Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(1,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.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: | \(1.92439468871\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} - 328 x^{3} - 45 x^{2} + 18 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.63125\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 241.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.63125 | 1.15347 | 0.576736 | − | 0.816931i | \(-0.304326\pi\) | ||||
0.576736 | + | 0.816931i | \(0.304326\pi\) | |||||||
\(3\) | −1.16790 | −0.674287 | −0.337144 | − | 0.941453i | \(-0.609461\pi\) | ||||
−0.337144 | + | 0.941453i | \(0.609461\pi\) | |||||||
\(4\) | 0.660992 | 0.330496 | ||||||||
\(5\) | 1.75438 | 0.784580 | 0.392290 | − | 0.919842i | \(-0.371683\pi\) | ||||
0.392290 | + | 0.919842i | \(0.371683\pi\) | |||||||
\(6\) | −1.90514 | −0.777771 | ||||||||
\(7\) | 5.06139 | 1.91302 | 0.956512 | − | 0.291693i | \(-0.0942184\pi\) | ||||
0.956512 | + | 0.291693i | \(0.0942184\pi\) | |||||||
\(8\) | −2.18426 | −0.772253 | ||||||||
\(9\) | −1.63601 | −0.545337 | ||||||||
\(10\) | 2.86183 | 0.904991 | ||||||||
\(11\) | 1.08118 | 0.325989 | 0.162995 | − | 0.986627i | \(-0.447885\pi\) | ||||
0.162995 | + | 0.986627i | \(0.447885\pi\) | |||||||
\(12\) | −0.771973 | −0.222849 | ||||||||
\(13\) | 3.01110 | 0.835129 | 0.417565 | − | 0.908647i | \(-0.362884\pi\) | ||||
0.417565 | + | 0.908647i | \(0.362884\pi\) | |||||||
\(14\) | 8.25641 | 2.20662 | ||||||||
\(15\) | −2.04893 | −0.529032 | ||||||||
\(16\) | −4.88507 | −1.22127 | ||||||||
\(17\) | 2.47710 | 0.600785 | 0.300393 | − | 0.953816i | \(-0.402882\pi\) | ||||
0.300393 | + | 0.953816i | \(0.402882\pi\) | |||||||
\(18\) | −2.66875 | −0.629030 | ||||||||
\(19\) | −7.12459 | −1.63449 | −0.817247 | − | 0.576287i | \(-0.804501\pi\) | ||||
−0.817247 | + | 0.576287i | \(0.804501\pi\) | |||||||
\(20\) | 1.15963 | 0.259301 | ||||||||
\(21\) | −5.91119 | −1.28993 | ||||||||
\(22\) | 1.76369 | 0.376019 | ||||||||
\(23\) | 5.33139 | 1.11167 | 0.555836 | − | 0.831292i | \(-0.312398\pi\) | ||||
0.555836 | + | 0.831292i | \(0.312398\pi\) | |||||||
\(24\) | 2.55100 | 0.520721 | ||||||||
\(25\) | −1.92217 | −0.384434 | ||||||||
\(26\) | 4.91187 | 0.963298 | ||||||||
\(27\) | 5.41439 | 1.04200 | ||||||||
\(28\) | 3.34554 | 0.632247 | ||||||||
\(29\) | −6.80248 | −1.26319 | −0.631595 | − | 0.775299i | \(-0.717599\pi\) | ||||
−0.631595 | + | 0.775299i | \(0.717599\pi\) | |||||||
\(30\) | −3.34233 | −0.610224 | ||||||||
\(31\) | −8.37871 | −1.50486 | −0.752430 | − | 0.658672i | \(-0.771119\pi\) | ||||
−0.752430 | + | 0.658672i | \(0.771119\pi\) | |||||||
\(32\) | −3.60028 | −0.636445 | ||||||||
\(33\) | −1.26271 | −0.219810 | ||||||||
\(34\) | 4.04078 | 0.692989 | ||||||||
\(35\) | 8.87957 | 1.50092 | ||||||||
\(36\) | −1.08139 | −0.180232 | ||||||||
\(37\) | −2.09398 | −0.344249 | −0.172124 | − | 0.985075i | \(-0.555063\pi\) | ||||
−0.172124 | + | 0.985075i | \(0.555063\pi\) | |||||||
\(38\) | −11.6220 | −1.88534 | ||||||||
\(39\) | −3.51666 | −0.563117 | ||||||||
\(40\) | −3.83202 | −0.605895 | ||||||||
\(41\) | −10.6564 | −1.66425 | −0.832124 | − | 0.554589i | \(-0.812875\pi\) | ||||
−0.832124 | + | 0.554589i | \(0.812875\pi\) | |||||||
\(42\) | −9.64266 | −1.48789 | ||||||||
\(43\) | −5.49791 | −0.838423 | −0.419211 | − | 0.907889i | \(-0.637693\pi\) | ||||
−0.419211 | + | 0.907889i | \(0.637693\pi\) | |||||||
\(44\) | 0.714654 | 0.107738 | ||||||||
\(45\) | −2.87018 | −0.427861 | ||||||||
\(46\) | 8.69686 | 1.28228 | ||||||||
\(47\) | 4.90386 | 0.715302 | 0.357651 | − | 0.933855i | \(-0.383578\pi\) | ||||
0.357651 | + | 0.933855i | \(0.383578\pi\) | |||||||
\(48\) | 5.70528 | 0.823486 | ||||||||
\(49\) | 18.6176 | 2.65966 | ||||||||
\(50\) | −3.13555 | −0.443433 | ||||||||
\(51\) | −2.89301 | −0.405102 | ||||||||
\(52\) | 1.99032 | 0.276007 | ||||||||
\(53\) | −4.04410 | −0.555500 | −0.277750 | − | 0.960653i | \(-0.589589\pi\) | ||||
−0.277750 | + | 0.960653i | \(0.589589\pi\) | |||||||
\(54\) | 8.83226 | 1.20192 | ||||||||
\(55\) | 1.89680 | 0.255765 | ||||||||
\(56\) | −11.0554 | −1.47734 | ||||||||
\(57\) | 8.32081 | 1.10212 | ||||||||
\(58\) | −11.0966 | −1.45705 | ||||||||
\(59\) | 5.64831 | 0.735347 | 0.367673 | − | 0.929955i | \(-0.380154\pi\) | ||||
0.367673 | + | 0.929955i | \(0.380154\pi\) | |||||||
\(60\) | −1.35433 | −0.174843 | ||||||||
\(61\) | −2.03784 | −0.260919 | −0.130459 | − | 0.991454i | \(-0.541645\pi\) | ||||
−0.130459 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(62\) | −13.6678 | −1.73581 | ||||||||
\(63\) | −8.28048 | −1.04324 | ||||||||
\(64\) | 3.89718 | 0.487148 | ||||||||
\(65\) | 5.28260 | 0.655226 | ||||||||
\(66\) | −2.05981 | −0.253545 | ||||||||
\(67\) | 7.65097 | 0.934715 | 0.467358 | − | 0.884068i | \(-0.345206\pi\) | ||||
0.467358 | + | 0.884068i | \(0.345206\pi\) | |||||||
\(68\) | 1.63735 | 0.198557 | ||||||||
\(69\) | −6.22653 | −0.749586 | ||||||||
\(70\) | 14.4848 | 1.73127 | ||||||||
\(71\) | 12.2631 | 1.45536 | 0.727682 | − | 0.685915i | \(-0.240598\pi\) | ||||
0.727682 | + | 0.685915i | \(0.240598\pi\) | |||||||
\(72\) | 3.57348 | 0.421138 | ||||||||
\(73\) | 0.733715 | 0.0858748 | 0.0429374 | − | 0.999078i | \(-0.486328\pi\) | ||||
0.0429374 | + | 0.999078i | \(0.486328\pi\) | |||||||
\(74\) | −3.41582 | −0.397081 | ||||||||
\(75\) | 2.24490 | 0.259219 | ||||||||
\(76\) | −4.70930 | −0.540194 | ||||||||
\(77\) | 5.47229 | 0.623625 | ||||||||
\(78\) | −5.73657 | −0.649539 | ||||||||
\(79\) | 6.86216 | 0.772053 | 0.386027 | − | 0.922488i | \(-0.373847\pi\) | ||||
0.386027 | + | 0.922488i | \(0.373847\pi\) | |||||||
\(80\) | −8.57025 | −0.958183 | ||||||||
\(81\) | −1.41544 | −0.157271 | ||||||||
\(82\) | −17.3833 | −1.91966 | ||||||||
\(83\) | 5.58812 | 0.613376 | 0.306688 | − | 0.951810i | \(-0.400779\pi\) | ||||
0.306688 | + | 0.951810i | \(0.400779\pi\) | |||||||
\(84\) | −3.90725 | −0.426316 | ||||||||
\(85\) | 4.34576 | 0.471364 | ||||||||
\(86\) | −8.96849 | −0.967097 | ||||||||
\(87\) | 7.94461 | 0.851752 | ||||||||
\(88\) | −2.36159 | −0.251746 | ||||||||
\(89\) | 9.62798 | 1.02056 | 0.510282 | − | 0.860007i | \(-0.329541\pi\) | ||||
0.510282 | + | 0.860007i | \(0.329541\pi\) | |||||||
\(90\) | −4.68199 | −0.493525 | ||||||||
\(91\) | 15.2403 | 1.59762 | ||||||||
\(92\) | 3.52401 | 0.367403 | ||||||||
\(93\) | 9.78549 | 1.01471 | ||||||||
\(94\) | 7.99945 | 0.825080 | ||||||||
\(95\) | −12.4992 | −1.28239 | ||||||||
\(96\) | 4.20476 | 0.429147 | ||||||||
\(97\) | −10.9185 | −1.10861 | −0.554303 | − | 0.832315i | \(-0.687015\pi\) | ||||
−0.554303 | + | 0.832315i | \(0.687015\pi\) | |||||||
\(98\) | 30.3701 | 3.06784 | ||||||||
\(99\) | −1.76883 | −0.177774 | ||||||||
\(100\) | −1.27054 | −0.127054 | ||||||||
\(101\) | −13.9401 | −1.38709 | −0.693545 | − | 0.720413i | \(-0.743952\pi\) | ||||
−0.693545 | + | 0.720413i | \(0.743952\pi\) | |||||||
\(102\) | −4.71923 | −0.467273 | ||||||||
\(103\) | −7.14621 | −0.704137 | −0.352068 | − | 0.935974i | \(-0.614522\pi\) | ||||
−0.352068 | + | 0.935974i | \(0.614522\pi\) | |||||||
\(104\) | −6.57703 | −0.644931 | ||||||||
\(105\) | −10.3704 | −1.01205 | ||||||||
\(106\) | −6.59695 | −0.640753 | ||||||||
