Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.211079\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −0.211079 | −0.121867 | −0.0609333 | − | 0.998142i | \(-0.519408\pi\) | ||||
−0.0609333 | + | 0.998142i | \(0.519408\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.211079 | 0.0861728 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.95545 | −0.985149 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.211079 | −0.0609333 | ||||||||
\(13\) | 0.384053 | 0.106517 | 0.0532585 | − | 0.998581i | \(-0.483039\pi\) | ||||
0.0532585 | + | 0.998581i | \(0.483039\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.211079 | 0.0545004 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.35151 | 0.812860 | 0.406430 | − | 0.913682i | \(-0.366774\pi\) | ||||
0.406430 | + | 0.913682i | \(0.366774\pi\) | |||||||
\(18\) | 2.95545 | 0.696605 | ||||||||
\(19\) | 4.82002 | 1.10579 | 0.552894 | − | 0.833251i | \(-0.313523\pi\) | ||||
0.552894 | + | 0.833251i | \(0.313523\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.211079 | −0.0460613 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.683067 | 0.142429 | 0.0712147 | − | 0.997461i | \(-0.477312\pi\) | ||||
0.0712147 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(24\) | 0.211079 | 0.0430864 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.384053 | −0.0753189 | ||||||||
\(27\) | 1.25707 | 0.241923 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.60685 | −0.298385 | −0.149193 | − | 0.988808i | \(-0.547667\pi\) | ||||
−0.149193 | + | 0.988808i | \(0.547667\pi\) | |||||||
\(30\) | −0.211079 | −0.0385376 | ||||||||
\(31\) | −1.25772 | −0.225893 | −0.112947 | − | 0.993601i | \(-0.536029\pi\) | ||||
−0.112947 | + | 0.993601i | \(0.536029\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.35151 | −0.574779 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.95545 | −0.492574 | ||||||||
\(37\) | 0.856889 | 0.140872 | 0.0704359 | − | 0.997516i | \(-0.477561\pi\) | ||||
0.0704359 | + | 0.997516i | \(0.477561\pi\) | |||||||
\(38\) | −4.82002 | −0.781911 | ||||||||
\(39\) | −0.0810656 | −0.0129809 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.62110 | −1.50256 | −0.751281 | − | 0.659982i | \(-0.770564\pi\) | ||||
−0.751281 | + | 0.659982i | \(0.770564\pi\) | |||||||
\(42\) | 0.211079 | 0.0325702 | ||||||||
\(43\) | −9.55155 | −1.45660 | −0.728299 | − | 0.685259i | \(-0.759689\pi\) | ||||
−0.728299 | + | 0.685259i | \(0.759689\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.95545 | 0.440572 | ||||||||
\(46\) | −0.683067 | −0.100713 | ||||||||
\(47\) | −7.55052 | −1.10136 | −0.550678 | − | 0.834718i | \(-0.685631\pi\) | ||||
−0.550678 | + | 0.834718i | \(0.685631\pi\) | |||||||
\(48\) | −0.211079 | −0.0304667 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.707434 | −0.0990605 | ||||||||
\(52\) | 0.384053 | 0.0532585 | ||||||||
\(53\) | −13.5386 | −1.85967 | −0.929837 | − | 0.367971i | \(-0.880053\pi\) | ||||
−0.929837 | + | 0.367971i | \(0.880053\pi\) | |||||||
\(54\) | −1.25707 | −0.171066 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.01741 | −0.134759 | ||||||||
\(58\) | 1.60685 | 0.210990 | ||||||||
\(59\) | 7.26925 | 0.946375 | 0.473188 | − | 0.880962i | \(-0.343103\pi\) | ||||
0.473188 | + | 0.880962i | \(0.343103\pi\) | |||||||
\(60\) | 0.211079 | 0.0272502 | ||||||||
\(61\) | −3.89131 | −0.498232 | −0.249116 | − | 0.968474i | \(-0.580140\pi\) | ||||
−0.249116 | + | 0.968474i | \(0.580140\pi\) | |||||||
\(62\) | 1.25772 | 0.159731 | ||||||||
\(63\) | −2.95545 | −0.372351 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.384053 | −0.0476359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.97372 | 0.607637 | 0.303818 | − | 0.952730i | \(-0.401738\pi\) | ||||
0.303818 | + | 0.952730i | \(0.401738\pi\) | |||||||
\(68\) | 3.35151 | 0.406430 | ||||||||
\(69\) | −0.144181 | −0.0173574 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 0.840435 | 0.0997413 | 0.0498707 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498707 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(72\) | 2.95545 | 0.348303 | ||||||||
\(73\) | 10.3485 | 1.21120 | 0.605602 | − | 0.795768i | \(-0.292932\pi\) | ||||
0.605602 | + | 0.795768i | \(0.292932\pi\) | |||||||
\(74\) | −0.856889 | −0.0996114 | ||||||||
\(75\) | −0.211079 | −0.0243733 | ||||||||
\(76\) | 4.82002 | 0.552894 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0810656 | 0.00917887 | ||||||||
\(79\) | −3.36771 | −0.378898 | −0.189449 | − | 0.981891i | \(-0.560670\pi\) | ||||
