Properties

Label 882.2.e.p.655.2
Level 882882
Weight 22
Character 882.655
Analytic conductor 7.0437.043
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(373,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 882=23272 882 = 2 \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 882.e (of order 33, degree 22, not 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: 7.042805458287.04280545828
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5+10x415x3+19x212x+3 x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 655.2
Root 0.5000002.05195i0.500000 - 2.05195i of defining polynomial
Character χ\chi == 882.655
Dual form 882.2.e.p.373.2

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+1.00000q2+(0.796790+1.53790i)q3+1.00000q4+(0.230252+0.398809i)q5+(0.796790+1.53790i)q6+1.00000q8+(1.73025+2.45076i)q9+(0.230252+0.398809i)q10+(1.82383+3.15897i)q11+(0.796790+1.53790i)q12+(0.7302521.26483i)q13+(0.7967900.0363376i)q15+1.00000q16+(1.866933.23361i)q17+(1.73025+2.45076i)q18+(2.02704+3.51094i)q19+(0.230252+0.398809i)q20+(1.82383+3.15897i)q22+(0.566537+0.981271i)q23+(0.796790+1.53790i)q24+(2.39397+4.14647i)q25+(0.7302521.26483i)q26+(5.147660.708209i)q27+(4.48755+7.77266i)q29+(0.7967900.0363376i)q30+0.514589q31+1.00000q32+(3.40496+5.32190i)q33+(1.866933.23361i)q34+(1.73025+2.45076i)q36+(4.554087.88791i)q37+(2.02704+3.51094i)q38+(1.363332.13086i)q39+(0.230252+0.398809i)q40+(0.472958+0.819187i)q41+(4.663728.07779i)q43+(1.82383+3.15897i)q44+(0.5789901.25433i)q45+(0.566537+0.981271i)q462.32743q47+(0.796790+1.53790i)q48+(2.39397+4.14647i)q50+(6.46050+0.294632i)q51+(0.7302521.26483i)q52+(6.2178010.7695i)q53+(5.147660.708209i)q541.67977q55+(3.78434+5.91486i)q57+(4.48755+7.77266i)q58+12.8961q59+(0.7967900.0363376i)q6012.0833q61+0.514589q62+1.00000q64+0.672570q65+(3.40496+5.32190i)q662.32023q67+(1.866933.23361i)q68+(1.960500.0894089i)q69+1.67977q71+(1.73025+2.45076i)q72+(6.6206211.4673i)q73+(4.554087.88791i)q74+(4.46936+6.98554i)q75+(2.02704+3.51094i)q76+(1.363332.13086i)q785.00720q79+(0.230252+0.398809i)q80+(3.012458.48087i)q81+(0.472958+0.819187i)q82+(3.32383+5.75705i)q83+(0.859728+1.48909i)q85+(4.663728.07779i)q86+(15.52920.708209i)q87+(1.82383+3.15897i)q88+(1.36333+2.36135i)q89+(0.5789901.25433i)q90+(0.566537+0.981271i)q92+(0.410019+0.791385i)q932.32743q941.86693q95+(0.796790+1.53790i)q96+(5.593589.68836i)q97+(10.89760.996040i)q99+O(q100)q+1.00000 q^{2} +(0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 + 1.53790i) q^{6} +1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.230252 + 0.398809i) q^{10} +(1.82383 + 3.15897i) q^{11} +(0.796790 + 1.53790i) q^{12} +(-0.730252 - 1.26483i) q^{13} +(-0.796790 - 0.0363376i) q^{15} +1.00000 q^{16} +(1.86693 - 3.23361i) q^{17} +(-1.73025 + 2.45076i) q^{18} +(2.02704 + 3.51094i) q^{19} +(-0.230252 + 0.398809i) q^{20} +(1.82383 + 3.15897i) q^{22} +(-0.566537 + 0.981271i) q^{23} +(0.796790 + 1.53790i) q^{24} +(2.39397 + 4.14647i) q^{25} +(-0.730252 - 1.26483i) q^{26} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +(-0.796790 - 0.0363376i) q^{30} +0.514589 q^{31} +1.00000 q^{32} +(-3.40496 + 5.32190i) q^{33} +(1.86693 - 3.23361i) q^{34} +(-1.73025 + 2.45076i) q^{36} +(-4.55408 - 7.88791i) q^{37} +(2.02704 + 3.51094i) q^{38} +(1.36333 - 2.13086i) q^{39} +(-0.230252 + 0.398809i) q^{40} +(0.472958 + 0.819187i) q^{41} +(4.66372 - 8.07779i) q^{43} +(1.82383 + 3.15897i) q^{44} +(-0.578990 - 1.25433i) q^{45} +(-0.566537 + 0.981271i) q^{46} -2.32743 q^{47} +(0.796790 + 1.53790i) q^{48} +(2.39397 + 4.14647i) q^{50} +(6.46050 + 0.294632i) q^{51} +(-0.730252 - 1.26483i) q^{52} +(6.21780 - 10.7695i) q^{53} +(-5.14766 - 0.708209i) q^{54} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +(-4.48755 + 7.77266i) q^{58} +12.8961 q^{59} +(-0.796790 - 0.0363376i) q^{60} -12.0833 q^{61} +0.514589 q^{62} +1.00000 q^{64} +0.672570 q^{65} +(-3.40496 + 5.32190i) q^{66} -2.32023 q^{67} +(1.86693 - 3.23361i) q^{68} +(-1.96050 - 0.0894089i) q^{69} +1.67977 q^{71} +(-1.73025 + 2.45076i) q^{72} +(6.62062 - 11.4673i) q^{73} +(-4.55408 - 7.88791i) q^{74} +(-4.46936 + 6.98554i) q^{75} +(2.02704 + 3.51094i) q^{76} +(1.36333 - 2.13086i) q^{78} -5.00720 q^{79} +(-0.230252 + 0.398809i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(0.472958 + 0.819187i) q^{82} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(4.66372 - 8.07779i) q^{86} +(-15.5292 - 0.708209i) q^{87} +(1.82383 + 3.15897i) q^{88} +(1.36333 + 2.36135i) q^{89} +(-0.578990 - 1.25433i) q^{90} +(-0.566537 + 0.981271i) q^{92} +(0.410019 + 0.791385i) q^{93} -2.32743 q^{94} -1.86693 q^{95} +(0.796790 + 1.53790i) q^{96} +(5.59358 - 9.68836i) q^{97} +(-10.8976 - 0.996040i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+6q2+2q3+6q4+5q5+2q6+6q84q9+5q10q11+2q12+2q132q15+6q16+4q174q18+3q19+5q20q227q23+41q99+O(q100) 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 6 q^{16} + 4 q^{17} - 4 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} - 7 q^{23}+ \cdots - 41 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/882Z)×\left(\mathbb{Z}/882\mathbb{Z}\right)^\times.

nn 199199 785785
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\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 1.00000 0.707107
33 0.796790 + 1.53790i 0.460027 + 0.887905i
44 1.00000 0.500000
55 −0.230252 + 0.398809i −0.102972 + 0.178353i −0.912908 0.408166i 0.866169π-0.866169\pi
0.809936 + 0.586519i 0.199502π0.199502\pi
66 0.796790 + 1.53790i 0.325288 + 0.627844i
77 0 0
88 1.00000 0.353553
99 −1.73025 + 2.45076i −0.576751 + 0.816920i
1010 −0.230252 + 0.398809i −0.0728122 + 0.126114i
1111 1.82383 + 3.15897i 0.549906 + 0.952465i 0.998280 + 0.0586193i 0.0186698π0.0186698\pi
−0.448374 + 0.893846i 0.647997π0.647997\pi
1212 0.796790 + 1.53790i 0.230013 + 0.443953i
1313 −0.730252 1.26483i −0.202536 0.350802i 0.746809 0.665038i 0.231585π-0.231585\pi
−0.949345 + 0.314236i 0.898252π0.898252\pi
1414 0 0
1515 −0.796790 0.0363376i −0.205730 0.00938234i
1616 1.00000 0.250000
1717 1.86693 3.23361i 0.452796 0.784266i −0.545763 0.837940i 0.683760π-0.683760\pi
0.998558 + 0.0536743i 0.0170933π0.0170933\pi
1818 −1.73025 + 2.45076i −0.407824 + 0.577650i
1919 2.02704 + 3.51094i 0.465035 + 0.805465i 0.999203 0.0399136i 0.0127083π-0.0127083\pi
−0.534168 + 0.845378i 0.679375π0.679375\pi
2020 −0.230252 + 0.398809i −0.0514860 + 0.0891764i
2121 0 0
2222 1.82383 + 3.15897i 0.388842 + 0.673495i
2323 −0.566537 + 0.981271i −0.118131 + 0.204609i −0.919027 0.394194i 0.871024π-0.871024\pi
0.800896 + 0.598804i 0.204357π0.204357\pi
2424 0.796790 + 1.53790i 0.162644 + 0.313922i
2525 2.39397 + 4.14647i 0.478794 + 0.829295i
2626 −0.730252 1.26483i −0.143214 0.248054i
2727 −5.14766 0.708209i −0.990668 0.136295i
2828 0 0
2929 −4.48755 + 7.77266i −0.833317 + 1.44335i 0.0620772 + 0.998071i 0.480228π0.480228\pi
−0.895394 + 0.445275i 0.853106π0.853106\pi
3030 −0.796790 0.0363376i −0.145473 0.00663431i
3131 0.514589 0.0924229 0.0462115 0.998932i 0.485285π-0.485285\pi
0.0462115 + 0.998932i 0.485285π0.485285\pi
3232 1.00000 0.176777
3333 −3.40496 + 5.32190i −0.592727 + 0.926424i
3434 1.86693 3.23361i 0.320175 0.554560i
3535 0 0
3636 −1.73025 + 2.45076i −0.288375 + 0.408460i
3737 −4.55408 7.88791i −0.748687 1.29676i −0.948452 0.316920i 0.897351π-0.897351\pi
0.199765 0.979844i 0.435982π-0.435982\pi
3838 2.02704 + 3.51094i 0.328830 + 0.569550i
3939 1.36333 2.13086i 0.218307 0.341211i
4040 −0.230252 + 0.398809i −0.0364061 + 0.0630572i
