Properties

Label 882.2.h.p.67.2
Level 882882
Weight 22
Character 882.67
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(67,882)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.67");
 
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.h (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 67.2
Root 0.5000002.05195i0.500000 - 2.05195i of defining polynomial
Character χ\chi == 882.67
Dual form 882.2.h.p.79.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q2+(0.796790+1.53790i)q3+(0.5000000.866025i)q40.593579q5+(0.933463+1.45899i)q61.00000q8+(1.730252.45076i)q9+(0.296790+0.514055i)q100.593579q11+(1.730250.0789082i)q12+(1.257292.17770i)q13+(0.4729580.912864i)q15+(0.500000+0.866025i)q16+(1.46050+2.52967i)q17+(2.98755+0.273062i)q18+(2.690764.66053i)q19+(0.296790+0.514055i)q20+(0.296790+0.514055i)q22+4.46050q23+(0.7967901.53790i)q244.64766q25+(1.257292.17770i)q26+(5.147660.708209i)q27+(3.097185.36447i)q29+(0.5540840.866025i)q30+(3.933466.81296i)q31+(0.500000+0.866025i)q32+(0.4729580.912864i)q33+(1.46050+2.52967i)q34+(1.25729+2.72382i)q36+(0.500000+0.866025i)q375.38151q38+(2.34728+3.66876i)q39+0.593579q40+(0.1366730.236725i)q41+(5.581139.66679i)q43+(0.296790+0.514055i)q44+(1.02704+1.45472i)q45+(2.230253.86291i)q46+(6.0811310.5328i)q47+(0.9334631.45899i)q48+(2.32383+4.02499i)q50+(2.726654.26172i)q512.51459q52+(4.027046.97504i)q53+(1.960504.81211i)q54+0.352336q55+(9.311380.424646i)q576.19436q58+(4.32383+7.48910i)q59+(1.02704+0.0468383i)q60+(3.32383+5.75705i)q617.86693q62+1.00000q64+(0.746304+1.29264i)q65+(0.5540840.866025i)q66+(0.956906+1.65741i)q67+2.92101q68+(3.55408+6.85980i)q6914.4107q71+(1.73025+2.45076i)q72+(3.95691+6.85356i)q73+1.00000q74+(3.703217.14763i)q75+(2.69076+4.66053i)q76+(4.350870.198422i)q78+(4.624228.00938i)q79+(0.2967900.514055i)q80+(3.01245+8.48087i)q81+(0.1366730.236725i)q82+(3.850876.66991i)q83+(0.8669261.50156i)q8511.1623q86+(10.71780.488786i)q87+0.593579q88+(6.21780+10.7695i)q89+(1.773350.162084i)q90+(2.230253.86291i)q92+(13.61180.620765i)q93+(6.0811310.5328i)q94+(1.59718+2.76639i)q95+(1.73025+0.0789082i)q96+(5.8669310.1618i)q97+(1.02704+1.45472i)q99+O(q100)q+(0.500000 - 0.866025i) q^{2} +(-0.796790 + 1.53790i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +(-0.296790 + 0.514055i) q^{10} -0.593579 q^{11} +(1.73025 - 0.0789082i) q^{12} +(1.25729 - 2.17770i) q^{13} +(0.472958 - 0.912864i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.46050 + 2.52967i) q^{17} +(-2.98755 + 0.273062i) q^{18} +(-2.69076 - 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +4.46050 q^{23} +(0.796790 - 1.53790i) q^{24} -4.64766 q^{25} +(-1.25729 - 2.17770i) q^{26} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(-0.554084 - 0.866025i) q^{30} +(-3.93346 - 6.81296i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.472958 - 0.912864i) q^{33} +(1.46050 + 2.52967i) q^{34} +(-1.25729 + 2.72382i) q^{36} +(0.500000 + 0.866025i) q^{37} -5.38151 q^{38} +(2.34728 + 3.66876i) q^{39} +0.593579 q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(0.296790 + 0.514055i) q^{44} +(1.02704 + 1.45472i) q^{45} +(2.23025 - 3.86291i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-0.933463 - 1.45899i) q^{48} +(-2.32383 + 4.02499i) q^{50} +(-2.72665 - 4.26172i) q^{51} -2.51459 q^{52} +(4.02704 - 6.97504i) q^{53} +(1.96050 - 4.81211i) q^{54} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} -6.19436 q^{58} +(4.32383 + 7.48910i) q^{59} +(-1.02704 + 0.0468383i) q^{60} +(-3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 + 1.29264i) q^{65} +(-0.554084 - 0.866025i) q^{66} +(0.956906 + 1.65741i) q^{67} +2.92101 q^{68} +(-3.55408 + 6.85980i) q^{69} -14.4107 q^{71} +(1.73025 + 2.45076i) q^{72} +(-3.95691 + 6.85356i) q^{73} +1.00000 q^{74} +(3.70321 - 7.14763i) q^{75} +(-2.69076 + 4.66053i) q^{76} +(4.35087 - 0.198422i) q^{78} +(4.62422 - 8.00938i) q^{79} +(0.296790 - 0.514055i) q^{80} +(-3.01245 + 8.48087i) q^{81} +(-0.136673 - 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} -11.1623 q^{86} +(10.7178 - 0.488786i) q^{87} +0.593579 q^{88} +(6.21780 + 10.7695i) q^{89} +(1.77335 - 0.162084i) q^{90} +(-2.23025 - 3.86291i) q^{92} +(13.6118 - 0.620765i) q^{93} +(-6.08113 - 10.5328i) q^{94} +(1.59718 + 2.76639i) q^{95} +(-1.73025 + 0.0789082i) q^{96} +(-5.86693 - 10.1618i) q^{97} +(1.02704 + 1.45472i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+3q22q33q4+2q5+2q66q84q9+q10+2q11+4q128q13+12q153q16+4q17+4q18+3q19q20+q22+14q23+3q99+O(q100) 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23}+ \cdots - 3 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(13)e\left(\frac{1}{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 0.500000 0.866025i 0.353553 0.612372i
33 −0.796790 + 1.53790i −0.460027 + 0.887905i
44 −0.500000 0.866025i −0.250000 0.433013i
55 −0.593579 −0.265457 −0.132728 0.991152i 0.542374π-0.542374\pi
−0.132728 + 0.991152i 0.542374π0.542374\pi
66 0.933463 + 1.45899i 0.381085 + 0.595630i
77 0 0
88 −1.00000 −0.353553
99 −1.73025 2.45076i −0.576751 0.816920i
1010 −0.296790 + 0.514055i −0.0938531 + 0.162558i
1111 −0.593579 −0.178971 −0.0894855 0.995988i 0.528522π-0.528522\pi
−0.0894855 + 0.995988i 0.528522π0.528522\pi
1212 1.73025 0.0789082i 0.499481 0.0227788i
1313 1.25729 2.17770i 0.348711 0.603985i −0.637310 0.770608i 0.719953π-0.719953\pi
0.986021 + 0.166623i 0.0532862π0.0532862\pi
1414 0 0
1515 0.472958 0.912864i 0.122117 0.235700i
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 −1.46050 + 2.52967i −0.354224 + 0.613535i −0.986985 0.160813i 0.948588π-0.948588\pi
0.632760 + 0.774348i 0.281922π0.281922\pi
1818 −2.98755 + 0.273062i −0.704172 + 0.0643614i
1919 −2.69076 4.66053i −0.617302 1.06920i −0.989976 0.141236i 0.954892π-0.954892\pi
0.372674 0.927962i 0.378441π-0.378441\pi
2020 0.296790 + 0.514055i 0.0663642 + 0.114946i
2121 0 0
2222 −0.296790 + 0.514055i −0.0632758 + 0.109597i
2323 4.46050 0.930080 0.465040 0.885290i 0.346040π-0.346040\pi
0.465040 + 0.885290i 0.346040π0.346040\pi
2424 0.796790 1.53790i 0.162644 0.313922i
2525 −4.64766 −0.929533
2626 −1.25729 2.17770i −0.246576 0.427082i
2727 5.14766 0.708209i 0.990668 0.136295i
2828 0 0
2929 −3.09718 5.36447i −0.575132 0.996157i −0.996027 0.0890480i 0.971618π-0.971618\pi
0.420896 0.907109i 0.361716π-0.361716\pi
3030 −0.554084 0.866025i −0.101161 0.158114i
3131 −3.93346 6.81296i −0.706471 1.22364i −0.966158 0.257951i 0.916953π-0.916953\pi
0.259687 0.965693i 0.416380π-0.416380\pi
3232 0.500000 + 0.866025i 0.0883883 + 0.153093i
3333 0.472958 0.912864i 0.0823314 0.158909i
3434 1.46050 + 2.52967i 0.250475 + 0.433835i
3535 0 0
3636 −1.25729 + 2.72382i −0.209549 + 0.453970i
3737 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i 0.140472π-0.140472\pi
−0.821995 + 0.569495i 0.807139π0.807139\pi
3838 −5.38151 −0.872997
3939 2.34728 + 3.66876i 0.375865 + 0.587471i
4040 0.593579 0.0938531
4141 0.136673 0.236725i 0.0213448 0.0369702i −0.855156 0.518371i 0.826539π-0.826539\pi
0.876500 + 0.481401i 0.159872π0.159872\pi
4242 0 0
4343 −5.58113 9.66679i −0.851114 1.47417i −0.880204 0.474596i 0.842594π-0.842594\pi
0.0290902 0.999577i 0.490739π-0.490739\pi
4444 0.296790 + 0.514055i 0.0447427 + 0.0774967i
4545 1.02704 + 1.45472i 0.153102 + 0.216857i
4646 2.23025 3.86291i 0.328833 0.569555i
4747 6.08113 10.5328i 0.887023 1.53637i 0.0436467 0.999047i 0.486102π-0.486102\pi
0.843377 0.537323i 0.180564π-0.180564\pi
