Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.34607\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34607 | −1.65892 | −0.829462 | − | 0.558564i | \(-0.811353\pi\) | ||||
−0.829462 | + | 0.558564i | \(0.811353\pi\) | |||||||
\(3\) | 0.967441 | 0.558552 | 0.279276 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279276 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(4\) | 3.50405 | 1.75203 | ||||||||
\(5\) | 3.03222 | 1.35605 | 0.678026 | − | 0.735038i | \(-0.262836\pi\) | ||||
0.678026 | + | 0.735038i | \(0.262836\pi\) | |||||||
\(6\) | −2.26969 | −0.926595 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.52861 | −1.24755 | ||||||||
\(9\) | −2.06406 | −0.688019 | ||||||||
\(10\) | −7.11381 | −2.24959 | ||||||||
\(11\) | 1.10360 | 0.332747 | 0.166373 | − | 0.986063i | \(-0.446794\pi\) | ||||
0.166373 | + | 0.986063i | \(0.446794\pi\) | |||||||
\(12\) | 3.38996 | 0.978598 | ||||||||
\(13\) | 6.46984 | 1.79441 | 0.897205 | − | 0.441613i | \(-0.145594\pi\) | ||||
0.897205 | + | 0.441613i | \(0.145594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.93350 | 0.757426 | ||||||||
\(16\) | 1.27027 | 0.317568 | ||||||||
\(17\) | −5.05976 | −1.22717 | −0.613587 | − | 0.789627i | \(-0.710274\pi\) | ||||
−0.613587 | + | 0.789627i | \(0.710274\pi\) | |||||||
\(18\) | 4.84243 | 1.14137 | ||||||||
\(19\) | −4.13340 | −0.948267 | −0.474134 | − | 0.880453i | \(-0.657239\pi\) | ||||
−0.474134 | + | 0.880453i | \(0.657239\pi\) | |||||||
\(20\) | 10.6251 | 2.37584 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.58911 | −0.552001 | ||||||||
\(23\) | 4.02275 | 0.838801 | 0.419401 | − | 0.907801i | \(-0.362240\pi\) | ||||
0.419401 | + | 0.907801i | \(0.362240\pi\) | |||||||
\(24\) | −3.41372 | −0.696823 | ||||||||
\(25\) | 4.19438 | 0.838876 | ||||||||
\(26\) | −15.1787 | −2.97679 | ||||||||
\(27\) | −4.89918 | −0.942847 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32970 | 0.246919 | 0.123460 | − | 0.992350i | \(-0.460601\pi\) | ||||
0.123460 | + | 0.992350i | \(0.460601\pi\) | |||||||
\(30\) | −6.88219 | −1.25651 | ||||||||
\(31\) | 7.45223 | 1.33846 | 0.669230 | − | 0.743055i | \(-0.266624\pi\) | ||||
0.669230 | + | 0.743055i | \(0.266624\pi\) | |||||||
\(32\) | 4.07707 | 0.720732 | ||||||||
\(33\) | 1.06766 | 0.185856 | ||||||||
\(34\) | 11.8706 | 2.03579 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.23256 | −1.20543 | ||||||||
\(37\) | −5.52598 | −0.908466 | −0.454233 | − | 0.890883i | \(-0.650087\pi\) | ||||
−0.454233 | + | 0.890883i | \(0.650087\pi\) | |||||||
\(38\) | 9.69726 | 1.57310 | ||||||||
\(39\) | 6.25919 | 1.00227 | ||||||||
\(40\) | −10.6995 | −1.69175 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7127 | 1.63368 | 0.816839 | − | 0.576865i | \(-0.195724\pi\) | ||||
0.816839 | + | 0.576865i | \(0.195724\pi\) | |||||||
\(44\) | 3.86706 | 0.582981 | ||||||||
\(45\) | −6.25868 | −0.932990 | ||||||||
\(46\) | −9.43766 | −1.39151 | ||||||||
\(47\) | −0.701294 | −0.102294 | −0.0511471 | − | 0.998691i | \(-0.516288\pi\) | ||||
−0.0511471 | + | 0.998691i | \(0.516288\pi\) | |||||||
\(48\) | 1.22891 | 0.177378 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.84031 | −1.39163 | ||||||||
\(51\) | −4.89502 | −0.685440 | ||||||||
\(52\) | 22.6707 | 3.14385 | ||||||||
\(53\) | 9.92442 | 1.36322 | 0.681612 | − | 0.731714i | \(-0.261279\pi\) | ||||
0.681612 | + | 0.731714i | \(0.261279\pi\) | |||||||
\(54\) | 11.4938 | 1.56411 | ||||||||
\(55\) | 3.34635 | 0.451222 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.99882 | −0.529657 | ||||||||
\(58\) | −3.11957 | −0.409620 | ||||||||
\(59\) | −1.64732 | −0.214462 | −0.107231 | − | 0.994234i | \(-0.534198\pi\) | ||||
−0.107231 | + | 0.994234i | \(0.534198\pi\) | |||||||
\(60\) | 10.2791 | 1.32703 | ||||||||
\(61\) | 7.03158 | 0.900302 | 0.450151 | − | 0.892952i | \(-0.351370\pi\) | ||||
0.450151 | + | 0.892952i | \(0.351370\pi\) | |||||||
\(62\) | −17.4835 | −2.22040 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.1056 | −1.51321 | ||||||||
\(65\) | 19.6180 | 2.43331 | ||||||||
\(66\) | −2.50482 | −0.308322 | ||||||||
\(67\) | 8.82578 | 1.07824 | 0.539120 | − | 0.842229i | \(-0.318757\pi\) | ||||
0.539120 | + | 0.842229i | \(0.318757\pi\) | |||||||
\(68\) | −17.7297 | −2.15004 | ||||||||
\(69\) | 3.89177 | 0.468515 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.62821 | 0.667946 | 0.333973 | − | 0.942583i | \(-0.391611\pi\) | ||||
0.333973 | + | 0.942583i | \(0.391611\pi\) | |||||||
\(72\) | 7.28326 | 0.858340 | ||||||||
\(73\) | 10.8521 | 1.27014 | 0.635072 | − | 0.772453i | \(-0.280970\pi\) | ||||
0.635072 | + | 0.772453i | \(0.280970\pi\) | |||||||
\(74\) | 12.9644 | 1.50708 | ||||||||
\(75\) | 4.05782 | 0.468556 | ||||||||
\(76\) | −14.4837 | −1.66139 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −14.6845 | −1.66269 | ||||||||
\(79\) | 3.37993 | 0.380272 | 0.190136 | − | 0.981758i | \(-0.439107\pi\) | ||||
0.190136 | + | 0.981758i | \(0.439107\pi\) | |||||||
\(80\) | 3.85175 | 0.430639 | ||||||||
\(81\) | 1.45251 | 0.161390 | ||||||||
\(82\) | −2.34607 | −0.259080 | ||||||||
\(83\) | −7.65029 | −0.839728 | −0.419864 | − | 0.907587i | \(-0.637922\pi\) | ||||
−0.419864 | + | 0.907587i | \(0.637922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.3423 | −1.66411 | ||||||||
\(86\) | −25.1329 | −2.71015 | ||||||||
\(87\) | 1.28641 | 0.137917 | ||||||||
\(88\) | −3.89416 | −0.415119 | ||||||||
\(89\) | 11.6819 | 1.23828 | 0.619141 | − | 0.785280i | \(-0.287481\pi\) | ||||
0.619141 | + | 0.785280i | \(0.287481\pi\) | |||||||
\(90\) | 14.6833 | 1.54776 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.0959 | 1.46960 | ||||||||
\(93\) | 7.20959 | 0.747600 | ||||||||
\(94\) | 1.64529 | 0.169698 | ||||||||
\(95\) | −12.5334 | −1.28590 | ||||||||
\(96\) | 3.94433 | 0.402566 | ||||||||
\(97\) | 3.66714 | 0.372342 | 0.186171 | − | 0.982517i | \(-0.440392\pi\) | ||||
0.186171 | + | 0.982517i | \(0.440392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.27789 | −0.228936 | ||||||||
\(100\) | 14.6973 | 1.46973 | ||||||||
\(101\) | −11.4922 | −1.14352 | −0.571759 | − | 0.820421i | \(-0.693739\pi\) | ||||
−0.571759 | + | 0.820421i | \(0.693739\pi\) | |||||||
\(102\) | 11.4841 | 1.13709 | ||||||||
\(103\) | −18.4372 | −1.81667 | −0.908335 | − | 0.418244i | \(-0.862646\pi\) | ||||
−0.908335 | + | 0.418244i | \(0.862646\pi\) | |||||||
\(104\) | −22.8296 | −2.23862 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.2834 | −2.26148 | ||||||||
\(107\) | −10.1064 | −0.977024 | −0.488512 | − | 0.872557i | \(-0.662460\pi\) | ||||
−0.488512 | + | 0.872557i | \(0.662460\pi\) | |||||||
\(108\) | −17.1670 | −1.65189 | ||||||||
\(109\) | −7.54678 | −0.722850 | −0.361425 | − | 0.932401i | \(-0.617710\pi\) | ||||
−0.361425 | + | 0.932401i | \(0.617710\pi\) | |||||||
\(110\) | −7.85077 | −0.748542 | ||||||||
