −3.75345 + 2.16706i −0.375345 + 0.216706i
1111 0.186168 0.322453i 0.0169244 0.0293139i −0.857439 0.514585i 0.827946π-0.827946\pi
0.874364 + 0.485271i 0.161279π0.161279\pi
1212 3.01319 0.530076i 0.251099 0.0441730i
1313 5.01827 + 2.89730i 0.386021 + 0.222869i 0.680435 0.732809i 0.261791π-0.261791\pi
−0.294414 + 0.955678i 0.595124π0.595124\pi
1414 −15.6530 + 0.976446i −1.11807 + 0.0697462i
1515 −4.44709 + 3.72855i −0.296472 + 0.248570i
1616 −19.0392 −1.18995
1717 9.96576 5.75374i 0.586221 0.338455i −0.177381 0.984142i 0.556762π-0.556762\pi
0.763602 + 0.645687i 0.223429π0.223429\pi
1818 18.9538 6.88165i 1.05299 0.382314i
1919 18.2323 + 10.5264i 0.959593 + 0.554021i 0.896048 0.443958i 0.146426π-0.146426\pi
0.0635451 + 0.997979i 0.479759π0.479759\pi
2020 −1.70848 + 0.986391i −0.0854239 + 0.0493195i
2121 −20.4158 + 4.91904i −0.972179 + 0.234240i
2222 0.417109 0.722455i 0.0189595 0.0328389i
2323 −13.6417 23.6282i −0.593119 1.02731i −0.993809 0.111099i 0.964563π-0.964563\pi
0.400690 0.916214i 0.368770π-0.368770\pi
2424 −19.7283 + 3.47058i −0.822013 + 0.144608i
2525 −10.6290 + 18.4099i −0.425159 + 0.736396i
2626 11.2434 + 6.49139i 0.432439 + 0.249669i
2727 23.3987 13.4722i 0.866619 0.498971i
2828 −7.12488 + 0.444454i −0.254460 + 0.0158734i
2929 −20.1404 34.8842i −0.694497 1.20290i −0.970350 0.241704i 0.922294π-0.922294\pi
0.275853 0.961200i 0.411040π-0.411040\pi
3030 −9.96367 + 8.35380i −0.332122 + 0.278460i
3131 48.8145i 1.57466i 0.616530 + 0.787331i 0.288538π0.288538\pi
−0.616530 + 0.787331i 0.711462π0.711462\pi
3232 −15.9490 −0.498406
3333 0.382456 1.04950i 0.0115896 0.0318029i
3434 22.3282 12.8912i 0.656713 0.379154i
3535 11.2827 7.48753i 0.322362 0.213929i
3636 8.62732 3.13236i 0.239648 0.0870099i
3737 14.7691 25.5809i 0.399166 0.691376i −0.594457 0.804127i 0.702633π-0.702633\pi
0.993623 + 0.112751i 0.0359663π0.0359663\pi
3838 40.8493 + 23.5844i 1.07498 + 0.620641i
3939 16.3331 + 5.95208i 0.418797 + 0.152617i
4040 11.1860 6.45822i 0.279649 0.161455i
4141 19.6397 + 11.3390i 0.479016 + 0.276560i 0.720006 0.693968i 0.244139π-0.244139\pi
−0.240990 + 0.970528i 0.577472π0.577472\pi
4242 −45.7414 + 11.0211i −1.08908 + 0.262407i
4343 10.7407 + 18.6035i 0.249785 + 0.432639i 0.963466 0.267831i 0.0863069π-0.0863069\pi
−0.713681 + 0.700470i 0.752974π0.752974\pi
4444 0.189858 0.328844i 0.00431495 0.00747372i
4545 −11.2015 + 13.3280i −0.248922 + 0.296177i
4646 −30.5642 52.9388i −0.664440 1.15084i
4747 53.3035i 1.13412i −0.823677 0.567059i 0.808081π-0.808081\pi
0.823677 0.567059i 0.191919π-0.191919\pi
4848 −56.2539 + 9.89612i −1.17196 + 0.206169i
4949 48.6201 6.08960i 0.992247 0.124278i
5050 −23.8141 + 41.2473i −0.476283 + 0.824946i
5151 26.4545 22.1801i 0.518716 0.434904i
5252 5.11773 + 2.95472i 0.0984178 + 0.0568216i
5353 43.7300 + 75.7426i 0.825094 + 1.42911i 0.901847 + 0.432055i 0.142211π0.142211\pi
−0.0767530 + 0.997050i 0.524455π0.524455\pi
5454 52.4247 30.1844i 0.970827 0.558971i
5555 0.720265i 0.0130957i
5656 46.6489 2.90999i 0.833016 0.0519641i
5757 59.3409 + 21.6249i 1.04107 + 0.379385i
5858 −45.1245 78.1579i −0.778008 1.34755i
5959 9.23111i 0.156460i 0.996935 + 0.0782298i 0.0249268π0.0249268\pi
−0.996935 + 0.0782298i 0.975073π0.975073\pi
6060 −4.53522 + 3.80244i −0.0755870 + 0.0633740i
6161 70.5346i 1.15631i −0.815929 0.578153i 0.803774π-0.803774\pi
0.815929 0.578153i 0.196226π-0.196226\pi
6262 109.369i 1.76401i
6363 −57.7642 + 25.1456i −0.916892 + 0.399136i
6464 40.4233 0.631614
6565 −11.2093 −0.172451
6666 0.856890 2.35139i 0.0129832 0.0356271i
6767 −75.5440 −1.12752 −0.563761 0.825938i 0.690646π-0.690646\pi
−0.563761 + 0.825938i 0.690646π0.690646\pi
6868 10.1633 5.86777i 0.149460 0.0862907i
6969 −52.5876 62.7219i −0.762139 0.909013i
7070 25.2787 16.7758i 0.361125 0.239654i
7171 −97.4729 −1.37286 −0.686429 0.727197i 0.740823π-0.740823\pi
−0.686429 + 0.727197i 0.740823π0.740823\pi
7272 −56.4859 + 20.5086i −0.784526 + 0.284841i
7373 −75.3269 + 43.4900i −1.03188 + 0.595754i −0.917521 0.397687i 0.869813π-0.869813\pi
−0.114354 + 0.993440i 0.536480π0.536480\pi
7474 33.0902 57.3139i 0.447165 0.774512i
7575 −21.8356 + 59.9191i −0.291142 + 0.798922i
7676 18.5936 + 10.7350i 0.244653 + 0.141250i
7777 −1.16012 + 2.33393i −0.0150665 + 0.0303108i
7878 36.5942 + 13.3356i 0.469156 + 0.170969i
7979 −47.1994 −0.597461 −0.298730 0.954338i 0.596563π-0.596563\pi
−0.298730 + 0.954338i 0.596563π0.596563\pi
8080 31.8960 18.4152i 0.398700 0.230190i
8181 62.1320 51.9675i 0.767061 0.641574i
8282 44.0025 + 25.4049i 0.536616 + 0.309816i
8383 −81.1770 + 46.8676i −0.978036 + 0.564669i −0.901677 0.432411i 0.857663π-0.857663\pi
−0.0763594 + 0.997080i 0.524330π0.524330\pi
8484 −20.8204 + 5.01653i −0.247861 + 0.0597206i
8585 −11.1303 + 19.2782i −0.130944 + 0.226802i
8686 24.0646 + 41.6810i 0.279821 + 0.484663i
8787 −77.6394 92.6014i −0.892407 1.06438i
8888 −1.24306 + 2.15305i −0.0141257 + 0.0244664i
8989 −25.6803 14.8266i −0.288543 0.166590i 0.348742 0.937219i 0.386609π-0.386609\pi
−0.637285 + 0.770628i 0.719942π0.719942\pi
9090 −25.0969 + 29.8612i −0.278854 + 0.331792i
9191 −36.3225 18.0547i −0.399148 0.198403i
9292 −13.9121 24.0965i −0.151218 0.261918i
9393 25.3726 + 144.229i 0.272823 + 1.55085i
9494 119.426i 1.27049i
9595 −40.7255 −0.428689
9696 −47.1234 + 8.28989i −0.490869 + 0.0863531i
9797 122.538 70.7471i 1.26327 0.729351i 0.289567 0.957158i 0.406489π-0.406489\pi
0.973706 + 0.227806i 0.0731553π0.0731553\pi
9898 108.933 13.6437i 1.11156 0.139222i
9999 0.584513 3.29966i 0.00590417 0.0333299i
100100 −10.8396 + 18.7748i −0.108396 + 0.187748i
101101 40.6345 + 23.4603i 0.402321 + 0.232280i 0.687485 0.726198i 0.258715π-0.258715\pi
−0.285164 + 0.958479i 0.592048π0.592048\pi
102102 59.2712 49.6944i 0.581090 0.487200i
103103 −113.923 + 65.7733i −1.10605 + 0.638576i −0.937802 0.347169i 0.887143π-0.887143\pi
−0.168244 + 0.985745i 0.553810π0.553810\pi
104104 −33.5074 19.3455i −0.322187 0.186015i
105105 29.4442 27.9873i 0.280421 0.266546i
106106 97.9768 + 169.701i 0.924310 + 1.60095i
107107 69.9586 121.172i 0.653819 1.13245i −0.328369 0.944549i 0.606499π-0.606499\pi
0.982188 0.187899i 0.0601676π-0.0601676\pi
108108 23.8624 13.7392i 0.220948 0.127215i
109109 55.5420 + 96.2016i 0.509560 + 0.882583i 0.999939 + 0.0110739i 0.00352500π0.00352500\pi
−0.490379 + 0.871509i 0.663142π0.663142\pi
110110 1.61375i 0.0146704i
111111 30.3410 83.2587i 0.273343 0.750079i
112112 133.016 8.29763i 1.18764 0.0740860i
113113 50.7636 87.9252i 0.449236 0.778099i −0.549101 0.835756i 0.685030π-0.685030\pi
0.998336 + 0.0576571i 0.0183630π0.0183630\pi
114114 132.953 + 48.4506i 1.16626 + 0.425005i
115115 45.7074 + 26.3892i 0.397456 + 0.229471i
116116 −20.5396 35.5756i −0.177065 0.306686i
117117 51.3519 + 9.09666i 0.438906 + 0.0777492i
118118 20.6823i 0.175273i
119119 −67.1174 + 44.5413i −0.564012 + 0.374296i
120120 29.6936 24.8958i 0.247446 0.207465i
121121 60.4307 + 104.669i 0.499427 + 0.865033i
122122 158.032i 1.29535i
123123 63.9216 + 23.2942i 0.519688 + 0.189384i
124124 49.7820i 0.401468i
125125 89.4834i 0.715867i
126126 −129.420 + 56.3385i −1.02715 + 0.447131i
127127 −49.1014 −0.386625 −0.193312 0.981137i 0.561923π-0.561923\pi
