Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [123,2,Mod(1,123)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(123, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("123.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 123 = 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 123.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: | \(0.982159944862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 123.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34292 | 1.65670 | 0.828348 | − | 0.560213i | \(-0.189281\pi\) | ||||
0.828348 | + | 0.560213i | \(0.189281\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.48929 | 1.74464 | ||||||||
\(5\) | 0.853635 | 0.381757 | 0.190878 | − | 0.981614i | \(-0.438866\pi\) | ||||
0.190878 | + | 0.981614i | \(0.438866\pi\) | |||||||
\(6\) | −2.34292 | −0.956494 | ||||||||
\(7\) | −3.83221 | −1.44844 | −0.724220 | − | 0.689569i | \(-0.757800\pi\) | ||||
−0.724220 | + | 0.689569i | \(0.757800\pi\) | |||||||
\(8\) | 3.48929 | 1.23365 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | −3.34292 | −1.00793 | −0.503965 | − | 0.863724i | \(-0.668126\pi\) | ||||
−0.503965 | + | 0.863724i | \(0.668126\pi\) | |||||||
\(12\) | −3.48929 | −1.00727 | ||||||||
\(13\) | 3.14637 | 0.872645 | 0.436322 | − | 0.899790i | \(-0.356281\pi\) | ||||
0.436322 | + | 0.899790i | \(0.356281\pi\) | |||||||
\(14\) | −8.97858 | −2.39963 | ||||||||
\(15\) | −0.853635 | −0.220407 | ||||||||
\(16\) | 1.19656 | 0.299139 | ||||||||
\(17\) | 3.63565 | 0.881776 | 0.440888 | − | 0.897562i | \(-0.354664\pi\) | ||||
0.440888 | + | 0.897562i | \(0.354664\pi\) | |||||||
\(18\) | 2.34292 | 0.552232 | ||||||||
\(19\) | 1.14637 | 0.262994 | 0.131497 | − | 0.991317i | \(-0.458022\pi\) | ||||
0.131497 | + | 0.991317i | \(0.458022\pi\) | |||||||
\(20\) | 2.97858 | 0.666030 | ||||||||
\(21\) | 3.83221 | 0.836257 | ||||||||
\(22\) | −7.83221 | −1.66983 | ||||||||
\(23\) | −2.85363 | −0.595024 | −0.297512 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297512 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(24\) | −3.48929 | −0.712248 | ||||||||
\(25\) | −4.27131 | −0.854262 | ||||||||
\(26\) | 7.37169 | 1.44571 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −13.3717 | −2.52701 | ||||||||
\(29\) | −8.02877 | −1.49091 | −0.745453 | − | 0.666559i | \(-0.767767\pi\) | ||||
−0.745453 | + | 0.666559i | \(0.767767\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | 9.86098 | 1.77108 | 0.885542 | − | 0.464559i | \(-0.153787\pi\) | ||||
0.885542 | + | 0.464559i | \(0.153787\pi\) | |||||||
\(32\) | −4.17513 | −0.738067 | ||||||||
\(33\) | 3.34292 | 0.581928 | ||||||||
\(34\) | 8.51806 | 1.46083 | ||||||||
\(35\) | −3.27131 | −0.552952 | ||||||||
\(36\) | 3.48929 | 0.581548 | ||||||||
\(37\) | 8.19656 | 1.34751 | 0.673753 | − | 0.738957i | \(-0.264681\pi\) | ||||
0.673753 | + | 0.738957i | \(0.264681\pi\) | |||||||
\(38\) | 2.68585 | 0.435702 | ||||||||
\(39\) | −3.14637 | −0.503822 | ||||||||
\(40\) | 2.97858 | 0.470954 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 8.97858 | 1.38542 | ||||||||
\(43\) | 11.7606 | 1.79347 | 0.896737 | − | 0.442564i | \(-0.145931\pi\) | ||||
0.896737 | + | 0.442564i | \(0.145931\pi\) | |||||||
\(44\) | −11.6644 | −1.75848 | ||||||||
\(45\) | 0.853635 | 0.127252 | ||||||||
\(46\) | −6.68585 | −0.985774 | ||||||||
\(47\) | 8.32150 | 1.21382 | 0.606908 | − | 0.794772i | \(-0.292410\pi\) | ||||
0.606908 | + | 0.794772i | \(0.292410\pi\) | |||||||
\(48\) | −1.19656 | −0.172708 | ||||||||
\(49\) | 7.68585 | 1.09798 | ||||||||
\(50\) | −10.0073 | −1.41525 | ||||||||
\(51\) | −3.63565 | −0.509093 | ||||||||
\(52\) | 10.9786 | 1.52245 | ||||||||
\(53\) | 1.60688 | 0.220723 | 0.110361 | − | 0.993892i | \(-0.464799\pi\) | ||||
0.110361 | + | 0.993892i | \(0.464799\pi\) | |||||||
\(54\) | −2.34292 | −0.318831 | ||||||||
\(55\) | −2.85363 | −0.384784 | ||||||||
\(56\) | −13.3717 | −1.78687 | ||||||||
\(57\) | −1.14637 | −0.151840 | ||||||||
\(58\) | −18.8108 | −2.46998 | ||||||||
\(59\) | −11.6644 | −1.51858 | −0.759289 | − | 0.650753i | \(-0.774453\pi\) | ||||
−0.759289 | + | 0.650753i | \(0.774453\pi\) | |||||||
\(60\) | −2.97858 | −0.384533 | ||||||||
\(61\) | −4.19656 | −0.537314 | −0.268657 | − | 0.963236i | \(-0.586580\pi\) | ||||
−0.268657 | + | 0.963236i | \(0.586580\pi\) | |||||||
\(62\) | 23.1035 | 2.93415 | ||||||||
\(63\) | −3.83221 | −0.482813 | ||||||||
\(64\) | −12.1751 | −1.52189 | ||||||||
\(65\) | 2.68585 | 0.333138 | ||||||||
\(66\) | 7.83221 | 0.964079 | ||||||||
\(67\) | 6.10038 | 0.745281 | 0.372640 | − | 0.927976i | \(-0.378453\pi\) | ||||
0.372640 | + | 0.927976i | \(0.378453\pi\) | |||||||
\(68\) | 12.6858 | 1.53838 | ||||||||
\(69\) | 2.85363 | 0.343537 | ||||||||
\(70\) | −7.66442 | −0.916074 | ||||||||
\(71\) | −8.65708 | −1.02741 | −0.513703 | − | 0.857968i | \(-0.671727\pi\) | ||||
−0.513703 | + | 0.857968i | \(0.671727\pi\) | |||||||
\(72\) | 3.48929 | 0.411217 | ||||||||
\(73\) | −10.1537 | −1.18840 | −0.594201 | − | 0.804317i | \(-0.702532\pi\) | ||||
−0.594201 | + | 0.804317i | \(0.702532\pi\) | |||||||
\(74\) | 19.2039 | 2.23241 | ||||||||
\(75\) | 4.27131 | 0.493208 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 12.8108 | 1.45992 | ||||||||
\(78\) | −7.37169 | −0.834680 | ||||||||
\(79\) | −3.60688 | −0.405806 | −0.202903 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202903 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(80\) | 1.02142 | 0.114199 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.34292 | 0.258733 | ||||||||
\(83\) | −10.1249 | −1.11136 | −0.555678 | − | 0.831397i | \(-0.687541\pi\) | ||||
−0.555678 | + | 0.831397i | \(0.687541\pi\) | |||||||
\(84\) | 13.3717 | 1.45897 | ||||||||
\(85\) | 3.10352 | 0.336624 | ||||||||
\(86\) | 27.5542 | 2.97124 | ||||||||
\(87\) | 8.02877 | 0.860774 | ||||||||
\(88\) | −11.6644 | −1.24343 | ||||||||
\(89\) | −3.37169 | −0.357399 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | −12.0575 | −1.26397 | ||||||||
\(92\) | −9.95715 | −1.03811 | ||||||||
\(93\) | −9.86098 | −1.02254 | ||||||||
\(94\) | 19.4966 | 2.01092 | ||||||||
\(95\) | 0.978577 | 0.100400 | ||||||||
\(96\) | 4.17513 | 0.426123 | ||||||||
\(97\) | −7.53948 | −0.765518 | −0.382759 | − | 0.923848i | \(-0.625026\pi\) | ||||
−0.382759 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(98\) | 18.0073 | 1.81902 | ||||||||
\(99\) | −3.34292 | −0.335976 | ||||||||
\(100\) | −14.9038 | −1.49038 | ||||||||
\(101\) | 5.00735 | 0.498250 | 0.249125 | − | 0.968471i | \(-0.419857\pi\) | ||||
0.249125 | + | 0.968471i | \(0.419857\pi\) | |||||||
\(102\) | −8.51806 | −0.843413 | ||||||||
\(103\) | 1.21798 | 0.120011 | 0.0600056 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600056 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(104\) | 10.9786 | 1.07654 | ||||||||
\(105\) | 3.27131 | 0.319247 | ||||||||
\(106\) | 3.76481 | 0.365670 | ||||||||
\(107\) | 13.7648 | 1.33069 | 0.665347 | − | 0.746534i | \(-0.268284\pi\) | ||||
0.665347 | + | 0.746534i | \(0.268284\pi\) | |||||||
\(108\) | −3.48929 | −0.335757 | ||||||||
\(109\) | 3.14637 | 0.301367 | 0.150684 | − | 0.988582i | \(-0.451853\pi\) | ||||
0.150684 | + | 0.988582i | \(0.451853\pi\) | |||||||
