Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4160,2,Mod(1,4160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4160 = 2^{6} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4160.a (trivial) |
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: | yes |
Analytic conductor: | \(33.2177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 260) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.35194 | 0.780542 | 0.390271 | − | 0.920700i | \(-0.372381\pi\) | ||||
0.390271 | + | 0.920700i | \(0.372381\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.17226 | −1.57697 | −0.788483 | − | 0.615056i | \(-0.789133\pi\) | ||||
−0.788483 | + | 0.615056i | \(0.789133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.17226 | −0.390753 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.52420 | −1.66561 | −0.832804 | − | 0.553567i | \(-0.813266\pi\) | ||||
−0.832804 | + | 0.553567i | \(0.813266\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.35194 | −0.349069 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.703878 | −0.170716 | −0.0853578 | − | 0.996350i | \(-0.527203\pi\) | ||||
−0.0853578 | + | 0.996350i | \(0.527203\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.82032 | 1.56469 | 0.782344 | − | 0.622846i | \(-0.214024\pi\) | ||||
0.782344 | + | 0.622846i | \(0.214024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.64064 | −1.23089 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.64806 | 0.552159 | 0.276079 | − | 0.961135i | \(-0.410965\pi\) | ||||
0.276079 | + | 0.961135i | \(0.410965\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64064 | −1.08554 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.17226 | −1.51755 | −0.758775 | − | 0.651352i | \(-0.774202\pi\) | ||||
−0.758775 | + | 0.651352i | \(0.774202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.52420 | 1.71060 | 0.855298 | − | 0.518136i | \(-0.173374\pi\) | ||||
0.855298 | + | 0.518136i | \(0.173374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.46838 | −1.30008 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.17226 | 0.705241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.87614 | 1.13043 | 0.565215 | − | 0.824944i | \(-0.308793\pi\) | ||||
0.565215 | + | 0.824944i | \(0.308793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.35194 | −0.216484 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.703878 | 0.109927 | 0.0549637 | − | 0.998488i | \(-0.482496\pi\) | ||||
0.0549637 | + | 0.998488i | \(0.482496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.35194 | −0.206169 | −0.103084 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103084 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.17226 | 0.174750 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.17226 | 1.19205 | 0.596023 | − | 0.802967i | \(-0.296747\pi\) | ||||
0.596023 | + | 0.802967i | \(0.296747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.4078 | 1.48682 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.951601 | −0.133251 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.04840 | −0.693451 | −0.346725 | − | 0.937967i | \(-0.612706\pi\) | ||||
−0.346725 | + | 0.937967i | \(0.612706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.52420 | 0.744883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.22066 | 1.22131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2281 | −1.59196 | −0.795980 | − | 0.605323i | \(-0.793044\pi\) | ||||
−0.795980 | + | 0.605323i | \(0.793044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.172260 | 0.0220557 | 0.0110278 | − | 0.999939i | \(-0.496490\pi\) | ||||
0.0110278 | + | 0.999939i | \(0.496490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.89098 | 0.616205 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8761 | 1.32873 | 0.664366 | − | 0.747407i | \(-0.268702\pi\) | ||||
0.664366 | + | 0.747407i | \(0.268702\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.58002 | 0.430983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.52420 | 0.655602 | 0.327801 | − | 0.944747i | \(-0.393692\pi\) | ||||
0.327801 | + | 0.944747i | \(0.393692\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.2207 | −1.31328 | −0.656639 | − | 0.754205i | \(-0.728023\pi\) | ||||
−0.656639 | + | 0.754205i | \(0.728023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.35194 | 0.156108 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.0484 | 2.62661 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.29612 | −0.145825 | −0.0729125 | − | 0.997338i | \(-0.523229\pi\) | ||||
−0.0729125 | + | 0.997338i | \(0.523229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.10902 | −0.456558 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.58002 | −1.05154 | −0.525772 | − | 0.850626i | \(-0.676223\pi\) | ||||
−0.525772 | + | 0.850626i | \(0.676223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.703878 | 0.0763463 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0484 | −1.18451 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.7523 | 1.24574 | 0.622869 | − | 0.782326i | \(-0.285967\pi\) | ||||
0.622869 | + | 0.782326i | \(0.285967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17226 | 0.437372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.8761 | 1.33519 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.82032 | −0.699750 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.3445 | 1.86260 | 0.931302 | − | 0.364248i | \(-0.118674\pi\) | ||||
0.931302 | + | 0.364248i | \(0.118674\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.47580 | 0.650842 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9926 | 1.08313 | 0.541566 | − | 0.840658i | \(-0.317832\pi\) | ||||
0.541566 | + | 0.840658i | \(0.317832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.64064 | 0.550470 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.99258 | 0.675998 | 0.337999 | − | 0.941146i | \(-0.390250\pi\) | ||||
0.337999 | + | 0.941146i | \(0.390250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40776 | −0.326404 | −0.163202 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163202 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.29612 | 0.882349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.64064 | 0.342483 | 0.171241 | − | 0.985229i | \(-0.445222\pi\) | ||||