−0.189449 | + | 0.981891i | \(0.560670\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.60099 | 0.955666 | ||||||||
\(82\) | 9.62110 | 1.06247 | ||||||||
\(83\) | 10.5195 | 1.15467 | 0.577334 | − | 0.816508i | \(-0.304093\pi\) | ||||
0.577334 | + | 0.816508i | \(0.304093\pi\) | |||||||
\(84\) | −0.211079 | −0.0230306 | ||||||||
\(85\) | −3.35151 | −0.363522 | ||||||||
\(86\) | 9.55155 | 1.02997 | ||||||||
\(87\) | 0.339174 | 0.0363632 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0365 | 1.59386 | 0.796931 | − | 0.604070i | \(-0.206455\pi\) | ||||
0.796931 | + | 0.604070i | \(0.206455\pi\) | |||||||
\(90\) | −2.95545 | −0.311531 | ||||||||
\(91\) | 0.384053 | 0.0402597 | ||||||||
\(92\) | 0.683067 | 0.0712147 | ||||||||
\(93\) | 0.265479 | 0.0275289 | ||||||||
\(94\) | 7.55052 | 0.778776 | ||||||||
\(95\) | −4.82002 | −0.494524 | ||||||||
\(96\) | 0.211079 | 0.0215432 | ||||||||
\(97\) | 11.2671 | 1.14400 | 0.572001 | − | 0.820253i | \(-0.306167\pi\) | ||||
0.572001 | + | 0.820253i | \(0.306167\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.707992 | −0.0704478 | −0.0352239 | − | 0.999379i | \(-0.511214\pi\) | ||||
−0.0352239 | + | 0.999379i | \(0.511214\pi\) | |||||||
\(102\) | 0.707434 | 0.0700464 | ||||||||
\(103\) | 0.602041 | 0.0593209 | 0.0296604 | − | 0.999560i | \(-0.490557\pi\) | ||||
0.0296604 | + | 0.999560i | \(0.490557\pi\) | |||||||
\(104\) | −0.384053 | −0.0376595 | ||||||||
\(105\) | 0.211079 | 0.0205992 | ||||||||
\(106\) | 13.5386 | 1.31499 | ||||||||
\(107\) | −10.2801 | −0.993819 | −0.496909 | − | 0.867802i | \(-0.665532\pi\) | ||||
−0.496909 | + | 0.867802i | \(0.665532\pi\) | |||||||
\(108\) | 1.25707 | 0.120962 | ||||||||
\(109\) | 2.65530 | 0.254331 | 0.127166 | − | 0.991881i | \(-0.459412\pi\) | ||||
0.127166 | + | 0.991881i | \(0.459412\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.180872 | −0.0171676 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.2264 | 0.962016 | 0.481008 | − | 0.876716i | \(-0.340271\pi\) | ||||
0.481008 | + | 0.876716i | \(0.340271\pi\) | |||||||
\(114\) | 1.01741 | 0.0952889 | ||||||||
\(115\) | −0.683067 | −0.0636963 | ||||||||
\(116\) | −1.60685 | −0.149193 | ||||||||
\(117\) | −1.13505 | −0.104935 | ||||||||
\(118\) | −7.26925 | −0.669188 | ||||||||
\(119\) | 3.35151 | 0.307232 | ||||||||
\(120\) | −0.211079 | −0.0192688 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.89131 | 0.352303 | ||||||||
\(123\) | 2.03081 | 0.183112 | ||||||||
\(124\) | −1.25772 | −0.112947 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.95545 | 0.263292 | ||||||||
\(127\) | −21.0499 | −1.86788 | −0.933938 | − | 0.357434i | \(-0.883652\pi\) | ||||
−0.933938 | + | 0.357434i | \(0.883652\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.01614 | 0.177511 | ||||||||
\(130\) | 0.384053 | 0.0336836 | ||||||||
\(131\) | −12.9629 | −1.13257 | −0.566287 | − | 0.824208i | \(-0.691621\pi\) | ||||
−0.566287 | + | 0.824208i | \(0.691621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.82002 | 0.417949 | ||||||||
\(134\) | −4.97372 | −0.429664 | ||||||||
\(135\) | −1.25707 | −0.108191 | ||||||||
\(136\) | −3.35151 | −0.287389 | ||||||||
\(137\) | 12.4469 | 1.06341 | 0.531704 | − | 0.846930i | \(-0.321552\pi\) | ||||
0.531704 | + | 0.846930i | \(0.321552\pi\) | |||||||
\(138\) | 0.144181 | 0.0122735 | ||||||||
\(139\) | 12.0205 | 1.01957 | 0.509784 | − | 0.860302i | \(-0.329725\pi\) | ||||
0.509784 | + | 0.860302i | \(0.329725\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 1.59376 | 0.134219 | ||||||||
\(142\) | −0.840435 | −0.0705278 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.95545 | −0.246287 | ||||||||
\(145\) | 1.60685 | 0.133442 | ||||||||
\(146\) | −10.3485 | −0.856450 | ||||||||
\(147\) | −0.211079 | −0.0174095 | ||||||||
\(148\) | 0.856889 | 0.0704359 | ||||||||
\(149\) | −12.1628 | −0.996419 | −0.498209 | − | 0.867057i | \(-0.666009\pi\) | ||||
−0.498209 | + | 0.867057i | \(0.666009\pi\) | |||||||
\(150\) | 0.211079 | 0.0172346 | ||||||||
\(151\) | 20.2628 | 1.64896 | 0.824481 | − | 0.565889i | \(-0.191467\pi\) | ||||
0.824481 | + | 0.565889i | \(0.191467\pi\) | |||||||
\(152\) | −4.82002 | −0.390955 | ||||||||
\(153\) | −9.90519 | −0.800787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.25772 | 0.101023 | ||||||||
\(156\) | −0.0810656 | −0.00649044 | ||||||||
\(157\) | −10.0988 | −0.805972 | −0.402986 | − | 0.915206i | \(-0.632028\pi\) | ||||