\(111\) | −5.34606 | −0.507426 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.75949 | −0.447735 | −0.223867 | − | 0.974620i | \(-0.571868\pi\) | ||||
−0.223867 | + | 0.974620i | \(0.571868\pi\) | |||||||
\(114\) | 9.38152 | 0.878660 | ||||||||
\(115\) | 12.1979 | 1.13746 | ||||||||
\(116\) | 4.65934 | 0.432609 | ||||||||
\(117\) | −13.3541 | −1.23459 | ||||||||
\(118\) | 3.86472 | 0.355776 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.3512 | −0.944929 | ||||||||
\(121\) | −9.78208 | −0.889280 | ||||||||
\(122\) | −16.4966 | −1.49353 | ||||||||
\(123\) | 0.967441 | 0.0872312 | ||||||||
\(124\) | 26.1130 | 2.34502 | ||||||||
\(125\) | −2.44282 | −0.218493 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7056 | 1.74859 | 0.874296 | − | 0.485393i | \(-0.161324\pi\) | ||||
0.874296 | + | 0.485393i | \(0.161324\pi\) | |||||||
\(128\) | 20.2466 | 1.78956 | ||||||||
\(129\) | 10.3640 | 0.912495 | ||||||||
\(130\) | −46.0252 | −4.03668 | ||||||||
\(131\) | 2.80070 | 0.244698 | 0.122349 | − | 0.992487i | \(-0.460957\pi\) | ||||
0.122349 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(132\) | 3.74115 | 0.325625 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.7059 | −1.78872 | ||||||||
\(135\) | −14.8554 | −1.27855 | ||||||||
\(136\) | 17.8539 | 1.53096 | ||||||||
\(137\) | −12.4549 | −1.06409 | −0.532047 | − | 0.846715i | \(-0.678577\pi\) | ||||
−0.532047 | + | 0.846715i | \(0.678577\pi\) | |||||||
\(138\) | −9.13038 | −0.777229 | ||||||||
\(139\) | −0.357926 | −0.0303589 | −0.0151794 | − | 0.999885i | \(-0.504832\pi\) | ||||
−0.0151794 | + | 0.999885i | \(0.504832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.678460 | −0.0571367 | ||||||||
\(142\) | −13.2042 | −1.10807 | ||||||||
\(143\) | 7.14009 | 0.597084 | ||||||||
\(144\) | −2.62192 | −0.218493 | ||||||||
\(145\) | 4.03195 | 0.334835 | ||||||||
\(146\) | −25.4598 | −2.10707 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.3633 | −1.59166 | ||||||||
\(149\) | −13.8665 | −1.13599 | −0.567995 | − | 0.823032i | \(-0.692281\pi\) | ||||
−0.567995 | + | 0.823032i | \(0.692281\pi\) | |||||||
\(150\) | −9.51992 | −0.777299 | ||||||||
\(151\) | −9.86597 | −0.802881 | −0.401441 | − | 0.915885i | \(-0.631490\pi\) | ||||
−0.401441 | + | 0.915885i | \(0.631490\pi\) | |||||||
\(152\) | 14.5852 | 1.18301 | ||||||||
\(153\) | 10.4436 | 0.844319 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.5968 | 1.81502 | ||||||||
\(156\) | 21.9325 | 1.75601 | ||||||||
\(157\) | 8.36035 | 0.667229 | 0.333614 | − | 0.942710i | \(-0.391732\pi\) | ||||
0.333614 | + | 0.942710i | \(0.391732\pi\) | |||||||
\(158\) | −7.92957 | −0.630843 | ||||||||
\(159\) | 9.60129 | 0.761432 | ||||||||
\(160\) | 12.3626 | 0.977349 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.40769 | −0.267733 | ||||||||
\(163\) | 12.1242 | 0.949644 | 0.474822 | − | 0.880082i | \(-0.342512\pi\) | ||||
0.474822 | + | 0.880082i | \(0.342512\pi\) | |||||||
\(164\) | 3.50405 | 0.273620 | ||||||||
\(165\) | 3.23740 | 0.252031 | ||||||||
\(166\) | 17.9481 | 1.39304 | ||||||||
\(167\) | 12.2976 | 0.951614 | 0.475807 | − | 0.879550i | \(-0.342156\pi\) | ||||
0.475807 | + | 0.879550i | \(0.342156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.8588 | 2.21991 | ||||||||
\(170\) | 35.9942 | 2.76063 | ||||||||
\(171\) | 8.53158 | 0.652426 | ||||||||
\(172\) | 37.5380 | 2.86225 | ||||||||
\(173\) | 4.20278 | 0.319532 | 0.159766 | − | 0.987155i | \(-0.448926\pi\) | ||||
0.159766 | + | 0.987155i | \(0.448926\pi\) | |||||||
\(174\) | −3.01800 | −0.228794 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.40187 | 0.105670 | ||||||||
\(177\) | −1.59368 | −0.119788 | ||||||||
\(178\) | −27.4066 | −2.05421 | ||||||||
\(179\) | 22.3986 | 1.67415 | 0.837076 | − | 0.547087i | \(-0.184263\pi\) | ||||
0.837076 | + | 0.547087i | \(0.184263\pi\) | |||||||
\(180\) | −21.9308 | −1.63462 | ||||||||
\(181\) | 18.9063 | 1.40529 | 0.702646 | − | 0.711539i | \(-0.252002\pi\) | ||||
0.702646 | + | 0.711539i | \(0.252002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.80264 | 0.502866 | ||||||||
\(184\) | −14.1947 | −1.04645 | ||||||||
\(185\) | −16.7560 | −1.23193 | ||||||||
\(186\) | −16.9142 | −1.24021 | ||||||||
\(187\) | −5.58393 | −0.408338 | ||||||||
\(188\) | −2.45737 | −0.179222 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 29.4042 | 2.13321 | ||||||||
\(191\) | −4.23571 | −0.306485 | −0.153243 | − | 0.988189i | \(-0.548972\pi\) | ||||
−0.153243 | + | 0.988189i | \(0.548972\pi\) | |||||||
\(192\) | −11.7115 | −0.845205 | ||||||||
\(193\) | −12.7881 | −0.920508 | −0.460254 | − | 0.887787i | \(-0.652242\pi\) | ||||
−0.460254 | + | 0.887787i | \(0.652242\pi\) | |||||||
\(194\) | −8.60338 | −0.617687 | ||||||||
\(195\) | 18.9793 | 1.35913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.6221 | −1.04178 | −0.520892 | − | 0.853622i | \(-0.674401\pi\) | ||||
−0.520892 | + | 0.853622i | \(0.674401\pi\) | |||||||
\(198\) | 5.34408 | 0.379787 | ||||||||
\(199\) | 17.2973 | 1.22617 | 0.613087 | − | 0.790016i | \(-0.289928\pi\) | ||||
0.613087 | + | 0.790016i | \(0.289928\pi\) | |||||||
\(200\) | −14.8003 | −1.04654 | ||||||||
\(201\) | 8.53842 | 0.602254 | ||||||||
\(202\) | 26.9616 | 1.89701 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −17.1524 | −1.20091 | ||||||||
\(205\) | 3.03222 | 0.211780 | ||||||||
\(206\) | 43.2549 | 3.01371 | ||||||||
\(207\) | −8.30319 | −0.577112 | ||||||||
\(208\) | 8.21846 | 0.569848 | ||||||||
\(209\) | −4.56161 | −0.315533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.72016 | −0.531478 | −0.265739 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265739 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(212\) | 34.7757 | 2.38840 | ||||||||
\(213\) | 5.44496 | 0.373083 | ||||||||
\(214\) | 23.7104 | 1.62081 | ||||||||
\(215\) | 32.4834 | 2.21535 | ||||||||
\(216\) | 17.2873 | 1.17625 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.7053 | 1.19915 | ||||||||
\(219\) | 10.4988 | 0.709442 | ||||||||
\(220\) | 11.7258 | 0.790552 | ||||||||
\(221\) | −32.7359 | −2.20205 | ||||||||
\(222\) | 12.5422 | 0.841780 | ||||||||
\(223\) | 13.5520 | 0.907509 | 0.453754 | − | 0.891127i | \(-0.350084\pi\) | ||||
0.453754 | + | 0.891127i | \(0.350084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.65744 | −0.577163 | ||||||||
\(226\) | 11.1661 | 0.742758 | ||||||||
\(227\) | −16.6512 | −1.10518 | −0.552590 | − | 0.833454i | \(-0.686360\pi\) | ||||
−0.552590 | + | 0.833454i | \(0.686360\pi\) | |||||||
\(228\) | −14.0121 | −0.927973 | ||||||||
\(229\) | 15.1282 | 0.999701 | 0.499850 | − | 0.866112i | \(-0.333388\pi\) | ||||
0.499850 | + | 0.866112i | \(0.333388\pi\) | |||||||
\(230\) | −28.6171 | −1.88696 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.69199 | −0.308045 | ||||||||
\(233\) | −8.22146 | −0.538605 | −0.269303 | − | 0.963056i | \(-0.586793\pi\) | ||||
−0.269303 | + | 0.963056i | \(0.586793\pi\) | |||||||
\(234\) | 31.3297 | 2.04809 | ||||||||