0.171241 | + | 0.985229i | \(0.445222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.64806 | −0.246933 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17226 | 0.108376 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.93676 | 0.269213 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5168 | 1.77425 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.951601 | 0.0858030 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.69646 | 0.505479 | 0.252740 | − | 0.967534i | \(-0.418668\pi\) | ||||
0.252740 | + | 0.967534i | \(0.418668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.82774 | −0.160923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7523 | 1.55102 | 0.775512 | − | 0.631333i | \(-0.217492\pi\) | ||||
0.775512 | + | 0.631333i | \(0.217492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.4562 | −2.46746 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.64064 | 0.485469 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.93676 | −0.763519 | −0.381760 | − | 0.924262i | \(-0.624682\pi\) | ||||
−0.381760 | + | 0.924262i | \(0.624682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2961 | 1.12776 | 0.563881 | − | 0.825856i | \(-0.309308\pi\) | ||||
0.563881 | + | 0.825856i | \(0.309308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0484 | 0.930443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.52420 | 0.461957 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.17226 | 0.678669 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.0707 | 1.16053 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.93676 | 0.732128 | 0.366064 | − | 0.930590i | \(-0.380705\pi\) | ||||
0.366064 | + | 0.930590i | \(0.380705\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.93196 | −0.238599 | −0.119300 | − | 0.992858i | \(-0.538065\pi\) | ||||
−0.119300 | + | 0.992858i | \(0.538065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.825129 | 0.0667077 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.52420 | −0.765002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.592243 | −0.0472662 | −0.0236331 | − | 0.999721i | \(-0.507523\pi\) | ||||
−0.0236331 | + | 0.999721i | \(0.507523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82513 | −0.541268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0484 | −0.870736 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6284 | 1.30244 | 0.651219 | − | 0.758890i | \(-0.274258\pi\) | ||||
0.651219 | + | 0.758890i | \(0.274258\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.46838 | 0.581413 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.82774 | 0.296199 | 0.148100 | − | 0.988972i | \(-0.452684\pi\) | ||||
0.148100 | + | 0.988972i | \(0.452684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.99519 | −0.611408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1116 | −1.07289 | −0.536444 | − | 0.843936i | \(-0.680233\pi\) | ||||
−0.536444 | + | 0.843936i | \(0.680233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.17226 | −0.315393 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.5316 | −1.24259 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.75228 | 0.429945 | 0.214973 | − | 0.976620i | \(-0.431034\pi\) | ||||
0.214973 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.76450 | −0.205484 | −0.102742 | − | 0.994708i | \(-0.532762\pi\) | ||||
−0.102742 | + | 0.994708i | \(0.532762\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.232886 | 0.0172154 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.87614 | −0.505544 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.88836 | 0.284345 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.5342 | 1.71186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3445 | −1.03254 | −0.516271 | − | 0.856426i | \(-0.672680\pi\) | ||||
−0.516271 | + | 0.856426i | \(0.672680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.35194 | 0.0968144 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.40776 | 0.527781 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.75228 | −0.124216 | −0.0621078 | − | 0.998069i | \(-0.519782\pi\) | ||||
−0.0621078 | + | 0.998069i | \(0.519782\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.7039 | 1.03713 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.0968 | 2.39313 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.703878 | −0.0491610 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.10422 | −0.215758 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.6768 | −2.60616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.75228 | −0.671374 | −0.335687 | − | 0.941974i | \(-0.608969\pi\) | ||||
−0.335687 | + | 0.941974i | \(0.608969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.46838 | 0.511725 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.35194 | 0.0922015 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −39.7374 | −2.69755 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.1696 | −1.02507 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.703878 | 0.0473480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.76450 | −0.185125 | −0.0925624 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925624 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.17226 | −0.0781507 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8129 | 1.18228 | 0.591142 | − | 0.806568i | \(-0.298677\pi\) | ||||
0.591142 | + | 0.806568i | \(0.298677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1116 | −0.668196 | −0.334098 | − | 0.942538i | \(-0.608432\pi\) | ||||
−0.334098 | + | 0.942538i | \(0.608432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.1600 | 2.05018 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.17226 | −0.533099 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.75228 | −0.113823 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.86872 | −0.638354 | −0.319177 | − | 0.947695i | \(-0.603407\pi\) | ||||
