Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, 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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.23607 | 0.390879 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23607 | −0.319151 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.23607 | −0.276393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −5.70820 | −1.19024 | −0.595121 | − | 0.803636i | \(-0.702896\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 5.23607 | 1.02688 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 1.23607 | 0.225674 | ||||||||
\(31\) | −7.70820 | −1.38443 | −0.692217 | − | 0.721689i | \(-0.743366\pi\) | ||||
−0.692217 | + | 0.721689i | \(0.743366\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 2.47214 | 0.423968 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.763932 | 0.125590 | 0.0627948 | − | 0.998026i | \(-0.479999\pi\) | ||||
0.0627948 | + | 0.998026i | \(0.479999\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.23607 | −0.838442 | ||||||||
\(40\) | 1.23607 | 0.195440 | ||||||||
\(41\) | 6.94427 | 1.08451 | 0.542257 | − | 0.840213i | \(-0.317570\pi\) | ||||
0.542257 | + | 0.840213i | \(0.317570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.52786 | 0.232997 | 0.116499 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116499 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −1.23607 | −0.184262 | ||||||||
\(46\) | 5.70820 | 0.841629 | ||||||||
\(47\) | −2.76393 | −0.403161 | −0.201580 | − | 0.979472i | \(-0.564608\pi\) | ||||
−0.201580 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.47214 | 0.491034 | ||||||||
\(51\) | −2.47214 | −0.346168 | ||||||||
\(52\) | −5.23607 | −0.726112 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.47214 | 0.333343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −8.47214 | −1.11245 | ||||||||
\(59\) | 12.9443 | 1.68520 | 0.842600 | − | 0.538539i | \(-0.181024\pi\) | ||||
0.842600 | + | 0.538539i | \(0.181024\pi\) | |||||||
\(60\) | −1.23607 | −0.159576 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 7.70820 | 0.978943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.47214 | 0.802770 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | 10.9443 | 1.33706 | 0.668528 | − | 0.743687i | \(-0.266925\pi\) | ||||
0.668528 | + | 0.743687i | \(0.266925\pi\) | |||||||
\(68\) | −2.47214 | −0.299791 | ||||||||
\(69\) | −5.70820 | −0.687187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4721 | 1.71753 | 0.858763 | − | 0.512373i | \(-0.171233\pi\) | ||||
0.858763 | + | 0.512373i | \(0.171233\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −0.763932 | −0.0888053 | ||||||||
\(75\) | −3.47214 | −0.400928 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.23607 | 0.592868 | ||||||||
\(79\) | 12.1803 | 1.37040 | 0.685198 | − | 0.728357i | \(-0.259716\pi\) | ||||
0.685198 | + | 0.728357i | \(0.259716\pi\) | |||||||
\(80\) | −1.23607 | −0.138197 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.94427 | −0.766867 | ||||||||
\(83\) | −8.94427 | −0.981761 | −0.490881 | − | 0.871227i | \(-0.663325\pi\) | ||||
−0.490881 | + | 0.871227i | \(0.663325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05573 | 0.331440 | ||||||||
\(86\) | −1.52786 | −0.164754 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 2.94427 | 0.312092 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(90\) | 1.23607 | 0.130293 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.70820 | −0.595121 | ||||||||
\(93\) | −7.70820 | −0.799304 | ||||||||
\(94\) | 2.76393 | 0.285078 | ||||||||
\(95\) | −1.23607 | −0.126818 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.4721 | −1.06328 | −0.531642 | − | 0.846969i | \(-0.678425\pi\) | ||||
−0.531642 | + | 0.846969i | \(0.678425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −3.47214 | −0.347214 | ||||||||
\(101\) | 19.7082 | 1.96104 | 0.980520 | − | 0.196420i | \(-0.0629317\pi\) | ||||
0.980520 | + | 0.196420i | \(0.0629317\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | 12.6525 | 1.24669 | 0.623343 | − | 0.781949i | \(-0.285774\pi\) | ||||
0.623343 | + | 0.781949i | \(0.285774\pi\) | |||||||
\(104\) | 5.23607 | 0.513439 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.47214 | −0.822887 | ||||||||
\(107\) | −8.94427 | −0.864675 | −0.432338 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.70820 | −0.163616 | −0.0818081 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818081 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(110\) | −2.47214 | −0.235709 | ||||||||
\(111\) | 0.763932 | 0.0725092 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4721 | 1.17328 | 0.586640 | − | 0.809848i | \(-0.300450\pi\) | ||||
0.586640 | + | 0.809848i | \(0.300450\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 7.05573 | 0.657950 | ||||||||
\(116\) | 8.47214 | 0.786618 | ||||||||
\(117\) | −5.23607 | −0.484075 | ||||||||
\(118\) | −12.9443 | −1.19162 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.23607 | 0.112837 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 12.4721 | 1.12917 | ||||||||
\(123\) | 6.94427 | 0.626144 | ||||||||
\(124\) | −7.70820 | −0.692217 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.7082 | 1.92629 | 0.963146 | − | 0.268980i | \(-0.0866865\pi\) | ||||
0.963146 | + | 0.268980i | \(0.0866865\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.52786 | 0.134521 | ||||||||
\(130\) | −6.47214 | −0.567644 | ||||||||
\(131\) | 3.05573 | 0.266980 | 0.133490 | − | 0.991050i | \(-0.457382\pi\) | ||||
0.133490 | + | 0.991050i | \(0.457382\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.9443 | −0.945441 | ||||||||
\(135\) | −1.23607 | −0.106384 | ||||||||
\(136\) | 2.47214 | 0.211984 | ||||||||
\(137\) | −9.41641 | −0.804498 | −0.402249 | − | 0.915530i | \(-0.631771\pi\) | ||||
−0.402249 | + | 0.915530i | \(0.631771\pi\) | |||||||
\(138\) | 5.70820 | 0.485915 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.76393 | −0.232765 | ||||||||
\(142\) | −14.4721 | −1.21447 | ||||||||
\(143\) | 10.4721 | 0.875724 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.4721 | −0.869664 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.763932 | 0.0627948 | ||||||||
\(149\) | 12.1803 | 0.997852 | 0.498926 | − | 0.866644i | \(-0.333728\pi\) | ||||
