Properties

Label 170.2.k.b.121.3
Level 170170
Weight 22
Character 170.121
Analytic conductor 1.3571.357
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(111,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.111");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 170=2517 170 = 2 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 170.k (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: 1.357456834361.35745683436
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ8)\Q(\zeta_{8})
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+28x14+286x12+1412x10+3709x8+5264x6+3780x4+1072x2+4 x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 121.3
Root 2.47571i2.47571i of defining polynomial
Character χ\chi == 170.121
Dual form 170.2.k.b.111.3

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+(0.707107+0.707107i)q2+(1.363380.564729i)q3+1.00000iq4+(0.382683+0.923880i)q5+(1.36338+0.564729i)q6+(1.357853.27815i)q7+(0.707107+0.707107i)q8+(0.581445+0.581445i)q9+(0.382683+0.923880i)q10+(4.350131.80188i)q11+(0.564729+1.36338i)q12+5.47699iq13+(3.278151.35785i)q14+(1.04348+1.04348i)q151.00000q16+(2.528943.25645i)q170.822287q18+(0.857748+0.857748i)q19+(0.923880+0.382683i)q205.23617iq21+(1.801884.35013i)q22+(5.284852.18906i)q23+(0.564729+1.36338i)q24+(0.707107+0.707107i)q25+(3.87282+3.87282i)q26+(2.15856+5.21121i)q27+(3.27815+1.35785i)q28+(1.777104.29029i)q29+1.47571iq30+(6.728922.78721i)q31+(0.7071070.707107i)q326.94843q33+(4.090890.514430i)q34+3.54824q35+(0.5814450.581445i)q36+(8.58444+3.55579i)q37+1.21304iq38+(3.09302+7.46720i)q39+(0.9238800.382683i)q40+(0.05475980.132202i)q41+(3.702533.70253i)q42+(0.587013+0.587013i)q43+(1.801884.35013i)q44+(0.7596950.314676i)q45+(2.189065.28485i)q465.85635iq47+(1.36338+0.564729i)q48+(3.952753.95275i)q491.00000q50+(1.608885.86793i)q515.47699q52+(6.54226+6.54226i)q53+(5.21121+2.15856i)q544.70854iq55+(1.35785+3.27815i)q56+(1.65383+0.685038i)q57+(1.777104.29029i)q58+(3.33507+3.33507i)q59+(1.04348+1.04348i)q60+(4.7626111.4980i)q61+(6.72892+2.78721i)q62+(1.11655+2.69558i)q631.00000iq64+(5.06008+2.09595i)q65+(4.913284.91328i)q66+8.66703q67+(3.25645+2.52894i)q688.44146q69+(2.50899+2.50899i)q70+(4.752351.96849i)q710.822287iq72+(6.17351+14.9042i)q73+(8.584443.55579i)q74+(0.564729+1.36338i)q75+(0.857748+0.857748i)q76+(11.8137+11.8137i)q77+(3.09302+7.46720i)q78+(9.34587+3.87118i)q79+(0.3826830.923880i)q80+5.85698iq81+(0.1322020.0547598i)q82+(2.40841+2.40841i)q83+5.23617q84+(3.97635+1.09024i)q850.830161q86+(4.845704.84570i)q87+(4.350131.80188i)q88+2.24175iq89+(0.3146760.759695i)q90+(17.9544+7.43696i)q91+(2.189065.28485i)q92+(7.600047.60004i)q93+(4.141064.14106i)q94+(0.464210+1.12070i)q95+(1.363380.564729i)q96+(1.66675+4.02389i)q975.59004iq98+(3.577051.48166i)q99+O(q100)q+(0.707107 + 0.707107i) q^{2} +(1.36338 - 0.564729i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(1.36338 + 0.564729i) q^{6} +(1.35785 - 3.27815i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.581445 + 0.581445i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(-4.35013 - 1.80188i) q^{11} +(0.564729 + 1.36338i) q^{12} +5.47699i q^{13} +(3.27815 - 1.35785i) q^{14} +(1.04348 + 1.04348i) q^{15} -1.00000 q^{16} +(2.52894 - 3.25645i) q^{17} -0.822287 q^{18} +(0.857748 + 0.857748i) q^{19} +(-0.923880 + 0.382683i) q^{20} -5.23617i q^{21} +(-1.80188 - 4.35013i) q^{22} +(-5.28485 - 2.18906i) q^{23} +(-0.564729 + 1.36338i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-3.87282 + 3.87282i) q^{26} +(-2.15856 + 5.21121i) q^{27} +(3.27815 + 1.35785i) q^{28} +(-1.77710 - 4.29029i) q^{29} +1.47571i q^{30} +(6.72892 - 2.78721i) q^{31} +(-0.707107 - 0.707107i) q^{32} -6.94843 q^{33} +(4.09089 - 0.514430i) q^{34} +3.54824 q^{35} +(-0.581445 - 0.581445i) q^{36} +(-8.58444 + 3.55579i) q^{37} +1.21304i q^{38} +(3.09302 + 7.46720i) q^{39} +(-0.923880 - 0.382683i) q^{40} +(0.0547598 - 0.132202i) q^{41} +(3.70253 - 3.70253i) q^{42} +(-0.587013 + 0.587013i) q^{43} +(1.80188 - 4.35013i) q^{44} +(-0.759695 - 0.314676i) q^{45} +(-2.18906 - 5.28485i) q^{46} -5.85635i q^{47} +(-1.36338 + 0.564729i) q^{48} +(-3.95275 - 3.95275i) q^{49} -1.00000 q^{50} +(1.60888 - 5.86793i) q^{51} -5.47699 q^{52} +(6.54226 + 6.54226i) q^{53} +(-5.21121 + 2.15856i) q^{54} -4.70854i q^{55} +(1.35785 + 3.27815i) q^{56} +(1.65383 + 0.685038i) q^{57} +(1.77710 - 4.29029i) q^{58} +(-3.33507 + 3.33507i) q^{59} +(-1.04348 + 1.04348i) q^{60} +(4.76261 - 11.4980i) q^{61} +(6.72892 + 2.78721i) q^{62} +(1.11655 + 2.69558i) q^{63} -1.00000i q^{64} +(-5.06008 + 2.09595i) q^{65} +(-4.91328 - 4.91328i) q^{66} +8.66703 q^{67} +(3.25645 + 2.52894i) q^{68} -8.44146 q^{69} +(2.50899 + 2.50899i) q^{70} +(4.75235 - 1.96849i) q^{71} -0.822287i q^{72} +(6.17351 + 14.9042i) q^{73} +(-8.58444 - 3.55579i) q^{74} +(-0.564729 + 1.36338i) q^{75} +(-0.857748 + 0.857748i) q^{76} +(-11.8137 + 11.8137i) q^{77} +(-3.09302 + 7.46720i) q^{78} +(9.34587 + 3.87118i) q^{79} +(-0.382683 - 0.923880i) q^{80} +5.85698i q^{81} +(0.132202 - 0.0547598i) q^{82} +(2.40841 + 2.40841i) q^{83} +5.23617 q^{84} +(3.97635 + 1.09024i) q^{85} -0.830161 q^{86} +(-4.84570 - 4.84570i) q^{87} +(4.35013 - 1.80188i) q^{88} +2.24175i q^{89} +(-0.314676 - 0.759695i) q^{90} +(17.9544 + 7.43696i) q^{91} +(2.18906 - 5.28485i) q^{92} +(7.60004 - 7.60004i) q^{93} +(4.14106 - 4.14106i) q^{94} +(-0.464210 + 1.12070i) q^{95} +(-1.36338 - 0.564729i) q^{96} +(1.66675 + 4.02389i) q^{97} -5.59004i q^{98} +(3.57705 - 1.48166i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q8q118q14+8q1516q16+8q188q22+8q2324q278q28+8q29+32q31+16q33+16q34+16q358q3732q3932q41+32q42+56q99+O(q100) 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42}+ \cdots - 56 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/170Z)×\left(\mathbb{Z}/170\mathbb{Z}\right)^\times.

nn 7171 137137
χ(n)\chi(n) e(78)e\left(\frac{7}{8}\right) 11

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 1.36338 0.564729i 0.787145 0.326046i 0.0473502 0.998878i 0.484922π-0.484922\pi
0.739795 + 0.672832i 0.234922π0.234922\pi
44 1.00000i 0.500000i
55 0.382683 + 0.923880i 0.171141 + 0.413171i
66 1.36338 + 0.564729i 0.556596 + 0.230550i
77 1.35785 3.27815i 0.513221 1.23902i −0.428779 0.903410i 0.641056π-0.641056\pi
0.941999 0.335615i 0.108944π-0.108944\pi
88 −0.707107 + 0.707107i −0.250000 + 0.250000i
99 −0.581445 + 0.581445i −0.193815 + 0.193815i
1010 −0.382683 + 0.923880i −0.121015 + 0.292156i
1111 −4.35013 1.80188i −1.31161 0.543288i −0.386258 0.922391i 0.626232π-0.626232\pi
−0.925354 + 0.379103i 0.876232π0.876232\pi
1212 0.564729 + 1.36338i 0.163023 + 0.393573i
1313 5.47699i 1.51904i 0.650481 + 0.759522i 0.274567π0.274567\pi
−0.650481 + 0.759522i 0.725433π0.725433\pi
1414 3.27815 1.35785i 0.876123 0.362902i
1515 1.04348 + 1.04348i 0.269426 + 0.269426i
1616 −1.00000 −0.250000
1717 2.52894 3.25645i 0.613358 0.789805i
1818 −0.822287 −0.193815
1919 0.857748 + 0.857748i 0.196781 + 0.196781i 0.798619 0.601838i 0.205565π-0.205565\pi
−0.601838 + 0.798619i 0.705565π0.705565\pi
2020 −0.923880 + 0.382683i −0.206586 + 0.0855706i
2121 5.23617i 1.14263i
2222 −1.80188 4.35013i −0.384162 0.927450i
2323 −5.28485 2.18906i −1.10197 0.456450i −0.243803 0.969825i 0.578395π-0.578395\pi
−0.858165 + 0.513375i 0.828395π0.828395\pi
2424 −0.564729 + 1.36338i −0.115275 + 0.278298i
2525 −0.707107 + 0.707107i −0.141421 + 0.141421i
2626 −3.87282 + 3.87282i −0.759522 + 0.759522i
2727 −2.15856 + 5.21121i −0.415414 + 1.00290i
2828 3.27815 + 1.35785i 0.619512 + 0.256610i
2929 −1.77710 4.29029i −0.329999 0.796687i −0.998591 0.0530586i 0.983103π-0.983103\pi
0.668593 0.743629i 0.266897π-0.266897\pi
3030 1.47571i 0.269426i
3131 6.72892 2.78721i 1.20855 0.500598i 0.314798 0.949159i 0.398063π-0.398063\pi
0.893752 + 0.448561i 0.148063π0.148063\pi
3232 −0.707107 0.707107i −0.125000 0.125000i