4848 −0.933463 1.45899i −0.134734 0.210587i
4949 0 0
5050 −2.32383 + 4.02499i −0.328639 + 0.569220i
5151 −2.72665 4.26172i −0.381808 0.596760i
5252 −2.51459 −0.348711
5353 4.02704 6.97504i 0.553157 0.958096i −0.444888 0.895586i 0.646756π-0.646756\pi
0.998044 0.0625092i 0.0199103π-0.0199103\pi
5454 1.96050 4.81211i 0.266791 0.654845i
5555 0.352336 0.0475090
5656 0 0
5757 9.31138 0.424646i 1.23332 0.0562457i
5858 −6.19436 −0.813359
5959 4.32383 + 7.48910i 0.562915 + 0.974997i 0.997240 + 0.0742412i 0.0236535π0.0236535\pi
−0.434325 + 0.900756i 0.643013π0.643013\pi
6060 −1.02704 + 0.0468383i −0.132591 + 0.00604680i
6161 −3.32383 + 5.75705i −0.425573 + 0.737114i −0.996474 0.0839050i 0.973261π-0.973261\pi
0.570901 + 0.821019i 0.306594π0.306594\pi
6262 −7.86693 −0.999101
6363 0 0
6464 1.00000 0.125000
6565 −0.746304 + 1.29264i −0.0925676 + 0.160332i
6666 −0.554084 0.866025i −0.0682031 0.106600i
6767 0.956906 + 1.65741i 0.116905 + 0.202485i 0.918540 0.395329i 0.129369π-0.129369\pi
−0.801635 + 0.597814i 0.796036π0.796036\pi
6868 2.92101 0.354224
6969 −3.55408 + 6.85980i −0.427861 + 0.825822i
7070 0 0
7171 −14.4107 −1.71023 −0.855117 0.518435i 0.826515π-0.826515\pi
−0.855117 + 0.518435i 0.826515π0.826515\pi
7272 1.73025 + 2.45076i 0.203912 + 0.288825i
7373 −3.95691 + 6.85356i −0.463121 + 0.802149i −0.999115 0.0420732i 0.986604π-0.986604\pi
0.535994 + 0.844222i 0.319937π0.319937\pi
7474 1.00000 0.116248
7575 3.70321 7.14763i 0.427610 0.825337i
7676 −2.69076 + 4.66053i −0.308651 + 0.534599i
7777 0 0
7878 4.35087 0.198422i 0.492639 0.0224668i
7979 4.62422 8.00938i 0.520265 0.901126i −0.479457 0.877565i 0.659166π-0.659166\pi
0.999722 0.0235607i 0.00750031π-0.00750031\pi
8080 0.296790 0.514055i 0.0331821 0.0574731i
8181 −3.01245 + 8.48087i −0.334717 + 0.942319i
8282 −0.136673 0.236725i −0.0150930 0.0261419i
8383 −3.85087 6.66991i −0.422688 0.732118i 0.573513 0.819196i 0.305580π-0.305580\pi
−0.996201 + 0.0870787i 0.972247π0.972247\pi
8484 0 0
8585 0.866926 1.50156i 0.0940313 0.162867i
8686 −11.1623 −1.20366
8787 10.7178 0.488786i 1.14907 0.0524033i
8888 0.593579 0.0632758
8989 6.21780 + 10.7695i 0.659085 + 1.14157i 0.980853 + 0.194751i 0.0623898π0.0623898\pi
−0.321767 + 0.946819i 0.604277π0.604277\pi
9090 1.77335 0.162084i 0.186927 0.0170852i
9191 0 0
9292 −2.23025 3.86291i −0.232520 0.402736i
9393 13.6118 0.620765i 1.41147 0.0643704i
9494 −6.08113 10.5328i −0.627220 1.08638i
9595 1.59718 + 2.76639i 0.163867 + 0.283826i
9696 −1.73025 + 0.0789082i −0.176593 + 0.00805354i
9797 −5.86693 10.1618i −0.595696 1.03178i −0.993448 0.114283i 0.963543π-0.963543\pi
0.397752 0.917493i 0.369790π-0.369790\pi
9898 0 0
9999 1.02704 + 1.45472i 0.103222 + 0.146205i
100100 2.32383 + 4.02499i 0.232383 + 0.402499i
101101 1.62276 0.161470 0.0807352 0.996736i 0.474273π-0.474273\pi
0.0807352 + 0.996736i 0.474273π0.474273\pi
102102 −5.05408 + 0.230492i −0.500429 + 0.0228221i
103103 −6.38151 −0.628789 −0.314395 0.949292i 0.601802π-0.601802\pi
−0.314395 + 0.949292i 0.601802π0.601802\pi
104104 −1.25729 + 2.17770i −0.123288 + 0.213541i
105105 0 0
106106 −4.02704 6.97504i −0.391141 0.677476i
107107 9.35447 + 16.2024i 0.904331 + 1.56635i 0.821813 + 0.569758i 0.192963π0.192963\pi
0.0825182 + 0.996590i 0.473704π0.473704\pi
108108 −3.18716 4.10390i −0.306684 0.394898i
109109 −1.43346 + 2.48283i −0.137301 + 0.237812i −0.926474 0.376359i 0.877176π-0.877176\pi
0.789173 + 0.614171i 0.210509π0.210509\pi
110110 0.176168 0.305132i 0.0167970 0.0290932i
111111 −1.73025 + 0.0789082i −0.164228 + 0.00748964i
112112 0 0
113113 −6.16012 + 10.6696i −0.579495 + 1.00371i 0.416042 + 0.909345i 0.363417π0.363417\pi
−0.995537 + 0.0943695i 0.969916π0.969916\pi
114114 4.28794 8.27621i 0.401602 0.775138i
115115 −2.64766 −0.246896
116116 −3.09718 + 5.36447i −0.287566 + 0.498078i
117117 −7.51245 + 0.686640i −0.694527 + 0.0634799i
118118 8.64766 0.796082
119119 0 0
120120 −0.472958 + 0.912864i −0.0431750 + 0.0833327i
121121 −10.6477 −0.967969
122122 3.32383 + 5.75705i 0.300926 + 0.521218i
123123 0.255158 + 0.398809i 0.0230069 + 0.0359594i
124124 −3.93346 + 6.81296i −0.353235 + 0.611822i
125125 5.72665 0.512207
126126 0 0
127127 12.3346 1.09452 0.547261 0.836962i 0.315671π-0.315671\pi
0.547261 + 0.836962i 0.315671π0.315671\pi
128128 0.500000 0.866025i 0.0441942 0.0765466i
129129 19.3135 0.880794i 1.70046 0.0775496i
130130 0.746304 + 1.29264i 0.0654552 + 0.113372i
131131 1.18716 0.103723 0.0518613 0.998654i 0.483485π-0.483485\pi
0.0518613 + 0.998654i 0.483485π0.483485\pi
132132 −1.02704 + 0.0468383i −0.0893925 + 0.00407675i
133133 0 0
134134 1.91381 0.165328
135135 −3.05555 + 0.420378i −0.262980 + 0.0361804i
136136 1.46050 2.52967i 0.125237 0.216917i
137137 2.52179 0.215451 0.107725 0.994181i 0.465643π-0.465643\pi
0.107725 + 0.994181i 0.465643π0.465643\pi
138138 4.16372 + 6.50783i 0.354439 + 0.553983i
139139 −2.45691 + 4.25549i −0.208392 + 0.360946i −0.951208 0.308550i 0.900156π-0.900156\pi
0.742816 + 0.669496i 0.233490π0.233490\pi
140140 0 0
141141 11.3530 + 17.7446i 0.956096 + 1.49436i
142142 −7.20535 + 12.4800i −0.604659 + 1.04730i
143143 −0.746304 + 1.29264i −0.0624091 + 0.108096i
144144 2.98755 0.273062i 0.248962 0.0227552i
145145 1.83842 + 3.18424i 0.152673 + 0.264437i
146146 3.95691 + 6.85356i 0.327476 + 0.567205i
147147 0 0
148148 0.500000 0.866025i 0.0410997 0.0711868i
149149 18.0512 1.47881 0.739404 0.673262i 0.235107π-0.235107\pi
0.739404 + 0.673262i 0.235107π0.235107\pi
150150 −4.33842 6.78089i −0.354231 0.553657i
151151 1.64766 0.134085 0.0670425 0.997750i 0.478644π-0.478644\pi
0.0670425 + 0.997750i 0.478644π0.478644\pi
152152 2.69076 + 4.66053i 0.218249 + 0.378019i
153153 8.72665 0.797618i 0.705508 0.0644836i
154154 0 0
155155 2.33482 + 4.04403i 0.187537 + 0.324824i
156156 2.00360 3.86718i 0.160416 0.309622i
157157 −3.30039 5.71644i −0.263400 0.456222i 0.703743 0.710454i 0.251510π-0.251510\pi
−0.967143 + 0.254233i 0.918177π0.918177\pi
158158 −4.62422 8.00938i −0.367883 0.637192i
159159 7.51819 + 11.7508i 0.596231 + 0.931900i
160160 −0.296790 0.514055i −0.0234633 0.0406396i
161161 0 0
162162 5.83842 + 6.84929i 0.458710 + 0.538131i
163163 −2.99115 5.18082i −0.234285 0.405793i 0.724780 0.688980i 0.241941π-0.241941\pi
−0.959065 + 0.283188i 0.908608π0.908608\pi
164164 −0.273346 −0.0213448
165165 −0.280738 + 0.541857i −0.0218554 + 0.0421835i
166166 −7.70175 −0.597772
167167 −3.73025 + 6.46099i −0.288656 + 0.499966i −0.973489 0.228733i 0.926542π-0.926542\pi
0.684833 + 0.728700i 0.259875π0.259875\pi
168168 0 0
169169 3.33842 + 5.78231i 0.256802 + 0.444793i
170170 −0.866926 1.50156i −0.0664902 0.115164i
171171 −6.76615 + 14.6583i −0.517420 + 1.12095i
172172 −5.58113 + 9.66679i −0.425557 + 0.737086i
173173 −12.8296 + 22.2215i −0.975414 + 1.68947i −0.296851 + 0.954924i 0.595937π0.595937\pi
−0.678562 + 0.734543i 0.737397π0.737397\pi
174174 4.93560 9.52628i 0.374167 0.722185i
175175 0 0
176176 0.296790 0.514055i 0.0223714 0.0387483i
177177 −14.9626 + 0.682372i −1.12466 + 0.0512902i
178178 12.4356 0.932088
179179 7.51819 13.0219i 0.561936 0.973301i −0.435392 0.900241i 0.643390π-0.643390\pi
0.997328 0.0730602i 0.0232765π-0.0232765\pi
180180 0.746304 1.61680i 0.0556262 0.120510i
181181 0.0861875 0.00640627 0.00320313 0.999995i 0.498980π-0.498980\pi
0.00320313 + 0.999995i 0.498980π0.498980\pi
182182 0 0
183183 −6.20535 9.69886i −0.458712 0.716961i
184184 −4.46050 −0.328833