−0.319177 | + | 0.947695i | \(0.603407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.88836 | −0.121640 | −0.0608201 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608201 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3668 | 0.729179 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.4078 | −0.664927 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.82032 | −0.433967 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9516 | −0.820774 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.35936 | 0.148921 | 0.0744607 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744607 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6284 | −0.919681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.951601 | 0.0595916 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.65548 | −0.103266 | −0.0516330 | − | 0.998666i | \(-0.516443\pi\) | ||||
−0.0516330 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.6890 | −1.78265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.58002 | 0.592988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.6332 | 1.02565 | 0.512824 | − | 0.858494i | \(-0.328599\pi\) | ||||
0.512824 | + | 0.858494i | \(0.328599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.04840 | 0.310121 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8884 | 0.972352 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0968 | −0.981439 | −0.490720 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490720 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4758 | 0.636360 | 0.318180 | − | 0.948030i | \(-0.396928\pi\) | ||||
0.318180 | + | 0.948030i | \(0.396928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.64064 | 0.341387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.52420 | −0.333122 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.3929 | −1.04504 | −0.522520 | − | 0.852627i | \(-0.675008\pi\) | ||||
−0.522520 | + | 0.852627i | \(0.675008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.1648 | −0.668422 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2961 | 0.673870 | 0.336935 | − | 0.941528i | \(-0.390610\pi\) | ||||
0.336935 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.24030 | 0.549279 | 0.274640 | − | 0.961547i | \(-0.411441\pi\) | ||||
0.274640 | + | 0.961547i | \(0.411441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.22066 | −0.546185 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.93676 | −0.173352 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5046 | −0.970856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.8007 | 1.45384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4051 | 0.958399 | 0.479199 | − | 0.877706i | \(-0.340927\pi\) | ||||
0.479199 | + | 0.877706i | \(0.340927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2281 | 0.711946 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.1600 | 1.80809 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.64806 | −0.153141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.64064 | 0.325121 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.11164 | −0.466001 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.172260 | −0.00986360 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.1090 | −0.862318 | −0.431159 | − | 0.902276i | \(-0.641895\pi\) | ||||
−0.431159 | + | 0.902276i | \(0.641895\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8613 | 0.845430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.11164 | 0.459969 | 0.229984 | − | 0.973194i | \(-0.426133\pi\) | ||||
0.229984 | + | 0.973194i | \(0.426133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.39292 | −0.0787325 | −0.0393662 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393662 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.89098 | −0.275575 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.8129 | 1.67446 | 0.837230 | − | 0.546851i | \(-0.184174\pi\) | ||||
0.837230 | + | 0.546851i | \(0.184174\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.1452 | 2.52765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.45355 | 0.527645 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.80068 | −0.267117 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.60708 | −0.254772 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.0968 | −1.87982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1648 | −1.05339 | −0.526697 | − | 0.850053i | \(-0.676570\pi\) | ||||
−0.526697 | + | 0.850053i | \(0.676570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.06063 | −0.441720 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.8761 | −0.594227 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6406 | 0.634106 | 0.317053 | − | 0.948408i | \(-0.397307\pi\) | ||||
0.317053 | + | 0.948408i | \(0.397307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.92193 | 0.267322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52.6136 | −2.84919 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2180 | −0.767702 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.58002 | −0.192742 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.7597 | −1.22180 | −0.610902 | − | 0.791706i | \(-0.709193\pi\) | ||||
−0.610902 | + | 0.791706i | \(0.709193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.04840 | −0.0561195 | −0.0280598 | − | 0.999606i | \(-0.508933\pi\) | ||||
−0.0280598 | + | 0.999606i | \(0.508933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.64064 | 0.301075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40515 | 0.234462 | 0.117231 | − | 0.993105i | \(-0.462598\pi\) | ||||
0.117231 | + | 0.993105i | \(0.462598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.52420 | −0.293194 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.97033 | 0.210132 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2281 | −1.27871 | −0.639355 | − | 0.768912i | \(-0.720798\pi\) | ||||
−0.639355 | + | 0.768912i | \(0.720798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.5168 | 1.44825 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.3855 | 1.38488 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2207 | 0.587316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3371 | 1.42699 | 0.713493 | − | 0.700663i | \(-0.247112\pi\) | ||||
0.713493 | + | 0.700663i | \(0.247112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.825129 | −0.0429545 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.0632 | 1.09355 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6890 | −1.17479 | −0.587397 | − | 0.809299i | \(-0.699847\pi\) | ||||