\(235\) | −2.12648 | −0.138716 | ||||||||
\(236\) | −5.77228 | −0.375743 | ||||||||
\(237\) | 3.26989 | 0.212402 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.9685 | −1.61508 | −0.807538 | − | 0.589815i | \(-0.799201\pi\) | ||||
−0.807538 | + | 0.589815i | \(0.799201\pi\) | |||||||
\(240\) | 3.72634 | 0.240534 | ||||||||
\(241\) | 5.88205 | 0.378896 | 0.189448 | − | 0.981891i | \(-0.439330\pi\) | ||||
0.189448 | + | 0.981891i | \(0.439330\pi\) | |||||||
\(242\) | 22.9494 | 1.47525 | ||||||||
\(243\) | 16.1027 | 1.03299 | ||||||||
\(244\) | 24.6390 | 1.57735 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.26969 | −0.144710 | ||||||||
\(247\) | −26.7425 | −1.70158 | ||||||||
\(248\) | −26.2960 | −1.66980 | ||||||||
\(249\) | −7.40120 | −0.469032 | ||||||||
\(250\) | 5.73103 | 0.362462 | ||||||||
\(251\) | 7.95766 | 0.502283 | 0.251141 | − | 0.967950i | \(-0.419194\pi\) | ||||
0.251141 | + | 0.967950i | \(0.419194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.43949 | 0.279108 | ||||||||
\(254\) | −46.2308 | −2.90078 | ||||||||
\(255\) | −14.8428 | −0.929493 | ||||||||
\(256\) | −23.2886 | −1.45554 | ||||||||
\(257\) | 1.35054 | 0.0842442 | 0.0421221 | − | 0.999112i | \(-0.486588\pi\) | ||||
0.0421221 | + | 0.999112i | \(0.486588\pi\) | |||||||
\(258\) | −24.3146 | −1.51376 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 68.7425 | 4.26323 | ||||||||
\(261\) | −2.74458 | −0.169885 | ||||||||
\(262\) | −6.57065 | −0.405936 | ||||||||
\(263\) | 7.78387 | 0.479974 | 0.239987 | − | 0.970776i | \(-0.422857\pi\) | ||||
0.239987 | + | 0.970776i | \(0.422857\pi\) | |||||||
\(264\) | −3.76737 | −0.231866 | ||||||||
\(265\) | 30.0931 | 1.84860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3016 | 0.691645 | ||||||||
\(268\) | 30.9260 | 1.88911 | ||||||||
\(269\) | −9.81220 | −0.598260 | −0.299130 | − | 0.954212i | \(-0.596696\pi\) | ||||
−0.299130 | + | 0.954212i | \(0.596696\pi\) | |||||||
\(270\) | 34.8518 | 2.12101 | ||||||||
\(271\) | 22.1543 | 1.34578 | 0.672888 | − | 0.739745i | \(-0.265054\pi\) | ||||
0.672888 | + | 0.739745i | \(0.265054\pi\) | |||||||
\(272\) | −6.42728 | −0.389711 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 29.2201 | 1.76525 | ||||||||
\(275\) | 4.62890 | 0.279133 | ||||||||
\(276\) | 13.6370 | 0.820849 | ||||||||
\(277\) | −20.2889 | −1.21904 | −0.609522 | − | 0.792769i | \(-0.708638\pi\) | ||||
−0.609522 | + | 0.792769i | \(0.708638\pi\) | |||||||
\(278\) | 0.839720 | 0.0503630 | ||||||||
\(279\) | −15.3818 | −0.920886 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1445 | 1.55965 | 0.779826 | − | 0.625997i | \(-0.215308\pi\) | ||||
0.779826 | + | 0.625997i | \(0.215308\pi\) | |||||||
\(282\) | 1.59172 | 0.0947853 | ||||||||
\(283\) | 19.8681 | 1.18104 | 0.590519 | − | 0.807024i | \(-0.298923\pi\) | ||||
0.590519 | + | 0.807024i | \(0.298923\pi\) | |||||||
\(284\) | 19.7215 | 1.17026 | ||||||||
\(285\) | −12.1253 | −0.718242 | ||||||||
\(286\) | −16.7512 | −0.990517 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.41531 | −0.495877 | ||||||||
\(289\) | 8.60122 | 0.505954 | ||||||||
\(290\) | −9.45924 | −0.555465 | ||||||||
\(291\) | 3.54774 | 0.207972 | ||||||||
\(292\) | 38.0264 | 2.22532 | ||||||||
\(293\) | −13.0491 | −0.762337 | −0.381169 | − | 0.924506i | \(-0.624478\pi\) | ||||
−0.381169 | + | 0.924506i | \(0.624478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.99503 | −0.290822 | ||||||||
\(296\) | 19.4991 | 1.13336 | ||||||||
\(297\) | −5.40671 | −0.313729 | ||||||||
\(298\) | 32.5318 | 1.88452 | ||||||||
\(299\) | 26.0266 | 1.50515 | ||||||||
\(300\) | 14.2188 | 0.820922 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 23.1463 | 1.33192 | ||||||||
\(303\) | −11.1180 | −0.638715 | ||||||||
\(304\) | −5.25055 | −0.301140 | ||||||||
\(305\) | 21.3213 | 1.22086 | ||||||||
\(306\) | −24.5015 | −1.40066 | ||||||||
\(307\) | −25.0334 | −1.42873 | −0.714366 | − | 0.699772i | \(-0.753285\pi\) | ||||
−0.714366 | + | 0.699772i | \(0.753285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.8369 | −1.01470 | ||||||||
\(310\) | −53.0138 | −3.01098 | ||||||||
\(311\) | 4.41939 | 0.250601 | 0.125300 | − | 0.992119i | \(-0.460011\pi\) | ||||
0.125300 | + | 0.992119i | \(0.460011\pi\) | |||||||
\(312\) | −22.0862 | −1.25039 | ||||||||
\(313\) | 23.5718 | 1.33236 | 0.666178 | − | 0.745793i | \(-0.267929\pi\) | ||||
0.666178 | + | 0.745793i | \(0.267929\pi\) | |||||||
\(314\) | −19.6140 | −1.10688 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8435 | 0.666247 | ||||||||
\(317\) | −17.6331 | −0.990373 | −0.495186 | − | 0.868787i | \(-0.664900\pi\) | ||||
−0.495186 | + | 0.868787i | \(0.664900\pi\) | |||||||
\(318\) | −22.5253 | −1.26316 | ||||||||
\(319\) | 1.46745 | 0.0821615 | ||||||||
\(320\) | −36.7070 | −2.05199 | ||||||||
\(321\) | −9.77736 | −0.545719 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9140 | 1.16369 | ||||||||
\(324\) | 5.08966 | 0.282759 | ||||||||
\(325\) | 27.1370 | 1.50529 | ||||||||
\(326\) | −28.4444 | −1.57539 | ||||||||
\(327\) | −7.30106 | −0.403750 | ||||||||
\(328\) | −3.52861 | −0.194835 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.59516 | −0.418100 | ||||||||
\(331\) | 21.7255 | 1.19414 | 0.597072 | − | 0.802188i | \(-0.296331\pi\) | ||||
0.597072 | + | 0.802188i | \(0.296331\pi\) | |||||||
\(332\) | −26.8070 | −1.47122 | ||||||||
\(333\) | 11.4059 | 0.625042 | ||||||||
\(334\) | −28.8510 | −1.57865 | ||||||||
\(335\) | 26.7617 | 1.46215 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0133 | −0.599933 | −0.299967 | − | 0.953950i | \(-0.596976\pi\) | ||||
−0.299967 | + | 0.953950i | \(0.596976\pi\) | |||||||
\(338\) | −67.7049 | −3.68266 | ||||||||
\(339\) | −4.60452 | −0.250083 | ||||||||
\(340\) | −53.7603 | −2.91556 | ||||||||
\(341\) | 8.22425 | 0.445368 | ||||||||
\(342\) | −20.0157 | −1.08232 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −37.8011 | −2.03810 | ||||||||
\(345\) | 11.8007 | 0.635330 | ||||||||
\(346\) | −9.86002 | −0.530078 | ||||||||
\(347\) | −28.6267 | −1.53676 | −0.768380 | − | 0.639994i | \(-0.778937\pi\) | ||||
−0.768380 | + | 0.639994i | \(0.778937\pi\) | |||||||
\(348\) | 4.50763 | 0.241635 | ||||||||
\(349\) | −33.9270 | −1.81607 | −0.908034 | − | 0.418895i | \(-0.862417\pi\) | ||||
−0.908034 | + | 0.418895i | \(0.862417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.6969 | −1.69186 | ||||||||
\(352\) | 4.49944 | 0.239821 | ||||||||
\(353\) | −15.1883 | −0.808393 | −0.404196 | − | 0.914672i | \(-0.632449\pi\) | ||||
−0.404196 | + | 0.914672i | \(0.632449\pi\) | |||||||
\(354\) | 3.73889 | 0.198720 | ||||||||
\(355\) | 17.0660 | 0.905769 | ||||||||
\(356\) | 40.9341 | 2.16950 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −52.5488 | −2.77729 | ||||||||
\(359\) | −23.0574 | −1.21692 | −0.608460 | − | 0.793584i | \(-0.708212\pi\) | ||||
−0.608460 | + | 0.793584i | \(0.708212\pi\) | |||||||