−0.193312 + 0.981137i 0.561923π0.561923\pi
128128 154.364 1.20597
129129 41.4045 + 49.3837i 0.320965 + 0.382819i
130130 −25.1145 −0.193188
131131 −107.596 + 62.1204i −0.821341 + 0.474202i −0.850879 0.525362i 0.823930π-0.823930\pi
0.0295376 + 0.999564i 0.490597π0.490597\pi
132132 0.390035 1.07029i 0.00295481 0.00810829i
133133 −131.966 65.5959i −0.992224 0.493203i
134134 −169.256 −1.26310
135135 −26.1687 + 45.2014i −0.193842 + 0.334826i
136136 −66.5422 + 38.4182i −0.489281 + 0.282487i
137137 −2.31536 + 4.01032i −0.0169004 + 0.0292724i −0.874352 0.485292i 0.838713π-0.838713\pi
0.857452 + 0.514565i 0.172046π0.172046\pi
138138 −117.822 140.528i −0.853785 1.01832i
139139 37.7043 + 21.7686i 0.271254 + 0.156608i 0.629457 0.777035i 0.283277π-0.283277\pi
−0.358204 + 0.933644i 0.616611π0.616611\pi
140140 11.5063 7.63592i 0.0821876 0.0545423i
141141 −27.7058 157.492i −0.196495 1.11697i
142142 −218.387 −1.53794
143143 1.86849 1.07877i 0.0130664 0.00754386i
144144 −161.066 + 58.4787i −1.11851 + 0.406102i
145145 67.4815 + 38.9605i 0.465390 + 0.268693i
146146 −168.770 + 97.4391i −1.15596 + 0.667391i
147147 140.489 43.2640i 0.955709 0.294313i
148148 15.0618 26.0879i 0.101769 0.176269i
149149 13.1304 + 22.7425i 0.0881232 + 0.152634i 0.906718 0.421738i 0.138580π-0.138580\pi
−0.818595 + 0.574372i 0.805246π0.805246\pi
150150 −48.9226 + 134.248i −0.326151 + 0.894990i
151151 −59.9365 + 103.813i −0.396931 + 0.687504i −0.993346 0.115172i 0.963258π-0.963258\pi
0.596415 + 0.802676i 0.296591π0.296591\pi
152152 −121.738 70.2857i −0.800910 0.462406i
153153 66.6345 79.2844i 0.435520 0.518199i
154154 −2.59924 + 5.22916i −0.0168782 + 0.0339556i
155155 −47.2145 81.7779i −0.304610 0.527599i
156156 16.6568 + 6.07004i 0.106774 + 0.0389105i
157157 195.955i 1.24812i −0.781377 0.624059i 0.785482π-0.785482\pi
0.781377 0.624059i 0.214518π-0.214518\pi
158158 −105.750 −0.669304
159159 168.575 + 201.061i 1.06022 + 1.26454i
160160 26.7190 15.4262i 0.166994 0.0964139i
161161 105.604 + 159.131i 0.655928 + 0.988392i
162162 139.206 116.433i 0.859299 0.718722i
163163 41.8418 72.4721i 0.256698 0.444614i −0.708657 0.705553i 0.750699π-0.750699\pi
0.965355 + 0.260939i 0.0840321π0.0840321\pi
164164 20.0289 + 11.5637i 0.122127 + 0.0705102i
165165 0.374376 + 2.12811i 0.00226894 + 0.0128977i
166166 −181.877 + 105.007i −1.09564 + 0.632569i
167167 215.835 + 124.612i 1.29242 + 0.746181i 0.979083 0.203460i 0.0652188π-0.0652188\pi
0.313340 + 0.949641i 0.398552π0.398552\pi
168168 136.318 32.8449i 0.811415 0.195505i
169169 −67.7113 117.279i −0.400659 0.693961i
170170 −24.9373 + 43.1927i −0.146690 + 0.254075i
171171 186.571 + 33.0497i 1.09106 + 0.193273i
172172 10.9536 + 18.9722i 0.0636837 + 0.110303i
173173 278.453i 1.60956i 0.593575 + 0.804779i 0.297716π0.297716\pi
−0.593575 + 0.804779i 0.702284π0.702284\pi
174174 −173.951 207.473i −0.999716 1.19237i
175175 66.2351 133.252i 0.378486 0.761438i
176176 −3.54451 + 6.13926i −0.0201392 + 0.0348822i
177177 4.79810 + 27.2745i 0.0271079 + 0.154093i
178178 −57.5367 33.2188i −0.323240 0.186623i
179179 −128.758 223.015i −0.719317 1.24589i −0.961271 0.275605i 0.911122π-0.911122\pi
0.241954 0.970288i 0.422212π-0.422212\pi
180180 −11.4235 + 13.5921i −0.0634638 + 0.0755117i
181181 29.2542i 0.161625i −0.996729 0.0808126i 0.974248π-0.974248\pi
0.996729 0.0808126i 0.0257515π-0.0257515\pi
182182 −81.3803 40.4515i −0.447144 0.222261i
183183 −36.6621 208.404i −0.200340 1.13882i
184184 91.0870 + 157.767i 0.495038 + 0.857431i
185185 57.1402i 0.308866i
186186 56.8471 + 323.144i 0.305630 + 1.73733i
187187 4.28466i 0.0229126i
188188 54.3599i 0.289149i
189189 −157.602 + 104.320i −0.833872 + 0.551959i
190190 −91.2452 −0.480238
191191 −60.7704 −0.318170 −0.159085 0.987265i 0.550854π-0.550854\pi
−0.159085 + 0.987265i 0.550854π0.550854\pi
192192 119.436 21.0110i 0.622062 0.109432i
193193 24.8767 0.128895 0.0644474 0.997921i 0.479472π-0.479472\pi
0.0644474 + 0.997921i 0.479472π0.479472\pi
194194 274.545 158.508i 1.41518 0.817054i
195195 −33.1194 + 5.82633i −0.169843 + 0.0298786i
196196 49.5837 6.21029i 0.252978 0.0316851i
197197 174.320 0.884873 0.442437 0.896800i 0.354114π-0.354114\pi
0.442437 + 0.896800i 0.354114π0.354114\pi
198198 1.30960 7.39287i 0.00661413 0.0373377i
199199 250.227 144.468i 1.25742 0.725972i 0.284848 0.958573i 0.408057π-0.408057\pi
0.972572 + 0.232600i 0.0747234π0.0747234\pi
200200 70.9705 122.924i 0.354852 0.614622i
201201 −223.204 + 39.2659i −1.11047 + 0.195353i
202202 91.0413 + 52.5627i 0.450699 + 0.260211i
203203 155.912 + 234.938i 0.768042 + 1.15733i
204204 26.9788 22.6197i 0.132249 0.110881i
205205 −43.8692 −0.213996
206206 −255.243 + 147.365i −1.23905 + 0.715363i
207207 −187.978 157.986i −0.908107 0.763218i
208208 −95.5441 55.1624i −0.459347 0.265204i
209209 6.78854 3.91937i 0.0324811 0.0187530i
210210 65.9697 62.7055i 0.314141 0.298597i
211211 −149.601 + 259.116i −0.709009 + 1.22804i 0.256217 + 0.966619i 0.417524π0.417524\pi
−0.965225 + 0.261419i 0.915809π0.915809\pi
212212 44.5967 + 77.2437i 0.210362 + 0.364357i
213213 −287.996 + 50.6640i −1.35209 + 0.237859i
214214 156.742 271.485i 0.732439 1.26862i
215215 −35.9874 20.7773i −0.167383 0.0966388i
216216 −156.235 + 89.9551i −0.723310 + 0.416459i
217217 −21.2742 341.039i −0.0980379 1.57161i
218218 124.442 + 215.539i 0.570833 + 0.988712i
219219 −199.958 + 167.650i −0.913050 + 0.765525i
220220 0.734539i 0.00333881i
221221 66.6812 0.301725
222222 67.9789 186.541i 0.306211 0.840274i
223223 14.0772 8.12745i 0.0631263 0.0364460i −0.468105 0.883673i 0.655063π-0.655063\pi
0.531231 + 0.847227i 0.321730π0.321730\pi
224224 111.426 6.95085i 0.497439 0.0310306i
225225 −33.3718 + 188.388i −0.148319 + 0.837282i
226226 113.736 196.996i 0.503255 0.871664i
227227 −26.4526 15.2724i −0.116531 0.0672793i 0.440602 0.897703i 0.354765π-0.354765\pi
−0.557133 + 0.830423i 0.688099π0.688099\pi
228228 60.5170 + 22.0535i 0.265425 + 0.0967259i
229229 158.134 91.2986i 0.690541 0.398684i −0.113274 0.993564i 0.536134π-0.536134\pi
0.803815 + 0.594880i 0.202800π0.202800\pi
230230 102.407 + 59.1248i 0.445249 + 0.257064i
231231 −2.21461 + 7.49890i −0.00958704 + 0.0324627i
232232 134.479 + 232.925i 0.579652 + 1.00399i
233233 174.898 302.932i 0.750635 1.30014i −0.196880 0.980428i 0.563081π-0.563081\pi
0.947515 0.319710i 0.103586π-0.103586\pi
234234 115.054 + 20.3810i 0.491683 + 0.0870984i
235235 51.5563 + 89.2982i 0.219389 + 0.379992i
236236 9.41406i 0.0398901i
237237 −139.457 + 24.5331i −0.588425 + 0.103515i
238238 −150.376 + 99.7945i −0.631833 + 0.419305i
239239 49.6154 85.9365i 0.207596 0.359567i −0.743361 0.668891i 0.766769π-0.766769\pi
0.950957 + 0.309324i 0.100103π0.100103\pi
240240 84.6692 70.9888i 0.352788 0.295786i
241241 243.343 + 140.494i 1.00972 + 0.582964i 0.911110 0.412162i 0.135226π-0.135226\pi
0.0986123 + 0.995126i 0.468560π0.468560\pi
242242 135.395 + 234.510i 0.559482 + 0.969051i
243243 156.566 185.839i 0.644303 0.764771i
244244 71.9325i 0.294805i
245245 −75.5622 + 57.2282i −0.308417 + 0.233585i
246246 143.216 + 52.1906i 0.582179 + 0.212157i
247247 60.9963 + 105.649i 0.246949 + 0.427728i
248248 325.939i 1.31427i
249249 −215.487 + 180.670i −0.865411 + 0.725582i
250250 200.487i 0.801948i