0.498926 | + | 0.866644i | \(0.333728\pi\) | |||||||
\(150\) | 3.47214 | 0.283499 | ||||||||
\(151\) | −13.7082 | −1.11556 | −0.557779 | − | 0.829990i | \(-0.688346\pi\) | ||||
−0.557779 | + | 0.829990i | \(0.688346\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.52786 | 0.765296 | ||||||||
\(156\) | −5.23607 | −0.419221 | ||||||||
\(157\) | 4.47214 | 0.356915 | 0.178458 | − | 0.983948i | \(-0.442889\pi\) | ||||
0.178458 | + | 0.983948i | \(0.442889\pi\) | |||||||
\(158\) | −12.1803 | −0.969016 | ||||||||
\(159\) | 8.47214 | 0.671884 | ||||||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −20.9443 | −1.64048 | −0.820241 | − | 0.572018i | \(-0.806161\pi\) | ||||
−0.820241 | + | 0.572018i | \(0.806161\pi\) | |||||||
\(164\) | 6.94427 | 0.542257 | ||||||||
\(165\) | 2.47214 | 0.192456 | ||||||||
\(166\) | 8.94427 | 0.694210 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | −3.05573 | −0.234364 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 1.52786 | 0.116499 | ||||||||
\(173\) | −11.8885 | −0.903869 | −0.451935 | − | 0.892051i | \(-0.649266\pi\) | ||||
−0.451935 | + | 0.892051i | \(0.649266\pi\) | |||||||
\(174\) | −8.47214 | −0.642271 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 12.9443 | 0.972951 | ||||||||
\(178\) | −2.94427 | −0.220683 | ||||||||
\(179\) | −15.4164 | −1.15228 | −0.576138 | − | 0.817352i | \(-0.695441\pi\) | ||||
−0.576138 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(180\) | −1.23607 | −0.0921311 | ||||||||
\(181\) | 9.23607 | 0.686512 | 0.343256 | − | 0.939242i | \(-0.388470\pi\) | ||||
0.343256 | + | 0.939242i | \(0.388470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4721 | −0.921967 | ||||||||
\(184\) | 5.70820 | 0.420814 | ||||||||
\(185\) | −0.944272 | −0.0694243 | ||||||||
\(186\) | 7.70820 | 0.565193 | ||||||||
\(187\) | 4.94427 | 0.361561 | ||||||||
\(188\) | −2.76393 | −0.201580 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.23607 | 0.0896738 | ||||||||
\(191\) | −3.81966 | −0.276381 | −0.138190 | − | 0.990406i | \(-0.544129\pi\) | ||||
−0.138190 | + | 0.990406i | \(0.544129\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.472136 | −0.0339851 | −0.0169925 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169925 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(194\) | 10.4721 | 0.751856 | ||||||||
\(195\) | 6.47214 | 0.463479 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.29180 | 0.163284 | 0.0816419 | − | 0.996662i | \(-0.473984\pi\) | ||||
0.0816419 | + | 0.996662i | \(0.473984\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | 5.52786 | 0.391860 | 0.195930 | − | 0.980618i | \(-0.437227\pi\) | ||||
0.195930 | + | 0.980618i | \(0.437227\pi\) | |||||||
\(200\) | 3.47214 | 0.245517 | ||||||||
\(201\) | 10.9443 | 0.771949 | ||||||||
\(202\) | −19.7082 | −1.38666 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.47214 | −0.173084 | ||||||||
\(205\) | −8.58359 | −0.599504 | ||||||||
\(206\) | −12.6525 | −0.881540 | ||||||||
\(207\) | −5.70820 | −0.396748 | ||||||||
\(208\) | −5.23607 | −0.363056 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.4164 | −1.74974 | −0.874869 | − | 0.484360i | \(-0.839053\pi\) | ||||
−0.874869 | + | 0.484360i | \(0.839053\pi\) | |||||||
\(212\) | 8.47214 | 0.581869 | ||||||||
\(213\) | 14.4721 | 0.991614 | ||||||||
\(214\) | 8.94427 | 0.611418 | ||||||||
\(215\) | −1.88854 | −0.128798 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.70820 | 0.115694 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 2.47214 | 0.166671 | ||||||||
\(221\) | 12.9443 | 0.870726 | ||||||||
\(222\) | −0.763932 | −0.0512718 | ||||||||
\(223\) | −3.70820 | −0.248320 | −0.124160 | − | 0.992262i | \(-0.539624\pi\) | ||||
−0.124160 | + | 0.992262i | \(0.539624\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47214 | −0.231476 | ||||||||
\(226\) | −12.4721 | −0.829634 | ||||||||
\(227\) | 7.05573 | 0.468305 | 0.234153 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234153 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 23.8885 | 1.57860 | 0.789300 | − | 0.614008i | \(-0.210444\pi\) | ||||
0.789300 | + | 0.614008i | \(0.210444\pi\) | |||||||
\(230\) | −7.05573 | −0.465241 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.47214 | −0.556223 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 5.23607 | 0.342292 | ||||||||
\(235\) | 3.41641 | 0.222862 | ||||||||
\(236\) | 12.9443 | 0.842600 | ||||||||
\(237\) | 12.1803 | 0.791198 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6525 | 1.46527 | 0.732633 | − | 0.680623i | \(-0.238291\pi\) | ||||
0.732633 | + | 0.680623i | \(0.238291\pi\) | |||||||
\(240\) | −1.23607 | −0.0797878 | ||||||||
\(241\) | 16.3607 | 1.05388 | 0.526942 | − | 0.849901i | \(-0.323338\pi\) | ||||
0.526942 | + | 0.849901i | \(0.323338\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.4721 | −0.798447 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.94427 | −0.442751 | ||||||||
\(247\) | −5.23607 | −0.333163 | ||||||||
\(248\) | 7.70820 | 0.489471 | ||||||||
\(249\) | −8.94427 | −0.566820 | ||||||||
\(250\) | −10.4721 | −0.662316 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.4164 | 0.717743 | ||||||||
\(254\) | −21.7082 | −1.36209 | ||||||||
\(255\) | 3.05573 | 0.191357 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.8885 | 1.24061 | 0.620307 | − | 0.784359i | \(-0.287008\pi\) | ||||
0.620307 | + | 0.784359i | \(0.287008\pi\) | |||||||
\(258\) | −1.52786 | −0.0951207 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.47214 | 0.401385 | ||||||||
\(261\) | 8.47214 | 0.524412 | ||||||||
\(262\) | −3.05573 | −0.188784 | ||||||||
\(263\) | −4.18034 | −0.257771 | −0.128885 | − | 0.991659i | \(-0.541140\pi\) | ||||
−0.128885 | + | 0.991659i | \(0.541140\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | −10.4721 | −0.643298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.94427 | 0.180187 | ||||||||
\(268\) | 10.9443 | 0.668528 | ||||||||
\(269\) | −28.4721 | −1.73598 | −0.867988 | − | 0.496584i | \(-0.834587\pi\) | ||||
−0.867988 | + | 0.496584i | \(0.834587\pi\) | |||||||
\(270\) | 1.23607 | 0.0752247 | ||||||||
\(271\) | −12.9443 | −0.786309 | −0.393154 | − | 0.919473i | \(-0.628616\pi\) | ||||