\(360\) | 22.0845 | 1.16395 | ||||||||
\(361\) | −1.91499 | −0.100789 | ||||||||
\(362\) | −44.3555 | −2.33127 | ||||||||
\(363\) | −9.46358 | −0.496709 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9060 | 1.72238 | ||||||||
\(366\) | −15.9595 | −0.834216 | ||||||||
\(367\) | −11.9305 | −0.622767 | −0.311383 | − | 0.950284i | \(-0.600792\pi\) | ||||
−0.311383 | + | 0.950284i | \(0.600792\pi\) | |||||||
\(368\) | 5.10999 | 0.266377 | ||||||||
\(369\) | −2.06406 | −0.107451 | ||||||||
\(370\) | 39.3108 | 2.04367 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 25.2628 | 1.30981 | ||||||||
\(373\) | 5.01702 | 0.259771 | 0.129886 | − | 0.991529i | \(-0.458539\pi\) | ||||
0.129886 | + | 0.991529i | \(0.458539\pi\) | |||||||
\(374\) | 13.1003 | 0.677401 | ||||||||
\(375\) | −2.36328 | −0.122040 | ||||||||
\(376\) | 2.47459 | 0.127617 | ||||||||
\(377\) | 8.60295 | 0.443074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1372 | 1.34258 | 0.671289 | − | 0.741196i | \(-0.265741\pi\) | ||||
0.671289 | + | 0.741196i | \(0.265741\pi\) | |||||||
\(380\) | −43.9177 | −2.25293 | ||||||||
\(381\) | 19.0640 | 0.976680 | ||||||||
\(382\) | 9.93729 | 0.508436 | ||||||||
\(383\) | −28.4070 | −1.45153 | −0.725765 | − | 0.687943i | \(-0.758514\pi\) | ||||
−0.725765 | + | 0.687943i | \(0.758514\pi\) | |||||||
\(384\) | 19.5874 | 0.999564 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.0018 | 1.52705 | ||||||||
\(387\) | −22.1117 | −1.12400 | ||||||||
\(388\) | 12.8499 | 0.652353 | ||||||||
\(389\) | −35.4596 | −1.79787 | −0.898936 | − | 0.438079i | \(-0.855659\pi\) | ||||
−0.898936 | + | 0.438079i | \(0.855659\pi\) | |||||||
\(390\) | −44.5267 | −2.25470 | ||||||||
\(391\) | −20.3542 | −1.02935 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.70951 | 0.136677 | ||||||||
\(394\) | 34.3046 | 1.72824 | ||||||||
\(395\) | 10.2487 | 0.515669 | ||||||||
\(396\) | −7.98183 | −0.401102 | ||||||||
\(397\) | −19.6169 | −0.984544 | −0.492272 | − | 0.870441i | \(-0.663834\pi\) | ||||
−0.492272 | + | 0.870441i | \(0.663834\pi\) | |||||||
\(398\) | −40.5807 | −2.03413 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.32801 | 0.266400 | ||||||||
\(401\) | 27.1076 | 1.35369 | 0.676844 | − | 0.736126i | \(-0.263347\pi\) | ||||
0.676844 | + | 0.736126i | \(0.263347\pi\) | |||||||
\(402\) | −20.0318 | −0.999093 | ||||||||
\(403\) | 48.2147 | 2.40175 | ||||||||
\(404\) | −40.2693 | −2.00347 | ||||||||
\(405\) | 4.40433 | 0.218853 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.09845 | −0.302289 | ||||||||
\(408\) | 17.2726 | 0.855123 | ||||||||
\(409\) | −10.5825 | −0.523271 | −0.261635 | − | 0.965167i | \(-0.584262\pi\) | ||||
−0.261635 | + | 0.965167i | \(0.584262\pi\) | |||||||
\(410\) | −7.11381 | −0.351326 | ||||||||
\(411\) | −12.0494 | −0.594352 | ||||||||
\(412\) | −64.6048 | −3.18285 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 19.4799 | 0.957384 | ||||||||
\(415\) | −23.1974 | −1.13871 | ||||||||
\(416\) | 26.3780 | 1.29329 | ||||||||
\(417\) | −0.346272 | −0.0169570 | ||||||||
\(418\) | 10.7019 | 0.523445 | ||||||||
\(419\) | 7.64322 | 0.373396 | 0.186698 | − | 0.982417i | \(-0.440221\pi\) | ||||
0.186698 | + | 0.982417i | \(0.440221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.5374 | 1.48830 | 0.744150 | − | 0.668012i | \(-0.232855\pi\) | ||||
0.744150 | + | 0.668012i | \(0.232855\pi\) | |||||||
\(422\) | 18.1120 | 0.881681 | ||||||||
\(423\) | 1.44751 | 0.0703804 | ||||||||
\(424\) | −35.0194 | −1.70069 | ||||||||
\(425\) | −21.2226 | −1.02945 | ||||||||
\(426\) | −12.7743 | −0.618916 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −35.4134 | −1.71177 | ||||||||
\(429\) | 6.90761 | 0.333503 | ||||||||
\(430\) | −76.2085 | −3.67510 | ||||||||
\(431\) | −15.7015 | −0.756314 | −0.378157 | − | 0.925741i | \(-0.623442\pi\) | ||||
−0.378157 | + | 0.925741i | \(0.623442\pi\) | |||||||
\(432\) | −6.22329 | −0.299418 | ||||||||
\(433\) | −21.3198 | −1.02457 | −0.512283 | − | 0.858817i | \(-0.671200\pi\) | ||||
−0.512283 | + | 0.858817i | \(0.671200\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.90067 | 0.187023 | ||||||||
\(436\) | −26.4443 | −1.26645 | ||||||||
\(437\) | −16.6276 | −0.795408 | ||||||||
\(438\) | −24.6309 | −1.17691 | ||||||||
\(439\) | 25.5265 | 1.21831 | 0.609156 | − | 0.793051i | \(-0.291508\pi\) | ||||
0.609156 | + | 0.793051i | \(0.291508\pi\) | |||||||
\(440\) | −11.8080 | −0.562923 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 76.8007 | 3.65304 | ||||||||
\(443\) | 22.7925 | 1.08291 | 0.541453 | − | 0.840731i | \(-0.317874\pi\) | ||||
0.541453 | + | 0.840731i | \(0.317874\pi\) | |||||||
\(444\) | −18.7329 | −0.889023 | ||||||||
\(445\) | 35.4222 | 1.67917 | ||||||||
\(446\) | −31.7939 | −1.50549 | ||||||||
\(447\) | −13.4150 | −0.634509 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.3934 | −1.43435 | −0.717176 | − | 0.696892i | \(-0.754566\pi\) | ||||
−0.717176 | + | 0.696892i | \(0.754566\pi\) | |||||||
\(450\) | 20.3110 | 0.957469 | ||||||||
\(451\) | 1.10360 | 0.0519663 | ||||||||
\(452\) | −16.6775 | −0.784443 | ||||||||
\(453\) | −9.54474 | −0.448451 | ||||||||
\(454\) | 39.0649 | 1.83341 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.1103 | 0.660775 | ||||||||
\(457\) | 34.3753 | 1.60801 | 0.804004 | − | 0.594624i | \(-0.202699\pi\) | ||||
0.804004 | + | 0.594624i | \(0.202699\pi\) | |||||||
\(458\) | −35.4919 | −1.65843 | ||||||||
\(459\) | 24.7887 | 1.15704 | ||||||||
\(460\) | 42.7420 | 1.99286 | ||||||||
\(461\) | 18.6176 | 0.867109 | 0.433555 | − | 0.901127i | \(-0.357259\pi\) | ||||
0.433555 | + | 0.901127i | \(0.357259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2529 | −1.12713 | −0.563564 | − | 0.826073i | \(-0.690570\pi\) | ||||
−0.563564 | + | 0.826073i | \(0.690570\pi\) | |||||||
\(464\) | 1.68908 | 0.0784136 | ||||||||
\(465\) | 21.8611 | 1.01378 | ||||||||
\(466\) | 19.2881 | 0.893505 | ||||||||
\(467\) | 17.8900 | 0.827850 | 0.413925 | − | 0.910311i | \(-0.364158\pi\) | ||||
0.413925 | + | 0.910311i | \(0.364158\pi\) | |||||||
\(468\) | −46.7935 | −2.16303 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.98887 | 0.230120 | ||||||||
\(471\) | 8.08815 | 0.372682 | ||||||||
\(472\) | 5.81274 | 0.267553 | ||||||||
\(473\) | 11.8225 | 0.543601 | ||||||||
\(474\) | −7.67139 | −0.352359 | ||||||||
\(475\) | −17.3371 | −0.795479 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.4846 | −0.937924 | ||||||||
\(478\) | 58.5778 | 2.67929 | ||||||||
\(479\) | 35.1547 | 1.60626 | 0.803130 | − | 0.595803i | \(-0.203166\pi\) | ||||
0.803130 | + | 0.595803i | \(0.203166\pi\) | |||||||
\(480\) | 11.9601 | 0.545901 | ||||||||
\(481\) | −35.7522 | −1.63016 | ||||||||
\(482\) | −13.7997 | −0.628559 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −34.2769 | −1.55804 | ||||||||
\(485\) | 11.1196 | 0.504915 | ||||||||
\(486\) | −37.7782 | −1.71365 | ||||||||
