Properties

Label 120.4.v.a.43.9
Level 120120
Weight 44
Character 120.43
Analytic conductor 7.0807.080
Analytic rank 00
Dimension 7272
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [120,4,Mod(43,120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(120, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("120.43");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 120=2335 120 = 2^{3} \cdot 3 \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 120.v (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: 7.080229200697.08022920069
Analytic rank: 00
Dimension: 7272
Relative dimension: 3636 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 43.9
Character χ\chi == 120.43
Dual form 120.4.v.a.67.9

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+(1.972042.02758i)q2+(2.12132+2.12132i)q3+(0.222122+7.99692i)q4+(8.640407.09531i)q5+(0.1178098.48446i)q6+(4.53056+4.53056i)q7+(16.652415.3199i)q8+9.00000iq9+(2.65294+31.5113i)q1012.4278q11+(17.4352+16.4928i)q12+(52.8453+52.8453i)q13+(0.25160918.1205i)q14+(3.2776333.3805i)q15+(63.90133.55259i)q16+(40.2091+40.2091i)q17+(18.248217.7484i)q18+31.1052iq19+(58.659867.5205i)q20+19.2216iq21+(24.5081+25.1983i)q22+(58.1146+58.1146i)q23+(67.8234+2.82670i)q24+(24.3131+122.613i)q25+(211.361+2.93481i)q26+(19.0919+19.0919i)q27+(37.2369+35.2242i)q2852.1723q29+(61.2178+72.4733i)q30+189.156iq31+(118.813+136.571i)q32+(26.363426.3634i)q33+(160.821+2.23305i)q34+(7.0001371.2917i)q35+(71.97221.99910i)q36+(36.576236.5762i)q37+(63.068161.3407i)q38224.204q39+(252.582+14.2159i)q40+459.943q41+(38.973237.9057i)q42+(243.635243.635i)q43+(2.7605099.3842i)q44+(63.857877.7636i)q45+(232.436+3.22745i)q46+(323.620323.620i)q47+(128.019143.091i)q48301.948iq49+(200.660291.094i)q50170.593q51+(410.861434.338i)q52+(157.044+157.044i)q53+(76.3602+1.06029i)q54+(107.381+88.1792i)q55+(144.852+6.03707i)q56+(65.9841+65.9841i)q57+(102.886+105.783i)q58509.630iq59+(267.66918.7964i)q60+60.4041iq61+(383.529373.024i)q62+(40.7751+40.7751i)q63+(42.6036510.224i)q64+(831.55981.6508i)q65+(1.46411+105.443i)q66+(508.552+508.552i)q67+(312.618330.480i)q68246.559q69+(130.745+154.783i)q70+433.818iq71+(137.879+149.871i)q72+(490.722+490.722i)q73+(2.03129+146.291i)q74+(208.525+311.677i)q75+(248.7466.90916i)q76+(56.305056.3050i)q77+(442.138+454.590i)q78+1095.03q79+(526.926+484.096i)q8081.0000q81+(907.025932.568i)q82+(665.401665.401i)q83+(153.7134.26954i)q84+(632.71962.1267i)q85+(13.5305+974.447i)q86+(110.674110.674i)q87+(206.953+190.392i)q88+667.040iq89+(283.602+23.8764i)q90478.838q91+(451.829477.646i)q92+(401.261+401.261i)q93+(17.9726+1294.36i)q94+(220.701268.761i)q95+(37.6700+541.750i)q96+(483.335483.335i)q97+(612.222+595.453i)q98111.850iq99+O(q100)q+(-1.97204 - 2.02758i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-0.222122 + 7.99692i) q^{4} +(-8.64040 - 7.09531i) q^{5} +(0.117809 - 8.48446i) q^{6} +(4.53056 + 4.53056i) q^{7} +(16.6524 - 15.3199i) q^{8} +9.00000i q^{9} +(2.65294 + 31.5113i) q^{10} -12.4278 q^{11} +(-17.4352 + 16.4928i) q^{12} +(-52.8453 + 52.8453i) q^{13} +(0.251609 - 18.1205i) q^{14} +(-3.27763 - 33.3805i) q^{15} +(-63.9013 - 3.55259i) q^{16} +(-40.2091 + 40.2091i) q^{17} +(18.2482 - 17.7484i) q^{18} +31.1052i q^{19} +(58.6598 - 67.5205i) q^{20} +19.2216i q^{21} +(24.5081 + 25.1983i) q^{22} +(-58.1146 + 58.1146i) q^{23} +(67.8234 + 2.82670i) q^{24} +(24.3131 + 122.613i) q^{25} +(211.361 + 2.93481i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(-37.2369 + 35.2242i) q^{28} -52.1723 q^{29} +(-61.2178 + 72.4733i) q^{30} +189.156i q^{31} +(118.813 + 136.571i) q^{32} +(-26.3634 - 26.3634i) q^{33} +(160.821 + 2.23305i) q^{34} +(-7.00013 - 71.2917i) q^{35} +(-71.9722 - 1.99910i) q^{36} +(-36.5762 - 36.5762i) q^{37} +(63.0681 - 61.3407i) q^{38} -224.204 q^{39} +(-252.582 + 14.2159i) q^{40} +459.943 q^{41} +(38.9732 - 37.9057i) q^{42} +(-243.635 - 243.635i) q^{43} +(2.76050 - 99.3842i) q^{44} +(63.8578 - 77.7636i) q^{45} +(232.436 + 3.22745i) q^{46} +(-323.620 - 323.620i) q^{47} +(-128.019 - 143.091i) q^{48} -301.948i q^{49} +(200.660 - 291.094i) q^{50} -170.593 q^{51} +(-410.861 - 434.338i) q^{52} +(-157.044 + 157.044i) q^{53} +(76.3602 + 1.06029i) q^{54} +(107.381 + 88.1792i) q^{55} +(144.852 + 6.03707i) q^{56} +(-65.9841 + 65.9841i) q^{57} +(102.886 + 105.783i) q^{58} -509.630i q^{59} +(267.669 - 18.7964i) q^{60} +60.4041i q^{61} +(383.529 - 373.024i) q^{62} +(-40.7751 + 40.7751i) q^{63} +(42.6036 - 510.224i) q^{64} +(831.559 - 81.6508i) q^{65} +(-1.46411 + 105.443i) q^{66} +(-508.552 + 508.552i) q^{67} +(-312.618 - 330.480i) q^{68} -246.559 q^{69} +(-130.745 + 154.783i) q^{70} +433.818i q^{71} +(137.879 + 149.871i) q^{72} +(490.722 + 490.722i) q^{73} +(-2.03129 + 146.291i) q^{74} +(-208.525 + 311.677i) q^{75} +(-248.746 - 6.90916i) q^{76} +(-56.3050 - 56.3050i) q^{77} +(442.138 + 454.590i) q^{78} +1095.03 q^{79} +(526.926 + 484.096i) q^{80} -81.0000 q^{81} +(-907.025 - 932.568i) q^{82} +(-665.401 - 665.401i) q^{83} +(-153.713 - 4.26954i) q^{84} +(632.719 - 62.1267i) q^{85} +(-13.5305 + 974.447i) q^{86} +(-110.674 - 110.674i) q^{87} +(-206.953 + 190.392i) q^{88} +667.040i q^{89} +(-283.602 + 23.8764i) q^{90} -478.838 q^{91} +(-451.829 - 477.646i) q^{92} +(-401.261 + 401.261i) q^{93} +(-17.9726 + 1294.36i) q^{94} +(220.701 - 268.761i) q^{95} +(-37.6700 + 541.750i) q^{96} +(483.335 - 483.335i) q^{97} +(-612.222 + 595.453i) q^{98} -111.850i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 72q+12q6+84q872q10+24q1220q16104q17+380q20+44q2288q25368q261068q28+408q30+340q32+912q35108q3640q38++7576q98+O(q100) 72 q + 12 q^{6} + 84 q^{8} - 72 q^{10} + 24 q^{12} - 20 q^{16} - 104 q^{17} + 380 q^{20} + 44 q^{22} - 88 q^{25} - 368 q^{26} - 1068 q^{28} + 408 q^{30} + 340 q^{32} + 912 q^{35} - 108 q^{36} - 40 q^{38}+ \cdots + 7576 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/120Z)×\left(\mathbb{Z}/120\mathbb{Z}\right)^\times.