3333 −6.94843 −1.20957
3434 4.09089 0.514430i 0.701581 0.0882239i
3535 3.54824 0.599763
3636 −0.581445 0.581445i −0.0969075 0.0969075i
3737 −8.58444 + 3.55579i −1.41127 + 0.584569i −0.952652 0.304063i 0.901657π-0.901657\pi
−0.458622 + 0.888631i 0.651657π0.651657\pi
3838 1.21304i 0.196781i
3939 3.09302 + 7.46720i 0.495279 + 1.19571i
4040 −0.923880 0.382683i −0.146078 0.0605076i
4141 0.0547598 0.132202i 0.00855205 0.0206465i −0.919546 0.392983i 0.871443π-0.871443\pi
0.928098 + 0.372336i 0.121443π0.121443\pi
4242 3.70253 3.70253i 0.571313 0.571313i
4343 −0.587013 + 0.587013i −0.0895186 + 0.0895186i −0.750448 0.660929i 0.770162π-0.770162\pi
0.660929 + 0.750448i 0.270162π0.270162\pi
4444 1.80188 4.35013i 0.271644 0.655806i
4545 −0.759695 0.314676i −0.113249 0.0469091i
4646 −2.18906 5.28485i −0.322759 0.779209i
4747 5.85635i 0.854236i −0.904196 0.427118i 0.859529π-0.859529\pi
0.904196 0.427118i 0.140471π-0.140471\pi
4848 −1.36338 + 0.564729i −0.196786 + 0.0815116i
4949 −3.95275 3.95275i −0.564679 0.564679i
5050 −1.00000 −0.141421
5151 1.60888 5.86793i 0.225288 0.821675i
5252 −5.47699 −0.759522
5353 6.54226 + 6.54226i 0.898648 + 0.898648i 0.995317 0.0966687i 0.0308187π-0.0308187\pi
−0.0966687 + 0.995317i 0.530819π0.530819\pi
5454 −5.21121 + 2.15856i −0.709156 + 0.293742i
5555 4.70854i 0.634900i
5656 1.35785 + 3.27815i 0.181451 + 0.438061i
5757 1.65383 + 0.685038i 0.219055 + 0.0907355i
5858 1.77710 4.29029i 0.233344 0.563343i
5959 −3.33507 + 3.33507i −0.434189 + 0.434189i −0.890051 0.455861i 0.849331π-0.849331\pi
0.455861 + 0.890051i 0.349331π0.349331\pi
6060 −1.04348 + 1.04348i −0.134713 + 0.134713i
6161 4.76261 11.4980i 0.609790 1.47216i −0.253439 0.967351i 0.581562π-0.581562\pi
0.863229 0.504812i 0.168438π-0.168438\pi
6262 6.72892 + 2.78721i 0.854574 + 0.353976i
6363 1.11655 + 2.69558i 0.140672 + 0.339611i
6464 1.00000i 0.125000i
6565 −5.06008 + 2.09595i −0.627626 + 0.259971i
6666 −4.91328 4.91328i −0.604783 0.604783i
6767 8.66703 1.05885 0.529423 0.848358i 0.322408π-0.322408\pi
0.529423 + 0.848358i 0.322408π0.322408\pi
6868 3.25645 + 2.52894i 0.394903 + 0.306679i
6969 −8.44146 −1.01623
7070 2.50899 + 2.50899i 0.299881 + 0.299881i
7171 4.75235 1.96849i 0.564000 0.233617i −0.0824206 0.996598i 0.526265π-0.526265\pi
0.646421 + 0.762981i 0.276265π0.276265\pi
7272 0.822287i 0.0969075i
7373 6.17351 + 14.9042i 0.722555 + 1.74440i 0.665939 + 0.746006i 0.268031π0.268031\pi
0.0566159 + 0.998396i 0.481969π0.481969\pi
7474 −8.58444 3.55579i −0.997921 0.413353i
7575 −0.564729 + 1.36338i −0.0652093 + 0.157429i
7676 −0.857748 + 0.857748i −0.0983905 + 0.0983905i
7777 −11.8137 + 11.8137i −1.34629 + 1.34629i
7878 −3.09302 + 7.46720i −0.350215 + 0.845494i
7979 9.34587 + 3.87118i 1.05149 + 0.435542i 0.840424 0.541929i 0.182306π-0.182306\pi
0.211068 + 0.977471i 0.432306π0.432306\pi
8080 −0.382683 0.923880i −0.0427853 0.103293i
8181 5.85698i 0.650776i
8282 0.132202 0.0547598i 0.0145993 0.00604721i
8383 2.40841 + 2.40841i 0.264358 + 0.264358i 0.826822 0.562464i 0.190147π-0.190147\pi
−0.562464 + 0.826822i 0.690147π0.690147\pi
8484 5.23617 0.571313
8585 3.97635 + 1.09024i 0.431296 + 0.118254i
8686 −0.830161 −0.0895186
8787 −4.84570 4.84570i −0.519514 0.519514i
8888 4.35013 1.80188i 0.463725 0.192081i
8989 2.24175i 0.237625i 0.992917 + 0.118813i 0.0379088π0.0379088\pi
−0.992917 + 0.118813i 0.962091π0.962091\pi
9090 −0.314676 0.759695i −0.0331697 0.0800788i
9191 17.9544 + 7.43696i 1.88213 + 0.779605i
9292 2.18906 5.28485i 0.228225 0.550984i
9393 7.60004 7.60004i 0.788087 0.788087i
9494 4.14106 4.14106i 0.427118 0.427118i
9595 −0.464210 + 1.12070i −0.0476269 + 0.114982i
9696 −1.36338 0.564729i −0.139149 0.0576374i
9797 1.66675 + 4.02389i 0.169233 + 0.408564i 0.985628 0.168929i 0.0540309π-0.0540309\pi
−0.816395 + 0.577493i 0.804031π0.804031\pi
9898 5.59004i 0.564679i
9999 3.57705 1.48166i 0.359507 0.148913i
100100 −0.707107 0.707107i −0.0707107 0.0707107i
101101 −10.7393 −1.06860 −0.534301 0.845294i 0.679425π-0.679425\pi
−0.534301 + 0.845294i 0.679425π0.679425\pi
102102 5.28690 3.01160i 0.523482 0.298193i
103103 −7.43306 −0.732401 −0.366200 0.930536i 0.619342π-0.619342\pi
−0.366200 + 0.930536i 0.619342π0.619342\pi
104104 −3.87282 3.87282i −0.379761 0.379761i
105105 4.83759 2.00380i 0.472101 0.195550i
106106 9.25215i 0.898648i
107107 6.01999 + 14.5335i 0.581974 + 1.40501i 0.891020 + 0.453963i 0.149990π0.149990\pi
−0.309046 + 0.951047i 0.600010π0.600010\pi
108108 −5.21121 2.15856i −0.501449 0.207707i
109109 2.46089 5.94112i 0.235711 0.569056i −0.761120 0.648611i 0.775350π-0.775350\pi
0.996830 + 0.0795553i 0.0253500π0.0253500\pi
110110 3.32944 3.32944i 0.317450 0.317450i
111111 −9.69577 + 9.69577i −0.920281 + 0.920281i
112112 −1.35785 + 3.27815i −0.128305 + 0.309756i
113113 −8.90782 3.68974i −0.837978 0.347102i −0.0779218 0.996959i 0.524828π-0.524828\pi
−0.760056 + 0.649858i 0.774828π0.774828\pi
114114 0.685038 + 1.65383i 0.0641597 + 0.154895i
115115 5.72028i 0.533419i
116116 4.29029 1.77710i 0.398344 0.164999i
117117 −3.18457 3.18457i −0.294414 0.294414i
118118 −4.71650 −0.434189
119119 −7.24121 12.7120i −0.663800 1.16531i
120120 −1.47571 −0.134713
121121 7.89864 + 7.89864i 0.718058 + 0.718058i
122122 11.4980 4.76261i 1.04098 0.431187i
123123 0.211165i 0.0190401i
124124 2.78721 + 6.72892i 0.250299 + 0.604275i
125125 −0.923880 0.382683i −0.0826343 0.0342282i
126126 −1.11655 + 2.69558i −0.0994699 + 0.240142i
127127 2.26692 2.26692i 0.201157 0.201157i −0.599339 0.800496i 0.704570π-0.704570\pi
0.800496 + 0.599339i 0.204570π0.204570\pi
128128 0.707107 0.707107i 0.0625000 0.0625000i
129129 −0.468816 + 1.13182i −0.0412769 + 0.0996513i
130130 −5.06008 2.09595i −0.443798 0.183827i
131131 −1.36747 3.30136i −0.119476 0.288441i 0.852815 0.522213i 0.174893π-0.174893\pi
−0.972292 + 0.233771i 0.924893π0.924893\pi
132132 6.94843i 0.604783i
133133 3.97653 1.64713i 0.344808 0.142824i
134134 6.12852 + 6.12852i 0.529423 + 0.529423i
135135 −5.64058 −0.485464
136136 0.514430 + 4.09089i 0.0441120 + 0.350791i
137137 3.30950 0.282750 0.141375 0.989956i 0.454848π-0.454848\pi
0.141375 + 0.989956i 0.454848π0.454848\pi
138138 −5.96902 5.96902i −0.508116 0.508116i
139139 −1.66295 + 0.688816i −0.141049 + 0.0584246i −0.452092 0.891972i 0.649322π-0.649322\pi
0.311042 + 0.950396i 0.399322π0.399322\pi
140140 3.54824i 0.299881i
141141 −3.30725 7.98440i −0.278520 0.672408i
142142 4.75235 + 1.96849i 0.398808 + 0.165192i
143143 9.86889 23.8256i 0.825278 1.99240i
144144 0.581445 0.581445i 0.0484538 0.0484538i
145145 3.28365 3.28365i 0.272692 0.272692i
146146 −6.17351 + 14.9042i −0.510924 + 1.23348i
147147 −7.62132 3.15686i −0.628596 0.260373i
148148 −3.55579 8.58444i −0.292284 0.705637i
149149 4.16768i 0.341430i −0.985320 0.170715i 0.945392π-0.945392\pi
0.985320 0.170715i 0.0546077π-0.0546077\pi
150150 −1.36338 + 0.564729i −0.111319 + 0.0461099i
151151 −3.24744 3.24744i −0.264273 0.264273i 0.562514 0.826788i 0.309834π-0.309834\pi
−0.826788 + 0.562514i 0.809834π0.809834\pi
152152 −1.21304 −0.0983905
153153 0.423009 + 3.36389i 0.0341982 + 0.271954i
154154 −16.7071 −1.34629
155155 5.15010 + 5.15010i 0.413666 + 0.413666i
156156 −7.46720 + 3.09302i −0.597854 + 0.247639i
157157 15.5482i 1.24088i −0.784253 0.620442i 0.786953π-0.786953\pi
0.784253 0.620442i 0.213047π-0.213047\pi
158158 3.87118 + 9.34587i 0.307975 + 0.743517i
159159 12.6142 + 5.22495i 1.00037 + 0.414366i
160160 0.382683 0.923880i 0.0302538 0.0730391i
161161 −14.3521 + 14.3521i −1.13111 + 1.13111i
162162 −4.14151 + 4.14151i −0.325388 + 0.325388i
163163 3.87956 9.36608i 0.303870 0.733608i −0.696008 0.718034i 0.745042π-0.745042\pi
0.999879 0.0155742i 0.00495762π-0.00495762\pi
164164 0.132202 + 0.0547598i 0.0103232 + 0.00427602i
165165 −2.65905 6.41951i −0.207007 0.499758i
166166 3.40601i 0.264358i