\(487\) | 3.62881 | 0.164437 | 0.0822185 | − | 0.996614i | \(-0.473799\pi\) | ||||
0.0822185 | + | 0.996614i | \(0.473799\pi\) | |||||||
\(488\) | −24.8117 | −1.12317 | ||||||||
\(489\) | 11.7295 | 0.530426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.5727 | 1.28947 | 0.644734 | − | 0.764407i | \(-0.276968\pi\) | ||||
0.644734 | + | 0.764407i | \(0.276968\pi\) | |||||||
\(492\) | 3.38996 | 0.152831 | ||||||||
\(493\) | −6.72797 | −0.303012 | ||||||||
\(494\) | 62.7397 | 2.82279 | ||||||||
\(495\) | −6.90706 | −0.310449 | ||||||||
\(496\) | 9.46636 | 0.425052 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.3637 | 0.778088 | ||||||||
\(499\) | 12.6897 | 0.568070 | 0.284035 | − | 0.958814i | \(-0.408327\pi\) | ||||
0.284035 | + | 0.958814i | \(0.408327\pi\) | |||||||
\(500\) | −8.55977 | −0.382804 | ||||||||
\(501\) | 11.8972 | 0.531526 | ||||||||
\(502\) | −18.6692 | −0.833248 | ||||||||
\(503\) | −41.3782 | −1.84496 | −0.922481 | − | 0.386042i | \(-0.873842\pi\) | ||||
−0.922481 | + | 0.386042i | \(0.873842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.8470 | −1.55067 | ||||||||
\(506\) | −10.4154 | −0.463019 | ||||||||
\(507\) | 27.9192 | 1.23994 | ||||||||
\(508\) | 69.0495 | 3.06358 | ||||||||
\(509\) | 10.5433 | 0.467324 | 0.233662 | − | 0.972318i | \(-0.424929\pi\) | ||||
0.233662 | + | 0.972318i | \(0.424929\pi\) | |||||||
\(510\) | 34.8223 | 1.54196 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.1436 | 0.625064 | ||||||||
\(513\) | 20.2503 | 0.894071 | ||||||||
\(514\) | −3.16846 | −0.139755 | ||||||||
\(515\) | −55.9056 | −2.46350 | ||||||||
\(516\) | 36.3158 | 1.59871 | ||||||||
\(517\) | −0.773945 | −0.0340381 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.06594 | 0.178475 | ||||||||
\(520\) | −69.2243 | −3.03569 | ||||||||
\(521\) | −4.57724 | −0.200532 | −0.100266 | − | 0.994961i | \(-0.531969\pi\) | ||||
−0.100266 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(522\) | 6.43897 | 0.281826 | ||||||||
\(523\) | −22.9021 | −1.00144 | −0.500720 | − | 0.865609i | \(-0.666931\pi\) | ||||
−0.500720 | + | 0.865609i | \(0.666931\pi\) | |||||||
\(524\) | 9.81380 | 0.428718 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.2615 | −0.796240 | ||||||||
\(527\) | −37.7065 | −1.64252 | ||||||||
\(528\) | 1.35622 | 0.0590221 | ||||||||
\(529\) | −6.81748 | −0.296412 | ||||||||
\(530\) | −70.6005 | −3.06669 | ||||||||
\(531\) | 3.40016 | 0.147554 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.46984 | 0.280240 | ||||||||
\(534\) | −26.5143 | −1.14739 | ||||||||
\(535\) | −30.6449 | −1.32490 | ||||||||
\(536\) | −31.1428 | −1.34516 | ||||||||
\(537\) | 21.6693 | 0.935101 | ||||||||
\(538\) | 23.0201 | 0.992468 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −52.0541 | −2.24005 | ||||||||
\(541\) | 39.6068 | 1.70283 | 0.851416 | − | 0.524491i | \(-0.175745\pi\) | ||||
0.851416 | + | 0.524491i | \(0.175745\pi\) | |||||||
\(542\) | −51.9755 | −2.23254 | ||||||||
\(543\) | 18.2907 | 0.784929 | ||||||||
\(544\) | −20.6290 | −0.884462 | ||||||||
\(545\) | −22.8835 | −0.980222 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7170 | −0.500981 | −0.250490 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250490 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(548\) | −43.6426 | −1.86432 | ||||||||
\(549\) | −14.5136 | −0.619425 | ||||||||
\(550\) | −10.8597 | −0.463060 | ||||||||
\(551\) | −5.49618 | −0.234145 | ||||||||
\(552\) | −13.7326 | −0.584496 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 47.5993 | 2.02230 | ||||||||
\(555\) | −16.2105 | −0.688096 | ||||||||
\(556\) | −1.25419 | −0.0531895 | ||||||||
\(557\) | −7.17660 | −0.304082 | −0.152041 | − | 0.988374i | \(-0.548585\pi\) | ||||
−0.152041 | + | 0.988374i | \(0.548585\pi\) | |||||||
\(558\) | 36.0869 | 1.52768 | ||||||||
\(559\) | 69.3098 | 2.93149 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.40213 | −0.228078 | ||||||||
\(562\) | −61.3369 | −2.58734 | ||||||||
\(563\) | 6.36752 | 0.268359 | 0.134180 | − | 0.990957i | \(-0.457160\pi\) | ||||
0.134180 | + | 0.990957i | \(0.457160\pi\) | |||||||
\(564\) | −2.37736 | −0.100105 | ||||||||
\(565\) | −14.4318 | −0.607151 | ||||||||
\(566\) | −46.6120 | −1.95925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.8598 | −0.833298 | ||||||||
\(569\) | −13.6027 | −0.570256 | −0.285128 | − | 0.958489i | \(-0.592036\pi\) | ||||
−0.285128 | + | 0.958489i | \(0.592036\pi\) | |||||||
\(570\) | 28.4469 | 1.19151 | ||||||||
\(571\) | −25.5078 | −1.06747 | −0.533735 | − | 0.845652i | \(-0.679212\pi\) | ||||
−0.533735 | + | 0.845652i | \(0.679212\pi\) | |||||||
\(572\) | 25.0192 | 1.04611 | ||||||||
\(573\) | −4.09780 | −0.171188 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8729 | 0.703650 | ||||||||
\(576\) | 24.9868 | 1.04112 | ||||||||
\(577\) | −10.0533 | −0.418526 | −0.209263 | − | 0.977859i | \(-0.567106\pi\) | ||||
−0.209263 | + | 0.977859i | \(0.567106\pi\) | |||||||
\(578\) | −20.1791 | −0.839339 | ||||||||
\(579\) | −12.3717 | −0.514152 | ||||||||
\(580\) | 14.1281 | 0.586639 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.32326 | −0.345010 | ||||||||
\(583\) | 10.9525 | 0.453608 | ||||||||
\(584\) | −38.2929 | −1.58457 | ||||||||
\(585\) | −40.4927 | −1.67417 | ||||||||
\(586\) | 30.6141 | 1.26466 | ||||||||
\(587\) | −11.6413 | −0.480488 | −0.240244 | − | 0.970713i | \(-0.577227\pi\) | ||||
−0.240244 | + | 0.970713i | \(0.577227\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.8031 | −1.26922 | ||||||||
\(590\) | 11.7187 | 0.482451 | ||||||||
\(591\) | −14.1461 | −0.581891 | ||||||||
\(592\) | −7.01950 | −0.288500 | ||||||||
\(593\) | 5.56228 | 0.228416 | 0.114208 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114208 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(594\) | 12.6845 | 0.520453 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −48.5890 | −1.99028 | ||||||||
\(597\) | 16.7341 | 0.684882 | ||||||||
\(598\) | −61.0602 | −2.49694 | ||||||||
\(599\) | 22.4110 | 0.915687 | 0.457843 | − | 0.889033i | \(-0.348622\pi\) | ||||
0.457843 | + | 0.889033i | \(0.348622\pi\) | |||||||
\(600\) | −14.3185 | −0.584548 | ||||||||
\(601\) | −16.7631 | −0.683782 | −0.341891 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341891 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.2169 | −0.741851 | ||||||||
\(604\) | −34.5709 | −1.40667 | ||||||||
\(605\) | −29.6614 | −1.20591 | ||||||||
\(606\) | 26.0837 | 1.05958 | ||||||||
\(607\) | 28.8510 | 1.17102 | 0.585512 | − | 0.810663i | \(-0.300893\pi\) | ||||
0.585512 | + | 0.810663i | \(0.300893\pi\) | |||||||
\(608\) | −16.8522 | −0.683446 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −50.0214 | −2.02531 | ||||||||
\(611\) | −4.53726 | −0.183558 | ||||||||
\(612\) | 36.5951 | 1.47927 | ||||||||
\(613\) | −44.8822 | −1.81278 | −0.906388 | − | 0.422447i | \(-0.861171\pi\) | ||||