−0.587397 | + | 0.809299i | \(0.699847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.35194 | −0.0698138 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.17226 | 0.420893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3249 | 1.55768 | 0.778842 | − | 0.627220i | \(-0.215807\pi\) | ||||
0.778842 | + | 0.627220i | \(0.215807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.70127 | 0.394548 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.23550 | 0.267521 | 0.133761 | − | 0.991014i | \(-0.457295\pi\) | ||||
0.133761 | + | 0.991014i | \(0.457295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.0484 | −1.17466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.58482 | 0.0805612 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8735 | −1.21044 | −0.605218 | − | 0.796060i | \(-0.706914\pi\) | ||||
−0.605218 | + | 0.796060i | \(0.706914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.86391 | −0.0942621 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.29612 | 0.0652150 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.2207 | −1.96843 | −0.984214 | − | 0.176981i | \(-0.943367\pi\) | ||||
−0.984214 | + | 0.176981i | \(0.943367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −38.4710 | −1.92596 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0336 | 1.54974 | 0.774871 | − | 0.632119i | \(-0.217815\pi\) | ||||
0.774871 | + | 0.632119i | \(0.217815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.52420 | −0.474434 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.10902 | 0.204179 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.9852 | −1.88285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1116 | −0.895563 | −0.447781 | − | 0.894143i | \(-0.647786\pi\) | ||||
−0.447781 | + | 0.894143i | \(0.647786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0820 | −0.595959 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 51.0187 | 2.51047 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.58002 | 0.470265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.9755 | 0.880266 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.0484 | −1.12599 | −0.562994 | − | 0.826461i | \(-0.690351\pi\) | ||||
−0.562994 | + | 0.826461i | \(0.690351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.9123 | 1.70152 | 0.850761 | − | 0.525553i | \(-0.176141\pi\) | ||||
0.850761 | + | 0.525553i | \(0.176141\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.58002 | −0.465796 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.703878 | −0.0341431 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.718715 | −0.0347811 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.46838 | 0.360577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.47580 | −0.311928 | −0.155964 | − | 0.987763i | \(-0.549848\pi\) | ||||
−0.155964 | + | 0.987763i | \(0.549848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.8155 | −1.19256 | −0.596279 | − | 0.802777i | \(-0.703355\pi\) | ||||
−0.596279 | + | 0.802777i | \(0.703355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0484 | 0.529730 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0606 | 0.863957 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8155 | −0.516196 | −0.258098 | − | 0.966119i | \(-0.583096\pi\) | ||||
−0.258098 | + | 0.966119i | \(0.583096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.2006 | −0.580981 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0410 | 0.857153 | 0.428576 | − | 0.903506i | \(-0.359015\pi\) | ||||
0.428576 | + | 0.903506i | \(0.359015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7523 | −0.557111 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0820 | 0.571457 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1452 | 1.28106 | 0.640531 | − | 0.767933i | \(-0.278714\pi\) | ||||
0.640531 | + | 0.767933i | \(0.278714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88836 | −0.183096 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.96383 | −0.186237 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.17226 | −0.195599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.75228 | −0.175524 | −0.0877621 | − | 0.996141i | \(-0.527972\pi\) | ||||
−0.0877621 | + | 0.996141i | \(0.527972\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.97033 | 0.185319 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.3297 | −1.69204 | −0.846021 | − | 0.533150i | \(-0.821008\pi\) | ||||
−0.846021 | + | 0.533150i | \(0.821008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4684 | 1.36951 | 0.684756 | − | 0.728772i | \(-0.259909\pi\) | ||||
0.684756 | + | 0.728772i | \(0.259909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.8761 | −0.597117 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5848 | −0.813729 | −0.406864 | − | 0.913489i | \(-0.633378\pi\) | ||||
−0.406864 | + | 0.913489i | \(0.633378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.3781 | −2.09537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.800677 | −0.0368932 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.46838 | 0.343397 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.82032 | 0.312938 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.91804 | 0.270968 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.2765 | 0.515235 | 0.257618 | − | 0.966247i | \(-0.417062\pi\) | ||||
0.257618 | + | 0.966247i | \(0.417062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.87614 | −0.313525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.9368 | −0.679646 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.3445 | −0.832982 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1574 | 1.18531 | 0.592653 | − | 0.805458i | \(-0.298081\pi\) | ||||
0.592653 | + | 0.805458i | \(0.298081\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.4806 | 1.01661 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.456156 | 0.0205860 | 0.0102930 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102930 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.75228 | 0.259070 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.47580 | −0.291066 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.0484 | −1.03386 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4610 | −0.557829 | −0.278915 | − | 0.960316i | \(-0.589975\pi\) | ||||