−0.393154 | + | 0.919473i | \(0.628616\pi\) | |||||||
\(272\) | −2.47214 | −0.149895 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.41641 | 0.568866 | ||||||||
\(275\) | 6.94427 | 0.418755 | ||||||||
\(276\) | −5.70820 | −0.343594 | ||||||||
\(277\) | 23.8885 | 1.43532 | 0.717662 | − | 0.696392i | \(-0.245212\pi\) | ||||
0.717662 | + | 0.696392i | \(0.245212\pi\) | |||||||
\(278\) | −16.0000 | −0.959616 | ||||||||
\(279\) | −7.70820 | −0.461478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.41641 | −0.323116 | −0.161558 | − | 0.986863i | \(-0.551652\pi\) | ||||
−0.161558 | + | 0.986863i | \(0.551652\pi\) | |||||||
\(282\) | 2.76393 | 0.164590 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | 14.4721 | 0.858763 | ||||||||
\(285\) | −1.23607 | −0.0732183 | ||||||||
\(286\) | −10.4721 | −0.619230 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 10.4721 | 0.614945 | ||||||||
\(291\) | −10.4721 | −0.613887 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 8.47214 | 0.494947 | 0.247474 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247474 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.0000 | −0.931556 | ||||||||
\(296\) | −0.763932 | −0.0444026 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | −12.1803 | −0.705588 | ||||||||
\(299\) | 29.8885 | 1.72850 | ||||||||
\(300\) | −3.47214 | −0.200464 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.7082 | 0.788818 | ||||||||
\(303\) | 19.7082 | 1.13221 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 15.4164 | 0.882741 | ||||||||
\(306\) | 2.47214 | 0.141323 | ||||||||
\(307\) | −5.52786 | −0.315492 | −0.157746 | − | 0.987480i | \(-0.550423\pi\) | ||||
−0.157746 | + | 0.987480i | \(0.550423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.6525 | 0.719774 | ||||||||
\(310\) | −9.52786 | −0.541146 | ||||||||
\(311\) | 17.2361 | 0.977368 | 0.488684 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488684 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(312\) | 5.23607 | 0.296434 | ||||||||
\(313\) | −30.0000 | −1.69570 | −0.847850 | − | 0.530236i | \(-0.822103\pi\) | ||||
−0.847850 | + | 0.530236i | \(0.822103\pi\) | |||||||
\(314\) | −4.47214 | −0.252377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1803 | 0.685198 | ||||||||
\(317\) | 12.4721 | 0.700505 | 0.350252 | − | 0.936655i | \(-0.386096\pi\) | ||||
0.350252 | + | 0.936655i | \(0.386096\pi\) | |||||||
\(318\) | −8.47214 | −0.475094 | ||||||||
\(319\) | −16.9443 | −0.948697 | ||||||||
\(320\) | −1.23607 | −0.0690983 | ||||||||
\(321\) | −8.94427 | −0.499221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.47214 | −0.137553 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 18.1803 | 1.00846 | ||||||||
\(326\) | 20.9443 | 1.16000 | ||||||||
\(327\) | −1.70820 | −0.0944639 | ||||||||
\(328\) | −6.94427 | −0.383433 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.47214 | −0.136087 | ||||||||
\(331\) | −18.9443 | −1.04127 | −0.520636 | − | 0.853779i | \(-0.674305\pi\) | ||||
−0.520636 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(332\) | −8.94427 | −0.490881 | ||||||||
\(333\) | 0.763932 | 0.0418632 | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | −13.5279 | −0.739106 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05573 | 0.0575092 | 0.0287546 | − | 0.999587i | \(-0.490846\pi\) | ||||
0.0287546 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(338\) | −14.4164 | −0.784149 | ||||||||
\(339\) | 12.4721 | 0.677393 | ||||||||
\(340\) | 3.05573 | 0.165720 | ||||||||
\(341\) | 15.4164 | 0.834845 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.52786 | −0.0823769 | ||||||||
\(345\) | 7.05573 | 0.379868 | ||||||||
\(346\) | 11.8885 | 0.639132 | ||||||||
\(347\) | 10.0000 | 0.536828 | 0.268414 | − | 0.963304i | \(-0.413500\pi\) | ||||
0.268414 | + | 0.963304i | \(0.413500\pi\) | |||||||
\(348\) | 8.47214 | 0.454154 | ||||||||
\(349\) | 22.3607 | 1.19694 | 0.598470 | − | 0.801145i | \(-0.295776\pi\) | ||||
0.598470 | + | 0.801145i | \(0.295776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.23607 | −0.279481 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | −8.00000 | −0.425797 | −0.212899 | − | 0.977074i | \(-0.568290\pi\) | ||||
−0.212899 | + | 0.977074i | \(0.568290\pi\) | |||||||
\(354\) | −12.9443 | −0.687980 | ||||||||
\(355\) | −17.8885 | −0.949425 | ||||||||
\(356\) | 2.94427 | 0.156046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.4164 | 0.814782 | ||||||||
\(359\) | 14.2918 | 0.754292 | 0.377146 | − | 0.926154i | \(-0.376905\pi\) | ||||
0.377146 | + | 0.926154i | \(0.376905\pi\) | |||||||
\(360\) | 1.23607 | 0.0651465 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.23607 | −0.485437 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.41641 | 0.388193 | ||||||||
\(366\) | 12.4721 | 0.651929 | ||||||||
\(367\) | 19.0557 | 0.994701 | 0.497350 | − | 0.867550i | \(-0.334306\pi\) | ||||
0.497350 | + | 0.867550i | \(0.334306\pi\) | |||||||
\(368\) | −5.70820 | −0.297561 | ||||||||
\(369\) | 6.94427 | 0.361504 | ||||||||
\(370\) | 0.944272 | 0.0490904 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.70820 | −0.399652 | ||||||||
\(373\) | 1.70820 | 0.0884474 | 0.0442237 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442237 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(374\) | −4.94427 | −0.255662 | ||||||||
\(375\) | 10.4721 | 0.540779 | ||||||||
\(376\) | 2.76393 | 0.142539 | ||||||||
\(377\) | −44.3607 | −2.28469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9443 | −0.562169 | −0.281085 | − | 0.959683i | \(-0.590694\pi\) | ||||
−0.281085 | + | 0.959683i | \(0.590694\pi\) | |||||||
\(380\) | −1.23607 | −0.0634089 | ||||||||
\(381\) | 21.7082 | 1.11214 | ||||||||
\(382\) | 3.81966 | 0.195431 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.472136 | 0.0240311 | ||||||||
\(387\) | 1.52786 | 0.0776657 | ||||||||
\(388\) | −10.4721 | −0.531642 | ||||||||
\(389\) | −7.23607 | −0.366883 | −0.183442 | − | 0.983031i | \(-0.558724\pi\) | ||||
−0.183442 | + | 0.983031i | \(0.558724\pi\) | |||||||
\(390\) | −6.47214 | −0.327729 | ||||||||
\(391\) | 14.1115 | 0.713647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.05573 | 0.154141 | ||||||||
\(394\) | −2.29180 | −0.115459 | ||||||||
