Properties

Label 74.2.f.b.71.2
Level 7474
Weight 22
Character 74.71
Analytic conductor 0.5910.591
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,2,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 74=237 74 = 2 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 74.f (of order 99, degree 66, 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: 0.5908929749570.590892974957
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ9)\Q(\zeta_{9})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1224x10+264x81687x6+6600x415000x2+15625 x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 71.2
Root 2.209760.342020i2.20976 - 0.342020i of defining polynomial
Character χ\chi == 74.71
Dual form 74.2.f.b.49.2

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+(0.766044+0.642788i)q2+(0.9729250.816381i)q3+(0.173648+0.984808i)q4+(1.439690.524005i)q5+1.27006q6+(1.828500.665520i)q7+(0.500000+0.866025i)q8+(0.240839+1.36587i)q9+(0.7660441.32683i)q10+(0.220544+0.381994i)q11+(0.972925+0.816381i)q12+(0.3675922.08472i)q13+(0.9729251.68516i)q14+(1.82850+0.665520i)q15+(0.939693+0.342020i)q16+(0.664245+3.76712i)q17+(1.06246+0.891507i)q18+(4.554793.82192i)q19+(0.2660441.50881i)q20+(2.32231+0.845253i)q21+(0.414488+0.150861i)q22+(2.855584.94600i)q23+(0.220544+1.25077i)q24+(2.032091.70513i)q25+(1.058441.83327i)q26+(2.78585+4.82523i)q27+(0.3378931.91629i)q28+(1.36712+2.36792i)q29+(1.828500.665520i)q30+9.87516q31+(0.9396930.342020i)q32+(0.0972795+0.551699i)q33+(2.93030+2.45881i)q34+(2.28374+1.91629i)q351.38694q36+(2.18831+5.67550i)q37+5.94585q38+(2.059561.72818i)q39+(1.173650.984808i)q40+(1.80615+10.2432i)q41+(2.322310.845253i)q42+3.84681q43+(0.4144880.150861i)q44+(1.062461.84023i)q45+(0.9917315.62439i)q46+(3.843166.65655i)q47+(0.635032+1.09991i)q48+(2.461812.06571i)q49+(0.4606372.61240i)q50+(2.42915+4.20740i)q51+(1.989210.724014i)q52+(1.62561+0.591673i)q53+(0.967514+5.48704i)q54+(0.5176830.434387i)q55+(1.490611.25077i)q56+(1.311327.43688i)q57+(2.56934+0.935163i)q58+(1.93027+0.702561i)q59+(0.9729251.68516i)q60+(1.8989410.7694i)q61+(7.56481+6.34763i)q62+(1.349392.33721i)q63+(0.5000000.866025i)q64+(0.563183+3.19397i)q65+(0.280105+0.485156i)q66+(1.57261+0.572384i)q673.82524q68+(6.816082.48085i)q69+(0.517683+2.93592i)q70+(7.70462+6.46494i)q71+(1.062460.891507i)q729.88570q73+(1.97180+5.75430i)q743.36910q75+(4.55479+3.82192i)q76+(0.6574900.551699i)q77+(0.4668652.64772i)q78+(12.53954.56401i)q79+1.53209q80+(2.73975+0.997189i)q81+(5.20061+9.00771i)q82+(0.6179993.50484i)q83+(1.235682.14025i)q84+(2.930305.07543i)q85+(2.94683+2.47268i)q86+(0.603020+3.41989i)q87+(0.2205440.381994i)q88+(11.15434.05982i)q89+(1.996770.726763i)q90+(0.715278+4.05654i)q91+(4.375003.67106i)q92+(9.607798.06190i)q93+(1.334727.56955i)q94+(8.56020+3.11566i)q95+(1.19347+0.434387i)q96+(0.296748+0.513983i)q97+(0.5580473.16484i)q98+(0.4686370.393233i)q99+O(q100)q+(0.766044 + 0.642788i) q^{2} +(0.972925 - 0.816381i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{5} +1.27006 q^{6} +(-1.82850 - 0.665520i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.240839 + 1.36587i) q^{9} +(-0.766044 - 1.32683i) q^{10} +(-0.220544 + 0.381994i) q^{11} +(0.972925 + 0.816381i) q^{12} +(-0.367592 - 2.08472i) q^{13} +(-0.972925 - 1.68516i) q^{14} +(-1.82850 + 0.665520i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.664245 + 3.76712i) q^{17} +(-1.06246 + 0.891507i) q^{18} +(4.55479 - 3.82192i) q^{19} +(0.266044 - 1.50881i) q^{20} +(-2.32231 + 0.845253i) q^{21} +(-0.414488 + 0.150861i) q^{22} +(-2.85558 - 4.94600i) q^{23} +(0.220544 + 1.25077i) q^{24} +(-2.03209 - 1.70513i) q^{25} +(1.05844 - 1.83327i) q^{26} +(2.78585 + 4.82523i) q^{27} +(0.337893 - 1.91629i) q^{28} +(-1.36712 + 2.36792i) q^{29} +(-1.82850 - 0.665520i) q^{30} +9.87516 q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.0972795 + 0.551699i) q^{33} +(-2.93030 + 2.45881i) q^{34} +(2.28374 + 1.91629i) q^{35} -1.38694 q^{36} +(2.18831 + 5.67550i) q^{37} +5.94585 q^{38} +(-2.05956 - 1.72818i) q^{39} +(1.17365 - 0.984808i) q^{40} +(1.80615 + 10.2432i) q^{41} +(-2.32231 - 0.845253i) q^{42} +3.84681 q^{43} +(-0.414488 - 0.150861i) q^{44} +(1.06246 - 1.84023i) q^{45} +(0.991731 - 5.62439i) q^{46} +(-3.84316 - 6.65655i) q^{47} +(-0.635032 + 1.09991i) q^{48} +(-2.46181 - 2.06571i) q^{49} +(-0.460637 - 2.61240i) q^{50} +(2.42915 + 4.20740i) q^{51} +(1.98921 - 0.724014i) q^{52} +(-1.62561 + 0.591673i) q^{53} +(-0.967514 + 5.48704i) q^{54} +(0.517683 - 0.434387i) q^{55} +(1.49061 - 1.25077i) q^{56} +(1.31132 - 7.43688i) q^{57} +(-2.56934 + 0.935163i) q^{58} +(-1.93027 + 0.702561i) q^{59} +(-0.972925 - 1.68516i) q^{60} +(-1.89894 - 10.7694i) q^{61} +(7.56481 + 6.34763i) q^{62} +(1.34939 - 2.33721i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.563183 + 3.19397i) q^{65} +(-0.280105 + 0.485156i) q^{66} +(1.57261 + 0.572384i) q^{67} -3.82524 q^{68} +(-6.81608 - 2.48085i) q^{69} +(0.517683 + 2.93592i) q^{70} +(-7.70462 + 6.46494i) q^{71} +(-1.06246 - 0.891507i) q^{72} -9.88570 q^{73} +(-1.97180 + 5.75430i) q^{74} -3.36910 q^{75} +(4.55479 + 3.82192i) q^{76} +(0.657490 - 0.551699i) q^{77} +(-0.466865 - 2.64772i) q^{78} +(-12.5395 - 4.56401i) q^{79} +1.53209 q^{80} +(2.73975 + 0.997189i) q^{81} +(-5.20061 + 9.00771i) q^{82} +(0.617999 - 3.50484i) q^{83} +(-1.23568 - 2.14025i) q^{84} +(2.93030 - 5.07543i) q^{85} +(2.94683 + 2.47268i) q^{86} +(0.603020 + 3.41989i) q^{87} +(-0.220544 - 0.381994i) q^{88} +(11.1543 - 4.05982i) q^{89} +(1.99677 - 0.726763i) q^{90} +(-0.715278 + 4.05654i) q^{91} +(4.37500 - 3.67106i) q^{92} +(9.60779 - 8.06190i) q^{93} +(1.33472 - 7.56955i) q^{94} +(-8.56020 + 3.11566i) q^{95} +(-1.19347 + 0.434387i) q^{96} +(0.296748 + 0.513983i) q^{97} +(-0.558047 - 3.16484i) q^{98} +(-0.468637 - 0.393233i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q3q36q5+6q76q83q9+3q113q126q13+3q14+6q153q17+6q183q196q2033q213q2221q233q246q25+33q99+O(q100) 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25}+ \cdots - 33 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/74Z)×\left(\mathbb{Z}/74\mathbb{Z}\right)^\times.