−0.278915 | + | 0.960316i | \(0.589975\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.17487 | 0.231196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7933 | 0.525835 | 0.262918 | − | 0.964818i | \(-0.415315\pi\) | ||||
0.262918 | + | 0.964818i | \(0.415315\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.35194 | 0.0600417 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.0484 | 1.28755 | 0.643774 | − | 0.765216i | \(-0.277368\pi\) | ||||
0.643774 | + | 0.765216i | \(0.277368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.8155 | 2.07100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.4710 | −1.69854 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.9926 | −0.484391 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.1452 | −1.98548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.0781 | −0.837434 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3323 | −0.671720 | −0.335860 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335860 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4487 | 0.675526 | 0.337763 | − | 0.941231i | \(-0.390330\pi\) | ||||
0.337763 | + | 0.941231i | \(0.390330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.64064 | −0.246178 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.70388 | −0.292026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9878 | −0.695121 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3345 | 0.622064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.703878 | −0.0304884 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.99258 | −0.302316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.77673 | 0.335591 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −57.4945 | −2.47646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.8007 | 1.66817 | 0.834086 | − | 0.551635i | \(-0.185996\pi\) | ||||
0.834086 | + | 0.551635i | \(0.185996\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.73744 | −0.160389 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.40776 | 0.145972 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9926 | 0.641036 | 0.320518 | − | 0.947242i | \(-0.396143\pi\) | ||||
0.320518 | + | 0.947242i | \(0.396143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.201934 | −0.00861833 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.7374 | −2.37449 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.40776 | 0.229961 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.29612 | −0.394598 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3807 | 1.11779 | 0.558893 | − | 0.829240i | \(-0.311226\pi\) | ||||
0.558893 | + | 0.829240i | \(0.311226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.35194 | 0.0571809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.25683 | 0.221944 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.0410 | −1.77182 | −0.885908 | − | 0.463861i | \(-0.846464\pi\) | ||||
−0.885908 | + | 0.463861i | \(0.846464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.64064 | −0.153163 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.1439 | 0.719977 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.2691 | 1.26894 | 0.634472 | − | 0.772945i | \(-0.281217\pi\) | ||||
0.634472 | + | 0.772945i | \(0.281217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1116 | −0.506856 | −0.253428 | − | 0.967354i | \(-0.581558\pi\) | ||||
−0.253428 | + | 0.967354i | \(0.581558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.2233 | −0.677737 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.64806 | 0.110432 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.40515 | −0.349911 | −0.174955 | − | 0.984576i | \(-0.555978\pi\) | ||||
−0.174955 | + | 0.984576i | \(0.555978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.3929 | −0.805942 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.9703 | 1.65825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.8884 | 1.15502 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.17226 | −0.0484670 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 47.4439 | 1.95822 | 0.979110 | − | 0.203330i | \(-0.0651764\pi\) | ||||
0.979110 | + | 0.203330i | \(0.0651764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.9581 | 2.67655 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0148 | 0.411955 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.4413 | 1.33221 | 0.666103 | − | 0.745860i | \(-0.267961\pi\) | ||||
0.666103 | + | 0.745860i | \(0.267961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.93676 | −0.120396 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.36897 | −0.0969556 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.6742 | 1.41675 | 0.708375 | − | 0.705836i | \(-0.249429\pi\) | ||||
0.708375 | + | 0.705836i | \(0.249429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.7497 | −0.519207 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.5168 | −0.793470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.30354 | 0.0934978 | 0.0467489 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467489 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 46.0968 | 1.86794 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.17226 | −0.330614 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8735 | 0.641126 | 0.320563 | − | 0.947227i | \(-0.396128\pi\) | ||||
0.320563 | + | 0.947227i | \(0.396128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.951601 | −0.0383722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3445 | 0.416455 | 0.208227 | − | 0.978080i | \(-0.433231\pi\) | ||||
0.208227 | + | 0.978080i | \(0.433231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.1500 | 1.49318 | 0.746592 | − | 0.665282i | \(-0.231689\pi\) | ||||
0.746592 | + | 0.665282i | \(0.231689\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.9368 | −0.599392 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.0336 | −1.96449 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −50.9368 | −2.03422 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.83997 | −0.192982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.2132 | −0.406583 | −0.203291 | − | 0.979118i | \(-0.565164\pi\) | ||||