167167 −11.5038 + 4.76501i −0.890187 + 0.368728i −0.780439 0.625232i 0.785004π-0.785004\pi
−0.109748 + 0.993959i 0.535004π0.535004\pi
168168 3.70253 + 3.70253i 0.285657 + 0.285657i
169169 −16.9974 −1.30750
170170 2.04079 + 3.58262i 0.156521 + 0.274775i
171171 −0.997467 −0.0762782
172172 −0.587013 0.587013i −0.0447593 0.0447593i
173173 −3.27672 + 1.35726i −0.249125 + 0.103191i −0.503752 0.863849i 0.668047π-0.668047\pi
0.254627 + 0.967039i 0.418047π0.418047\pi
174174 6.85286i 0.519514i
175175 1.35785 + 3.27815i 0.102644 + 0.247805i
176176 4.35013 + 1.80188i 0.327903 + 0.135822i
177177 −2.66354 + 6.43037i −0.200204 + 0.483336i
178178 −1.58516 + 1.58516i −0.118813 + 0.118813i
179179 −9.26485 + 9.26485i −0.692487 + 0.692487i −0.962779 0.270291i 0.912880π-0.912880\pi
0.270291 + 0.962779i 0.412880π0.412880\pi
180180 0.314676 0.759695i 0.0234545 0.0566243i
181181 1.68821 + 0.699281i 0.125484 + 0.0519772i 0.444542 0.895758i 0.353366π-0.353366\pi
−0.319058 + 0.947735i 0.603366π0.603366\pi
182182 7.43696 + 17.9544i 0.551264 + 1.33087i
183183 18.3656i 1.35763i
184184 5.28485 2.18906i 0.389604 0.161379i
185185 −6.57025 6.57025i −0.483054 0.483054i
186186 10.7481 0.788087
187187 −16.8689 + 9.60913i −1.23358 + 0.702689i
188188 5.85635 0.427118
189189 14.1521 + 14.1521i 1.02942 + 1.02942i
190190 −1.12070 + 0.464210i −0.0813043 + 0.0336773i
191191 16.8319i 1.21791i −0.793205 0.608955i 0.791589π-0.791589\pi
0.793205 0.608955i 0.208411π-0.208411\pi
192192 −0.564729 1.36338i −0.0407558 0.0983932i
193193 −5.38504 2.23056i −0.387624 0.160559i 0.180356 0.983601i 0.442275π-0.442275\pi
−0.567980 + 0.823042i 0.692275π0.692275\pi
194194 −1.66675 + 4.02389i −0.119666 + 0.288899i
195195 −5.71515 + 5.71515i −0.409270 + 0.409270i
196196 3.95275 3.95275i 0.282340 0.282340i
197197 1.34760 3.25339i 0.0960123 0.231794i −0.868575 0.495557i 0.834964π-0.834964\pi
0.964587 + 0.263763i 0.0849638π0.0849638\pi
198198 3.57705 + 1.48166i 0.254210 + 0.105297i
199199 −6.42910 15.5212i −0.455747 1.10027i −0.970103 0.242694i 0.921969π-0.921969\pi
0.514356 0.857577i 0.328031π-0.328031\pi
200200 1.00000i 0.0707107i
201201 11.8164 4.89452i 0.833466 0.345233i
202202 −7.59384 7.59384i −0.534301 0.534301i
203203 −16.4773 −1.15648
204204 5.86793 + 1.60888i 0.410837 + 0.112644i
205205 0.143094 0.00999414
206206 −5.25597 5.25597i −0.366200 0.366200i
207207 4.34567 1.80003i 0.302045 0.125111i
208208 5.47699i 0.379761i
209209 −2.18575 5.27687i −0.151192 0.365009i
210210 4.83759 + 2.00380i 0.333826 + 0.138275i
211211 −8.73280 + 21.0828i −0.601191 + 1.45140i 0.271166 + 0.962533i 0.412591π0.412591\pi
−0.872357 + 0.488870i 0.837409π0.837409\pi
212212 −6.54226 + 6.54226i −0.449324 + 0.449324i
213213 5.36758 5.36758i 0.367780 0.367780i
214214 −6.01999 + 14.5335i −0.411518 + 0.993492i
215215 −0.766969 0.317689i −0.0523068 0.0216662i
216216 −2.15856 5.21121i −0.146871 0.354578i
217217 25.8431i 1.75434i
218218 5.94112 2.46089i 0.402383 0.166673i
219219 16.8336 + 16.8336i 1.13751 + 1.13751i
220220 4.70854 0.317450
221221 17.8356 + 13.8510i 1.19975 + 0.931717i
222222 −13.7119 −0.920281
223223 −6.41246 6.41246i −0.429410 0.429410i 0.459017 0.888427i 0.348202π-0.348202\pi
−0.888427 + 0.459017i 0.848202π0.848202\pi
224224 −3.27815 + 1.35785i −0.219031 + 0.0907255i
225225 0.822287i 0.0548192i
226226 −3.68974 8.90782i −0.245438 0.592540i
227227 14.5491 + 6.02643i 0.965658 + 0.399988i 0.809094 0.587679i 0.199958π-0.199958\pi
0.156564 + 0.987668i 0.449958π0.449958\pi
228228 −0.685038 + 1.65383i −0.0453678 + 0.109527i
229229 14.2262 14.2262i 0.940092 0.940092i −0.0582124 0.998304i 0.518540π-0.518540\pi
0.998304 + 0.0582124i 0.0185401π0.0185401\pi
230230 4.04485 4.04485i 0.266710 0.266710i
231231 −9.43496 + 22.7780i −0.620775 + 1.49868i
232232 4.29029 + 1.77710i 0.281672 + 0.116672i
233233 −7.37613 17.8076i −0.483227 1.16661i −0.958068 0.286541i 0.907495π-0.907495\pi
0.474841 0.880071i 0.342505π-0.342505\pi
234234 4.50366i 0.294414i
235235 5.41056 2.24113i 0.352946 0.146195i
236236 −3.33507 3.33507i −0.217095 0.217095i
237237 14.9281 0.969684
238238 3.86845 14.1091i 0.250755 0.914555i
239239 14.2040 0.918778 0.459389 0.888235i 0.348068π-0.348068\pi
0.459389 + 0.888235i 0.348068π0.348068\pi
240240 −1.04348 1.04348i −0.0673565 0.0673565i
241241 −4.22633 + 1.75060i −0.272242 + 0.112766i −0.514628 0.857414i 0.672070π-0.672070\pi
0.242386 + 0.970180i 0.422070π0.422070\pi
242242 11.1704i 0.718058i
243243 −3.16806 7.64838i −0.203231 0.490644i
244244 11.4980 + 4.76261i 0.736082 + 0.304895i
245245 2.13922 5.16452i 0.136669 0.329949i
246246 0.149316 0.149316i 0.00952007 0.00952007i
247247 −4.69788 + 4.69788i −0.298919 + 0.298919i
248248 −2.78721 + 6.72892i −0.176988 + 0.427287i
249249 4.64367 + 1.92347i 0.294281 + 0.121895i
250250 −0.382683 0.923880i −0.0242030 0.0584313i
251251 9.00712i 0.568524i −0.958747 0.284262i 0.908251π-0.908251\pi
0.958747 0.284262i 0.0917486π-0.0917486\pi
252252 −2.69558 + 1.11655i −0.169806 + 0.0703358i
253253 19.0453 + 19.0453i 1.19737 + 1.19737i
254254 3.20591 0.201157
255255 6.03695 0.759148i 0.378049 0.0475397i
256256 1.00000 0.0625000
257257 20.2643 + 20.2643i 1.26405 + 1.26405i 0.949112 + 0.314938i 0.101984π0.101984\pi
0.314938 + 0.949112i 0.398016π0.398016\pi
258258 −1.13182 + 0.468816i −0.0704641 + 0.0291872i
259259 32.9693i 2.04862i
260260 −2.09595 5.06008i −0.129986 0.313813i
261261 3.52785 + 1.46129i 0.218369 + 0.0904513i
262262 1.36747 3.30136i 0.0844825 0.203959i
263263 −4.27498 + 4.27498i −0.263606 + 0.263606i −0.826517 0.562911i 0.809681π-0.809681\pi
0.562911 + 0.826517i 0.309681π0.309681\pi
264264 4.91328 4.91328i 0.302392 0.302392i
265265 −3.54064 + 8.54787i −0.217500 + 0.525091i
266266 3.97653 + 1.64713i 0.243816 + 0.100992i
267267 1.26598 + 3.05635i 0.0774769 + 0.187046i
268268 8.66703i 0.529423i
269269 −15.6073 + 6.46477i −0.951596 + 0.394164i −0.803830 0.594858i 0.797208π-0.797208\pi
−0.147765 + 0.989022i 0.547208π0.547208\pi
270270 −3.98849 3.98849i −0.242732 0.242732i
271271 −22.9305 −1.39293 −0.696463 0.717593i 0.745244π-0.745244\pi
−0.696463 + 0.717593i 0.745244π0.745244\pi
272272 −2.52894 + 3.25645i −0.153339 + 0.197451i
273273 28.6785 1.73570
274274 2.34017 + 2.34017i 0.141375 + 0.141375i
275275 4.35013 1.80188i 0.262322 0.108658i
276276 8.44146i 0.508116i
277277 7.65435 + 18.4792i 0.459905 + 1.11031i 0.968435 + 0.249265i 0.0801891π0.0801891\pi
−0.508530 + 0.861044i 0.669811π0.669811\pi
278278 −1.66295 0.688816i −0.0997370 0.0413124i
279279 −2.29189 + 5.53311i −0.137212 + 0.331259i
280280 −2.50899 + 2.50899i −0.149941 + 0.149941i
281281 16.4633 16.4633i 0.982118 0.982118i −0.0177247 0.999843i 0.505642π-0.505642\pi
0.999843 + 0.0177247i 0.00564226π0.00564226\pi
282282 3.30725 7.98440i 0.196944 0.475464i
283283 −23.2363 9.62478i −1.38125 0.572134i −0.436437 0.899735i 0.643760π-0.643760\pi
−0.944816 + 0.327601i 0.893760π0.893760\pi
284284 1.96849 + 4.75235i 0.116808 + 0.282000i
285285 1.79009i 0.106036i
286286 23.8256 9.86889i 1.40884 0.583560i
287287 −0.359022 0.359022i −0.0211924 0.0211924i
288288 0.822287 0.0484538
289289 −4.20895 16.4707i −0.247585 0.968866i
290290 4.64378 0.272692
291291 4.54481 + 4.54481i 0.266422 + 0.266422i
292292 −14.9042 + 6.17351i −0.872201 + 0.361278i
293293 25.5251i 1.49119i 0.666399 + 0.745595i 0.267835π0.267835\pi
−0.666399 + 0.745595i 0.732165π0.732165\pi
294294 −3.15686 7.62132i −0.184112 0.444485i
295295 −4.35748 1.80493i −0.253702 0.105087i
296296 3.55579 8.58444i 0.206676 0.498961i
297297 18.7800 18.7800i 1.08972 1.08972i
298298 2.94700 2.94700i 0.170715 0.170715i
299299 11.9894 28.9451i 0.693368 1.67394i
300300 −1.36338 0.564729i −0.0787145 0.0326046i
301301 1.12724 + 2.72139i 0.0649729 + 0.156858i
302302 4.59258i 0.264273i
303303 −14.6417 + 6.06480i −0.841145 + 0.348414i