\(107\) | 17.8929 | 1.72977 | 0.864886 | − | 0.501968i | \(-0.167390\pi\) | ||||
0.864886 | + | 0.501968i | \(0.167390\pi\) | |||||||
\(108\) | 3.57887 | 0.344377 | ||||||||
\(109\) | −14.9297 | −1.43001 | −0.715004 | − | 0.699120i | \(-0.753575\pi\) | ||||
−0.715004 | + | 0.699120i | \(0.753575\pi\) | |||||||
\(110\) | 3.09417 | 0.295017 | ||||||||
\(111\) | 2.44556 | 0.232123 | ||||||||
\(112\) | −24.7252 | −2.33632 | ||||||||
\(113\) | 0.859306 | 0.0808367 | 0.0404184 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404184 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(114\) | 13.5734 | 1.27126 | ||||||||
\(115\) | 9.35326 | 0.872196 | ||||||||
\(116\) | −4.49639 | −0.417479 | ||||||||
\(117\) | −4.92619 | −0.455427 | ||||||||
\(118\) | 9.21383 | 0.848201 | ||||||||
\(119\) | 12.5376 | 1.14932 | ||||||||
\(120\) | 4.47541 | 0.408547 | ||||||||
\(121\) | −9.83104 | −0.893731 | ||||||||
\(122\) | −3.32424 | −0.300962 | ||||||||
\(123\) | 12.4456 | 1.12218 | ||||||||
\(124\) | −5.53826 | −0.497351 | ||||||||
\(125\) | −12.1441 | −1.08620 | ||||||||
\(126\) | −13.5076 | −1.20335 | ||||||||
\(127\) | −3.01886 | −0.267880 | −0.133940 | − | 0.990989i | \(-0.542763\pi\) | ||||
−0.133940 | + | 0.990989i | \(0.542763\pi\) | |||||||
\(128\) | 13.5578 | 1.19836 | ||||||||
\(129\) | 6.42100 | 0.565338 | ||||||||
\(130\) | 8.61727 | 0.755784 | ||||||||
\(131\) | −2.17519 | −0.190047 | −0.0950234 | − | 0.995475i | \(-0.530293\pi\) | ||||
−0.0950234 | + | 0.995475i | \(0.530293\pi\) | |||||||
\(132\) | −0.834644 | −0.0726464 | ||||||||
\(133\) | −36.0603 | −3.12683 | ||||||||
\(134\) | 12.4807 | 1.07817 | ||||||||
\(135\) | 9.49888 | 0.817533 | ||||||||
\(136\) | −5.41064 | −0.463958 | ||||||||
\(137\) | 15.9150 | 1.35971 | 0.679854 | − | 0.733347i | \(-0.262043\pi\) | ||||
0.679854 | + | 0.733347i | \(0.262043\pi\) | |||||||
\(138\) | −10.1571 | −0.864626 | ||||||||
\(139\) | −15.0721 | −1.27840 | −0.639201 | − | 0.769040i | \(-0.720735\pi\) | ||||
−0.639201 | + | 0.769040i | \(0.720735\pi\) | |||||||
\(140\) | 5.86933 | 0.496049 | ||||||||
\(141\) | −5.72722 | −0.482319 | ||||||||
\(142\) | 20.0043 | 1.67872 | ||||||||
\(143\) | 3.25555 | 0.272243 | ||||||||
\(144\) | 7.99203 | 0.666003 | ||||||||
\(145\) | −11.9341 | −0.991073 | ||||||||
\(146\) | 1.19688 | 0.0990542 | ||||||||
\(147\) | −21.7435 | −1.79338 | ||||||||
\(148\) | −1.38411 | −0.113773 | ||||||||
\(149\) | −1.36774 | −0.112050 | −0.0560250 | − | 0.998429i | \(-0.517843\pi\) | ||||
−0.0560250 | + | 0.998429i | \(0.517843\pi\) | |||||||
\(150\) | 3.66200 | 0.299001 | ||||||||
\(151\) | 17.1854 | 1.39853 | 0.699264 | − | 0.714864i | \(-0.253511\pi\) | ||||
0.699264 | + | 0.714864i | \(0.253511\pi\) | |||||||
\(152\) | 15.5620 | 1.26224 | ||||||||
\(153\) | −4.05256 | −0.327630 | ||||||||
\(154\) | 8.92669 | 0.719334 | ||||||||
\(155\) | −14.6994 | −1.18068 | ||||||||
\(156\) | −2.32449 | −0.186108 | ||||||||
\(157\) | 12.1279 | 0.967909 | 0.483955 | − | 0.875093i | \(-0.339200\pi\) | ||||
0.483955 | + | 0.875093i | \(0.339200\pi\) | |||||||
\(158\) | 11.1939 | 0.890541 | ||||||||
\(159\) | 4.72310 | 0.374566 | ||||||||
\(160\) | −6.31623 | −0.499342 | ||||||||
\(161\) | 26.9842 | 2.12665 | ||||||||
\(162\) | −2.30894 | −0.181407 | ||||||||
\(163\) | 10.7083 | 0.838737 | 0.419369 | − | 0.907816i | \(-0.362251\pi\) | ||||
0.419369 | + | 0.907816i | \(0.362251\pi\) | |||||||
\(164\) | −7.04379 | −0.550028 | ||||||||
\(165\) | −2.21527 | −0.172459 | ||||||||
\(166\) | 9.11564 | 0.707511 | ||||||||
\(167\) | −10.5539 | −0.816684 | −0.408342 | − | 0.912829i | \(-0.633893\pi\) | ||||
−0.408342 | + | 0.912829i | \(0.633893\pi\) | |||||||
\(168\) | 12.9116 | 0.996151 | ||||||||
\(169\) | −3.93327 | −0.302559 | ||||||||
\(170\) | 7.08905 | 0.543705 | ||||||||
\(171\) | 11.6559 | 0.891350 | ||||||||
\(172\) | −3.63407 | −0.277096 | ||||||||
\(173\) | −2.07621 | −0.157851 | −0.0789255 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789255 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(174\) | 12.9597 | 0.982472 | ||||||||
\(175\) | −9.72883 | −0.735431 | ||||||||
\(176\) | −5.28166 | −0.398120 | ||||||||
\(177\) | −6.59665 | −0.495835 | ||||||||
\(178\) | 15.7057 | 1.17719 | ||||||||
\(179\) | −3.06922 | −0.229405 | −0.114702 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114702 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(180\) | −1.89717 | −0.141406 | ||||||||
\(181\) | −0.391403 | −0.0290927 | −0.0145464 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145464 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(182\) | 24.8609 | 1.84281 | ||||||||
\(183\) | 2.37999 | 0.175934 | ||||||||
\(184\) | −11.6452 | −0.858492 | ||||||||
\(185\) | −3.67363 | −0.270091 | ||||||||
\(186\) | 15.9626 | 1.17044 | ||||||||
\(187\) | 2.67820 | 0.195849 | ||||||||
\(188\) | 3.24142 | 0.236405 | ||||||||
\(189\) | 27.4043 | 1.99337 | ||||||||
\(190\) | −20.3894 | −1.47920 | ||||||||
\(191\) | 4.99018 | 0.361077 | 0.180538 | − | 0.983568i | \(-0.442216\pi\) | ||||
0.180538 | + | 0.983568i | \(0.442216\pi\) | |||||||
\(192\) | −4.55152 | −0.328477 | ||||||||
\(193\) | 13.5209 | 0.973254 | 0.486627 | − | 0.873610i | \(-0.338227\pi\) | ||||
0.486627 | + | 0.873610i | \(0.338227\pi\) | |||||||
\(194\) | −17.8109 | −1.27874 | ||||||||
\(195\) | −6.16955 | −0.441810 | ||||||||
\(196\) | 12.3061 | 0.879008 | ||||||||
\(197\) | 5.86751 | 0.418043 | 0.209021 | − | 0.977911i | \(-0.432972\pi\) | ||||
0.209021 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(198\) | −2.88541 | −0.205057 | ||||||||
\(199\) | 12.5774 | 0.891585 | 0.445792 | − | 0.895136i | \(-0.352922\pi\) | ||||
0.445792 | + | 0.895136i | \(0.352922\pi\) | |||||||
\(200\) | 4.19852 | 0.296880 | ||||||||
\(201\) | −8.93557 | −0.630266 | ||||||||
\(202\) | −22.7398 | −1.59997 | ||||||||
\(203\) | −34.4300 | −2.41651 | ||||||||
\(204\) | −1.91225 | −0.133885 | ||||||||
\(205\) | −18.6953 | −1.30574 | ||||||||
\(206\) | −11.6573 | −0.812201 | ||||||||
\(207\) | −8.72221 | −0.606236 | ||||||||
\(208\) | −14.7095 | −1.01992 | ||||||||
\(209\) | −7.70299 | −0.532827 | ||||||||
\(210\) | −16.9168 | −1.16737 | ||||||||
\(211\) | 6.00657 | 0.413509 | 0.206755 | − | 0.978393i | \(-0.433710\pi\) | ||||
0.206755 | + | 0.978393i | \(0.433710\pi\) | |||||||
\(212\) | −2.67312 | −0.183591 | ||||||||
\(213\) | −14.3221 | −0.981333 | ||||||||
\(214\) | 29.1879 | 1.99524 | ||||||||
\(215\) | −9.64539 | −0.657810 | ||||||||
\(216\) | −11.8265 | −0.804689 | ||||||||
\(217\) | −42.4079 | −2.87884 | ||||||||
\(218\) | −24.3542 | −1.64947 | ||||||||
\(219\) | −0.856905 | −0.0579043 | ||||||||
\(220\) | 1.25377 | 0.0845292 | ||||||||
\(221\) | 7.45880 | 0.501733 | ||||||||
\(222\) | 3.98934 | 0.267747 | ||||||||
\(223\) | −25.7624 | −1.72518 | −0.862590 | − | 0.505904i | \(-0.831159\pi\) | ||||
−0.862590 | + | 0.505904i | \(0.831159\pi\) | |||||||
\(224\) | −18.2224 | −1.21753 | ||||||||
\(225\) | 3.14469 | 0.209646 | ||||||||
\(226\) | 1.40175 | 0.0932429 | ||||||||
\(227\) | 5.03720 | 0.334331 | 0.167165 | − | 0.985929i | \(-0.446539\pi\) | ||||
0.167165 | + | 0.985929i | \(0.446539\pi\) | |||||||
\(228\) | 5.49999 | 0.364246 | ||||||||