nn 3939
χ(n)\chi(n) e(29)e\left(\frac{2}{9}\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 0.766044 + 0.642788i 0.541675 + 0.454519i
33 0.972925 0.816381i 0.561719 0.471338i −0.317168 0.948370i 0.602732π-0.602732\pi
0.878886 + 0.477032i 0.158287π0.158287\pi
44 0.173648 + 0.984808i 0.0868241 + 0.492404i
55 −1.43969 0.524005i −0.643850 0.234342i −0.000601695 1.00000i 0.500192π-0.500192\pi
−0.643248 + 0.765658i 0.722414π0.722414\pi
66 1.27006 0.518501
77 −1.82850 0.665520i −0.691108 0.251543i −0.0274987 0.999622i 0.508754π-0.508754\pi
−0.663610 + 0.748079i 0.730976π0.730976\pi
88 −0.500000 + 0.866025i −0.176777 + 0.306186i
99 −0.240839 + 1.36587i −0.0802798 + 0.455289i
1010 −0.766044 1.32683i −0.242245 0.419580i
1111 −0.220544 + 0.381994i −0.0664966 + 0.115175i −0.897357 0.441306i 0.854515π-0.854515\pi
0.830860 + 0.556481i 0.187849π0.187849\pi
1212 0.972925 + 0.816381i 0.280859 + 0.235669i
1313 −0.367592 2.08472i −0.101952 0.578196i −0.992394 0.123100i 0.960716π-0.960716\pi
0.890443 0.455095i 0.150395π-0.150395\pi
1414 −0.972925 1.68516i −0.260025 0.450377i
1515 −1.82850 + 0.665520i −0.472117 + 0.171837i
1616 −0.939693 + 0.342020i −0.234923 + 0.0855050i
1717 −0.664245 + 3.76712i −0.161103 + 0.913661i 0.791889 + 0.610665i 0.209098π0.209098\pi
−0.952992 + 0.302996i 0.902013π0.902013\pi
1818 −1.06246 + 0.891507i −0.250423 + 0.210130i
1919 4.55479 3.82192i 1.04494 0.876808i 0.0523871 0.998627i 0.483317π-0.483317\pi
0.992552 + 0.121819i 0.0388726π0.0388726\pi
2020 0.266044 1.50881i 0.0594893 0.337381i
2121 −2.32231 + 0.845253i −0.506770 + 0.184449i
2222 −0.414488 + 0.150861i −0.0883690 + 0.0321637i
2323 −2.85558 4.94600i −0.595429 1.03131i −0.993486 0.113952i 0.963649π-0.963649\pi
0.398057 0.917360i 0.369684π-0.369684\pi
2424 0.220544 + 1.25077i 0.0450184 + 0.255312i
2525 −2.03209 1.70513i −0.406418 0.341025i
2626 1.05844 1.83327i 0.207577 0.359533i
2727 2.78585 + 4.82523i 0.536136 + 0.928615i
2828 0.337893 1.91629i 0.0638558 0.362144i
2929 −1.36712 + 2.36792i −0.253867 + 0.439711i −0.964587 0.263764i 0.915036π-0.915036\pi
0.710720 + 0.703475i 0.248369π0.248369\pi
3030 −1.82850 0.665520i −0.333837 0.121507i
3131 9.87516 1.77363 0.886816 0.462123i 0.152912π-0.152912\pi
0.886816 + 0.462123i 0.152912π0.152912\pi
3232 −0.939693 0.342020i −0.166116 0.0604612i
3333 0.0972795 + 0.551699i 0.0169342 + 0.0960386i
3434 −2.93030 + 2.45881i −0.502542 + 0.421683i
3535 2.28374 + 1.91629i 0.386023 + 0.323912i
3636 −1.38694 −0.231156
3737 2.18831 + 5.67550i 0.359755 + 0.933047i
3838 5.94585 0.964544
3939 −2.05956 1.72818i −0.329794 0.276730i
4040 1.17365 0.984808i 0.185570 0.155712i
4141 1.80615 + 10.2432i 0.282073 + 1.59972i 0.715556 + 0.698556i 0.246174π0.246174\pi
−0.433482 + 0.901162i 0.642715π0.642715\pi
4242 −2.32231 0.845253i −0.358341 0.130425i
4343 3.84681 0.586633 0.293317 0.956015i 0.405241π-0.405241\pi
0.293317 + 0.956015i 0.405241π0.405241\pi
4444 −0.414488 0.150861i −0.0624863 0.0227432i
4545 1.06246 1.84023i 0.158382 0.274325i
4646 0.991731 5.62439i 0.146223 0.829271i
4747 −3.84316 6.65655i −0.560582 0.970957i −0.997446 0.0714293i 0.977244π-0.977244\pi
0.436863 0.899528i 0.356089π-0.356089\pi
4848 −0.635032 + 1.09991i −0.0916589 + 0.158758i
4949 −2.46181 2.06571i −0.351687 0.295101i
5050 −0.460637 2.61240i −0.0651439 0.369450i
5151 2.42915 + 4.20740i 0.340148 + 0.589154i
5252 1.98921 0.724014i 0.275854 0.100403i
5353 −1.62561 + 0.591673i −0.223295 + 0.0812726i −0.451245 0.892400i 0.649020π-0.649020\pi
0.227950 + 0.973673i 0.426798π0.426798\pi
5454 −0.967514 + 5.48704i −0.131662 + 0.746692i
5555 0.517683 0.434387i 0.0698043 0.0585728i
5656 1.49061 1.25077i 0.199191 0.167141i
5757 1.31132 7.43688i 0.173689 0.985039i
5858 −2.56934 + 0.935163i −0.337371 + 0.122793i
5959 −1.93027 + 0.702561i −0.251300 + 0.0914656i −0.464599 0.885521i 0.653801π-0.653801\pi
0.213299 + 0.976987i 0.431579π0.431579\pi
6060 −0.972925 1.68516i −0.125604 0.217553i
6161 −1.89894 10.7694i −0.243134 1.37888i −0.824786 0.565444i 0.808705π-0.808705\pi
0.581652 0.813437i 0.302406π-0.302406\pi
6262 7.56481 + 6.34763i 0.960732 + 0.806150i
6363 1.34939 2.33721i 0.170007 0.294460i
6464 −0.500000 0.866025i −0.0625000 0.108253i
6565 −0.563183 + 3.19397i −0.0698542 + 0.396163i
6666 −0.280105 + 0.485156i −0.0344786 + 0.0597186i
6767 1.57261 + 0.572384i 0.192125 + 0.0699279i 0.436291 0.899806i 0.356292π-0.356292\pi
−0.244166 + 0.969734i 0.578514π0.578514\pi
6868 −3.82524 −0.463878
6969 −6.81608 2.48085i −0.820560 0.298659i
7070 0.517683 + 2.93592i 0.0618749 + 0.350910i
7171 −7.70462 + 6.46494i −0.914370 + 0.767248i −0.972945 0.231035i 0.925789π-0.925789\pi
0.0585751 + 0.998283i 0.481344π0.481344\pi
7272 −1.06246 0.891507i −0.125212 0.105065i
7373 −9.88570 −1.15703 −0.578517 0.815671i 0.696368π-0.696368\pi
−0.578517 + 0.815671i 0.696368π0.696368\pi
7474 −1.97180 + 5.75430i −0.229217 + 0.668924i
7575 −3.36910 −0.389030
7676 4.55479 + 3.82192i 0.522470 + 0.438404i
7777 0.657490 0.551699i 0.0749279 0.0628720i
7878 −0.466865 2.64772i −0.0528620 0.299795i
7979 −12.5395 4.56401i −1.41081 0.513491i −0.479439 0.877575i 0.659160π-0.659160\pi
−0.931366 + 0.364084i 0.881382π0.881382\pi
8080 1.53209 0.171293
8181 2.73975 + 0.997189i 0.304417 + 0.110799i
8282 −5.20061 + 9.00771i −0.574311 + 0.994735i
8383 0.617999 3.50484i 0.0678341 0.384707i −0.931923 0.362657i 0.881870π-0.881870\pi
0.999757 0.0220497i 0.00701920π-0.00701920\pi
8484 −1.23568 2.14025i −0.134823 0.233521i
8585 2.93030 5.07543i 0.317836 0.550508i
8686 2.94683 + 2.47268i 0.317765 + 0.266636i
8787 0.603020 + 3.41989i 0.0646505 + 0.366651i
8888 −0.220544 0.381994i −0.0235101 0.0407207i
8989 11.1543 4.05982i 1.18235 0.430340i 0.325319 0.945604i 0.394528π-0.394528\pi
0.857031 + 0.515264i 0.172306π0.172306\pi
9090 1.99677 0.726763i 0.210478 0.0766076i
9191 −0.715278 + 4.05654i −0.0749815 + 0.425241i
9292 4.37500 3.67106i 0.456125 0.382734i
9393 9.60779 8.06190i 0.996282 0.835980i
9494 1.33472 7.56955i 0.137665 0.780739i
9595 −8.56020 + 3.11566i −0.878258 + 0.319660i
9696 −1.19347 + 0.434387i −0.121808 + 0.0443345i
9797 0.296748 + 0.513983i 0.0301302 + 0.0521871i 0.880697 0.473679i 0.157074π-0.157074\pi
−0.850567 + 0.525867i 0.823741π0.823741\pi
9898 −0.558047 3.16484i −0.0563713 0.319698i
9999 −0.468637 0.393233i −0.0470998 0.0395214i
100100 1.32635 2.29731i 0.132635 0.229731i
101101 6.61396 + 11.4557i 0.658113 + 1.13989i 0.981104 + 0.193483i 0.0619785π0.0619785\pi
−0.322990 + 0.946402i 0.604688π0.604688\pi
102102 −0.843634 + 4.78448i −0.0835322 + 0.473734i
103103 1.57500 2.72797i 0.155189 0.268795i −0.777939 0.628340i 0.783735π-0.783735\pi
0.933128 + 0.359545i 0.117068π0.117068\pi
104104 1.98921 + 0.724014i 0.195058 + 0.0709954i
105105 3.78633 0.369508
106106 −1.62561 0.591673i −0.157893 0.0574684i
107107 −0.643654 3.65035i −0.0622244 0.352892i −0.999984 0.00560785i 0.998215π-0.998215\pi
0.937760 0.347284i 0.112896π-0.112896\pi
108108 −4.26816 + 3.58141i −0.410704 + 0.344622i
109109 11.4667 + 9.62169i 1.09831 + 0.921591i 0.997310 0.0732954i 0.0233516π-0.0233516\pi
0.100999 + 0.994887i 0.467796π0.467796\pi
110110 0.675787 0.0644337
111111 6.76243 + 3.73535i 0.641861 + 0.354543i
112112 1.94585 0.183866
113113 −15.2648 12.8087i −1.43599 1.20494i −0.942062 0.335438i 0.891116π-0.891116\pi
−0.493929 0.869502i 0.664440π-0.664440\pi
114114 5.78487 4.85408i 0.541802 0.454626i
115115 1.51942 + 8.61706i 0.141687 + 0.803545i
116116 −2.56934 0.935163i −0.238557 0.0868277i
117117 2.93598 0.271431
118118 −1.93027 0.702561i −0.177696 0.0646759i
119119 3.72167 6.44612i 0.341165 0.590915i
120120 0.337893 1.91629i 0.0308453 0.174932i
121121 5.40272 + 9.35779i 0.491156 + 0.850708i
122122 5.46777 9.47046i 0.495029 0.857415i
123123 10.1196 + 8.49135i 0.912454 + 0.765639i
124124 1.71480 + 9.72514i 0.153994 + 0.873343i
125125 5.86231 + 10.1538i 0.524341 + 0.908185i
126126 2.53602 0.923035i 0.225927 0.0822305i
127127 −4.60748 + 1.67699i −0.408848 + 0.148808i −0.538253 0.842783i 0.680916π-0.680916\pi
0.129405 + 0.991592i 0.458693π0.458693\pi
128128 0.173648 0.984808i 0.0153485 0.0870455i
129129 3.74266 3.14046i 0.329523 0.276502i
130130 −2.48447 + 2.08472i −0.217902 + 0.182842i
131131 0.0536454 0.304238i 0.00468702 0.0265814i −0.982375 0.186923i 0.940148π-0.940148\pi
0.987062 + 0.160342i 0.0512596π0.0512596\pi
132132 −0.526426 + 0.191603i −0.0458195 + 0.0166769i
133133 −10.8720 + 3.95708i −0.942721 + 0.343123i
134134 0.836770 + 1.44933i 0.0722859 + 0.125203i
