Properties

Label 56.2.m.a.19.3
Level 5656
Weight 22
Character 56.19
Analytic conductor 0.4470.447
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [56,2,Mod(3,56)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(56, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("56.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 56=237 56 = 2^{3} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 56.m (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: 0.4471622513190.447162251319
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.144054149089536.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x123x11+x9+48x8189x7+431x6654x5+624x4340x3+96x212x+4 x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 19.3
Root 0.609850+0.457915i0.609850 + 0.457915i of defining polynomial
Character χ\chi == 56.19
Dual form 56.2.m.a.3.4

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+(0.1699381.40397i)q2+(0.416472+0.240450i)q3+(1.942240.477176i)q4+(1.597132.76632i)q5+(0.266810+0.625575i)q6+(0.694153+2.55307i)q7+(1.00000+2.64575i)q8+(1.38437+2.39779i)q9+(3.612402.71243i)q10+(0.800840+1.38709i)q11+(0.9236270.268282i)q121.38831q13+(3.702380.540703i)q14+1.53613iq15+(3.54461+1.85358i)q16+(3.486052.01267i)q17+(3.13116+2.35108i)q18+(4.569572.63824i)q19+(4.42204+4.61075i)q20+(0.9029820.896373i)q21+(2.083530.888631i)q22+(3.830442.21151i)q23+(0.2197001.34233i)q24+(2.601684.50624i)q25+(0.235927+1.94913i)q262.77419iq27+(0.1299525.28991i)q28+5.10613iq29+(2.15667+0.261047i)q30+(0.05798090.100426i)q31+(3.204734.66151i)q32+(0.6670550.385124i)q33+(2.233315.23632i)q34+(8.17125+2.15734i)q35+(3.832943.99651i)q36+(4.630872.67363i)q37+(4.48055+5.96719i)q38+(0.5781910.333819i)q39+(5.72186+6.99194i)q40+4.21689iq41+(1.41193+1.11543i)q42+(0.8935363.07621i)q44+(4.42204+7.65920i)q45+(3.75582+5.00199i)q46+(5.058218.76108i)q47+(1.92193+0.0803370i)q48+(6.03630+3.54444i)q49+(6.76873+2.88689i)q50+(0.967895+1.67644i)q51+(2.69643+0.662466i)q52+(6.135143.54212i)q53+(3.894870.471441i)q54+5.11619q55+(7.448930.716511i)q56+2.53747q57+(7.16884+0.867728i)q58+(4.38856+2.53374i)q59+(0.7330022.98353i)q60+(4.21321+7.29750i)q61+(0.150848+0.0643370i)q62+(7.082691.86995i)q63+(6.000005.29150i)q64+(2.21731+3.84050i)q65+(0.654060+0.871075i)q66+(5.01815+8.69169i)q67+(7.73114+2.24564i)q68+2.12703q69+(4.4174511.1055i)q705.29150iq71+(4.959606.06049i)q72+(9.305045.37227i)q73+(4.54066+6.04723i)q74+(2.16706+1.25115i)q75+(7.61631+7.30460i)q76+(2.98544+3.00745i)q77+(0.3704130.868490i)q78+(10.3349+5.96688i)q79+(10.78886.84509i)q80+(3.486056.03801i)q81+(5.92037+0.716612i)q8214.9789iq83+(1.32608+2.17185i)q8412.8580iq85+(1.227772.12656i)q87+(4.47075+0.731728i)q88+(1.50000+0.866025i)q89+(11.50474.90680i)q90+(0.9636973.54444i)q91+(6.38437+6.12307i)q92+(0.0482949+0.0278831i)q93+(11.44078.59041i)q94+(14.5965+8.42726i)q95+(0.213819+2.71197i)q96+2.87198iq97+(3.95047+9.07710i)q984.43462q99+O(q100)q+(0.169938 - 1.40397i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(-1.94224 - 0.477176i) q^{4} +(1.59713 - 2.76632i) q^{5} +(0.266810 + 0.625575i) q^{6} +(0.694153 + 2.55307i) q^{7} +(-1.00000 + 2.64575i) q^{8} +(-1.38437 + 2.39779i) q^{9} +(-3.61240 - 2.71243i) q^{10} +(0.800840 + 1.38709i) q^{11} +(0.923627 - 0.268282i) q^{12} -1.38831 q^{13} +(3.70238 - 0.540703i) q^{14} +1.53613i q^{15} +(3.54461 + 1.85358i) q^{16} +(3.48605 - 2.01267i) q^{17} +(3.13116 + 2.35108i) q^{18} +(-4.56957 - 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(-0.902982 - 0.896373i) q^{21} +(2.08353 - 0.888631i) q^{22} +(-3.83044 - 2.21151i) q^{23} +(-0.219700 - 1.34233i) q^{24} +(-2.60168 - 4.50624i) q^{25} +(-0.235927 + 1.94913i) q^{26} -2.77419i q^{27} +(-0.129952 - 5.28991i) q^{28} +5.10613i q^{29} +(2.15667 + 0.261047i) q^{30} +(-0.0579809 - 0.100426i) q^{31} +(3.20473 - 4.66151i) q^{32} +(-0.667055 - 0.385124i) q^{33} +(-2.23331 - 5.23632i) q^{34} +(8.17125 + 2.15734i) q^{35} +(3.83294 - 3.99651i) q^{36} +(-4.63087 - 2.67363i) q^{37} +(-4.48055 + 5.96719i) q^{38} +(0.578191 - 0.333819i) q^{39} +(5.72186 + 6.99194i) q^{40} +4.21689i q^{41} +(-1.41193 + 1.11543i) q^{42} +(-0.893536 - 3.07621i) q^{44} +(4.42204 + 7.65920i) q^{45} +(-3.75582 + 5.00199i) q^{46} +(5.05821 - 8.76108i) q^{47} +(-1.92193 + 0.0803370i) q^{48} +(-6.03630 + 3.54444i) q^{49} +(-6.76873 + 2.88689i) q^{50} +(-0.967895 + 1.67644i) q^{51} +(2.69643 + 0.662466i) q^{52} +(6.13514 - 3.54212i) q^{53} +(-3.89487 - 0.471441i) q^{54} +5.11619 q^{55} +(-7.44893 - 0.716511i) q^{56} +2.53747 q^{57} +(7.16884 + 0.867728i) q^{58} +(-4.38856 + 2.53374i) q^{59} +(0.733002 - 2.98353i) q^{60} +(-4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-7.08269 - 1.86995i) q^{63} +(-6.00000 - 5.29150i) q^{64} +(-2.21731 + 3.84050i) q^{65} +(-0.654060 + 0.871075i) q^{66} +(5.01815 + 8.69169i) q^{67} +(-7.73114 + 2.24564i) q^{68} +2.12703 q^{69} +(4.41745 - 11.1055i) q^{70} -5.29150i q^{71} +(-4.95960 - 6.06049i) q^{72} +(9.30504 - 5.37227i) q^{73} +(-4.54066 + 6.04723i) q^{74} +(2.16706 + 1.25115i) q^{75} +(7.61631 + 7.30460i) q^{76} +(-2.98544 + 3.00745i) q^{77} +(-0.370413 - 0.868490i) q^{78} +(10.3349 + 5.96688i) q^{79} +(10.7888 - 6.84509i) q^{80} +(-3.48605 - 6.03801i) q^{81} +(5.92037 + 0.716612i) q^{82} -14.9789i q^{83} +(1.32608 + 2.17185i) q^{84} -12.8580i q^{85} +(-1.22777 - 2.12656i) q^{87} +(-4.47075 + 0.731728i) q^{88} +(1.50000 + 0.866025i) q^{89} +(11.5047 - 4.90680i) q^{90} +(-0.963697 - 3.54444i) q^{91} +(6.38437 + 6.12307i) q^{92} +(0.0482949 + 0.0278831i) q^{93} +(-11.4407 - 8.59041i) q^{94} +(-14.5965 + 8.42726i) q^{95} +(-0.213819 + 2.71197i) q^{96} +2.87198i q^{97} +(3.95047 + 9.07710i) q^{98} -4.43462 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q6q312q8+6q106q1118q12+6q146q17+6q186q19+24q22+6q24+6q26+6q2812q306q33+18q35+48q3624q38+24q99+O(q100) 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/56Z)×\left(\mathbb{Z}/56\mathbb{Z}\right)^\times.

nn 1515 1717 2929
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\right) 1-1

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 0.169938 1.40397i 0.120165 0.992754i
33 −0.416472 + 0.240450i −0.240450 + 0.138824i −0.615384 0.788228i 0.710999π-0.710999\pi
0.374933 + 0.927052i 0.377666π0.377666\pi
44 −1.94224 0.477176i −0.971121 0.238588i
55 1.59713 2.76632i 0.714260 1.23714i −0.248984 0.968508i 0.580097π-0.580097\pi
0.963244 0.268628i 0.0865701π-0.0865701\pi
66 0.266810 + 0.625575i 0.108925 + 0.255390i
77 0.694153 + 2.55307i 0.262365 + 0.964969i
88 −1.00000 + 2.64575i −0.353553 + 0.935414i
99 −1.38437 + 2.39779i −0.461456 + 0.799265i
1010 −3.61240 2.71243i −1.14234 0.857745i
1111 0.800840 + 1.38709i 0.241462 + 0.418225i 0.961131 0.276093i 0.0890397π-0.0890397\pi
−0.719669 + 0.694318i 0.755706π0.755706\pi
1212 0.923627 0.268282i 0.266628 0.0774465i
1313 −1.38831 −0.385047 −0.192523 0.981292i 0.561667π-0.561667\pi
−0.192523 + 0.981292i 0.561667π0.561667\pi
1414 3.70238 0.540703i 0.989503 0.144509i
1515 1.53613i 0.396626i
1616 3.54461 + 1.85358i 0.886152 + 0.463395i
1717 3.48605 2.01267i 0.845490 0.488144i −0.0136363 0.999907i 0.504341π-0.504341\pi
0.859127 + 0.511763i 0.171007π0.171007\pi
1818 3.13116 + 2.35108i 0.738023 + 0.554155i
1919 −4.56957 2.63824i −1.04833 0.605255i −0.126150 0.992011i 0.540262π-0.540262\pi
−0.922182 + 0.386756i 0.873595π0.873595\pi
2020 −4.42204 + 4.61075i −0.988799 + 1.03099i
2121 −0.902982 0.896373i −0.197047 0.195605i
2222 2.08353 0.888631i 0.444210 0.189457i
2323 −3.83044 2.21151i −0.798702 0.461131i 0.0443149 0.999018i 0.485890π-0.485890\pi
−0.843017 + 0.537887i 0.819223π0.819223\pi
2424 −0.219700 1.34233i −0.0448460 0.274003i
2525 −2.60168 4.50624i −0.520336 0.901248i
2626 −0.235927 + 1.94913i −0.0462690 + 0.382257i
2727 2.77419i 0.533893i
2828 −0.129952 5.28991i −0.0245586 0.999698i
2929 5.10613i 0.948185i 0.880475 + 0.474093i 0.157224π0.157224\pi
−0.880475 + 0.474093i 0.842776π0.842776\pi
3030 2.15667 + 0.261047i 0.393752 + 0.0476605i
3131 −0.0579809 0.100426i −0.0104137 0.0180370i 0.860772 0.508991i 0.169982π-0.169982\pi
−0.871185 + 0.490954i 0.836648π0.836648\pi
3232 3.20473 4.66151i 0.566522 0.824047i
3333 −0.667055 0.385124i −0.116119 0.0670416i