−0.402986 | + | 0.915206i | \(0.632028\pi\) | |||||||
\(158\) | 3.36771 | 0.267921 | ||||||||
\(159\) | 2.85773 | 0.226632 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.683067 | 0.0538332 | ||||||||
\(162\) | −8.60099 | −0.675758 | ||||||||
\(163\) | 20.9868 | 1.64381 | 0.821905 | − | 0.569625i | \(-0.192911\pi\) | ||||
0.821905 | + | 0.569625i | \(0.192911\pi\) | |||||||
\(164\) | −9.62110 | −0.751281 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.5195 | −0.816474 | ||||||||
\(167\) | −21.8752 | −1.69276 | −0.846378 | − | 0.532582i | \(-0.821222\pi\) | ||||
−0.846378 | + | 0.532582i | \(0.821222\pi\) | |||||||
\(168\) | 0.211079 | 0.0162851 | ||||||||
\(169\) | −12.8525 | −0.988654 | ||||||||
\(170\) | 3.35151 | 0.257049 | ||||||||
\(171\) | −14.2453 | −1.08937 | ||||||||
\(172\) | −9.55155 | −0.728299 | ||||||||
\(173\) | −0.216594 | −0.0164673 | −0.00823366 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823366 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(174\) | −0.339174 | −0.0257127 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.53439 | −0.115332 | ||||||||
\(178\) | −15.0365 | −1.12703 | ||||||||
\(179\) | −17.0592 | −1.27507 | −0.637534 | − | 0.770422i | \(-0.720045\pi\) | ||||
−0.637534 | + | 0.770422i | \(0.720045\pi\) | |||||||
\(180\) | 2.95545 | 0.220286 | ||||||||
\(181\) | 3.45754 | 0.256997 | 0.128498 | − | 0.991710i | \(-0.458984\pi\) | ||||
0.128498 | + | 0.991710i | \(0.458984\pi\) | |||||||
\(182\) | −0.384053 | −0.0284679 | ||||||||
\(183\) | 0.821376 | 0.0607178 | ||||||||
\(184\) | −0.683067 | −0.0503564 | ||||||||
\(185\) | −0.856889 | −0.0629998 | ||||||||
\(186\) | −0.265479 | −0.0194658 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.55052 | −0.550678 | ||||||||
\(189\) | 1.25707 | 0.0914385 | ||||||||
\(190\) | 4.82002 | 0.349681 | ||||||||
\(191\) | 2.95839 | 0.214062 | 0.107031 | − | 0.994256i | \(-0.465866\pi\) | ||||
0.107031 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(192\) | −0.211079 | −0.0152333 | ||||||||
\(193\) | 9.47612 | 0.682106 | 0.341053 | − | 0.940044i | \(-0.389216\pi\) | ||||
0.341053 | + | 0.940044i | \(0.389216\pi\) | |||||||
\(194\) | −11.2671 | −0.808931 | ||||||||
\(195\) | 0.0810656 | 0.00580522 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −5.06389 | −0.360787 | −0.180394 | − | 0.983594i | \(-0.557737\pi\) | ||||
−0.180394 | + | 0.983594i | \(0.557737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.7104 | −1.53901 | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||||
−0.769506 | + | 0.638639i | \(0.779498\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −1.04985 | −0.0740507 | ||||||||
\(202\) | 0.707992 | 0.0498141 | ||||||||
\(203\) | −1.60685 | −0.112779 | ||||||||
\(204\) | −0.707434 | −0.0495303 | ||||||||
\(205\) | 9.62110 | 0.671967 | ||||||||
\(206\) | −0.602041 | −0.0419462 | ||||||||
\(207\) | −2.01877 | −0.140314 | ||||||||
\(208\) | 0.384053 | 0.0266293 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.211079 | −0.0145659 | ||||||||
\(211\) | −15.9979 | −1.10134 | −0.550671 | − | 0.834723i | \(-0.685628\pi\) | ||||
−0.550671 | + | 0.834723i | \(0.685628\pi\) | |||||||
\(212\) | −13.5386 | −0.929837 | ||||||||
\(213\) | −0.177399 | −0.0121551 | ||||||||
\(214\) | 10.2801 | 0.702736 | ||||||||
\(215\) | 9.55155 | 0.651411 | ||||||||
\(216\) | −1.25707 | −0.0855329 | ||||||||
\(217\) | −1.25772 | −0.0853796 | ||||||||
\(218\) | −2.65530 | −0.179839 | ||||||||
\(219\) | −2.18436 | −0.147605 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.28715 | 0.0865834 | ||||||||
\(222\) | 0.180872 | 0.0121393 | ||||||||
\(223\) | 2.78387 | 0.186422 | 0.0932109 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932109 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.95545 | −0.197030 | ||||||||
\(226\) | −10.2264 | −0.680248 | ||||||||
\(227\) | 15.7137 | 1.04295 | 0.521476 | − | 0.853266i | \(-0.325382\pi\) | ||||
0.521476 | + | 0.853266i | \(0.325382\pi\) | |||||||
\(228\) | −1.01741 | −0.0673794 | ||||||||
\(229\) | 17.0716 | 1.12812 | 0.564060 | − | 0.825734i | \(-0.309239\pi\) | ||||
0.564060 | + | 0.825734i | \(0.309239\pi\) | |||||||
\(230\) | 0.683067 | 0.0450401 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.60685 | 0.105495 | ||||||||
\(233\) | 7.21602 | 0.472737 | 0.236369 | − | 0.971663i | \(-0.424043\pi\) | ||||
0.236369 | + | 0.971663i | \(0.424043\pi\) | |||||||
\(234\) | 1.13505 | 0.0742003 | ||||||||
\(235\) | 7.55052 | 0.492541 | ||||||||