304304 −0.857748 0.857748i −0.0491952 0.0491952i
305305 12.4453 0.712616
306306 −2.07951 + 2.67774i −0.118878 + 0.153076i
307307 −14.2382 −0.812616 −0.406308 0.913736i 0.633184π-0.633184\pi
−0.406308 + 0.913736i 0.633184π0.633184\pi
308308 −11.8137 11.8137i −0.673147 0.673147i
309309 −10.1341 + 4.19766i −0.576506 + 0.238797i
310310 7.28334i 0.413666i
311311 −4.65012 11.2264i −0.263684 0.636590i 0.735477 0.677550i 0.236958π-0.236958\pi
−0.999161 + 0.0409602i 0.986958π0.986958\pi
312312 −7.46720 3.09302i −0.422747 0.175108i
313313 −8.33854 + 20.1310i −0.471322 + 1.13787i 0.492257 + 0.870450i 0.336172π0.336172\pi
−0.963579 + 0.267422i 0.913828π0.913828\pi
314314 10.9943 10.9943i 0.620442 0.620442i
315315 −2.06311 + 2.06311i −0.116243 + 0.116243i
316316 −3.87118 + 9.34587i −0.217771 + 0.525746i
317317 9.47130 + 3.92314i 0.531961 + 0.220346i 0.632462 0.774591i 0.282044π-0.282044\pi
−0.100501 + 0.994937i 0.532044π0.532044\pi
318318 5.22495 + 12.6142i 0.293001 + 0.707367i
319319 21.8654i 1.22423i
320320 0.923880 0.382683i 0.0516464 0.0213927i
321321 16.4150 + 16.4150i 0.916197 + 0.916197i
322322 −20.2970 −1.13111
323323 4.96241 0.624023i 0.276116 0.0347216i
324324 −5.85698 −0.325388
325325 −3.87282 3.87282i −0.214825 0.214825i
326326 9.36608 3.87956i 0.518739 0.214869i
327327 9.48972i 0.524783i
328328 0.0547598 + 0.132202i 0.00302360 + 0.00729963i
329329 −19.1980 7.95207i −1.05842 0.438412i
330330 2.65905 6.41951i 0.146376 0.353383i
331331 −0.209438 + 0.209438i −0.0115117 + 0.0115117i −0.712839 0.701327i 0.752591π-0.752591\pi
0.701327 + 0.712839i 0.252591π0.252591\pi
332332 −2.40841 + 2.40841i −0.132179 + 0.132179i
333333 2.92388 7.05888i 0.160228 0.386824i
334334 −11.5038 4.76501i −0.629457 0.260730i
335335 3.31673 + 8.00729i 0.181212 + 0.437485i
336336 5.23617i 0.285657i
337337 −12.9824 + 5.37748i −0.707196 + 0.292930i −0.707144 0.707070i 0.750017π-0.750017\pi
−5.22341e−5 1.00000i 0.500017π0.500017\pi
338338 −12.0190 12.0190i −0.653748 0.653748i
339339 −14.2284 −0.772782
340340 −1.09024 + 3.97635i −0.0591268 + 0.215648i
341341 −34.2939 −1.85712
342342 −0.705316 0.705316i −0.0381391 0.0381391i
343343 4.62206 1.91452i 0.249568 0.103374i
344344 0.830161i 0.0447593i
345345 −3.23041 7.79889i −0.173919 0.419878i
346346 −3.27672 1.35726i −0.176158 0.0729669i
347347 −4.26669 + 10.3007i −0.229048 + 0.552971i −0.996062 0.0886594i 0.971742π-0.971742\pi
0.767014 + 0.641631i 0.221742π0.221742\pi
348348 4.84570 4.84570i 0.259757 0.259757i
349349 −1.77671 + 1.77671i −0.0951051 + 0.0951051i −0.753059 0.657953i 0.771422π-0.771422\pi
0.657953 + 0.753059i 0.271422π0.271422\pi
350350 −1.35785 + 3.27815i −0.0725804 + 0.175225i
351351 −28.5418 11.8224i −1.52345 0.631033i
352352 1.80188 + 4.35013i 0.0960406 + 0.231862i
353353 10.0823i 0.536629i −0.963331 0.268314i 0.913533π-0.913533\pi
0.963331 0.268314i 0.0864666π-0.0864666\pi
354354 −6.43037 + 2.66354i −0.341770 + 0.141566i
355355 3.63729 + 3.63729i 0.193047 + 0.193047i
356356 −2.24175 −0.118813
357357 −17.0513 13.2420i −0.902452 0.700838i
358358 −13.1025 −0.692487
359359 −17.4429 17.4429i −0.920599 0.920599i 0.0764723 0.997072i 0.475634π-0.475634\pi
−0.997072 + 0.0764723i 0.975634π0.975634\pi
360360 0.759695 0.314676i 0.0400394 0.0165849i
361361 17.5285i 0.922555i
362362 0.699281 + 1.68821i 0.0367534 + 0.0887306i
363363 15.2294 + 6.30823i 0.799337 + 0.331096i
364364 −7.43696 + 17.9544i −0.389803 + 0.941067i
365365 −11.4072 + 11.4072i −0.597078 + 0.597078i
366366 12.9865 12.9865i 0.678813 0.678813i
367367 11.3939 27.5072i 0.594755 1.43587i −0.284108 0.958792i 0.591698π-0.591698\pi
0.878863 0.477073i 0.158302π-0.158302\pi
368368 5.28485 + 2.18906i 0.275492 + 0.114112i
369369 0.0450283 + 0.108708i 0.00234408 + 0.00565911i
370370 9.29174i 0.483054i
371371 30.3299 12.5631i 1.57465 0.652242i
372372 7.60004 + 7.60004i 0.394043 + 0.394043i
373373 20.8039 1.07718 0.538592 0.842567i 0.318956π-0.318956\pi
0.538592 + 0.842567i 0.318956π0.318956\pi
374374 −18.7228 5.13346i −0.968134 0.265445i
375375 −1.47571 −0.0762052
376376 4.14106 + 4.14106i 0.213559 + 0.213559i
377377 23.4979 9.73315i 1.21020 0.501283i
378378 20.0142i 1.02942i
379379 3.99706 + 9.64974i 0.205315 + 0.495674i 0.992674 0.120820i 0.0385524π-0.0385524\pi
−0.787359 + 0.616494i 0.788552π0.788552\pi
380380 −1.12070 0.464210i −0.0574908 0.0238135i
381381 1.81047 4.37087i 0.0927533 0.223926i
382382 11.9019 11.9019i 0.608955 0.608955i
383383 −14.2495 + 14.2495i −0.728113 + 0.728113i −0.970244 0.242130i 0.922154π-0.922154\pi
0.242130 + 0.970244i 0.422154π0.422154\pi
384384 0.564729 1.36338i 0.0288187 0.0695745i
385385 −15.4353 6.39351i −0.786656 0.325844i
386386 −2.23056 5.38504i −0.113532 0.274091i
387387 0.682631i 0.0347001i
388388 −4.02389 + 1.66675i −0.204282 + 0.0846164i
389389 −13.9058 13.9058i −0.705051 0.705051i 0.260440 0.965490i 0.416133π-0.416133\pi
−0.965490 + 0.260440i 0.916133π0.916133\pi
390390 −8.08244 −0.409270
391391 −20.4936 + 11.6739i −1.03641 + 0.590373i
392392 5.59004 0.282340
393393 −3.72875 3.72875i −0.188090 0.188090i
394394 3.25339 1.34760i 0.163903 0.0678909i
395395 10.1159i 0.508986i
396396 1.48166 + 3.57705i 0.0744564 + 0.179754i
397397 −22.1250 9.16446i −1.11042 0.459951i −0.249338 0.968416i 0.580213π-0.580213\pi
−0.861083 + 0.508465i 0.830213π0.830213\pi
398398 6.42910 15.5212i 0.322262 0.778009i
399399 4.49132 4.49132i 0.224847 0.224847i
400400 0.707107 0.707107i 0.0353553 0.0353553i
401401 −8.81734 + 21.2869i −0.440317 + 1.06302i 0.535521 + 0.844522i 0.320115π0.320115\pi
−0.975838 + 0.218497i 0.929885π0.929885\pi
402402 11.8164 + 4.89452i 0.589350 + 0.244117i
403403 15.2655 + 36.8543i 0.760431 + 1.83584i
404404 10.7393i 0.534301i
405405 −5.41114 + 2.24137i −0.268882 + 0.111375i
406406 −11.6512 11.6512i −0.578239 0.578239i
407407 43.7505 2.16863
408408 3.01160 + 5.28690i 0.149097 + 0.261741i
409409 12.7488 0.630389 0.315195 0.949027i 0.397930π-0.397930\pi
0.315195 + 0.949027i 0.397930π0.397930\pi
410410 0.101183 + 0.101183i 0.00499707 + 0.00499707i
411411 4.51209 1.86897i 0.222565 0.0921895i
412412 7.43306i 0.366200i
413413 6.40432 + 15.4614i 0.315136 + 0.760806i
414414 4.34567 + 1.80003i 0.213578 + 0.0884669i
415415 −1.30342 + 3.14674i −0.0639826 + 0.154468i
416416 3.87282 3.87282i 0.189881 0.189881i
417417 −1.87823 + 1.87823i −0.0919773 + 0.0919773i
418418 2.18575 5.27687i 0.106909 0.258100i
419419 25.2883 + 10.4748i 1.23541 + 0.511725i 0.902279 0.431153i 0.141893π-0.141893\pi
0.333136 + 0.942879i 0.391893π0.391893\pi
420420 2.00380 + 4.83759i 0.0977752 + 0.236050i
421421 33.6813i 1.64153i 0.571268 + 0.820764i 0.306452π0.306452\pi
−0.571268 + 0.820764i 0.693548π0.693548\pi
422422 −21.0828 + 8.73280i −1.02630 + 0.425106i
423423 3.40514 + 3.40514i 0.165564 + 0.165564i
424424 −9.25215 −0.449324
425425 0.514430 + 4.09089i 0.0249535 + 0.198437i
426426 7.59090 0.367780
427427 −31.2251 31.2251i −1.51109 1.51109i
428428 −14.5335 + 6.01999i −0.702505 + 0.290987i
429429 38.0565i 1.83739i
430430 −0.317689 0.766969i −0.0153203 0.0369865i
431431 −16.7963 6.95725i −0.809049 0.335119i −0.0604746 0.998170i 0.519261π-0.519261\pi
−0.748575 + 0.663051i 0.769261π0.769261\pi
432432 2.15856 5.21121i 0.103854 0.250725i
433433 −5.73034 + 5.73034i −0.275382 + 0.275382i −0.831262 0.555880i 0.812381π-0.812381\pi
0.555880 + 0.831262i 0.312381π0.312381\pi
434434 18.2738 18.2738i 0.877170 0.877170i
435435 2.62248 6.33122i 0.125738 0.303559i
436436 5.94112 + 2.46089i 0.284528 + 0.117855i
437437 −2.65541 6.41073i −0.127026 0.306667i
438438 23.8064i 1.13751i
439439 22.1522 9.17574i 1.05727 0.437934i 0.214786 0.976661i 0.431095π-0.431095\pi
0.842480 + 0.538727i 0.181095π0.181095\pi
440440 3.32944 + 3.32944i 0.158725 + 0.158725i
441441 4.59662 0.218887
442442 2.81753 + 22.4058i 0.134016 + 1.06573i
443443 0.244075 0.0115964 0.00579819 0.999983i 0.498154π-0.498154\pi