nn 3131 4141 6161 9797
χ(n)\chi(n) 1-1 11 1-1 e(34)e\left(\frac{3}{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 −1.97204 2.02758i −0.697221 0.716856i
33 2.12132 + 2.12132i 0.408248 + 0.408248i
44 −0.222122 + 7.99692i −0.0277653 + 0.999614i
55 −8.64040 7.09531i −0.772821 0.634624i
66 0.117809 8.48446i 0.00801592 0.577295i
77 4.53056 + 4.53056i 0.244627 + 0.244627i 0.818761 0.574134i 0.194661π-0.194661\pi
−0.574134 + 0.818761i 0.694661π0.694661\pi
88 16.6524 15.3199i 0.735938 0.677049i
99 9.00000i 0.333333i
1010 2.65294 + 31.5113i 0.0838932 + 0.996475i
1111 −12.4278 −0.340648 −0.170324 0.985388i 0.554481π-0.554481\pi
−0.170324 + 0.985388i 0.554481π0.554481\pi
1212 −17.4352 + 16.4928i −0.419426 + 0.396756i
1313 −52.8453 + 52.8453i −1.12743 + 1.12743i −0.136842 + 0.990593i 0.543695π0.543695\pi
−0.990593 + 0.136842i 0.956305π0.956305\pi
1414 0.251609 18.1205i 0.00480324 0.345922i
1515 −3.27763 33.3805i −0.0564188 0.574587i
1616 −63.9013 3.55259i −0.998458 0.0555092i
1717 −40.2091 + 40.2091i −0.573655 + 0.573655i −0.933148 0.359493i 0.882950π-0.882950\pi
0.359493 + 0.933148i 0.382950π0.382950\pi
1818 18.2482 17.7484i 0.238952 0.232407i
1919 31.1052i 0.375580i 0.982209 + 0.187790i 0.0601324π0.0601324\pi
−0.982209 + 0.187790i 0.939868π0.939868\pi
2020 58.6598 67.5205i 0.655837 0.754903i
2121 19.2216i 0.199737i
2222 24.5081 + 25.1983i 0.237507 + 0.244196i
2323 −58.1146 + 58.1146i −0.526858 + 0.526858i −0.919634 0.392776i 0.871515π-0.871515\pi
0.392776 + 0.919634i 0.371515π0.371515\pi
2424 67.8234 + 2.82670i 0.576849 + 0.0240416i
2525 24.3131 + 122.613i 0.194505 + 0.980902i
2626 211.361 + 2.93481i 1.59428 + 0.0221371i
2727 −19.0919 + 19.0919i −0.136083 + 0.136083i
2828 −37.2369 + 35.2242i −0.251325 + 0.237741i
2929 −52.1723 −0.334075 −0.167037 0.985951i 0.553420π-0.553420\pi
−0.167037 + 0.985951i 0.553420π0.553420\pi
3030 −61.2178 + 72.4733i −0.372560 + 0.441058i
3131 189.156i 1.09592i 0.836505 + 0.547960i 0.184595π0.184595\pi
−0.836505 + 0.547960i 0.815405π0.815405\pi
3232 118.813 + 136.571i 0.656354 + 0.754453i
3333 −26.3634 26.3634i −0.139069 0.139069i
3434 160.821 + 2.23305i 0.811193 + 0.0112637i
3535 −7.00013 71.2917i −0.0338068 0.344300i
3636 −71.9722 1.99910i −0.333205 0.00925510i
3737 −36.5762 36.5762i −0.162516 0.162516i 0.621164 0.783680i 0.286660π-0.286660\pi
−0.783680 + 0.621164i 0.786660π0.786660\pi
3838 63.0681 61.3407i 0.269237 0.261862i
3939 −224.204 −0.920547
4040 −252.582 + 14.2159i −0.998420 + 0.0561934i
4141 459.943 1.75197 0.875987 0.482334i 0.160211π-0.160211\pi
0.875987 + 0.482334i 0.160211π0.160211\pi
4242 38.9732 37.9057i 0.143183 0.139261i
4343 −243.635 243.635i −0.864047 0.864047i 0.127759 0.991805i 0.459222π-0.459222\pi
−0.991805 + 0.127759i 0.959222π0.959222\pi
4444 2.76050 99.3842i 0.00945819 0.340517i
4545 63.8578 77.7636i 0.211541 0.257607i
4646 232.436 + 3.22745i 0.745018 + 0.0103448i
4747 −323.620 323.620i −1.00436 1.00436i −0.999990 0.00436910i 0.998609π-0.998609\pi
−0.00436910 0.999990i 0.501391π-0.501391\pi
4848 −128.019 143.091i −0.384957 0.430280i
4949 301.948i 0.880315i
5050 200.660 291.094i 0.567552 0.823337i
5151 −170.593 −0.468388
5252 −410.861 434.338i −1.09570 1.15830i
5353 −157.044 + 157.044i −0.407012 + 0.407012i −0.880695 0.473683i 0.842924π-0.842924\pi
0.473683 + 0.880695i 0.342924π0.342924\pi
5454 76.3602 + 1.06029i 0.192432 + 0.00267197i
5555 107.381 + 88.1792i 0.263260 + 0.216183i
5656 144.852 + 6.03707i 0.345655 + 0.0144060i
5757 −65.9841 + 65.9841i −0.153330 + 0.153330i
5858 102.886 + 105.783i 0.232924 + 0.239483i
5959 509.630i 1.12454i −0.826952 0.562272i 0.809927π-0.809927\pi
0.826952 0.562272i 0.190073π-0.190073\pi
6060 267.669 18.7964i 0.575932 0.0404434i
6161 60.4041i 0.126786i 0.997989 + 0.0633931i 0.0201922π0.0201922\pi
−0.997989 + 0.0633931i 0.979808π0.979808\pi
6262 383.529 373.024i 0.785617 0.764098i
6363 −40.7751 + 40.7751i −0.0815425 + 0.0815425i
6464 42.6036 510.224i 0.0832102 0.996532i
6565 831.559 81.6508i 1.58680 0.155808i
6666 −1.46411 + 105.443i −0.00273061 + 0.196654i
6767 −508.552 + 508.552i −0.927306 + 0.927306i −0.997531 0.0702255i 0.977628π-0.977628\pi
0.0702255 + 0.997531i 0.477628π0.477628\pi
6868 −312.618 330.480i −0.557507 0.589362i
6969 −246.559 −0.430178
7070 −130.745 + 154.783i −0.223243 + 0.264288i
7171 433.818i 0.725137i 0.931957 + 0.362569i 0.118100π0.118100\pi
−0.931957 + 0.362569i 0.881900π0.881900\pi
7272 137.879 + 149.871i 0.225683 + 0.245313i
7373 490.722 + 490.722i 0.786777 + 0.786777i 0.980964 0.194187i 0.0622070π-0.0622070\pi
−0.194187 + 0.980964i 0.562207π0.562207\pi
7474 −2.03129 + 146.291i −0.00319099 + 0.229810i
7575 −208.525 + 311.677i −0.321045 + 0.479858i
7676 −248.746 6.90916i −0.375435 0.0104281i
7777 −56.3050 56.3050i −0.0833319 0.0833319i
7878 442.138 + 454.590i 0.641825 + 0.659899i
7979 1095.03 1.55950 0.779752 0.626088i 0.215345π-0.215345\pi
0.779752 + 0.626088i 0.215345π0.215345\pi
8080 526.926 + 484.096i 0.736402 + 0.676544i
8181 −81.0000 −0.111111
8282 −907.025 932.568i −1.22151 1.25591i
8383 −665.401 665.401i −0.879967 0.879967i 0.113564 0.993531i 0.463773π-0.463773\pi
−0.993531 + 0.113564i 0.963773π0.963773\pi
8484 −153.713 4.26954i −0.199660 0.00554577i
8585 632.719 62.1267i 0.807388 0.0792775i
8686 −13.5305 + 974.447i −0.0169655 + 1.22183i
8787 −110.674 110.674i −0.136385 0.136385i
8888 −206.953 + 190.392i −0.250696 + 0.230635i
8989 667.040i 0.794451i 0.917721 + 0.397226i 0.130027π0.130027\pi
−0.917721 + 0.397226i 0.869973π0.869973\pi
9090 −283.602 + 23.8764i −0.332158 + 0.0279644i
9191 −478.838 −0.551603
9292 −451.829 477.646i −0.512027 0.541283i
9393 −401.261 + 401.261i −0.447407 + 0.447407i
9494 −17.9726 + 1294.36i −0.0197205 + 1.42024i
9595 220.701 268.761i 0.238352 0.290256i
9696 −37.6700 + 541.750i −0.0400487 + 0.575960i
9797 483.335 483.335i 0.505930 0.505930i −0.407345 0.913275i 0.633545π-0.633545\pi
0.913275 + 0.407345i 0.133545π0.133545\pi
9898 −612.222 + 595.453i −0.631059 + 0.613774i
9999 111.850i 0.113549i
100100 −985.924 + 167.195i −0.985924 + 0.167195i
101101 359.937i 0.354604i −0.984156 0.177302i 0.943263π-0.943263\pi
0.984156 0.177302i 0.0567370π-0.0567370\pi
102102 336.416 + 345.890i 0.326570 + 0.335767i
103103 764.676 764.676i 0.731512 0.731512i −0.239407 0.970919i 0.576953π-0.576953\pi
0.970919 + 0.239407i 0.0769531π0.0769531\pi
104104 −70.4174 + 1689.58i −0.0663942 + 1.59305i
105105 136.383 166.082i 0.126758 0.154361i
106106 628.116 + 8.72159i 0.575547 + 0.00799165i
107107 −517.656 + 517.656i −0.467698 + 0.467698i −0.901168 0.433470i 0.857289π-0.857289\pi
0.433470 + 0.901168i 0.357289π0.357289\pi
108108 −148.435 156.917i −0.132252 0.139809i
109109 2149.97 1.88926 0.944632 0.328132i 0.106419π-0.106419\pi
0.944632 + 0.328132i 0.106419π0.106419\pi
110110 −32.9702 391.617i −0.0285781 0.339447i
111111 155.180i 0.132694i
112112 −273.414 305.604i −0.230671 0.257829i
113113 843.602 + 843.602i 0.702296 + 0.702296i 0.964903 0.262607i 0.0845823π-0.0845823\pi
−0.262607 + 0.964903i 0.584582π0.584582\pi
114114 263.911 + 3.66449i 0.216820 + 0.00301062i
115115 914.475 89.7924i 0.741524 0.0728103i
116116 11.5886 417.218i 0.00927567 0.333946i
117117 −475.608 475.608i −0.375812 0.375812i
118118 −1033.31 + 1005.01i −0.806137 + 0.784056i
119119 −364.340 −0.280664
120120 −565.965 505.652i −0.430544 0.384662i
121121 −1176.55 −0.883959
122122 122.474 119.119i 0.0908874 0.0883980i
123123 975.686 + 975.686i 0.715241 + 0.715241i
124124 −1512.67 42.0159i −1.09550 0.0304285i
125125 659.900 1231.93i 0.472186 0.881499i
126126 163.085 + 2.26448i 0.115307 + 0.00160108i
127127 −597.375 597.375i −0.417390 0.417390i 0.466913 0.884303i 0.345366π-0.345366\pi
−0.884303 + 0.466913i 0.845366π0.845366\pi
128128 −1118.53 + 919.800i −0.772386 + 0.635153i
129129 1033.66i 0.705491i
130130 −1805.42 1525.03i −1.21804 1.02888i
131131 −1796.00 −1.19784 −0.598921 0.800808i 0.704403π-0.704403\pi
−0.598921 + 0.800808i 0.704403π0.704403\pi
132132 216.682 204.970i 0.142877 0.135154i
133133 −140.924 + 140.924i −0.0918772 + 0.0918772i
134134 2034.01 + 28.2429i 1.31128 + 0.0182076i
135135 300.424 29.4987i 0.191529 0.0188063i
136136 −53.5794 + 1285.58i −0.0337823 + 0.810568i
