Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, 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("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.07227\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.756417 | −0.534868 | −0.267434 | − | 0.963576i | \(-0.586176\pi\) | ||||
−0.267434 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(3\) | −3.07227 | −1.77378 | −0.886888 | − | 0.461985i | \(-0.847137\pi\) | ||||
−0.886888 | + | 0.461985i | \(0.847137\pi\) | |||||||
\(4\) | −1.42783 | −0.713916 | ||||||||
\(5\) | 0.386144 | 0.172689 | 0.0863445 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863445 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(6\) | 2.32392 | 0.948736 | ||||||||
\(7\) | 0.194914 | 0.0736704 | 0.0368352 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368352 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(8\) | 2.59287 | 0.916719 | ||||||||
\(9\) | 6.43884 | 2.14628 | ||||||||
\(10\) | −0.292086 | −0.0923657 | ||||||||
\(11\) | 2.36326 | 0.712549 | 0.356275 | − | 0.934381i | \(-0.384047\pi\) | ||||
0.356275 | + | 0.934381i | \(0.384047\pi\) | |||||||
\(12\) | 4.38669 | 1.26633 | ||||||||
\(13\) | −1.22636 | −0.340131 | −0.170065 | − | 0.985433i | \(-0.554398\pi\) | ||||
−0.170065 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(14\) | −0.147436 | −0.0394039 | ||||||||
\(15\) | −1.18634 | −0.306311 | ||||||||
\(16\) | 0.894372 | 0.223593 | ||||||||
\(17\) | −5.04830 | −1.22439 | −0.612197 | − | 0.790705i | \(-0.709714\pi\) | ||||
−0.612197 | + | 0.790705i | \(0.709714\pi\) | |||||||
\(18\) | −4.87045 | −1.14798 | ||||||||
\(19\) | 4.24460 | 0.973779 | 0.486890 | − | 0.873464i | \(-0.338131\pi\) | ||||
0.486890 | + | 0.873464i | \(0.338131\pi\) | |||||||
\(20\) | −0.551349 | −0.123285 | ||||||||
\(21\) | −0.598827 | −0.130675 | ||||||||
\(22\) | −1.78761 | −0.381120 | ||||||||
\(23\) | 1.53457 | 0.319980 | 0.159990 | − | 0.987119i | \(-0.448854\pi\) | ||||
0.159990 | + | 0.987119i | \(0.448854\pi\) | |||||||
\(24\) | −7.96600 | −1.62605 | ||||||||
\(25\) | −4.85089 | −0.970179 | ||||||||
\(26\) | 0.927639 | 0.181925 | ||||||||
\(27\) | −10.5650 | −2.03324 | ||||||||
\(28\) | −0.278304 | −0.0525945 | ||||||||
\(29\) | −7.31602 | −1.35855 | −0.679275 | − | 0.733883i | \(-0.737706\pi\) | ||||
−0.679275 | + | 0.733883i | \(0.737706\pi\) | |||||||
\(30\) | 0.897367 | 0.163836 | ||||||||
\(31\) | 3.33893 | 0.599690 | 0.299845 | − | 0.953988i | \(-0.403065\pi\) | ||||
0.299845 | + | 0.953988i | \(0.403065\pi\) | |||||||
\(32\) | −5.86226 | −1.03631 | ||||||||
\(33\) | −7.26057 | −1.26390 | ||||||||
\(34\) | 3.81863 | 0.654889 | ||||||||
\(35\) | 0.0752647 | 0.0127221 | ||||||||
\(36\) | −9.19358 | −1.53226 | ||||||||
\(37\) | −2.17138 | −0.356973 | −0.178487 | − | 0.983942i | \(-0.557120\pi\) | ||||
−0.178487 | + | 0.983942i | \(0.557120\pi\) | |||||||
\(38\) | −3.21069 | −0.520843 | ||||||||
\(39\) | 3.76771 | 0.603316 | ||||||||
\(40\) | 1.00122 | 0.158307 | ||||||||
\(41\) | −1.04840 | −0.163733 | −0.0818663 | − | 0.996643i | \(-0.526088\pi\) | ||||
−0.0818663 | + | 0.996643i | \(0.526088\pi\) | |||||||
\(42\) | 0.452963 | 0.0698937 | ||||||||
\(43\) | −1.53067 | −0.233425 | −0.116712 | − | 0.993166i | \(-0.537236\pi\) | ||||
−0.116712 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(44\) | −3.37434 | −0.508701 | ||||||||
\(45\) | 2.48632 | 0.370639 | ||||||||
\(46\) | −1.16077 | −0.171147 | ||||||||
\(47\) | −1.08422 | −0.158150 | −0.0790748 | − | 0.996869i | \(-0.525197\pi\) | ||||
−0.0790748 | + | 0.996869i | \(0.525197\pi\) | |||||||
\(48\) | −2.74775 | −0.396604 | ||||||||
\(49\) | −6.96201 | −0.994573 | ||||||||
\(50\) | 3.66930 | 0.518917 | ||||||||
\(51\) | 15.5098 | 2.17180 | ||||||||
\(52\) | 1.75104 | 0.242825 | ||||||||
\(53\) | 1.55308 | 0.213332 | 0.106666 | − | 0.994295i | \(-0.465983\pi\) | ||||
0.106666 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(54\) | 7.99158 | 1.08752 | ||||||||
\(55\) | 0.912558 | 0.123049 | ||||||||
\(56\) | 0.505386 | 0.0675350 | ||||||||
\(57\) | −13.0406 | −1.72727 | ||||||||
\(58\) | 5.53396 | 0.726645 | ||||||||
\(59\) | 14.8451 | 1.93267 | 0.966334 | − | 0.257293i | \(-0.0828304\pi\) | ||||
0.966334 | + | 0.257293i | \(0.0828304\pi\) | |||||||
\(60\) | 1.69389 | 0.218681 | ||||||||
\(61\) | −5.45056 | −0.697873 | −0.348936 | − | 0.937146i | \(-0.613457\pi\) | ||||
−0.348936 | + | 0.937146i | \(0.613457\pi\) | |||||||
\(62\) | −2.52563 | −0.320755 | ||||||||
\(63\) | 1.25502 | 0.158117 | ||||||||
\(64\) | 2.64557 | 0.330697 | ||||||||
\(65\) | −0.473551 | −0.0587368 | ||||||||
\(66\) | 5.49202 | 0.676021 | ||||||||
\(67\) | −11.3202 | −1.38298 | −0.691490 | − | 0.722386i | \(-0.743045\pi\) | ||||
−0.691490 | + | 0.722386i | \(0.743045\pi\) | |||||||
\(68\) | 7.20814 | 0.874115 | ||||||||
\(69\) | −4.71461 | −0.567572 | ||||||||
\(70\) | −0.0569315 | −0.00680462 | ||||||||
\(71\) | −11.4236 | −1.35573 | −0.677864 | − | 0.735187i | \(-0.737094\pi\) | ||||
−0.677864 | + | 0.735187i | \(0.737094\pi\) | |||||||
\(72\) | 16.6951 | 1.96753 | ||||||||
\(73\) | −0.902229 | −0.105598 | −0.0527990 | − | 0.998605i | \(-0.516814\pi\) | ||||
−0.0527990 | + | 0.998605i | \(0.516814\pi\) | |||||||
\(74\) | 1.64247 | 0.190933 | ||||||||
\(75\) | 14.9032 | 1.72088 | ||||||||
\(76\) | −6.06059 | −0.695197 | ||||||||
\(77\) | 0.460631 | 0.0524938 | ||||||||
\(78\) | −2.84996 | −0.322694 | ||||||||
\(79\) | −12.7431 | −1.43371 | −0.716853 | − | 0.697225i | \(-0.754418\pi\) | ||||
−0.716853 | + | 0.697225i | \(0.754418\pi\) | |||||||
\(80\) | 0.345356 | 0.0386120 | ||||||||
\(81\) | 13.1421 | 1.46024 | ||||||||
\(82\) | 0.793029 | 0.0875753 | ||||||||
\(83\) | 6.10241 | 0.669826 | 0.334913 | − | 0.942249i | \(-0.391293\pi\) | ||||
0.334913 | + | 0.942249i | \(0.391293\pi\) | |||||||
\(84\) | 0.855025 | 0.0932908 | ||||||||
\(85\) | −1.94937 | −0.211439 | ||||||||
\(86\) | 1.15782 | 0.124851 | ||||||||
\(87\) | 22.4768 | 2.40976 | ||||||||
\(88\) | 6.12763 | 0.653207 | ||||||||
\(89\) | 6.44432 | 0.683097 | 0.341548 | − | 0.939864i | \(-0.389049\pi\) | ||||
0.341548 | + | 0.939864i | \(0.389049\pi\) | |||||||
\(90\) | −1.88070 | −0.198243 | ||||||||
\(91\) | −0.239034 | −0.0250576 | ||||||||
\(92\) | −2.19111 | −0.228439 | ||||||||
\(93\) | −10.2581 | −1.06372 | ||||||||
\(94\) | 0.820122 | 0.0845892 | ||||||||
\(95\) | 1.63903 | 0.168161 | ||||||||
\(96\) | 18.0105 | 1.83818 | ||||||||
\(97\) | −12.9886 | −1.31879 | −0.659394 | − | 0.751797i | \(-0.729187\pi\) | ||||
−0.659394 | + | 0.751797i | \(0.729187\pi\) | |||||||
\(98\) | 5.26618 | 0.531965 | ||||||||
\(99\) | 15.2166 | 1.52933 | ||||||||
\(100\) | 6.92626 | 0.692626 | ||||||||
\(101\) | 6.18139 | 0.615072 | 0.307536 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307536 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(102\) | −11.7318 | −1.16163 | ||||||||
\(103\) | 7.78250 | 0.766833 | 0.383416 | − | 0.923576i | \(-0.374747\pi\) | ||||
0.383416 | + | 0.923576i | \(0.374747\pi\) | |||||||
\(104\) | −3.17979 | −0.311804 | ||||||||
\(105\) | −0.231233 | −0.0225661 | ||||||||
\(106\) | −1.17477 | −0.114104 | ||||||||
\(107\) | −8.18217 | −0.791000 | −0.395500 | − | 0.918466i | \(-0.629429\pi\) | ||||