135135 −1.48232 8.40664i −0.127578 0.723528i
136136 −2.93030 2.45881i −0.251271 0.210842i
137137 10.1508 17.5818i 0.867245 1.50211i 0.00244359 0.999997i 0.499222π-0.499222\pi
0.864801 0.502115i 0.167444π-0.167444\pi
138138 −3.62676 6.28174i −0.308731 0.534737i
139139 −2.28137 + 12.9383i −0.193503 + 1.09741i 0.721031 + 0.692903i 0.243668π0.243668\pi
−0.914534 + 0.404508i 0.867443π0.867443\pi
140140 −1.49061 + 2.58181i −0.125979 + 0.218203i
141141 −9.17339 3.33884i −0.772538 0.281181i
142142 −10.0577 −0.844021
143143 0.877418 + 0.319354i 0.0733734 + 0.0267057i
144144 −0.240839 1.36587i −0.0200699 0.113822i
145145 3.20903 2.69270i 0.266495 0.223616i
146146 −7.57288 6.35440i −0.626736 0.525894i
147147 −4.08156 −0.336641
148148 −5.20928 + 3.14060i −0.428200 + 0.258156i
149149 −3.98826 −0.326731 −0.163366 0.986566i 0.552235π-0.552235\pi
−0.163366 + 0.986566i 0.552235π0.552235\pi
150150 −2.58088 2.16562i −0.210728 0.176822i
151151 −15.0525 + 12.6306i −1.22496 + 1.02786i −0.226408 + 0.974032i 0.572698π0.572698\pi
−0.998550 + 0.0538298i 0.982857π0.982857\pi
152152 1.03249 + 5.85552i 0.0837457 + 0.474945i
153153 −4.98541 1.81454i −0.403047 0.146697i
154154 0.858292 0.0691631
155155 −14.2172 5.17464i −1.14195 0.415637i
156156 1.34428 2.32837i 0.107629 0.186419i
157157 1.58561 8.99242i 0.126545 0.717674i −0.853833 0.520547i 0.825728π-0.825728\pi
0.980378 0.197126i 0.0631609π-0.0631609\pi
158158 −6.67213 11.5565i −0.530807 0.919384i
159159 −1.09856 + 1.90277i −0.0871218 + 0.150899i
160160 1.17365 + 0.984808i 0.0927850 + 0.0778559i
161161 1.92976 + 10.9442i 0.152086 + 0.862525i
162162 1.45779 + 2.52497i 0.114535 + 0.198380i
163163 1.76208 0.641343i 0.138016 0.0502339i −0.272088 0.962272i 0.587714π-0.587714\pi
0.410105 + 0.912038i 0.365492π0.365492\pi
164164 −9.77394 + 3.55742i −0.763217 + 0.277788i
165165 0.149041 0.845253i 0.0116028 0.0658028i
166166 2.72628 2.28762i 0.211601 0.177554i
167167 3.52918 2.96133i 0.273096 0.229155i −0.495945 0.868354i 0.665178π-0.665178\pi
0.769041 + 0.639199i 0.220734π0.220734\pi
168168 0.429146 2.43381i 0.0331093 0.187772i
169169 8.00509 2.91361i 0.615776 0.224124i
170170 5.50716 2.00444i 0.422380 0.153734i
171171 4.12326 + 7.14170i 0.315314 + 0.546140i
172172 0.667992 + 3.78837i 0.0509339 + 0.288860i
173173 −11.5656 9.70473i −0.879320 0.737837i 0.0867194 0.996233i 0.472362π-0.472362\pi
−0.966039 + 0.258396i 0.916806π0.916806\pi
174174 −1.73633 + 3.00740i −0.131631 + 0.227991i
175175 2.58088 + 4.47022i 0.195096 + 0.337917i
176176 0.0765942 0.434387i 0.00577351 0.0327432i
177177 −1.30445 + 2.25937i −0.0980485 + 0.169825i
178178 11.1543 + 4.05982i 0.836048 + 0.304296i
179179 20.1143 1.50342 0.751708 0.659496i 0.229230π-0.229230\pi
0.751708 + 0.659496i 0.229230π0.229230\pi
180180 1.99677 + 0.726763i 0.148830 + 0.0541697i
181181 1.61762 + 9.17397i 0.120237 + 0.681896i 0.984024 + 0.178038i 0.0569751π0.0569751\pi
−0.863787 + 0.503857i 0.831914π0.831914\pi
182182 −3.15543 + 2.64772i −0.233896 + 0.196262i
183183 −10.6395 8.92757i −0.786492 0.659945i
184184 5.71115 0.421032
185185 −0.176496 9.31766i −0.0129763 0.685048i
186186 12.5421 0.919630
187187 −1.29252 1.08455i −0.0945185 0.0793105i
188188 5.88806 4.94067i 0.429431 0.360335i
189189 −1.88264 10.6770i −0.136942 0.776635i
190190 −8.56020 3.11566i −0.621022 0.226034i
191191 −10.6491 −0.770541 −0.385271 0.922804i 0.625892π-0.625892\pi
−0.385271 + 0.922804i 0.625892π0.625892\pi
192192 −1.19347 0.434387i −0.0861312 0.0313492i
193193 −6.12636 + 10.6112i −0.440985 + 0.763809i −0.997763 0.0668528i 0.978704π-0.978704\pi
0.556778 + 0.830662i 0.312038π0.312038\pi
194194 −0.103060 + 0.584480i −0.00739925 + 0.0419632i
195195 2.05956 + 3.56726i 0.147488 + 0.255457i
196196 1.60683 2.78312i 0.114774 0.198794i
197197 12.3511 + 10.3638i 0.879978 + 0.738389i 0.966175 0.257889i 0.0830269π-0.0830269\pi
−0.0861968 + 0.996278i 0.527471π0.527471\pi
198198 −0.106231 0.602469i −0.00754954 0.0428156i
199199 0.995370 + 1.72403i 0.0705599 + 0.122213i 0.899147 0.437647i 0.144188π-0.144188\pi
−0.828587 + 0.559860i 0.810855π0.810855\pi
200200 2.49273 0.907278i 0.176262 0.0641542i
201201 1.99732 0.726964i 0.140880 0.0512761i
202202 −2.29700 + 13.0270i −0.161617 + 0.916573i
203203 4.07567 3.41989i 0.286056 0.240030i
204204 −3.72167 + 3.12285i −0.260569 + 0.218643i
205205 2.76718 15.6935i 0.193269 1.09608i
206206 2.96003 1.07736i 0.206235 0.0750633i
207207 7.44332 2.70915i 0.517347 0.188299i
208208 1.05844 + 1.83327i 0.0733894 + 0.127114i
209209 0.455418 + 2.58280i 0.0315019 + 0.178656i
210210 2.90050 + 2.43381i 0.200153 + 0.167949i
211211 6.30255 10.9163i 0.433885 0.751512i −0.563319 0.826240i 0.690476π-0.690476\pi
0.997204 + 0.0747282i 0.0238089π0.0238089\pi
212212 −0.864968 1.49817i −0.0594063 0.102895i
213213 −2.21816 + 12.5798i −0.151986 + 0.861955i
214214 1.85333 3.21006i 0.126691 0.219435i
215215 −5.53823 2.01575i −0.377704 0.137473i
216216 −5.57169 −0.379106
217217 −18.0567 6.57212i −1.22577 0.446144i
218218 2.59929 + 14.7413i 0.176046 + 0.998406i
219219 −9.61804 + 8.07049i −0.649927 + 0.545353i
220220 0.517683 + 0.434387i 0.0349022 + 0.0292864i
221221 8.09755 0.544700
222222 2.77929 + 7.20825i 0.186534 + 0.483786i
223223 20.3949 1.36575 0.682873 0.730538i 0.260730π-0.260730\pi
0.682873 + 0.730538i 0.260730π0.260730\pi
224224 1.49061 + 1.25077i 0.0995954 + 0.0835705i
225225 2.81838 2.36490i 0.187892 0.157660i
226226 −3.46025 19.6240i −0.230172 1.30537i
227227 7.11595 + 2.58999i 0.472302 + 0.171904i 0.567195 0.823584i 0.308029π-0.308029\pi
−0.0948927 + 0.995488i 0.530251π0.530251\pi
228228 7.55161 0.500117
229229 0.294030 + 0.107018i 0.0194301 + 0.00707197i 0.351717 0.936106i 0.385598π-0.385598\pi
−0.332287 + 0.943178i 0.607820π0.607820\pi
230230 −4.37500 + 7.57772i −0.288479 + 0.499660i
231231 0.189291 1.07352i 0.0124545 0.0706327i
232232 −1.36712 2.36792i −0.0897557 0.155461i
233233 0.341583 0.591640i 0.0223779 0.0387596i −0.854620 0.519255i 0.826210π-0.826210\pi
0.876997 + 0.480495i 0.159543π0.159543\pi
234234 2.24909 + 1.88721i 0.147027 + 0.123371i
235235 2.04490 + 11.5972i 0.133395 + 0.756519i
236236 −1.02707 1.77895i −0.0668569 0.115800i
237237 −15.9260 + 5.79658i −1.03450 + 0.376528i
238238 6.99445 2.54577i 0.453383 0.165018i
239239 1.94597 11.0361i 0.125874 0.713869i −0.854910 0.518776i 0.826388π-0.826388\pi
0.980785 0.195093i 0.0625009π-0.0625009\pi
240240 1.49061 1.25077i 0.0962183 0.0807368i
241241 −3.96856 + 3.33002i −0.255638 + 0.214505i −0.761595 0.648053i 0.775584π-0.775584\pi
0.505958 + 0.862558i 0.331139π0.331139\pi
242242 −1.87635 + 10.6413i −0.120616 + 0.684048i
243243 −12.2274 + 4.45040i −0.784386 + 0.285493i
244244 10.2761 3.74018i 0.657857 0.239440i
245245 2.46181 + 4.26398i 0.157279 + 0.272416i
246246 2.29393 + 13.0095i 0.146255 + 0.829456i
247247 −9.64191 8.09052i −0.613500 0.514788i
248248 −4.93758 + 8.55214i −0.313537 + 0.543062i
249249 −2.26002 3.91447i −0.143223 0.248070i
250250 −2.03596 + 11.5465i −0.128765 + 0.730265i
251251 15.2460 26.4069i 0.962321 1.66679i 0.245675 0.969352i 0.420991π-0.420991\pi
0.716646 0.697437i 0.245676π-0.245676\pi
252252 2.53602 + 0.923035i 0.159754 + 0.0581458i
253253 2.51912 0.158376
254254 −4.60748 1.67699i −0.289099 0.105223i
255255 −1.29252 7.33025i −0.0809408 0.459038i
256256 0.766044 0.642788i 0.0478778 0.0401742i
257257 4.49488 + 3.77165i 0.280383 + 0.235269i 0.772123 0.635473i 0.219195π-0.219195\pi
−0.491741 + 0.870742i 0.663639π0.663639\pi
258258 4.88570 0.304170
259259 −0.224162 11.8340i −0.0139287 0.735330i
260260 −3.24324 −0.201137
261261 −2.90501 2.43759i −0.179815 0.150883i
262262 0.236655 0.198577i 0.0146206 0.0122681i
263263 2.83262 + 16.0646i 0.174667 + 0.990586i 0.938528 + 0.345204i 0.112190π0.112190\pi
−0.763861 + 0.645381i 0.776698π0.776698\pi
264264 −0.526426 0.191603i −0.0323993 0.0117924i
265265 2.65042 0.162814
266266 −10.8720 3.95708i −0.666605 0.242624i
267267 7.53791 13.0560i 0.461312 0.799016i
268268 −0.290607 + 1.64812i −0.0177517 + 0.100675i
269269 5.00302 + 8.66548i 0.305039 + 0.528344i 0.977270 0.211998i 0.0679970π-0.0679970\pi
−0.672231 + 0.740342i 0.734664π0.734664\pi
270270 4.26816 7.39267i 0.259752 0.449904i
271271 −9.47356 7.94926i −0.575478 0.482883i 0.307981 0.951393i 0.400347π-0.400347\pi
−0.883459 + 0.468509i 0.844791π0.844791\pi
272272 −0.664245 3.76712i −0.0402758 0.228415i
273273 2.61577 + 4.53065i 0.158314 + 0.274208i
274274 19.0773 6.94358i 1.15250 0.419477i
275275 1.09951 0.400190i 0.0663031 0.0241324i
276276 1.25956 7.14333i 0.0758167 0.429978i
