Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.32283 | −1.34109 | −0.670543 | − | 0.741870i | \(-0.733939\pi\) | ||||
−0.670543 | + | 0.741870i | \(0.733939\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.89591 | 1.74230 | 0.871152 | − | 0.491013i | \(-0.163373\pi\) | ||||
0.871152 | + | 0.491013i | \(0.163373\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0996640 | 0.0376694 | 0.0188347 | − | 0.999823i | \(-0.494004\pi\) | ||||
0.0188347 | + | 0.999823i | \(0.494004\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.39554 | 0.798514 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.90464 | −1.78032 | −0.890159 | − | 0.455651i | \(-0.849407\pi\) | ||||
−0.890159 | + | 0.455651i | \(0.849407\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.114246 | −0.0316861 | −0.0158431 | − | 0.999874i | \(-0.505043\pi\) | ||||
−0.0158431 | + | 0.999874i | \(0.505043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.04954 | −2.33658 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.599000 | −0.145279 | −0.0726394 | − | 0.997358i | \(-0.523142\pi\) | ||||
−0.0726394 | + | 0.997358i | \(0.523142\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.75876 | −0.862318 | −0.431159 | − | 0.902276i | \(-0.641895\pi\) | ||||
−0.431159 | + | 0.902276i | \(0.641895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.231503 | −0.0505180 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.45024 | 1.76200 | 0.880998 | − | 0.473119i | \(-0.156872\pi\) | ||||
0.880998 | + | 0.473119i | \(0.156872\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1781 | 2.03562 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.40405 | 0.270210 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.82511 | −0.896001 | −0.448001 | − | 0.894033i | \(-0.647864\pi\) | ||||
−0.448001 | + | 0.894033i | \(0.647864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.02204 | −0.901986 | −0.450993 | − | 0.892528i | \(-0.648930\pi\) | ||||
−0.450993 | + | 0.892528i | \(0.648930\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.7155 | 2.38756 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.388282 | 0.0656316 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.30770 | 0.708181 | 0.354090 | − | 0.935211i | \(-0.384791\pi\) | ||||
0.354090 | + | 0.935211i | \(0.384791\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.265374 | 0.0424938 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.72885 | −0.270001 | −0.135000 | − | 0.990846i | \(-0.543104\pi\) | ||||
−0.135000 | + | 0.990846i | \(0.543104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.69072 | 1.17282 | 0.586412 | − | 0.810013i | \(-0.300540\pi\) | ||||
0.586412 | + | 0.810013i | \(0.300540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.33282 | 1.39125 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.57421 | 0.521353 | 0.260676 | − | 0.965426i | \(-0.416054\pi\) | ||||
0.260676 | + | 0.965426i | \(0.416054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99007 | −0.998581 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39138 | 0.194832 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.09824 | 1.11238 | 0.556189 | − | 0.831056i | \(-0.312263\pi\) | ||||
0.556189 | + | 0.831056i | \(0.312263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −23.0040 | −3.10185 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.73095 | 1.15644 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.16867 | −1.06347 | −0.531735 | − | 0.846911i | \(-0.678460\pi\) | ||||
−0.531735 | + | 0.846911i | \(0.678460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5579 | 1.60787 | 0.803937 | − | 0.594715i | \(-0.202735\pi\) | ||||
0.803937 | + | 0.594715i | \(0.202735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.238749 | 0.0300796 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.445092 | −0.0552068 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.648145 | 0.0791835 | 0.0395917 | − | 0.999216i | \(-0.487394\pi\) | ||||
0.0395917 | + | 0.999216i | \(0.487394\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.6285 | −2.36299 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7524 | −1.27607 | −0.638037 | − | 0.770006i | \(-0.720253\pi\) | ||||
−0.638037 | + | 0.770006i | \(0.720253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.5173 | −1.93320 | −0.966601 | − | 0.256286i | \(-0.917501\pi\) | ||||
−0.966601 | + | 0.256286i | \(0.917501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23.6420 | −2.72995 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.588480 | −0.0670635 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.11173 | −0.350097 | −0.175049 | − | 0.984560i | \(-0.556008\pi\) | ||||
−0.175049 | + | 0.984560i | \(0.556008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4480 | −1.16089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1879 | −1.33779 | −0.668896 | − | 0.743356i | \(-0.733233\pi\) | ||||
−0.668896 | + | 0.743356i | \(0.733233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.33365 | −0.253120 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.2079 | 1.20162 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.53075 | −0.480258 | −0.240129 | − | 0.970741i | \(-0.577190\pi\) | ||||
−0.240129 | + | 0.970741i | \(0.577190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0113862 | −0.00119360 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.6654 | 1.20964 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.6438 | −1.50242 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9395 | −1.31381 | −0.656904 | − | 0.753974i | \(-0.728134\pi\) | ||||
−0.656904 | + | 0.753974i | \(0.728134\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.1448 | −1.42161 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0137 | 0.996398 | 0.498199 | − | 0.867063i | \(-0.333995\pi\) | ||||
0.498199 | + | 0.867063i | \(0.333995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.2251 | −1.89430 | −0.947152 | − | 0.320786i | \(-0.896053\pi\) | ||||
−0.947152 | + | 0.320786i | \(0.896053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.901913 | −0.0880177 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.515605 | 0.0498454 | 0.0249227 | − | 0.999689i | \(-0.492066\pi\) | ||||
0.0249227 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9042 | 1.33178 | 0.665892 | − | 0.746048i | \(-0.268051\pi\) | ||||
