Properties

Label 102.2.h.a.49.2
Level 102102
Weight 22
Character 102.49
Analytic conductor 0.8140.814
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [102,2,Mod(19,102)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(102, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("102.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 102=2317 102 = 2 \cdot 3 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 102.h (of order 88, degree 44, 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: 0.8144741006170.814474100617
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ8)\Q(\zeta_{8})
Coefficient field: Q(ζ16)\Q(\zeta_{16})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+1 x^{8} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 49.2
Root 0.923880+0.382683i0.923880 + 0.382683i of defining polynomial
Character χ\chi == 102.49
Dual form 102.2.h.a.25.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.7071070.707107i)q2+(0.382683+0.923880i)q3+1.00000iq4+(0.4005440.165911i)q5+(0.3826830.923880i)q6+(3.15432+1.30656i)q7+(0.7071070.707107i)q8+(0.707107+0.707107i)q9+(0.4005440.165911i)q10+(0.6488471.56645i)q11+(0.923880+0.382683i)q12+0.331821iq13+(1.306563.15432i)q14+(0.306563+0.306563i)q151.00000q16+(3.944951.19891i)q17+1.00000q18+(1.515941.51594i)q19+(0.165911+0.400544i)q20+3.41421iq21+(1.56645+0.648847i)q22+(0.7207771.74011i)q23+(0.923880+0.382683i)q24+(3.40262+3.40262i)q25+(0.2346330.234633i)q26+(0.9238800.382683i)q27+(1.30656+3.15432i)q28+(7.88877+3.26763i)q290.433546iq30+(0.9895382.38896i)q31+(0.707107+0.707107i)q32+1.69552q33+(1.94174+3.63726i)q34+1.48022q35+(0.7071070.707107i)q36+(4.061939.80638i)q37+2.14386iq38+(0.306563+0.126983i)q39+(0.1659110.400544i)q40+(11.1953+4.63726i)q41+(2.414212.41421i)q42+(7.137077.13707i)q43+(1.56645+0.648847i)q44+(0.165911+0.400544i)q45+(1.74011+0.720777i)q462.38009iq47+(0.3826830.923880i)q48+(3.29289+3.29289i)q49+4.81204q50+(0.4020154.10346i)q510.331821q52+(2.21371+2.21371i)q53+(0.382683+0.923880i)q540.735084iq55+(3.154321.30656i)q56+(0.8204201.98067i)q57+(7.88877+3.26763i)q58+(5.42676+5.42676i)q59+(0.306563+0.306563i)q60+(7.427883.07673i)q61+(0.989538+2.38896i)q62+(3.15432+1.30656i)q631.00000iq64+(0.0550527+0.132909i)q65+(1.198911.19891i)q66+15.7711q67+(1.198913.94495i)q68+1.88348q69+(1.046671.04667i)q70+(0.0867259+0.209375i)q71+1.00000iq72+(11.2147+4.64527i)q73+(4.06193+9.80638i)q74+(4.445741.84149i)q75+(1.515941.51594i)q76+(4.093344.09334i)q77+(0.306563+0.126983i)q78+(4.79863+11.5849i)q79+(0.400544+0.165911i)q801.00000iq81+(4.6372611.1953i)q82+(0.7380270.738027i)q833.41421q84+(1.77904+0.174292i)q8510.0933q86+(6.037806.03780i)q87+(0.6488471.56645i)q88+13.8281iq89+(0.4005440.165911i)q90+(0.433546+1.04667i)q91+(1.74011+0.720777i)q92+(1.828431.82843i)q93+(1.68297+1.68297i)q94+(0.8587100.355689i)q95+(0.382683+0.923880i)q96+(3.469531.43713i)q974.65685iq98+(0.648847+1.56645i)q99+O(q100)q+(-0.707107 - 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.400544 - 0.165911i) q^{5} +(0.382683 - 0.923880i) q^{6} +(3.15432 + 1.30656i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.400544 - 0.165911i) q^{10} +(0.648847 - 1.56645i) q^{11} +(-0.923880 + 0.382683i) q^{12} +0.331821i q^{13} +(-1.30656 - 3.15432i) q^{14} +(0.306563 + 0.306563i) q^{15} -1.00000 q^{16} +(-3.94495 - 1.19891i) q^{17} +1.00000 q^{18} +(-1.51594 - 1.51594i) q^{19} +(0.165911 + 0.400544i) q^{20} +3.41421i q^{21} +(-1.56645 + 0.648847i) q^{22} +(0.720777 - 1.74011i) q^{23} +(0.923880 + 0.382683i) q^{24} +(-3.40262 + 3.40262i) q^{25} +(0.234633 - 0.234633i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.30656 + 3.15432i) q^{28} +(-7.88877 + 3.26763i) q^{29} -0.433546i q^{30} +(-0.989538 - 2.38896i) q^{31} +(0.707107 + 0.707107i) q^{32} +1.69552 q^{33} +(1.94174 + 3.63726i) q^{34} +1.48022 q^{35} +(-0.707107 - 0.707107i) q^{36} +(-4.06193 - 9.80638i) q^{37} +2.14386i q^{38} +(-0.306563 + 0.126983i) q^{39} +(0.165911 - 0.400544i) q^{40} +(11.1953 + 4.63726i) q^{41} +(2.41421 - 2.41421i) q^{42} +(7.13707 - 7.13707i) q^{43} +(1.56645 + 0.648847i) q^{44} +(-0.165911 + 0.400544i) q^{45} +(-1.74011 + 0.720777i) q^{46} -2.38009i q^{47} +(-0.382683 - 0.923880i) q^{48} +(3.29289 + 3.29289i) q^{49} +4.81204 q^{50} +(-0.402015 - 4.10346i) q^{51} -0.331821 q^{52} +(2.21371 + 2.21371i) q^{53} +(0.382683 + 0.923880i) q^{54} -0.735084i q^{55} +(3.15432 - 1.30656i) q^{56} +(0.820420 - 1.98067i) q^{57} +(7.88877 + 3.26763i) q^{58} +(-5.42676 + 5.42676i) q^{59} +(-0.306563 + 0.306563i) q^{60} +(-7.42788 - 3.07673i) q^{61} +(-0.989538 + 2.38896i) q^{62} +(-3.15432 + 1.30656i) q^{63} -1.00000i q^{64} +(0.0550527 + 0.132909i) q^{65} +(-1.19891 - 1.19891i) q^{66} +15.7711 q^{67} +(1.19891 - 3.94495i) q^{68} +1.88348 q^{69} +(-1.04667 - 1.04667i) q^{70} +(0.0867259 + 0.209375i) q^{71} +1.00000i q^{72} +(-11.2147 + 4.64527i) q^{73} +(-4.06193 + 9.80638i) q^{74} +(-4.44574 - 1.84149i) q^{75} +(1.51594 - 1.51594i) q^{76} +(4.09334 - 4.09334i) q^{77} +(0.306563 + 0.126983i) q^{78} +(-4.79863 + 11.5849i) q^{79} +(-0.400544 + 0.165911i) q^{80} -1.00000i q^{81} +(-4.63726 - 11.1953i) q^{82} +(-0.738027 - 0.738027i) q^{83} -3.41421 q^{84} +(-1.77904 + 0.174292i) q^{85} -10.0933 q^{86} +(-6.03780 - 6.03780i) q^{87} +(-0.648847 - 1.56645i) q^{88} +13.8281i q^{89} +(0.400544 - 0.165911i) q^{90} +(-0.433546 + 1.04667i) q^{91} +(1.74011 + 0.720777i) q^{92} +(1.82843 - 1.82843i) q^{93} +(-1.68297 + 1.68297i) q^{94} +(-0.858710 - 0.355689i) q^{95} +(-0.382683 + 0.923880i) q^{96} +(3.46953 - 1.43713i) q^{97} -4.65685i q^{98} +(0.648847 + 1.56645i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+8q58q108q158q168q17+8q1816q2216q23+8q25+8q2616q33+16q3416q35+8q39+16q41+8q4216q43+16q44++16q97+O(q100) 8 q + 8 q^{5} - 8 q^{10} - 8 q^{15} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{22} - 16 q^{23} + 8 q^{25} + 8 q^{26} - 16 q^{33} + 16 q^{34} - 16 q^{35} + 8 q^{39} + 16 q^{41} + 8 q^{42} - 16 q^{43} + 16 q^{44}+ \cdots + 16 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/102Z)×\left(\mathbb{Z}/102\mathbb{Z}\right)^\times.