4141 0.472958 + 0.819187i 0.0738636 + 0.127936i 0.900592 0.434666i 0.143134π-0.143134\pi
−0.826728 + 0.562602i 0.809800π0.809800\pi
4242 0 0
4343 4.66372 8.07779i 0.711210 1.23185i −0.253193 0.967416i 0.581481π-0.581481\pi
0.964403 0.264436i 0.0851858π-0.0851858\pi
4444 1.82383 + 3.15897i 0.274953 + 0.476233i
4545 −0.578990 1.25433i −0.0863108 0.186985i
4646 −0.566537 + 0.981271i −0.0835314 + 0.144681i
4747 −2.32743 −0.339491 −0.169745 0.985488i 0.554295π-0.554295\pi
−0.169745 + 0.985488i 0.554295π0.554295\pi
4848 0.796790 + 1.53790i 0.115007 + 0.221976i
4949 0 0
5050 2.39397 + 4.14647i 0.338558 + 0.586400i
5151 6.46050 + 0.294632i 0.904652 + 0.0412567i
5252 −0.730252 1.26483i −0.101268 0.175401i
5353 6.21780 10.7695i 0.854080 1.47931i −0.0234151 0.999726i 0.507454π-0.507454\pi
0.877495 0.479585i 0.159213π-0.159213\pi
5454 −5.14766 0.708209i −0.700508 0.0963750i
5555 −1.67977 −0.226500
5656 0 0
5757 −3.78434 + 5.91486i −0.501248 + 0.783443i
5858 −4.48755 + 7.77266i −0.589244 + 1.02060i
5959 12.8961 1.67893 0.839465 0.543414i 0.182869π-0.182869\pi
0.839465 + 0.543414i 0.182869π0.182869\pi
6060 −0.796790 0.0363376i −0.102865 0.00469117i
6161 −12.0833 −1.54710 −0.773552 0.633733i 0.781522π-0.781522\pi
−0.773552 + 0.633733i 0.781522π0.781522\pi
6262 0.514589 0.0653529
6363 0 0
6464 1.00000 0.125000
6565 0.672570 0.0834220
6666 −3.40496 + 5.32190i −0.419121 + 0.655080i
6767 −2.32023 −0.283462 −0.141731 0.989905i 0.545267π-0.545267\pi
−0.141731 + 0.989905i 0.545267π0.545267\pi
6868 1.86693 3.23361i 0.226398 0.392133i
6969 −1.96050 0.0894089i −0.236017 0.0107636i
7070 0 0
7171 1.67977 0.199352 0.0996758 0.995020i 0.468219π-0.468219\pi
0.0996758 + 0.995020i 0.468219π0.468219\pi
7272 −1.73025 + 2.45076i −0.203912 + 0.288825i
7373 6.62062 11.4673i 0.774885 1.34214i −0.159974 0.987121i 0.551141π-0.551141\pi
0.934859 0.355019i 0.115526π-0.115526\pi
7474 −4.55408 7.88791i −0.529402 0.916950i
7575 −4.46936 + 6.98554i −0.516077 + 0.806621i
7676 2.02704 + 3.51094i 0.232518 + 0.402732i
7777 0 0
7878 1.36333 2.13086i 0.154366 0.241272i
7979 −5.00720 −0.563354 −0.281677 0.959509i 0.590891π-0.590891\pi
−0.281677 + 0.959509i 0.590891π0.590891\pi
8080 −0.230252 + 0.398809i −0.0257430 + 0.0445882i
8181 −3.01245 8.48087i −0.334717 0.942319i
8282 0.472958 + 0.819187i 0.0522295 + 0.0904641i
8383 −3.32383 + 5.75705i −0.364838 + 0.631918i −0.988750 0.149577i 0.952209π-0.952209\pi
0.623912 + 0.781494i 0.285542π0.285542\pi
8484 0 0
8585 0.859728 + 1.48909i 0.0932506 + 0.161515i
8686 4.66372 8.07779i 0.502901 0.871051i
8787 −15.5292 0.708209i −1.66490 0.0759280i
8888 1.82383 + 3.15897i 0.194421 + 0.336747i
8989 1.36333 + 2.36135i 0.144512 + 0.250303i 0.929191 0.369600i 0.120505π-0.120505\pi
−0.784679 + 0.619903i 0.787172π0.787172\pi
9090 −0.578990 1.25433i −0.0610309 0.132218i
9191 0 0
9292 −0.566537 + 0.981271i −0.0590656 + 0.102305i
9393 0.410019 + 0.791385i 0.0425170 + 0.0820628i
9494 −2.32743 −0.240056
9595 −1.86693 −0.191543
9696 0.796790 + 1.53790i 0.0813220 + 0.156961i
9797 5.59358 9.68836i 0.567942 0.983704i −0.428827 0.903386i 0.641073π-0.641073\pi
0.996769 0.0803178i 0.0255935π-0.0255935\pi
9898 0 0
9999 −10.8976 0.996040i −1.09525 0.100106i
100100 2.39397 + 4.14647i 0.239397 + 0.414647i
101101 6.87792 + 11.9129i 0.684378 + 1.18538i 0.973632 + 0.228125i 0.0732596π0.0732596\pi
−0.289254 + 0.957253i 0.593407π0.593407\pi
102102 6.46050 + 0.294632i 0.639685 + 0.0291729i
103103 5.58113 9.66679i 0.549925 0.952498i −0.448354 0.893856i 0.647990π-0.647990\pi
0.998279 0.0586417i 0.0186769π-0.0186769\pi
104104 −0.730252 1.26483i −0.0716071 0.124027i
105105 0 0
106106 6.21780 10.7695i 0.603926 1.04603i
107107 −3.89037 6.73832i −0.376096 0.651418i 0.614394 0.788999i 0.289400π-0.289400\pi
−0.990490 + 0.137581i 0.956067π0.956067\pi
108108 −5.14766 0.708209i −0.495334 0.0681474i
109109 −3.75729 + 6.50783i −0.359884 + 0.623337i −0.987941 0.154830i 0.950517π-0.950517\pi
0.628058 + 0.778167i 0.283850π0.283850\pi
110110 −1.67977 −0.160159
111111 8.50214 13.2887i 0.806987 1.26131i
112112 0 0
113113 3.03064 + 5.24922i 0.285099 + 0.493805i 0.972633 0.232346i 0.0746403π-0.0746403\pi
−0.687534 + 0.726152i 0.741307π0.741307\pi
114114 −3.78434 + 5.91486i −0.354436 + 0.553978i
115115 −0.260893 0.451880i −0.0243284 0.0421380i
116116 −4.48755 + 7.77266i −0.416658 + 0.721673i
117117 4.36333 + 0.398809i 0.403390 + 0.0368699i
118118 12.8961 1.18718
119119 0 0
120120 −0.796790 0.0363376i −0.0727366 0.00331716i
121121 −1.15272 + 1.99658i −0.104793 + 0.181507i
122122 −12.0833 −1.09397
123123 −0.882977 + 1.38008i −0.0796154 + 0.124438i
124124 0.514589 0.0462115
125125 −4.50739 −0.403153
126126 0 0
127127 8.80992 0.781754 0.390877 0.920443i 0.372172π-0.372172\pi
0.390877 + 0.920443i 0.372172π0.372172\pi
128128 1.00000 0.0883883
129129 16.1388 + 0.736011i 1.42094 + 0.0648022i
130130 0.672570 0.0589883
131131 10.5687 18.3055i 0.923389 1.59936i 0.129258 0.991611i 0.458740π-0.458740\pi
0.794131 0.607746i 0.207926π-0.207926\pi
132132 −3.40496 + 5.32190i −0.296364 + 0.463212i
133133 0 0
134134 −2.32023 −0.200438
135135 1.46770 1.88987i 0.126320 0.162654i
136136 1.86693 3.23361i 0.160088 0.277280i
137137 2.20321 + 3.81607i 0.188233 + 0.326029i 0.944661 0.328048i 0.106391π-0.106391\pi
−0.756428 + 0.654077i 0.773057π0.773057\pi
138138 −1.96050 0.0894089i −0.166889 0.00761099i
139139 1.01245 + 1.75362i 0.0858751 + 0.148740i 0.905764 0.423783i 0.139298π-0.139298\pi
−0.819889 + 0.572523i 0.805965π0.805965\pi
140140 0 0
141141 −1.85447 3.57935i −0.156175 0.301435i
142142 1.67977 0.140963
143143 2.66372 4.61369i 0.222751 0.385816i
144144 −1.73025 + 2.45076i −0.144188 + 0.204230i
145145 −2.06654 3.57935i −0.171617 0.297249i
146146 6.62062 11.4673i 0.547927 0.949037i
147147 0 0
148148 −4.55408 7.88791i −0.374343 0.648382i
149149 4.58113 7.93474i 0.375300 0.650040i −0.615071 0.788471i 0.710873π-0.710873\pi
0.990372 + 0.138432i 0.0442062π0.0442062\pi
150150 −4.46936 + 6.98554i −0.364922 + 0.570367i
151151 0.0519482 + 0.0899768i 0.00422748 + 0.00732221i 0.868131 0.496334i 0.165321π-0.165321\pi
−0.863904 + 0.503657i 0.831988π0.831988\pi
152152 2.02704 + 3.51094i 0.164415 + 0.284775i
153153 4.69455 + 10.1703i 0.379532 + 0.822224i
154154 0 0
155155 −0.118485 + 0.205223i −0.00951698 + 0.0164839i
156156 1.36333 2.13086i 0.109154 0.170605i
157157 −20.9823 −1.67457 −0.837285 0.546767i 0.815858π-0.815858\pi
−0.837285 + 0.546767i 0.815858π0.815858\pi
158158 −5.00720 −0.398351
159159 21.5167 + 0.981271i 1.70639 + 0.0778199i
160160 −0.230252 + 0.398809i −0.0182031 + 0.0315286i
161161 0 0
162162 −3.01245 8.48087i −0.236681 0.666320i
163163 −11.5182 19.9501i −0.902174 1.56261i −0.824666 0.565620i 0.808637π-0.808637\pi
−0.0775078 0.996992i 0.524696π-0.524696\pi
164164 0.472958 + 0.819187i 0.0369318 + 0.0639678i
165165 −1.33842 2.58331i −0.104196 0.201110i
166166 −3.32383 + 5.75705i −0.257979 + 0.446833i
167167 5.31498 + 9.20581i 0.411285 + 0.712367i 0.995031 0.0995698i 0.0317467π-0.0317467\pi
−0.583745 + 0.811937i 0.698413π0.698413\pi
168168 0 0
169169 5.43346 9.41103i 0.417959 0.723926i
170170 0.859728 + 1.48909i 0.0659382 + 0.114208i
171171 −12.1118 1.10702i −0.926210 0.0846558i
172172 4.66372 8.07779i 0.355605 0.615926i
173173 −2.93872 −0.223427 −0.111713 0.993740i 0.535634π-0.535634\pi
−0.111713 + 0.993740i 0.535634π0.535634\pi
174174 −15.5292 0.708209i −1.17726 0.0536892i
175175 0 0
176176 1.82383 + 3.15897i 0.137476 + 0.238116i
177177 10.2755 + 19.8329i 0.772353 + 1.49073i