0.665892 | + | 0.746048i | \(0.268051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0060 | −0.949732 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.7994 | 1.67442 | 0.837212 | − | 0.546879i | \(-0.184184\pi\) | ||||
0.837212 | + | 0.546879i | \(0.184184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.9214 | 3.06993 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.273681 | −0.0253018 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0596987 | −0.00547257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.8648 | 2.16953 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.01583 | 0.362095 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.1735 | 1.80437 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9798 | 1.15177 | 0.575883 | − | 0.817532i | \(-0.304658\pi\) | ||||
0.575883 | + | 0.817532i | \(0.304658\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.8642 | −1.57286 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3554 | −1.16687 | −0.583435 | − | 0.812160i | \(-0.698292\pi\) | ||||
−0.583435 | + | 0.812160i | \(0.698292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.374612 | −0.0324830 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.47006 | 0.470788 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.0945 | −1.37505 | −0.687523 | − | 0.726163i | \(-0.741302\pi\) | ||||
−0.687523 | + | 0.726163i | \(0.741302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3178 | −1.04478 | −0.522390 | − | 0.852706i | \(-0.674960\pi\) | ||||
−0.522390 | + | 0.852706i | \(0.674960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.30230 | −0.699179 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.674581 | 0.0564113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.7982 | −1.56111 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.2367 | 1.33918 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6426 | −0.953799 | −0.476899 | − | 0.878958i | \(-0.658239\pi\) | ||||
−0.476899 | + | 0.878958i | \(0.658239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7102 | −1.44123 | −0.720617 | − | 0.693334i | \(-0.756141\pi\) | ||||
−0.720617 | + | 0.693334i | \(0.756141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.43493 | −0.116007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.5654 | −1.57153 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6610 | −0.850843 | −0.425422 | − | 0.904995i | \(-0.639874\pi\) | ||||
−0.425422 | + | 0.904995i | \(0.639874\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.8108 | −1.49180 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.842184 | 0.0663734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.7667 | 1.93988 | 0.969939 | − | 0.243347i | \(-0.0782453\pi\) | ||||
0.969939 | + | 0.243347i | \(0.0782453\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 53.4343 | 4.15986 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2172 | 1.40969 | 0.704845 | − | 0.709361i | \(-0.251016\pi\) | ||||
0.704845 | + | 0.709361i | \(0.251016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9869 | −0.998996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.00426 | −0.688573 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.92966 | 0.754938 | 0.377469 | − | 0.926022i | \(-0.376794\pi\) | ||||
0.377469 | + | 0.926022i | \(0.376794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.01439 | 0.0766808 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.9744 | 1.42621 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.765250 | −0.0571975 | −0.0285987 | − | 0.999591i | \(-0.509104\pi\) | ||||
−0.0285987 | + | 0.999591i | \(0.509104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4570 | −1.52055 | −0.760277 | − | 0.649599i | \(-0.774937\pi\) | ||||
−0.760277 | + | 0.649599i | \(0.774937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.1699 | −2.15630 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.7824 | 1.23387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.53688 | 0.258642 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.139933 | 0.0101787 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.64057 | 0.625210 | 0.312605 | − | 0.949883i | \(-0.398798\pi\) | ||||
0.312605 | + | 0.949883i | \(0.398798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.0662 | 1.94827 | 0.974135 | − | 0.225968i | \(-0.0725545\pi\) | ||||
0.974135 | + | 0.225968i | \(0.0725545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.03387 | 0.0740371 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.1750 | −1.43741 | −0.718705 | − | 0.695315i | \(-0.755265\pi\) | ||||
−0.718705 | + | 0.695315i | \(0.755265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.33390 | −0.378110 | −0.189055 | − | 0.981966i | \(-0.560543\pi\) | ||||
−0.189055 | + | 0.981966i | \(0.560543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.50553 | −0.106192 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.480890 | −0.0337519 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.73544 | −0.470424 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.2429 | 1.40698 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.1941 | 1.53520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.74619 | 0.464427 | 0.232213 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232213 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.9760 | 1.71133 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.9624 | 2.04342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.500517 | −0.0339773 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 38.3669 | 2.59259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0684333 | 0.00460332 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0288 | −1.47516 | −0.737580 | − | 0.675260i | \(-0.764032\pi\) | ||||
−0.737580 | + | 0.675260i | \(0.764032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.3821 | 1.62547 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.3582 | −0.952990 | −0.476495 | − | 0.879177i | \(-0.658093\pi\) | ||||
−0.476495 | + | 0.879177i | \(0.658093\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.58291 | −0.633256 | −0.316628 | − | 0.948550i | \(-0.602551\pi\) | ||||
