Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.02984\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.55594 | 0.898320 | 0.449160 | − | 0.893451i | \(-0.351723\pi\) | ||||
0.449160 | + | 0.893451i | \(0.351723\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.24033 | 1.00191 | 0.500953 | − | 0.865475i | \(-0.332983\pi\) | ||||
0.500953 | + | 0.865475i | \(0.332983\pi\) | |||||||
\(6\) | −1.55594 | −0.635208 | ||||||||
\(7\) | 2.27752 | 0.860821 | 0.430410 | − | 0.902633i | \(-0.358369\pi\) | ||||
0.430410 | + | 0.902633i | \(0.358369\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.579065 | −0.193022 | ||||||||
\(10\) | −2.24033 | −0.708454 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.55594 | 0.449160 | ||||||||
\(13\) | −2.75611 | −0.764406 | −0.382203 | − | 0.924078i | \(-0.624835\pi\) | ||||
−0.382203 | + | 0.924078i | \(0.624835\pi\) | |||||||
\(14\) | −2.27752 | −0.608692 | ||||||||
\(15\) | 3.48581 | 0.900031 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.571514 | 0.138612 | 0.0693062 | − | 0.997595i | \(-0.477921\pi\) | ||||
0.0693062 | + | 0.997595i | \(0.477921\pi\) | |||||||
\(18\) | 0.579065 | 0.136487 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.24033 | 0.500953 | ||||||||
\(21\) | 3.54367 | 0.773292 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.47493 | 1.97566 | 0.987830 | − | 0.155537i | \(-0.0497107\pi\) | ||||
0.987830 | + | 0.155537i | \(0.0497107\pi\) | |||||||
\(24\) | −1.55594 | −0.317604 | ||||||||
\(25\) | 0.0190711 | 0.00381423 | ||||||||
\(26\) | 2.75611 | 0.540517 | ||||||||
\(27\) | −5.56879 | −1.07171 | ||||||||
\(28\) | 2.27752 | 0.430410 | ||||||||
\(29\) | −1.99533 | −0.370523 | −0.185261 | − | 0.982689i | \(-0.559313\pi\) | ||||
−0.185261 | + | 0.982689i | \(0.559313\pi\) | |||||||
\(30\) | −3.48581 | −0.636418 | ||||||||
\(31\) | 8.92659 | 1.60326 | 0.801631 | − | 0.597819i | \(-0.203966\pi\) | ||||
0.801631 | + | 0.597819i | \(0.203966\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.571514 | −0.0980138 | ||||||||
\(35\) | 5.10239 | 0.862461 | ||||||||
\(36\) | −0.579065 | −0.0965108 | ||||||||
\(37\) | 7.48207 | 1.23004 | 0.615022 | − | 0.788510i | \(-0.289147\pi\) | ||||
0.615022 | + | 0.788510i | \(0.289147\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −4.28832 | −0.686681 | ||||||||
\(40\) | −2.24033 | −0.354227 | ||||||||
\(41\) | 0.0862369 | 0.0134679 | 0.00673397 | − | 0.999977i | \(-0.497856\pi\) | ||||
0.00673397 | + | 0.999977i | \(0.497856\pi\) | |||||||
\(42\) | −3.54367 | −0.546800 | ||||||||
\(43\) | −5.53342 | −0.843839 | −0.421920 | − | 0.906633i | \(-0.638644\pi\) | ||||
−0.421920 | + | 0.906633i | \(0.638644\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.29730 | −0.193389 | ||||||||
\(46\) | −9.47493 | −1.39700 | ||||||||
\(47\) | −9.68313 | −1.41243 | −0.706215 | − | 0.707997i | \(-0.749599\pi\) | ||||
−0.706215 | + | 0.707997i | \(0.749599\pi\) | |||||||
\(48\) | 1.55594 | 0.224580 | ||||||||
\(49\) | −1.81292 | −0.258988 | ||||||||
\(50\) | −0.0190711 | −0.00269706 | ||||||||
\(51\) | 0.889238 | 0.124518 | ||||||||
\(52\) | −2.75611 | −0.382203 | ||||||||
\(53\) | 4.40072 | 0.604485 | 0.302243 | − | 0.953231i | \(-0.402265\pi\) | ||||
0.302243 | + | 0.953231i | \(0.402265\pi\) | |||||||
\(54\) | 5.56879 | 0.757817 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.27752 | −0.304346 | ||||||||
\(57\) | 1.55594 | 0.206089 | ||||||||
\(58\) | 1.99533 | 0.261999 | ||||||||
\(59\) | 8.02502 | 1.04477 | 0.522384 | − | 0.852710i | \(-0.325043\pi\) | ||||
0.522384 | + | 0.852710i | \(0.325043\pi\) | |||||||
\(60\) | 3.48581 | 0.450016 | ||||||||
\(61\) | −3.73883 | −0.478709 | −0.239354 | − | 0.970932i | \(-0.576936\pi\) | ||||
−0.239354 | + | 0.970932i | \(0.576936\pi\) | |||||||
\(62\) | −8.92659 | −1.13368 | ||||||||
\(63\) | −1.31883 | −0.166157 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.17458 | −0.765863 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.91634 | 0.844965 | 0.422483 | − | 0.906371i | \(-0.361159\pi\) | ||||
0.422483 | + | 0.906371i | \(0.361159\pi\) | |||||||
\(68\) | 0.571514 | 0.0693062 | ||||||||
\(69\) | 14.7424 | 1.77477 | ||||||||
\(70\) | −5.10239 | −0.609852 | ||||||||
\(71\) | 4.91454 | 0.583248 | 0.291624 | − | 0.956533i | \(-0.405804\pi\) | ||||
0.291624 | + | 0.956533i | \(0.405804\pi\) | |||||||
\(72\) | 0.579065 | 0.0682435 | ||||||||
\(73\) | 10.7414 | 1.25719 | 0.628593 | − | 0.777734i | \(-0.283631\pi\) | ||||
0.628593 | + | 0.777734i | \(0.283631\pi\) | |||||||
\(74\) | −7.48207 | −0.869773 | ||||||||
\(75\) | 0.0296734 | 0.00342639 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.28832 | 0.485557 | ||||||||
\(79\) | 5.92179 | 0.666254 | 0.333127 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333127 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(80\) | 2.24033 | 0.250476 | ||||||||
\(81\) | −6.92749 | −0.769721 | ||||||||
\(82\) | −0.0862369 | −0.00952328 | ||||||||
\(83\) | 16.8470 | 1.84920 | 0.924601 | − | 0.380938i | \(-0.124399\pi\) | ||||
0.924601 | + | 0.380938i | \(0.124399\pi\) | |||||||
\(84\) | 3.54367 | 0.386646 | ||||||||
\(85\) | 1.28038 | 0.138877 | ||||||||
\(86\) | 5.53342 | 0.596684 | ||||||||
\(87\) | −3.10460 | −0.332848 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.14468 | 0.545335 | 0.272668 | − | 0.962108i | \(-0.412094\pi\) | ||||
0.272668 | + | 0.962108i | \(0.412094\pi\) | |||||||
\(90\) | 1.29730 | 0.136747 | ||||||||
\(91\) | −6.27708 | −0.658017 | ||||||||
\(92\) | 9.47493 | 0.987830 | ||||||||
\(93\) | 13.8892 | 1.44024 | ||||||||
\(94\) | 9.68313 | 0.998739 | ||||||||
\(95\) | 2.24033 | 0.229853 | ||||||||
\(96\) | −1.55594 | −0.158802 | ||||||||
\(97\) | 3.98358 | 0.404471 | 0.202236 | − | 0.979337i | \(-0.435179\pi\) | ||||
0.202236 | + | 0.979337i | \(0.435179\pi\) | |||||||
\(98\) | 1.81292 | 0.183132 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0190711 | 0.00190711 | ||||||||
\(101\) | −1.22629 | −0.122021 | −0.0610104 | − | 0.998137i | \(-0.519432\pi\) | ||||
−0.0610104 | + | 0.998137i | \(0.519432\pi\) | |||||||
\(102\) | −0.889238 | −0.0880477 | ||||||||
\(103\) | 6.31633 | 0.622367 | 0.311183 | − | 0.950350i | \(-0.399275\pi\) | ||||
0.311183 | + | 0.950350i | \(0.399275\pi\) | |||||||
\(104\) | 2.75611 | 0.270258 | ||||||||
\(105\) | 7.93898 | 0.774765 | ||||||||
\(106\) | −4.40072 | −0.427436 | ||||||||
\(107\) | −15.9287 | −1.53988 | −0.769940 | − | 0.638116i | \(-0.779714\pi\) | ||||
−0.769940 | + | 0.638116i | \(0.779714\pi\) | |||||||
\(108\) | −5.56879 | −0.535857 | ||||||||
\(109\) | −8.67279 | −0.830703 | −0.415352 | − | 0.909661i | \(-0.636341\pi\) | ||||
−0.415352 | + | 0.909661i | \(0.636341\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.6416 | 1.10497 | ||||||||
\(112\) | 2.27752 | 0.215205 | ||||||||
\(113\) | −0.297807 | −0.0280153 | −0.0140077 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140077 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(114\) | −1.55594 | −0.145727 | ||||||||
\(115\) | 21.2270 | 1.97942 | ||||||||