\(110\) | −6.68585 | −0.637470 | ||||||||
\(111\) | −8.19656 | −0.777983 | ||||||||
\(112\) | −4.58546 | −0.433285 | ||||||||
\(113\) | −7.73183 | −0.727349 | −0.363675 | − | 0.931526i | \(-0.618478\pi\) | ||||
−0.363675 | + | 0.931526i | \(0.618478\pi\) | |||||||
\(114\) | −2.68585 | −0.251553 | ||||||||
\(115\) | −2.43596 | −0.227155 | ||||||||
\(116\) | −28.0147 | −2.60110 | ||||||||
\(117\) | 3.14637 | 0.290882 | ||||||||
\(118\) | −27.3288 | −2.51582 | ||||||||
\(119\) | −13.9326 | −1.27720 | ||||||||
\(120\) | −2.97858 | −0.271906 | ||||||||
\(121\) | 0.175135 | 0.0159213 | ||||||||
\(122\) | −9.83221 | −0.890167 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 34.4078 | 3.08991 | ||||||||
\(125\) | −7.91431 | −0.707877 | ||||||||
\(126\) | −8.97858 | −0.799875 | ||||||||
\(127\) | −12.0575 | −1.06993 | −0.534967 | − | 0.844873i | \(-0.679676\pi\) | ||||
−0.534967 | + | 0.844873i | \(0.679676\pi\) | |||||||
\(128\) | −20.1751 | −1.78325 | ||||||||
\(129\) | −11.7606 | −1.03546 | ||||||||
\(130\) | 6.29273 | 0.551909 | ||||||||
\(131\) | 12.2253 | 1.06813 | 0.534066 | − | 0.845443i | \(-0.320663\pi\) | ||||
0.534066 | + | 0.845443i | \(0.320663\pi\) | |||||||
\(132\) | 11.6644 | 1.01526 | ||||||||
\(133\) | −4.39312 | −0.380931 | ||||||||
\(134\) | 14.2927 | 1.23470 | ||||||||
\(135\) | −0.853635 | −0.0734692 | ||||||||
\(136\) | 12.6858 | 1.08780 | ||||||||
\(137\) | 7.69319 | 0.657274 | 0.328637 | − | 0.944456i | \(-0.393411\pi\) | ||||
0.328637 | + | 0.944456i | \(0.393411\pi\) | |||||||
\(138\) | 6.68585 | 0.569137 | ||||||||
\(139\) | −18.0147 | −1.52799 | −0.763993 | − | 0.645224i | \(-0.776764\pi\) | ||||
−0.763993 | + | 0.645224i | \(0.776764\pi\) | |||||||
\(140\) | −11.4145 | −0.964705 | ||||||||
\(141\) | −8.32150 | −0.700797 | ||||||||
\(142\) | −20.2829 | −1.70210 | ||||||||
\(143\) | −10.5181 | −0.879564 | ||||||||
\(144\) | 1.19656 | 0.0997131 | ||||||||
\(145\) | −6.85363 | −0.569163 | ||||||||
\(146\) | −23.7894 | −1.96882 | ||||||||
\(147\) | −7.68585 | −0.633918 | ||||||||
\(148\) | 28.6002 | 2.35092 | ||||||||
\(149\) | 12.5426 | 1.02753 | 0.513766 | − | 0.857931i | \(-0.328250\pi\) | ||||
0.513766 | + | 0.857931i | \(0.328250\pi\) | |||||||
\(150\) | 10.0073 | 0.817096 | ||||||||
\(151\) | 2.62831 | 0.213889 | 0.106944 | − | 0.994265i | \(-0.465893\pi\) | ||||
0.106944 | + | 0.994265i | \(0.465893\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 3.63565 | 0.293925 | ||||||||
\(154\) | 30.0147 | 2.41865 | ||||||||
\(155\) | 8.41767 | 0.676124 | ||||||||
\(156\) | −10.9786 | −0.878990 | ||||||||
\(157\) | 20.1579 | 1.60878 | 0.804389 | − | 0.594103i | \(-0.202493\pi\) | ||||
0.804389 | + | 0.594103i | \(0.202493\pi\) | |||||||
\(158\) | −8.45065 | −0.672298 | ||||||||
\(159\) | −1.60688 | −0.127434 | ||||||||
\(160\) | −3.56404 | −0.281762 | ||||||||
\(161\) | 10.9357 | 0.861856 | ||||||||
\(162\) | 2.34292 | 0.184077 | ||||||||
\(163\) | 18.2541 | 1.42977 | 0.714886 | − | 0.699241i | \(-0.246479\pi\) | ||||
0.714886 | + | 0.699241i | \(0.246479\pi\) | |||||||
\(164\) | 3.48929 | 0.272468 | ||||||||
\(165\) | 2.85363 | 0.222155 | ||||||||
\(166\) | −23.7220 | −1.84118 | ||||||||
\(167\) | 1.31415 | 0.101692 | 0.0508461 | − | 0.998706i | \(-0.483808\pi\) | ||||
0.0508461 | + | 0.998706i | \(0.483808\pi\) | |||||||
\(168\) | 13.3717 | 1.03165 | ||||||||
\(169\) | −3.10038 | −0.238491 | ||||||||
\(170\) | 7.27131 | 0.557684 | ||||||||
\(171\) | 1.14637 | 0.0876648 | ||||||||
\(172\) | 41.0361 | 3.12897 | ||||||||
\(173\) | 1.18921 | 0.0904141 | 0.0452070 | − | 0.998978i | \(-0.485605\pi\) | ||||
0.0452070 | + | 0.998978i | \(0.485605\pi\) | |||||||
\(174\) | 18.8108 | 1.42604 | ||||||||
\(175\) | 16.3686 | 1.23735 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 11.6644 | 0.876752 | ||||||||
\(178\) | −7.89962 | −0.592101 | ||||||||
\(179\) | −19.0073 | −1.42068 | −0.710338 | − | 0.703861i | \(-0.751458\pi\) | ||||
−0.710338 | + | 0.703861i | \(0.751458\pi\) | |||||||
\(180\) | 2.97858 | 0.222010 | ||||||||
\(181\) | 10.3931 | 0.772514 | 0.386257 | − | 0.922391i | \(-0.373768\pi\) | ||||
0.386257 | + | 0.922391i | \(0.373768\pi\) | |||||||
\(182\) | −28.2499 | −2.09402 | ||||||||
\(183\) | 4.19656 | 0.310218 | ||||||||
\(184\) | −9.95715 | −0.734051 | ||||||||
\(185\) | 6.99686 | 0.514420 | ||||||||
\(186\) | −23.1035 | −1.69403 | ||||||||
\(187\) | −12.1537 | −0.888767 | ||||||||
\(188\) | 29.0361 | 2.11768 | ||||||||
\(189\) | 3.83221 | 0.278752 | ||||||||
\(190\) | 2.29273 | 0.166332 | ||||||||
\(191\) | −6.87819 | −0.497689 | −0.248844 | − | 0.968544i | \(-0.580051\pi\) | ||||
−0.248844 | + | 0.968544i | \(0.580051\pi\) | |||||||
\(192\) | 12.1751 | 0.878665 | ||||||||
\(193\) | −19.5970 | −1.41062 | −0.705312 | − | 0.708897i | \(-0.749193\pi\) | ||||
−0.705312 | + | 0.708897i | \(0.749193\pi\) | |||||||
\(194\) | −17.6644 | −1.26823 | ||||||||
\(195\) | −2.68585 | −0.192337 | ||||||||
\(196\) | 26.8181 | 1.91558 | ||||||||
\(197\) | −24.7679 | −1.76464 | −0.882321 | − | 0.470647i | \(-0.844020\pi\) | ||||
−0.882321 | + | 0.470647i | \(0.844020\pi\) | |||||||
\(198\) | −7.83221 | −0.556611 | ||||||||
\(199\) | 12.8108 | 0.908133 | 0.454066 | − | 0.890968i | \(-0.349973\pi\) | ||||
0.454066 | + | 0.890968i | \(0.349973\pi\) | |||||||
\(200\) | −14.9038 | −1.05386 | ||||||||
\(201\) | −6.10038 | −0.430288 | ||||||||
\(202\) | 11.7318 | 0.825448 | ||||||||
\(203\) | 30.7679 | 2.15949 | ||||||||
\(204\) | −12.6858 | −0.888187 | ||||||||
\(205\) | 0.853635 | 0.0596204 | ||||||||
\(206\) | 2.85363 | 0.198822 | ||||||||
\(207\) | −2.85363 | −0.198341 | ||||||||
\(208\) | 3.76481 | 0.261042 | ||||||||
\(209\) | −3.83221 | −0.265080 | ||||||||
\(210\) | 7.66442 | 0.528895 | ||||||||
\(211\) | 3.66442 | 0.252269 | 0.126135 | − | 0.992013i | \(-0.459743\pi\) | ||||
0.126135 | + | 0.992013i | \(0.459743\pi\) | |||||||
\(212\) | 5.60688 | 0.385082 | ||||||||
\(213\) | 8.65708 | 0.593173 | ||||||||
\(214\) | 32.2499 | 2.20456 | ||||||||
\(215\) | 10.0393 | 0.684671 | ||||||||
\(216\) | −3.48929 | −0.237416 | ||||||||
\(217\) | −37.7894 | −2.56531 | ||||||||
\(218\) | 7.37169 | 0.499274 | ||||||||
\(219\) | 10.1537 | 0.686124 | ||||||||
\(220\) | −9.95715 | −0.671311 | ||||||||
\(221\) | 11.4391 | 0.769477 | ||||||||
\(222\) | −19.2039 | −1.28888 | ||||||||
\(223\) | 9.17092 | 0.614130 | 0.307065 | − | 0.951688i | \(-0.400653\pi\) | ||||
0.307065 | + | 0.951688i | \(0.400653\pi\) | |||||||
\(224\) | 16.0000 | 1.06904 | ||||||||
\(225\) | −4.27131 | −0.284754 | ||||||||
\(226\) | −18.1151 | −1.20500 | ||||||||
\(227\) | 0.263962 | 0.0175198 | 0.00875988 | − | 0.999962i | \(-0.497212\pi\) | ||||
0.00875988 | + | 0.999962i | \(0.497212\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | 7.20390 | 0.476047 | 0.238024 | − | 0.971259i | \(-0.423500\pi\) | ||||
0.238024 | + | 0.971259i | \(0.423500\pi\) | |||||||
\(230\) | −5.70727 | −0.376326 | ||||||||
\(231\) | −12.8108 | −0.842888 | ||||||||
\(232\) | −28.0147 | −1.83925 | ||||||||
\(233\) | 16.1579 | 1.05854 | 0.529270 | − | 0.848453i | \(-0.322466\pi\) | ||||
0.529270 | + | 0.848453i | \(0.322466\pi\) | |||||||
\(234\) | 7.37169 | 0.481903 | ||||||||
\(235\) | 7.10352 | 0.463383 | ||||||||
\(236\) | −40.7005 | −2.64938 | ||||||||