−0.316628 | + | 0.948550i | \(0.602551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36694 | 0.0899380 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0682 | −1.18369 | −0.591844 | − | 0.806053i | \(-0.701600\pi\) | ||||
−0.591844 | + | 0.806053i | \(0.701600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9248 | 0.908355 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.22803 | 0.469511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7459 | −0.953832 | −0.476916 | − | 0.878949i | \(-0.658245\pi\) | ||||
−0.476916 | + | 0.878949i | \(0.658245\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2052 | −0.915038 | −0.457519 | − | 0.889200i | \(-0.651262\pi\) | ||||
−0.457519 | + | 0.889200i | \(0.651262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.0568 | 1.28664 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −27.2327 | −1.73983 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.429422 | 0.0273235 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.3103 | 1.79409 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0204 | 1.38991 | 0.694956 | − | 0.719052i | \(-0.255424\pi\) | ||||
0.694956 | + | 0.719052i | \(0.255424\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −49.8957 | −3.13691 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.42067 | 0.339456 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2542 | −0.702016 | −0.351008 | − | 0.936373i | \(-0.614161\pi\) | ||||
−0.351008 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.429322 | 0.0266768 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.5588 | −0.715470 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2942 | 0.634766 | 0.317383 | − | 0.948297i | \(-0.397196\pi\) | ||||
0.317383 | + | 0.948297i | \(0.397196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.5500 | 1.93810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5242 | 0.644068 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6473 | 0.710151 | 0.355076 | − | 0.934838i | \(-0.384455\pi\) | ||||
0.355076 | + | 0.934838i | \(0.384455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.40010 | −0.145796 | −0.0728978 | − | 0.997339i | \(-0.523225\pi\) | ||||
−0.0728978 | + | 0.997339i | \(0.523225\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0264482 | 0.00160072 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −60.0982 | −3.62405 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.93482 | −0.296504 | −0.148252 | − | 0.988950i | \(-0.547365\pi\) | ||||
−0.148252 | + | 0.988950i | \(0.547365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0305 | −0.720248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2937 | −0.852693 | −0.426346 | − | 0.904560i | \(-0.640200\pi\) | ||||
−0.426346 | + | 0.904560i | \(0.640200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1385 | 0.840448 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 34.0150 | 2.01488 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.172304 | −0.0101708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6412 | −0.978894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.0563 | 1.76193 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6522 | −0.972830 | −0.486415 | − | 0.873728i | \(-0.661696\pi\) | ||||
−0.486415 | + | 0.873728i | \(0.661696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.8244 | −1.85289 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.29043 | −0.481059 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.965405 | −0.0558308 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.766488 | 0.0441796 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.2601 | −1.33626 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.9244 | 2.80140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.76420 | 0.328980 | 0.164490 | − | 0.986379i | \(-0.447402\pi\) | ||||
0.164490 | + | 0.986379i | \(0.447402\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.6566 | 2.54043 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.5164 | −1.50361 | −0.751803 | − | 0.659388i | \(-0.770816\pi\) | ||||
−0.751803 | + | 0.659388i | \(0.770816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4430 | −1.43813 | −0.719063 | − | 0.694945i | \(-0.755429\pi\) | ||||
−0.719063 | + | 0.694945i | \(0.755429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.930146 | 0.0524078 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.15542 | 0.345723 | 0.172861 | − | 0.984946i | \(-0.444699\pi\) | ||||
0.172861 | + | 0.984946i | \(0.444699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.4906 | 1.59517 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.19766 | −0.0668470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.25149 | 0.125276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.16281 | −0.0645010 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −32.2972 | −1.78604 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.356220 | 0.0196391 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3803 | −1.06524 | −0.532619 | − | 0.846355i | \(-0.678792\pi\) | ||||
−0.532619 | + | 0.846355i | \(0.678792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.3193 | 0.565492 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.52511 | 0.137962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2283 | 1.37427 | 0.687136 | − | 0.726529i | \(-0.258868\pi\) | ||||
0.687136 | + | 0.726529i | \(0.258868\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.3449 | −2.24555 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.6534 | 1.60582 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.39431 | −0.0752854 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −76.4708 | −4.11705 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3526 | 0.555757 | 0.277879 | − | 0.960616i | \(-0.410369\pi\) | ||||
0.277879 | + | 0.960616i | \(0.410369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1171 | −0.541555 | −0.270778 | − | 0.962642i | \(-0.587281\pi\) | ||||
−0.270778 | + | 0.962642i | \(0.587281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.160407 | −0.00856190 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.85827 | 0.311804 | 0.155902 | − | 0.987773i | \(-0.450172\pi\) | ||||
0.155902 | + | 0.987773i | \(0.450172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.8903 | −2.22331 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.138670 | 0.00733919 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.3184 | 1.17792 | 0.588959 | − | 0.808163i | \(-0.299538\pi\) | ||||