\(229\) | 21.1245 | 1.39594 | 0.697972 | − | 0.716125i | \(-0.254086\pi\) | ||||
0.697972 | + | 0.716125i | \(0.254086\pi\) | |||||||
\(230\) | 15.2575 | 1.00605 | ||||||||
\(231\) | −6.39108 | −0.420502 | ||||||||
\(232\) | 14.8584 | 0.975502 | ||||||||
\(233\) | 20.9468 | 1.37227 | 0.686135 | − | 0.727474i | \(-0.259306\pi\) | ||||
0.686135 | + | 0.727474i | \(0.259306\pi\) | |||||||
\(234\) | −8.03588 | −0.525322 | ||||||||
\(235\) | 8.60322 | 0.561212 | ||||||||
\(236\) | 3.73349 | 0.243029 | ||||||||
\(237\) | −8.01431 | −0.520586 | ||||||||
\(238\) | 20.4520 | 1.32570 | ||||||||
\(239\) | −7.83541 | −0.506831 | −0.253415 | − | 0.967358i | \(-0.581554\pi\) | ||||
−0.253415 | + | 0.967358i | \(0.581554\pi\) | |||||||
\(240\) | 10.0092 | 0.646091 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −16.0369 | −1.03089 | ||||||||
\(243\) | −14.5901 | −0.935955 | ||||||||
\(244\) | −1.34700 | −0.0862326 | ||||||||
\(245\) | 32.6623 | 2.08672 | ||||||||
\(246\) | 20.3019 | 1.29440 | ||||||||
\(247\) | −21.4529 | −1.36501 | ||||||||
\(248\) | 18.3013 | 1.16213 | ||||||||
\(249\) | −6.52636 | −0.413591 | ||||||||
\(250\) | −19.8101 | −1.25290 | ||||||||
\(251\) | −7.01648 | −0.442876 | −0.221438 | − | 0.975174i | \(-0.571075\pi\) | ||||
−0.221438 | + | 0.975174i | \(0.571075\pi\) | |||||||
\(252\) | −5.47334 | −0.344788 | ||||||||
\(253\) | 5.76421 | 0.362393 | ||||||||
\(254\) | −4.92453 | −0.308992 | ||||||||
\(255\) | −5.07542 | −0.317835 | ||||||||
\(256\) | 14.3219 | 0.895121 | ||||||||
\(257\) | 11.3057 | 0.705229 | 0.352615 | − | 0.935769i | \(-0.385293\pi\) | ||||
0.352615 | + | 0.935769i | \(0.385293\pi\) | |||||||
\(258\) | 10.4743 | 0.652101 | ||||||||
\(259\) | −10.5985 | −0.658556 | ||||||||
\(260\) | 3.49176 | 0.216550 | ||||||||
\(261\) | 11.1289 | 0.688864 | ||||||||
\(262\) | −3.54828 | −0.219214 | ||||||||
\(263\) | 19.8667 | 1.22503 | 0.612516 | − | 0.790458i | \(-0.290158\pi\) | ||||
0.612516 | + | 0.790458i | \(0.290158\pi\) | |||||||
\(264\) | 2.75810 | 0.169749 | ||||||||
\(265\) | −7.09487 | −0.435834 | ||||||||
\(266\) | −58.8236 | −3.60671 | ||||||||
\(267\) | −11.2445 | −0.688153 | ||||||||
\(268\) | 5.05724 | 0.308920 | ||||||||
\(269\) | −20.2533 | −1.23486 | −0.617431 | − | 0.786625i | \(-0.711827\pi\) | ||||
−0.617431 | + | 0.786625i | \(0.711827\pi\) | |||||||
\(270\) | 15.4951 | 0.943001 | ||||||||
\(271\) | −4.23892 | −0.257496 | −0.128748 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128748 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(272\) | −12.1008 | −0.733720 | ||||||||
\(273\) | −17.7992 | −1.07726 | ||||||||
\(274\) | 25.9614 | 1.56839 | ||||||||
\(275\) | −2.07822 | −0.125321 | ||||||||
\(276\) | −4.11569 | −0.247735 | ||||||||
\(277\) | −0.369469 | −0.0221992 | −0.0110996 | − | 0.999938i | \(-0.503533\pi\) | ||||
−0.0110996 | + | 0.999938i | \(0.503533\pi\) | |||||||
\(278\) | −24.5865 | −1.47460 | ||||||||
\(279\) | 13.7077 | 0.820656 | ||||||||
\(280\) | −19.3953 | −1.15909 | ||||||||
\(281\) | 24.6918 | 1.47299 | 0.736494 | − | 0.676444i | \(-0.236480\pi\) | ||||
0.736494 | + | 0.676444i | \(0.236480\pi\) | |||||||
\(282\) | −9.34255 | −0.556341 | ||||||||
\(283\) | 0.0696775 | 0.00414190 | 0.00207095 | − | 0.999998i | \(-0.499341\pi\) | ||||
0.00207095 | + | 0.999998i | \(0.499341\pi\) | |||||||
\(284\) | 8.10583 | 0.480992 | ||||||||
\(285\) | 14.5978 | 0.864700 | ||||||||
\(286\) | 5.31064 | 0.314024 | ||||||||
\(287\) | −53.9361 | −3.18375 | ||||||||
\(288\) | 5.89009 | 0.347077 | ||||||||
\(289\) | −10.8640 | −0.639057 | ||||||||
\(290\) | −19.4676 | −1.14317 | ||||||||
\(291\) | 12.7517 | 0.747518 | ||||||||
\(292\) | 0.484980 | 0.0283813 | ||||||||
\(293\) | −7.59140 | −0.443494 | −0.221747 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221747 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(294\) | −35.4692 | −2.06861 | ||||||||
\(295\) | 9.90925 | 0.576939 | ||||||||
\(296\) | 4.57381 | 0.265847 | ||||||||
\(297\) | 5.85395 | 0.339681 | ||||||||
\(298\) | −2.23114 | −0.129246 | ||||||||
\(299\) | 16.0534 | 0.928389 | ||||||||
\(300\) | 1.48386 | 0.0856708 | ||||||||
\(301\) | −27.8270 | −1.60392 | ||||||||
\(302\) | 28.0338 | 1.61316 | ||||||||
\(303\) | 16.2806 | 0.935297 | ||||||||
\(304\) | 34.8042 | 1.99616 | ||||||||
\(305\) | −3.57514 | −0.204712 | ||||||||
\(306\) | −6.61076 | −0.377912 | ||||||||
\(307\) | −20.6437 | −1.17820 | −0.589100 | − | 0.808060i | \(-0.700518\pi\) | ||||
−0.589100 | + | 0.808060i | \(0.700518\pi\) | |||||||
\(308\) | 3.61714 | 0.206106 | ||||||||
\(309\) | 8.34605 | 0.474790 | ||||||||
\(310\) | −23.9785 | −1.36189 | ||||||||
\(311\) | 24.0882 | 1.36592 | 0.682959 | − | 0.730456i | \(-0.260693\pi\) | ||||
0.682959 | + | 0.730456i | \(0.260693\pi\) | |||||||
\(312\) | 7.68132 | 0.434869 | ||||||||
\(313\) | 16.3804 | 0.925876 | 0.462938 | − | 0.886391i | \(-0.346795\pi\) | ||||
0.462938 | + | 0.886391i | \(0.346795\pi\) | |||||||
\(314\) | 19.7836 | 1.11646 | ||||||||
\(315\) | −14.5271 | −0.818508 | ||||||||
\(316\) | 4.53584 | 0.255161 | ||||||||
\(317\) | −1.59833 | −0.0897714 | −0.0448857 | − | 0.998992i | \(-0.514292\pi\) | ||||
−0.0448857 | + | 0.998992i | \(0.514292\pi\) | |||||||
\(318\) | 7.70458 | 0.432051 | ||||||||
\(319\) | −7.35473 | −0.411786 | ||||||||
\(320\) | 6.83712 | 0.382206 | ||||||||
\(321\) | −20.8971 | −1.16636 | ||||||||
\(322\) | 44.0181 | 2.45304 | ||||||||
\(323\) | −17.6483 | −0.981980 | ||||||||
\(324\) | −0.935593 | −0.0519774 | ||||||||
\(325\) | −5.78784 | −0.321052 | ||||||||
\(326\) | 17.4679 | 0.967460 | ||||||||
\(327\) | 17.4364 | 0.964236 | ||||||||
\(328\) | 23.2764 | 1.28522 | ||||||||
\(329\) | 24.8203 | 1.36839 | ||||||||
\(330\) | −3.61368 | −0.198926 | ||||||||
\(331\) | −26.9070 | −1.47894 | −0.739472 | − | 0.673188i | \(-0.764925\pi\) | ||||
−0.739472 | + | 0.673188i | \(0.764925\pi\) | |||||||
\(332\) | 3.69370 | 0.202718 | ||||||||
\(333\) | 3.42578 | 0.187732 | ||||||||
\(334\) | −17.2161 | −0.942022 | ||||||||
\(335\) | 13.4227 | 0.733359 | ||||||||
\(336\) | 28.8766 | 1.57535 | ||||||||
\(337\) | −10.8794 | −0.592640 | −0.296320 | − | 0.955089i | \(-0.595760\pi\) | ||||
−0.296320 | + | 0.955089i | \(0.595760\pi\) | |||||||
\(338\) | −6.41617 | −0.348994 | ||||||||
\(339\) | −1.00358 | −0.0545072 | ||||||||
\(340\) | 2.87252 | 0.155784 | ||||||||
\(341\) | −9.05892 | −0.490568 | ||||||||
\(342\) | 19.0138 | 1.02815 | ||||||||
\(343\) | 58.8013 | 3.17497 | ||||||||
\(344\) | 12.0089 | 0.647475 | ||||||||
\(345\) | −10.9237 | −0.588110 | ||||||||
\(346\) | −3.38682 | −0.182077 | ||||||||
\(347\) | 12.9007 | 0.692546 | 0.346273 | − | 0.938134i | \(-0.387447\pi\) | ||||
0.346273 | + | 0.938134i | \(0.387447\pi\) | |||||||
\(348\) | 5.25133 | 0.281501 | ||||||||
\(349\) | −10.7803 | −0.577058 | −0.288529 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288529 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(350\) | −15.8702 | −0.848298 | ||||||||
\(351\) | 16.3033 | 0.870205 | ||||||||
\(352\) | −3.89256 | −0.207474 | ||||||||
\(353\) | 6.56859 | 0.349611 | 0.174805 | − | 0.984603i | \(-0.444070\pi\) | ||||
0.174805 | + | 0.984603i | \(0.444070\pi\) | |||||||
\(354\) | −10.7608 | −0.571931 | ||||||||
\(355\) | 21.5141 | 1.14185 | ||||||||