178178 1.36333 + 2.36135i 0.102186 + 0.176991i
179179 −4.58113 + 7.93474i −0.342409 + 0.593071i −0.984880 0.173240i 0.944576π-0.944576\pi
0.642470 + 0.766311i 0.277910π0.277910\pi
180180 −0.578990 1.25433i −0.0431554 0.0934925i
181181 −22.4284 −1.66709 −0.833545 0.552452i 0.813692π-0.813692\pi
−0.833545 + 0.552452i 0.813692π0.813692\pi
182182 0 0
183183 −9.62782 18.5828i −0.711709 1.37368i
184184 −0.566537 + 0.981271i −0.0417657 + 0.0723403i
185185 4.19436 0.308375
186186 0.410019 + 0.791385i 0.0300641 + 0.0580272i
187187 13.6198 0.995981
188188 −2.32743 −0.169745
189189 0 0
190190 −1.86693 −0.135441
191191 2.48968 0.180147 0.0900736 0.995935i 0.471290π-0.471290\pi
0.0900736 + 0.995935i 0.471290π0.471290\pi
192192 0.796790 + 1.53790i 0.0575033 + 0.110988i
193193 4.48968 0.323174 0.161587 0.986858i 0.448339π-0.448339\pi
0.161587 + 0.986858i 0.448339π0.448339\pi
194194 5.59358 9.68836i 0.401596 0.695584i
195195 0.535897 + 1.03434i 0.0383763 + 0.0740708i
196196 0 0
197197 12.7339 0.907249 0.453625 0.891193i 0.350131π-0.350131\pi
0.453625 + 0.891193i 0.350131π0.350131\pi
198198 −10.8976 0.996040i −0.774456 0.0707855i
199199 1.47296 2.55124i 0.104415 0.180852i −0.809084 0.587693i 0.800036π-0.800036\pi
0.913499 + 0.406841i 0.133370π0.133370\pi
200200 2.39397 + 4.14647i 0.169279 + 0.293200i
201201 −1.84874 3.56828i −0.130400 0.251687i
202202 6.87792 + 11.9129i 0.483928 + 0.838189i
203203 0 0
204204 6.46050 + 0.294632i 0.452326 + 0.0206283i
205205 −0.435599 −0.0304235
206206 5.58113 9.66679i 0.388855 0.673517i
207207 −1.42461 3.08629i −0.0990171 0.214512i
208208 −0.730252 1.26483i −0.0506339 0.0877005i
209209 −7.39397 + 12.8067i −0.511451 + 0.885860i
210210 0 0
211211 −0.608168 1.05338i −0.0418680 0.0725176i 0.844332 0.535820i 0.179998π-0.179998\pi
−0.886200 + 0.463303i 0.846664π0.846664\pi
212212 6.21780 10.7695i 0.427040 0.739655i
213213 1.33842 + 2.58331i 0.0917071 + 0.177005i
214214 −3.89037 6.73832i −0.265940 0.460622i
215215 2.14766 + 3.71986i 0.146469 + 0.253693i
216216 −5.14766 0.708209i −0.350254 0.0481875i
217217 0 0
218218 −3.75729 + 6.50783i −0.254476 + 0.440766i
219219 22.9107 + 1.04484i 1.54816 + 0.0706040i
220220 −1.67977 −0.113250
221221 −5.45331 −0.366829
222222 8.50214 13.2887i 0.570626 0.891880i
223223 0.445916 0.772349i 0.0298607 0.0517203i −0.850709 0.525637i 0.823827π-0.823827\pi
0.880570 + 0.473917i 0.157160π0.157160\pi
224224 0 0
225225 −14.3042 1.30740i −0.953612 0.0871603i
226226 3.03064 + 5.24922i 0.201595 + 0.349173i
227227 −7.32597 12.6889i −0.486242 0.842195i 0.513633 0.858010i 0.328299π-0.328299\pi
−0.999875 + 0.0158147i 0.994966π0.994966\pi
228228 −3.78434 + 5.91486i −0.250624 + 0.391721i
229229 −4.78794 + 8.29295i −0.316396 + 0.548013i −0.979733 0.200307i 0.935806π-0.935806\pi
0.663338 + 0.748320i 0.269139π0.269139\pi
230230 −0.260893 0.451880i −0.0172028 0.0297961i
231231 0 0
232232 −4.48755 + 7.77266i −0.294622 + 0.510300i
233233 7.21420 + 12.4954i 0.472618 + 0.818598i 0.999509 0.0313345i 0.00997571π-0.00997571\pi
−0.526891 + 0.849933i 0.676642π0.676642\pi
234234 4.36333 + 0.398809i 0.285240 + 0.0260710i
235235 0.535897 0.928200i 0.0349580 0.0605491i
236236 12.8961 0.839465
237237 −3.98968 7.70055i −0.259158 0.500205i
238238 0 0
239239 −9.15486 15.8567i −0.592179 1.02568i −0.993938 0.109938i 0.964935π-0.964935\pi
0.401760 0.915745i 0.368399π-0.368399\pi
240240 −0.796790 0.0363376i −0.0514326 0.00234558i
241241 0.0466924 + 0.0808735i 0.00300772 + 0.00520952i 0.867525 0.497393i 0.165709π-0.165709\pi
−0.864518 + 0.502602i 0.832376π0.832376\pi
242242 −1.15272 + 1.99658i −0.0741000 + 0.128345i
243243 10.6424 11.3903i 0.682711 0.730689i
244244 −12.0833 −0.773552
245245 0 0
246246 −0.882977 + 1.38008i −0.0562966 + 0.0879907i
247247 2.96050 5.12774i 0.188372 0.326271i
248248 0.514589 0.0326764
249249 −11.5021 0.524555i −0.728918 0.0332424i
250250 −4.50739 −0.285072
251251 18.2733 1.15340 0.576702 0.816955i 0.304339π-0.304339\pi
0.576702 + 0.816955i 0.304339π0.304339\pi
252252 0 0
253253 −4.13307 −0.259844
254254 8.80992 0.552783
255255 −1.60505 + 2.50867i −0.100512 + 0.157099i
256256 1.00000 0.0625000
257257 −10.5256 + 18.2308i −0.656568 + 1.13721i 0.324931 + 0.945738i 0.394659π0.394659\pi
−0.981498 + 0.191471i 0.938674π0.938674\pi
258258 16.1388 + 0.736011i 1.00476 + 0.0458221i
259259 0 0
260260 0.672570 0.0417110
261261 −11.2843 24.4466i −0.698483 1.51320i
262262 10.5687 18.3055i 0.652935 1.13092i
263263 2.58259 + 4.47318i 0.159249 + 0.275828i 0.934598 0.355705i 0.115759π-0.115759\pi
−0.775349 + 0.631533i 0.782426π0.782426\pi
264264 −3.40496 + 5.32190i −0.209561 + 0.327540i
265265 2.86333 + 4.95943i 0.175893 + 0.304655i
266266 0 0
267267 −2.54523 + 3.97816i −0.155766 + 0.243459i
268268 −2.32023 −0.141731
269269 −8.42840 + 14.5984i −0.513889 + 0.890081i 0.485981 + 0.873969i 0.338462π0.338462\pi
−0.999870 + 0.0161123i 0.994871π0.994871\pi
270270 1.46770 1.88987i 0.0893215 0.115014i
271271 −12.5562 21.7480i −0.762736 1.32110i −0.941435 0.337194i 0.890522π-0.890522\pi
0.178699 0.983904i 0.442811π-0.442811\pi
272272 1.86693 3.23361i 0.113199 0.196066i
273273 0 0
274274 2.20321 + 3.81607i 0.133101 + 0.230537i
275275 −8.73239 + 15.1249i −0.526583 + 0.912068i
276276 −1.96050 0.0894089i −0.118009 0.00538178i
277277 −1.69076 2.92848i −0.101588 0.175955i 0.810751 0.585391i 0.199059π-0.199059\pi
−0.912339 + 0.409436i 0.865726π0.865726\pi
278278 1.01245 + 1.75362i 0.0607229 + 0.105175i
279279 −0.890369 + 1.26113i −0.0533050 + 0.0755022i
280280 0 0
281281 −10.1388 + 17.5609i −0.604831 + 1.04760i 0.387248 + 0.921976i 0.373426π0.373426\pi
−0.992078 + 0.125622i 0.959907π0.959907\pi
282282 −1.85447 3.57935i −0.110432 0.213147i
283283 −17.3494 −1.03132 −0.515658 0.856795i 0.672452π-0.672452\pi
−0.515658 + 0.856795i 0.672452π0.672452\pi
284284 1.67977 0.0996758
285285 −1.48755 2.87114i −0.0881147 0.170072i
286286 2.66372 4.61369i 0.157509 0.272813i
287287 0 0
288288 −1.73025 + 2.45076i −0.101956 + 0.144412i
289289 1.52918 + 2.64861i 0.0899517 + 0.155801i
290290 −2.06654 3.57935i −0.121351 0.210187i
291291 19.3566 + 0.882759i 1.13470 + 0.0517483i
292292 6.62062 11.4673i 0.387443 0.671070i
293293 4.93560 + 8.54871i 0.288341 + 0.499421i 0.973414 0.229054i 0.0735631π-0.0735631\pi
−0.685073 + 0.728474i 0.740230π0.740230\pi
294294 0 0
295295 −2.96936 + 5.14308i −0.172883 + 0.299442i
296296 −4.55408 7.88791i −0.264701 0.458475i
297297 −7.15126 17.5530i −0.414958 1.01853i
298298 4.58113 7.93474i 0.265378 0.459647i
299299 1.65486 0.0957031
300300 −4.46936 + 6.98554i −0.258039 + 0.403310i
301301 0 0
302302 0.0519482 + 0.0899768i 0.00298928 + 0.00517759i
303303 −12.8406 + 20.0696i −0.737671 + 1.15297i
304304 2.02704 + 3.51094i 0.116259 + 0.201366i
305305 2.78220 4.81891i 0.159308 0.275930i
306306 4.69455 + 10.1703i 0.268370 + 0.581400i
307307 −7.78794 −0.444481 −0.222240 0.974992i 0.571337π-0.571337\pi
−0.222240 + 0.974992i 0.571337π0.571337\pi
308308 0 0
309309 19.3135 + 0.880794i 1.09871 + 0.0501066i
310310 −0.118485 + 0.205223i −0.00672952 + 0.0116559i
311311 −15.4107 −0.873860 −0.436930 0.899495i 0.643934π-0.643934\pi
−0.436930 + 0.899495i 0.643934π0.643934\pi
312312 1.36333 2.13086i 0.0771832 0.120636i
313313 −8.49688 −0.480272 −0.240136 0.970739i 0.577192π-0.577192\pi
−0.240136 + 0.970739i 0.577192π0.577192\pi
314314 −20.9823 −1.18410
315315 0 0
316316 −5.00720 −0.281677
317317 −14.1052 −0.792229 −0.396115 0.918201i 0.629642π-0.629642\pi
−0.396115 + 0.918201i 0.629642π0.629642\pi