185185 −0.296790 0.514055i −0.0218204 0.0377941i
186186 6.26829 12.0985i 0.459613 0.887106i
187187 0.866926 1.50156i 0.0633959 0.109805i
188188 −12.1623 −0.887023
189189 0 0
190190 3.19436 0.231743
191191 −1.99115 + 3.44877i −0.144074 + 0.249544i −0.929027 0.370011i 0.879354π-0.879354\pi
0.784953 + 0.619555i 0.212687π0.212687\pi
192192 −0.796790 + 1.53790i −0.0575033 + 0.110988i
193193 −3.39037 5.87229i −0.244044 0.422697i 0.717818 0.696230i 0.245141π-0.245141\pi
−0.961862 + 0.273534i 0.911808π0.911808\pi
194194 −11.7339 −0.842441
195195 −1.39329 2.17770i −0.0997759 0.155948i
196196 0 0
197197 11.0584 0.787875 0.393938 0.919137i 0.371113π-0.371113\pi
0.393938 + 0.919137i 0.371113π0.371113\pi
198198 1.77335 0.162084i 0.126026 0.0115188i
199199 −2.80924 + 4.86575i −0.199142 + 0.344924i −0.948250 0.317523i 0.897149π-0.897149\pi
0.749109 + 0.662447i 0.230482π0.230482\pi
200200 4.64766 0.328639
201201 −3.31138 + 0.151016i −0.233567 + 0.0106518i
202202 0.811379 1.40535i 0.0570884 0.0988800i
203203 0 0
204204 −2.32743 + 4.49221i −0.162953 + 0.314518i
205205 −0.0811263 + 0.140515i −0.00566611 + 0.00981399i
206206 −3.19076 + 5.52655i −0.222311 + 0.385053i
207207 −7.71780 10.9316i −0.536424 0.759801i
208208 1.25729 + 2.17770i 0.0871777 + 0.150996i
209209 1.59718 + 2.76639i 0.110479 + 0.191355i
210210 0 0
211211 9.66225 16.7355i 0.665177 1.15212i −0.314060 0.949403i 0.601689π-0.601689\pi
0.979237 0.202717i 0.0649772π-0.0649772\pi
212212 −8.05408 −0.553157
213213 11.4823 22.1622i 0.786754 1.51853i
214214 18.7089 1.27892
215215 3.31284 + 5.73801i 0.225934 + 0.391329i
216216 −5.14766 + 0.708209i −0.350254 + 0.0481875i
217217 0 0
218218 1.43346 + 2.48283i 0.0970863 + 0.168158i
219219 −7.38725 11.5462i −0.499184 0.780217i
220220 −0.176168 0.305132i −0.0118773 0.0205720i
221221 3.67257 + 6.36108i 0.247044 + 0.427892i
222222 −0.796790 + 1.53790i −0.0534770 + 0.103217i
223223 −12.6623 21.9317i −0.847927 1.46865i −0.883055 0.469270i 0.844517π-0.844517\pi
0.0351275 0.999383i 0.488816π-0.488816\pi
224224 0 0
225225 8.04163 + 11.3903i 0.536109 + 0.759354i
226226 6.16012 + 10.6696i 0.409765 + 0.709734i
227227 −4.81711 −0.319723 −0.159862 0.987139i 0.551105π-0.551105\pi
−0.159862 + 0.987139i 0.551105π0.551105\pi
228228 −5.02344 7.85157i −0.332686 0.519983i
229229 9.29533 0.614253 0.307126 0.951669i 0.400633π-0.400633\pi
0.307126 + 0.951669i 0.400633π0.400633\pi
230230 −1.32383 + 2.29294i −0.0872909 + 0.151192i
231231 0 0
232232 3.09718 + 5.36447i 0.203340 + 0.352195i
233233 0.0971780 + 0.168317i 0.00636634 + 0.0110268i 0.869191 0.494476i 0.164640π-0.164640\pi
−0.862825 + 0.505503i 0.831307π0.831307\pi
234234 −3.16158 + 6.84929i −0.206679 + 0.447752i
235235 −3.60963 + 6.25206i −0.235466 + 0.407840i
236236 4.32383 7.48910i 0.281457 0.487499i
237237 8.63307 + 13.4934i 0.560778 + 0.876488i
238238 0 0
239239 −6.82743 + 11.8255i −0.441630 + 0.764925i −0.997811 0.0661361i 0.978933π-0.978933\pi
0.556181 + 0.831061i 0.312266π0.312266\pi
240240 0.554084 + 0.866025i 0.0357660 + 0.0559017i
241241 13.0000 0.837404 0.418702 0.908124i 0.362485π-0.362485\pi
0.418702 + 0.908124i 0.362485π0.362485\pi
242242 −5.32383 + 9.22115i −0.342229 + 0.592758i
243243 −10.6424 11.3903i −0.682711 0.730689i
244244 6.64766 0.425573
245245 0 0
246246 0.472958 0.0215693i 0.0301547 0.00137521i
247247 −13.5323 −0.861039
248248 3.93346 + 6.81296i 0.249775 + 0.432623i
249249 13.3260 0.607731i 0.844499 0.0385134i
250250 2.86333 4.95943i 0.181093 0.313662i
251251 19.5438 1.23359 0.616796 0.787123i 0.288430π-0.288430\pi
0.616796 + 0.787123i 0.288430π0.288430\pi
252252 0 0
253253 −2.64766 −0.166457
254254 6.16731 10.6821i 0.386972 0.670255i
255255 1.61849 + 2.52967i 0.101353 + 0.158414i
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 −8.32743 −0.519451 −0.259725 0.965683i 0.583632π-0.583632\pi
−0.259725 + 0.965683i 0.583632π0.583632\pi
258258 8.89397 17.1664i 0.553714 1.06873i
259259 0 0
260260 1.49261 0.0925676
261261 −7.78813 + 16.8723i −0.482073 + 1.04437i
262262 0.593579 1.02811i 0.0366715 0.0635168i
263263 −17.0905 −1.05384 −0.526921 0.849914i 0.676654π-0.676654\pi
−0.526921 + 0.849914i 0.676654π0.676654\pi
264264 −0.472958 + 0.912864i −0.0291085 + 0.0561829i
265265 −2.39037 + 4.14024i −0.146839 + 0.254333i
266266 0 0
267267 −21.5167 + 0.981271i −1.31680 + 0.0600528i
268268 0.956906 1.65741i 0.0584524 0.101242i
269269 5.00720 8.67272i 0.305294 0.528785i −0.672033 0.740522i 0.734579π-0.734579\pi
0.977327 + 0.211737i 0.0679119π0.0679119\pi
270270 −1.16372 + 2.85637i −0.0708215 + 0.173833i
271271 −5.10457 8.84137i −0.310081 0.537075i 0.668299 0.743893i 0.267023π-0.267023\pi
−0.978380 + 0.206818i 0.933689π0.933689\pi
272272 −1.46050 2.52967i −0.0885561 0.153384i
273273 0 0
274274 1.26089 2.18393i 0.0761733 0.131936i
275275 2.75876 0.166359
276276 7.71780 0.351971i 0.464557 0.0211861i
277277 19.3422 1.16216 0.581081 0.813846i 0.302630π-0.302630\pi
0.581081 + 0.813846i 0.302630π0.302630\pi
278278 2.45691 + 4.25549i 0.147355 + 0.255227i
279279 −9.89104 + 21.4281i −0.592161 + 1.28287i
280280 0 0
281281 −6.40136 11.0875i −0.381873 0.661424i 0.609457 0.792819i 0.291388π-0.291388\pi
−0.991330 + 0.131396i 0.958054π0.958054\pi
282282 21.0438 0.959702i 1.25314 0.0571494i
283283 −8.17617 14.1615i −0.486023 0.841816i 0.513848 0.857881i 0.328219π-0.328219\pi
−0.999871 + 0.0160650i 0.994886π0.994886\pi
284284 7.20535 + 12.4800i 0.427559 + 0.740553i
285285 −5.52704 + 0.252061i −0.327394 + 0.0149308i
286286 0.746304 + 1.29264i 0.0441299 + 0.0764352i
287287 0 0
288288 1.25729 2.72382i 0.0740868 0.160503i
289289 4.23385 + 7.33325i 0.249050 + 0.431367i
290290 3.67684 0.215912
291291 20.3025 0.925898i 1.19016 0.0542771i
292292 7.91381 0.463121
293293 10.3889 17.9941i 0.606926 1.05123i −0.384817 0.922993i 0.625736π-0.625736\pi
0.991744 0.128235i 0.0409311π-0.0409311\pi
294294 0 0
295295 −2.56654 4.44537i −0.149430 0.258820i
296296 −0.500000 0.866025i −0.0290619 0.0503367i
297297 −3.05555 + 0.420378i −0.177301 + 0.0243928i
298298 9.02558 15.6328i 0.522838 0.905582i
299299 5.60817 9.71363i 0.324329 0.561754i
300300 −8.04163 + 0.366739i −0.464284 + 0.0211737i
301301 0 0
302302 0.823832 1.42692i 0.0474062 0.0821099i
303303 −1.29300 + 2.49563i −0.0742807 + 0.143370i
304304 5.38151 0.308651
305305 1.97296 3.41726i 0.112971 0.195672i
306306 3.67257 7.95631i 0.209947 0.454832i
307307 22.6768 1.29424 0.647118 0.762390i 0.275974π-0.275974\pi
0.647118 + 0.762390i 0.275974π0.275974\pi
308308 0 0
309309 5.08472 9.81411i 0.289260 0.558305i
310310 4.66964 0.265218
311311 −3.25729 5.64180i −0.184704 0.319917i 0.758773 0.651356i 0.225799π-0.225799\pi
−0.943477 + 0.331439i 0.892466π0.892466\pi
312312 −2.34728 3.66876i −0.132888 0.207702i
313313 0.133074 0.230492i 0.00752181 0.0130282i −0.862240 0.506500i 0.830939π-0.830939\pi
0.869762 + 0.493472i 0.164272π0.164272\pi
314314 −6.60078 −0.372503
315315 0 0
316316 −9.24844 −0.520265
317317 −7.86186 + 13.6171i −0.441566 + 0.764815i −0.997806 0.0662067i 0.978910π-0.978910\pi
0.556240 + 0.831022i 0.312244π0.312244\pi
318318 13.9356 0.635534i 0.781470 0.0356390i
319319 1.83842 + 3.18424i 0.102932 + 0.178283i
320320 −0.593579 −0.0331821
321321 −32.3712 + 1.47629i −1.80678 + 0.0823985i
322322 0 0
323323 15.7195 0.874654
324324 8.85087 1.63157i 0.491715 0.0906430i
325325 −5.84348 + 10.1212i −0.324138 + 0.561424i
326326 −5.98229 −0.331328