0.00579819 + 0.999983i 0.498154π0.498154\pi
444444 −9.69577 9.69577i −0.460141 0.460141i
445445 −2.07111 + 0.857882i −0.0981800 + 0.0406675i
446446 9.06859i 0.429410i
447447 −2.35361 5.68212i −0.111322 0.268755i
448448 −3.27815 1.35785i −0.154878 0.0641526i
449449 −0.0315454 + 0.0761574i −0.00148872 + 0.00359409i −0.924622 0.380886i 0.875619π-0.875619\pi
0.923133 + 0.384480i 0.125619π0.125619\pi
450450 0.581445 0.581445i 0.0274096 0.0274096i
451451 −0.476424 + 0.476424i −0.0224339 + 0.0224339i
452452 3.68974 8.90782i 0.173551 0.418989i
453453 −6.26141 2.59356i −0.294187 0.121856i
454454 6.02643 + 14.5491i 0.282835 + 0.682823i
455455 19.4337i 0.911066i
456456 −1.65383 + 0.685038i −0.0774476 + 0.0320799i
457457 17.2461 + 17.2461i 0.806737 + 0.806737i 0.984139 0.177402i 0.0567692π-0.0567692\pi
−0.177402 + 0.984139i 0.556769π0.556769\pi
458458 20.1188 0.940092
459459 11.5112 + 20.2081i 0.537297 + 0.943232i
460460 5.72028 0.266710
461461 20.5839 + 20.5839i 0.958687 + 0.958687i 0.999180 0.0404924i 0.0128926π-0.0128926\pi
−0.0404924 + 0.999180i 0.512893π0.512893\pi
462462 −22.7780 + 9.43496i −1.05973 + 0.438954i
463463 27.9762i 1.30016i 0.759865 + 0.650081i 0.225265π0.225265\pi
−0.759865 + 0.650081i 0.774735π0.774735\pi
464464 1.77710 + 4.29029i 0.0824997 + 0.199172i
465465 9.92992 + 4.11311i 0.460489 + 0.190741i
466466 7.37613 17.8076i 0.341693 0.824919i
467467 22.1173 22.1173i 1.02347 1.02347i 0.0237504 0.999718i 0.492439π-0.492439\pi
0.999718 0.0237504i 0.00756069π-0.00756069\pi
468468 3.18457 3.18457i 0.147207 0.147207i
469469 11.7686 28.4118i 0.543422 1.31194i
470470 5.41056 + 2.24113i 0.249570 + 0.103375i
471471 −8.78053 21.1981i −0.404586 0.976756i
472472 4.71650i 0.217095i
473473 3.61131 1.49585i 0.166048 0.0687793i
474474 10.5558 + 10.5558i 0.484842 + 0.484842i
475475 −1.21304 −0.0556581
476476 12.7120 7.24121i 0.582655 0.331900i
477477 −7.60792 −0.348343
478478 10.0437 + 10.0437i 0.459389 + 0.459389i
479479 −11.1564 + 4.62112i −0.509748 + 0.211144i −0.622707 0.782455i 0.713967π-0.713967\pi
0.112959 + 0.993600i 0.463967π0.463967\pi
480480 1.47571i 0.0673565i
481481 −19.4751 47.0169i −0.887986 2.14379i
482482 −4.22633 1.75060i −0.192504 0.0797378i
483483 −11.4623 + 27.6724i −0.521552 + 1.25914i
484484 −7.89864 + 7.89864i −0.359029 + 0.359029i
485485 −3.07975 + 3.07975i −0.139844 + 0.139844i
486486 3.16806 7.64838i 0.143706 0.346937i
487487 4.63377 + 1.91937i 0.209976 + 0.0869749i 0.485192 0.874407i 0.338750π-0.338750\pi
−0.275217 + 0.961382i 0.588750π0.588750\pi
488488 4.76261 + 11.4980i 0.215593 + 0.520488i
489489 14.9604i 0.676532i
490490 5.16452 2.13922i 0.233309 0.0966399i
491491 −18.6988 18.6988i −0.843865 0.843865i 0.145494 0.989359i 0.453523π-0.453523\pi
−0.989359 + 0.145494i 0.953523π0.953523\pi
492492 0.211165 0.00952007
493493 −18.4653 5.06285i −0.831635 0.228019i
494494 −6.64381 −0.298919
495495 2.73776 + 2.73776i 0.123053 + 0.123053i
496496 −6.72892 + 2.78721i −0.302138 + 0.125150i
497497 18.2518i 0.818707i
498498 1.92347 + 4.64367i 0.0861929 + 0.208088i
499499 −27.6595 11.4569i −1.23821 0.512882i −0.335053 0.942199i 0.608754π-0.608754\pi
−0.903154 + 0.429317i 0.858754π0.858754\pi
500500 0.382683 0.923880i 0.0171141 0.0413171i
501501 −12.9930 + 12.9930i −0.580484 + 0.580484i
502502 6.36899 6.36899i 0.284262 0.284262i
503503 13.0499 31.5052i 0.581865 1.40475i −0.309255 0.950979i 0.600080π-0.600080\pi
0.891120 0.453768i 0.149920π-0.149920\pi
504504 −2.69558 1.11655i −0.120071 0.0497349i
505505 −4.10976 9.92183i −0.182882 0.441516i
506506 26.9342i 1.19737i
507507 −23.1739 + 9.59895i −1.02919 + 0.426304i
508508 2.26692 + 2.26692i 0.100578 + 0.100578i
509509 28.0939 1.24524 0.622620 0.782525i 0.286068π-0.286068\pi
0.622620 + 0.782525i 0.286068π0.286068\pi
510510 4.80557 + 3.73197i 0.212794 + 0.165255i
511511 57.2409 2.53219
512512 0.707107 + 0.707107i 0.0312500 + 0.0312500i
513513 −6.32141 + 2.61841i −0.279097 + 0.115606i
514514 28.6580i 1.26405i
515515 −2.84451 6.86725i −0.125344 0.302607i
516516 −1.13182 0.468816i −0.0498257 0.0206385i
517517 −10.5524 + 25.4758i −0.464096 + 1.12043i
518518 −23.3129 + 23.3129i −1.02431 + 1.02431i
519519 −3.70092 + 3.70092i −0.162452 + 0.162452i
520520 2.09595 5.06008i 0.0919137 0.221899i
521521 17.6215 + 7.29907i 0.772013 + 0.319778i 0.733687 0.679487i 0.237798π-0.237798\pi
0.0383252 + 0.999265i 0.487798π0.487798\pi
522522 1.46129 + 3.52785i 0.0639587 + 0.154410i
523523 6.69653i 0.292819i 0.989224 + 0.146409i 0.0467717π0.0467717\pi
−0.989224 + 0.146409i 0.953228π0.953228\pi
524524 3.30136 1.36747i 0.144221 0.0597381i
525525 3.70253 + 3.70253i 0.161592 + 0.161592i
526526 −6.04573 −0.263606
527527 7.94061 28.9611i 0.345899 1.26157i
528528 6.94843 0.302392
529529 6.87423 + 6.87423i 0.298879 + 0.298879i
530530 −8.54787 + 3.54064i −0.371296 + 0.153796i
531531 3.87832i 0.168305i
532532 1.64713 + 3.97653i 0.0714122 + 0.172404i
533533 0.724069 + 0.299919i 0.0313629 + 0.0129909i
534534 −1.26598 + 3.05635i −0.0547844 + 0.132261i
535535 −11.1235 + 11.1235i −0.480910 + 0.480910i
536536 −6.12852 + 6.12852i −0.264712 + 0.264712i
537537 −7.39935 + 17.8636i −0.319305 + 0.770871i
538538 −15.6073 6.46477i −0.672880 0.278716i
539539 10.0726 + 24.3174i 0.433857 + 1.04742i
540540 5.64058i 0.242732i
541541 −6.32639 + 2.62047i −0.271993 + 0.112663i −0.514511 0.857484i 0.672027π-0.672027\pi
0.242518 + 0.970147i 0.422027π0.422027\pi
542542 −16.2143 16.2143i −0.696463 0.696463i
543543 2.69657 0.115721
544544 −4.09089 + 0.514430i −0.175395 + 0.0220560i
545545 6.43062 0.275458
546546 20.2787 + 20.2787i 0.867850 + 0.867850i
547547 −3.26202 + 1.35117i −0.139474 + 0.0577719i −0.451329 0.892358i 0.649050π-0.649050\pi
0.311855 + 0.950130i 0.399050π0.399050\pi
548548 3.30950i 0.141375i
549549 3.91624 + 9.45463i 0.167141 + 0.403514i
550550 4.35013 + 1.80188i 0.185490 + 0.0768325i
551551 2.15569 5.20429i 0.0918355 0.221710i
552552 5.96902 5.96902i 0.254058 0.254058i
553553 25.3806 25.3806i 1.07929 1.07929i
554554 −7.65435 + 18.4792i −0.325202 + 0.785108i
555555 −12.6681 5.24731i −0.537732 0.222736i
556556 −0.688816 1.66295i −0.0292123 0.0705247i
557557 45.7591i 1.93888i 0.245338 + 0.969438i 0.421101π0.421101\pi
−0.245338 + 0.969438i 0.578899π0.578899\pi
558558 −5.53311 + 2.29189i −0.234235 + 0.0970234i
559559 −3.21506 3.21506i −0.135983 0.135983i
560560 −3.54824 −0.149941
561561 −17.5721 + 22.6272i −0.741897 + 0.955322i
562562 23.2826 0.982118
563563 −7.05601 7.05601i −0.297375 0.297375i 0.542610 0.839985i 0.317436π-0.317436\pi
−0.839985 + 0.542610i 0.817436π0.817436\pi
564564 7.98440 3.30725i 0.336204 0.139260i
565565 9.64176i 0.405632i
566566 −9.62478 23.2363i −0.404560 0.976693i
567567 19.2001 + 7.95293i 0.806327 + 0.333992i
568568 −1.96849 + 4.75235i −0.0825959 + 0.199404i
569569 −9.56020 + 9.56020i −0.400784 + 0.400784i −0.878509 0.477725i 0.841462π-0.841462\pi
0.477725 + 0.878509i 0.341462π0.341462\pi
570570 −1.26579 + 1.26579i −0.0530179 + 0.0530179i
571571 6.49469 15.6796i 0.271794 0.656169i −0.727766 0.685826i 0.759441π-0.759441\pi
0.999560 + 0.0296562i 0.00944125π0.00944125\pi
572572 23.8256 + 9.86889i 0.996199 + 0.412639i
573573 −9.50543 22.9481i −0.397095 0.958673i
574574 0.507734i 0.0211924i
575575 5.28485 2.18906i 0.220394 0.0912900i
576576 0.581445 + 0.581445i 0.0242269 + 0.0242269i
577577 −9.67374 −0.402723 −0.201361 0.979517i 0.564537π-0.564537\pi
−0.201361 + 0.979517i 0.564537π0.564537\pi
578578 8.67039 14.6227i 0.360641 0.608226i
579579 −8.60150 −0.357466
580580 3.28365 + 3.28365i 0.136346 + 0.136346i
581581 11.1654 4.62487i 0.463220 0.191872i
582582 6.42734i 0.266422i
583583 −16.6713 40.2480i −0.690453 1.66690i
584584 −14.9042 6.17351i −0.616739 0.255462i
585585 1.72348 4.16084i 0.0712570 0.172030i
586586 −18.0489 + 18.0489i −0.745595 + 0.745595i