\(116\) | −1.99533 | −0.185261 | ||||||||
\(117\) | 1.59596 | 0.147547 | ||||||||
\(118\) | −8.02502 | −0.738763 | ||||||||
\(119\) | 1.30163 | 0.119320 | ||||||||
\(120\) | −3.48581 | −0.318209 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.73883 | 0.338498 | ||||||||
\(123\) | 0.134179 | 0.0120985 | ||||||||
\(124\) | 8.92659 | 0.801631 | ||||||||
\(125\) | −11.1589 | −0.998084 | ||||||||
\(126\) | 1.31883 | 0.117491 | ||||||||
\(127\) | 0.637264 | 0.0565480 | 0.0282740 | − | 0.999600i | \(-0.490999\pi\) | ||||
0.0282740 | + | 0.999600i | \(0.490999\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.60965 | −0.758037 | ||||||||
\(130\) | 6.17458 | 0.541547 | ||||||||
\(131\) | 21.8110 | 1.90564 | 0.952818 | − | 0.303542i | \(-0.0981693\pi\) | ||||
0.952818 | + | 0.303542i | \(0.0981693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.27752 | 0.197486 | ||||||||
\(134\) | −6.91634 | −0.597481 | ||||||||
\(135\) | −12.4759 | −1.07376 | ||||||||
\(136\) | −0.571514 | −0.0490069 | ||||||||
\(137\) | −1.60089 | −0.136773 | −0.0683866 | − | 0.997659i | \(-0.521785\pi\) | ||||
−0.0683866 | + | 0.997659i | \(0.521785\pi\) | |||||||
\(138\) | −14.7424 | −1.25496 | ||||||||
\(139\) | 15.9213 | 1.35043 | 0.675214 | − | 0.737621i | \(-0.264051\pi\) | ||||
0.675214 | + | 0.737621i | \(0.264051\pi\) | |||||||
\(140\) | 5.10239 | 0.431230 | ||||||||
\(141\) | −15.0663 | −1.26881 | ||||||||
\(142\) | −4.91454 | −0.412419 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.579065 | −0.0482554 | ||||||||
\(145\) | −4.47019 | −0.371229 | ||||||||
\(146\) | −10.7414 | −0.888965 | ||||||||
\(147\) | −2.82078 | −0.232654 | ||||||||
\(148\) | 7.48207 | 0.615022 | ||||||||
\(149\) | −4.19884 | −0.343982 | −0.171991 | − | 0.985098i | \(-0.555020\pi\) | ||||
−0.171991 | + | 0.985098i | \(0.555020\pi\) | |||||||
\(150\) | −0.0296734 | −0.00242283 | ||||||||
\(151\) | 0.918503 | 0.0747467 | 0.0373733 | − | 0.999301i | \(-0.488101\pi\) | ||||
0.0373733 | + | 0.999301i | \(0.488101\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −0.330944 | −0.0267552 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.9985 | 1.60632 | ||||||||
\(156\) | −4.28832 | −0.343341 | ||||||||
\(157\) | −11.8346 | −0.944505 | −0.472252 | − | 0.881463i | \(-0.656559\pi\) | ||||
−0.472252 | + | 0.881463i | \(0.656559\pi\) | |||||||
\(158\) | −5.92179 | −0.471113 | ||||||||
\(159\) | 6.84723 | 0.543021 | ||||||||
\(160\) | −2.24033 | −0.177114 | ||||||||
\(161\) | 21.5793 | 1.70069 | ||||||||
\(162\) | 6.92749 | 0.544275 | ||||||||
\(163\) | −7.54426 | −0.590912 | −0.295456 | − | 0.955356i | \(-0.595472\pi\) | ||||
−0.295456 | + | 0.955356i | \(0.595472\pi\) | |||||||
\(164\) | 0.0862369 | 0.00673397 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.8470 | −1.30758 | ||||||||
\(167\) | 9.75174 | 0.754612 | 0.377306 | − | 0.926089i | \(-0.376850\pi\) | ||||
0.377306 | + | 0.926089i | \(0.376850\pi\) | |||||||
\(168\) | −3.54367 | −0.273400 | ||||||||
\(169\) | −5.40388 | −0.415683 | ||||||||
\(170\) | −1.28038 | −0.0982005 | ||||||||
\(171\) | −0.579065 | −0.0442822 | ||||||||
\(172\) | −5.53342 | −0.421920 | ||||||||
\(173\) | −9.90137 | −0.752787 | −0.376393 | − | 0.926460i | \(-0.622836\pi\) | ||||
−0.376393 | + | 0.926460i | \(0.622836\pi\) | |||||||
\(174\) | 3.10460 | 0.235359 | ||||||||
\(175\) | 0.0434348 | 0.00328336 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4864 | 0.938536 | ||||||||
\(178\) | −5.14468 | −0.385610 | ||||||||
\(179\) | 15.8720 | 1.18633 | 0.593164 | − | 0.805081i | \(-0.297878\pi\) | ||||
0.593164 | + | 0.805081i | \(0.297878\pi\) | |||||||
\(180\) | −1.29730 | −0.0966947 | ||||||||
\(181\) | −17.7160 | −1.31682 | −0.658410 | − | 0.752660i | \(-0.728771\pi\) | ||||
−0.658410 | + | 0.752660i | \(0.728771\pi\) | |||||||
\(182\) | 6.27708 | 0.465288 | ||||||||
\(183\) | −5.81738 | −0.430033 | ||||||||
\(184\) | −9.47493 | −0.698501 | ||||||||
\(185\) | 16.7623 | 1.23239 | ||||||||
\(186\) | −13.8892 | −1.01841 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.68313 | −0.706215 | ||||||||
\(189\) | −12.6830 | −0.922554 | ||||||||
\(190\) | −2.24033 | −0.162531 | ||||||||
\(191\) | −17.5478 | −1.26971 | −0.634857 | − | 0.772629i | \(-0.718941\pi\) | ||||
−0.634857 | + | 0.772629i | \(0.718941\pi\) | |||||||
\(192\) | 1.55594 | 0.112290 | ||||||||
\(193\) | 13.1066 | 0.943437 | 0.471719 | − | 0.881749i | \(-0.343634\pi\) | ||||
0.471719 | + | 0.881749i | \(0.343634\pi\) | |||||||
\(194\) | −3.98358 | −0.286004 | ||||||||
\(195\) | −9.60725 | −0.687990 | ||||||||
\(196\) | −1.81292 | −0.129494 | ||||||||
\(197\) | −15.2492 | −1.08646 | −0.543230 | − | 0.839584i | \(-0.682799\pi\) | ||||
−0.543230 | + | 0.839584i | \(0.682799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4862 | 0.956009 | 0.478005 | − | 0.878357i | \(-0.341360\pi\) | ||||
0.478005 | + | 0.878357i | \(0.341360\pi\) | |||||||
\(200\) | −0.0190711 | −0.00134853 | ||||||||
\(201\) | 10.7614 | 0.759049 | ||||||||
\(202\) | 1.22629 | 0.0862818 | ||||||||
\(203\) | −4.54439 | −0.318954 | ||||||||
\(204\) | 0.889238 | 0.0622591 | ||||||||
\(205\) | 0.193199 | 0.0134936 | ||||||||
\(206\) | −6.31633 | −0.440080 | ||||||||
\(207\) | −5.48660 | −0.381345 | ||||||||
\(208\) | −2.75611 | −0.191102 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −7.93898 | −0.547842 | ||||||||
\(211\) | −2.15813 | −0.148572 | −0.0742858 | − | 0.997237i | \(-0.523668\pi\) | ||||
−0.0742858 | + | 0.997237i | \(0.523668\pi\) | |||||||
\(212\) | 4.40072 | 0.302243 | ||||||||
\(213\) | 7.64670 | 0.523943 | ||||||||
\(214\) | 15.9287 | 1.08886 | ||||||||
\(215\) | −12.3967 | −0.845447 | ||||||||
\(216\) | 5.56879 | 0.378908 | ||||||||
\(217\) | 20.3305 | 1.38012 | ||||||||
\(218\) | 8.67279 | 0.587396 | ||||||||
\(219\) | 16.7129 | 1.12936 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.57515 | −0.105956 | ||||||||
\(222\) | −11.6416 | −0.781334 | ||||||||
\(223\) | 6.76418 | 0.452963 | 0.226482 | − | 0.974015i | \(-0.427278\pi\) | ||||
0.226482 | + | 0.974015i | \(0.427278\pi\) | |||||||
\(224\) | −2.27752 | −0.152173 | ||||||||
\(225\) | −0.0110434 | −0.000736228 0 | ||||||||
\(226\) | 0.297807 | 0.0198098 | ||||||||
\(227\) | 6.68912 | 0.443973 | 0.221986 | − | 0.975050i | \(-0.428746\pi\) | ||||
0.221986 | + | 0.975050i | \(0.428746\pi\) | |||||||
\(228\) | 1.55594 | 0.103044 | ||||||||
\(229\) | 0.645439 | 0.0426518 | 0.0213259 | − | 0.999773i | \(-0.493211\pi\) | ||||
0.0213259 | + | 0.999773i | \(0.493211\pi\) | |||||||
\(230\) | −21.2270 | −1.39966 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.99533 | 0.131000 | ||||||||
\(233\) | −5.52617 | −0.362031 | −0.181016 | − | 0.983480i | \(-0.557938\pi\) | ||||
−0.181016 | + | 0.983480i | \(0.557938\pi\) | |||||||
\(234\) | −1.59596 | −0.104331 | ||||||||
\(235\) | −21.6934 | −1.41512 | ||||||||
\(236\) | 8.02502 | 0.522384 | ||||||||
\(237\) | 9.21393 | 0.598509 | ||||||||
\(238\) | −1.30163 | −0.0843723 | ||||||||
\(239\) | −24.0112 | −1.55316 | −0.776578 | − | 0.630021i | \(-0.783046\pi\) | ||||