137137 −1991.32 + 1991.32i −1.24183 + 1.24183i −0.282583 + 0.959243i 0.591191π0.591191\pi
−0.959243 + 0.282583i 0.908809π0.908809\pi
138138 486.225 + 499.918i 0.299929 + 0.308376i
139139 877.478i 0.535444i −0.963496 0.267722i 0.913729π-0.913729\pi
0.963496 0.267722i 0.0862708π-0.0862708\pi
140140 571.668 40.1440i 0.345106 0.0242342i
141141 1373.01i 0.820056i
142142 879.599 855.506i 0.519819 0.505581i
143143 656.752 656.752i 0.384058 0.384058i
144144 31.9733 575.112i 0.0185031 0.332819i
145145 450.790 + 370.179i 0.258180 + 0.212012i
146146 27.2527 1962.70i 0.0154483 1.11256i
147147 640.528 640.528i 0.359387 0.359387i
148148 300.621 284.372i 0.166966 0.157941i
149149 −852.565 −0.468757 −0.234379 0.972145i 0.575306π-0.575306\pi
−0.234379 + 0.972145i 0.575306π0.575306\pi
150150 1043.17 191.839i 0.567828 0.104424i
151151 2744.98i 1.47936i 0.672958 + 0.739681i 0.265023π0.265023\pi
−0.672958 + 0.739681i 0.734977π0.734977\pi
152152 476.527 + 517.976i 0.254286 + 0.276404i
153153 −361.882 361.882i −0.191218 0.191218i
154154 −3.12695 + 225.198i −0.00163621 + 0.117838i
155155 1342.12 1634.39i 0.695497 0.846950i
156156 49.8006 1792.94i 0.0255592 0.920192i
157157 1443.33 + 1443.33i 0.733697 + 0.733697i 0.971350 0.237653i 0.0763783π-0.0763783\pi
−0.237653 + 0.971350i 0.576378π0.576378\pi
158158 −2159.45 2220.26i −1.08732 1.11794i
159159 −666.281 −0.332324
160160 −57.5795 2023.04i −0.0284504 0.999595i
161161 −526.584 −0.257768
162162 159.735 + 164.234i 0.0774690 + 0.0796507i
163163 2920.30 + 2920.30i 1.40329 + 1.40329i 0.789378 + 0.613908i 0.210403π0.210403\pi
0.613908 + 0.789378i 0.289597π0.289597\pi
164164 −102.163 + 3678.12i −0.0486441 + 1.75130i
165165 40.7338 + 414.847i 0.0192189 + 0.195732i
166166 −36.9537 + 2661.35i −0.0172781 + 1.24434i
167167 −448.699 448.699i −0.207912 0.207912i 0.595467 0.803380i 0.296967π-0.296967\pi
−0.803380 + 0.595467i 0.796967π0.796967\pi
168168 294.472 + 320.085i 0.135232 + 0.146994i
169169 3388.25i 1.54222i
170170 −1373.71 1160.37i −0.619759 0.523507i
171171 −279.947 −0.125193
172172 2002.45 1894.21i 0.887704 0.839723i
173173 −2422.59 + 2422.59i −1.06466 + 1.06466i −0.0668998 + 0.997760i 0.521311π0.521311\pi
−0.997760 + 0.0668998i 0.978689π0.978689\pi
174174 −6.14640 + 442.654i −0.00267791 + 0.192859i
175175 −445.353 + 665.657i −0.192374 + 0.287537i
176176 794.154 + 44.1509i 0.340123 + 0.0189091i
177177 1081.09 1081.09i 0.459093 0.459093i
178178 1352.47 1315.43i 0.569507 0.553908i
179179 3084.37i 1.28791i −0.765062 0.643956i 0.777292π-0.777292\pi
0.765062 0.643956i 0.222708π-0.222708\pi
180180 607.685 + 527.939i 0.251634 + 0.218612i
181181 2051.43i 0.842439i 0.906959 + 0.421219i 0.138398π0.138398\pi
−0.906959 + 0.421219i 0.861602π0.861602\pi
182182 944.288 + 970.880i 0.384589 + 0.395420i
183183 −128.137 + 128.137i −0.0517602 + 0.0517602i
184184 −77.4389 + 1858.05i −0.0310265 + 0.744444i
185185 56.5136 + 575.553i 0.0224592 + 0.228732i
186186 1604.89 + 22.2844i 0.632668 + 0.00878480i
187187 499.712 499.712i 0.195415 0.195415i
188188 2659.85 2516.08i 1.03186 0.976086i
189189 −172.994 −0.0665792
190190 −980.165 + 82.5201i −0.374256 + 0.0315086i
191191 391.206i 0.148202i −0.997251 0.0741012i 0.976391π-0.976391\pi
0.997251 0.0741012i 0.0236088π-0.0236088\pi
192192 1172.73 991.973i 0.440803 0.372862i
193193 −2085.33 2085.33i −0.777749 0.777749i 0.201699 0.979448i 0.435354π-0.435354\pi
−0.979448 + 0.201699i 0.935354π0.935354\pi
194194 −1933.15 26.8424i −0.715424 0.00993389i
195195 1937.21 + 1590.79i 0.711418 + 0.584201i
196196 2414.65 + 67.0694i 0.879975 + 0.0244422i
197197 815.019 + 815.019i 0.294760 + 0.294760i 0.838957 0.544197i 0.183166π-0.183166\pi
−0.544197 + 0.838957i 0.683166π0.683166\pi
198198 −226.785 + 220.573i −0.0813985 + 0.0791690i
199199 −1675.60 −0.596886 −0.298443 0.954428i 0.596467π-0.596467\pi
−0.298443 + 0.954428i 0.596467π0.596467\pi
200200 2283.28 + 1669.32i 0.807262 + 0.590194i
201201 −2157.60 −0.757142
202202 −729.799 + 709.809i −0.254200 + 0.247238i
203203 −236.370 236.370i −0.0817238 0.0817238i
204204 37.8925 1364.22i 0.0130049 0.468207i
205205 −3974.09 3263.44i −1.35396 1.11185i
206206 −3058.41 42.4670i −1.03441 0.0143632i
207207 −523.032 523.032i −0.175619 0.175619i
208208 3564.62 3189.15i 1.18828 1.06311i
209209 386.570i 0.127941i
210210 −605.696 + 50.9936i −0.199033 + 0.0167566i
211211 1254.42 0.409277 0.204639 0.978838i 0.434398π-0.434398\pi
0.204639 + 0.978838i 0.434398π0.434398\pi
212212 −1220.99 1290.75i −0.395555 0.418156i
213213 −920.267 + 920.267i −0.296036 + 0.296036i
214214 2070.43 + 28.7485i 0.661362 + 0.00918322i
215215 376.438 + 3833.77i 0.119409 + 1.21610i
216216 −25.4403 + 610.410i −0.00801386 + 0.192283i
217217 −856.986 + 856.986i −0.268092 + 0.268092i
218218 −4239.82 4359.23i −1.31723 1.35433i
219219 2081.96i 0.642401i
220220 −729.014 + 839.133i −0.223410 + 0.257156i
221221 4249.73i 1.29352i
222222 −314.639 + 306.020i −0.0951223 + 0.0925169i
223223 3024.01 3024.01i 0.908085 0.908085i −0.0880328 0.996118i 0.528058π-0.528058\pi
0.996118 + 0.0880328i 0.0280580π0.0280580\pi
224224 −80.4528 + 1157.03i −0.0239977 + 0.345122i
225225 −1103.51 + 218.818i −0.326967 + 0.0648350i
226226 46.8502 3374.08i 0.0137895 0.993101i
227227 −2043.74 + 2043.74i −0.597568 + 0.597568i −0.939665 0.342097i 0.888863π-0.888863\pi
0.342097 + 0.939665i 0.388863π0.388863\pi
228228 −513.013 542.326i −0.149014 0.157528i
229229 −3898.97 −1.12511 −0.562557 0.826758i 0.690182π-0.690182\pi
−0.562557 + 0.826758i 0.690182π0.690182\pi
230230 −1985.44 1677.09i −0.569201 0.480801i
231231 238.882i 0.0680402i
232232 −868.794 + 799.273i −0.245858 + 0.226185i
233233 2788.90 + 2788.90i 0.784151 + 0.784151i 0.980528 0.196377i 0.0629177π-0.0629177\pi
−0.196377 + 0.980528i 0.562918π0.562918\pi
234234 −26.4133 + 1902.25i −0.00737903 + 0.531427i
235235 500.023 + 5092.40i 0.138800 + 1.41358i
236236 4075.46 + 113.200i 1.12411 + 0.0312233i
237237 2322.92 + 2322.92i 0.636665 + 0.636665i
238238 718.493 + 738.727i 0.195685 + 0.201196i
239239 −5389.60 −1.45868 −0.729339 0.684152i 0.760172π-0.760172\pi
−0.729339 + 0.684152i 0.760172π0.760172\pi
240240 90.8580 + 2144.70i 0.0244369 + 0.576833i
241241 −4663.59 −1.24651 −0.623253 0.782020i 0.714189π-0.714189\pi
−0.623253 + 0.782020i 0.714189π0.714189\pi
242242 2320.20 + 2385.54i 0.616315 + 0.633671i
243243 −171.827 171.827i −0.0453609 0.0453609i
244244 −483.047 13.4171i −0.126737 0.00352025i
245245 −2142.41 + 2608.95i −0.558669 + 0.680326i
246246 54.1856 3902.37i 0.0140437 1.01141i
247247 −1643.76 1643.76i −0.423442 0.423442i
248248 2897.85 + 3149.91i 0.741991 + 0.806529i
249249 2823.06i 0.718490i
250250 −3799.18 + 1091.42i −0.961126 + 0.276110i
251251 4059.10 1.02075 0.510374 0.859952i 0.329507π-0.329507\pi
0.510374 + 0.859952i 0.329507π0.329507\pi
252252 −317.018 335.132i −0.0792470 0.0837751i
253253 722.238 722.238i 0.179473 0.179473i
254254 −33.1758 + 2389.27i −0.00819541 + 0.590221i
255255 1473.99 + 1210.41i 0.361980 + 0.297250i
256256 4070.76 + 454.030i 0.993837 + 0.110847i
257257 −3381.26 + 3381.26i −0.820689 + 0.820689i −0.986207 0.165517i 0.947071π-0.947071\pi
0.165517 + 0.986207i 0.447071π0.447071\pi
258258 −2095.82 + 2038.41i −0.505736 + 0.491883i
259259 331.422i 0.0795117i
260260 468.247 + 6668.04i 0.111690 + 1.59052i
261261 469.551i 0.111358i
262262 3541.78 + 3641.52i 0.835160 + 0.858680i
263263 1684.34 1684.34i 0.394909 0.394909i −0.481524 0.876433i 0.659916π-0.659916\pi
0.876433 + 0.481524i 0.159916π0.159916\pi
264264 −842.897 35.1297i −0.196503 0.00818972i
265265 2471.20 242.647i 0.572848 0.0562480i
266266 563.642 + 7.82635i 0.129921 + 0.00180400i
267267 −1415.01 + 1415.01i −0.324333 + 0.324333i
268268 −3953.88 4179.81i −0.901201 0.952695i
269269 7976.91 1.80803 0.904016 0.427499i 0.140605π-0.140605\pi
0.904016 + 0.427499i 0.140605π0.140605\pi
270270 −652.260 550.960i −0.147019 0.124187i
271271 652.119i 0.146175i 0.997326 + 0.0730875i 0.0232852π0.0232852\pi
−0.997326 + 0.0730875i 0.976715π0.976715\pi
272272 2712.26 2426.57i 0.604614 0.540928i
273273 −1015.77 1015.77i −0.225191 0.225191i
274274 7964.52 + 110.590i 1.75604 + 0.0243831i
275275 −302.159 1523.81i −0.0662577 0.334142i