\(356\) | 6.36402 | 0.337292 | ||||||||
\(357\) | −14.6426 | −0.774970 | ||||||||
\(358\) | −5.00669 | −0.264612 | ||||||||
\(359\) | 15.8305 | 0.835504 | 0.417752 | − | 0.908561i | \(-0.362818\pi\) | ||||
0.417752 | + | 0.908561i | \(0.362818\pi\) | |||||||
\(360\) | 6.26922 | 0.330417 | ||||||||
\(361\) | 31.7598 | 1.67157 | ||||||||
\(362\) | −0.638477 | −0.0335576 | ||||||||
\(363\) | 11.4817 | 0.602631 | ||||||||
\(364\) | 10.0738 | 0.528008 | ||||||||
\(365\) | 1.28721 | 0.0673757 | ||||||||
\(366\) | 3.88237 | 0.202935 | ||||||||
\(367\) | −5.63657 | −0.294226 | −0.147113 | − | 0.989120i | \(-0.546998\pi\) | ||||
−0.147113 | + | 0.989120i | \(0.546998\pi\) | |||||||
\(368\) | −26.0442 | −1.35765 | ||||||||
\(369\) | 17.4340 | 0.907576 | ||||||||
\(370\) | −5.99263 | −0.311542 | ||||||||
\(371\) | −20.4687 | −1.06268 | ||||||||
\(372\) | 6.46814 | 0.335357 | ||||||||
\(373\) | 1.29504 | 0.0670548 | 0.0335274 | − | 0.999438i | \(-0.489326\pi\) | ||||
0.0335274 | + | 0.999438i | \(0.489326\pi\) | |||||||
\(374\) | 4.36883 | 0.225907 | ||||||||
\(375\) | 14.1831 | 0.732410 | ||||||||
\(376\) | −10.7113 | −0.552394 | ||||||||
\(377\) | −20.4830 | −1.05493 | ||||||||
\(378\) | 44.7035 | 2.29930 | ||||||||
\(379\) | −13.8155 | −0.709656 | −0.354828 | − | 0.934932i | \(-0.615461\pi\) | ||||
−0.354828 | + | 0.934932i | \(0.615461\pi\) | |||||||
\(380\) | −8.26188 | −0.423826 | ||||||||
\(381\) | 3.52572 | 0.180628 | ||||||||
\(382\) | 8.14026 | 0.416492 | ||||||||
\(383\) | 12.0143 | 0.613900 | 0.306950 | − | 0.951726i | \(-0.400692\pi\) | ||||
0.306950 | + | 0.951726i | \(0.400692\pi\) | |||||||
\(384\) | −15.8342 | −0.808036 | ||||||||
\(385\) | 9.60044 | 0.489284 | ||||||||
\(386\) | 22.0560 | 1.12262 | ||||||||
\(387\) | 8.99463 | 0.457223 | ||||||||
\(388\) | −7.21704 | −0.366390 | ||||||||
\(389\) | 4.86222 | 0.246524 | 0.123262 | − | 0.992374i | \(-0.460664\pi\) | ||||
0.123262 | + | 0.992374i | \(0.460664\pi\) | |||||||
\(390\) | −10.0641 | −0.509616 | ||||||||
\(391\) | 13.2064 | 0.667876 | ||||||||
\(392\) | −40.6658 | −2.05393 | ||||||||
\(393\) | 2.54040 | 0.128146 | ||||||||
\(394\) | 9.57141 | 0.482201 | ||||||||
\(395\) | 12.0388 | 0.605738 | ||||||||
\(396\) | −1.16918 | −0.0587536 | ||||||||
\(397\) | 9.17854 | 0.460658 | 0.230329 | − | 0.973113i | \(-0.426020\pi\) | ||||
0.230329 | + | 0.973113i | \(0.426020\pi\) | |||||||
\(398\) | 20.5169 | 1.02842 | ||||||||
\(399\) | 42.1148 | 2.10838 | ||||||||
\(400\) | 9.38993 | 0.469497 | ||||||||
\(401\) | −28.0569 | −1.40109 | −0.700547 | − | 0.713607i | \(-0.747060\pi\) | ||||
−0.700547 | + | 0.713607i | \(0.747060\pi\) | |||||||
\(402\) | −14.5762 | −0.726994 | ||||||||
\(403\) | −25.2291 | −1.25675 | ||||||||
\(404\) | −9.21429 | −0.458428 | ||||||||
\(405\) | −2.48321 | −0.123392 | ||||||||
\(406\) | −56.1641 | −2.78738 | ||||||||
\(407\) | −2.26398 | −0.112221 | ||||||||
\(408\) | 6.31908 | 0.312841 | ||||||||
\(409\) | −11.6170 | −0.574422 | −0.287211 | − | 0.957867i | \(-0.592728\pi\) | ||||
−0.287211 | + | 0.957867i | \(0.592728\pi\) | |||||||
\(410\) | −30.4968 | −1.50613 | ||||||||
\(411\) | −18.5871 | −0.916834 | ||||||||
\(412\) | −4.72359 | −0.232714 | ||||||||
\(413\) | 28.5883 | 1.40674 | ||||||||
\(414\) | −14.2281 | −0.699275 | ||||||||
\(415\) | 9.80365 | 0.481242 | ||||||||
\(416\) | −10.8408 | −0.531514 | ||||||||
\(417\) | 17.6027 | 0.862010 | ||||||||
\(418\) | −12.5655 | −0.614601 | ||||||||
\(419\) | 15.5789 | 0.761080 | 0.380540 | − | 0.924765i | \(-0.375738\pi\) | ||||
0.380540 | + | 0.924765i | \(0.375738\pi\) | |||||||
\(420\) | −6.85479 | −0.334479 | ||||||||
\(421\) | 7.53596 | 0.367280 | 0.183640 | − | 0.982994i | \(-0.441212\pi\) | ||||
0.183640 | + | 0.982994i | \(0.441212\pi\) | |||||||
\(422\) | 9.79824 | 0.476971 | ||||||||
\(423\) | −8.02277 | −0.390081 | ||||||||
\(424\) | 8.83337 | 0.428986 | ||||||||
\(425\) | −4.76140 | −0.230962 | ||||||||
\(426\) | −23.3630 | −1.13194 | ||||||||
\(427\) | −10.3143 | −0.499144 | ||||||||
\(428\) | 11.8271 | 0.571683 | ||||||||
\(429\) | −3.80216 | −0.183570 | ||||||||
\(430\) | −15.7341 | −0.758765 | ||||||||
\(431\) | 24.2144 | 1.16636 | 0.583182 | − | 0.812341i | \(-0.301807\pi\) | ||||
0.583182 | + | 0.812341i | \(0.301807\pi\) | |||||||
\(432\) | −26.4497 | −1.27256 | ||||||||
\(433\) | 1.90821 | 0.0917025 | 0.0458512 | − | 0.998948i | \(-0.485400\pi\) | ||||
0.0458512 | + | 0.998948i | \(0.485400\pi\) | |||||||
\(434\) | −69.1781 | −3.32065 | ||||||||
\(435\) | 13.9378 | 0.668268 | ||||||||
\(436\) | −9.86844 | −0.472612 | ||||||||
\(437\) | −37.9840 | −1.81702 | ||||||||
\(438\) | −1.39783 | −0.0667910 | ||||||||
\(439\) | −14.9135 | −0.711784 | −0.355892 | − | 0.934527i | \(-0.615823\pi\) | ||||
−0.355892 | + | 0.934527i | \(0.615823\pi\) | |||||||
\(440\) | −4.14311 | −0.197515 | ||||||||
\(441\) | −30.4586 | −1.45041 | ||||||||
\(442\) | 12.1672 | 0.578735 | ||||||||
\(443\) | −23.0698 | −1.09608 | −0.548039 | − | 0.836453i | \(-0.684625\pi\) | ||||
−0.548039 | + | 0.836453i | \(0.684625\pi\) | |||||||
\(444\) | 1.61650 | 0.0767156 | ||||||||
\(445\) | 16.8911 | 0.800714 | ||||||||
\(446\) | −42.0251 | −1.98995 | ||||||||
\(447\) | 1.59739 | 0.0755539 | ||||||||
\(448\) | 19.7251 | 0.931925 | ||||||||
\(449\) | 14.5420 | 0.686277 | 0.343139 | − | 0.939285i | \(-0.388510\pi\) | ||||
0.343139 | + | 0.939285i | \(0.388510\pi\) | |||||||
\(450\) | 5.12979 | 0.241820 | ||||||||
\(451\) | −11.5215 | −0.542527 | ||||||||
\(452\) | 0.567995 | 0.0267162 | ||||||||
\(453\) | −20.0708 | −0.943009 | ||||||||
\(454\) | 8.21696 | 0.385641 | ||||||||
\(455\) | 26.7373 | 1.25346 | ||||||||
\(456\) | −18.1748 | −0.851115 | ||||||||
\(457\) | 11.8002 | 0.551991 | 0.275995 | − | 0.961159i | \(-0.410993\pi\) | ||||
0.275995 | + | 0.961159i | \(0.410993\pi\) | |||||||
\(458\) | 34.4594 | 1.61018 | ||||||||
\(459\) | 13.4120 | 0.626019 | ||||||||
\(460\) | 6.18243 | 0.288257 | ||||||||
\(461\) | 15.0722 | 0.701985 | 0.350992 | − | 0.936378i | \(-0.385844\pi\) | ||||
0.350992 | + | 0.936378i | \(0.385844\pi\) | |||||||
\(462\) | −10.4255 | −0.485037 | ||||||||
\(463\) | 24.3295 | 1.13069 | 0.565344 | − | 0.824855i | \(-0.308743\pi\) | ||||
0.565344 | + | 0.824855i | \(0.308743\pi\) | |||||||
\(464\) | 33.2306 | 1.54269 | ||||||||
\(465\) | 17.1674 | 0.796120 | ||||||||
\(466\) | 34.1695 | 1.58287 | ||||||||
\(467\) | 29.7743 | 1.37779 | 0.688895 | − | 0.724862i | \(-0.258096\pi\) | ||||
0.688895 | + | 0.724862i | \(0.258096\pi\) | |||||||
\(468\) | −3.25618 | −0.150517 | ||||||||
\(469\) | 38.7245 | 1.78813 | ||||||||
\(470\) | 14.0340 | 0.647342 | ||||||||
\(471\) | −14.1641 | −0.652649 | ||||||||
\(472\) | −12.3374 | −0.567874 | ||||||||
\(473\) | −5.94424 | −0.273317 | ||||||||
\(474\) | −13.0734 | −0.600481 | ||||||||
\(475\) | 13.6947 | 0.628354 | ||||||||
\(476\) | 8.28724 | 0.379845 | ||||||||
\(477\) | 6.61619 | 0.302934 | ||||||||
\(478\) | −12.7816 | −0.584615 | ||||||||
\(479\) | −10.1987 | −0.465991 | −0.232996 | − | 0.972478i | \(-0.574853\pi\) | ||||
−0.232996 | + | 0.972478i | \(0.574853\pi\) | |||||||
\(480\) | 7.37673 | 0.336700 | ||||||||
\(481\) | −6.30520 | −0.287492 | ||||||||
\(482\) | 1.63125 | 0.0743016 | ||||||||