\(237\) | 3.60688 | 0.234292 | ||||||||
\(238\) | −32.6430 | −2.11593 | ||||||||
\(239\) | −15.6644 | −1.01325 | −0.506624 | − | 0.862167i | \(-0.669107\pi\) | ||||
−0.506624 | + | 0.862167i | \(0.669107\pi\) | |||||||
\(240\) | −1.02142 | −0.0659326 | ||||||||
\(241\) | 10.5468 | 0.679381 | 0.339690 | − | 0.940537i | \(-0.389678\pi\) | ||||
0.339690 | + | 0.940537i | \(0.389678\pi\) | |||||||
\(242\) | 0.410327 | 0.0263768 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.6430 | −0.937422 | ||||||||
\(245\) | 6.56090 | 0.419161 | ||||||||
\(246\) | −2.34292 | −0.149379 | ||||||||
\(247\) | 3.60688 | 0.229501 | ||||||||
\(248\) | 34.4078 | 2.18490 | ||||||||
\(249\) | 10.1249 | 0.641642 | ||||||||
\(250\) | −18.5426 | −1.17274 | ||||||||
\(251\) | 21.4292 | 1.35260 | 0.676301 | − | 0.736626i | \(-0.263582\pi\) | ||||
0.676301 | + | 0.736626i | \(0.263582\pi\) | |||||||
\(252\) | −13.3717 | −0.842337 | ||||||||
\(253\) | 9.53948 | 0.599742 | ||||||||
\(254\) | −28.2499 | −1.77256 | ||||||||
\(255\) | −3.10352 | −0.194350 | ||||||||
\(256\) | −22.9185 | −1.43241 | ||||||||
\(257\) | −7.10773 | −0.443368 | −0.221684 | − | 0.975119i | \(-0.571155\pi\) | ||||
−0.221684 | + | 0.975119i | \(0.571155\pi\) | |||||||
\(258\) | −27.5542 | −1.71545 | ||||||||
\(259\) | −31.4109 | −1.95178 | ||||||||
\(260\) | 9.37169 | 0.581208 | ||||||||
\(261\) | −8.02877 | −0.496968 | ||||||||
\(262\) | 28.6430 | 1.76957 | ||||||||
\(263\) | −9.97123 | −0.614852 | −0.307426 | − | 0.951572i | \(-0.599468\pi\) | ||||
−0.307426 | + | 0.951572i | \(0.599468\pi\) | |||||||
\(264\) | 11.6644 | 0.717896 | ||||||||
\(265\) | 1.37169 | 0.0842624 | ||||||||
\(266\) | −10.2927 | −0.631088 | ||||||||
\(267\) | 3.37169 | 0.206344 | ||||||||
\(268\) | 21.2860 | 1.30025 | ||||||||
\(269\) | −0.685846 | −0.0418168 | −0.0209084 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209084 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 13.8034 | 0.838499 | 0.419250 | − | 0.907871i | \(-0.362293\pi\) | ||||
0.419250 | + | 0.907871i | \(0.362293\pi\) | |||||||
\(272\) | 4.35027 | 0.263774 | ||||||||
\(273\) | 12.0575 | 0.729755 | ||||||||
\(274\) | 18.0246 | 1.08890 | ||||||||
\(275\) | 14.2787 | 0.861035 | ||||||||
\(276\) | 9.95715 | 0.599350 | ||||||||
\(277\) | 22.2113 | 1.33454 | 0.667272 | − | 0.744814i | \(-0.267462\pi\) | ||||
0.667272 | + | 0.744814i | \(0.267462\pi\) | |||||||
\(278\) | −42.2070 | −2.53141 | ||||||||
\(279\) | 9.86098 | 0.590361 | ||||||||
\(280\) | −11.4145 | −0.682149 | ||||||||
\(281\) | 4.61423 | 0.275262 | 0.137631 | − | 0.990484i | \(-0.456051\pi\) | ||||
0.137631 | + | 0.990484i | \(0.456051\pi\) | |||||||
\(282\) | −19.4966 | −1.16101 | ||||||||
\(283\) | 9.13229 | 0.542858 | 0.271429 | − | 0.962458i | \(-0.412504\pi\) | ||||
0.271429 | + | 0.962458i | \(0.412504\pi\) | |||||||
\(284\) | −30.2070 | −1.79246 | ||||||||
\(285\) | −0.978577 | −0.0579659 | ||||||||
\(286\) | −24.6430 | −1.45717 | ||||||||
\(287\) | −3.83221 | −0.226208 | ||||||||
\(288\) | −4.17513 | −0.246022 | ||||||||
\(289\) | −3.78202 | −0.222472 | ||||||||
\(290\) | −16.0575 | −0.942931 | ||||||||
\(291\) | 7.53948 | 0.441972 | ||||||||
\(292\) | −35.4292 | −2.07334 | ||||||||
\(293\) | 23.4433 | 1.36957 | 0.684786 | − | 0.728744i | \(-0.259896\pi\) | ||||
0.684786 | + | 0.728744i | \(0.259896\pi\) | |||||||
\(294\) | −18.0073 | −1.05021 | ||||||||
\(295\) | −9.95715 | −0.579728 | ||||||||
\(296\) | 28.6002 | 1.66235 | ||||||||
\(297\) | 3.34292 | 0.193976 | ||||||||
\(298\) | 29.3864 | 1.70231 | ||||||||
\(299\) | −8.97858 | −0.519245 | ||||||||
\(300\) | 14.9038 | 0.860473 | ||||||||
\(301\) | −45.0691 | −2.59774 | ||||||||
\(302\) | 6.15792 | 0.354349 | ||||||||
\(303\) | −5.00735 | −0.287665 | ||||||||
\(304\) | 1.37169 | 0.0786720 | ||||||||
\(305\) | −3.58233 | −0.205123 | ||||||||
\(306\) | 8.51806 | 0.486945 | ||||||||
\(307\) | 18.2541 | 1.04182 | 0.520908 | − | 0.853613i | \(-0.325593\pi\) | ||||
0.520908 | + | 0.853613i | \(0.325593\pi\) | |||||||
\(308\) | 44.7005 | 2.54705 | ||||||||
\(309\) | −1.21798 | −0.0692885 | ||||||||
\(310\) | 19.7220 | 1.12013 | ||||||||
\(311\) | 14.8782 | 0.843665 | 0.421832 | − | 0.906674i | \(-0.361387\pi\) | ||||
0.421832 | + | 0.906674i | \(0.361387\pi\) | |||||||
\(312\) | −10.9786 | −0.621540 | ||||||||
\(313\) | −26.4752 | −1.49647 | −0.748234 | − | 0.663435i | \(-0.769098\pi\) | ||||
−0.748234 | + | 0.663435i | \(0.769098\pi\) | |||||||
\(314\) | 47.2285 | 2.66526 | ||||||||
\(315\) | −3.27131 | −0.184317 | ||||||||
\(316\) | −12.5855 | −0.707988 | ||||||||
\(317\) | 29.6503 | 1.66533 | 0.832665 | − | 0.553777i | \(-0.186814\pi\) | ||||
0.832665 | + | 0.553777i | \(0.186814\pi\) | |||||||
\(318\) | −3.76481 | −0.211120 | ||||||||
\(319\) | 26.8396 | 1.50273 | ||||||||
\(320\) | −10.3931 | −0.580993 | ||||||||
\(321\) | −13.7648 | −0.768277 | ||||||||
\(322\) | 25.6216 | 1.42783 | ||||||||
\(323\) | 4.16779 | 0.231902 | ||||||||
\(324\) | 3.48929 | 0.193849 | ||||||||
\(325\) | −13.4391 | −0.745467 | ||||||||
\(326\) | 42.7679 | 2.36870 | ||||||||
\(327\) | −3.14637 | −0.173994 | ||||||||
\(328\) | 3.48929 | 0.192664 | ||||||||
\(329\) | −31.8898 | −1.75814 | ||||||||
\(330\) | 6.68585 | 0.368044 | ||||||||
\(331\) | 2.60375 | 0.143115 | 0.0715575 | − | 0.997436i | \(-0.477203\pi\) | ||||
0.0715575 | + | 0.997436i | \(0.477203\pi\) | |||||||
\(332\) | −35.3288 | −1.93892 | ||||||||
\(333\) | 8.19656 | 0.449169 | ||||||||
\(334\) | 3.07896 | 0.168473 | ||||||||
\(335\) | 5.20750 | 0.284516 | ||||||||
\(336\) | 4.58546 | 0.250157 | ||||||||
\(337\) | −1.51071 | −0.0822937 | −0.0411468 | − | 0.999153i | \(-0.513101\pi\) | ||||
−0.0411468 | + | 0.999153i | \(0.513101\pi\) | |||||||
\(338\) | −7.26396 | −0.395107 | ||||||||
\(339\) | 7.73183 | 0.419935 | ||||||||
\(340\) | 10.8291 | 0.587289 | ||||||||
\(341\) | −32.9645 | −1.78513 | ||||||||
\(342\) | 2.68585 | 0.145234 | ||||||||
\(343\) | −2.62831 | −0.141915 | ||||||||
\(344\) | 41.0361 | 2.21252 | ||||||||
\(345\) | 2.43596 | 0.131148 | ||||||||
\(346\) | 2.78623 | 0.149789 | ||||||||
\(347\) | −14.2787 | −0.766518 | −0.383259 | − | 0.923641i | \(-0.625198\pi\) | ||||
−0.383259 | + | 0.923641i | \(0.625198\pi\) | |||||||
\(348\) | 28.0147 | 1.50175 | ||||||||
\(349\) | −16.2541 | −0.870062 | −0.435031 | − | 0.900416i | \(-0.643263\pi\) | ||||
−0.435031 | + | 0.900416i | \(0.643263\pi\) | |||||||
\(350\) | 38.3503 | 2.04991 | ||||||||
\(351\) | −3.14637 | −0.167941 | ||||||||
\(352\) | 13.9572 | 0.743919 | ||||||||
\(353\) | 11.1709 | 0.594568 | 0.297284 | − | 0.954789i | \(-0.403919\pi\) | ||||
0.297284 | + | 0.954789i | \(0.403919\pi\) | |||||||
\(354\) | 27.3288 | 1.45251 | ||||||||
\(355\) | −7.38998 | −0.392219 | ||||||||
\(356\) | −11.7648 | −0.623534 | ||||||||
\(357\) | 13.9326 | 0.737391 | ||||||||
\(358\) | −44.5328 | −2.35363 | ||||||||
\(359\) | −16.2253 | −0.856340 | −0.428170 | − | 0.903698i | \(-0.640842\pi\) | ||||
−0.428170 | + | 0.903698i | \(0.640842\pi\) | |||||||
\(360\) | 2.97858 | 0.156985 | ||||||||
\(361\) | −17.6858 | −0.930834 | ||||||||
\(362\) | 24.3503 | 1.27982 | ||||||||
\(363\) | −0.175135 | −0.00919219 | ||||||||
\(364\) | −42.0722 | −2.20518 | ||||||||
\(365\) | −8.66756 | −0.453681 | ||||||||