277277 −16.2756 + 13.6568i −0.977905 + 0.820559i −0.983772 0.179423i 0.942577π-0.942577\pi
0.00586739 + 0.999983i 0.498132π0.498132\pi
278278 −10.0642 + 8.44487i −0.603611 + 0.506489i
279279 −2.37833 + 13.4882i −0.142387 + 0.807515i
280280 −2.80143 + 1.01964i −0.167417 + 0.0609349i
281281 −15.2217 + 5.54025i −0.908052 + 0.330504i −0.753475 0.657477i 0.771624π-0.771624\pi
−0.154577 + 0.987981i 0.549401π0.549401\pi
282282 −4.88106 8.45424i −0.290663 0.503443i
283283 −0.866198 4.91245i −0.0514901 0.292015i 0.948179 0.317737i 0.102923π-0.102923\pi
−0.999669 + 0.0257216i 0.991812π0.991812\pi
284284 −7.70462 6.46494i −0.457185 0.383624i
285285 −5.78487 + 10.0197i −0.342666 + 0.593515i
286286 0.466865 + 0.808633i 0.0276063 + 0.0478155i
287287 3.51450 19.9317i 0.207454 1.17653i
288288 0.693469 1.20112i 0.0408631 0.0707769i
289289 2.22479 + 0.809758i 0.130870 + 0.0476328i
290290 4.18909 0.245992
291291 0.708320 + 0.257807i 0.0415224 + 0.0151129i
292292 −1.71663 9.73551i −0.100458 0.569728i
293293 4.25093 3.56696i 0.248342 0.208384i −0.510116 0.860106i 0.670397π-0.670397\pi
0.758458 + 0.651722i 0.225953π0.225953\pi
294294 −3.12666 2.62358i −0.182350 0.153010i
295295 3.14714 0.183234
296296 −6.00928 0.942621i −0.349282 0.0547888i
297297 −2.45761 −0.142605
298298 −3.05519 2.56361i −0.176982 0.148506i
299299 −9.26132 + 7.77117i −0.535596 + 0.449418i
300300 −0.585038 3.31792i −0.0337772 0.191560i
301301 −7.03390 2.56013i −0.405427 0.147563i
302302 −19.6497 −1.13071
303303 15.7871 + 5.74604i 0.906946 + 0.330101i
304304 −2.97293 + 5.14926i −0.170509 + 0.295330i
305305 −2.90934 + 16.4997i −0.166588 + 0.944770i
306306 −2.65268 4.59458i −0.151644 0.262655i
307307 −7.58074 + 13.1302i −0.432656 + 0.749382i −0.997101 0.0760888i 0.975757π-0.975757\pi
0.564445 + 0.825470i 0.309090π0.309090\pi
308308 0.657490 + 0.551699i 0.0374640 + 0.0314360i
309309 −0.694713 3.93991i −0.0395208 0.224134i
310310 −7.56481 13.1026i −0.429653 0.744180i
311311 −14.2914 + 5.20165i −0.810392 + 0.294959i −0.713786 0.700364i 0.753021π-0.753021\pi
−0.0966062 + 0.995323i 0.530799π0.530799\pi
312312 2.52643 0.919544i 0.143031 0.0520589i
313313 5.06559 28.7284i 0.286324 1.62382i −0.414193 0.910189i 0.635936π-0.635936\pi
0.700517 0.713636i 0.252953π-0.252953\pi
314314 6.99486 5.86939i 0.394743 0.331229i
315315 −3.16741 + 2.65777i −0.178463 + 0.149749i
316316 2.31721 13.1415i 0.130353 0.739269i
317317 18.0323 6.56322i 1.01279 0.368627i 0.218289 0.975884i 0.429952π-0.429952\pi
0.794505 + 0.607257i 0.207730π0.207730\pi
318318 −2.06463 + 0.751462i −0.115778 + 0.0421399i
319319 −0.603020 1.04446i −0.0337626 0.0584786i
320320 0.266044 + 1.50881i 0.0148723 + 0.0843452i
321321 −3.60630 3.02605i −0.201284 0.168897i
322322 −5.55652 + 9.62418i −0.309653 + 0.536335i
323323 11.3721 + 19.6971i 0.632763 + 1.09598i
324324 −0.506286 + 2.87129i −0.0281270 + 0.159516i
325325 −2.80772 + 4.86312i −0.155744 + 0.269757i
326326 1.76208 + 0.641343i 0.0975924 + 0.0355207i
327327 19.0112 1.05132
328328 −9.77394 3.55742i −0.539676 0.196426i
329329 2.59716 + 14.7292i 0.143186 + 0.812047i
330330 0.657490 0.551699i 0.0361936 0.0303701i
331331 −6.00049 5.03501i −0.329817 0.276749i 0.462808 0.886458i 0.346842π-0.346842\pi
−0.792625 + 0.609709i 0.791286π0.791286\pi
332332 3.55891 0.195321
333333 −8.27902 + 1.62205i −0.453687 + 0.0888880i
334334 4.60701 0.252085
335335 −1.96415 1.64812i −0.107313 0.0900461i
336336 1.89317 1.58856i 0.103281 0.0866628i
337337 3.41476 + 19.3661i 0.186014 + 1.05494i 0.924646 + 0.380828i 0.124361π0.124361\pi
−0.738632 + 0.674109i 0.764528π0.764528\pi
338338 8.00509 + 2.91361i 0.435420 + 0.158480i
339339 −25.3083 −1.37456
340340 5.50716 + 2.00444i 0.298668 + 0.108706i
341341 −2.17791 + 3.77225i −0.117940 + 0.204279i
342342 −1.43199 + 8.12125i −0.0774334 + 0.439147i
343343 9.93713 + 17.2116i 0.536555 + 0.929340i
344344 −1.92341 + 3.33144i −0.103703 + 0.179619i
345345 8.51309 + 7.14333i 0.458329 + 0.384584i
346346 −2.62172 14.8685i −0.140944 0.799336i
347347 −10.7822 18.6753i −0.578817 1.00254i −0.995615 0.0935416i 0.970181π-0.970181\pi
0.416798 0.908999i 0.363152π-0.363152\pi
348348 −3.26323 + 1.18772i −0.174927 + 0.0636683i
349349 25.2549 9.19201i 1.35186 0.492037i 0.438333 0.898813i 0.355569π-0.355569\pi
0.913528 + 0.406775i 0.133347π0.133347\pi
350350 −0.896331 + 5.08335i −0.0479109 + 0.271716i
351351 9.03517 7.58141i 0.482262 0.404666i
352352 0.337893 0.283526i 0.0180098 0.0151120i
353353 −2.28842 + 12.9783i −0.121800 + 0.690763i 0.861357 + 0.508000i 0.169615π0.169615\pi
−0.983157 + 0.182763i 0.941496π0.941496\pi
354354 −2.45156 + 0.892297i −0.130299 + 0.0474250i
355355 14.4800 5.27027i 0.768516 0.279717i
356356 5.93506 + 10.2798i 0.314558 + 0.544830i
357357 −1.64158 9.30989i −0.0868819 0.492732i
358358 15.4085 + 12.9293i 0.814364 + 0.683332i
359359 −1.69284 + 2.93209i −0.0893448 + 0.154750i −0.907234 0.420626i 0.861811π-0.861811\pi
0.817890 + 0.575375i 0.195144π0.195144\pi
360360 1.06246 + 1.84023i 0.0559964 + 0.0969886i
361361 2.83969 16.1047i 0.149457 0.847615i
362362 −4.65774 + 8.06745i −0.244806 + 0.424016i
363363 12.8960 + 4.69375i 0.676862 + 0.246358i
364364 −4.11912 −0.215901
365365 14.2324 + 5.18016i 0.744956 + 0.271142i
366366 −2.41177 13.6778i −0.126065 0.714952i
367367 5.05350 4.24039i 0.263790 0.221347i −0.501293 0.865278i 0.667142π-0.667142\pi
0.765083 + 0.643931i 0.222698π0.222698\pi
368368 4.37500 + 3.67106i 0.228062 + 0.191367i
369369 −14.4258 −0.750979
370370 5.85407 7.25119i 0.304339 0.376972i
371371 3.36620 0.174764
372372 9.60779 + 8.06190i 0.498141 + 0.417990i
373373 0.809650 0.679377i 0.0419221 0.0351768i −0.621586 0.783346i 0.713511π-0.713511\pi
0.663508 + 0.748169i 0.269067π0.269067\pi
374374 −0.292991 1.66163i −0.0151502 0.0859210i
375375 13.9930 + 5.09303i 0.722594 + 0.263003i
376376 7.68632 0.396392
377377 5.43897 + 1.97962i 0.280121 + 0.101956i
378378 5.42084 9.38917i 0.278818 0.482927i
379379 3.85749 21.8769i 0.198146 1.12374i −0.709721 0.704482i 0.751179π-0.751179\pi
0.907867 0.419258i 0.137710π-0.137710\pi
380380 −4.55479 7.88912i −0.233656 0.404703i
381381 −3.11368 + 5.39304i −0.159518 + 0.276294i
382382 −8.15768 6.84510i −0.417383 0.350226i
383383 1.62312 + 9.20517i 0.0829375 + 0.470362i 0.997783 + 0.0665572i 0.0212015π0.0212015\pi
−0.914845 + 0.403805i 0.867687π0.867687\pi
384384 −0.635032 1.09991i −0.0324063 0.0561294i
385385 −1.23568 + 0.449750i −0.0629759 + 0.0229214i
386386 −11.5138 + 4.19068i −0.586037 + 0.213300i
387387 −0.926464 + 5.25424i −0.0470948 + 0.267088i
388388 −0.454645 + 0.381492i −0.0230811 + 0.0193673i
389389 1.85358 1.55534i 0.0939804 0.0788589i −0.594587 0.804031i 0.702684π-0.702684\pi
0.688567 + 0.725172i 0.258240π0.258240\pi
390390 −0.715278 + 4.05654i −0.0362195 + 0.205411i
391391 20.5290 7.47194i 1.03820 0.377872i
392392 3.01986 1.09914i 0.152526 0.0555149i
393393 −0.196181 0.339796i −0.00989603 0.0171404i
394394 2.79976 + 15.8782i 0.141050 + 0.799934i
395395 15.6615 + 13.1415i 0.788014 + 0.661223i
396396 0.305881 0.529802i 0.0153711 0.0266235i
397397 −9.85205 17.0643i −0.494460 0.856430i 0.505519 0.862815i 0.331301π-0.331301\pi
−0.999980 + 0.00638497i 0.997968π0.997968\pi
398398 −0.345688 + 1.96050i −0.0173278 + 0.0982707i
399399 −7.34715 + 12.7256i −0.367817 + 0.637079i
400400 2.49273 + 0.907278i 0.124636 + 0.0453639i
401401 −29.2178 −1.45907 −0.729534 0.683944i 0.760263π-0.760263\pi
−0.729534 + 0.683944i 0.760263π0.760263\pi
402402 1.99732 + 0.726964i 0.0996172 + 0.0362577i
403403 −3.63003 20.5869i −0.180824 1.02551i
404404 −10.1332 + 8.50274i −0.504144 + 0.423027i
405405 −3.42187 2.87129i −0.170034 0.142676i
406406 5.32041 0.264048
407407 −2.65062 0.415779i −0.131387 0.0206094i
408408 −4.85829 −0.240521
409409 −2.89098 2.42582i −0.142950 0.119949i 0.568509 0.822677i 0.307521π-0.307521\pi
−0.711458 + 0.702728i 0.751965π0.751965\pi
410410 12.2074 10.2432i 0.602879 0.505875i
411411 −4.47742 25.3927i −0.220855 1.25253i
412412 2.96003 + 1.07736i 0.145830 + 0.0530778i
413413 3.99707 0.196683
414414 7.44332 + 2.70915i 0.365819 + 0.133147i
415415 −2.72628 + 4.72206i −0.133828 + 0.231797i
416416 −0.367592 + 2.08472i −0.0180227 + 0.102212i
417417 8.34297 + 14.4504i 0.408557 + 0.707642i
418418 −1.31132 + 2.27128i −0.0641389 + 0.111092i
419419 −27.7696 23.3015i −1.35663 1.13835i −0.977006 0.213213i 0.931607π-0.931607\pi
−0.379629 0.925139i 0.623948π-0.623948\pi
420420 0.657490 + 3.72881i 0.0320822 + 0.181947i
421421 −8.08913 14.0108i −0.394240 0.682844i 0.598764 0.800926i 0.295659π-0.295659\pi