327327 −2.67617 4.18281i −0.147992 0.231310i
328328 −0.136673 + 0.236725i −0.00754651 + 0.0130709i
329329 0 0
330330 0.328893 + 0.514055i 0.0181050 + 0.0282978i
331331 12.5811 21.7912i 0.691521 1.19775i −0.279818 0.960053i 0.590274π-0.590274\pi
0.971339 0.237697i 0.0763925π-0.0763925\pi
332332 −3.85087 + 6.66991i −0.211344 + 0.366059i
333333 1.25729 2.72382i 0.0688993 0.149265i
334334 3.73025 + 6.46099i 0.204110 + 0.353529i
335335 −0.568000 0.983804i −0.0310331 0.0537510i
336336 0 0
337337 −9.36693 + 16.2240i −0.510249 + 0.883777i 0.489681 + 0.871902i 0.337113π0.337113\pi
−0.999929 + 0.0118752i 0.996220π0.996220\pi
338338 6.67684 0.363172
339339 −11.5005 17.9751i −0.624620 0.976272i
340340 −1.73385 −0.0940313
341341 2.33482 + 4.04403i 0.126438 + 0.218997i
342342 9.31138 + 13.1888i 0.503502 + 0.713169i
343343 0 0
344344 5.58113 + 9.66679i 0.300914 + 0.521199i
345345 2.10963 4.07183i 0.113579 0.219220i
346346 12.8296 + 22.2215i 0.689722 + 1.19463i
347347 −11.2719 19.5235i −0.605106 1.04808i −0.992035 0.125965i 0.959797π-0.959797\pi
0.386928 0.922110i 0.373536π-0.373536\pi
348348 −5.78220 9.03749i −0.309958 0.484461i
349349 −1.89543 3.28298i −0.101460 0.175734i 0.810826 0.585287i 0.199018π-0.199018\pi
−0.912286 + 0.409553i 0.865685π0.865685\pi
350350 0 0
351351 4.92986 12.1005i 0.263137 0.645876i
352352 −0.296790 0.514055i −0.0158189 0.0273992i
353353 −6.83482 −0.363781 −0.181890 0.983319i 0.558222π-0.558222\pi
−0.181890 + 0.983319i 0.558222π0.558222\pi
354354 −6.89037 + 13.2992i −0.366219 + 0.706845i
355355 8.55389 0.453993
356356 6.21780 10.7695i 0.329543 0.570785i
357357 0 0
358358 −7.51819 13.0219i −0.397349 0.688228i
359359 −6.32237 10.9507i −0.333682 0.577954i 0.649549 0.760320i 0.274958π-0.274958\pi
−0.983231 + 0.182366i 0.941624π0.941624\pi
360360 −1.02704 1.45472i −0.0541299 0.0766705i
361361 −4.98035 + 8.62622i −0.262124 + 0.454012i
362362 0.0430937 0.0746406i 0.00226496 0.00392302i
363363 8.48395 16.3750i 0.445292 0.859465i
364364 0 0
365365 2.34874 4.06813i 0.122939 0.212936i
366366 −11.5021 + 0.524555i −0.601226 + 0.0274190i
367367 −6.54377 −0.341582 −0.170791 0.985307i 0.554632π-0.554632\pi
−0.170791 + 0.985307i 0.554632π0.554632\pi
368368 −2.23025 + 3.86291i −0.116260 + 0.201368i
369369 −0.816635 + 0.0746406i −0.0425123 + 0.00388563i
370370 −0.593579 −0.0308587
371371 0 0
372372 −7.34348 11.4778i −0.380742 0.595094i
373373 9.42840 0.488184 0.244092 0.969752i 0.421510π-0.421510\pi
0.244092 + 0.969752i 0.421510π0.421510\pi
374374 −0.866926 1.50156i −0.0448277 0.0776438i
375375 −4.56294 + 8.80700i −0.235629 + 0.454792i
376376 −6.08113 + 10.5328i −0.313610 + 0.543189i
377377 −15.5763 −0.802218
378378 0 0
379379 −7.27762 −0.373826 −0.186913 0.982376i 0.559848π-0.559848\pi
−0.186913 + 0.982376i 0.559848π0.559848\pi
380380 1.59718 2.76639i 0.0819335 0.141913i
381381 −9.82810 + 18.9694i −0.503509 + 0.971831i
382382 1.99115 + 3.44877i 0.101876 + 0.176454i
383383 24.0833 1.23060 0.615299 0.788294i 0.289035π-0.289035\pi
0.615299 + 0.788294i 0.289035π0.289035\pi
384384 0.933463 + 1.45899i 0.0476356 + 0.0744537i
385385 0 0
386386 −6.78074 −0.345130
387387 −14.0342 + 30.4040i −0.713400 + 1.54552i
388388 −5.86693 + 10.1618i −0.297848 + 0.515888i
389389 −16.2983 −0.826354 −0.413177 0.910651i 0.635581π-0.635581\pi
−0.413177 + 0.910651i 0.635581π0.635581\pi
390390 −2.58259 + 0.117779i −0.130774 + 0.00596398i
391391 −6.51459 + 11.2836i −0.329457 + 0.570636i
392392 0 0
393393 −0.945916 + 1.82573i −0.0477151 + 0.0920958i
394394 5.52918 9.57682i 0.278556 0.482473i
395395 −2.74484 + 4.75420i −0.138108 + 0.239210i
396396 0.746304 1.61680i 0.0375032 0.0812475i
397397 6.08619 + 10.5416i 0.305457 + 0.529067i 0.977363 0.211569i 0.0678574π-0.0678574\pi
−0.671906 + 0.740636i 0.734524π0.734524\pi
398398 2.80924 + 4.86575i 0.140815 + 0.243898i
399399 0 0
400400 2.32383 4.02499i 0.116192 0.201250i
401401 −33.3609 −1.66596 −0.832981 0.553301i 0.813368π-0.813368\pi
−0.832981 + 0.553301i 0.813368π0.813368\pi
402402 −1.52491 + 2.94325i −0.0760554 + 0.146796i
403403 −19.7821 −0.985416
404404 −0.811379 1.40535i −0.0403676 0.0699187i
405405 1.78813 5.03407i 0.0888529 0.250145i
406406 0 0
407407 −0.296790 0.514055i −0.0147113 0.0254808i
408408 2.72665 + 4.26172i 0.134989 + 0.210987i
409409 −2.89037 5.00627i −0.142920 0.247544i 0.785675 0.618639i 0.212316π-0.212316\pi
−0.928595 + 0.371095i 0.878982π0.878982\pi
410410 0.0811263 + 0.140515i 0.00400654 + 0.00693954i
411411 −2.00933 + 3.87825i −0.0991131 + 0.191300i
412412 3.19076 + 5.52655i 0.157197 + 0.272274i
413413 0 0
414414 −13.3260 + 1.21800i −0.654936 + 0.0598612i
415415 2.28580 + 3.95912i 0.112205 + 0.194346i
416416 2.51459 0.123288
417417 −4.58686 7.16920i −0.224620 0.351077i
418418 3.19436 0.156241
419419 −15.4356 + 26.7352i −0.754078 + 1.30610i 0.191753 + 0.981443i 0.438583π0.438583\pi
−0.945831 + 0.324659i 0.894751π0.894751\pi
420420 0 0
421421 −1.86693 3.23361i −0.0909884 0.157597i 0.816939 0.576724i 0.195669π-0.195669\pi
−0.907927 + 0.419128i 0.862336π0.862336\pi
422422 −9.66225 16.7355i −0.470351 0.814672i
423423 −36.3353 + 3.32105i −1.76668 + 0.161475i
424424 −4.02704 + 6.97504i −0.195570 + 0.338738i
425425 6.78794 11.7570i 0.329263 0.570301i
426426 −13.4518 21.0250i −0.651744 1.01867i
427427 0 0
428428 9.35447 16.2024i 0.452165 0.783174i
429429 −1.39329 2.17770i −0.0672689 0.105140i
430430 6.62568 0.319519
431431 −14.0979 + 24.4182i −0.679070 + 1.17618i 0.296192 + 0.955128i 0.404283π0.404283\pi
−0.975261 + 0.221055i 0.929050π0.929050\pi
432432 −1.96050 + 4.81211i −0.0943248 + 0.231523i
433433 −12.5438 −0.602815 −0.301407 0.953495i 0.597456π-0.597456\pi
−0.301407 + 0.953495i 0.597456π0.597456\pi
434434 0 0
435435 −6.36186 + 0.290133i −0.305028 + 0.0139108i
436436 2.86693 0.137301
437437 −12.0021 20.7883i −0.574140 0.994440i
438438 −13.6929 + 0.624465i −0.654272 + 0.0298381i
439439 13.0203 22.5519i 0.621426 1.07634i −0.367794 0.929907i 0.619887π-0.619887\pi
0.989220 0.146434i 0.0467797π-0.0467797\pi
440440 −0.352336 −0.0167970
441441 0 0
442442 7.34514 0.349373
443443 11.7865 20.4148i 0.559992 0.969935i −0.437504 0.899216i 0.644137π-0.644137\pi
0.997496 0.0707186i 0.0225292π-0.0225292\pi
444444 0.933463 + 1.45899i 0.0443002 + 0.0692405i
445445 −3.69076 6.39258i −0.174959 0.303037i
446446 −25.3245 −1.19915
447447 −14.3830 + 27.7608i −0.680291 + 1.31304i
448448 0 0
449449 13.6870 0.645928 0.322964 0.946411i 0.395321π-0.395321\pi
0.322964 + 0.946411i 0.395321π0.395321\pi
450450 13.8851 1.26910i 0.654551 0.0598260i
451451 −0.0811263 + 0.140515i −0.00382009 + 0.00661659i
452452 12.3202 0.579495
453453 −1.31284 + 2.53394i −0.0616827 + 0.119055i
454454 −2.40856 + 4.17174i −0.113039 + 0.195790i
455455 0 0
456456 −9.31138 + 0.424646i −0.436045 + 0.0198859i
457457 11.1762 19.3577i 0.522799 0.905515i −0.476849 0.878985i 0.658221π-0.658221\pi
0.999648 0.0265293i 0.00844554π-0.00844554\pi
458458 4.64766 8.04999i 0.217171 0.376151i
459459 −5.72665 + 14.0562i −0.267297 + 0.656088i
460460 1.32383 + 2.29294i 0.0617240 + 0.106909i
461461 3.98755 + 6.90663i 0.185719 + 0.321674i 0.943818 0.330464i 0.107205π-0.107205\pi
−0.758100 + 0.652138i 0.773872π0.773872\pi
462462 0 0
463463 −14.3676 + 24.8854i −0.667719 + 1.15652i 0.310821 + 0.950468i 0.399396π0.399396\pi
−0.978540 + 0.206055i 0.933937π0.933937\pi
464464 6.19436 0.287566
465465 −8.07966 + 0.368473i −0.374685 + 0.0170875i