\(366\) | 9.83221 | 0.513938 | ||||||||
\(367\) | 0.431750 | 0.0225372 | 0.0112686 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112686 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(368\) | −3.41454 | −0.177995 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 16.3931 | 0.852237 | ||||||||
\(371\) | −6.15792 | −0.319703 | ||||||||
\(372\) | −34.4078 | −1.78396 | ||||||||
\(373\) | −3.66863 | −0.189955 | −0.0949773 | − | 0.995479i | \(-0.530278\pi\) | ||||
−0.0949773 | + | 0.995479i | \(0.530278\pi\) | |||||||
\(374\) | −28.4752 | −1.47242 | ||||||||
\(375\) | 7.91431 | 0.408693 | ||||||||
\(376\) | 29.0361 | 1.49742 | ||||||||
\(377\) | −25.2614 | −1.30103 | ||||||||
\(378\) | 8.97858 | 0.461808 | ||||||||
\(379\) | −9.89962 | −0.508509 | −0.254255 | − | 0.967137i | \(-0.581830\pi\) | ||||
−0.254255 | + | 0.967137i | \(0.581830\pi\) | |||||||
\(380\) | 3.41454 | 0.175162 | ||||||||
\(381\) | 12.0575 | 0.617726 | ||||||||
\(382\) | −16.1151 | −0.824519 | ||||||||
\(383\) | −31.3148 | −1.60011 | −0.800055 | − | 0.599927i | \(-0.795196\pi\) | ||||
−0.800055 | + | 0.599927i | \(0.795196\pi\) | |||||||
\(384\) | 20.1751 | 1.02956 | ||||||||
\(385\) | 10.9357 | 0.557336 | ||||||||
\(386\) | −45.9143 | −2.33698 | ||||||||
\(387\) | 11.7606 | 0.597825 | ||||||||
\(388\) | −26.3074 | −1.33556 | ||||||||
\(389\) | 7.39625 | 0.375005 | 0.187502 | − | 0.982264i | \(-0.439961\pi\) | ||||
0.187502 | + | 0.982264i | \(0.439961\pi\) | |||||||
\(390\) | −6.29273 | −0.318645 | ||||||||
\(391\) | −10.3748 | −0.524678 | ||||||||
\(392\) | 26.8181 | 1.35452 | ||||||||
\(393\) | −12.2253 | −0.616686 | ||||||||
\(394\) | −58.0294 | −2.92348 | ||||||||
\(395\) | −3.07896 | −0.154919 | ||||||||
\(396\) | −11.6644 | −0.586159 | ||||||||
\(397\) | 11.9326 | 0.598880 | 0.299440 | − | 0.954115i | \(-0.403200\pi\) | ||||
0.299440 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(398\) | 30.0147 | 1.50450 | ||||||||
\(399\) | 4.39312 | 0.219931 | ||||||||
\(400\) | −5.11087 | −0.255543 | ||||||||
\(401\) | −15.7648 | −0.787257 | −0.393628 | − | 0.919270i | \(-0.628780\pi\) | ||||
−0.393628 | + | 0.919270i | \(0.628780\pi\) | |||||||
\(402\) | −14.2927 | −0.712857 | ||||||||
\(403\) | 31.0263 | 1.54553 | ||||||||
\(404\) | 17.4721 | 0.869268 | ||||||||
\(405\) | 0.853635 | 0.0424174 | ||||||||
\(406\) | 72.0869 | 3.57761 | ||||||||
\(407\) | −27.4005 | −1.35819 | ||||||||
\(408\) | −12.6858 | −0.628043 | ||||||||
\(409\) | −7.55356 | −0.373499 | −0.186750 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186750 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | −7.69319 | −0.379477 | ||||||||
\(412\) | 4.24989 | 0.209377 | ||||||||
\(413\) | 44.7005 | 2.19957 | ||||||||
\(414\) | −6.68585 | −0.328591 | ||||||||
\(415\) | −8.64300 | −0.424268 | ||||||||
\(416\) | −13.1365 | −0.644070 | ||||||||
\(417\) | 18.0147 | 0.882183 | ||||||||
\(418\) | −8.97858 | −0.439157 | ||||||||
\(419\) | 9.59702 | 0.468845 | 0.234423 | − | 0.972135i | \(-0.424680\pi\) | ||||
0.234423 | + | 0.972135i | \(0.424680\pi\) | |||||||
\(420\) | 11.4145 | 0.556972 | ||||||||
\(421\) | 12.3503 | 0.601915 | 0.300958 | − | 0.953638i | \(-0.402694\pi\) | ||||
0.300958 | + | 0.953638i | \(0.402694\pi\) | |||||||
\(422\) | 8.58546 | 0.417934 | ||||||||
\(423\) | 8.32150 | 0.404605 | ||||||||
\(424\) | 5.60688 | 0.272294 | ||||||||
\(425\) | −15.5290 | −0.753267 | ||||||||
\(426\) | 20.2829 | 0.982708 | ||||||||
\(427\) | 16.0821 | 0.778267 | ||||||||
\(428\) | 48.0294 | 2.32159 | ||||||||
\(429\) | 10.5181 | 0.507817 | ||||||||
\(430\) | 23.5212 | 1.13429 | ||||||||
\(431\) | 5.14637 | 0.247892 | 0.123946 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123946 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(432\) | −1.19656 | −0.0575694 | ||||||||
\(433\) | 17.0894 | 0.821266 | 0.410633 | − | 0.911801i | \(-0.365308\pi\) | ||||
0.410633 | + | 0.911801i | \(0.365308\pi\) | |||||||
\(434\) | −88.5376 | −4.24994 | ||||||||
\(435\) | 6.85363 | 0.328607 | ||||||||
\(436\) | 10.9786 | 0.525778 | ||||||||
\(437\) | −3.27131 | −0.156488 | ||||||||
\(438\) | 23.7894 | 1.13670 | ||||||||
\(439\) | −22.3503 | −1.06672 | −0.533360 | − | 0.845888i | \(-0.679071\pi\) | ||||
−0.533360 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(440\) | −9.95715 | −0.474689 | ||||||||
\(441\) | 7.68585 | 0.365993 | ||||||||
\(442\) | 26.8009 | 1.27479 | ||||||||
\(443\) | 23.4145 | 1.11246 | 0.556229 | − | 0.831029i | \(-0.312248\pi\) | ||||
0.556229 | + | 0.831029i | \(0.312248\pi\) | |||||||
\(444\) | −28.6002 | −1.35730 | ||||||||
\(445\) | −2.87819 | −0.136439 | ||||||||
\(446\) | 21.4868 | 1.01743 | ||||||||
\(447\) | −12.5426 | −0.593245 | ||||||||
\(448\) | 46.6577 | 2.20437 | ||||||||
\(449\) | −33.2713 | −1.57017 | −0.785085 | − | 0.619388i | \(-0.787381\pi\) | ||||
−0.785085 | + | 0.619388i | \(0.787381\pi\) | |||||||
\(450\) | −10.0073 | −0.471751 | ||||||||
\(451\) | −3.34292 | −0.157412 | ||||||||
\(452\) | −26.9786 | −1.26897 | ||||||||
\(453\) | −2.62831 | −0.123489 | ||||||||
\(454\) | 0.618442 | 0.0290249 | ||||||||
\(455\) | −10.2927 | −0.482531 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | −26.3931 | −1.23462 | −0.617309 | − | 0.786721i | \(-0.711777\pi\) | ||||
−0.617309 | + | 0.786721i | \(0.711777\pi\) | |||||||
\(458\) | 16.8782 | 0.788666 | ||||||||
\(459\) | −3.63565 | −0.169698 | ||||||||
\(460\) | −8.49977 | −0.396304 | ||||||||
\(461\) | 2.20077 | 0.102500 | 0.0512500 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512500 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(462\) | −30.0147 | −1.39641 | ||||||||
\(463\) | 24.5328 | 1.14013 | 0.570067 | − | 0.821598i | \(-0.306917\pi\) | ||||
0.570067 | + | 0.821598i | \(0.306917\pi\) | |||||||
\(464\) | −9.60688 | −0.445988 | ||||||||
\(465\) | −8.41767 | −0.390360 | ||||||||
\(466\) | 37.8568 | 1.75368 | ||||||||
\(467\) | −22.9357 | −1.06134 | −0.530670 | − | 0.847579i | \(-0.678059\pi\) | ||||
−0.530670 | + | 0.847579i | \(0.678059\pi\) | |||||||
\(468\) | 10.9786 | 0.507485 | ||||||||
\(469\) | −23.3780 | −1.07949 | ||||||||
\(470\) | 16.6430 | 0.767684 | ||||||||
\(471\) | −20.1579 | −0.928828 | ||||||||
\(472\) | −40.7005 | −1.87339 | ||||||||
\(473\) | −39.3148 | −1.80770 | ||||||||
\(474\) | 8.45065 | 0.388151 | ||||||||
\(475\) | −4.89648 | −0.224666 | ||||||||
\(476\) | −48.6148 | −2.22826 | ||||||||
\(477\) | 1.60688 | 0.0735742 | ||||||||
\(478\) | −36.7005 | −1.67864 | ||||||||
\(479\) | 41.6075 | 1.90110 | 0.950548 | − | 0.310579i | \(-0.100523\pi\) | ||||
0.950548 | + | 0.310579i | \(0.100523\pi\) | |||||||
\(480\) | 3.56404 | 0.162675 | ||||||||
\(481\) | 25.7894 | 1.17589 | ||||||||
\(482\) | 24.7104 | 1.12553 | ||||||||
\(483\) | −10.9357 | −0.497593 | ||||||||
\(484\) | 0.611096 | 0.0277771 | ||||||||
\(485\) | −6.43596 | −0.292242 | ||||||||
\(486\) | −2.34292 | −0.106277 | ||||||||
\(487\) | 40.4036 | 1.83086 | 0.915431 | − | 0.402475i | \(-0.131850\pi\) | ||||
0.915431 | + | 0.402475i | \(0.131850\pi\) | |||||||
\(488\) | −14.6430 | −0.662857 | ||||||||
\(489\) | −18.2541 | −0.825479 | ||||||||
\(490\) | 15.3717 | 0.694422 | ||||||||
\(491\) | −16.6184 | −0.749980 | −0.374990 | − | 0.927029i | \(-0.622354\pi\) | ||||