\(236\) | 7.26925 | 0.473188 | ||||||||
\(237\) | 0.710855 | 0.0461750 | ||||||||
\(238\) | −3.35151 | −0.217246 | ||||||||
\(239\) | 4.90570 | 0.317324 | 0.158662 | − | 0.987333i | \(-0.449282\pi\) | ||||
0.158662 | + | 0.987333i | \(0.449282\pi\) | |||||||
\(240\) | 0.211079 | 0.0136251 | ||||||||
\(241\) | −23.5063 | −1.51417 | −0.757086 | − | 0.653315i | \(-0.773378\pi\) | ||||
−0.757086 | + | 0.653315i | \(0.773378\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.58671 | −0.358387 | ||||||||
\(244\) | −3.89131 | −0.249116 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −2.03081 | −0.129480 | ||||||||
\(247\) | 1.85114 | 0.117785 | ||||||||
\(248\) | 1.25772 | 0.0798653 | ||||||||
\(249\) | −2.22046 | −0.140716 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.08639 | −0.384170 | −0.192085 | − | 0.981378i | \(-0.561525\pi\) | ||||
−0.192085 | + | 0.981378i | \(0.561525\pi\) | |||||||
\(252\) | −2.95545 | −0.186176 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.0499 | 1.32079 | ||||||||
\(255\) | 0.707434 | 0.0443012 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.76924 | 0.110362 | 0.0551811 | − | 0.998476i | \(-0.482426\pi\) | ||||
0.0551811 | + | 0.998476i | \(0.482426\pi\) | |||||||
\(258\) | −2.01614 | −0.125519 | ||||||||
\(259\) | 0.856889 | 0.0532445 | ||||||||
\(260\) | −0.384053 | −0.0238179 | ||||||||
\(261\) | 4.74897 | 0.293954 | ||||||||
\(262\) | 12.9629 | 0.800851 | ||||||||
\(263\) | −20.9446 | −1.29150 | −0.645750 | − | 0.763549i | \(-0.723455\pi\) | ||||
−0.645750 | + | 0.763549i | \(0.723455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5386 | 0.831672 | ||||||||
\(266\) | −4.82002 | −0.295534 | ||||||||
\(267\) | −3.17389 | −0.194239 | ||||||||
\(268\) | 4.97372 | 0.303818 | ||||||||
\(269\) | −28.7266 | −1.75149 | −0.875745 | − | 0.482774i | \(-0.839629\pi\) | ||||
−0.875745 | + | 0.482774i | \(0.839629\pi\) | |||||||
\(270\) | 1.25707 | 0.0765029 | ||||||||
\(271\) | 4.59932 | 0.279389 | 0.139694 | − | 0.990195i | \(-0.455388\pi\) | ||||
0.139694 | + | 0.990195i | \(0.455388\pi\) | |||||||
\(272\) | 3.35151 | 0.203215 | ||||||||
\(273\) | −0.0810656 | −0.00490631 | ||||||||
\(274\) | −12.4469 | −0.751943 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.144181 | −0.00867869 | ||||||||
\(277\) | −23.9175 | −1.43707 | −0.718533 | − | 0.695493i | \(-0.755186\pi\) | ||||
−0.718533 | + | 0.695493i | \(0.755186\pi\) | |||||||
\(278\) | −12.0205 | −0.720944 | ||||||||
\(279\) | 3.71712 | 0.222538 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −24.2413 | −1.44611 | −0.723056 | − | 0.690790i | \(-0.757263\pi\) | ||||
−0.723056 | + | 0.690790i | \(0.757263\pi\) | |||||||
\(282\) | −1.59376 | −0.0949069 | ||||||||
\(283\) | −2.20835 | −0.131273 | −0.0656364 | − | 0.997844i | \(-0.520908\pi\) | ||||
−0.0656364 | + | 0.997844i | \(0.520908\pi\) | |||||||
\(284\) | 0.840435 | 0.0498707 | ||||||||
\(285\) | 1.01741 | 0.0602660 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.62110 | −0.567915 | ||||||||
\(288\) | 2.95545 | 0.174151 | ||||||||
\(289\) | −5.76741 | −0.339259 | ||||||||
\(290\) | −1.60685 | −0.0943578 | ||||||||
\(291\) | −2.37825 | −0.139416 | ||||||||
\(292\) | 10.3485 | 0.605602 | ||||||||
\(293\) | 21.8741 | 1.27790 | 0.638950 | − | 0.769248i | \(-0.279369\pi\) | ||||
0.638950 | + | 0.769248i | \(0.279369\pi\) | |||||||
\(294\) | 0.211079 | 0.0123104 | ||||||||
\(295\) | −7.26925 | −0.423232 | ||||||||
\(296\) | −0.856889 | −0.0498057 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.1628 | 0.704575 | ||||||||
\(299\) | 0.262334 | 0.0151711 | ||||||||
\(300\) | −0.211079 | −0.0121867 | ||||||||
\(301\) | −9.55155 | −0.550542 | ||||||||
\(302\) | −20.2628 | −1.16599 | ||||||||
\(303\) | 0.149442 | 0.00858524 | ||||||||
\(304\) | 4.82002 | 0.276447 | ||||||||
\(305\) | 3.89131 | 0.222816 | ||||||||
\(306\) | 9.90519 | 0.566242 | ||||||||
\(307\) | 0.917520 | 0.0523656 | 0.0261828 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261828 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.127078 | −0.00722924 | ||||||||
\(310\) | −1.25772 | −0.0714337 | ||||||||
\(311\) | 2.96958 | 0.168390 | 0.0841949 | − | 0.996449i | \(-0.473168\pi\) | ||||
0.0841949 | + | 0.996449i | \(0.473168\pi\) | |||||||
\(312\) | 0.0810656 | 0.00458943 | ||||||||
\(313\) | −1.00800 | −0.0569757 | −0.0284878 | − | 0.999594i | \(-0.509069\pi\) | ||||
−0.0284878 | + | 0.999594i | \(0.509069\pi\) | |||||||
\(314\) | 10.0988 | 0.569908 | ||||||||