−0.203291 | + | 0.979118i | \(0.565164\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.1845 | −0.524036 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.69646 | −0.226057 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4078 | −0.412370 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.47580 | −0.256179 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0968 | −0.635785 | −0.317893 | − | 0.948127i | \(-0.602975\pi\) | ||||
−0.317893 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0458 | −0.711656 | −0.355828 | − | 0.934551i | \(-0.615801\pi\) | ||||
−0.355828 | + | 0.934551i | \(0.615801\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.82774 | 0.0719672 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.5700 | 1.71291 | 0.856456 | − | 0.516219i | \(-0.172661\pi\) | ||||
0.856456 | + | 0.516219i | \(0.172661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.5503 | 2.65158 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.7226 | −2.10555 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.3445 | 0.874409 | 0.437204 | − | 0.899362i | \(-0.355969\pi\) | ||||
0.437204 | + | 0.899362i | \(0.355969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.7523 | −0.693639 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1535 | 0.513168 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9219 | 1.12664 | 0.563319 | − | 0.826239i | \(-0.309524\pi\) | ||||
0.563319 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.6890 | 0.726919 | 0.363460 | − | 0.931610i | \(-0.381595\pi\) | ||||
0.363460 | + | 0.931610i | \(0.381595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.951601 | 0.0369571 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.4562 | 1.10348 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.6406 | −0.837929 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.73744 | −0.144498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.951601 | −0.0367361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5194 | 0.906606 | 0.453303 | − | 0.891357i | \(-0.350246\pi\) | ||||
0.453303 | + | 0.891357i | \(0.350246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.64064 | −0.217108 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.35936 | 0.321276 | 0.160638 | − | 0.987013i | \(-0.448645\pi\) | ||||
0.160638 | + | 0.987013i | \(0.448645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −76.5381 | −2.93726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0820 | 0.922823 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.9394 | −0.456847 | −0.228424 | − | 0.973562i | \(-0.573357\pi\) | ||||
−0.228424 | + | 0.973562i | \(0.573357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.93676 | 0.341456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.6703 | −0.521555 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.04840 | 0.192329 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4274 | 0.586886 | 0.293443 | − | 0.955977i | \(-0.405199\pi\) | ||||
0.293443 | + | 0.955977i | \(0.405199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.0187 | −1.02636 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.2961 | −0.504351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.495445 | −0.0187663 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.11164 | −0.306810 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.2813 | −1.40809 | −0.704047 | − | 0.710153i | \(-0.748626\pi\) | ||||
−0.704047 | + | 0.710153i | \(0.748626\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.8975 | 1.76877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0484 | −0.416107 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.0336 | 0.941484 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9852 | 0.450112 | 0.225056 | − | 0.974346i | \(-0.427743\pi\) | ||||
0.225056 | + | 0.974346i | \(0.427743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.51939 | 0.0569817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.2207 | 0.944521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.52420 | −0.206593 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.3419 | −0.498263 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6258 | −0.881094 | −0.440547 | − | 0.897730i | \(-0.645215\pi\) | ||||
−0.440547 | + | 0.897730i | \(0.645215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.8639 | −1.70806 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.55295 | −0.0949454 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.17226 | −0.303510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1526 | −0.821595 | −0.410798 | − | 0.911727i | \(-0.634750\pi\) | ||||
−0.410798 | + | 0.911727i | \(0.634750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6943 | 1.02571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.951601 | 0.0351962 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000 | 0.369358 | 0.184679 | − | 0.982799i | \(-0.440875\pi\) | ||||
0.184679 | + | 0.982799i | \(0.440875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.0707 | −0.519004 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −60.0820 | −2.21315 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0436 | −0.700530 | −0.350265 | − | 0.936651i | \(-0.613908\pi\) | ||||
−0.350265 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.22066 | −0.338729 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.26906 | −0.229989 | −0.114995 | − | 0.993366i | \(-0.536685\pi\) | ||||
−0.114995 | + | 0.993366i | \(0.536685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.93676 | −0.327418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2303 | 0.410894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.1749 | −1.06603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9219 | 0.763452 | 0.381726 | − | 0.924276i | \(-0.375330\pi\) | ||||
0.381726 | + | 0.924276i | \(0.375330\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.18971 | 0.116239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.93196 | 0.106705 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.8975 | 1.77721 | 0.888604 | − | 0.458674i | \(-0.151676\pi\) | ||||
0.888604 | + | 0.458674i | \(0.151676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.7767 | −0.717850 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.09680 | −0.148509 | −0.0742544 | − | 0.997239i | \(-0.523658\pi\) | ||||