nn 3535 3737
χ(n)\chi(n) 11 e(38)e\left(\frac{3}{8}\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 −0.707107 0.707107i −0.500000 0.500000i
33 0.382683 + 0.923880i 0.220942 + 0.533402i
44 1.00000i 0.500000i
55 0.400544 0.165911i 0.179129 0.0741975i −0.291317 0.956627i 0.594093π-0.594093\pi
0.470445 + 0.882429i 0.344093π0.344093\pi
66 0.382683 0.923880i 0.156230 0.377172i
77 3.15432 + 1.30656i 1.19222 + 0.493834i 0.888478 0.458919i 0.151763π-0.151763\pi
0.303744 + 0.952754i 0.401763π0.401763\pi
88 0.707107 0.707107i 0.250000 0.250000i
99 −0.707107 + 0.707107i −0.235702 + 0.235702i
1010 −0.400544 0.165911i −0.126663 0.0524656i
1111 0.648847 1.56645i 0.195635 0.472304i −0.795371 0.606123i 0.792724π-0.792724\pi
0.991006 + 0.133819i 0.0427240π0.0427240\pi
1212 −0.923880 + 0.382683i −0.266701 + 0.110471i
1313 0.331821i 0.0920307i 0.998941 + 0.0460153i 0.0146523π0.0146523\pi
−0.998941 + 0.0460153i 0.985348π0.985348\pi
1414 −1.30656 3.15432i −0.349194 0.843028i
1515 0.306563 + 0.306563i 0.0791542 + 0.0791542i
1616 −1.00000 −0.250000
1717 −3.94495 1.19891i −0.956790 0.290779i
1818 1.00000 0.235702
1919 −1.51594 1.51594i −0.347780 0.347780i 0.511502 0.859282i 0.329089π-0.329089\pi
−0.859282 + 0.511502i 0.829089π0.829089\pi
2020 0.165911 + 0.400544i 0.0370988 + 0.0895643i
2121 3.41421i 0.745042i
2222 −1.56645 + 0.648847i −0.333969 + 0.138335i
2323 0.720777 1.74011i 0.150292 0.362838i −0.830746 0.556652i 0.812086π-0.812086\pi
0.981038 + 0.193814i 0.0620858π0.0620858\pi
2424 0.923880 + 0.382683i 0.188586 + 0.0781149i
2525 −3.40262 + 3.40262i −0.680525 + 0.680525i
2626 0.234633 0.234633i 0.0460153 0.0460153i
2727 −0.923880 0.382683i −0.177801 0.0736475i
2828 −1.30656 + 3.15432i −0.246917 + 0.596111i
2929 −7.88877 + 3.26763i −1.46491 + 0.606785i −0.965691 0.259693i 0.916379π-0.916379\pi
−0.499216 + 0.866477i 0.666379π0.666379\pi
3030 0.433546i 0.0791542i
3131 −0.989538 2.38896i −0.177726 0.429069i 0.809763 0.586758i 0.199596π-0.199596\pi
−0.987489 + 0.157688i 0.949596π0.949596\pi
3232 0.707107 + 0.707107i 0.125000 + 0.125000i
3333 1.69552 0.295152
3434 1.94174 + 3.63726i 0.333006 + 0.623785i
3535 1.48022 0.250202
3636 −0.707107 0.707107i −0.117851 0.117851i
3737 −4.06193 9.80638i −0.667778 1.61216i −0.785320 0.619090i 0.787501π-0.787501\pi
0.117542 0.993068i 0.462499π-0.462499\pi
3838 2.14386i 0.347780i
3939 −0.306563 + 0.126983i −0.0490894 + 0.0203335i
4040 0.165911 0.400544i 0.0262328 0.0633315i
4141 11.1953 + 4.63726i 1.74842 + 0.724218i 0.997997 + 0.0632564i 0.0201486π0.0201486\pi
0.750420 + 0.660962i 0.229851π0.229851\pi
4242 2.41421 2.41421i 0.372521 0.372521i
4343 7.13707 7.13707i 1.08839 1.08839i 0.0926990 0.995694i 0.470451π-0.470451\pi
0.995694 0.0926990i 0.0295494π-0.0295494\pi
4444 1.56645 + 0.648847i 0.236152 + 0.0978173i
4545 −0.165911 + 0.400544i −0.0247325 + 0.0597095i
4646 −1.74011 + 0.720777i −0.256565 + 0.106273i
4747 2.38009i 0.347171i −0.984819 0.173586i 0.944465π-0.944465\pi
0.984819 0.173586i 0.0555353π-0.0555353\pi
4848 −0.382683 0.923880i −0.0552356 0.133351i
4949 3.29289 + 3.29289i 0.470413 + 0.470413i
5050 4.81204 0.680525
5151 −0.402015 4.10346i −0.0562934 0.574599i
5252 −0.331821 −0.0460153
5353 2.21371 + 2.21371i 0.304076 + 0.304076i 0.842606 0.538530i 0.181020π-0.181020\pi
−0.538530 + 0.842606i 0.681020π0.681020\pi
5454 0.382683 + 0.923880i 0.0520766 + 0.125724i
5555 0.735084i 0.0991187i
5656 3.15432 1.30656i 0.421514 0.174597i
5757 0.820420 1.98067i 0.108667 0.262346i
5858 7.88877 + 3.26763i 1.03585 + 0.429061i
5959 −5.42676 + 5.42676i −0.706504 + 0.706504i −0.965798 0.259295i 0.916510π-0.916510\pi
0.259295 + 0.965798i 0.416510π0.416510\pi
6060 −0.306563 + 0.306563i −0.0395771 + 0.0395771i
6161 −7.42788 3.07673i −0.951043 0.393935i −0.147420 0.989074i 0.547097π-0.547097\pi
−0.803623 + 0.595139i 0.797097π0.797097\pi
6262 −0.989538 + 2.38896i −0.125671 + 0.303398i
6363 −3.15432 + 1.30656i −0.397407 + 0.164611i
6464 1.00000i 0.125000i
6565 0.0550527 + 0.132909i 0.00682845 + 0.0164853i
6666 −1.19891 1.19891i −0.147576 0.147576i
6767 15.7711 1.92675 0.963375 0.268159i 0.0864153π-0.0864153\pi
0.963375 + 0.268159i 0.0864153π0.0864153\pi
6868 1.19891 3.94495i 0.145389 0.478395i
6969 1.88348 0.226744
7070 −1.04667 1.04667i −0.125101 0.125101i
7171 0.0867259 + 0.209375i 0.0102925 + 0.0248482i 0.928942 0.370225i 0.120719π-0.120719\pi
−0.918650 + 0.395073i 0.870719π0.870719\pi
7272 1.00000i 0.117851i
7373 −11.2147 + 4.64527i −1.31258 + 0.543687i −0.925635 0.378417i 0.876469π-0.876469\pi
−0.386942 + 0.922104i 0.626469π0.626469\pi
7474 −4.06193 + 9.80638i −0.472190 + 1.13997i
7575 −4.44574 1.84149i −0.513350 0.212637i
7676 1.51594 1.51594i 0.173890 0.173890i
7777 4.09334 4.09334i 0.466480 0.466480i
7878 0.306563 + 0.126983i 0.0347114 + 0.0143779i
7979 −4.79863 + 11.5849i −0.539888 + 1.30341i 0.384912 + 0.922953i 0.374232π0.374232\pi
−0.924800 + 0.380453i 0.875768π0.875768\pi
8080 −0.400544 + 0.165911i −0.0447822 + 0.0185494i
8181 1.00000i 0.111111i
8282 −4.63726 11.1953i −0.512099 1.23632i
8383 −0.738027 0.738027i −0.0810090 0.0810090i 0.665441 0.746450i 0.268243π-0.268243\pi
−0.746450 + 0.665441i 0.768243π0.768243\pi
8484 −3.41421 −0.372521
8585 −1.77904 + 0.174292i −0.192964 + 0.0189046i
8686 −10.0933 −1.08839
8787 −6.03780 6.03780i −0.647320 0.647320i
8888 −0.648847 1.56645i −0.0691673 0.166985i
8989 13.8281i 1.46577i 0.680352 + 0.732885i 0.261827π0.261827\pi
−0.680352 + 0.732885i 0.738173π0.738173\pi
9090 0.400544 0.165911i 0.0422210 0.0174885i
9191 −0.433546 + 1.04667i −0.0454479 + 0.109721i
9292 1.74011 + 0.720777i 0.181419 + 0.0751461i
9393 1.82843 1.82843i 0.189599 0.189599i
9494 −1.68297 + 1.68297i −0.173586 + 0.173586i
9595 −0.858710 0.355689i −0.0881018 0.0364929i
9696 −0.382683 + 0.923880i −0.0390575 + 0.0942931i
9797 3.46953 1.43713i 0.352277 0.145918i −0.199525 0.979893i 0.563940π-0.563940\pi
0.551803 + 0.833975i 0.313940π0.313940\pi
9898 4.65685i 0.470413i
9999 0.648847 + 1.56645i 0.0652115 + 0.157435i
100100 −3.40262 3.40262i −0.340262 0.340262i
101101 −0.636303 −0.0633145 −0.0316573 0.999499i 0.510079π-0.510079\pi
−0.0316573 + 0.999499i 0.510079π0.510079\pi
102102 −2.61732 + 3.18585i −0.259153 + 0.315446i
103103 8.59955 0.847339 0.423669 0.905817i 0.360742π-0.360742\pi
0.423669 + 0.905817i 0.360742π0.360742\pi
104104 0.234633 + 0.234633i 0.0230077 + 0.0230077i
105105 0.566454 + 1.36754i 0.0552803 + 0.133458i
106106 3.13066i 0.304076i
107107 2.00000 0.828427i 0.193347 0.0800871i −0.283909 0.958851i 0.591631π-0.591631\pi
0.477256 + 0.878764i 0.341631π0.341631\pi
108108 0.382683 0.923880i 0.0368237 0.0889003i
109109 −7.31136 3.02847i −0.700302 0.290074i 0.00398311 0.999992i 0.498732π-0.498732\pi
−0.704285 + 0.709918i 0.748732π0.748732\pi
110110 −0.519783 + 0.519783i −0.0495594 + 0.0495594i
111111 7.50548 7.50548i 0.712388 0.712388i
112112 −3.15432 1.30656i −0.298055 0.123459i
113113 3.51620 8.48886i 0.330776 0.798565i −0.667755 0.744382i 0.732744π-0.732744\pi
0.998531 0.0541835i 0.0172556π-0.0172556\pi
114114 −1.98067 + 0.820420i −0.185507 + 0.0768393i
115115 0.816574i 0.0761459i
116116 −3.26763 7.88877i −0.303392 0.732454i
117117 −0.234633 0.234633i −0.0216918 0.0216918i
118118 7.67459 0.706504
119119 −10.8772 8.93608i −0.997109 0.819169i
120120 0.433546 0.0395771
121121 5.74540 + 5.74540i 0.522309 + 0.522309i
122122 3.07673 + 7.42788i 0.278554 + 0.672489i
123123 12.1177i 1.09262i
124124 2.38896 0.989538i 0.214535 0.0888631i
125125 −1.62792 + 3.93015i −0.145606 + 0.351523i
126126 3.15432 + 1.30656i 0.281009 + 0.116398i
127127 −8.54487 + 8.54487i −0.758235 + 0.758235i −0.976001 0.217766i 0.930123π-0.930123\pi
0.217766 + 0.976001i 0.430123π0.430123\pi
128128 −0.707107 + 0.707107i −0.0625000 + 0.0625000i
129129 9.32503 + 3.86256i 0.821023 + 0.340079i
130130 0.0550527 0.132909i 0.00482844 0.0116569i
131131 −0.828427 + 0.343146i −0.0723800 + 0.0299808i −0.418580 0.908180i 0.637472π-0.637472\pi
0.346200 + 0.938161i 0.387472π0.387472\pi
132132 1.69552i 0.147576i
133133 −2.80109 6.76242i −0.242885 0.586377i
134134 −11.1519 11.1519i −0.963375 0.963375i
135135 −0.433546 −0.0373137
136136 −3.63726 + 1.94174i −0.311892 + 0.166503i
137137 12.6109 1.07742 0.538710 0.842491i 0.318912π-0.318912\pi