\(315\) | 2.95545 | 0.166520 | ||||||||
\(316\) | −3.36771 | −0.189449 | ||||||||
\(317\) | −3.47654 | −0.195262 | −0.0976309 | − | 0.995223i | \(-0.531126\pi\) | ||||
−0.0976309 | + | 0.995223i | \(0.531126\pi\) | |||||||
\(318\) | −2.85773 | −0.160253 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 2.16992 | 0.121113 | ||||||||
\(322\) | −0.683067 | −0.0380658 | ||||||||
\(323\) | 16.1543 | 0.898851 | ||||||||
\(324\) | 8.60099 | 0.477833 | ||||||||
\(325\) | 0.384053 | 0.0213034 | ||||||||
\(326\) | −20.9868 | −1.16235 | ||||||||
\(327\) | −0.560478 | −0.0309945 | ||||||||
\(328\) | 9.62110 | 0.531236 | ||||||||
\(329\) | −7.55052 | −0.416274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3885 | 0.955758 | 0.477879 | − | 0.878426i | \(-0.341406\pi\) | ||||
0.477879 | + | 0.878426i | \(0.341406\pi\) | |||||||
\(332\) | 10.5195 | 0.577334 | ||||||||
\(333\) | −2.53249 | −0.138780 | ||||||||
\(334\) | 21.8752 | 1.19696 | ||||||||
\(335\) | −4.97372 | −0.271743 | ||||||||
\(336\) | −0.211079 | −0.0115153 | ||||||||
\(337\) | 16.4320 | 0.895109 | 0.447555 | − | 0.894257i | \(-0.352295\pi\) | ||||
0.447555 | + | 0.894257i | \(0.352295\pi\) | |||||||
\(338\) | 12.8525 | 0.699084 | ||||||||
\(339\) | −2.15858 | −0.117238 | ||||||||
\(340\) | −3.35151 | −0.181761 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 14.2453 | 0.770298 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.55155 | 0.514985 | ||||||||
\(345\) | 0.144181 | 0.00776246 | ||||||||
\(346\) | 0.216594 | 0.0116442 | ||||||||
\(347\) | −32.0372 | −1.71985 | −0.859925 | − | 0.510421i | \(-0.829489\pi\) | ||||
−0.859925 | + | 0.510421i | \(0.829489\pi\) | |||||||
\(348\) | 0.339174 | 0.0181816 | ||||||||
\(349\) | −35.8054 | −1.91662 | −0.958309 | − | 0.285733i | \(-0.907763\pi\) | ||||
−0.958309 | + | 0.285733i | \(0.907763\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 0.482781 | 0.0257690 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4312 | −0.821322 | −0.410661 | − | 0.911788i | \(-0.634702\pi\) | ||||
−0.410661 | + | 0.911788i | \(0.634702\pi\) | |||||||
\(354\) | 1.53439 | 0.0815518 | ||||||||
\(355\) | −0.840435 | −0.0446057 | ||||||||
\(356\) | 15.0365 | 0.796931 | ||||||||
\(357\) | −0.707434 | −0.0374414 | ||||||||
\(358\) | 17.0592 | 0.901609 | ||||||||
\(359\) | −16.8842 | −0.891115 | −0.445558 | − | 0.895253i | \(-0.646995\pi\) | ||||
−0.445558 | + | 0.895253i | \(0.646995\pi\) | |||||||
\(360\) | −2.95545 | −0.155766 | ||||||||
\(361\) | 4.23260 | 0.222768 | ||||||||
\(362\) | −3.45754 | −0.181724 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.384053 | 0.0201298 | ||||||||
\(365\) | −10.3485 | −0.541667 | ||||||||
\(366\) | −0.821376 | −0.0429340 | ||||||||
\(367\) | −8.94654 | −0.467006 | −0.233503 | − | 0.972356i | \(-0.575019\pi\) | ||||
−0.233503 | + | 0.972356i | \(0.575019\pi\) | |||||||
\(368\) | 0.683067 | 0.0356073 | ||||||||
\(369\) | 28.4346 | 1.48025 | ||||||||
\(370\) | 0.856889 | 0.0445476 | ||||||||
\(371\) | −13.5386 | −0.702891 | ||||||||
\(372\) | 0.265479 | 0.0137644 | ||||||||
\(373\) | −13.2408 | −0.685583 | −0.342792 | − | 0.939411i | \(-0.611373\pi\) | ||||
−0.342792 | + | 0.939411i | \(0.611373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.211079 | 0.0109001 | ||||||||
\(376\) | 7.55052 | 0.389388 | ||||||||
\(377\) | −0.617117 | −0.0317831 | ||||||||
\(378\) | −1.25707 | −0.0646568 | ||||||||
\(379\) | −15.8412 | −0.813708 | −0.406854 | − | 0.913493i | \(-0.633374\pi\) | ||||
−0.406854 | + | 0.913493i | \(0.633374\pi\) | |||||||
\(380\) | −4.82002 | −0.247262 | ||||||||
\(381\) | 4.44320 | 0.227632 | ||||||||
\(382\) | −2.95839 | −0.151365 | ||||||||
\(383\) | −0.127136 | −0.00649637 | −0.00324818 | − | 0.999995i | \(-0.501034\pi\) | ||||
−0.00324818 | + | 0.999995i | \(0.501034\pi\) | |||||||
\(384\) | 0.211079 | 0.0107716 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.47612 | −0.482322 | ||||||||
\(387\) | 28.2291 | 1.43497 | ||||||||
\(388\) | 11.2671 | 0.572001 | ||||||||
\(389\) | 10.0764 | 0.510891 | 0.255446 | − | 0.966823i | \(-0.417778\pi\) | ||||
0.255446 | + | 0.966823i | \(0.417778\pi\) | |||||||
\(390\) | −0.0810656 | −0.00410491 | ||||||||
\(391\) | 2.28930 | 0.115775 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 2.73620 | 0.138023 | ||||||||
\(394\) | 5.06389 | 0.255115 | ||||||||
\(395\) | 3.36771 | 0.169448 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.42050 | 0.422613 | 0.211306 | − | 0.977420i | \(-0.432228\pi\) | ||||