3434 −2.23331 5.23632i −0.383009 0.898022i
3535 8.17125 + 2.15734i 1.38119 + 0.364658i
3636 3.83294 3.99651i 0.638824 0.666085i
3737 −4.63087 2.67363i −0.761310 0.439543i 0.0684556 0.997654i 0.478193π-0.478193\pi
−0.829766 + 0.558111i 0.811526π0.811526\pi
3838 −4.48055 + 5.96719i −0.726842 + 0.968006i
3939 0.578191 0.333819i 0.0925847 0.0534538i
4040 5.72186 + 6.99194i 0.904705 + 1.10552i
4141 4.21689i 0.658568i 0.944231 + 0.329284i 0.106807π0.106807\pi
−0.944231 + 0.329284i 0.893193π0.893193\pi
4242 −1.41193 + 1.11543i −0.217865 + 0.172114i
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 −0.893536 3.07621i −0.134706 0.463757i
4545 4.42204 + 7.65920i 0.659199 + 1.14177i
4646 −3.75582 + 5.00199i −0.553765 + 0.737503i
4747 5.05821 8.76108i 0.737816 1.27794i −0.215660 0.976468i 0.569190π-0.569190\pi
0.953477 0.301467i 0.0974763π-0.0974763\pi
4848 −1.92193 + 0.0803370i −0.277406 + 0.0115956i
4949 −6.03630 + 3.54444i −0.862329 + 0.506348i
5050 −6.76873 + 2.88689i −0.957244 + 0.408267i
5151 −0.967895 + 1.67644i −0.135532 + 0.234749i
5252 2.69643 + 0.662466i 0.373927 + 0.0918675i
5353 6.13514 3.54212i 0.842726 0.486548i −0.0154638 0.999880i 0.504922π-0.504922\pi
0.858190 + 0.513332i 0.171589π0.171589\pi
5454 −3.89487 0.471441i −0.530024 0.0641551i
5555 5.11619 0.689868
5656 −7.44893 0.716511i −0.995406 0.0957478i
5757 2.53747 0.336096
5858 7.16884 + 0.867728i 0.941315 + 0.113938i
5959 −4.38856 + 2.53374i −0.571342 + 0.329865i −0.757685 0.652620i 0.773670π-0.773670\pi
0.186343 + 0.982485i 0.440336π0.440336\pi
6060 0.733002 2.98353i 0.0946302 0.385172i
6161 −4.21321 + 7.29750i −0.539447 + 0.934349i 0.459487 + 0.888184i 0.348033π0.348033\pi
−0.998934 + 0.0461646i 0.985300π0.985300\pi
6262 −0.150848 + 0.0643370i −0.0191577 + 0.00817081i
6363 −7.08269 1.86995i −0.892335 0.235591i
6464 −6.00000 5.29150i −0.750000 0.661438i
6565 −2.21731 + 3.84050i −0.275024 + 0.476355i
6666 −0.654060 + 0.871075i −0.0805092 + 0.107222i
6767 5.01815 + 8.69169i 0.613065 + 1.06186i 0.990721 + 0.135913i 0.0433969π0.0433969\pi
−0.377656 + 0.925946i 0.623270π0.623270\pi
6868 −7.73114 + 2.24564i −0.937539 + 0.272323i
6969 2.12703 0.256064
7070 4.41745 11.1055i 0.527986 1.32737i
7171 5.29150i 0.627986i −0.949425 0.313993i 0.898333π-0.898333\pi
0.949425 0.313993i 0.101667π-0.101667\pi
7272 −4.95960 6.06049i −0.584494 0.714235i
7373 9.30504 5.37227i 1.08907 0.628776i 0.155743 0.987798i 0.450223π-0.450223\pi
0.933329 + 0.359021i 0.116890π0.116890\pi
7474 −4.54066 + 6.04723i −0.527840 + 0.702976i
7575 2.16706 + 1.25115i 0.250230 + 0.144470i
7676 7.61631 + 7.30460i 0.873651 + 0.837895i
7777 −2.98544 + 3.00745i −0.340223 + 0.342731i
7878 −0.370413 0.868490i −0.0419411 0.0983371i
7979 10.3349 + 5.96688i 1.16277 + 0.671327i 0.951967 0.306201i 0.0990581π-0.0990581\pi
0.210805 + 0.977528i 0.432391π0.432391\pi
8080 10.7888 6.84509i 1.20623 0.765305i
8181 −3.48605 6.03801i −0.387338 0.670890i
8282 5.92037 + 0.716612i 0.653796 + 0.0791366i
8383 14.9789i 1.64415i −0.569382 0.822073i 0.692818π-0.692818\pi
0.569382 0.822073i 0.307182π-0.307182\pi
8484 1.32608 + 2.17185i 0.144687 + 0.236969i
8585 12.8580i 1.39465i
8686 0 0
8787 −1.22777 2.12656i −0.131631 0.227992i
8888 −4.47075 + 0.731728i −0.476583 + 0.0780024i
8989 1.50000 + 0.866025i 0.159000 + 0.0917985i 0.577389 0.816469i 0.304072π-0.304072\pi
−0.418389 + 0.908268i 0.637405π0.637405\pi
9090 11.5047 4.90680i 1.21271 0.517223i
9191 −0.963697 3.54444i −0.101023 0.371558i
9292 6.38437 + 6.12307i 0.665616 + 0.638375i
9393 0.0482949 + 0.0278831i 0.00500795 + 0.00289134i
9494 −11.4407 8.59041i −1.18002 0.886033i
9595 −14.5965 + 8.42726i −1.49756 + 0.864619i
9696 −0.213819 + 2.71197i −0.0218228 + 0.276789i
9797 2.87198i 0.291606i 0.989314 + 0.145803i 0.0465765π0.0465765\pi
−0.989314 + 0.145803i 0.953423π0.953423\pi
9898 3.95047 + 9.07710i 0.399058 + 0.916926i
9999 −4.43462 −0.445696
100100 2.90282 + 9.99367i 0.290282 + 0.999367i
101101 −3.40310 5.89434i −0.338621 0.586509i 0.645553 0.763716i 0.276627π-0.276627\pi
−0.984174 + 0.177207i 0.943294π0.943294\pi
102102 2.18919 + 1.64378i 0.216762 + 0.162759i
103103 −7.02471 + 12.1672i −0.692165 + 1.19887i 0.278962 + 0.960302i 0.410010π0.410010\pi
−0.971127 + 0.238563i 0.923324π0.923324\pi
104104 1.38831 3.67311i 0.136135 0.360178i
105105 −3.92184 + 1.06631i −0.382732 + 0.104061i
106106 −3.93043 9.21547i −0.381757 0.895086i
107107 2.56957 4.45063i 0.248410 0.430259i −0.714675 0.699457i 0.753425π-0.753425\pi
0.963085 + 0.269198i 0.0867586π0.0867586\pi
108108 −1.32378 + 5.38815i −0.127380 + 0.518475i
109109 −2.45182 + 1.41556i −0.234842 + 0.135586i −0.612804 0.790235i 0.709958π-0.709958\pi
0.377962 + 0.925821i 0.376625π0.376625\pi
110110 0.869438 7.18296i 0.0828977 0.684869i
111111 2.57151 0.244077
112112 −2.27182 + 10.3363i −0.214667 + 0.976687i
113113 −1.43695 −0.135177 −0.0675887 0.997713i 0.521531π-0.521531\pi
−0.0675887 + 0.997713i 0.521531π0.521531\pi
114114 0.431213 3.56252i 0.0403868 0.333661i
115115 −12.2355 + 7.06415i −1.14096 + 0.658735i
116116 2.43652 9.91735i 0.226225 0.920803i
117117 1.92193 3.32887i 0.177682 0.307754i
118118 2.81150 + 6.59198i 0.258819 + 0.606841i
119119 7.55833 + 7.50301i 0.692871 + 0.687800i
120120 −4.06421 1.53613i −0.371010 0.140229i
121121 4.21731 7.30460i 0.383392 0.664054i
122122 9.52946 + 7.15533i 0.862756 + 0.647814i
123123 −1.01395 1.75622i −0.0914251 0.158353i
124124 0.0646922 + 0.222719i 0.00580953 + 0.0200007i
125125 −0.649581 −0.0581003
126126 −3.82896 + 9.62608i −0.341111 + 0.857560i
127127 4.92077i 0.436647i 0.975876 + 0.218324i 0.0700589π0.0700589\pi
−0.975876 + 0.218324i 0.929941π0.929941\pi
128128 −8.44872 + 7.52457i −0.746769 + 0.665084i
129129 0 0
130130 5.01512 + 3.76568i 0.439855 + 0.330272i
131131 −3.41647 1.97250i −0.298499 0.172338i 0.343270 0.939237i 0.388466π-0.388466\pi
−0.641768 + 0.766899i 0.721799π0.721799\pi
132132 1.11181 + 1.06631i 0.0967707 + 0.0928101i
133133 3.56363 13.4978i 0.309006 1.17041i
134134 13.0556 5.56826i 1.12783 0.481025i
135135 −7.67429 4.43075i −0.660498 0.381339i
136136 1.83898 + 11.2359i 0.157691 + 0.963469i
137137 0.0514223 + 0.0890661i 0.00439331 + 0.00760943i 0.868214 0.496190i 0.165268π-0.165268\pi
−0.863820 + 0.503800i 0.831935π0.831935\pi
138138 0.361464 2.98628i 0.0307699 0.254209i
139139 14.9789i 1.27049i 0.772310 + 0.635246i 0.219101π0.219101\pi
−0.772310 + 0.635246i 0.780899π0.780899\pi
140140 −14.8411 8.08921i −1.25430 0.683663i
141141 4.86500i 0.409707i
142142 −7.42909 0.899230i −0.623435 0.0754617i
143143 −1.11181 1.92571i −0.0929743 0.161036i
144144 −9.35154 + 5.93320i −0.779295 + 0.494433i
145145 14.1252 + 8.15518i 1.17303 + 0.677251i
146146 −5.96120 13.9769i −0.493352 1.15674i
147147 1.66169 2.92759i 0.137054 0.241464i
148148 7.71848 + 7.40258i 0.634455 + 0.608489i
149149 9.79164 + 5.65320i 0.802162 + 0.463129i 0.844227 0.535986i 0.180060π-0.180060\pi
−0.0420645 + 0.999115i 0.513393π0.513393\pi
150150 2.12484 2.82985i 0.173492 0.231057i
151151 12.8351 7.41032i 1.04450 0.603044i 0.123397 0.992357i 0.460621π-0.460621\pi
0.921105 + 0.389314i 0.127288π0.127288\pi
152152 11.5497 9.45171i 0.936805 0.766635i
153153 11.1451i 0.901028i
154154 3.71502 + 4.70254i 0.299365 + 0.378941i
155155 −0.370413 −0.0297523
156156 −1.28228 + 0.372458i −0.102664 + 0.0298205i
157157 −0.369362 0.639755i −0.0294783 0.0510580i 0.850910 0.525312i 0.176051π-0.176051\pi
−0.880388 + 0.474254i 0.842718π0.842718\pi
158158 10.1336 13.4959i 0.806186 1.07368i
159159 −1.70341 + 2.95039i −0.135089 + 0.233981i
160160 −7.77685 16.3104i −0.614814 1.28945i
161161 2.98721 11.3145i 0.235425 0.891707i
162162 −9.06957 + 3.86820i −0.712573 + 0.303915i
163163 4.35226 7.53834i 0.340895 0.590448i −0.643704 0.765275i 0.722603π-0.722603\pi
0.984599 + 0.174826i 0.0559364π0.0559364\pi
164164 2.01220 8.19022i 0.157126 0.639549i
165165 −2.13075 + 1.23019i −0.165879 + 0.0957703i
166166 −21.0298 2.54549i −1.63223 0.197568i
167167 −1.38831 −0.107430 −0.0537152 0.998556i 0.517106π-0.517106\pi
−0.0537152 + 0.998556i 0.517106π0.517106\pi
168168 3.27456 1.49269i 0.252638 0.115164i
169169 −11.0726 −0.851739
170170 −18.0522 2.18507i −1.38454 0.167587i