318318 21.5167 + 0.981271i 1.20660 + 0.0550270i
319319 −32.7381 −1.83298
320320 −0.230252 + 0.398809i −0.0128715 + 0.0222941i
321321 7.26303 11.3520i 0.405383 0.633607i
322322 0 0
323323 15.1373 0.842264
324324 −3.01245 8.48087i −0.167359 0.471159i
325325 3.49640 6.05594i 0.193945 0.335923i
326326 −11.5182 19.9501i −0.637933 1.10493i
327327 −13.0021 0.592963i −0.719020 0.0327909i
328328 0.472958 + 0.819187i 0.0261147 + 0.0452320i
329329 0 0
330330 −1.33842 2.58331i −0.0736776 0.142206i
331331 27.5438 1.51394 0.756971 0.653448i 0.226678π-0.226678\pi
0.756971 + 0.653448i 0.226678π0.226678\pi
332332 −3.32383 + 5.75705i −0.182419 + 0.315959i
333333 27.2111 + 2.48710i 1.49116 + 0.136292i
334334 5.31498 + 9.20581i 0.290823 + 0.503720i
335335 0.534239 0.925330i 0.0291886 0.0505562i
336336 0 0
337337 0.748440 + 1.29634i 0.0407701 + 0.0706159i 0.885690 0.464276i 0.153686π-0.153686\pi
−0.844920 + 0.534892i 0.820352π0.820352\pi
338338 5.43346 9.41103i 0.295541 0.511893i
339339 −5.65798 + 8.84334i −0.307299 + 0.480304i
340340 0.859728 + 1.48909i 0.0466253 + 0.0807574i
341341 0.938524 + 1.62557i 0.0508239 + 0.0880296i
342342 −12.1118 1.10702i −0.654929 0.0598607i
343343 0 0
344344 4.66372 8.07779i 0.251451 0.435525i
345345 0.487068 0.761280i 0.0262229 0.0409859i
346346 −2.93872 −0.157986
347347 −18.2881 −0.981758 −0.490879 0.871228i 0.663324π-0.663324\pi
−0.490879 + 0.871228i 0.663324π0.663324\pi
348348 −15.5292 0.708209i −0.832451 0.0379640i
349349 3.90136 6.75735i 0.208835 0.361713i −0.742513 0.669832i 0.766366π-0.766366\pi
0.951348 + 0.308119i 0.0996995π0.0996995\pi
350350 0 0
351351 2.86333 + 7.02811i 0.152833 + 0.375133i
352352 1.82383 + 3.15897i 0.0972106 + 0.168374i
353353 13.4626 + 23.3180i 0.716544 + 1.24109i 0.962361 + 0.271774i 0.0876105π0.0876105\pi
−0.245817 + 0.969316i 0.579056π0.579056\pi
354354 10.2755 + 19.8329i 0.546136 + 1.05411i
355355 −0.386770 + 0.669906i −0.0205276 + 0.0355549i
356356 1.36333 + 2.36135i 0.0722562 + 0.125151i
357357 0 0
358358 −4.58113 + 7.93474i −0.242120 + 0.419364i
359359 −3.13161 5.42411i −0.165280 0.286274i 0.771475 0.636260i 0.219519π-0.219519\pi
−0.936755 + 0.349987i 0.886186π0.886186\pi
360360 −0.578990 1.25433i −0.0305155 0.0661092i
361361 1.28220 2.22084i 0.0674842 0.116886i
362362 −22.4284 −1.17881
363363 −3.98901 0.181919i −0.209369 0.00954827i
364364 0 0
365365 3.04883 + 5.28073i 0.159583 + 0.276406i
366366 −9.62782 18.5828i −0.503254 0.971339i
367367 14.6367 + 25.3515i 0.764028 + 1.32334i 0.940759 + 0.339076i 0.110114π0.110114\pi
−0.176731 + 0.984259i 0.556552π0.556552\pi
368368 −0.566537 + 0.981271i −0.0295328 + 0.0511523i
369369 −2.82597 0.258294i −0.147114 0.0134462i
370370 4.19436 0.218054
371371 0 0
372372 0.410019 + 0.791385i 0.0212585 + 0.0410314i
373373 −8.92986 + 15.4670i −0.462371 + 0.800850i −0.999079 0.0429184i 0.986334π-0.986334\pi
0.536708 + 0.843768i 0.319668π0.319668\pi
374374 13.6198 0.704265
375375 −3.59144 6.93190i −0.185461 0.357962i
376376 −2.32743 −0.120028
377377 13.1082 0.675105
378378 0 0
379379 −22.4255 −1.15192 −0.575960 0.817478i 0.695371π-0.695371\pi
−0.575960 + 0.817478i 0.695371π0.695371\pi
380380 −1.86693 −0.0957713
381381 7.01965 + 13.5487i 0.359628 + 0.694123i
382382 2.48968 0.127383
383383 −7.07014 + 12.2458i −0.361267 + 0.625733i −0.988170 0.153365i 0.950989π-0.950989\pi
0.626903 + 0.779098i 0.284322π0.284322\pi
384384 0.796790 + 1.53790i 0.0406610 + 0.0784805i
385385 0 0
386386 4.48968 0.228519
387387 11.7273 + 25.4063i 0.596134 + 1.29147i
388388 5.59358 9.68836i 0.283971 0.491852i
389389 11.5651 + 20.0313i 0.586373 + 1.01563i 0.994703 + 0.102793i 0.0327779π0.0327779\pi
−0.408330 + 0.912834i 0.633889π0.633889\pi
390390 0.535897 + 1.03434i 0.0271362 + 0.0523760i
391391 2.11537 + 3.66392i 0.106979 + 0.185292i
392392 0 0
393393 36.5729 + 1.66791i 1.84486 + 0.0841350i
394394 12.7339 0.641522
395395 1.15292 1.99691i 0.0580097 0.100476i
396396 −10.8976 0.996040i −0.547623 0.0500529i
397397 5.13307 + 8.89075i 0.257622 + 0.446214i 0.965604 0.260016i 0.0837279π-0.0837279\pi
−0.707983 + 0.706230i 0.750395π0.750395\pi
398398 1.47296 2.55124i 0.0738327 0.127882i
399399 0 0
400400 2.39397 + 4.14647i 0.119698 + 0.207324i
401401 −17.0167 + 29.4738i −0.849775 + 1.47185i 0.0316345 + 0.999500i 0.489929π0.489929\pi
−0.881409 + 0.472353i 0.843405π0.843405\pi
402402 −1.84874 3.56828i −0.0922067 0.177970i
403403 −0.375780 0.650870i −0.0187189 0.0324221i
404404 6.87792 + 11.9129i 0.342189 + 0.592689i
405405 4.07587 + 0.751347i 0.202532 + 0.0373348i
406406 0 0
407407 16.6118 28.7724i 0.823415 1.42620i
408408 6.46050 + 0.294632i 0.319843 + 0.0145864i
409409 3.48968 0.172554 0.0862769 0.996271i 0.472503π-0.472503\pi
0.0862769 + 0.996271i 0.472503π0.472503\pi
410410 −0.435599 −0.0215127
411411 −4.11323 + 6.42892i −0.202891 + 0.317115i
412412 5.58113 9.66679i 0.274962 0.476249i
413413 0 0
414414 −1.42461 3.08629i −0.0700157 0.151683i
415415 −1.53064 2.65115i −0.0751362 0.130140i
416416 −0.730252 1.26483i −0.0358036 0.0620136i
417417 −1.89017 + 2.95431i −0.0925622 + 0.144673i
418418 −7.39397 + 12.8067i −0.361651 + 0.626398i
419419 −14.4897 25.0969i −0.707867 1.22606i −0.965647 0.259858i 0.916324π-0.916324\pi
0.257779 0.966204i 0.417009π-0.417009\pi
420420 0 0
421421 −1.06128 + 1.83819i −0.0517237 + 0.0895881i −0.890728 0.454537i 0.849805π-0.849805\pi
0.839004 + 0.544125i 0.183138π0.183138\pi
422422 −0.608168 1.05338i −0.0296052 0.0512777i
423423 4.02704 5.70397i 0.195801 0.277337i
424424 6.21780 10.7695i 0.301963 0.523015i
425425 17.8774 0.867183
426426 1.33842 + 2.58331i 0.0648467 + 0.125162i
427427 0 0
428428 −3.89037 6.73832i −0.188048 0.325709i
429429 9.21780 + 0.420378i 0.445040 + 0.0202960i
430430 2.14766 + 3.71986i 0.103570 + 0.179388i
431431 10.9356 18.9410i 0.526749 0.912356i −0.472765 0.881189i 0.656744π-0.656744\pi
0.999514 0.0311679i 0.00992265π-0.00992265\pi
432432 −5.14766 0.708209i −0.247667 0.0340737i
433433 13.0512 0.627199 0.313599 0.949555i 0.398465π-0.398465\pi
0.313599 + 0.949555i 0.398465π0.398465\pi
434434 0 0
435435 3.85807 6.03011i 0.184980 0.289122i
436436 −3.75729 + 6.50783i −0.179942 + 0.311668i
437437 −4.59358 −0.219741
438438 22.9107 + 1.04484i 1.09472 + 0.0499245i
439439 −4.86400 −0.232146 −0.116073 0.993241i 0.537031π-0.537031\pi
−0.116073 + 0.993241i 0.537031π0.537031\pi
440440 −1.67977 −0.0800797
441441 0 0
442442 −5.45331 −0.259387
443443 −11.5395 −0.548258 −0.274129 0.961693i 0.588390π-0.588390\pi
−0.274129 + 0.961693i 0.588390π0.588390\pi
444444 8.50214 13.2887i 0.403494 0.630654i
445445 −1.25564 −0.0595229
446446 0.445916 0.772349i 0.0211147 0.0365718i
447447 15.8530 + 0.722977i 0.749822 + 0.0341957i
448448 0 0
449449 −26.4251 −1.24708 −0.623538 0.781793i 0.714306π-0.714306\pi
−0.623538 + 0.781793i 0.714306π0.714306\pi
450450 −14.3042 1.30740i −0.674306 0.0616317i
451451 −1.72519 + 2.98812i −0.0812361 + 0.140705i
452452 3.03064 + 5.24922i 0.142549 + 0.246903i
453453 −0.0969833 + 0.151584i −0.00455667 + 0.00712201i
454454 −7.32597 12.6889i −0.343825 0.595522i
455455 0 0
456456 −3.78434 + 5.91486i −0.177218 + 0.276989i
457457 −3.73812 −0.174862 −0.0874310 0.996171i 0.527866π-0.527866\pi
−0.0874310 + 0.996171i 0.527866π0.527866\pi
458458 −4.78794 + 8.29295i −0.223726 + 0.387504i
459459 −11.9004 + 15.3234i −0.555462 + 0.715233i
460460 −0.260893 0.451880i −0.0121642 0.0210690i
461461 7.90496 13.6918i 0.368171 0.637690i −0.621109 0.783724i 0.713318π-0.713318\pi