0.211306 | + | 0.977420i | \(0.432228\pi\) | |||||||
\(398\) | 21.7104 | 1.08825 | ||||||||
\(399\) | −1.01741 | −0.0509340 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −18.9810 | −0.947866 | −0.473933 | − | 0.880561i | \(-0.657166\pi\) | ||||
−0.473933 | + | 0.880561i | \(0.657166\pi\) | |||||||
\(402\) | 1.04985 | 0.0523617 | ||||||||
\(403\) | −0.483031 | −0.0240615 | ||||||||
\(404\) | −0.707992 | −0.0352239 | ||||||||
\(405\) | −8.60099 | −0.427387 | ||||||||
\(406\) | 1.60685 | 0.0797469 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.707434 | 0.0350232 | ||||||||
\(409\) | −23.6931 | −1.17155 | −0.585775 | − | 0.810474i | \(-0.699210\pi\) | ||||
−0.585775 | + | 0.810474i | \(0.699210\pi\) | |||||||
\(410\) | −9.62110 | −0.475152 | ||||||||
\(411\) | −2.62728 | −0.129594 | ||||||||
\(412\) | 0.602041 | 0.0296604 | ||||||||
\(413\) | 7.26925 | 0.357696 | ||||||||
\(414\) | 2.01877 | 0.0992170 | ||||||||
\(415\) | −10.5195 | −0.516384 | ||||||||
\(416\) | −0.384053 | −0.0188297 | ||||||||
\(417\) | −2.53729 | −0.124251 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.81468 | −0.137506 | −0.0687531 | − | 0.997634i | \(-0.521902\pi\) | ||||
−0.0687531 | + | 0.997634i | \(0.521902\pi\) | |||||||
\(420\) | 0.211079 | 0.0102996 | ||||||||
\(421\) | −2.78939 | −0.135946 | −0.0679732 | − | 0.997687i | \(-0.521653\pi\) | ||||
−0.0679732 | + | 0.997687i | \(0.521653\pi\) | |||||||
\(422\) | 15.9979 | 0.778766 | ||||||||
\(423\) | 22.3151 | 1.08500 | ||||||||
\(424\) | 13.5386 | 0.657494 | ||||||||
\(425\) | 3.35151 | 0.162572 | ||||||||
\(426\) | 0.177399 | 0.00859499 | ||||||||
\(427\) | −3.89131 | −0.188314 | ||||||||
\(428\) | −10.2801 | −0.496909 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.55155 | −0.460617 | ||||||||
\(431\) | 6.27580 | 0.302295 | 0.151147 | − | 0.988511i | \(-0.451703\pi\) | ||||
0.151147 | + | 0.988511i | \(0.451703\pi\) | |||||||
\(432\) | 1.25707 | 0.0604809 | ||||||||
\(433\) | 25.3703 | 1.21922 | 0.609609 | − | 0.792702i | \(-0.291326\pi\) | ||||
0.609609 | + | 0.792702i | \(0.291326\pi\) | |||||||
\(434\) | 1.25772 | 0.0603725 | ||||||||
\(435\) | −0.339174 | −0.0162621 | ||||||||
\(436\) | 2.65530 | 0.127166 | ||||||||
\(437\) | 3.29240 | 0.157497 | ||||||||
\(438\) | 2.18436 | 0.104373 | ||||||||
\(439\) | −14.4302 | −0.688715 | −0.344357 | − | 0.938839i | \(-0.611903\pi\) | ||||
−0.344357 | + | 0.938839i | \(0.611903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.95545 | −0.140736 | ||||||||
\(442\) | −1.28715 | −0.0612237 | ||||||||
\(443\) | 23.5142 | 1.11719 | 0.558597 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558597 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(444\) | −0.180872 | −0.00858379 | ||||||||
\(445\) | −15.0365 | −0.712797 | ||||||||
\(446\) | −2.78387 | −0.131820 | ||||||||
\(447\) | 2.56732 | 0.121430 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −6.33865 | −0.299140 | −0.149570 | − | 0.988751i | \(-0.547789\pi\) | ||||
−0.149570 | + | 0.988751i | \(0.547789\pi\) | |||||||
\(450\) | 2.95545 | 0.139321 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.2264 | 0.481008 | ||||||||
\(453\) | −4.27706 | −0.200954 | ||||||||
\(454\) | −15.7137 | −0.737478 | ||||||||
\(455\) | −0.384053 | −0.0180047 | ||||||||
\(456\) | 1.01741 | 0.0476444 | ||||||||
\(457\) | 4.08335 | 0.191011 | 0.0955056 | − | 0.995429i | \(-0.469553\pi\) | ||||
0.0955056 | + | 0.995429i | \(0.469553\pi\) | |||||||
\(458\) | −17.0716 | −0.797701 | ||||||||
\(459\) | 4.21308 | 0.196650 | ||||||||
\(460\) | −0.683067 | −0.0318482 | ||||||||
\(461\) | −27.7053 | −1.29037 | −0.645183 | − | 0.764028i | \(-0.723219\pi\) | ||||
−0.645183 | + | 0.764028i | \(0.723219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.6895 | −1.42626 | −0.713131 | − | 0.701030i | \(-0.752724\pi\) | ||||
−0.713131 | + | 0.701030i | \(0.752724\pi\) | |||||||
\(464\) | −1.60685 | −0.0745964 | ||||||||
\(465\) | −0.265479 | −0.0123113 | ||||||||
\(466\) | −7.21602 | −0.334276 | ||||||||
\(467\) | −5.78418 | −0.267660 | −0.133830 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133830 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(468\) | −1.13505 | −0.0524675 | ||||||||
\(469\) | 4.97372 | 0.229665 | ||||||||
\(470\) | −7.55052 | −0.348279 | ||||||||
\(471\) | 2.13165 | 0.0982212 | ||||||||
\(472\) | −7.26925 | −0.334594 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.710855 | −0.0326506 | ||||||||
\(475\) | 4.82002 | 0.221158 | ||||||||