−0.993004 + 0.118082i 0.962325π0.962325\pi
422422 11.8449 4.31120i 0.576602 0.209866i
423423 10.0175 3.64609i 0.487070 0.177279i
424424 0.300400 1.70365i 0.0145887 0.0827368i
425425 7.77322 6.52250i 0.377056 0.316388i
426426 −9.78536 + 8.21089i −0.474102 + 0.397819i
427427 −3.69505 + 20.9557i −0.178816 + 1.01412i
428428 3.48312 1.26775i 0.168363 0.0612791i
429429 1.11438 0.405600i 0.0538026 0.0195826i
430430 −2.94683 5.10406i −0.142109 0.246139i
431431 3.59966 + 20.4147i 0.173390 + 0.983342i 0.939986 + 0.341213i 0.110838π0.110838\pi
−0.766596 + 0.642129i 0.778051π0.778051\pi
432432 −4.26816 3.58141i −0.205352 0.172311i
433433 −13.3927 + 23.1968i −0.643611 + 1.11477i 0.341010 + 0.940060i 0.389231π0.389231\pi
−0.984621 + 0.174707i 0.944102π0.944102\pi
434434 −9.60779 16.6412i −0.461189 0.798803i
435435 0.923880 5.23958i 0.0442966 0.251219i
436436 −7.48435 + 12.9633i −0.358435 + 0.620828i
437437 −31.9098 11.6142i −1.52645 0.555583i
438438 −12.5555 −0.599923
439439 7.88952 + 2.87155i 0.376546 + 0.137052i 0.523358 0.852113i 0.324679π-0.324679\pi
−0.146812 + 0.989164i 0.546901π0.546901\pi
440440 0.117349 + 0.665520i 0.00559440 + 0.0317274i
441441 3.41438 2.86501i 0.162590 0.136429i
442442 6.20308 + 5.20500i 0.295050 + 0.247577i
443443 −19.6599 −0.934068 −0.467034 0.884239i 0.654677π-0.654677\pi
−0.467034 + 0.884239i 0.654677π0.654677\pi
444444 −2.50431 + 7.30833i −0.118849 + 0.346838i
445445 −18.1861 −0.862103
446446 15.6234 + 13.1096i 0.739790 + 0.620758i
447447 −3.88028 + 3.25594i −0.183531 + 0.154001i
448448 0.337893 + 1.91629i 0.0159640 + 0.0905361i
449449 25.5337 + 9.29349i 1.20501 + 0.438587i 0.864970 0.501824i 0.167338π-0.167338\pi
0.340039 + 0.940411i 0.389560π0.389560\pi
450450 3.67914 0.173436
451451 −4.31117 1.56914i −0.203005 0.0738878i
452452 9.96339 17.2571i 0.468639 0.811706i
453453 −4.33363 + 24.5772i −0.203612 + 1.15474i
454454 3.78632 + 6.55810i 0.177701 + 0.307787i
455455 3.15543 5.46537i 0.147929 0.256220i
456456 5.78487 + 4.85408i 0.270901 + 0.227313i
457457 −3.46724 19.6637i −0.162191 0.919829i −0.951914 0.306366i 0.900887π-0.900887\pi
0.789723 0.613463i 0.210224π-0.210224\pi
458458 0.156450 + 0.270980i 0.00731044 + 0.0126621i
459459 −20.0277 + 7.28949i −0.934813 + 0.340244i
460460 −8.22230 + 2.99267i −0.383367 + 0.139534i
461461 1.36552 7.74427i 0.0635987 0.360686i −0.936355 0.351055i 0.885823π-0.885823\pi
0.999954 0.00963149i 0.00306585π-0.00306585\pi
462462 0.835054 0.700693i 0.0388502 0.0325992i
463463 −4.62851 + 3.88378i −0.215105 + 0.180495i −0.743973 0.668209i 0.767061π-0.767061\pi
0.528868 + 0.848704i 0.322617π0.322617\pi
464464 0.474795 2.69270i 0.0220418 0.125005i
465465 −18.0567 + 6.57212i −0.837362 + 0.304775i
466466 0.641967 0.233657i 0.0297385 0.0108239i
467467 −14.6623 25.3958i −0.678489 1.17518i −0.975436 0.220283i 0.929302π-0.929302\pi
0.296947 0.954894i 0.404032π-0.404032\pi
468468 0.509827 + 2.89137i 0.0235668 + 0.133654i
469469 −2.49459 2.09321i −0.115190 0.0966555i
470470 −5.88806 + 10.1984i −0.271596 + 0.470418i
471471 −5.79857 10.0434i −0.267184 0.462776i
472472 0.356699 2.02294i 0.0164184 0.0931135i
473473 −0.848392 + 1.46946i −0.0390091 + 0.0675658i
474474 −15.9260 5.79658i −0.731504 0.266246i
475475 −15.7726 −0.723696
476476 6.99445 + 2.54577i 0.320590 + 0.116685i
477477 −0.416637 2.36286i −0.0190765 0.108188i
478478 8.58460 7.20333i 0.392650 0.329473i
479479 −3.16884 2.65897i −0.144788 0.121492i 0.567517 0.823362i 0.307904π-0.307904\pi
−0.712305 + 0.701870i 0.752349π0.752349\pi
480480 1.94585 0.0888155
481481 11.0274 6.64826i 0.502806 0.303135i
482482 −5.18059 −0.235969
483483 10.8122 + 9.07248i 0.491970 + 0.412812i
484484 −8.27745 + 6.94560i −0.376248 + 0.315709i
485485 −0.157896 0.895475i −0.00716971 0.0406614i
486486 −12.2274 4.45040i −0.554645 0.201874i
487487 28.9347 1.31116 0.655579 0.755126i 0.272425π-0.272425\pi
0.655579 + 0.755126i 0.272425π0.272425\pi
488488 10.2761 + 3.74018i 0.465175 + 0.169310i
489489 1.19079 2.06251i 0.0538493 0.0932697i
490490 −0.854978 + 4.84882i −0.0386240 + 0.219047i
491491 −9.77117 16.9242i −0.440967 0.763776i 0.556795 0.830650i 0.312031π-0.312031\pi
−0.997761 + 0.0668736i 0.978698π0.978698\pi
492492 −6.60510 + 11.4404i −0.297781 + 0.515772i
493493 −8.01213 6.72298i −0.360848 0.302788i
494494 −2.18564 12.3954i −0.0983368 0.557696i
495495 0.468637 + 0.811704i 0.0210637 + 0.0364834i
496496 −9.27962 + 3.37750i −0.416667 + 0.151654i
497497 18.3905 6.69358i 0.824925 0.300248i
498498 0.784897 4.45137i 0.0351721 0.199471i
499499 −32.3469 + 27.1423i −1.44805 + 1.21505i −0.514056 + 0.857757i 0.671858π0.671858\pi
−0.933990 + 0.357298i 0.883698π0.883698\pi
500500 −8.98158 + 7.53644i −0.401669 + 0.337040i
501501 1.01605 5.76231i 0.0453938 0.257441i
502502 28.6532 10.4289i 1.27885 0.465465i
503503 12.5255 4.55890i 0.558483 0.203271i −0.0473286 0.998879i 0.515071π-0.515071\pi
0.605811 + 0.795608i 0.292849π0.292849\pi
504504 1.34939 + 2.33721i 0.0601065 + 0.104108i
505505 −3.51921 19.9584i −0.156603 0.888139i
506506 1.92976 + 1.61926i 0.0857883 + 0.0719849i
507507 5.40973 9.36993i 0.240255 0.416133i
508508 −2.45159 4.24628i −0.108772 0.188398i
509509 4.74665 26.9196i 0.210392 1.19319i −0.678335 0.734753i 0.737298π-0.737298\pi
0.888727 0.458438i 0.151591π-0.151591\pi
510510 3.72167 6.44612i 0.164798 0.285439i
511511 18.0760 + 6.57913i 0.799635 + 0.291043i
512512 1.00000 0.0441942
513513 31.1305 + 11.3306i 1.37445 + 0.500258i
514514 1.01891 + 5.77851i 0.0449420 + 0.254879i
515515 −3.69698 + 3.10214i −0.162909 + 0.136697i
516516 3.74266 + 3.14046i 0.164761 + 0.138251i
517517 3.39035 0.149107
518518 7.43504 9.20948i 0.326677 0.404641i
519519 −19.1753 −0.841701
520520 −2.48447 2.08472i −0.108951 0.0914208i
521521 16.9953 14.2607i 0.744576 0.624773i −0.189487 0.981883i 0.560682π-0.560682\pi
0.934062 + 0.357110i 0.116238π0.116238\pi
522522 −0.658511 3.73460i −0.0288223 0.163459i
523523 36.0869 + 13.1346i 1.57797 + 0.574335i 0.974762 0.223247i 0.0716658π-0.0716658\pi
0.603210 + 0.797582i 0.293888π0.293888\pi
524524 0.308931 0.0134957
525525 6.16041 + 2.24220i 0.268862 + 0.0978578i
526526 −8.15621 + 14.1270i −0.355628 + 0.615965i
527527 −6.55953 + 37.2009i −0.285738 + 1.62050i
528528 −0.280105 0.485156i −0.0121900 0.0211137i
529529 −4.80863 + 8.32879i −0.209071 + 0.362121i
530530 2.03034 + 1.70365i 0.0881922 + 0.0740020i
531531 −0.494720 2.80570i −0.0214690 0.121757i
532532 −5.78487 10.0197i −0.250806 0.434408i
533533 20.6902 7.53062i 0.896193 0.326187i
534534 14.1666 5.15623i 0.613050 0.223132i
535535 −0.986136 + 5.59265i −0.0426344 + 0.241792i
536536 −1.28201 + 1.07573i −0.0553742 + 0.0464645i
537537 19.5698 16.4210i 0.844497 0.708617i
538538 −1.73753 + 9.85402i −0.0749103 + 0.424837i
539539 1.33202 0.484817i 0.0573744 0.0208826i
540540 8.02152 2.91960i 0.345191 0.125639i
541541 17.7662 + 30.7719i 0.763827 + 1.32299i 0.940865 + 0.338783i 0.110015π0.110015\pi
−0.177038 + 0.984204i 0.556651π0.556651\pi
542542 −2.14748 12.1790i −0.0922422 0.523132i
543543 9.06327 + 7.60499i 0.388942 + 0.326361i
544544 1.91262 3.31275i 0.0820028 0.142033i
545545 −11.4667 19.8609i −0.491179 0.850747i
546546 −0.908449 + 5.15207i −0.0388780 + 0.220488i
547547 −19.9167 + 34.4968i −0.851579 + 1.47498i 0.0282043 + 0.999602i 0.491021π0.491021\pi
−0.879783 + 0.475375i 0.842312π0.842312\pi
548548 19.0773 + 6.94358i 0.814943 + 0.296615i
549549 15.1669 0.647309
550550 1.09951 + 0.400190i 0.0468834 + 0.0170642i
551551 2.82306 + 16.0104i 0.120266 + 0.682065i
552552 5.55652 4.66248i 0.236501 0.198448i
553553 19.8911 + 16.6906i 0.845854 + 0.709756i
554554 −21.2463 −0.902667
555555 −7.77848 8.92130i −0.330178 0.378688i
556556 −13.1379 −0.557170
557557 −5.98445 5.02155i −0.253569 0.212770i 0.507138 0.861865i 0.330703π-0.330703\pi
−0.760708 + 0.649095i 0.775148π0.775148\pi
558558 −10.4919 + 8.80378i −0.444159 + 0.372694i
559559 −1.41406 8.01951i −0.0598082 0.339189i
560560 −2.80143 1.01964i −0.118382 0.0430875i
561561 −2.14294 −0.0904748
562562 −15.2217 5.54025i −0.642089 0.233701i
563563 17.5698 30.4318i 0.740479 1.28255i −0.211799 0.977313i 0.567932π-0.567932\pi
0.952278 0.305233i 0.0987345π-0.0987345\pi
564564 1.69517 9.61381i 0.0713797 0.404814i
565565 15.2648 + 26.4394i 0.642195 + 1.11231i
566566 2.49412 4.31994i 0.104836 0.181581i
567567 −4.34599 3.64672i −0.182515 0.153148i
568568 −1.74650 9.90487i −0.0732813 0.415599i
569569 13.4402 + 23.2792i 0.563444 + 0.975913i 0.997193 + 0.0748791i 0.0238571π0.0238571\pi