251251 16.5983i 0.0661286i 0.999453 + 0.0330643i 0.0105266π0.0105266\pi
−0.999453 + 0.0330643i 0.989473π0.989473\pi
252252 −58.9090 + 25.6439i −0.233766 + 0.101761i
253253 −10.1586 −0.0401527
254254 −110.011 −0.433116
255255 −22.8655 + 62.7452i −0.0896687 + 0.246060i
256256 184.159 0.719371
257257 73.7864 42.6006i 0.287106 0.165761i −0.349530 0.936925i 0.613659π-0.613659\pi
0.636636 + 0.771164i 0.280325π0.280325\pi
258258 92.7666 + 110.644i 0.359561 + 0.428852i
259259 −92.0349 + 185.156i −0.355347 + 0.714887i
260260 −11.4315 −0.0439672
261261 −277.527 233.248i −1.06332 0.893670i
262262 −241.068 + 139.180i −0.920105 + 0.531223i
263263 178.327 308.872i 0.678050 1.17442i −0.297517 0.954717i 0.596158π-0.596158\pi
0.975567 0.219701i 0.0705082π-0.0705082\pi
264264 −2.55369 + 7.00757i −0.00967306 + 0.0265438i
265265 −146.520 84.5932i −0.552905 0.319220i
266266 −295.669 146.967i −1.11154 0.552509i
267267 −83.5824 30.4590i −0.313043 0.114079i
268268 −77.0412 −0.287467
269269 −333.500 + 192.546i −1.23978 + 0.715785i −0.969048 0.246871i 0.920597π-0.920597\pi
−0.270727 + 0.962656i 0.587264π0.587264\pi
270270 −58.6308 + 101.274i −0.217151 + 0.375087i
271271 53.9536 + 31.1502i 0.199091 + 0.114945i 0.596231 0.802813i 0.296664π-0.296664\pi
−0.397140 + 0.917758i 0.629997π0.629997\pi
272272 −189.741 + 109.547i −0.697576 + 0.402746i
273273 −116.704 34.4655i −0.427486 0.126247i
274274 −5.18755 + 8.98509i −0.0189327 + 0.0327923i
275275 3.95755 + 6.85469i 0.0143911 + 0.0249261i
276276 −53.6298 63.9649i −0.194311 0.231757i
277277 −42.5057 + 73.6221i −0.153450 + 0.265784i −0.932494 0.361186i 0.882372π-0.882372\pi
0.779043 + 0.626970i 0.215705π0.215705\pi
278278 84.4762 + 48.7724i 0.303871 + 0.175440i
279279 149.933 + 412.955i 0.537395 + 1.48012i
280280 −75.3352 + 49.9949i −0.269054 + 0.178553i
281281 73.8831 + 127.969i 0.262929 + 0.455407i 0.967019 0.254704i 0.0819781π-0.0819781\pi
−0.704090 + 0.710111i 0.748645π0.748645\pi
282282 −62.0748 352.861i −0.220123 1.25128i
283283 350.815i 1.23963i −0.784748 0.619815i 0.787208π-0.787208\pi
0.784748 0.619815i 0.212792π-0.212792\pi
284284 −99.4046 −0.350016
285285 −120.329 + 21.1681i −0.422206 + 0.0742740i
286286 4.18634 2.41698i 0.0146375 0.00845099i
287287 −142.153 70.6594i −0.495305 0.246200i
288288 −134.923 + 48.9871i −0.468484 + 0.170094i
289289 −78.2890 + 135.601i −0.270896 + 0.469206i
290290 151.192 + 87.2908i 0.521352 + 0.301003i
291291 325.280 272.723i 1.11780 0.937194i
292292 −76.8198 + 44.3519i −0.263081 + 0.151890i
293293 −42.7689 24.6927i −0.145969 0.0842753i 0.425237 0.905082i 0.360191π-0.360191\pi
−0.571206 + 0.820807i 0.693524π0.693524\pi
294294 314.765 96.9329i 1.07063 0.329704i
295295 −8.92853 15.4647i −0.0302662 0.0524226i
296296 −98.6148 + 170.806i −0.333158 + 0.577047i
297297 0.0119384 10.0531i 4.01967e−5 0.0338488i
298298 29.4185 + 50.9544i 0.0987198 + 0.170988i
299299 158.097i 0.528752i
300300 −22.2684 + 61.1066i −0.0742280 + 0.203689i
301301 −83.1470 125.291i −0.276236 0.416249i
302302 −134.288 + 232.593i −0.444661 + 0.770175i
303303 132.254 + 48.1958i 0.436481 + 0.159062i
304304 −347.129 200.415i −1.14187 0.659259i
305305 68.2226 + 118.165i 0.223681 + 0.387426i
306306 149.294 177.636i 0.487890 0.580511i
307307 432.680i 1.40938i 0.709515 + 0.704691i 0.248914π0.248914\pi
−0.709515 + 0.704691i 0.751086π0.751086\pi
308308 −1.18311 + 2.38018i −0.00384127 + 0.00772787i
309309 −302.412 + 253.550i −0.978680 + 0.820550i
310310 −105.784 183.223i −0.341238 0.591042i
311311 167.189i 0.537586i 0.963198 + 0.268793i 0.0866248π0.0866248\pi
−0.963198 + 0.268793i 0.913375π0.913375\pi
312312 −109.057 39.7425i −0.349543 0.127380i
313313 258.585i 0.826151i −0.910697 0.413075i 0.864455π-0.864455\pi
0.910697 0.413075i 0.135545π-0.135545\pi
314314 439.035i 1.39820i
315315 72.4497 97.9966i 0.229999 0.311100i
316316 −48.1348 −0.152325
317317 −202.513 −0.638844 −0.319422 0.947613i 0.603489π-0.603489\pi
−0.319422 + 0.947613i 0.603489π0.603489\pi
318318 377.691 + 450.477i 1.18771 + 1.41660i
319319 −14.9980 −0.0470158
320320 −67.7203 + 39.0983i −0.211626 + 0.122182i
321321 143.720 394.381i 0.447725 1.22860i
322322 236.606 + 356.532i 0.734802 + 1.10724i
323323 242.265 0.750045
324324 63.3633 52.9974i 0.195566 0.163572i
325325 −106.678 + 61.5906i −0.328240 + 0.189510i
326326 93.7463 162.373i 0.287565 0.498078i
327327 214.109 + 255.371i 0.654768 + 0.780950i
328328 −131.136 75.7112i −0.399804 0.230827i
329329 23.2306 + 372.401i 0.0706097 + 1.13192i
330330 0.838787 + 4.76803i 0.00254178 + 0.0144486i
331331 34.1563 0.103191 0.0515956 0.998668i 0.483569π-0.483569\pi
0.0515956 + 0.998668i 0.483569π0.483569\pi
332332 −82.7858 + 47.7964i −0.249355 + 0.143965i
333333 46.3707 261.769i 0.139251 0.786094i
334334 483.576 + 279.193i 1.44783 + 0.835907i
335335 126.557 73.0678i 0.377783 0.218113i
336336 388.701 93.6549i 1.15685 0.278735i
337337 205.854 356.550i 0.610844 1.05801i −0.380255 0.924882i 0.624164π-0.624164\pi
0.991099 0.133130i 0.0425029π-0.0425029\pi
338338 −151.707 262.764i −0.448837 0.777408i
339339 104.286 286.172i 0.307629 0.844165i
340340 −11.3509 + 19.6603i −0.0333849 + 0.0578243i
341341 15.7404 + 9.08773i 0.0461595 + 0.0266502i
342342 418.010 + 74.0478i 1.22225 + 0.216514i
343343 −337.027 + 63.7340i −0.982585 + 0.185813i
344344 −71.7168 124.217i −0.208479 0.361096i
345345 148.765 + 54.2127i 0.431202 + 0.157138i
346346 623.874i 1.80310i
347347 −597.488 −1.72187 −0.860933 0.508718i 0.830119π-0.830119\pi
−0.860933 + 0.508718i 0.830119π0.830119\pi
348348 −79.1781 94.4366i −0.227523 0.271370i
349349 −72.8266 + 42.0465i −0.208672 + 0.120477i −0.600694 0.799479i 0.705109π-0.705109\pi
0.392022 + 0.919956i 0.371776π0.371776\pi
350350 148.399 298.550i 0.423998 0.852999i
351351 156.454 + 0.185795i 0.445738 + 0.000529331i
352352 −2.96920 + 5.14281i −0.00843523 + 0.0146102i
353353 397.017 + 229.218i 1.12469 + 0.649343i 0.942595 0.333937i 0.108377π-0.108377\pi
0.182099 + 0.983280i 0.441711π0.441711\pi
354354 10.7501 + 61.1084i 0.0303676 + 0.172623i
355355 163.294 94.2779i 0.459983 0.265572i
356356 −26.1893 15.1204i −0.0735654 0.0424730i
357357 −175.156 + 166.489i −0.490632 + 0.466356i
358358 −288.481 499.664i −0.805813 1.39571i
359359 6.42758 11.1329i 0.0179041 0.0310109i −0.856935 0.515425i 0.827634π-0.827634\pi
0.874839 + 0.484414i 0.160967π0.160967\pi
360360 74.7932 88.9919i 0.207759 0.247200i
361361 41.1103 + 71.2051i 0.113879 + 0.197244i
362362 65.5438i 0.181060i
363363 232.955 + 277.848i 0.641748 + 0.765421i
364364 −37.0423 18.4125i −0.101765 0.0505839i
365365 84.1290 145.716i 0.230490 0.399221i
366366 −82.1413 466.927i −0.224430 1.27576i
367367 535.505 + 309.174i 1.45914 + 0.842436i 0.998969 0.0453934i 0.0144541π-0.0144541\pi
0.460173 + 0.887829i 0.347787π0.347787\pi
368368 259.728 + 449.863i 0.705784 + 1.22245i
369369 200.972 + 35.6009i 0.544641 + 0.0964795i
370370 128.022i 0.346006i
371371 −338.526 510.111i −0.912469 1.37496i
372372 25.8754 + 147.087i 0.0695576 + 0.395396i
373373 −0.289633 0.501659i −0.000776495 0.00134493i 0.865637 0.500672i 0.166914π-0.166914\pi
−0.866413 + 0.499327i 0.833580π0.833580\pi
374374 9.59975i 0.0256678i
375375 −46.5112 264.390i −0.124030 0.705040i