0.588959 | + | 0.808163i | \(0.299538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.87176 | −0.256408 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −55.4339 | −2.90953 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −64.3499 | −3.36823 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9832 | 0.938717 | 0.469358 | − | 0.883008i | \(-0.344485\pi\) | ||||
0.469358 | + | 0.883008i | \(0.344485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.14153 | −0.215600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.807102 | 0.0419027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.1695 | −0.681893 | −0.340946 | − | 0.940083i | \(-0.610747\pi\) | ||||
−0.340946 | + | 0.940083i | \(0.610747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −46.8596 | −2.41982 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.551249 | 0.0283908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7348 | 0.859610 | 0.429805 | − | 0.902922i | \(-0.358582\pi\) | ||||
0.429805 | + | 0.902922i | \(0.358582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.1498 | −1.54462 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.0825 | −1.02617 | −0.513084 | − | 0.858338i | \(-0.671497\pi\) | ||||
−0.513084 | + | 0.858338i | \(0.671497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.29267 | −0.116845 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.4235 | 0.936517 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.8905 | −1.71832 | −0.859158 | − | 0.511710i | \(-0.829012\pi\) | ||||
−0.859158 | + | 0.511710i | \(0.829012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.06169 | −0.255981 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.0224 | 1.56488 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.1230 | −0.609976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1181 | 1.41121 | 0.705605 | − | 0.708606i | \(-0.250676\pi\) | ||||
0.705605 | + | 0.708606i | \(0.250676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.870161 | 0.0435626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.63888 | −0.281592 | −0.140796 | − | 0.990039i | \(-0.544966\pi\) | ||||
−0.140796 | + | 0.990039i | \(0.544966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.573748 | 0.0285804 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −40.7045 | −2.02262 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.4354 | −1.26079 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.2320 | 0.852067 | 0.426033 | − | 0.904707i | \(-0.359911\pi\) | ||||
0.426033 | + | 0.904707i | \(0.359911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 37.3848 | 1.84406 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.814122 | −0.0400603 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −47.4828 | −2.33084 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.6121 | 1.40114 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.82680 | 0.186951 | 0.0934756 | − | 0.995622i | \(-0.470202\pi\) | ||||
0.0934756 | + | 0.995622i | \(0.470202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7975 | −1.01361 | −0.506804 | − | 0.862061i | \(-0.669173\pi\) | ||||
−0.506804 | + | 0.862061i | \(0.669173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.56218 | 0.416308 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.09669 | −0.295733 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.25157 | 0.0605677 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.56694 | −0.0756525 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9927 | −1.44470 | −0.722348 | − | 0.691530i | \(-0.756937\pi\) | ||||
−0.722348 | + | 0.691530i | \(0.756937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7873 | −1.14314 | −0.571571 | − | 0.820552i | \(-0.693666\pi\) | ||||
−0.571571 | + | 0.820552i | \(0.693666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 43.6651 | 2.09358 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.7624 | −1.51940 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.55479 | −0.408298 | −0.204149 | − | 0.978940i | \(-0.565443\pi\) | ||||
−0.204149 | + | 0.978940i | \(0.565443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.7450 | −0.797381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.6606 | 1.31420 | 0.657098 | − | 0.753806i | \(-0.271784\pi\) | ||||
0.657098 | + | 0.753806i | \(0.271784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.6514 | −0.836756 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.0438 | 1.27913 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.96415 | 0.328659 | 0.164329 | − | 0.986406i | \(-0.447454\pi\) | ||||
0.164329 | + | 0.986406i | \(0.447454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.2082 | 0.480687 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 41.1377 | 1.93282 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0443596 | −0.00207961 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.2530 | 1.41517 | 0.707587 | − | 0.706626i | \(-0.249784\pi\) | ||||
0.707587 | + | 0.706626i | \(0.249784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.841027 | −0.0392558 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3323 | −1.17984 | −0.589922 | − | 0.807460i | \(-0.700841\pi\) | ||||
−0.589922 | + | 0.807460i | \(0.700841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7879 | 1.19847 | 0.599233 | − | 0.800575i | \(-0.295472\pi\) | ||||
0.599233 | + | 0.800575i | \(0.295472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.4472 | 2.10756 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.68313 | −0.170435 | −0.0852174 | − | 0.996362i | \(-0.527158\pi\) | ||||
−0.0852174 | + | 0.996362i | \(0.527158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0645967 | 0.00298280 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.7638 | 1.14106 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −45.4110 | −2.08800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.2570 | −1.75535 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.3997 | 0.888250 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.25673 | 0.148804 | 0.0744020 | − | 0.997228i | \(-0.476295\pi\) | ||||
