Properties

Label 525.2.t.j.26.5
Level 525525
Weight 22
Character 525.26
Analytic conductor 4.1924.192
Analytic rank 00
Dimension 2424
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(26,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 525=3527 525 = 3 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 525.t (of order 66, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.192146106124.19214610612
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 26.5
Character χ\chi == 525.26
Dual form 525.2.t.j.101.5

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+(0.5584180.322403i)q2+(1.288381.15761i)q3+(0.7921131.37198i)q4+(0.346239+1.06181i)q6+(0.105130+2.64366i)q7+2.31113iq8+(0.319861+2.98290i)q9+(3.510442.02675i)q11+(0.567678+2.68460i)q12+4.21339iq13+(0.7936181.51016i)q14+(0.839111+1.45338i)q16+(1.088301.88498i)q17+(0.7830791.76883i)q18+(3.87634+2.23800i)q19+(2.924893.52775i)q212.61372q22+(0.5584180.322403i)q23+(2.675402.97762i)q24+(1.358412.35284i)q26+(3.040944.21339i)q27+(3.543772.23831i)q281.16875iq29+(0.339111+0.195786i)q31+(4.940142.85219i)q32+(6.868981.45250i)q33+1.40348iq34+(3.839112.80164i)q36+(2.131783.69236i)q37+(1.443082.49949i)q38+(4.877485.42846i)q39+2.27971q41+(2.77067+1.02697i)q42+6.54419q43+(5.561323.21083i)q44+(0.207887+0.360071i)q46+(3.90070+6.75621i)q47+(2.763550.901147i)q48+(6.97790+0.555857i)q49+(0.779941+3.68841i)q51+(5.780693.33748i)q52+(6.236673.60074i)q53+(3.05653+1.37243i)q54+(6.10984+0.242969i)q56+(2.403467.37071i)q57+(0.376810+0.652654i)q58+(5.66247+9.80768i)q59+(6.05456+3.49560i)q61+0.252487q62+(7.85215+1.15920i)q630.321779q64+(3.36748+3.02568i)q66+(4.36870+7.56680i)q67+(1.72411+2.98624i)q68+(0.346239+1.06181i)q69+8.13766iq71+(6.89387+0.739241i)q72+(4.535252.61843i)q73+(2.38085+1.37459i)q747.09101iq76+(5.72710+9.06734i)q77+(4.47383+1.45884i)q78+(1.876343.24991i)q79+(8.79538+1.90823i)q81+(1.273030.734986i)q825.27461q83+(7.156841.21852i)q84+(3.654392.10987i)q86+(1.35297+1.50580i)q87+(4.68409+8.11308i)q88+(0.4473790.774883i)q89+(11.1388+0.442954i)q91+1.02152iq92+(0.663548+0.140312i)q93+(4.356442.51519i)q94+(9.666532.04406i)q96+3.89968iq97+(4.07579+1.93929i)q98+(7.16845+9.82300i)q99+O(q100)q+(-0.558418 - 0.322403i) q^{2} +(-1.28838 - 1.15761i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(0.346239 + 1.06181i) q^{6} +(0.105130 + 2.64366i) q^{7} +2.31113i q^{8} +(0.319861 + 2.98290i) q^{9} +(3.51044 - 2.02675i) q^{11} +(-0.567678 + 2.68460i) q^{12} +4.21339i q^{13} +(0.793618 - 1.51016i) q^{14} +(-0.839111 + 1.45338i) q^{16} +(-1.08830 - 1.88498i) q^{17} +(0.783079 - 1.76883i) q^{18} +(3.87634 + 2.23800i) q^{19} +(2.92489 - 3.52775i) q^{21} -2.61372 q^{22} +(-0.558418 - 0.322403i) q^{23} +(2.67540 - 2.97762i) q^{24} +(1.35841 - 2.35284i) q^{26} +(3.04094 - 4.21339i) q^{27} +(3.54377 - 2.23831i) q^{28} -1.16875i q^{29} +(-0.339111 + 0.195786i) q^{31} +(4.94014 - 2.85219i) q^{32} +(-6.86898 - 1.45250i) q^{33} +1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +(2.13178 - 3.69236i) q^{37} +(-1.44308 - 2.49949i) q^{38} +(4.87748 - 5.42846i) q^{39} +2.27971 q^{41} +(-2.77067 + 1.02697i) q^{42} +6.54419 q^{43} +(-5.56132 - 3.21083i) q^{44} +(0.207887 + 0.360071i) q^{46} +(-3.90070 + 6.75621i) q^{47} +(2.76355 - 0.901147i) q^{48} +(-6.97790 + 0.555857i) q^{49} +(-0.779941 + 3.68841i) q^{51} +(5.78069 - 3.33748i) q^{52} +(6.23667 - 3.60074i) q^{53} +(-3.05653 + 1.37243i) q^{54} +(-6.10984 + 0.242969i) q^{56} +(-2.40346 - 7.37071i) q^{57} +(-0.376810 + 0.652654i) q^{58} +(5.66247 + 9.80768i) q^{59} +(6.05456 + 3.49560i) q^{61} +0.252487 q^{62} +(-7.85215 + 1.15920i) q^{63} -0.321779 q^{64} +(3.36748 + 3.02568i) q^{66} +(4.36870 + 7.56680i) q^{67} +(-1.72411 + 2.98624i) q^{68} +(0.346239 + 1.06181i) q^{69} +8.13766i q^{71} +(-6.89387 + 0.739241i) q^{72} +(4.53525 - 2.61843i) q^{73} +(-2.38085 + 1.37459i) q^{74} -7.09101i q^{76} +(5.72710 + 9.06734i) q^{77} +(-4.47383 + 1.45884i) q^{78} +(1.87634 - 3.24991i) q^{79} +(-8.79538 + 1.90823i) q^{81} +(-1.27303 - 0.734986i) q^{82} -5.27461 q^{83} +(-7.15684 - 1.21852i) q^{84} +(-3.65439 - 2.10987i) q^{86} +(-1.35297 + 1.50580i) q^{87} +(4.68409 + 8.11308i) q^{88} +(0.447379 - 0.774883i) q^{89} +(-11.1388 + 0.442954i) q^{91} +1.02152i q^{92} +(0.663548 + 0.140312i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-9.66653 - 2.04406i) q^{96} +3.89968i q^{97} +(4.07579 + 1.93929i) q^{98} +(7.16845 + 9.82300i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+12q4+6q912q166q2118q24+84q36+12q39+36q46+12q4912q51+36q54+36q6124q6472q6648q796q8148q84++48q99+O(q100) 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/525Z)×\left(\mathbb{Z}/525\mathbb{Z}\right)^\times.

nn 127127 176176 451451
χ(n)\chi(n) 11 1-1 e(56)e\left(\frac{5}{6}\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 −0.558418 0.322403i −0.394861 0.227973i 0.289403 0.957207i 0.406543π-0.406543\pi
−0.684264 + 0.729234i 0.739877π0.739877\pi
33 −1.28838 1.15761i −0.743848 0.668349i
44 −0.792113 1.37198i −0.396056 0.685990i
55 0 0
66 0.346239 + 1.06181i 0.141351 + 0.433483i
77 0.105130 + 2.64366i 0.0397354 + 0.999210i
88 2.31113i 0.817108i
99 0.319861 + 2.98290i 0.106620 + 0.994300i
1010 0 0
1111 3.51044 2.02675i 1.05844 0.611089i 0.133437 0.991057i 0.457398π-0.457398\pi
0.924999 + 0.379968i 0.124065π0.124065\pi
1212 −0.567678 + 2.68460i −0.163874 + 0.774976i
1313 4.21339i 1.16858i 0.811543 + 0.584292i 0.198628π0.198628\pi
−0.811543 + 0.584292i 0.801372π0.801372\pi
1414 0.793618 1.51016i 0.212103 0.403608i
1515 0 0
1616 −0.839111 + 1.45338i −0.209778 + 0.363346i
1717 −1.08830 1.88498i −0.263951 0.457176i 0.703338 0.710856i 0.251692π-0.251692\pi
−0.967288 + 0.253680i 0.918359π0.918359\pi
1818 0.783079 1.76883i 0.184574 0.416917i
1919 3.87634 + 2.23800i 0.889293 + 0.513434i 0.873711 0.486445i 0.161707π-0.161707\pi
0.0155818 + 0.999879i 0.495040π0.495040\pi
2020 0 0
2121 2.92489 3.52775i 0.638264 0.769818i
2222 −2.61372 −0.557248
2323 −0.558418 0.322403i −0.116438 0.0672257i 0.440650 0.897679i 0.354748π-0.354748\pi
−0.557088 + 0.830453i 0.688081π0.688081\pi
2424 2.67540 2.97762i 0.546113 0.607804i
2525 0 0
2626 1.35841 2.35284i 0.266406 0.461429i
2727 3.04094 4.21339i 0.585229 0.810868i
2828 3.54377 2.23831i 0.669710 0.423002i
2929 1.16875i 0.217032i −0.994095 0.108516i 0.965390π-0.965390\pi
0.994095 0.108516i 0.0346099π-0.0346099\pi
3030 0 0
3131 −0.339111 + 0.195786i −0.0609061 + 0.0351641i −0.530144 0.847908i 0.677862π-0.677862\pi
0.469238 + 0.883072i 0.344529π0.344529\pi
3232 4.94014 2.85219i 0.873302 0.504201i
3333 −6.86898 1.45250i −1.19574 0.252847i
3434 1.40348i 0.240695i
3535 0 0
3636 3.83911 2.80164i 0.639852 0.466939i
3737 2.13178 3.69236i 0.350463 0.607020i −0.635868 0.771798i 0.719358π-0.719358\pi
0.986331 + 0.164778i 0.0526909π0.0526909\pi
3838 −1.44308 2.49949i −0.234098 0.405470i
3939 4.87748 5.42846i 0.781022 0.869250i
4040 0 0
4141 2.27971 0.356031 0.178016 0.984028i 0.443032π-0.443032\pi
0.178016 + 0.984028i 0.443032π0.443032\pi
4242 −2.77067 + 1.02697i −0.427524 + 0.158464i
4343 6.54419 0.997980 0.498990 0.866608i 0.333705π-0.333705\pi
0.498990 + 0.866608i 0.333705π0.333705\pi
4444 −5.56132 3.21083i −0.838401 0.484051i
4545 0 0