587587 3.24694 3.24694i 0.134015 0.134015i −0.636917 0.770932i 0.719791π-0.719791\pi
0.770932 + 0.636917i 0.219791π0.219791\pi
588588 3.15686 7.62132i 0.130187 0.314298i
589589 8.16245 + 3.38100i 0.336328 + 0.139312i
590590 −1.80493 4.35748i −0.0743077 0.179395i
591591 5.19661i 0.213760i
592592 8.58444 3.55579i 0.352818 0.146142i
593593 −0.550724 0.550724i −0.0226155 0.0226155i 0.695709 0.718324i 0.255090π-0.255090\pi
−0.718324 + 0.695709i 0.755090π0.755090\pi
594594 26.5589 1.08972
595595 8.97329 11.5547i 0.367869 0.473696i
596596 4.16768 0.170715
597597 −17.5306 17.5306i −0.717478 0.717478i
598598 28.9451 11.9894i 1.18365 0.490285i
599599 10.4846i 0.428391i −0.976791 0.214196i 0.931287π-0.931287\pi
0.976791 0.214196i 0.0687130π-0.0687130\pi
600600 −0.564729 1.36338i −0.0230550 0.0556596i
601601 −14.1755 5.87170i −0.578233 0.239512i 0.0743464 0.997232i 0.476313π-0.476313\pi
−0.652579 + 0.757721i 0.726313π0.726313\pi
602602 −1.12724 + 2.72139i −0.0459428 + 0.110916i
603603 −5.03940 + 5.03940i −0.205220 + 0.205220i
604604 3.24744 3.24744i 0.132137 0.132137i
605605 −4.27471 + 10.3201i −0.173792 + 0.419571i
606606 −14.6417 6.06480i −0.594779 0.246366i
607607 8.27458 + 19.9766i 0.335855 + 0.810825i 0.998105 + 0.0615418i 0.0196018π0.0196018\pi
−0.662250 + 0.749283i 0.730398π0.730398\pi
608608 1.21304i 0.0491952i
609609 −22.4647 + 9.30519i −0.910316 + 0.377065i
610610 8.80016 + 8.80016i 0.356308 + 0.356308i
611611 32.0752 1.29762
612612 −3.36389 + 0.423009i −0.135977 + 0.0170991i
613613 −18.6071 −0.751535 −0.375768 0.926714i 0.622621π-0.622621\pi
−0.375768 + 0.926714i 0.622621π0.622621\pi
614614 −10.0679 10.0679i −0.406308 0.406308i
615615 0.195091 0.0808095i 0.00786684 0.00325855i
616616 16.7071i 0.673147i
617617 2.18286 + 5.26989i 0.0878787 + 0.212158i 0.961709 0.274074i 0.0883712π-0.0883712\pi
−0.873830 + 0.486231i 0.838371π0.838371\pi
618618 −10.1341 4.19766i −0.407651 0.168855i
619619 11.1868 27.0073i 0.449635 1.08552i −0.522823 0.852441i 0.675121π-0.675121\pi
0.972459 0.233075i 0.0748787π-0.0748787\pi
620620 −5.15010 + 5.15010i −0.206833 + 0.206833i
621621 22.8153 22.8153i 0.915546 0.915546i
622622 4.65012 11.2264i 0.186453 0.450137i
623623 7.34881 + 3.04397i 0.294424 + 0.121954i
624624 −3.09302 7.46720i −0.123820 0.298927i
625625 1.00000i 0.0400000i
626626 −20.1310 + 8.33854i −0.804597 + 0.333275i
627627 −5.96000 5.96000i −0.238020 0.238020i
628628 15.5482 0.620442
629629 −10.1303 + 36.9472i −0.403920 + 1.47318i
630630 −2.91768 −0.116243
631631 30.9574 + 30.9574i 1.23239 + 1.23239i 0.963042 + 0.269351i 0.0868092π0.0868092\pi
0.269351 + 0.963042i 0.413191π0.413191\pi
632632 −9.34587 + 3.87118i −0.371759 + 0.153987i
633633 33.6755i 1.33848i
634634 3.92314 + 9.47130i 0.155808 + 0.376153i
635635 2.96188 + 1.22685i 0.117539 + 0.0486861i
636636 −5.22495 + 12.6142i −0.207183 + 0.500184i
637637 21.6492 21.6492i 0.857773 0.857773i
638638 −15.4612 + 15.4612i −0.612115 + 0.612115i
639639 −1.61866 + 3.90780i −0.0640333 + 0.154590i
640640 0.923880 + 0.382683i 0.0365195 + 0.0151269i
641641 −16.6913 40.2963i −0.659265 1.59161i −0.798941 0.601410i 0.794606π-0.794606\pi
0.139676 0.990197i 0.455394π-0.455394\pi
642642 23.2143i 0.916197i
643643 −5.12401 + 2.12244i −0.202071 + 0.0837007i −0.481424 0.876488i 0.659880π-0.659880\pi
0.279353 + 0.960189i 0.409880π0.409880\pi
644644 −14.3521 14.3521i −0.565553 0.565553i
645645 −1.22508 −0.0482373
646646 3.95020 + 3.06770i 0.155419 + 0.120697i
647647 −25.3893 −0.998155 −0.499078 0.866557i 0.666328π-0.666328\pi
−0.499078 + 0.866557i 0.666328π0.666328\pi
648648 −4.14151 4.14151i −0.162694 0.162694i
649649 20.5174 8.49858i 0.805378 0.333598i
650650 5.47699i 0.214825i
651651 −14.5943 35.2338i −0.571996 1.38092i
652652 9.36608 + 3.87956i 0.366804 + 0.151935i
653653 15.0457 36.3236i 0.588784 1.42145i −0.295882 0.955225i 0.595613π-0.595613\pi
0.884666 0.466226i 0.154387π-0.154387\pi
654654 6.71024 6.71024i 0.262391 0.262391i
655655 2.52675 2.52675i 0.0987284 0.0987284i
656656 −0.0547598 + 0.132202i −0.00213801 + 0.00516162i
657657 −12.2555 5.07640i −0.478133 0.198049i
658658 −7.95207 19.1980i −0.310004 0.748415i
659659 39.5179i 1.53940i 0.638408 + 0.769698i 0.279593π0.279593\pi
−0.638408 + 0.769698i 0.720407π0.720407\pi
660660 6.41951 2.65905i 0.249879 0.103503i
661661 −2.21986 2.21986i −0.0863427 0.0863427i 0.662616 0.748959i 0.269446π-0.269446\pi
−0.748959 + 0.662616i 0.769446π0.769446\pi
662662 −0.296190 −0.0115117
663663 32.1386 + 8.81183i 1.24816 + 0.342223i
664664 −3.40601 −0.132179
665665 3.04350 + 3.04350i 0.118022 + 0.118022i
666666 7.05888 2.92388i 0.273526 0.113298i
667667 26.5637i 1.02855i
668668 −4.76501 11.5038i −0.184364 0.445093i
669669 −12.3639 5.12129i −0.478016 0.198001i
670670 −3.31673 + 8.00729i −0.128136 + 0.309349i
671671 −41.4359 + 41.4359i −1.59962 + 1.59962i
672672 −3.70253 + 3.70253i −0.142828 + 0.142828i
673673 −8.91195 + 21.5153i −0.343530 + 0.829355i 0.653823 + 0.756647i 0.273164π0.273164\pi
−0.997353 + 0.0727079i 0.976836π0.976836\pi
674674 −12.9824 5.37748i −0.500063 0.207133i
675675 −2.15856 5.21121i −0.0830829 0.200580i
676676 16.9974i 0.653748i
677677 −38.1349 + 15.7960i −1.46564 + 0.607089i −0.965861 0.259062i 0.916587π-0.916587\pi
−0.499782 + 0.866151i 0.666587π0.666587\pi
678678 −10.0610 10.0610i −0.386391 0.386391i
679679 15.4541 0.593075
680680 −3.58262 + 2.04079i −0.137387 + 0.0782606i
681681 23.2392 0.890528
682682 −24.2494 24.2494i −0.928559 0.928559i
683683 5.77636 2.39265i 0.221026 0.0915521i −0.269423 0.963022i 0.586833π-0.586833\pi
0.490449 + 0.871470i 0.336833π0.336833\pi
684684 0.997467i 0.0381391i
685685 1.26649 + 3.05758i 0.0483901 + 0.116824i
686686 4.62206 + 1.91452i 0.176471 + 0.0730968i
687687 11.3617 27.4295i 0.433476 1.04650i
688688 0.587013 0.587013i 0.0223796 0.0223796i
689689 −35.8319 + 35.8319i −1.36509 + 1.36509i
690690 3.23041 7.79889i 0.122980 0.296899i
691691 −29.6992 12.3018i −1.12981 0.467983i −0.262094 0.965042i 0.584413π-0.584413\pi
−0.867716 + 0.497060i 0.834413π0.834413\pi
692692 −1.35726 3.27672i −0.0515954 0.124562i
693693 13.7380i 0.521864i
694694 −10.3007 + 4.26669i −0.391010 + 0.161961i
695695 −1.27277 1.27277i −0.0482788 0.0482788i
696696 6.85286 0.259757
697697 −0.292025 0.512653i −0.0110612 0.0194181i
698698 −2.51265 −0.0951051
699699 −20.1129 20.1129i −0.760739 0.760739i
700700 −3.27815 + 1.35785i −0.123902 + 0.0513221i
701701 12.7609i 0.481972i −0.970529 0.240986i 0.922529π-0.922529\pi
0.970529 0.240986i 0.0774708π-0.0774708\pi
702702 −11.8224 28.5418i −0.446208 1.07724i
703703 −10.4133 4.31332i −0.392744 0.162680i
704704 −1.80188 + 4.35013i −0.0679109 + 0.163952i
705705 6.11100 6.11100i 0.230153 0.230153i
706706 7.12929 7.12929i 0.268314 0.268314i
707707 −14.5824 + 35.2051i −0.548429 + 1.32402i
708708 −6.43037 2.66354i −0.241668 0.100102i
709709 12.8274 + 30.9681i 0.481744 + 1.16303i 0.958780 + 0.284149i 0.0917110π0.0917110\pi
−0.477036 + 0.878884i 0.658289π0.658289\pi
710710 5.14391i 0.193047i
711711 −7.68499 + 3.18323i −0.288210 + 0.119380i
712712 −1.58516 1.58516i −0.0594063 0.0594063i
713713 −41.6627 −1.56028
714714 −2.69364 21.4206i −0.100807 0.801645i
715715 25.7886 0.964441
716716 −9.26485 9.26485i −0.346244 0.346244i
717717 19.3653 8.02139i 0.723212 0.299564i
718718 24.6679i 0.920599i
719719 −10.9707 26.4857i −0.409140 0.987750i −0.985365 0.170459i 0.945475π-0.945475\pi
0.576225 0.817291i 0.304525π-0.304525\pi
720720 0.759695 + 0.314676i 0.0283121 + 0.0117273i
721721 −10.0930 + 24.3667i −0.375883 + 0.907463i
722722 12.3945 12.3945i 0.461277 0.461277i
723723 −4.77346 + 4.77346i −0.177527 + 0.177527i
724724 −0.699281 + 1.68821i −0.0259886 + 0.0627420i
725725 4.29029 + 1.77710i 0.159337 + 0.0659998i
726726 6.30823 + 15.2294i 0.234120 + 0.565216i
727727 21.0302i 0.779966i 0.920822 + 0.389983i 0.127519π0.127519\pi