0.0744020 | + | 0.997228i | \(0.476295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.492136 | −0.0224395 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.95625 | −0.0890125 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −50.4112 | −2.28905 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5037 | −0.974427 | −0.487214 | − | 0.873283i | \(-0.661987\pi\) | ||||
−0.487214 | + | 0.873283i | \(0.661987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −57.5289 | −2.60155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.7292 | −1.38679 | −0.693395 | − | 0.720558i | \(-0.743886\pi\) | ||||
−0.693395 | + | 0.720558i | \(0.743886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.89024 | 0.130170 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −55.1070 | −2.47687 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.07163 | −0.0480690 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5918 | −1.77237 | −0.886187 | − | 0.463327i | \(-0.846655\pi\) | ||||
−0.886187 | + | 0.463327i | \(0.846655\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.3155 | −1.89052 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.51630 | −0.245960 | −0.122980 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122980 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.0124 | 1.73603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.1665 | 1.33974 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.4619 | −0.862634 | −0.431317 | − | 0.902201i | \(-0.641951\pi\) | ||||
−0.431317 | + | 0.902201i | \(0.641951\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.64618 | −0.0728226 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.27749 | −0.233007 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −74.8992 | −3.30045 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.1045 | −0.928173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0649 | −1.01244 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.94769 | −0.348195 | −0.174097 | − | 0.984728i | \(-0.555701\pi\) | ||||
−0.174097 | + | 0.984728i | \(0.555701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.6974 | −1.38603 | −0.693016 | − | 0.720922i | \(-0.743719\pi\) | ||||
−0.693016 | + | 0.720922i | \(0.743719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.35626 | −0.102836 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00820 | 0.131039 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.4066 | 2.10463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.5684 | −0.849196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.197514 | 0.00855528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.00875 | 0.0868458 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.77755 | 0.0767068 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.2739 | 1.77779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7350 | 0.848475 | 0.424237 | − | 0.905551i | \(-0.360542\pi\) | ||||
0.424237 | + | 0.905551i | \(0.360542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 47.5181 | 2.03920 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.1697 | 2.32037 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3389 | −0.655845 | −0.327923 | − | 0.944705i | \(-0.606349\pi\) | ||||
−0.327923 | + | 0.944705i | \(0.606349\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.0830 | 1.28391 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.1364 | 0.772638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.310128 | −0.0131880 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −38.9827 | −1.65472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.1757 | 1.15147 | 0.575736 | − | 0.817636i | \(-0.304716\pi\) | ||||
0.575736 | + | 0.817636i | \(0.304716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.878633 | −0.0371622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.21558 | −0.346862 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.4502 | 1.03045 | 0.515227 | − | 0.857054i | \(-0.327708\pi\) | ||||
0.515227 | + | 0.857054i | \(0.327708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 69.3447 | 2.91735 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.04129 | −0.0437300 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.17990 | 0.259075 | 0.129537 | − | 0.991575i | \(-0.458651\pi\) | ||||
0.129537 | + | 0.991575i | \(0.458651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8635 | 0.622019 | 0.311009 | − | 0.950407i | \(-0.399333\pi\) | ||||
0.311009 | + | 0.950407i | \(0.399333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0706 | −0.838461 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 86.0075 | 3.58676 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.4466 | −0.809572 | −0.404786 | − | 0.914411i | \(-0.632654\pi\) | ||||
−0.404786 | + | 0.914411i | \(0.632654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −62.8703 | −2.61280 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.21469 | −0.0503938 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.8172 | −1.98039 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.06624 | −0.0440834 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.6478 | 0.604578 | 0.302289 | − | 0.953216i | \(-0.402249\pi\) | ||||
0.302289 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8766 | 0.777798 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.8632 | 1.92769 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0984 | 1.07173 | 0.535867 | − | 0.844303i | \(-0.319985\pi\) | ||||
0.535867 | + | 0.844303i | \(0.319985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.232581 | −0.00953488 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.3898 | 0.507079 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.8440 | −1.26025 | −0.630126 | − | 0.776493i | \(-0.716997\pi\) | ||||
−0.630126 | + | 0.776493i | \(0.716997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3212 | −0.421008 | −0.210504 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210504 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.55266 | 0.0632291 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 92.9752 | 3.77998 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.14177 | 0.0869318 | 0.0434659 | − | 0.999055i | \(-0.486160\pi\) | ||||