−0.433749 + 0.901034i 0.642810π0.642810\pi
570570 −10.8720 + 3.95708i −0.455378 + 0.165744i
571571 −37.5779 + 13.6772i −1.57259 + 0.572375i −0.973575 0.228366i 0.926662π-0.926662\pi
−0.599011 + 0.800741i 0.704440π0.704440\pi
572572 −0.162140 + 0.919544i −0.00677943 + 0.0384481i
573573 −10.3608 + 8.69372i −0.432827 + 0.363185i
574574 15.5041 13.0095i 0.647130 0.543006i
575575 −2.63077 + 14.9198i −0.109711 + 0.622200i
576576 1.30330 0.474361i 0.0543040 0.0197650i
577577 −15.5041 + 5.64304i −0.645445 + 0.234923i −0.643940 0.765076i 0.722701π-0.722701\pi
−0.00150512 + 0.999999i 0.500479π0.500479\pi
578578 1.18379 + 2.05038i 0.0492390 + 0.0852845i
579579 2.70227 + 15.3253i 0.112302 + 0.636899i
580580 3.20903 + 2.69270i 0.133248 + 0.111808i
581581 −3.46255 + 5.99732i −0.143651 + 0.248811i
582582 0.376889 + 0.652791i 0.0156226 + 0.0270591i
583583 0.132503 0.751462i 0.00548772 0.0311224i
584584 4.94285 8.56126i 0.204536 0.354268i
585585 −4.22690 1.53847i −0.174761 0.0636078i
586586 5.54920 0.229235
587587 26.0305 + 9.47432i 1.07439 + 0.391047i 0.817818 0.575477i 0.195184π-0.195184\pi
0.256575 + 0.966524i 0.417406π0.417406\pi
588588 −0.708756 4.01955i −0.0292286 0.165764i
589589 44.9792 37.7421i 1.85334 1.55513i
590590 2.41085 + 2.02294i 0.0992531 + 0.0832832i
591591 20.4775 0.842331
592592 −3.99747 4.58478i −0.164295 0.188433i
593593 −43.2875 −1.77760 −0.888802 0.458292i 0.848461π-0.848461\pi
−0.888802 + 0.458292i 0.848461π0.848461\pi
594594 −1.88264 1.57972i −0.0772455 0.0648167i
595595 −8.73586 + 7.33025i −0.358135 + 0.300511i
596596 −0.692555 3.92767i −0.0283681 0.160884i
597597 2.37589 + 0.864752i 0.0972385 + 0.0353919i
598598 −12.0898 −0.494389
599599 −2.17628 0.792102i −0.0889205 0.0323644i 0.297177 0.954822i 0.403955π-0.403955\pi
−0.386097 + 0.922458i 0.626177π0.626177\pi
600600 1.68455 2.91773i 0.0687715 0.119116i
601601 2.32161 13.1665i 0.0947005 0.537073i −0.900138 0.435604i 0.856535π-0.856535\pi
0.994839 0.101469i 0.0323542π-0.0323542\pi
602602 −3.74266 6.48248i −0.152539 0.264206i
603603 −1.16055 + 2.01013i −0.0472612 + 0.0818588i
604604 −15.0525 12.6306i −0.612479 0.513931i
605605 −2.87473 16.3034i −0.116874 0.662827i
606606 8.40014 + 14.5495i 0.341233 + 0.591032i
607607 −33.6174 + 12.2357i −1.36449 + 0.496633i −0.917439 0.397877i 0.869747π-0.869747\pi
−0.447048 + 0.894510i 0.647525π0.647525\pi
608608 −5.58727 + 2.03360i −0.226594 + 0.0824734i
609609 1.17339 6.65460i 0.0475480 0.269658i
610610 −12.8345 + 10.7694i −0.519653 + 0.436041i
611611 −12.4643 + 10.4588i −0.504251 + 0.423117i
612612 0.921267 5.22477i 0.0372400 0.211199i
613613 −4.73396 + 1.72302i −0.191203 + 0.0695921i −0.435847 0.900021i 0.643551π-0.643551\pi
0.244644 + 0.969613i 0.421329π0.421329\pi
614614 −14.2471 + 5.18553i −0.574967 + 0.209271i
615615 −10.1196 17.5277i −0.408062 0.706783i
616616 0.149041 + 0.845253i 0.00600503 + 0.0340562i
617617 22.8182 + 19.1467i 0.918625 + 0.770818i 0.973740 0.227662i 0.0731082π-0.0731082\pi
−0.0551152 + 0.998480i 0.517553π0.517553\pi
618618 2.00035 3.46470i 0.0804657 0.139371i
619619 −5.82105 10.0823i −0.233968 0.405244i 0.725005 0.688744i 0.241838π-0.241838\pi
−0.958972 + 0.283500i 0.908504π0.908504\pi
620620 2.62723 14.8998i 0.105512 0.598389i
621621 15.9104 27.5576i 0.638462 1.10585i
622622 −14.2914 5.20165i −0.573034 0.208567i
623623 −23.0975 −0.925381
624624 2.52643 + 0.919544i 0.101138 + 0.0368112i
625625 −0.816085 4.62825i −0.0326434 0.185130i
626626 22.3467 18.7511i 0.893155 0.749446i
627627 2.55164 + 2.14108i 0.101903 + 0.0855064i
628628 9.13115 0.364372
629629 −22.8339 + 4.47369i −0.910446 + 0.178378i
630630 −4.13476 −0.164733
631631 25.1488 + 21.1023i 1.00116 + 0.840070i 0.987144 0.159832i 0.0510952π-0.0510952\pi
0.0140121 + 0.999902i 0.495540π0.495540\pi
632632 10.2223 8.57753i 0.406621 0.341196i
633633 −2.77998 15.7661i −0.110494 0.626645i
634634 18.0323 + 6.56322i 0.716154 + 0.260659i
635635 7.51211 0.298109
636636 −2.06463 0.751462i −0.0818678 0.0297974i
637637 −3.40147 + 5.89151i −0.134771 + 0.233430i
638638 0.209427 1.18772i 0.00829128 0.0470222i
639639 −6.97468 12.0805i −0.275914 0.477897i
640640 −0.766044 + 1.32683i −0.0302806 + 0.0524475i
641641 −7.75179 6.50452i −0.306177 0.256913i 0.476733 0.879048i 0.341821π-0.341821\pi
−0.782910 + 0.622135i 0.786265π0.786265\pi
642642 −0.817482 4.63617i −0.0322634 0.182975i
643643 −9.94109 17.2185i −0.392038 0.679030i 0.600680 0.799490i 0.294897π-0.294897\pi
−0.992718 + 0.120459i 0.961563π0.961563\pi
644644 −10.4428 + 3.80089i −0.411506 + 0.149776i
645645 −7.03390 + 2.56013i −0.276960 + 0.100805i
646646 −3.94950 + 22.3987i −0.155391 + 0.881267i
647647 −6.83200 + 5.73273i −0.268594 + 0.225377i −0.767129 0.641492i 0.778316π-0.778316\pi
0.498536 + 0.866869i 0.333871π0.333871\pi
648648 −2.23347 + 1.87410i −0.0877389 + 0.0736217i
649649 0.157336 0.892297i 0.00617598 0.0350257i
650650 −5.27679 + 1.92059i −0.206973 + 0.0753319i
651651 −22.9332 + 8.34701i −0.898824 + 0.327145i
652652 0.937581 + 1.62394i 0.0367185 + 0.0635983i
653653 6.58685 + 37.3559i 0.257763 + 1.46185i 0.788879 + 0.614549i 0.210662π0.210662\pi
−0.531115 + 0.847300i 0.678227π0.678227\pi
654654 14.5634 + 12.2202i 0.569475 + 0.477846i
655655 −0.236655 + 0.409899i −0.00924688 + 0.0160161i
656656 −5.20061 9.00771i −0.203050 0.351692i
657657 2.38086 13.5026i 0.0928864 0.526785i
658658 −7.47821 + 12.9526i −0.291531 + 0.504947i
659659 −6.16662 2.24447i −0.240217 0.0874320i 0.219106 0.975701i 0.429686π-0.429686\pi
−0.459324 + 0.888269i 0.651908π0.651908\pi
660660 0.858292 0.0334090
661661 −15.8047 5.75246i −0.614733 0.223745i 0.0158397 0.999875i 0.494958π-0.494958\pi
−0.630573 + 0.776130i 0.717180π0.717180\pi
662662 −1.36020 7.71408i −0.0528657 0.299816i
663663 7.87831 6.61068i 0.305968 0.256738i
664664 2.72628 + 2.28762i 0.105800 + 0.0887770i
665665 17.7259 0.687379
666666 −7.38473 4.07908i −0.286152 0.158061i
667667 15.6156 0.604640
668668 3.52918 + 2.96133i 0.136548 + 0.114577i
669669 19.8427 16.6500i 0.767164 0.643727i
670670 −0.445236 2.52506i −0.0172010 0.0975515i
671671 4.53265 + 1.64975i 0.174981 + 0.0636878i
672672 2.47135 0.0953345
673673 7.68493 + 2.79709i 0.296232 + 0.107820i 0.485861 0.874036i 0.338506π-0.338506\pi
−0.189629 + 0.981856i 0.560728π0.560728\pi
674674 −9.83241 + 17.0302i −0.378730 + 0.655980i
675675 2.56653 14.5555i 0.0987857 0.560242i
676676 4.25942 + 7.37753i 0.163824 + 0.283751i
677677 −13.2217 + 22.9007i −0.508152 + 0.880145i 0.491804 + 0.870706i 0.336338π0.336338\pi
−0.999955 + 0.00943859i 0.996996π0.996996\pi
678678 −19.3873 16.2678i −0.744563 0.624763i
679679 −0.200539 1.13731i −0.00769596 0.0436460i
680680 2.93030 + 5.07543i 0.112372 + 0.194634i
681681 9.03771 3.28946i 0.346326 0.126052i
682682 −4.09313 + 1.48978i −0.156734 + 0.0570466i
683683 2.15766 12.2367i 0.0825604 0.468223i −0.915296 0.402782i 0.868043π-0.868043\pi
0.997856 0.0654415i 0.0208456π-0.0208456\pi
684684 −6.31721 + 5.30077i −0.241544 + 0.202680i
685685 −23.8270 + 19.9932i −0.910384 + 0.763903i
686686 −3.45113 + 19.5723i −0.131765 + 0.747275i
687687 0.373437 0.135920i 0.0142475 0.00518567i
688688 −3.61482 + 1.31569i −0.137814 + 0.0501601i
689689 1.83103 + 3.17144i 0.0697567 + 0.120822i
690690 1.92976 + 10.9442i 0.0734647 + 0.416639i
691691 −21.0501 17.6632i −0.800785 0.671938i 0.147605 0.989046i 0.452844π-0.452844\pi
−0.948389 + 0.317108i 0.897288π0.897288\pi
692692 7.54894 13.0751i 0.286968 0.497042i
693693 0.595199 + 1.03092i 0.0226097 + 0.0391612i
694694 3.74461 21.2367i 0.142143 0.806135i
695695 10.0642 17.4317i 0.381757 0.661222i
696696 −3.26323 1.18772i −0.123692 0.0450203i
697697 −39.7871 −1.50704
698698 25.2549 + 9.19201i 0.955910 + 0.347923i
699699 −0.150668 0.854483i −0.00569881 0.0323195i
700700 −3.95414 + 3.31792i −0.149452 + 0.125406i
701701 −15.0052 12.5909i −0.566739 0.475551i 0.313823 0.949482i 0.398390π-0.398390\pi
−0.880562 + 0.473931i 0.842835π0.842835\pi
702702 11.7946 0.445157
703703 31.6586 + 17.4872i 1.19403 + 0.659541i
704704 0.441088 0.0166241
705705 11.4573 + 9.61381i 0.431506 + 0.362077i
706706 −10.0953 + 8.47096i −0.379941 + 0.318809i
707707 −4.46962 25.3485i −0.168097 0.953328i
708708 −2.45156 0.892297i −0.0921354 0.0335346i
709709 18.8660 0.708528 0.354264 0.935145i 0.384731π-0.384731\pi
0.354264 + 0.935145i 0.384731π0.384731\pi
710710 14.4800 + 5.27027i 0.543423 + 0.197790i
711711 9.25384 16.0281i 0.347046 0.601102i
712712 −2.06123 + 11.6898i −0.0772477 + 0.438093i
713713 −28.1993 48.8426i −1.05607 1.82917i