466466 0.194356 0.00900336
467467 −16.7829 29.0688i −0.776619 1.34514i −0.933880 0.357586i 0.883600π-0.883600\pi
0.157261 0.987557i 0.449733π-0.449733\pi
468468 4.35087 + 6.16266i 0.201119 + 0.284869i
469469 0 0
470470 3.60963 + 6.25206i 0.166500 + 0.288386i
471471 11.4210 0.520856i 0.526252 0.0239998i
472472 −4.32383 7.48910i −0.199020 0.344714i
473473 3.31284 + 5.73801i 0.152325 + 0.263834i
474474 16.0021 0.729778i 0.735002 0.0335198i
475475 12.5057 + 21.6606i 0.573802 + 0.993855i
476476 0 0
477477 −24.0620 + 2.19927i −1.10172 + 0.100698i
478478 6.82743 + 11.8255i 0.312279 + 0.540884i
479479 −0.367120 −0.0167741 −0.00838707 0.999965i 0.502670π-0.502670\pi
−0.00838707 + 0.999965i 0.502670π0.502670\pi
480480 1.02704 0.0468383i 0.0468778 0.00213787i
481481 2.51459 0.114655
482482 6.50000 11.2583i 0.296067 0.512803i
483483 0 0
484484 5.32383 + 9.22115i 0.241992 + 0.419143i
485485 3.48249 + 6.03184i 0.158132 + 0.273892i
486486 −15.1855 + 3.52144i −0.688828 + 0.159736i
487487 −14.9538 + 25.9007i −0.677621 + 1.17367i 0.298075 + 0.954543i 0.403656π0.403656\pi
−0.975695 + 0.219131i 0.929678π0.929678\pi
488488 3.32383 5.75705i 0.150463 0.260609i
489489 10.3509 0.472052i 0.468083 0.0213469i
490490 0 0
491491 −0.255158 + 0.441947i −0.0115151 + 0.0199448i −0.871726 0.489994i 0.836999π-0.836999\pi
0.860210 + 0.509939i 0.170332π0.170332\pi
492492 0.217799 0.420378i 0.00981916 0.0189521i
493493 18.0938 0.814903
494494 −6.76615 + 11.7193i −0.304423 + 0.527277i
495495 −0.609631 0.863492i −0.0274009 0.0388111i
496496 7.86693 0.353235
497497 0 0
498498 6.13667 11.8445i 0.274991 0.530764i
499499 −19.0191 −0.851410 −0.425705 0.904862i 0.639974π-0.639974\pi
−0.425705 + 0.904862i 0.639974π0.639974\pi
500500 −2.86333 4.95943i −0.128052 0.221792i
501501 −6.96410 10.8848i −0.311133 0.486297i
502502 9.77188 16.9254i 0.436141 0.755418i
503503 37.7807 1.68456 0.842280 0.539040i 0.181213π-0.181213\pi
0.842280 + 0.539040i 0.181213π0.181213\pi
504504 0 0
505505 −0.963235 −0.0428634
506506 −1.32383 + 2.29294i −0.0588515 + 0.101934i
507507 −11.5526 + 0.526858i −0.513070 + 0.0233986i
508508 −6.16731 10.6821i −0.273630 0.473942i
509509 11.2163 0.497155 0.248578 0.968612i 0.420037π-0.420037\pi
0.248578 + 0.968612i 0.420037π0.420037\pi
510510 3.00000 0.136815i 0.132842 0.00605828i
511511 0 0
512512 −1.00000 −0.0441942
513513 −17.1517 22.0852i −0.757268 0.975086i
514514 −4.16372 + 7.21177i −0.183654 + 0.318097i
515515 3.78794 0.166916
516516 −10.4195 16.2856i −0.458695 0.716933i
517517 −3.60963 + 6.25206i −0.158751 + 0.274965i
518518 0 0
519519 −23.9518 37.4364i −1.05137 1.64327i
520520 0.746304 1.29264i 0.0327276 0.0566859i
521521 13.7360 23.7914i 0.601785 1.04232i −0.390766 0.920490i 0.627790π-0.627790\pi
0.992551 0.121831i 0.0388767π-0.0388767\pi
522522 10.7178 + 15.1809i 0.469105 + 0.664449i
523523 −11.0919 19.2118i −0.485016 0.840072i 0.514836 0.857289i 0.327853π-0.327853\pi
−0.999852 + 0.0172166i 0.994520π0.994520\pi
524524 −0.593579 1.02811i −0.0259306 0.0449132i
525525 0 0
526526 −8.54523 + 14.8008i −0.372590 + 0.645344i
527527 22.9794 1.00100
528528 0.554084 + 0.866025i 0.0241134 + 0.0376889i
529529 −3.10390 −0.134952
530530 2.39037 + 4.14024i 0.103831 + 0.179841i
531531 10.8727 23.5547i 0.471833 1.02219i
532532 0 0
533533 −0.343677 0.595265i −0.0148863 0.0257838i
534534 −9.90856 + 19.1247i −0.428785 + 0.827605i
535535 −5.55262 9.61742i −0.240061 0.415797i
536536 −0.956906 1.65741i −0.0413321 0.0715892i
537537 14.0359 + 21.9379i 0.605694 + 0.946690i
538538 −5.00720 8.67272i −0.215876 0.373908i
539539 0 0
540540 1.89183 + 2.43599i 0.0814115 + 0.104828i
541541 14.9246 + 25.8502i 0.641659 + 1.11139i 0.985062 + 0.172198i 0.0550869π0.0550869\pi
−0.343403 + 0.939188i 0.611580π0.611580\pi
542542 −10.2091 −0.438520
543543 −0.0686733 + 0.132547i −0.00294705 + 0.00568816i
544544 −2.92101 −0.125237
545545 0.850874 1.47376i 0.0364474 0.0631288i
546546 0 0
547547 8.84348 + 15.3174i 0.378120 + 0.654923i 0.990789 0.135417i 0.0432373π-0.0432373\pi
−0.612669 + 0.790340i 0.709904π0.709904\pi
548548 −1.26089 2.18393i −0.0538627 0.0932929i
549549 19.8602 1.81523i 0.847613 0.0774720i
550550 1.37938 2.38915i 0.0588169 0.101874i
551551 −16.6675 + 28.8690i −0.710060 + 1.22986i
552552 3.55408 6.85980i 0.151272 0.291972i
553553 0 0
554554 9.67111 16.7508i 0.410886 0.711675i
555555 1.02704 0.0468383i 0.0435955 0.00198818i
556556 4.91381 0.208392
557557 15.0651 26.0935i 0.638328 1.10562i −0.347472 0.937690i 0.612960π-0.612960\pi
0.985800 0.167926i 0.0537069π-0.0537069\pi
558558 13.6118 + 19.2799i 0.576232 + 0.816185i
559559 −28.0685 −1.18717
560560 0 0
561561 1.61849 + 2.52967i 0.0683325 + 0.106803i
562562 −12.8027 −0.540050
563563 2.04883 + 3.54867i 0.0863478 + 0.149559i 0.905965 0.423353i 0.139147π-0.139147\pi
−0.819617 + 0.572912i 0.805814π0.805814\pi
564564 9.69076 18.7043i 0.408054 0.787593i
565565 3.65652 6.33327i 0.153831 0.266443i
566566 −16.3523 −0.687340
567567 0 0
568568 14.4107 0.604659
569569 −3.11849 + 5.40138i −0.130734 + 0.226437i −0.923960 0.382490i 0.875067π-0.875067\pi
0.793226 + 0.608927i 0.208400π0.208400\pi
570570 −2.54523 + 4.91259i −0.106608 + 0.205766i
571571 −17.8011 30.8323i −0.744951 1.29029i −0.950218 0.311587i 0.899139π-0.899139\pi
0.205266 0.978706i 0.434194π-0.434194\pi
572572 1.49261 0.0624091
573573 −3.71732 5.81012i −0.155293 0.242721i
574574 0 0
575575 −20.7309 −0.864539
576576 −1.73025 2.45076i −0.0720939 0.102115i
577577 −23.1388 + 40.0776i −0.963281 + 1.66845i −0.249118 + 0.968473i 0.580141π0.580141\pi
−0.714164 + 0.699979i 0.753193π0.753193\pi
578578 8.46770 0.352210
579579 11.7324 0.535056i 0.487581 0.0222362i
580580 1.83842 3.18424i 0.0763363 0.132218i
581581 0 0
582582 9.34941 18.0455i 0.387546 0.748008i
583583 −2.39037 + 4.14024i −0.0989990 + 0.171471i
584584 3.95691 6.85356i 0.163738 0.283602i
585585 4.45924 0.407575i 0.184367 0.0168512i
586586 −10.3889 17.9941i −0.429162 0.743330i
587587 −1.13161 1.96001i −0.0467066 0.0808982i 0.841727 0.539903i 0.181539π-0.181539\pi
−0.888434 + 0.459005i 0.848206π0.848206\pi
588588 0 0
589589 −21.1680 + 36.6640i −0.872212 + 1.51072i
590590 −5.13307 −0.211325
591591 −8.81118 + 17.0066i −0.362444 + 0.699558i
592592 −1.00000 −0.0410997
593593 −23.0979 40.0067i −0.948515 1.64288i −0.748555 0.663072i 0.769252π-0.769252\pi
−0.199960 0.979804i 0.564081π-0.564081\pi
594594 −1.16372 + 2.85637i −0.0477478 + 0.117198i
595595 0 0
596596 −9.02558 15.6328i −0.369702 0.640343i
597597 −5.24465 8.19731i −0.214649 0.335493i
598598 −5.60817 9.71363i −0.229335 0.397220i
599599 8.39037 + 14.5325i 0.342821 + 0.593784i 0.984955 0.172808i 0.0552842π-0.0552842\pi
−0.642134 + 0.766592i 0.721951π0.721951\pi
600600 −3.70321 + 7.14763i −0.151183 + 0.291801i
601601 5.69961 + 9.87202i 0.232492 + 0.402688i 0.958541 0.284955i 0.0919787π-0.0919787\pi
−0.726049 + 0.687643i 0.758645π0.758645\pi
602602 0 0
603603 2.40623 5.21289i 0.0979891 0.212285i
604604 −0.823832 1.42692i −0.0335212 0.0580605i
605605 6.32023 0.256954
606606 1.51478 + 2.36758i 0.0615339 + 0.0961765i
607607 14.4284 0.585631 0.292815 0.956169i 0.405408π-0.405408\pi
0.292815 + 0.956169i 0.405408π0.405408\pi
608608 2.69076 4.66053i 0.109125 0.189009i
609609 0 0
610610 −1.97296 3.41726i −0.0798827 0.138361i
611611 −15.2915 26.4857i −0.618629 1.07150i
612612 −5.05408 7.15869i −0.204299 0.289373i