\(483\) | −31.5149 | −1.43398 | ||||||||
\(484\) | −6.49825 | −0.295375 | ||||||||
\(485\) | −19.1551 | −0.869790 | ||||||||
\(486\) | −23.8002 | −1.07960 | ||||||||
\(487\) | −24.9246 | −1.12944 | −0.564720 | − | 0.825282i | \(-0.691016\pi\) | ||||
−0.564720 | + | 0.825282i | \(0.691016\pi\) | |||||||
\(488\) | 4.45118 | 0.201495 | ||||||||
\(489\) | −12.5062 | −0.565550 | ||||||||
\(490\) | 53.2806 | 2.40697 | ||||||||
\(491\) | −26.8710 | −1.21267 | −0.606335 | − | 0.795209i | \(-0.707361\pi\) | ||||
−0.606335 | + | 0.795209i | \(0.707361\pi\) | |||||||
\(492\) | 8.22644 | 0.370877 | ||||||||
\(493\) | −16.8504 | −0.758905 | ||||||||
\(494\) | −34.9951 | −1.57450 | ||||||||
\(495\) | −3.10319 | −0.139478 | ||||||||
\(496\) | 40.9306 | 1.83784 | ||||||||
\(497\) | 62.0684 | 2.78415 | ||||||||
\(498\) | −10.6462 | −0.477066 | ||||||||
\(499\) | −37.6147 | −1.68387 | −0.841933 | − | 0.539582i | \(-0.818582\pi\) | ||||
−0.841933 | + | 0.539582i | \(0.818582\pi\) | |||||||
\(500\) | −8.02714 | −0.358985 | ||||||||
\(501\) | 12.3259 | 0.550680 | ||||||||
\(502\) | −11.4457 | −0.510845 | ||||||||
\(503\) | −38.0897 | −1.69834 | −0.849168 | − | 0.528123i | \(-0.822896\pi\) | ||||
−0.849168 | + | 0.528123i | \(0.822896\pi\) | |||||||
\(504\) | 18.0867 | 0.805648 | ||||||||
\(505\) | −24.4561 | −1.08828 | ||||||||
\(506\) | 9.40290 | 0.418010 | ||||||||
\(507\) | 4.59367 | 0.204012 | ||||||||
\(508\) | −1.99544 | −0.0885334 | ||||||||
\(509\) | −37.4493 | −1.65991 | −0.829954 | − | 0.557831i | \(-0.811634\pi\) | ||||
−0.829954 | + | 0.557831i | \(0.811634\pi\) | |||||||
\(510\) | −8.27930 | −0.366613 | ||||||||
\(511\) | 3.71362 | 0.164281 | ||||||||
\(512\) | −3.75296 | −0.165859 | ||||||||
\(513\) | −38.5754 | −1.70314 | ||||||||
\(514\) | 18.4424 | 0.813462 | ||||||||
\(515\) | −12.5371 | −0.552452 | ||||||||
\(516\) | 4.24423 | 0.186842 | ||||||||
\(517\) | 5.30198 | 0.233181 | ||||||||
\(518\) | −17.2888 | −0.759626 | ||||||||
\(519\) | 2.42480 | 0.106437 | ||||||||
\(520\) | −11.5386 | −0.506001 | ||||||||
\(521\) | 14.8226 | 0.649391 | 0.324695 | − | 0.945819i | \(-0.394738\pi\) | ||||
0.324695 | + | 0.945819i | \(0.394738\pi\) | |||||||
\(522\) | 18.1541 | 0.794584 | ||||||||
\(523\) | 23.8624 | 1.04343 | 0.521715 | − | 0.853120i | \(-0.325292\pi\) | ||||
0.521715 | + | 0.853120i | \(0.325292\pi\) | |||||||
\(524\) | −1.43778 | −0.0628098 | ||||||||
\(525\) | 11.3623 | 0.495891 | ||||||||
\(526\) | 32.4076 | 1.41304 | ||||||||
\(527\) | −20.7549 | −0.904098 | ||||||||
\(528\) | 6.16845 | 0.268447 | ||||||||
\(529\) | 5.42372 | 0.235814 | ||||||||
\(530\) | −11.5735 | −0.502722 | ||||||||
\(531\) | −9.24069 | −0.401012 | ||||||||
\(532\) | −23.8356 | −1.03340 | ||||||||
\(533\) | −32.0875 | −1.38986 | ||||||||
\(534\) | −18.3427 | −0.793765 | ||||||||
\(535\) | 31.3909 | 1.35715 | ||||||||
\(536\) | −16.7117 | −0.721837 | ||||||||
\(537\) | 3.58454 | 0.154685 | ||||||||
\(538\) | −33.0382 | −1.42438 | ||||||||
\(539\) | 20.1291 | 0.867021 | ||||||||
\(540\) | 6.27869 | 0.270192 | ||||||||
\(541\) | −12.9272 | −0.555782 | −0.277891 | − | 0.960613i | \(-0.589635\pi\) | ||||
−0.277891 | + | 0.960613i | \(0.589635\pi\) | |||||||
\(542\) | −6.91477 | −0.297015 | ||||||||
\(543\) | 0.457119 | 0.0196168 | ||||||||
\(544\) | −8.91825 | −0.382367 | ||||||||
\(545\) | −26.1923 | −1.12196 | ||||||||
\(546\) | −29.0350 | −1.24258 | ||||||||
\(547\) | −9.03128 | −0.386150 | −0.193075 | − | 0.981184i | \(-0.561846\pi\) | ||||
−0.193075 | + | 0.981184i | \(0.561846\pi\) | |||||||
\(548\) | 10.5197 | 0.449379 | ||||||||
\(549\) | 3.33393 | 0.142289 | ||||||||
\(550\) | −3.39010 | −0.144554 | ||||||||
\(551\) | 48.4649 | 2.06467 | ||||||||
\(552\) | 13.6004 | 0.578870 | ||||||||
\(553\) | 34.7320 | 1.47696 | ||||||||
\(554\) | −0.602698 | −0.0256062 | ||||||||
\(555\) | 4.29043 | 0.182119 | ||||||||
\(556\) | −9.96256 | −0.422507 | ||||||||
\(557\) | −4.33616 | −0.183729 | −0.0918644 | − | 0.995772i | \(-0.529283\pi\) | ||||
−0.0918644 | + | 0.995772i | \(0.529283\pi\) | |||||||
\(558\) | 22.3607 | 0.946603 | ||||||||
\(559\) | −16.5547 | −0.700191 | ||||||||
\(560\) | −43.3774 | −1.83303 | ||||||||
\(561\) | −3.12787 | −0.132059 | ||||||||
\(562\) | 40.2786 | 1.69905 | ||||||||
\(563\) | 6.56701 | 0.276767 | 0.138383 | − | 0.990379i | \(-0.455809\pi\) | ||||
0.138383 | + | 0.990379i | \(0.455809\pi\) | |||||||
\(564\) | −3.78565 | −0.159405 | ||||||||
\(565\) | 1.50755 | 0.0634229 | ||||||||
\(566\) | 0.113662 | 0.00477756 | ||||||||
\(567\) | −7.16407 | −0.300863 | ||||||||
\(568\) | −26.7859 | −1.12391 | ||||||||
\(569\) | 18.1137 | 0.759366 | 0.379683 | − | 0.925117i | \(-0.376033\pi\) | ||||
0.379683 | + | 0.925117i | \(0.376033\pi\) | |||||||
\(570\) | 23.8128 | 0.997407 | ||||||||
\(571\) | 6.26298 | 0.262098 | 0.131049 | − | 0.991376i | \(-0.458166\pi\) | ||||
0.131049 | + | 0.991376i | \(0.458166\pi\) | |||||||
\(572\) | 2.15190 | 0.0899753 | ||||||||
\(573\) | −5.82803 | −0.243470 | ||||||||
\(574\) | −87.9835 | −3.67236 | ||||||||
\(575\) | −10.2478 | −0.427364 | ||||||||
\(576\) | −6.37583 | −0.265660 | ||||||||
\(577\) | −1.76988 | −0.0736810 | −0.0368405 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368405 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(578\) | −17.7219 | −0.737134 | ||||||||
\(579\) | −15.7910 | −0.656253 | ||||||||
\(580\) | −7.88835 | −0.327546 | ||||||||
\(581\) | 28.2836 | 1.17340 | ||||||||
\(582\) | 20.8013 | 0.862241 | ||||||||
\(583\) | −4.37241 | −0.181087 | ||||||||
\(584\) | −1.60263 | −0.0663171 | ||||||||
\(585\) | −8.64239 | −0.357319 | ||||||||
\(586\) | −12.3835 | −0.511558 | ||||||||
\(587\) | 11.9082 | 0.491502 | 0.245751 | − | 0.969333i | \(-0.420965\pi\) | ||||
0.245751 | + | 0.969333i | \(0.420965\pi\) | |||||||
\(588\) | −14.3723 | −0.592704 | ||||||||
\(589\) | 59.6949 | 2.45969 | ||||||||
\(590\) | 16.1645 | 0.665482 | ||||||||
\(591\) | −6.85266 | −0.281881 | ||||||||
\(592\) | 10.2293 | 0.420420 | ||||||||
\(593\) | −34.2932 | −1.40825 | −0.704126 | − | 0.710075i | \(-0.748661\pi\) | ||||
−0.704126 | + | 0.710075i | \(0.748661\pi\) | |||||||
\(594\) | 9.54929 | 0.391812 | ||||||||
\(595\) | 21.9956 | 0.901731 | ||||||||
\(596\) | −0.904069 | −0.0370321 | ||||||||
\(597\) | −14.6891 | −0.601184 | ||||||||
\(598\) | 26.1871 | 1.07087 | ||||||||
\(599\) | −18.2245 | −0.744632 | −0.372316 | − | 0.928106i | \(-0.621436\pi\) | ||||
−0.372316 | + | 0.928106i | \(0.621436\pi\) | |||||||
\(600\) | −4.90345 | −0.200182 | ||||||||
\(601\) | −19.2591 | −0.785595 | −0.392797 | − | 0.919625i | \(-0.628493\pi\) | ||||
−0.392797 | + | 0.919625i | \(0.628493\pi\) | |||||||
\(602\) | −45.3930 | −1.85008 | ||||||||
\(603\) | −12.5171 | −0.509735 | ||||||||
\(604\) | 11.3594 | 0.462208 | ||||||||
\(605\) | −17.2473 | −0.701204 | ||||||||
\(606\) | 26.5578 | 1.07884 | ||||||||
\(607\) | 39.9799 | 1.62273 | 0.811367 | − | 0.584536i | \(-0.198724\pi\) | ||||
0.811367 | + | 0.584536i | \(0.198724\pi\) | |||||||
\(608\) | 25.6505 | 1.04027 | ||||||||
\(609\) | 40.2108 | 1.62942 | ||||||||
\(610\) | −5.83196 | −0.236129 | ||||||||
\(611\) | 14.7660 | 0.597369 | ||||||||
\(612\) | −2.67871 | −0.108281 | ||||||||