−0.920822 + 0.389983i 0.872481π0.872481\pi
728728 −17.9544 + 7.43696i −0.665435 + 0.275632i
729729 −21.0631 21.0631i −0.780113 0.780113i
730730 −16.1322 −0.597078
731731 0.427059 + 3.39610i 0.0157954 + 0.125609i
732732 18.3656 0.678813
733733 −6.38248 6.38248i −0.235742 0.235742i 0.579342 0.815084i 0.303310π-0.303310\pi
−0.815084 + 0.579342i 0.803310π0.803310\pi
734734 27.5072 11.3939i 1.01531 0.420555i
735735 8.24926i 0.304279i
736736 2.18906 + 5.28485i 0.0806897 + 0.194802i
737737 −37.7027 15.6170i −1.38880 0.575258i
738738 −0.0450283 + 0.108708i −0.00165751 + 0.00400160i
739739 10.1850 10.1850i 0.374662 0.374662i −0.494510 0.869172i 0.664653π-0.664653\pi
0.869172 + 0.494510i 0.164653π0.164653\pi
740740 6.57025 6.57025i 0.241527 0.241527i
741741 −3.75195 + 9.05801i −0.137831 + 0.332754i
742742 30.3299 + 12.5631i 1.11345 + 0.461205i
743743 12.6717 + 30.5921i 0.464879 + 1.12232i 0.966370 + 0.257154i 0.0827847π0.0827847\pi
−0.501492 + 0.865162i 0.667215π0.667215\pi
744744 10.7481i 0.394043i
745745 3.85044 1.59490i 0.141069 0.0584327i
746746 14.7106 + 14.7106i 0.538592 + 0.538592i
747747 −2.80072 −0.102473
748748 −9.60913 16.8689i −0.351344 0.616789i
749749 55.8174 2.03952
750750 −1.04348 1.04348i −0.0381026 0.0381026i
751751 −5.92242 + 2.45315i −0.216112 + 0.0895166i −0.488113 0.872780i 0.662315π-0.662315\pi
0.272001 + 0.962297i 0.412315π0.412315\pi
752752 5.85635i 0.213559i
753753 −5.08658 12.2801i −0.185365 0.447511i
754754 23.4979 + 9.73315i 0.855743 + 0.354460i
755755 1.75750 4.24299i 0.0639621 0.154418i
756756 −14.1521 + 14.1521i −0.514708 + 0.514708i
757757 34.6660 34.6660i 1.25996 1.25996i 0.308847 0.951112i 0.400057π-0.400057\pi
0.951112 0.308847i 0.0999430π-0.0999430\pi
758758 −3.99706 + 9.64974i −0.145180 + 0.350495i
759759 36.7214 + 15.2105i 1.33290 + 0.552107i
760760 −0.464210 1.12070i −0.0168387 0.0406521i
761761 42.6819i 1.54722i 0.633662 + 0.773610i 0.281551π0.281551\pi
−0.633662 + 0.773610i 0.718449π0.718449\pi
762762 4.37087 1.81047i 0.158340 0.0655865i
763763 −16.1344 16.1344i −0.584103 0.584103i
764764 16.8319 0.608955
765765 −2.94595 + 1.67811i −0.106511 + 0.0606723i
766766 −20.1518 −0.728113
767767 −18.2662 18.2662i −0.659553 0.659553i
768768 1.36338 0.564729i 0.0491966 0.0203779i
769769 14.6429i 0.528035i 0.964518 + 0.264018i 0.0850477π0.0850477\pi
−0.964518 + 0.264018i 0.914952π0.914952\pi
770770 −6.39351 15.4353i −0.230406 0.556250i
771771 39.0716 + 16.1840i 1.40713 + 0.582853i
772772 2.23056 5.38504i 0.0802795 0.193812i
773773 10.5010 10.5010i 0.377696 0.377696i −0.492575 0.870270i 0.663944π-0.663944\pi
0.870270 + 0.492575i 0.163944π0.163944\pi
774774 0.482693 0.482693i 0.0173500 0.0173500i
775775 −2.78721 + 6.72892i −0.100120 + 0.241710i
776776 −4.02389 1.66675i −0.144449 0.0598328i
777777 18.6187 + 44.9496i 0.667944 + 1.61256i
778778 19.6657i 0.705051i
779779 0.160366 0.0664258i 0.00574571 0.00237995i
780780 −5.71515 5.71515i −0.204635 0.204635i
781781 −24.2203 −0.866670
782782 −22.7458 6.23650i −0.813390 0.223017i
783783 26.1936 0.936083
784784 3.95275 + 3.95275i 0.141170 + 0.141170i
785785 14.3647 5.95005i 0.512698 0.212366i
786786 5.27324i 0.188090i
787787 8.22589 + 19.8591i 0.293221 + 0.707899i 1.00000 0.000464022i 0.000147703π0.000147703\pi
−0.706779 + 0.707435i 0.749852π0.749852\pi
788788 3.25339 + 1.34760i 0.115897 + 0.0480061i
789789 −3.41420 + 8.24261i −0.121549 + 0.293445i
790790 −7.15302 + 7.15302i −0.254493 + 0.254493i
791791 −24.1911 + 24.1911i −0.860135 + 0.860135i
792792 −1.48166 + 3.57705i −0.0526486 + 0.127105i
793793 62.9743 + 26.0848i 2.23628 + 0.926298i
794794 −9.16446 22.1250i −0.325235 0.785186i
795795 13.6535i 0.484238i
796796 15.5212 6.42910i 0.550135 0.227874i
797797 14.8934 + 14.8934i 0.527550 + 0.527550i 0.919841 0.392291i 0.128317π-0.128317\pi
−0.392291 + 0.919841i 0.628317π0.628317\pi
798798 6.35168 0.224847
799799 −19.0709 14.8103i −0.674680 0.523952i
800800 1.00000 0.0353553
801801 −1.30346 1.30346i −0.0460554 0.0460554i
802802 −21.2869 + 8.81734i −0.751668 + 0.311351i
803803 75.9590i 2.68053i
804804 4.89452 + 11.8164i 0.172617 + 0.416733i
805805 −18.7519 7.76731i −0.660919 0.273762i
806806 −15.2655 + 36.8543i −0.537706 + 1.29814i
807807 −17.6278 + 17.6278i −0.620529 + 0.620529i
808808 7.59384 7.59384i 0.267150 0.267150i
809809 −6.98690 + 16.8679i −0.245646 + 0.593042i −0.997825 0.0659166i 0.979003π-0.979003\pi
0.752179 + 0.658959i 0.229003π0.229003\pi
810810 −5.41114 2.24137i −0.190128 0.0787537i
811811 −5.56638 13.4384i −0.195462 0.471887i 0.795512 0.605937i 0.207202π-0.207202\pi
−0.990975 + 0.134050i 0.957202π0.957202\pi
812812 16.4773i 0.578239i
813813 −31.2628 + 12.9495i −1.09644 + 0.454158i
814814 30.9363 + 30.9363i 1.08432 + 1.08432i
815815 10.1378 0.355111
816816 −1.60888 + 5.86793i −0.0563221 + 0.205419i
817817 −1.00702 −0.0352311
818818 9.01479 + 9.01479i 0.315195 + 0.315195i
819819 −14.7637 + 6.11532i −0.515885 + 0.213686i
820820 0.143094i 0.00499707i
821821 15.6230 + 37.7172i 0.545246 + 1.31634i 0.920979 + 0.389613i 0.127391π0.127391\pi
−0.375733 + 0.926728i 0.622609π0.622609\pi
822822 4.51209 + 1.86897i 0.157377 + 0.0651878i
823823 0.697439 1.68377i 0.0243112 0.0586925i −0.911258 0.411837i 0.864887π-0.864887\pi
0.935569 + 0.353144i 0.114887π0.114887\pi
824824 5.25597 5.25597i 0.183100 0.183100i
825825 4.91328 4.91328i 0.171059 0.171059i
826826 −6.40432 + 15.4614i −0.222835 + 0.537971i
827827 42.9008 + 17.7701i 1.49181 + 0.617927i 0.971709 0.236180i 0.0758955π-0.0758955\pi
0.520098 + 0.854107i 0.325896π0.325896\pi
828828 1.80003 + 4.34567i 0.0625555 + 0.151022i
829829 34.9749i 1.21473i −0.794424 0.607364i 0.792227π-0.792227\pi
0.794424 0.607364i 0.207773π-0.207773\pi
830830 −3.14674 + 1.30342i −0.109225 + 0.0452425i
831831 20.8715 + 20.8715i 0.724025 + 0.724025i
832832 5.47699 0.189881
833833 −22.8682 + 2.87568i −0.792337 + 0.0996365i
834834 −2.65622 −0.0919773
835835 −8.80459 8.80459i −0.304695 0.304695i
836836 5.27687 2.18575i 0.182504 0.0755958i
837837 41.0822i 1.42001i
838838 10.4748 + 25.2883i 0.361845 + 0.873570i
839839 39.6860 + 16.4385i 1.37011 + 0.567520i 0.941819 0.336120i 0.109115π-0.109115\pi
0.428294 + 0.903639i 0.359115π0.359115\pi
840840 −2.00380 + 4.83759i −0.0691375 + 0.166913i
841841 5.25756 5.25756i 0.181295 0.181295i
842842 −23.8163 + 23.8163i −0.820764 + 0.820764i
843843 13.1484 31.7430i 0.452854 1.09329i
844844 −21.0828 8.73280i −0.725701 0.300595i
845845 −6.50464 15.7036i −0.223766 0.540220i
846846 4.81560i 0.165564i
847847 36.6181 15.1677i 1.25821 0.521169i
848848 −6.54226 6.54226i −0.224662 0.224662i
849849 −37.1152 −1.27379
850850 −2.52894 + 3.25645i −0.0867419 + 0.111695i
851851 53.1513 1.82200
852852 5.36758 + 5.36758i 0.183890 + 0.183890i
853853 −8.59031 + 3.55822i −0.294127 + 0.121831i −0.524867 0.851184i 0.675885π-0.675885\pi
0.230741 + 0.973015i 0.425885π0.425885\pi
854854 44.1590i 1.51109i
855855 −0.381714 0.921539i −0.0130543 0.0315160i
856856 −14.5335 6.01999i −0.496746 0.205759i
857857 −11.8527 + 28.6150i −0.404881 + 0.977469i 0.581582 + 0.813488i 0.302434π0.302434\pi
−0.986463 + 0.163982i 0.947566π0.947566\pi
858858 26.9100 26.9100i 0.918693 0.918693i
859859 13.1008 13.1008i 0.446994 0.446994i −0.447360 0.894354i 0.647636π-0.647636\pi
0.894354 + 0.447360i 0.147636π0.147636\pi
860860 0.317689 0.766969i 0.0108331 0.0261534i
861861 −0.692232 0.286732i −0.0235912 0.00977179i
862862 −6.95725 16.7963i −0.236965 0.572084i
863863 18.5377i 0.631030i −0.948921 0.315515i 0.897823π-0.897823\pi
0.948921 0.315515i 0.102177π-0.102177\pi
864864 5.21121 2.15856i 0.177289 0.0734356i
865865 −2.50790 2.50790i −0.0852710 0.0852710i
866866 −8.10392 −0.275382
867867 −15.0399 20.0789i −0.510781 0.681914i
868868 25.8431 0.877170
869869 −33.6803 33.6803i −1.14253 1.14253i