\(395\) | −15.0557 | −0.757536 | ||||||||
\(396\) | −2.00000 | −0.100504 | ||||||||
\(397\) | 6.94427 | 0.348523 | 0.174262 | − | 0.984699i | \(-0.444246\pi\) | ||||
0.174262 | + | 0.984699i | \(0.444246\pi\) | |||||||
\(398\) | −5.52786 | −0.277087 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | −20.4721 | −1.02233 | −0.511165 | − | 0.859483i | \(-0.670786\pi\) | ||||
−0.511165 | + | 0.859483i | \(0.670786\pi\) | |||||||
\(402\) | −10.9443 | −0.545851 | ||||||||
\(403\) | 40.3607 | 2.01051 | ||||||||
\(404\) | 19.7082 | 0.980520 | ||||||||
\(405\) | −1.23607 | −0.0614207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52786 | −0.0757334 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | −5.52786 | −0.273335 | −0.136668 | − | 0.990617i | \(-0.543639\pi\) | ||||
−0.136668 | + | 0.990617i | \(0.543639\pi\) | |||||||
\(410\) | 8.58359 | 0.423913 | ||||||||
\(411\) | −9.41641 | −0.464477 | ||||||||
\(412\) | 12.6525 | 0.623343 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.70820 | 0.280543 | ||||||||
\(415\) | 11.0557 | 0.542704 | ||||||||
\(416\) | 5.23607 | 0.256719 | ||||||||
\(417\) | 16.0000 | 0.783523 | ||||||||
\(418\) | 2.00000 | 0.0978232 | ||||||||
\(419\) | 20.3607 | 0.994684 | 0.497342 | − | 0.867554i | \(-0.334309\pi\) | ||||
0.497342 | + | 0.867554i | \(0.334309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2361 | −0.547612 | −0.273806 | − | 0.961785i | \(-0.588283\pi\) | ||||
−0.273806 | + | 0.961785i | \(0.588283\pi\) | |||||||
\(422\) | 25.4164 | 1.23725 | ||||||||
\(423\) | −2.76393 | −0.134387 | ||||||||
\(424\) | −8.47214 | −0.411443 | ||||||||
\(425\) | 8.58359 | 0.416365 | ||||||||
\(426\) | −14.4721 | −0.701177 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.94427 | −0.432338 | ||||||||
\(429\) | 10.4721 | 0.505599 | ||||||||
\(430\) | 1.88854 | 0.0910737 | ||||||||
\(431\) | −9.52786 | −0.458941 | −0.229471 | − | 0.973316i | \(-0.573699\pi\) | ||||
−0.229471 | + | 0.973316i | \(0.573699\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 13.5279 | 0.650108 | 0.325054 | − | 0.945696i | \(-0.394618\pi\) | ||||
0.325054 | + | 0.945696i | \(0.394618\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4721 | −0.502100 | ||||||||
\(436\) | −1.70820 | −0.0818081 | ||||||||
\(437\) | −5.70820 | −0.273060 | ||||||||
\(438\) | 6.00000 | 0.286691 | ||||||||
\(439\) | −12.6525 | −0.603870 | −0.301935 | − | 0.953329i | \(-0.597633\pi\) | ||||
−0.301935 | + | 0.953329i | \(0.597633\pi\) | |||||||
\(440\) | −2.47214 | −0.117854 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.9443 | −0.615696 | ||||||||
\(443\) | −11.8885 | −0.564842 | −0.282421 | − | 0.959291i | \(-0.591137\pi\) | ||||
−0.282421 | + | 0.959291i | \(0.591137\pi\) | |||||||
\(444\) | 0.763932 | 0.0362546 | ||||||||
\(445\) | −3.63932 | −0.172520 | ||||||||
\(446\) | 3.70820 | 0.175589 | ||||||||
\(447\) | 12.1803 | 0.576110 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 3.47214 | 0.163678 | ||||||||
\(451\) | −13.8885 | −0.653986 | ||||||||
\(452\) | 12.4721 | 0.586640 | ||||||||
\(453\) | −13.7082 | −0.644068 | ||||||||
\(454\) | −7.05573 | −0.331142 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | −23.8885 | −1.11624 | ||||||||
\(459\) | −2.47214 | −0.115389 | ||||||||
\(460\) | 7.05573 | 0.328975 | ||||||||
\(461\) | 25.2361 | 1.17536 | 0.587680 | − | 0.809093i | \(-0.300041\pi\) | ||||
0.587680 | + | 0.809093i | \(0.300041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 8.47214 | 0.393309 | ||||||||
\(465\) | 9.52786 | 0.441844 | ||||||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | −29.8885 | −1.38308 | −0.691538 | − | 0.722340i | \(-0.743067\pi\) | ||||
−0.691538 | + | 0.722340i | \(0.743067\pi\) | |||||||
\(468\) | −5.23607 | −0.242037 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.41641 | −0.157587 | ||||||||
\(471\) | 4.47214 | 0.206065 | ||||||||
\(472\) | −12.9443 | −0.595808 | ||||||||
\(473\) | −3.05573 | −0.140503 | ||||||||
\(474\) | −12.1803 | −0.559462 | ||||||||
\(475\) | −3.47214 | −0.159313 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.47214 | 0.387912 | ||||||||
\(478\) | −22.6525 | −1.03610 | ||||||||
\(479\) | −1.23607 | −0.0564774 | −0.0282387 | − | 0.999601i | \(-0.508990\pi\) | ||||
−0.0282387 | + | 0.999601i | \(0.508990\pi\) | |||||||
\(480\) | 1.23607 | 0.0564185 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | −16.3607 | −0.745209 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 12.9443 | 0.587769 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 19.2361 | 0.871669 | 0.435835 | − | 0.900027i | \(-0.356453\pi\) | ||||
0.435835 | + | 0.900027i | \(0.356453\pi\) | |||||||
\(488\) | 12.4721 | 0.564587 | ||||||||
\(489\) | −20.9443 | −0.947133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5279 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(492\) | 6.94427 | 0.313072 | ||||||||
\(493\) | −20.9443 | −0.943283 | ||||||||
\(494\) | 5.23607 | 0.235582 | ||||||||
\(495\) | 2.47214 | 0.111114 | ||||||||
\(496\) | −7.70820 | −0.346109 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.94427 | 0.400802 | ||||||||
\(499\) | 8.36068 | 0.374275 | 0.187138 | − | 0.982334i | \(-0.440079\pi\) | ||||
0.187138 | + | 0.982334i | \(0.440079\pi\) | |||||||
\(500\) | 10.4721 | 0.468328 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.1246 | 0.496022 | 0.248011 | − | 0.968757i | \(-0.420223\pi\) | ||||
0.248011 | + | 0.968757i | \(0.420223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.3607 | −1.08404 | ||||||||
\(506\) | −11.4164 | −0.507521 | ||||||||
\(507\) | 14.4164 | 0.640255 | ||||||||
\(508\) | 21.7082 | 0.963146 | ||||||||
\(509\) | 24.4721 | 1.08471 | 0.542354 | − | 0.840150i | \(-0.317533\pi\) | ||||
0.542354 | + | 0.840150i | \(0.317533\pi\) | |||||||
\(510\) | −3.05573 | −0.135310 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −19.8885 | −0.877246 | ||||||||
\(515\) | −15.6393 | −0.689151 | ||||||||
\(516\) | 1.52786 | 0.0672605 | ||||||||
\(517\) | 5.52786 | 0.243115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.8885 | −0.521849 | ||||||||
\(520\) | −6.47214 | −0.283822 | ||||||||
\(521\) | 28.8328 | 1.26319 | 0.631594 | − | 0.775299i | \(-0.282401\pi\) | ||||
0.631594 | + | 0.775299i | \(0.282401\pi\) | |||||||