613613 12.2053 21.1403i 0.492969 0.853848i −0.506998 0.861947i 0.669245π-0.669245\pi
0.999967 + 0.00809942i 0.00257815π0.00257815\pi
614614 11.3384 19.6387i 0.457581 0.792554i
615615 −0.151457 0.236725i −0.00610733 0.00954566i
616616 0 0
617617 24.4698 42.3830i 0.985119 1.70628i 0.343710 0.939076i 0.388316π-0.388316\pi
0.641408 0.767200i 0.278350π-0.278350\pi
618618 −5.95691 9.31056i −0.239622 0.374525i
619619 44.6591 1.79500 0.897501 0.441012i 0.145380π-0.145380\pi
0.897501 + 0.441012i 0.145380π0.145380\pi
620620 2.33482 4.04403i 0.0937687 0.162412i
621621 22.9612 3.15897i 0.921400 0.126765i
622622 −6.51459 −0.261211
623623 0 0
624624 −4.35087 + 0.198422i −0.174174 + 0.00794323i
625625 19.8391 0.793564
626626 −0.133074 0.230492i −0.00531873 0.00921230i
627627 −5.52704 + 0.252061i −0.220729 + 0.0100663i
628628 −3.30039 + 5.71644i −0.131700 + 0.228111i
629629 −2.92101 −0.116468
630630 0 0
631631 33.2852 1.32506 0.662532 0.749034i 0.269482π-0.269482\pi
0.662532 + 0.749034i 0.269482π0.269482\pi
632632 −4.62422 + 8.00938i −0.183942 + 0.318596i
633633 18.0387 + 28.1942i 0.716974 + 1.12062i
634634 7.86186 + 13.6171i 0.312235 + 0.540806i
635635 −7.32158 −0.290548
636636 6.41741 12.3863i 0.254467 0.491151i
637637 0 0
638638 3.67684 0.145568
639639 24.9341 + 35.3172i 0.986379 + 1.39713i
640640 −0.296790 + 0.514055i −0.0117316 + 0.0203198i
641641 30.7879 1.21605 0.608025 0.793918i 0.291962π-0.291962\pi
0.608025 + 0.793918i 0.291962π0.291962\pi
642642 −14.9071 + 28.7724i −0.588336 + 1.13556i
643643 13.7345 23.7889i 0.541637 0.938142i −0.457174 0.889378i 0.651138π-0.651138\pi
0.998810 0.0487649i 0.0155285π-0.0155285\pi
644644 0 0
645645 −11.4641 + 0.522821i −0.451399 + 0.0205861i
646646 7.85973 13.6134i 0.309237 0.535614i
647647 6.63521 11.4925i 0.260857 0.451818i −0.705613 0.708598i 0.749328π-0.749328\pi
0.966470 + 0.256780i 0.0826615π0.0826615\pi
648648 3.01245 8.48087i 0.118340 0.333160i
649649 −2.56654 4.44537i −0.100745 0.174496i
650650 5.84348 + 10.1212i 0.229200 + 0.396986i
651651 0 0
652652 −2.99115 + 5.18082i −0.117142 + 0.202896i
653653 −17.1416 −0.670803 −0.335402 0.942075i 0.608872π-0.608872\pi
−0.335402 + 0.942075i 0.608872π0.608872\pi
654654 −4.96050 + 0.226224i −0.193971 + 0.00884606i
655655 −0.704673 −0.0275338
656656 0.136673 + 0.236725i 0.00533619 + 0.00924255i
657657 23.6429 2.16096i 0.922397 0.0843072i
658658 0 0
659659 4.26089 + 7.38008i 0.165981 + 0.287487i 0.937003 0.349321i 0.113588π-0.113588\pi
−0.771022 + 0.636808i 0.780254π0.780254\pi
660660 0.609631 0.0278023i 0.0237299 0.00108220i
661661 17.1680 + 29.7358i 0.667757 + 1.15659i 0.978530 + 0.206105i 0.0660789π0.0660789\pi
−0.310773 + 0.950484i 0.600588π0.600588\pi
662662 −12.5811 21.7912i −0.488979 0.846937i
663663 −12.7089 + 0.579592i −0.493575 + 0.0225095i
664664 3.85087 + 6.66991i 0.149443 + 0.258843i
665665 0 0
666666 −1.73025 2.45076i −0.0670459 0.0949650i
667667 −13.8150 23.9282i −0.534918 0.926505i
668668 7.46050 0.288656
669669 43.8178 1.99831i 1.69409 0.0772592i
670670 −1.13600 −0.0438875
671671 1.97296 3.41726i 0.0761652 0.131922i
672672 0 0
673673 −7.70155 13.3395i −0.296873 0.514199i 0.678546 0.734558i 0.262610π-0.262610\pi
−0.975419 + 0.220359i 0.929277π0.929277\pi
674674 9.36693 + 16.2240i 0.360800 + 0.624925i
675675 −23.9246 + 3.29152i −0.920859 + 0.126691i
676676 3.33842 5.78231i 0.128401 0.222397i
677677 −3.69076 + 6.39258i −0.141847 + 0.245687i −0.928192 0.372101i 0.878638π-0.878638\pi
0.786345 + 0.617788i 0.211971π0.211971\pi
678678 −21.3171 + 0.972168i −0.818679 + 0.0373359i
679679 0 0
680680 −0.866926 + 1.50156i −0.0332451 + 0.0575822i
681681 3.83823 7.40822i 0.147081 0.283884i
682682 4.66964 0.178810
683683 4.79893 8.31198i 0.183626 0.318049i −0.759487 0.650523i 0.774550π-0.774550\pi
0.943113 + 0.332474i 0.107883π0.107883\pi
684684 16.0775 1.46949i 0.614740 0.0561873i
685685 −1.49688 −0.0571929
686686 0 0
687687 −7.40642 + 14.2953i −0.282573 + 0.545398i
688688 11.1623 0.425557
689689 −10.1264 17.5394i −0.385783 0.668197i
690690 −2.47150 3.86291i −0.0940882 0.147058i
691691 −7.07227 + 12.2495i −0.269042 + 0.465994i −0.968615 0.248567i 0.920040π-0.920040\pi
0.699573 + 0.714561i 0.253374π0.253374\pi
692692 25.6591 0.975414
693693 0 0
694694 −22.5438 −0.855750
695695 1.45837 2.52597i 0.0553191 0.0958155i
696696 −10.7178 + 0.488786i −0.406257 + 0.0185274i
697697 0.399223 + 0.691475i 0.0151217 + 0.0261915i
698698 −3.79086 −0.143486
699699 −0.336285 + 0.0153363i −0.0127195 + 0.000580072i
700700 0 0
701701 37.3753 1.41164 0.705822 0.708389i 0.250578π-0.250578\pi
0.705822 + 0.708389i 0.250578π0.250578\pi
702702 −8.01439 10.3196i −0.302484 0.389489i
703703 2.69076 4.66053i 0.101484 0.175775i
704704 −0.593579 −0.0223714
705705 −6.73891 10.5328i −0.253802 0.396689i
706706 −3.41741 + 5.91913i −0.128616 + 0.222769i
707707 0 0
708708 8.07227 + 12.6168i 0.303375 + 0.474170i
709709 5.24338 9.08180i 0.196919 0.341074i −0.750609 0.660747i 0.770240π-0.770240\pi
0.947528 + 0.319673i 0.103573π0.103573\pi
710710 4.27694 7.40789i 0.160511 0.278013i
711711 −27.6301 + 2.52540i −1.03621 + 0.0947099i
712712 −6.21780 10.7695i −0.233022 0.403606i
713713 −17.5452 30.3892i −0.657074 1.13809i
714714 0 0
715715 0.442991 0.767282i 0.0165669 0.0286947i
716716 −15.0364 −0.561936
717717 −12.7463 19.9223i −0.476019 0.744011i
718718 −12.6447 −0.471897
719719 −1.11995 1.93981i −0.0417670 0.0723426i 0.844386 0.535735i 0.179965π-0.179965\pi
−0.886153 + 0.463392i 0.846632π0.846632\pi
720720 −1.77335 + 0.162084i −0.0660887 + 0.00604052i
721721 0 0
722722 4.98035 + 8.62622i 0.185349 + 0.321035i
723723 −10.3583 + 19.9927i −0.385228 + 0.743535i
724724 −0.0430937 0.0746406i −0.00160157 0.00277399i
725725 14.3946 + 24.9322i 0.534604 + 0.925961i
726726 −9.93920 15.5348i −0.368878 0.576551i
727727 −0.185023 0.320469i −0.00686211 0.0118855i 0.862574 0.505931i 0.168851π-0.168851\pi
−0.869436 + 0.494045i 0.835518π0.835518\pi
728728 0 0
729729 25.9969 7.29124i 0.962847 0.270046i
730730 −2.34874 4.06813i −0.0869307 0.150568i
731731 32.6050 1.20594
732732 −5.29679 + 10.2234i −0.195775 + 0.377868i
733733 −14.0191 −0.517806 −0.258903 0.965903i 0.583361π-0.583361\pi
−0.258903 + 0.965903i 0.583361π0.583361\pi
734734 −3.27188 + 5.66707i −0.120767 + 0.209175i
735735 0 0
736736 2.23025 + 3.86291i 0.0822082 + 0.142389i
737737 −0.568000 0.983804i −0.0209225 0.0362389i
738738 −0.343677 + 0.744547i −0.0126509 + 0.0274071i
739739 13.3872 23.1874i 0.492458 0.852962i −0.507504 0.861649i 0.669432π-0.669432\pi
0.999962 + 0.00868705i 0.00276521π0.00276521\pi
740740 −0.296790 + 0.514055i −0.0109102 + 0.0188970i
741741 10.7824 20.8113i 0.396101 0.764521i
742742 0 0
743743 −5.04669 + 8.74113i −0.185145 + 0.320681i −0.943625 0.331015i 0.892609π-0.892609\pi
0.758480 + 0.651696i 0.225942π0.225942\pi
744744 −13.6118 + 0.620765i −0.499032 + 0.0227584i
745745 −10.7148 −0.392560
746746 4.71420 8.16524i 0.172599 0.298951i
747747 −9.68337 + 20.9782i −0.354296 + 0.767552i
748748 −1.73385 −0.0633959
749749 0 0
750750 5.34562 + 8.35512i 0.195194 + 0.305086i
751751 11.5146 0.420173 0.210087 0.977683i 0.432625π-0.432625\pi
0.210087 + 0.977683i 0.432625π0.432625\pi
752752 6.08113 + 10.5328i 0.221756 + 0.384092i
753753 −15.5723 + 30.0563i −0.567485 + 1.09531i
754754 −7.78813 + 13.4894i −0.283627 + 0.491256i
755755 −0.978019 −0.0355938
756756 0 0
757757 −15.2484 −0.554214 −0.277107 0.960839i 0.589376π-0.589376\pi