4646 0.207887 + 0.360071i 0.0306513 + 0.0530896i
4747 −3.90070 + 6.75621i −0.568975 + 0.985494i 0.427692 + 0.903924i 0.359327π0.359327\pi
−0.996668 + 0.0815698i 0.974007π0.974007\pi
4848 2.76355 0.901147i 0.398884 0.130069i
4949 −6.97790 + 0.555857i −0.996842 + 0.0794081i
5050 0 0
5151 −0.779941 + 3.68841i −0.109214 + 0.516480i
5252 5.78069 3.33748i 0.801637 0.462825i
5353 6.23667 3.60074i 0.856672 0.494600i −0.00622439 0.999981i 0.501981π-0.501981\pi
0.862896 + 0.505381i 0.168648π0.168648\pi
5454 −3.05653 + 1.37243i −0.415941 + 0.186764i
5555 0 0
5656 −6.10984 + 0.242969i −0.816462 + 0.0324681i
5757 −2.40346 7.37071i −0.318346 0.976274i
5858 −0.376810 + 0.652654i −0.0494776 + 0.0856977i
5959 5.66247 + 9.80768i 0.737190 + 1.27685i 0.953756 + 0.300583i 0.0971812π0.0971812\pi
−0.216566 + 0.976268i 0.569485π0.569485\pi
6060 0 0
6161 6.05456 + 3.49560i 0.775207 + 0.447566i 0.834729 0.550661i 0.185624π-0.185624\pi
−0.0595220 + 0.998227i 0.518958π0.518958\pi
6262 0.252487 0.0320659
6363 −7.85215 + 1.15920i −0.989278 + 0.146045i
6464 −0.321779 −0.0402224
6565 0 0
6666 3.36748 + 3.02568i 0.414508 + 0.372436i
6767 4.36870 + 7.56680i 0.533721 + 0.924432i 0.999224 + 0.0393859i 0.0125402π0.0125402\pi
−0.465503 + 0.885046i 0.654127π0.654127\pi
6868 −1.72411 + 2.98624i −0.209079 + 0.362135i
6969 0.346239 + 1.06181i 0.0416822 + 0.127827i
7070 0 0
7171 8.13766i 0.965762i 0.875686 + 0.482881i 0.160410π0.160410\pi
−0.875686 + 0.482881i 0.839590π0.839590\pi
7272 −6.89387 + 0.739241i −0.812450 + 0.0871204i
7373 4.53525 2.61843i 0.530810 0.306464i −0.210536 0.977586i 0.567521π-0.567521\pi
0.741346 + 0.671123i 0.234188π0.234188\pi
7474 −2.38085 + 1.37459i −0.276769 + 0.159792i
7575 0 0
7676 7.09101i 0.813394i
7777 5.72710 + 9.06734i 0.652664 + 1.03332i
7878 −4.47383 + 1.45884i −0.506561 + 0.165181i
7979 1.87634 3.24991i 0.211105 0.365644i −0.740956 0.671554i 0.765627π-0.765627\pi
0.952060 + 0.305910i 0.0989606π0.0989606\pi
8080 0 0
8181 −8.79538 + 1.90823i −0.977264 + 0.212025i
8282 −1.27303 0.734986i −0.140583 0.0811656i
8383 −5.27461 −0.578964 −0.289482 0.957183i 0.593483π-0.593483\pi
−0.289482 + 0.957183i 0.593483π0.593483\pi
8484 −7.15684 1.21852i −0.780876 0.132951i
8585 0 0
8686 −3.65439 2.10987i −0.394064 0.227513i
8787 −1.35297 + 1.50580i −0.145053 + 0.161439i
8888 4.68409 + 8.11308i 0.499325 + 0.864857i
8989 0.447379 0.774883i 0.0474221 0.0821375i −0.841340 0.540506i 0.818233π-0.818233\pi
0.888762 + 0.458369i 0.151566π0.151566\pi
9090 0 0
9191 −11.1388 + 0.442954i −1.16766 + 0.0464342i
9292 1.02152i 0.106501i
9393 0.663548 + 0.140312i 0.0688068 + 0.0145497i
9494 4.35644 2.51519i 0.449333 0.259422i
9595 0 0
9696 −9.66653 2.04406i −0.986586 0.208621i
9797 3.89968i 0.395953i 0.980207 + 0.197976i 0.0634370π0.0634370\pi
−0.980207 + 0.197976i 0.936563π0.936563\pi
9898 4.07579 + 1.93929i 0.411717 + 0.195898i
9999 7.16845 + 9.82300i 0.720456 + 0.987249i
100100 0 0
101101 −3.29188 5.70171i −0.327555 0.567341i 0.654471 0.756087i 0.272891π-0.272891\pi
−0.982026 + 0.188745i 0.939558π0.939558\pi
102102 1.62469 1.80822i 0.160868 0.179040i
103103 8.49954 + 4.90721i 0.837485 + 0.483522i 0.856408 0.516299i 0.172691π-0.172691\pi
−0.0189238 + 0.999821i 0.506024π0.506024\pi
104104 −9.73770 −0.954860
105105 0 0
106106 −4.64356 −0.451022
107107 −16.2635 9.38974i −1.57225 0.907740i −0.995892 0.0905447i 0.971139π-0.971139\pi
−0.576360 0.817196i 0.695527π-0.695527\pi
108108 −8.18946 0.834627i −0.788031 0.0803120i
109109 0.453002 + 0.784623i 0.0433897 + 0.0751532i 0.886905 0.461952i 0.152851π-0.152851\pi
−0.843515 + 0.537106i 0.819518π0.819518\pi
110110 0 0
111111 −7.02088 + 2.28939i −0.666392 + 0.217299i
112112 −3.93047 2.06553i −0.371394 0.195174i
113113 8.82955i 0.830614i −0.909681 0.415307i 0.863674π-0.863674\pi
0.909681 0.415307i 0.136326π-0.136326\pi
114114 −1.03420 + 4.89082i −0.0968618 + 0.458067i
115115 0 0
116116 −1.60351 + 0.925786i −0.148882 + 0.0859570i
117117 −12.5681 + 1.34770i −1.16192 + 0.124595i
118118 7.30238i 0.672239i
119119 4.86885 3.07526i 0.446327 0.281908i
120120 0 0
121121 2.71545 4.70330i 0.246859 0.427572i
122122 −2.25398 3.90402i −0.204066 0.353453i
123123 −2.93714 2.63903i −0.264833 0.237953i
124124 0.537228 + 0.310168i 0.0482445 + 0.0278540i
125125 0 0
126126 4.75851 + 1.88424i 0.423922 + 0.167861i
127127 15.8249 1.40424 0.702118 0.712060i 0.252238π-0.252238\pi
0.702118 + 0.712060i 0.252238π0.252238\pi
128128 −9.70060 5.60064i −0.857420 0.495032i
129129 −8.43142 7.57564i −0.742345 0.666998i
130130 0 0
131131 −8.27814 + 14.3382i −0.723265 + 1.25273i 0.236419 + 0.971651i 0.424026π0.424026\pi
−0.959684 + 0.281080i 0.909307π0.909307\pi
132132 3.44821 + 10.5746i 0.300128 + 0.920405i
133133 −5.50901 + 10.4830i −0.477692 + 0.908992i
134134 5.63392i 0.486697i
135135 0 0
136136 4.35644 2.51519i 0.373562 0.215676i
137137 17.2007 9.93080i 1.46955 0.848446i 0.470135 0.882595i 0.344205π-0.344205\pi
0.999417 + 0.0341490i 0.0108721π0.0108721\pi
138138 0.148985 0.704563i 0.0126825 0.0599764i
139139 0.228766i 0.0194037i 0.999953 + 0.00970183i 0.00308824π0.00308824\pi
−0.999953 + 0.00970183i 0.996912π0.996912\pi
140140 0 0
141141 12.8467 4.18908i 1.08188 0.352784i
142142 2.62361 4.54422i 0.220168 0.381342i
143143 8.53950 + 14.7909i 0.714109 + 1.23687i
144144 −4.60369 2.03810i −0.383641 0.169842i
145145 0 0
146146 −3.37675 −0.279462
147147 9.63367 + 7.36155i 0.794572 + 0.607170i
148148 −6.75445 −0.555212
149149 8.62438 + 4.97929i 0.706537 + 0.407919i 0.809777 0.586737i 0.199588π-0.199588\pi
−0.103240 + 0.994656i 0.532921π0.532921\pi
150150 0 0
151151 2.53723 + 4.39461i 0.206477 + 0.357628i 0.950602 0.310412i 0.100467π-0.100467\pi
−0.744126 + 0.668040i 0.767134π0.767134\pi
152152 −5.17232 + 8.95872i −0.419530 + 0.726648i
153153 5.27461 3.84921i 0.426427 0.311190i
154154 −0.274781 6.90980i −0.0221425 0.556808i
155155 0 0
156156 −11.3113 2.39185i −0.905625 0.191501i
157157 −14.5956 + 8.42678i −1.16486 + 0.672531i −0.952463 0.304653i 0.901459π-0.901459\pi
−0.212394 + 0.977184i 0.568126π0.568126\pi
158158 −2.09556 + 1.20987i −0.166714 + 0.0962524i
159159 −12.2035 2.58052i −0.967799 0.204648i
160160 0 0
161161 0.793618 1.51016i 0.0625458 0.119018i
162162 5.52672 + 1.77007i 0.434220 + 0.139070i
163163 2.40346 4.16292i 0.188254 0.326065i −0.756414 0.654093i 0.773051π-0.773051\pi
0.944668 + 0.328028i 0.106384π0.106384\pi
164164 −1.80579 3.12772i −0.141008 0.244234i
165165 0 0
166166 2.94544 + 1.70055i 0.228611 + 0.131988i
167167 4.45089 0.344420 0.172210 0.985060i 0.444909π-0.444909\pi
0.172210 + 0.985060i 0.444909π0.444909\pi
168168 8.15308 + 6.75980i 0.629024 + 0.521530i
169169 −4.75268 −0.365590
170170 0 0
171171 −5.43585 + 12.2786i −0.415690 + 0.938966i
172172 −5.18374 8.97849i −0.395256 0.684604i
173173 −5.72710 + 9.91963i −0.435423 + 0.754175i −0.997330 0.0730252i 0.976735π-0.976735\pi
0.561907 + 0.827201i 0.310068π0.310068\pi
174174 1.24100 0.404668i 0.0940797 0.0306778i
175175 0 0
176176 6.80268i 0.512771i
177177 4.05808 19.1910i 0.305024 1.44248i
178178 −0.499649 + 0.288473i −0.0374503 + 0.0216219i
179179 −9.04522 + 5.22226i −0.676071 + 0.390330i −0.798373 0.602163i 0.794306π-0.794306\pi
0.122302 + 0.992493i 0.460972π0.460972\pi
180180 0 0