−0.906388 | + | 0.422447i | \(0.861171\pi\) | |||||||
\(614\) | 58.7302 | 2.37016 | ||||||||
\(615\) | 2.93350 | 0.118290 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.5219 | −1.71187 | −0.855933 | − | 0.517087i | \(-0.827016\pi\) | ||||
−0.855933 | + | 0.517087i | \(0.827016\pi\) | |||||||
\(618\) | 41.8466 | 1.68332 | ||||||||
\(619\) | −13.0509 | −0.524560 | −0.262280 | − | 0.964992i | \(-0.584474\pi\) | ||||
−0.262280 | + | 0.964992i | \(0.584474\pi\) | |||||||
\(620\) | 79.1804 | 3.17996 | ||||||||
\(621\) | −19.7082 | −0.790862 | ||||||||
\(622\) | −10.3682 | −0.415727 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.95088 | 0.318290 | ||||||||
\(625\) | −28.3791 | −1.13516 | ||||||||
\(626\) | −55.3011 | −2.21028 | ||||||||
\(627\) | −4.41308 | −0.176242 | ||||||||
\(628\) | 29.2951 | 1.16900 | ||||||||
\(629\) | 27.9602 | 1.11485 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6364 | −1.25943 | −0.629713 | − | 0.776828i | \(-0.716828\pi\) | ||||
−0.629713 | + | 0.776828i | \(0.716828\pi\) | |||||||
\(632\) | −11.9265 | −0.474410 | ||||||||
\(633\) | −7.46880 | −0.296858 | ||||||||
\(634\) | 41.3685 | 1.64295 | ||||||||
\(635\) | 59.7519 | 2.37118 | ||||||||
\(636\) | 33.6434 | 1.33405 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.44275 | −0.136300 | ||||||||
\(639\) | −11.6170 | −0.459560 | ||||||||
\(640\) | 61.3921 | 2.42674 | ||||||||
\(641\) | 6.06719 | 0.239640 | 0.119820 | − | 0.992796i | \(-0.461768\pi\) | ||||
0.119820 | + | 0.992796i | \(0.461768\pi\) | |||||||
\(642\) | 22.9384 | 0.905306 | ||||||||
\(643\) | 31.9549 | 1.26018 | 0.630088 | − | 0.776523i | \(-0.283019\pi\) | ||||
0.630088 | + | 0.776523i | \(0.283019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.4258 | 1.23739 | ||||||||
\(646\) | −49.0658 | −1.93047 | ||||||||
\(647\) | −8.92703 | −0.350958 | −0.175479 | − | 0.984483i | \(-0.556147\pi\) | ||||
−0.175479 | + | 0.984483i | \(0.556147\pi\) | |||||||
\(648\) | −5.12534 | −0.201342 | ||||||||
\(649\) | −1.81797 | −0.0713616 | ||||||||
\(650\) | −63.6653 | −2.49716 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.4840 | 1.66380 | ||||||||
\(653\) | 18.4326 | 0.721325 | 0.360662 | − | 0.932696i | \(-0.382551\pi\) | ||||
0.360662 | + | 0.932696i | \(0.382551\pi\) | |||||||
\(654\) | 17.1288 | 0.669790 | ||||||||
\(655\) | 8.49235 | 0.331824 | ||||||||
\(656\) | 1.27027 | 0.0495958 | ||||||||
\(657\) | −22.3994 | −0.873884 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.4381 | 0.913020 | 0.456510 | − | 0.889718i | \(-0.349099\pi\) | ||||
0.456510 | + | 0.889718i | \(0.349099\pi\) | |||||||
\(660\) | 11.3440 | 0.441565 | ||||||||
\(661\) | −13.1414 | −0.511142 | −0.255571 | − | 0.966790i | \(-0.582263\pi\) | ||||
−0.255571 | + | 0.966790i | \(0.582263\pi\) | |||||||
\(662\) | −50.9697 | −1.98099 | ||||||||
\(663\) | −31.6700 | −1.22996 | ||||||||
\(664\) | 26.9949 | 1.04760 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.7592 | −1.03690 | ||||||||
\(667\) | 5.34905 | 0.207116 | ||||||||
\(668\) | 43.0913 | 1.66725 | ||||||||
\(669\) | 13.1108 | 0.506891 | ||||||||
\(670\) | −62.7850 | −2.42560 | ||||||||
\(671\) | 7.76003 | 0.299573 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.7536 | −1.26256 | −0.631279 | − | 0.775556i | \(-0.717470\pi\) | ||||
−0.631279 | + | 0.775556i | \(0.717470\pi\) | |||||||
\(674\) | 25.8380 | 0.995243 | ||||||||
\(675\) | −20.5490 | −0.790932 | ||||||||
\(676\) | 101.123 | 3.88934 | ||||||||
\(677\) | −39.5121 | −1.51857 | −0.759286 | − | 0.650757i | \(-0.774452\pi\) | ||||
−0.759286 | + | 0.650757i | \(0.774452\pi\) | |||||||
\(678\) | 10.8025 | 0.414869 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 54.1371 | 2.07606 | ||||||||
\(681\) | −16.1091 | −0.617300 | ||||||||
\(682\) | −19.2947 | −0.738831 | ||||||||
\(683\) | −18.8293 | −0.720484 | −0.360242 | − | 0.932859i | \(-0.617306\pi\) | ||||
−0.360242 | + | 0.932859i | \(0.617306\pi\) | |||||||
\(684\) | 29.8951 | 1.14307 | ||||||||
\(685\) | −37.7660 | −1.44297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.6357 | 0.558385 | ||||||||
\(688\) | 13.6081 | 0.518804 | ||||||||
\(689\) | 64.2094 | 2.44618 | ||||||||
\(690\) | −27.6854 | −1.05396 | ||||||||
\(691\) | 3.93863 | 0.149833 | 0.0749163 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749163 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(692\) | 14.7268 | 0.559827 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 67.1602 | 2.54937 | ||||||||
\(695\) | −1.08531 | −0.0411682 | ||||||||
\(696\) | −4.53923 | −0.172059 | ||||||||
\(697\) | −5.05976 | −0.191652 | ||||||||
\(698\) | 79.5951 | 3.01272 | ||||||||
\(699\) | −7.95377 | −0.300839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0119 | 1.36015 | 0.680076 | − | 0.733142i | \(-0.261947\pi\) | ||||
0.680076 | + | 0.733142i | \(0.261947\pi\) | |||||||
\(702\) | 74.3632 | 2.80666 | ||||||||
\(703\) | 22.8411 | 0.861469 | ||||||||
\(704\) | −13.3597 | −0.503514 | ||||||||
\(705\) | −2.05724 | −0.0774803 | ||||||||
\(706\) | 35.6329 | 1.34106 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.58434 | −0.209872 | ||||||||
\(709\) | −48.2255 | −1.81115 | −0.905573 | − | 0.424190i | \(-0.860559\pi\) | ||||
−0.905573 | + | 0.424190i | \(0.860559\pi\) | |||||||
\(710\) | −40.0381 | −1.50260 | ||||||||
\(711\) | −6.97638 | −0.261635 | ||||||||
\(712\) | −41.2210 | −1.54482 | ||||||||
\(713\) | 29.9785 | 1.12270 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.6503 | 0.809677 | ||||||||
\(716\) | 78.4859 | 2.93316 | ||||||||
\(717\) | −24.1555 | −0.902105 | ||||||||
\(718\) | 54.0942 | 2.01878 | ||||||||
\(719\) | −31.9531 | −1.19165 | −0.595824 | − | 0.803115i | \(-0.703175\pi\) | ||||
−0.595824 | + | 0.803115i | \(0.703175\pi\) | |||||||
\(720\) | −7.95023 | −0.296288 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.49270 | 0.167201 | ||||||||
\(723\) | 5.69053 | 0.211633 | ||||||||
\(724\) | 66.2485 | 2.46211 | ||||||||
\(725\) | 5.57727 | 0.207134 | ||||||||
\(726\) | 22.2022 | 0.824002 | ||||||||
\(727\) | 27.5763 | 1.02275 | 0.511374 | − | 0.859359i | \(-0.329137\pi\) | ||||
0.511374 | + | 0.859359i | \(0.329137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.2209 | 0.415590 | ||||||||
\(730\) | −77.1999 | −2.85730 | ||||||||
\(731\) | −54.2040 | −2.00481 | ||||||||
\(732\) | 23.8368 | 0.881034 | ||||||||
\(733\) | −40.3227 | −1.48935 | −0.744676 | − | 0.667426i | \(-0.767396\pi\) | ||||
−0.744676 | + | 0.667426i | \(0.767396\pi\) | |||||||
\(734\) | 27.9898 | 1.03312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.4010 | 0.604551 | ||||||||
\(737\) | 9.74010 | 0.358781 | ||||||||
\(738\) | 4.84243 | 0.178252 | ||||||||
\(739\) | −11.1228 | −0.409158 | −0.204579 | − | 0.978850i | \(-0.565583\pi\) | ||||
−0.204579 | + | 0.978850i | \(0.565583\pi\) | |||||||
\(740\) | −58.7139 | −2.15837 | ||||||||