−0.395500 | + | 0.918466i | \(0.629429\pi\) | |||||||
\(108\) | 15.0851 | 1.45157 | ||||||||
\(109\) | −5.32486 | −0.510029 | −0.255015 | − | 0.966937i | \(-0.582080\pi\) | ||||
−0.255015 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(110\) | −0.690275 | −0.0658151 | ||||||||
\(111\) | 6.67107 | 0.633190 | ||||||||
\(112\) | 0.174325 | 0.0164722 | ||||||||
\(113\) | −3.60573 | −0.339199 | −0.169599 | − | 0.985513i | \(-0.554247\pi\) | ||||
−0.169599 | + | 0.985513i | \(0.554247\pi\) | |||||||
\(114\) | 9.86411 | 0.923859 | ||||||||
\(115\) | 0.592565 | 0.0552570 | ||||||||
\(116\) | 10.4461 | 0.969892 | ||||||||
\(117\) | −7.89633 | −0.730016 | ||||||||
\(118\) | −11.2291 | −1.03372 | ||||||||
\(119\) | −0.983983 | −0.0902016 | ||||||||
\(120\) | −3.07602 | −0.280801 | ||||||||
\(121\) | −5.41501 | −0.492274 | ||||||||
\(122\) | 4.12290 | 0.373270 | ||||||||
\(123\) | 3.22097 | 0.290425 | ||||||||
\(124\) | −4.76744 | −0.428129 | ||||||||
\(125\) | −3.80386 | −0.340228 | ||||||||
\(126\) | −0.949316 | −0.0845718 | ||||||||
\(127\) | −17.8352 | −1.58262 | −0.791308 | − | 0.611418i | \(-0.790599\pi\) | ||||
−0.791308 | + | 0.611418i | \(0.790599\pi\) | |||||||
\(128\) | 9.72337 | 0.859432 | ||||||||
\(129\) | 4.70262 | 0.414043 | ||||||||
\(130\) | 0.358202 | 0.0314164 | ||||||||
\(131\) | −12.1841 | −1.06453 | −0.532267 | − | 0.846577i | \(-0.678660\pi\) | ||||
−0.532267 | + | 0.846577i | \(0.678660\pi\) | |||||||
\(132\) | 10.3669 | 0.902321 | ||||||||
\(133\) | 0.827331 | 0.0717387 | ||||||||
\(134\) | 8.56278 | 0.739711 | ||||||||
\(135\) | −4.07963 | −0.351118 | ||||||||
\(136\) | −13.0896 | −1.12242 | ||||||||
\(137\) | −13.9009 | −1.18764 | −0.593819 | − | 0.804599i | \(-0.702380\pi\) | ||||
−0.593819 | + | 0.804599i | \(0.702380\pi\) | |||||||
\(138\) | 3.56621 | 0.303576 | ||||||||
\(139\) | 4.99920 | 0.424027 | 0.212013 | − | 0.977267i | \(-0.431998\pi\) | ||||
0.212013 | + | 0.977267i | \(0.431998\pi\) | |||||||
\(140\) | −0.107465 | −0.00908249 | ||||||||
\(141\) | 3.33101 | 0.280522 | ||||||||
\(142\) | 8.64099 | 0.725135 | ||||||||
\(143\) | −2.89820 | −0.242360 | ||||||||
\(144\) | 5.75872 | 0.479893 | ||||||||
\(145\) | −2.82504 | −0.234607 | ||||||||
\(146\) | 0.682462 | 0.0564809 | ||||||||
\(147\) | 21.3892 | 1.76415 | ||||||||
\(148\) | 3.10037 | 0.254849 | ||||||||
\(149\) | 17.4937 | 1.43314 | 0.716570 | − | 0.697515i | \(-0.245711\pi\) | ||||
0.716570 | + | 0.697515i | \(0.245711\pi\) | |||||||
\(150\) | −11.2731 | −0.920443 | ||||||||
\(151\) | 0.480306 | 0.0390867 | 0.0195434 | − | 0.999809i | \(-0.493779\pi\) | ||||
0.0195434 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(152\) | 11.0057 | 0.892682 | ||||||||
\(153\) | −32.5052 | −2.62789 | ||||||||
\(154\) | −0.348429 | −0.0280772 | ||||||||
\(155\) | 1.28931 | 0.103560 | ||||||||
\(156\) | −5.37965 | −0.430717 | ||||||||
\(157\) | 0.117389 | 0.00936869 | 0.00468434 | − | 0.999989i | \(-0.498509\pi\) | ||||
0.00468434 | + | 0.999989i | \(0.498509\pi\) | |||||||
\(158\) | 9.63907 | 0.766843 | ||||||||
\(159\) | −4.77147 | −0.378402 | ||||||||
\(160\) | −2.26368 | −0.178959 | ||||||||
\(161\) | 0.299108 | 0.0235730 | ||||||||
\(162\) | −9.94093 | −0.781033 | ||||||||
\(163\) | −12.5273 | −0.981210 | −0.490605 | − | 0.871382i | \(-0.663224\pi\) | ||||
−0.490605 | + | 0.871382i | \(0.663224\pi\) | |||||||
\(164\) | 1.49694 | 0.116891 | ||||||||
\(165\) | −2.80362 | −0.218262 | ||||||||
\(166\) | −4.61597 | −0.358268 | ||||||||
\(167\) | −0.744061 | −0.0575772 | −0.0287886 | − | 0.999586i | \(-0.509165\pi\) | ||||
−0.0287886 | + | 0.999586i | \(0.509165\pi\) | |||||||
\(168\) | −1.55268 | −0.119792 | ||||||||
\(169\) | −11.4960 | −0.884311 | ||||||||
\(170\) | 1.47454 | 0.113092 | ||||||||
\(171\) | 27.3303 | 2.09000 | ||||||||
\(172\) | 2.18554 | 0.166646 | ||||||||
\(173\) | 11.6073 | 0.882484 | 0.441242 | − | 0.897388i | \(-0.354538\pi\) | ||||
0.441242 | + | 0.897388i | \(0.354538\pi\) | |||||||
\(174\) | −17.0018 | −1.28891 | ||||||||
\(175\) | −0.945505 | −0.0714734 | ||||||||
\(176\) | 2.11363 | 0.159321 | ||||||||
\(177\) | −45.6081 | −3.42812 | ||||||||
\(178\) | −4.87460 | −0.365367 | ||||||||
\(179\) | −21.1974 | −1.58437 | −0.792183 | − | 0.610284i | \(-0.791055\pi\) | ||||
−0.792183 | + | 0.610284i | \(0.791055\pi\) | |||||||
\(180\) | −3.55005 | −0.264605 | ||||||||
\(181\) | 11.9508 | 0.888299 | 0.444150 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444150 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(182\) | 0.180809 | 0.0134025 | ||||||||
\(183\) | 16.7456 | 1.23787 | ||||||||
\(184\) | 3.97894 | 0.293332 | ||||||||
\(185\) | −0.838467 | −0.0616453 | ||||||||
\(186\) | 7.75941 | 0.568948 | ||||||||
\(187\) | −11.9304 | −0.872441 | ||||||||
\(188\) | 1.54808 | 0.112906 | ||||||||
\(189\) | −2.05927 | −0.149790 | ||||||||
\(190\) | −1.23979 | −0.0899438 | ||||||||
\(191\) | 24.2243 | 1.75281 | 0.876406 | − | 0.481574i | \(-0.159935\pi\) | ||||
0.876406 | + | 0.481574i | \(0.159935\pi\) | |||||||
\(192\) | −8.12792 | −0.586582 | ||||||||
\(193\) | −5.78545 | −0.416446 | −0.208223 | − | 0.978081i | \(-0.566768\pi\) | ||||
−0.208223 | + | 0.978081i | \(0.566768\pi\) | |||||||
\(194\) | 9.82478 | 0.705378 | ||||||||
\(195\) | 1.45488 | 0.104186 | ||||||||
\(196\) | 9.94058 | 0.710042 | ||||||||
\(197\) | 4.06793 | 0.289828 | 0.144914 | − | 0.989444i | \(-0.453709\pi\) | ||||
0.144914 | + | 0.989444i | \(0.453709\pi\) | |||||||
\(198\) | −11.5101 | −0.817989 | ||||||||
\(199\) | −11.4204 | −0.809571 | −0.404785 | − | 0.914412i | \(-0.632654\pi\) | ||||
−0.404785 | + | 0.914412i | \(0.632654\pi\) | |||||||
\(200\) | −12.5777 | −0.889381 | ||||||||
\(201\) | 34.7786 | 2.45310 | ||||||||
\(202\) | −4.67571 | −0.328982 | ||||||||
\(203\) | −1.42599 | −0.100085 | ||||||||
\(204\) | −22.1453 | −1.55048 | ||||||||
\(205\) | −0.404834 | −0.0282748 | ||||||||
\(206\) | −5.88682 | −0.410154 | ||||||||
\(207\) | 9.88084 | 0.686766 | ||||||||
\(208\) | −1.09682 | −0.0760509 | ||||||||
\(209\) | 10.0311 | 0.693866 | ||||||||
\(210\) | 0.174909 | 0.0120699 | ||||||||
\(211\) | 18.0941 | 1.24565 | 0.622824 | − | 0.782362i | \(-0.285985\pi\) | ||||
0.622824 | + | 0.782362i | \(0.285985\pi\) | |||||||
\(212\) | −2.21753 | −0.152301 | ||||||||
\(213\) | 35.0963 | 2.40476 | ||||||||
\(214\) | 6.18913 | 0.423080 | ||||||||
\(215\) | −0.591058 | −0.0403098 | ||||||||
\(216\) | −27.3938 | −1.86391 | ||||||||
\(217\) | 0.650804 | 0.0441794 | ||||||||
\(218\) | 4.02782 | 0.272798 | ||||||||
\(219\) | 2.77189 | 0.187307 | ||||||||
\(220\) | −1.30298 | −0.0878469 | ||||||||
\(221\) | 6.19103 | 0.416454 | ||||||||
\(222\) | −5.04611 | −0.338673 | ||||||||
\(223\) | −21.1665 | −1.41741 | −0.708706 | − | 0.705504i | \(-0.750721\pi\) | ||||
−0.708706 | + | 0.705504i | \(0.750721\pi\) | |||||||
\(224\) | −1.14263 | −0.0763455 | ||||||||
\(225\) | −31.2341 | −2.08227 | ||||||||
\(226\) | 2.72744 | 0.181426 | ||||||||
\(227\) | −13.3828 | −0.888248 | −0.444124 | − | 0.895965i | \(-0.646485\pi\) | ||||
−0.444124 | + | 0.895965i | \(0.646485\pi\) | |||||||
\(228\) | 18.6198 | 1.23312 | ||||||||
\(229\) | −12.5484 | −0.829225 | −0.414612 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414612 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(230\) | −0.448226 | −0.0295552 | ||||||||