−0.277107 + 0.960839i 0.589376π0.589376\pi
758758 −3.63881 + 6.30260i −0.132168 + 0.228921i
759759 2.10963 4.07183i 0.0765748 0.147798i
760760 −1.59718 2.76639i −0.0579357 0.100348i
761761 1.70175 0.0616883 0.0308442 0.999524i 0.490180π-0.490180\pi
0.0308442 + 0.999524i 0.490180π0.490180\pi
762762 11.5139 + 17.9961i 0.417105 + 0.651929i
763763 0 0
764764 3.98229 0.144074
765765 −5.17996 + 0.473449i −0.187282 + 0.0171176i
766766 12.0416 20.8567i 0.435082 0.753584i
767767 21.7453 0.785178
768768 1.73025 0.0789082i 0.0624351 0.00284736i
769769 −24.1211 + 41.7790i −0.869829 + 1.50659i −0.00765823 + 0.999971i 0.502438π0.502438\pi
−0.862171 + 0.506618i 0.830896π0.830896\pi
770770 0 0
771771 6.63521 12.8067i 0.238961 0.461223i
772772 −3.39037 + 5.87229i −0.122022 + 0.211348i
773773 −3.10243 + 5.37357i −0.111587 + 0.193274i −0.916410 0.400240i 0.868927π-0.868927\pi
0.804823 + 0.593514i 0.202260π0.202260\pi
774774 19.3135 + 27.3560i 0.694210 + 0.983291i
775775 18.2814 + 31.6643i 0.656688 + 1.13742i
776776 5.86693 + 10.1618i 0.210610 + 0.364788i
777777 0 0
778778 −8.14913 + 14.1147i −0.292160 + 0.506037i
779779 −1.47102 −0.0527046
780780 −1.18929 + 2.29548i −0.0425836 + 0.0821913i
781781 8.55389 0.306082
782782 6.51459 + 11.2836i 0.232961 + 0.403501i
783783 −19.7424 25.4210i −0.705536 0.908474i
784784 0 0
785785 1.95904 + 3.39316i 0.0699212 + 0.121107i
786786 1.10817 + 1.73205i 0.0395271 + 0.0617802i
787787 3.04883 + 5.28073i 0.108679 + 0.188238i 0.915235 0.402920i 0.132005π-0.132005\pi
−0.806556 + 0.591157i 0.798671π0.798671\pi
788788 −5.52918 9.57682i −0.196969 0.341160i
789789 13.6175 26.2834i 0.484796 0.935712i
790790 2.74484 + 4.75420i 0.0976571 + 0.169147i
791791 0 0
792792 −1.02704 1.45472i −0.0364944 0.0516913i
793793 8.35807 + 14.4766i 0.296804 + 0.514079i
794794 12.1724 0.431981
795795 −4.46264 6.97504i −0.158274 0.247379i
796796 5.61849 0.199142
797797 6.22860 10.7882i 0.220628 0.382139i −0.734371 0.678749i 0.762523π-0.762523\pi
0.954999 + 0.296609i 0.0958559π0.0958559\pi
798798 0 0
799799 17.7630 + 30.7665i 0.628411 + 1.08844i
800800 −2.32383 4.02499i −0.0821599 0.142305i
801801 15.6352 33.8724i 0.552443 1.19682i
802802 −16.6804 + 28.8914i −0.589007 + 1.02019i
803803 2.34874 4.06813i 0.0828852 0.143561i
804804 1.78647 + 2.79223i 0.0630040 + 0.0984744i
805805 0 0
806806 −9.89104 + 17.1318i −0.348397 + 0.603442i
807807 9.34806 + 14.6109i 0.329067 + 0.514328i
808808 −1.62276 −0.0570884
809809 −2.81644 + 4.87822i −0.0990208 + 0.171509i −0.911280 0.411788i 0.864904π-0.864904\pi
0.812259 + 0.583297i 0.198238π0.198238\pi
810810 −3.46557 4.06560i −0.121768 0.142851i
811811 45.6414 1.60269 0.801344 0.598204i 0.204119π-0.204119\pi
0.801344 + 0.598204i 0.204119π0.204119\pi
812812 0 0
813813 17.6644 0.805585i 0.619517 0.0282531i
814814 −0.593579 −0.0208049
815815 1.77548 + 3.07523i 0.0621924 + 0.107720i
816816 5.05408 0.230492i 0.176928 0.00806883i
817817 −30.0349 + 52.0220i −1.05079 + 1.82002i
818818 −5.78074 −0.202119
819819 0 0
820820 0.162253 0.00566611
821821 −16.3473 + 28.3143i −0.570524 + 0.988176i 0.425988 + 0.904729i 0.359926π0.359926\pi
−0.996512 + 0.0834476i 0.973407π0.973407\pi
822822 2.35399 + 3.67926i 0.0821050 + 0.128329i
823823 5.21994 + 9.04119i 0.181956 + 0.315156i 0.942546 0.334075i 0.108424π-0.108424\pi
−0.760591 + 0.649231i 0.775091π0.775091\pi
824824 6.38151 0.222311
825825 −2.19815 + 4.24268i −0.0765297 + 0.147711i
826826 0 0
827827 16.7060 0.580925 0.290463 0.956886i 0.406191π-0.406191\pi
0.290463 + 0.956886i 0.406191π0.406191\pi
828828 −5.60817 + 12.1496i −0.194897 + 0.422229i
829829 13.1046 22.6978i 0.455141 0.788327i −0.543556 0.839373i 0.682922π-0.682922\pi
0.998696 + 0.0510466i 0.0162557π0.0162557\pi
830830 4.57160 0.158682
831831 −15.4117 + 29.7463i −0.534625 + 1.03189i
832832 1.25729 2.17770i 0.0435888 0.0754981i
833833 0 0
834834 −8.50214 + 0.387740i −0.294405 + 0.0134263i
835835 2.21420 3.83511i 0.0766256 0.132719i
836836 1.59718 2.76639i 0.0552396 0.0956777i
837837 −25.0731 32.2851i −0.866655 1.11594i
838838 15.4356 + 26.7352i 0.533214 + 0.923554i
839839 −11.1886 19.3793i −0.386274 0.669046i 0.605671 0.795715i 0.292905π-0.292905\pi
−0.991945 + 0.126669i 0.959571π0.959571\pi
840840 0 0
841841 −4.68502 + 8.11470i −0.161553 + 0.279817i
842842 −3.73385 −0.128677
843843 22.1519 1.01024i 0.762953 0.0347945i
844844 −19.3245 −0.665177
845845 −1.98162 3.43226i −0.0681697 0.118073i
846846 −15.2915 + 33.1278i −0.525734 + 1.13896i
847847 0 0
848848 4.02704 + 6.97504i 0.138289 + 0.239524i
849849 28.2937 1.29033i 0.971036 0.0442842i
850850 −6.78794 11.7570i −0.232824 0.403263i
851851 2.23025 + 3.86291i 0.0764521 + 0.132419i
852852 −24.9341 + 1.13712i −0.854229 + 0.0389572i
853853 −4.96264 8.59555i −0.169918 0.294306i 0.768473 0.639882i 0.221017π-0.221017\pi
−0.938391 + 0.345576i 0.887683π0.887683\pi
854854 0 0
855855 4.01625 8.70086i 0.137353 0.297563i
856856 −9.35447 16.2024i −0.319729 0.553787i
857857 −7.79552 −0.266290 −0.133145 0.991097i 0.542508π-0.542508\pi
−0.133145 + 0.991097i 0.542508π0.542508\pi
858858 −2.58259 + 0.117779i −0.0881681 + 0.00402091i
859859 −16.3422 −0.557589 −0.278795 0.960351i 0.589935π-0.589935\pi
−0.278795 + 0.960351i 0.589935π0.589935\pi
860860 3.31284 5.73801i 0.112967 0.195664i
861861 0 0
862862 14.0979 + 24.4182i 0.480175 + 0.831687i
863863 0.730252 + 1.26483i 0.0248581 + 0.0430555i 0.878187 0.478318i 0.158753π-0.158753\pi
−0.853329 + 0.521373i 0.825420π0.825420\pi
864864 3.18716 + 4.10390i 0.108429 + 0.139618i
865865 7.61537 13.1902i 0.258930 0.448480i
866866 −6.27188 + 10.8632i −0.213127 + 0.369147i
867867 −14.6513 + 0.668172i −0.497583 + 0.0226923i
868868 0 0
869869 −2.74484 + 4.75420i −0.0931124 + 0.161275i
870870 −2.92967 + 5.65460i −0.0993251 + 0.191709i
871871 4.81245 0.163064
872872 1.43346 2.48283i 0.0485432 0.0840792i
873873 −14.7529 + 31.9609i −0.499310 + 1.08171i
874874 −24.0043 −0.811957
875875 0 0
876876 −6.30564 + 12.1706i −0.213048 + 0.411207i
877877 −2.40935 −0.0813578 −0.0406789 0.999172i 0.512952π-0.512952\pi
−0.0406789 + 0.999172i 0.512952π0.512952\pi
878878 −13.0203 22.5519i −0.439415 0.761088i
879879 19.3953 + 30.3146i 0.654188 + 1.02249i
880880 −0.176168 + 0.305132i −0.00593863 + 0.0102860i
881881 18.9607 0.638802 0.319401 0.947620i 0.396518π-0.396518\pi
0.319401 + 0.947620i 0.396518π0.396518\pi
882882 0 0
883883 3.64008 0.122498 0.0612492 0.998123i 0.480492π-0.480492\pi
0.0612492 + 0.998123i 0.480492π0.480492\pi
884884 3.67257 6.36108i 0.123522 0.213946i
885885 8.88151 0.405042i 0.298549 0.0136153i
886886 −11.7865 20.4148i −0.395974 0.685848i
887887 24.4572 0.821192 0.410596 0.911817i 0.365321π-0.365321\pi
0.410596 + 0.911817i 0.365321π0.365321\pi
888888 1.73025 0.0789082i 0.0580635 0.00264799i
889889 0 0
890890 −7.38151 −0.247429
891891 1.78813 5.03407i 0.0599046 0.168648i
892892 −12.6623 + 21.9317i −0.423964 + 0.734326i
893893 −65.4513 −2.19025
894894 16.8501 + 26.3364i 0.563551 + 0.880822i
895895 −4.46264 + 7.72952i −0.149170 + 0.258369i
896896 0 0
897897 10.4700 + 16.3645i 0.349584 + 0.546395i
898898 6.84348 11.8533i 0.228370 0.395548i
899899 −24.3653 + 42.2019i −0.812627 + 1.40751i
900900 5.84348 12.6594i 0.194783 0.421980i
901901 11.7630 + 20.3742i 0.391883 + 0.678762i
902902 0.0811263 + 0.140515i 0.00270121 + 0.00467863i
903903 0 0
904904 6.16012 10.6696i 0.204882 0.354867i
905905 −0.0511591 −0.00170059