0.538710 + 0.842491i 0.318912π0.318912\pi
138138 −1.33182 1.33182i −0.113372 0.113372i
139139 6.52273 + 15.7473i 0.553250 + 1.33566i 0.915024 + 0.403399i 0.132171π0.132171\pi
−0.361774 + 0.932266i 0.617829π0.617829\pi
140140 1.48022i 0.125101i
141141 2.19891 0.910819i 0.185182 0.0767048i
142142 0.0867259 0.209375i 0.00727787 0.0175703i
143143 0.519783 + 0.215301i 0.0434664 + 0.0180044i
144144 0.707107 0.707107i 0.0589256 0.0589256i
145145 −2.61766 + 2.61766i −0.217385 + 0.217385i
146146 11.2147 + 4.64527i 0.928132 + 0.384445i
147147 −1.78210 + 4.30237i −0.146985 + 0.354854i
148148 9.80638 4.06193i 0.806079 0.333889i
149149 17.5004i 1.43369i −0.697234 0.716844i 0.745586π-0.745586\pi
0.697234 0.716844i 0.254414π-0.254414\pi
150150 1.84149 + 4.44574i 0.150357 + 0.362993i
151151 6.81657 + 6.81657i 0.554725 + 0.554725i 0.927801 0.373076i 0.121697π-0.121697\pi
−0.373076 + 0.927801i 0.621697π0.621697\pi
152152 −2.14386 −0.173890
153153 3.63726 1.94174i 0.294055 0.156980i
154154 −5.78886 −0.466480
155155 −0.792706 0.792706i −0.0636717 0.0636717i
156156 −0.126983 0.306563i −0.0101667 0.0245447i
157157 4.78976i 0.382265i −0.981564 0.191132i 0.938784π-0.938784\pi
0.981564 0.191132i 0.0612160π-0.0612160\pi
158158 11.5849 4.79863i 0.921647 0.381759i
159159 −1.19805 + 2.89235i −0.0950116 + 0.229378i
160160 0.400544 + 0.165911i 0.0316658 + 0.0131164i
161161 4.54712 4.54712i 0.358363 0.358363i
162162 −0.707107 + 0.707107i −0.0555556 + 0.0555556i
163163 −16.4496 6.81363i −1.28843 0.533685i −0.369912 0.929067i 0.620612π-0.620612\pi
−0.918517 + 0.395382i 0.870612π0.870612\pi
164164 −4.63726 + 11.1953i −0.362109 + 0.874208i
165165 0.679129 0.281305i 0.0528701 0.0218995i
166166 1.04373i 0.0810090i
167167 6.73332 + 16.2557i 0.521040 + 1.25790i 0.937258 + 0.348637i 0.113355π0.113355\pi
−0.416218 + 0.909265i 0.636645π0.636645\pi
168168 2.41421 + 2.41421i 0.186261 + 0.186261i
169169 12.8899 0.991530
170170 1.38121 + 1.13473i 0.105934 + 0.0870295i
171171 2.14386 0.163945
172172 7.13707 + 7.13707i 0.544197 + 0.544197i
173173 −7.40349 17.8736i −0.562877 1.35890i −0.907456 0.420147i 0.861978π-0.861978\pi
0.344579 0.938757i 0.388022π-0.388022\pi
174174 8.53874i 0.647320i
175175 −15.1787 + 6.28723i −1.14740 + 0.475270i
176176 −0.648847 + 1.56645i −0.0489087 + 0.118076i
177177 −7.09040 2.93694i −0.532947 0.220754i
178178 9.77791 9.77791i 0.732885 0.732885i
179179 6.44834 6.44834i 0.481972 0.481972i −0.423789 0.905761i 0.639300π-0.639300\pi
0.905761 + 0.423789i 0.139300π0.139300\pi
180180 −0.400544 0.165911i −0.0298548 0.0123663i
181181 0.297227 0.717569i 0.0220927 0.0533365i −0.912448 0.409192i 0.865811π-0.865811\pi
0.934541 + 0.355856i 0.115811π0.115811\pi
182182 1.04667 0.433546i 0.0775844 0.0321365i
183183 8.03988i 0.594325i
184184 −0.720777 1.74011i −0.0531364 0.128282i
185185 −3.25397 3.25397i −0.239236 0.239236i
186186 −2.58579 −0.189599
187187 −4.43771 + 5.40167i −0.324517 + 0.395009i
188188 2.38009 0.173586
189189 −2.41421 2.41421i −0.175608 0.175608i
190190 0.355689 + 0.858710i 0.0258044 + 0.0622974i
191191 13.4248i 0.971384i −0.874130 0.485692i 0.838568π-0.838568\pi
0.874130 0.485692i 0.161432π-0.161432\pi
192192 0.923880 0.382683i 0.0666753 0.0276178i
193193 1.94749 4.70167i 0.140184 0.338434i −0.838159 0.545426i 0.816368π-0.816368\pi
0.978342 + 0.206993i 0.0663677π0.0663677\pi
194194 −3.46953 1.43713i −0.249098 0.103180i
195195 −0.101724 + 0.101724i −0.00728462 + 0.00728462i
196196 −3.29289 + 3.29289i −0.235207 + 0.235207i
197197 3.83825 + 1.58986i 0.273464 + 0.113273i 0.515201 0.857069i 0.327717π-0.327717\pi
−0.241737 + 0.970342i 0.577717π0.577717\pi
198198 0.648847 1.56645i 0.0461115 0.111323i
199199 9.89357 4.09805i 0.701336 0.290503i −0.00337780 0.999994i 0.501075π-0.501075\pi
0.704714 + 0.709491i 0.251075π0.251075\pi
200200 4.81204i 0.340262i
201201 6.03535 + 14.5706i 0.425701 + 1.02773i
202202 0.449934 + 0.449934i 0.0316573 + 0.0316573i
203203 −29.1531 −2.04615
204204 4.10346 0.402015i 0.287300 0.0281467i
205205 5.25359 0.366927
206206 −6.08080 6.08080i −0.423669 0.423669i
207207 0.720777 + 1.74011i 0.0500974 + 0.120946i
208208 0.331821i 0.0230077i
209209 −3.35826 + 1.39104i −0.232296 + 0.0962200i
210210 0.566454 1.36754i 0.0390891 0.0943694i
211211 −4.36210 1.80684i −0.300300 0.124388i 0.227446 0.973791i 0.426963π-0.426963\pi
−0.527746 + 0.849403i 0.676963π0.676963\pi
212212 −2.21371 + 2.21371i −0.152038 + 0.152038i
213213 −0.160248 + 0.160248i −0.0109800 + 0.0109800i
214214 −2.00000 0.828427i −0.136717 0.0566301i
215215 1.67459 4.04283i 0.114206 0.275718i
216216 −0.923880 + 0.382683i −0.0628620 + 0.0260383i
217217 8.82843i 0.599313i
218218 3.02847 + 7.31136i 0.205114 + 0.495188i
219219 −8.58333 8.58333i −0.580008 0.580008i
220220 0.735084 0.0495594
221221 0.397825 1.30902i 0.0267606 0.0880541i
222222 −10.6143 −0.712388
223223 11.0563 + 11.0563i 0.740383 + 0.740383i 0.972652 0.232269i 0.0746149π-0.0746149\pi
−0.232269 + 0.972652i 0.574615π0.574615\pi
224224 1.30656 + 3.15432i 0.0872984 + 0.210757i
225225 4.81204i 0.320803i
226226 −8.48886 + 3.51620i −0.564671 + 0.233894i
227227 −4.23304 + 10.2195i −0.280957 + 0.678290i −0.999858 0.0168221i 0.994645π-0.994645\pi
0.718902 + 0.695112i 0.244645π0.244645\pi
228228 1.98067 + 0.820420i 0.131173 + 0.0543336i
229229 −10.8789 + 10.8789i −0.718901 + 0.718901i −0.968380 0.249479i 0.919741π-0.919741\pi
0.249479 + 0.968380i 0.419741π0.419741\pi
230230 −0.577405 + 0.577405i −0.0380730 + 0.0380730i
231231 5.34821 + 2.21530i 0.351886 + 0.145756i
232232 −3.26763 + 7.88877i −0.214531 + 0.517923i
233233 −9.58764 + 3.97133i −0.628107 + 0.260171i −0.673949 0.738778i 0.735403π-0.735403\pi
0.0458413 + 0.998949i 0.485403π0.485403\pi
234234 0.331821i 0.0216918i
235235 −0.394882 0.953329i −0.0257592 0.0621883i
236236 −5.42676 5.42676i −0.353252 0.353252i
237237 −12.5394 −0.814524
238238 1.37257 + 14.0101i 0.0889703 + 0.908139i
239239 −24.7803 −1.60291 −0.801454 0.598057i 0.795940π-0.795940\pi
−0.801454 + 0.598057i 0.795940π0.795940\pi
240240 −0.306563 0.306563i −0.0197886 0.0197886i
241241 −1.64752 3.97746i −0.106126 0.256211i 0.861892 0.507092i 0.169280π-0.169280\pi
−0.968018 + 0.250881i 0.919280π0.919280\pi
242242 8.12522i 0.522309i
243243 0.923880 0.382683i 0.0592669 0.0245492i
244244 3.07673 7.42788i 0.196967 0.475522i
245245 1.86527 + 0.772622i 0.119168 + 0.0493610i
246246 8.56854 8.56854i 0.546310 0.546310i
247247 0.503021 0.503021i 0.0320064 0.0320064i
248248 −2.38896 0.989538i −0.151699 0.0628357i
249249 0.399418 0.964279i 0.0253121 0.0611087i
250250 3.93015 1.62792i 0.248565 0.102959i
251251 19.0639i 1.20330i 0.798759 + 0.601652i 0.205490π0.205490\pi
−0.798759 + 0.601652i 0.794510π0.794510\pi
252252 −1.30656 3.15432i −0.0823057 0.198704i
253253 −2.25813 2.25813i −0.141967 0.141967i
254254 12.0843 0.758235
255255 −0.841833 1.57692i −0.0527176 0.0987504i
256256 1.00000 0.0625000
257257 18.9218 + 18.9218i 1.18031 + 1.18031i 0.979664 + 0.200643i 0.0643032π0.0643032\pi
0.200643 + 0.979664i 0.435697π0.435697\pi
258258 −3.86256 9.32503i −0.240472 0.580551i
259259 36.2396i 2.25182i
260260 −0.132909 + 0.0550527i −0.00824267 + 0.00341422i
261261 3.26763 7.88877i 0.202262 0.488302i
262262 0.828427 + 0.343146i 0.0511804 + 0.0211996i
263263 19.4541 19.4541i 1.19959 1.19959i 0.225302 0.974289i 0.427663π-0.427663\pi
0.974289 0.225302i 0.0723369π-0.0723369\pi
264264 1.19891 1.19891i 0.0737880 0.0737880i
265265 1.25397 + 0.519409i 0.0770305 + 0.0319071i
266266 −2.80109 + 6.76242i −0.171746 + 0.414631i
267267 −12.7755 + 5.29177i −0.781845 + 0.323851i
268268 15.7711i 0.963375i
269269 3.83250 + 9.25247i 0.233671 + 0.564133i 0.996604 0.0823455i 0.0262411π-0.0262411\pi
−0.762932 + 0.646478i 0.776241π0.776241\pi
270270 0.306563 + 0.306563i 0.0186568 + 0.0186568i
271271 −9.20949 −0.559437 −0.279718 0.960082i 0.590241π-0.590241\pi
−0.279718 + 0.960082i 0.590241π0.590241\pi
272272 3.94495 + 1.19891i 0.239198 + 0.0726947i
273273 −1.13291 −0.0685668
274274 −8.91723 8.91723i −0.538710 0.538710i
275275 3.12228 + 7.53784i 0.188280 + 0.454549i
276276 1.88348i 0.113372i
277277 −7.72852 + 3.20126i −0.464362 + 0.192345i −0.602583 0.798056i 0.705862π-0.705862\pi