376376 355.912i 0.946575i
377377 233.411i 0.619128i
378378 −353.106 + 233.729i −0.934143 + 0.618330i
379379 18.5015 0.0488165 0.0244083 0.999702i 0.492230π-0.492230\pi
0.0244083 + 0.999702i 0.492230π0.492230\pi
380380 −41.5326 −0.109296
381381 −145.076 + 25.5217i −0.380778 + 0.0669860i
382382 −136.156 −0.356429
383383 49.0332 28.3093i 0.128024 0.0739147i −0.434620 0.900614i 0.643117π-0.643117\pi
0.562644 + 0.826699i 0.309784π0.309784\pi
384384 456.089 80.2347i 1.18773 0.208944i
385385 −0.313904 5.03207i −0.000815334 0.0130703i
386386 55.7361 0.144394
387387 148.003 + 124.389i 0.382438 + 0.321420i
388388 124.966 72.1492i 0.322077 0.185951i
389389 −206.783 + 358.158i −0.531575 + 0.920715i 0.467746 + 0.883863i 0.345066π0.345066\pi
−0.999321 + 0.0368521i 0.988267π0.988267\pi
390390 −74.2039 + 13.0539i −0.190266 + 0.0334715i
391391 −271.901 156.982i −0.695398 0.401488i
392392 −324.641 + 40.6608i −0.828165 + 0.103726i
393393 −285.617 + 239.468i −0.726760 + 0.609334i
394394 390.563 0.991277
395395 79.0721 45.6523i 0.200182 0.115575i
396396 0.596097 3.36505i 0.00150530 0.00849761i
397397 −540.503 312.059i −1.36147 0.786044i −0.371648 0.928374i 0.621207π-0.621207\pi
−0.989819 + 0.142330i 0.954541π0.954541\pi
398398 560.632 323.681i 1.40862 0.813269i
399399 −424.005 125.219i −1.06267 0.313832i
400400 202.367 350.511i 0.505919 0.876277i
401401 −63.4372 109.876i −0.158198 0.274006i 0.776021 0.630707i 0.217235π-0.217235\pi
−0.934219 + 0.356701i 0.883902π0.883902\pi
402402 −500.089 + 87.9750i −1.24400 + 0.218843i
403403 −141.430 + 244.965i −0.350944 + 0.607853i
404404 41.4398 + 23.9253i 0.102574 + 0.0592209i
405405 −53.8242 + 147.155i −0.132899 + 0.363347i
406406 349.321 + 526.378i 0.860397 + 1.29650i
407407 −5.49910 9.52472i −0.0135113 0.0234023i
408408 −176.639 + 148.098i −0.432938 + 0.362986i
409409 432.530i 1.05753i 0.848768 + 0.528765i 0.177345π0.177345\pi
−0.848768 + 0.528765i 0.822655π0.822655\pi
410410 −98.2886 −0.239728
411411 −4.75656 + 13.0525i −0.0115731 + 0.0317578i
412412 −116.181 + 67.0769i −0.281992 + 0.162808i
413413 −4.02308 64.4924i −0.00974110 0.156156i
414414 −421.164 353.967i −1.01730 0.854993i
415415 90.6626 157.032i 0.218464 0.378391i
416416 −80.0365 46.2091i −0.192395 0.111080i
417417 122.717 + 44.7203i 0.294285 + 0.107243i
418418 15.2097 8.78132i 0.0363868 0.0210080i
419419 −150.801 87.0648i −0.359906 0.207792i 0.309134 0.951019i 0.399961π-0.399961\pi
−0.669040 + 0.743227i 0.733294π0.733294\pi
420420 30.0278 28.5420i 0.0714947 0.0679571i
421421 −175.470 303.923i −0.416793 0.721907i 0.578822 0.815454i 0.303513π-0.303513\pi
−0.995615 + 0.0935470i 0.970179π0.970179\pi
422422 −335.180 + 580.549i −0.794265 + 1.37571i
423423 −163.721 450.930i −0.387047 1.06603i
424424 −291.989 505.739i −0.688653 1.19278i
425425 244.625i 0.575588i
426426 −645.254 + 113.512i −1.51468 + 0.266461i
427427 30.7402 + 492.785i 0.0719911 + 1.15406i
428428 71.3451 123.573i 0.166694 0.288723i
429429 4.95997 4.15856i 0.0115617 0.00969362i
430430 −80.6296 46.5515i −0.187511 0.108259i
431431 367.837 + 637.113i 0.853451 + 1.47822i 0.878075 + 0.478524i 0.158828π0.158828\pi
−0.0246236 + 0.999697i 0.507839π0.507839\pi
432432 −445.494 + 256.501i −1.03124 + 0.593752i
433433 134.778i 0.311266i −0.987815 0.155633i 0.950258π-0.950258\pi
0.987815 0.155633i 0.0497417π-0.0497417\pi
434434 −47.6648 764.096i −0.109827 1.76059i
435435 219.634 + 80.0386i 0.504905 + 0.183997i
436436 56.6427 + 98.1081i 0.129915 + 0.225019i
437437 574.394i 1.31440i
438438 −448.005 + 375.619i −1.02284 + 0.857577i
439439 5.84694i 0.0133188i 0.999978 + 0.00665939i 0.00211977π0.00211977\pi
−0.999978 + 0.00665939i 0.997880π0.997880\pi
440440 4.80927i 0.0109302i
441441 392.606 200.852i 0.890263 0.455447i
442442 149.399 0.338007
443443 −160.318 −0.361892 −0.180946 0.983493i 0.557916π-0.557916\pi
−0.180946 + 0.983493i 0.557916π0.557916\pi
444444 30.9423 84.9088i 0.0696900 0.191236i
445445 57.3623 0.128904
446446 31.5398 18.2095i 0.0707170 0.0408285i
447447 50.6163 + 60.3707i 0.113236 + 0.135057i
448448 −282.414 + 17.6172i −0.630389 + 0.0393240i
449449 46.7901 0.104209 0.0521047 0.998642i 0.483407π-0.483407\pi
0.0521047 + 0.998642i 0.483407π0.483407\pi
450450 −74.7693 + 422.083i −0.166154 + 0.937963i
451451 7.31257 4.22191i 0.0162141 0.00936122i
452452 51.7697 89.6677i 0.114535 0.198380i
453453 −123.131 + 337.883i −0.271812 + 0.745878i
454454 −59.2669 34.2177i −0.130544 0.0753695i
455455 78.3131 4.88522i 0.172117 0.0107367i
456456 −396.224 144.392i −0.868913 0.316648i
457457 554.340 1.21300 0.606499 0.795084i 0.292573π-0.292573\pi
0.606499 + 0.795084i 0.292573π0.292573\pi
458458 354.298 204.554i 0.773577 0.446625i
459459 155.670 268.891i 0.339151 0.585819i
460460 46.6132 + 26.9122i 0.101333 + 0.0585047i
461461 −117.654 + 67.9273i −0.255214 + 0.147348i −0.622149 0.782899i 0.713740π-0.713740\pi
0.366935 + 0.930246i 0.380407π0.380407\pi
462462 −4.96182 + 16.8012i −0.0107399 + 0.0363663i
463463 0.952160 1.64919i 0.00205650 0.00356196i −0.864995 0.501780i 0.832679π-0.832679\pi
0.867052 + 0.498218i 0.166012π0.166012\pi
464464 383.458 + 664.169i 0.826418 + 1.43140i
465465 −182.007 217.082i −0.391414 0.466844i
466466 391.858 678.718i 0.840897 1.45648i
467467 −89.3271 51.5730i −0.191278 0.110435i 0.401302 0.915946i 0.368558π-0.368558\pi
−0.592581 + 0.805511i 0.701891π0.701891\pi
468468 52.3697 + 9.27694i 0.111901 + 0.0198225i
469469 527.782 32.9234i 1.12533 0.0701991i
470470 115.512 + 200.072i 0.245770 + 0.425686i
471471 −101.852 578.973i −0.216247 1.22924i
472472 61.6369i 0.130587i
473473 7.99834 0.0169098
474474 −312.452 + 54.9662i −0.659182 + 0.115962i
475475 −387.580 + 223.769i −0.815958 + 0.471094i
476476 −68.4476 + 45.4240i −0.143797 + 0.0954286i
477477 602.583 + 506.441i 1.26328 + 1.06172i
478478 111.163 192.540i 0.232559 0.402804i
479479 165.785 + 95.7160i 0.346106 + 0.199825i 0.662969 0.748647i 0.269296π-0.269296\pi
−0.316863 + 0.948471i 0.602629π0.602629\pi
480480 70.9266 59.4666i 0.147764 0.123889i
481481 148.231 85.5813i 0.308173 0.177924i
482482 545.209 + 314.777i 1.13114 + 0.653064i
483483 394.734 + 415.283i 0.817255 + 0.859799i
484484 61.6283 + 106.743i 0.127331 + 0.220544i
485485 −136.856 + 237.042i −0.282178 + 0.488746i
486486 350.784 416.372i 0.721778 0.856733i
487487 −224.406 388.683i −0.460794 0.798118i 0.538207 0.842813i 0.319102π-0.319102\pi
−0.999001 + 0.0446948i 0.985768π0.985768\pi
488488 470.966i 0.965093i
489489 85.9578 235.876i 0.175783 0.482365i
490490 −169.297 + 128.220i −0.345504 + 0.261673i
491491 −40.8828 + 70.8111i −0.0832644 + 0.144218i −0.904650 0.426155i 0.859868π-0.859868\pi
0.821386 + 0.570373i 0.193201π0.193201\pi
492492 65.1884 + 23.7559i 0.132497 + 0.0482843i
493493 −401.429 231.765i −0.814258 0.470112i
494494 136.662 + 236.705i 0.276644 + 0.479161i
495495 2.21228 + 6.09320i 0.00446926 + 0.0123095i
496496 929.392i 1.87377i
497497 680.986 42.4803i 1.37019 0.0854735i
498498 −482.798 + 404.790i −0.969474 + 0.812832i
499499 13.7715 + 23.8529i 0.0275982 + 0.0478014i 0.879495 0.475909i 0.157881π-0.157881\pi
−0.851896 + 0.523710i 0.824547π0.824547\pi
500500 91.2568i 0.182514i