\(231\) | −1.41518 | −0.0931122 | ||||||||
\(232\) | −18.9695 | −1.24541 | ||||||||
\(233\) | 15.6538 | 1.02551 | 0.512757 | − | 0.858534i | \(-0.328624\pi\) | ||||
0.512757 | + | 0.858534i | \(0.328624\pi\) | |||||||
\(234\) | 5.97292 | 0.390462 | ||||||||
\(235\) | −0.418665 | −0.0273107 | ||||||||
\(236\) | −21.1963 | −1.37976 | ||||||||
\(237\) | 39.1501 | 2.54307 | ||||||||
\(238\) | 0.744302 | 0.0482459 | ||||||||
\(239\) | 3.45659 | 0.223588 | 0.111794 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111794 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(240\) | −1.06103 | −0.0684891 | ||||||||
\(241\) | 28.7843 | 1.85416 | 0.927080 | − | 0.374864i | \(-0.122311\pi\) | ||||
0.927080 | + | 0.374864i | \(0.122311\pi\) | |||||||
\(242\) | 4.09601 | 0.263301 | ||||||||
\(243\) | −8.68104 | −0.556889 | ||||||||
\(244\) | 7.78249 | 0.498223 | ||||||||
\(245\) | −2.68834 | −0.171752 | ||||||||
\(246\) | −2.43640 | −0.155339 | ||||||||
\(247\) | −5.20541 | −0.331212 | ||||||||
\(248\) | 8.65743 | 0.549747 | ||||||||
\(249\) | −18.7482 | −1.18812 | ||||||||
\(250\) | 2.87731 | 0.181977 | ||||||||
\(251\) | −1.82824 | −0.115397 | −0.0576986 | − | 0.998334i | \(-0.518376\pi\) | ||||
−0.0576986 | + | 0.998334i | \(0.518376\pi\) | |||||||
\(252\) | −1.79195 | −0.112882 | ||||||||
\(253\) | 3.62658 | 0.228001 | ||||||||
\(254\) | 13.4908 | 0.846490 | ||||||||
\(255\) | 5.98900 | 0.375046 | ||||||||
\(256\) | −12.6461 | −0.790380 | ||||||||
\(257\) | 3.65882 | 0.228231 | 0.114116 | − | 0.993467i | \(-0.463597\pi\) | ||||
0.114116 | + | 0.993467i | \(0.463597\pi\) | |||||||
\(258\) | −3.55714 | −0.221458 | ||||||||
\(259\) | −0.423232 | −0.0262983 | ||||||||
\(260\) | 0.676152 | 0.0419332 | ||||||||
\(261\) | −47.1067 | −2.91583 | ||||||||
\(262\) | 9.21630 | 0.569385 | ||||||||
\(263\) | −13.1581 | −0.811362 | −0.405681 | − | 0.914015i | \(-0.632966\pi\) | ||||
−0.405681 | + | 0.914015i | \(0.632966\pi\) | |||||||
\(264\) | −18.8257 | −1.15864 | ||||||||
\(265\) | 0.599712 | 0.0368400 | ||||||||
\(266\) | −0.625807 | −0.0383707 | ||||||||
\(267\) | −19.7987 | −1.21166 | ||||||||
\(268\) | 16.1633 | 0.987332 | ||||||||
\(269\) | −30.0225 | −1.83050 | −0.915251 | − | 0.402885i | \(-0.868008\pi\) | ||||
−0.915251 | + | 0.402885i | \(0.868008\pi\) | |||||||
\(270\) | 3.08590 | 0.187802 | ||||||||
\(271\) | −9.04876 | −0.549673 | −0.274837 | − | 0.961491i | \(-0.588624\pi\) | ||||
−0.274837 | + | 0.961491i | \(0.588624\pi\) | |||||||
\(272\) | −4.51506 | −0.273766 | ||||||||
\(273\) | 0.734377 | 0.0444465 | ||||||||
\(274\) | 10.5149 | 0.635229 | ||||||||
\(275\) | −11.4639 | −0.691300 | ||||||||
\(276\) | 6.73168 | 0.405199 | ||||||||
\(277\) | 10.3482 | 0.621762 | 0.310881 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310881 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(278\) | −3.78148 | −0.226798 | ||||||||
\(279\) | 21.4989 | 1.28710 | ||||||||
\(280\) | 0.195152 | 0.0116625 | ||||||||
\(281\) | −19.3686 | −1.15543 | −0.577716 | − | 0.816238i | \(-0.696056\pi\) | ||||
−0.577716 | + | 0.816238i | \(0.696056\pi\) | |||||||
\(282\) | −2.51964 | −0.150042 | ||||||||
\(283\) | 9.72949 | 0.578358 | 0.289179 | − | 0.957275i | \(-0.406618\pi\) | ||||
0.289179 | + | 0.957275i | \(0.406618\pi\) | |||||||
\(284\) | 16.3109 | 0.967876 | ||||||||
\(285\) | −5.03554 | −0.298280 | ||||||||
\(286\) | 2.19225 | 0.129631 | ||||||||
\(287\) | −0.204347 | −0.0120622 | ||||||||
\(288\) | −37.7462 | −2.22421 | ||||||||
\(289\) | 8.48538 | 0.499140 | ||||||||
\(290\) | 2.13691 | 0.125484 | ||||||||
\(291\) | 39.9044 | 2.33924 | ||||||||
\(292\) | 1.28823 | 0.0753881 | ||||||||
\(293\) | 26.2321 | 1.53249 | 0.766247 | − | 0.642546i | \(-0.222122\pi\) | ||||
0.766247 | + | 0.642546i | \(0.222122\pi\) | |||||||
\(294\) | −16.1791 | −0.943586 | ||||||||
\(295\) | 5.73235 | 0.333750 | ||||||||
\(296\) | −5.63012 | −0.327244 | ||||||||
\(297\) | −24.9679 | −1.44879 | ||||||||
\(298\) | −13.2325 | −0.766540 | ||||||||
\(299\) | −1.88193 | −0.108835 | ||||||||
\(300\) | −21.2793 | −1.22856 | ||||||||
\(301\) | −0.298348 | −0.0171965 | ||||||||
\(302\) | −0.363312 | −0.0209062 | ||||||||
\(303\) | −18.9909 | −1.09100 | ||||||||
\(304\) | 3.79626 | 0.217730 | ||||||||
\(305\) | −2.10470 | −0.120515 | ||||||||
\(306\) | 24.5875 | 1.40557 | ||||||||
\(307\) | −13.7097 | −0.782455 | −0.391228 | − | 0.920294i | \(-0.627950\pi\) | ||||
−0.391228 | + | 0.920294i | \(0.627950\pi\) | |||||||
\(308\) | −0.657704 | −0.0374762 | ||||||||
\(309\) | −23.9099 | −1.36019 | ||||||||
\(310\) | −0.975257 | −0.0553909 | ||||||||
\(311\) | 30.9043 | 1.75242 | 0.876212 | − | 0.481926i | \(-0.160063\pi\) | ||||
0.876212 | + | 0.481926i | \(0.160063\pi\) | |||||||
\(312\) | 9.76918 | 0.553071 | ||||||||
\(313\) | −28.2287 | −1.59558 | −0.797790 | − | 0.602935i | \(-0.793998\pi\) | ||||
−0.797790 | + | 0.602935i | \(0.793998\pi\) | |||||||
\(314\) | −0.0887953 | −0.00501101 | ||||||||
\(315\) | 0.484617 | 0.0273051 | ||||||||
\(316\) | 18.1949 | 1.02355 | ||||||||
\(317\) | −7.55793 | −0.424496 | −0.212248 | − | 0.977216i | \(-0.568078\pi\) | ||||
−0.212248 | + | 0.977216i | \(0.568078\pi\) | |||||||
\(318\) | 3.60922 | 0.202395 | ||||||||
\(319\) | −17.2896 | −0.968034 | ||||||||
\(320\) | 1.02157 | 0.0571077 | ||||||||
\(321\) | 25.1378 | 1.40306 | ||||||||
\(322\) | −0.226251 | −0.0126085 | ||||||||
\(323\) | −21.4281 | −1.19229 | ||||||||
\(324\) | −18.7648 | −1.04249 | ||||||||
\(325\) | 5.94894 | 0.329988 | ||||||||
\(326\) | 9.47583 | 0.524818 | ||||||||
\(327\) | 16.3594 | 0.904678 | ||||||||
\(328\) | −2.71837 | −0.150097 | ||||||||
\(329\) | −0.211329 | −0.0116509 | ||||||||
\(330\) | 2.12071 | 0.116741 | ||||||||
\(331\) | 20.4225 | 1.12252 | 0.561260 | − | 0.827640i | \(-0.310317\pi\) | ||||
0.561260 | + | 0.827640i | \(0.310317\pi\) | |||||||
\(332\) | −8.71322 | −0.478200 | ||||||||
\(333\) | −13.9812 | −0.766164 | ||||||||
\(334\) | 0.562821 | 0.0307962 | ||||||||
\(335\) | −4.37122 | −0.238825 | ||||||||
\(336\) | −0.535574 | −0.0292179 | ||||||||
\(337\) | 16.7603 | 0.912994 | 0.456497 | − | 0.889725i | \(-0.349104\pi\) | ||||
0.456497 | + | 0.889725i | \(0.349104\pi\) | |||||||
\(338\) | 8.69581 | 0.472990 | ||||||||
\(339\) | 11.0778 | 0.601662 | ||||||||
\(340\) | 2.78338 | 0.150950 | ||||||||
\(341\) | 7.89077 | 0.427309 | ||||||||
\(342\) | −20.6731 | −1.11788 | ||||||||
\(343\) | −2.72138 | −0.146941 | ||||||||
\(344\) | −3.96882 | −0.213985 | ||||||||
\(345\) | −1.82052 | −0.0980135 | ||||||||
\(346\) | −8.77994 | −0.472012 | ||||||||
\(347\) | 14.1418 | 0.759171 | 0.379586 | − | 0.925157i | \(-0.376067\pi\) | ||||
0.379586 | + | 0.925157i | \(0.376067\pi\) | |||||||
\(348\) | −32.0931 | −1.72037 | ||||||||
\(349\) | −22.1523 | −1.18579 | −0.592893 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592893 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(350\) | 0.715196 | 0.0382288 | ||||||||
\(351\) | 12.9565 | 0.691568 | ||||||||
\(352\) | −13.8540 | −0.738423 | ||||||||
\(353\) | 17.2209 | 0.916574 | 0.458287 | − | 0.888804i | \(-0.348463\pi\) | ||||
0.458287 | + | 0.888804i | \(0.348463\pi\) | |||||||