0.138221 + 0.990401i 0.455862π0.455862\pi
278278 6.52273 15.7473i 0.391207 0.944458i
279279 2.38896 + 0.989538i 0.143023 + 0.0592421i
280280 1.04667 1.04667i 0.0625506 0.0625506i
281281 −7.77791 + 7.77791i −0.463991 + 0.463991i −0.899961 0.435970i 0.856405π-0.856405\pi
0.435970 + 0.899961i 0.356405π0.356405\pi
282282 −2.19891 0.910819i −0.130943 0.0542385i
283283 8.08918 19.5290i 0.480852 1.16088i −0.478353 0.878168i 0.658766π-0.658766\pi
0.959205 0.282712i 0.0912339π-0.0912339\pi
284284 −0.209375 + 0.0867259i −0.0124241 + 0.00514623i
285285 0.929461i 0.0550565i
286286 −0.215301 0.519783i −0.0127310 0.0307354i
287287 29.2548 + 29.2548i 1.72686 + 1.72686i
288288 −1.00000 −0.0589256
289289 14.1252 + 9.45929i 0.830895 + 0.556429i
290290 3.70193 0.217385
291291 2.65546 + 2.65546i 0.155666 + 0.155666i
292292 −4.64527 11.2147i −0.271844 0.656289i
293293 25.1277i 1.46797i 0.679164 + 0.733987i 0.262343π0.262343\pi
−0.679164 + 0.733987i 0.737657π0.737657\pi
294294 4.30237 1.78210i 0.250919 0.103934i
295295 −1.27330 + 3.07401i −0.0741342 + 0.178976i
296296 −9.80638 4.06193i −0.569984 0.236095i
297297 −1.19891 + 1.19891i −0.0695680 + 0.0695680i
298298 −12.3746 + 12.3746i −0.716844 + 0.716844i
299299 0.577405 + 0.239169i 0.0333922 + 0.0138315i
300300 1.84149 4.44574i 0.106318 0.256675i
301301 31.8377 13.1876i 1.83509 0.760120i
302302 9.64009i 0.554725i
303303 −0.243503 0.587868i −0.0139889 0.0337721i
304304 1.51594 + 1.51594i 0.0869450 + 0.0869450i
305305 −3.48566 −0.199588
306306 −3.94495 1.19891i −0.225518 0.0685373i
307307 15.3433 0.875688 0.437844 0.899051i 0.355742π-0.355742\pi
0.437844 + 0.899051i 0.355742π0.355742\pi
308308 4.09334 + 4.09334i 0.233240 + 0.233240i
309309 3.29090 + 7.94495i 0.187213 + 0.451972i
310310 1.12106i 0.0636717i
311311 20.0320 8.29752i 1.13591 0.470509i 0.266124 0.963939i 0.414257π-0.414257\pi
0.869786 + 0.493429i 0.164257π0.164257\pi
312312 −0.126983 + 0.306563i −0.00718897 + 0.0173557i
313313 −7.74993 3.21013i −0.438052 0.181447i 0.152748 0.988265i 0.451188π-0.451188\pi
−0.590800 + 0.806818i 0.701188π0.701188\pi
314314 −3.38687 + 3.38687i −0.191132 + 0.191132i
315315 −1.04667 + 1.04667i −0.0589733 + 0.0589733i
316316 −11.5849 4.79863i −0.651703 0.269944i
317317 9.17686 22.1549i 0.515424 1.24434i −0.425264 0.905069i 0.639819π-0.639819\pi
0.940688 0.339274i 0.110181π-0.110181\pi
318318 2.89235 1.19805i 0.162195 0.0671833i
319319 14.4776i 0.810589i
320320 −0.165911 0.400544i −0.00927469 0.0223911i
321321 1.53073 + 1.53073i 0.0854372 + 0.0854372i
322322 −6.43060 −0.358363
323323 4.16282 + 7.79777i 0.231625 + 0.433880i
324324 1.00000 0.0555556
325325 −1.12906 1.12906i −0.0626292 0.0626292i
326326 6.81363 + 16.4496i 0.377372 + 0.911057i
327327 7.91376i 0.437632i
328328 11.1953 4.63726i 0.618159 0.256050i
329329 3.10973 7.50756i 0.171445 0.413905i
330330 −0.679129 0.281305i −0.0373848 0.0154853i
331331 −2.88311 + 2.88311i −0.158470 + 0.158470i −0.781888 0.623418i 0.785743π-0.785743\pi
0.623418 + 0.781888i 0.285743π0.285743\pi
332332 0.738027 0.738027i 0.0405045 0.0405045i
333333 9.80638 + 4.06193i 0.537386 + 0.222593i
334334 6.73332 16.2557i 0.368431 0.889471i
335335 6.31703 2.61660i 0.345136 0.142960i
336336 3.41421i 0.186261i
337337 −3.83323 9.25423i −0.208809 0.504110i 0.784427 0.620221i 0.212957π-0.212957\pi
−0.993236 + 0.116111i 0.962957π0.962957\pi
338338 −9.11453 9.11453i −0.495765 0.495765i
339339 9.18828 0.499039
340340 −0.174292 1.77904i −0.00945231 0.0964818i
341341 −4.38425 −0.237420
342342 −1.51594 1.51594i −0.0819725 0.0819725i
343343 −3.06147 7.39104i −0.165304 0.399078i
344344 10.0933i 0.544197i
345345 0.754416 0.312489i 0.0406164 0.0168239i
346346 −7.40349 + 17.8736i −0.398014 + 0.960891i
347347 −7.98618 3.30798i −0.428721 0.177582i 0.157880 0.987458i 0.449534π-0.449534\pi
−0.586601 + 0.809876i 0.699534π0.699534\pi
348348 6.03780 6.03780i 0.323660 0.323660i
349349 −14.7167 + 14.7167i −0.787768 + 0.787768i −0.981128 0.193360i 0.938062π-0.938062\pi
0.193360 + 0.981128i 0.438062π0.438062\pi
350350 15.1787 + 6.28723i 0.811337 + 0.336067i
351351 0.126983 0.306563i 0.00677783 0.0163631i
352352 1.56645 0.648847i 0.0834923 0.0345836i
353353 20.1049i 1.07007i 0.844829 + 0.535037i 0.179702π0.179702\pi
−0.844829 + 0.535037i 0.820298π0.820298\pi
354354 2.93694 + 7.09040i 0.156097 + 0.376850i
355355 0.0694750 + 0.0694750i 0.00368735 + 0.00368735i
356356 −13.8281 −0.732885
357357 4.09334 13.4689i 0.216643 0.712849i
358358 −9.11933 −0.481972
359359 −17.8899 17.8899i −0.944193 0.944193i 0.0543305 0.998523i 0.482698π-0.482698\pi
−0.998523 + 0.0543305i 0.982698π0.982698\pi
360360 0.165911 + 0.400544i 0.00874426 + 0.0211105i
361361 14.4039i 0.758098i
362362 −0.717569 + 0.297227i −0.0377146 + 0.0156219i
363363 −3.10939 + 7.50672i −0.163200 + 0.394001i
364364 −1.04667 0.433546i −0.0548605 0.0227240i
365365 −3.72126 + 3.72126i −0.194780 + 0.194780i
366366 −5.68506 + 5.68506i −0.297163 + 0.297163i
367367 −9.53441 3.94928i −0.497692 0.206151i 0.119694 0.992811i 0.461809π-0.461809\pi
−0.617386 + 0.786660i 0.711809π0.711809\pi
368368 −0.720777 + 1.74011i −0.0375731 + 0.0907094i
369369 −11.1953 + 4.63726i −0.582806 + 0.241406i
370370 4.60180i 0.239236i
371371 4.09040 + 9.87510i 0.212363 + 0.512690i
372372 1.82843 + 1.82843i 0.0947995 + 0.0947995i
373373 −18.2719 −0.946083 −0.473041 0.881040i 0.656844π-0.656844\pi
−0.473041 + 0.881040i 0.656844π0.656844\pi
374374 6.95749 0.681624i 0.359763 0.0352460i
375375 −4.25397 −0.219674
376376 −1.68297 1.68297i −0.0867928 0.0867928i
377377 −1.08427 2.61766i −0.0558428 0.134816i
378378 3.41421i 0.175608i
379379 19.3386 8.01029i 0.993355 0.411461i 0.173999 0.984746i 0.444331π-0.444331\pi
0.819356 + 0.573285i 0.194331π0.194331\pi
380380 0.355689 0.858710i 0.0182465 0.0440509i
381381 −11.1644 4.62445i −0.571970 0.236918i
382382 −9.49276 + 9.49276i −0.485692 + 0.485692i
383383 −16.2616 + 16.2616i −0.830929 + 0.830929i −0.987644 0.156715i 0.949910π-0.949910\pi
0.156715 + 0.987644i 0.449910π0.449910\pi
384384 −0.923880 0.382683i −0.0471465 0.0195287i
385385 0.960434 2.31869i 0.0489482 0.118172i
386386 −4.70167 + 1.94749i −0.239309 + 0.0991249i
387387 10.0933i 0.513073i
388388 1.43713 + 3.46953i 0.0729590 + 0.176139i
389389 −6.41875 6.41875i −0.325444 0.325444i 0.525407 0.850851i 0.323913π-0.323913\pi
−0.850851 + 0.525407i 0.823913π0.823913\pi
390390 0.143860 0.00728462
391391 −4.92966 + 6.00049i −0.249304 + 0.303458i
392392 4.65685 0.235207
393393 −0.634051 0.634051i −0.0319836 0.0319836i
394394 −1.58986 3.83825i −0.0800958 0.193368i
395395 5.43641i 0.273536i
396396 −1.56645 + 0.648847i −0.0787173 + 0.0326058i
397397 −2.98821 + 7.21417i −0.149974 + 0.362069i −0.980956 0.194230i 0.937779π-0.937779\pi
0.830982 + 0.556299i 0.187779π0.187779\pi
398398 −9.89357 4.09805i −0.495920 0.205417i
399399 5.17574 5.17574i 0.259111 0.259111i
400400 3.40262 3.40262i 0.170131 0.170131i
401401 −16.0392 6.64367i −0.800962 0.331769i −0.0556201 0.998452i 0.517714π-0.517714\pi
−0.745342 + 0.666683i 0.767714π0.767714\pi
402402 6.03535 14.5706i 0.301016 0.726716i
403403 0.792706 0.328350i 0.0394875 0.0163563i
404404 0.636303i 0.0316573i
405405 −0.165911 0.400544i −0.00824417 0.0199032i
406406 20.6143 + 20.6143i 1.02307 + 1.02307i
407407 −17.9968 −0.892069
408408 −3.18585 2.61732i −0.157723 0.129576i
409409 4.42153 0.218631 0.109315 0.994007i 0.465134π-0.465134\pi
0.109315 + 0.994007i 0.465134π0.465134\pi
410410 −3.71485 3.71485i −0.183463 0.183463i
411411 4.82597 + 11.6509i 0.238048 + 0.574698i
412412 8.59955i 0.423669i
413413 −24.2081 + 10.0273i −1.19120 + 0.493413i
414414 0.720777 1.74011i 0.0354242 0.0855217i
415415 −0.418059 0.173166i −0.0205217 0.00850037i
416416 −0.234633 + 0.234633i −0.0115038 + 0.0115038i
417417 −12.0524 + 12.0524i −0.590210 + 0.590210i
418418 3.35826 + 1.39104i 0.164258 + 0.0680378i
419419 8.86537 21.4029i 0.433102 1.04560i −0.545180 0.838319i 0.683539π-0.683539\pi
0.978282 0.207281i 0.0664613π-0.0664613\pi
420420 −1.36754 + 0.566454i −0.0667292 + 0.0276401i
421421 20.0524i 0.977295i 0.872481 + 0.488648i 0.162510π0.162510\pi
−0.872481 + 0.488648i 0.837490π0.837490\pi
422422 1.80684 + 4.36210i 0.0879557 + 0.212344i
423423 1.68297 + 1.68297i 0.0818290 + 0.0818290i