−0.776578 | + | 0.630021i | \(0.783046\pi\) | |||||||
\(240\) | 3.48581 | 0.225008 | ||||||||
\(241\) | 12.5817 | 0.810461 | 0.405231 | − | 0.914214i | \(-0.367191\pi\) | ||||
0.405231 | + | 0.914214i | \(0.367191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.92766 | 0.380259 | ||||||||
\(244\) | −3.73883 | −0.239354 | ||||||||
\(245\) | −4.06153 | −0.259481 | ||||||||
\(246\) | −0.134179 | −0.00855495 | ||||||||
\(247\) | −2.75611 | −0.175367 | ||||||||
\(248\) | −8.92659 | −0.566839 | ||||||||
\(249\) | 26.2129 | 1.66117 | ||||||||
\(250\) | 11.1589 | 0.705752 | ||||||||
\(251\) | −27.2335 | −1.71896 | −0.859480 | − | 0.511169i | \(-0.829213\pi\) | ||||
−0.859480 | + | 0.511169i | \(0.829213\pi\) | |||||||
\(252\) | −1.31883 | −0.0830785 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.637264 | −0.0399855 | ||||||||
\(255\) | 1.99219 | 0.124756 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.8288 | −1.73591 | −0.867956 | − | 0.496641i | \(-0.834567\pi\) | ||||
−0.867956 | + | 0.496641i | \(0.834567\pi\) | |||||||
\(258\) | 8.60965 | 0.536013 | ||||||||
\(259\) | 17.0405 | 1.05885 | ||||||||
\(260\) | −6.17458 | −0.382931 | ||||||||
\(261\) | 1.15542 | 0.0715189 | ||||||||
\(262\) | −21.8110 | −1.34749 | ||||||||
\(263\) | −29.9986 | −1.84979 | −0.924895 | − | 0.380222i | \(-0.875848\pi\) | ||||
−0.924895 | + | 0.380222i | \(0.875848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.85905 | 0.605637 | ||||||||
\(266\) | −2.27752 | −0.139644 | ||||||||
\(267\) | 8.00479 | 0.489885 | ||||||||
\(268\) | 6.91634 | 0.422483 | ||||||||
\(269\) | −1.89146 | −0.115325 | −0.0576623 | − | 0.998336i | \(-0.518365\pi\) | ||||
−0.0576623 | + | 0.998336i | \(0.518365\pi\) | |||||||
\(270\) | 12.4759 | 0.759261 | ||||||||
\(271\) | −18.2983 | −1.11154 | −0.555772 | − | 0.831335i | \(-0.687577\pi\) | ||||
−0.555772 | + | 0.831335i | \(0.687577\pi\) | |||||||
\(272\) | 0.571514 | 0.0346531 | ||||||||
\(273\) | −9.76673 | −0.591109 | ||||||||
\(274\) | 1.60089 | 0.0967132 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.7424 | 0.887387 | ||||||||
\(277\) | 3.69005 | 0.221714 | 0.110857 | − | 0.993836i | \(-0.464640\pi\) | ||||
0.110857 | + | 0.993836i | \(0.464640\pi\) | |||||||
\(278\) | −15.9213 | −0.954897 | ||||||||
\(279\) | −5.16908 | −0.309464 | ||||||||
\(280\) | −5.10239 | −0.304926 | ||||||||
\(281\) | 23.5460 | 1.40463 | 0.702317 | − | 0.711864i | \(-0.252149\pi\) | ||||
0.702317 | + | 0.711864i | \(0.252149\pi\) | |||||||
\(282\) | 15.0663 | 0.897187 | ||||||||
\(283\) | 15.4242 | 0.916871 | 0.458435 | − | 0.888728i | \(-0.348410\pi\) | ||||
0.458435 | + | 0.888728i | \(0.348410\pi\) | |||||||
\(284\) | 4.91454 | 0.291624 | ||||||||
\(285\) | 3.48581 | 0.206481 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.196406 | 0.0115935 | ||||||||
\(288\) | 0.579065 | 0.0341217 | ||||||||
\(289\) | −16.6734 | −0.980787 | ||||||||
\(290\) | 4.47019 | 0.262498 | ||||||||
\(291\) | 6.19819 | 0.363344 | ||||||||
\(292\) | 10.7414 | 0.628593 | ||||||||
\(293\) | 15.3414 | 0.896251 | 0.448126 | − | 0.893971i | \(-0.352092\pi\) | ||||
0.448126 | + | 0.893971i | \(0.352092\pi\) | |||||||
\(294\) | 2.82078 | 0.164511 | ||||||||
\(295\) | 17.9787 | 1.04676 | ||||||||
\(296\) | −7.48207 | −0.434887 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.19884 | 0.243232 | ||||||||
\(299\) | −26.1139 | −1.51021 | ||||||||
\(300\) | 0.0296734 | 0.00171320 | ||||||||
\(301\) | −12.6025 | −0.726394 | ||||||||
\(302\) | −0.918503 | −0.0528539 | ||||||||
\(303\) | −1.90803 | −0.109614 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −8.37622 | −0.479621 | ||||||||
\(306\) | 0.330944 | 0.0189188 | ||||||||
\(307\) | 23.5750 | 1.34550 | 0.672749 | − | 0.739870i | \(-0.265113\pi\) | ||||
0.672749 | + | 0.739870i | \(0.265113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.82780 | 0.559084 | ||||||||
\(310\) | −19.9985 | −1.13584 | ||||||||
\(311\) | −4.17781 | −0.236902 | −0.118451 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118451 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(312\) | 4.28832 | 0.242779 | ||||||||
\(313\) | −30.2227 | −1.70829 | −0.854144 | − | 0.520036i | \(-0.825919\pi\) | ||||
−0.854144 | + | 0.520036i | \(0.825919\pi\) | |||||||
\(314\) | 11.8346 | 0.667866 | ||||||||
\(315\) | −2.95461 | −0.166474 | ||||||||
\(316\) | 5.92179 | 0.333127 | ||||||||
\(317\) | 17.3175 | 0.972647 | 0.486324 | − | 0.873779i | \(-0.338338\pi\) | ||||
0.486324 | + | 0.873779i | \(0.338338\pi\) | |||||||
\(318\) | −6.84723 | −0.383974 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.24033 | 0.125238 | ||||||||
\(321\) | −24.7840 | −1.38331 | ||||||||
\(322\) | −21.5793 | −1.20257 | ||||||||
\(323\) | 0.571514 | 0.0317999 | ||||||||
\(324\) | −6.92749 | −0.384860 | ||||||||
\(325\) | −0.0525621 | −0.00291562 | ||||||||
\(326\) | 7.54426 | 0.417838 | ||||||||
\(327\) | −13.4943 | −0.746237 | ||||||||
\(328\) | −0.0862369 | −0.00476164 | ||||||||
\(329\) | −22.0535 | −1.21585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.13686 | −0.502207 | −0.251104 | − | 0.967960i | \(-0.580793\pi\) | ||||
−0.251104 | + | 0.967960i | \(0.580793\pi\) | |||||||
\(332\) | 16.8470 | 0.924601 | ||||||||
\(333\) | −4.33261 | −0.237425 | ||||||||
\(334\) | −9.75174 | −0.533591 | ||||||||
\(335\) | 15.4949 | 0.846575 | ||||||||
\(336\) | 3.54367 | 0.193323 | ||||||||
\(337\) | −9.49487 | −0.517219 | −0.258609 | − | 0.965982i | \(-0.583264\pi\) | ||||
−0.258609 | + | 0.965982i | \(0.583264\pi\) | |||||||
\(338\) | 5.40388 | 0.293932 | ||||||||
\(339\) | −0.463368 | −0.0251667 | ||||||||
\(340\) | 1.28038 | 0.0694383 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.579065 | 0.0313122 | ||||||||
\(343\) | −20.0716 | −1.08376 | ||||||||
\(344\) | 5.53342 | 0.298342 | ||||||||
\(345\) | 33.0278 | 1.77816 | ||||||||
\(346\) | 9.90137 | 0.532301 | ||||||||
\(347\) | 12.4664 | 0.669234 | 0.334617 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334617 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(348\) | −3.10460 | −0.166424 | ||||||||
\(349\) | 29.2430 | 1.56534 | 0.782672 | − | 0.622434i | \(-0.213856\pi\) | ||||
0.782672 | + | 0.622434i | \(0.213856\pi\) | |||||||
\(350\) | −0.0434348 | −0.00232169 | ||||||||
\(351\) | 15.3482 | 0.819226 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.95957 | −0.530095 | −0.265047 | − | 0.964235i | \(-0.585388\pi\) | ||||
−0.265047 | + | 0.964235i | \(0.585388\pi\) | |||||||
\(354\) | −12.4864 | −0.663646 | ||||||||
\(355\) | 11.0102 | 0.584359 | ||||||||
\(356\) | 5.14468 | 0.272668 | ||||||||
\(357\) | 2.02526 | 0.107188 | ||||||||
\(358\) | −15.8720 | −0.838861 | ||||||||
\(359\) | 9.89422 | 0.522197 | 0.261099 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261099 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(360\) | 1.29730 | 0.0683735 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.7160 | 0.931132 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.27708 | −0.329008 | ||||||||