0.0434659 | + | 0.999055i | \(0.486160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.11703 | 0.0452642 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.408339 | −0.0165196 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.807877 | 0.0326298 | 0.0163149 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163149 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.6453 | 0.630879 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.2375 | −1.90171 | −0.950855 | − | 0.309637i | \(-0.899792\pi\) | ||||
−0.950855 | + | 0.309637i | \(0.899792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.6928 | 1.87674 | 0.938371 | − | 0.345628i | \(-0.112334\pi\) | ||||
0.938371 | + | 0.345628i | \(0.112334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8646 | 0.476109 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.451552 | −0.0180911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.7035 | 1.10814 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −51.5532 | −2.05884 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.58031 | −0.102884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5243 | 0.538392 | 0.269196 | − | 0.963085i | \(-0.413242\pi\) | ||||
0.269196 | + | 0.963085i | \(0.413242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.6703 | −0.622837 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.5680 | 2.00673 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.798586 | 0.0316411 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.7578 | −1.01896 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1372 | −0.874368 | −0.437184 | − | 0.899372i | \(-0.644024\pi\) | ||||
−0.437184 | + | 0.899372i | \(0.644024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.1941 | 0.835815 | 0.417907 | − | 0.908490i | \(-0.362764\pi\) | ||||
0.417907 | + | 0.908490i | \(0.362764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −69.5975 | −2.74040 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0194 | 0.511846 | 0.255923 | − | 0.966697i | \(-0.417621\pi\) | ||||
0.255923 | + | 0.966697i | \(0.417621\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.2331 | 1.89331 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.16262 | 0.0455665 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.73363 | −0.146108 | −0.0730542 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730542 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.0316 | −2.03304 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.5679 | −1.54369 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5240 | 1.18905 | 0.594524 | − | 0.804078i | \(-0.297341\pi\) | ||||
0.594524 | + | 0.804078i | \(0.297341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6436 | −0.608464 | −0.304232 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304232 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.158959 | −0.00617345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.45946 | −0.0565953 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.7734 | −1.57875 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51.1693 | 1.97832 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −74.1499 | −2.86252 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.1808 | −0.430989 | −0.215495 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215495 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.2906 | 0.550046 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.4148 | −1.39954 | −0.699768 | − | 0.714371i | \(-0.746713\pi\) | ||||
−0.699768 | + | 0.714371i | \(0.746713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.28960 | −0.0494904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.3518 | 1.27804 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.27488 | 0.278365 | 0.139183 | − | 0.990267i | \(-0.455552\pi\) | ||||
0.139183 | + | 0.990267i | \(0.455552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62.7027 | −2.39575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.2595 | 0.849252 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.925190 | −0.0352469 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.68549 | −0.102161 | −0.0510804 | − | 0.998695i | \(-0.516266\pi\) | ||||
−0.0510804 | + | 0.998695i | \(0.516266\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.40973 | −0.0535512 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.9890 | −1.82033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03558 | 0.0392254 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.9694 | 1.58743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.5715 | 0.512588 | 0.256294 | − | 0.966599i | \(-0.417498\pi\) | ||||
0.256294 | + | 0.966599i | \(0.417498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1916 | −0.610677 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.3450 | −1.21818 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.998002 | 0.0375337 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5915 | 0.472884 | 0.236442 | − | 0.971646i | \(-0.424019\pi\) | ||||
0.236442 | + | 0.971646i | \(0.424019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.45429 | −0.279558 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.4375 | −1.58930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.62811 | 0.0982857 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.2522 | 1.27917 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.8803 | 0.965172 | 0.482586 | − | 0.875849i | \(-0.339698\pi\) | ||||
0.482586 | + | 0.875849i | \(0.339698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.91605 | −0.0713573 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.9963 | 1.22715 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −49.1106 | −1.82392 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8980 | −0.700889 | −0.350445 | − | 0.936583i | \(-0.613970\pi\) | ||||
−0.350445 | + | 0.936583i | \(0.613970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.2445 | −0.564612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.60674 | −0.170387 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.61256 | −0.244240 | −0.122120 | − | 0.992515i | \(-0.538969\pi\) | ||||
−0.122120 | + | 0.992515i | \(0.538969\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 63.2569 | 2.33327 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.82706 | −0.140972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.28543 | −0.0840709 | −0.0420354 | − | 0.999116i | \(-0.513384\pi\) | ||||