\(354\) | 34.4988 | 1.83359 | ||||||||
\(355\) | −4.41114 | −0.234119 | ||||||||
\(356\) | −9.20141 | −0.487674 | ||||||||
\(357\) | 3.02306 | 0.159997 | ||||||||
\(358\) | 16.0341 | 0.847426 | ||||||||
\(359\) | 21.9672 | 1.15938 | 0.579692 | − | 0.814836i | \(-0.303173\pi\) | ||||
0.579692 | + | 0.814836i | \(0.303173\pi\) | |||||||
\(360\) | 6.44671 | 0.339771 | ||||||||
\(361\) | −0.983329 | −0.0517541 | ||||||||
\(362\) | −9.03983 | −0.475123 | ||||||||
\(363\) | 16.6364 | 0.873183 | ||||||||
\(364\) | 0.341300 | 0.0178890 | ||||||||
\(365\) | −0.348390 | −0.0182356 | ||||||||
\(366\) | −12.6667 | −0.662097 | ||||||||
\(367\) | −13.1841 | −0.688202 | −0.344101 | − | 0.938933i | \(-0.611816\pi\) | ||||
−0.344101 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(368\) | 1.37248 | 0.0715452 | ||||||||
\(369\) | −6.75048 | −0.351416 | ||||||||
\(370\) | 0.634231 | 0.0329721 | ||||||||
\(371\) | 0.302716 | 0.0157162 | ||||||||
\(372\) | 14.6469 | 0.759404 | ||||||||
\(373\) | −35.2516 | −1.82526 | −0.912630 | − | 0.408787i | \(-0.865952\pi\) | ||||
−0.912630 | + | 0.408787i | \(0.865952\pi\) | |||||||
\(374\) | 9.02440 | 0.466641 | ||||||||
\(375\) | 11.6865 | 0.603488 | ||||||||
\(376\) | −2.81124 | −0.144979 | ||||||||
\(377\) | 8.97207 | 0.462085 | ||||||||
\(378\) | 1.55767 | 0.0801177 | ||||||||
\(379\) | 23.6003 | 1.21227 | 0.606134 | − | 0.795363i | \(-0.292720\pi\) | ||||
0.606134 | + | 0.795363i | \(0.292720\pi\) | |||||||
\(380\) | −2.34026 | −0.120053 | ||||||||
\(381\) | 54.7945 | 2.80721 | ||||||||
\(382\) | −18.3237 | −0.937522 | ||||||||
\(383\) | −13.1311 | −0.670970 | −0.335485 | − | 0.942046i | \(-0.608900\pi\) | ||||
−0.335485 | + | 0.942046i | \(0.608900\pi\) | |||||||
\(384\) | −29.8728 | −1.52444 | ||||||||
\(385\) | 0.177870 | 0.00906509 | ||||||||
\(386\) | 4.37622 | 0.222744 | ||||||||
\(387\) | −9.85572 | −0.500994 | ||||||||
\(388\) | 18.5455 | 0.941505 | ||||||||
\(389\) | 29.2216 | 1.48159 | 0.740797 | − | 0.671729i | \(-0.234448\pi\) | ||||
0.740797 | + | 0.671729i | \(0.234448\pi\) | |||||||
\(390\) | −1.10049 | −0.0557257 | ||||||||
\(391\) | −7.74697 | −0.391781 | ||||||||
\(392\) | −18.0516 | −0.911743 | ||||||||
\(393\) | 37.4330 | 1.88824 | ||||||||
\(394\) | −3.07706 | −0.155020 | ||||||||
\(395\) | −4.92065 | −0.247585 | ||||||||
\(396\) | −21.7268 | −1.09181 | ||||||||
\(397\) | 26.2129 | 1.31559 | 0.657795 | − | 0.753197i | \(-0.271489\pi\) | ||||
0.657795 | + | 0.753197i | \(0.271489\pi\) | |||||||
\(398\) | 8.63859 | 0.433013 | ||||||||
\(399\) | −2.54178 | −0.127248 | ||||||||
\(400\) | −4.33850 | −0.216925 | ||||||||
\(401\) | −24.3910 | −1.21803 | −0.609014 | − | 0.793160i | \(-0.708435\pi\) | ||||
−0.609014 | + | 0.793160i | \(0.708435\pi\) | |||||||
\(402\) | −26.3072 | −1.31208 | ||||||||
\(403\) | −4.09473 | −0.203973 | ||||||||
\(404\) | −8.82599 | −0.439110 | ||||||||
\(405\) | 5.07476 | 0.252167 | ||||||||
\(406\) | 1.07864 | 0.0535322 | ||||||||
\(407\) | −5.13154 | −0.254361 | ||||||||
\(408\) | 40.2148 | 1.99093 | ||||||||
\(409\) | 13.2071 | 0.653051 | 0.326526 | − | 0.945188i | \(-0.394122\pi\) | ||||
0.326526 | + | 0.945188i | \(0.394122\pi\) | |||||||
\(410\) | 0.306223 | 0.0151233 | ||||||||
\(411\) | 42.7074 | 2.10660 | ||||||||
\(412\) | −11.1121 | −0.547454 | ||||||||
\(413\) | 2.89351 | 0.142380 | ||||||||
\(414\) | −7.47404 | −0.367329 | ||||||||
\(415\) | 2.35641 | 0.115672 | ||||||||
\(416\) | 7.18924 | 0.352481 | ||||||||
\(417\) | −15.3589 | −0.752129 | ||||||||
\(418\) | −7.58770 | −0.371126 | ||||||||
\(419\) | 15.8597 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(420\) | 0.330163 | 0.0161103 | ||||||||
\(421\) | −4.53957 | −0.221245 | −0.110622 | − | 0.993863i | \(-0.535284\pi\) | ||||
−0.110622 | + | 0.993863i | \(0.535284\pi\) | |||||||
\(422\) | −13.6867 | −0.666257 | ||||||||
\(423\) | −6.98111 | −0.339433 | ||||||||
\(424\) | 4.02693 | 0.195565 | ||||||||
\(425\) | 24.4888 | 1.18788 | ||||||||
\(426\) | −26.5474 | −1.28623 | ||||||||
\(427\) | −1.06239 | −0.0514126 | ||||||||
\(428\) | 11.6828 | 0.564708 | ||||||||
\(429\) | 8.90406 | 0.429892 | ||||||||
\(430\) | 0.447087 | 0.0215604 | ||||||||
\(431\) | −24.0460 | −1.15825 | −0.579126 | − | 0.815238i | \(-0.696606\pi\) | ||||
−0.579126 | + | 0.815238i | \(0.696606\pi\) | |||||||
\(432\) | −9.44907 | −0.454619 | ||||||||
\(433\) | −20.8069 | −0.999914 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(434\) | −0.492279 | −0.0236302 | ||||||||
\(435\) | 8.67928 | 0.416140 | ||||||||
\(436\) | 7.60301 | 0.364118 | ||||||||
\(437\) | 6.51364 | 0.311590 | ||||||||
\(438\) | −2.09671 | −0.100185 | ||||||||
\(439\) | −27.0822 | −1.29256 | −0.646282 | − | 0.763098i | \(-0.723677\pi\) | ||||
−0.646282 | + | 0.763098i | \(0.723677\pi\) | |||||||
\(440\) | 2.36615 | 0.112802 | ||||||||
\(441\) | −44.8273 | −2.13463 | ||||||||
\(442\) | −4.68301 | −0.222748 | ||||||||
\(443\) | 26.1108 | 1.24056 | 0.620282 | − | 0.784379i | \(-0.287018\pi\) | ||||
0.620282 | + | 0.784379i | \(0.287018\pi\) | |||||||
\(444\) | −9.52517 | −0.452045 | ||||||||
\(445\) | 2.48844 | 0.117963 | ||||||||
\(446\) | 16.0107 | 0.758129 | ||||||||
\(447\) | −53.7454 | −2.54207 | ||||||||
\(448\) | 0.515658 | 0.0243626 | ||||||||
\(449\) | 18.4224 | 0.869407 | 0.434703 | − | 0.900574i | \(-0.356853\pi\) | ||||
0.434703 | + | 0.900574i | \(0.356853\pi\) | |||||||
\(450\) | 23.6260 | 1.11374 | ||||||||
\(451\) | −2.47764 | −0.116668 | ||||||||
\(452\) | 5.14838 | 0.242159 | ||||||||
\(453\) | −1.47563 | −0.0693311 | ||||||||
\(454\) | 10.1230 | 0.475095 | ||||||||
\(455\) | −0.0923016 | −0.00432716 | ||||||||
\(456\) | −33.8125 | −1.58342 | ||||||||
\(457\) | −3.55147 | −0.166131 | −0.0830654 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830654 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(458\) | 9.49186 | 0.443526 | ||||||||
\(459\) | 53.3355 | 2.48949 | ||||||||
\(460\) | −0.846084 | −0.0394489 | ||||||||
\(461\) | −2.86665 | −0.133513 | −0.0667565 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667565 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(462\) | 1.07047 | 0.0498027 | ||||||||
\(463\) | 30.5287 | 1.41879 | 0.709395 | − | 0.704811i | \(-0.248968\pi\) | ||||
0.709395 | + | 0.704811i | \(0.248968\pi\) | |||||||
\(464\) | −6.54324 | −0.303762 | ||||||||
\(465\) | −3.96111 | −0.183692 | ||||||||
\(466\) | −11.8408 | −0.548515 | ||||||||
\(467\) | 18.7000 | 0.865332 | 0.432666 | − | 0.901554i | \(-0.357573\pi\) | ||||
0.432666 | + | 0.901554i | \(0.357573\pi\) | |||||||
\(468\) | 11.2746 | 0.521170 | ||||||||
\(469\) | −2.20646 | −0.101885 | ||||||||
\(470\) | 0.316685 | 0.0146076 | ||||||||
\(471\) | −0.360652 | −0.0166179 | ||||||||
\(472\) | 38.4914 | 1.77171 | ||||||||
\(473\) | −3.61736 | −0.166326 | ||||||||
\(474\) | −29.6138 | −1.36021 | ||||||||
\(475\) | −20.5901 | −0.944740 | ||||||||
\(476\) | 1.40496 | 0.0643964 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | −2.61463 | −0.119590 | ||||||||
\(479\) | 7.50976 | 0.343130 | 0.171565 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171565 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(480\) | 6.95463 | 0.317434 | ||||||||
\(481\) | 2.66289 | 0.121418 | ||||||||