\(476\) | 3.35151 | 0.153616 | ||||||||
\(477\) | 40.0127 | 1.83206 | ||||||||
\(478\) | −4.90570 | −0.224382 | ||||||||
\(479\) | −6.65632 | −0.304135 | −0.152068 | − | 0.988370i | \(-0.548593\pi\) | ||||
−0.152068 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(480\) | −0.211079 | −0.00963441 | ||||||||
\(481\) | 0.329091 | 0.0150052 | ||||||||
\(482\) | 23.5063 | 1.07068 | ||||||||
\(483\) | −0.144181 | −0.00656048 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.2671 | −0.511613 | ||||||||
\(486\) | 5.58671 | 0.253418 | ||||||||
\(487\) | −3.19787 | −0.144910 | −0.0724548 | − | 0.997372i | \(-0.523083\pi\) | ||||
−0.0724548 | + | 0.997372i | \(0.523083\pi\) | |||||||
\(488\) | 3.89131 | 0.176152 | ||||||||
\(489\) | −4.42987 | −0.200326 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −2.50327 | −0.112971 | −0.0564854 | − | 0.998403i | \(-0.517989\pi\) | ||||
−0.0564854 | + | 0.998403i | \(0.517989\pi\) | |||||||
\(492\) | 2.03081 | 0.0915562 | ||||||||
\(493\) | −5.38538 | −0.242545 | ||||||||
\(494\) | −1.85114 | −0.0832868 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.25772 | −0.0564733 | ||||||||
\(497\) | 0.840435 | 0.0376987 | ||||||||
\(498\) | 2.22046 | 0.0995010 | ||||||||
\(499\) | 21.6925 | 0.971088 | 0.485544 | − | 0.874212i | \(-0.338622\pi\) | ||||
0.485544 | + | 0.874212i | \(0.338622\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 4.61741 | 0.206291 | ||||||||
\(502\) | 6.08639 | 0.271649 | ||||||||
\(503\) | 1.50610 | 0.0671536 | 0.0335768 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335768 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(504\) | 2.95545 | 0.131646 | ||||||||
\(505\) | 0.707992 | 0.0315052 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.71290 | 0.120484 | ||||||||
\(508\) | −21.0499 | −0.933938 | ||||||||
\(509\) | 11.6817 | 0.517781 | 0.258891 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258891 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(510\) | −0.707434 | −0.0313257 | ||||||||
\(511\) | 10.3485 | 0.457792 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.05911 | 0.267516 | ||||||||
\(514\) | −1.76924 | −0.0780378 | ||||||||
\(515\) | −0.602041 | −0.0265291 | ||||||||
\(516\) | 2.01614 | 0.0887554 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.856889 | −0.0376496 | ||||||||
\(519\) | 0.0457185 | 0.00200682 | ||||||||
\(520\) | 0.384053 | 0.0168418 | ||||||||
\(521\) | −6.10991 | −0.267680 | −0.133840 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(522\) | −4.74897 | −0.207857 | ||||||||
\(523\) | −5.86885 | −0.256627 | −0.128314 | − | 0.991734i | \(-0.540956\pi\) | ||||
−0.128314 | + | 0.991734i | \(0.540956\pi\) | |||||||
\(524\) | −12.9629 | −0.566287 | ||||||||
\(525\) | −0.211079 | −0.00921226 | ||||||||
\(526\) | 20.9446 | 0.913228 | ||||||||
\(527\) | −4.21526 | −0.183619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5334 | −0.979714 | ||||||||
\(530\) | −13.5386 | −0.588081 | ||||||||
\(531\) | −21.4839 | −0.932320 | ||||||||
\(532\) | 4.82002 | 0.208974 | ||||||||
\(533\) | −3.69501 | −0.160049 | ||||||||
\(534\) | 3.17389 | 0.137347 | ||||||||
\(535\) | 10.2801 | 0.444449 | ||||||||
\(536\) | −4.97372 | −0.214832 | ||||||||
\(537\) | 3.60085 | 0.155388 | ||||||||
\(538\) | 28.7266 | 1.23849 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.25707 | −0.0540957 | ||||||||
\(541\) | 2.51357 | 0.108067 | 0.0540333 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540333 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(542\) | −4.59932 | −0.197558 | ||||||||
\(543\) | −0.729814 | −0.0313193 | ||||||||
\(544\) | −3.35151 | −0.143695 | ||||||||
\(545\) | −2.65530 | −0.113740 | ||||||||
\(546\) | 0.0810656 | 0.00346929 | ||||||||
\(547\) | 14.6785 | 0.627608 | 0.313804 | − | 0.949488i | \(-0.398397\pi\) | ||||
0.313804 | + | 0.949488i | \(0.398397\pi\) | |||||||
\(548\) | 12.4469 | 0.531704 | ||||||||
\(549\) | 11.5006 | 0.490832 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.74507 | −0.329951 | ||||||||
\(552\) | 0.144181 | 0.00613676 | ||||||||
\(553\) | −3.36771 | −0.143210 | ||||||||
\(554\) | 23.9175 | 1.01616 | ||||||||
\(555\) | 0.180872 | 0.00767757 | ||||||||
\(556\) | 12.0205 | 0.509784 | ||||||||
\(557\) | 21.3175 | 0.903252 | 0.451626 | − | 0.892207i | \(-0.350844\pi\) | ||||
0.451626 | + | 0.892207i | \(0.350844\pi\) | |||||||
\(558\) | −3.71712 | −0.157358 | ||||||||
\(559\) | −3.66830 | −0.155153 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.2413 | 1.02256 | ||||||||