276276 54.7664 1971.72i 0.0119440 0.430012i
277277 −219.968 219.968i −0.0477133 0.0477133i 0.682848 0.730561i 0.260741π-0.260741\pi
−0.730561 + 0.682848i 0.760741π0.760741\pi
278278 −1779.15 + 1730.42i −0.383836 + 0.373323i
279279 −1702.41 −0.365307
280280 −1208.75 1079.93i −0.257987 0.230494i
281281 2786.67 0.591598 0.295799 0.955250i 0.404414π-0.404414\pi
0.295799 + 0.955250i 0.404414π0.404414\pi
282282 −2783.87 + 2707.62i −0.587862 + 0.571761i
283283 827.696 + 827.696i 0.173857 + 0.173857i 0.788671 0.614815i 0.210769π-0.210769\pi
−0.614815 + 0.788671i 0.710769π0.710769\pi
284284 −3469.21 96.3607i −0.724858 0.0201336i
285285 1038.31 101.951i 0.215803 0.0211898i
286286 −2626.75 36.4733i −0.543088 0.00754095i
287287 2083.80 + 2083.80i 0.428581 + 0.428581i
288288 −1229.14 + 1069.32i −0.251484 + 0.218785i
289289 1679.45i 0.341839i
290290 −138.410 1644.02i −0.0280266 0.332897i
291291 2050.62 0.413090
292292 −4033.27 + 3815.27i −0.808319 + 0.764629i
293293 −1645.09 + 1645.09i −0.328012 + 0.328012i −0.851830 0.523818i 0.824507π-0.824507\pi
0.523818 + 0.851830i 0.324507π0.324507\pi
294294 −2561.87 35.5723i −0.508201 0.00705653i
295295 −3615.98 + 4403.40i −0.713663 + 0.869072i
296296 −1169.42 48.7385i −0.229633 0.00957050i
297297 237.270 237.270i 0.0463563 0.0463563i
298298 1681.29 + 1728.64i 0.326827 + 0.336031i
299299 6142.17i 1.18800i
300300 −2446.13 1736.79i −0.470759 0.334245i
301301 2207.61i 0.422739i
302302 5565.66 5413.22i 1.06049 1.03144i
303303 763.541 763.541i 0.144767 0.144767i
304304 110.504 1987.66i 0.0208481 0.375001i
305305 428.586 521.916i 0.0804615 0.0979830i
306306 −20.0975 + 1447.39i −0.00375456 + 0.270398i
307307 147.043 147.043i 0.0273361 0.0273361i −0.693307 0.720643i 0.743847π-0.743847\pi
0.720643 + 0.693307i 0.243847π0.243847\pi
308308 462.773 437.760i 0.0856135 0.0809860i
309309 3244.24 0.597277
310310 −5960.57 + 501.820i −1.09206 + 0.0919402i
311311 3070.62i 0.559869i −0.960019 0.279934i 0.909687π-0.909687\pi
0.960019 0.279934i 0.0903127π-0.0903127\pi
312312 −3733.53 + 3434.77i −0.677466 + 0.623255i
313313 −4446.65 4446.65i −0.803001 0.803001i 0.180562 0.983564i 0.442208π-0.442208\pi
−0.983564 + 0.180562i 0.942208π0.942208\pi
314314 80.1567 5772.77i 0.0144061 1.03750i
315315 641.625 63.0012i 0.114767 0.0112689i
316316 −243.231 + 8756.89i −0.0433001 + 1.55890i
317317 5560.16 + 5560.16i 0.985142 + 0.985142i 0.999891 0.0147495i 0.00469508π-0.00469508\pi
−0.0147495 + 0.999891i 0.504695π0.504695\pi
318318 1313.93 + 1350.94i 0.231704 + 0.238229i
319319 648.388 0.113802
320320 −3988.31 + 4106.26i −0.696730 + 0.717334i
321321 −2196.23 −0.381874
322322 1038.44 + 1067.69i 0.179721 + 0.184783i
323323 −1250.71 1250.71i −0.215454 0.215454i
324324 17.9919 647.750i 0.00308503 0.111068i
325325 −7764.34 5194.67i −1.32519 0.886611i
326326 162.182 11680.1i 0.0275534 1.98435i
327327 4560.77 + 4560.77i 0.771289 + 0.771289i
328328 7659.14 7046.26i 1.28935 1.18617i
329329 2932.37i 0.491388i
330330 760.804 900.685i 0.126912 0.150246i
331331 −3732.10 −0.619742 −0.309871 0.950779i 0.600286π-0.600286\pi
−0.309871 + 0.950779i 0.600286π0.600286\pi
332332 5468.96 5173.35i 0.904060 0.855195i
333333 329.186 329.186i 0.0541720 0.0541720i
334334 −24.9189 + 1794.62i −0.00408234 + 0.294004i
335335 8002.42 785.759i 1.30513 0.128151i
336336 68.2862 1228.28i 0.0110873 0.199430i
337337 231.262 231.262i 0.0373818 0.0373818i −0.688169 0.725551i 0.741585π-0.741585\pi
0.725551 + 0.688169i 0.241585π0.241585\pi
338338 −6869.94 + 6681.77i −1.10555 + 1.07527i
339339 3579.10i 0.573422i
340340 356.281 + 5073.60i 0.0568296 + 0.809278i
341341 2350.80i 0.373323i
342342 552.066 + 567.613i 0.0872874 + 0.0897456i
343343 2921.98 2921.98i 0.459977 0.459977i
344344 −7789.56 324.649i −1.22089 0.0508834i
345345 2130.37 + 1749.42i 0.332451 + 0.273001i
346346 9689.43 + 134.541i 1.50551 + 0.0209045i
347347 2975.42 2975.42i 0.460314 0.460314i −0.438444 0.898758i 0.644470π-0.644470\pi
0.898758 + 0.438444i 0.144470π0.144470\pi
348348 909.636 860.469i 0.140120 0.132546i
349349 8875.23 1.36126 0.680630 0.732627i 0.261706π-0.261706\pi
0.680630 + 0.732627i 0.261706π0.261706\pi
350350 2227.92 409.716i 0.340250 0.0625720i
351351 2017.83i 0.306849i
352352 −1476.58 1697.27i −0.223586 0.257003i
353353 5543.31 + 5543.31i 0.835810 + 0.835810i 0.988304 0.152494i 0.0487306π-0.0487306\pi
−0.152494 + 0.988304i 0.548731π0.548731\pi
354354 −4323.93 60.0392i −0.649193 0.00901426i
355355 3078.07 3748.36i 0.460189 0.560401i
356356 −5334.27 148.165i −0.794145 0.0220582i
357357 −772.882 772.882i −0.114580 0.114580i
358358 −6253.79 + 6082.49i −0.923248 + 0.897960i
359359 −1090.27 −0.160285 −0.0801425 0.996783i 0.525538π-0.525538\pi
−0.0801425 + 0.996783i 0.525538π0.525538\pi
360360 −127.943 2273.24i −0.0187311 0.332807i
361361 5891.47 0.858940
362362 4159.42 4045.50i 0.603907 0.587366i
363363 −2495.84 2495.84i −0.360875 0.360875i
364364 106.361 3829.23i 0.0153154 0.551390i
365365 −758.211 7721.87i −0.108730 1.10735i
366366 512.497 + 7.11618i 0.0731930 + 0.00101631i
367367 −7890.78 7890.78i −1.12233 1.12233i −0.991390 0.130941i 0.958200π-0.958200\pi
−0.130941 0.991390i 0.541800π-0.541800\pi
368368 3920.06 3507.14i 0.555291 0.496800i
369369 4139.48i 0.583992i
370370 1055.53 1249.60i 0.148309 0.175577i
371371 −1423.00 −0.199133
372372 −3119.73 3297.98i −0.434812 0.459657i
373373 −4686.39 + 4686.39i −0.650542 + 0.650542i −0.953123 0.302582i 0.902152π-0.902152\pi
0.302582 + 0.953123i 0.402152π0.402152\pi
374374 −1998.65 27.7519i −0.276331 0.00383695i
375375 4013.18 1213.46i 0.552640 0.167101i
376376 −10346.9 431.231i −1.41915 0.0591463i
377377 2757.06 2757.06i 0.376647 0.376647i
378378 341.151 + 350.758i 0.0464204 + 0.0477277i
379379 7284.17i 0.987237i 0.869679 + 0.493618i 0.164326π0.164326\pi
−0.869679 + 0.493618i 0.835674π0.835674\pi
380380 2100.24 + 1824.63i 0.283526 + 0.246319i
381381 2534.45i 0.340797i
382382 −793.200 + 771.474i −0.106240 + 0.103330i
383383 6182.97 6182.97i 0.824896 0.824896i −0.161910 0.986806i 0.551765π-0.551765\pi
0.986806 + 0.161910i 0.0517654π0.0517654\pi
384384 −4323.96 421.578i −0.574626 0.0560249i
385385 86.9964 + 886.000i 0.0115162 + 0.117285i
386386 −115.811 + 8340.53i −0.0152710 + 1.09980i
387387 2192.72 2192.72i 0.288016 0.288016i
388388 3757.83 + 3972.55i 0.491688 + 0.519782i
389389 −2699.90 −0.351903 −0.175951 0.984399i 0.556300π-0.556300\pi
−0.175951 + 0.984399i 0.556300π0.556300\pi
390390 −594.798 7064.95i −0.0772276 0.917302i
391391 4673.47i 0.604470i
392392 −4625.80 5028.15i −0.596016 0.647857i
393393 −3809.89 3809.89i −0.489017 0.489017i
394394 45.2628 3259.76i 0.00578758 0.416813i
395395 −9461.53 7769.60i −1.20522 0.989699i
396396 894.458 + 24.8445i 0.113506 + 0.00315273i
397397 1077.34 + 1077.34i 0.136197 + 0.136197i 0.771918 0.635722i 0.219297π-0.219297\pi
−0.635722 + 0.771918i 0.719297π0.719297\pi
398398 3304.35 + 3397.41i 0.416161 + 0.427881i
399399 −597.890 −0.0750174
400400 −1118.05 7921.49i −0.139756 0.990186i
401401 9896.69 1.23246 0.616231 0.787566i 0.288659π-0.288659\pi
0.616231 + 0.787566i 0.288659π0.288659\pi
402402 4254.88 + 4374.70i 0.527895 + 0.542762i
403403 −9996.03 9996.03i −1.23558 1.23558i
404404 2878.38 + 79.9500i 0.354468 + 0.00984569i
405405 699.873 + 574.720i 0.0858690 + 0.0705138i
406406 −13.1270 + 945.390i −0.00160464 + 0.115564i
407407 454.562 + 454.562i 0.0553607 + 0.0553607i
408408 −2840.78 + 2613.46i −0.344704 + 0.317121i
409409 5960.14i 0.720562i 0.932844 + 0.360281i 0.117319π0.117319\pi
−0.932844 + 0.360281i 0.882681π0.882681\pi
410410 1220.20 + 14493.4i 0.146979 + 1.74580i
411411 −8448.46 −1.01395
412412 5945.20 + 6284.90i 0.710919 + 0.751541i
413413 2308.91 2308.91i 0.275094 0.275094i
414414 −29.0470 + 2091.92i −0.00344827 + 0.248339i
415415 1028.11 + 10470.6i 0.121609 + 1.23850i
416416 −13495.8 938.416i −1.59059 0.110600i
417417 1861.41 1861.41i 0.218594 0.218594i
418418 −783.799 + 762.331i −0.0917150 + 0.0892029i
419419 2470.57i 0.288056i 0.989574 + 0.144028i 0.0460055π0.0460055\pi
−0.989574 + 0.144028i 0.953994π0.953994\pi
420420 1297.85 + 1127.53i 0.150782 + 0.130995i
421421 10190.0i 1.17965i 0.807532 + 0.589824i 0.200803π0.200803\pi