\(365\) | 24.0643 | 1.25958 | ||||||||
\(366\) | 5.81738 | 0.304080 | ||||||||
\(367\) | −1.78588 | −0.0932222 | −0.0466111 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466111 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(368\) | 9.47493 | 0.493915 | ||||||||
\(369\) | −0.0499368 | −0.00259961 | ||||||||
\(370\) | −16.7623 | −0.871430 | ||||||||
\(371\) | 10.0227 | 0.520353 | ||||||||
\(372\) | 13.8892 | 0.720121 | ||||||||
\(373\) | 11.8730 | 0.614762 | 0.307381 | − | 0.951586i | \(-0.400547\pi\) | ||||
0.307381 | + | 0.951586i | \(0.400547\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.3626 | −0.896598 | ||||||||
\(376\) | 9.68313 | 0.499369 | ||||||||
\(377\) | 5.49933 | 0.283230 | ||||||||
\(378\) | 12.6830 | 0.652344 | ||||||||
\(379\) | 14.5469 | 0.747226 | 0.373613 | − | 0.927585i | \(-0.378119\pi\) | ||||
0.373613 | + | 0.927585i | \(0.378119\pi\) | |||||||
\(380\) | 2.24033 | 0.114926 | ||||||||
\(381\) | 0.991542 | 0.0507982 | ||||||||
\(382\) | 17.5478 | 0.897824 | ||||||||
\(383\) | 10.9005 | 0.556988 | 0.278494 | − | 0.960438i | \(-0.410165\pi\) | ||||
0.278494 | + | 0.960438i | \(0.410165\pi\) | |||||||
\(384\) | −1.55594 | −0.0794010 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1066 | −0.667111 | ||||||||
\(387\) | 3.20421 | 0.162879 | ||||||||
\(388\) | 3.98358 | 0.202236 | ||||||||
\(389\) | 2.85935 | 0.144975 | 0.0724874 | − | 0.997369i | \(-0.476906\pi\) | ||||
0.0724874 | + | 0.997369i | \(0.476906\pi\) | |||||||
\(390\) | 9.60725 | 0.486482 | ||||||||
\(391\) | 5.41505 | 0.273851 | ||||||||
\(392\) | 1.81292 | 0.0915661 | ||||||||
\(393\) | 33.9365 | 1.71187 | ||||||||
\(394\) | 15.2492 | 0.768244 | ||||||||
\(395\) | 13.2668 | 0.667523 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.34242 | −0.0673741 | −0.0336870 | − | 0.999432i | \(-0.510725\pi\) | ||||
−0.0336870 | + | 0.999432i | \(0.510725\pi\) | |||||||
\(398\) | −13.4862 | −0.676001 | ||||||||
\(399\) | 3.54367 | 0.177405 | ||||||||
\(400\) | 0.0190711 | 0.000953556 0 | ||||||||
\(401\) | −25.2632 | −1.26159 | −0.630793 | − | 0.775951i | \(-0.717270\pi\) | ||||
−0.630793 | + | 0.775951i | \(0.717270\pi\) | |||||||
\(402\) | −10.7614 | −0.536729 | ||||||||
\(403\) | −24.6026 | −1.22554 | ||||||||
\(404\) | −1.22629 | −0.0610104 | ||||||||
\(405\) | −15.5198 | −0.771188 | ||||||||
\(406\) | 4.54439 | 0.225534 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.889238 | −0.0440239 | ||||||||
\(409\) | −10.9069 | −0.539312 | −0.269656 | − | 0.962957i | \(-0.586910\pi\) | ||||
−0.269656 | + | 0.962957i | \(0.586910\pi\) | |||||||
\(410\) | −0.193199 | −0.00954142 | ||||||||
\(411\) | −2.49088 | −0.122866 | ||||||||
\(412\) | 6.31633 | 0.311183 | ||||||||
\(413\) | 18.2771 | 0.899358 | ||||||||
\(414\) | 5.48660 | 0.269652 | ||||||||
\(415\) | 37.7429 | 1.85272 | ||||||||
\(416\) | 2.75611 | 0.135129 | ||||||||
\(417\) | 24.7725 | 1.21312 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.08955 | 0.444054 | 0.222027 | − | 0.975041i | \(-0.428733\pi\) | ||||
0.222027 | + | 0.975041i | \(0.428733\pi\) | |||||||
\(420\) | 7.93898 | 0.387383 | ||||||||
\(421\) | 34.5218 | 1.68249 | 0.841244 | − | 0.540655i | \(-0.181824\pi\) | ||||
0.841244 | + | 0.540655i | \(0.181824\pi\) | |||||||
\(422\) | 2.15813 | 0.105056 | ||||||||
\(423\) | 5.60716 | 0.272630 | ||||||||
\(424\) | −4.40072 | −0.213718 | ||||||||
\(425\) | 0.0108994 | 0.000528699 0 | ||||||||
\(426\) | −7.64670 | −0.370484 | ||||||||
\(427\) | −8.51526 | −0.412082 | ||||||||
\(428\) | −15.9287 | −0.769940 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.3967 | 0.597821 | ||||||||
\(431\) | 3.67160 | 0.176855 | 0.0884273 | − | 0.996083i | \(-0.471816\pi\) | ||||
0.0884273 | + | 0.996083i | \(0.471816\pi\) | |||||||
\(432\) | −5.56879 | −0.267929 | ||||||||
\(433\) | −9.59701 | −0.461203 | −0.230602 | − | 0.973048i | \(-0.574069\pi\) | ||||
−0.230602 | + | 0.973048i | \(0.574069\pi\) | |||||||
\(434\) | −20.3305 | −0.975893 | ||||||||
\(435\) | −6.95532 | −0.333482 | ||||||||
\(436\) | −8.67279 | −0.415352 | ||||||||
\(437\) | 9.47493 | 0.453248 | ||||||||
\(438\) | −16.7129 | −0.798575 | ||||||||
\(439\) | 5.20790 | 0.248560 | 0.124280 | − | 0.992247i | \(-0.460338\pi\) | ||||
0.124280 | + | 0.992247i | \(0.460338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.04980 | 0.0499903 | ||||||||
\(442\) | 1.57515 | 0.0749224 | ||||||||
\(443\) | −11.5968 | −0.550981 | −0.275490 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275490 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(444\) | 11.6416 | 0.552487 | ||||||||
\(445\) | 11.5258 | 0.546374 | ||||||||
\(446\) | −6.76418 | −0.320293 | ||||||||
\(447\) | −6.53312 | −0.309006 | ||||||||
\(448\) | 2.27752 | 0.107603 | ||||||||
\(449\) | −19.1493 | −0.903711 | −0.451856 | − | 0.892091i | \(-0.649238\pi\) | ||||
−0.451856 | + | 0.892091i | \(0.649238\pi\) | |||||||
\(450\) | 0.0110434 | 0.000520592 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.297807 | −0.0140077 | ||||||||
\(453\) | 1.42913 | 0.0671464 | ||||||||
\(454\) | −6.68912 | −0.313936 | ||||||||
\(455\) | −14.0627 | −0.659270 | ||||||||
\(456\) | −1.55594 | −0.0728634 | ||||||||
\(457\) | −15.2474 | −0.713243 | −0.356622 | − | 0.934249i | \(-0.616071\pi\) | ||||
−0.356622 | + | 0.934249i | \(0.616071\pi\) | |||||||
\(458\) | −0.645439 | −0.0301594 | ||||||||
\(459\) | −3.18264 | −0.148553 | ||||||||
\(460\) | 21.2270 | 0.989712 | ||||||||
\(461\) | −13.1903 | −0.614336 | −0.307168 | − | 0.951655i | \(-0.599381\pi\) | ||||
−0.307168 | + | 0.951655i | \(0.599381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8312 | −0.735740 | −0.367870 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367870 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(464\) | −1.99533 | −0.0926307 | ||||||||
\(465\) | 31.1164 | 1.44299 | ||||||||
\(466\) | 5.52617 | 0.255995 | ||||||||
\(467\) | −14.8060 | −0.685140 | −0.342570 | − | 0.939492i | \(-0.611297\pi\) | ||||
−0.342570 | + | 0.939492i | \(0.611297\pi\) | |||||||
\(468\) | 1.59596 | 0.0737735 | ||||||||
\(469\) | 15.7521 | 0.727363 | ||||||||
\(470\) | 21.6934 | 1.00064 | ||||||||
\(471\) | −18.4139 | −0.848467 | ||||||||
\(472\) | −8.02502 | −0.369382 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9.21393 | −0.423210 | ||||||||
\(475\) | 0.0190711 | 0.000875043 0 | ||||||||
\(476\) | 1.30163 | 0.0596602 | ||||||||
\(477\) | −2.54830 | −0.116679 | ||||||||
\(478\) | 24.0112 | 1.09825 | ||||||||
\(479\) | −21.4058 | −0.978055 | −0.489028 | − | 0.872268i | \(-0.662648\pi\) | ||||
−0.489028 | + | 0.872268i | \(0.662648\pi\) | |||||||
\(480\) | −3.48581 | −0.159105 | ||||||||
\(481\) | −20.6214 | −0.940254 | ||||||||
\(482\) | −12.5817 | −0.573083 | ||||||||
\(483\) | 33.5760 | 1.52776 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.92453 | 0.405242 | ||||||||
\(486\) | −5.92766 | −0.268884 | ||||||||
\(487\) | −18.0587 | −0.818320 | −0.409160 | − | 0.912463i | \(-0.634178\pi\) | ||||
−0.409160 | + | 0.912463i | \(0.634178\pi\) | |||||||