171171 12.6519 7.30460i 0.967518 0.558597i
172172 0 0
173173 0.485324 0.840606i 0.0368985 0.0639101i −0.846986 0.531615i 0.821586π-0.821586\pi
0.883885 + 0.467704i 0.154919π0.154919\pi
174174 −3.19427 + 1.36237i −0.242157 + 0.103281i
175175 9.69877 9.77028i 0.733158 0.738564i
176176 0.267569 + 6.40113i 0.0201688 + 0.482503i
177177 1.21848 2.11046i 0.0915864 0.158632i
178178 1.47078 1.95878i 0.110239 0.146817i
179179 7.13495 + 12.3581i 0.533291 + 0.923687i 0.999244 + 0.0388779i 0.0123783π0.0123783\pi
−0.465953 + 0.884810i 0.654288π0.654288\pi
180180 −4.93389 16.9861i −0.367750 1.26607i
181181 −15.3218 −1.13886 −0.569429 0.822041i 0.692836π-0.692836\pi
−0.569429 + 0.822041i 0.692836π0.692836\pi
182182 −5.14004 + 0.750661i −0.381005 + 0.0556427i
183183 4.05228i 0.299553i
184184 9.68154 7.92289i 0.713732 0.584083i
185185 −14.7922 + 8.54031i −1.08755 + 0.627896i
186186 0.0473541 0.0630660i 0.00347217 0.00462422i
187187 5.58353 + 3.22365i 0.408308 + 0.235737i
188188 −14.0049 + 14.6025i −1.02141 + 1.06500i
189189 7.08269 1.92571i 0.515190 0.140075i
190190 9.35110 + 21.9250i 0.678400 + 1.59061i
191191 2.16564 + 1.25033i 0.156700 + 0.0904709i 0.576300 0.817238i 0.304496π-0.304496\pi
−0.419599 + 0.907709i 0.637829π0.637829\pi
192192 3.77118 + 0.761062i 0.272161 + 0.0549249i
193193 1.55026 + 2.68512i 0.111590 + 0.193279i 0.916411 0.400237i 0.131072π-0.131072\pi
−0.804822 + 0.593517i 0.797739π0.797739\pi
194194 4.03217 + 0.488061i 0.289493 + 0.0350407i
195195 2.13261i 0.152720i
196196 13.4153 4.00378i 0.958234 0.285984i
197197 15.6891i 1.11780i 0.829233 + 0.558902i 0.188777π0.188777\pi
−0.829233 + 0.558902i 0.811223π0.811223\pi
198198 −0.753613 + 6.22606i −0.0535570 + 0.442467i
199199 −5.91290 10.2414i −0.419154 0.725997i 0.576700 0.816956i 0.304340π-0.304340\pi
−0.995855 + 0.0909591i 0.971007π0.971007\pi
200200 14.5241 2.37716i 1.02701 0.168090i
201201 −4.17984 2.41323i −0.294823 0.170216i
202202 −8.85377 + 3.77616i −0.622949 + 0.265690i
203203 −13.0363 + 3.54444i −0.914969 + 0.248771i
204204 2.67984 2.79420i 0.187627 0.195633i
205205 11.6653 + 6.73495i 0.814738 + 0.470389i
206206 15.8885 + 11.9301i 1.10700 + 0.831211i
207207 10.6055 6.12307i 0.737131 0.425583i
208208 −4.92100 2.57334i −0.341210 0.178429i
209209 8.45124i 0.584585i
210210 0.830589 + 5.68733i 0.0573161 + 0.392463i
211211 10.0726 0.693427 0.346713 0.937971i 0.387298π-0.387298\pi
0.346713 + 0.937971i 0.387298π0.387298\pi
212212 −13.6061 + 3.95212i −0.934473 + 0.271433i
213213 1.27234 + 2.20376i 0.0871796 + 0.150999i
214214 −5.81187 4.36393i −0.397291 0.298312i
215215 0 0
216216 7.33982 + 2.77419i 0.499411 + 0.188760i
217217 0.216146 0.217740i 0.0146730 0.0147812i
218218 1.57074 + 3.68283i 0.106384 + 0.249433i
219219 −2.58353 + 4.47480i −0.174579 + 0.302379i
220220 −9.93689 2.44132i −0.669945 0.164594i
221221 −4.83970 + 2.79420i −0.325553 + 0.187958i
222222 0.436998 3.61031i 0.0293294 0.242308i
223223 −24.3086 −1.62783 −0.813913 0.580987i 0.802667π-0.802667\pi
−0.813913 + 0.580987i 0.802667π0.802667\pi
224224 14.1257 + 4.94609i 0.943815 + 0.330474i
225225 14.4067 0.960448
226226 −0.244194 + 2.01744i −0.0162435 + 0.134198i
227227 −12.4048 + 7.16194i −0.823339 + 0.475355i −0.851566 0.524247i 0.824347π-0.824347\pi
0.0282277 + 0.999602i 0.491014π0.491014\pi
228228 −4.92838 1.21082i −0.326390 0.0801884i
229229 −5.32502 + 9.22321i −0.351887 + 0.609487i −0.986580 0.163278i 0.947793π-0.947793\pi
0.634693 + 0.772765i 0.281127π0.281127\pi
230230 7.83855 + 18.3786i 0.516859 + 1.21185i
231231 0.520210 1.97037i 0.0342273 0.129641i
232232 −13.5096 5.10613i −0.886946 0.335234i
233233 0.318991 0.552509i 0.0208978 0.0361961i −0.855387 0.517989i 0.826681π-0.826681\pi
0.876285 + 0.481793i 0.160014π0.160014\pi
234234 −4.34702 3.26402i −0.284173 0.213376i
235235 −16.1573 27.9853i −1.05399 1.82556i
236236 9.73269 2.82702i 0.633544 0.184023i
237237 −5.73896 −0.372785
238238 11.8184 9.33659i 0.766075 0.605201i
239239 4.73540i 0.306307i −0.988202 0.153154i 0.951057π-0.951057\pi
0.988202 0.153154i 0.0489430π-0.0489430\pi
240240 −2.84734 + 5.44497i −0.183795 + 0.351471i
241241 −10.1380 + 5.85317i −0.653045 + 0.377036i −0.789622 0.613594i 0.789723π-0.789723\pi
0.136577 + 0.990629i 0.456390π0.456390\pi
242242 −9.53873 7.16230i −0.613173 0.460410i
243243 10.1112 + 5.83773i 0.648636 + 0.374490i
244244 11.6653 12.1631i 0.746792 0.778661i
245245 0.164257 + 22.3593i 0.0104940 + 1.42848i
246246 −2.63798 + 1.12511i −0.168192 + 0.0717342i
247247 6.34397 + 3.66269i 0.403657 + 0.233051i
248248 0.323683 0.0529772i 0.0205539 0.00336406i
249249 3.60168 + 6.23829i 0.228247 + 0.395336i
250250 −0.110389 + 0.911990i −0.00698160 + 0.0576793i
251251 11.5631i 0.729858i 0.931035 + 0.364929i 0.118907π0.118907\pi
−0.931035 + 0.364929i 0.881093π0.881093\pi
252252 12.8640 + 7.01158i 0.810356 + 0.441688i
253253 7.08425i 0.445383i
254254 6.90859 + 0.836227i 0.433483 + 0.0524696i
255255 3.09172 + 5.35501i 0.193611 + 0.335344i
256256 9.12847 + 13.1404i 0.570530 + 0.821277i
257257 −20.4302 11.7954i −1.27440 0.735777i −0.298589 0.954382i 0.596516π-0.596516\pi
−0.975813 + 0.218605i 0.929849π0.929849\pi
258258 0 0
259259 3.61144 13.6788i 0.224404 0.849961i
260260 6.13915 6.40113i 0.380734 0.396981i
261261 −12.2435 7.06876i −0.757851 0.437546i
262262 −3.34991 + 4.46141i −0.206958 + 0.275627i
263263 −9.24833 + 5.33953i −0.570277 + 0.329249i −0.757260 0.653114i 0.773462π-0.773462\pi
0.186983 + 0.982363i 0.440129π0.440129\pi
264264 1.68600 1.37974i 0.103766 0.0849170i
265265 22.6290i 1.39009i
266266 −18.3448 7.29701i −1.12479 0.447408i
267267 −0.832945 −0.0509754
268268 −5.59900 19.2759i −0.342013 1.17746i
269269 −11.6690 20.2113i −0.711471 1.23230i −0.964305 0.264794i 0.914696π-0.914696\pi
0.252834 0.967510i 0.418637π-0.418637\pi
270270 −7.52479 + 10.0215i −0.457944 + 0.609889i
271271 6.81961 11.8119i 0.414262 0.717522i −0.581089 0.813840i 0.697373π-0.697373\pi
0.995351 + 0.0963179i 0.0307066π0.0307066\pi
272272 16.0873 0.672454i 0.975436 0.0407735i
273273 1.25362 + 1.24444i 0.0758722 + 0.0753169i
274274 0.133784 0.0570595i 0.00808221 0.00344709i
275275 4.16706 7.21755i 0.251283 0.435235i
276276 −4.13121 1.01497i −0.248670 0.0610939i
277277 −0.396180 + 0.228735i −0.0238042 + 0.0137433i −0.511855 0.859072i 0.671041π-0.671041\pi
0.488051 + 0.872815i 0.337708π0.337708\pi
278278 21.0298 + 2.54549i 1.26129 + 0.152668i
279279 0.321068 0.0192218
280280 −13.8790 + 19.4618i −0.829432 + 1.16306i
281281 1.43695 0.0857215 0.0428608 0.999081i 0.486353π-0.486353\pi
0.0428608 + 0.999081i 0.486353π0.486353\pi
282282 6.83029 + 0.826750i 0.406738 + 0.0492323i
283283 27.0428 15.6132i 1.60753 0.928108i 0.617609 0.786486i 0.288102π-0.288102\pi
0.989921 0.141622i 0.0452318π-0.0452318\pi
284284 −2.52498 + 10.2774i −0.149830 + 0.609850i
285285 4.05268 7.01945i 0.240060 0.415796i
286286 −2.89257 + 1.23369i −0.171041 + 0.0729497i
287287 −10.7660 + 2.92717i −0.635497 + 0.172785i
288288 6.74083 + 14.1375i 0.397207 + 0.833062i
289289 −0.398321 + 0.689912i −0.0234306 + 0.0405831i
290290 13.8500 18.4454i 0.813301 1.08315i
291291 −0.690570 1.19610i −0.0404819 0.0701168i
292292 −20.6361 + 5.99410i −1.20764 + 0.350778i
293293 31.3006 1.82860 0.914299 0.405040i 0.132742π-0.132742\pi
0.914299 + 0.405040i 0.132742π0.132742\pi
294294 −3.82786 2.83047i −0.223245 0.165076i
295295 16.1869i 0.942437i
296296 11.7046 9.57850i 0.680319 0.556739i
297297 3.84806 2.22168i 0.223287 0.128915i
298298 9.60088 12.7864i 0.556164 0.740698i
299299 5.31783 + 3.07025i 0.307538 + 0.177557i
300300 −3.61193 3.46410i −0.208535 0.200000i
301301 0 0
302302 −8.22268 19.2793i −0.473162 1.10940i
303303 2.83459 + 1.63655i 0.162843 + 0.0940175i
304304 −11.3071 17.8216i −0.648509 1.02214i
305305 13.4581 + 23.3102i 0.770611 + 1.33474i
306306 15.6473 + 1.89398i 0.894499 + 0.108272i
307307 14.7215i 0.840202i 0.907477 + 0.420101i 0.138005π0.138005\pi
−0.907477 + 0.420101i 0.861995π0.861995\pi
308308 7.23353 4.41662i 0.412169 0.251660i
309309 6.75638i 0.384357i
310310 −0.0629475 + 0.520048i −0.00357518 + 0.0295367i
311311 7.79025 + 13.4931i 0.441745 + 0.765124i 0.997819 0.0660082i 0.0210263π-0.0210263\pi