−0.0742544 | + | 0.997239i | \(0.523658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2180 | 0.514728 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.825129 | −0.0298326 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2281 | 0.441530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7858 | −1.03804 | −0.519022 | − | 0.854761i | \(-0.673704\pi\) | ||||
−0.519022 | + | 0.854761i | \(0.673704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.23811 | −0.0806035 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.22066 | −0.259709 | −0.129855 | − | 0.991533i | \(-0.541451\pi\) | ||||
−0.129855 | + | 0.991533i | \(0.541451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.52420 | 0.342119 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −38.7858 | −1.39143 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.80068 | 0.172002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.5168 | −1.09198 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.0968 | 1.64737 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.592243 | 0.0211381 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5800 | 1.48217 | 0.741084 | − | 0.671413i | \(-0.234312\pi\) | ||||
0.741084 | + | 0.671413i | \(0.234312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.4871 | 0.800562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.1897 | −0.540084 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.172260 | −0.00611715 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.82513 | 0.242062 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.4078 | −0.687458 | −0.343729 | − | 0.939069i | \(-0.611690\pi\) | ||||
−0.343729 | + | 0.939069i | \(0.611690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.75228 | −0.203501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.7767 | −0.486777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 61.9852 | 2.18741 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0484 | 0.389405 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.7619 | −0.766055 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.7981 | 1.53986 | 0.769929 | − | 0.638130i | \(-0.220292\pi\) | ||||
0.769929 | + | 0.638130i | \(0.220292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.75709 | −0.202159 | −0.101079 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101079 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.1626 | 0.496706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.6284 | −0.582468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.22066 | −0.322590 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.89098 | −0.170905 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9368 | 1.14950 | 0.574750 | − | 0.818329i | \(-0.305099\pi\) | ||||
0.574750 | + | 0.818329i | \(0.305099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 57.0894 | 1.99001 | 0.995005 | − | 0.0998217i | \(-0.0318272\pi\) | ||||
0.995005 | + | 0.0998217i | \(0.0318272\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.46838 | −0.260016 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4535 | −0.954653 | −0.477327 | − | 0.878726i | \(-0.658394\pi\) | ||||
−0.477327 | + | 0.878726i | \(0.658394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4200 | −0.361901 | −0.180950 | − | 0.983492i | \(-0.557917\pi\) | ||||
−0.180950 | + | 0.983492i | \(0.557917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.5142 | −0.815698 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.32580 | −0.253824 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.82774 | −0.132464 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −53.7226 | −1.85692 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.1984 | −1.38780 | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||||
−0.693902 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7858 | 1.30296 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.2717 | 0.525984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −81.4291 | −2.79794 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.4923 | 0.428736 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.2084 | 0.624177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.8761 | −1.19414 | −0.597068 | − | 0.802191i | \(-0.703668\pi\) | ||||
−0.597068 | + | 0.802191i | \(0.703668\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.99519 | 0.273430 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.1600 | 0.859450 | 0.429725 | − | 0.902960i | \(-0.358610\pi\) | ||||
0.429725 | + | 0.902960i | \(0.358610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0484 | −0.513445 | −0.256722 | − | 0.966485i | \(-0.582643\pi\) | ||||
−0.256722 | + | 0.966485i | \(0.582643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.97033 | −0.135308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.29873 | −0.0782498 | −0.0391249 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391249 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.1116 | 0.479810 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.3132 | −0.757794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.16003 | 0.242888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8761 | −0.368524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.5046 | −0.727819 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.17226 | 0.141048 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0000 | 0.337676 | 0.168838 | − | 0.985644i | \(-0.445999\pi\) | ||||
0.168838 | + | 0.985644i | \(0.445999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1788 | 0.748071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1426 | −1.62196 | −0.810982 | − | 0.585070i | \(-0.801067\pi\) | ||||
−0.810982 | + | 0.585070i | \(0.801067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8565 | −0.432655 | −0.216328 | − | 0.976321i | \(-0.569408\pi\) | ||||
−0.216328 | + | 0.976321i | \(0.569408\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.5316 | 0.555704 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.5216 | 1.09197 | 0.545984 | − | 0.837796i | \(-0.316156\pi\) | ||||