870870 6.33122 2.62248i 0.214648 0.0889103i
871871 47.4693i 1.60843i
872872 2.46089 + 5.94112i 0.0833363 + 0.201192i
873873 −3.30880 1.37055i −0.111986 0.0463860i
874874 2.65541 6.41073i 0.0898207 0.216846i
875875 −2.50899 + 2.50899i −0.0848193 + 0.0848193i
876876 −16.8336 + 16.8336i −0.568756 + 0.568756i
877877 16.3998 39.5926i 0.553781 1.33695i −0.360837 0.932629i 0.617509π-0.617509\pi
0.914619 0.404318i 0.132491π-0.132491\pi
878878 22.1522 + 9.17574i 0.747600 + 0.309666i
879879 14.4147 + 34.8003i 0.486197 + 1.17378i
880880 4.70854i 0.158725i
881881 37.7646 15.6426i 1.27232 0.527014i 0.358653 0.933471i 0.383236π-0.383236\pi
0.913670 + 0.406457i 0.133236π0.133236\pi
882882 3.25030 + 3.25030i 0.109443 + 0.109443i
883883 52.3174 1.76062 0.880310 0.474398i 0.157334π-0.157334\pi
0.880310 + 0.474398i 0.157334π0.157334\pi
884884 −13.8510 + 17.8356i −0.465859 + 0.599875i
885885 −6.96018 −0.233964
886886 0.172587 + 0.172587i 0.00579819 + 0.00579819i
887887 −13.9607 + 5.78272i −0.468755 + 0.194165i −0.604542 0.796573i 0.706644π-0.706644\pi
0.135787 + 0.990738i 0.456644π0.456644\pi
888888 13.7119i 0.460141i
889889 −4.35317 10.5095i −0.146000 0.352476i
890890 −2.07111 0.857882i −0.0694238 0.0287563i
891891 10.5536 25.4786i 0.353558 0.853565i
892892 6.41246 6.41246i 0.214705 0.214705i
893893 5.02327 5.02327i 0.168097 0.168097i
894894 2.35361 5.68212i 0.0787165 0.190038i
895895 −12.1051 5.01410i −0.404629 0.167603i
896896 −1.35785 3.27815i −0.0453627 0.109515i
897897 46.2338i 1.54370i
898898 −0.0761574 + 0.0315454i −0.00254140 + 0.00105268i
899899 −23.9159 23.9159i −0.797640 0.797640i
900900 0.822287 0.0274096
901901 37.8495 4.75958i 1.26095 0.158565i
902902 −0.673765 −0.0224339
903903 3.07370 + 3.07370i 0.102286 + 0.102286i
904904 8.90782 3.68974i 0.296270 0.122719i
905905 1.82731i 0.0607418i
906906 −2.59356 6.26141i −0.0861653 0.208022i
907907 −23.1561 9.59155i −0.768884 0.318482i −0.0364638 0.999335i 0.511609π-0.511609\pi
−0.732420 + 0.680853i 0.761609π0.761609\pi
908908 −6.02643 + 14.5491i −0.199994 + 0.482829i
909909 6.24432 6.24432i 0.207111 0.207111i
910910 −13.7417 + 13.7417i −0.455533 + 0.455533i
911911 −1.10387 + 2.66499i −0.0365730 + 0.0882950i −0.941111 0.338099i 0.890216π-0.890216\pi
0.904538 + 0.426394i 0.140216π0.140216\pi
912912 −1.65383 0.685038i −0.0547637 0.0226839i
913913 −6.13723 14.8166i −0.203113 0.490357i
914914 24.3896i 0.806737i
915915 16.9676 7.02822i 0.560933 0.232346i
916916 14.2262 + 14.2262i 0.470046 + 0.470046i
917917 −12.6792 −0.418703
918918 −6.14961 + 22.4289i −0.202967 + 0.740265i
919919 −48.0746 −1.58584 −0.792918 0.609328i 0.791439π-0.791439\pi
−0.792918 + 0.609328i 0.791439π0.791439\pi
920920 4.04485 + 4.04485i 0.133355 + 0.133355i
921921 −19.4120 + 8.04071i −0.639647 + 0.264950i
922922 29.1100i 0.958687i
923923 10.7814 + 26.0286i 0.354874 + 0.856741i
924924 −22.7780 9.43496i −0.749341 0.310387i
925925 3.55579 8.58444i 0.116914 0.282255i
926926 −19.7821 + 19.7821i −0.650081 + 0.650081i
927927 4.32191 4.32191i 0.141950 0.141950i
928928 −1.77710 + 4.29029i −0.0583361 + 0.140836i
929929 25.3430 + 10.4974i 0.831478 + 0.344409i 0.757487 0.652850i 0.226427π-0.226427\pi
0.0739901 + 0.997259i 0.476427π0.476427\pi
930930 4.11311 + 9.92992i 0.134874 + 0.325615i
931931 6.78094i 0.222236i
932932 17.8076 7.37613i 0.583306 0.241613i
933933 −12.6797 12.6797i −0.415116 0.415116i
934934 31.2786 1.02347
935935 −15.3331 11.9076i −0.501447 0.389420i
936936 4.50366 0.147207
937937 −10.3762 10.3762i −0.338975 0.338975i 0.517007 0.855981i 0.327046π-0.327046\pi
−0.855981 + 0.517007i 0.827046π0.827046\pi
938938 28.4118 11.7686i 0.927679 0.384257i
939939 32.1552i 1.04934i
940940 2.24113 + 5.41056i 0.0730975 + 0.176473i
941941 22.8397 + 9.46050i 0.744552 + 0.308404i 0.722517 0.691354i 0.242985π-0.242985\pi
0.0220356 + 0.999757i 0.492985π0.492985\pi
942942 8.78053 21.1981i 0.286085 0.690671i
943943 −0.578795 + 0.578795i −0.0188482 + 0.0188482i
944944 3.33507 3.33507i 0.108547 0.108547i
945945 −7.65908 + 18.4907i −0.249150 + 0.601501i
946946 3.61131 + 1.49585i 0.117414 + 0.0486343i
947947 −2.49335 6.01947i −0.0810228 0.195606i 0.878177 0.478336i 0.158760π-0.158760\pi
−0.959200 + 0.282730i 0.908760π0.908760\pi
948948 14.9281i 0.484842i
949949 −81.6301 + 33.8123i −2.64982 + 1.09759i
950950 −0.857748 0.857748i −0.0278290 0.0278290i
951951 15.1285 0.490574
952952 14.1091 + 3.86845i 0.457277 + 0.125377i
953953 13.6944 0.443607 0.221803 0.975091i 0.428806π-0.428806\pi
0.221803 + 0.975091i 0.428806π0.428806\pi
954954 −5.37961 5.37961i −0.174171 0.174171i
955955 15.5506 6.44127i 0.503206 0.208435i
956956 14.2040i 0.459389i
957957 12.3480 + 29.8108i 0.399155 + 0.963646i
958958 −11.1564 4.62112i −0.360446 0.149302i
959959 4.49382 10.8490i 0.145113 0.350334i
960960 1.04348 1.04348i 0.0336783 0.0336783i
961961 15.5896 15.5896i 0.502889 0.502889i
962962 19.4751 47.0169i 0.627901 1.51589i
963963 −11.9507 4.95016i −0.385107 0.159517i
964964 −1.75060 4.22633i −0.0563832 0.136121i
965965 5.82873i 0.187633i
966966 −27.6724 + 11.4623i −0.890344 + 0.368793i
967967 11.5376 + 11.5376i 0.371026 + 0.371026i 0.867851 0.496825i 0.165501π-0.165501\pi
−0.496825 + 0.867851i 0.665501π0.665501\pi
968968 −11.1704 −0.359029
969969 6.41322 3.65319i 0.206022 0.117357i
970970 −4.35543 −0.139844
971971 −19.0136 19.0136i −0.610176 0.610176i 0.332816 0.942992i 0.392001π-0.392001\pi
−0.942992 + 0.332816i 0.892001π0.892001\pi
972972 7.64838 3.16806i 0.245322 0.101616i
973973 6.38671i 0.204748i
974974 1.91937 + 4.63377i 0.0615005 + 0.148475i
975975 −7.46720 3.09302i −0.239142 0.0990558i
976976 −4.76261 + 11.4980i −0.152448 + 0.368041i
977977 −14.1423 + 14.1423i −0.452451 + 0.452451i −0.896167 0.443716i 0.853660π-0.853660\pi
0.443716 + 0.896167i 0.353660π0.353660\pi
978978 10.5786 10.5786i 0.338266 0.338266i
979979 4.03937 9.75191i 0.129099 0.311672i
980980 5.16452 + 2.13922i 0.164975 + 0.0683347i
981981 2.02356 + 4.88531i 0.0646073 + 0.155976i
982982 26.4441i 0.843865i
983983 −26.6406 + 11.0349i −0.849704 + 0.351959i −0.764672 0.644419i 0.777099π-0.777099\pi
−0.0850316 + 0.996378i 0.527099π0.527099\pi
984984 0.149316 + 0.149316i 0.00476003 + 0.00476003i
985985 3.52144 0.112202
986986 −9.47696 16.6369i −0.301808 0.529827i
987987 −30.6648 −0.976072
988988 −4.69788 4.69788i −0.149460 0.149460i
989989 4.38728 1.81727i 0.139507 0.0577858i
990990 3.87177i 0.123053i
991991 −10.2929 24.8494i −0.326966 0.789366i −0.998815 0.0486775i 0.984499π-0.984499\pi
0.671848 0.740689i 0.265501π-0.265501\pi
992992 −6.72892 2.78721i −0.213644 0.0884941i
993993 −0.167267 + 0.403818i −0.00530805 + 0.0128148i
994994 12.9060 12.9060i 0.409353 0.409353i
995995 11.8794 11.8794i 0.376603 0.376603i
996996 −1.92347 + 4.64367i −0.0609476 + 0.147140i
997997 28.1434 + 11.6574i 0.891310 + 0.369193i 0.780872 0.624690i 0.214775π-0.214775\pi
0.110437 + 0.993883i 0.464775π0.464775\pi
998998 −11.4569 27.6595i −0.362663 0.875545i
999999 52.4108i 1.65820i
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 170.2.k.b.121.3 yes 16
5.2 odd 4 850.2.o.g.699.2 16
5.3 odd 4 850.2.o.j.699.3 16
5.4 even 2 850.2.l.e.801.2 16
17.3 odd 16 2890.2.a.bi.1.7 8
17.5 odd 16 2890.2.b.r.2311.12 16
17.9 even 8 inner 170.2.k.b.111.3 16
17.12 odd 16 2890.2.b.r.2311.5 16
17.14 odd 16 2890.2.a.bj.1.2 8
85.9 even 8 850.2.l.e.451.2 16
85.43 odd 8 850.2.o.g.349.2 16
85.77 odd 8 850.2.o.j.349.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.k.b.111.3 16 17.9 even 8 inner
170.2.k.b.121.3 yes 16 1.1 even 1 trivial
850.2.l.e.451.2 16 85.9 even 8
850.2.l.e.801.2 16 5.4 even 2
850.2.o.g.349.2 16 85.43 odd 8
850.2.o.g.699.2 16 5.2 odd 4
850.2.o.j.349.3 16 85.77 odd 8
850.2.o.j.699.3 16 5.3 odd 4
2890.2.a.bi.1.7 8 17.3 odd 16
2890.2.a.bj.1.2 8 17.14 odd 16
2890.2.b.r.2311.5 16 17.12 odd 16
2890.2.b.r.2311.12 16 17.5 odd 16