−0.556074 + 0.831133i 0.687693π0.687693\pi
312312 0.305010 + 1.86357i 0.0172678 + 0.105504i
313313 11.3329 + 6.54308i 0.640576 + 0.369837i 0.784836 0.619703i 0.212747π-0.212747\pi
−0.144260 + 0.989540i 0.546080π0.546080\pi
314314 −0.960963 + 0.409854i −0.0542303 + 0.0231294i
315315 −16.4849 + 16.6064i −0.928818 + 0.935666i
316316 −17.2257 16.5207i −0.969022 0.929363i
317317 −20.3971 11.7763i −1.14562 0.661422i −0.197801 0.980242i 0.563380π-0.563380\pi
−0.947815 + 0.318821i 0.896713π0.896713\pi
318318 3.85278 + 2.89292i 0.216053 + 0.162227i
319319 −7.08269 + 4.08919i −0.396555 + 0.228951i
320320 −24.2208 + 8.14667i −1.35398 + 0.455413i
321321 2.47142i 0.137941i
322322 −15.3775 6.11671i −0.856956 0.340871i
323323 −21.2397 −1.18181
324324 3.88955 + 13.3907i 0.216086 + 0.743929i
325325 3.61193 + 6.25604i 0.200354 + 0.347023i
326326 −9.84396 7.39148i −0.545206 0.409376i
327327 0.680744 1.17908i 0.0376452 0.0652035i
328328 −11.1568 4.21689i −0.616034 0.232839i
329329 25.8788 + 6.83243i 1.42674 + 0.376684i
330330 1.36505 + 3.20056i 0.0751435 + 0.176185i
331331 −16.5277 + 28.6268i −0.908445 + 1.57347i −0.0922207 + 0.995739i 0.529397π0.529397\pi
−0.816225 + 0.577735i 0.803937π0.803937\pi
332332 −7.14756 + 29.0926i −0.392273 + 1.59666i
333333 12.8217 7.40258i 0.702622 0.405659i
334334 −0.235927 + 1.94913i −0.0129093 + 0.106652i
335335 32.0587 1.75155
336336 −1.53922 4.85104i −0.0839711 0.264646i
337337 −15.5096 −0.844860 −0.422430 0.906396i 0.638823π-0.638823\pi
−0.422430 + 0.906396i 0.638823π0.638823\pi
338338 −1.88166 + 15.5456i −0.102349 + 0.845567i
339339 0.598452 0.345516i 0.0325035 0.0187659i
340340 −6.13553 + 24.9734i −0.332746 + 1.35437i
341341 0.0928668 0.160850i 0.00502902 0.00871052i
342342 −8.10536 19.0042i −0.438288 1.02763i
343343 −13.2393 12.9507i −0.714855 0.699272i
344344 0 0
345345 3.39716 5.88405i 0.182897 0.316786i
346346 −1.09771 0.824230i −0.0590131 0.0443109i
347347 −11.2494 19.4846i −0.603900 1.04599i −0.992224 0.124463i 0.960279π-0.960279\pi
0.388324 0.921523i 0.373054π-0.373054\pi
348348 1.36989 + 4.71616i 0.0734336 + 0.252813i
349349 28.4735 1.52415 0.762077 0.647486i 0.224180π-0.224180\pi
0.762077 + 0.647486i 0.224180π0.224180\pi
350350 −12.0690 15.2771i −0.645113 0.816595i
351351 3.85142i 0.205574i
352352 9.03244 + 0.712140i 0.481430 + 0.0379572i
353353 −8.29108 + 4.78686i −0.441290 + 0.254779i −0.704145 0.710057i 0.748669π-0.748669\pi
0.262855 + 0.964835i 0.415336π0.415336\pi
354354 −2.75596 2.06935i −0.146477 0.109985i
355355 −14.6380 8.45124i −0.776903 0.448545i
356356 −2.50012 2.39779i −0.132506 0.127083i
357357 −4.95194 1.30739i −0.262084 0.0691945i
358358 18.5629 7.91711i 0.981077 0.418432i
359359 3.25225 + 1.87769i 0.171647 + 0.0991006i 0.583362 0.812212i 0.301737π-0.301737\pi
−0.411715 + 0.911313i 0.635070π0.635070\pi
360360 −24.6864 + 4.04042i −1.30109 + 0.212949i
361361 4.42067 + 7.65683i 0.232667 + 0.402991i
362362 −2.60376 + 21.5112i −0.136850 + 1.13061i
363363 4.05622i 0.212896i
364364 0.180413 + 7.34401i 0.00945620 + 0.384931i
365365 34.3209i 1.79644i
366366 −5.68926 0.688638i −0.297382 0.0359957i
367367 8.41302 + 14.5718i 0.439156 + 0.760640i 0.997625 0.0688852i 0.0219442π-0.0219442\pi
−0.558469 + 0.829526i 0.688611π0.688611\pi
368368 −9.47820 14.9390i −0.494086 0.778747i
369369 −10.1112 5.83773i −0.526370 0.303900i
370370 9.47653 + 22.2191i 0.492661 + 1.15512i
371371 13.3020 + 13.2046i 0.690606 + 0.685551i
372372 −0.0804953 0.0772008i −0.00417349 0.00400268i
373373 11.1354 + 6.42901i 0.576568 + 0.332882i 0.759768 0.650194i 0.225312π-0.225312\pi
−0.183200 + 0.983076i 0.558646π0.558646\pi
374374 5.47475 7.29126i 0.283093 0.377022i
375375 0.270533 0.156192i 0.0139702 0.00806572i
376376 18.1214 + 22.1439i 0.934542 + 1.14198i
377377 7.08888i 0.365096i
378378 −1.50001 10.2711i −0.0771523 0.528289i
379379 25.5822 1.31407 0.657034 0.753861i 0.271811π-0.271811\pi
0.657034 + 0.753861i 0.271811π0.271811\pi
380380 32.3711 9.40272i 1.66060 0.482349i
381381 −1.18320 2.04936i −0.0606172 0.104992i
382382 2.12345 2.82801i 0.108645 0.144693i
383383 −13.4846 + 23.3561i −0.689033 + 1.19344i 0.283118 + 0.959085i 0.408631π0.408631\pi
−0.972151 + 0.234355i 0.924702π0.924702\pi
384384 1.70937 5.16527i 0.0872311 0.263589i
385385 3.55142 + 13.0620i 0.180997 + 0.665701i
386386 4.03327 1.72020i 0.205288 0.0875560i
387387 0 0
388388 1.37044 5.57809i 0.0695736 0.283185i
389389 −27.7043 + 15.9951i −1.40466 + 0.810983i −0.994867 0.101195i 0.967734π-0.967734\pi
−0.409796 + 0.912177i 0.634400π0.634400\pi
390390 −2.99412 0.362413i −0.151613 0.0183515i
391391 −17.8041 −0.900394
392392 −3.34140 19.5150i −0.168766 0.985656i
393393 1.89716 0.0956988
394394 22.0270 + 2.66619i 1.10971 + 0.134321i
395395 33.0126 19.0598i 1.66104 0.959004i
396396 8.61311 + 2.11609i 0.432825 + 0.106338i
397397 8.51929 14.7558i 0.427571 0.740575i −0.569086 0.822278i 0.692703π-0.692703\pi
0.996657 + 0.0817035i 0.0260360π0.0260360\pi
398398 −15.3835 + 6.56110i −0.771104 + 0.328878i
399399 1.76139 + 6.47833i 0.0881799 + 0.324322i
400400 −0.869248 20.7953i −0.0434624 1.03976i
401401 2.94858 5.10709i 0.147245 0.255036i −0.782963 0.622068i 0.786293π-0.786293\pi
0.930208 + 0.367032i 0.119626π0.119626\pi
402402 −4.09841 + 5.45826i −0.204410 + 0.272233i
403403 0.0804953 + 0.139422i 0.00400976 + 0.00694510i
404404 3.79700 + 13.0721i 0.188908 + 0.650362i
405405 −22.2707 −1.10664
406406 2.76090 + 18.9049i 0.137021 + 0.938233i
407407 8.56461i 0.424532i
408408 −3.46756 4.23725i −0.171670 0.209775i
409409 −0.207751 + 0.119945i −0.0102726 + 0.00593090i −0.505128 0.863045i 0.668555π-0.668555\pi
0.494855 + 0.868976i 0.335221π0.335221\pi
410410 11.4380 15.2331i 0.564883 0.752310i
411411 −0.0428320 0.0247290i −0.00211274 0.00121979i
412412 19.4496 20.2795i 0.958211 0.999101i
413413 −9.51514 9.44550i −0.468210 0.464783i
414414 −6.79431 15.9303i −0.333922 0.782930i
415415 −41.4364 23.9233i −2.03403 1.17435i
416416 −4.44915 + 6.47161i −0.218137 + 0.317297i
417417 −3.60168 6.23829i −0.176375 0.305490i
418418 −11.8653 1.43619i −0.580349 0.0702464i
419419 29.4140i 1.43697i −0.695544 0.718484i 0.744837π-0.744837\pi
0.695544 0.718484i 0.255163π-0.255163\pi
420420 8.12597 0.199622i 0.396507 0.00974057i
421421 32.1265i 1.56575i 0.622180 + 0.782874i 0.286247π0.286247\pi
−0.622180 + 0.782874i 0.713753π0.713753\pi
422422 1.71172 14.1416i 0.0833254 0.688402i
423423 14.0049 + 24.2571i 0.680939 + 1.17942i
424424 3.23644 + 19.7742i 0.157175 + 0.960319i
425425 −18.1391 10.4726i −0.879878 0.507998i
426426 3.31023 1.41182i 0.160381 0.0684031i
427427 −21.5556 5.69103i −1.04315 0.275408i
428428 −7.11447 + 7.41807i −0.343891 + 0.358566i
429429 0.926077 + 0.534671i 0.0447114 + 0.0258141i
430430 0 0
431431 32.7662 18.9176i 1.57829 0.911228i 0.583196 0.812332i 0.301802π-0.301802\pi
0.995098 0.0988962i 0.0315312π-0.0315312\pi
432432 5.14219 9.83341i 0.247404 0.473110i
433433 25.4835i 1.22466i −0.790602 0.612330i 0.790232π-0.790232\pi
0.790602 0.612330i 0.209768π-0.209768\pi
434434 −0.268968 0.340465i −0.0129109 0.0163428i
435435 −7.84367 −0.376075
436436 5.43750 1.57941i 0.260409 0.0756400i
437437 11.6690 + 20.2113i 0.558204 + 0.966837i
438438 5.84343 + 4.38763i 0.279210 + 0.209649i
439439 11.9804 20.7506i 0.571792 0.990373i −0.424590 0.905386i 0.639582π-0.639582\pi
0.996382 0.0849871i 0.0270849π-0.0270849\pi
440440 −5.11619 + 13.5362i −0.243905 + 0.645312i
441441 −0.142375 19.3806i −0.00677975 0.922887i
442442 3.10051 + 7.26962i 0.147476 + 0.345780i
443443 −5.13495 + 8.89399i −0.243969 + 0.422566i −0.961841 0.273608i 0.911783π-0.911783\pi
0.717872 + 0.696175i 0.245116π0.245116\pi
444444 −4.99449 1.22706i −0.237028 0.0582337i
445445 4.79140 2.76632i 0.227134 0.131136i
446446 −4.13097 + 34.1285i −0.195607 + 1.61603i
447447 −5.43726 −0.257174
448448 9.34464 18.9915i 0.441493 0.897265i
449449 11.5096 0.543170 0.271585 0.962414i 0.412452π-0.412452\pi
0.271585 + 0.962414i 0.412452π0.412452\pi
450450 2.44825 20.2265i 0.115412 0.953488i
451451 −5.84923 + 3.37705i −0.275429 + 0.159019i
452452 2.79091 + 0.685680i 0.131274 + 0.0322517i
453453 −3.56363 + 6.17239i −0.167434 + 0.290004i