−0.807532 + 0.589824i 0.799197π0.799197\pi
422422 −2473.76 2543.42i −0.285357 0.293393i
423423 2912.58 2912.58i 0.334787 0.334787i
424424 −209.264 + 5021.05i −0.0239688 + 0.575103i
425425 −5907.76 3952.54i −0.674278 0.451121i
426426 3680.71 + 51.1079i 0.418618 + 0.00581264i
427427 −273.665 + 273.665i −0.0310154 + 0.0310154i
428428 −4024.67 4254.64i −0.454532 0.480504i
429429 2786.36 0.313582
430430 7030.91 8323.61i 0.788513 0.933488i
431431 13623.7i 1.52258i 0.648412 + 0.761290i 0.275434π0.275434\pi
−0.648412 + 0.761290i 0.724566π0.724566\pi
432432 1287.82 1152.17i 0.143427 0.128319i
433433 6541.91 + 6541.91i 0.726060 + 0.726060i 0.969832 0.243772i 0.0783850π-0.0783850\pi
−0.243772 + 0.969832i 0.578385π0.578385\pi
434434 3427.61 + 47.5935i 0.379103 + 0.00526396i
435435 171.002 + 1741.54i 0.0188481 + 0.191955i
436436 −477.556 + 17193.1i −0.0524559 + 1.88854i
437437 −1807.67 1807.67i −0.197877 0.197877i
438438 4221.33 4105.71i 0.460509 0.447895i
439439 −6238.92 −0.678286 −0.339143 0.940735i 0.610137π-0.610137\pi
−0.339143 + 0.940735i 0.610137π0.610137\pi
440440 3139.05 176.673i 0.340110 0.0191422i
441441 2717.53 0.293438
442442 −8616.64 + 8380.63i −0.927266 + 0.901868i
443443 9265.28 + 9265.28i 0.993695 + 0.993695i 0.999980 0.00628571i 0.00200082π-0.00200082\pi
−0.00628571 + 0.999980i 0.502001π0.502001\pi
444444 1240.96 + 34.4689i 0.132643 + 0.00368428i
445445 4732.86 5763.50i 0.504178 0.613969i
446446 −12094.9 167.941i −1.28410 0.0178302i
447447 −1808.56 1808.56i −0.191369 0.191369i
448448 2504.62 2118.59i 0.264135 0.223424i
449449 5672.62i 0.596230i 0.954530 + 0.298115i 0.0963579π0.0963579\pi
−0.954530 + 0.298115i 0.903642π0.903642\pi
450450 2619.84 + 1805.94i 0.274446 + 0.189184i
451451 −5716.08 −0.596807
452452 −6933.60 + 6558.83i −0.721525 + 0.682526i
453453 −5822.99 + 5822.99i −0.603947 + 0.603947i
454454 8174.18 + 113.501i 0.845007 + 0.0117332i
455455 4137.35 + 3397.51i 0.426290 + 0.350061i
456456 −87.9251 + 2109.66i −0.00902954 + 0.216653i
457457 6993.10 6993.10i 0.715806 0.715806i −0.251938 0.967743i 0.581068π-0.581068\pi
0.967743 + 0.251938i 0.0810678π0.0810678\pi
458458 7688.92 + 7905.46i 0.784454 + 0.806545i
459459 1535.34i 0.156129i
460460 514.937 + 7332.93i 0.0521936 + 0.743260i
461461 2825.86i 0.285496i 0.989759 + 0.142748i 0.0455938π0.0455938\pi
−0.989759 + 0.142748i 0.954406π0.954406\pi
462462 −484.351 + 471.085i −0.0487750 + 0.0474391i
463463 −4393.24 + 4393.24i −0.440975 + 0.440975i −0.892339 0.451365i 0.850937π-0.850937\pi
0.451365 + 0.892339i 0.350937π0.350937\pi
464464 3333.88 + 185.347i 0.333559 + 0.0185442i
465465 6314.14 619.986i 0.629701 0.0618304i
466466 154.884 11154.5i 0.0153967 1.10885i
467467 −13479.9 + 13479.9i −1.33571 + 1.33571i −0.435540 + 0.900169i 0.643442π0.643442\pi
−0.900169 + 0.435540i 0.856558π0.856558\pi
468468 3909.04 3697.75i 0.386101 0.365232i
469469 −4608.05 −0.453689
470470 9339.16 11056.2i 0.916560 1.08508i
471471 6123.53i 0.599061i
472472 −7807.46 8486.55i −0.761371 0.827595i
473473 3027.85 + 3027.85i 0.294336 + 0.294336i
474474 129.005 9290.77i 0.0125009 0.900293i
475475 −3813.89 + 756.264i −0.368407 + 0.0730522i
476476 80.9280 2913.60i 0.00779271 0.280556i
477477 −1413.40 1413.40i −0.135671 0.135671i
478478 10628.5 + 10927.8i 1.01702 + 1.04566i
479479 −16772.7 −1.59993 −0.799965 0.600047i 0.795149π-0.795149\pi
−0.799965 + 0.600047i 0.795149π0.795149\pi
480480 4169.37 4413.66i 0.396468 0.419698i
481481 3865.76 0.366452
482482 9196.78 + 9455.78i 0.869091 + 0.893566i
483483 −1117.05 1117.05i −0.105233 0.105233i
484484 261.338 9408.77i 0.0245434 0.883618i
485485 −7605.62 + 746.796i −0.712069 + 0.0699181i
486486 −9.54257 + 687.242i −0.000890658 + 0.0641438i
487487 −8030.17 8030.17i −0.747191 0.747191i 0.226760 0.973951i 0.427187π-0.427187\pi
−0.973951 + 0.226760i 0.927187π0.927187\pi
488488 925.383 + 1005.87i 0.0858404 + 0.0933068i
489489 12389.8i 1.14578i
490490 9514.77 801.049i 0.877211 0.0738524i
491491 −499.341 −0.0458960 −0.0229480 0.999737i 0.507305π-0.507305\pi
−0.0229480 + 0.999737i 0.507305π0.507305\pi
492492 −8019.20 + 7585.75i −0.734824 + 0.695106i
493493 2097.80 2097.80i 0.191644 0.191644i
494494 −91.2879 + 6574.42i −0.00831425 + 0.598780i
495495 −793.613 + 966.432i −0.0720611 + 0.0877533i
496496 671.995 12087.3i 0.0608336 1.09423i
497497 −1965.44 + 1965.44i −0.177388 + 0.177388i
498498 −5723.96 + 5567.18i −0.515054 + 0.500946i
499499 7718.28i 0.692420i 0.938157 + 0.346210i 0.112532π0.112532\pi
−0.938157 + 0.346210i 0.887468π0.887468\pi
500500 9705.08 + 5550.81i 0.868049 + 0.496479i
501501 1903.67i 0.169760i
502502 −8004.70 8230.12i −0.711688 0.731730i
503503 −859.315 + 859.315i −0.0761729 + 0.0761729i −0.744167 0.667994i 0.767153π-0.767153\pi
0.667994 + 0.744167i 0.267153π0.267153\pi
504504 −54.3336 + 1303.67i −0.00480200 + 0.115218i
505505 −2553.86 + 3110.00i −0.225040 + 0.274046i
506506 −2888.67 40.1102i −0.253789 0.00352394i
507507 7187.57 7187.57i 0.629608 0.629608i
508508 4909.85 4644.47i 0.428818 0.405640i
509509 14547.6 1.26682 0.633410 0.773816i 0.281655π-0.281655\pi
0.633410 + 0.773816i 0.281655π0.281655\pi
510510 −452.572 5375.60i −0.0392945 0.466736i
511511 4446.50i 0.384935i
512512 −7107.12 9149.13i −0.613463 0.789723i
513513 −593.857 593.857i −0.0511100 0.0511100i
514514 13523.7 + 187.781i 1.16052 + 0.0161142i
515515 −12032.7 + 1181.49i −1.02956 + 0.101093i
516516 8266.06 + 229.598i 0.705219 + 0.0195882i
517517 4021.90 + 4021.90i 0.342133 + 0.342133i
518518 −671.982 + 653.577i −0.0569985 + 0.0554373i
519519 −10278.2 −0.869291
520520 12596.6 14099.0i 1.06230 1.18901i
521521 −4286.58 −0.360458 −0.180229 0.983625i 0.557684π-0.557684\pi
−0.180229 + 0.983625i 0.557684π0.557684\pi
522522 −952.050 + 925.973i −0.0798278 + 0.0776413i
523523 −9413.82 9413.82i −0.787070 0.787070i 0.193943 0.981013i 0.437872π-0.437872\pi
−0.981013 + 0.193943i 0.937872π0.937872\pi
524524 398.931 14362.5i 0.0332584 1.19738i
525525 −2356.81 + 467.336i −0.195923 + 0.0388499i
526526 −6736.73 93.5416i −0.558432 0.00775401i
527527 −7605.81 7605.81i −0.628680 0.628680i
528528 1591.00 + 1778.31i 0.131135 + 0.146574i
529529 5412.38i 0.444841i
530530 −5365.29 4532.03i −0.439723 0.371432i
531531 4586.67 0.374848
532532 −1095.66 1158.26i −0.0892908 0.0943928i
533533 −24305.8 + 24305.8i −1.97524 + 1.97524i
534534 5659.48 + 78.5837i 0.458632 + 0.00636826i
535535 8145.69 799.826i 0.658260 0.0646346i
536536 −677.655 + 16259.5i −0.0546087 + 1.31027i
537537 6542.93 6542.93i 0.525788 0.525788i
538538 −15730.8 16173.8i −1.26060 1.29610i
539539 3752.55i 0.299877i
540540 169.168 + 2409.02i 0.0134811 + 0.191977i
541541 4696.82i 0.373257i −0.982431 0.186628i 0.940244π-0.940244\pi
0.982431 0.186628i 0.0597560π-0.0597560\pi
542542 1322.22 1286.00i 0.104786 0.101916i
543543 −4351.74 + 4351.74i −0.343924 + 0.343924i
544544 −10268.7 714.025i −0.809317 0.0562750i
545545 −18576.6 15254.7i −1.46006 1.19897i
546546 −56.4117 + 4062.69i −0.00442161 + 0.318437i
547547 14320.7 14320.7i 1.11939 1.11939i 0.127564 0.991830i 0.459284π-0.459284\pi
0.991830 0.127564i 0.0407158π-0.0407158\pi
548548 −15482.1 16366.8i −1.20687 1.27583i
549549 −543.637 −0.0422621
550550 −2493.77 + 3617.66i −0.193336 + 0.280468i
551551 1622.83i 0.125472i
552552 −4105.80 + 3777.26i −0.316584 + 0.291251i
553553 4961.12 + 4961.12i 0.381498 + 0.381498i
554554 −12.2161 + 879.787i −0.000936847 + 0.0674703i
555555 −1101.05 + 1340.82i −0.0842106 + 0.102549i
556556 7017.11 + 194.907i 0.535237 + 0.0148667i
557557 −9214.52 9214.52i −0.700955 0.700955i 0.263661 0.964616i 0.415070π-0.415070\pi
−0.964616 + 0.263661i 0.915070π0.915070\pi
558558 3357.22 + 3451.76i 0.254699 + 0.261872i
559559 25749.9 1.94831
560560 194.048 + 4580.50i 0.0146429 + 0.345645i
561561 2120.10 0.159555
562562 −5495.43 5650.19i −0.412474 0.424090i
563563 3971.85 + 3971.85i 0.297324 + 0.297324i 0.839965 0.542641i 0.182575π-0.182575\pi
−0.542641 + 0.839965i 0.682575π0.682575\pi
564564 10979.8 + 304.975i 0.819740 + 0.0227691i
565565 −1303.44 13274.7i −0.0970553 0.988443i
566566 45.9669 3310.47i 0.00341366 0.245847i
567567 −366.976 366.976i −0.0271808 0.0271808i
568568 6646.03 + 7224.10i 0.490953 + 0.533656i