0.989280 + 0.146034i 0.0466509π0.0466509\pi
462462 0 0
463463 19.1965 + 33.2493i 0.892137 + 1.54523i 0.837309 + 0.546730i 0.184128π0.184128\pi
0.0548278 + 0.998496i 0.482539π0.482539\pi
464464 −4.48755 + 7.77266i −0.208329 + 0.360837i
465465 −0.410019 0.0186989i −0.0190142 0.000867143i
466466 7.21420 + 12.4954i 0.334191 + 0.578836i
467467 −3.15652 5.46725i −0.146066 0.252994i 0.783704 0.621134i 0.213328π-0.213328\pi
−0.929770 + 0.368140i 0.879995π0.879995\pi
468468 4.36333 + 0.398809i 0.201695 + 0.0184349i
469469 0 0
470470 0.535897 0.928200i 0.0247191 0.0428147i
471471 −16.7185 32.2686i −0.770347 1.48686i
472472 12.8961 0.593591
473473 34.0233 1.56439
474474 −3.98968 7.70055i −0.183252 0.353698i
475475 −9.70535 + 16.8102i −0.445312 + 0.771303i
476476 0 0
477477 15.6352 + 33.8724i 0.715887 + 1.55091i
478478 −9.15486 15.8567i −0.418734 0.725268i
479479 −10.2068 17.6787i −0.466361 0.807761i 0.532901 0.846178i 0.321102π-0.321102\pi
−0.999262 + 0.0384168i 0.987769π0.987769\pi
480480 −0.796790 0.0363376i −0.0363683 0.00165858i
481481 −6.65126 + 11.5203i −0.303271 + 0.525282i
482482 0.0466924 + 0.0808735i 0.00212678 + 0.00368369i
483483 0 0
484484 −1.15272 + 1.99658i −0.0523966 + 0.0907535i
485485 2.57587 + 4.46154i 0.116964 + 0.202588i
486486 10.6424 11.3903i 0.482749 0.516675i
487487 6.18190 10.7074i 0.280129 0.485197i −0.691287 0.722580i 0.742956π-0.742956\pi
0.971416 + 0.237383i 0.0762895π0.0762895\pi
488488 −12.0833 −0.546984
489489 21.5036 33.6098i 0.972426 1.51989i
490490 0 0
491491 0.207004 + 0.358541i 0.00934194 + 0.0161807i 0.870659 0.491888i 0.163693π-0.163693\pi
−0.861317 + 0.508069i 0.830360π0.830360\pi
492492 −0.882977 + 1.38008i −0.0398077 + 0.0622188i
493493 16.7558 + 29.0220i 0.754645 + 1.30708i
494494 2.96050 5.12774i 0.133199 0.230708i
495495 2.90642 4.11671i 0.130634 0.185032i
496496 0.514589 0.0231057
497497 0 0
498498 −11.5021 0.524555i −0.515423 0.0235059i
499499 0.461967 0.800151i 0.0206805 0.0358197i −0.855500 0.517803i 0.826750π-0.826750\pi
0.876180 + 0.481983i 0.160083π0.160083\pi
500500 −4.50739 −0.201577
501501 −9.92267 + 15.5090i −0.443312 + 0.692890i
502502 18.2733 0.815579
503503 23.8142 1.06182 0.530911 0.847428i 0.321850π-0.321850\pi
0.530911 + 0.847428i 0.321850π0.321850\pi
504504 0 0
505505 −6.33463 −0.281887
506506 −4.13307 −0.183738
507507 18.8025 + 0.857490i 0.835049 + 0.0380825i
508508 8.80992 0.390877
509509 −15.3171 + 26.5300i −0.678919 + 1.17592i 0.296388 + 0.955068i 0.404218π0.404218\pi
−0.975307 + 0.220855i 0.929115π0.929115\pi
510510 −1.60505 + 2.50867i −0.0710728 + 0.111086i
511511 0 0
512512 1.00000 0.0441942
513513 −7.94805 19.5087i −0.350915 0.861330i
514514 −10.5256 + 18.2308i −0.464263 + 0.804128i
515515 2.57014 + 4.45161i 0.113254 + 0.196161i
516516 16.1388 + 0.736011i 0.710471 + 0.0324011i
517517 −4.24484 7.35228i −0.186688 0.323353i
518518 0 0
519519 −2.34154 4.51945i −0.102782 0.198382i
520520 0.672570 0.0294941
521521 13.4518 23.2993i 0.589336 1.02076i −0.404984 0.914324i 0.632723π-0.632723\pi
0.994320 0.106436i 0.0339439π-0.0339439\pi
522522 −11.2843 24.4466i −0.493902 1.07000i
523523 7.85301 + 13.6018i 0.343388 + 0.594766i 0.985060 0.172214i 0.0550920π-0.0550920\pi
−0.641671 + 0.766980i 0.721759π0.721759\pi
524524 10.5687 18.3055i 0.461695 0.799679i
525525 0 0
526526 2.58259 + 4.47318i 0.112606 + 0.195040i
527527 0.960699 1.66398i 0.0418487 0.0724841i
528528 −3.40496 + 5.32190i −0.148182 + 0.231606i
529529 10.8581 + 18.8067i 0.472090 + 0.817684i
530530 2.86333 + 4.95943i 0.124375 + 0.215424i
531531 −22.3135 + 31.6053i −0.968324 + 1.37155i
532532 0 0
533533 0.690757 1.19643i 0.0299200 0.0518230i
534534 −2.54523 + 3.97816i −0.110143 + 0.172152i
535535 3.58307 0.154910
536536 −2.32023 −0.100219
537537 −15.8530 0.722977i −0.684108 0.0311988i
538538 −8.42840 + 14.5984i −0.363374 + 0.629383i
539539 0 0
540540 1.46770 1.88987i 0.0631598 0.0813269i
541541 −2.05934 3.56688i −0.0885379 0.153352i 0.818355 0.574713i 0.194886π-0.194886\pi
−0.906893 + 0.421360i 0.861553π0.861553\pi
542542 −12.5562 21.7480i −0.539336 0.934157i
543543 −17.8707 34.4926i −0.766906 1.48022i
544544 1.86693 3.23361i 0.0800438 0.138640i
545545 −1.73025 2.99689i −0.0741159 0.128372i
546546 0 0
547547 −11.8602 + 20.5425i −0.507106 + 0.878333i 0.492860 + 0.870108i 0.335951π0.335951\pi
−0.999966 + 0.00822465i 0.997382π0.997382\pi
548548 2.20321 + 3.81607i 0.0941165 + 0.163015i
549549 20.9071 29.6132i 0.892293 1.26386i
550550 −8.73239 + 15.1249i −0.372350 + 0.644930i
551551 −36.3858 −1.55009
552552 −1.96050 0.0894089i −0.0834446 0.00380550i
553553 0 0
554554 −1.69076 2.92848i −0.0718334 0.124419i
555555 3.34202 + 6.45049i 0.141861 + 0.273808i
556556 1.01245 + 1.75362i 0.0429376 + 0.0743701i
557557 −21.0313 + 36.4273i −0.891125 + 1.54347i −0.0525975 + 0.998616i 0.516750π0.516750\pi
−0.838528 + 0.544859i 0.816583π0.816583\pi
558558 −0.890369 + 1.26113i −0.0376923 + 0.0533881i
559559 −13.6228 −0.576181
560560 0 0
561561 10.8521 + 20.9459i 0.458178 + 0.884336i
562562 −10.1388 + 17.5609i −0.427680 + 0.740763i
563563 −11.8243 −0.498335 −0.249168 0.968460i 0.580157π-0.580157\pi
−0.249168 + 0.968460i 0.580157π0.580157\pi
564564 −1.85447 3.57935i −0.0780874 0.150718i
565565 −2.79125 −0.117429
566566 −17.3494 −0.729250
567567 0 0
568568 1.67977 0.0704815
569569 14.2016 0.595360 0.297680 0.954666i 0.403787π-0.403787\pi
0.297680 + 0.954666i 0.403787π0.403787\pi
570570 −1.48755 2.87114i −0.0623065 0.120259i
571571 11.9574 0.500401 0.250200 0.968194i 0.419503π-0.419503\pi
0.250200 + 0.968194i 0.419503π0.419503\pi
572572 2.66372 4.61369i 0.111376 0.192908i
573573 1.98375 + 3.82888i 0.0828725 + 0.159954i
574574 0 0
575575 −5.42509 −0.226242
576576 −1.73025 + 2.45076i −0.0720939 + 0.102115i
577577 −21.3135 + 36.9161i −0.887293 + 1.53684i −0.0442307 + 0.999021i 0.514084π0.514084\pi
−0.843062 + 0.537816i 0.819250π0.819250\pi
578578 1.52918 + 2.64861i 0.0636054 + 0.110168i
579579 3.57733 + 6.90467i 0.148669 + 0.286948i
580580 −2.06654 3.57935i −0.0858083 0.148624i
581581 0 0
582582 19.3566 + 0.882759i 0.802357 + 0.0365915i
583583 45.3609 1.87866
584584 6.62062 11.4673i 0.273963 0.474518i
585585 −1.16372 + 1.64831i −0.0481137 + 0.0681491i
586586 4.93560 + 8.54871i 0.203888 + 0.353144i
587587 −20.5328 + 35.5638i −0.847478 + 1.46788i 0.0359730 + 0.999353i 0.488547π0.488547\pi
−0.883451 + 0.468523i 0.844786π0.844786\pi
588588 0 0
589589 1.04309 + 1.80669i 0.0429799 + 0.0744434i
590590 −2.96936 + 5.14308i −0.122247 + 0.211737i
591591 10.1462 + 19.5833i 0.417359 + 0.805551i
592592 −4.55408 7.88791i −0.187172 0.324191i
593593 −16.1008 27.8874i −0.661180 1.14520i −0.980306 0.197485i 0.936723π-0.936723\pi
0.319126 0.947712i 0.396611π-0.396611\pi
594594 −7.15126 17.5530i −0.293420 0.720207i
595595 0 0
596596 4.58113 7.93474i 0.187650 0.325020i
597597 5.09718 + 0.232457i 0.208614 + 0.00951383i
598598 1.65486 0.0676723
599599 19.0718 0.779252 0.389626 0.920973i 0.372604π-0.372604\pi
0.389626 + 0.920973i 0.372604π0.372604\pi
600600 −4.46936 + 6.98554i −0.182461 + 0.285184i
601601 −4.27188 + 7.39912i −0.174254 + 0.301816i −0.939903 0.341442i 0.889085π-0.889085\pi
0.765649 + 0.643259i 0.222418π0.222418\pi
602602 0 0
603603 4.01459 5.68634i 0.163487 0.231565i
604604 0.0519482 + 0.0899768i 0.00211374 + 0.00366111i
605605 −0.530835 0.919434i −0.0215815 0.0373803i
606606 −12.8406 + 20.0696i −0.521612 + 0.815272i
607607 19.0057 32.9189i 0.771419 1.33614i −0.165366 0.986232i 0.552881π-0.552881\pi