181181 11.9616i 0.889095i −0.895755 0.444548i 0.853364π-0.853364\pi
0.895755 0.444548i 0.146636π-0.146636\pi
182182 6.36291 + 3.34382i 0.471650 + 0.247861i
183183 −3.75404 11.5125i −0.277506 0.851030i
184184 0.745115 1.29058i 0.0549306 0.0951426i
185185 0 0
186186 −0.325300 0.292283i −0.0238522 0.0214312i
187187 −7.64079 4.41141i −0.558750 0.322594i
188188 12.3592 0.901385
189189 11.4585 + 7.59627i 0.833482 + 0.552547i
190190 0 0
191191 12.2522 + 7.07383i 0.886541 + 0.511844i 0.872809 0.488061i 0.162296π-0.162296\pi
0.0137312 + 0.999906i 0.495629π0.495629\pi
192192 0.414574 + 0.372496i 0.0299193 + 0.0268826i
193193 −3.09566 5.36185i −0.222831 0.385954i 0.732836 0.680406i 0.238196π-0.238196\pi
−0.955666 + 0.294452i 0.904863π0.904863\pi
194194 1.25727 2.17765i 0.0902667 0.156346i
195195 0 0
196196 6.28990 + 9.13323i 0.449279 + 0.652373i
197197 13.0751i 0.931562i −0.884900 0.465781i 0.845773π-0.845773\pi
0.884900 0.465781i 0.154227π-0.154227\pi
198198 −0.836029 7.79647i −0.0594140 0.554071i
199199 −14.6810 + 8.47608i −1.04071 + 0.600854i −0.920034 0.391838i 0.871839π-0.871839\pi
−0.120675 + 0.992692i 0.538506π0.538506\pi
200200 0 0
201201 3.13088 14.8062i 0.220835 1.04435i
202202 4.24525i 0.298695i
203203 3.08979 0.122871i 0.216861 0.00862388i
204204 5.67822 1.85157i 0.397555 0.129636i
205205 0 0
206206 −3.16420 5.48055i −0.220460 0.381848i
207207 0.783079 1.76883i 0.0544278 0.122942i
208208 −6.12367 3.53550i −0.424600 0.245143i
209209 18.1435 1.25501
210210 0 0
211211 −18.4309 −1.26884 −0.634418 0.772990i 0.718760π-0.718760\pi
−0.634418 + 0.772990i 0.718760π0.718760\pi
212212 −9.88029 5.70439i −0.678581 0.391779i
213213 9.42027 10.4844i 0.645466 0.718381i
214214 6.05456 + 10.4868i 0.413881 + 0.716863i
215215 0 0
216216 9.73770 + 7.02801i 0.662566 + 0.478195i
217217 −0.553242 0.875911i −0.0375565 0.0594607i
218218 0.584197i 0.0395668i
219219 −8.87426 1.87653i −0.599667 0.126804i
220220 0 0
221221 7.94218 4.58542i 0.534249 0.308449i
222222 4.65869 + 0.985115i 0.312671 + 0.0661166i
223223 0.627418i 0.0420150i 0.999779 + 0.0210075i 0.00668739π0.00668739\pi
−0.999779 + 0.0210075i 0.993313π0.993313\pi
224224 8.05959 + 12.7602i 0.538504 + 0.852578i
225225 0 0
226226 −2.84667 + 4.93058i −0.189358 + 0.327977i
227227 2.71470 + 4.70200i 0.180181 + 0.312082i 0.941942 0.335776i 0.108998π-0.108998\pi
−0.761761 + 0.647858i 0.775665π0.775665\pi
228228 −8.20865 + 9.13593i −0.543631 + 0.605042i
229229 12.4482 + 7.18699i 0.822602 + 0.474930i 0.851313 0.524658i 0.175807π-0.175807\pi
−0.0287108 + 0.999588i 0.509140π0.509140\pi
230230 0 0
231231 3.11778 18.3120i 0.205135 1.20484i
232232 2.70114 0.177339
233233 −7.30101 4.21524i −0.478305 0.276150i 0.241405 0.970425i 0.422392π-0.422392\pi
−0.719710 + 0.694275i 0.755725π0.755725\pi
234234 7.45277 + 3.29942i 0.487203 + 0.215690i
235235 0 0
236236 8.97062 15.5376i 0.583938 1.01141i
237237 −6.17959 + 2.01506i −0.401407 + 0.130892i
238238 −3.71032 + 0.147548i −0.240505 + 0.00956411i
239239 2.71852i 0.175847i −0.996127 0.0879233i 0.971977π-0.971977\pi
0.996127 0.0879233i 0.0280230π-0.0280230\pi
240240 0 0
241241 −1.32457 + 0.764739i −0.0853229 + 0.0492612i −0.542054 0.840343i 0.682353π-0.682353\pi
0.456732 + 0.889605i 0.349020π0.349020\pi
242242 −3.03271 + 1.75094i −0.194950 + 0.112555i
243243 13.5408 + 7.72312i 0.868643 + 0.495438i
244244 11.0756i 0.709045i
245245 0 0
246246 0.789324 + 2.42062i 0.0503255 + 0.154333i
247247 −9.42959 + 16.3325i −0.599991 + 1.03921i
248248 −0.452486 0.783728i −0.0287329 0.0497668i
249249 6.79572 + 6.10597i 0.430661 + 0.386950i
250250 0 0
251251 8.81039 0.556107 0.278054 0.960566i 0.410311π-0.410311\pi
0.278054 + 0.960566i 0.410311π0.410311\pi
252252 7.81018 + 9.85477i 0.491995 + 0.620792i
253253 −2.61372 −0.164323
254254 −8.83694 5.10201i −0.554479 0.320128i
255255 0 0
256256 3.93311 + 6.81234i 0.245819 + 0.425771i
257257 −10.0517 + 17.4101i −0.627011 + 1.08601i 0.361138 + 0.932512i 0.382388π0.382388\pi
−0.988148 + 0.153502i 0.950945π0.950945\pi
258258 2.26585 + 6.94869i 0.141066 + 0.432607i
259259 9.98546 + 5.24754i 0.620466 + 0.326066i
260260 0 0
261261 3.48628 0.373839i 0.215795 0.0231401i
262262 9.24533 5.33780i 0.571179 0.329770i
263263 7.58568 4.37959i 0.467753 0.270057i −0.247546 0.968876i 0.579624π-0.579624\pi
0.715299 + 0.698819i 0.246291π0.246291\pi
264264 3.35691 15.8751i 0.206604 0.977046i
265265 0 0
266266 6.45608 4.07778i 0.395848 0.250025i
267267 −1.47341 + 0.480454i −0.0901713 + 0.0294033i
268268 6.92100 11.9875i 0.422767 0.732255i
269269 −8.62438 14.9379i −0.525838 0.910778i −0.999547 0.0300966i 0.990419π-0.990419\pi
0.473709 0.880681i 0.342915π-0.342915\pi
270270 0 0
271271 19.6117 + 11.3228i 1.19132 + 0.687812i 0.958607 0.284733i 0.0919048π-0.0919048\pi
0.232718 + 0.972544i 0.425238π0.425238\pi
272272 3.65280 0.221484
273273 14.8638 + 12.3237i 0.899598 + 0.745865i
274274 −12.8069 −0.773692
275275 0 0
276276 1.18252 1.31611i 0.0711795 0.0792203i
277277 6.60561 + 11.4413i 0.396893 + 0.687438i 0.993341 0.115213i 0.0367552π-0.0367552\pi
−0.596448 + 0.802652i 0.703422π0.703422\pi
278278 0.0737548 0.127747i 0.00442352 0.00766176i
279279 −0.692477 0.948908i −0.0414575 0.0568097i
280280 0 0
281281 32.8703i 1.96088i −0.196817 0.980440i 0.563060π-0.563060\pi
0.196817 0.980440i 0.436940π-0.436940\pi
282282 −8.52439 1.80255i −0.507620 0.107340i
283283 −13.6932 + 7.90575i −0.813974 + 0.469948i −0.848334 0.529462i 0.822394π-0.822394\pi
0.0343601 + 0.999410i 0.489061π0.489061\pi
284284 11.1647 6.44594i 0.662503 0.382496i
285285 0 0
286286 11.0126i 0.651191i
287287 0.239666 + 6.02679i 0.0141471 + 0.355750i
288288 10.0880 + 13.8236i 0.594439 + 0.814566i
289289 6.13122 10.6196i 0.360660 0.624682i
290290 0 0
291291 4.51433 5.02429i 0.264635 0.294529i
292292 −7.18485 4.14818i −0.420462 0.242754i
293293 −20.7797 −1.21396 −0.606982 0.794716i 0.707620π-0.707620\pi
−0.606982 + 0.794716i 0.707620π0.707620\pi
294294 −3.00623 7.21675i −0.175327 0.420889i
295295 0 0
296296 8.53351 + 4.92683i 0.496000 + 0.286366i
297297 2.13553 20.9541i 0.123916 1.21588i
298298 −3.21068 5.56105i −0.185989 0.322143i
299299 1.35841 2.35284i 0.0785589 0.136068i
300300 0 0
301301 0.687991 + 17.3006i 0.0396552 + 0.997191i
302302 3.27204i 0.188285i
303303 −2.35917 + 11.1567i −0.135531 + 0.640937i
304304 −6.50535 + 3.75587i −0.373108 + 0.215414i
305305 0 0
306306 −4.18644 + 0.448919i −0.239323 + 0.0256630i
307307 12.9857i 0.741136i −0.928805 0.370568i 0.879163π-0.879163\pi
0.928805 0.370568i 0.120837π-0.120837\pi
308308 7.90369 15.0398i 0.450355 0.856973i
309309 −5.27001 16.1616i −0.299800 0.919399i
310310 0 0
311311 0.228825 + 0.396337i 0.0129755 + 0.0224742i 0.872440 0.488721i 0.162536π-0.162536\pi
−0.859465 + 0.511195i 0.829203π0.829203\pi
312312 12.5459 + 11.2725i 0.710271 + 0.638179i
313313 −24.0252 13.8710i −1.35799 0.784033i −0.368633 0.929575i 0.620174π-0.620174\pi
−0.989352 + 0.145542i 0.953507π0.953507\pi
314314 10.8673 0.613276
315315 0 0
316316 −5.94509 −0.334437
317317 3.91737 + 2.26170i 0.220022 + 0.127030i 0.605960 0.795495i 0.292789π-0.292789\pi
−0.385939 + 0.922524i 0.626122π0.626122\pi
318318 5.98268 + 5.37545i 0.335492 + 0.301440i
319319 −2.36878 4.10284i −0.132626 0.229715i