501501 702.482 + 255.997i 1.40216 + 0.510973i
502502 37.1884i 0.0740805i
503503 49.4903i 0.0983902i 0.998789 + 0.0491951i 0.0156656π0.0156656\pi
−0.998789 + 0.0491951i 0.984334π0.984334\pi
504504 385.696 167.899i 0.765270 0.333133i
505505 −90.7653 −0.179733
506506 −22.7604 −0.0449810
507507 −261.021 311.322i −0.514834 0.614048i
508508 −50.0745 −0.0985718
509509 −108.850 + 62.8447i −0.213851 + 0.123467i −0.603100 0.797666i 0.706068π-0.706068\pi
0.389249 + 0.921133i 0.372735π0.372735\pi
510510 −51.2301 + 140.580i −0.100451 + 0.275648i
511511 507.312 336.668i 0.992782 0.658842i
512512 −204.849 −0.400097
513513 568.425 + 0.675026i 1.10804 + 0.00131584i
514514 165.318 95.4464i 0.321630 0.185693i
515515 127.235 220.377i 0.247058 0.427917i
516516 42.2251 + 50.3624i 0.0818316 + 0.0976015i
517517 −17.1879 9.92344i −0.0332454 0.0191943i
518518 −206.204 + 414.840i −0.398077 + 0.800850i
519519 144.733 + 822.727i 0.278869 + 1.58522i
520520 74.8456 0.143934
521521 −606.831 + 350.354i −1.16474 + 0.672464i −0.952436 0.304739i 0.901431π-0.901431\pi
−0.212306 + 0.977203i 0.568097π0.568097\pi
522522 −621.799 522.591i −1.19119 1.00113i
523523 −302.754 174.795i −0.578879 0.334216i 0.181809 0.983334i 0.441805π-0.441805\pi
−0.760688 + 0.649118i 0.775138π0.775138\pi
524524 −109.728 + 63.3515i −0.209405 + 0.120900i
525525 126.439 428.136i 0.240837 0.815498i
526526 399.541 692.026i 0.759584 1.31564i
527527 280.866 + 486.474i 0.532953 + 0.923101i
528528 −7.28166 + 19.9816i −0.0137910 + 0.0378439i
529529 −107.694 + 186.531i −0.203580 + 0.352611i
530530 −328.277 189.531i −0.619390 0.357605i
531531 28.3532 + 78.0921i 0.0533959 + 0.147066i
532532 −134.581 66.8959i −0.252972 0.125744i
533533 65.7048 + 113.804i 0.123273 + 0.213516i
534534 −187.266 68.2432i −0.350685 0.127796i
535535 270.662i 0.505911i
536536 504.413 0.941070
537537 −496.349 592.001i −0.924299 1.10242i
538538 −747.204 + 431.399i −1.38886 + 0.801856i
539539 7.08792 16.8114i 0.0131501 0.0311900i
540540 −26.6873 + 46.0973i −0.0494209 + 0.0853653i
541541 −350.723 + 607.469i −0.648286 + 1.12286i 0.335246 + 0.942131i 0.391180π0.391180\pi
−0.983532 + 0.180734i 0.942153π0.942153\pi
542542 120.883 + 69.7918i 0.223031 + 0.128767i
543543 −15.2056 86.4352i −0.0280029 0.159181i
544544 −158.944 + 91.7664i −0.292177 + 0.168688i
545545 −186.096 107.443i −0.341461 0.197143i
546546 −261.474 77.2197i −0.478891 0.141428i
547547 −202.629 350.964i −0.370437 0.641616i 0.619195 0.785237i 0.287459π-0.287459\pi
−0.989633 + 0.143620i 0.954126π0.954126\pi
548548 −2.36124 + 4.08979i −0.00430884 + 0.00746313i
549549 −216.646 596.700i −0.394619 1.08688i
550550 8.86688 + 15.3579i 0.0161216 + 0.0279234i
551551 848.024i 1.53906i
552552 351.132 + 418.799i 0.636108 + 0.758694i
553553 329.755 20.5703i 0.596302 0.0371977i
554554 −95.2339 + 164.950i −0.171902 + 0.297744i
555555 29.7000 + 168.828i 0.0535136 + 0.304195i
556556 38.4515 + 22.2000i 0.0691574 + 0.0399280i
557557 −51.7943 89.7104i −0.0929880 0.161060i 0.815779 0.578364i 0.196308π-0.196308\pi
−0.908767 + 0.417304i 0.862975π0.862975\pi
558558 335.924 + 925.223i 0.602015 + 1.65811i
559559 124.477i 0.222677i
560560 −214.813 + 142.557i −0.383595 + 0.254566i
561561 −2.22706 12.6596i −0.00396980 0.0225661i
562562 165.535 + 286.715i 0.294546 + 0.510168i
563563 130.812i 0.232348i −0.993229 0.116174i 0.962937π-0.962937\pi
0.993229 0.116174i 0.0370630π-0.0370630\pi
564564 −28.2549 160.613i −0.0500974 0.284776i
565565 196.399i 0.347608i
566566 786.000i 1.38869i
567567 −411.432 + 390.145i −0.725629 + 0.688086i
568568 650.834 1.14584
569569 −635.580 −1.11701 −0.558506 0.829500i 0.688625π-0.688625\pi
−0.558506 + 0.829500i 0.688625π0.688625\pi
570570 −269.596 + 47.4270i −0.472975 + 0.0832052i
571571 172.059 0.301330 0.150665 0.988585i 0.451859π-0.451859\pi
0.150665 + 0.988585i 0.451859π0.451859\pi
572572 1.90552 1.10015i 0.00333133 0.00192334i
573573 −179.554 + 31.5869i −0.313358 + 0.0551255i
574574 −318.492 158.312i −0.554864 0.275805i
575575 579.990 1.00868
576576 341.968 124.160i 0.593694 0.215555i
577577 27.4829 15.8672i 0.0476306 0.0274996i −0.475996 0.879448i 0.657912π-0.657912\pi
0.523626 + 0.851948i 0.324579π0.324579\pi
578578 −175.406 + 303.812i −0.303471 + 0.525627i
579579 73.5014 12.9303i 0.126946 0.0223321i
580580 68.8189 + 39.7326i 0.118653 + 0.0685045i
581581 546.711 362.815i 0.940983 0.624466i
582582 728.789 611.035i 1.25222 1.04989i
583583 32.5646 0.0558569
584584 502.964 290.386i 0.861240 0.497237i
585585 −94.8272 + 34.4293i −0.162098 + 0.0588535i
586586 −95.8236 55.3238i −0.163521 0.0944092i
587587 −780.765 + 450.775i −1.33009 + 0.767929i −0.985314 0.170754i 0.945380π-0.945380\pi
−0.344779 + 0.938684i 0.612046π0.612046\pi
588588 143.273 44.1215i 0.243662 0.0750365i
589589 −513.842 + 890.000i −0.872396 + 1.51104i
590590 −20.0043 34.6485i −0.0339056 0.0587263i
591591 515.051 90.6072i 0.871491 0.153312i
592592 −281.193 + 487.041i −0.474989 + 0.822705i
593593 −92.1847 53.2228i −0.155455 0.0897518i 0.420255 0.907406i 0.361941π-0.361941\pi
−0.575709 + 0.817654i 0.695274π0.695274\pi
594594 0.0267479 22.5239i 4.50302e−5 0.0379190i
595595 69.3590 139.536i 0.116570 0.234515i
596596 13.3906 + 23.1932i 0.0224674 + 0.0389147i
597597 664.236 556.912i 1.11262 0.932852i
598598 354.215i 0.592333i
599599 −815.080 −1.36073 −0.680367 0.732871i 0.738180π-0.738180\pi
−0.680367 + 0.732871i 0.738180π0.738180\pi
600600 145.798 400.085i 0.242997 0.666808i
601601 −222.029 + 128.189i −0.369433 + 0.213292i −0.673211 0.739451i 0.735085π-0.735085\pi
0.303778 + 0.952743i 0.401752π0.401752\pi
602602 −186.290 280.714i −0.309453 0.466302i
603603 −639.077 + 232.032i −1.05983 + 0.384796i
604604 −61.1244 + 105.871i −0.101199 + 0.175282i
605605 −202.476 116.900i −0.334672 0.193223i
606606 296.314 + 107.982i 0.488967 + 0.178189i
607607 280.441 161.913i 0.462012 0.266742i −0.250878 0.968019i 0.580719π-0.580719\pi
0.712890 + 0.701276i 0.247386π0.247386\pi
608608 −290.786 167.886i −0.478267 0.276128i
609609 582.779 + 613.116i 0.956944 + 1.00676i
610610 152.852 + 264.748i 0.250578 + 0.434014i
611611 154.436 267.492i 0.252760 0.437793i
612612 67.9551 80.8557i 0.111038 0.132117i
613613 310.620 + 538.010i 0.506721 + 0.877667i 0.999970 + 0.00777855i 0.00247602π0.00247602\pi
−0.493248 + 0.869888i 0.664191π0.664191\pi
614614 969.418i 1.57886i
615615 −129.617 + 22.8021i −0.210759 + 0.0370766i
616616 7.74622 15.5838i 0.0125750 0.0252984i
617617 372.353 644.935i 0.603490 1.04527i −0.388799 0.921323i 0.627110π-0.627110\pi
0.992288 0.123952i 0.0395569π-0.0395569\pi
618618 −677.553 + 568.078i −1.09636 + 0.919219i
619619 −159.035 91.8186i −0.256922 0.148334i 0.366008 0.930612i 0.380724π-0.380724\pi
−0.622930 + 0.782278i 0.714058π0.714058\pi
620620 −48.1502 83.3986i −0.0776616 0.134514i
621621 −637.523 369.084i −1.02661 0.594339i
622622 374.587i 0.602230i
623623 185.875 + 92.3926i 0.298355 + 0.148303i
624624 −310.970 113.323i −0.498349 0.181607i
625625 −179.174 310.338i −0.286678 0.496541i
626626 579.359i 0.925493i
627627 18.0204 15.1088i 0.0287407 0.0240970i
628628 199.838i 0.318214i
629629 339.911i 0.540399i
630630 162.323 219.561i 0.257656 0.348509i
631631 325.873 0.516439 0.258220 0.966086i 0.416864π-0.416864\pi