−0.374990 | + | 0.927029i | \(0.622354\pi\) | |||||||
\(492\) | −3.48929 | −0.157309 | ||||||||
\(493\) | −29.1898 | −1.31464 | ||||||||
\(494\) | 8.45065 | 0.380213 | ||||||||
\(495\) | −2.85363 | −0.128261 | ||||||||
\(496\) | 11.7992 | 0.529801 | ||||||||
\(497\) | 33.1758 | 1.48814 | ||||||||
\(498\) | 23.7220 | 1.06301 | ||||||||
\(499\) | −0.921039 | −0.0412314 | −0.0206157 | − | 0.999787i | \(-0.506563\pi\) | ||||
−0.0206157 | + | 0.999787i | \(0.506563\pi\) | |||||||
\(500\) | −27.6153 | −1.23499 | ||||||||
\(501\) | −1.31415 | −0.0587121 | ||||||||
\(502\) | 50.2070 | 2.24085 | ||||||||
\(503\) | 18.9217 | 0.843675 | 0.421837 | − | 0.906671i | \(-0.361385\pi\) | ||||
0.421837 | + | 0.906671i | \(0.361385\pi\) | |||||||
\(504\) | −13.3717 | −0.595623 | ||||||||
\(505\) | 4.27444 | 0.190210 | ||||||||
\(506\) | 22.3503 | 0.993591 | ||||||||
\(507\) | 3.10038 | 0.137693 | ||||||||
\(508\) | −42.0722 | −1.86665 | ||||||||
\(509\) | 27.8855 | 1.23600 | 0.618002 | − | 0.786176i | \(-0.287942\pi\) | ||||
0.618002 | + | 0.786176i | \(0.287942\pi\) | |||||||
\(510\) | −7.27131 | −0.321979 | ||||||||
\(511\) | 38.9112 | 1.72133 | ||||||||
\(512\) | −13.3461 | −0.589818 | ||||||||
\(513\) | −1.14637 | −0.0506133 | ||||||||
\(514\) | −16.6529 | −0.734526 | ||||||||
\(515\) | 1.03971 | 0.0458151 | ||||||||
\(516\) | −41.0361 | −1.80651 | ||||||||
\(517\) | −27.8181 | −1.22344 | ||||||||
\(518\) | −73.5934 | −3.23351 | ||||||||
\(519\) | −1.18921 | −0.0522006 | ||||||||
\(520\) | 9.37169 | 0.410976 | ||||||||
\(521\) | 9.93681 | 0.435339 | 0.217670 | − | 0.976022i | \(-0.430154\pi\) | ||||
0.217670 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(522\) | −18.8108 | −0.823326 | ||||||||
\(523\) | −35.9718 | −1.57294 | −0.786470 | − | 0.617629i | \(-0.788093\pi\) | ||||
−0.786470 | + | 0.617629i | \(0.788093\pi\) | |||||||
\(524\) | 42.6577 | 1.86351 | ||||||||
\(525\) | −16.3686 | −0.714382 | ||||||||
\(526\) | −23.3618 | −1.01862 | ||||||||
\(527\) | 35.8511 | 1.56170 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | −14.8568 | −0.645947 | ||||||||
\(530\) | 3.21377 | 0.139597 | ||||||||
\(531\) | −11.6644 | −0.506193 | ||||||||
\(532\) | −15.3288 | −0.664590 | ||||||||
\(533\) | 3.14637 | 0.136284 | ||||||||
\(534\) | 7.89962 | 0.341850 | ||||||||
\(535\) | 11.7501 | 0.508002 | ||||||||
\(536\) | 21.2860 | 0.919415 | ||||||||
\(537\) | 19.0073 | 0.820228 | ||||||||
\(538\) | −1.60688 | −0.0692777 | ||||||||
\(539\) | −25.6932 | −1.10668 | ||||||||
\(540\) | −2.97858 | −0.128178 | ||||||||
\(541\) | 9.79923 | 0.421302 | 0.210651 | − | 0.977561i | \(-0.432442\pi\) | ||||
0.210651 | + | 0.977561i | \(0.432442\pi\) | |||||||
\(542\) | 32.3404 | 1.38914 | ||||||||
\(543\) | −10.3931 | −0.446011 | ||||||||
\(544\) | −15.1793 | −0.650809 | ||||||||
\(545\) | 2.68585 | 0.115049 | ||||||||
\(546\) | 28.2499 | 1.20898 | ||||||||
\(547\) | −33.8223 | −1.44614 | −0.723070 | − | 0.690775i | \(-0.757269\pi\) | ||||
−0.723070 | + | 0.690775i | \(0.757269\pi\) | |||||||
\(548\) | 26.8438 | 1.14671 | ||||||||
\(549\) | −4.19656 | −0.179105 | ||||||||
\(550\) | 33.4538 | 1.42647 | ||||||||
\(551\) | −9.20390 | −0.392099 | ||||||||
\(552\) | 9.95715 | 0.423805 | ||||||||
\(553\) | 13.8223 | 0.587786 | ||||||||
\(554\) | 52.0393 | 2.21094 | ||||||||
\(555\) | −6.99686 | −0.297000 | ||||||||
\(556\) | −62.8585 | −2.66579 | ||||||||
\(557\) | −20.9217 | −0.886479 | −0.443239 | − | 0.896403i | \(-0.646171\pi\) | ||||
−0.443239 | + | 0.896403i | \(0.646171\pi\) | |||||||
\(558\) | 23.1035 | 0.978050 | ||||||||
\(559\) | 37.0031 | 1.56507 | ||||||||
\(560\) | −3.91431 | −0.165410 | ||||||||
\(561\) | 12.1537 | 0.513130 | ||||||||
\(562\) | 10.8108 | 0.456026 | ||||||||
\(563\) | −28.6289 | −1.20657 | −0.603283 | − | 0.797527i | \(-0.706141\pi\) | ||||
−0.603283 | + | 0.797527i | \(0.706141\pi\) | |||||||
\(564\) | −29.0361 | −1.22264 | ||||||||
\(565\) | −6.60015 | −0.277671 | ||||||||
\(566\) | 21.3963 | 0.899352 | ||||||||
\(567\) | −3.83221 | −0.160938 | ||||||||
\(568\) | −30.2070 | −1.26746 | ||||||||
\(569\) | −20.9603 | −0.878701 | −0.439351 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439351 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(570\) | −2.29273 | −0.0960319 | ||||||||
\(571\) | −13.2860 | −0.556002 | −0.278001 | − | 0.960581i | \(-0.589672\pi\) | ||||
−0.278001 | + | 0.960581i | \(0.589672\pi\) | |||||||
\(572\) | −36.7005 | −1.53453 | ||||||||
\(573\) | 6.87819 | 0.287341 | ||||||||
\(574\) | −8.97858 | −0.374759 | ||||||||
\(575\) | 12.1888 | 0.508306 | ||||||||
\(576\) | −12.1751 | −0.507297 | ||||||||
\(577\) | 1.35700 | 0.0564926 | 0.0282463 | − | 0.999601i | \(-0.491008\pi\) | ||||
0.0282463 | + | 0.999601i | \(0.491008\pi\) | |||||||
\(578\) | −8.86098 | −0.368568 | ||||||||
\(579\) | 19.5970 | 0.814424 | ||||||||
\(580\) | −23.9143 | −0.992988 | ||||||||
\(581\) | 38.8009 | 1.60973 | ||||||||
\(582\) | 17.6644 | 0.732214 | ||||||||
\(583\) | −5.37169 | −0.222473 | ||||||||
\(584\) | −35.4292 | −1.46607 | ||||||||
\(585\) | 2.68585 | 0.111046 | ||||||||
\(586\) | 54.9259 | 2.26897 | ||||||||
\(587\) | 29.9431 | 1.23588 | 0.617942 | − | 0.786224i | \(-0.287967\pi\) | ||||
0.617942 | + | 0.786224i | \(0.287967\pi\) | |||||||
\(588\) | −26.8181 | −1.10596 | ||||||||
\(589\) | 11.3043 | 0.465785 | ||||||||
\(590\) | −23.3288 | −0.960433 | ||||||||
\(591\) | 24.7679 | 1.01882 | ||||||||
\(592\) | 9.80765 | 0.403092 | ||||||||
\(593\) | −6.01408 | −0.246969 | −0.123484 | − | 0.992347i | \(-0.539407\pi\) | ||||
−0.123484 | + | 0.992347i | \(0.539407\pi\) | |||||||
\(594\) | 7.83221 | 0.321360 | ||||||||
\(595\) | −11.8933 | −0.487580 | ||||||||
\(596\) | 43.7648 | 1.79268 | ||||||||
\(597\) | −12.8108 | −0.524311 | ||||||||
\(598\) | −21.0361 | −0.860231 | ||||||||
\(599\) | 30.0477 | 1.22771 | 0.613857 | − | 0.789417i | \(-0.289617\pi\) | ||||
0.613857 | + | 0.789417i | \(0.289617\pi\) | |||||||
\(600\) | 14.9038 | 0.608446 | ||||||||
\(601\) | −38.1642 | −1.55675 | −0.778375 | − | 0.627800i | \(-0.783956\pi\) | ||||
−0.778375 | + | 0.627800i | \(0.783956\pi\) | |||||||
\(602\) | −105.593 | −4.30367 | ||||||||
\(603\) | 6.10038 | 0.248427 | ||||||||
\(604\) | 9.17092 | 0.373160 | ||||||||
\(605\) | 0.149501 | 0.00607808 | ||||||||
\(606\) | −11.7318 | −0.476573 | ||||||||
\(607\) | 35.7220 | 1.44991 | 0.724955 | − | 0.688796i | \(-0.241861\pi\) | ||||
0.724955 | + | 0.688796i | \(0.241861\pi\) | |||||||
\(608\) | −4.78623 | −0.194107 | ||||||||
\(609\) | −30.7679 | −1.24678 | ||||||||
\(610\) | −8.39312 | −0.339827 | ||||||||
\(611\) | 26.1825 | 1.05923 | ||||||||
\(612\) | 12.6858 | 0.512795 | ||||||||
\(613\) | −8.68585 | −0.350818 | −0.175409 | − | 0.984496i | \(-0.556125\pi\) | ||||
−0.175409 | + | 0.984496i | \(0.556125\pi\) | |||||||
\(614\) | 42.7679 | 1.72597 | ||||||||
\(615\) | −0.853635 | −0.0344219 | ||||||||
\(616\) | 44.7005 | 1.80104 | ||||||||
\(617\) | 25.4391 | 1.02414 | 0.512070 | − | 0.858944i | \(-0.328879\pi\) | ||||
0.512070 | + | 0.858944i | \(0.328879\pi\) | |||||||
\(618\) | −2.85363 | −0.114790 | ||||||||
\(619\) | 4.28852 | 0.172370 | 0.0861851 | − | 0.996279i | \(-0.472532\pi\) | ||||
0.0861851 | + | 0.996279i | \(0.472532\pi\) | |||||||