\(488\) | 3.73883 | 0.169249 | ||||||||
\(489\) | −11.7384 | −0.530828 | ||||||||
\(490\) | 4.06153 | 0.183481 | ||||||||
\(491\) | −26.9808 | −1.21763 | −0.608813 | − | 0.793314i | \(-0.708354\pi\) | ||||
−0.608813 | + | 0.793314i | \(0.708354\pi\) | |||||||
\(492\) | 0.134179 | 0.00604926 | ||||||||
\(493\) | −1.14036 | −0.0513590 | ||||||||
\(494\) | 2.75611 | 0.124003 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.92659 | 0.400816 | ||||||||
\(497\) | 11.1929 | 0.502072 | ||||||||
\(498\) | −26.2129 | −1.17463 | ||||||||
\(499\) | 41.4218 | 1.85429 | 0.927147 | − | 0.374699i | \(-0.122254\pi\) | ||||
0.927147 | + | 0.374699i | \(0.122254\pi\) | |||||||
\(500\) | −11.1589 | −0.499042 | ||||||||
\(501\) | 15.1731 | 0.677883 | ||||||||
\(502\) | 27.2335 | 1.21549 | ||||||||
\(503\) | −36.6381 | −1.63361 | −0.816806 | − | 0.576912i | \(-0.804258\pi\) | ||||
−0.816806 | + | 0.576912i | \(0.804258\pi\) | |||||||
\(504\) | 1.31883 | 0.0587454 | ||||||||
\(505\) | −2.74730 | −0.122253 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.40808 | −0.373416 | ||||||||
\(508\) | 0.637264 | 0.0282740 | ||||||||
\(509\) | −1.94309 | −0.0861260 | −0.0430630 | − | 0.999072i | \(-0.513712\pi\) | ||||
−0.0430630 | + | 0.999072i | \(0.513712\pi\) | |||||||
\(510\) | −1.99219 | −0.0882155 | ||||||||
\(511\) | 24.4637 | 1.08221 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.56879 | −0.245868 | ||||||||
\(514\) | 27.8288 | 1.22748 | ||||||||
\(515\) | 14.1507 | 0.623552 | ||||||||
\(516\) | −8.60965 | −0.379019 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17.0405 | −0.748719 | ||||||||
\(519\) | −15.4059 | −0.676243 | ||||||||
\(520\) | 6.17458 | 0.270773 | ||||||||
\(521\) | −42.3465 | −1.85523 | −0.927616 | − | 0.373535i | \(-0.878145\pi\) | ||||
−0.927616 | + | 0.373535i | \(0.878145\pi\) | |||||||
\(522\) | −1.15542 | −0.0505715 | ||||||||
\(523\) | −40.4000 | −1.76657 | −0.883284 | − | 0.468838i | \(-0.844673\pi\) | ||||
−0.883284 | + | 0.468838i | \(0.844673\pi\) | |||||||
\(524\) | 21.8110 | 0.952818 | ||||||||
\(525\) | 0.0675818 | 0.00294951 | ||||||||
\(526\) | 29.9986 | 1.30800 | ||||||||
\(527\) | 5.10167 | 0.222232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.7744 | 2.90323 | ||||||||
\(530\) | −9.85905 | −0.428250 | ||||||||
\(531\) | −4.64701 | −0.201663 | ||||||||
\(532\) | 2.27752 | 0.0987429 | ||||||||
\(533\) | −0.237678 | −0.0102950 | ||||||||
\(534\) | −8.00479 | −0.346401 | ||||||||
\(535\) | −35.6854 | −1.54281 | ||||||||
\(536\) | −6.91634 | −0.298740 | ||||||||
\(537\) | 24.6958 | 1.06570 | ||||||||
\(538\) | 1.89146 | 0.0815468 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.4759 | −0.536878 | ||||||||
\(541\) | −4.72409 | −0.203104 | −0.101552 | − | 0.994830i | \(-0.532381\pi\) | ||||
−0.101552 | + | 0.994830i | \(0.532381\pi\) | |||||||
\(542\) | 18.2983 | 0.785981 | ||||||||
\(543\) | −27.5649 | −1.18293 | ||||||||
\(544\) | −0.571514 | −0.0245034 | ||||||||
\(545\) | −19.4299 | −0.832286 | ||||||||
\(546\) | 9.76673 | 0.417978 | ||||||||
\(547\) | −26.5069 | −1.13335 | −0.566677 | − | 0.823940i | \(-0.691771\pi\) | ||||
−0.566677 | + | 0.823940i | \(0.691771\pi\) | |||||||
\(548\) | −1.60089 | −0.0683866 | ||||||||
\(549\) | 2.16503 | 0.0924011 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.99533 | −0.0850037 | ||||||||
\(552\) | −14.7424 | −0.627478 | ||||||||
\(553\) | 13.4870 | 0.573525 | ||||||||
\(554\) | −3.69005 | −0.156775 | ||||||||
\(555\) | 26.0811 | 1.10708 | ||||||||
\(556\) | 15.9213 | 0.675214 | ||||||||
\(557\) | 19.2433 | 0.815364 | 0.407682 | − | 0.913124i | \(-0.366337\pi\) | ||||
0.407682 | + | 0.913124i | \(0.366337\pi\) | |||||||
\(558\) | 5.16908 | 0.218824 | ||||||||
\(559\) | 15.2507 | 0.645036 | ||||||||
\(560\) | 5.10239 | 0.215615 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.5460 | −0.993226 | ||||||||
\(563\) | −3.50880 | −0.147878 | −0.0739391 | − | 0.997263i | \(-0.523557\pi\) | ||||
−0.0739391 | + | 0.997263i | \(0.523557\pi\) | |||||||
\(564\) | −15.0663 | −0.634407 | ||||||||
\(565\) | −0.667185 | −0.0280687 | ||||||||
\(566\) | −15.4242 | −0.648326 | ||||||||
\(567\) | −15.7775 | −0.662592 | ||||||||
\(568\) | −4.91454 | −0.206209 | ||||||||
\(569\) | −34.8083 | −1.45924 | −0.729620 | − | 0.683852i | \(-0.760303\pi\) | ||||
−0.729620 | + | 0.683852i | \(0.760303\pi\) | |||||||
\(570\) | −3.48581 | −0.146004 | ||||||||
\(571\) | 8.86605 | 0.371033 | 0.185516 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185516 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.3033 | −1.14061 | ||||||||
\(574\) | −0.196406 | −0.00819783 | ||||||||
\(575\) | 0.180698 | 0.00753561 | ||||||||
\(576\) | −0.579065 | −0.0241277 | ||||||||
\(577\) | 15.5873 | 0.648910 | 0.324455 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324455 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(578\) | 16.6734 | 0.693521 | ||||||||
\(579\) | 20.3931 | 0.847508 | ||||||||
\(580\) | −4.47019 | −0.185614 | ||||||||
\(581\) | 38.3694 | 1.59183 | ||||||||
\(582\) | −6.19819 | −0.256923 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.7414 | −0.444483 | ||||||||
\(585\) | 3.57549 | 0.147828 | ||||||||
\(586\) | −15.3414 | −0.633745 | ||||||||
\(587\) | 26.9304 | 1.11154 | 0.555769 | − | 0.831337i | \(-0.312424\pi\) | ||||
0.555769 | + | 0.831337i | \(0.312424\pi\) | |||||||
\(588\) | −2.82078 | −0.116327 | ||||||||
\(589\) | 8.92659 | 0.367814 | ||||||||
\(590\) | −17.9787 | −0.740171 | ||||||||
\(591\) | −23.7268 | −0.975989 | ||||||||
\(592\) | 7.48207 | 0.307511 | ||||||||
\(593\) | 23.7386 | 0.974826 | 0.487413 | − | 0.873172i | \(-0.337941\pi\) | ||||
0.487413 | + | 0.873172i | \(0.337941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.91608 | 0.119548 | ||||||||
\(596\) | −4.19884 | −0.171991 | ||||||||
\(597\) | 20.9836 | 0.858802 | ||||||||
\(598\) | 26.1139 | 1.06788 | ||||||||
\(599\) | 21.9522 | 0.896944 | 0.448472 | − | 0.893797i | \(-0.351968\pi\) | ||||
0.448472 | + | 0.893797i | \(0.351968\pi\) | |||||||
\(600\) | −0.0296734 | −0.00121141 | ||||||||
\(601\) | 9.40878 | 0.383792 | 0.191896 | − | 0.981415i | \(-0.438536\pi\) | ||||
0.191896 | + | 0.981415i | \(0.438536\pi\) | |||||||
\(602\) | 12.6025 | 0.513638 | ||||||||
\(603\) | −4.00501 | −0.163097 | ||||||||
\(604\) | 0.918503 | 0.0373733 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.90803 | 0.0775086 | ||||||||
\(607\) | 29.5786 | 1.20056 | 0.600278 | − | 0.799791i | \(-0.295056\pi\) | ||||
0.600278 | + | 0.799791i | \(0.295056\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −7.07078 | −0.286522 | ||||||||
\(610\) | 8.37622 | 0.339143 | ||||||||
\(611\) | 26.6877 | 1.07967 | ||||||||
\(612\) | −0.330944 | −0.0133776 | ||||||||
\(613\) | 43.1876 | 1.74433 | 0.872166 | − | 0.489211i | \(-0.162715\pi\) | ||||
0.872166 | + | 0.489211i | \(0.162715\pi\) | |||||||
\(614\) | −23.5750 | −0.951411 | ||||||||
\(615\) | 0.300605 | 0.0121216 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.5678 | −1.19036 | −0.595178 | − | 0.803594i | \(-0.702919\pi\) | ||||