320320 0 0
321321 10.0839 + 30.9244i 0.562830 + 1.72603i
322322 −0.930052 + 0.587438i −0.0518297 + 0.0327366i
323323 9.74245i 0.542084i
324324 9.58498 + 10.5555i 0.532499 + 0.586419i
325325 0 0
326326 −2.68428 + 1.54977i −0.148668 + 0.0858337i
327327 0.324650 1.53530i 0.0179532 0.0849021i
328328 5.26871i 0.290916i
329329 −18.2712 9.60185i −1.00732 0.529367i
330330 0 0
331331 11.4482 19.8289i 0.629252 1.08990i −0.358451 0.933549i 0.616695π-0.616695\pi
0.987702 0.156347i 0.0499718π-0.0499718\pi
332332 4.17809 + 7.23666i 0.229302 + 0.397163i
333333 11.6958 + 5.17785i 0.640926 + 0.283745i
334334 −2.48546 1.43498i −0.135998 0.0785186i
335335 0 0
336336 2.67286 + 7.21116i 0.145816 + 0.393401i
337337 −31.2616 −1.70293 −0.851464 0.524413i 0.824285π-0.824285\pi
−0.851464 + 0.524413i 0.824285π0.824285\pi
338338 2.65398 + 1.53228i 0.144358 + 0.0833449i
339339 −10.2212 + 11.3758i −0.555140 + 0.617851i
340340 0 0
341341 −0.793618 + 1.37459i −0.0429768 + 0.0744380i
342342 6.99413 5.10405i 0.378199 0.275995i
343343 −2.20308 18.3888i −0.118955 0.992900i
344344 15.1245i 0.815457i
345345 0 0
346346 6.39623 3.69287i 0.343864 0.198530i
347347 2.41336 1.39335i 0.129556 0.0747992i −0.433821 0.900999i 0.642835π-0.642835\pi
0.563377 + 0.826200i 0.309502π0.309502\pi
348348 3.13763 + 0.663476i 0.168195 + 0.0355661i
349349 16.5636i 0.886627i −0.896367 0.443314i 0.853803π-0.853803\pi
0.896367 0.443314i 0.146197π-0.146197\pi
350350 0 0
351351 17.7527 + 12.8127i 0.947568 + 0.683890i
352352 11.5614 20.0249i 0.616223 1.06733i
353353 −1.63849 2.83794i −0.0872078 0.151048i 0.819122 0.573619i 0.194461π-0.194461\pi
−0.906330 + 0.422571i 0.861128π0.861128\pi
354354 −8.45334 + 9.40826i −0.449290 + 0.500044i
355355 0 0
356356 −1.41750 −0.0751273
357357 −9.83290 1.67414i −0.520412 0.0886048i
358358 6.73469 0.355939
359359 14.7282 + 8.50335i 0.777326 + 0.448789i 0.835482 0.549518i 0.185189π-0.185189\pi
−0.0581557 + 0.998308i 0.518522π0.518522\pi
360360 0 0
361361 0.517332 + 0.896045i 0.0272280 + 0.0471603i
362362 −3.85644 + 6.67955i −0.202690 + 0.351069i
363363 −8.94314 + 2.91620i −0.469393 + 0.153061i
364364 9.43090 + 14.9313i 0.494313 + 0.782614i
365365 0 0
366366 −1.61535 + 7.63911i −0.0844355 + 0.399303i
367367 14.8236 8.55840i 0.773785 0.446745i −0.0604381 0.998172i 0.519250π-0.519250\pi
0.834223 + 0.551427i 0.185916π0.185916\pi
368368 0.937149 0.541063i 0.0488523 0.0282049i
369369 0.729192 + 6.80015i 0.0379602 + 0.354002i
370370 0 0
371371 10.1748 + 16.1091i 0.528249 + 0.836342i
372372 −0.333100 1.02152i −0.0172704 0.0529632i
373373 −14.4567 + 25.0397i −0.748538 + 1.29651i 0.199986 + 0.979799i 0.435910π0.435910\pi
−0.948524 + 0.316706i 0.897423π0.897423\pi
374374 2.84450 + 4.92683i 0.147086 + 0.254760i
375375 0 0
376376 −15.6145 9.01502i −0.805255 0.464914i
377377 4.92442 0.253621
378378 −3.94957 7.93614i −0.203144 0.408191i
379379 0.559557 0.0287425 0.0143712 0.999897i 0.495425π-0.495425\pi
0.0143712 + 0.999897i 0.495425π0.495425\pi
380380 0 0
381381 −20.3886 18.3192i −1.04454 0.938519i
382382 −4.56125 7.90031i −0.233374 0.404215i
383383 1.89920 3.28951i 0.0970447 0.168086i −0.813415 0.581683i 0.802394π-0.802394\pi
0.910460 + 0.413597i 0.135728π0.135728\pi
384384 6.01470 + 18.4453i 0.306937 + 0.941284i
385385 0 0
386386 3.99220i 0.203198i
387387 2.09323 + 19.5207i 0.106405 + 0.992291i
388388 5.35029 3.08899i 0.271620 0.156820i
389389 −7.88909 + 4.55477i −0.399993 + 0.230936i −0.686481 0.727148i 0.740845π-0.740845\pi
0.286488 + 0.958084i 0.407512π0.407512\pi
390390 0 0
391391 1.40348i 0.0709770i
392392 −1.28466 16.1268i −0.0648850 0.814527i
393393 27.2635 8.89016i 1.37526 0.448449i
394394 −4.21545 + 7.30137i −0.212371 + 0.367838i
395395 0 0
396396 7.79874 17.6159i 0.391901 0.885232i
397397 20.9910 + 12.1191i 1.05351 + 0.608242i 0.923629 0.383288i 0.125208π-0.125208\pi
0.129878 + 0.991530i 0.458542π0.458542\pi
398398 10.9309 0.547914
399399 19.2330 7.12883i 0.962854 0.356888i
400400 0 0
401401 −26.1500 15.0977i −1.30587 0.753944i −0.324466 0.945897i 0.605185π-0.605185\pi
−0.981404 + 0.191953i 0.938518π0.938518\pi
402402 −6.52190 + 7.25865i −0.325283 + 0.362028i
403403 −0.824921 1.42881i −0.0410923 0.0711739i
404404 −5.21509 + 9.03279i −0.259460 + 0.449398i
405405 0 0
406406 −1.76501 0.927545i −0.0875960 0.0460333i
407407 17.2824i 0.856656i
408408 −8.52439 1.80255i −0.422020 0.0892393i
409409 21.3618 12.3332i 1.05627 0.609839i 0.131874 0.991267i 0.457901π-0.457901\pi
0.924399 + 0.381427i 0.124567π0.124567\pi
410410 0 0
411411 −33.6571 7.11704i −1.66018 0.351058i
412412 15.5483i 0.766008i
413413 −25.3329 + 16.0007i −1.24655 + 0.787344i
414414 −1.00756 + 0.735280i −0.0495189 + 0.0361370i
415415 0 0
416416 12.0174 + 20.8148i 0.589202 + 1.02053i
417417 0.264822 0.294738i 0.0129684 0.0144334i
418418 −10.1317 5.84953i −0.495556 0.286110i
419419 −39.4615 −1.92782 −0.963911 0.266226i 0.914223π-0.914223\pi
−0.963911 + 0.266226i 0.914223π0.914223\pi
420420 0 0
421421 −30.9363 −1.50774 −0.753870 0.657023i 0.771815π-0.771815\pi
−0.753870 + 0.657023i 0.771815π0.771815\pi
422422 10.2921 + 5.94218i 0.501014 + 0.289261i
423423 −21.4008 9.47434i −1.04054 0.460658i
424424 8.32178 + 14.4137i 0.404141 + 0.699993i
425425 0 0
426426 −8.64066 + 2.81757i −0.418641 + 0.136512i
427427 −8.60467 + 16.3737i −0.416409 + 0.792379i
428428 29.7509i 1.43807i
429429 6.11994 28.9417i 0.295474 1.39732i
430430 0 0
431431 −26.6240 + 15.3713i −1.28243 + 0.740412i −0.977292 0.211896i 0.932036π-0.932036\pi
−0.305138 + 0.952308i 0.598703π0.598703\pi
432432 3.57198 + 7.95515i 0.171857 + 0.382742i
433433 2.95856i 0.142179i −0.997470 0.0710896i 0.977352π-0.977352\pi
0.997470 0.0710896i 0.0226476π-0.0226476\pi
434434 0.0265440 + 0.667491i 0.00127415 + 0.0320406i
435435 0 0
436436 0.717658 1.24302i 0.0343696 0.0595298i
437437 −1.44308 2.49949i −0.0690318 0.119567i
438438 4.35055 + 3.90897i 0.207877 + 0.186778i
439439 −15.0772 8.70485i −0.719598 0.415460i 0.0950070 0.995477i 0.469713π-0.469713\pi
−0.814605 + 0.580017i 0.803046π0.803046\pi
440440 0 0
441441 −3.89002 20.6366i −0.185239 0.982693i
442442 −5.91341 −0.281272
443443 27.5344 + 15.8970i 1.30820 + 0.755288i 0.981795 0.189942i 0.0608301π-0.0608301\pi
0.326403 + 0.945231i 0.394163π0.394163\pi
444444 8.70232 + 7.81904i 0.412994 + 0.371075i
445445 0 0
446446 0.202281 0.350362i 0.00957830 0.0165901i
447447 −5.34741 16.3989i −0.252924 0.775643i
448448 −0.0338286 0.850674i −0.00159825 0.0401906i
449449 2.99461i 0.141324i 0.997500 + 0.0706621i 0.0225112π0.0225112\pi
−0.997500 + 0.0706621i 0.977489π0.977489\pi
450450 0 0
451451 8.00279 4.62041i 0.376837 0.217567i
452452 −12.1140 + 6.99400i −0.569793 + 0.328970i
453453 1.81834 8.59907i 0.0854329 0.404019i
454454 3.50091i 0.164306i
455455 0 0
456456 17.0347 5.55471i 0.797721 0.260123i
457457 4.40252 7.62540i 0.205941 0.356701i −0.744491 0.667633i 0.767308π-0.767308\pi
0.950432 + 0.310932i 0.100641π0.100641\pi
458458 −4.63421 8.02669i −0.216543 0.375063i
459459 −11.2516 1.14671i −0.525181 0.0535237i
460460 0 0
461461 −31.9710 −1.48904 −0.744519 0.667602i 0.767321π-0.767321\pi
−0.744519 + 0.667602i 0.767321π0.767321\pi
462462 −7.64486 + 9.22056i −0.355671 + 0.428979i