\(613\) | −18.3233 | −0.740070 | −0.370035 | − | 0.929018i | \(-0.620654\pi\) | ||||
−0.370035 | + | 0.929018i | \(0.620654\pi\) | |||||||
\(614\) | −33.6752 | −1.35902 | ||||||||
\(615\) | 21.8342 | 0.880442 | ||||||||
\(616\) | −11.9529 | −0.481597 | ||||||||
\(617\) | 12.3769 | 0.498273 | 0.249137 | − | 0.968468i | \(-0.419853\pi\) | ||||
0.249137 | + | 0.968468i | \(0.419853\pi\) | |||||||
\(618\) | 13.6145 | 0.547657 | ||||||||
\(619\) | −8.87878 | −0.356868 | −0.178434 | − | 0.983952i | \(-0.557103\pi\) | ||||
−0.178434 | + | 0.983952i | \(0.557103\pi\) | |||||||
\(620\) | −9.71619 | −0.390212 | ||||||||
\(621\) | 28.8662 | 1.15836 | ||||||||
\(622\) | 39.2941 | 1.57555 | ||||||||
\(623\) | 48.7309 | 1.95236 | ||||||||
\(624\) | 17.1792 | 0.687717 | ||||||||
\(625\) | −11.6944 | −0.467777 | ||||||||
\(626\) | 26.7206 | 1.06797 | ||||||||
\(627\) | 8.99632 | 0.359278 | ||||||||
\(628\) | 8.01643 | 0.319890 | ||||||||
\(629\) | −5.18701 | −0.206820 | ||||||||
\(630\) | −23.6974 | −0.944125 | ||||||||
\(631\) | 34.5564 | 1.37567 | 0.687835 | − | 0.725867i | \(-0.258561\pi\) | ||||
0.687835 | + | 0.725867i | \(0.258561\pi\) | |||||||
\(632\) | −14.9888 | −0.596221 | ||||||||
\(633\) | −7.01507 | −0.278824 | ||||||||
\(634\) | −2.60729 | −0.103549 | ||||||||
\(635\) | −5.29621 | −0.210174 | ||||||||
\(636\) | 3.12193 | 0.123793 | ||||||||
\(637\) | 56.0596 | 2.22116 | ||||||||
\(638\) | −11.9974 | −0.474983 | ||||||||
\(639\) | −20.0626 | −0.793664 | ||||||||
\(640\) | 23.7855 | 0.940206 | ||||||||
\(641\) | −1.70265 | −0.0672505 | −0.0336253 | − | 0.999435i | \(-0.510705\pi\) | ||||
−0.0336253 | + | 0.999435i | \(0.510705\pi\) | |||||||
\(642\) | −34.0885 | −1.34537 | ||||||||
\(643\) | 40.7018 | 1.60512 | 0.802561 | − | 0.596571i | \(-0.203470\pi\) | ||||
0.802561 | + | 0.596571i | \(0.203470\pi\) | |||||||
\(644\) | 17.8364 | 0.702851 | ||||||||
\(645\) | 11.2648 | 0.443553 | ||||||||
\(646\) | −28.7889 | −1.13269 | ||||||||
\(647\) | −30.3915 | −1.19481 | −0.597406 | − | 0.801939i | \(-0.703802\pi\) | ||||
−0.597406 | + | 0.801939i | \(0.703802\pi\) | |||||||
\(648\) | 3.09169 | 0.121453 | ||||||||
\(649\) | 6.10685 | 0.239715 | ||||||||
\(650\) | −9.44144 | −0.370324 | ||||||||
\(651\) | 49.5282 | 1.94116 | ||||||||
\(652\) | 7.07809 | 0.277200 | ||||||||
\(653\) | 6.95225 | 0.272062 | 0.136031 | − | 0.990705i | \(-0.456565\pi\) | ||||
0.136031 | + | 0.990705i | \(0.456565\pi\) | |||||||
\(654\) | 28.4432 | 1.11222 | ||||||||
\(655\) | −3.81609 | −0.149107 | ||||||||
\(656\) | 52.0573 | 2.03249 | ||||||||
\(657\) | −1.20037 | −0.0468307 | ||||||||
\(658\) | 40.4883 | 1.57840 | ||||||||
\(659\) | −38.2304 | −1.48924 | −0.744622 | − | 0.667486i | \(-0.767370\pi\) | ||||
−0.744622 | + | 0.667486i | \(0.767370\pi\) | |||||||
\(660\) | −1.46428 | −0.0569970 | ||||||||
\(661\) | 35.0225 | 1.36222 | 0.681109 | − | 0.732182i | \(-0.261498\pi\) | ||||
0.681109 | + | 0.732182i | \(0.261498\pi\) | |||||||
\(662\) | −43.8922 | −1.70592 | ||||||||
\(663\) | −8.71113 | −0.338312 | ||||||||
\(664\) | −12.2059 | −0.473681 | ||||||||
\(665\) | −63.2633 | −2.45325 | ||||||||
\(666\) | 5.58832 | 0.216543 | ||||||||
\(667\) | −36.2667 | −1.40425 | ||||||||
\(668\) | −6.97604 | −0.269911 | ||||||||
\(669\) | 30.0879 | 1.16327 | ||||||||
\(670\) | 21.8958 | 0.845909 | ||||||||
\(671\) | −2.20328 | −0.0850566 | ||||||||
\(672\) | 21.2819 | 0.820968 | ||||||||
\(673\) | −19.3765 | −0.746909 | −0.373454 | − | 0.927649i | \(-0.621827\pi\) | ||||
−0.373454 | + | 0.927649i | \(0.621827\pi\) | |||||||
\(674\) | −17.7471 | −0.683594 | ||||||||
\(675\) | −10.4074 | −0.400580 | ||||||||
\(676\) | −2.59986 | −0.0999947 | ||||||||
\(677\) | −3.01738 | −0.115967 | −0.0579837 | − | 0.998318i | \(-0.518467\pi\) | ||||
−0.0579837 | + | 0.998318i | \(0.518467\pi\) | |||||||
\(678\) | −1.63710 | −0.0628725 | ||||||||
\(679\) | −55.2627 | −2.12079 | ||||||||
\(680\) | −9.49229 | −0.364013 | ||||||||
\(681\) | −5.88294 | −0.225435 | ||||||||
\(682\) | −14.7774 | −0.565856 | ||||||||
\(683\) | −5.60316 | −0.214399 | −0.107199 | − | 0.994238i | \(-0.534188\pi\) | ||||
−0.107199 | + | 0.994238i | \(0.534188\pi\) | |||||||
\(684\) | 7.70447 | 0.294588 | ||||||||
\(685\) | 27.9209 | 1.06680 | ||||||||
\(686\) | 95.9200 | 3.66224 | ||||||||
\(687\) | −24.6713 | −0.941267 | ||||||||
\(688\) | 26.8577 | 1.02394 | ||||||||
\(689\) | −12.1772 | −0.463914 | ||||||||
\(690\) | −17.8193 | −0.678368 | ||||||||
\(691\) | 49.0976 | 1.86776 | 0.933881 | − | 0.357583i | \(-0.116399\pi\) | ||||
0.933881 | + | 0.357583i | \(0.116399\pi\) | |||||||
\(692\) | −1.37236 | −0.0521691 | ||||||||
\(693\) | −8.95272 | −0.340086 | ||||||||
\(694\) | 21.0443 | 0.798832 | ||||||||
\(695\) | −26.4422 | −1.00301 | ||||||||
\(696\) | −17.3531 | −0.657768 | ||||||||
\(697\) | −26.3970 | −0.999856 | ||||||||
\(698\) | −17.5855 | −0.665619 | ||||||||
\(699\) | −24.4637 | −0.925304 | ||||||||
\(700\) | −6.43069 | −0.243057 | ||||||||
\(701\) | 14.0248 | 0.529709 | 0.264855 | − | 0.964288i | \(-0.414676\pi\) | ||||
0.264855 | + | 0.964288i | \(0.414676\pi\) | |||||||
\(702\) | 26.5948 | 1.00376 | ||||||||
\(703\) | 14.9188 | 0.562673 | ||||||||
\(704\) | 4.21357 | 0.158805 | ||||||||
\(705\) | −10.0477 | −0.378418 | ||||||||
\(706\) | 10.7150 | 0.403266 | ||||||||
\(707\) | −70.5561 | −2.65354 | ||||||||
\(708\) | −4.36034 | −0.163872 | ||||||||
\(709\) | −10.0074 | −0.375835 | −0.187918 | − | 0.982185i | \(-0.560174\pi\) | ||||
−0.187918 | + | 0.982185i | \(0.560174\pi\) | |||||||
\(710\) | 35.0950 | 1.31709 | ||||||||
\(711\) | −11.2266 | −0.421029 | ||||||||
\(712\) | −21.0300 | −0.788134 | ||||||||
\(713\) | −44.6702 | −1.67291 | ||||||||
\(714\) | −23.8858 | −0.893905 | ||||||||
\(715\) | 5.71146 | 0.213596 | ||||||||
\(716\) | −2.02873 | −0.0758173 | ||||||||
\(717\) | 9.15098 | 0.341749 | ||||||||
\(718\) | 25.8236 | 0.963730 | ||||||||
\(719\) | 32.3086 | 1.20491 | 0.602454 | − | 0.798154i | \(-0.294190\pi\) | ||||
0.602454 | + | 0.798154i | \(0.294190\pi\) | |||||||
\(720\) | 14.0210 | 0.522533 | ||||||||
\(721\) | −36.1697 | −1.34703 | ||||||||
\(722\) | 51.8084 | 1.92811 | ||||||||
\(723\) | −1.16790 | −0.0434347 | ||||||||
\(724\) | −0.258714 | −0.00961504 | ||||||||
\(725\) | 13.0755 | 0.485612 | ||||||||
\(726\) | 18.7295 | 0.695118 | ||||||||
\(727\) | 14.7153 | 0.545762 | 0.272881 | − | 0.962048i | \(-0.412023\pi\) | ||||
0.272881 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(728\) | −33.2889 | −1.23377 | ||||||||
\(729\) | 21.2861 | 0.788373 | ||||||||
\(730\) | 2.09977 | 0.0777160 | ||||||||
\(731\) | −13.6189 | −0.503712 | ||||||||
\(732\) | 1.57316 | 0.0581455 | ||||||||
\(733\) | 28.2634 | 1.04393 | 0.521966 | − | 0.852966i | \(-0.325199\pi\) | ||||
0.521966 | + | 0.852966i | \(0.325199\pi\) | |||||||
\(734\) | −9.19468 | −0.339382 | ||||||||
\(735\) | −38.1463 | −1.40705 | ||||||||
\(736\) | −19.1945 | −0.707518 | ||||||||
\(737\) | 8.27210 | 0.304707 | ||||||||
\(738\) | 28.4392 | 1.04686 | ||||||||
\(739\) | −34.0536 | −1.25268 | −0.626340 | − | 0.779550i | \(-0.715448\pi\) | ||||
−0.626340 | + | 0.779550i | \(0.715448\pi\) | |||||||
\(740\) | −2.42824 | −0.0892640 | ||||||||
\(741\) | 25.0548 | 0.920411 | ||||||||
\(742\) | −33.3897 | −1.22578 | ||||||||