\(522\) | −8.47214 | −0.370815 | ||||||||
\(523\) | 2.47214 | 0.108099 | 0.0540495 | − | 0.998538i | \(-0.482787\pi\) | ||||
0.0540495 | + | 0.998538i | \(0.482787\pi\) | |||||||
\(524\) | 3.05573 | 0.133490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.18034 | 0.182271 | ||||||||
\(527\) | 19.0557 | 0.830081 | ||||||||
\(528\) | −2.00000 | −0.0870388 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 10.4721 | 0.454881 | ||||||||
\(531\) | 12.9443 | 0.561734 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.3607 | −1.57496 | ||||||||
\(534\) | −2.94427 | −0.127411 | ||||||||
\(535\) | 11.0557 | 0.477981 | ||||||||
\(536\) | −10.9443 | −0.472721 | ||||||||
\(537\) | −15.4164 | −0.665267 | ||||||||
\(538\) | 28.4721 | 1.22752 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.23607 | −0.0531919 | ||||||||
\(541\) | 24.8328 | 1.06765 | 0.533823 | − | 0.845596i | \(-0.320755\pi\) | ||||
0.533823 | + | 0.845596i | \(0.320755\pi\) | |||||||
\(542\) | 12.9443 | 0.556004 | ||||||||
\(543\) | 9.23607 | 0.396358 | ||||||||
\(544\) | 2.47214 | 0.105992 | ||||||||
\(545\) | 2.11146 | 0.0904448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0000 | −0.769624 | −0.384812 | − | 0.922995i | \(-0.625734\pi\) | ||||
−0.384812 | + | 0.922995i | \(0.625734\pi\) | |||||||
\(548\) | −9.41641 | −0.402249 | ||||||||
\(549\) | −12.4721 | −0.532298 | ||||||||
\(550\) | −6.94427 | −0.296105 | ||||||||
\(551\) | 8.47214 | 0.360925 | ||||||||
\(552\) | 5.70820 | 0.242957 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23.8885 | −1.01493 | ||||||||
\(555\) | −0.944272 | −0.0400821 | ||||||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | −36.5410 | −1.54829 | −0.774146 | − | 0.633007i | \(-0.781821\pi\) | ||||
−0.774146 | + | 0.633007i | \(0.781821\pi\) | |||||||
\(558\) | 7.70820 | 0.326314 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.94427 | 0.208747 | ||||||||
\(562\) | 5.41641 | 0.228477 | ||||||||
\(563\) | 9.88854 | 0.416752 | 0.208376 | − | 0.978049i | \(-0.433182\pi\) | ||||
0.208376 | + | 0.978049i | \(0.433182\pi\) | |||||||
\(564\) | −2.76393 | −0.116383 | ||||||||
\(565\) | −15.4164 | −0.648573 | ||||||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.4721 | −0.607237 | ||||||||
\(569\) | 13.0557 | 0.547325 | 0.273662 | − | 0.961826i | \(-0.411765\pi\) | ||||
0.273662 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(570\) | 1.23607 | 0.0517732 | ||||||||
\(571\) | −26.4721 | −1.10782 | −0.553912 | − | 0.832575i | \(-0.686866\pi\) | ||||
−0.553912 | + | 0.832575i | \(0.686866\pi\) | |||||||
\(572\) | 10.4721 | 0.437862 | ||||||||
\(573\) | −3.81966 | −0.159569 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.8197 | 0.826537 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 10.8885 | 0.452904 | ||||||||
\(579\) | −0.472136 | −0.0196213 | ||||||||
\(580\) | −10.4721 | −0.434832 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.4721 | 0.434084 | ||||||||
\(583\) | −16.9443 | −0.701760 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 6.47214 | 0.267590 | ||||||||
\(586\) | −8.47214 | −0.349981 | ||||||||
\(587\) | −19.4164 | −0.801401 | −0.400700 | − | 0.916209i | \(-0.631233\pi\) | ||||
−0.400700 | + | 0.916209i | \(0.631233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.70820 | −0.317611 | ||||||||
\(590\) | 16.0000 | 0.658710 | ||||||||
\(591\) | 2.29180 | 0.0942719 | ||||||||
\(592\) | 0.763932 | 0.0313974 | ||||||||
\(593\) | 4.00000 | 0.164260 | 0.0821302 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821302 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.1803 | 0.498926 | ||||||||
\(597\) | 5.52786 | 0.226240 | ||||||||
\(598\) | −29.8885 | −1.22223 | ||||||||
\(599\) | 32.3607 | 1.32222 | 0.661111 | − | 0.750288i | \(-0.270085\pi\) | ||||
0.661111 | + | 0.750288i | \(0.270085\pi\) | |||||||
\(600\) | 3.47214 | 0.141749 | ||||||||
\(601\) | 12.9443 | 0.528008 | 0.264004 | − | 0.964522i | \(-0.414957\pi\) | ||||
0.264004 | + | 0.964522i | \(0.414957\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.9443 | 0.445685 | ||||||||
\(604\) | −13.7082 | −0.557779 | ||||||||
\(605\) | 8.65248 | 0.351773 | ||||||||
\(606\) | −19.7082 | −0.800591 | ||||||||
\(607\) | 42.5410 | 1.72669 | 0.863343 | − | 0.504617i | \(-0.168366\pi\) | ||||
0.863343 | + | 0.504617i | \(0.168366\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.4164 | −0.624192 | ||||||||
\(611\) | 14.4721 | 0.585480 | ||||||||
\(612\) | −2.47214 | −0.0999302 | ||||||||
\(613\) | −14.3607 | −0.580022 | −0.290011 | − | 0.957023i | \(-0.593659\pi\) | ||||
−0.290011 | + | 0.957023i | \(0.593659\pi\) | |||||||
\(614\) | 5.52786 | 0.223086 | ||||||||
\(615\) | −8.58359 | −0.346124 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9443 | 1.08474 | 0.542368 | − | 0.840141i | \(-0.317528\pi\) | ||||
0.542368 | + | 0.840141i | \(0.317528\pi\) | |||||||
\(618\) | −12.6525 | −0.508957 | ||||||||
\(619\) | 26.8328 | 1.07850 | 0.539251 | − | 0.842145i | \(-0.318707\pi\) | ||||
0.539251 | + | 0.842145i | \(0.318707\pi\) | |||||||
\(620\) | 9.52786 | 0.382648 | ||||||||
\(621\) | −5.70820 | −0.229062 | ||||||||
\(622\) | −17.2361 | −0.691103 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.23607 | −0.209610 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 30.0000 | 1.19904 | ||||||||
\(627\) | −2.00000 | −0.0798723 | ||||||||
\(628\) | 4.47214 | 0.178458 | ||||||||
\(629\) | −1.88854 | −0.0753012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3607 | 1.28826 | 0.644129 | − | 0.764917i | \(-0.277220\pi\) | ||||
0.644129 | + | 0.764917i | \(0.277220\pi\) | |||||||
\(632\) | −12.1803 | −0.484508 | ||||||||
\(633\) | −25.4164 | −1.01021 | ||||||||
\(634\) | −12.4721 | −0.495332 | ||||||||
\(635\) | −26.8328 | −1.06483 | ||||||||
\(636\) | 8.47214 | 0.335942 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.9443 | 0.670830 | ||||||||
\(639\) | 14.4721 | 0.572509 | ||||||||
\(640\) | 1.23607 | 0.0488599 | ||||||||
\(641\) | −29.0557 | −1.14763 | −0.573816 | − | 0.818984i | \(-0.694538\pi\) | ||||
−0.573816 | + | 0.818984i | \(0.694538\pi\) | |||||||
\(642\) | 8.94427 | 0.353002 | ||||||||
\(643\) | 48.7214 | 1.92138 | 0.960691 | − | 0.277618i | \(-0.0895451\pi\) | ||||