454454 7.94707 + 18.6331i 0.372974 + 0.874494i
455455 −11.3442 2.99505i −0.531824 0.140410i
456456 −2.53747 + 6.71351i −0.118828 + 0.314389i
457457 −15.3050 + 26.5091i −0.715939 + 1.24004i 0.246657 + 0.969103i 0.420668π0.420668\pi
−0.962596 + 0.270941i 0.912665π0.912665\pi
458458 12.0442 + 9.04353i 0.562786 + 0.422576i
459459 −5.58353 9.67095i −0.260617 0.451401i
460460 27.1351 7.88182i 1.26518 0.367492i
461461 −17.3671 −0.808866 −0.404433 0.914568i 0.632531π-0.632531\pi
−0.404433 + 0.914568i 0.632531π0.632531\pi
462462 −2.67793 1.06520i −0.124589 0.0495576i
463463 21.7288i 1.00983i −0.863171 0.504913i 0.831525π-0.831525\pi
0.863171 0.504913i 0.168475π-0.168475\pi
464464 −9.46463 + 18.0992i −0.439385 + 0.840236i
465465 0.154267 0.0890661i 0.00715396 0.00413034i
466466 −0.721495 0.541745i −0.0334226 0.0250959i
467467 −0.585859 0.338246i −0.0271103 0.0156521i 0.486384 0.873745i 0.338316π-0.338316\pi
−0.513494 + 0.858093i 0.671649π0.671649\pi
468468 −5.32130 + 5.54838i −0.245977 + 0.256474i
469469 −18.7071 + 18.8450i −0.863814 + 0.870183i
470470 −42.0361 + 17.9285i −1.93898 + 0.826981i
471471 0.307659 + 0.177627i 0.0141762 + 0.00818461i
472472 −2.31508 14.1448i −0.106560 0.651067i
473473 0 0
474474 −0.975270 + 8.05730i −0.0447956 + 0.370084i
475475 27.4555i 1.25974i
476476 −11.0999 18.1793i −0.508761 0.833247i
477477 19.6144i 0.898082i
478478 −6.64834 0.804726i −0.304088 0.0368073i
479479 −14.3839 24.9136i −0.657217 1.13833i −0.981333 0.192316i 0.938400π-0.938400\pi
0.324116 0.946017i 0.394933π-0.394933\pi
480480 7.16068 + 4.92287i 0.326839 + 0.224697i
481481 6.42907 + 3.71182i 0.293140 + 0.169245i
482482 6.49482 + 15.2281i 0.295831 + 0.693619i
483483 1.47649 + 5.43045i 0.0671824 + 0.247094i
484484 −11.6766 + 12.1749i −0.530755 + 0.553404i
485485 7.94483 + 4.58695i 0.360756 + 0.208283i
486486 9.91426 13.2038i 0.449720 0.598936i
487487 1.58745 0.916514i 0.0719342 0.0415312i −0.463602 0.886044i 0.653443π-0.653443\pi
0.535536 + 0.844513i 0.320110π0.320110\pi
488488 −15.0942 18.4446i −0.683280 0.834948i
489489 4.18601i 0.189298i
490490 31.4196 + 3.56909i 1.41939 + 0.161235i
491491 13.4370 0.606401 0.303201 0.952927i 0.401945π-0.401945\pi
0.303201 + 0.952927i 0.401945π0.401945\pi
492492 1.13132 + 3.89484i 0.0510038 + 0.175593i
493493 10.2770 + 17.8002i 0.462851 + 0.801682i
494494 6.22038 8.28428i 0.279868 0.372728i
495495 −7.08269 + 12.2676i −0.318343 + 0.551387i
496496 −0.0193720 0.463443i −0.000869830 0.0208092i
497497 13.5096 3.67311i 0.605987 0.164762i
498498 9.37041 3.99651i 0.419898 0.179088i
499499 5.68404 9.84505i 0.254453 0.440725i −0.710294 0.703905i 0.751438π-0.751438\pi
0.964747 + 0.263180i 0.0847714π0.0847714\pi
500500 1.26164 + 0.309964i 0.0564224 + 0.0138620i
501501 0.578191 0.333819i 0.0258317 0.0149139i
502502 16.2342 + 1.96502i 0.724569 + 0.0877031i
503503 13.2022 0.588656 0.294328 0.955704i 0.404904π-0.404904\pi
0.294328 + 0.955704i 0.404904π0.404904\pi
504504 12.0301 16.8691i 0.535863 0.751409i
505505 −21.7408 −0.967454
506506 −9.94604 1.20389i −0.442156 0.0535193i
507507 4.61144 2.66241i 0.204801 0.118242i
508508 2.34807 9.55732i 0.104179 0.424037i
509509 13.2178 22.8940i 0.585870 1.01476i −0.408896 0.912581i 0.634086π-0.634086\pi
0.994766 0.102176i 0.0325804π-0.0325804\pi
510510 8.04365 3.43064i 0.356179 0.151911i
511511 20.1749 + 20.0272i 0.892484 + 0.885952i
512512 20.0000 10.5830i 0.883883 0.467707i
513513 −7.31899 + 12.6769i −0.323141 + 0.559697i
514514 −20.0322 + 26.6789i −0.883583 + 1.17675i
515515 22.4388 + 38.8652i 0.988773 + 1.71260i
516516 0 0
517517 16.2033 0.712619
518518 −18.5909 7.39489i −0.816837 0.324913i
519519 0.466786i 0.0204896i
520520 −7.94369 9.70695i −0.348354 0.425678i
521521 −10.4163 + 6.01384i −0.456345 + 0.263471i −0.710506 0.703691i 0.751534π-0.751534\pi
0.254161 + 0.967162i 0.418201π0.418201\pi
522522 −12.0049 + 15.9881i −0.525442 + 0.699782i
523523 2.43276 + 1.40455i 0.106377 + 0.0614168i 0.552245 0.833682i 0.313771π-0.313771\pi
−0.445868 + 0.895099i 0.647105π0.647105\pi
524524 5.69439 + 5.46133i 0.248760 + 0.238579i
525525 −1.69000 + 6.40113i −0.0737577 + 0.279368i
526526 5.92487 + 13.8917i 0.258337 + 0.605708i
527527 −0.404248 0.233393i −0.0176093 0.0101668i
528528 −1.65059 2.60156i −0.0718327 0.113218i
529529 −1.71848 2.97649i −0.0747164 0.129413i
530530 −31.7703 3.84554i −1.38002 0.167039i
531531 14.0305i 0.608872i
532532 −13.3622 + 24.5155i −0.579327 + 1.06288i
533533 5.85434i 0.253580i
534534 −0.141549 + 1.16943i −0.00612544 + 0.0506060i
535535 −8.20791 14.2165i −0.354859 0.614634i
536536 −28.0142 + 4.58509i −1.21003 + 0.198046i
537537 −5.94302 3.43120i −0.256460 0.148067i
538538 −30.3590 + 12.9482i −1.30887 + 0.558236i
539539 −9.75058 5.53440i −0.419987 0.238383i
540540 12.7911 + 12.2676i 0.550441 + 0.527913i
541541 −1.68628 0.973573i −0.0724988 0.0418572i 0.463312 0.886195i 0.346661π-0.346661\pi
−0.535811 + 0.844338i 0.679994π0.679994\pi
542542 −15.4246 11.5818i −0.662543 0.497481i
543543 6.38109 3.68413i 0.273839 0.158101i
544544 1.78975 22.7003i 0.0767349 0.973268i
545545 9.04336i 0.387375i
546546 1.96019 1.54855i 0.0838883 0.0662720i
547547 28.4561 1.21669 0.608347 0.793671i 0.291833π-0.291833\pi
0.608347 + 0.793671i 0.291833π0.291833\pi
548548 −0.0573744 0.197525i −0.00245091 0.00843786i
549549 −11.6653 20.2048i −0.497862 0.862321i
550550 −9.42505 7.07694i −0.401886 0.301762i
551551 13.4712 23.3329i 0.573894 0.994013i
552552 −2.12703 + 5.62760i −0.0905325 + 0.239526i
553553 −8.05982 + 30.5277i −0.342738 + 1.29817i
554554 0.253810 + 0.595095i 0.0107833 + 0.0252832i
555555 4.10704 7.11361i 0.174334 0.301956i
556556 7.14756 29.0926i 0.303124 1.23380i
557557 −7.96630 + 4.59935i −0.337543 + 0.194881i −0.659185 0.751981i 0.729099π-0.729099\pi
0.321642 + 0.946861i 0.395765π0.395765\pi
558558 0.0545617 0.450768i 0.00230978 0.0190825i
559559 0 0
560560 24.9651 + 22.7930i 1.05497 + 0.963181i
561561 −3.10051 −0.130904
562562 0.244194 2.01744i 0.0103007 0.0851004i
563563 −23.5533 + 13.5985i −0.992653 + 0.573108i −0.906066 0.423136i 0.860929π-0.860929\pi
−0.0865866 + 0.996244i 0.527596π0.527596\pi
564564 2.32146 9.44901i 0.0977511 0.397875i
565565 −2.29501 + 3.97508i −0.0965518 + 0.167233i
566566 −17.3248 40.6205i −0.728214 1.70741i
567567 12.9956 13.0914i 0.545764 0.549788i
568568 14.0000 + 5.29150i 0.587427 + 0.222027i
569569 11.7699 20.3861i 0.493420 0.854628i −0.506551 0.862210i 0.669080π-0.669080\pi
0.999971 + 0.00758149i 0.00241329π0.00241329\pi
570570 −9.16636 6.88270i −0.383937 0.288285i
571571 −15.1713 26.2774i −0.634897 1.09967i −0.986537 0.163539i 0.947709π-0.947709\pi
0.351640 0.936135i 0.385624π-0.385624\pi
572572 1.24050 + 4.27073i 0.0518680 + 0.178568i
573573 −1.20257 −0.0502382
574574 2.28009 + 15.6126i 0.0951690 + 0.651655i
575575 23.0145i 0.959772i
576576 20.9941 7.06138i 0.874756 0.294224i
577577 24.7760 14.3044i 1.03144 0.595500i 0.114041 0.993476i 0.463620π-0.463620\pi
0.917396 + 0.397976i 0.130287π0.130287\pi
578578 0.900923 + 0.676472i 0.0374735 + 0.0281375i
579579 −1.29128 0.745520i −0.0536637 0.0309828i
580580 −23.5431 22.5795i −0.977574 0.937564i
581581 38.2421 10.3976i 1.58655 0.431367i
582582 −1.79664 + 0.766273i −0.0744732 + 0.0317630i
583583 9.82652 + 5.67335i 0.406973 + 0.234966i
584584 4.90864 + 29.9911i 0.203121 + 1.24104i
585585 −6.13915 10.6333i −0.253823 0.439634i
586586 5.31917 43.9449i 0.219733 1.81535i
587587 15.2362i 0.628867i 0.949280 + 0.314433i 0.101814π0.101814\pi
−0.949280 + 0.314433i 0.898186π0.898186\pi
588588 −4.62438 + 4.89317i −0.190706 + 0.201791i
589589 0.611872i 0.0252117i
590590 22.7258 + 2.75078i 0.935608 + 0.113248i
591591 −3.77246 6.53409i −0.155178 0.268777i
592592 −11.4588 18.0607i −0.470955 0.742289i
593593 18.2934 + 10.5617i 0.751221 + 0.433717i 0.826135 0.563473i 0.190535π-0.190535\pi
−0.0749142 + 0.997190i 0.523868π0.523868\pi
594594 −2.46523 5.78010i −0.101150 0.237160i
595595 32.8274 8.92543i 1.34579 0.365907i
596596 −16.3202 15.6522i −0.668500 0.641140i
597597 4.92512 + 2.84352i 0.201572 + 0.116378i
598598 5.21423 6.94429i 0.213226 0.283973i
599599 −29.1795 + 16.8468i −1.19224 + 0.688341i −0.958814 0.284033i 0.908327π-0.908327\pi