0.258220 + 0.966086i 0.416864π0.416864\pi
632632 315.154 0.498662
633633 −307.333 + 843.351i −0.485518 + 1.33231i
634634 −453.730 −0.715663
635635 82.2584 47.4919i 0.129541 0.0747904i
636636 171.916 + 205.046i 0.270308 + 0.322400i
637637 261.633 + 110.308i 0.410726 + 0.173168i
638638 −33.6030 −0.0526693
639639 −824.588 + 299.386i −1.29044 + 0.468523i
640640 −258.603 + 149.304i −0.404067 + 0.233288i
641641 89.3312 154.726i 0.139362 0.241383i −0.787893 0.615812i 0.788828π-0.788828\pi
0.927255 + 0.374429i 0.122161π0.122161\pi
642642 322.003 883.608i 0.501563 1.37634i
643643 −60.1837 34.7471i −0.0935983 0.0540390i 0.452470 0.891780i 0.350543π-0.350543\pi
−0.546069 + 0.837740i 0.683876π0.683876\pi
644644 107.697 + 162.285i 0.167232 + 0.251995i
645645 −117.129 42.6840i −0.181595 0.0661767i
646646 542.793 0.840236
647647 −712.875 + 411.579i −1.10182 + 0.636134i −0.936697 0.350140i 0.886134π-0.886134\pi
−0.165119 + 0.986274i 0.552801π0.552801\pi
648648 −414.860 + 346.991i −0.640216 + 0.535480i
649649 2.97660 + 1.71854i 0.00458644 + 0.00264798i
650650 −239.012 + 137.993i −0.367710 + 0.212298i
651651 −240.121 996.586i −0.368849 1.53085i
652652 42.6710 73.9084i 0.0654463 0.113356i
653653 −391.218 677.609i −0.599108 1.03769i −0.992953 0.118509i 0.962189π-0.962189\pi
0.393845 0.919177i 0.371145π-0.371145\pi
654654 479.711 + 572.157i 0.733502 + 0.874857i
655655 120.168 208.138i 0.183463 0.317768i
656656 −373.924 215.885i −0.570006 0.329093i
657657 −503.662 + 599.276i −0.766608 + 0.912141i
658658 52.0480 + 834.362i 0.0791004 + 1.26803i
659659 90.6800 + 157.062i 0.137602 + 0.238334i 0.926589 0.376077i 0.122727π-0.122727\pi
−0.788986 + 0.614411i 0.789394π0.789394\pi
660660 0.381795 + 2.17029i 0.000578477 + 0.00328832i
661661 192.972i 0.291940i 0.989289 + 0.145970i 0.0466303π0.0466303\pi
−0.989289 + 0.145970i 0.953370π0.953370\pi
662662 76.5270 0.115600
663663 197.018 34.6592i 0.297162 0.0522764i
664664 542.025 312.939i 0.816303 0.471293i
665665 284.525 17.7489i 0.427857 0.0266900i
666666 103.893 586.493i 0.155996 0.880620i
667667 −549.500 + 951.762i −0.823839 + 1.42693i
668668 220.112 + 127.082i 0.329509 + 0.190242i
669669 37.3683 31.3306i 0.0558570 0.0468319i
670670 283.551 163.708i 0.423210 0.244340i
671671 −22.7441 13.1313i −0.0338958 0.0195698i
672672 325.611 78.4539i 0.484540 0.116747i
673673 −41.9447 72.6503i −0.0623249 0.107950i 0.833179 0.553003i 0.186518π-0.186518\pi
−0.895504 + 0.445053i 0.853185π0.853185\pi
674674 461.215 798.849i 0.684296 1.18524i
675675 −0.681603 + 573.964i −0.00100978 + 0.850317i
676676 −69.0532 119.604i −0.102150 0.176929i
677677 207.203i 0.306060i −0.988222 0.153030i 0.951097π-0.951097\pi
0.988222 0.153030i 0.0489031π-0.0489031\pi
678678 233.653 641.167i 0.344621 0.945674i
679679 −825.266 + 547.673i −1.21541 + 0.806587i
680680 74.3178 128.722i 0.109291 0.189297i
681681 −86.0958 31.3749i −0.126425 0.0460718i
682682 35.2663 + 20.3610i 0.0517101 + 0.0298549i
683683 −639.939 1108.41i −0.936953 1.62285i −0.771113 0.636698i 0.780300π-0.780300\pi
−0.165841 0.986153i 0.553034π-0.553034\pi
684684 190.268 + 33.7047i 0.278170 + 0.0492759i
685685 8.95786i 0.0130772i
686686 −755.107 + 142.796i −1.10074 + 0.208157i
687687 419.772 351.948i 0.611022 0.512296i
688688 −204.495 354.197i −0.297232 0.514821i
689689 506.796i 0.735553i
690690 333.307 + 121.463i 0.483053 + 0.176034i
691691 1215.74i 1.75939i 0.475538 + 0.879695i 0.342253π0.342253\pi
−0.475538 + 0.879695i 0.657747π0.657747\pi
692692 283.972i 0.410364i
693693 −2.64560 + 23.3076i −0.00381761 + 0.0336328i
694694 −1338.67 −1.92892
695695 −84.2201 −0.121180
696696 518.405 + 618.307i 0.744834 + 0.888373i
697697 260.966 0.374413
698698 −163.168 + 94.2049i −0.233765 + 0.134964i
699699 359.302 985.960i 0.514023 1.41053i
700700 67.5477 135.892i 0.0964967 0.194132i
701701 −1171.72 −1.67149 −0.835747 0.549114i 0.814965π-0.814965\pi
−0.835747 + 0.549114i 0.814965π0.814965\pi
702702 350.535 + 0.416273i 0.499337 + 0.000592981i
703703 538.550 310.932i 0.766074 0.442293i
704704 7.52554 13.0346i 0.0106897 0.0185151i
705705 198.745 + 237.045i 0.281908 + 0.336235i
706706 889.515 + 513.562i 1.25994 + 0.727425i
707707 −294.114 146.194i −0.416002 0.206781i
708708 4.89319 + 27.8150i 0.00691129 + 0.0392868i
709709 −111.673 −0.157508 −0.0787540 0.996894i 0.525094π-0.525094\pi
−0.0787540 + 0.996894i 0.525094π0.525094\pi
710710 365.860 211.229i 0.515295 0.297506i
711711 −399.291 + 144.972i −0.561591 + 0.203899i
712712 171.470 + 98.9981i 0.240828 + 0.139042i
713713 1153.40 665.915i 1.61767 0.933962i
714714 −392.436 + 373.018i −0.549630 + 0.522434i
715715 −2.08682 + 3.61448i −0.00291863 + 0.00505522i
716716 −131.309 227.435i −0.183393 0.317646i
717717 101.928 279.699i 0.142158 0.390097i
718718 14.4010 24.9432i 0.0200571 0.0347398i
719719 1204.35 + 695.331i 1.67503 + 0.967081i 0.964751 + 0.263164i 0.0847662π0.0847662\pi
0.710283 + 0.703917i 0.248567π0.248567\pi
720720 213.268 253.754i 0.296205 0.352437i
721721 767.247 509.170i 1.06414 0.706199i
722722 92.1074 + 159.535i 0.127573 + 0.220962i
723723 792.014 + 288.625i 1.09546 + 0.399204i
724724 29.8339i 0.0412071i
725725 856.287 1.18109
726726 521.934 + 622.517i 0.718917 + 0.857461i
727727 570.198 329.204i 0.784317 0.452826i −0.0536411 0.998560i 0.517083π-0.517083\pi
0.837958 + 0.545735i 0.183749π0.183749\pi
728728 242.528 + 120.553i 0.333143 + 0.165595i
729729 365.998 630.465i 0.502055 0.864835i
730730 188.491 326.475i 0.258206 0.447226i
731731 214.079 + 123.599i 0.292858 + 0.169082i
732732 −37.3887 212.534i −0.0510775 0.290347i
733733 322.167 186.003i 0.439518 0.253756i −0.263875 0.964557i 0.585001π-0.585001\pi
0.703393 + 0.710801i 0.251667π0.251667\pi
734734 1199.80 + 692.703i 1.63460 + 0.943737i
735735 −193.512 + 208.364i −0.263282 + 0.283488i
736736 217.572 + 376.846i 0.295614 + 0.512019i
737737 −14.0639 + 24.3594i −0.0190826 + 0.0330521i
738738 450.278 + 79.7637i 0.610132 + 0.108081i
739739 470.172 + 814.362i 0.636227 + 1.10198i 0.986254 + 0.165238i 0.0528393π0.0528393\pi
−0.350026 + 0.936740i 0.613827π0.613827\pi
740740 58.2726i 0.0787467i
741741 235.135 + 280.448i 0.317321 + 0.378473i
742742 −758.466 1142.90i −1.02219 1.54030i
743743 −103.438 + 179.161i −0.139217 + 0.241131i −0.927201 0.374565i 0.877792π-0.877792\pi
0.787983 + 0.615697i 0.211125π0.211125\pi
744744 −169.415 963.028i −0.227708 1.29439i
745745 −43.9940 25.3999i −0.0590523 0.0340939i
746746 −0.648921 1.12396i −0.000869867 0.00150665i
747747 −542.777 + 645.818i −0.726610 + 0.864549i
748748 4.36957i 0.00584167i
749749 −435.952 + 877.047i −0.582045 + 1.17096i
750750 −104.208 592.365i −0.138944 0.789820i
751751 −724.153 1254.27i −0.964252 1.67013i −0.711611 0.702574i 0.752034π-0.752034\pi
−0.252641 0.967560i 0.581299π-0.581299\pi
752752 1014.86i 1.34955i
753753 8.62738 + 49.0418i 0.0114573 + 0.0651285i
754754 522.957i 0.693577i
755755 231.888i 0.307136i
756756 −160.725 + 106.388i −0.212599 + 0.140724i
757757 −296.987 −0.392321 −0.196161 0.980572i 0.562847π-0.562847\pi
−0.196161 + 0.980572i 0.562847π0.562847\pi
758758 41.4524 0.0546866
759759 −30.0150 + 5.28021i −0.0395455 + 0.00695680i
760760 271.927 0.357799