463463 −6.94495 −0.322759 −0.161380 0.986892i 0.551594π-0.551594\pi
−0.161380 + 0.986892i 0.551594π0.551594\pi
464464 1.69865 + 0.980715i 0.0788577 + 0.0455285i
465465 0 0
466466 2.71801 + 4.70774i 0.125910 + 0.218082i
467467 12.2366 21.1944i 0.566241 0.980758i −0.430692 0.902499i 0.641731π-0.641731\pi
0.996933 0.0782589i 0.0249361π-0.0249361\pi
468468 11.8044 + 16.1757i 0.545658 + 0.747721i
469469 −19.5448 + 12.3449i −0.902495 + 0.570032i
470470 0 0
471471 28.5597 + 6.03916i 1.31596 + 0.278270i
472472 −22.6668 + 13.0867i −1.04332 + 0.602364i
473473 22.9730 13.2635i 1.05630 0.609854i
474474 4.10045 + 0.867071i 0.188340 + 0.0398259i
475475 0 0
476476 −8.07586 4.24401i −0.370157 0.194524i
477477 12.7355 + 17.4516i 0.583119 + 0.799054i
478478 −0.876459 + 1.51807i −0.0400883 + 0.0694350i
479479 −12.1451 21.0359i −0.554923 0.961156i −0.997909 0.0646271i 0.979414π-0.979414\pi
0.442986 0.896529i 0.353919π-0.353919\pi
480480 0 0
481481 15.5573 + 8.98204i 0.709354 + 0.409546i
482482 0.986217 0.0449209
483483 −2.77067 + 1.02697i −0.126070 + 0.0467286i
484484 −8.60377 −0.391080
485485 0 0
486486 −5.07148 8.67833i −0.230047 0.393657i
487487 −4.87823 8.44934i −0.221054 0.382876i 0.734075 0.679069i 0.237616π-0.237616\pi
−0.955128 + 0.296193i 0.904283π0.904283\pi
488488 −8.07879 + 13.9929i −0.365710 + 0.633427i
489489 −7.91563 + 2.58115i −0.357957 + 0.116724i
490490 0 0
491491 23.6689i 1.06816i 0.845434 + 0.534080i 0.179342π0.179342\pi
−0.845434 + 0.534080i 0.820658π0.820658\pi
492492 −1.29414 + 6.12011i −0.0583444 + 0.275916i
493493 −2.20308 + 1.27195i −0.0992219 + 0.0572858i
494494 10.5313 6.08026i 0.473826 0.273564i
495495 0 0
496496 0.657143i 0.0295066i
497497 −21.5132 + 0.855513i −0.965000 + 0.0383750i
498498 −1.82627 5.60064i −0.0818373 0.250971i
499499 −5.73534 + 9.93391i −0.256749 + 0.444703i −0.965369 0.260888i 0.915985π-0.915985\pi
0.708620 + 0.705590i 0.249318π0.249318\pi
500500 0 0
501501 −5.73445 5.15241i −0.256196 0.230193i
502502 −4.91988 2.84050i −0.219585 0.126778i
503503 −16.8580 −0.751659 −0.375830 0.926689i 0.622642π-0.622642\pi
−0.375830 + 0.926689i 0.622642π0.622642\pi
504504 −2.67906 18.1473i −0.119335 0.808347i
505505 0 0
506506 1.45955 + 0.842672i 0.0648849 + 0.0374613i
507507 6.12327 + 5.50176i 0.271944 + 0.244342i
508508 −12.5351 21.7115i −0.556157 0.963292i
509509 −1.47582 + 2.55620i −0.0654147 + 0.113302i −0.896878 0.442278i 0.854170π-0.854170\pi
0.831463 + 0.555580i 0.187504π0.187504\pi
510510 0 0
511511 7.39902 + 11.7144i 0.327313 + 0.518214i
512512 17.3304i 0.765902i
513513 21.2173 9.52689i 0.936767 0.420623i
514514 11.2262 6.48142i 0.495164 0.285883i
515515 0 0
516516 −3.71499 + 17.5685i −0.163543 + 0.773410i
517517 31.6230i 1.39078i
518518 −3.88424 6.14966i −0.170664 0.270201i
519519 18.8618 6.15051i 0.827941 0.269977i
520520 0 0
521521 7.91563 + 13.7103i 0.346790 + 0.600658i 0.985677 0.168642i 0.0539382π-0.0539382\pi
−0.638887 + 0.769300i 0.720605π0.720605\pi
522522 −2.06733 0.915228i −0.0904845 0.0400584i
523523 19.0179 + 10.9800i 0.831595 + 0.480122i 0.854398 0.519618i 0.173926π-0.173926\pi
−0.0228034 + 0.999740i 0.507259π0.507259\pi
524524 26.2289 1.14581
525525 0 0
526526 −5.64798 −0.246263
527527 0.738105 + 0.426145i 0.0321524 + 0.0185632i
528528 7.87487 8.76445i 0.342710 0.381424i
529529 −11.2921 19.5585i −0.490961 0.850370i
530530 0 0
531531 −27.4441 + 20.0277i −1.19097 + 0.869126i
532532 18.7462 0.745479i 0.812752 0.0323206i
533533 9.60532i 0.416053i
534534 0.977680 + 0.206738i 0.0423083 + 0.00894641i
535535 0 0
536536 −17.4879 + 10.0966i −0.755361 + 0.436108i
537537 17.6991 + 3.74260i 0.763771 + 0.161505i
538538 11.1221i 0.479508i
539539 −23.3689 + 16.0938i −1.00657 + 0.693208i
540540 0 0
541541 −2.34667 + 4.06456i −0.100891 + 0.174749i −0.912052 0.410074i 0.865503π-0.865503\pi
0.811161 + 0.584823i 0.198836π0.198836\pi
542542 −7.30101 12.6457i −0.313605 0.543181i
543543 −13.8469 + 15.4111i −0.594225 + 0.661352i
544544 −10.7527 6.20806i −0.461017 0.266168i
545545 0 0
546546 −4.32701 11.6739i −0.185179 0.499597i
547547 14.9485 0.639151 0.319575 0.947561i 0.396460π-0.396460\pi
0.319575 + 0.947561i 0.396460π0.396460\pi
548548 −27.2497 15.7326i −1.16405 0.672065i
549549 −8.49041 + 19.1782i −0.362362 + 0.818508i
550550 0 0
551551 2.61568 4.53049i 0.111432 0.193005i
552552 −2.45398 + 0.800202i −0.104448 + 0.0340589i
553553 8.78893 + 4.61874i 0.373743 + 0.196409i
554554 8.51867i 0.361924i
555555 0 0
556556 0.313862 0.181208i 0.0133107 0.00768494i
557557 1.06435 0.614501i 0.0450979 0.0260373i −0.477282 0.878750i 0.658378π-0.658378\pi
0.522379 + 0.852713i 0.325044π0.325044\pi
558558 0.0807609 + 0.753144i 0.00341888 + 0.0318831i
559559 27.5732i 1.16622i
560560 0 0
561561 4.73755 + 14.5287i 0.200020 + 0.613401i
562562 −10.5975 + 18.3554i −0.447028 + 0.774276i
563563 −2.10379 3.64387i −0.0886643 0.153571i 0.818282 0.574816i 0.194926π-0.194926\pi
−0.906947 + 0.421245i 0.861593π0.861593\pi
564564 −15.9233 14.3071i −0.670494 0.602440i
565565 0 0
566566 10.1953 0.428542
567567 −5.96937 23.0514i −0.250690 0.968067i
568568 −18.8072 −0.789132
569569 −22.3139 12.8829i −0.935447 0.540081i −0.0469169 0.998899i 0.514940π-0.514940\pi
−0.888530 + 0.458818i 0.848273π0.848273\pi
570570 0 0
571571 −12.3419 21.3768i −0.516492 0.894591i −0.999817 0.0191497i 0.993904π-0.993904\pi
0.483324 0.875441i 0.339429π-0.339429\pi
572572 13.5285 23.4320i 0.565655 0.979743i
573573 −7.59681 23.2972i −0.317361 0.973253i
574574 1.80922 3.44274i 0.0755154 0.143697i
575575 0 0
576576 −0.102925 0.959834i −0.00428852 0.0399931i
577577 4.96565 2.86692i 0.206723 0.119351i −0.393065 0.919511i 0.628585π-0.628585\pi
0.599787 + 0.800159i 0.295252π0.295252\pi
578578 −6.84757 + 3.95345i −0.284822 + 0.164442i
579579 −2.21855 + 10.4917i −0.0921996 + 0.436020i
580580 0 0
581581 −0.554521 13.9443i −0.0230054 0.578507i
582582 −4.14073 + 1.35022i −0.171639 + 0.0559684i
583583 14.5956 25.2804i 0.604489 1.04701i
584584 6.05152 + 10.4815i 0.250414 + 0.433729i
585585 0 0
586586 11.6038 + 6.69944i 0.479347 + 0.276751i
587587 −31.0435 −1.28130 −0.640652 0.767832i 0.721336π-0.721336\pi
−0.640652 + 0.767832i 0.721336π0.721336\pi
588588 2.46894 19.0484i 0.101818 0.785542i
589589 −1.75268 −0.0722178
590590 0 0
591591 −15.1359 + 16.8457i −0.622608 + 0.692941i
592592 3.57760 + 6.19659i 0.147039 + 0.254678i
593593 16.2884 28.2124i 0.668885 1.15854i −0.309331 0.950954i 0.600105π-0.600105\pi
0.978216 0.207588i 0.0665614π-0.0665614\pi
594594 −7.94818 + 11.0126i −0.326118 + 0.451854i
595595 0 0
596596 15.7766i 0.646236i
597597 28.7268 + 6.07449i 1.17571 + 0.248612i
598598 −1.51712 + 0.875911i −0.0620397 + 0.0358187i
599599 31.8553 18.3917i 1.30157 0.751463i 0.320899 0.947113i 0.396015π-0.396015\pi
0.980674 + 0.195650i 0.0626817π0.0626817\pi
600600 0 0
601601 42.5075i 1.73392i −0.498380 0.866959i 0.666071π-0.666071\pi
0.498380 0.866959i 0.333929π-0.333929\pi
602602 5.19358 9.88279i 0.211675 0.402793i
603603 −21.1736 + 15.4517i −0.862257 + 0.629242i
604604 4.01954 6.96205i 0.163553 0.283282i
605605 0 0
606606 4.91436 5.46951i 0.199632 0.222184i
607607 −14.6810 8.47607i −0.595883 0.344033i 0.171537 0.985178i 0.445127π-0.445127\pi
−0.767420 + 0.641144i 0.778460π0.778460\pi