0.960691 | + | 0.277618i | \(0.0895451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.88854 | −0.0743613 | ||||||||
\(646\) | 2.47214 | 0.0972649 | ||||||||
\(647\) | 4.87539 | 0.191671 | 0.0958356 | − | 0.995397i | \(-0.469448\pi\) | ||||
0.0958356 | + | 0.995397i | \(0.469448\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −25.8885 | −1.01621 | ||||||||
\(650\) | −18.1803 | −0.713092 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.9443 | −0.820241 | ||||||||
\(653\) | −2.87539 | −0.112523 | −0.0562613 | − | 0.998416i | \(-0.517918\pi\) | ||||
−0.0562613 | + | 0.998416i | \(0.517918\pi\) | |||||||
\(654\) | 1.70820 | 0.0667961 | ||||||||
\(655\) | −3.77709 | −0.147583 | ||||||||
\(656\) | 6.94427 | 0.271128 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.4721 | 1.65448 | 0.827240 | − | 0.561849i | \(-0.189910\pi\) | ||||
0.827240 | + | 0.561849i | \(0.189910\pi\) | |||||||
\(660\) | 2.47214 | 0.0962278 | ||||||||
\(661\) | −37.0132 | −1.43964 | −0.719822 | − | 0.694158i | \(-0.755777\pi\) | ||||
−0.719822 | + | 0.694158i | \(0.755777\pi\) | |||||||
\(662\) | 18.9443 | 0.736290 | ||||||||
\(663\) | 12.9443 | 0.502714 | ||||||||
\(664\) | 8.94427 | 0.347105 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.763932 | −0.0296018 | ||||||||
\(667\) | −48.3607 | −1.87253 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | −3.70820 | −0.143367 | ||||||||
\(670\) | 13.5279 | 0.522627 | ||||||||
\(671\) | 24.9443 | 0.962963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.4721 | −1.40590 | −0.702949 | − | 0.711240i | \(-0.748134\pi\) | ||||
−0.702949 | + | 0.711240i | \(0.748134\pi\) | |||||||
\(674\) | −1.05573 | −0.0406651 | ||||||||
\(675\) | −3.47214 | −0.133643 | ||||||||
\(676\) | 14.4164 | 0.554477 | ||||||||
\(677\) | 46.3607 | 1.78179 | 0.890893 | − | 0.454214i | \(-0.150080\pi\) | ||||
0.890893 | + | 0.454214i | \(0.150080\pi\) | |||||||
\(678\) | −12.4721 | −0.478989 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.05573 | −0.117182 | ||||||||
\(681\) | 7.05573 | 0.270376 | ||||||||
\(682\) | −15.4164 | −0.590325 | ||||||||
\(683\) | 40.3607 | 1.54436 | 0.772179 | − | 0.635405i | \(-0.219167\pi\) | ||||
0.772179 | + | 0.635405i | \(0.219167\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 11.6393 | 0.444716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.8885 | 0.911405 | ||||||||
\(688\) | 1.52786 | 0.0582493 | ||||||||
\(689\) | −44.3607 | −1.69001 | ||||||||
\(690\) | −7.05573 | −0.268607 | ||||||||
\(691\) | 13.8885 | 0.528345 | 0.264173 | − | 0.964475i | \(-0.414901\pi\) | ||||
0.264173 | + | 0.964475i | \(0.414901\pi\) | |||||||
\(692\) | −11.8885 | −0.451935 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0000 | −0.379595 | ||||||||
\(695\) | −19.7771 | −0.750188 | ||||||||
\(696\) | −8.47214 | −0.321135 | ||||||||
\(697\) | −17.1672 | −0.650253 | ||||||||
\(698\) | −22.3607 | −0.846364 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.2361 | −1.48193 | −0.740963 | − | 0.671546i | \(-0.765631\pi\) | ||||
−0.740963 | + | 0.671546i | \(0.765631\pi\) | |||||||
\(702\) | 5.23607 | 0.197623 | ||||||||
\(703\) | 0.763932 | 0.0288122 | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 3.41641 | 0.128669 | ||||||||
\(706\) | 8.00000 | 0.301084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.9443 | 0.486476 | ||||||||
\(709\) | 10.5836 | 0.397475 | 0.198738 | − | 0.980053i | \(-0.436316\pi\) | ||||
0.198738 | + | 0.980053i | \(0.436316\pi\) | |||||||
\(710\) | 17.8885 | 0.671345 | ||||||||
\(711\) | 12.1803 | 0.456798 | ||||||||
\(712\) | −2.94427 | −0.110341 | ||||||||
\(713\) | 44.0000 | 1.64781 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.9443 | −0.484088 | ||||||||
\(716\) | −15.4164 | −0.576138 | ||||||||
\(717\) | 22.6525 | 0.845972 | ||||||||
\(718\) | −14.2918 | −0.533365 | ||||||||
\(719\) | −18.5410 | −0.691463 | −0.345732 | − | 0.938333i | \(-0.612369\pi\) | ||||
−0.345732 | + | 0.938333i | \(0.612369\pi\) | |||||||
\(720\) | −1.23607 | −0.0460655 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 16.3607 | 0.608460 | ||||||||
\(724\) | 9.23607 | 0.343256 | ||||||||
\(725\) | −29.4164 | −1.09250 | ||||||||
\(726\) | 7.00000 | 0.259794 | ||||||||
\(727\) | 10.4721 | 0.388390 | 0.194195 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194195 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.41641 | −0.274494 | ||||||||
\(731\) | −3.77709 | −0.139701 | ||||||||
\(732\) | −12.4721 | −0.460983 | ||||||||
\(733\) | 19.3050 | 0.713045 | 0.356522 | − | 0.934287i | \(-0.383962\pi\) | ||||
0.356522 | + | 0.934287i | \(0.383962\pi\) | |||||||
\(734\) | −19.0557 | −0.703360 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.70820 | 0.210407 | ||||||||
\(737\) | −21.8885 | −0.806275 | ||||||||
\(738\) | −6.94427 | −0.255622 | ||||||||
\(739\) | 32.9443 | 1.21187 | 0.605937 | − | 0.795512i | \(-0.292798\pi\) | ||||
0.605937 | + | 0.795512i | \(0.292798\pi\) | |||||||
\(740\) | −0.944272 | −0.0347121 | ||||||||
\(741\) | −5.23607 | −0.192352 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.0557 | −1.28607 | −0.643035 | − | 0.765837i | \(-0.722325\pi\) | ||||
−0.643035 | + | 0.765837i | \(0.722325\pi\) | |||||||
\(744\) | 7.70820 | 0.282596 | ||||||||
\(745\) | −15.0557 | −0.551599 | ||||||||
\(746\) | −1.70820 | −0.0625418 | ||||||||
\(747\) | −8.94427 | −0.327254 | ||||||||
\(748\) | 4.94427 | 0.180780 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.4721 | −0.382388 | ||||||||
\(751\) | −53.4853 | −1.95171 | −0.975853 | − | 0.218428i | \(-0.929907\pi\) | ||||
−0.975853 | + | 0.218428i | \(0.929907\pi\) | |||||||
\(752\) | −2.76393 | −0.100790 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44.3607 | 1.61552 | ||||||||
\(755\) | 16.9443 | 0.616665 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3050 | 1.42856 | 0.714281 | − | 0.699859i | \(-0.246754\pi\) | ||||
0.714281 | + | 0.699859i | \(0.246754\pi\) | |||||||
\(758\) | 10.9443 | 0.397514 | ||||||||
\(759\) | 11.4164 | 0.414389 | ||||||||
\(760\) | 1.23607 | 0.0448369 | ||||||||
\(761\) | −16.3607 | −0.593074 | −0.296537 | − | 0.955021i | \(-0.595832\pi\) | ||||
−0.296537 | + | 0.955021i | \(0.595832\pi\) | |||||||
\(762\) | −21.7082 | −0.786405 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.81966 | −0.138190 | ||||||||