−0.0420354 | + | 0.999116i | \(0.513384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.997475 | −0.0366432 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.3889 | −1.22492 | −0.612460 | − | 0.790502i | \(-0.709820\pi\) | ||||
−0.612460 | + | 0.790502i | \(0.709820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.3585 | −1.66181 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.1965 | −1.06825 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0513872 | 0.00187765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −51.1496 | −1.86399 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −68.9972 | −2.51107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3287 | −0.956932 | −0.478466 | − | 0.878106i | \(-0.658807\pi\) | ||||
−0.478466 | + | 0.878106i | \(0.658807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 115.899 | 4.20687 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0302 | 1.37859 | 0.689297 | − | 0.724479i | \(-0.257920\pi\) | ||||
0.689297 | + | 0.724479i | \(0.257920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38575 | 0.0501676 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.59036 | −0.202120 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.933237 | 0.0336972 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.02534 | 0.253340 | 0.126670 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126670 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.1415 | 0.941464 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.4211 | −1.05820 | −0.529102 | − | 0.848558i | \(-0.677471\pi\) | ||||
−0.529102 | + | 0.848558i | \(0.677471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −51.1149 | −1.83610 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.997242 | −0.0357759 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.49832 | 0.232827 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63.4890 | 2.27182 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.77471 | −0.242108 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.5344 | −1.48243 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5990 | 0.377812 | 0.188906 | − | 0.981995i | \(-0.439506\pi\) | ||||
0.188906 | + | 0.981995i | \(0.439506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.9116 | −0.851277 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.77396 | 0.0630746 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.43469 | −0.0509472 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −73.2853 | −2.59916 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.3456 | 1.11032 | 0.555158 | − | 0.831745i | \(-0.312658\pi\) | ||||
0.555158 | + | 0.831745i | \(0.312658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.14095 | −0.0757415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.8536 | −0.383493 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 97.5287 | 3.44171 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.28107 | 0.115643 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.0548 | −0.952375 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.02698 | −0.247056 | −0.123528 | − | 0.992341i | \(-0.539421\pi\) | ||||
−0.123528 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0298 | 0.703342 | 0.351671 | − | 0.936124i | \(-0.385614\pi\) | ||||
0.351671 | + | 0.936124i | \(0.385614\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.57502 | 0.195525 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 96.4889 | 3.37986 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.9075 | −1.01135 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0272761 | −0.000953105 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4064 | 0.502786 | 0.251393 | − | 0.967885i | \(-0.419111\pi\) | ||||
0.251393 | + | 0.967885i | \(0.419111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.7218 | 0.757175 | 0.378587 | − | 0.925566i | \(-0.376410\pi\) | ||||
0.378587 | + | 0.925566i | \(0.376410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 139.598 | 4.86017 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.99954 | −0.139078 | −0.0695388 | − | 0.997579i | \(-0.522153\pi\) | ||||
−0.0695388 | + | 0.997579i | \(0.522153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.3387 | 1.19263 | 0.596317 | − | 0.802749i | \(-0.296630\pi\) | ||||
0.596317 | + | 0.802749i | \(0.296630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.4627 | 0.397638 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.18705 | 0.145073 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 70.9727 | 2.45611 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.05121 | −0.243725 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.38671 | 0.0478744 | 0.0239372 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239372 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.71827 | −0.197182 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.2019 | 1.14354 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.5960 | −1.74055 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.37846 | 0.0817250 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.8414 | −1.12711 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.4011 | 1.24781 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.3362 | −1.10717 | −0.553584 | − | 0.832793i | \(-0.686740\pi\) | ||||
−0.553584 | + | 0.832793i | \(0.686740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −35.0798 | −1.19970 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.7240 | −1.83518 | −0.917588 | − | 0.397532i | \(-0.869867\pi\) | ||||
−0.917588 | + | 0.397532i | \(0.869867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4809 | 1.44943 | 0.724715 | − | 0.689049i | \(-0.241972\pi\) | ||||
0.724715 | + | 0.689049i | \(0.241972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.400233 | 0.0136399 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.5249 | 1.34544 | 0.672722 | − | 0.739895i | \(-0.265125\pi\) | ||||
0.672722 | + | 0.739895i | \(0.265125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.6851 | 1.31533 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.6547 | 1.31278 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.3737 | 0.623284 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0740479 | −0.00250902 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.9972 | −1.04909 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.01057 | 0.0679696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.0978 | −1.21894 | −0.609468 | − | 0.792811i | \(-0.708617\pi\) | ||||