608608 25.5329 1.03550
609609 −4.12307 3.41848i −0.167075 0.138524i
610610 0 0
611611 −28.4666 16.4352i −1.15163 0.664896i
612612 −9.45913 4.18765i −0.382363 0.169276i
613613 17.3421 + 30.0373i 0.700439 + 1.21320i 0.968312 + 0.249742i 0.0803459π0.0803459\pi
−0.267873 + 0.963454i 0.586321π0.586321\pi
614614 −4.18664 + 7.25148i −0.168959 + 0.292646i
615615 0 0
616616 −20.9558 + 13.2361i −0.844333 + 0.533296i
617617 45.7116i 1.84028i 0.391590 + 0.920140i 0.371925π0.371925\pi
−0.391590 + 0.920140i 0.628075π0.628075\pi
618618 −2.26766 + 10.7240i −0.0912188 + 0.431381i
619619 34.2356 19.7659i 1.37604 0.794459i 0.384363 0.923182i 0.374421π-0.374421\pi
0.991681 + 0.128723i 0.0410877π0.0410877\pi
620620 0 0
621621 −3.05653 + 1.37243i −0.122654 + 0.0550736i
622622 0.295096i 0.0118323i
623623 2.09556 + 1.10126i 0.0839570 + 0.0441209i
624624 3.79689 + 11.6439i 0.151997 + 0.466130i
625625 0 0
626626 8.94408 + 15.4916i 0.357477 + 0.619169i
627627 −23.3758 21.0032i −0.933540 0.838787i
628628 23.1228 + 13.3499i 0.922698 + 0.532720i
629629 −9.28004 −0.370020
630630 0 0
631631 −21.1685 −0.842703 −0.421351 0.906897i 0.638444π-0.638444\pi
−0.421351 + 0.906897i 0.638444π0.638444\pi
632632 7.51097 + 4.33646i 0.298770 + 0.172495i
633633 23.7461 + 21.3359i 0.943821 + 0.848024i
634634 −1.45835 2.52594i −0.0579187 0.100318i
635635 0 0
636636 6.12612 + 18.7870i 0.242916 + 0.744952i
637637 −2.34204 29.4006i −0.0927951 1.16489i
638638 3.05480i 0.120941i
639639 −24.2738 + 2.60292i −0.960257 + 0.102970i
640640 0 0
641641 30.6083 17.6717i 1.20896 0.697991i 0.246424 0.969162i 0.420744π-0.420744\pi
0.962531 + 0.271171i 0.0874109π0.0874109\pi
642642 4.33908 20.5199i 0.171250 0.809854i
643643 26.0538i 1.02746i −0.857951 0.513731i 0.828263π-0.828263\pi
0.857951 0.513731i 0.171737π-0.171737\pi
644644 −2.70055 + 0.107392i −0.106416 + 0.00423185i
645645 0 0
646646 −3.14099 + 5.44036i −0.123581 + 0.214048i
647647 20.4213 + 35.3707i 0.802844 + 1.39057i 0.917737 + 0.397188i 0.130014π0.130014\pi
−0.114894 + 0.993378i 0.536653π0.536653\pi
648648 −4.41016 20.3273i −0.173248 0.798530i
649649 39.7555 + 22.9528i 1.56054 + 0.900977i
650650 0 0
651651 −0.301179 + 1.76895i −0.0118041 + 0.0693306i
652652 −7.61525 −0.298236
653653 20.7918 + 12.0041i 0.813645 + 0.469758i 0.848220 0.529644i 0.177674π-0.177674\pi
−0.0345747 + 0.999402i 0.511008π0.511008\pi
654654 −0.676274 + 0.752669i −0.0264444 + 0.0294317i
655655 0 0
656656 −1.91293 + 3.31329i −0.0746874 + 0.129362i
657657 9.26115 + 12.6906i 0.361312 + 0.495109i
658658 7.10731 + 11.2525i 0.277072 + 0.438670i
659659 38.7398i 1.50909i 0.656248 + 0.754545i 0.272142π0.272142\pi
−0.656248 + 0.754545i 0.727858π0.727858\pi
660660 0 0
661661 44.0826 25.4511i 1.71461 0.989933i 0.786539 0.617541i 0.211871π-0.211871\pi
0.928075 0.372392i 0.121462π-0.121462\pi
662662 −12.7858 + 7.38188i −0.496934 + 0.286905i
663663 −15.5407 3.28620i −0.603551 0.127625i
664664 12.1903i 0.473076i
665665 0 0
666666 −4.86179 6.66217i −0.188391 0.258154i
667667 −0.376810 + 0.652654i −0.0145901 + 0.0252709i
668668 −3.52560 6.10653i −0.136410 0.236269i
669669 0.726307 0.808354i 0.0280807 0.0312528i
670670 0 0
671671 28.3389 1.09401
672672 4.38756 25.7699i 0.169254 0.994097i
673673 −3.33192 −0.128436 −0.0642181 0.997936i 0.520455π-0.520455\pi
−0.0642181 + 0.997936i 0.520455π0.520455\pi
674674 17.4570 + 10.0788i 0.672420 + 0.388222i
675675 0 0
676676 3.76466 + 6.52057i 0.144794 + 0.250791i
677677 16.1861 28.0352i 0.622083 1.07748i −0.367014 0.930215i 0.619620π-0.619620\pi
0.989097 0.147264i 0.0470467π-0.0470467\pi
678678 9.37531 3.05713i 0.360057 0.117408i
679679 −10.3094 + 0.409974i −0.395640 + 0.0157334i
680680 0 0
681681 1.94552 9.20055i 0.0745526 0.352566i
682682 0.886341 0.511729i 0.0339398 0.0195951i
683683 −18.8566 + 10.8868i −0.721526 + 0.416573i −0.815314 0.579019i 0.803436π-0.803436\pi
0.0937881 + 0.995592i 0.470102π0.470102\pi
684684 21.1518 2.26814i 0.808758 0.0867245i
685685 0 0
686686 −4.69835 + 10.9789i −0.179384 + 0.419176i
687687 −7.71833 23.6698i −0.294473 0.903060i
688688 −5.49130 + 9.51121i −0.209354 + 0.362611i
689689 15.1713 + 26.2775i 0.577982 + 1.00109i
690690 0 0
691691 5.15554 + 2.97655i 0.196126 + 0.113233i 0.594847 0.803839i 0.297213π-0.297213\pi
−0.398721 + 0.917072i 0.630546π0.630546\pi
692692 18.1460 0.689809
693693 −25.2151 + 19.9837i −0.957842 + 0.759116i
694694 −1.79689 −0.0682088
695695 0 0
696696 −3.48011 3.12688i −0.131913 0.118524i
697697 −2.48100 4.29722i −0.0939747 0.162769i
698698 −5.34014 + 9.24939i −0.202127 + 0.350095i
699699 4.52688 + 13.8826i 0.171222 + 0.525088i
700700 0 0
701701 19.3393i 0.730434i −0.930922 0.365217i 0.880995π-0.880995\pi
0.930922 0.365217i 0.119005π-0.119005\pi
702702 −5.78257 12.8783i −0.218249 0.486062i
703703 16.5270 9.54188i 0.623329 0.359879i
704704 −1.12958 + 0.652166i −0.0425728 + 0.0245794i
705705 0 0
706706 2.11301i 0.0795242i
707707 14.7273 9.30205i 0.553878 0.349840i
708708 −29.5441 + 9.63383i −1.11034 + 0.362061i
709709 −16.9012 + 29.2738i −0.634739 + 1.09940i 0.351831 + 0.936063i 0.385559π0.385559\pi
−0.986570 + 0.163337i 0.947774π0.947774\pi
710710 0 0
711711 10.2943 + 4.55741i 0.386068 + 0.170916i
712712 1.79086 + 1.03395i 0.0671152 + 0.0387490i
713713 0.252487 0.00945573
714714 4.95112 + 4.10502i 0.185291 + 0.153627i
715715 0 0
716716 14.3297 + 8.27324i 0.535525 + 0.309185i
717717 −3.14700 + 3.50250i −0.117527 + 0.130803i
718718 −5.48301 9.49685i −0.204624 0.354419i
719719 13.7118 23.7495i 0.511363 0.885707i −0.488550 0.872536i 0.662474π-0.662474\pi
0.999913 0.0131713i 0.00419267π-0.00419267\pi
720720 0 0
721721 −12.0795 + 22.9858i −0.449862 + 0.856036i
722722 0.667157i 0.0248290i
723723 2.59182 + 0.548060i 0.0963909 + 0.0203826i
724724 −16.4110 + 9.47490i −0.609910 + 0.352132i
725725 0 0
726726 5.93420 + 1.25483i 0.220239 + 0.0465712i
727727 6.14612i 0.227947i 0.993484 + 0.113973i 0.0363579π0.0363579\pi
−0.993484 + 0.113973i 0.963642π0.963642\pi
728728 −1.02372 25.7432i −0.0379418 0.954105i
729729 −8.50535 25.6254i −0.315013 0.949087i
730730 0 0
731731 −7.12202 12.3357i −0.263417 0.456252i
732732 −12.8213 + 14.2697i −0.473889 + 0.527422i
733733 14.5795 + 8.41748i 0.538506 + 0.310907i 0.744473 0.667652i 0.232701π-0.232701\pi
−0.205967 + 0.978559i 0.566034π0.566034\pi
734734 −11.0370 −0.407384
735735 0 0
736736 −3.67822 −0.135581
737737 30.6721 + 17.7085i 1.12982 + 0.652302i
738738 1.78520 4.03242i 0.0657139 0.148436i
739739 −19.3419 33.5012i −0.711503 1.23236i −0.964293 0.264838i 0.914681π-0.914681\pi
0.252790 0.967521i 0.418652π-0.418652\pi
740740 0 0
741741 31.0557 10.1267i 1.14086 0.372015i
742742 −0.488178 12.2760i −0.0179216 0.450666i
743743 39.3563i 1.44384i −0.691976 0.721920i 0.743260π-0.743260\pi
0.691976 0.721920i 0.256740π-0.256740\pi
744744 −0.324280 + 1.53355i −0.0118887 + 0.0562225i
745745 0 0
746746 16.1457 9.32174i 0.591137 0.341293i
747747 −1.68714 15.7336i −0.0617294 0.575664i
748748 13.9773i 0.511062i
749749 23.1135 43.9824i 0.844549 1.60708i
750750 0 0
751751 −16.1416 + 27.9580i −0.589014 + 1.02020i 0.405347 + 0.914163i 0.367151π0.367151\pi
−0.994362 + 0.106040i 0.966183π0.966183\pi
752752 −6.54623 11.3384i −0.238717 0.413469i