569569 10888.3i 0.802218i −0.916030 0.401109i 0.868625π-0.868625\pi
0.916030 0.401109i 0.131375π-0.131375\pi
570570 −2254.30 1904.19i −0.165653 0.139926i
571571 14962.4 1.09660 0.548298 0.836283i 0.315276π-0.315276\pi
0.548298 + 0.836283i 0.315276π0.315276\pi
572572 5106.11 + 5397.87i 0.373247 + 0.394574i
573573 829.873 829.873i 0.0605034 0.0605034i
574574 115.726 8334.39i 0.00841515 0.606047i
575575 −8538.54 5712.64i −0.619272 0.414319i
576576 4592.02 + 383.433i 0.332177 + 0.0277367i
577577 11929.8 11929.8i 0.860734 0.860734i −0.130689 0.991423i 0.541719π-0.541719\pi
0.991423 + 0.130689i 0.0417191π0.0417191\pi
578578 3405.22 3311.95i 0.245049 0.238337i
579579 8847.32i 0.635029i
580580 −3060.42 + 3522.71i −0.219098 + 0.252194i
581581 6029.28i 0.430528i
582582 −4043.89 4157.78i −0.288015 0.296126i
583583 1951.71 1951.71i 0.138648 0.138648i
584584 15689.5 + 653.897i 1.11171 + 0.0463330i
585585 734.857 + 7484.03i 0.0519361 + 0.528934i
586586 6579.74 + 91.3619i 0.463834 + 0.00644048i
587587 2020.70 2020.70i 0.142084 0.142084i −0.632487 0.774571i 0.717966π-0.717966\pi
0.774571 + 0.632487i 0.217966π0.217966\pi
588588 4979.98 + 5264.53i 0.349270 + 0.369227i
589589 −5883.75 −0.411605
590590 16059.1 1352.01i 1.12058 0.0943416i
591591 3457.83i 0.240670i
592592 2207.33 + 2467.21i 0.153244 + 0.171287i
593593 −18128.7 18128.7i −1.25541 1.25541i −0.953263 0.302143i 0.902298π-0.902298\pi
−0.302143 0.953263i 0.597702π-0.597702\pi
594594 −948.990 13.1770i −0.0655514 0.000910202i
595595 3148.04 + 2585.11i 0.216903 + 0.178116i
596596 189.374 6817.89i 0.0130152 0.468576i
597597 −3554.49 3554.49i −0.243678 0.243678i
598598 −12453.7 + 12112.6i −0.851622 + 0.828296i
599599 16943.4 1.15574 0.577869 0.816129i 0.303884π-0.303884\pi
0.577869 + 0.816129i 0.303884π0.303884\pi
600600 1302.41 + 8384.73i 0.0886176 + 0.570509i
601601 −8319.55 −0.564661 −0.282331 0.959317i 0.591108π-0.591108\pi
−0.282331 + 0.959317i 0.591108π0.591108\pi
602602 −4476.09 + 4353.49i −0.303043 + 0.294743i
603603 −4576.97 4576.97i −0.309102 0.309102i
604604 −21951.4 609.722i −1.47879 0.0410749i
605605 10165.9 + 8347.98i 0.683142 + 0.560982i
606606 −3053.87 42.4040i −0.204711 0.00284248i
607607 9133.72 + 9133.72i 0.610752 + 0.610752i 0.943142 0.332390i 0.107855π-0.107855\pi
−0.332390 + 0.943142i 0.607855π0.607855\pi
608608 −4248.05 + 3695.69i −0.283357 + 0.246513i
609609 1002.83i 0.0667272i
610610 −1903.41 + 160.248i −0.126339 + 0.0106365i
611611 34203.7 2.26470
612612 2974.32 2813.56i 0.196454 0.185836i
613613 −7504.73 + 7504.73i −0.494475 + 0.494475i −0.909713 0.415238i 0.863698π-0.863698\pi
0.415238 + 0.909713i 0.363698π0.363698\pi
614614 −588.115 8.16616i −0.0386553 0.000536742i
615615 −1507.52 15353.1i −0.0988442 1.00666i
616616 −1800.20 75.0276i −0.117747 0.00490738i
617617 −10138.0 + 10138.0i −0.661494 + 0.661494i −0.955732 0.294238i 0.904934π-0.904934\pi
0.294238 + 0.955732i 0.404934π0.404934\pi
618618 −6397.78 6577.95i −0.416434 0.428162i
619619 11914.3i 0.773627i −0.922158 0.386814i 0.873576π-0.873576\pi
0.922158 0.386814i 0.126424π-0.126424\pi
620620 12771.9 + 11095.9i 0.827313 + 0.718744i
621621 2219.04i 0.143393i
622622 −6225.92 + 6055.39i −0.401345 + 0.390352i
623623 −3022.07 + 3022.07i −0.194345 + 0.194345i
624624 14326.9 + 796.503i 0.919127 + 0.0510988i
625625 −14442.7 + 5962.19i −0.924336 + 0.381580i
626626 −246.949 + 17784.9i −0.0157669 + 1.13551i
627627 820.038 820.038i 0.0522315 0.0522315i
628628 −11862.8 + 11221.6i −0.753785 + 0.713042i
629629 2941.39 0.186456
630630 −1393.05 1176.70i −0.0880959 0.0744142i
631631 2376.23i 0.149915i 0.997187 + 0.0749574i 0.0238821π0.0238821\pi
−0.997187 + 0.0749574i 0.976118π0.976118\pi
632632 18234.9 16775.8i 1.14770 1.05586i
633633 2661.02 + 2661.02i 0.167087 + 0.167087i
634634 308.789 22238.5i 0.0193432 1.39307i
635635 922.999 + 9400.12i 0.0576820 + 0.587453i
636636 147.996 5328.20i 0.00922708 0.332196i
637637 15956.5 + 15956.5i 0.992498 + 0.992498i
638638 −1278.65 1314.66i −0.0793450 0.0815795i
639639 −3904.36 −0.241712
640640 16190.9 11.0965i 1.00000 0.000685355i
641641 7046.51 0.434197 0.217099 0.976150i 0.430341π-0.430341\pi
0.217099 + 0.976150i 0.430341π0.430341\pi
642642 4331.05 + 4453.02i 0.266251 + 0.273749i
643643 4714.67 + 4714.67i 0.289158 + 0.289158i 0.836747 0.547589i 0.184454π-0.184454\pi
−0.547589 + 0.836747i 0.684454π0.684454\pi
644644 116.966 4211.05i 0.00715700 0.257669i
645645 −7334.11 + 8931.21i −0.447722 + 0.545218i
646646 −69.4595 + 5002.37i −0.00423041 + 0.304668i
647647 −9404.06 9404.06i −0.571425 0.571425i 0.361102 0.932526i 0.382401π-0.382401\pi
−0.932526 + 0.361102i 0.882401π0.882401\pi
648648 −1348.84 + 1240.91i −0.0817709 + 0.0752276i
649649 6333.58i 0.383074i
650650 4779.00 + 25986.9i 0.288381 + 1.56814i
651651 −3635.88 −0.218896
652652 −24002.1 + 22704.7i −1.44171 + 1.36378i
653653 21869.3 21869.3i 1.31059 1.31059i 0.389605 0.920982i 0.372612π-0.372612\pi
0.920982 0.389605i 0.127388π-0.127388\pi
654654 253.287 18241.3i 0.0151442 1.09066i
655655 15518.2 + 12743.2i 0.925717 + 0.760179i
656656 −29390.9 1633.99i −1.74927 0.0972506i
657657 −4416.50 + 4416.50i −0.262259 + 0.262259i
658658 −5945.59 + 5782.74i −0.352254 + 0.342606i
659659 20051.7i 1.18528i 0.805466 + 0.592642i 0.201915π0.201915\pi
−0.805466 + 0.592642i 0.798085π0.798085\pi
660660 −3326.54 + 233.598i −0.196190 + 0.0137770i
661661 8405.80i 0.494626i 0.968936 + 0.247313i 0.0795475π0.0795475\pi
−0.968936 + 0.247313i 0.920452π0.920452\pi
662662 7359.85 + 7567.11i 0.432098 + 0.444266i
663663 9015.03 9015.03i 0.528077 0.528077i
664664 −21274.4 886.660i −1.24338 0.0518209i
665665 2217.54 217.741i 0.129312 0.0126972i
666666 −1316.62 18.2816i −0.0766034 0.00106366i
667667 3031.98 3031.98i 0.176010 0.176010i
668668 3687.87 3488.54i 0.213605 0.202059i
669669 12829.8 0.741448
670670 −17374.3 14676.0i −1.00183 0.846242i
671671 750.692i 0.0431895i
672672 −2625.10 + 2283.77i −0.150693 + 0.131099i
673673 −16587.1 16587.1i −0.950051 0.950051i 0.0487593 0.998811i 0.484473π-0.484473\pi
−0.998811 + 0.0487593i 0.984473π0.984473\pi
674674 −924.960 12.8434i −0.0528607 0.000733988i
675675 −2805.09 1876.72i −0.159953 0.107015i
676676 27095.6 + 752.607i 1.54162 + 0.0428201i
677677 −3107.71 3107.71i −0.176424 0.176424i 0.613371 0.789795i 0.289813π-0.289813\pi
−0.789795 + 0.613371i 0.789813π0.789813\pi
678678 7256.90 7058.13i 0.411061 0.399802i
679679 4379.56 0.247529
680680 9584.51 10727.7i 0.540513 0.604985i
681681 −8670.86 −0.487912
682682 −4766.43 + 4635.87i −0.267619 + 0.260289i
683683 20235.7 + 20235.7i 1.13367 + 1.13367i 0.989562 + 0.144111i 0.0460321π0.0460321\pi
0.144111 + 0.989562i 0.453968π0.453968\pi
684684 62.1824 2238.71i 0.00347603 0.125145i
685685 31334.9 3076.77i 1.74780 0.171617i
686686 −11686.8 162.275i −0.650443 0.00903160i
687687 −8270.96 8270.96i −0.459326 0.459326i
688688 14703.1 + 16434.1i 0.814752 + 0.910677i
689689 16598.1i 0.917760i
690690 −654.106 7769.41i −0.0360890 0.428661i
691691 −9571.90 −0.526964 −0.263482 0.964664i 0.584871π-0.584871\pi
−0.263482 + 0.964664i 0.584871π0.584871\pi
692692 −18835.1 19911.4i −1.03469 1.09381i
693693 506.745 506.745i 0.0277773 0.0277773i
694694 −11900.5 165.243i −0.650919 0.00903822i
695695 −6225.98 + 7581.76i −0.339805 + 0.413802i
696696 −3538.50 147.476i −0.192711 0.00803168i
697697 −18493.9 + 18493.9i −1.00503 + 1.00503i
698698 −17502.3 17995.2i −0.949100 0.975828i
699699 11832.3i 0.640257i
700700 −5224.28 3709.30i −0.282085 0.200284i
701701 8233.56i 0.443620i −0.975090 0.221810i 0.928804π-0.928804\pi
0.975090 0.221810i 0.0711964π-0.0711964\pi
702702 −4091.31 + 3979.25i −0.219966 + 0.213942i
703703 1137.71 1137.71i 0.0610378 0.0610378i
704704 −529.470 + 6340.98i −0.0283454 + 0.339467i
705705 −9741.90 + 11863.3i −0.520427 + 0.633757i
706706 307.853 22171.1i 0.0164111 1.18190i
707707 1630.72 1630.72i 0.0867460 0.0867460i
708708 8405.23 + 8885.50i 0.446169 + 0.471663i
709709 −22460.1 −1.18971 −0.594857 0.803832i 0.702791π-0.702791\pi
−0.594857 + 0.803832i 0.702791π0.702791\pi
710710 −13670.2 + 1150.89i −0.722581 + 0.0608341i
711711 9855.30i 0.519835i
712712 10219.0 + 11107.8i 0.537882 + 0.584667i
713713 −10992.8 10992.8i −0.577394 0.577394i