0.936785 0.349905i 0.113786π-0.113786\pi
608608 2.02704 + 3.51094i 0.0822074 + 0.142387i
609609 0 0
610610 2.78220 4.81891i 0.112648 0.195112i
611611 1.69961 + 2.94381i 0.0687589 + 0.119094i
612612 4.69455 + 10.1703i 0.189766 + 0.411112i
613613 11.3296 19.6234i 0.457597 0.792581i −0.541237 0.840870i 0.682044π-0.682044\pi
0.998833 + 0.0482894i 0.0153770π0.0153770\pi
614614 −7.78794 −0.314295
615615 −0.347081 0.669906i −0.0139956 0.0270132i
616616 0 0
617617 −10.1388 17.5609i −0.408173 0.706977i 0.586512 0.809941i 0.300501π-0.300501\pi
−0.994685 + 0.102964i 0.967167π0.967167\pi
618618 19.3135 + 0.880794i 0.776904 + 0.0354307i
619619 1.03064 + 1.78512i 0.0414249 + 0.0717501i 0.885994 0.463696i 0.153477π-0.153477\pi
−0.844570 + 0.535446i 0.820144π0.820144\pi
620620 −0.118485 + 0.205223i −0.00475849 + 0.00824194i
621621 3.61129 4.65003i 0.144916 0.186599i
622622 −15.4107 −0.617912
623623 0 0
624624 1.36333 2.13086i 0.0545768 0.0853027i
625625 −10.9320 + 18.9348i −0.437280 + 0.757391i
626626 −8.49688 −0.339604
627627 −25.5869 1.16689i −1.02184 0.0466011i
628628 −20.9823 −0.837285
629629 −34.0085 −1.35601
630630 0 0
631631 1.63715 0.0651740 0.0325870 0.999469i 0.489625π-0.489625\pi
0.0325870 + 0.999469i 0.489625π0.489625\pi
632632 −5.00720 −0.199176
633633 1.13541 1.77462i 0.0451283 0.0705349i
634634 −14.1052 −0.560191
635635 −2.02850 + 3.51347i −0.0804988 + 0.139428i
636636 21.5167 + 0.981271i 0.853194 + 0.0389099i
637637 0 0
638638 −32.7381 −1.29611
639639 −2.90642 + 4.11671i −0.114976 + 0.162854i
640640 −0.230252 + 0.398809i −0.00910153 + 0.0157643i
641641 −10.9662 18.9941i −0.433140 0.750221i 0.564001 0.825774i 0.309261π-0.309261\pi
−0.997142 + 0.0755526i 0.975928π0.975928\pi
642642 7.26303 11.3520i 0.286649 0.448028i
643643 14.1819 + 24.5638i 0.559280 + 0.968701i 0.997557 + 0.0698609i 0.0222555π0.0222555\pi
−0.438277 + 0.898840i 0.644411π0.644411\pi
644644 0 0
645645 −4.00953 + 6.26683i −0.157875 + 0.246756i
646646 15.1373 0.595571
647647 −17.3904 + 30.1210i −0.683686 + 1.18418i 0.290162 + 0.956978i 0.406291π0.406291\pi
−0.973848 + 0.227201i 0.927042π0.927042\pi
648648 −3.01245 8.48087i −0.118340 0.333160i
649649 23.5203 + 40.7384i 0.923253 + 1.59912i
650650 3.49640 6.05594i 0.137140 0.237534i
651651 0 0
652652 −11.5182 19.9501i −0.451087 0.781306i
653653 1.59931 2.77009i 0.0625860 0.108402i −0.833035 0.553221i 0.813399π-0.813399\pi
0.895621 + 0.444819i 0.146732π0.146732\pi
654654 −13.0021 0.592963i −0.508424 0.0231867i
655655 4.86693 + 8.42976i 0.190167 + 0.329378i
656656 0.472958 + 0.819187i 0.0184659 + 0.0319839i
657657 16.6481 + 36.0668i 0.649506 + 1.40710i
658658 0 0
659659 5.30418 9.18711i 0.206622 0.357879i −0.744027 0.668150i 0.767086π-0.767086\pi
0.950648 + 0.310271i 0.100420π0.100420\pi
660660 −1.33842 2.58331i −0.0520980 0.100555i
661661 −10.1301 −0.394017 −0.197009 0.980402i 0.563123π-0.563123\pi
−0.197009 + 0.980402i 0.563123π0.563123\pi
662662 27.5438 1.07052
663663 −4.34514 8.38662i −0.168751 0.325709i
664664 −3.32383 + 5.75705i −0.128990 + 0.223417i
665665 0 0
666666 27.2111 + 2.48710i 1.05441 + 0.0963731i
667667 −5.08472 8.80700i −0.196881 0.341008i
668668 5.31498 + 9.20581i 0.205643 + 0.356184i
669669 1.54309 + 0.0703729i 0.0596595 + 0.00272077i
670670 0.534239 0.925330i 0.0206395 0.0357486i
671671 −22.0378 38.1707i −0.850761 1.47356i
672672 0 0
673673 1.60817 2.78543i 0.0619903 0.107370i −0.833365 0.552724i 0.813589π-0.813589\pi
0.895355 + 0.445353i 0.146922π0.146922\pi
674674 0.748440 + 1.29634i 0.0288288 + 0.0499330i
675675 −9.38677 23.0401i −0.361297 0.886813i
676676 5.43346 9.41103i 0.208979 0.361963i
677677 29.3638 1.12854 0.564271 0.825589i 0.309157π-0.309157\pi
0.564271 + 0.825589i 0.309157π0.309157\pi
678678 −5.65798 + 8.84334i −0.217293 + 0.339626i
679679 0 0
680680 0.859728 + 1.48909i 0.0329691 + 0.0571041i
681681 13.6770 21.3770i 0.524105 0.819169i
682682 0.938524 + 1.62557i 0.0359379 + 0.0622463i
683683 12.6278 21.8720i 0.483190 0.836910i −0.516624 0.856213i 0.672811π-0.672811\pi
0.999814 + 0.0193029i 0.00614468π0.00614468\pi
684684 −12.1118 1.10702i −0.463105 0.0423279i
685685 −2.02918 −0.0775309
686686 0 0
687687 −16.5687 0.755615i −0.632134 0.0288285i
688688 4.66372 8.07779i 0.177802 0.307963i
689689 −18.1623 −0.691927
690690 0.487068 0.761280i 0.0185424 0.0289814i
691691 15.3638 0.584467 0.292233 0.956347i 0.405602π-0.405602\pi
0.292233 + 0.956347i 0.405602π0.405602\pi
692692 −2.93872 −0.111713
693693 0 0
694694 −18.2881 −0.694208
695695 −0.932479 −0.0353709
696696 −15.5292 0.708209i −0.588632 0.0268446i
697697 3.53191 0.133781
698698 3.90136 6.75735i 0.147669 0.255770i
699699 −13.4684 + 21.0509i −0.509421 + 0.796217i
700700 0 0
701701 −13.3700 −0.504980 −0.252490 0.967600i 0.581249π-0.581249\pi
−0.252490 + 0.967600i 0.581249π0.581249\pi
702702 2.86333 + 7.02811i 0.108069 + 0.265259i
703703 18.4626 31.9782i 0.696332 1.20608i
704704 1.82383 + 3.15897i 0.0687382 + 0.119058i
705705 1.85447 + 0.0845733i 0.0698435 + 0.00318522i
706706 13.4626 + 23.3180i 0.506673 + 0.877584i
707707 0 0
708708 10.2755 + 19.8329i 0.386176 + 0.745365i
709709 −1.12588 −0.0422832 −0.0211416 0.999776i 0.506730π-0.506730\pi
−0.0211416 + 0.999776i 0.506730π0.506730\pi
710710 −0.386770 + 0.669906i −0.0145152 + 0.0251411i
711711 8.66372 12.2714i 0.324915 0.460215i
712712 1.36333 + 2.36135i 0.0510928 + 0.0884954i
713713 −0.291534 + 0.504951i −0.0109180 + 0.0189106i
714714 0 0
715715 1.22665 + 2.12463i 0.0458743 + 0.0794565i
716716 −4.58113 + 7.93474i −0.171205 + 0.296535i
717717 17.0914 26.7137i 0.638292 0.997640i
718718 −3.13161 5.42411i −0.116871 0.202426i
719719 −9.13667 15.8252i −0.340740 0.590180i 0.643830 0.765169i 0.277344π-0.277344\pi
−0.984570 + 0.174989i 0.944011π0.944011\pi
720720 −0.578990 1.25433i −0.0215777 0.0467463i
721721 0 0
722722 1.28220 2.22084i 0.0477186 0.0826510i
723723 −0.0871712 + 0.136247i −0.00324193 + 0.00506709i
724724 −22.4284 −0.833545
725725 −42.9722 −1.59595
726726 −3.98901 0.181919i −0.148046 0.00675165i
727727 14.8478 25.7171i 0.550673 0.953793i −0.447553 0.894257i 0.647705π-0.647705\pi
0.998226 0.0595359i 0.0189621π-0.0189621\pi
728728 0 0
729729 25.9969 + 7.29124i 0.962847 + 0.270046i
730730 3.04883 + 5.28073i 0.112842 + 0.195448i
731731 −17.4136 30.1613i −0.644066 1.11555i
732732 −9.62782 18.5828i −0.355854 0.686840i
733733 9.61390 16.6518i 0.355098 0.615047i −0.632037 0.774938i 0.717781π-0.717781\pi
0.987135 + 0.159891i 0.0511143π0.0511143\pi
734734 14.6367 + 25.3515i 0.540249 + 0.935740i
735735 0 0
736736 −0.566537 + 0.981271i −0.0208828 + 0.0361701i
737737 −4.23171 7.32955i −0.155877 0.269987i
738738 −2.82597 0.258294i −0.104025 0.00950793i
739739 −15.1336 + 26.2121i −0.556697 + 0.964227i 0.441073 + 0.897471i 0.354598π0.354598\pi
−0.997769 + 0.0667556i 0.978735π0.978735\pi
740740 4.19436 0.154188
741741 10.2448 + 0.467216i 0.376354 + 0.0171636i
742742 0 0
743743 −11.8815 20.5794i −0.435890 0.754984i 0.561477 0.827492i 0.310233π-0.310233\pi
−0.997368 + 0.0725076i 0.976900π0.976900\pi
744744 0.410019 + 0.791385i 0.0150320 + 0.0290136i
745745 2.10963 + 3.65399i 0.0772909 + 0.133872i
746746 −8.92986 + 15.4670i −0.326946 + 0.566286i
747747 −8.35807 18.1071i −0.305806 0.662503i
748748 13.6198 0.497990
749749 0 0
750750 −3.59144 6.93190i −0.131141 0.253117i
751751 −6.33415 + 10.9711i −0.231136 + 0.400340i −0.958143 0.286291i 0.907578π-0.907578\pi
0.727006 + 0.686631i 0.240911π0.240911\pi
752752 −2.32743 −0.0848727
753753 14.5600 + 28.1025i 0.530596 + 1.02411i