\(765\) | 3.05573 | 0.110480 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | −67.7771 | −2.44729 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −23.8885 | −0.861443 | −0.430721 | − | 0.902485i | \(-0.641741\pi\) | ||||
−0.430721 | + | 0.902485i | \(0.641741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8885 | 0.716268 | ||||||||
\(772\) | −0.472136 | −0.0169925 | ||||||||
\(773\) | −31.5279 | −1.13398 | −0.566989 | − | 0.823725i | \(-0.691892\pi\) | ||||
−0.566989 | + | 0.823725i | \(0.691892\pi\) | |||||||
\(774\) | −1.52786 | −0.0549179 | ||||||||
\(775\) | 26.7639 | 0.961389 | ||||||||
\(776\) | 10.4721 | 0.375928 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.23607 | 0.259426 | ||||||||
\(779\) | 6.94427 | 0.248804 | ||||||||
\(780\) | 6.47214 | 0.231740 | ||||||||
\(781\) | −28.9443 | −1.03571 | ||||||||
\(782\) | −14.1115 | −0.504625 | ||||||||
\(783\) | 8.47214 | 0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.52786 | −0.197298 | ||||||||
\(786\) | −3.05573 | −0.108994 | ||||||||
\(787\) | 38.8328 | 1.38424 | 0.692120 | − | 0.721782i | \(-0.256677\pi\) | ||||
0.692120 | + | 0.721782i | \(0.256677\pi\) | |||||||
\(788\) | 2.29180 | 0.0816419 | ||||||||
\(789\) | −4.18034 | −0.148824 | ||||||||
\(790\) | 15.0557 | 0.535659 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 65.3050 | 2.31905 | ||||||||
\(794\) | −6.94427 | −0.246443 | ||||||||
\(795\) | −10.4721 | −0.371408 | ||||||||
\(796\) | 5.52786 | 0.195930 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.83282 | 0.241728 | ||||||||
\(800\) | 3.47214 | 0.122759 | ||||||||
\(801\) | 2.94427 | 0.104031 | ||||||||
\(802\) | 20.4721 | 0.722896 | ||||||||
\(803\) | 12.0000 | 0.423471 | ||||||||
\(804\) | 10.9443 | 0.385975 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −40.3607 | −1.42164 | ||||||||
\(807\) | −28.4721 | −1.00227 | ||||||||
\(808\) | −19.7082 | −0.693332 | ||||||||
\(809\) | 33.4164 | 1.17486 | 0.587429 | − | 0.809276i | \(-0.300140\pi\) | ||||
0.587429 | + | 0.809276i | \(0.300140\pi\) | |||||||
\(810\) | 1.23607 | 0.0434310 | ||||||||
\(811\) | 31.4164 | 1.10318 | 0.551590 | − | 0.834116i | \(-0.314021\pi\) | ||||
0.551590 | + | 0.834116i | \(0.314021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.9443 | −0.453975 | ||||||||
\(814\) | 1.52786 | 0.0535516 | ||||||||
\(815\) | 25.8885 | 0.906836 | ||||||||
\(816\) | −2.47214 | −0.0865421 | ||||||||
\(817\) | 1.52786 | 0.0534532 | ||||||||
\(818\) | 5.52786 | 0.193277 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.58359 | −0.299752 | ||||||||
\(821\) | −22.2918 | −0.777989 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(822\) | 9.41641 | 0.328435 | ||||||||
\(823\) | 51.7771 | 1.80484 | 0.902418 | − | 0.430862i | \(-0.141790\pi\) | ||||
0.902418 | + | 0.430862i | \(0.141790\pi\) | |||||||
\(824\) | −12.6525 | −0.440770 | ||||||||
\(825\) | 6.94427 | 0.241769 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.47214 | −0.0859646 | −0.0429823 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429823 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(828\) | −5.70820 | −0.198374 | ||||||||
\(829\) | −13.8197 | −0.479977 | −0.239988 | − | 0.970776i | \(-0.577144\pi\) | ||||
−0.239988 | + | 0.970776i | \(0.577144\pi\) | |||||||
\(830\) | −11.0557 | −0.383750 | ||||||||
\(831\) | 23.8885 | 0.828684 | ||||||||
\(832\) | −5.23607 | −0.181528 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.0000 | −0.554035 | ||||||||
\(835\) | 9.88854 | 0.342207 | ||||||||
\(836\) | −2.00000 | −0.0691714 | ||||||||
\(837\) | −7.70820 | −0.266435 | ||||||||
\(838\) | −20.3607 | −0.703348 | ||||||||
\(839\) | −41.8885 | −1.44615 | −0.723077 | − | 0.690768i | \(-0.757273\pi\) | ||||
−0.723077 | + | 0.690768i | \(0.757273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 11.2361 | 0.387220 | ||||||||
\(843\) | −5.41641 | −0.186551 | ||||||||
\(844\) | −25.4164 | −0.874869 | ||||||||
\(845\) | −17.8197 | −0.613015 | ||||||||
\(846\) | 2.76393 | 0.0950259 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.47214 | 0.290934 | ||||||||
\(849\) | 8.00000 | 0.274559 | ||||||||
\(850\) | −8.58359 | −0.294415 | ||||||||
\(851\) | −4.36068 | −0.149482 | ||||||||
\(852\) | 14.4721 | 0.495807 | ||||||||
\(853\) | 37.4164 | 1.28111 | 0.640557 | − | 0.767911i | \(-0.278704\pi\) | ||||
0.640557 | + | 0.767911i | \(0.278704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.23607 | −0.0422726 | ||||||||
\(856\) | 8.94427 | 0.305709 | ||||||||
\(857\) | −11.8885 | −0.406105 | −0.203052 | − | 0.979168i | \(-0.565086\pi\) | ||||
−0.203052 | + | 0.979168i | \(0.565086\pi\) | |||||||
\(858\) | −10.4721 | −0.357513 | ||||||||
\(859\) | −53.8885 | −1.83865 | −0.919327 | − | 0.393495i | \(-0.871266\pi\) | ||||
−0.919327 | + | 0.393495i | \(0.871266\pi\) | |||||||
\(860\) | −1.88854 | −0.0643988 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.52786 | 0.324520 | ||||||||
\(863\) | 44.9443 | 1.52992 | 0.764960 | − | 0.644077i | \(-0.222759\pi\) | ||||
0.764960 | + | 0.644077i | \(0.222759\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 14.6950 | 0.499647 | ||||||||
\(866\) | −13.5279 | −0.459696 | ||||||||
\(867\) | −10.8885 | −0.369794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.3607 | −0.826379 | ||||||||
\(870\) | 10.4721 | 0.355039 | ||||||||
\(871\) | −57.3050 | −1.94170 | ||||||||
\(872\) | 1.70820 | 0.0578471 | ||||||||
\(873\) | −10.4721 | −0.354428 | ||||||||
\(874\) | 5.70820 | 0.193083 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −2.29180 | −0.0773885 | −0.0386942 | − | 0.999251i | \(-0.512320\pi\) | ||||
−0.0386942 | + | 0.999251i | \(0.512320\pi\) | |||||||
\(878\) | 12.6525 | 0.427000 | ||||||||
\(879\) | 8.47214 | 0.285758 | ||||||||
\(880\) | 2.47214 | 0.0833357 | ||||||||
\(881\) | 36.9443 | 1.24468 | 0.622342 | − | 0.782745i | \(-0.286181\pi\) | ||||
0.622342 | + | 0.782745i | \(0.286181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.360680 | −0.0121378 | −0.00606892 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00606892 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(884\) | 12.9443 | 0.435363 | ||||||||
\(885\) | −16.0000 | −0.537834 | ||||||||
\(886\) | 11.8885 | 0.399403 | ||||||||