−0.233427 + 0.972374i 0.574994π0.574994\pi
600600 −5.47729 + 4.48234i −0.223609 + 0.182991i
601601 24.3960i 0.995132i 0.867426 + 0.497566i 0.165773π0.165773\pi
−0.867426 + 0.497566i 0.834227π0.834227\pi
602602 0 0
603603 −27.7879 −1.13161
604604 −28.4648 + 8.26807i −1.15822 + 0.336423i
605605 −13.4712 23.3329i −0.547683 0.948616i
606606 2.77937 3.70156i 0.112904 0.150366i
607607 −4.08757 + 7.07987i −0.165909 + 0.287363i −0.936978 0.349389i 0.886389π-0.886389\pi
0.771069 + 0.636752i 0.219723π0.219723\pi
608608 −26.9425 + 12.8463i −1.09266 + 0.520985i
609609 4.57700 4.61075i 0.185469 0.186837i
610610 35.0138 14.9335i 1.41767 0.604639i
611611 −7.02235 + 12.1631i −0.284094 + 0.492065i
612612 5.31817 21.6465i 0.214974 0.875007i
613613 14.7221 8.49981i 0.594620 0.343304i −0.172302 0.985044i 0.555121π-0.555121\pi
0.766922 + 0.641740i 0.221787π0.221787\pi
614614 20.6685 + 2.50175i 0.834114 + 0.100963i
615615 −6.47768 −0.261205
616616 −4.97153 10.9062i −0.200309 0.439423i
617617 39.6548 1.59644 0.798221 0.602365i 0.205775π-0.205775\pi
0.798221 + 0.602365i 0.205775π0.205775\pi
618618 −9.48573 1.14817i −0.381572 0.0461861i
619619 −12.4719 + 7.20065i −0.501288 + 0.289419i −0.729245 0.684252i 0.760129π-0.760129\pi
0.227957 + 0.973671i 0.426795π0.426795\pi
620620 0.719432 + 0.176752i 0.0288931 + 0.00709854i
621621 −6.13514 + 10.6264i −0.246195 + 0.426422i
622622 20.2677 8.64425i 0.812662 0.346603i
623623 −1.16979 + 4.43075i −0.0468667 + 0.177514i
624624 2.66822 0.111532i 0.106814 0.00446487i
625625 11.9709 20.7343i 0.478837 0.829370i
626626 11.1122 14.7992i 0.444131 0.591493i
627627 2.03211 + 3.51971i 0.0811545 + 0.140564i
628628 0.412116 + 1.41881i 0.0164452 + 0.0566166i
629629 −21.5246 −0.858241
630630 20.5134 + 25.9663i 0.817275 + 1.03452i
631631 36.6698i 1.45980i 0.683553 + 0.729900i 0.260434π0.260434\pi
−0.683553 + 0.729900i 0.739566π0.739566\pi
632632 −26.1218 + 21.3768i −1.03907 + 0.850324i
633633 −4.19496 + 2.42196i −0.166735 + 0.0962644i
634634 −19.9998 + 26.6356i −0.794292 + 1.05784i
635635 13.6124 + 7.85913i 0.540192 + 0.311880i
636636 4.71629 4.91755i 0.187013 0.194994i
637637 8.38024 4.92077i 0.332037 0.194968i
638638 4.53747 + 10.6388i 0.179640 + 0.421193i
639639 12.6879 + 7.32538i 0.501927 + 0.289788i
640640 7.32160 + 35.3896i 0.289412 + 1.39890i
641641 −9.13798 15.8274i −0.360929 0.625147i 0.627185 0.778870i 0.284207π-0.284207\pi
−0.988114 + 0.153723i 0.950874π0.950874\pi
642642 3.46979 + 0.419989i 0.136942 + 0.0165757i
643643 13.6340i 0.537671i −0.963186 0.268836i 0.913361π-0.913361\pi
0.963186 0.268836i 0.0866389π-0.0866389\pi
644644 −11.2009 + 20.5501i −0.441377 + 0.809786i
645645 0 0
646646 −3.60943 + 29.8198i −0.142011 + 1.17324i
647647 −8.74153 15.1408i −0.343665 0.595245i 0.641445 0.767169i 0.278335π-0.278335\pi
−0.985110 + 0.171923i 0.945002π0.945002\pi
648648 19.4611 3.18520i 0.764505 0.125127i
649649 −7.02907 4.05824i −0.275915 0.159300i
650650 9.39708 4.00788i 0.368584 0.157202i
651651 −0.0376633 + 0.142655i −0.00147614 + 0.00559110i
652652 −12.0503 + 12.5645i −0.471924 + 0.492063i
653653 −8.40495 4.85260i −0.328911 0.189897i 0.326446 0.945216i 0.394149π-0.394149\pi
−0.655358 + 0.755319i 0.727482π0.727482\pi
654654 −1.53971 1.15611i −0.0602074 0.0452076i
655655 −10.9131 + 6.30070i −0.426411 + 0.246189i
656656 −7.81635 + 14.9472i −0.305177 + 0.583591i
657657 29.7488i 1.16061i
658658 13.9903 35.1719i 0.545399 1.37114i
659659 −28.9465 −1.12760 −0.563798 0.825913i 0.690660π-0.690660\pi
−0.563798 + 0.825913i 0.690660π0.690660\pi
660660 4.72546 1.37259i 0.183938 0.0534278i
661661 −6.43683 11.1489i −0.250364 0.433643i 0.713262 0.700897i 0.247217π-0.247217\pi
−0.963626 + 0.267254i 0.913884π0.913884\pi
662662 37.3824 + 28.0691i 1.45291 + 1.09094i
663663 1.34373 2.32742i 0.0521863 0.0903893i
664664 39.6304 + 14.9789i 1.53796 + 0.581293i
665665 −31.6475 31.4159i −1.22724 1.21826i
666666 −8.21408 19.2591i −0.318289 0.746277i
667667 11.2922 19.5587i 0.437238 0.757318i
668668 2.69643 + 0.662466i 0.104328 + 0.0256316i
669669 10.1239 5.84502i 0.391412 0.225982i
670670 5.44800 45.0093i 0.210475 1.73886i
671671 −13.4964 −0.521024
672672 −7.07227 + 1.33663i −0.272819 + 0.0515616i
673673 −23.6548 −0.911825 −0.455912 0.890025i 0.650687π-0.650687\pi
−0.455912 + 0.890025i 0.650687π0.650687\pi
674674 −2.63567 + 21.7749i −0.101522 + 0.838738i
675675 −12.5012 + 7.21755i −0.481170 + 0.277804i
676676 21.5057 + 5.28358i 0.827142 + 0.203215i
677677 −1.80224 + 3.12157i −0.0692657 + 0.119972i −0.898578 0.438813i 0.855399π-0.855399\pi
0.829313 + 0.558785i 0.188732π0.188732\pi
678678 −0.383393 0.898923i −0.0147241 0.0345229i
679679 −7.33237 + 1.99360i −0.281391 + 0.0765072i
680680 34.0191 + 12.8580i 1.30457 + 0.493083i
681681 3.44419 5.96550i 0.131981 0.228599i
682682 −0.210046 0.157717i −0.00804309 0.00603928i
683683 3.80924 + 6.59779i 0.145756 + 0.252457i 0.929655 0.368432i 0.120105π-0.120105\pi
−0.783899 + 0.620889i 0.786772π0.786772\pi
684684 −28.0587 + 8.15010i −1.07285 + 0.311627i
685685 0.328514 0.0125519
686686 −20.4322 + 16.3867i −0.780106 + 0.625648i
687687 5.12162i 0.195402i
688688 0 0
689689 −8.51745 + 4.91755i −0.324489 + 0.187344i
690690 −7.68369 5.76942i −0.292513 0.219638i
691691 −44.9707 25.9639i −1.71077 0.987712i −0.933526 0.358509i 0.883285π-0.883285\pi
−0.777241 0.629203i 0.783381π-0.783381\pi
692692 −1.34373 + 1.40108i −0.0510811 + 0.0532609i
693693 −3.07831 11.3219i −0.116935 0.430083i
694694 −29.2674 + 12.4826i −1.11097 + 0.473834i
695695 41.4364 + 23.9233i 1.57177 + 0.907462i
696696 6.85413 1.12182i 0.259805 0.0425223i
697697 8.48721 + 14.7003i 0.321476 + 0.556813i
698698 4.83875 39.9759i 0.183149 1.51311i
699699 0.306806i 0.0116045i
700700 −23.4995 + 14.3482i −0.888198 + 0.542312i
701701 0.741474i 0.0280051i −0.999902 0.0140025i 0.995543π-0.995543\pi
0.999902 0.0140025i 0.00445729π-0.00445729\pi
702702 5.40727 + 0.654505i 0.204084 + 0.0247027i
703703 14.1074 + 24.4347i 0.532071 + 0.921574i
704704 2.53478 12.5602i 0.0955331 0.473381i
705705 13.4581 + 7.77006i 0.506863 + 0.292637i
706706 5.31161 + 12.4539i 0.199905 + 0.468708i
707707 12.6864 12.7799i 0.477120 0.480638i
708708 −3.37364 + 3.51761i −0.126789 + 0.132200i
709709 −35.6491 20.5820i −1.33883 0.772974i −0.352196 0.935926i 0.614565π-0.614565\pi
−0.986634 + 0.162952i 0.947898π0.947898\pi
710710 −14.3528 + 19.1150i −0.538652 + 0.717375i
711711 −28.6147 + 16.5207i −1.07314 + 0.619575i
712712 −3.79129 + 3.10260i −0.142085 + 0.116275i
713713 0.512901i 0.0192083i
714714 −2.67706 + 6.73018i −0.100186 + 0.251871i
715715 −7.10284 −0.265631
716716 −7.96082 27.4070i −0.297510 1.02425i
717717 1.13863 + 1.97216i 0.0425229 + 0.0736518i
718718 3.18889 4.24696i 0.119008 0.158495i
719719 −7.02471 + 12.1672i −0.261978 + 0.453758i −0.966767 0.255658i 0.917708π-0.917708\pi
0.704790 + 0.709416i 0.251041π0.251041\pi
720720 1.47745 + 35.3455i 0.0550613 + 1.31725i
721721 −35.9398 9.48869i −1.33847 0.353377i
722722 11.5012 4.90528i 0.428029 0.182556i
723723 2.81479 4.87536i 0.104683 0.181317i
724724 29.7586 + 7.31117i 1.10597 + 0.271718i
725725 23.0095 13.2845i 0.854550 0.493375i
726726 5.69479 + 0.689307i 0.211354 + 0.0255826i
727727 −13.2022 −0.489642 −0.244821 0.969568i 0.578729π-0.578729\pi
−0.244821 + 0.969568i 0.578729π0.578729\pi
728728 10.3414 + 0.994736i 0.383278 + 0.0368674i
729729 15.3015 0.566724
730730 −48.1854 5.83245i −1.78342 0.215868i
731731 0 0
732732 −1.93365 + 7.87050i −0.0714697 + 0.290902i
733733 −24.9797 + 43.2661i −0.922646 + 1.59807i −0.127342 + 0.991859i 0.540644π0.540644\pi
−0.795304 + 0.606211i 0.792689π0.792689\pi
734734 21.8880 9.33529i 0.807900 0.344572i
735735 −5.44471 9.27253i −0.200831 0.342022i
736736 −22.5845 + 10.7684i −0.832476 + 0.396928i
737737 −8.03747 + 13.9213i −0.296064 + 0.512798i
738738 −9.91426 + 13.2038i −0.364949 + 0.486038i
739739 18.2718 + 31.6476i 0.672138 + 1.16418i 0.977297 + 0.211875i 0.0679571π0.0679571\pi
−0.305159 + 0.952301i 0.598710π0.598710\pi
740740 32.8054 9.52884i 1.20595 0.350287i
741741 −3.52278 −0.129413
742742 20.7994 16.4316i 0.763570 0.603223i
743743 15.1330i 0.555177i −0.960700 0.277589i 0.910465π-0.910465\pi