\(741\) | −25.8717 | −0.950422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3765 | −1.18778 | −0.593889 | − | 0.804547i | \(-0.702408\pi\) | ||||
−0.593889 | + | 0.804547i | \(0.702408\pi\) | |||||||
\(744\) | −25.4399 | −0.932670 | ||||||||
\(745\) | −42.0464 | −1.54046 | ||||||||
\(746\) | −11.7703 | −0.430941 | ||||||||
\(747\) | 15.7906 | 0.577749 | ||||||||
\(748\) | −19.5664 | −0.715418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.54444 | 0.202454 | ||||||||
\(751\) | −18.8396 | −0.687466 | −0.343733 | − | 0.939067i | \(-0.611692\pi\) | ||||
−0.343733 | + | 0.939067i | \(0.611692\pi\) | |||||||
\(752\) | −0.890834 | −0.0324854 | ||||||||
\(753\) | 7.69856 | 0.280551 | ||||||||
\(754\) | −20.1831 | −0.735026 | ||||||||
\(755\) | −29.9158 | −1.08875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.9592 | 1.59772 | 0.798862 | − | 0.601514i | \(-0.205436\pi\) | ||||
0.798862 | + | 0.601514i | \(0.205436\pi\) | |||||||
\(758\) | −61.3197 | −2.22723 | ||||||||
\(759\) | 4.29495 | 0.155897 | ||||||||
\(760\) | 44.2255 | 1.60423 | ||||||||
\(761\) | 11.9192 | 0.432069 | 0.216035 | − | 0.976386i | \(-0.430688\pi\) | ||||
0.216035 | + | 0.976386i | \(0.430688\pi\) | |||||||
\(762\) | −44.7256 | −1.62024 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.8422 | −0.536970 | ||||||||
\(765\) | 31.6675 | 1.14494 | ||||||||
\(766\) | 66.6448 | 2.40798 | ||||||||
\(767\) | −10.6579 | −0.384834 | ||||||||
\(768\) | −22.5304 | −0.812994 | ||||||||
\(769\) | −17.1165 | −0.617236 | −0.308618 | − | 0.951186i | \(-0.599866\pi\) | ||||
−0.308618 | + | 0.951186i | \(0.599866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30657 | 0.0470548 | ||||||||
\(772\) | −44.8102 | −1.61275 | ||||||||
\(773\) | 27.3944 | 0.985307 | 0.492653 | − | 0.870226i | \(-0.336027\pi\) | ||||
0.492653 | + | 0.870226i | \(0.336027\pi\) | |||||||
\(774\) | 51.8757 | 1.86463 | ||||||||
\(775\) | 31.2575 | 1.12280 | ||||||||
\(776\) | −12.9399 | −0.464516 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 83.1908 | 2.98253 | ||||||||
\(779\) | −4.13340 | −0.148094 | ||||||||
\(780\) | 66.5043 | 2.38124 | ||||||||
\(781\) | 6.21127 | 0.222257 | ||||||||
\(782\) | 47.7523 | 1.70762 | ||||||||
\(783\) | −6.51444 | −0.232807 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.3504 | 0.904796 | ||||||||
\(786\) | −6.35671 | −0.226736 | ||||||||
\(787\) | 19.5519 | 0.696949 | 0.348475 | − | 0.937318i | \(-0.386700\pi\) | ||||
0.348475 | + | 0.937318i | \(0.386700\pi\) | |||||||
\(788\) | −51.2367 | −1.82523 | ||||||||
\(789\) | 7.53043 | 0.268091 | ||||||||
\(790\) | −24.0442 | −0.855455 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.03777 | 0.285610 | ||||||||
\(793\) | 45.4932 | 1.61551 | ||||||||
\(794\) | 46.0227 | 1.63328 | ||||||||
\(795\) | 29.1133 | 1.03254 | ||||||||
\(796\) | 60.6106 | 2.14829 | ||||||||
\(797\) | 2.98961 | 0.105898 | 0.0529488 | − | 0.998597i | \(-0.483138\pi\) | ||||
0.0529488 | + | 0.998597i | \(0.483138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.54838 | 0.125533 | ||||||||
\(800\) | 17.1008 | 0.604604 | ||||||||
\(801\) | −24.1122 | −0.851962 | ||||||||
\(802\) | −63.5963 | −2.24566 | ||||||||
\(803\) | 11.9763 | 0.422636 | ||||||||
\(804\) | 29.9191 | 1.05516 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −113.115 | −3.98431 | ||||||||
\(807\) | −9.49273 | −0.334160 | ||||||||
\(808\) | 40.5516 | 1.42660 | ||||||||
\(809\) | −38.4129 | −1.35052 | −0.675262 | − | 0.737578i | \(-0.735970\pi\) | ||||
−0.675262 | + | 0.737578i | \(0.735970\pi\) | |||||||
\(810\) | −10.3329 | −0.363060 | ||||||||
\(811\) | 21.8757 | 0.768159 | 0.384079 | − | 0.923300i | \(-0.374519\pi\) | ||||
0.384079 | + | 0.923300i | \(0.374519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.4329 | 0.751686 | ||||||||
\(814\) | 14.3074 | 0.501474 | ||||||||
\(815\) | 36.7634 | 1.28777 | ||||||||
\(816\) | −6.21801 | −0.217674 | ||||||||
\(817\) | −44.2801 | −1.54916 | ||||||||
\(818\) | 24.8273 | 0.868066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.6251 | 0.371043 | ||||||||
\(821\) | 30.1818 | 1.05335 | 0.526676 | − | 0.850066i | \(-0.323438\pi\) | ||||
0.526676 | + | 0.850066i | \(0.323438\pi\) | |||||||
\(822\) | 28.2687 | 0.985984 | ||||||||
\(823\) | −10.3448 | −0.360599 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(824\) | 65.0576 | 2.26639 | ||||||||
\(825\) | 4.47819 | 0.155910 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4610 | 0.502858 | 0.251429 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251429 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(828\) | −29.0948 | −1.01111 | ||||||||
\(829\) | −1.47563 | −0.0512507 | −0.0256253 | − | 0.999672i | \(-0.508158\pi\) | ||||
−0.0256253 | + | 0.999672i | \(0.508158\pi\) | |||||||
\(830\) | 54.4227 | 1.88904 | ||||||||
\(831\) | −19.6283 | −0.680900 | ||||||||
\(832\) | −78.3216 | −2.71531 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.812379 | 0.0281304 | ||||||||
\(835\) | 37.2890 | 1.29044 | ||||||||
\(836\) | −15.9841 | −0.552822 | ||||||||
\(837\) | −36.5098 | −1.26196 | ||||||||
\(838\) | −17.9315 | −0.619435 | ||||||||
\(839\) | 22.0657 | 0.761794 | 0.380897 | − | 0.924617i | \(-0.375615\pi\) | ||||
0.380897 | + | 0.924617i | \(0.375615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2319 | −0.939031 | ||||||||
\(842\) | −71.6429 | −2.46898 | ||||||||
\(843\) | 25.2933 | 0.871147 | ||||||||
\(844\) | −27.0518 | −0.931163 | ||||||||
\(845\) | 87.5064 | 3.01031 | ||||||||
\(846\) | −3.39596 | −0.116756 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.6067 | 0.432916 | ||||||||
\(849\) | 19.2212 | 0.659671 | ||||||||
\(850\) | 49.7897 | 1.70777 | ||||||||
\(851\) | −22.2297 | −0.762023 | ||||||||
\(852\) | 19.0794 | 0.653651 | ||||||||
\(853\) | 46.2038 | 1.58199 | 0.790994 | − | 0.611824i | \(-0.209564\pi\) | ||||
0.790994 | + | 0.611824i | \(0.209564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.8697 | 0.884724 | ||||||||
\(856\) | 35.6616 | 1.21889 | ||||||||
\(857\) | −39.5203 | −1.34999 | −0.674994 | − | 0.737823i | \(-0.735854\pi\) | ||||
−0.674994 | + | 0.737823i | \(0.735854\pi\) | |||||||
\(858\) | −16.2058 | −0.553255 | ||||||||
\(859\) | 14.6171 | 0.498729 | 0.249364 | − | 0.968410i | \(-0.419778\pi\) | ||||
0.249364 | + | 0.968410i | \(0.419778\pi\) | |||||||
\(860\) | 113.824 | 3.88135 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.8368 | 1.25467 | ||||||||
\(863\) | 6.76865 | 0.230408 | 0.115204 | − | 0.993342i | \(-0.463248\pi\) | ||||
0.115204 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(864\) | −19.9743 | −0.679540 | ||||||||
\(865\) | 12.7438 | 0.433301 | ||||||||
\(866\) | 50.0179 | 1.69968 | ||||||||
\(867\) | 8.32117 | 0.282602 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.73008 | 0.126534 | ||||||||
\(870\) | −9.15125 | −0.310257 | ||||||||
\(871\) | 57.1014 | 1.93481 | ||||||||
\(872\) | 26.6296 | 0.901794 | ||||||||