714714 −42.9227 + 3091.23i −0.00224978 + 0.162026i
715715 −10334.5 + 1014.74i −0.540541 + 0.0530758i
716716 24665.4 + 685.107i 1.28742 + 0.0357593i
717717 −11433.1 11433.1i −0.595503 0.595503i
718718 2150.06 + 2210.61i 0.111754 + 0.114901i
719719 −14177.6 −0.735377 −0.367688 0.929949i 0.619851π-0.619851\pi
−0.367688 + 0.929949i 0.619851π0.619851\pi
720720 −4356.86 + 4742.34i −0.225515 + 0.245467i
721721 6928.83 0.357896
722722 −11618.2 11945.4i −0.598871 0.615736i
723723 −9892.97 9892.97i −0.508884 0.508884i
724724 −16405.1 455.668i −0.842114 0.0233906i
725725 −1268.47 6396.99i −0.0649791 0.327694i
726726 −138.609 + 9982.39i −0.00708574 + 0.510305i
727727 48.4942 + 48.4942i 0.00247393 + 0.00247393i 0.708343 0.705869i 0.249443π-0.249443\pi
−0.705869 + 0.708343i 0.749443π0.749443\pi
728728 −7973.80 + 7335.73i −0.405946 + 0.373462i
729729 729.000i 0.0370370i
730730 −14161.4 + 16765.2i −0.717998 + 0.850009i
731731 19592.7 0.991330
732732 −996.235 1053.16i −0.0503031 0.0531774i
733733 22687.5 22687.5i 1.14322 1.14322i 0.155367 0.987857i 0.450344π-0.450344\pi
0.987857 0.155367i 0.0496561π-0.0496561\pi
734734 −438.222 + 31560.1i −0.0220369 + 1.58706i
735735 −10079.2 + 989.675i −0.505817 + 0.0496663i
736736 −14841.5 1031.99i −0.743295 0.0516842i
737737 6320.19 6320.19i 0.315885 0.315885i
738738 8393.11 8163.22i 0.418638 0.407171i
739739 18302.4i 0.911046i 0.890224 + 0.455523i 0.150548π0.150548\pi
−0.890224 + 0.455523i 0.849452π0.849452\pi
740740 −4615.20 + 324.091i −0.229268 + 0.0160998i
741741 6973.90i 0.345739i
742742 2806.20 + 2885.23i 0.138840 + 0.142750i
743743 18251.9 18251.9i 0.901207 0.901207i −0.0943332 0.995541i 0.530072π-0.530072\pi
0.995541 + 0.0943332i 0.0300719π0.0300719\pi
744744 −534.689 + 12829.2i −0.0263476 + 0.632181i
745745 7366.50 + 6049.21i 0.362265 + 0.297484i
746746 18743.8 + 260.263i 0.919916 + 0.0127733i
747747 5988.61 5988.61i 0.293322 0.293322i
748748 3885.15 + 4107.15i 0.189913 + 0.200765i
749749 −4690.55 −0.228824
750750 −10374.5 5744.03i −0.505100 0.279657i
751751 21816.5i 1.06005i −0.847982 0.530024i 0.822183π-0.822183\pi
0.847982 0.530024i 0.177817π-0.177817\pi
752752 19530.1 + 21829.5i 0.947060 + 1.05856i
753753 8610.64 + 8610.64i 0.416719 + 0.416719i
754754 −11027.2 153.116i −0.532608 0.00739544i
755755 19476.5 23717.8i 0.938838 1.14328i
756756 38.4258 1383.42i 0.00184859 0.0665535i
757757 17383.8 + 17383.8i 0.834644 + 0.834644i 0.988148 0.153504i 0.0490557π-0.0490557\pi
−0.153504 + 0.988148i 0.549056π0.549056\pi
758758 14769.2 14364.7i 0.707707 0.688323i
759759 3064.20 0.146539
760760 −442.190 7856.63i −0.0211051 0.374987i
761761 426.712 0.0203263 0.0101631 0.999948i 0.496765π-0.496765\pi
0.0101631 + 0.999948i 0.496765π0.496765\pi
762762 −5138.78 + 4998.03i −0.244302 + 0.237611i
763763 9740.58 + 9740.58i 0.462166 + 0.462166i
764764 3128.44 + 86.8956i 0.148145 + 0.00411488i
765765 559.141 + 5694.47i 0.0264258 + 0.269129i
766766 −24729.5 343.377i −1.16647 0.0161968i
767767 26931.5 + 26931.5i 1.26785 + 1.26785i
768768 7672.24 + 9598.53i 0.360479 + 0.450986i
769769 15349.4i 0.719786i 0.932994 + 0.359893i 0.117187π0.117187\pi
−0.932994 + 0.359893i 0.882813π0.882813\pi
770770 1624.87 1923.62i 0.0760471 0.0900291i
771771 −14345.5 −0.670090
772772 17139.4 16213.0i 0.799044 0.755855i
773773 −9844.65 + 9844.65i −0.458069 + 0.458069i −0.898021 0.439952i 0.854995π-0.854995\pi
0.439952 + 0.898021i 0.354995π0.354995\pi
774774 −8770.02 121.775i −0.407276 0.00565516i
775775 −23193.0 + 4598.98i −1.07499 + 0.213162i
776776 644.053 15453.3i 0.0297940 0.714872i
777777 703.052 703.052i 0.0324605 0.0324605i
778778 5324.30 + 5474.24i 0.245354 + 0.252264i
779779 14306.6i 0.658007i
780780 −13151.8 + 15138.4i −0.603728 + 0.694923i
781781 5391.41i 0.247017i
782782 −9475.82 + 9216.28i −0.433318 + 0.421449i
783783 996.068 996.068i 0.0454618 0.0454618i
784784 −1072.70 + 19294.9i −0.0488655 + 0.878958i
785785 −2230.08 22711.8i −0.101395 1.03264i
786786 −211.586 + 15238.1i −0.00960180 + 0.691507i
787787 3192.68 3192.68i 0.144608 0.144608i −0.631096 0.775705i 0.717395π-0.717395\pi
0.775705 + 0.631096i 0.217395π0.217395\pi
788788 −6698.67 + 6336.60i −0.302830 + 0.286462i
789789 7146.07 0.322442
790790 2905.05 + 34505.9i 0.130832 + 1.55401i
791791 7643.99i 0.343602i
792792 −1713.53 1862.57i −0.0768784 0.0835653i
793793 −3192.08 3192.08i −0.142943 0.142943i
794794 59.8310 4308.94i 0.00267421 0.192593i
795795 5756.94 + 4727.47i 0.256827 + 0.210901i
796796 372.188 13399.6i 0.0165727 0.596656i
797797 1431.93 + 1431.93i 0.0636407 + 0.0636407i 0.738211 0.674570i 0.235671π-0.235671\pi
−0.674570 + 0.738211i 0.735671π0.735671\pi
798798 1179.06 + 1212.27i 0.0523037 + 0.0537767i
799799 26025.0 1.15231
800800 −13856.6 + 17888.4i −0.612380 + 0.790564i
801801 −6003.36 −0.264817
802802 −19516.7 20066.3i −0.859298 0.883497i
803803 −6098.61 6098.61i −0.268014 0.268014i
804804 479.252 17254.2i 0.0210223 0.756850i
805805 4549.90 + 3736.28i 0.199209 + 0.163586i
806806 −555.139 + 39980.3i −0.0242605 + 1.74720i
807807 16921.6 + 16921.6i 0.738126 + 0.738126i
808808 −5514.18 5993.80i −0.240084 0.260967i
809809 15866.9i 0.689556i −0.938684 0.344778i 0.887954π-0.887954\pi
0.938684 0.344778i 0.112046π-0.112046\pi
810810 −214.888 2552.42i −0.00932147 0.110719i
811811 −21359.2 −0.924812 −0.462406 0.886668i 0.653014π-0.653014\pi
−0.462406 + 0.886668i 0.653014π0.653014\pi
812812 1942.74 1837.73i 0.0839614 0.0794232i
813813 −1383.35 + 1383.35i −0.0596757 + 0.0596757i
814814 25.2445 1818.07i 0.00108700 0.0782844i
815815 −4512.13 45953.0i −0.193930 1.97505i
816816 10901.1 + 606.046i 0.467666 + 0.0259998i
817817 7578.32 7578.32i 0.324519 0.324519i
818818 12084.6 11753.6i 0.516539 0.502391i
819819 4309.54i 0.183868i
820820 26980.2 31055.6i 1.14901 1.32257i
821821 4564.28i 0.194025i 0.995283 + 0.0970126i 0.0309287π0.0309287\pi
−0.995283 + 0.0970126i 0.969071π0.969071\pi
822822 16660.7 + 17129.9i 0.706945 + 0.726854i
823823 −21363.8 + 21363.8i −0.904857 + 0.904857i −0.995851 0.0909949i 0.970995π-0.970995\pi
0.0909949 + 0.995851i 0.470995π0.470995\pi
824824 1018.95 24448.4i 0.0430785 1.03362i
825825 2591.51 3873.46i 0.109363 0.163463i
826826 −9234.75 128.227i −0.389005 0.00540146i
827827 −26808.3 + 26808.3i −1.12722 + 1.12722i −0.136598 + 0.990626i 0.543617π0.543617\pi
−0.990626 + 0.136598i 0.956383π0.956383\pi
828828 4298.82 4066.46i 0.180428 0.170676i
829829 −23938.0 −1.00290 −0.501448 0.865188i 0.667199π-0.667199\pi
−0.501448 + 0.865188i 0.667199π0.667199\pi
830830 19202.4 22732.9i 0.803041 0.950688i
831831 933.245i 0.0389578i
832832 24711.6 + 29214.4i 1.02971 + 1.21734i
833833 12141.1 + 12141.1i 0.504997 + 0.504997i
834834 −7444.93 103.375i −0.309109 0.00429207i
835835 693.281 + 7060.60i 0.0287329 + 0.292625i
836836 3091.36 + 85.8657i 0.127891 + 0.00355231i
837837 −3611.35 3611.35i −0.149136 0.149136i
838838 5009.27 4872.07i 0.206495 0.200839i
839839 −2924.94 −0.120358 −0.0601789 0.998188i 0.519167π-0.519167\pi
−0.0601789 + 0.998188i 0.519167π0.519167\pi
840840 −273.253 4855.03i −0.0112239 0.199422i
841841 −21667.0 −0.888394
842842 20661.0 20095.1i 0.845637 0.822475i
843843 5911.42 + 5911.42i 0.241519 + 0.241519i
844844 −278.634 + 10031.5i −0.0113637 + 0.409120i
845845 −24040.7 + 29275.9i −0.978729 + 1.19186i
846846 −11649.2 161.753i −0.473414 0.00657350i
847847 −5330.43 5330.43i −0.216241 0.216241i
848848 10593.2 9477.41i 0.428978 0.383792i
849849 3511.62i 0.141953i
850850 3636.26 + 19773.0i 0.146732 + 0.797891i
851851 4251.22 0.171246
852852 −7154.89 7563.71i −0.287702 0.304141i
853853 −6388.44 + 6388.44i −0.256431 + 0.256431i −0.823601 0.567170i 0.808038π-0.808038\pi
0.567170 + 0.823601i 0.308038π0.308038\pi
854854 1094.55 + 15.1982i 0.0438581 + 0.000608984i
855855 2418.85 + 1986.31i 0.0967521 + 0.0794507i
856856 −689.787 + 16550.6i −0.0275426 + 0.660852i
857857 −10121.5 + 10121.5i −0.403434 + 0.403434i −0.879441 0.476007i 0.842084π-0.842084\pi
0.476007 + 0.879441i 0.342084π0.342084\pi
858858 −5494.82 5649.56i −0.218636 0.224793i
859859 41062.1i 1.63099i −0.578764 0.815495i 0.696465π-0.696465\pi
0.578764 0.815495i 0.303535π-0.303535\pi
860860 −30742.0 + 2158.78i −1.21894 + 0.0855974i