\(743\) | −47.2361 | −1.73293 | −0.866463 | − | 0.499241i | \(-0.833612\pi\) | ||||
−0.866463 | + | 0.499241i | \(0.833612\pi\) | |||||||
\(744\) | −21.3741 | −0.783612 | ||||||||
\(745\) | −2.39954 | −0.0879122 | ||||||||
\(746\) | 2.11255 | 0.0773458 | ||||||||
\(747\) | −9.14222 | −0.334496 | ||||||||
\(748\) | 1.77027 | 0.0647275 | ||||||||
\(749\) | 90.5629 | 3.30910 | ||||||||
\(750\) | 23.1362 | 0.844814 | ||||||||
\(751\) | 36.7588 | 1.34135 | 0.670674 | − | 0.741752i | \(-0.266005\pi\) | ||||
0.670674 | + | 0.741752i | \(0.266005\pi\) | |||||||
\(752\) | −23.9557 | −0.873576 | ||||||||
\(753\) | 8.19454 | 0.298626 | ||||||||
\(754\) | −33.4129 | −1.21683 | ||||||||
\(755\) | 30.1496 | 1.09726 | ||||||||
\(756\) | 18.1141 | 0.658802 | ||||||||
\(757\) | 7.43315 | 0.270162 | 0.135081 | − | 0.990835i | \(-0.456870\pi\) | ||||
0.135081 | + | 0.990835i | \(0.456870\pi\) | |||||||
\(758\) | −22.5367 | −0.818568 | ||||||||
\(759\) | −6.73202 | −0.244357 | ||||||||
\(760\) | 27.3016 | 0.990332 | ||||||||
\(761\) | 1.06982 | 0.0387809 | 0.0193905 | − | 0.999812i | \(-0.493827\pi\) | ||||
0.0193905 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(762\) | 5.75135 | 0.208350 | ||||||||
\(763\) | −75.5651 | −2.73564 | ||||||||
\(764\) | 3.29847 | 0.119335 | ||||||||
\(765\) | −7.10972 | −0.257052 | ||||||||
\(766\) | 19.5983 | 0.708116 | ||||||||
\(767\) | 17.0076 | 0.614109 | ||||||||
\(768\) | −16.7266 | −0.603569 | ||||||||
\(769\) | −26.2212 | −0.945562 | −0.472781 | − | 0.881180i | \(-0.656750\pi\) | ||||
−0.472781 | + | 0.881180i | \(0.656750\pi\) | |||||||
\(770\) | 15.6608 | 0.564375 | ||||||||
\(771\) | −13.2039 | −0.475527 | ||||||||
\(772\) | 8.93720 | 0.321657 | ||||||||
\(773\) | −15.9051 | −0.572065 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(774\) | 14.6725 | 0.527394 | ||||||||
\(775\) | 16.1053 | 0.578519 | ||||||||
\(776\) | 23.8489 | 0.856124 | ||||||||
\(777\) | 12.3779 | 0.444056 | ||||||||
\(778\) | 7.93152 | 0.284359 | ||||||||
\(779\) | 75.9225 | 2.72020 | ||||||||
\(780\) | −4.07802 | −0.146017 | ||||||||
\(781\) | 13.2587 | 0.474433 | ||||||||
\(782\) | 21.5430 | 0.770376 | ||||||||
\(783\) | −36.8313 | −1.31624 | ||||||||
\(784\) | −90.9485 | −3.24816 | ||||||||
\(785\) | 21.2768 | 0.759403 | ||||||||
\(786\) | 4.14404 | 0.147813 | ||||||||
\(787\) | −44.7474 | −1.59507 | −0.797536 | − | 0.603272i | \(-0.793863\pi\) | ||||
−0.797536 | + | 0.603272i | \(0.793863\pi\) | |||||||
\(788\) | 3.87838 | 0.138162 | ||||||||
\(789\) | −23.2023 | −0.826023 | ||||||||
\(790\) | 19.6384 | 0.698701 | ||||||||
\(791\) | 4.34928 | 0.154643 | ||||||||
\(792\) | 3.86358 | 0.137286 | ||||||||
\(793\) | −6.13614 | −0.217901 | ||||||||
\(794\) | 14.9725 | 0.531356 | ||||||||
\(795\) | 8.28609 | 0.293877 | ||||||||
\(796\) | 8.31354 | 0.294665 | ||||||||
\(797\) | −20.2003 | −0.715530 | −0.357765 | − | 0.933812i | \(-0.616461\pi\) | ||||
−0.357765 | + | 0.933812i | \(0.616461\pi\) | |||||||
\(798\) | 68.7000 | 2.43195 | ||||||||
\(799\) | 12.1474 | 0.429743 | ||||||||
\(800\) | 6.92033 | 0.244671 | ||||||||
\(801\) | −15.7515 | −0.556551 | ||||||||
\(802\) | −45.7679 | −1.61612 | ||||||||
\(803\) | 0.793280 | 0.0279943 | ||||||||
\(804\) | −5.90634 | −0.208301 | ||||||||
\(805\) | 47.3405 | 1.66853 | ||||||||
\(806\) | −41.1552 | −1.44963 | ||||||||
\(807\) | 23.6538 | 0.832652 | ||||||||
\(808\) | 30.4488 | 1.07118 | ||||||||
\(809\) | 31.3338 | 1.10164 | 0.550818 | − | 0.834625i | \(-0.314316\pi\) | ||||
0.550818 | + | 0.834625i | \(0.314316\pi\) | |||||||
\(810\) | −4.05074 | −0.142329 | ||||||||
\(811\) | −28.2192 | −0.990909 | −0.495454 | − | 0.868634i | \(-0.664998\pi\) | ||||
−0.495454 | + | 0.868634i | \(0.664998\pi\) | |||||||
\(812\) | −22.7580 | −0.798648 | ||||||||
\(813\) | 4.95064 | 0.173626 | ||||||||
\(814\) | −3.69313 | −0.129444 | ||||||||
\(815\) | 18.7863 | 0.658057 | ||||||||
\(816\) | 14.1325 | 0.494738 | ||||||||
\(817\) | 39.1704 | 1.37040 | ||||||||
\(818\) | −18.9502 | −0.662579 | ||||||||
\(819\) | −24.9334 | −0.871242 | ||||||||
\(820\) | −12.3575 | −0.431541 | ||||||||
\(821\) | −36.8115 | −1.28473 | −0.642365 | − | 0.766399i | \(-0.722047\pi\) | ||||
−0.642365 | + | 0.766399i | \(0.722047\pi\) | |||||||
\(822\) | −30.3203 | −1.05754 | ||||||||
\(823\) | −34.8680 | −1.21542 | −0.607711 | − | 0.794158i | \(-0.707912\pi\) | ||||
−0.607711 | + | 0.794158i | \(0.707912\pi\) | |||||||
\(824\) | 15.6092 | 0.543772 | ||||||||
\(825\) | 2.42715 | 0.0845024 | ||||||||
\(826\) | 46.6347 | 1.62263 | ||||||||
\(827\) | −11.6305 | −0.404431 | −0.202216 | − | 0.979341i | \(-0.564814\pi\) | ||||
−0.202216 | + | 0.979341i | \(0.564814\pi\) | |||||||
\(828\) | −5.76532 | −0.200359 | ||||||||
\(829\) | −45.8232 | −1.59150 | −0.795752 | − | 0.605622i | \(-0.792924\pi\) | ||||
−0.795752 | + | 0.605622i | \(0.792924\pi\) | |||||||
\(830\) | 15.9923 | 0.555099 | ||||||||
\(831\) | 0.431502 | 0.0149686 | ||||||||
\(832\) | 11.7348 | 0.406831 | ||||||||
\(833\) | 46.1178 | 1.59789 | ||||||||
\(834\) | 28.7145 | 0.994303 | ||||||||
\(835\) | −18.5155 | −0.640755 | ||||||||
\(836\) | −5.09162 | −0.176097 | ||||||||
\(837\) | −45.3656 | −1.56807 | ||||||||
\(838\) | 25.4132 | 0.877884 | ||||||||
\(839\) | −3.48632 | −0.120361 | −0.0601806 | − | 0.998188i | \(-0.519168\pi\) | ||||
−0.0601806 | + | 0.998188i | \(0.519168\pi\) | |||||||
\(840\) | 22.6518 | 0.781561 | ||||||||
\(841\) | 17.2737 | 0.595646 | ||||||||
\(842\) | 12.2931 | 0.423647 | ||||||||
\(843\) | −28.8375 | −0.993216 | ||||||||
\(844\) | 3.97030 | 0.136663 | ||||||||
\(845\) | −6.90043 | −0.237382 | ||||||||
\(846\) | −13.0872 | −0.449947 | ||||||||
\(847\) | −49.7587 | −1.70973 | ||||||||
\(848\) | 19.7557 | 0.678414 | ||||||||
\(849\) | −0.0813764 | −0.00279283 | ||||||||
\(850\) | −7.76706 | −0.266408 | ||||||||
\(851\) | −11.1638 | −0.382692 | ||||||||
\(852\) | −9.46679 | −0.324327 | ||||||||
\(853\) | −44.6130 | −1.52752 | −0.763760 | − | 0.645500i | \(-0.776649\pi\) | ||||
−0.763760 | + | 0.645500i | \(0.776649\pi\) | |||||||
\(854\) | −16.8252 | −0.575748 | ||||||||
\(855\) | 20.4488 | 0.699336 | ||||||||
\(856\) | −39.0828 | −1.33582 | ||||||||
\(857\) | 21.1188 | 0.721404 | 0.360702 | − | 0.932681i | \(-0.382537\pi\) | ||||
0.360702 | + | 0.932681i | \(0.382537\pi\) | |||||||
\(858\) | −6.20229 | −0.211743 | ||||||||
\(859\) | −36.4020 | −1.24202 | −0.621011 | − | 0.783802i | \(-0.713278\pi\) | ||||
−0.621011 | + | 0.783802i | \(0.713278\pi\) | |||||||
\(860\) | −6.37553 | −0.217404 | ||||||||
\(861\) | 62.9920 | 2.14676 | ||||||||
\(862\) | 39.4998 | 1.34537 | ||||||||
\(863\) | −4.01817 | −0.136780 | −0.0683900 | − | 0.997659i | \(-0.521786\pi\) | ||||
−0.0683900 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(864\) | −19.4933 | −0.663176 | ||||||||
\(865\) | −3.64244 | −0.123847 | ||||||||
\(866\) | 3.11277 | 0.105776 | ||||||||
\(867\) | 12.6880 | 0.430908 | ||||||||
\(868\) | −28.0313 | −0.951444 | ||||||||
\(869\) | 7.41925 | 0.251681 | ||||||||
\(870\) | 22.7362 | 0.770828 | ||||||||
\(871\) | 23.0379 | 0.780608 | ||||||||
\(872\) | 32.6104 | 1.10433 | ||||||||
\(873\) | 17.8628 | 0.604563 | ||||||||
\(874\) | −61.9616 | −2.09588 | ||||||||