754754 13.1082 0.477371
755755 −0.0478448 −0.00174125
756756 0 0
757757 −29.0799 −1.05693 −0.528464 0.848955i 0.677232π-0.677232\pi
−0.528464 + 0.848955i 0.677232π0.677232\pi
758758 −22.4255 −0.814530
759759 −3.29319 6.35624i −0.119535 0.230717i
760760 −1.86693 −0.0677205
761761 14.6015 25.2905i 0.529302 0.916778i −0.470114 0.882606i 0.655787π-0.655787\pi
0.999416 0.0341724i 0.0108795π-0.0108795\pi
762762 7.01965 + 13.5487i 0.254295 + 0.490819i
763763 0 0
764764 2.48968 0.0900736
765765 −5.13696 0.469519i −0.185727 0.0169755i
766766 −7.07014 + 12.2458i −0.255454 + 0.442460i
767767 −9.41741 16.3114i −0.340043 0.588972i
768768 0.796790 + 1.53790i 0.0287517 + 0.0554941i
769769 −12.5869 21.8011i −0.453894 0.786167i 0.544730 0.838611i 0.316632π-0.316632\pi
−0.998624 + 0.0524443i 0.983299π0.983299\pi
770770 0 0
771771 −36.4238 1.66111i −1.31177 0.0598234i
772772 4.48968 0.161587
773773 0.752039 1.30257i 0.0270490 0.0468502i −0.852184 0.523242i 0.824722π-0.824722\pi
0.879233 + 0.476392i 0.158056π0.158056\pi
774774 11.7273 + 25.4063i 0.421530 + 0.913209i
775775 1.23191 + 2.13373i 0.0442515 + 0.0766458i
776776 5.59358 9.68836i 0.200798 0.347792i
777777 0 0
778778 11.5651 + 20.0313i 0.414628 + 0.718157i
779779 −1.91741 + 3.32105i −0.0686984 + 0.118989i
780780 0.535897 + 1.03434i 0.0191882 + 0.0370354i
781781 3.06361 + 5.30633i 0.109625 + 0.189875i
782782 2.11537 + 3.66392i 0.0756453 + 0.131022i
783783 28.6050 36.8329i 1.02226 1.31630i
784784 0 0
785785 4.83122 8.36792i 0.172434 0.298664i
786786 36.5729 + 1.66791i 1.30451 + 0.0594924i
787787 14.9531 0.533021 0.266510 0.963832i 0.414129π-0.414129\pi
0.266510 + 0.963832i 0.414129π0.414129\pi
788788 12.7339 0.453625
789789 −4.82150 + 7.53593i −0.171650 + 0.268286i
790790 1.15292 1.99691i 0.0410190 0.0710470i
791791 0 0
792792 −10.8976 0.996040i −0.387228 0.0353927i
793793 8.82383 + 15.2833i 0.313343 + 0.542727i
794794 5.13307 + 8.89075i 0.182166 + 0.315521i
795795 −5.34562 + 8.35512i −0.189590 + 0.296326i
796796 1.47296 2.55124i 0.0522076 0.0904262i
797797 4.56294 + 7.90324i 0.161628 + 0.279947i 0.935453 0.353452i 0.114992π-0.114992\pi
−0.773825 + 0.633400i 0.781659π0.781659\pi
798798 0 0
799799 −4.34514 + 7.52600i −0.153720 + 0.266251i
800800 2.39397 + 4.14647i 0.0846395 + 0.146600i
801801 −8.14601 0.744547i −0.287825 0.0263073i
802802 −17.0167 + 29.4738i −0.600881 + 1.04076i
803803 48.2996 1.70446
804804 −1.84874 3.56828i −0.0652000 0.125843i
805805 0 0
806806 −0.375780 0.650870i −0.0132363 0.0229259i
807807 −29.1665 1.33014i −1.02671 0.0468232i
808808 6.87792 + 11.9129i 0.241964 + 0.419094i
809809 17.7755 30.7880i 0.624953 1.08245i −0.363597 0.931556i 0.618452π-0.618452\pi
0.988550 0.150894i 0.0482151π-0.0482151\pi
810810 4.07587 + 0.751347i 0.143211 + 0.0263997i
811811 13.5070 0.474295 0.237148 0.971474i 0.423788π-0.423788\pi
0.237148 + 0.971474i 0.423788π0.423788\pi
812812 0 0
813813 23.4415 36.6388i 0.822130 1.28498i
814814 16.6118 28.7724i 0.582242 1.00847i
815815 10.6084 0.371595
816816 6.46050 + 0.294632i 0.226163 + 0.0103142i
817817 37.8142 1.32295
818818 3.48968 0.122014
819819 0 0
820820 −0.435599 −0.0152118
821821 21.6228 0.754639 0.377320 0.926083i 0.376846π-0.376846\pi
0.377320 + 0.926083i 0.376846π0.376846\pi
822822 −4.11323 + 6.42892i −0.143465 + 0.224234i
823823 −1.50700 −0.0525308 −0.0262654 0.999655i 0.508361π-0.508361\pi
−0.0262654 + 0.999655i 0.508361π0.508361\pi
824824 5.58113 9.66679i 0.194428 0.336759i
825825 −30.2185 1.37811i −1.05207 0.0479798i
826826 0 0
827827 23.3786 0.812953 0.406477 0.913661i 0.366757π-0.366757\pi
0.406477 + 0.913661i 0.366757π0.366757\pi
828828 −1.42461 3.08629i −0.0495086 0.107256i
829829 11.0095 19.0691i 0.382377 0.662296i −0.609025 0.793151i 0.708439π-0.708439\pi
0.991401 + 0.130855i 0.0417723π0.0417723\pi
830830 −1.53064 2.65115i −0.0531293 0.0920227i
831831 3.15652 4.93359i 0.109498 0.171144i
832832 −0.730252 1.26483i −0.0253169 0.0438502i
833833 0 0
834834 −1.89017 + 2.95431i −0.0654514 + 0.102300i
835835 −4.89515 −0.169404
836836 −7.39397 + 12.8067i −0.255726 + 0.442930i
837837 −2.64893 0.364437i −0.0915605 0.0125968i
838838 −14.4897 25.0969i −0.500538 0.866957i
839839 1.06507 1.84476i 0.0367705 0.0636883i −0.847055 0.531506i 0.821626π-0.821626\pi
0.883825 + 0.467818i 0.154960π0.154960\pi
840840 0 0
841841 −25.7762 44.6456i −0.888833 1.53950i
842842 −1.06128 + 1.83819i −0.0365742 + 0.0633483i
843843 −35.0854 1.60007i −1.20841 0.0551094i
844844 −0.608168 1.05338i −0.0209340 0.0362588i
845845 2.50214 + 4.33383i 0.0860761 + 0.149088i
846846 4.02704 5.70397i 0.138453 0.196107i
847847 0 0
848848 6.21780 10.7695i 0.213520 0.369828i
849849 −13.8238 26.6816i −0.474433 0.915710i
850850 17.8774 0.613191
851851 10.3202 0.353773
852852 1.33842 + 2.58331i 0.0458535 + 0.0885027i
853853 3.50146 6.06471i 0.119888 0.207652i −0.799835 0.600220i 0.795080π-0.795080\pi
0.919723 + 0.392568i 0.128413π0.128413\pi
854854 0 0
855855 3.23025 4.57539i 0.110472 0.156475i
856856 −3.89037 6.73832i −0.132970 0.230311i
857857 5.46410 + 9.46410i 0.186650 + 0.323288i 0.944131 0.329569i 0.106904π-0.106904\pi
−0.757481 + 0.652857i 0.773570π0.773570\pi
858858 9.21780 + 0.420378i 0.314690 + 0.0143515i
859859 −6.95379 + 12.0443i −0.237260 + 0.410947i −0.959927 0.280250i 0.909583π-0.909583\pi
0.722667 + 0.691196i 0.242916π0.242916\pi
860860 2.14766 + 3.71986i 0.0732347 + 0.126846i
861861 0 0
862862 10.9356 18.9410i 0.372468 0.645133i
863863 −18.4231 31.9098i −0.627131 1.08622i −0.988125 0.153655i 0.950896π-0.950896\pi
0.360993 0.932568i 0.382438π-0.382438\pi
864864 −5.14766 0.708209i −0.175127 0.0240938i
865865 0.676647 1.17199i 0.0230067 0.0398488i
866866 13.0512 0.443496
867867 −2.85486 + 4.46211i −0.0969562 + 0.151541i
868868 0 0
869869 −9.13229 15.8176i −0.309792 0.536575i
870870 3.85807 6.03011i 0.130801 0.204440i
871871 1.69436 + 2.93471i 0.0574111 + 0.0994389i
872872 −3.75729 + 6.50783i −0.127238 + 0.220383i
873873 14.0656 + 30.4718i 0.476047 + 1.03132i
874874 −4.59358 −0.155380
875875 0 0
876876 22.9107 + 1.04484i 0.774081 + 0.0353020i
877877 5.17977 8.97162i 0.174908 0.302950i −0.765221 0.643767i 0.777370π-0.777370\pi
0.940130 + 0.340817i 0.110704π0.110704\pi
878878 −4.86400 −0.164152
879879 −9.21440 + 14.4020i −0.310794 + 0.485766i
880880 −1.67977 −0.0566249
881881 −9.34806 −0.314944 −0.157472 0.987523i 0.550334π-0.550334\pi
−0.157472 + 0.987523i 0.550334π0.550334\pi
882882 0 0
883883 2.29494 0.0772308 0.0386154 0.999254i 0.487705π-0.487705\pi
0.0386154 + 0.999254i 0.487705π0.487705\pi
884884 −5.45331 −0.183415
885885 −10.2755 0.468614i −0.345407 0.0157523i
886886 −11.5395 −0.387677
887887 −13.8363 + 23.9651i −0.464577 + 0.804671i −0.999182 0.0404309i 0.987127π-0.987127\pi
0.534605 + 0.845102i 0.320460π0.320460\pi
888888 8.50214 13.2887i 0.285313 0.445940i
889889 0 0
890890 −1.25564 −0.0420891
891891 21.2966 24.9839i 0.713463 0.836993i
892892 0.445916 0.772349i 0.0149304 0.0258602i
893893 −4.71780 8.17147i −0.157875 0.273448i
894894 15.8530 + 0.722977i 0.530204 + 0.0241800i
895895 −2.10963 3.65399i −0.0705172 0.122139i
896896 0 0
897897 1.31858 + 2.54500i 0.0440260 + 0.0849752i
898898 −26.4251 −0.881817
899899 −2.30924 + 3.99973i −0.0770176 + 0.133398i
900900 −14.3042 1.30740i −0.476806 0.0435802i
901901 −23.2163 40.2119i −0.773448 1.33965i
902902 −1.72519 + 2.98812i −0.0574426 + 0.0994935i
903903 0 0
904904 3.03064 + 5.24922i 0.100798 + 0.174587i
905905 5.16419 8.94465i 0.171664 0.297330i