−0.609468 | + | 0.792811i | \(0.708617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.6802 | 1.30465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9091 | 1.37826 | 0.689131 | − | 0.724637i | \(-0.257992\pi\) | ||||
0.689131 | + | 0.724637i | \(0.257992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.3239 | −0.683953 | −0.341976 | − | 0.939709i | \(-0.611096\pi\) | ||||
−0.341976 | + | 0.939709i | \(0.611096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 73.9227 | 2.48488 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.44332 | 0.0484618 | 0.0242309 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242309 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.29361 | 0.0433864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 61.6917 | 2.06675 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.4346 | −0.449572 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.98134 | −0.0996554 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.24247 | 0.0748740 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.2319 | 0.808180 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.85084 | −0.161605 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.78042 | −0.0592487 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −79.6985 | −2.64927 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.2840 | −0.972359 | −0.486180 | − | 0.873859i | \(-0.661610\pi\) | ||||
−0.486180 | + | 0.873859i | \(0.661610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.9882 | 0.795638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.0149 | −1.35888 | −0.679441 | − | 0.733730i | \(-0.737778\pi\) | ||||
−0.679441 | + | 0.733730i | \(0.737778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.9650 | 2.38169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −113.643 | −3.75693 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.33106 | −0.0439554 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8345 | −0.588306 | −0.294153 | − | 0.955758i | \(-0.595038\pi\) | ||||
−0.294153 | + | 0.955758i | \(0.595038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3893 | −0.441191 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.22842 | 0.0404338 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.8442 | 1.44159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46.0545 | −1.51263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.9029 | −1.76850 | −0.884248 | − | 0.467018i | \(-0.845328\pi\) | ||||
−0.884248 | + | 0.467018i | \(0.845328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.2740 | 0.861094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.5931 | 2.01647 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.7794 | 0.450634 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8413 | −1.36690 | −0.683448 | − | 0.729999i | \(-0.739521\pi\) | ||||
−0.683448 | + | 0.729999i | \(0.739521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.0999 | 1.92865 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0296 | 0.587749 | 0.293875 | − | 0.955844i | \(-0.405055\pi\) | ||||
0.293875 | + | 0.955844i | \(0.405055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6092 | −0.475741 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.545168 | 0.0177343 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.0916 | 1.49778 | 0.748889 | − | 0.662696i | \(-0.230588\pi\) | ||||
0.748889 | + | 0.662696i | \(0.230588\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.88703 | 0.0612556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.2980 | −0.463644 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9333 | −0.548525 | −0.274262 | − | 0.961655i | \(-0.588434\pi\) | ||||
−0.274262 | + | 0.961655i | \(0.588434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.6629 | 1.08931 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −66.1788 | −2.13926 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.60404 | −0.0517972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.77908 | −0.186422 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.23515 | 0.0398022 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 105.448 | 3.39448 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.61718 | 0.277110 | 0.138555 | − | 0.990355i | \(-0.455754\pi\) | ||||
0.138555 | + | 0.990355i | \(0.455754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.22984 | −0.168007 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5073 | −0.465562 | −0.232781 | − | 0.972529i | \(-0.574782\pi\) | ||||
−0.232781 | + | 0.972529i | \(0.574782\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.22764 | −0.0393563 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.70101 | 0.0865014 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.2892 | 1.44893 | 0.724465 | − | 0.689312i | \(-0.242087\pi\) | ||||
0.724465 | + | 0.689312i | \(0.242087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.7525 | 0.855012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.3082 | 1.06345 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.2655 | −1.47564 | −0.737819 | − | 0.674998i | \(-0.764144\pi\) | ||||
−0.737819 | + | 0.674998i | \(0.764144\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −78.6001 | −2.50441 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.827440 | −0.0263377 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.9885 | 2.06651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.2575 | −1.05646 | −0.528229 | − | 0.849102i | \(-0.677144\pi\) | ||||
−0.528229 | + | 0.849102i | \(0.677144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.0172 | 1.42858 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.7804 | −0.658783 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5830 | −0.556858 | −0.278429 | − | 0.960457i | \(-0.589814\pi\) | ||||
−0.278429 | + | 0.960457i | \(0.589814\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.04823 | 0.191357 |
(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 | 6008.2.a.b.1.8 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.8 | ✓ | 44 | 1.1 | even | 1 | trivial |