424424 3.13066 0.152038
425425 17.5026 9.34373i 0.849002 0.453237i
426426 0.226626 0.0109800
427427 −19.4100 19.4100i −0.939315 0.939315i
428428 0.828427 + 2.00000i 0.0400435 + 0.0966736i
429429 0.562609i 0.0271630i
430430 −4.04283 + 1.67459i −0.194962 + 0.0807561i
431431 15.3635 37.0908i 0.740033 1.78660i 0.134285 0.990943i 0.457126π-0.457126\pi
0.605749 0.795656i 0.292874π-0.292874\pi
432432 0.923880 + 0.382683i 0.0444502 + 0.0184119i
433433 −15.4502 + 15.4502i −0.742490 + 0.742490i −0.973057 0.230566i 0.925942π-0.925942\pi
0.230566 + 0.973057i 0.425942π0.425942\pi
434434 −6.24264 + 6.24264i −0.299656 + 0.299656i
435435 −3.42014 1.41667i −0.163983 0.0679240i
436436 3.02847 7.31136i 0.145037 0.350151i
437437 −3.73055 + 1.54524i −0.178456 + 0.0739190i
438438 12.1387i 0.580008i
439439 0.320985 + 0.774927i 0.0153198 + 0.0369852i 0.931354 0.364114i 0.118628π-0.118628\pi
−0.916035 + 0.401099i 0.868628π0.868628\pi
440440 −0.519783 0.519783i −0.0247797 0.0247797i
441441 −4.65685 −0.221755
442442 −1.20692 + 0.644311i −0.0574073 + 0.0306467i
443443 −3.21267 −0.152639 −0.0763194 0.997083i 0.524317π-0.524317\pi
−0.0763194 + 0.997083i 0.524317π0.524317\pi
444444 7.50548 + 7.50548i 0.356194 + 0.356194i
445445 2.29422 + 5.53874i 0.108757 + 0.262562i
446446 15.6359i 0.740383i
447447 16.1683 6.69711i 0.764732 0.316762i
448448 1.30656 3.15432i 0.0617293 0.149028i
449449 −26.5599 11.0015i −1.25344 0.519192i −0.345550 0.938400i 0.612308π-0.612308\pi
−0.907890 + 0.419208i 0.862308π0.862308\pi
450450 −3.40262 + 3.40262i −0.160401 + 0.160401i
451451 14.5281 14.5281i 0.684102 0.684102i
452452 8.48886 + 3.51620i 0.399283 + 0.165388i
453453 −3.68910 + 8.90628i −0.173329 + 0.418454i
454454 10.2195 4.23304i 0.479623 0.198666i
455455 0.491168i 0.0230263i
456456 −0.820420 1.98067i −0.0384197 0.0927533i
457457 −5.26863 5.26863i −0.246456 0.246456i 0.573058 0.819515i 0.305757π-0.305757\pi
−0.819515 + 0.573058i 0.805757π0.805757\pi
458458 15.3852 0.718901
459459 3.18585 + 2.61732i 0.148703 + 0.122166i
460460 0.816574 0.0380730
461461 −18.1287 18.1287i −0.844337 0.844337i 0.145082 0.989420i 0.453655π-0.453655\pi
−0.989420 + 0.145082i 0.953655π0.953655\pi
462462 −2.21530 5.34821i −0.103065 0.248821i
463463 10.7747i 0.500744i −0.968150 0.250372i 0.919447π-0.919447\pi
0.968150 0.250372i 0.0805529π-0.0805529\pi
464464 7.88877 3.26763i 0.366227 0.151696i
465465 0.429010 1.03572i 0.0198948 0.0480304i
466466 9.58764 + 3.97133i 0.444139 + 0.183968i
467467 25.2078 25.2078i 1.16648 1.16648i 0.183447 0.983030i 0.441275π-0.441275\pi
0.983030 0.183447i 0.0587254π-0.0587254\pi
468468 0.234633 0.234633i 0.0108459 0.0108459i
469469 49.7472 + 20.6060i 2.29711 + 0.951495i
470470 −0.394882 + 0.953329i −0.0182145 + 0.0439738i
471471 4.42516 1.83296i 0.203901 0.0844585i
472472 7.67459i 0.353252i
473473 −6.54903 15.8108i −0.301125 0.726980i
474474 8.86672 + 8.86672i 0.407262 + 0.407262i
475475 10.3163 0.473346
476476 8.93608 10.8772i 0.409584 0.498555i
477477 −3.13066 −0.143343
478478 17.5224 + 17.5224i 0.801454 + 0.801454i
479479 −5.38442 12.9991i −0.246020 0.593946i 0.751839 0.659347i 0.229167π-0.229167\pi
−0.997859 + 0.0654014i 0.979167π0.979167\pi
480480 0.433546i 0.0197886i
481481 3.25397 1.34784i 0.148368 0.0614561i
482482 −1.64752 + 3.97746i −0.0750424 + 0.181168i
483483 5.94110 + 2.46088i 0.270329 + 0.111974i
484484 −5.74540 + 5.74540i −0.261154 + 0.261154i
485485 1.15126 1.15126i 0.0522762 0.0522762i
486486 −0.923880 0.382683i −0.0419080 0.0173589i
487487 −9.23512 + 22.2956i −0.418483 + 1.01031i 0.564304 + 0.825567i 0.309145π0.309145\pi
−0.982787 + 0.184741i 0.940855π0.940855\pi
488488 −7.42788 + 3.07673i −0.336244 + 0.139277i
489489 17.8049i 0.805164i
490490 −0.772622 1.86527i −0.0349035 0.0842645i
491491 18.7525 + 18.7525i 0.846288 + 0.846288i 0.989668 0.143380i 0.0457971π-0.0457971\pi
−0.143380 + 0.989668i 0.545797π0.545797\pi
492492 −12.1177 −0.546310
493493 35.0384 3.43271i 1.57805 0.154601i
494494 −0.711378 −0.0320064
495495 0.519783 + 0.519783i 0.0233625 + 0.0233625i
496496 0.989538 + 2.38896i 0.0444316 + 0.107267i
497497 0.773748i 0.0347073i
498498 −0.964279 + 0.399418i −0.0432104 + 0.0178983i
499499 −1.73737 + 4.19438i −0.0777753 + 0.187766i −0.957985 0.286819i 0.907402π-0.907402\pi
0.880209 + 0.474585i 0.157402π0.157402\pi
500500 −3.93015 1.62792i −0.175762 0.0728029i
501501 −12.4416 + 12.4416i −0.555848 + 0.555848i
502502 13.4802 13.4802i 0.601652 0.601652i
503503 3.69306 + 1.52972i 0.164666 + 0.0682067i 0.463494 0.886100i 0.346596π-0.346596\pi
−0.298828 + 0.954307i 0.596596π0.596596\pi
504504 −1.30656 + 3.15432i −0.0581989 + 0.140505i
505505 −0.254867 + 0.105570i −0.0113414 + 0.00469778i
506506 3.19347i 0.141967i
507507 4.93275 + 11.9087i 0.219071 + 0.528884i
508508 −8.54487 8.54487i −0.379117 0.379117i
509509 22.9751 1.01835 0.509176 0.860662i 0.329950π-0.329950\pi
0.509176 + 0.860662i 0.329950π0.329950\pi
510510 −0.519783 + 1.71031i −0.0230164 + 0.0757340i
511511 −41.4440 −1.83337
512512 −0.707107 0.707107i −0.0312500 0.0312500i
513513 0.820420 + 1.98067i 0.0362224 + 0.0874486i
514514 26.7594i 1.18031i
515515 3.44450 1.42676i 0.151783 0.0628704i
516516 −3.86256 + 9.32503i −0.170040 + 0.410512i
517517 −3.72830 1.54431i −0.163970 0.0679187i
518518 −25.6253 + 25.6253i −1.12591 + 1.12591i
519519 13.6799 13.6799i 0.600479 0.600479i
520520 0.132909 + 0.0550527i 0.00582844 + 0.00241422i
521521 −6.46078 + 15.5977i −0.283052 + 0.683347i −0.999904 0.0138781i 0.995582π-0.995582\pi
0.716852 + 0.697225i 0.245582π0.245582\pi
522522 −7.88877 + 3.26763i −0.345282 + 0.143020i
523523 15.5903i 0.681717i 0.940115 + 0.340859i 0.110718π0.110718\pi
−0.940115 + 0.340859i 0.889282π0.889282\pi
524524 −0.343146 0.828427i −0.0149904 0.0361900i
525525 −11.6173 11.6173i −0.507020 0.507020i
526526 −27.5122 −1.19959
527527 1.03953 + 10.6107i 0.0452825 + 0.462208i
528528 −1.69552 −0.0737880
529529 13.7550 + 13.7550i 0.598043 + 0.598043i
530530 −0.519409 1.25397i −0.0225617 0.0544688i
531531 7.67459i 0.333049i
532532 6.76242 2.80109i 0.293188 0.121443i
533533 −1.53874 + 3.71485i −0.0666503 + 0.160908i
534534 12.7755 + 5.29177i 0.552848 + 0.228997i
535535 0.663643 0.663643i 0.0286918 0.0286918i
536536 11.1519 11.1519i 0.481687 0.481687i
537537 8.42516 + 3.48982i 0.363573 + 0.150597i
538538 3.83250 9.25247i 0.165231 0.398902i
539539 7.29475 3.02158i 0.314207 0.130149i
540540 0.433546i 0.0186568i
541541 5.79023 + 13.9789i 0.248941 + 0.600998i 0.998115 0.0613763i 0.0195490π-0.0195490\pi
−0.749173 + 0.662374i 0.769549π0.769549\pi
542542 6.51209 + 6.51209i 0.279718 + 0.279718i
543543 0.776691 0.0333310
544544 −1.94174 3.63726i −0.0832514 0.155946i
545545 −3.43098 −0.146967
546546 0.801088 + 0.801088i 0.0342834 + 0.0342834i
547547 −1.01292 2.44540i −0.0433092 0.104558i 0.900745 0.434349i 0.143022π-0.143022\pi
−0.944054 + 0.329791i 0.893022π0.893022\pi
548548 12.6109i 0.538710i
549549 7.42788 3.07673i 0.317014 0.131312i
550550 3.12228 7.53784i 0.133134 0.321415i
551551 16.9124 + 7.00535i 0.720493 + 0.298438i
552552 1.33182 1.33182i 0.0566861 0.0566861i
553553 −30.2729 + 30.2729i −1.28733 + 1.28733i
554554 7.72852 + 3.20126i 0.328353 + 0.136008i
555555 1.76103 4.25151i 0.0747517 0.180467i
556556 −15.7473 + 6.52273i −0.667832 + 0.276625i
557557 12.4900i 0.529217i 0.964356 + 0.264609i 0.0852427π0.0852427\pi
−0.964356 + 0.264609i 0.914757π0.914757\pi
558558 −0.989538 2.38896i −0.0418905 0.101133i
559559 2.36823 + 2.36823i 0.100166 + 0.100166i
560560 −1.48022 −0.0625506
561561 −6.68873 2.03278i −0.282398 0.0858239i
562562 10.9996 0.463991
563563 −1.40167 1.40167i −0.0590734 0.0590734i 0.676953 0.736026i 0.263300π-0.263300\pi
−0.736026 + 0.676953i 0.763300π0.763300\pi
564564 0.910819 + 2.19891i 0.0383524 + 0.0925909i
565565 3.98354i 0.167589i
566566 −19.5290 + 8.08918i −0.820866 + 0.340014i
567567 1.30656 3.15432i 0.0548705 0.132469i
568568 0.209375 + 0.0867259i 0.00878517 + 0.00363894i
569569 11.8558 11.8558i 0.497020 0.497020i −0.413489 0.910509i 0.635690π-0.635690\pi
0.910509 + 0.413489i 0.135690π0.135690\pi
570570 −0.657228 + 0.657228i −0.0275283 + 0.0275283i
571571 −27.8300 11.5275i −1.16465 0.482413i −0.285228 0.958460i 0.592069π-0.592069\pi