\(875\) | −61.4659 | −2.07793 | ||||||||
\(876\) | −0.566408 | −0.0191372 | ||||||||
\(877\) | 48.0234 | 1.62163 | 0.810817 | − | 0.585300i | \(-0.199023\pi\) | ||||
0.810817 | + | 0.585300i | \(0.199023\pi\) | |||||||
\(878\) | −24.3278 | −0.821022 | ||||||||
\(879\) | 8.86599 | 0.299042 | ||||||||
\(880\) | −9.26601 | −0.312357 | ||||||||
\(881\) | −56.8752 | −1.91617 | −0.958087 | − | 0.286479i | \(-0.907515\pi\) | ||||
−0.958087 | + | 0.286479i | \(0.907515\pi\) | |||||||
\(882\) | −49.6858 | −1.67301 | ||||||||
\(883\) | 44.7065 | 1.50449 | 0.752246 | − | 0.658882i | \(-0.228970\pi\) | ||||
0.752246 | + | 0.658882i | \(0.228970\pi\) | |||||||
\(884\) | 4.93021 | 0.165821 | ||||||||
\(885\) | −11.5730 | −0.389022 | ||||||||
\(886\) | −37.6327 | −1.26429 | ||||||||
\(887\) | 5.64866 | 0.189663 | 0.0948317 | − | 0.995493i | \(-0.469769\pi\) | ||||
0.0948317 | + | 0.995493i | \(0.469769\pi\) | |||||||
\(888\) | −5.34175 | −0.179257 | ||||||||
\(889\) | −15.2796 | −0.512462 | ||||||||
\(890\) | 27.5537 | 0.923601 | ||||||||
\(891\) | −1.53035 | −0.0512686 | ||||||||
\(892\) | −17.0288 | −0.570165 | ||||||||
\(893\) | −34.9380 | −1.16916 | ||||||||
\(894\) | 2.60575 | 0.0871492 | ||||||||
\(895\) | −5.38457 | −0.179986 | ||||||||
\(896\) | 68.6215 | 2.29248 | ||||||||
\(897\) | −18.7487 | −0.626001 | ||||||||
\(898\) | 23.7216 | 0.791601 | ||||||||
\(899\) | 56.9960 | 1.90092 | ||||||||
\(900\) | 2.07861 | 0.0692871 | ||||||||
\(901\) | −10.0176 | −0.333736 | ||||||||
\(902\) | −18.7945 | −0.625789 | ||||||||
\(903\) | 32.4992 | 1.08150 | ||||||||
\(904\) | −1.87695 | −0.0624265 | ||||||||
\(905\) | −0.686667 | −0.0228256 | ||||||||
\(906\) | −32.7406 | −1.08773 | ||||||||
\(907\) | 25.2839 | 0.839538 | 0.419769 | − | 0.907631i | \(-0.362111\pi\) | ||||
0.419769 | + | 0.907631i | \(0.362111\pi\) | |||||||
\(908\) | 3.32955 | 0.110495 | ||||||||
\(909\) | 22.8061 | 0.756431 | ||||||||
\(910\) | 43.6153 | 1.44583 | ||||||||
\(911\) | 27.3571 | 0.906380 | 0.453190 | − | 0.891414i | \(-0.350286\pi\) | ||||
0.453190 | + | 0.891414i | \(0.350286\pi\) | |||||||
\(912\) | −40.6478 | −1.34598 | ||||||||
\(913\) | 6.04178 | 0.199954 | ||||||||
\(914\) | 19.2492 | 0.636705 | ||||||||
\(915\) | 4.17540 | 0.138034 | ||||||||
\(916\) | 13.9631 | 0.461354 | ||||||||
\(917\) | −11.0095 | −0.363564 | ||||||||
\(918\) | 21.8784 | 0.722095 | ||||||||
\(919\) | −44.3463 | −1.46285 | −0.731424 | − | 0.681923i | \(-0.761144\pi\) | ||||
−0.731424 | + | 0.681923i | \(0.761144\pi\) | |||||||
\(920\) | −20.4300 | −0.673556 | ||||||||
\(921\) | 24.1098 | 0.794445 | ||||||||
\(922\) | 24.5867 | 0.809719 | ||||||||
\(923\) | 36.9255 | 1.21542 | ||||||||
\(924\) | −4.22446 | −0.138974 | ||||||||
\(925\) | 4.02499 | 0.132341 | ||||||||
\(926\) | 39.6876 | 1.30422 | ||||||||
\(927\) | 11.6913 | 0.383992 | ||||||||
\(928\) | 24.4908 | 0.803950 | ||||||||
\(929\) | −33.2552 | −1.09107 | −0.545535 | − | 0.838088i | \(-0.683673\pi\) | ||||
−0.545535 | + | 0.838088i | \(0.683673\pi\) | |||||||
\(930\) | 28.0044 | 0.918302 | ||||||||
\(931\) | −132.643 | −4.34720 | ||||||||
\(932\) | 13.8457 | 0.453530 | ||||||||
\(933\) | −28.1326 | −0.921021 | ||||||||
\(934\) | 48.5694 | 1.58924 | ||||||||
\(935\) | 4.69857 | 0.153660 | ||||||||
\(936\) | 10.7601 | 0.351705 | ||||||||
\(937\) | −51.9272 | −1.69639 | −0.848194 | − | 0.529686i | \(-0.822310\pi\) | ||||
−0.848194 | + | 0.529686i | \(0.822310\pi\) | |||||||
\(938\) | 63.1696 | 2.06256 | ||||||||
\(939\) | −19.1307 | −0.624306 | ||||||||
\(940\) | 5.68666 | 0.185478 | ||||||||
\(941\) | 21.0604 | 0.686549 | 0.343274 | − | 0.939235i | \(-0.388464\pi\) | ||||
0.343274 | + | 0.939235i | \(0.388464\pi\) | |||||||
\(942\) | −23.1053 | −0.752812 | ||||||||
\(943\) | −56.8134 | −1.85010 | ||||||||
\(944\) | −27.5924 | −0.898056 | ||||||||
\(945\) | 48.0775 | 1.56396 | ||||||||
\(946\) | −9.69658 | −0.315263 | ||||||||
\(947\) | −22.4529 | −0.729621 | −0.364810 | − | 0.931082i | \(-0.618866\pi\) | ||||
−0.364810 | + | 0.931082i | \(0.618866\pi\) | |||||||
\(948\) | −5.29740 | −0.172052 | ||||||||
\(949\) | 2.20929 | 0.0717166 | ||||||||
\(950\) | 22.3395 | 0.724789 | ||||||||
\(951\) | 1.86669 | 0.0605317 | ||||||||
\(952\) | −27.3853 | −0.887564 | ||||||||
\(953\) | 29.3558 | 0.950927 | 0.475463 | − | 0.879736i | \(-0.342280\pi\) | ||||
0.475463 | + | 0.879736i | \(0.342280\pi\) | |||||||
\(954\) | 10.7927 | 0.349426 | ||||||||
\(955\) | 8.75465 | 0.283294 | ||||||||
\(956\) | −5.17915 | −0.167506 | ||||||||
\(957\) | 8.58958 | 0.277662 | ||||||||
\(958\) | −16.6367 | −0.537508 | ||||||||
\(959\) | 80.5519 | 2.60116 | ||||||||
\(960\) | −7.98507 | −0.257717 | ||||||||
\(961\) | 39.2028 | 1.26461 | ||||||||
\(962\) | −10.2854 | −0.331614 | ||||||||
\(963\) | −29.2730 | −0.943309 | ||||||||
\(964\) | 0.660992 | 0.0212891 | ||||||||
\(965\) | 23.7207 | 0.763596 | ||||||||
\(966\) | −51.4088 | −1.65405 | ||||||||
\(967\) | 26.9397 | 0.866324 | 0.433162 | − | 0.901316i | \(-0.357398\pi\) | ||||
0.433162 | + | 0.901316i | \(0.357398\pi\) | |||||||
\(968\) | 21.4736 | 0.690187 | ||||||||
\(969\) | 20.6115 | 0.662136 | ||||||||
\(970\) | −31.2469 | −1.00328 | ||||||||
\(971\) | −38.3427 | −1.23047 | −0.615237 | − | 0.788342i | \(-0.710940\pi\) | ||||
−0.615237 | + | 0.788342i | \(0.710940\pi\) | |||||||
\(972\) | −9.64394 | −0.309330 | ||||||||
\(973\) | −76.2859 | −2.44561 | ||||||||
\(974\) | −40.6583 | −1.30278 | ||||||||
\(975\) | 6.75962 | 0.216481 | ||||||||
\(976\) | 9.95500 | 0.318652 | ||||||||
\(977\) | −13.7841 | −0.440991 | −0.220496 | − | 0.975388i | \(-0.570767\pi\) | ||||
−0.220496 | + | 0.975388i | \(0.570767\pi\) | |||||||
\(978\) | −20.4008 | −0.652346 | ||||||||
\(979\) | 10.4096 | 0.332693 | ||||||||
\(980\) | 21.5895 | 0.689653 | ||||||||
\(981\) | 24.4252 | 0.779836 | ||||||||
\(982\) | −43.8334 | −1.39878 | ||||||||
\(983\) | 14.8201 | 0.472688 | 0.236344 | − | 0.971669i | \(-0.424051\pi\) | ||||
0.236344 | + | 0.971669i | \(0.424051\pi\) | |||||||
\(984\) | −27.1844 | −0.866608 | ||||||||
\(985\) | 10.2938 | 0.327988 | ||||||||
\(986\) | −27.4874 | −0.875376 | ||||||||
\(987\) | −28.9877 | −0.922688 | ||||||||
\(988\) | −14.1802 | −0.451132 | ||||||||
\(989\) | −29.3115 | −0.932051 | ||||||||
\(990\) | −5.06209 | −0.160884 | ||||||||
\(991\) | −52.3768 | −1.66380 | −0.831902 | − | 0.554923i | \(-0.812748\pi\) | ||||
−0.831902 | + | 0.554923i | \(0.812748\pi\) | |||||||
\(992\) | 30.1657 | 0.957761 | ||||||||
\(993\) | 31.4247 | 0.997233 | ||||||||
\(994\) | 101.249 | 3.21143 | ||||||||
\(995\) | 22.0654 | 0.699520 | ||||||||
\(996\) | −4.31387 | −0.136690 | ||||||||
\(997\) | 23.1646 | 0.733630 | 0.366815 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366815 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(998\) | −61.3592 | −1.94229 | ||||||||
\(999\) | −11.3377 | −0.358708 |
(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 | 241.2.a.b.1.9 | ✓ | 12 | |
3.2 | odd | 2 | 2169.2.a.h.1.4 | 12 | |||
4.3 | odd | 2 | 3856.2.a.n.1.8 | 12 | |||
5.4 | even | 2 | 6025.2.a.h.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2169.2.a.h.1.4 | 12 | 3.2 | odd | 2 | |||
3856.2.a.n.1.8 | 12 | 4.3 | odd | 2 | |||
6025.2.a.h.1.4 | 12 | 5.4 | even | 2 |