861861 8840.81i 0.349935i
862862 27623.1 26866.5i 1.09147 1.06157i
863863 −837.975 + 837.975i −0.0330533 + 0.0330533i −0.723440 0.690387i 0.757440π-0.757440\pi
0.690387 + 0.723440i 0.257440π0.257440\pi
864864 −4875.75 339.030i −0.191987 0.0133496i
865865 38121.2 3743.12i 1.49845 0.147133i
866866 363.311 26165.1i 0.0142561 1.02671i
867867 −3562.66 + 3562.66i −0.139555 + 0.139555i
868868 −6662.89 7043.60i −0.260545 0.275432i
869869 −13608.9 −0.531242
870870 3193.88 3781.10i 0.124463 0.147346i
871871 53749.1i 2.09095i
872872 35802.1 32937.2i 1.39038 1.27912i
873873 4350.01 + 4350.01i 0.168643 + 0.168643i
874874 −100.390 + 7229.97i −0.00388531 + 0.279814i
875875 8571.07 2591.63i 0.331149 0.100129i
876876 −16649.3 462.450i −0.642153 0.0178364i
877877 1659.56 + 1659.56i 0.0638990 + 0.0638990i 0.738334 0.674435i 0.235613π-0.235613\pi
−0.674435 + 0.738334i 0.735613π0.735613\pi
878878 12303.4 + 12649.9i 0.472915 + 0.486234i
879879 −6979.55 −0.267821
880880 −6548.55 6016.25i −0.250854 0.230463i
881881 −3948.49 −0.150997 −0.0754983 0.997146i 0.524055π-0.524055\pi
−0.0754983 + 0.997146i 0.524055π0.524055\pi
882882 −5359.08 5510.00i −0.204591 0.210353i
883883 −9143.59 9143.59i −0.348478 0.348478i 0.511064 0.859543i 0.329251π-0.329251\pi
−0.859543 + 0.511064i 0.829251π0.829251\pi
884884 33984.7 + 943.959i 1.29302 + 0.0359149i
885885 −17011.7 + 1670.38i −0.646149 + 0.0634454i
886886 514.556 37057.5i 0.0195111 1.40516i
887887 19332.9 + 19332.9i 0.731834 + 0.731834i 0.970983 0.239149i 0.0768685π-0.0768685\pi
−0.239149 + 0.970983i 0.576868π0.576868\pi
888888 −2377.33 2584.11i −0.0898401 0.0976544i
889889 5412.89i 0.204210i
890890 −21019.3 + 1769.62i −0.791650 + 0.0666490i
891891 1006.65 0.0378498
892892 23511.1 + 24854.5i 0.882521 + 0.932948i
893893 10066.3 10066.3i 0.377217 0.377217i
894894 −100.440 + 7233.55i −0.00375752 + 0.270611i
895895 −21884.5 + 26650.2i −0.817340 + 0.995326i
896896 −9234.81 900.377i −0.344323 0.0335708i
897897 13029.5 13029.5i 0.484997 0.484997i
898898 11501.7 11186.6i 0.427411 0.415704i
899899 9868.74i 0.366119i
900900 −1504.75 8873.31i −0.0557316 0.328641i
901901 12629.2i 0.466970i
902902 11272.3 + 11589.8i 0.416106 + 0.427824i
903903 4683.05 4683.05i 0.172583 0.172583i
904904 26971.9 + 1124.12i 0.992335 + 0.0413579i
905905 14555.5 17725.2i 0.534632 0.651054i
906906 23289.7 + 323.385i 0.854027 + 0.0118584i
907907 11929.3 11929.3i 0.436721 0.436721i −0.454186 0.890907i 0.650070π-0.650070\pi
0.890907 + 0.454186i 0.150070π0.150070\pi
908908 −15889.7 16797.6i −0.580746 0.613929i
909909 3239.43 0.118201
910910 −1270.33 15088.8i −0.0462757 0.549659i
911911 34862.0i 1.26787i 0.773386 + 0.633935i 0.218561π0.218561\pi
−0.773386 + 0.633935i 0.781439π0.781439\pi
912912 4450.88 3982.06i 0.161605 0.144582i
913913 8269.48 + 8269.48i 0.299759 + 0.299759i
914914 −27969.7 388.368i −1.01220 0.0140548i
915915 2016.32 197.983i 0.0728497 0.00715312i
916916 866.048 31179.7i 0.0312391 1.12468i
917917 −8136.89 8136.89i −0.293025 0.293025i
918918 −3113.01 + 3027.74i −0.111922 + 0.108857i
919919 −13149.4 −0.471990 −0.235995 0.971754i 0.575835π-0.575835\pi
−0.235995 + 0.971754i 0.575835π0.575835\pi
920920 13852.6 15504.9i 0.496420 0.555632i
921921 623.850 0.0223198
922922 5729.65 5572.71i 0.204659 0.199054i
923923 −22925.3 22925.3i −0.817545 0.817545i
924924 1910.32 + 53.0610i 0.0680140 + 0.00188916i
925925 3595.43 5373.99i 0.127802 0.191022i
926926 17571.3 + 243.983i 0.623572 + 0.00865850i
927927 6882.08 + 6882.08i 0.243837 + 0.243837i
928928 −6198.74 7125.21i −0.219271 0.252044i
929929 25537.5i 0.901892i 0.892551 + 0.450946i 0.148913π0.148913\pi
−0.892551 + 0.450946i 0.851087π0.851087\pi
930930 −13708.8 11579.7i −0.483364 0.408296i
931931 9392.15 0.330629
932932 −22922.1 + 21683.2i −0.805621 + 0.762077i
933933 6513.78 6513.78i 0.228565 0.228565i
934934 53914.5 + 748.620i 1.88880 + 0.0262265i
935935 −7863.32 + 772.100i −0.275035 + 0.0270057i
936936 −15206.2 633.757i −0.531017 0.0221314i
937937 8008.02 8008.02i 0.279200 0.279200i −0.553589 0.832790i 0.686742π-0.686742\pi
0.832790 + 0.553589i 0.186742π0.186742\pi
938938 9087.26 + 9343.17i 0.316321 + 0.325230i
939939 18865.5i 0.655648i
940940 −40834.6 + 2867.51i −1.41689 + 0.0994976i
941941 10838.0i 0.375460i −0.982221 0.187730i 0.939887π-0.939887\pi
0.982221 0.187730i 0.0601130π-0.0601130\pi
942942 12415.9 12075.9i 0.429440 0.417678i
943943 −26729.4 + 26729.4i −0.923042 + 0.923042i
944944 −1810.50 + 32566.0i −0.0624225 + 1.12281i
945945 1494.74 + 1227.45i 0.0514538 + 0.0422527i
946946 168.155 12110.2i 0.00577926 0.416214i
947947 −1009.18 + 1009.18i −0.0346292 + 0.0346292i −0.724209 0.689580i 0.757795π-0.757795\pi
0.689580 + 0.724209i 0.257795π0.257795\pi
948948 −19092.1 + 18060.2i −0.654097 + 0.618742i
949949 −51864.8 −1.77408
950950 9054.53 + 6241.57i 0.309229 + 0.213161i
951951 23589.8i 0.804365i
952952 −6067.13 + 5581.64i −0.206551 + 0.190023i
953953 16368.4 + 16368.4i 0.556373 + 0.556373i 0.928273 0.371900i 0.121294π-0.121294\pi
−0.371900 + 0.928273i 0.621294π0.621294\pi
954954 −78.4943 + 5653.04i −0.00266388 + 0.191849i
955955 −2775.73 + 3380.18i −0.0940528 + 0.114534i
956956 1197.15 43100.2i 0.0405006 1.45812i
957957 1375.44 + 1375.44i 0.0464594 + 0.0464594i
958958 33076.5 + 34008.0i 1.11551 + 1.14692i
959959 −18043.6 −0.607569
960960 −17171.2 + 250.198i −0.577289 + 0.00841157i
961961 −5989.17 −0.201040
962962 −7623.43 7838.12i −0.255498 0.262694i
963963 −4658.91 4658.91i −0.155899 0.155899i
964964 1035.89 37294.3i 0.0346096 1.24603i
965965 3222.03 + 32814.2i 0.107483 + 1.09464i
966966 −62.0366 + 4467.78i −0.00206625 + 0.148808i
967967 −23863.5 23863.5i −0.793586 0.793586i 0.188489 0.982075i 0.439641π-0.439641\pi
−0.982075 + 0.188489i 0.939641π0.939641\pi
968968 −19592.3 + 18024.6i −0.650539 + 0.598483i
969969 5306.32i 0.175917i
970970 16512.8 + 13948.2i 0.546590 + 0.461702i
971971 −49836.4 −1.64709 −0.823547 0.567249i 0.808008π-0.808008\pi
−0.823547 + 0.567249i 0.808008π0.808008\pi
972972 1412.25 1335.92i 0.0466029 0.0440840i
973973 3975.47 3975.47i 0.130984 0.130984i
974974 −445.963 + 32117.6i −0.0146710 + 1.05659i
975975 −5451.09 27490.2i −0.179051 0.902966i
976976 214.591 3859.90i 0.00703779 0.126591i
977977 −13522.5 + 13522.5i −0.442807 + 0.442807i −0.892954 0.450147i 0.851371π-0.851371\pi
0.450147 + 0.892954i 0.351371π0.351371\pi
978978 25121.2 24433.1i 0.821358 0.798861i
979979 8289.86i 0.270628i
980980 −20387.7 17712.2i −0.664552 0.577343i
981981 19349.7i 0.629755i
982982 984.720 + 1012.45i 0.0319997 + 0.0329008i
983983 −36477.6 + 36477.6i −1.18358 + 1.18358i −0.204766 + 0.978811i 0.565643π0.565643\pi
−0.978811 + 0.204766i 0.934357π0.934357\pi
984984 31194.9 + 1300.12i 1.01063 + 0.0421202i
985985 −1259.28 12824.9i −0.0407350 0.414858i
986986 −8390.41 116.503i −0.270999 0.00376291i
987987 6220.49 6220.49i 0.200608 0.200608i
988988 13510.2 12779.9i 0.435036 0.411522i
989989 28317.5 0.910460
990990 3524.55 296.732i 0.113149 0.00952602i
991991 36474.0i 1.16916i −0.811337 0.584579i 0.801260π-0.801260\pi
0.811337 0.584579i 0.198740π-0.198740\pi
992992 −25833.2 + 22474.2i −0.826820 + 0.719311i
993993 −7916.98 7916.98i −0.253009 0.253009i
994994 7861.00 + 109.153i 0.250841 + 0.00348301i
995995 14477.9 + 11888.9i 0.461286 + 0.378798i
996996 22575.7 + 627.064i 0.718213 + 0.0199491i
997997 −16586.0 16586.0i −0.526865 0.526865i 0.392771 0.919636i 0.371516π-0.371516\pi
−0.919636 + 0.392771i 0.871516π0.871516\pi
998998 15649.4 15220.7i 0.496365 0.482770i
999999 1396.62 0.0442312
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 120.4.v.a.43.9 72
4.3 odd 2 480.4.bh.a.463.9 72
5.2 odd 4 inner 120.4.v.a.67.27 yes 72
8.3 odd 2 inner 120.4.v.a.43.27 yes 72
8.5 even 2 480.4.bh.a.463.10 72
20.7 even 4 480.4.bh.a.367.10 72
40.27 even 4 inner 120.4.v.a.67.9 yes 72
40.37 odd 4 480.4.bh.a.367.9 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.v.a.43.9 72 1.1 even 1 trivial
120.4.v.a.43.27 yes 72 8.3 odd 2 inner
120.4.v.a.67.9 yes 72 40.27 even 4 inner
120.4.v.a.67.27 yes 72 5.2 odd 4 inner
480.4.bh.a.367.9 72 40.37 odd 4
480.4.bh.a.367.10 72 20.7 even 4
480.4.bh.a.463.9 72 4.3 odd 2
480.4.bh.a.463.10 72 8.5 even 2