−0.879420 + 0.476047i 0.842069π0.842069\pi
572572 −0.215301 + 0.519783i −0.00900220 + 0.0217332i
573573 12.4029 5.13744i 0.518138 0.214620i
574574 41.3725i 1.72686i
575575 3.46840 + 8.37347i 0.144642 + 0.349198i
576576 0.707107 + 0.707107i 0.0294628 + 0.0294628i
577577 19.8204 0.825132 0.412566 0.910928i 0.364633π-0.364633\pi
0.412566 + 0.910928i 0.364633π0.364633\pi
578578 −3.29931 16.6768i −0.137233 0.693662i
579579 5.08905 0.211494
580580 −2.61766 2.61766i −0.108692 0.108692i
581581 −1.36370 3.29226i −0.0565757 0.136586i
582582 3.75539i 0.155666i
583583 4.90403 2.03132i 0.203104 0.0841285i
584584 −4.64527 + 11.2147i −0.192222 + 0.464066i
585585 −0.132909 0.0550527i −0.00549511 0.00227615i
586586 17.7679 17.7679i 0.733987 0.733987i
587587 −9.09425 + 9.09425i −0.375360 + 0.375360i −0.869425 0.494065i 0.835510π-0.835510\pi
0.494065 + 0.869425i 0.335510π0.335510\pi
588588 −4.30237 1.78210i −0.177427 0.0734926i
589589 −2.12143 + 5.12158i −0.0874120 + 0.211031i
590590 3.07401 1.27330i 0.126555 0.0524208i
591591 4.15449i 0.170893i
592592 4.06193 + 9.80638i 0.166944 + 0.403040i
593593 −25.3356 25.3356i −1.04041 1.04041i −0.999148 0.0412617i 0.986862π-0.986862\pi
−0.0412617 0.999148i 0.513138π-0.513138\pi
594594 1.69552 0.0695680
595595 −5.83938 1.77465i −0.239391 0.0727536i
596596 17.5004 0.716844
597597 7.57221 + 7.57221i 0.309910 + 0.309910i
598598 −0.239169 0.577405i −0.00978035 0.0236119i
599599 21.1148i 0.862728i −0.902178 0.431364i 0.858032π-0.858032\pi
0.902178 0.431364i 0.141968π-0.141968\pi
600600 −4.44574 + 1.84149i −0.181497 + 0.0751784i
601601 5.83004 14.0750i 0.237812 0.574130i −0.759244 0.650806i 0.774431π-0.774431\pi
0.997056 + 0.0766767i 0.0244309π0.0244309\pi
602602 −31.8377 13.1876i −1.29761 0.537486i
603603 −11.1519 + 11.1519i −0.454139 + 0.454139i
604604 −6.81657 + 6.81657i −0.277362 + 0.277362i
605605 3.25451 + 1.34806i 0.132314 + 0.0548065i
606606 −0.243503 + 0.587868i −0.00989162 + 0.0238805i
607607 −35.4629 + 14.6892i −1.43940 + 0.596217i −0.959652 0.281192i 0.909270π-0.909270\pi
−0.479743 + 0.877409i 0.659270π0.659270\pi
608608 2.14386i 0.0869450i
609609 −11.1564 26.9339i −0.452080 1.09142i
610610 2.46473 + 2.46473i 0.0997940 + 0.0997940i
611611 0.789763 0.0319504
612612 1.94174 + 3.63726i 0.0784902 + 0.147027i
613613 −1.39554 −0.0563654 −0.0281827 0.999603i 0.508972π-0.508972\pi
−0.0281827 + 0.999603i 0.508972π0.508972\pi
614614 −10.8494 10.8494i −0.437844 0.437844i
615615 2.01046 + 4.85369i 0.0810697 + 0.195719i
616616 5.78886i 0.233240i
617617 7.77433 3.22023i 0.312983 0.129642i −0.220662 0.975350i 0.570822π-0.570822\pi
0.533645 + 0.845709i 0.320822π0.320822\pi
618618 3.29090 7.94495i 0.132380 0.319593i
619619 −4.93657 2.04479i −0.198417 0.0821872i 0.281262 0.959631i 0.409247π-0.409247\pi
−0.479679 + 0.877444i 0.659247π0.659247\pi
620620 0.792706 0.792706i 0.0318359 0.0318359i
621621 −1.33182 + 1.33182i −0.0534442 + 0.0534442i
622622 −20.0320 8.29752i −0.803210 0.332700i
623623 −18.0672 + 43.6181i −0.723848 + 1.74752i
624624 0.306563 0.126983i 0.0122723 0.00508337i
625625 22.2159i 0.888636i
626626 3.21013 + 7.74993i 0.128302 + 0.309750i
627627 −2.57030 2.57030i −0.102648 0.102648i
628628 4.78976 0.191132
629629 4.26713 + 43.5555i 0.170142 + 1.73667i
630630 1.48022 0.0589733
631631 1.03437 + 1.03437i 0.0411776 + 0.0411776i 0.727396 0.686218i 0.240730π-0.240730\pi
−0.686218 + 0.727396i 0.740730π0.740730\pi
632632 4.79863 + 11.5849i 0.190879 + 0.460824i
633633 4.72151i 0.187663i
634634 −22.1549 + 9.17686i −0.879884 + 0.364460i
635635 −2.00491 + 4.84028i −0.0795624 + 0.192081i
636636 −2.89235 1.19805i −0.114689 0.0475058i
637637 −1.09265 + 1.09265i −0.0432925 + 0.0432925i
638638 10.2372 10.2372i 0.405295 0.405295i
639639 −0.209375 0.0867259i −0.00828274 0.00343082i
640640 −0.165911 + 0.400544i −0.00655820 + 0.0158329i
641641 −0.442882 + 0.183448i −0.0174928 + 0.00724574i −0.391413 0.920215i 0.628013π-0.628013\pi
0.373920 + 0.927461i 0.378013π0.378013\pi
642642 2.16478i 0.0854372i
643643 −12.2860 29.6610i −0.484512 1.16972i −0.957444 0.288617i 0.906804π-0.906804\pi
0.472932 0.881099i 0.343196π-0.343196\pi
644644 4.54712 + 4.54712i 0.179182 + 0.179182i
645645 4.37592 0.172302
646646 2.57030 8.45741i 0.101127 0.332752i
647647 23.4802 0.923103 0.461551 0.887114i 0.347293π-0.347293\pi
0.461551 + 0.887114i 0.347293π0.347293\pi
648648 −0.707107 0.707107i −0.0277778 0.0277778i
649649 4.97963 + 12.0219i 0.195468 + 0.471901i
650650 1.59674i 0.0626292i
651651 8.15640 3.37849i 0.319675 0.132414i
652652 6.81363 16.4496i 0.266842 0.644215i
653653 41.9154 + 17.3619i 1.64027 + 0.679424i 0.996326 0.0856443i 0.0272949π-0.0272949\pi
0.643949 + 0.765068i 0.277295π0.277295\pi
654654 −5.59588 + 5.59588i −0.218816 + 0.218816i
655655 −0.274890 + 0.274890i −0.0107408 + 0.0107408i
656656 −11.1953 4.63726i −0.437104 0.181055i
657657 4.64527 11.2147i 0.181229 0.437526i
658658 −7.50756 + 3.10973i −0.292675 + 0.121230i
659659 12.8417i 0.500240i −0.968215 0.250120i 0.919530π-0.919530\pi
0.968215 0.250120i 0.0804701π-0.0804701\pi
660660 0.281305 + 0.679129i 0.0109498 + 0.0264351i
661661 −19.2247 19.2247i −0.747753 0.747753i 0.226304 0.974057i 0.427336π-0.427336\pi
−0.974057 + 0.226304i 0.927336π0.927336\pi
662662 4.07733 0.158470
663663 1.36162 0.133397i 0.0528808 0.00518072i
664664 −1.04373 −0.0405045
665665 −2.24392 2.24392i −0.0870154 0.0870154i
666666 −4.06193 9.80638i −0.157397 0.379989i
667667 16.0825i 0.622719i
668668 −16.2557 + 6.73332i −0.628951 + 0.260520i
669669 −5.98361 + 14.4457i −0.231340 + 0.558504i
670670 −6.31703 2.61660i −0.244048 0.101088i
671671 −9.63912 + 9.63912i −0.372114 + 0.372114i
672672 −2.41421 + 2.41421i −0.0931303 + 0.0931303i
673673 15.4077 + 6.38207i 0.593923 + 0.246011i 0.659337 0.751847i 0.270837π-0.270837\pi
−0.0654145 + 0.997858i 0.520837π0.520837\pi
674674 −3.83323 + 9.25423i −0.147650 + 0.356460i
675675 4.44574 1.84149i 0.171117 0.0708789i
676676 12.8899i 0.495765i
677677 0.996062 + 2.40471i 0.0382818 + 0.0924204i 0.941864 0.335994i 0.109072π-0.109072\pi
−0.903582 + 0.428415i 0.859072π0.859072\pi
678678 −6.49709 6.49709i −0.249519 0.249519i
679679 12.8217 0.492052
680680 −1.13473 + 1.38121i −0.0435147 + 0.0529671i
681681 −11.0615 −0.423876
682682 3.10013 + 3.10013i 0.118710 + 0.118710i
683683 4.68507 + 11.3108i 0.179269 + 0.432794i 0.987814 0.155641i 0.0497442π-0.0497442\pi
−0.808544 + 0.588435i 0.799744π0.799744\pi
684684 2.14386i 0.0819725i
685685 5.05121 2.09228i 0.192997 0.0799419i
686686 −3.06147 + 7.39104i −0.116887 + 0.282191i
687687 −14.2140 5.88764i −0.542299 0.224628i
688688 −7.13707 + 7.13707i −0.272098 + 0.272098i
689689 −0.734556 + 0.734556i −0.0279843 + 0.0279843i
690690 −0.754416 0.312489i −0.0287201 0.0118963i
691691 −5.99803 + 14.4805i −0.228176 + 0.550865i −0.995955 0.0898487i 0.971362π-0.971362\pi
0.767779 + 0.640714i 0.221362π0.221362\pi
692692 17.8736 7.40349i 0.679452 0.281438i
693693 5.78886i 0.219901i
694694 3.30798 + 7.98618i 0.125569 + 0.303151i
695695 5.22528 + 5.22528i 0.198206 + 0.198206i
696696 −8.53874 −0.323660
697697 −38.6053 31.7160i −1.46228 1.20133i
698698 20.8126 0.787768
699699 −7.33806 7.33806i −0.277551 0.277551i
700700 −6.28723 15.1787i −0.237635 0.573702i
701701 30.8222i 1.16414i 0.813139 + 0.582070i 0.197757π0.197757\pi
−0.813139 + 0.582070i 0.802243π0.802243\pi
702702 −0.306563 + 0.126983i −0.0115705 + 0.00479265i
703703 −8.70822 + 21.0235i −0.328437 + 0.792916i
704704 −1.56645 0.648847i −0.0590380 0.0244543i
705705 0.729646 0.729646i 0.0274801 0.0274801i
706706 14.2163 14.2163i 0.535037 0.535037i
707707 −2.00711 0.831370i −0.0754850 0.0312669i
708708 2.93694 7.09040i 0.110377 0.266474i
709709 0.364823 0.151115i 0.0137012 0.00567523i −0.375822 0.926692i 0.622640π-0.622640\pi
0.389524 + 0.921017i 0.372640π0.372640\pi
710710 0.0982525i 0.00368735i
711711 −4.79863 11.5849i −0.179963 0.434469i
712712 9.77791 + 9.77791i 0.366443 + 0.366443i
713713 −4.87028 −0.182393
714714 −12.4184 + 6.62951i −0.464746 + 0.248103i
715715 0.243917 0.00912197
716716 6.44834 + 6.44834i 0.240986 + 0.240986i
717717 −9.48303 22.8941i −0.354150 0.854994i
718718 25.3001i 0.944193i
719719 −10.2515 + 4.24631i −0.382317 + 0.158361i −0.565561 0.824707i 0.691340π-0.691340\pi