753753 −11.3512 10.1990i −0.413659 0.371673i
754754 −2.74989 1.58765i −0.100145 0.0578187i
755755 0 0
756756 1.34551 21.7379i 0.0489359 0.790600i
757757 40.0667 1.45625 0.728124 0.685446i 0.240393π-0.240393\pi
0.728124 + 0.685446i 0.240393π0.240393\pi
758758 −0.312467 0.180403i −0.0113493 0.00655252i
759759 3.36748 + 3.02568i 0.122232 + 0.109825i
760760 0 0
761761 6.58977 11.4138i 0.238879 0.413750i −0.721514 0.692400i 0.756553π-0.756553\pi
0.960393 + 0.278649i 0.0898868π0.0898868\pi
762762 5.47920 + 16.8031i 0.198491 + 0.608712i
763763 −2.02665 + 1.28007i −0.0733698 + 0.0463417i
764764 22.4131i 0.810877i
765765 0 0
766766 −2.12110 + 1.22462i −0.0766384 + 0.0442472i
767767 −41.3236 + 23.8582i −1.49211 + 0.861469i
768768 2.81871 13.3299i 0.101711 0.481002i
769769 12.7709i 0.460530i −0.973128 0.230265i 0.926041π-0.926041\pi
0.973128 0.230265i 0.0739593π-0.0739593\pi
770770 0 0
771771 33.1047 10.7949i 1.19224 0.388768i
772772 −4.90423 + 8.49437i −0.176507 + 0.305719i
773773 9.09428 + 15.7518i 0.327099 + 0.566551i 0.981935 0.189219i 0.0605957π-0.0605957\pi
−0.654836 + 0.755771i 0.727262π0.727262\pi
774774 5.12462 11.5756i 0.184201 0.416075i
775775 0 0
776776 −9.01267 −0.323536
777777 −6.79047 18.3201i −0.243607 0.657231i
778778 5.87388 0.210589
779779 8.83694 + 5.10201i 0.316616 + 0.182798i
780780 0 0
781781 16.4930 + 28.5667i 0.590167 + 1.02220i
782782 0.452486 0.783728i 0.0161809 0.0280261i
783783 −4.92442 3.55412i −0.175985 0.127014i
784784 5.04735 10.6080i 0.180263 0.378856i
785785 0 0
786786 −18.0906 3.82540i −0.645272 0.136447i
787787 −1.07265 + 0.619297i −0.0382360 + 0.0220756i −0.518996 0.854777i 0.673694π-0.673694\pi
0.480760 + 0.876852i 0.340361π0.340361\pi
788788 −17.9388 + 10.3569i −0.639042 + 0.368951i
789789 −14.8431 3.13869i −0.528430 0.111740i
790790 0 0
791791 23.3423 0.928251i 0.829958 0.0330048i
792792 −22.7022 + 16.5672i −0.806689 + 0.588690i
793793 −14.7283 + 25.5102i −0.523019 + 0.905895i
794794 −7.81449 13.5351i −0.277326 0.480343i
795795 0 0
796796 23.2580 + 13.4280i 0.824359 + 0.475944i
797797 −51.4416 −1.82216 −0.911078 0.412235i 0.864748π-0.864748\pi
−0.911078 + 0.412235i 0.864748π0.864748\pi
798798 −13.0384 2.21990i −0.461555 0.0785837i
799799 16.9805 0.600725
800800 0 0
801801 2.45450 + 1.08663i 0.0867254 + 0.0383942i
802802 9.73510 + 16.8617i 0.343758 + 0.595407i
803803 10.6138 18.3836i 0.374553 0.648745i
804804 −22.7938 + 7.43268i −0.803876 + 0.262130i
805805 0 0
806806 1.06383i 0.0374718i
807807 −6.18077 + 29.2294i −0.217574 + 1.02892i
808808 13.1774 7.60797i 0.463579 0.267647i
809809 2.44518 1.41172i 0.0859679 0.0496336i −0.456400 0.889775i 0.650861π-0.650861\pi
0.542368 + 0.840141i 0.317528π0.317528\pi
810810 0 0
811811 0.162805i 0.00571687i −0.999996 0.00285843i 0.999090π-0.999090\pi
0.999996 0.00285843i 0.000909869π-0.000909869\pi
812812 −2.61604 4.14180i −0.0918050 0.145349i
813813 −12.1599 37.2909i −0.426467 1.30785i
814814 −5.57189 + 9.65080i −0.195295 + 0.338260i
815815 0 0
816816 −4.70621 4.22853i −0.164750 0.148028i
817817 25.3675 + 14.6459i 0.887496 + 0.512396i
818818 −15.9051 −0.556108
819819 −4.88415 33.0842i −0.170666 1.15606i
820820 0 0
821821 43.3765 + 25.0434i 1.51385 + 0.874022i 0.999868 + 0.0162217i 0.00516375π0.00516375\pi
0.513983 + 0.857801i 0.328170π0.328170\pi
822822 16.5002 + 14.8254i 0.575509 + 0.517096i
823823 19.1132 + 33.1050i 0.666243 + 1.15397i 0.978947 + 0.204116i 0.0654319π0.0654319\pi
−0.312704 + 0.949851i 0.601235π0.601235\pi
824824 −11.3412 + 19.6435i −0.395090 + 0.684315i
825825 0 0
826826 19.3050 0.767700i 0.671708 0.0267117i
827827 7.13112i 0.247973i −0.992284 0.123987i 0.960432π-0.960432\pi
0.992284 0.123987i 0.0395680π-0.0395680\pi
828828 −3.04708 + 0.326744i −0.105894 + 0.0113551i
829829 −0.876338 + 0.505954i −0.0304365 + 0.0175725i −0.515141 0.857105i 0.672260π-0.672260\pi
0.484705 + 0.874678i 0.338927π0.338927\pi
830830 0 0
831831 4.73399 22.3875i 0.164220 0.776612i
832832 1.35578i 0.0470032i
833833 8.64180 + 12.5483i 0.299421 + 0.434772i
834834 −0.242906 + 0.0792075i −0.00841115 + 0.00274273i
835835 0 0
836836 −14.3717 24.8925i −0.497056 0.860927i
837837 −0.206294 + 2.02418i −0.00713056 + 0.0699658i
838838 22.0360 + 12.7225i 0.761222 + 0.439492i
839839 29.5215 1.01920 0.509598 0.860412i 0.329794π-0.329794\pi
0.509598 + 0.860412i 0.329794π0.329794\pi
840840 0 0
841841 27.6340 0.952897
842842 17.2754 + 9.97394i 0.595348 + 0.343725i
843843 −38.0512 + 42.3496i −1.31055 + 1.45860i
844844 14.5993 + 25.2868i 0.502530 + 0.870408i
845845 0 0
846846 8.89603 + 12.1903i 0.305852 + 0.419112i
847847 12.7194 + 6.68427i 0.437044 + 0.229674i
848848 12.0857i 0.415024i
849849 26.7938 + 5.66576i 0.919562 + 0.194448i
850850 0 0
851851 −2.38085 + 1.37459i −0.0816146 + 0.0471202i
852852 −21.8463 4.61957i −0.748443 0.158264i
853853 22.0904i 0.756362i −0.925732 0.378181i 0.876550π-0.876550\pi
0.925732 0.378181i 0.123450π-0.123450\pi
854854 10.0839 6.36920i 0.345065 0.217950i
855855 0 0
856856 21.7009 37.5871i 0.741722 1.28470i
857857 −7.16559 12.4112i −0.244772 0.423957i 0.717296 0.696769i 0.245380π-0.245380\pi
−0.962067 + 0.272812i 0.912046π0.912046\pi
858858 −12.7484 + 14.1885i −0.435223 + 0.484387i
859859 −23.7901 13.7352i −0.811709 0.468640i 0.0358402 0.999358i 0.488589π-0.488589\pi
−0.847549 + 0.530717i 0.821923π0.821923\pi
860860 0 0
861861 6.66791 8.04225i 0.227242 0.274079i
862862 19.8231 0.675176
863863 14.0492 + 8.11130i 0.478240 + 0.276112i 0.719683 0.694303i 0.244287π-0.244287\pi
−0.241443 + 0.970415i 0.577621π0.577621\pi
864864 3.00528 29.4881i 0.102242 1.00321i
865865 0 0
866866 −0.953847 + 1.65211i −0.0324131 + 0.0561411i
867867 −20.1927 + 6.58451i −0.685782 + 0.223622i
868868 −0.763502 + 1.45286i −0.0259149 + 0.0493131i
869869 15.2115i 0.516014i
870870 0 0
871871 −31.8819 + 18.4070i −1.08028 + 0.623698i
872872 −1.81336 + 1.04695i −0.0614083 + 0.0354541i
873873 −11.6324 + 1.24736i −0.393696 + 0.0422167i
874874 1.86101i 0.0629496i
875875 0 0
876876 4.45486 + 13.6617i 0.150516 + 0.461587i
877877 −22.2463 + 38.5317i −0.751204 + 1.30112i 0.196036 + 0.980597i 0.437193π0.437193\pi
−0.947240 + 0.320527i 0.896140π0.896140\pi
878878 5.61294 + 9.72189i 0.189427 + 0.328098i
879879 26.7722 + 24.0549i 0.903004 + 0.811351i
880880 0 0
881881 −0.841670 −0.0283566 −0.0141783 0.999899i 0.504513π-0.504513\pi
−0.0141783 + 0.999899i 0.504513π0.504513\pi
882882 −4.48103 + 12.7780i −0.150884 + 0.430257i
883883 51.7706 1.74222 0.871110 0.491088i 0.163400π-0.163400\pi
0.871110 + 0.491088i 0.163400π0.163400\pi
884884 −12.5822 7.26434i −0.423185 0.244326i
885885 0 0
886886 −10.2505 17.7543i −0.344371 0.596468i
887887 27.9867 48.4743i 0.939700 1.62761i 0.173669 0.984804i 0.444438π-0.444438\pi
0.766031 0.642804i 0.222229π-0.222229\pi
888888 −5.29107 16.2262i −0.177557 0.544514i
889889 1.66368 + 41.8358i 0.0557980 + 1.40313i
890890 0 0
891891 −27.0081 + 24.5248i −0.904806 + 0.821611i
892892 0.860804 0.496986i 0.0288219 0.0166403i
893893 −30.2409 + 17.4596i −1.01197 + 0.584262i
894894 −2.30097 + 10.8815i −0.0769560 + 0.363931i
895895 0 0
896896 13.7864 26.2339i 0.460571 0.876413i
897897 −4.47383 + 1.45884i −0.149377 + 0.0487092i
898898 0.965470 1.67224i 0.0322182 0.0558035i