714714 4.72675 8.18698i 0.176894 0.306390i
715715 −1.09587 0.919544i −0.0409832 0.0343890i
716716 3.49282 + 19.8088i 0.130533 + 0.740288i
717717 −7.11642 12.3260i −0.265767 0.460323i
718718 −3.18150 + 1.15797i −0.118733 + 0.0432151i
719719 −15.2536 + 5.55186i −0.568863 + 0.207049i −0.610408 0.792087i 0.708994π-0.708994\pi
0.0415444 + 0.999137i 0.486772π0.486772\pi
720720 −0.368987 + 2.09263i −0.0137513 + 0.0779878i
721721 −4.69540 + 3.93991i −0.174866 + 0.146730i
722722 12.5272 10.5116i 0.466215 0.391201i
723723 −1.14255 + 6.47972i −0.0424919 + 0.240983i
724724 −8.75370 + 3.18609i −0.325329 + 0.118410i
725725 6.81570 2.48071i 0.253129 0.0921313i
726726 6.86180 + 11.8850i 0.254665 + 0.441093i
727727 −2.94600 16.7076i −0.109261 0.619650i −0.989433 0.144994i 0.953684π-0.953684\pi
0.880172 0.474656i 0.157427π-0.157427\pi
728728 −3.15543 2.64772i −0.116948 0.0981311i
729729 −12.6365 + 21.8870i −0.468017 + 0.810630i
730730 7.57288 + 13.1166i 0.280285 + 0.485468i
731731 −2.55523 + 14.4914i −0.0945084 + 0.535984i
732732 6.94442 12.0281i 0.256673 0.444571i
733733 31.7060 + 11.5400i 1.17109 + 0.426241i 0.853046 0.521835i 0.174753π-0.174753\pi
0.318042 + 0.948077i 0.396975π0.396975\pi
734734 6.59687 0.243495
735735 5.87619 + 2.13876i 0.216747 + 0.0788893i
736736 0.991731 + 5.62439i 0.0365557 + 0.207318i
737737 −0.565478 + 0.474492i −0.0208296 + 0.0174782i
738738 −11.0508 9.27275i −0.406787 0.341335i
739739 15.5694 0.572730 0.286365 0.958121i 0.407553π-0.407553\pi
0.286365 + 0.958121i 0.407553π0.407553\pi
740740 9.14546 1.79181i 0.336194 0.0658682i
741741 −15.9858 −0.587253
742742 2.57866 + 2.16375i 0.0946655 + 0.0794338i
743743 −36.6033 + 30.7138i −1.34285 + 1.12678i −0.361961 + 0.932193i 0.617893π0.617893\pi
−0.980885 + 0.194588i 0.937663π0.937663\pi
744744 2.17791 + 12.3515i 0.0798461 + 0.452829i
745745 5.74187 + 2.08987i 0.210366 + 0.0765669i
746746 1.05692 0.0386967
747747 4.63832 + 1.68821i 0.169707 + 0.0617683i
748748 0.843634 1.46122i 0.0308463 0.0534274i
749749 −1.25246 + 7.10303i −0.0457637 + 0.259539i
750750 7.44551 + 12.8960i 0.271871 + 0.470895i
751751 13.6489 23.6406i 0.498055 0.862657i −0.501942 0.864901i 0.667381π-0.667381\pi
0.999997 + 0.00224411i 0.000714323π0.000714323\pi
752752 5.88806 + 4.94067i 0.214716 + 0.180168i
753753 −6.72485 38.1385i −0.245067 1.38984i
754754 2.89402 + 5.01258i 0.105394 + 0.182548i
755755 28.2895 10.2965i 1.02956 0.374730i
756756 10.1878 3.70807i 0.370528 0.134861i
757757 −8.23710 + 46.7149i −0.299383 + 1.69788i 0.349453 + 0.936954i 0.386367π0.386367\pi
−0.648835 + 0.760929i 0.724744π0.724744\pi
758758 17.0172 14.2791i 0.618092 0.518641i
759759 2.45092 2.05656i 0.0889627 0.0746486i
760760 1.58186 8.97118i 0.0573801 0.325419i
761761 −8.81599 + 3.20876i −0.319579 + 0.116317i −0.496829 0.867849i 0.665502π-0.665502\pi
0.177249 + 0.984166i 0.443280π0.443280\pi
762762 −5.85180 + 2.12988i −0.211988 + 0.0771574i
763763 −14.5634 25.2246i −0.527231 0.913191i
764764 −1.84920 10.4873i −0.0669015 0.379417i
765765 6.22663 + 5.22477i 0.225124 + 0.188902i
766766 −4.67359 + 8.09489i −0.168864 + 0.292480i
767767 2.17419 + 3.76581i 0.0785054 + 0.135975i
768768 0.220544 1.25077i 0.00795820 0.0451332i
769769 −1.14862 + 1.98947i −0.0414203 + 0.0717420i −0.885992 0.463700i 0.846522π-0.846522\pi
0.844572 + 0.535442i 0.179855π0.179855\pi
770770 −1.23568 0.449750i −0.0445307 0.0162078i
771771 7.45229 0.268388
772772 −11.5138 4.19068i −0.414391 0.150826i
773773 −3.65406 20.7232i −0.131427 0.745361i −0.977281 0.211947i 0.932020π-0.932020\pi
0.845854 0.533414i 0.179091π-0.179091\pi
774774 −4.08707 + 3.42946i −0.146907 + 0.123269i
775775 −20.0672 16.8384i −0.720835 0.604853i
776776 −0.593497 −0.0213053
777777 −9.87916 11.3306i −0.354413 0.406484i
778778 2.41968 0.0867497
779779 47.3753 + 39.7526i 1.69740 + 1.42428i
780780 −3.15543 + 2.64772i −0.112983 + 0.0948036i
781781 −0.770359 4.36892i −0.0275656 0.156332i
782782 20.5290 + 7.47194i 0.734115 + 0.267196i
783783 −15.2343 −0.544430
784784 3.01986 + 1.09914i 0.107852 + 0.0392550i
785785 −6.99486 + 12.1155i −0.249657 + 0.432419i
786786 0.0681330 0.386402i 0.00243022 0.0137825i
787787 9.94650 + 17.2278i 0.354555 + 0.614106i 0.987042 0.160464i 0.0512992π-0.0512992\pi
−0.632487 + 0.774571i 0.717966π0.717966\pi
788788 −8.06159 + 13.9631i −0.287182 + 0.497414i
789789 15.8708 + 13.3172i 0.565014 + 0.474103i
790790 3.55017 + 20.1340i 0.126309 + 0.716336i
791791 19.3873 + 33.5797i 0.689332 + 1.19396i
792792 0.574869 0.209235i 0.0204271 0.00743485i
793793 −21.7531 + 7.91749i −0.772476 + 0.281158i
794794 3.42158 19.4048i 0.121427 0.688649i
795795 2.57866 2.16375i 0.0914555 0.0767403i
796796 −1.52499 + 1.27962i −0.0540520 + 0.0453550i
797797 −3.96311 + 22.4759i −0.140380 + 0.796137i 0.830580 + 0.556899i 0.188009π0.188009\pi
−0.970961 + 0.239238i 0.923102π0.923102\pi
798798 −13.8081 + 5.02575i −0.488802 + 0.177909i
799799 27.6288 10.0561i 0.977438 0.355758i
800800 1.32635 + 2.29731i 0.0468936 + 0.0812221i
801801 2.85879 + 16.2130i 0.101010 + 0.572859i
802802 −22.3822 18.7809i −0.790341 0.663175i
803803 2.18023 3.77627i 0.0769387 0.133262i
804804 1.06275 + 1.84074i 0.0374803 + 0.0649178i
805805 2.95656 16.7675i 0.104205 0.590977i
806806 10.4522 18.1038i 0.368165 0.637680i
807807 11.9419 + 4.34650i 0.420375 + 0.153004i
808808 −13.2279 −0.465356
809809 −8.00473 2.91348i −0.281431 0.102433i 0.197448 0.980313i 0.436735π-0.436735\pi
−0.478879 + 0.877881i 0.658957π0.658957\pi
810810 −0.775675 4.39907i −0.0272545 0.154568i
811811 42.0356 35.2721i 1.47607 1.23857i 0.565807 0.824538i 0.308565π-0.308565\pi
0.910263 0.414031i 0.135880π-0.135880\pi
812812 4.07567 + 3.41989i 0.143028 + 0.120015i
813813 −15.7067 −0.550858
814814 −1.76324 2.02229i −0.0618015 0.0708814i
815815 −2.87292 −0.100634
816816 −3.72167 3.12285i −0.130284 0.109322i
817817 17.5214 14.7022i 0.612996 0.514365i
818818 −0.655331 3.71657i −0.0229131 0.129947i
819819 −5.36844 1.95395i −0.187588 0.0682766i
820820 15.9356 0.556495
821821 23.4205 + 8.52435i 0.817380 + 0.297502i 0.716669 0.697414i 0.245666π-0.245666\pi
0.100711 + 0.994916i 0.467888π0.467888\pi
822822 12.8922 22.3300i 0.449667 0.778847i
823823 6.03516 34.2271i 0.210373 1.19308i −0.678386 0.734706i 0.737320π-0.737320\pi
0.888758 0.458376i 0.151569π-0.151569\pi
824824 1.57500 + 2.72797i 0.0548676 + 0.0950335i
825825 0.743036 1.28698i 0.0258692 0.0448068i
826826 3.06193 + 2.56927i 0.106538 + 0.0893962i
827827 2.07962 + 11.7941i 0.0723156 + 0.410122i 0.999380 + 0.0352192i 0.0112129π0.0112129\pi
−0.927064 + 0.374903i 0.877676π0.877676\pi
828828 3.96051 + 6.85980i 0.137637 + 0.238395i
829829 6.74182 2.45382i 0.234153 0.0852248i −0.222279 0.974983i 0.571349π-0.571349\pi
0.456432 + 0.889758i 0.349127π0.349127\pi
830830 −5.12374 + 1.86489i −0.177848 + 0.0647312i
831831 −4.68574 + 26.5741i −0.162546 + 0.921847i
832832 −1.62162 + 1.36070i −0.0562196 + 0.0471738i
833833 9.41701 7.90181i 0.326280 0.273781i
834834 −2.89748 + 16.4324i −0.100332 + 0.569009i
835835 −6.63268 + 2.41410i −0.229533 + 0.0835433i
836836 −2.46448 + 0.896998i −0.0852359 + 0.0310233i
837837 27.5107 + 47.6499i 0.950908 + 1.64702i
838838 −6.29486 35.6999i −0.217452 1.23323i
839839 16.6124 + 13.9395i 0.573525 + 0.481244i 0.882813 0.469724i 0.155647π-0.155647\pi
−0.309289 + 0.950968i 0.600091π0.600091\pi
840840 −1.89317 + 3.27906i −0.0653205 + 0.113138i
841841 10.7620 + 18.6403i 0.371103 + 0.642769i
842842 2.80932 15.9325i 0.0968157 0.549069i
843843 −10.2866 + 17.8170i −0.354291 + 0.613649i
844844 11.8449 + 4.31120i 0.407719 + 0.148398i
845845 −13.0516 −0.448989
846846 10.0175 + 3.64609i 0.344410 + 0.125355i
847847 −3.65109 20.7063i −0.125453 0.711478i
848848 1.32521 1.11198i 0.0455078 0.0381856i
849849 −4.85318 4.07230i −0.166561 0.139761i
850850 10.1472 0.348047
851851 21.8222 27.0302i 0.748054 0.926583i
852852 −12.7739 −0.437626
853853 −27.4605 23.0421i −0.940231 0.788948i 0.0373944 0.999301i 0.488094π-0.488094\pi
−0.977625 + 0.210353i 0.932539π0.932539\pi
854854 −16.3006 + 13.6778i −0.557795 + 0.468046i
855855 −2.19394 12.4425i −0.0750313 0.425524i
856856 3.48312 + 1.26775i 0.119051 + 0.0433309i
857857 −16.3281 −0.557757 −0.278879 0.960326i 0.589963π-0.589963\pi
−0.278879 + 0.960326i 0.589963π0.589963\pi
858858 1.11438 + 0.405600i 0.0380442 + 0.0138470i
859859 −6.97836 + 12.0869i −0.238099 + 0.412399i −0.960169 0.279421i 0.909857π-0.909857\pi
0.722070 + 0.691820i 0.243191π0.243191\pi
860860 1.02342 5.80412i 0.0348984 0.197919i