\(887\) | 43.1935 | 1.45030 | 0.725148 | − | 0.688593i | \(-0.241771\pi\) | ||||
0.725148 | + | 0.688593i | \(0.241771\pi\) | |||||||
\(888\) | −0.763932 | −0.0256359 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.63932 | 0.121990 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | −3.70820 | −0.124160 | ||||||||
\(893\) | −2.76393 | −0.0924915 | ||||||||
\(894\) | −12.1803 | −0.407372 | ||||||||
\(895\) | 19.0557 | 0.636963 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.8885 | 0.997949 | ||||||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | −65.3050 | −2.17804 | ||||||||
\(900\) | −3.47214 | −0.115738 | ||||||||
\(901\) | −20.9443 | −0.697755 | ||||||||
\(902\) | 13.8885 | 0.462438 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.4721 | −0.414817 | ||||||||
\(905\) | −11.4164 | −0.379494 | ||||||||
\(906\) | 13.7082 | 0.455425 | ||||||||
\(907\) | 34.0000 | 1.12895 | 0.564476 | − | 0.825450i | \(-0.309078\pi\) | ||||
0.564476 | + | 0.825450i | \(0.309078\pi\) | |||||||
\(908\) | 7.05573 | 0.234153 | ||||||||
\(909\) | 19.7082 | 0.653680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.4721 | −0.744535 | −0.372268 | − | 0.928125i | \(-0.621420\pi\) | ||||
−0.372268 | + | 0.928125i | \(0.621420\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 17.8885 | 0.592024 | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 15.4164 | 0.509651 | ||||||||
\(916\) | 23.8885 | 0.789300 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.47214 | 0.0815926 | ||||||||
\(919\) | 22.8328 | 0.753185 | 0.376593 | − | 0.926379i | \(-0.377096\pi\) | ||||
0.376593 | + | 0.926379i | \(0.377096\pi\) | |||||||
\(920\) | −7.05573 | −0.232620 | ||||||||
\(921\) | −5.52786 | −0.182149 | ||||||||
\(922\) | −25.2361 | −0.831106 | ||||||||
\(923\) | −75.7771 | −2.49423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.65248 | −0.0872129 | ||||||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | 12.6525 | 0.415562 | ||||||||
\(928\) | −8.47214 | −0.278111 | ||||||||
\(929\) | 39.4164 | 1.29321 | 0.646605 | − | 0.762825i | \(-0.276188\pi\) | ||||
0.646605 | + | 0.762825i | \(0.276188\pi\) | |||||||
\(930\) | −9.52786 | −0.312431 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 17.2361 | 0.564284 | ||||||||
\(934\) | 29.8885 | 0.977983 | ||||||||
\(935\) | −6.11146 | −0.199866 | ||||||||
\(936\) | 5.23607 | 0.171146 | ||||||||
\(937\) | 33.7771 | 1.10345 | 0.551725 | − | 0.834026i | \(-0.313970\pi\) | ||||
0.551725 | + | 0.834026i | \(0.313970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.0000 | −0.979013 | ||||||||
\(940\) | 3.41641 | 0.111431 | ||||||||
\(941\) | 16.4721 | 0.536976 | 0.268488 | − | 0.963283i | \(-0.413476\pi\) | ||||
0.268488 | + | 0.963283i | \(0.413476\pi\) | |||||||
\(942\) | −4.47214 | −0.145710 | ||||||||
\(943\) | −39.6393 | −1.29083 | ||||||||
\(944\) | 12.9443 | 0.421300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.05573 | 0.0993503 | ||||||||
\(947\) | 32.2492 | 1.04796 | 0.523979 | − | 0.851731i | \(-0.324447\pi\) | ||||
0.523979 | + | 0.851731i | \(0.324447\pi\) | |||||||
\(948\) | 12.1803 | 0.395599 | ||||||||
\(949\) | 31.4164 | 1.01982 | ||||||||
\(950\) | 3.47214 | 0.112651 | ||||||||
\(951\) | 12.4721 | 0.404437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.5836 | 0.601982 | 0.300991 | − | 0.953627i | \(-0.402683\pi\) | ||||
0.300991 | + | 0.953627i | \(0.402683\pi\) | |||||||
\(954\) | −8.47214 | −0.274296 | ||||||||
\(955\) | 4.72136 | 0.152780 | ||||||||
\(956\) | 22.6525 | 0.732633 | ||||||||
\(957\) | −16.9443 | −0.547731 | ||||||||
\(958\) | 1.23607 | 0.0399355 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.23607 | −0.0398939 | ||||||||
\(961\) | 28.4164 | 0.916658 | ||||||||
\(962\) | 4.00000 | 0.128965 | ||||||||
\(963\) | −8.94427 | −0.288225 | ||||||||
\(964\) | 16.3607 | 0.526942 | ||||||||
\(965\) | 0.583592 | 0.0187865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.4164 | −0.624390 | −0.312195 | − | 0.950018i | \(-0.601064\pi\) | ||||
−0.312195 | + | 0.950018i | \(0.601064\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | −2.47214 | −0.0794164 | ||||||||
\(970\) | −12.9443 | −0.415616 | ||||||||
\(971\) | 44.7214 | 1.43518 | 0.717588 | − | 0.696467i | \(-0.245246\pi\) | ||||
0.717588 | + | 0.696467i | \(0.245246\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.2361 | −0.616363 | ||||||||
\(975\) | 18.1803 | 0.582237 | ||||||||
\(976\) | −12.4721 | −0.399223 | ||||||||
\(977\) | 5.41641 | 0.173286 | 0.0866431 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866431 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(978\) | 20.9443 | 0.669724 | ||||||||
\(979\) | −5.88854 | −0.188199 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.70820 | −0.0545388 | ||||||||
\(982\) | −23.5279 | −0.750804 | ||||||||
\(983\) | −17.3050 | −0.551942 | −0.275971 | − | 0.961166i | \(-0.588999\pi\) | ||||
−0.275971 | + | 0.961166i | \(0.588999\pi\) | |||||||
\(984\) | −6.94427 | −0.221375 | ||||||||
\(985\) | −2.83282 | −0.0902610 | ||||||||
\(986\) | 20.9443 | 0.667001 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.23607 | −0.166582 | ||||||||
\(989\) | −8.72136 | −0.277323 | ||||||||
\(990\) | −2.47214 | −0.0785696 | ||||||||
\(991\) | 49.7082 | 1.57903 | 0.789517 | − | 0.613729i | \(-0.210331\pi\) | ||||
0.789517 | + | 0.613729i | \(0.210331\pi\) | |||||||
\(992\) | 7.70820 | 0.244736 | ||||||||
\(993\) | −18.9443 | −0.601178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.83282 | −0.216615 | ||||||||
\(996\) | −8.94427 | −0.283410 | ||||||||
\(997\) | −48.4721 | −1.53513 | −0.767564 | − | 0.640972i | \(-0.778531\pi\) | ||||
−0.767564 | + | 0.640972i | \(0.778531\pi\) | |||||||
\(998\) | −8.36068 | −0.264653 | ||||||||
\(999\) | 0.763932 | 0.0241697 |
(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 | 5586.2.a.be.1.1 | 2 | ||
7.6 | odd | 2 | 798.2.a.j.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 2394.2.a.z.1.1 | 2 | |||
28.27 | even | 2 | 6384.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.a.j.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
2394.2.a.z.1.1 | 2 | 21.20 | even | 2 | |||
5586.2.a.be.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6384.2.a.bn.1.2 | 2 | 28.27 | even | 2 |