0.960700 0.277589i 0.0895352π-0.0895352\pi
744744 −0.122067 + 0.0998933i −0.00447518 + 0.00366226i
745745 31.2771 18.0579i 1.14591 0.661589i
746746 10.9184 14.5411i 0.399752 0.532389i
747747 35.9163 + 20.7363i 1.31411 + 0.758701i
748748 −9.30631 8.92543i −0.340273 0.326346i
749749 13.1464 + 3.47087i 0.480360 + 0.126823i
750750 −0.173314 0.406362i −0.00632855 0.0148382i
751751 −11.9997 6.92806i −0.437877 0.252808i 0.264820 0.964298i 0.414688π-0.414688\pi
−0.702697 + 0.711490i 0.748021π0.748021\pi
752752 34.1688 21.6788i 1.24601 0.790544i
753753 −2.78036 4.81572i −0.101322 0.175495i
754754 −9.95254 1.20467i −0.362450 0.0438716i
755755 47.3412i 1.72292i
756756 −14.6752 + 0.360511i −0.533732 + 0.0131116i
757757 46.6967i 1.69722i −0.529019 0.848610i 0.677440π-0.677440\pi
0.529019 0.848610i 0.322560π-0.322560\pi
758758 4.34739 35.9165i 0.157904 1.30455i
759759 1.70341 + 2.95039i 0.0618299 + 0.107093i
760760 −7.70000 47.0458i −0.279308 1.70653i
761761 40.7899 + 23.5501i 1.47863 + 0.853689i 0.999708 0.0241662i 0.00769309π-0.00769309\pi
0.478925 + 0.877856i 0.341026π0.341026\pi
762762 −3.07831 + 1.31291i −0.111515 + 0.0475616i
763763 −5.31596 5.27705i −0.192451 0.191042i
764764 −3.60957 3.46184i −0.130590 0.125245i
765765 30.8309 + 17.8002i 1.11469 + 0.643568i
766766 30.4996 + 22.9011i 1.10199 + 0.827449i
767767 6.09267 3.51761i 0.219994 0.127013i
768768 −6.96138 3.27768i −0.251197 0.118273i
769769 17.3071i 0.624110i −0.950064 0.312055i 0.898983π-0.898983\pi
0.950064 0.312055i 0.101017π-0.101017\pi
770770 18.9421 2.76634i 0.682626 0.0996921i
771771 11.3448 0.408574
772772 −1.72970 5.95490i −0.0622532 0.214322i
773773 13.5389 + 23.4501i 0.486960 + 0.843440i 0.999888 0.0149920i 0.00477229π-0.00477229\pi
−0.512927 + 0.858432i 0.671439π0.671439\pi
774774 0 0
775775 −0.301696 + 0.522552i −0.0108372 + 0.0187706i
776776 −7.59856 2.87198i −0.272772 0.103098i
777777 1.78502 + 6.56523i 0.0640372 + 0.235526i
778778 17.7485 + 41.6141i 0.636315 + 1.49194i
779779 11.1252 19.2694i 0.398601 0.690398i
780780 −1.01763 + 4.14205i −0.0364371 + 0.148309i
781781 7.33982 4.23764i 0.262639 0.151635i
782782 −3.02561 + 24.9964i −0.108195 + 0.893869i
783783 14.1654 0.506230
784784 −27.9662 + 1.37486i −0.998794 + 0.0491023i
785785 −2.35969 −0.0842208
786786 0.322400 2.66354i 0.0114996 0.0950054i
787787 −46.9684 + 27.1172i −1.67424 + 0.966624i −0.709023 + 0.705186i 0.750864π0.750864\pi
−0.965220 + 0.261439i 0.915803π0.915803\pi
788788 7.48648 30.4721i 0.266695 1.08552i
789789 2.56778 4.44753i 0.0914155 0.158336i
790790 −21.1492 49.5876i −0.752456 1.76425i
791791 −0.997467 3.66864i −0.0354658 0.130442i
792792 4.43462 11.7329i 0.157578 0.416911i
793793 5.84923 10.1312i 0.207712 0.359768i
794794 −19.2690 14.4684i −0.683830 0.513464i
795795 5.44115 + 9.42435i 0.192978 + 0.334247i
796796 6.59732 + 22.7129i 0.233836 + 0.805036i
797797 −20.1437 −0.713527 −0.356763 0.934195i 0.616120π-0.616120\pi
−0.356763 + 0.934195i 0.616120π0.616120\pi
798798 9.39468 1.37202i 0.332568 0.0485689i
799799 40.7221i 1.44064i
800800 −29.3436 2.31352i −1.03745 0.0817953i
801801 −4.15310 + 2.39779i −0.146743 + 0.0847219i
802802 −6.66910 5.00759i −0.235494 0.176824i
803803 14.9037 + 8.60465i 0.525940 + 0.303651i
804804 6.96673 + 6.68160i 0.245698 + 0.235642i
805805 −26.5285 26.3344i −0.935008 0.928164i
806806 0.209423 0.0893195i 0.00737661 0.00314615i
807807 9.71963 + 5.61163i 0.342147 + 0.197539i
808808 18.9981 3.10941i 0.668349 0.109389i
809809 −17.2771 29.9249i −0.607432 1.05210i −0.991662 0.128865i 0.958867π-0.958867\pi
0.384231 0.923237i 0.374467π-0.374467\pi
810810 −3.78466 + 31.2674i −0.132979 + 1.09862i
811811 13.6340i 0.478754i 0.970927 + 0.239377i 0.0769431π0.0769431\pi
−0.970927 + 0.239377i 0.923057π0.923057\pi
812812 27.0110 0.663551i 0.947899 0.0232861i
813813 6.55911i 0.230038i
814814 −12.0244 1.45546i −0.421456 0.0510137i
815815 −13.9023 24.0795i −0.486976 0.843468i
816816 −6.53823 + 4.14826i −0.228884 + 0.145218i
817817 0 0
818818 0.133094 + 0.312058i 0.00465352 + 0.0109109i
819819 9.83294 + 2.59606i 0.343591 + 0.0907136i
820820 −19.4430 18.6473i −0.678980 0.651191i
821821 27.7311 + 16.0106i 0.967822 + 0.558772i 0.898572 0.438827i 0.144606π-0.144606\pi
0.0692505 + 0.997599i 0.477939π0.477939\pi
822822 −0.0419975 + 0.0559322i −0.00146483 + 0.00195086i
823823 26.8399 15.4960i 0.935580 0.540158i 0.0470083 0.998894i 0.485031π-0.485031\pi
0.888572 + 0.458737i 0.151698π0.151698\pi
824824 −25.1666 30.7528i −0.876719 1.07132i
825825 4.00788i 0.139537i
826826 −14.8781 + 11.7538i −0.517677 + 0.408966i
827827 −11.0191 −0.383172 −0.191586 0.981476i 0.561363π-0.561363\pi
−0.191586 + 0.981476i 0.561363π0.561363\pi
828828 −23.5202 + 6.83182i −0.817383 + 0.237422i
829829 18.9836 + 32.8806i 0.659328 + 1.14199i 0.980790 + 0.195067i 0.0624924π0.0624924\pi
−0.321462 + 0.946922i 0.604174π0.604174\pi
830830 −40.6291 + 54.1098i −1.41026 + 1.87818i
831831 0.109999 0.190524i 0.00381582 0.00660919i
832832 8.32984 + 7.34623i 0.288785 + 0.254685i
833833 −13.9090 + 24.5052i −0.481920 + 0.849054i
834834 −9.37041 + 3.99651i −0.324471 + 0.138388i
835835 −2.21731 + 3.84050i −0.0767332 + 0.132906i
836836 −4.03273 + 16.4144i −0.139475 + 0.567702i
837837 −0.278601 + 0.160850i −0.00962984 + 0.00555979i
838838 −41.2962 4.99857i −1.42655 0.172673i
839839 8.32984 0.287578 0.143789 0.989608i 0.454071π-0.454071\pi
0.143789 + 0.989608i 0.454071π0.454071\pi
840840 1.10065 11.4425i 0.0379761 0.394804i
841841 2.92739 0.100945
842842 45.1045 + 5.45952i 1.55440 + 0.188148i
843843 −0.598452 + 0.345516i −0.0206118 + 0.0119002i
844844 −19.5634 4.80640i −0.673401 0.165443i
845845 −17.6844 + 30.6304i −0.608363 + 1.05372i
846846 36.4361 15.5401i 1.25270 0.534280i
847847 21.5766 + 5.69657i 0.741380 + 0.195736i
848848 28.3123 1.18346i 0.972247 0.0406402i
849849 −7.50840 + 13.0049i −0.257687 + 0.446328i
850850 −17.7858 + 23.6870i −0.610047 + 0.812459i
851851 11.8255 + 20.4824i 0.405374 + 0.702128i
852852 −1.41962 4.88738i −0.0486353 0.167439i
853853 6.94153 0.237673 0.118837 0.992914i 0.462083π-0.462083\pi
0.118837 + 0.992914i 0.462083π0.462083\pi
854854 −11.6531 + 29.2962i −0.398763 + 1.00250i
855855 46.6657i 1.59593i
856856 9.20569 + 11.2491i 0.314644 + 0.384486i
857857 1.91744 1.10704i 0.0654986 0.0378156i −0.466893 0.884314i 0.654627π-0.654627\pi
0.532392 + 0.846498i 0.321293π0.321293\pi
858858 0.908036 1.20932i 0.0309998 0.0412855i
859859 5.26337 + 3.03881i 0.179584 + 0.103683i 0.587097 0.809516i 0.300271π-0.300271\pi
−0.407513 + 0.913199i 0.633604π0.633604\pi
860860 0 0
861861 3.77991 3.80778i 0.128819 0.129769i
862862 −20.9914 49.2175i −0.714970 1.67635i
863863 7.64747 + 4.41527i 0.260323 + 0.150298i 0.624482 0.781039i 0.285310π-0.285310\pi
−0.364159 + 0.931337i 0.618643π0.618643\pi
864864 −12.9319 8.89053i −0.439953 0.302462i
865865 −1.55026 2.68512i −0.0527103 0.0912969i
866866 −35.7780 4.33063i −1.21579 0.147161i
867867 0.383106i 0.0130110i
868868 −0.523709 + 0.319764i −0.0177758 + 0.0108535i
869869 19.1141i 0.648400i
870870 −1.33294 + 11.0122i −0.0451909 + 0.373350i
871871 −6.96673 12.0667i −0.236059 0.408866i
872872 −1.29340 7.90247i −0.0438000 0.267611i
873873 −6.88643 3.97588i −0.233070 0.134563i
874874 30.3590 12.9482i 1.02691 0.437979i
875875 −0.450909 1.65842i −0.0152435 0.0560650i
876876 7.15310 7.45835i 0.241681 0.251994i
877877 10.3059 + 5.95011i 0.348005 + 0.200921i 0.663806 0.747905i 0.268940π-0.268940\pi
−0.315801 + 0.948825i 0.602273π0.602273\pi
878878 −27.0972 20.3464i −0.914487 0.686657i
879879 −13.0358 + 7.52623i −0.439687 + 0.253854i
880880 18.1349 + 9.48328i 0.611327 + 0.319681i
881881 53.9142i 1.81642i 0.418519 + 0.908208i 0.362549π0.362549\pi
−0.418519 + 0.908208i 0.637451π0.637451\pi
882882 −27.2339 3.09362i −0.917014 0.104168i
883883 11.1987 0.376866 0.188433 0.982086i 0.439659π-0.439659\pi
0.188433 + 0.982086i 0.439659π0.439659\pi
884884 10.7332 3.11763i 0.360996 0.104857i
885885 −3.89215 6.74139i −0.130833 0.226609i
886886 11.6142 + 8.72073i 0.390188 + 0.292979i
887887 −18.1832 + 31.4942i −0.610531 + 1.05747i 0.380620 + 0.924732i 0.375711π0.375711\pi
−0.991151 + 0.132740i 0.957623π0.957623\pi