861861 −12.8525 22.2612i −0.438013 0.758661i
862862 −10.3648 + 17.9524i −0.353027 + 0.611461i
863863 −37.6158 31.5634i −1.28046 1.07443i −0.993181 0.116583i 0.962806π-0.962806\pi
−0.287276 0.957848i 0.592750π-0.592750\pi
864864 −0.967514 5.48704i −0.0329155 0.186673i
865865 11.5656 + 20.0323i 0.393244 + 0.681118i
866866 −25.1700 + 9.16113i −0.855311 + 0.311308i
867867 2.82563 1.02844i 0.0959633 0.0349278i
868868 3.33675 18.9237i 0.113257 0.642311i
869869 4.50894 3.78345i 0.152955 0.128345i
870870 4.07567 3.41989i 0.138178 0.115945i
871871 0.615179 3.48885i 0.0208445 0.118215i
872872 −14.0660 + 5.11960i −0.476334 + 0.173371i
873873 −0.773502 + 0.281532i −0.0261791 + 0.00952840i
874874 −16.9788 29.4082i −0.574317 0.994747i
875875 −3.96167 22.4678i −0.133929 0.759549i
876876 −9.61804 8.07049i −0.324963 0.272677i
877877 −17.0002 + 29.4453i −0.574057 + 0.994297i 0.422086 + 0.906556i 0.361298π0.361298\pi
−0.996143 + 0.0877408i 0.972035π0.972035\pi
878878 4.19793 + 7.27102i 0.141673 + 0.245385i
879879 1.22384 6.94076i 0.0412792 0.234106i
880880 −0.337893 + 0.585248i −0.0113904 + 0.0197287i
881881 −49.9500 18.1803i −1.68286 0.612510i −0.689161 0.724609i 0.742021π-0.742021\pi
−0.993697 + 0.112098i 0.964243π0.964243\pi
882882 4.45716 0.150080
883883 −14.5551 5.29763i −0.489819 0.178279i 0.0852904 0.996356i 0.472818π-0.472818\pi
−0.575109 + 0.818077i 0.695040π0.695040\pi
884884 1.40612 + 7.97453i 0.0472931 + 0.268212i
885885 3.06193 2.56927i 0.102926 0.0863649i
886886 −15.0603 12.6371i −0.505961 0.424552i
887887 17.6841 0.593774 0.296887 0.954913i 0.404052π-0.404052\pi
0.296887 + 0.954913i 0.404052π0.404052\pi
888888 −6.61612 + 3.98876i −0.222022 + 0.133854i
889889 9.54086 0.319990
890890 −13.9313 11.6898i −0.466980 0.391843i
891891 −0.985157 + 0.826645i −0.0330040 + 0.0276936i
892892 3.54154 + 20.0851i 0.118580 + 0.672498i
893893 −42.9456 15.6309i −1.43712 0.523068i
894894 −5.06535 −0.169411
895895 −28.9585 10.5400i −0.967975 0.352314i
896896 −0.972925 + 1.68516i −0.0325031 + 0.0562971i
897897 −2.66633 + 15.1215i −0.0890263 + 0.504893i
898898 13.5862 + 23.5320i 0.453377 + 0.785271i
899899 −13.5005 + 23.3836i −0.450267 + 0.779886i
900900 2.81838 + 2.36490i 0.0939461 + 0.0788301i
901901 −1.14910 6.51688i −0.0382821 0.217109i
902902 −2.29393 3.97320i −0.0763794 0.132293i
903903 −8.93350 + 3.25153i −0.297288 + 0.108204i
904904 18.7251 6.81536i 0.622786 0.226676i
905905 2.47833 14.0553i 0.0823826 0.467215i
906906 −19.1177 + 16.0416i −0.635143 + 0.532948i
907907 −27.9435 + 23.4474i −0.927850 + 0.778558i −0.975430 0.220309i 0.929293π-0.929293\pi
0.0475804 + 0.998867i 0.484849π0.484849\pi
908908 −1.31497 + 7.45759i −0.0436390 + 0.247489i
909909 −17.2399 + 6.27481i −0.571811 + 0.208122i
910910 5.93027 2.15844i 0.196587 0.0715516i
911911 3.84129 + 6.65330i 0.127267 + 0.220434i 0.922617 0.385717i 0.126046π-0.126046\pi
−0.795350 + 0.606151i 0.792713π0.792713\pi
912912 1.31132 + 7.43688i 0.0434222 + 0.246260i
913913 1.20253 + 1.00904i 0.0397980 + 0.0333945i
914914 9.98352 17.2920i 0.330225 0.571967i
915915 10.6395 + 18.4281i 0.351730 + 0.609214i
916916 −0.0543346 + 0.308147i −0.00179527 + 0.0101815i
917917 −0.300567 + 0.520597i −0.00992560 + 0.0171916i
918918 −20.0277 7.28949i −0.661012 0.240589i
919919 −0.166200 −0.00548242 −0.00274121 0.999996i 0.500873π-0.500873\pi
−0.00274121 + 0.999996i 0.500873π0.500873\pi
920920 −8.22230 2.99267i −0.271081 0.0986655i
921921 3.34378 + 18.9635i 0.110181 + 0.624869i
922922 6.02397 5.05471i 0.198389 0.166468i
923923 16.3097 + 13.6855i 0.536841 + 0.450463i
924924 1.09009 0.0358612
925925 5.23061 15.2645i 0.171981 0.501892i
926926 −6.04210 −0.198556
927927 3.34673 + 2.80824i 0.109921 + 0.0922347i
928928 2.09455 1.75753i 0.0687568 0.0576938i
929929 6.14457 + 34.8476i 0.201597 + 1.14331i 0.902706 + 0.430258i 0.141577π0.141577\pi
−0.701109 + 0.713054i 0.747311π0.747311\pi
930930 −18.0567 6.57212i −0.592104 0.215508i
931931 −19.1080 −0.626239
932932 0.641967 + 0.233657i 0.0210283 + 0.00765368i
933933 −9.65795 + 16.7281i −0.316187 + 0.547652i
934934 5.09215 28.8790i 0.166620 0.944951i
935935 1.29252 + 2.23871i 0.0422700 + 0.0732137i
936936 −1.46799 + 2.54263i −0.0479827 + 0.0831085i
937937 11.8267 + 9.92376i 0.386361 + 0.324195i 0.815193 0.579189i 0.196631π-0.196631\pi
−0.428833 + 0.903384i 0.641075π0.641075\pi
938938 −0.565478 3.20699i −0.0184635 0.104712i
939939 −18.5249 32.0860i −0.604537 1.04709i
940940 −11.0659 + 4.02767i −0.360931 + 0.131368i
941941 21.9764 7.99875i 0.716410 0.260752i 0.0420089 0.999117i 0.486624π-0.486624\pi
0.674401 + 0.738365i 0.264402π0.264402\pi
942942 2.01382 11.4210i 0.0656139 0.372115i
943943 45.5053 38.1834i 1.48186 1.24342i
944944 1.57357 1.32038i 0.0512153 0.0429748i
945945 −2.88437 + 16.3581i −0.0938285 + 0.532128i
946946 −1.59446 + 0.580334i −0.0518402 + 0.0188683i
947947 25.1514 9.15437i 0.817311 0.297477i 0.100671 0.994920i 0.467901π-0.467901\pi
0.716640 + 0.697443i 0.245679π0.245679\pi
948948 −8.47403 14.6775i −0.275224 0.476702i
949949 3.63390 + 20.6089i 0.117961 + 0.668992i
950950 −12.0825 10.1384i −0.392008 0.328934i
951951 12.1860 21.1067i 0.395158 0.684433i
952952 3.72167 + 6.44612i 0.120620 + 0.208920i
953953 −7.42555 + 42.1124i −0.240537 + 1.36415i 0.590095 + 0.807334i 0.299090π0.299090\pi
−0.830632 + 0.556821i 0.812021π0.812021\pi
954954 1.19966 2.07787i 0.0388404 0.0672735i
955955 15.3314 + 5.58018i 0.496113 + 0.180570i
956956 11.2064 0.362441
957957 −1.43937 0.523888i −0.0465283 0.0169349i
958958 −0.718317 4.07378i −0.0232078 0.131618i
959959 −30.2618 + 25.3927i −0.977206 + 0.819973i
960960 1.49061 + 1.25077i 0.0481092 + 0.0403684i
961961 66.5188 2.14577
962962 12.7209 + 1.99541i 0.410138 + 0.0643347i
963963 5.14091 0.165663
964964 −3.96856 3.33002i −0.127819 0.107253i
965965 14.3804 12.0666i 0.462921 0.388437i
966966 2.45092 + 13.8998i 0.0788570 + 0.447220i
967967 3.28122 + 1.19426i 0.105517 + 0.0384050i 0.394239 0.919008i 0.371008π-0.371008\pi
−0.288722 + 0.957413i 0.593230π0.593230\pi
968968 −10.8054 −0.347300
969969 27.1446 + 9.87983i 0.872010 + 0.317386i
970970 0.454645 0.787468i 0.0145978 0.0252841i
971971 1.07928 6.12087i 0.0346356 0.196428i −0.962580 0.270997i 0.912647π-0.912647\pi
0.997216 + 0.0745684i 0.0237579π0.0237579\pi
972972 −6.50605 11.2688i −0.208682 0.361447i
973973 12.7822 22.1394i 0.409778 0.709756i
974974 22.1653 + 18.5989i 0.710222 + 0.595947i
975975 1.23845 + 7.02362i 0.0396622 + 0.224936i
976976 5.46777 + 9.47046i 0.175019 + 0.303142i
977977 0.127278 0.0463253i 0.00407198 0.00148208i −0.339983 0.940431i 0.610421π-0.610421\pi
0.344055 + 0.938949i 0.388199π0.388199\pi
978978 2.23795 0.814547i 0.0715617 0.0260463i
979979 −0.909183 + 5.15623i −0.0290576 + 0.164794i
980980 −3.77171 + 3.16484i −0.120483 + 0.101097i
981981 −15.9036 + 13.3447i −0.507763 + 0.426063i
982982 3.39349 19.2454i 0.108291 0.614147i
983983 1.92791 0.701702i 0.0614908 0.0223808i −0.311092 0.950380i 0.600695π-0.600695\pi
0.372582 + 0.927999i 0.378472π0.378472\pi
984984 −12.4135 + 4.51815i −0.395729 + 0.144033i
985985 −12.3511 21.3927i −0.393538 0.681628i
986986 −1.81620 10.3002i −0.0578397 0.328025i
987987 14.5515 + 12.2101i 0.463179 + 0.388653i
988988 6.29331 10.9003i 0.200217 0.346786i
989989 −10.9849 19.0263i −0.349298 0.605002i
990990 −0.162756 + 0.923035i −0.00517273 + 0.0293360i
991991 −8.69906 + 15.0672i −0.276335 + 0.478626i −0.970471 0.241218i 0.922453π-0.922453\pi
0.694136 + 0.719844i 0.255787π0.255787\pi
992992 −9.27962 3.37750i −0.294628 0.107236i
993993 −9.94851 −0.315707
994994 18.3905 + 6.69358i 0.583310 + 0.212307i
995995 −0.529625 3.00365i −0.0167902 0.0952222i
996996 3.46255 2.90543i 0.109715 0.0920620i
997997 5.44281 + 4.56706i 0.172376 + 0.144640i 0.724894 0.688860i 0.241889π-0.241889\pi
−0.552518 + 0.833501i 0.686333π0.686333\pi
998998 −42.2259 −1.33664
999999 −21.2893 + 26.3701i −0.673563 + 0.834314i
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 74.2.f.b.71.2 yes 12
3.2 odd 2 666.2.x.g.145.1 12
4.3 odd 2 592.2.bc.d.145.1 12
37.7 even 9 2738.2.a.t.1.4 6
37.12 even 9 inner 74.2.f.b.49.2 12
37.30 even 18 2738.2.a.q.1.4 6
111.86 odd 18 666.2.x.g.271.1 12
148.123 odd 18 592.2.bc.d.49.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.f.b.49.2 12 37.12 even 9 inner
74.2.f.b.71.2 yes 12 1.1 even 1 trivial
592.2.bc.d.49.1 12 148.123 odd 18
592.2.bc.d.145.1 12 4.3 odd 2
666.2.x.g.145.1 12 3.2 odd 2
666.2.x.g.271.1 12 111.86 odd 18
2738.2.a.q.1.4 6 37.30 even 18
2738.2.a.t.1.4 6 37.7 even 9