\(482\) | −21.7729 | −0.991730 | ||||||||
\(483\) | −0.918941 | −0.0418133 | ||||||||
\(484\) | 7.73173 | 0.351442 | ||||||||
\(485\) | −5.01546 | −0.227740 | ||||||||
\(486\) | 6.56649 | 0.297862 | ||||||||
\(487\) | 32.6786 | 1.48081 | 0.740404 | − | 0.672162i | \(-0.234634\pi\) | ||||
0.740404 | + | 0.672162i | \(0.234634\pi\) | |||||||
\(488\) | −14.1326 | −0.639753 | ||||||||
\(489\) | 38.4871 | 1.74045 | ||||||||
\(490\) | 2.03351 | 0.0918644 | ||||||||
\(491\) | 2.81716 | 0.127137 | 0.0635683 | − | 0.997977i | \(-0.479752\pi\) | ||||
0.0635683 | + | 0.997977i | \(0.479752\pi\) | |||||||
\(492\) | −4.59901 | −0.207339 | ||||||||
\(493\) | 36.9335 | 1.66340 | ||||||||
\(494\) | 3.93746 | 0.177155 | ||||||||
\(495\) | 5.87582 | 0.264098 | ||||||||
\(496\) | 2.98625 | 0.134087 | ||||||||
\(497\) | −2.22661 | −0.0998770 | ||||||||
\(498\) | 14.1815 | 0.635488 | ||||||||
\(499\) | 29.0591 | 1.30086 | 0.650432 | − | 0.759564i | \(-0.274588\pi\) | ||||
0.650432 | + | 0.759564i | \(0.274588\pi\) | |||||||
\(500\) | 5.43128 | 0.242894 | ||||||||
\(501\) | 2.28596 | 0.102129 | ||||||||
\(502\) | 1.38291 | 0.0617223 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 3.25410 | 0.144949 | ||||||||
\(505\) | 2.38691 | 0.106216 | ||||||||
\(506\) | −2.74321 | −0.121951 | ||||||||
\(507\) | 35.3189 | 1.56857 | ||||||||
\(508\) | 25.4656 | 1.12986 | ||||||||
\(509\) | 7.58042 | 0.335996 | 0.167998 | − | 0.985787i | \(-0.446270\pi\) | ||||
0.167998 | + | 0.985787i | \(0.446270\pi\) | |||||||
\(510\) | −4.53018 | −0.200600 | ||||||||
\(511\) | −0.175857 | −0.00777944 | ||||||||
\(512\) | −9.88103 | −0.436684 | ||||||||
\(513\) | −44.8444 | −1.97993 | ||||||||
\(514\) | −2.76760 | −0.122074 | ||||||||
\(515\) | 3.00517 | 0.132423 | ||||||||
\(516\) | −6.71456 | −0.295592 | ||||||||
\(517\) | −2.56229 | −0.112689 | ||||||||
\(518\) | 0.320140 | 0.0140661 | ||||||||
\(519\) | −35.6607 | −1.56533 | ||||||||
\(520\) | −1.22786 | −0.0538451 | ||||||||
\(521\) | −8.90148 | −0.389981 | −0.194990 | − | 0.980805i | \(-0.562468\pi\) | ||||
−0.194990 | + | 0.980805i | \(0.562468\pi\) | |||||||
\(522\) | 35.6323 | 1.55958 | ||||||||
\(523\) | 37.7311 | 1.64986 | 0.824932 | − | 0.565232i | \(-0.191213\pi\) | ||||
0.824932 | + | 0.565232i | \(0.191213\pi\) | |||||||
\(524\) | 17.3969 | 0.759988 | ||||||||
\(525\) | 2.90484 | 0.126778 | ||||||||
\(526\) | 9.95301 | 0.433972 | ||||||||
\(527\) | −16.8560 | −0.734257 | ||||||||
\(528\) | −6.49365 | −0.282600 | ||||||||
\(529\) | −20.6451 | −0.897613 | ||||||||
\(530\) | −0.453632 | −0.0197045 | ||||||||
\(531\) | 95.5852 | 4.14804 | ||||||||
\(532\) | −1.18129 | −0.0512154 | ||||||||
\(533\) | 1.28572 | 0.0556905 | ||||||||
\(534\) | 14.9761 | 0.648078 | ||||||||
\(535\) | −3.15950 | −0.136597 | ||||||||
\(536\) | −29.3518 | −1.26780 | ||||||||
\(537\) | 65.1240 | 2.81031 | ||||||||
\(538\) | 22.7095 | 0.979076 | ||||||||
\(539\) | −16.4530 | −0.708682 | ||||||||
\(540\) | 5.82503 | 0.250669 | ||||||||
\(541\) | 11.6293 | 0.499981 | 0.249990 | − | 0.968248i | \(-0.419573\pi\) | ||||
0.249990 | + | 0.968248i | \(0.419573\pi\) | |||||||
\(542\) | 6.84464 | 0.294003 | ||||||||
\(543\) | −36.7162 | −1.57564 | ||||||||
\(544\) | 29.5945 | 1.26885 | ||||||||
\(545\) | −2.05616 | −0.0880764 | ||||||||
\(546\) | −0.555495 | −0.0237730 | ||||||||
\(547\) | −13.4958 | −0.577040 | −0.288520 | − | 0.957474i | \(-0.593163\pi\) | ||||
−0.288520 | + | 0.957474i | \(0.593163\pi\) | |||||||
\(548\) | 19.8482 | 0.847874 | ||||||||
\(549\) | −35.0953 | −1.49783 | ||||||||
\(550\) | 8.67150 | 0.369754 | ||||||||
\(551\) | −31.0536 | −1.32293 | ||||||||
\(552\) | −12.2244 | −0.520304 | ||||||||
\(553\) | −2.48379 | −0.105622 | ||||||||
\(554\) | −7.82754 | −0.332560 | ||||||||
\(555\) | 2.57599 | 0.109345 | ||||||||
\(556\) | −7.13803 | −0.302720 | ||||||||
\(557\) | −34.2002 | −1.44911 | −0.724554 | − | 0.689218i | \(-0.757954\pi\) | ||||
−0.724554 | + | 0.689218i | \(0.757954\pi\) | |||||||
\(558\) | −16.2621 | −0.688430 | ||||||||
\(559\) | 1.87715 | 0.0793949 | ||||||||
\(560\) | 0.0673146 | 0.00284456 | ||||||||
\(561\) | 36.6536 | 1.54751 | ||||||||
\(562\) | 14.6507 | 0.618003 | ||||||||
\(563\) | 25.6005 | 1.07893 | 0.539467 | − | 0.842007i | \(-0.318626\pi\) | ||||
0.539467 | + | 0.842007i | \(0.318626\pi\) | |||||||
\(564\) | −4.75613 | −0.200269 | ||||||||
\(565\) | −1.39233 | −0.0585758 | ||||||||
\(566\) | −7.35956 | −0.309345 | ||||||||
\(567\) | 2.56158 | 0.107576 | ||||||||
\(568\) | −29.6199 | −1.24282 | ||||||||
\(569\) | −17.2311 | −0.722363 | −0.361182 | − | 0.932495i | \(-0.617627\pi\) | ||||
−0.361182 | + | 0.932495i | \(0.617627\pi\) | |||||||
\(570\) | 3.80897 | 0.159540 | ||||||||
\(571\) | 2.79325 | 0.116894 | 0.0584470 | − | 0.998291i | \(-0.481385\pi\) | ||||
0.0584470 | + | 0.998291i | \(0.481385\pi\) | |||||||
\(572\) | 4.13815 | 0.173025 | ||||||||
\(573\) | −74.4237 | −3.10909 | ||||||||
\(574\) | 0.154572 | 0.00645171 | ||||||||
\(575\) | −7.44403 | −0.310438 | ||||||||
\(576\) | 17.0344 | 0.709768 | ||||||||
\(577\) | −40.1143 | −1.66998 | −0.834991 | − | 0.550264i | \(-0.814527\pi\) | ||||
−0.834991 | + | 0.550264i | \(0.814527\pi\) | |||||||
\(578\) | −6.41849 | −0.266974 | ||||||||
\(579\) | 17.7745 | 0.738682 | ||||||||
\(580\) | 4.03368 | 0.167490 | ||||||||
\(581\) | 1.18944 | 0.0493464 | ||||||||
\(582\) | −30.1844 | −1.25118 | ||||||||
\(583\) | 3.67032 | 0.152009 | ||||||||
\(584\) | −2.33936 | −0.0968036 | ||||||||
\(585\) | −3.04912 | −0.126066 | ||||||||
\(586\) | −19.8424 | −0.819682 | ||||||||
\(587\) | −38.5445 | −1.59090 | −0.795451 | − | 0.606018i | \(-0.792766\pi\) | ||||
−0.795451 | + | 0.606018i | \(0.792766\pi\) | |||||||
\(588\) | −30.5402 | −1.25945 | ||||||||
\(589\) | 14.1725 | 0.583966 | ||||||||
\(590\) | −4.33605 | −0.178512 | ||||||||
\(591\) | −12.4978 | −0.514090 | ||||||||
\(592\) | −1.94202 | −0.0798167 | ||||||||
\(593\) | −25.0372 | −1.02816 | −0.514078 | − | 0.857744i | \(-0.671866\pi\) | ||||
−0.514078 | + | 0.857744i | \(0.671866\pi\) | |||||||
\(594\) | 18.8862 | 0.774909 | ||||||||
\(595\) | −0.379959 | −0.0155768 | ||||||||
\(596\) | −24.9781 | −1.02314 | ||||||||
\(597\) | 35.0865 | 1.43600 | ||||||||
\(598\) | 1.42353 | 0.0582123 | ||||||||
\(599\) | −23.0220 | −0.940655 | −0.470328 | − | 0.882492i | \(-0.655864\pi\) | ||||
−0.470328 | + | 0.882492i | \(0.655864\pi\) | |||||||
\(600\) | 38.6422 | 1.57756 | ||||||||
\(601\) | −33.9451 | −1.38465 | −0.692326 | − | 0.721585i | \(-0.743414\pi\) | ||||
−0.692326 | + | 0.721585i | \(0.743414\pi\) | |||||||
\(602\) | 0.225675 | 0.00919784 | ||||||||
\(603\) | −72.8888 | −2.96826 | ||||||||
\(604\) | −0.685796 | −0.0279046 | ||||||||
\(605\) | −2.09097 | −0.0850102 | ||||||||
\(606\) | 14.3650 | 0.583540 | ||||||||
\(607\) | 24.3039 | 0.986467 | 0.493233 | − | 0.869897i | \(-0.335815\pi\) | ||||
0.493233 | + | 0.869897i | \(0.335815\pi\) | |||||||
\(608\) | −24.8830 | −1.00914 | ||||||||
\(609\) | 4.38103 | 0.177528 | ||||||||
\(610\) | 1.59203 | 0.0644595 | ||||||||
\(611\) | 1.32964 | 0.0537916 | ||||||||
\(612\) | 46.4120 | 1.87609 | ||||||||
\(613\) | 34.5604 | 1.39588 | 0.697940 | − | 0.716156i | \(-0.254100\pi\) | ||||
0.697940 | + | 0.716156i | \(0.254100\pi\) | |||||||