906906 −0.0969833 + 0.151584i −0.00322206 + 0.00503602i
907907 1.46576 + 2.53877i 0.0486698 + 0.0842985i 0.889334 0.457258i 0.151168π-0.151168\pi
−0.840664 + 0.541557i 0.817835π0.817835\pi
908908 −7.32597 12.6889i −0.243121 0.421098i
909909 −41.0962 3.75620i −1.36307 0.124585i
910910 0 0
911911 15.3171 26.5300i 0.507479 0.878979i −0.492484 0.870322i 0.663911π-0.663911\pi
0.999963 0.00865719i 0.00275570π-0.00275570\pi
912912 −3.78434 + 5.91486i −0.125312 + 0.195861i
913913 −24.2484 −0.802506
914914 −3.73812 −0.123646
915915 9.62782 + 0.439077i 0.318286 + 0.0145154i
916916 −4.78794 + 8.29295i −0.158198 + 0.274007i
917917 0 0
918918 −11.9004 + 15.3234i −0.392771 + 0.505746i
919919 13.1857 + 22.8383i 0.434956 + 0.753366i 0.997292 0.0735429i 0.0234306π-0.0234306\pi
−0.562336 + 0.826909i 0.690097π0.690097\pi
920920 −0.260893 0.451880i −0.00860139 0.0148980i
921921 −6.20535 11.9770i −0.204473 0.394657i
922922 7.90496 13.6918i 0.260336 0.450915i
923923 −1.22665 2.12463i −0.0403758 0.0699329i
924924 0 0
925925 21.8047 37.7668i 0.716933 1.24176i
926926 19.1965 + 33.2493i 0.630836 + 1.09264i
927927 14.0342 + 30.4040i 0.460945 + 0.998598i
928928 −4.48755 + 7.77266i −0.147311 + 0.255150i
929929 −17.8741 −0.586431 −0.293215 0.956046i 0.594725π-0.594725\pi
−0.293215 + 0.956046i 0.594725π0.594725\pi
930930 −0.410019 0.0186989i −0.0134451 0.000613163i
931931 0 0
932932 7.21420 + 12.4954i 0.236309 + 0.409299i
933933 −12.2791 23.7001i −0.401999 0.775905i
934934 −3.15652 5.46725i −0.103284 0.178894i
935935 −3.13600 + 5.43171i −0.102558 + 0.177636i
936936 4.36333 + 0.398809i 0.142620 + 0.0130355i
937937 −15.9134 −0.519869 −0.259934 0.965626i 0.583701π-0.583701\pi
−0.259934 + 0.965626i 0.583701π0.583701\pi
938938 0 0
939939 −6.77023 13.0673i −0.220938 0.426436i
940940 0.535897 0.928200i 0.0174790 0.0302745i
941941 16.2805 0.530731 0.265365 0.964148i 0.414507π-0.414507\pi
0.265365 + 0.964148i 0.414507π0.414507\pi
942942 −16.7185 32.2686i −0.544717 1.05137i
943943 −1.07179 −0.0349024
944944 12.8961 0.419732
945945 0 0
946946 34.0233 1.10619
947947 −28.5903 −0.929059 −0.464529 0.885558i 0.653776π-0.653776\pi
−0.464529 + 0.885558i 0.653776π0.653776\pi
948948 −3.98968 7.70055i −0.129579 0.250102i
949949 −19.3389 −0.627767
950950 −9.70535 + 16.8102i −0.314883 + 0.545393i
951951 −11.2389 21.6924i −0.364447 0.703424i
952952 0 0
953953 −29.3537 −0.950859 −0.475430 0.879754i 0.657707π-0.657707\pi
−0.475430 + 0.879754i 0.657707π0.657707\pi
954954 15.6352 + 33.8724i 0.506209 + 1.09666i
955955 −0.573256 + 0.992908i −0.0185501 + 0.0321297i
956956 −9.15486 15.8567i −0.296089 0.512842i
957957 −26.0854 50.3479i −0.843221 1.62751i
958958 −10.2068 17.6787i −0.329767 0.571173i
959959 0 0
960960 −0.796790 0.0363376i −0.0257163 0.00117279i
961961 −30.7352 −0.991458
962962 −6.65126 + 11.5203i −0.214445 + 0.371430i
963963 23.2453 + 2.12463i 0.749070 + 0.0684651i
964964 0.0466924 + 0.0808735i 0.00150386 + 0.00260476i
965965 −1.03376 + 1.79053i −0.0332779 + 0.0576391i
966966 0 0
967967 −4.69815 8.13743i −0.151082 0.261682i 0.780543 0.625102i 0.214943π-0.214943\pi
−0.931626 + 0.363419i 0.881609π0.881609\pi
968968 −1.15272 + 1.99658i −0.0370500 + 0.0641724i
969969 12.0613 + 23.2797i 0.387464 + 0.747851i
970970 2.57587 + 4.46154i 0.0827062 + 0.143251i
971971 −7.77335 13.4638i −0.249459 0.432075i 0.713917 0.700230i 0.246919π-0.246919\pi
−0.963376 + 0.268155i 0.913586π0.913586\pi
972972 10.6424 11.3903i 0.341355 0.365344i
973973 0 0
974974 6.18190 10.7074i 0.198081 0.343086i
975975 12.0993 + 0.551790i 0.387488 + 0.0176714i
976976 −12.0833 −0.386776
977977 −9.59785 −0.307062 −0.153531 0.988144i 0.549065π-0.549065\pi
−0.153531 + 0.988144i 0.549065π0.549065\pi
978978 21.5036 33.6098i 0.687609 1.07472i
979979 −4.97296 + 8.61342i −0.158936 + 0.275286i
980980 0 0
981981 −9.44805 20.4684i −0.301653 0.653506i
982982 0.207004 + 0.358541i 0.00660575 + 0.0114415i
983983 −23.4267 40.5763i −0.747197 1.29418i −0.949161 0.314790i 0.898066π-0.898066\pi
0.201964 0.979393i 0.435268π-0.435268\pi
984984 −0.882977 + 1.38008i −0.0281483 + 0.0439953i
985985 −2.93200 + 5.07837i −0.0934213 + 0.161810i
986986 16.7558 + 29.0220i 0.533614 + 0.924247i
987987 0 0
988988 2.96050 5.12774i 0.0941862 0.163135i
989989 5.28434 + 9.15274i 0.168032 + 0.291040i
990990 2.90642 4.11671i 0.0923721 0.130838i
991991 10.8260 18.7511i 0.343898 0.595649i −0.641255 0.767328i 0.721586π-0.721586\pi
0.985153 + 0.171679i 0.0549192π0.0549192\pi
992992 0.514589 0.0163382
993993 21.9466 + 42.3595i 0.696454 + 1.34424i
994994 0 0
995995 0.678304 + 1.17486i 0.0215037 + 0.0372455i
996996 −11.5021 0.524555i −0.364459 0.0166212i
997997 −28.6190 49.5695i −0.906372 1.56988i −0.819065 0.573700i 0.805507π-0.805507\pi
−0.0873064 0.996182i 0.527826π-0.527826\pi
998998 0.461967 0.800151i 0.0146233 0.0253283i
999999 17.8566 + 43.8295i 0.564958 + 1.38670i
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 882.2.e.p.655.2 6
3.2 odd 2 2646.2.e.o.2125.3 6
7.2 even 3 882.2.h.o.79.1 6
7.3 odd 6 882.2.f.l.295.2 6
7.4 even 3 882.2.f.m.295.2 6
7.5 odd 6 126.2.h.c.79.3 yes 6
7.6 odd 2 126.2.e.d.25.2 6
9.4 even 3 882.2.h.o.67.1 6
9.5 odd 6 2646.2.h.p.361.1 6
21.2 odd 6 2646.2.h.p.667.1 6
21.5 even 6 378.2.h.d.289.3 6
21.11 odd 6 2646.2.f.n.883.3 6
21.17 even 6 2646.2.f.o.883.1 6
21.20 even 2 378.2.e.c.235.1 6
28.19 even 6 1008.2.t.g.961.1 6
28.27 even 2 1008.2.q.h.529.2 6
63.4 even 3 882.2.f.m.589.2 6
63.5 even 6 378.2.e.c.37.1 6
63.11 odd 6 7938.2.a.bx.1.1 3
63.13 odd 6 126.2.h.c.67.3 yes 6
63.20 even 6 1134.2.g.n.487.1 6
63.23 odd 6 2646.2.e.o.1549.3 6
63.25 even 3 7938.2.a.by.1.3 3
63.31 odd 6 882.2.f.l.589.2 6
63.32 odd 6 2646.2.f.n.1765.3 6
63.34 odd 6 1134.2.g.k.487.3 6
63.38 even 6 7938.2.a.bu.1.3 3
63.40 odd 6 126.2.e.d.121.2 yes 6
63.41 even 6 378.2.h.d.361.3 6
63.47 even 6 1134.2.g.n.163.1 6
63.52 odd 6 7938.2.a.cb.1.1 3
63.58 even 3 inner 882.2.e.p.373.2 6
63.59 even 6 2646.2.f.o.1765.1 6
63.61 odd 6 1134.2.g.k.163.3 6
84.47 odd 6 3024.2.t.g.289.3 6
84.83 odd 2 3024.2.q.h.2881.1 6
252.103 even 6 1008.2.q.h.625.2 6
252.131 odd 6 3024.2.q.h.2305.1 6
252.139 even 6 1008.2.t.g.193.1 6
252.167 odd 6 3024.2.t.g.1873.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.2 6 7.6 odd 2
126.2.e.d.121.2 yes 6 63.40 odd 6
126.2.h.c.67.3 yes 6 63.13 odd 6
126.2.h.c.79.3 yes 6 7.5 odd 6
378.2.e.c.37.1 6 63.5 even 6
378.2.e.c.235.1 6 21.20 even 2
378.2.h.d.289.3 6 21.5 even 6
378.2.h.d.361.3 6 63.41 even 6
882.2.e.p.373.2 6 63.58 even 3 inner
882.2.e.p.655.2 6 1.1 even 1 trivial
882.2.f.l.295.2 6 7.3 odd 6
882.2.f.l.589.2 6 63.31 odd 6
882.2.f.m.295.2 6 7.4 even 3
882.2.f.m.589.2 6 63.4 even 3
882.2.h.o.67.1 6 9.4 even 3
882.2.h.o.79.1 6 7.2 even 3
1008.2.q.h.529.2 6 28.27 even 2
1008.2.q.h.625.2 6 252.103 even 6
1008.2.t.g.193.1 6 252.139 even 6
1008.2.t.g.961.1 6 28.19 even 6
1134.2.g.k.163.3 6 63.61 odd 6
1134.2.g.k.487.3 6 63.34 odd 6
1134.2.g.n.163.1 6 63.47 even 6
1134.2.g.n.487.1 6 63.20 even 6
2646.2.e.o.1549.3 6 63.23 odd 6
2646.2.e.o.2125.3 6 3.2 odd 2
2646.2.f.n.883.3 6 21.11 odd 6
2646.2.f.n.1765.3 6 63.32 odd 6
2646.2.f.o.883.1 6 21.17 even 6
2646.2.f.o.1765.1 6 63.59 even 6
2646.2.h.p.361.1 6 9.5 odd 6
2646.2.h.p.667.1 6 21.2 odd 6
3024.2.q.h.2305.1 6 252.131 odd 6
3024.2.q.h.2881.1 6 84.83 odd 2
3024.2.t.g.289.3 6 84.47 odd 6
3024.2.t.g.1873.3 6 252.167 odd 6
7938.2.a.bu.1.3 3 63.38 even 6
7938.2.a.bx.1.1 3 63.11 odd 6
7938.2.a.by.1.3 3 63.25 even 3
7938.2.a.cb.1.1 3 63.52 odd 6