−0.595178 | + | 0.803594i | \(0.702919\pi\) | |||||||
\(618\) | −9.82780 | −0.395332 | ||||||||
\(619\) | 6.02976 | 0.242357 | 0.121178 | − | 0.992631i | \(-0.461333\pi\) | ||||
0.121178 | + | 0.992631i | \(0.461333\pi\) | |||||||
\(620\) | 19.9985 | 0.803159 | ||||||||
\(621\) | −52.7640 | −2.11734 | ||||||||
\(622\) | 4.17781 | 0.167515 | ||||||||
\(623\) | 11.7171 | 0.469436 | ||||||||
\(624\) | −4.28832 | −0.171670 | ||||||||
\(625\) | −25.0950 | −1.00380 | ||||||||
\(626\) | 30.2227 | 1.20794 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.8346 | −0.472252 | ||||||||
\(629\) | 4.27611 | 0.170500 | ||||||||
\(630\) | 2.95461 | 0.117715 | ||||||||
\(631\) | −41.8326 | −1.66533 | −0.832665 | − | 0.553777i | \(-0.813186\pi\) | ||||
−0.832665 | + | 0.553777i | \(0.813186\pi\) | |||||||
\(632\) | −5.92179 | −0.235556 | ||||||||
\(633\) | −3.35791 | −0.133465 | ||||||||
\(634\) | −17.3175 | −0.687766 | ||||||||
\(635\) | 1.42768 | 0.0566558 | ||||||||
\(636\) | 6.84723 | 0.271510 | ||||||||
\(637\) | 4.99659 | 0.197972 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.84584 | −0.112580 | ||||||||
\(640\) | −2.24033 | −0.0885568 | ||||||||
\(641\) | 46.1632 | 1.82334 | 0.911668 | − | 0.410928i | \(-0.134795\pi\) | ||||
0.911668 | + | 0.410928i | \(0.134795\pi\) | |||||||
\(642\) | 24.7840 | 0.978145 | ||||||||
\(643\) | 15.9119 | 0.627504 | 0.313752 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313752 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(644\) | 21.5793 | 0.850344 | ||||||||
\(645\) | −19.2884 | −0.759482 | ||||||||
\(646\) | −0.571514 | −0.0224859 | ||||||||
\(647\) | 4.91972 | 0.193414 | 0.0967071 | − | 0.995313i | \(-0.469169\pi\) | ||||
0.0967071 | + | 0.995313i | \(0.469169\pi\) | |||||||
\(648\) | 6.92749 | 0.272137 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.0525621 | 0.00206165 | ||||||||
\(651\) | 31.6329 | 1.23979 | ||||||||
\(652\) | −7.54426 | −0.295456 | ||||||||
\(653\) | 8.25465 | 0.323029 | 0.161515 | − | 0.986870i | \(-0.448362\pi\) | ||||
0.161515 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(654\) | 13.4943 | 0.527669 | ||||||||
\(655\) | 48.8638 | 1.90927 | ||||||||
\(656\) | 0.0862369 | 0.00336699 | ||||||||
\(657\) | −6.21997 | −0.242664 | ||||||||
\(658\) | 22.0535 | 0.859735 | ||||||||
\(659\) | −49.5250 | −1.92922 | −0.964611 | − | 0.263677i | \(-0.915065\pi\) | ||||
−0.964611 | + | 0.263677i | \(0.915065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.1275 | 1.91084 | 0.955420 | − | 0.295252i | \(-0.0954035\pi\) | ||||
0.955420 | + | 0.295252i | \(0.0954035\pi\) | |||||||
\(662\) | 9.13686 | 0.355114 | ||||||||
\(663\) | −2.45084 | −0.0951826 | ||||||||
\(664\) | −16.8470 | −0.653791 | ||||||||
\(665\) | 5.10239 | 0.197862 | ||||||||
\(666\) | 4.33261 | 0.167885 | ||||||||
\(667\) | −18.9056 | −0.732027 | ||||||||
\(668\) | 9.75174 | 0.377306 | ||||||||
\(669\) | 10.5246 | 0.406906 | ||||||||
\(670\) | −15.4949 | −0.598619 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.54367 | −0.136700 | ||||||||
\(673\) | 39.5853 | 1.52590 | 0.762951 | − | 0.646457i | \(-0.223750\pi\) | ||||
0.762951 | + | 0.646457i | \(0.223750\pi\) | |||||||
\(674\) | 9.49487 | 0.365729 | ||||||||
\(675\) | −0.106203 | −0.00408776 | ||||||||
\(676\) | −5.40388 | −0.207841 | ||||||||
\(677\) | −44.3011 | −1.70263 | −0.851315 | − | 0.524655i | \(-0.824194\pi\) | ||||
−0.851315 | + | 0.524655i | \(0.824194\pi\) | |||||||
\(678\) | 0.463368 | 0.0177955 | ||||||||
\(679\) | 9.07267 | 0.348177 | ||||||||
\(680\) | −1.28038 | −0.0491003 | ||||||||
\(681\) | 10.4078 | 0.398829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.18585 | 0.160167 | 0.0800835 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800835 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(684\) | −0.579065 | −0.0221411 | ||||||||
\(685\) | −3.58652 | −0.137034 | ||||||||
\(686\) | 20.0716 | 0.766336 | ||||||||
\(687\) | 1.00426 | 0.0383149 | ||||||||
\(688\) | −5.53342 | −0.210960 | ||||||||
\(689\) | −12.1288 | −0.462072 | ||||||||
\(690\) | −33.0278 | −1.25735 | ||||||||
\(691\) | −17.3471 | −0.659916 | −0.329958 | − | 0.943996i | \(-0.607035\pi\) | ||||
−0.329958 | + | 0.943996i | \(0.607035\pi\) | |||||||
\(692\) | −9.90137 | −0.376393 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.4664 | −0.473220 | ||||||||
\(695\) | 35.6690 | 1.35300 | ||||||||
\(696\) | 3.10460 | 0.117679 | ||||||||
\(697\) | 0.0492856 | 0.00186682 | ||||||||
\(698\) | −29.2430 | −1.10687 | ||||||||
\(699\) | −8.59836 | −0.325220 | ||||||||
\(700\) | 0.0434348 | 0.00164168 | ||||||||
\(701\) | 30.9365 | 1.16845 | 0.584227 | − | 0.811590i | \(-0.301398\pi\) | ||||
0.584227 | + | 0.811590i | \(0.301398\pi\) | |||||||
\(702\) | −15.3482 | −0.579280 | ||||||||
\(703\) | 7.48207 | 0.282192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.7535 | −1.27123 | ||||||||
\(706\) | 9.95957 | 0.374833 | ||||||||
\(707\) | −2.79291 | −0.105038 | ||||||||
\(708\) | 12.4864 | 0.469268 | ||||||||
\(709\) | −17.4009 | −0.653505 | −0.326752 | − | 0.945110i | \(-0.605954\pi\) | ||||
−0.326752 | + | 0.945110i | \(0.605954\pi\) | |||||||
\(710\) | −11.0102 | −0.413205 | ||||||||
\(711\) | −3.42910 | −0.128601 | ||||||||
\(712\) | −5.14468 | −0.192805 | ||||||||
\(713\) | 84.5788 | 3.16750 | ||||||||
\(714\) | −2.02526 | −0.0757933 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.8720 | 0.593164 | ||||||||
\(717\) | −37.3599 | −1.39523 | ||||||||
\(718\) | −9.89422 | −0.369249 | ||||||||
\(719\) | −15.1001 | −0.563138 | −0.281569 | − | 0.959541i | \(-0.590855\pi\) | ||||
−0.281569 | + | 0.959541i | \(0.590855\pi\) | |||||||
\(720\) | −1.29730 | −0.0483474 | ||||||||
\(721\) | 14.3856 | 0.535746 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 19.5764 | 0.728053 | ||||||||
\(724\) | −17.7160 | −0.658410 | ||||||||
\(725\) | −0.0380531 | −0.00141326 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.5584 | 0.465764 | 0.232882 | − | 0.972505i | \(-0.425184\pi\) | ||||
0.232882 | + | 0.972505i | \(0.425184\pi\) | |||||||
\(728\) | 6.27708 | 0.232644 | ||||||||
\(729\) | 30.0055 | 1.11132 | ||||||||
\(730\) | −24.0643 | −0.890659 | ||||||||
\(731\) | −3.16243 | −0.116967 | ||||||||
\(732\) | −5.81738 | −0.215017 | ||||||||
\(733\) | −8.63342 | −0.318883 | −0.159441 | − | 0.987207i | \(-0.550969\pi\) | ||||
−0.159441 | + | 0.987207i | \(0.550969\pi\) | |||||||
\(734\) | 1.78588 | 0.0659180 | ||||||||
\(735\) | −6.31947 | −0.233097 | ||||||||
\(736\) | −9.47493 | −0.349251 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0499368 | 0.00183820 | ||||||||
\(739\) | 25.8140 | 0.949584 | 0.474792 | − | 0.880098i | \(-0.342523\pi\) | ||||
0.474792 | + | 0.880098i | \(0.342523\pi\) | |||||||
\(740\) | 16.7623 | 0.616194 | ||||||||
\(741\) | −4.28832 | −0.157536 | ||||||||
\(742\) | −10.0227 | −0.367945 | ||||||||
\(743\) | −27.8252 | −1.02081 | −0.510404 | − | 0.859935i | \(-0.670504\pi\) | ||||
−0.510404 | + | 0.859935i | \(0.670504\pi\) | |||||||
\(744\) | −13.8892 | −0.509203 | ||||||||