761761 254.681 147.040i 0.334666 0.193220i −0.323245 0.946315i 0.604774π-0.604774\pi
0.657911 + 0.753096i 0.271440π0.271440\pi
762762 −325.043 + 57.1812i −0.426565 + 0.0750409i
763763 −429.966 647.898i −0.563520 0.849146i
764764 −61.9748 −0.0811188
765765 −34.9457 + 197.274i −0.0456807 + 0.257874i
766766 109.859 63.4270i 0.143419 0.0828028i
767767 −26.7453 + 46.3242i −0.0348700 + 0.0603967i
768768 544.122 95.7213i 0.708492 0.124637i
769769 91.6783 + 52.9305i 0.119218 + 0.0688303i 0.558423 0.829556i 0.311407π-0.311407\pi
−0.439205 + 0.898387i 0.644740π0.644740\pi
770770 −0.703300 11.2743i −0.000913376 0.0146420i
771771 195.869 164.221i 0.254045 0.212998i
772772 25.3697 0.0328623
773773 −1070.93 + 618.299i −1.38541 + 0.799869i −0.992794 0.119832i 0.961765π-0.961765\pi
−0.392620 + 0.919701i 0.628431π0.628431\pi
774774 331.601 + 278.694i 0.428425 + 0.360070i
775775 −898.671 518.848i −1.15958 0.669481i
776776 −818.193 + 472.384i −1.05437 + 0.608742i
777777 −175.690 + 594.904i −0.226113 + 0.765642i
778778 −463.296 + 802.452i −0.595496 + 1.03143i
779779 238.717 + 413.470i 0.306440 + 0.530770i
780780 −33.7758 + 5.94180i −0.0433023 + 0.00761769i
781781 −18.1464 + 31.4304i −0.0232348 + 0.0402438i
782782 −609.192 351.717i −0.779018 0.449766i
783783 −941.227 544.909i −1.20208 0.695925i
784784 −925.690 + 115.941i −1.18073 + 0.147884i
785785 189.532 + 328.278i 0.241442 + 0.418189i
786786 −639.923 + 536.528i −0.814151 + 0.682605i
787787 841.649i 1.06944i −0.845029 0.534720i 0.820417π-0.820417\pi
0.845029 0.534720i 0.179583π-0.179583\pi
788788 177.775 0.225602
789789 366.347 1005.29i 0.464318 1.27413i
790790 177.161 102.284i 0.224254 0.129473i
791791 −316.337 + 636.406i −0.399920 + 0.804559i
792792 −3.90284 + 22.0321i −0.00492783 + 0.0278183i
793793 204.360 353.962i 0.257705 0.446358i
794794 −1210.99 699.167i −1.52518 0.880564i
795795 −476.881 173.784i −0.599850 0.218597i
796796 255.186 147.332i 0.320585 0.185090i
797797 138.377 + 79.8921i 0.173622 + 0.100241i 0.584293 0.811543i 0.301372π-0.301372\pi
−0.410670 + 0.911784i 0.634705π0.634705\pi
798798 −949.982 280.553i −1.19045 0.351570i
799799 −306.695 531.211i −0.383848 0.664844i
800800 169.521 293.620i 0.211902 0.367025i
801801 −262.787 46.5509i −0.328073 0.0581160i
802802 −142.131 246.178i −0.177220 0.306955i
803803 32.3859i 0.0403311i
804804 −227.628 + 40.0441i −0.283119 + 0.0498061i
805805 −330.832 164.446i −0.410971 0.204280i
806806 −316.874 + 548.842i −0.393144 + 0.680946i
807807 −885.287 + 742.247i −1.09701 + 0.919761i
808808 −271.320 156.646i −0.335792 0.193869i
809809 −17.7511 30.7458i −0.0219420 0.0380046i 0.854846 0.518882i 0.173652π-0.173652\pi
−0.876788 + 0.480877i 0.840318π0.840318\pi
810810 −120.593 + 329.701i −0.148880 + 0.407038i
811811 264.939i 0.326682i 0.986570 + 0.163341i 0.0522271π0.0522271\pi
−0.986570 + 0.163341i 0.947773π0.947773\pi
812812 159.002 + 239.594i 0.195816 + 0.295067i
813813 175.604 + 63.9934i 0.215995 + 0.0787127i
814814 −12.3207 21.3401i −0.0151360 0.0262163i
815815 161.881i 0.198627i
816816 −503.674 + 422.293i −0.617247 + 0.517515i
817817 452.245i 0.553544i
818818 969.081i 1.18470i
819819 −362.731 41.1730i −0.442895 0.0502723i
820820 −44.7386 −0.0545592
821821 1507.56 1.83625 0.918126 0.396289i 0.129702π-0.129702\pi
0.918126 + 0.396289i 0.129702π0.129702\pi
822822 −10.6570 + 29.2440i −0.0129648 + 0.0355766i
823823 1234.84 1.50041 0.750207 0.661203i 0.229954π-0.229954\pi
0.750207 + 0.661203i 0.229954π0.229954\pi
824824 760.672 439.174i 0.923145 0.532978i
825825 15.2560 + 18.1960i 0.0184921 + 0.0220558i
826826 −9.01368 144.495i −0.0109124 0.174933i
827827 642.770 0.777231 0.388616 0.921400i 0.372953π-0.372953\pi
0.388616 + 0.921400i 0.372953π0.372953\pi
828828 −191.704 161.117i −0.231526 0.194586i
829829 831.340 479.974i 1.00282 0.578980i 0.0937403 0.995597i 0.470118π-0.470118\pi
0.909082 + 0.416617i 0.136784π0.136784\pi
830830 203.129 351.830i 0.244734 0.423892i
831831 −87.3218 + 239.619i −0.105080 + 0.288351i
832832 202.855 + 117.119i 0.243816 + 0.140767i
833833 449.499 340.435i 0.539614 0.408685i
834834 274.947 + 100.196i 0.329672 + 0.120139i
835835 −482.110 −0.577378
836836 6.92308 3.99704i 0.00828120 0.00478115i
837837 657.640 + 1142.20i 0.785711 + 1.36463i
838838 −337.868 195.068i −0.403184 0.232778i
839839 −409.757 + 236.574i −0.488388 + 0.281971i −0.723905 0.689899i 0.757655π-0.757655\pi
0.235518 + 0.971870i 0.424321π0.424321\pi
840840 −196.602 + 186.874i −0.234050 + 0.222469i
841841 −390.772 + 676.837i −0.464652 + 0.804800i
842842 −393.140 680.938i −0.466912 0.808715i
843843 284.812 + 339.699i 0.337856 + 0.402965i
844844 −152.566 + 264.251i −0.180765 + 0.313094i
845845 226.870 + 130.984i 0.268486 + 0.155010i
846846 −366.816 1010.31i −0.433589 1.19422i
847847 −467.811 704.925i −0.552315 0.832261i
848848 −832.586 1442.08i −0.981823 1.70057i
849849 −182.345 1036.53i −0.214776 1.22088i
850850 548.081i 0.644801i
851851 −805.907 −0.947012
852852 −293.704 + 51.6680i −0.344723 + 0.0606432i
853853 1068.57 616.937i 1.25271 0.723255i 0.281067 0.959688i 0.409312π-0.409312\pi
0.971648 + 0.236433i 0.0759783π0.0759783\pi
854854 68.8733 + 1104.08i 0.0806479 + 1.29284i
855855 −344.524 + 125.088i −0.402952 + 0.146301i
856856 −467.120 + 809.075i −0.545701 + 0.945181i
857857 344.080 + 198.655i 0.401493 + 0.231802i 0.687128 0.726536i 0.258871π-0.258871\pi
−0.285635 + 0.958339i 0.592204π0.592204\pi
858858 11.1128 9.31724i 0.0129520 0.0108593i
859859 −473.197 + 273.200i −0.550870 + 0.318045i −0.749473 0.662035i 0.769693π-0.769693\pi
0.198603 + 0.980080i 0.436360π0.436360\pi
860860 −36.7006 21.1891i −0.0426752 0.0246385i
861861 −456.735 134.885i −0.530471 0.156661i
862862 824.138 + 1427.45i 0.956076 + 1.65597i
863863 −7.86960 + 13.6305i −0.00911888 + 0.0157944i −0.870549 0.492082i 0.836236π-0.836236\pi
0.861430 + 0.507876i 0.169569π0.169569\pi
864864 −373.186 + 214.869i −0.431928 + 0.248690i
865865 −269.326 466.487i −0.311360 0.539291i
866866 301.969i 0.348695i
867867 −160.833 + 441.342i −0.185505 + 0.509045i
868868 −21.6958 347.798i −0.0249952 0.400689i
869869 −8.78704 + 15.2196i −0.0101117 + 0.0175139i
870870 492.088 + 179.326i 0.565618 + 0.206122i
871871 −379.100 218.874i −0.435247 0.251290i
872872 −370.858 642.346i −0.425296 0.736635i
873873 819.328 974.869i 0.938520 1.11669i
874874 1286.93i 1.47246i
875875 38.9984 + 625.168i 0.0445696 + 0.714478i
876876 −203.921 + 170.972i −0.232786 + 0.195174i
877877 86.7339 + 150.227i 0.0988984 + 0.171297i 0.911229 0.411900i 0.135135π-0.135135\pi
−0.812331 + 0.583197i 0.801801π0.801801\pi
878878 13.1000i 0.0149203i
879879 −139.201 50.7274i −0.158363 0.0577104i
880880 13.7133i 0.0155833i
881881 1381.76i 1.56840i 0.620507 + 0.784201i 0.286927π0.286927\pi
−0.620507 + 0.784201i 0.713073π0.713073\pi
882882 879.632 450.008i 0.997315 0.510213i
883883 1346.90 1.52537 0.762685 0.646771i 0.223881π-0.223881\pi
0.762685 + 0.646771i 0.223881π0.223881\pi
884884 68.0028 0.0769262
885885 −34.4187 41.0515i −0.0388911 0.0463859i
886886 −359.192 −0.405408
887887 532.683 307.545i 0.600544 0.346724i −0.168711 0.985665i 0.553961π-0.553961\pi
0.769256 + 0.638941i 0.220627π0.220627\pi