\(873\) | −7.56920 | −0.256178 | ||||||||
\(874\) | 39.0096 | 1.31952 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 36.7883 | 1.24296 | ||||||||
\(877\) | −21.5235 | −0.726796 | −0.363398 | − | 0.931634i | \(-0.618383\pi\) | ||||
−0.363398 | + | 0.931634i | \(0.618383\pi\) | |||||||
\(878\) | −59.8869 | −2.02108 | ||||||||
\(879\) | −12.6242 | −0.425805 | ||||||||
\(880\) | 4.25078 | 0.143294 | ||||||||
\(881\) | −5.37272 | −0.181011 | −0.0905057 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905057 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.9943 | −0.942082 | −0.471041 | − | 0.882111i | \(-0.656122\pi\) | ||||
−0.471041 | + | 0.882111i | \(0.656122\pi\) | |||||||
\(884\) | −114.708 | −3.85805 | ||||||||
\(885\) | −4.83240 | −0.162439 | ||||||||
\(886\) | −53.4729 | −1.79646 | ||||||||
\(887\) | −49.1470 | −1.65020 | −0.825098 | − | 0.564989i | \(-0.808880\pi\) | ||||
−0.825098 | + | 0.564989i | \(0.808880\pi\) | |||||||
\(888\) | 18.8642 | 0.633040 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −83.1031 | −2.78562 | ||||||||
\(891\) | 1.60298 | 0.0537019 | ||||||||
\(892\) | 47.4869 | 1.58998 | ||||||||
\(893\) | 2.89873 | 0.0970023 | ||||||||
\(894\) | 31.4726 | 1.05260 | ||||||||
\(895\) | 67.9176 | 2.27024 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.1792 | 0.840708 | ||||||||
\(898\) | 71.3050 | 2.37948 | ||||||||
\(899\) | 9.90923 | 0.330491 | ||||||||
\(900\) | −30.3361 | −1.01120 | ||||||||
\(901\) | −50.2152 | −1.67291 | ||||||||
\(902\) | −2.58911 | −0.0862081 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.7944 | 0.558573 | ||||||||
\(905\) | 57.3280 | 1.90565 | ||||||||
\(906\) | 22.3927 | 0.743946 | ||||||||
\(907\) | 47.2961 | 1.57044 | 0.785220 | − | 0.619217i | \(-0.212550\pi\) | ||||
0.785220 | + | 0.619217i | \(0.212550\pi\) | |||||||
\(908\) | −58.3467 | −1.93630 | ||||||||
\(909\) | 23.7206 | 0.786763 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.45674 | −0.280184 | −0.140092 | − | 0.990138i | \(-0.544740\pi\) | ||||
−0.140092 | + | 0.990138i | \(0.544740\pi\) | |||||||
\(912\) | −5.07959 | −0.168202 | ||||||||
\(913\) | −8.44282 | −0.279417 | ||||||||
\(914\) | −80.6469 | −2.66756 | ||||||||
\(915\) | 20.6271 | 0.681912 | ||||||||
\(916\) | 53.0100 | 1.75150 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −58.1560 | −1.91943 | ||||||||
\(919\) | −11.3509 | −0.374433 | −0.187217 | − | 0.982319i | \(-0.559947\pi\) | ||||
−0.187217 | + | 0.982319i | \(0.559947\pi\) | |||||||
\(920\) | −43.0416 | −1.41904 | ||||||||
\(921\) | −24.2183 | −0.798021 | ||||||||
\(922\) | −43.6783 | −1.43847 | ||||||||
\(923\) | 36.4136 | 1.19857 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.1781 | −0.762090 | ||||||||
\(926\) | 56.8990 | 1.86982 | ||||||||
\(927\) | 38.0554 | 1.24990 | ||||||||
\(928\) | 5.42128 | 0.177962 | ||||||||
\(929\) | 16.7500 | 0.549549 | 0.274774 | − | 0.961509i | \(-0.411397\pi\) | ||||
0.274774 | + | 0.961509i | \(0.411397\pi\) | |||||||
\(930\) | −51.2877 | −1.68179 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.8084 | −0.943651 | ||||||||
\(933\) | 4.27550 | 0.139974 | ||||||||
\(934\) | −41.9712 | −1.37334 | ||||||||
\(935\) | −16.9317 | −0.553727 | ||||||||
\(936\) | 47.1215 | 1.54022 | ||||||||
\(937\) | −19.9865 | −0.652930 | −0.326465 | − | 0.945209i | \(-0.605858\pi\) | ||||
−0.326465 | + | 0.945209i | \(0.605858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.8043 | 0.744191 | ||||||||
\(940\) | −7.45129 | −0.243034 | ||||||||
\(941\) | −24.5244 | −0.799473 | −0.399736 | − | 0.916630i | \(-0.630898\pi\) | ||||
−0.399736 | + | 0.916630i | \(0.630898\pi\) | |||||||
\(942\) | −18.9754 | −0.618251 | ||||||||
\(943\) | 4.02275 | 0.130999 | ||||||||
\(944\) | −2.09254 | −0.0681064 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7365 | −0.901792 | ||||||||
\(947\) | 8.85782 | 0.287841 | 0.143920 | − | 0.989589i | \(-0.454029\pi\) | ||||
0.143920 | + | 0.989589i | \(0.454029\pi\) | |||||||
\(948\) | 11.4579 | 0.372134 | ||||||||
\(949\) | 70.2115 | 2.27916 | ||||||||
\(950\) | 40.6740 | 1.31964 | ||||||||
\(951\) | −17.0590 | −0.553175 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.9215 | −1.81148 | −0.905738 | − | 0.423839i | \(-0.860682\pi\) | ||||
−0.905738 | + | 0.423839i | \(0.860682\pi\) | |||||||
\(954\) | 48.0583 | 1.55594 | ||||||||
\(955\) | −12.8436 | −0.415610 | ||||||||
\(956\) | −87.4908 | −2.82965 | ||||||||
\(957\) | 1.41967 | 0.0458915 | ||||||||
\(958\) | −82.4755 | −2.66466 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −35.5119 | −1.14614 | ||||||||
\(961\) | 24.5357 | 0.791476 | ||||||||
\(962\) | 83.8773 | 2.70431 | ||||||||
\(963\) | 20.8602 | 0.672211 | ||||||||
\(964\) | 20.6110 | 0.663835 | ||||||||
\(965\) | −38.7764 | −1.24826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.6898 | −1.08339 | −0.541696 | − | 0.840575i | \(-0.682217\pi\) | ||||
−0.541696 | + | 0.840575i | \(0.682217\pi\) | |||||||
\(968\) | 34.5171 | 1.10942 | ||||||||
\(969\) | 20.2331 | 0.649981 | ||||||||
\(970\) | −26.0874 | −0.837615 | ||||||||
\(971\) | −10.2936 | −0.330339 | −0.165169 | − | 0.986265i | \(-0.552817\pi\) | ||||
−0.165169 | + | 0.986265i | \(0.552817\pi\) | |||||||
\(972\) | 56.4249 | 1.80983 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.51344 | −0.272788 | ||||||||
\(975\) | 26.2534 | 0.840782 | ||||||||
\(976\) | 8.93203 | 0.285907 | ||||||||
\(977\) | 1.35123 | 0.0432297 | 0.0216149 | − | 0.999766i | \(-0.493119\pi\) | ||||
0.0216149 | + | 0.999766i | \(0.493119\pi\) | |||||||
\(978\) | −27.5182 | −0.879936 | ||||||||
\(979\) | 12.8921 | 0.412034 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5770 | 0.497335 | ||||||||
\(982\) | −67.0336 | −2.13913 | ||||||||
\(983\) | −35.8190 | −1.14245 | −0.571225 | − | 0.820794i | \(-0.693531\pi\) | ||||
−0.571225 | + | 0.820794i | \(0.693531\pi\) | |||||||
\(984\) | −3.41372 | −0.108826 | ||||||||
\(985\) | −44.3376 | −1.41271 | ||||||||
\(986\) | 15.7843 | 0.502674 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −93.7069 | −2.98121 | ||||||||
\(989\) | 43.0947 | 1.37033 | ||||||||
\(990\) | 16.2045 | 0.515011 | ||||||||
\(991\) | −9.70619 | −0.308327 | −0.154164 | − | 0.988045i | \(-0.549268\pi\) | ||||
−0.154164 | + | 0.988045i | \(0.549268\pi\) | |||||||
\(992\) | 30.3833 | 0.964670 | ||||||||
\(993\) | 21.0182 | 0.666992 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.4493 | 1.66275 | ||||||||
\(996\) | −25.9342 | −0.821756 | ||||||||
\(997\) | 19.0659 | 0.603825 | 0.301912 | − | 0.953336i | \(-0.402375\pi\) | ||||
0.301912 | + | 0.953336i | \(0.402375\pi\) | |||||||
\(998\) | −29.7710 | −0.942384 | ||||||||
\(999\) | 27.0728 | 0.856545 |
(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 | 2009.2.a.u.1.2 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.2 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.2 | yes | 20 | 1.1 | even | 1 | trivial |