\(614\) | 10.3703 | 0.418510 | ||||||||
\(615\) | 1.24376 | 0.0501532 | ||||||||
\(616\) | 1.19436 | 0.0481220 | ||||||||
\(617\) | 34.3607 | 1.38331 | 0.691655 | − | 0.722228i | \(-0.256882\pi\) | ||||
0.691655 | + | 0.722228i | \(0.256882\pi\) | |||||||
\(618\) | 18.0859 | 0.727521 | ||||||||
\(619\) | 1.08451 | 0.0435902 | 0.0217951 | − | 0.999762i | \(-0.493062\pi\) | ||||
0.0217951 | + | 0.999762i | \(0.493062\pi\) | |||||||
\(620\) | −1.84092 | −0.0739331 | ||||||||
\(621\) | −16.2128 | −0.650597 | ||||||||
\(622\) | −23.3766 | −0.937315 | ||||||||
\(623\) | 1.25609 | 0.0503240 | ||||||||
\(624\) | 3.36973 | 0.134897 | ||||||||
\(625\) | 22.7856 | 0.911425 | ||||||||
\(626\) | 21.3527 | 0.853425 | ||||||||
\(627\) | −30.8182 | −1.23076 | ||||||||
\(628\) | −0.167612 | −0.00668846 | ||||||||
\(629\) | 10.9618 | 0.437076 | ||||||||
\(630\) | −0.366573 | −0.0146046 | ||||||||
\(631\) | −6.03426 | −0.240220 | −0.120110 | − | 0.992761i | \(-0.538325\pi\) | ||||
−0.120110 | + | 0.992761i | \(0.538325\pi\) | |||||||
\(632\) | −33.0411 | −1.31430 | ||||||||
\(633\) | −55.5899 | −2.20950 | ||||||||
\(634\) | 5.71695 | 0.227049 | ||||||||
\(635\) | −6.88695 | −0.273300 | ||||||||
\(636\) | 6.81286 | 0.270148 | ||||||||
\(637\) | 8.53792 | 0.338285 | ||||||||
\(638\) | 13.0782 | 0.517770 | ||||||||
\(639\) | −73.5545 | −2.90977 | ||||||||
\(640\) | 3.75462 | 0.148414 | ||||||||
\(641\) | −22.0716 | −0.871778 | −0.435889 | − | 0.900001i | \(-0.643566\pi\) | ||||
−0.435889 | + | 0.900001i | \(0.643566\pi\) | |||||||
\(642\) | −19.0147 | −0.750450 | ||||||||
\(643\) | −40.6373 | −1.60258 | −0.801290 | − | 0.598277i | \(-0.795852\pi\) | ||||
−0.801290 | + | 0.598277i | \(0.795852\pi\) | |||||||
\(644\) | −0.427077 | −0.0168292 | ||||||||
\(645\) | 1.81589 | 0.0715006 | ||||||||
\(646\) | 16.2086 | 0.637717 | ||||||||
\(647\) | 22.9719 | 0.903118 | 0.451559 | − | 0.892241i | \(-0.350868\pi\) | ||||
0.451559 | + | 0.892241i | \(0.350868\pi\) | |||||||
\(648\) | 34.0759 | 1.33863 | ||||||||
\(649\) | 35.0828 | 1.37712 | ||||||||
\(650\) | −4.49988 | −0.176500 | ||||||||
\(651\) | −1.99944 | −0.0783644 | ||||||||
\(652\) | 17.8868 | 0.700502 | ||||||||
\(653\) | −39.0459 | −1.52798 | −0.763992 | − | 0.645226i | \(-0.776763\pi\) | ||||
−0.763992 | + | 0.645226i | \(0.776763\pi\) | |||||||
\(654\) | −12.3745 | −0.483883 | ||||||||
\(655\) | −4.70483 | −0.183833 | ||||||||
\(656\) | −0.937660 | −0.0366095 | ||||||||
\(657\) | −5.80931 | −0.226643 | ||||||||
\(658\) | 0.159853 | 0.00623172 | ||||||||
\(659\) | −26.6054 | −1.03640 | −0.518199 | − | 0.855260i | \(-0.673397\pi\) | ||||
−0.518199 | + | 0.855260i | \(0.673397\pi\) | |||||||
\(660\) | 4.00311 | 0.155821 | ||||||||
\(661\) | −39.3661 | −1.53116 | −0.765582 | − | 0.643338i | \(-0.777549\pi\) | ||||
−0.765582 | + | 0.643338i | \(0.777549\pi\) | |||||||
\(662\) | −15.4479 | −0.600400 | ||||||||
\(663\) | −19.0205 | −0.738696 | ||||||||
\(664\) | 15.8228 | 0.614042 | ||||||||
\(665\) | 0.319469 | 0.0123885 | ||||||||
\(666\) | 10.5756 | 0.409796 | ||||||||
\(667\) | −11.2269 | −0.434709 | ||||||||
\(668\) | 1.06239 | 0.0411053 | ||||||||
\(669\) | 65.0291 | 2.51417 | ||||||||
\(670\) | 3.30647 | 0.127740 | ||||||||
\(671\) | −12.8811 | −0.497269 | ||||||||
\(672\) | 3.51048 | 0.135420 | ||||||||
\(673\) | −13.4145 | −0.517090 | −0.258545 | − | 0.965999i | \(-0.583243\pi\) | ||||
−0.258545 | + | 0.965999i | \(0.583243\pi\) | |||||||
\(674\) | −12.6778 | −0.488331 | ||||||||
\(675\) | 51.2499 | 1.97261 | ||||||||
\(676\) | 16.4144 | 0.631324 | ||||||||
\(677\) | −2.13435 | −0.0820299 | −0.0410149 | − | 0.999159i | \(-0.513059\pi\) | ||||
−0.0410149 | + | 0.999159i | \(0.513059\pi\) | |||||||
\(678\) | −8.37942 | −0.321810 | ||||||||
\(679\) | −2.53165 | −0.0971557 | ||||||||
\(680\) | −5.05448 | −0.193830 | ||||||||
\(681\) | 41.1156 | 1.57555 | ||||||||
\(682\) | −5.96871 | −0.228554 | ||||||||
\(683\) | 21.3544 | 0.817105 | 0.408552 | − | 0.912735i | \(-0.366034\pi\) | ||||
0.408552 | + | 0.912735i | \(0.366034\pi\) | |||||||
\(684\) | −39.0231 | −1.49209 | ||||||||
\(685\) | −5.36777 | −0.205092 | ||||||||
\(686\) | 2.05850 | 0.0785940 | ||||||||
\(687\) | 38.5522 | 1.47086 | ||||||||
\(688\) | −1.36899 | −0.0521921 | ||||||||
\(689\) | −1.90463 | −0.0725606 | ||||||||
\(690\) | 1.37707 | 0.0524242 | ||||||||
\(691\) | 13.8167 | 0.525614 | 0.262807 | − | 0.964848i | \(-0.415352\pi\) | ||||
0.262807 | + | 0.964848i | \(0.415352\pi\) | |||||||
\(692\) | −16.5732 | −0.630020 | ||||||||
\(693\) | 2.96593 | 0.112666 | ||||||||
\(694\) | −10.6971 | −0.406056 | ||||||||
\(695\) | 1.93041 | 0.0732247 | ||||||||
\(696\) | 58.2794 | 2.20908 | ||||||||
\(697\) | 5.29265 | 0.200473 | ||||||||
\(698\) | 16.7564 | 0.634238 | ||||||||
\(699\) | −48.0927 | −1.81903 | ||||||||
\(700\) | 1.35002 | 0.0510260 | ||||||||
\(701\) | 45.1209 | 1.70419 | 0.852097 | − | 0.523385i | \(-0.175331\pi\) | ||||
0.852097 | + | 0.523385i | \(0.175331\pi\) | |||||||
\(702\) | −9.80054 | −0.369898 | ||||||||
\(703\) | −9.21666 | −0.347613 | ||||||||
\(704\) | 6.25217 | 0.235638 | ||||||||
\(705\) | 1.28625 | 0.0484430 | ||||||||
\(706\) | −13.0262 | −0.490246 | ||||||||
\(707\) | 1.20484 | 0.0453126 | ||||||||
\(708\) | 65.1208 | 2.44739 | ||||||||
\(709\) | −37.6350 | −1.41341 | −0.706706 | − | 0.707507i | \(-0.749820\pi\) | ||||
−0.706706 | + | 0.707507i | \(0.749820\pi\) | |||||||
\(710\) | 3.33667 | 0.125223 | ||||||||
\(711\) | −82.0505 | −3.07713 | ||||||||
\(712\) | 16.7093 | 0.626208 | ||||||||
\(713\) | 5.12383 | 0.191889 | ||||||||
\(714\) | −2.28670 | −0.0855774 | ||||||||
\(715\) | −1.11912 | −0.0418529 | ||||||||
\(716\) | 30.2663 | 1.13110 | ||||||||
\(717\) | −10.6196 | −0.396596 | ||||||||
\(718\) | −16.6164 | −0.620117 | ||||||||
\(719\) | −34.9860 | −1.30476 | −0.652380 | − | 0.757892i | \(-0.726229\pi\) | ||||
−0.652380 | + | 0.757892i | \(0.726229\pi\) | |||||||
\(720\) | 2.22369 | 0.0828722 | ||||||||
\(721\) | 1.51691 | 0.0564929 | ||||||||
\(722\) | 0.743807 | 0.0276816 | ||||||||
\(723\) | −88.4331 | −3.28886 | ||||||||
\(724\) | −17.0638 | −0.634171 | ||||||||
\(725\) | 35.4892 | 1.31804 | ||||||||
\(726\) | −12.5840 | −0.467038 | ||||||||
\(727\) | 0.0594046 | 0.00220319 | 0.00110160 | − | 0.999999i | \(-0.499649\pi\) | ||||
0.00110160 | + | 0.999999i | \(0.499649\pi\) | |||||||
\(728\) | −0.619784 | −0.0229707 | ||||||||
\(729\) | −12.7559 | −0.472440 | ||||||||
\(730\) | 0.263529 | 0.00975363 | ||||||||
\(731\) | 7.72727 | 0.285804 | ||||||||
\(732\) | −23.9099 | −0.883736 | ||||||||
\(733\) | −23.6914 | −0.875060 | −0.437530 | − | 0.899204i | \(-0.644147\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(734\) | 9.97265 | 0.368097 | ||||||||
\(735\) | 8.25930 | 0.304649 | ||||||||
\(736\) | −8.99605 | −0.331599 | ||||||||
\(737\) | −26.7525 | −0.985441 | ||||||||
\(738\) | 5.10618 | 0.187961 | ||||||||
\(739\) | −13.2539 | −0.487551 | −0.243776 | − | 0.969832i | \(-0.578386\pi\) | ||||
−0.243776 | + | 0.969832i | \(0.578386\pi\) | |||||||
\(740\) | 1.19719 | 0.0440096 | ||||||||
\(741\) | 15.9924 | 0.587496 | ||||||||
\(742\) | −0.228979 | −0.00840610 | ||||||||
\(743\) | −13.7983 | −0.506210 | −0.253105 | − | 0.967439i | \(-0.581452\pi\) | ||||