\(620\) | 29.3717 | 1.17960 | ||||||||
\(621\) | 2.85363 | 0.114512 | ||||||||
\(622\) | 34.8585 | 1.39770 | ||||||||
\(623\) | 12.9210 | 0.517670 | ||||||||
\(624\) | −3.76481 | −0.150713 | ||||||||
\(625\) | 14.6006 | 0.584025 | ||||||||
\(626\) | −62.0294 | −2.47919 | ||||||||
\(627\) | 3.83221 | 0.153044 | ||||||||
\(628\) | 70.3368 | 2.80674 | ||||||||
\(629\) | 29.7998 | 1.18820 | ||||||||
\(630\) | −7.66442 | −0.305358 | ||||||||
\(631\) | −3.17513 | −0.126400 | −0.0632001 | − | 0.998001i | \(-0.520131\pi\) | ||||
−0.0632001 | + | 0.998001i | \(0.520131\pi\) | |||||||
\(632\) | −12.5855 | −0.500623 | ||||||||
\(633\) | −3.66442 | −0.145648 | ||||||||
\(634\) | 69.4685 | 2.75895 | ||||||||
\(635\) | −10.2927 | −0.408455 | ||||||||
\(636\) | −5.60688 | −0.222327 | ||||||||
\(637\) | 24.1825 | 0.958145 | ||||||||
\(638\) | 62.8830 | 2.48956 | ||||||||
\(639\) | −8.65708 | −0.342469 | ||||||||
\(640\) | −17.2222 | −0.680767 | ||||||||
\(641\) | −21.0565 | −0.831680 | −0.415840 | − | 0.909438i | \(-0.636512\pi\) | ||||
−0.415840 | + | 0.909438i | \(0.636512\pi\) | |||||||
\(642\) | −32.2499 | −1.27280 | ||||||||
\(643\) | −18.2070 | −0.718016 | −0.359008 | − | 0.933335i | \(-0.616885\pi\) | ||||
−0.359008 | + | 0.933335i | \(0.616885\pi\) | |||||||
\(644\) | 38.1579 | 1.50363 | ||||||||
\(645\) | −10.0393 | −0.395295 | ||||||||
\(646\) | 9.76481 | 0.384191 | ||||||||
\(647\) | −19.6890 | −0.774054 | −0.387027 | − | 0.922068i | \(-0.626498\pi\) | ||||
−0.387027 | + | 0.922068i | \(0.626498\pi\) | |||||||
\(648\) | 3.48929 | 0.137072 | ||||||||
\(649\) | 38.9933 | 1.53062 | ||||||||
\(650\) | −31.4868 | −1.23501 | ||||||||
\(651\) | 37.7894 | 1.48108 | ||||||||
\(652\) | 63.6938 | 2.49444 | ||||||||
\(653\) | −2.80031 | −0.109584 | −0.0547922 | − | 0.998498i | \(-0.517450\pi\) | ||||
−0.0547922 | + | 0.998498i | \(0.517450\pi\) | |||||||
\(654\) | −7.37169 | −0.288256 | ||||||||
\(655\) | 10.4360 | 0.407767 | ||||||||
\(656\) | 1.19656 | 0.0467177 | ||||||||
\(657\) | −10.1537 | −0.396134 | ||||||||
\(658\) | −74.7152 | −2.91270 | ||||||||
\(659\) | −7.07896 | −0.275757 | −0.137879 | − | 0.990449i | \(-0.544028\pi\) | ||||
−0.137879 | + | 0.990449i | \(0.544028\pi\) | |||||||
\(660\) | 9.95715 | 0.387582 | ||||||||
\(661\) | −15.6791 | −0.609847 | −0.304923 | − | 0.952377i | \(-0.598631\pi\) | ||||
−0.304923 | + | 0.952377i | \(0.598631\pi\) | |||||||
\(662\) | 6.10038 | 0.237098 | ||||||||
\(663\) | −11.4391 | −0.444258 | ||||||||
\(664\) | −35.3288 | −1.37103 | ||||||||
\(665\) | −3.75011 | −0.145423 | ||||||||
\(666\) | 19.2039 | 0.744136 | ||||||||
\(667\) | 22.9112 | 0.887124 | ||||||||
\(668\) | 4.58546 | 0.177417 | ||||||||
\(669\) | −9.17092 | −0.354568 | ||||||||
\(670\) | 12.2008 | 0.471357 | ||||||||
\(671\) | 14.0288 | 0.541575 | ||||||||
\(672\) | −16.0000 | −0.617213 | ||||||||
\(673\) | −12.2070 | −0.470547 | −0.235273 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235273 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(674\) | −3.53948 | −0.136336 | ||||||||
\(675\) | 4.27131 | 0.164403 | ||||||||
\(676\) | −10.8181 | −0.416082 | ||||||||
\(677\) | −39.7121 | −1.52626 | −0.763130 | − | 0.646245i | \(-0.776338\pi\) | ||||
−0.763130 | + | 0.646245i | \(0.776338\pi\) | |||||||
\(678\) | 18.1151 | 0.695705 | ||||||||
\(679\) | 28.8929 | 1.10881 | ||||||||
\(680\) | 10.8291 | 0.415276 | ||||||||
\(681\) | −0.263962 | −0.0101150 | ||||||||
\(682\) | −77.2333 | −2.95742 | ||||||||
\(683\) | 9.22846 | 0.353117 | 0.176559 | − | 0.984290i | \(-0.443503\pi\) | ||||
0.176559 | + | 0.984290i | \(0.443503\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 6.56717 | 0.250919 | ||||||||
\(686\) | −6.15792 | −0.235111 | ||||||||
\(687\) | −7.20390 | −0.274846 | ||||||||
\(688\) | 14.0722 | 0.536499 | ||||||||
\(689\) | 5.05585 | 0.192612 | ||||||||
\(690\) | 5.70727 | 0.217272 | ||||||||
\(691\) | −4.75325 | −0.180822 | −0.0904111 | − | 0.995905i | \(-0.528818\pi\) | ||||
−0.0904111 | + | 0.995905i | \(0.528818\pi\) | |||||||
\(692\) | 4.14950 | 0.157740 | ||||||||
\(693\) | 12.8108 | 0.486642 | ||||||||
\(694\) | −33.4538 | −1.26989 | ||||||||
\(695\) | −15.3780 | −0.583319 | ||||||||
\(696\) | 28.0147 | 1.06189 | ||||||||
\(697\) | 3.63565 | 0.137710 | ||||||||
\(698\) | −38.0821 | −1.44143 | ||||||||
\(699\) | −16.1579 | −0.611149 | ||||||||
\(700\) | 57.1146 | 2.15873 | ||||||||
\(701\) | −21.0790 | −0.796141 | −0.398071 | − | 0.917355i | \(-0.630320\pi\) | ||||
−0.398071 | + | 0.917355i | \(0.630320\pi\) | |||||||
\(702\) | −7.37169 | −0.278227 | ||||||||
\(703\) | 9.39625 | 0.354386 | ||||||||
\(704\) | 40.7005 | 1.53396 | ||||||||
\(705\) | −7.10352 | −0.267534 | ||||||||
\(706\) | 26.1726 | 0.985019 | ||||||||
\(707\) | −19.1892 | −0.721685 | ||||||||
\(708\) | 40.7005 | 1.52962 | ||||||||
\(709\) | 42.7497 | 1.60550 | 0.802749 | − | 0.596318i | \(-0.203370\pi\) | ||||
0.802749 | + | 0.596318i | \(0.203370\pi\) | |||||||
\(710\) | −17.3142 | −0.649789 | ||||||||
\(711\) | −3.60688 | −0.135269 | ||||||||
\(712\) | −11.7648 | −0.440905 | ||||||||
\(713\) | −28.1396 | −1.05384 | ||||||||
\(714\) | 32.6430 | 1.22163 | ||||||||
\(715\) | −8.97858 | −0.335780 | ||||||||
\(716\) | −66.3221 | −2.47857 | ||||||||
\(717\) | 15.6644 | 0.584999 | ||||||||
\(718\) | −38.0147 | −1.41870 | ||||||||
\(719\) | −7.00735 | −0.261330 | −0.130665 | − | 0.991427i | \(-0.541711\pi\) | ||||
−0.130665 | + | 0.991427i | \(0.541711\pi\) | |||||||
\(720\) | 1.02142 | 0.0380662 | ||||||||
\(721\) | −4.66756 | −0.173829 | ||||||||
\(722\) | −41.4366 | −1.54211 | ||||||||
\(723\) | −10.5468 | −0.392241 | ||||||||
\(724\) | 36.2646 | 1.34776 | ||||||||
\(725\) | 34.2933 | 1.27362 | ||||||||
\(726\) | −0.410327 | −0.0152287 | ||||||||
\(727\) | −33.3963 | −1.23860 | −0.619299 | − | 0.785155i | \(-0.712583\pi\) | ||||
−0.619299 | + | 0.785155i | \(0.712583\pi\) | |||||||
\(728\) | −42.0722 | −1.55930 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.3074 | −0.751611 | ||||||||
\(731\) | 42.7575 | 1.58144 | ||||||||
\(732\) | 14.6430 | 0.541221 | ||||||||
\(733\) | 13.1176 | 0.484509 | 0.242255 | − | 0.970213i | \(-0.422113\pi\) | ||||
0.242255 | + | 0.970213i | \(0.422113\pi\) | |||||||
\(734\) | 1.01156 | 0.0373373 | ||||||||
\(735\) | −6.56090 | −0.242003 | ||||||||
\(736\) | 11.9143 | 0.439167 | ||||||||
\(737\) | −20.3931 | −0.751190 | ||||||||
\(738\) | 2.34292 | 0.0862442 | ||||||||
\(739\) | −47.2902 | −1.73960 | −0.869799 | − | 0.493406i | \(-0.835752\pi\) | ||||
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(740\) | 24.4141 | 0.897479 | ||||||||
\(741\) | −3.60688 | −0.132502 | ||||||||
\(742\) | −14.4275 | −0.529652 | ||||||||
\(743\) | −18.5510 | −0.680572 | −0.340286 | − | 0.940322i | \(-0.610524\pi\) | ||||
−0.340286 | + | 0.940322i | \(0.610524\pi\) | |||||||
\(744\) | −34.4078 | −1.26145 | ||||||||
\(745\) | 10.7068 | 0.392267 | ||||||||
\(746\) | −8.59533 | −0.314697 | ||||||||
\(747\) | −10.1249 | −0.370452 | ||||||||
\(748\) | −42.4078 | −1.55058 | ||||||||
\(749\) | −52.7497 | −1.92743 | ||||||||
\(750\) | 18.5426 | 0.677081 | ||||||||
\(751\) | −13.6791 | −0.499158 | −0.249579 | − | 0.968354i | \(-0.580292\pi\) | ||||
−0.249579 | + | 0.968354i | \(0.580292\pi\) | |||||||