0.183244 + 0.983067i 0.441340π0.441340\pi
720720 0.165911 0.400544i 0.00618313 0.0149274i
721721 27.1257 + 11.2359i 1.01022 + 0.418445i
722722 −10.1851 + 10.1851i −0.379049 + 0.379049i
723723 3.04422 3.04422i 0.113216 0.113216i
724724 0.717569 + 0.297227i 0.0266682 + 0.0110463i
725725 15.7240 37.9611i 0.583974 1.40984i
726726 7.50672 3.10939i 0.278601 0.115400i
727727 27.2866i 1.01200i −0.862533 0.506001i 0.831123π-0.831123\pi
0.862533 0.506001i 0.168877π-0.168877\pi
728728 0.433546 + 1.04667i 0.0160683 + 0.0387922i
729729 0.707107 + 0.707107i 0.0261891 + 0.0261891i
730730 5.26266 0.194780
731731 −36.7121 + 19.5986i −1.35785 + 0.724882i
732732 8.03988 0.297163
733733 20.7090 + 20.7090i 0.764906 + 0.764906i 0.977205 0.212299i 0.0680951π-0.0680951\pi
−0.212299 + 0.977205i 0.568095π0.568095\pi
734734 3.94928 + 9.53441i 0.145771 + 0.351921i
735735 2.01896i 0.0744704i
736736 1.74011 0.720777i 0.0641412 0.0265682i
737737 10.2330 24.7047i 0.376939 0.910011i
738738 11.1953 + 4.63726i 0.412106 + 0.170700i
739739 26.2007 26.2007i 0.963810 0.963810i −0.0355580 0.999368i 0.511321π-0.511321\pi
0.999368 + 0.0355580i 0.0113209π0.0113209\pi
740740 3.25397 3.25397i 0.119618 0.119618i
741741 0.657228 + 0.272233i 0.0241439 + 0.0100007i
742742 4.09040 9.87510i 0.150163 0.362526i
743743 13.3844 5.54401i 0.491027 0.203390i −0.123410 0.992356i 0.539383π-0.539383\pi
0.614437 + 0.788966i 0.289383π0.289383\pi
744744 2.58579i 0.0947995i
745745 −2.90350 7.00967i −0.106376 0.256815i
746746 12.9202 + 12.9202i 0.473041 + 0.473041i
747747 1.04373 0.0381880
748748 −5.40167 4.43771i −0.197505 0.162259i
749749 7.39104 0.270063
750750 3.00801 + 3.00801i 0.109837 + 0.109837i
751751 16.8240 + 40.6167i 0.613917 + 1.48213i 0.858664 + 0.512539i 0.171295π0.171295\pi
−0.244747 + 0.969587i 0.578705π0.578705\pi
752752 2.38009i 0.0867928i
753753 −17.6128 + 7.29544i −0.641844 + 0.265861i
754754 −1.08427 + 2.61766i −0.0394868 + 0.0953296i
755755 3.86128 + 1.59939i 0.140526 + 0.0582079i
756756 2.41421 2.41421i 0.0878041 0.0878041i
757757 26.7702 26.7702i 0.972980 0.972980i −0.0266643 0.999644i 0.508489π-0.508489\pi
0.999644 + 0.0266643i 0.00848850π0.00848850\pi
758758 −19.3386 8.01029i −0.702408 0.290947i
759759 1.22209 2.95039i 0.0443590 0.107092i
760760 −0.858710 + 0.355689i −0.0311487 + 0.0129022i
761761 9.82880i 0.356294i 0.984004 + 0.178147i 0.0570102π0.0570102\pi
−0.984004 + 0.178147i 0.942990π0.942990\pi
762762 4.62445 + 11.1644i 0.167526 + 0.404444i
763763 −19.1055 19.1055i −0.691666 0.691666i
764764 13.4248 0.485692
765765 1.13473 1.38121i 0.0410261 0.0499378i
766766 22.9974 0.830929
767767 −1.80071 1.80071i −0.0650200 0.0650200i
768768 0.382683 + 0.923880i 0.0138089 + 0.0333376i
769769 41.1522i 1.48398i 0.670408 + 0.741992i 0.266119π0.266119\pi
−0.670408 + 0.741992i 0.733881π0.733881\pi
770770 −2.31869 + 0.960434i −0.0835599 + 0.0346116i
771771 −10.2404 + 24.7225i −0.368799 + 0.890359i
772772 4.70167 + 1.94749i 0.169217 + 0.0700919i
773773 15.3765 15.3765i 0.553054 0.553054i −0.374267 0.927321i 0.622106π-0.622106\pi
0.927321 + 0.374267i 0.122106π0.122106\pi
774774 7.13707 7.13707i 0.256537 0.256537i
775775 11.4957 + 4.76169i 0.412939 + 0.171045i
776776 1.43713 3.46953i 0.0515898 0.124549i
777777 33.4811 13.8683i 1.20113 0.497523i
778778 9.07748i 0.325444i
779779 −9.94163 24.0012i −0.356196 0.859933i
780780 −0.101724 0.101724i −0.00364231 0.00364231i
781781 0.384248 0.0137495
782782 7.72878 0.757188i 0.276381 0.0270770i
783783 8.53874 0.305150
784784 −3.29289 3.29289i −0.117603 0.117603i
785785 −0.794673 1.91851i −0.0283631 0.0684746i
786786 0.896683i 0.0319836i
787787 43.9786 18.2165i 1.56767 0.649349i 0.581267 0.813713i 0.302557π-0.302557\pi
0.986400 + 0.164364i 0.0525572π0.0525572\pi
788788 −1.58986 + 3.83825i −0.0566363 + 0.136732i
789789 25.4180 + 10.5285i 0.904905 + 0.374824i
790790 3.84413 3.84413i 0.136768 0.136768i
791791 22.1825 22.1825i 0.788718 0.788718i
792792 1.56645 + 0.648847i 0.0556615 + 0.0230558i
793793 1.02092 2.46473i 0.0362541 0.0875251i
794794 7.21417 2.98821i 0.256021 0.106048i
795795 1.35728i 0.0481378i
796796 4.09805 + 9.89357i 0.145252 + 0.350668i
797797 −26.7982 26.7982i −0.949242 0.949242i 0.0495310 0.998773i 0.484227π-0.484227\pi
−0.998773 + 0.0495310i 0.984227π0.984227\pi
798798 −7.31959 −0.259111
799799 −2.85351 + 9.38931i −0.100950 + 0.332170i
800800 −4.81204 −0.170131
801801 −9.77791 9.77791i −0.345485 0.345485i
802802 6.64367 + 16.0392i 0.234596 + 0.566365i
803803 20.5813i 0.726299i
804804 −14.5706 + 6.03535i −0.513866 + 0.212850i
805805 1.06691 2.57574i 0.0376035 0.0907828i
806806 −0.792706 0.328350i −0.0279219 0.0115656i
807807 −7.08153 + 7.08153i −0.249282 + 0.249282i
808808 −0.449934 + 0.449934i −0.0158286 + 0.0158286i
809809 −35.6369 14.7613i −1.25293 0.518979i −0.345195 0.938531i 0.612187π-0.612187\pi
−0.907731 + 0.419552i 0.862187π0.862187\pi
810810 −0.165911 + 0.400544i −0.00582951 + 0.0140737i
811811 −17.9596 + 7.43911i −0.630647 + 0.261223i −0.675028 0.737792i 0.735869π-0.735869\pi
0.0443808 + 0.999015i 0.485869π0.485869\pi
812812 29.1531i 1.02307i
813813 −3.52432 8.50846i −0.123603 0.298405i
814814 12.7257 + 12.7257i 0.446034 + 0.446034i
815815 −7.71922 −0.270393
816816 0.402015 + 4.10346i 0.0140734 + 0.143650i
817817 −21.6387 −0.757043
818818 −3.12649 3.12649i −0.109315 0.109315i
819819 −0.433546 1.04667i −0.0151493 0.0365737i
820820 5.25359i 0.183463i
821821 0.214175 0.0887142i 0.00747476 0.00309615i −0.378943 0.925420i 0.623712π-0.623712\pi
0.386418 + 0.922324i 0.373712π0.373712\pi
822822 4.82597 11.6509i 0.168325 0.406373i
823823 −20.7809 8.60773i −0.724376 0.300047i −0.0101376 0.999949i 0.503227π-0.503227\pi
−0.714239 + 0.699902i 0.753227π0.753227\pi
824824 6.08080 6.08080i 0.211835 0.211835i
825825 −5.76921 + 5.76921i −0.200858 + 0.200858i
826826 24.2081 + 10.0273i 0.842309 + 0.348896i
827827 −20.0190 + 48.3300i −0.696127 + 1.68060i 0.0359274 + 0.999354i 0.488561π0.488561\pi
−0.732055 + 0.681246i 0.761439π0.761439\pi
828828 −1.74011 + 0.720777i −0.0604729 + 0.0250487i
829829 23.3260i 0.810144i −0.914285 0.405072i 0.867246π-0.867246\pi
0.914285 0.405072i 0.132754π-0.132754\pi
830830 0.173166 + 0.418059i 0.00601067 + 0.0145110i
831831 −5.91515 5.91515i −0.205194 0.205194i
832832 0.331821 0.0115038
833833 −9.04240 16.9382i −0.313301 0.586873i
834834 17.0447 0.590210
835835 5.39398 + 5.39398i 0.186666 + 0.186666i
836836 −1.39104 3.35826i −0.0481100 0.116148i
837837 2.58579i 0.0893779i
838838 −21.4029 + 8.86537i −0.739351 + 0.306249i
839839 −5.13605 + 12.3995i −0.177316 + 0.428079i −0.987402 0.158232i 0.949421π-0.949421\pi
0.810086 + 0.586312i 0.199421π0.199421\pi
840840 1.36754 + 0.566454i 0.0471847 + 0.0195445i
841841 31.0491 31.0491i 1.07066 1.07066i
842842 14.1792 14.1792i 0.488648 0.488648i
843843 −10.1623 4.20937i −0.350009 0.144979i
844844 1.80684 4.36210i 0.0621941 0.150150i
845845 5.16297 2.13857i 0.177611 0.0735691i
846846 2.38009i 0.0818290i
847847 10.6161 + 25.6296i 0.364774 + 0.880642i
848848 −2.21371 2.21371i −0.0760191 0.0760191i
849849 21.1380 0.725456
850850 −18.9832 5.76921i −0.651120 0.197882i
851851 −19.9919 −0.685314
852852 −0.160248 0.160248i −0.00549002 0.00549002i
853853 −19.1093 46.1339i −0.654290 1.57960i −0.806491 0.591246i 0.798636π-0.798636\pi
0.152202 0.988349i 0.451364π-0.451364\pi
854854 27.4499i 0.939315i
855855 0.858710 0.355689i 0.0293673 0.0121643i
856856 0.828427 2.00000i 0.0283151 0.0683586i
857857 15.8686 + 6.57298i 0.542060 + 0.224529i 0.636876 0.770966i 0.280226π-0.280226\pi
−0.0948160 + 0.995495i 0.530226π0.530226\pi
858858 0.397825 0.397825i 0.0135815 0.0135815i
859859 −6.19681 + 6.19681i −0.211433 + 0.211433i −0.804876 0.593443i 0.797768π-0.797768\pi
0.593443 + 0.804876i 0.297768π0.297768\pi
860860 4.04283 + 1.67459i 0.137859 + 0.0571032i
861861 −15.8326 + 38.2233i −0.539573 + 1.30264i
862862 −37.0908 + 15.3635i −1.26332 + 0.523283i
863863 35.9177i 1.22265i −0.791379 0.611326i 0.790636π-0.790636\pi
0.791379 0.611326i 0.209364π-0.209364\pi
864864 −0.382683 0.923880i −0.0130192 0.0314310i
865865 −5.93084 5.93084i −0.201655 0.201655i
866866 21.8499 0.742490
867867 −3.33376 + 16.6699i −0.113220 + 0.566140i
868868 8.82843 0.299656