−0.253105 | + | 0.967439i | \(0.581452\pi\) | |||||||
\(744\) | −26.5980 | −0.975129 | ||||||||
\(745\) | 6.75509 | 0.247487 | ||||||||
\(746\) | 26.6649 | 0.976273 | ||||||||
\(747\) | 39.2924 | 1.43763 | ||||||||
\(748\) | 17.0347 | 0.622850 | ||||||||
\(749\) | −1.59481 | −0.0582733 | ||||||||
\(750\) | −8.83987 | −0.322786 | ||||||||
\(751\) | 3.82043 | 0.139410 | 0.0697048 | − | 0.997568i | \(-0.477794\pi\) | ||||
0.0697048 | + | 0.997568i | \(0.477794\pi\) | |||||||
\(752\) | −0.969695 | −0.0353611 | ||||||||
\(753\) | 5.61683 | 0.204689 | ||||||||
\(754\) | −6.78663 | −0.247154 | ||||||||
\(755\) | 0.185467 | 0.00674984 | ||||||||
\(756\) | 2.94029 | 0.106937 | ||||||||
\(757\) | 19.6215 | 0.713157 | 0.356578 | − | 0.934265i | \(-0.383943\pi\) | ||||
0.356578 | + | 0.934265i | \(0.383943\pi\) | |||||||
\(758\) | −17.8517 | −0.648403 | ||||||||
\(759\) | −11.1418 | −0.404423 | ||||||||
\(760\) | 4.24979 | 0.154156 | ||||||||
\(761\) | 47.5141 | 1.72238 | 0.861192 | − | 0.508280i | \(-0.169719\pi\) | ||||
0.861192 | + | 0.508280i | \(0.169719\pi\) | |||||||
\(762\) | −41.4475 | −1.50148 | ||||||||
\(763\) | −1.03789 | −0.0375741 | ||||||||
\(764\) | −34.5883 | −1.25136 | ||||||||
\(765\) | −12.5517 | −0.453808 | ||||||||
\(766\) | 9.93262 | 0.358880 | ||||||||
\(767\) | −18.2054 | −0.657360 | ||||||||
\(768\) | 38.8521 | 1.40196 | ||||||||
\(769\) | −10.0139 | −0.361111 | −0.180556 | − | 0.983565i | \(-0.557790\pi\) | ||||
−0.180556 | + | 0.983565i | \(0.557790\pi\) | |||||||
\(770\) | −0.134544 | −0.00484863 | ||||||||
\(771\) | −11.2409 | −0.404831 | ||||||||
\(772\) | 8.26066 | 0.297308 | ||||||||
\(773\) | −35.8956 | −1.29108 | −0.645538 | − | 0.763728i | \(-0.723367\pi\) | ||||
−0.645538 | + | 0.763728i | \(0.723367\pi\) | |||||||
\(774\) | 7.45504 | 0.267966 | ||||||||
\(775\) | −16.1968 | −0.581807 | ||||||||
\(776\) | −33.6777 | −1.20896 | ||||||||
\(777\) | 1.30028 | 0.0466474 | ||||||||
\(778\) | −22.1037 | −0.792457 | ||||||||
\(779\) | −4.45005 | −0.159439 | ||||||||
\(780\) | −2.07732 | −0.0743800 | ||||||||
\(781\) | −26.9968 | −0.966023 | ||||||||
\(782\) | 5.85995 | 0.209551 | ||||||||
\(783\) | 77.2940 | 2.76226 | ||||||||
\(784\) | −6.22662 | −0.222379 | ||||||||
\(785\) | 0.0453292 | 0.00161787 | ||||||||
\(786\) | −28.3149 | −1.00996 | ||||||||
\(787\) | 1.89211 | 0.0674464 | 0.0337232 | − | 0.999431i | \(-0.489264\pi\) | ||||
0.0337232 | + | 0.999431i | \(0.489264\pi\) | |||||||
\(788\) | −5.80833 | −0.206913 | ||||||||
\(789\) | 40.4252 | 1.43917 | ||||||||
\(790\) | 3.72207 | 0.132425 | ||||||||
\(791\) | −0.702806 | −0.0249889 | ||||||||
\(792\) | 39.4548 | 1.40197 | ||||||||
\(793\) | 6.68434 | 0.237368 | ||||||||
\(794\) | −19.8279 | −0.703667 | ||||||||
\(795\) | −1.84248 | −0.0653459 | ||||||||
\(796\) | 16.3064 | 0.577966 | ||||||||
\(797\) | 24.4028 | 0.864393 | 0.432197 | − | 0.901779i | \(-0.357739\pi\) | ||||
0.432197 | + | 0.901779i | \(0.357739\pi\) | |||||||
\(798\) | 1.92265 | 0.0680610 | ||||||||
\(799\) | 5.47347 | 0.193637 | ||||||||
\(800\) | 28.4372 | 1.00541 | ||||||||
\(801\) | 41.4940 | 1.46612 | ||||||||
\(802\) | 18.4498 | 0.651484 | ||||||||
\(803\) | −2.13220 | −0.0752437 | ||||||||
\(804\) | −49.6581 | −1.75131 | ||||||||
\(805\) | 0.115499 | 0.00407080 | ||||||||
\(806\) | 3.09733 | 0.109099 | ||||||||
\(807\) | 92.2371 | 3.24690 | ||||||||
\(808\) | 16.0276 | 0.563848 | ||||||||
\(809\) | −32.9341 | −1.15790 | −0.578951 | − | 0.815363i | \(-0.696538\pi\) | ||||
−0.578951 | + | 0.815363i | \(0.696538\pi\) | |||||||
\(810\) | −3.83863 | −0.134876 | ||||||||
\(811\) | −42.8145 | −1.50342 | −0.751711 | − | 0.659493i | \(-0.770771\pi\) | ||||
−0.751711 | + | 0.659493i | \(0.770771\pi\) | |||||||
\(812\) | 2.03608 | 0.0714523 | ||||||||
\(813\) | 27.8002 | 0.974997 | ||||||||
\(814\) | 3.88158 | 0.136049 | ||||||||
\(815\) | −4.83732 | −0.169444 | ||||||||
\(816\) | 13.8715 | 0.485599 | ||||||||
\(817\) | −6.49708 | −0.227304 | ||||||||
\(818\) | −9.99011 | −0.349296 | ||||||||
\(819\) | −1.53910 | −0.0537805 | ||||||||
\(820\) | 0.578035 | 0.0201859 | ||||||||
\(821\) | −28.2632 | −0.986393 | −0.493196 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493196 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(822\) | −32.3046 | −1.12675 | ||||||||
\(823\) | 10.4127 | 0.362962 | 0.181481 | − | 0.983394i | \(-0.441911\pi\) | ||||
0.181481 | + | 0.983394i | \(0.441911\pi\) | |||||||
\(824\) | 20.1790 | 0.702970 | ||||||||
\(825\) | 35.2202 | 1.22621 | ||||||||
\(826\) | −2.18870 | −0.0761547 | ||||||||
\(827\) | −0.0841446 | −0.00292600 | −0.00146300 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146300 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(828\) | −14.1082 | −0.490294 | ||||||||
\(829\) | 46.3470 | 1.60970 | 0.804850 | − | 0.593479i | \(-0.202246\pi\) | ||||
0.804850 | + | 0.593479i | \(0.202246\pi\) | |||||||
\(830\) | −1.78243 | −0.0618690 | ||||||||
\(831\) | −31.7924 | −1.10287 | ||||||||
\(832\) | −3.24442 | −0.112480 | ||||||||
\(833\) | 35.1463 | 1.21775 | ||||||||
\(834\) | 11.6177 | 0.402289 | ||||||||
\(835\) | −0.287315 | −0.00994294 | ||||||||
\(836\) | −14.3227 | −0.495362 | ||||||||
\(837\) | −35.2760 | −1.21932 | ||||||||
\(838\) | −11.9966 | −0.414415 | ||||||||
\(839\) | −13.9611 | −0.481990 | −0.240995 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240995 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(840\) | −0.599559 | −0.0206867 | ||||||||
\(841\) | 24.5241 | 0.845660 | ||||||||
\(842\) | 3.43381 | 0.118337 | ||||||||
\(843\) | 59.5054 | 2.04948 | ||||||||
\(844\) | −25.8353 | −0.889289 | ||||||||
\(845\) | −4.43913 | −0.152711 | ||||||||
\(846\) | 5.28063 | 0.181552 | ||||||||
\(847\) | −1.05546 | −0.0362660 | ||||||||
\(848\) | 1.38903 | 0.0476994 | ||||||||
\(849\) | −29.8916 | −1.02588 | ||||||||
\(850\) | −18.5237 | −0.635359 | ||||||||
\(851\) | −3.33214 | −0.114224 | ||||||||
\(852\) | −50.1116 | −1.71680 | ||||||||
\(853\) | −54.5527 | −1.86785 | −0.933924 | − | 0.357472i | \(-0.883639\pi\) | ||||
−0.933924 | + | 0.357472i | \(0.883639\pi\) | |||||||
\(854\) | 0.803609 | 0.0274989 | ||||||||
\(855\) | 10.5534 | 0.360920 | ||||||||
\(856\) | −21.2153 | −0.725124 | ||||||||
\(857\) | 27.6798 | 0.945525 | 0.472762 | − | 0.881190i | \(-0.343257\pi\) | ||||
0.472762 | + | 0.881190i | \(0.343257\pi\) | |||||||
\(858\) | −6.73519 | −0.229935 | ||||||||
\(859\) | 27.1497 | 0.926336 | 0.463168 | − | 0.886270i | \(-0.346713\pi\) | ||||
0.463168 | + | 0.886270i | \(0.346713\pi\) | |||||||
\(860\) | 0.843932 | 0.0287778 | ||||||||
\(861\) | 0.627810 | 0.0213957 | ||||||||
\(862\) | 18.1888 | 0.619512 | ||||||||
\(863\) | 25.9641 | 0.883827 | 0.441913 | − | 0.897058i | \(-0.354300\pi\) | ||||
0.441913 | + | 0.897058i | \(0.354300\pi\) | |||||||
\(864\) | 61.9350 | 2.10707 | ||||||||
\(865\) | 4.48208 | 0.152395 | ||||||||
\(866\) | 15.7387 | 0.534822 | ||||||||
\(867\) | −26.0694 | −0.885363 | ||||||||
\(868\) | −0.929239 | −0.0315404 | ||||||||
\(869\) | −30.1151 | −1.02159 | ||||||||
\(870\) | −6.56516 | −0.222580 | ||||||||
\(871\) | 13.8826 | 0.470394 | ||||||||
\(872\) | −13.8067 | −0.467554 | ||||||||
\(873\) | −83.6313 | −2.83049 | ||||||||