\(752\) | 9.95715 | 0.363100 | ||||||||
\(753\) | −21.4292 | −0.780925 | ||||||||
\(754\) | −59.1856 | −2.15541 | ||||||||
\(755\) | 2.24361 | 0.0816535 | ||||||||
\(756\) | 13.3717 | 0.486324 | ||||||||
\(757\) | −23.0031 | −0.836063 | −0.418032 | − | 0.908432i | \(-0.637280\pi\) | ||||
−0.418032 | + | 0.908432i | \(0.637280\pi\) | |||||||
\(758\) | −23.1940 | −0.842445 | ||||||||
\(759\) | −9.53948 | −0.346261 | ||||||||
\(760\) | 3.41454 | 0.123858 | ||||||||
\(761\) | 20.4851 | 0.742583 | 0.371292 | − | 0.928516i | \(-0.378915\pi\) | ||||
0.371292 | + | 0.928516i | \(0.378915\pi\) | |||||||
\(762\) | 28.2499 | 1.02339 | ||||||||
\(763\) | −12.0575 | −0.436512 | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 3.10352 | 0.112208 | ||||||||
\(766\) | −73.3681 | −2.65090 | ||||||||
\(767\) | −36.7005 | −1.32518 | ||||||||
\(768\) | 22.9185 | 0.827001 | ||||||||
\(769\) | −17.5107 | −0.631452 | −0.315726 | − | 0.948850i | \(-0.602248\pi\) | ||||
−0.315726 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(770\) | 25.6216 | 0.923338 | ||||||||
\(771\) | 7.10773 | 0.255979 | ||||||||
\(772\) | −68.3797 | −2.46104 | ||||||||
\(773\) | −31.8083 | −1.14406 | −0.572032 | − | 0.820231i | \(-0.693845\pi\) | ||||
−0.572032 | + | 0.820231i | \(0.693845\pi\) | |||||||
\(774\) | 27.5542 | 0.990414 | ||||||||
\(775\) | −42.1193 | −1.51297 | ||||||||
\(776\) | −26.3074 | −0.944381 | ||||||||
\(777\) | 31.4109 | 1.12686 | ||||||||
\(778\) | 17.3288 | 0.621269 | ||||||||
\(779\) | 1.14637 | 0.0410728 | ||||||||
\(780\) | −9.37169 | −0.335560 | ||||||||
\(781\) | 28.9399 | 1.03555 | ||||||||
\(782\) | −24.3074 | −0.869232 | ||||||||
\(783\) | 8.02877 | 0.286925 | ||||||||
\(784\) | 9.19656 | 0.328448 | ||||||||
\(785\) | 17.2075 | 0.614162 | ||||||||
\(786\) | −28.6430 | −1.02166 | ||||||||
\(787\) | 14.5040 | 0.517011 | 0.258506 | − | 0.966010i | \(-0.416770\pi\) | ||||
0.258506 | + | 0.966010i | \(0.416770\pi\) | |||||||
\(788\) | −86.4225 | −3.07867 | ||||||||
\(789\) | 9.97123 | 0.354985 | ||||||||
\(790\) | −7.21377 | −0.256654 | ||||||||
\(791\) | 29.6300 | 1.05352 | ||||||||
\(792\) | −11.6644 | −0.414477 | ||||||||
\(793\) | −13.2039 | −0.468884 | ||||||||
\(794\) | 27.9572 | 0.992162 | ||||||||
\(795\) | −1.37169 | −0.0486489 | ||||||||
\(796\) | 44.7005 | 1.58437 | ||||||||
\(797\) | 50.3650 | 1.78402 | 0.892009 | − | 0.452017i | \(-0.149295\pi\) | ||||
0.892009 | + | 0.452017i | \(0.149295\pi\) | |||||||
\(798\) | 10.2927 | 0.364359 | ||||||||
\(799\) | 30.2541 | 1.07031 | ||||||||
\(800\) | 17.8333 | 0.630502 | ||||||||
\(801\) | −3.37169 | −0.119133 | ||||||||
\(802\) | −36.9357 | −1.30425 | ||||||||
\(803\) | 33.9431 | 1.19783 | ||||||||
\(804\) | −21.2860 | −0.750699 | ||||||||
\(805\) | 9.33512 | 0.329020 | ||||||||
\(806\) | 72.6921 | 2.56047 | ||||||||
\(807\) | 0.685846 | 0.0241429 | ||||||||
\(808\) | 17.4721 | 0.614666 | ||||||||
\(809\) | 35.2369 | 1.23886 | 0.619431 | − | 0.785051i | \(-0.287363\pi\) | ||||
0.619431 | + | 0.785051i | \(0.287363\pi\) | |||||||
\(810\) | 2.00000 | 0.0702728 | ||||||||
\(811\) | −13.8610 | −0.486725 | −0.243362 | − | 0.969935i | \(-0.578250\pi\) | ||||
−0.243362 | + | 0.969935i | \(0.578250\pi\) | |||||||
\(812\) | 107.358 | 3.76754 | ||||||||
\(813\) | −13.8034 | −0.484108 | ||||||||
\(814\) | −64.1972 | −2.25011 | ||||||||
\(815\) | 15.5823 | 0.545825 | ||||||||
\(816\) | −4.35027 | −0.152290 | ||||||||
\(817\) | 13.4819 | 0.471673 | ||||||||
\(818\) | −17.6974 | −0.618775 | ||||||||
\(819\) | −12.0575 | −0.421324 | ||||||||
\(820\) | 2.97858 | 0.104016 | ||||||||
\(821\) | 7.20390 | 0.251418 | 0.125709 | − | 0.992067i | \(-0.459879\pi\) | ||||
0.125709 | + | 0.992067i | \(0.459879\pi\) | |||||||
\(822\) | −18.0246 | −0.628679 | ||||||||
\(823\) | −9.81392 | −0.342092 | −0.171046 | − | 0.985263i | \(-0.554715\pi\) | ||||
−0.171046 | + | 0.985263i | \(0.554715\pi\) | |||||||
\(824\) | 4.24989 | 0.148052 | ||||||||
\(825\) | −14.2787 | −0.497119 | ||||||||
\(826\) | 104.730 | 3.64402 | ||||||||
\(827\) | 24.8788 | 0.865121 | 0.432560 | − | 0.901605i | \(-0.357610\pi\) | ||||
0.432560 | + | 0.901605i | \(0.357610\pi\) | |||||||
\(828\) | −9.95715 | −0.346035 | ||||||||
\(829\) | 13.3759 | 0.464564 | 0.232282 | − | 0.972648i | \(-0.425381\pi\) | ||||
0.232282 | + | 0.972648i | \(0.425381\pi\) | |||||||
\(830\) | −20.2499 | −0.702884 | ||||||||
\(831\) | −22.2113 | −0.770500 | ||||||||
\(832\) | −38.3074 | −1.32807 | ||||||||
\(833\) | 27.9431 | 0.968170 | ||||||||
\(834\) | 42.2070 | 1.46151 | ||||||||
\(835\) | 1.12181 | 0.0388217 | ||||||||
\(836\) | −13.3717 | −0.462470 | ||||||||
\(837\) | −9.86098 | −0.340845 | ||||||||
\(838\) | 22.4851 | 0.776734 | ||||||||
\(839\) | −12.9210 | −0.446084 | −0.223042 | − | 0.974809i | \(-0.571599\pi\) | ||||
−0.223042 | + | 0.974809i | \(0.571599\pi\) | |||||||
\(840\) | 11.4145 | 0.393839 | ||||||||
\(841\) | 35.4611 | 1.22280 | ||||||||
\(842\) | 28.9357 | 0.997191 | ||||||||
\(843\) | −4.61423 | −0.158923 | ||||||||
\(844\) | 12.7862 | 0.440120 | ||||||||
\(845\) | −2.64659 | −0.0910456 | ||||||||
\(846\) | 19.4966 | 0.670308 | ||||||||
\(847\) | −0.671153 | −0.0230611 | ||||||||
\(848\) | 1.92273 | 0.0660268 | ||||||||
\(849\) | −9.13229 | −0.313419 | ||||||||
\(850\) | −36.3832 | −1.24794 | ||||||||
\(851\) | −23.3900 | −0.801798 | ||||||||
\(852\) | 30.2070 | 1.03488 | ||||||||
\(853\) | 16.4851 | 0.564438 | 0.282219 | − | 0.959350i | \(-0.408929\pi\) | ||||
0.282219 | + | 0.959350i | \(0.408929\pi\) | |||||||
\(854\) | 37.6791 | 1.28935 | ||||||||
\(855\) | 0.978577 | 0.0334666 | ||||||||
\(856\) | 48.0294 | 1.64161 | ||||||||
\(857\) | −11.5149 | −0.393342 | −0.196671 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196671 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(858\) | 24.6430 | 0.841298 | ||||||||
\(859\) | −28.7392 | −0.980568 | −0.490284 | − | 0.871563i | \(-0.663107\pi\) | ||||
−0.490284 | + | 0.871563i | \(0.663107\pi\) | |||||||
\(860\) | 35.0298 | 1.19451 | ||||||||
\(861\) | 3.83221 | 0.130601 | ||||||||
\(862\) | 12.0575 | 0.410681 | ||||||||
\(863\) | 51.1611 | 1.74154 | 0.870771 | − | 0.491688i | \(-0.163620\pi\) | ||||
0.870771 | + | 0.491688i | \(0.163620\pi\) | |||||||
\(864\) | 4.17513 | 0.142041 | ||||||||
\(865\) | 1.01515 | 0.0345162 | ||||||||
\(866\) | 40.0393 | 1.36059 | ||||||||
\(867\) | 3.78202 | 0.128444 | ||||||||
\(868\) | −131.858 | −4.47555 | ||||||||
\(869\) | 12.0575 | 0.409024 | ||||||||
\(870\) | 16.0575 | 0.544402 | ||||||||
\(871\) | 19.1940 | 0.650365 | ||||||||
\(872\) | 10.9786 | 0.371782 | ||||||||
\(873\) | −7.53948 | −0.255173 | ||||||||
\(874\) | −7.66442 | −0.259253 | ||||||||
\(875\) | 30.3293 | 1.02532 | ||||||||
\(876\) | 35.4292 | 1.19704 | ||||||||
\(877\) | 34.3179 | 1.15883 | 0.579417 | − | 0.815031i | \(-0.303280\pi\) | ||||
0.579417 | + | 0.815031i | \(0.303280\pi\) | |||||||
\(878\) | −52.3650 | −1.76723 | ||||||||
\(879\) | −23.4433 | −0.790723 | ||||||||
\(880\) | −3.41454 | −0.115104 | ||||||||
\(881\) | −38.9786 | −1.31322 | −0.656611 | − | 0.754230i | \(-0.728011\pi\) | ||||
−0.656611 | + | 0.754230i | \(0.728011\pi\) | |||||||
\(882\) | 18.0073 | 0.606339 | ||||||||
\(883\) | −28.2253 | −0.949858 | −0.474929 | − | 0.880024i | \(-0.657526\pi\) | ||||