888888 −202.590 + 555.926i −0.228141 + 0.626042i
889889 343.043 21.3992i 0.385875 0.0240711i
890890 128.520 0.144404
891891 −5.19007 29.7094i −0.00582499 0.0333438i
892892 14.3561 8.28852i 0.0160943 0.00929206i
893893 561.095 971.844i 0.628325 1.08829i
894894 113.406 + 135.260i 0.126852 + 0.151298i
895895 431.410 + 249.074i 0.482022 + 0.278295i
896896 −1078.45 + 67.2746i −1.20363 + 0.0750832i
897897 −82.1748 467.118i −0.0916107 0.520756i
898898 104.833 0.116740
899899 1702.86 983.145i 1.89417 1.09360i
900900 −34.0331 + 192.122i −0.0378146 + 0.213469i
901901 871.606 + 503.222i 0.967376 + 0.558515i
902902 16.3838 9.45917i 0.0181638 0.0104869i
903903 −310.792 326.970i −0.344177 0.362093i
904904 −338.953 + 587.084i −0.374948 + 0.649429i
905905 28.2953 + 49.0089i 0.0312655 + 0.0541534i
906906 −275.874 + 757.025i −0.304497 + 0.835568i
907907 249.391 431.958i 0.274962 0.476249i −0.695163 0.718852i 0.744668π-0.744668\pi
0.970126 + 0.242603i 0.0780012π0.0780012\pi
908908 −26.9768 15.5751i −0.0297102 0.0171532i
909909 415.812 + 73.6583i 0.457439 + 0.0810323i
910910 175.460 10.9453i 0.192813 0.0120278i
911911 462.758 + 801.521i 0.507967 + 0.879825i 0.999957 + 0.00922428i 0.00293622π0.00293622\pi
−0.491990 + 0.870601i 0.663730π0.663730\pi
912912 −1129.81 411.723i −1.23882 0.451450i
913913 34.9010i 0.0382268i
914914 1242.00 1.35886
915915 262.992 + 313.674i 0.287423 + 0.342813i
916916 161.268 93.1080i 0.176057 0.101646i
917917 724.636 480.891i 0.790224 0.524418i
918918 348.779 602.449i 0.379933 0.656262i
919919 544.947 943.877i 0.592979 1.02707i −0.400850 0.916144i 0.631285π-0.631285\pi
0.993829 0.110925i 0.0353815π-0.0353815\pi
920920 −305.192 176.203i −0.331730 0.191525i
921921 224.896 + 1278.41i 0.244187 + 1.38807i
922922 −263.602 + 152.191i −0.285903 + 0.165066i
923923 −489.146 282.408i −0.529952 0.305968i
924924 −2.25850 + 7.64751i −0.00244426 + 0.00827653i
925925 313.961 + 543.797i 0.339418 + 0.587889i
926926 2.13331 3.69500i 0.00230379 0.00399028i
927927 −761.727 + 906.333i −0.821712 + 0.977705i
928928 321.219 + 556.368i 0.346142 + 0.599535i
929929 537.759i 0.578858i −0.957199 0.289429i 0.906535π-0.906535\pi
0.957199 0.289429i 0.0934654π-0.0934654\pi
930930 −407.787 486.372i −0.438480 0.522981i
931931 950.557 + 400.768i 1.02101 + 0.430470i
932932 178.364 308.936i 0.191378 0.331476i
933933 86.9008 + 493.982i 0.0931413 + 0.529456i
934934 −200.137 115.549i −0.214279 0.123714i
935935 4.14421 + 7.17799i 0.00443231 + 0.00767699i
936936 −342.881 60.7391i −0.366326 0.0648922i
937937 647.389i 0.690917i 0.938434 + 0.345459i 0.112277π0.112277\pi
−0.938434 + 0.345459i 0.887723π0.887723\pi
938938 1182.49 73.7646i 1.26065 0.0786403i
939939 −134.406 764.023i −0.143137 0.813656i
940940 52.5781 + 91.0680i 0.0559342 + 0.0968808i
941941 131.133i 0.139355i 0.997570 + 0.0696777i 0.0221971π0.0221971\pi
−0.997570 + 0.0696777i 0.977803π0.977803\pi
942942 −228.200 1297.19i −0.242250 1.37706i
943943 618.732i 0.656132i
944944 175.753i 0.186179i
945945 163.126 327.201i 0.172620 0.346244i
946946 17.9202 0.0189432
947947 418.984 0.442433 0.221217 0.975225i 0.428997π-0.428997\pi
0.221217 + 0.975225i 0.428997π0.428997\pi
948948 −142.221 + 25.0193i −0.150022 + 0.0263916i
949949 −504.015 −0.531101
950950 −868.371 + 501.354i −0.914075 + 0.527742i
951951 −598.352 + 105.261i −0.629182 + 0.110685i
952952 448.149 297.406i 0.470744 0.312401i
953953 −1131.25 −1.18704 −0.593520 0.804819i 0.702262π-0.702262\pi
−0.593520 + 0.804819i 0.702262π0.702262\pi
954954 1350.09 + 1134.68i 1.41518 + 1.18939i
955955 101.807 58.7785i 0.106604 0.0615481i
956956 50.5987 87.6396i 0.0529275 0.0916732i
957957 −44.3136 + 7.79560i −0.0463047 + 0.00814587i
958958 371.440 + 214.451i 0.387725 + 0.223853i
959959 14.4283 29.0268i 0.0150451 0.0302678i
960960 −179.766 + 150.720i −0.187256 + 0.157000i
961961 −1421.86 −1.47956
962962 332.111 191.745i 0.345230 0.199319i
963963 219.649 1239.95i 0.228088 1.28759i
964964 248.166 + 143.279i 0.257433 + 0.148629i
965965 −41.6754 + 24.0613i −0.0431869 + 0.0249340i
966966 884.401 + 930.439i 0.915528 + 0.963187i
967967 −115.840 + 200.640i −0.119793 + 0.207488i −0.919686 0.392656i 0.871556π-0.871556\pi
0.799893 + 0.600143i 0.204890π0.204890\pi
968968 −403.501 698.884i −0.416840 0.721987i
969969 715.802 125.923i 0.738702 0.129952i
970970 −306.626 + 531.091i −0.316109 + 0.547517i
971971 402.557 + 232.416i 0.414579 + 0.239358i 0.692755 0.721173i 0.256397π-0.256397\pi
−0.278176 + 0.960530i 0.589730π0.589730\pi
972972 159.668 189.522i 0.164268 0.194982i
973973 −272.905 135.652i −0.280478 0.139416i
974974 −502.782 870.843i −0.516203 0.894089i
975975 −283.181 + 237.426i −0.290442 + 0.243514i
976976 1342.93i 1.37595i
977977 −1778.98 −1.82086 −0.910429 0.413666i 0.864248π-0.864248\pi
−0.910429 + 0.413666i 0.864248π0.864248\pi
978978 192.588 528.480i 0.196920 0.540368i
979979 −9.56174 + 5.52047i −0.00976684 + 0.00563889i
980980 −77.0597 + 58.3624i −0.0786324 + 0.0595535i
981981 765.348 + 643.237i 0.780172 + 0.655695i
982982 −91.5977 + 158.652i −0.0932767 + 0.161560i
983983 199.156 + 114.983i 0.202601 + 0.116972i 0.597868 0.801595i 0.296015π-0.296015\pi
−0.395267 + 0.918566i 0.629348π0.629348\pi
984984 −426.810 155.537i −0.433750 0.158066i
985985 −292.034 + 168.606i −0.296482 + 0.171174i
986986 −899.400 519.269i −0.912170 0.526642i
987987 262.202 + 1088.23i 0.265656 + 1.10257i
988988 62.2052 + 107.743i 0.0629607 + 0.109051i
989989 293.045 507.568i 0.296304 0.513213i
990990 4.95661 + 13.6518i 0.00500667 + 0.0137897i
991991 −561.974 973.368i −0.567078 0.982208i −0.996853 0.0792720i 0.974740π-0.974740\pi
0.429775 0.902936i 0.358593π-0.358593\pi
992992 778.543i 0.784822i
993993 100.919 17.7536i 0.101631 0.0178787i
994994 1525.75 95.1770i 1.53496 0.0957515i
995995 −279.466 + 484.050i −0.280870 + 0.486482i
996996 −219.758 + 184.251i −0.220640 + 0.184991i
997997 −554.198 319.966i −0.555866 0.320929i 0.195619 0.980680i 0.437328π-0.437328\pi
−0.751484 + 0.659751i 0.770662π0.770662\pi
998998 30.8550 + 53.4424i 0.0309168 + 0.0535495i
999999 0.947100 797.533i 0.000948048 0.798332i
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 63.3.t.a.40.11 yes 28
3.2 odd 2 189.3.t.a.145.4 28
7.2 even 3 441.3.l.b.391.4 28
7.3 odd 6 63.3.k.a.31.4 28
7.4 even 3 441.3.k.b.31.4 28
7.5 odd 6 441.3.l.a.391.4 28
7.6 odd 2 441.3.t.a.166.11 28
9.2 odd 6 189.3.k.a.19.11 28
9.7 even 3 63.3.k.a.61.4 yes 28
21.17 even 6 189.3.k.a.10.11 28
63.16 even 3 441.3.l.a.97.4 28
63.25 even 3 441.3.t.a.178.11 28
63.34 odd 6 441.3.k.b.313.4 28
63.38 even 6 189.3.t.a.73.4 28
63.52 odd 6 inner 63.3.t.a.52.11 yes 28
63.61 odd 6 441.3.l.b.97.4 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.3.k.a.31.4 28 7.3 odd 6
63.3.k.a.61.4 yes 28 9.7 even 3
63.3.t.a.40.11 yes 28 1.1 even 1 trivial
63.3.t.a.52.11 yes 28 63.52 odd 6 inner
189.3.k.a.10.11 28 21.17 even 6
189.3.k.a.19.11 28 9.2 odd 6
189.3.t.a.73.4 28 63.38 even 6
189.3.t.a.145.4 28 3.2 odd 2
441.3.k.b.31.4 28 7.4 even 3
441.3.k.b.313.4 28 63.34 odd 6
441.3.l.a.97.4 28 63.16 even 3
441.3.l.a.391.4 28 7.5 odd 6
441.3.l.b.97.4 28 63.61 odd 6
441.3.l.b.391.4 28 7.2 even 3
441.3.t.a.166.11 28 7.6 odd 2
441.3.t.a.178.11 28 63.25 even 3