899899 0.228825 + 0.396337i 0.00763175 + 0.0132186i
900900 0 0
901901 −13.5747 7.83734i −0.452238 0.261100i
902902 −5.95854 −0.198398
903903 19.1410 23.0863i 0.636974 0.768263i
904904 20.4062 0.678701
905905 0 0
906906 −3.78776 + 4.21564i −0.125840 + 0.140055i
907907 −18.1332 31.4075i −0.602102 1.04287i −0.992502 0.122226i 0.960997π-0.960997\pi
0.390401 0.920645i 0.372336π-0.372336\pi
908908 4.30070 7.44902i 0.142724 0.247205i
909909 15.9547 11.6431i 0.529183 0.386178i
910910 0 0
911911 5.35784i 0.177513i −0.996053 0.0887565i 0.971711π-0.971711\pi
0.996053 0.0887565i 0.0282893π-0.0282893\pi
912912 12.7292 + 2.69169i 0.421507 + 0.0891308i
913913 −18.5162 + 10.6903i −0.612797 + 0.353798i
914914 −4.91690 + 2.83877i −0.162637 + 0.0938983i
915915 0 0
916916 22.7716i 0.752396i
917917 −38.7755 20.3772i −1.28048 0.672916i
918918 5.91341 + 4.26790i 0.195172 + 0.140862i
919919 10.0571 17.4194i 0.331754 0.574615i −0.651102 0.758990i 0.725693π-0.725693\pi
0.982856 + 0.184376i 0.0590263π0.0590263\pi
920920 0 0
921921 −15.0325 + 16.7306i −0.495337 + 0.551292i
922922 17.8532 + 10.3075i 0.587963 + 0.339461i
923923 −34.2872 −1.12858
924924 −27.5933 + 10.2276i −0.907752 + 0.336464i
925925 0 0
926926 3.87818 + 2.23907i 0.127445 + 0.0735804i
927927 −11.9190 + 26.9229i −0.391473 + 0.884264i
928928 −3.33351 5.77382i −0.109428 0.189535i
929929 −3.39903 + 5.88728i −0.111518 + 0.193156i −0.916383 0.400303i 0.868905π-0.868905\pi
0.804864 + 0.593459i 0.202238π0.202238\pi
930930 0 0
931931 −28.2927 13.4619i −0.927256 0.441195i
932932 13.3558i 0.437483i
933933 0.163991 0.775525i 0.00536881 0.0253896i
934934 −13.6662 + 7.89021i −0.447173 + 0.258176i
935935 0 0
936936 −3.11471 29.0466i −0.101808 0.949417i
937937 44.1327i 1.44175i −0.693063 0.720877i 0.743739π-0.743739\pi
0.693063 0.720877i 0.256261π-0.256261\pi
938938 14.8942 0.592295i 0.486312 0.0193391i
939939 14.8965 + 45.6830i 0.486128 + 1.49081i
940940 0 0
941941 −4.53288 7.85118i −0.147768 0.255941i 0.782634 0.622482i 0.213875π-0.213875\pi
−0.930402 + 0.366540i 0.880542π0.880542\pi
942942 −14.0012 12.5801i −0.456184 0.409882i
943943 −1.27303 0.734986i −0.0414557 0.0239344i
944944 −19.0057 −0.618584
945945 0 0
946946 −17.1047 −0.556122
947947 30.7330 + 17.7437i 0.998689 + 0.576593i 0.907860 0.419273i 0.137715π-0.137715\pi
0.0908285 + 0.995867i 0.471048π0.471048\pi
948948 7.65955 + 6.88211i 0.248771 + 0.223521i
949949 11.0325 + 19.1088i 0.358129 + 0.620297i
950950 0 0
951951 −2.42891 7.44873i −0.0787627 0.241542i
952952 7.10731 + 11.2525i 0.230349 + 0.364697i
953953 10.8726i 0.352198i 0.984373 + 0.176099i 0.0563478π0.0563478\pi
−0.984373 + 0.176099i 0.943652π0.943652\pi
954954 −1.48529 13.8513i −0.0480882 0.448451i
955955 0 0
956956 −3.72976 + 2.15338i −0.120629 + 0.0696452i
957957 −1.69761 + 8.02816i −0.0548761 + 0.259514i
958958 15.6625i 0.506031i
959959 28.0620 + 44.4287i 0.906169 + 1.43468i
960960 0 0
961961 −15.4233 + 26.7140i −0.497527 + 0.861742i
962962 −5.79167 10.0315i −0.186731 0.323428i
963963 22.8066 51.5158i 0.734932 1.66007i
964964 2.09841 + 1.21152i 0.0675853 + 0.0390204i
965965 0 0
966966 1.87829 + 0.319795i 0.0604330 + 0.0102892i
967967 −21.3855 −0.687711 −0.343855 0.939023i 0.611733π-0.611733\pi
−0.343855 + 0.939023i 0.611733π0.611733\pi
968968 10.8699 + 6.27575i 0.349373 + 0.201710i
969969 −11.2780 + 12.5520i −0.362301 + 0.403228i
970970 0 0
971971 −4.43174 + 7.67600i −0.142221 + 0.246335i −0.928333 0.371750i 0.878758π-0.878758\pi
0.786112 + 0.618085i 0.212091π0.212091\pi
972972 −0.129881 24.6953i −0.00416593 0.792102i
973973 −0.604779 + 0.0240502i −0.0193883 + 0.000771013i
974974 6.29102i 0.201577i
975975 0 0
976976 −10.1609 + 5.86639i −0.325242 + 0.187779i
977977 −0.633128 + 0.365536i −0.0202555 + 0.0116945i −0.510094 0.860119i 0.670389π-0.670389\pi
0.489838 + 0.871813i 0.337056π0.337056\pi
978978 5.25241 + 1.11066i 0.167953 + 0.0355150i
979979 3.62691i 0.115916i
980980 0 0
981981 −2.19555 + 1.60223i −0.0700986 + 0.0511553i
982982 7.63091 13.2171i 0.243512 0.421775i
983983 1.86607 + 3.23213i 0.0595184 + 0.103089i 0.894249 0.447569i 0.147710π-0.147710\pi
−0.834731 + 0.550658i 0.814377π0.814377\pi
984984 6.09913 6.78812i 0.194433 0.216397i
985985 0 0
986986 1.64032 0.0522385
987987 12.4251 + 33.5219i 0.395495 + 1.06701i
988988 29.8772 0.950520
989989 −3.65439 2.10987i −0.116203 0.0670898i
990990 0 0
991991 2.74255 + 4.75024i 0.0871200 + 0.150896i 0.906293 0.422651i 0.138900π-0.138900\pi
−0.819173 + 0.573547i 0.805567π0.805567\pi
992992 −1.11684 + 1.93442i −0.0354596 + 0.0614178i
993993 −37.7039 + 12.2946i −1.19650 + 0.390158i
994994 12.2892 + 6.45819i 0.389790 + 0.204841i
995995 0 0
996996 2.99428 14.1602i 0.0948774 0.448683i
997997 −4.39264 + 2.53609i −0.139116 + 0.0803189i −0.567943 0.823068i 0.692261π-0.692261\pi
0.428826 + 0.903387i 0.358927π0.358927\pi
998998 6.40544 3.69818i 0.202761 0.117064i
999999 −9.07472 20.2103i −0.287111 0.639425i
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 525.2.t.j.26.5 24
3.2 odd 2 inner 525.2.t.j.26.7 24
5.2 odd 4 105.2.p.a.89.8 yes 24
5.3 odd 4 105.2.p.a.89.5 yes 24
5.4 even 2 inner 525.2.t.j.26.8 24
7.3 odd 6 inner 525.2.t.j.101.7 24
15.2 even 4 105.2.p.a.89.6 yes 24
15.8 even 4 105.2.p.a.89.7 yes 24
15.14 odd 2 inner 525.2.t.j.26.6 24
21.17 even 6 inner 525.2.t.j.101.5 24
35.2 odd 12 735.2.g.b.734.9 24
35.3 even 12 105.2.p.a.59.6 yes 24
35.12 even 12 735.2.g.b.734.12 24
35.13 even 4 735.2.p.f.509.6 24
35.17 even 12 105.2.p.a.59.7 yes 24
35.18 odd 12 735.2.p.f.374.5 24
35.23 odd 12 735.2.g.b.734.16 24
35.24 odd 6 inner 525.2.t.j.101.6 24
35.27 even 4 735.2.p.f.509.7 24
35.32 odd 12 735.2.p.f.374.8 24
35.33 even 12 735.2.g.b.734.13 24
105.2 even 12 735.2.g.b.734.14 24
105.17 odd 12 105.2.p.a.59.5 24
105.23 even 12 735.2.g.b.734.11 24
105.32 even 12 735.2.p.f.374.6 24
105.38 odd 12 105.2.p.a.59.8 yes 24
105.47 odd 12 735.2.g.b.734.15 24
105.53 even 12 735.2.p.f.374.7 24
105.59 even 6 inner 525.2.t.j.101.8 24
105.62 odd 4 735.2.p.f.509.5 24
105.68 odd 12 735.2.g.b.734.10 24
105.83 odd 4 735.2.p.f.509.8 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.p.a.59.5 24 105.17 odd 12
105.2.p.a.59.6 yes 24 35.3 even 12
105.2.p.a.59.7 yes 24 35.17 even 12
105.2.p.a.59.8 yes 24 105.38 odd 12
105.2.p.a.89.5 yes 24 5.3 odd 4
105.2.p.a.89.6 yes 24 15.2 even 4
105.2.p.a.89.7 yes 24 15.8 even 4
105.2.p.a.89.8 yes 24 5.2 odd 4
525.2.t.j.26.5 24 1.1 even 1 trivial
525.2.t.j.26.6 24 15.14 odd 2 inner
525.2.t.j.26.7 24 3.2 odd 2 inner
525.2.t.j.26.8 24 5.4 even 2 inner
525.2.t.j.101.5 24 21.17 even 6 inner
525.2.t.j.101.6 24 35.24 odd 6 inner
525.2.t.j.101.7 24 7.3 odd 6 inner
525.2.t.j.101.8 24 105.59 even 6 inner
735.2.g.b.734.9 24 35.2 odd 12
735.2.g.b.734.10 24 105.68 odd 12
735.2.g.b.734.11 24 105.23 even 12
735.2.g.b.734.12 24 35.12 even 12
735.2.g.b.734.13 24 35.33 even 12
735.2.g.b.734.14 24 105.2 even 12
735.2.g.b.734.15 24 105.47 odd 12
735.2.g.b.734.16 24 35.23 odd 12
735.2.p.f.374.5 24 35.18 odd 12
735.2.p.f.374.6 24 105.32 even 12
735.2.p.f.374.7 24 105.53 even 12
735.2.p.f.374.8 24 35.32 odd 12
735.2.p.f.509.5 24 105.62 odd 4
735.2.p.f.509.6 24 35.13 even 4
735.2.p.f.509.7 24 35.27 even 4
735.2.p.f.509.8 24 105.83 odd 4