\(745\) | −9.40678 | −0.344638 | ||||||||
\(746\) | −11.8730 | −0.434703 | ||||||||
\(747\) | −9.75552 | −0.356936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.2778 | −1.32556 | ||||||||
\(750\) | 17.3626 | 0.633991 | ||||||||
\(751\) | 16.8060 | 0.613259 | 0.306630 | − | 0.951829i | \(-0.400799\pi\) | ||||
0.306630 | + | 0.951829i | \(0.400799\pi\) | |||||||
\(752\) | −9.68313 | −0.353107 | ||||||||
\(753\) | −42.3735 | −1.54418 | ||||||||
\(754\) | −5.49933 | −0.200274 | ||||||||
\(755\) | 2.05775 | 0.0748891 | ||||||||
\(756\) | −12.6830 | −0.461277 | ||||||||
\(757\) | −41.6137 | −1.51248 | −0.756238 | − | 0.654296i | \(-0.772965\pi\) | ||||
−0.756238 | + | 0.654296i | \(0.772965\pi\) | |||||||
\(758\) | −14.5469 | −0.528369 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.24033 | −0.0812653 | ||||||||
\(761\) | 17.3354 | 0.628409 | 0.314204 | − | 0.949355i | \(-0.398262\pi\) | ||||
0.314204 | + | 0.949355i | \(0.398262\pi\) | |||||||
\(762\) | −0.991542 | −0.0359198 | ||||||||
\(763\) | −19.7524 | −0.715086 | ||||||||
\(764\) | −17.5478 | −0.634857 | ||||||||
\(765\) | −0.741422 | −0.0268062 | ||||||||
\(766\) | −10.9005 | −0.393850 | ||||||||
\(767\) | −22.1178 | −0.798628 | ||||||||
\(768\) | 1.55594 | 0.0561450 | ||||||||
\(769\) | 6.63601 | 0.239301 | 0.119650 | − | 0.992816i | \(-0.461823\pi\) | ||||
0.119650 | + | 0.992816i | \(0.461823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.2998 | −1.55940 | ||||||||
\(772\) | 13.1066 | 0.471719 | ||||||||
\(773\) | −23.1698 | −0.833360 | −0.416680 | − | 0.909053i | \(-0.636807\pi\) | ||||
−0.416680 | + | 0.909053i | \(0.636807\pi\) | |||||||
\(774\) | −3.20421 | −0.115173 | ||||||||
\(775\) | 0.170240 | 0.00611521 | ||||||||
\(776\) | −3.98358 | −0.143002 | ||||||||
\(777\) | 26.5140 | 0.951184 | ||||||||
\(778\) | −2.85935 | −0.102513 | ||||||||
\(779\) | 0.0862369 | 0.00308976 | ||||||||
\(780\) | −9.60725 | −0.343995 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.41505 | −0.193642 | ||||||||
\(783\) | 11.1116 | 0.397095 | ||||||||
\(784\) | −1.81292 | −0.0647470 | ||||||||
\(785\) | −26.5134 | −0.946305 | ||||||||
\(786\) | −33.9365 | −1.21048 | ||||||||
\(787\) | −35.8057 | −1.27634 | −0.638168 | − | 0.769897i | \(-0.720307\pi\) | ||||
−0.638168 | + | 0.769897i | \(0.720307\pi\) | |||||||
\(788\) | −15.2492 | −0.543230 | ||||||||
\(789\) | −46.6758 | −1.66170 | ||||||||
\(790\) | −13.2668 | −0.472010 | ||||||||
\(791\) | −0.678260 | −0.0241162 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3046 | 0.365928 | ||||||||
\(794\) | 1.34242 | 0.0476407 | ||||||||
\(795\) | 15.3400 | 0.544056 | ||||||||
\(796\) | 13.4862 | 0.478005 | ||||||||
\(797\) | 12.9247 | 0.457816 | 0.228908 | − | 0.973448i | \(-0.426485\pi\) | ||||
0.228908 | + | 0.973448i | \(0.426485\pi\) | |||||||
\(798\) | −3.54367 | −0.125445 | ||||||||
\(799\) | −5.53404 | −0.195780 | ||||||||
\(800\) | −0.0190711 | −0.000674266 0 | ||||||||
\(801\) | −2.97910 | −0.105261 | ||||||||
\(802\) | 25.2632 | 0.892076 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 10.7614 | 0.379524 | ||||||||
\(805\) | 48.3448 | 1.70393 | ||||||||
\(806\) | 24.6026 | 0.866591 | ||||||||
\(807\) | −2.94300 | −0.103598 | ||||||||
\(808\) | 1.22629 | 0.0431409 | ||||||||
\(809\) | 1.69221 | 0.0594950 | 0.0297475 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297475 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(810\) | 15.5198 | 0.545312 | ||||||||
\(811\) | 14.2119 | 0.499048 | 0.249524 | − | 0.968369i | \(-0.419726\pi\) | ||||
0.249524 | + | 0.968369i | \(0.419726\pi\) | |||||||
\(812\) | −4.54439 | −0.159477 | ||||||||
\(813\) | −28.4710 | −0.998523 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9016 | −0.592038 | ||||||||
\(816\) | 0.889238 | 0.0311296 | ||||||||
\(817\) | −5.53342 | −0.193590 | ||||||||
\(818\) | 10.9069 | 0.381351 | ||||||||
\(819\) | 3.63484 | 0.127011 | ||||||||
\(820\) | 0.193199 | 0.00674680 | ||||||||
\(821\) | −36.7897 | −1.28397 | −0.641985 | − | 0.766717i | \(-0.721889\pi\) | ||||
−0.641985 | + | 0.766717i | \(0.721889\pi\) | |||||||
\(822\) | 2.49088 | 0.0868794 | ||||||||
\(823\) | 16.9368 | 0.590379 | 0.295189 | − | 0.955439i | \(-0.404617\pi\) | ||||
0.295189 | + | 0.955439i | \(0.404617\pi\) | |||||||
\(824\) | −6.31633 | −0.220040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.2771 | −0.635942 | ||||||||
\(827\) | 28.9883 | 1.00802 | 0.504012 | − | 0.863697i | \(-0.331857\pi\) | ||||
0.504012 | + | 0.863697i | \(0.331857\pi\) | |||||||
\(828\) | −5.48660 | −0.190673 | ||||||||
\(829\) | 38.3557 | 1.33215 | 0.666074 | − | 0.745886i | \(-0.267973\pi\) | ||||
0.666074 | + | 0.745886i | \(0.267973\pi\) | |||||||
\(830\) | −37.7429 | −1.31007 | ||||||||
\(831\) | 5.74148 | 0.199170 | ||||||||
\(832\) | −2.75611 | −0.0955508 | ||||||||
\(833\) | −1.03611 | −0.0358990 | ||||||||
\(834\) | −24.7725 | −0.857803 | ||||||||
\(835\) | 21.8471 | 0.756050 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −49.7103 | −1.71824 | ||||||||
\(838\) | −9.08955 | −0.313993 | ||||||||
\(839\) | 13.1347 | 0.453462 | 0.226731 | − | 0.973957i | \(-0.427196\pi\) | ||||
0.226731 | + | 0.973957i | \(0.427196\pi\) | |||||||
\(840\) | −7.93898 | −0.273921 | ||||||||
\(841\) | −25.0187 | −0.862713 | ||||||||
\(842\) | −34.5218 | −1.18970 | ||||||||
\(843\) | 36.6360 | 1.26181 | ||||||||
\(844\) | −2.15813 | −0.0742858 | ||||||||
\(845\) | −12.1065 | −0.416475 | ||||||||
\(846\) | −5.60716 | −0.192778 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.40072 | 0.151121 | ||||||||
\(849\) | 23.9990 | 0.823643 | ||||||||
\(850\) | −0.0108994 | −0.000373847 0 | ||||||||
\(851\) | 70.8921 | 2.43015 | ||||||||
\(852\) | 7.64670 | 0.261972 | ||||||||
\(853\) | 47.1433 | 1.61415 | 0.807077 | − | 0.590446i | \(-0.201048\pi\) | ||||
0.807077 | + | 0.590446i | \(0.201048\pi\) | |||||||
\(854\) | 8.51526 | 0.291386 | ||||||||
\(855\) | −1.29730 | −0.0443666 | ||||||||
\(856\) | 15.9287 | 0.544430 | ||||||||
\(857\) | −4.63462 | −0.158316 | −0.0791579 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791579 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.6906 | −0.978911 | −0.489456 | − | 0.872028i | \(-0.662805\pi\) | ||||
−0.489456 | + | 0.872028i | \(0.662805\pi\) | |||||||
\(860\) | −12.3967 | −0.422723 | ||||||||
\(861\) | 0.305595 | 0.0104147 | ||||||||
\(862\) | −3.67160 | −0.125055 | ||||||||
\(863\) | −29.7927 | −1.01416 | −0.507078 | − | 0.861900i | \(-0.669275\pi\) | ||||
−0.507078 | + | 0.861900i | \(0.669275\pi\) | |||||||
\(864\) | 5.56879 | 0.189454 | ||||||||
\(865\) | −22.1823 | −0.754221 | ||||||||
\(866\) | 9.59701 | 0.326120 | ||||||||
\(867\) | −25.9427 | −0.881060 | ||||||||
\(868\) | 20.3305 | 0.690061 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.95532 | 0.235807 | ||||||||
\(871\) | −19.0622 | −0.645897 | ||||||||
\(872\) | 8.67279 | 0.293698 | ||||||||
\(873\) | −2.30675 | −0.0780717 | ||||||||
\(874\) | −9.47493 | −0.320494 | ||||||||
\(875\) | −25.4146 | −0.859171 | ||||||||