0.545984 | + | 0.837796i | \(0.316156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.7671 | −0.797123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.6991 | 0.760447 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.7374 | 1.86518 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.75228 | −0.192277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.58002 | −0.119533 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −77.8342 | −2.59592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.55346 | 0.118383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.62581 | 0.253771 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.76450 | 0.0918952 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0894 | −0.700261 | −0.350131 | − | 0.936701i | \(-0.613863\pi\) | ||||
−0.350131 | + | 0.936701i | \(0.613863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.03356 | 0.233289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1600 | −1.42996 | −0.714978 | − | 0.699147i | \(-0.753563\pi\) | ||||
−0.714978 | + | 0.699147i | \(0.753563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.9219 | 1.75146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.232886 | −0.00769896 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −74.0671 | −2.44591 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8884 | −0.392161 | −0.196080 | − | 0.980588i | \(-0.562821\pi\) | ||||
−0.196080 | + | 0.980588i | \(0.562821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.4265 | −0.673075 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.52420 | −0.181831 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.87614 | 0.226086 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.8862 | −0.423237 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.4265 | −1.12950 | −0.564748 | − | 0.825263i | \(-0.691027\pi\) | ||||
−0.564748 | + | 0.825263i | \(0.691027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70.9842 | 2.32641 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9664 | 0.359025 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.88836 | −0.127163 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.88314 | −0.0614541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1116 | 1.24240 | 0.621202 | − | 0.783651i | \(-0.286645\pi\) | ||||
0.621202 | + | 0.783651i | \(0.286645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.86391 | 0.0606974 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −23.5342 | −0.765569 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.9245 | 0.452487 | 0.226243 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2207 | 0.364238 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.3052 | 1.30699 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.7523 | −0.769412 | −0.384706 | − | 0.923039i | \(-0.625697\pi\) | ||||
−0.384706 | + | 0.923039i | \(0.625697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | 0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 61.0336 | 1.97293 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.2865 | 1.20404 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.7104 | 1.92614 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.19713 | −0.264149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3445 | 0.461766 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.87614 | 0.221122 | 0.110561 | − | 0.993869i | \(-0.464735\pi\) | ||||
0.110561 | + | 0.993869i | \(0.464735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.49022 | −0.208496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.24772 | 0.200499 | 0.100249 | − | 0.994962i | \(-0.468036\pi\) | ||||
0.100249 | + | 0.994962i | \(0.468036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55.4749 | −1.77844 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.35194 | −0.0432967 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.5316 | −1.10476 | −0.552382 | − | 0.833591i | \(-0.686281\pi\) | ||||
−0.552382 | + | 0.833591i | \(0.686281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.9219 | −2.07491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.99478 | 0.127543 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.5652 | 0.368872 | 0.184436 | − | 0.982845i | \(-0.440954\pi\) | ||||
0.184436 | + | 0.982845i | \(0.440954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.40776 | −0.236031 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −46.0968 | −1.46728 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.58002 | −0.113838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.77673 | −0.119972 | −0.0599859 | − | 0.998199i | \(-0.519106\pi\) | ||||
−0.0599859 | + | 0.998199i | \(0.519106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.9097 | −0.822220 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.75228 | 0.0555509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.4265 | −1.72370 | −0.861852 | − | 0.507160i | \(-0.830695\pi\) | ||||
−0.861852 | + | 0.507160i | \(0.830695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.7858 | −1.22713 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4160.2.a.br.1.2 | 3 | ||
4.3 | odd | 2 | 4160.2.a.bo.1.2 | 3 | |||
8.3 | odd | 2 | 260.2.a.b.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 1040.2.a.o.1.2 | 3 | |||
24.5 | odd | 2 | 9360.2.a.da.1.1 | 3 | |||
24.11 | even | 2 | 2340.2.a.n.1.3 | 3 | |||
40.3 | even | 4 | 1300.2.c.f.1249.4 | 6 | |||
40.19 | odd | 2 | 1300.2.a.i.1.2 | 3 | |||
40.27 | even | 4 | 1300.2.c.f.1249.3 | 6 | |||
40.29 | even | 2 | 5200.2.a.ci.1.2 | 3 | |||
104.51 | odd | 2 | 3380.2.a.o.1.2 | 3 | |||
104.83 | even | 4 | 3380.2.f.h.3041.3 | 6 | |||
104.99 | even | 4 | 3380.2.f.h.3041.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.a.b.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
1040.2.a.o.1.2 | 3 | 8.5 | even | 2 | |||
1300.2.a.i.1.2 | 3 | 40.19 | odd | 2 | |||
1300.2.c.f.1249.3 | 6 | 40.27 | even | 4 | |||
1300.2.c.f.1249.4 | 6 | 40.3 | even | 4 | |||
2340.2.a.n.1.3 | 3 | 24.11 | even | 2 | |||
3380.2.a.o.1.2 | 3 | 104.51 | odd | 2 | |||
3380.2.f.h.3041.3 | 6 | 104.83 | even | 4 | |||
3380.2.f.h.3041.4 | 6 | 104.99 | even | 4 | |||
4160.2.a.bo.1.2 | 3 | 4.3 | odd | 2 | |||
4160.2.a.br.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5200.2.a.ci.1.2 | 3 | 40.29 | even | 2 | |||
9360.2.a.da.1.1 | 3 | 24.5 | odd | 2 |