906906 1.53803 + 2.40392i 0.0510977 + 0.0798650i
907907 10.0368 0.333265 0.166633 0.986019i 0.446711π-0.446711\pi
0.166633 + 0.986019i 0.446711π0.446711\pi
908908 2.40856 + 4.17174i 0.0799308 + 0.138444i
909909 −2.80778 3.97699i −0.0931282 0.131908i
910910 0 0
911911 11.4459 + 19.8249i 0.379220 + 0.656828i 0.990949 0.134239i 0.0428590π-0.0428590\pi
−0.611729 + 0.791067i 0.709526π0.709526\pi
912912 −4.28794 + 8.27621i −0.141988 + 0.274053i
913913 2.28580 + 3.95912i 0.0756489 + 0.131028i
914914 −11.1762 19.3577i −0.369675 0.640296i
915915 3.68337 + 5.75705i 0.121768 + 0.190322i
916916 −4.64766 8.04999i −0.153563 0.265979i
917917 0 0
918918 9.30972 + 11.9875i 0.307267 + 0.395648i
919919 10.8910 + 18.8638i 0.359262 + 0.622261i 0.987838 0.155488i 0.0496950π-0.0496950\pi
−0.628575 + 0.777749i 0.716362π0.716362\pi
920920 2.64766 0.0872909
921921 −18.0687 + 34.8746i −0.595383 + 1.14916i
922922 7.97509 0.262646
923923 −18.1185 + 31.3821i −0.596377 + 1.03296i
924924 0 0
925925 −2.32383 4.02499i −0.0764071 0.132341i
926926 14.3676 + 24.8854i 0.472149 + 0.817785i
927927 11.0416 + 15.6396i 0.362655 + 0.513671i
928928 3.09718 5.36447i 0.101670 0.176097i
929929 −16.4189 + 28.4383i −0.538686 + 0.933031i 0.460289 + 0.887769i 0.347746π0.347746\pi
−0.998975 + 0.0452622i 0.985588π0.985588\pi
930930 −3.72072 + 7.18143i −0.122007 + 0.235488i
931931 0 0
932932 0.0971780 0.168317i 0.00318317 0.00551341i
933933 11.2719 0.514055i 0.369025 0.0168294i
934934 −33.5657 −1.09830
935935 −0.514589 + 0.891294i −0.0168289 + 0.0291484i
936936 7.51245 0.686640i 0.245552 0.0224435i
937937 8.78074 0.286854 0.143427 0.989661i 0.454188π-0.454188\pi
0.143427 + 0.989661i 0.454188π0.454188\pi
938938 0 0
939939 0.248440 + 0.388308i 0.00810754 + 0.0126720i
940940 7.21926 0.235466
941941 2.13307 + 3.69459i 0.0695362 + 0.120440i 0.898697 0.438570i 0.144515π-0.144515\pi
−0.829161 + 0.559010i 0.811181π0.811181\pi
942942 5.25943 10.1513i 0.171362 0.330748i
943943 0.609631 1.05591i 0.0198523 0.0343852i
944944 −8.64766 −0.281457
945945 0 0
946946 6.62568 0.215420
947947 11.5292 19.9691i 0.374648 0.648909i −0.615626 0.788038i 0.711097π-0.711097\pi
0.990274 + 0.139129i 0.0444302π0.0444302\pi
948948 7.36906 14.2231i 0.239336 0.461946i
949949 9.94999 + 17.2339i 0.322990 + 0.559436i
950950 25.0115 0.811479
951951 −14.6775 22.9407i −0.475951 0.743904i
952952 0 0
953953 −36.5552 −1.18414 −0.592070 0.805886i 0.701689π-0.701689\pi
−0.592070 + 0.805886i 0.701689π0.701689\pi
954954 −10.1264 + 21.9379i −0.327853 + 0.710266i
955955 1.18190 2.04712i 0.0382455 0.0662431i
956956 13.6549 0.441630
957957 −6.36186 + 0.290133i −0.205650 + 0.00937867i
958958 −0.183560 + 0.317935i −0.00593056 + 0.0102720i
959959 0 0
960960 0.472958 0.912864i 0.0152647 0.0294625i
961961 −15.4443 + 26.7502i −0.498202 + 0.862911i
962962 1.25729 2.17770i 0.0405368 0.0702118i
963963 23.5227 50.9599i 0.758007 1.64216i
964964 −6.50000 11.2583i −0.209351 0.362606i
965965 2.01245 + 3.48567i 0.0647832 + 0.112208i
966966 0 0
967967 26.7719 46.3703i 0.860926 1.49117i −0.0101108 0.999949i 0.503218π-0.503218\pi
0.871037 0.491218i 0.163448π-0.163448\pi
968968 10.6477 0.342229
969969 −12.5251 + 24.1749i −0.402364 + 0.776610i
970970 6.96497 0.223632
971971 15.9897 + 27.6949i 0.513133 + 0.888773i 0.999884 + 0.0152321i 0.00484870π0.00484870\pi
−0.486751 + 0.873541i 0.661818π0.661818\pi
972972 −4.54309 + 14.9118i −0.145720 + 0.478295i
973973 0 0
974974 14.9538 + 25.9007i 0.479150 + 0.829913i
975975 −10.9093 17.0511i −0.349379 0.546074i
976976 −3.32383 5.75705i −0.106393 0.184279i
977977 13.7104 + 23.7471i 0.438635 + 0.759738i 0.997584 0.0694638i 0.0221288π-0.0221288\pi
−0.558950 + 0.829202i 0.688796π0.688796\pi
978978 4.76663 9.20015i 0.152420 0.294188i
979979 −3.69076 6.39258i −0.117957 0.204308i
980980 0 0
981981 8.56507 0.782849i 0.273462 0.0249945i
982982 0.255158 + 0.441947i 0.00814243 + 0.0141031i
983983 59.1564 1.88680 0.943398 0.331662i 0.107610π-0.107610\pi
0.943398 + 0.331662i 0.107610π0.107610\pi
984984 −0.255158 0.398809i −0.00813416 0.0127136i
985985 −6.56401 −0.209147
986986 9.04689 15.6697i 0.288112 0.499024i
987987 0 0
988988 6.76615 + 11.7193i 0.215260 + 0.372841i
989989 −24.8946 43.1188i −0.791604 1.37110i
990990 −1.05262 + 0.0962098i −0.0334545 + 0.00305775i
991991 6.41887 11.1178i 0.203902 0.353169i −0.745880 0.666080i 0.767971π-0.767971\pi
0.949782 + 0.312911i 0.101304π0.101304\pi
992992 3.93346 6.81296i 0.124888 0.216312i
993993 23.4880 + 36.7114i 0.745370 + 1.16500i
994994 0 0
995995 1.66751 2.88821i 0.0528636 0.0915624i
996996 −7.18929 11.2368i −0.227802 0.356050i
997997 5.78074 0.183078 0.0915389 0.995802i 0.470821π-0.470821\pi
0.0915389 + 0.995802i 0.470821π0.470821\pi
998998 −9.50953 + 16.4710i −0.301019 + 0.521380i
999999 3.18716 + 4.10390i 0.100837 + 0.129842i
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.h.p.67.2 6
3.2 odd 2 2646.2.h.o.361.2 6
7.2 even 3 882.2.e.o.373.2 6
7.3 odd 6 882.2.f.n.589.1 6
7.4 even 3 882.2.f.o.589.3 6
7.5 odd 6 126.2.e.c.121.2 yes 6
7.6 odd 2 126.2.h.d.67.2 yes 6
9.2 odd 6 2646.2.e.p.2125.2 6
9.7 even 3 882.2.e.o.655.2 6
21.2 odd 6 2646.2.e.p.1549.2 6
21.5 even 6 378.2.e.d.37.2 6
21.11 odd 6 2646.2.f.m.1765.2 6
21.17 even 6 2646.2.f.l.1765.2 6
21.20 even 2 378.2.h.c.361.2 6
28.19 even 6 1008.2.q.g.625.2 6
28.27 even 2 1008.2.t.h.193.2 6
63.2 odd 6 2646.2.h.o.667.2 6
63.4 even 3 7938.2.a.bw.1.2 3
63.5 even 6 1134.2.g.l.163.2 6
63.11 odd 6 2646.2.f.m.883.2 6
63.13 odd 6 1134.2.g.m.487.2 6
63.16 even 3 inner 882.2.h.p.79.2 6
63.20 even 6 378.2.e.d.235.2 6
63.25 even 3 882.2.f.o.295.3 6
63.31 odd 6 7938.2.a.bv.1.2 3
63.32 odd 6 7938.2.a.bz.1.2 3
63.34 odd 6 126.2.e.c.25.2 6
63.38 even 6 2646.2.f.l.883.2 6
63.40 odd 6 1134.2.g.m.163.2 6
63.41 even 6 1134.2.g.l.487.2 6
63.47 even 6 378.2.h.c.289.2 6
63.52 odd 6 882.2.f.n.295.1 6
63.59 even 6 7938.2.a.ca.1.2 3
63.61 odd 6 126.2.h.d.79.2 yes 6
84.47 odd 6 3024.2.q.g.2305.2 6
84.83 odd 2 3024.2.t.h.1873.2 6
252.47 odd 6 3024.2.t.h.289.2 6
252.83 odd 6 3024.2.q.g.2881.2 6
252.187 even 6 1008.2.t.h.961.2 6
252.223 even 6 1008.2.q.g.529.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.2 6 63.34 odd 6
126.2.e.c.121.2 yes 6 7.5 odd 6
126.2.h.d.67.2 yes 6 7.6 odd 2
126.2.h.d.79.2 yes 6 63.61 odd 6
378.2.e.d.37.2 6 21.5 even 6
378.2.e.d.235.2 6 63.20 even 6
378.2.h.c.289.2 6 63.47 even 6
378.2.h.c.361.2 6 21.20 even 2
882.2.e.o.373.2 6 7.2 even 3
882.2.e.o.655.2 6 9.7 even 3
882.2.f.n.295.1 6 63.52 odd 6
882.2.f.n.589.1 6 7.3 odd 6
882.2.f.o.295.3 6 63.25 even 3
882.2.f.o.589.3 6 7.4 even 3
882.2.h.p.67.2 6 1.1 even 1 trivial
882.2.h.p.79.2 6 63.16 even 3 inner
1008.2.q.g.529.2 6 252.223 even 6
1008.2.q.g.625.2 6 28.19 even 6
1008.2.t.h.193.2 6 28.27 even 2
1008.2.t.h.961.2 6 252.187 even 6
1134.2.g.l.163.2 6 63.5 even 6
1134.2.g.l.487.2 6 63.41 even 6
1134.2.g.m.163.2 6 63.40 odd 6
1134.2.g.m.487.2 6 63.13 odd 6
2646.2.e.p.1549.2 6 21.2 odd 6
2646.2.e.p.2125.2 6 9.2 odd 6
2646.2.f.l.883.2 6 63.38 even 6
2646.2.f.l.1765.2 6 21.17 even 6
2646.2.f.m.883.2 6 63.11 odd 6
2646.2.f.m.1765.2 6 21.11 odd 6
2646.2.h.o.361.2 6 3.2 odd 2
2646.2.h.o.667.2 6 63.2 odd 6
3024.2.q.g.2305.2 6 84.47 odd 6
3024.2.q.g.2881.2 6 252.83 odd 6
3024.2.t.h.289.2 6 252.47 odd 6
3024.2.t.h.1873.2 6 84.83 odd 2
7938.2.a.bv.1.2 3 63.31 odd 6
7938.2.a.bw.1.2 3 63.4 even 3
7938.2.a.bz.1.2 3 63.32 odd 6
7938.2.a.ca.1.2 3 63.59 even 6