869869 15.0337 + 15.0337i 0.509983 + 0.509983i
870870 1.41667 + 3.42014i 0.0480296 + 0.115954i
871871 5.23320i 0.177320i
872872 −7.31136 + 3.02847i −0.247594 + 0.102557i
873873 −1.43713 + 3.46953i −0.0486394 + 0.117426i
874874 3.73055 + 1.54524i 0.126188 + 0.0522686i
875875 −10.2700 + 10.2700i −0.347189 + 0.347189i
876876 8.58333 8.58333i 0.290004 0.290004i
877877 −3.90356 1.61691i −0.131814 0.0545991i 0.315801 0.948825i 0.397727π-0.397727\pi
−0.447615 + 0.894226i 0.647727π0.647727\pi
878878 0.320985 0.774927i 0.0108327 0.0261525i
879879 −23.2149 + 9.61594i −0.783020 + 0.324338i
880880 0.735084i 0.0247797i
881881 −11.4789 27.7125i −0.386734 0.933657i −0.990627 0.136593i 0.956385π-0.956385\pi
0.603894 0.797065i 0.293615π-0.293615\pi
882882 3.29289 + 3.29289i 0.110877 + 0.110877i
883883 −13.9714 −0.470175 −0.235087 0.971974i 0.575538π-0.575538\pi
−0.235087 + 0.971974i 0.575538π0.575538\pi
884884 1.30902 + 0.397825i 0.0440270 + 0.0133803i
885885 −3.32729 −0.111845
886886 2.27170 + 2.27170i 0.0763194 + 0.0763194i
887887 −8.42959 20.3508i −0.283038 0.683314i 0.716866 0.697211i 0.245576π-0.245576\pi
−0.999903 + 0.0138977i 0.995576π0.995576\pi
888888 10.6143i 0.356194i
889889 −38.1177 + 15.7889i −1.27843 + 0.529541i
890890 2.29422 5.53874i 0.0769025 0.185659i
891891 −1.56645 0.648847i −0.0524782 0.0217372i
892892 −11.0563 + 11.0563i −0.370191 + 0.370191i
893893 −3.60806 + 3.60806i −0.120739 + 0.120739i
894894 −16.1683 6.69711i −0.540747 0.223985i
895895 1.51299 3.65269i 0.0505738 0.122096i
896896 −3.15432 + 1.30656i −0.105379 + 0.0436492i
897897 0.624979i 0.0208674i
898898 11.0015 + 26.5599i 0.367124 + 0.886316i
899899 15.6125 + 15.6125i 0.520705 + 0.520705i
900900 4.81204 0.160401
901901 −6.07892 11.3870i −0.202518 0.379356i
902902 −20.5458 −0.684102
903903 24.3675 + 24.3675i 0.810899 + 0.810899i
904904 −3.51620 8.48886i −0.116947 0.282335i
905905 0.336731i 0.0111933i
906906 8.90628 3.68910i 0.295891 0.122562i
907907 −10.2983 + 24.8622i −0.341948 + 0.825535i 0.655571 + 0.755134i 0.272428π0.272428\pi
−0.997519 + 0.0704015i 0.977572π0.977572\pi
908908 −10.2195 4.23304i −0.339145 0.140478i
909909 0.449934 0.449934i 0.0149234 0.0149234i
910910 0.347308 0.347308i 0.0115131 0.0115131i
911911 −32.7838 13.5795i −1.08618 0.449908i −0.233504 0.972356i 0.575019π-0.575019\pi
−0.852671 + 0.522447i 0.825019π0.825019\pi
912912 −0.820420 + 1.98067i −0.0271668 + 0.0655865i
913913 −1.63495 + 0.677220i −0.0541090 + 0.0224127i
914914 7.45097i 0.246456i
915915 −1.33390 3.22033i −0.0440975 0.106461i
916916 −10.8789 10.8789i −0.359450 0.359450i
917917 −3.06147 −0.101099
918918 −0.402015 4.10346i −0.0132685 0.135434i
919919 −38.6107 −1.27365 −0.636824 0.771009i 0.719752π-0.719752\pi
−0.636824 + 0.771009i 0.719752π0.719752\pi
920920 −0.577405 0.577405i −0.0190365 0.0190365i
921921 5.87163 + 14.1754i 0.193477 + 0.467094i
922922 25.6378i 0.844337i
923923 −0.0694750 + 0.0287775i −0.00228680 + 0.000947223i
924924 −2.21530 + 5.34821i −0.0728781 + 0.175943i
925925 47.1887 + 19.5462i 1.55155 + 0.642675i
926926 −7.61888 + 7.61888i −0.250372 + 0.250372i
927927 −6.08080 + 6.08080i −0.199720 + 0.199720i
928928 −7.88877 3.26763i −0.258962 0.107265i
929929 8.76150 21.1521i 0.287455 0.693979i −0.712515 0.701657i 0.752444π-0.752444\pi
0.999971 + 0.00767791i 0.00244398π0.00244398\pi
930930 −1.03572 + 0.429010i −0.0339626 + 0.0140678i
931931 9.98364i 0.327201i
932932 −3.97133 9.58764i −0.130085 0.314054i
933933 15.3318 + 15.3318i 0.501941 + 0.501941i
934934 −35.6492 −1.16648
935935 −0.881302 + 2.89987i −0.0288216 + 0.0948358i
936936 −0.331821 −0.0108459
937937 −28.0575 28.0575i −0.916598 0.916598i 0.0801820 0.996780i 0.474450π-0.474450\pi
−0.996780 + 0.0801820i 0.974450π0.974450\pi
938938 −20.6060 49.7472i −0.672809 1.62430i
939939 8.38847i 0.273747i
940940 0.953329 0.394882i 0.0310941 0.0128796i
941941 −20.1541 + 48.6562i −0.657004 + 1.58615i 0.145405 + 0.989372i 0.453551π0.453551\pi
−0.802409 + 0.596775i 0.796449π0.796449\pi
942942 −4.42516 1.83296i −0.144180 0.0597212i
943943 16.1387 16.1387i 0.525547 0.525547i
944944 5.42676 5.42676i 0.176626 0.176626i
945945 −1.36754 0.566454i −0.0444861 0.0184268i
946946 −6.54903 + 15.8108i −0.212927 + 0.514052i
947947 −1.41074 + 0.584348i −0.0458430 + 0.0189888i −0.405487 0.914101i 0.632898π-0.632898\pi
0.359644 + 0.933090i 0.382898π0.382898\pi
948948 12.5394i 0.407262i
949949 −1.54140 3.72126i −0.0500359 0.120797i
950950 −7.29475 7.29475i −0.236673 0.236673i
951951 23.9803 0.777614
952952 −14.0101 + 1.37257i −0.454070 + 0.0444851i
953953 9.95360 0.322429 0.161214 0.986919i 0.448459π-0.448459\pi
0.161214 + 0.986919i 0.448459π0.448459\pi
954954 2.21371 + 2.21371i 0.0716715 + 0.0716715i
955955 −2.22732 5.37722i −0.0720743 0.174003i
956956 24.7803i 0.801454i
957957 −13.3755 + 5.54033i −0.432370 + 0.179094i
958958 −5.38442 + 12.9991i −0.173963 + 0.419983i
959959 39.7788 + 16.4769i 1.28452 + 0.532067i
960960 0.306563 0.306563i 0.00989428 0.00989428i
961961 17.1924 17.1924i 0.554593 0.554593i
962962 −3.25397 1.34784i −0.104912 0.0434560i
963963 −0.828427 + 2.00000i −0.0266957 + 0.0644491i
964964 3.97746 1.64752i 0.128105 0.0530630i
965965 2.20633i 0.0710244i
966966 −2.46088 5.94110i −0.0791777 0.191152i
967967 4.16375 + 4.16375i 0.133897 + 0.133897i 0.770879 0.636982i 0.219817π-0.219817\pi
−0.636982 + 0.770879i 0.719817π0.719817\pi
968968 8.12522 0.261154
969969 −5.61116 + 6.83002i −0.180256 + 0.219412i
970970 −1.62813 −0.0522762
971971 −13.4117 13.4117i −0.430403 0.430403i 0.458363 0.888765i 0.348436π-0.348436\pi
−0.888765 + 0.458363i 0.848436π0.848436\pi
972972 0.382683 + 0.923880i 0.0122746 + 0.0296334i
973973 58.1943i 1.86562i
974974 22.2956 9.23512i 0.714396 0.295912i
975975 0.611045 1.47519i 0.0195691 0.0472440i
976976 7.42788 + 3.07673i 0.237761 + 0.0984837i
977977 22.8517 22.8517i 0.731090 0.731090i −0.239746 0.970836i 0.577064π-0.577064\pi
0.970836 + 0.239746i 0.0770641π0.0770641\pi
978978 −12.5899 + 12.5899i −0.402582 + 0.402582i
979979 21.6610 + 8.97229i 0.692289 + 0.286756i
980980 −0.772622 + 1.86527i −0.0246805 + 0.0595840i
981981 7.31136 3.02847i 0.233434 0.0966915i
982982 26.5200i 0.846288i
983983 −12.4128 29.9672i −0.395908 0.955805i −0.988626 0.150396i 0.951945π-0.951945\pi
0.592718 0.805410i 0.298055π-0.298055\pi
984984 8.56854 + 8.56854i 0.273155 + 0.273155i
985985 1.80116 0.0573898
986986 −27.2032 22.3486i −0.866325 0.711724i
987987 8.12612 0.258657
988988 0.503021 + 0.503021i 0.0160032 + 0.0160032i
989989 −7.27504 17.5635i −0.231333 0.558487i
990990 0.735084i 0.0233625i
991991 43.3309 17.9482i 1.37645 0.570145i 0.432921 0.901432i 0.357483π-0.357483\pi
0.943530 + 0.331287i 0.107483π0.107483\pi
992992 0.989538 2.38896i 0.0314179 0.0758494i
993993 −3.76696 1.56033i −0.119541 0.0495154i
994994 0.547123 0.547123i 0.0173537 0.0173537i
995995 3.28290 3.28290i 0.104075 0.104075i
996996 0.964279 + 0.399418i 0.0305544 + 0.0126560i
997997 −18.1610 + 43.8446i −0.575166 + 1.38857i 0.321941 + 0.946760i 0.395665π0.395665\pi
−0.897107 + 0.441813i 0.854335π0.854335\pi
998998 4.19438 1.73737i 0.132771 0.0549954i
999999 10.6143i 0.335823i
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 102.2.h.a.49.2 yes 8
3.2 odd 2 306.2.l.d.253.2 8
4.3 odd 2 816.2.bq.b.49.1 8
17.3 odd 16 1734.2.b.k.577.6 8
17.5 odd 16 1734.2.a.v.1.3 4
17.6 odd 16 1734.2.f.m.829.3 8
17.7 odd 16 1734.2.f.m.1483.3 8
17.8 even 8 inner 102.2.h.a.25.2 8
17.10 odd 16 1734.2.f.j.1483.2 8
17.11 odd 16 1734.2.f.j.829.2 8
17.12 odd 16 1734.2.a.w.1.2 4
17.14 odd 16 1734.2.b.k.577.3 8
51.5 even 16 5202.2.a.br.1.2 4
51.8 odd 8 306.2.l.d.127.2 8
51.29 even 16 5202.2.a.bt.1.3 4
68.59 odd 8 816.2.bq.b.433.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.h.a.25.2 8 17.8 even 8 inner
102.2.h.a.49.2 yes 8 1.1 even 1 trivial
306.2.l.d.127.2 8 51.8 odd 8
306.2.l.d.253.2 8 3.2 odd 2
816.2.bq.b.49.1 8 4.3 odd 2
816.2.bq.b.433.1 8 68.59 odd 8
1734.2.a.v.1.3 4 17.5 odd 16
1734.2.a.w.1.2 4 17.12 odd 16
1734.2.b.k.577.3 8 17.14 odd 16
1734.2.b.k.577.6 8 17.3 odd 16
1734.2.f.j.829.2 8 17.11 odd 16
1734.2.f.j.1483.2 8 17.10 odd 16
1734.2.f.m.829.3 8 17.6 odd 16
1734.2.f.m.1483.3 8 17.7 odd 16
5202.2.a.br.1.2 4 51.5 even 16
5202.2.a.bt.1.3 4 51.29 even 16