888888 −2.57151 + 6.80357i −0.0862941 + 0.228313i
889889 −12.5630 + 3.41576i −0.421351 + 0.114561i
890890 −3.06957 7.19707i −0.102892 0.241246i
891891 5.58353 9.67095i 0.187055 0.323989i
892892 47.2132 + 11.5995i 1.58082 + 0.388380i
893893 −46.2278 + 26.6896i −1.54695 + 0.893134i
894894 −0.924000 + 7.63373i −0.0309032 + 0.255310i
895895 45.5819 1.52364
896896 −25.0754 16.3470i −0.837711 0.546113i
897897 −2.95297 −0.0985968
898898 1.95592 16.1590i 0.0652698 0.539234i
899899 0.512788 0.296058i 0.0171024 0.00987410i
900900 −27.9813 6.87453i −0.932711 0.229151i
901901 14.2583 24.6960i 0.475011 0.822744i
902902 3.74726 + 8.78601i 0.124770 + 0.292542i
903903 0 0
904904 1.43695 3.80183i 0.0477924 0.126447i
905905 −24.4709 + 42.3849i −0.813441 + 1.40892i
906906 8.06023 + 6.05215i 0.267783 + 0.201069i
907907 8.92370 + 15.4563i 0.296307 + 0.513218i 0.975288 0.220937i 0.0709116π-0.0709116\pi
−0.678981 + 0.734156i 0.737578π0.737578\pi
908908 27.5107 7.99093i 0.912975 0.265188i
909909 18.8446 0.625034
910910 −6.13277 + 15.4179i −0.203299 + 0.511098i
911911 11.1458i 0.369278i 0.982806 + 0.184639i 0.0591116π0.0591116\pi
−0.982806 + 0.184639i 0.940888π0.940888\pi
912912 8.99433 + 4.70340i 0.297832 + 0.155745i
913913 20.7771 11.9957i 0.687623 0.396999i
914914 34.6170 + 25.9927i 1.14503 + 0.859761i
915915 −11.2099 6.47203i −0.370587 0.213959i
916916 14.7436 15.3727i 0.487141 0.507929i
917917 2.66437 10.0917i 0.0879854 0.333257i
918918 −14.5265 + 6.19562i −0.479448 + 0.204486i
919919 −28.2802 16.3276i −0.932879 0.538598i −0.0451579 0.998980i 0.514379π-0.514379\pi
−0.887721 + 0.460382i 0.847712π0.847712\pi
920920 −6.45452 39.4361i −0.212799 1.30017i
921921 −3.53980 6.13111i −0.116640 0.202027i
922922 −2.95134 + 24.3828i −0.0971971 + 0.803005i
923923 7.34623i 0.241804i
924924 −1.95059 + 3.57871i −0.0641696 + 0.117731i
925925 27.8238i 0.914839i
926926 −30.5066 3.69257i −1.00251 0.121345i
927927 −19.4496 33.6876i −0.638807 1.10645i
928928 23.8023 + 16.3638i 0.781349 + 0.537167i
929929 −23.3027 13.4538i −0.764537 0.441406i 0.0663853 0.997794i 0.478853π-0.478853\pi
−0.830922 + 0.556388i 0.812187π0.812187\pi
930930 −0.0988299 0.231721i −0.00324076 0.00759844i
931931 36.9344 0.271329i 1.21048 0.00889246i
932932 −0.883202 + 0.920891i −0.0289302 + 0.0301648i
933933 −6.48885 3.74634i −0.212435 0.122650i
934934 −0.574445 + 0.765045i −0.0187964 + 0.0250330i
935935 17.8353 10.2972i 0.583276 0.336755i
936936 6.88544 + 8.41381i 0.225058 + 0.275014i
937937 32.6476i 1.06655i −0.845942 0.533275i 0.820961π-0.820961\pi
0.845942 0.533275i 0.179039π-0.179039\pi
938938 23.2787 + 29.4666i 0.760078 + 0.962120i
939939 −6.29315 −0.205369
940940 18.0275 + 62.0640i 0.587992 + 2.02431i
941941 6.32087 + 10.9481i 0.206055 + 0.356897i 0.950468 0.310822i 0.100604π-0.100604\pi
−0.744414 + 0.667719i 0.767271π0.767271\pi
942942 0.301665 0.401757i 0.00982878 0.0130899i
943943 9.32569 16.1526i 0.303686 0.526000i
944944 −20.2522 + 0.846548i −0.659154 + 0.0275528i
945945 5.98488 22.6686i 0.194688 0.737410i
946946 0 0
947947 21.1271 36.5931i 0.686537 1.18912i −0.286414 0.958106i 0.592463π-0.592463\pi
0.972951 0.231011i 0.0742035π-0.0742035\pi
948948 11.1464 + 2.73849i 0.362020 + 0.0889421i
949949 −12.9182 + 7.45835i −0.419344 + 0.242108i
950950 38.5465 + 4.66574i 1.25061 + 0.151377i
951951 11.3264 0.367285
952952 −27.4094 + 12.4945i −0.888345 + 0.404948i
953953 −44.4561 −1.44007 −0.720037 0.693936i 0.755875π-0.755875\pi
−0.720037 + 0.693936i 0.755875π0.755875\pi
954954 27.5380 + 3.33324i 0.891574 + 0.107918i
955955 6.91764 3.99390i 0.223850 0.129240i
956956 −2.25962 + 9.19729i −0.0730812 + 0.297462i
957957 1.96650 3.40607i 0.0635678 0.110103i
958958 −37.4223 + 15.9607i −1.20906 + 0.515668i
959959 −0.191697 + 0.193110i −0.00619021 + 0.00623585i
960960 8.12842 9.21676i 0.262344 0.297470i
961961 15.4933 26.8351i 0.499783 0.865650i
962962 6.30382 8.39541i 0.203243 0.270679i
963963 7.11447 + 12.3226i 0.229261 + 0.397091i
964964 22.4834 6.53067i 0.724142 0.210339i
965965 9.90388 0.318817
966966 7.87508 1.15009i 0.253377 0.0370036i
967967 25.7160i 0.826972i 0.910510 + 0.413486i 0.135689π0.135689\pi
−0.910510 + 0.413486i 0.864311π0.864311\pi
968968 15.1088 + 18.4626i 0.485616 + 0.593409i
969969 8.84573 5.10709i 0.284166 0.164063i
970970 7.79005 10.3748i 0.250123 0.333114i
971971 −40.2746 23.2526i −1.29247 0.746210i −0.313381 0.949627i 0.601462π-0.601462\pi
−0.979092 + 0.203417i 0.934795π0.934795\pi
972972 −16.8529 16.1631i −0.540556 0.518432i
973973 −38.2421 + 10.3976i −1.22599 + 0.333333i
974974 −1.01699 2.38448i −0.0325863 0.0764035i
975975 −3.00854 1.73698i −0.0963503 0.0556278i
976976 −28.4607 + 18.0572i −0.911004 + 0.577998i
977977 −17.1348 29.6783i −0.548189 0.949492i −0.998399 0.0565688i 0.981984π-0.981984\pi
0.450209 0.892923i 0.351349π-0.351349\pi
978978 5.87702 + 0.711365i 0.187926 + 0.0227469i
979979 2.77419i 0.0886635i
980980 10.3503 43.5055i 0.330628 1.38973i
981981 7.83862i 0.250268i
982982 2.28346 18.8650i 0.0728680 0.602007i
983983 0.777334 + 1.34638i 0.0247931 + 0.0429429i 0.878156 0.478375i 0.158774π-0.158774\pi
−0.853363 + 0.521318i 0.825441π0.825441\pi
984984 5.66047 0.926450i 0.180449 0.0295341i
985985 43.4012 + 25.0577i 1.38288 + 0.798404i
986986 26.7374 11.4036i 0.851491 0.363163i
987987 −12.4207 + 3.37705i −0.395354 + 0.107493i
988988 −10.5738 10.1410i −0.336396 0.322629i
989989 0 0
990990 16.0196 + 12.0286i 0.509138 + 0.382294i
991991 −22.6482 + 13.0759i −0.719443 + 0.415371i −0.814548 0.580097i 0.803015π-0.803015\pi
0.0951047 + 0.995467i 0.469681π0.469681\pi
992992 −0.653950 0.0515591i −0.0207629 0.00163700i
993993 15.8964i 0.504457i
994994 −2.86113 19.5912i −0.0907496 0.621394i
995995 −37.7748 −1.19754
996996 −4.01857 13.8349i −0.127333 0.438376i
997997 −18.1467 31.4310i −0.574711 0.995429i −0.996073 0.0885360i 0.971781π-0.971781\pi
0.421362 0.906893i 0.361552π-0.361552\pi
998998 −12.8562 9.65325i −0.406955 0.305568i
999999 −7.41717 + 12.8469i −0.234669 + 0.406458i
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 56.2.m.a.19.3 yes 12
3.2 odd 2 504.2.bk.a.19.4 12
4.3 odd 2 224.2.q.a.47.4 12
7.2 even 3 392.2.e.e.195.3 12
7.3 odd 6 inner 56.2.m.a.3.6 yes 12
7.4 even 3 392.2.m.g.227.6 12
7.5 odd 6 392.2.e.e.195.4 12
7.6 odd 2 392.2.m.g.19.3 12
8.3 odd 2 inner 56.2.m.a.19.5 yes 12
8.5 even 2 224.2.q.a.47.3 12
12.11 even 2 2016.2.bs.a.271.1 12
21.17 even 6 504.2.bk.a.451.1 12
24.5 odd 2 2016.2.bs.a.271.6 12
24.11 even 2 504.2.bk.a.19.2 12
28.3 even 6 224.2.q.a.143.3 12
28.11 odd 6 1568.2.q.g.815.4 12
28.19 even 6 1568.2.e.e.783.6 12
28.23 odd 6 1568.2.e.e.783.7 12
28.27 even 2 1568.2.q.g.1391.3 12
56.3 even 6 inner 56.2.m.a.3.4 12
56.5 odd 6 1568.2.e.e.783.5 12
56.11 odd 6 392.2.m.g.227.4 12
56.13 odd 2 1568.2.q.g.1391.4 12
56.19 even 6 392.2.e.e.195.2 12
56.27 even 2 392.2.m.g.19.5 12
56.37 even 6 1568.2.e.e.783.8 12
56.45 odd 6 224.2.q.a.143.4 12
56.51 odd 6 392.2.e.e.195.1 12
56.53 even 6 1568.2.q.g.815.3 12
84.59 odd 6 2016.2.bs.a.1711.6 12
168.59 odd 6 504.2.bk.a.451.3 12
168.101 even 6 2016.2.bs.a.1711.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.m.a.3.4 12 56.3 even 6 inner
56.2.m.a.3.6 yes 12 7.3 odd 6 inner
56.2.m.a.19.3 yes 12 1.1 even 1 trivial
56.2.m.a.19.5 yes 12 8.3 odd 2 inner
224.2.q.a.47.3 12 8.5 even 2
224.2.q.a.47.4 12 4.3 odd 2
224.2.q.a.143.3 12 28.3 even 6
224.2.q.a.143.4 12 56.45 odd 6
392.2.e.e.195.1 12 56.51 odd 6
392.2.e.e.195.2 12 56.19 even 6
392.2.e.e.195.3 12 7.2 even 3
392.2.e.e.195.4 12 7.5 odd 6
392.2.m.g.19.3 12 7.6 odd 2
392.2.m.g.19.5 12 56.27 even 2
392.2.m.g.227.4 12 56.11 odd 6
392.2.m.g.227.6 12 7.4 even 3
504.2.bk.a.19.2 12 24.11 even 2
504.2.bk.a.19.4 12 3.2 odd 2
504.2.bk.a.451.1 12 21.17 even 6
504.2.bk.a.451.3 12 168.59 odd 6
1568.2.e.e.783.5 12 56.5 odd 6
1568.2.e.e.783.6 12 28.19 even 6
1568.2.e.e.783.7 12 28.23 odd 6
1568.2.e.e.783.8 12 56.37 even 6
1568.2.q.g.815.3 12 56.53 even 6
1568.2.q.g.815.4 12 28.11 odd 6
1568.2.q.g.1391.3 12 28.27 even 2
1568.2.q.g.1391.4 12 56.13 odd 2
2016.2.bs.a.271.1 12 12.11 even 2
2016.2.bs.a.271.6 12 24.5 odd 2
2016.2.bs.a.1711.1 12 168.101 even 6
2016.2.bs.a.1711.6 12 84.59 odd 6