−0.474929 | + | 0.880024i | \(0.657526\pi\) | |||||||
\(884\) | 39.9143 | 1.34246 | ||||||||
\(885\) | 9.95715 | 0.334706 | ||||||||
\(886\) | 54.8585 | 1.84301 | ||||||||
\(887\) | −30.1438 | −1.01213 | −0.506066 | − | 0.862495i | \(-0.668901\pi\) | ||||
−0.506066 | + | 0.862495i | \(0.668901\pi\) | |||||||
\(888\) | −28.6002 | −0.959758 | ||||||||
\(889\) | 46.2070 | 1.54973 | ||||||||
\(890\) | −6.74338 | −0.226039 | ||||||||
\(891\) | −3.34292 | −0.111992 | ||||||||
\(892\) | 32.0000 | 1.07144 | ||||||||
\(893\) | 9.53948 | 0.319227 | ||||||||
\(894\) | −29.3864 | −0.982828 | ||||||||
\(895\) | −16.2253 | −0.542353 | ||||||||
\(896\) | 77.3154 | 2.58293 | ||||||||
\(897\) | 8.97858 | 0.299786 | ||||||||
\(898\) | −77.9521 | −2.60130 | ||||||||
\(899\) | −79.1715 | −2.64052 | ||||||||
\(900\) | −14.9038 | −0.496794 | ||||||||
\(901\) | 5.84208 | 0.194628 | ||||||||
\(902\) | −7.83221 | −0.260784 | ||||||||
\(903\) | 45.0691 | 1.49981 | ||||||||
\(904\) | −26.9786 | −0.897294 | ||||||||
\(905\) | 8.87192 | 0.294913 | ||||||||
\(906\) | −6.15792 | −0.204583 | ||||||||
\(907\) | 41.3435 | 1.37279 | 0.686395 | − | 0.727229i | \(-0.259192\pi\) | ||||
0.686395 | + | 0.727229i | \(0.259192\pi\) | |||||||
\(908\) | 0.921039 | 0.0305657 | ||||||||
\(909\) | 5.00735 | 0.166083 | ||||||||
\(910\) | −24.1151 | −0.799407 | ||||||||
\(911\) | −1.23206 | −0.0408199 | −0.0204099 | − | 0.999792i | \(-0.506497\pi\) | ||||
−0.0204099 | + | 0.999792i | \(0.506497\pi\) | |||||||
\(912\) | −1.37169 | −0.0454213 | ||||||||
\(913\) | 33.8469 | 1.12017 | ||||||||
\(914\) | −61.8370 | −2.04539 | ||||||||
\(915\) | 3.58233 | 0.118428 | ||||||||
\(916\) | 25.1365 | 0.830533 | ||||||||
\(917\) | −46.8500 | −1.54712 | ||||||||
\(918\) | −8.51806 | −0.281138 | ||||||||
\(919\) | −21.4047 | −0.706075 | −0.353037 | − | 0.935609i | \(-0.614851\pi\) | ||||
−0.353037 | + | 0.935609i | \(0.614851\pi\) | |||||||
\(920\) | −8.49977 | −0.280229 | ||||||||
\(921\) | −18.2541 | −0.601493 | ||||||||
\(922\) | 5.15623 | 0.169811 | ||||||||
\(923\) | −27.2383 | −0.896560 | ||||||||
\(924\) | −44.7005 | −1.47054 | ||||||||
\(925\) | −35.0100 | −1.15112 | ||||||||
\(926\) | 57.4783 | 1.88886 | ||||||||
\(927\) | 1.21798 | 0.0400037 | ||||||||
\(928\) | 33.5212 | 1.10039 | ||||||||
\(929\) | 32.8150 | 1.07663 | 0.538313 | − | 0.842745i | \(-0.319062\pi\) | ||||
0.538313 | + | 0.842745i | \(0.319062\pi\) | |||||||
\(930\) | −19.7220 | −0.646709 | ||||||||
\(931\) | 8.81079 | 0.288762 | ||||||||
\(932\) | 56.3797 | 1.84678 | ||||||||
\(933\) | −14.8782 | −0.487090 | ||||||||
\(934\) | −53.7367 | −1.75832 | ||||||||
\(935\) | −10.3748 | −0.339293 | ||||||||
\(936\) | 10.9786 | 0.358846 | ||||||||
\(937\) | 27.4783 | 0.897678 | 0.448839 | − | 0.893613i | \(-0.351838\pi\) | ||||
0.448839 | + | 0.893613i | \(0.351838\pi\) | |||||||
\(938\) | −54.7728 | −1.78839 | ||||||||
\(939\) | 26.4752 | 0.863986 | ||||||||
\(940\) | 24.7862 | 0.808438 | ||||||||
\(941\) | 38.1151 | 1.24252 | 0.621258 | − | 0.783606i | \(-0.286622\pi\) | ||||
0.621258 | + | 0.783606i | \(0.286622\pi\) | |||||||
\(942\) | −47.2285 | −1.53879 | ||||||||
\(943\) | −2.85363 | −0.0929271 | ||||||||
\(944\) | −13.9572 | −0.454267 | ||||||||
\(945\) | 3.27131 | 0.106416 | ||||||||
\(946\) | −92.1115 | −2.99480 | ||||||||
\(947\) | −9.85050 | −0.320098 | −0.160049 | − | 0.987109i | \(-0.551165\pi\) | ||||
−0.160049 | + | 0.987109i | \(0.551165\pi\) | |||||||
\(948\) | 12.5855 | 0.408757 | ||||||||
\(949\) | −31.9473 | −1.03705 | ||||||||
\(950\) | −11.4721 | −0.372203 | ||||||||
\(951\) | −29.6503 | −0.961478 | ||||||||
\(952\) | −48.6148 | −1.57562 | ||||||||
\(953\) | 3.92417 | 0.127116 | 0.0635582 | − | 0.997978i | \(-0.479755\pi\) | ||||
0.0635582 | + | 0.997978i | \(0.479755\pi\) | |||||||
\(954\) | 3.76481 | 0.121890 | ||||||||
\(955\) | −5.87146 | −0.189996 | ||||||||
\(956\) | −54.6577 | −1.76776 | ||||||||
\(957\) | −26.8396 | −0.867600 | ||||||||
\(958\) | 97.4832 | 3.14954 | ||||||||
\(959\) | −29.4819 | −0.952022 | ||||||||
\(960\) | 10.3931 | 0.335436 | ||||||||
\(961\) | 66.2389 | 2.13674 | ||||||||
\(962\) | 60.4225 | 1.94810 | ||||||||
\(963\) | 13.7648 | 0.443565 | ||||||||
\(964\) | 36.8009 | 1.18528 | ||||||||
\(965\) | −16.7287 | −0.538516 | ||||||||
\(966\) | −25.6216 | −0.824361 | ||||||||
\(967\) | −40.3074 | −1.29620 | −0.648100 | − | 0.761556i | \(-0.724436\pi\) | ||||
−0.648100 | + | 0.761556i | \(0.724436\pi\) | |||||||
\(968\) | 0.611096 | 0.0196414 | ||||||||
\(969\) | −4.16779 | −0.133889 | ||||||||
\(970\) | −15.0790 | −0.484156 | ||||||||
\(971\) | 37.8280 | 1.21396 | 0.606979 | − | 0.794718i | \(-0.292381\pi\) | ||||
0.606979 | + | 0.794718i | \(0.292381\pi\) | |||||||
\(972\) | −3.48929 | −0.111919 | ||||||||
\(973\) | 69.0361 | 2.21320 | ||||||||
\(974\) | 94.6625 | 3.03318 | ||||||||
\(975\) | 13.4391 | 0.430396 | ||||||||
\(976\) | −5.02142 | −0.160732 | ||||||||
\(977\) | 8.89227 | 0.284489 | 0.142244 | − | 0.989832i | \(-0.454568\pi\) | ||||
0.142244 | + | 0.989832i | \(0.454568\pi\) | |||||||
\(978\) | −42.7679 | −1.36757 | ||||||||
\(979\) | 11.2713 | 0.360233 | ||||||||
\(980\) | 22.8929 | 0.731286 | ||||||||
\(981\) | 3.14637 | 0.100456 | ||||||||
\(982\) | −38.9357 | −1.24249 | ||||||||
\(983\) | −30.6247 | −0.976777 | −0.488388 | − | 0.872626i | \(-0.662415\pi\) | ||||
−0.488388 | + | 0.872626i | \(0.662415\pi\) | |||||||
\(984\) | −3.48929 | −0.111234 | ||||||||
\(985\) | −21.1428 | −0.673665 | ||||||||
\(986\) | −68.3895 | −2.17797 | ||||||||
\(987\) | 31.8898 | 1.01506 | ||||||||
\(988\) | 12.5855 | 0.400397 | ||||||||
\(989\) | −33.5604 | −1.06716 | ||||||||
\(990\) | −6.68585 | −0.212490 | ||||||||
\(991\) | −53.1512 | −1.68840 | −0.844202 | − | 0.536026i | \(-0.819925\pi\) | ||||
−0.844202 | + | 0.536026i | \(0.819925\pi\) | |||||||
\(992\) | −41.1709 | −1.30718 | ||||||||
\(993\) | −2.60375 | −0.0826275 | ||||||||
\(994\) | 77.7282 | 2.46539 | ||||||||
\(995\) | 10.9357 | 0.346686 | ||||||||
\(996\) | 35.3288 | 1.11944 | ||||||||
\(997\) | −44.5181 | −1.40990 | −0.704951 | − | 0.709256i | \(-0.749031\pi\) | ||||
−0.704951 | + | 0.709256i | \(0.749031\pi\) | |||||||
\(998\) | −2.15792 | −0.0683078 | ||||||||
\(999\) | −8.19656 | −0.259328 |
(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 | 123.2.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 369.2.a.e.1.1 | 3 | |||
4.3 | odd | 2 | 1968.2.a.w.1.2 | 3 | |||
5.4 | even | 2 | 3075.2.a.t.1.1 | 3 | |||
7.6 | odd | 2 | 6027.2.a.s.1.3 | 3 | |||
8.3 | odd | 2 | 7872.2.a.bs.1.2 | 3 | |||
8.5 | even | 2 | 7872.2.a.bx.1.2 | 3 | |||
12.11 | even | 2 | 5904.2.a.bd.1.2 | 3 | |||
15.14 | odd | 2 | 9225.2.a.bx.1.3 | 3 | |||
41.40 | even | 2 | 5043.2.a.n.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
123.2.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
369.2.a.e.1.1 | 3 | 3.2 | odd | 2 | |||
1968.2.a.w.1.2 | 3 | 4.3 | odd | 2 | |||
3075.2.a.t.1.1 | 3 | 5.4 | even | 2 | |||
5043.2.a.n.1.3 | 3 | 41.40 | even | 2 | |||
5904.2.a.bd.1.2 | 3 | 12.11 | even | 2 | |||
6027.2.a.s.1.3 | 3 | 7.6 | odd | 2 | |||
7872.2.a.bs.1.2 | 3 | 8.3 | odd | 2 | |||
7872.2.a.bx.1.2 | 3 | 8.5 | even | 2 | |||
9225.2.a.bx.1.3 | 3 | 15.14 | odd | 2 |