\(874\) | −4.92703 | −0.166659 | ||||||||
\(875\) | −0.741425 | −0.0250647 | ||||||||
\(876\) | −3.95780 | −0.133722 | ||||||||
\(877\) | 37.2176 | 1.25675 | 0.628374 | − | 0.777911i | \(-0.283721\pi\) | ||||
0.628374 | + | 0.777911i | \(0.283721\pi\) | |||||||
\(878\) | 20.4855 | 0.691351 | ||||||||
\(879\) | −80.5920 | −2.71830 | ||||||||
\(880\) | 0.816166 | 0.0275130 | ||||||||
\(881\) | −6.44185 | −0.217031 | −0.108516 | − | 0.994095i | \(-0.534610\pi\) | ||||
−0.108516 | + | 0.994095i | \(0.534610\pi\) | |||||||
\(882\) | 33.9081 | 1.14175 | ||||||||
\(883\) | 45.9727 | 1.54711 | 0.773553 | − | 0.633732i | \(-0.218478\pi\) | ||||
0.773553 | + | 0.633732i | \(0.218478\pi\) | |||||||
\(884\) | −8.83976 | −0.297313 | ||||||||
\(885\) | −17.6113 | −0.591998 | ||||||||
\(886\) | −19.7507 | −0.663538 | ||||||||
\(887\) | −28.3187 | −0.950849 | −0.475425 | − | 0.879756i | \(-0.657706\pi\) | ||||
−0.475425 | + | 0.879756i | \(0.657706\pi\) | |||||||
\(888\) | 17.2972 | 0.580457 | ||||||||
\(889\) | −3.47632 | −0.116592 | ||||||||
\(890\) | −1.88230 | −0.0630947 | ||||||||
\(891\) | 31.0582 | 1.04049 | ||||||||
\(892\) | 30.2222 | 1.01191 | ||||||||
\(893\) | −4.60208 | −0.154003 | ||||||||
\(894\) | 40.6539 | 1.35967 | ||||||||
\(895\) | −8.18524 | −0.273602 | ||||||||
\(896\) | 1.89522 | 0.0633147 | ||||||||
\(897\) | 5.78181 | 0.193049 | ||||||||
\(898\) | −13.9350 | −0.465018 | ||||||||
\(899\) | −24.4277 | −0.814710 | ||||||||
\(900\) | 44.5971 | 1.48657 | ||||||||
\(901\) | −7.84041 | −0.261202 | ||||||||
\(902\) | 1.87413 | 0.0624017 | ||||||||
\(903\) | 0.916604 | 0.0305027 | ||||||||
\(904\) | −9.34920 | −0.310950 | ||||||||
\(905\) | 4.61475 | 0.153399 | ||||||||
\(906\) | 1.11619 | 0.0370830 | ||||||||
\(907\) | −12.5099 | −0.415384 | −0.207692 | − | 0.978194i | \(-0.566595\pi\) | ||||
−0.207692 | + | 0.978194i | \(0.566595\pi\) | |||||||
\(908\) | 19.1084 | 0.634135 | ||||||||
\(909\) | 39.8010 | 1.32012 | ||||||||
\(910\) | 0.0698185 | 0.00231446 | ||||||||
\(911\) | 2.41940 | 0.0801584 | 0.0400792 | − | 0.999197i | \(-0.487239\pi\) | ||||
0.0400792 | + | 0.999197i | \(0.487239\pi\) | |||||||
\(912\) | −11.6631 | −0.386204 | ||||||||
\(913\) | 14.4216 | 0.477284 | ||||||||
\(914\) | 2.68639 | 0.0888580 | ||||||||
\(915\) | 6.46621 | 0.213766 | ||||||||
\(916\) | 17.9171 | 0.591997 | ||||||||
\(917\) | −2.37485 | −0.0784246 | ||||||||
\(918\) | −40.3439 | −1.33155 | ||||||||
\(919\) | 50.3462 | 1.66077 | 0.830384 | − | 0.557192i | \(-0.188121\pi\) | ||||
0.830384 | + | 0.557192i | \(0.188121\pi\) | |||||||
\(920\) | 1.53645 | 0.0506551 | ||||||||
\(921\) | 42.1200 | 1.38790 | ||||||||
\(922\) | 2.16838 | 0.0714118 | ||||||||
\(923\) | 14.0094 | 0.461125 | ||||||||
\(924\) | 2.02064 | 0.0664743 | ||||||||
\(925\) | 10.5331 | 0.346328 | ||||||||
\(926\) | −23.0924 | −0.758865 | ||||||||
\(927\) | 50.1103 | 1.64584 | ||||||||
\(928\) | 42.8884 | 1.40788 | ||||||||
\(929\) | −32.9858 | −1.08223 | −0.541115 | − | 0.840948i | \(-0.681998\pi\) | ||||
−0.541115 | + | 0.840948i | \(0.681998\pi\) | |||||||
\(930\) | 2.99625 | 0.0982509 | ||||||||
\(931\) | −29.5510 | −0.968494 | ||||||||
\(932\) | −22.3510 | −0.732131 | ||||||||
\(933\) | −94.9464 | −3.10841 | ||||||||
\(934\) | −14.1450 | −0.462838 | ||||||||
\(935\) | −4.60687 | −0.150661 | ||||||||
\(936\) | −20.4742 | −0.669219 | ||||||||
\(937\) | 47.9023 | 1.56490 | 0.782450 | − | 0.622714i | \(-0.213970\pi\) | ||||
0.782450 | + | 0.622714i | \(0.213970\pi\) | |||||||
\(938\) | 1.66900 | 0.0544948 | ||||||||
\(939\) | 86.7262 | 2.83020 | ||||||||
\(940\) | 0.597783 | 0.0194975 | ||||||||
\(941\) | −4.42362 | −0.144206 | −0.0721030 | − | 0.997397i | \(-0.522971\pi\) | ||||
−0.0721030 | + | 0.997397i | \(0.522971\pi\) | |||||||
\(942\) | 0.272803 | 0.00888841 | ||||||||
\(943\) | −1.60884 | −0.0523912 | ||||||||
\(944\) | 13.2770 | 0.432131 | ||||||||
\(945\) | −0.795175 | −0.0258670 | ||||||||
\(946\) | 2.73624 | 0.0889627 | ||||||||
\(947\) | 19.3253 | 0.627987 | 0.313994 | − | 0.949425i | \(-0.398333\pi\) | ||||
0.313994 | + | 0.949425i | \(0.398333\pi\) | |||||||
\(948\) | −55.8998 | −1.81554 | ||||||||
\(949\) | 1.10646 | 0.0359171 | ||||||||
\(950\) | 15.5747 | 0.505311 | ||||||||
\(951\) | 23.2200 | 0.752960 | ||||||||
\(952\) | −2.55134 | −0.0826895 | ||||||||
\(953\) | 30.0968 | 0.974931 | 0.487465 | − | 0.873142i | \(-0.337922\pi\) | ||||
0.487465 | + | 0.873142i | \(0.337922\pi\) | |||||||
\(954\) | −7.56418 | −0.244899 | ||||||||
\(955\) | 9.35408 | 0.302691 | ||||||||
\(956\) | −4.93544 | −0.159623 | ||||||||
\(957\) | 53.1184 | 1.71708 | ||||||||
\(958\) | −5.68051 | −0.183529 | ||||||||
\(959\) | −2.70948 | −0.0874937 | ||||||||
\(960\) | −3.13855 | −0.101296 | ||||||||
\(961\) | −19.8515 | −0.640371 | ||||||||
\(962\) | −2.01426 | −0.0649423 | ||||||||
\(963\) | −52.6836 | −1.69771 | ||||||||
\(964\) | −41.0992 | −1.32372 | ||||||||
\(965\) | −2.23402 | −0.0719156 | ||||||||
\(966\) | 0.695103 | 0.0223646 | ||||||||
\(967\) | −42.6607 | −1.37187 | −0.685937 | − | 0.727661i | \(-0.740608\pi\) | ||||
−0.685937 | + | 0.727661i | \(0.740608\pi\) | |||||||
\(968\) | −14.0404 | −0.451277 | ||||||||
\(969\) | 65.8328 | 2.11485 | ||||||||
\(970\) | 3.79378 | 0.121811 | ||||||||
\(971\) | 33.0050 | 1.05918 | 0.529591 | − | 0.848253i | \(-0.322345\pi\) | ||||
0.529591 | + | 0.848253i | \(0.322345\pi\) | |||||||
\(972\) | 12.3951 | 0.397572 | ||||||||
\(973\) | 0.974412 | 0.0312382 | ||||||||
\(974\) | −24.7187 | −0.792037 | ||||||||
\(975\) | −18.2767 | −0.585324 | ||||||||
\(976\) | −4.87483 | −0.156039 | ||||||||
\(977\) | −5.79949 | −0.185542 | −0.0927710 | − | 0.995687i | \(-0.529572\pi\) | ||||
−0.0927710 | + | 0.995687i | \(0.529572\pi\) | |||||||
\(978\) | −29.1123 | −0.930909 | ||||||||
\(979\) | 15.2296 | 0.486740 | ||||||||
\(980\) | 3.83850 | 0.122616 | ||||||||
\(981\) | −34.2859 | −1.09467 | ||||||||
\(982\) | −2.13095 | −0.0680013 | ||||||||
\(983\) | −35.2304 | −1.12367 | −0.561837 | − | 0.827248i | \(-0.689905\pi\) | ||||
−0.561837 | + | 0.827248i | \(0.689905\pi\) | |||||||
\(984\) | 8.35156 | 0.266238 | ||||||||
\(985\) | 1.57081 | 0.0500501 | ||||||||
\(986\) | −27.9371 | −0.889700 | ||||||||
\(987\) | 0.649260 | 0.0206662 | ||||||||
\(988\) | 7.43245 | 0.236458 | ||||||||
\(989\) | −2.34891 | −0.0746911 | ||||||||
\(990\) | −4.44457 | −0.141258 | ||||||||
\(991\) | 9.08023 | 0.288443 | 0.144221 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144221 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(992\) | −19.5737 | −0.621466 | ||||||||
\(993\) | −62.7433 | −1.99110 | ||||||||
\(994\) | 1.68424 | 0.0534210 | ||||||||
\(995\) | −4.40992 | −0.139804 | ||||||||
\(996\) | 26.7693 | 0.848219 | ||||||||
\(997\) | 59.6440 | 1.88894 | 0.944472 | − | 0.328591i | \(-0.106574\pi\) | ||||
0.944472 | + | 0.328591i | \(0.106574\pi\) | |||||||
\(998\) | −21.9808 | −0.695791 | ||||||||
\(999\) | 22.9407 | 0.725813 |
(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 | 503.2.a.e.1.5 | ✓ | 10 | |
3.2 | odd | 2 | 4527.2.a.k.1.6 | 10 | |||
4.3 | odd | 2 | 8048.2.a.p.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4527.2.a.k.1.6 | 10 | 3.2 | odd | 2 | |||
8048.2.a.p.1.10 | 10 | 4.3 | odd | 2 |