\(876\) | 16.7129 | 0.564678 | ||||||||
\(877\) | −35.2763 | −1.19120 | −0.595598 | − | 0.803283i | \(-0.703085\pi\) | ||||
−0.595598 | + | 0.803283i | \(0.703085\pi\) | |||||||
\(878\) | −5.20790 | −0.175758 | ||||||||
\(879\) | 23.8702 | 0.805120 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.536228 | −0.0180660 | −0.00903300 | − | 0.999959i | \(-0.502875\pi\) | ||||
−0.00903300 | + | 0.999959i | \(0.502875\pi\) | |||||||
\(882\) | −1.04980 | −0.0353485 | ||||||||
\(883\) | 9.43044 | 0.317360 | 0.158680 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158680 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(884\) | −1.57515 | −0.0529781 | ||||||||
\(885\) | 27.9737 | 0.940325 | ||||||||
\(886\) | 11.5968 | 0.389602 | ||||||||
\(887\) | 15.7866 | 0.530062 | 0.265031 | − | 0.964240i | \(-0.414618\pi\) | ||||
0.265031 | + | 0.964240i | \(0.414618\pi\) | |||||||
\(888\) | −11.6416 | −0.390667 | ||||||||
\(889\) | 1.45138 | 0.0486777 | ||||||||
\(890\) | −11.5258 | −0.386345 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.76418 | 0.226482 | ||||||||
\(893\) | −9.68313 | −0.324034 | ||||||||
\(894\) | 6.53312 | 0.218500 | ||||||||
\(895\) | 35.5585 | 1.18859 | ||||||||
\(896\) | −2.27752 | −0.0760865 | ||||||||
\(897\) | −40.6316 | −1.35665 | ||||||||
\(898\) | 19.1493 | 0.639020 | ||||||||
\(899\) | −17.8115 | −0.594045 | ||||||||
\(900\) | −0.0110434 | −0.000368114 0 | ||||||||
\(901\) | 2.51507 | 0.0837891 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.6086 | −0.652534 | ||||||||
\(904\) | 0.297807 | 0.00990491 | ||||||||
\(905\) | −39.6896 | −1.31933 | ||||||||
\(906\) | −1.42913 | −0.0474797 | ||||||||
\(907\) | −44.7761 | −1.48677 | −0.743383 | − | 0.668866i | \(-0.766780\pi\) | ||||
−0.743383 | + | 0.668866i | \(0.766780\pi\) | |||||||
\(908\) | 6.68912 | 0.221986 | ||||||||
\(909\) | 0.710104 | 0.0235527 | ||||||||
\(910\) | 14.0627 | 0.466175 | ||||||||
\(911\) | 3.05935 | 0.101361 | 0.0506804 | − | 0.998715i | \(-0.483861\pi\) | ||||
0.0506804 | + | 0.998715i | \(0.483861\pi\) | |||||||
\(912\) | 1.55594 | 0.0515222 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 15.2474 | 0.504339 | ||||||||
\(915\) | −13.0329 | −0.430853 | ||||||||
\(916\) | 0.645439 | 0.0213259 | ||||||||
\(917\) | 49.6749 | 1.64041 | ||||||||
\(918\) | 3.18264 | 0.105043 | ||||||||
\(919\) | 55.2774 | 1.82343 | 0.911717 | − | 0.410818i | \(-0.134757\pi\) | ||||
0.911717 | + | 0.410818i | \(0.134757\pi\) | |||||||
\(920\) | −21.2270 | −0.699832 | ||||||||
\(921\) | 36.6812 | 1.20869 | ||||||||
\(922\) | 13.1903 | 0.434401 | ||||||||
\(923\) | −13.5450 | −0.445839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.142692 | 0.00469167 | ||||||||
\(926\) | 15.8312 | 0.520247 | ||||||||
\(927\) | −3.65757 | −0.120130 | ||||||||
\(928\) | 1.99533 | 0.0654998 | ||||||||
\(929\) | −29.1942 | −0.957832 | −0.478916 | − | 0.877861i | \(-0.658970\pi\) | ||||
−0.478916 | + | 0.877861i | \(0.658970\pi\) | |||||||
\(930\) | −31.1164 | −1.02035 | ||||||||
\(931\) | −1.81292 | −0.0594159 | ||||||||
\(932\) | −5.52617 | −0.181016 | ||||||||
\(933\) | −6.50041 | −0.212814 | ||||||||
\(934\) | 14.8060 | 0.484467 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.59596 | −0.0521657 | ||||||||
\(937\) | 18.6969 | 0.610801 | 0.305401 | − | 0.952224i | \(-0.401210\pi\) | ||||
0.305401 | + | 0.952224i | \(0.401210\pi\) | |||||||
\(938\) | −15.7521 | −0.514324 | ||||||||
\(939\) | −47.0246 | −1.53459 | ||||||||
\(940\) | −21.6934 | −0.707561 | ||||||||
\(941\) | −4.47168 | −0.145773 | −0.0728863 | − | 0.997340i | \(-0.523221\pi\) | ||||
−0.0728863 | + | 0.997340i | \(0.523221\pi\) | |||||||
\(942\) | 18.4139 | 0.599957 | ||||||||
\(943\) | 0.817089 | 0.0266081 | ||||||||
\(944\) | 8.02502 | 0.261192 | ||||||||
\(945\) | −28.4141 | −0.924312 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.78679 | 0.285532 | 0.142766 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142766 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(948\) | 9.21393 | 0.299254 | ||||||||
\(949\) | −29.6045 | −0.961002 | ||||||||
\(950\) | −0.0190711 | −0.000618749 0 | ||||||||
\(951\) | 26.9449 | 0.873748 | ||||||||
\(952\) | −1.30163 | −0.0421861 | ||||||||
\(953\) | 33.1114 | 1.07258 | 0.536292 | − | 0.844033i | \(-0.319825\pi\) | ||||
0.536292 | + | 0.844033i | \(0.319825\pi\) | |||||||
\(954\) | 2.54830 | 0.0825043 | ||||||||
\(955\) | −39.3129 | −1.27213 | ||||||||
\(956\) | −24.0112 | −0.776578 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.4058 | 0.691590 | ||||||||
\(959\) | −3.64605 | −0.117737 | ||||||||
\(960\) | 3.48581 | 0.112504 | ||||||||
\(961\) | 48.6840 | 1.57045 | ||||||||
\(962\) | 20.6214 | 0.664860 | ||||||||
\(963\) | 9.22372 | 0.297230 | ||||||||
\(964\) | 12.5817 | 0.405231 | ||||||||
\(965\) | 29.3632 | 0.945235 | ||||||||
\(966\) | −33.5760 | −1.08029 | ||||||||
\(967\) | 39.9996 | 1.28630 | 0.643150 | − | 0.765740i | \(-0.277627\pi\) | ||||
0.643150 | + | 0.765740i | \(0.277627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.889238 | 0.0285665 | ||||||||
\(970\) | −8.92453 | −0.286549 | ||||||||
\(971\) | 4.06604 | 0.130486 | 0.0652428 | − | 0.997869i | \(-0.479218\pi\) | ||||
0.0652428 | + | 0.997869i | \(0.479218\pi\) | |||||||
\(972\) | 5.92766 | 0.190130 | ||||||||
\(973\) | 36.2611 | 1.16248 | ||||||||
\(974\) | 18.0587 | 0.578639 | ||||||||
\(975\) | −0.0817832 | −0.00261916 | ||||||||
\(976\) | −3.73883 | −0.119677 | ||||||||
\(977\) | −37.4002 | −1.19654 | −0.598270 | − | 0.801295i | \(-0.704145\pi\) | ||||
−0.598270 | + | 0.801295i | \(0.704145\pi\) | |||||||
\(978\) | 11.7384 | 0.375352 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.06153 | −0.129741 | ||||||||
\(981\) | 5.02211 | 0.160344 | ||||||||
\(982\) | 26.9808 | 0.860992 | ||||||||
\(983\) | −52.9556 | −1.68902 | −0.844511 | − | 0.535538i | \(-0.820109\pi\) | ||||
−0.844511 | + | 0.535538i | \(0.820109\pi\) | |||||||
\(984\) | −0.134179 | −0.00427747 | ||||||||
\(985\) | −34.1632 | −1.08853 | ||||||||
\(986\) | 1.14036 | 0.0363163 | ||||||||
\(987\) | −34.3138 | −1.09222 | ||||||||
\(988\) | −2.75611 | −0.0876834 | ||||||||
\(989\) | −52.4288 | −1.66714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.98829 | −0.126692 | −0.0633461 | − | 0.997992i | \(-0.520177\pi\) | ||||
−0.0633461 | + | 0.997992i | \(0.520177\pi\) | |||||||
\(992\) | −8.92659 | −0.283420 | ||||||||
\(993\) | −14.2164 | −0.451143 | ||||||||
\(994\) | −11.1929 | −0.355019 | ||||||||
\(995\) | 30.2135 | 0.957831 | ||||||||
\(996\) | 26.2129 | 0.830587 | ||||||||
\(997\) | −32.7194 | −1.03623 | −0.518117 | − | 0.855309i | \(-0.673367\pi\) | ||||
−0.518117 | + | 0.855309i | \(0.673367\pi\) | |||||||
\(998\) | −41.4218 | −1.31118 | ||||||||
\(999\) | −41.6661 | −1.31826 |
(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 | 4598.2.a.by.1.4 | ✓ | 8 | |
11.10 | odd | 2 | 4598.2.a.cb.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.by.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4598.2.a.cb.1.4 | yes | 8 | 11.10 | odd | 2 |