\(563\) | −33.0588 | −1.39326 | −0.696630 | − | 0.717430i | \(-0.745318\pi\) | ||||
−0.696630 | + | 0.717430i | \(0.745318\pi\) | |||||||
\(564\) | 1.59376 | 0.0671093 | ||||||||
\(565\) | −10.2264 | −0.430227 | ||||||||
\(566\) | 2.20835 | 0.0928239 | ||||||||
\(567\) | 8.60099 | 0.361208 | ||||||||
\(568\) | −0.840435 | −0.0352639 | ||||||||
\(569\) | −46.0666 | −1.93121 | −0.965606 | − | 0.260011i | \(-0.916274\pi\) | ||||
−0.965606 | + | 0.260011i | \(0.916274\pi\) | |||||||
\(570\) | −1.01741 | −0.0426145 | ||||||||
\(571\) | −24.0901 | −1.00814 | −0.504070 | − | 0.863663i | \(-0.668165\pi\) | ||||
−0.504070 | + | 0.863663i | \(0.668165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.624456 | −0.0260870 | ||||||||
\(574\) | 9.62110 | 0.401577 | ||||||||
\(575\) | 0.683067 | 0.0284859 | ||||||||
\(576\) | −2.95545 | −0.123144 | ||||||||
\(577\) | −9.62623 | −0.400745 | −0.200373 | − | 0.979720i | \(-0.564215\pi\) | ||||
−0.200373 | + | 0.979720i | \(0.564215\pi\) | |||||||
\(578\) | 5.76741 | 0.239893 | ||||||||
\(579\) | −2.00021 | −0.0831260 | ||||||||
\(580\) | 1.60685 | 0.0667210 | ||||||||
\(581\) | 10.5195 | 0.436424 | ||||||||
\(582\) | 2.37825 | 0.0985818 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.3485 | −0.428225 | ||||||||
\(585\) | 1.13505 | 0.0469284 | ||||||||
\(586\) | −21.8741 | −0.903612 | ||||||||
\(587\) | −48.2830 | −1.99285 | −0.996425 | − | 0.0844765i | \(-0.973078\pi\) | ||||
−0.996425 | + | 0.0844765i | \(0.973078\pi\) | |||||||
\(588\) | −0.211079 | −0.00870476 | ||||||||
\(589\) | −6.06224 | −0.249790 | ||||||||
\(590\) | 7.26925 | 0.299270 | ||||||||
\(591\) | 1.06888 | 0.0439680 | ||||||||
\(592\) | 0.856889 | 0.0352179 | ||||||||
\(593\) | 22.5234 | 0.924924 | 0.462462 | − | 0.886639i | \(-0.346966\pi\) | ||||
0.462462 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.35151 | −0.137398 | ||||||||
\(596\) | −12.1628 | −0.498209 | ||||||||
\(597\) | 4.58263 | 0.187554 | ||||||||
\(598\) | −0.262334 | −0.0107276 | ||||||||
\(599\) | −26.8704 | −1.09789 | −0.548947 | − | 0.835857i | \(-0.684971\pi\) | ||||
−0.548947 | + | 0.835857i | \(0.684971\pi\) | |||||||
\(600\) | 0.211079 | 0.00861728 | ||||||||
\(601\) | −42.6062 | −1.73794 | −0.868972 | − | 0.494862i | \(-0.835219\pi\) | ||||
−0.868972 | + | 0.494862i | \(0.835219\pi\) | |||||||
\(602\) | 9.55155 | 0.389292 | ||||||||
\(603\) | −14.6996 | −0.598613 | ||||||||
\(604\) | 20.2628 | 0.824481 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.149442 | −0.00607068 | ||||||||
\(607\) | 16.8446 | 0.683701 | 0.341851 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341851 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(608\) | −4.82002 | −0.195478 | ||||||||
\(609\) | 0.339174 | 0.0137440 | ||||||||
\(610\) | −3.89131 | −0.157555 | ||||||||
\(611\) | −2.89980 | −0.117313 | ||||||||
\(612\) | −9.90519 | −0.400394 | ||||||||
\(613\) | 29.9604 | 1.21009 | 0.605044 | − | 0.796192i | \(-0.293155\pi\) | ||||
0.605044 | + | 0.796192i | \(0.293155\pi\) | |||||||
\(614\) | −0.917520 | −0.0370281 | ||||||||
\(615\) | −2.03081 | −0.0818903 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.21777 | −0.371093 | −0.185547 | − | 0.982635i | \(-0.559406\pi\) | ||||
−0.185547 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(618\) | 0.127078 | 0.00511184 | ||||||||
\(619\) | −34.1356 | −1.37202 | −0.686012 | − | 0.727590i | \(-0.740640\pi\) | ||||
−0.686012 | + | 0.727590i | \(0.740640\pi\) | |||||||
\(620\) | 1.25772 | 0.0505113 | ||||||||
\(621\) | 0.858664 | 0.0344570 | ||||||||
\(622\) | −2.96958 | −0.119070 | ||||||||
\(623\) | 15.0365 | 0.602423 | ||||||||
\(624\) | −0.0810656 | −0.00324522 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.00800 | 0.0402879 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0988 | −0.402986 | ||||||||
\(629\) | 2.87187 | 0.114509 | ||||||||
\(630\) | −2.95545 | −0.117748 | ||||||||
\(631\) | −19.6717 | −0.783119 | −0.391559 | − | 0.920153i | \(-0.628064\pi\) | ||||
−0.391559 | + | 0.920153i | \(0.628064\pi\) | |||||||
\(632\) | 3.36771 | 0.133960 | ||||||||
\(633\) | 3.37683 | 0.134217 | ||||||||
\(634\) | 3.47654 | 0.138071 | ||||||||
\(635\) | 21.0499 | 0.835340 | ||||||||
\(636\) | 2.85773 | 0.113316 | ||||||||
\(637\) | 0.384053 | 0.0152167 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.48386 | −0.0982600 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −6.78428 | −0.267963 | −0.133982 | − | 0.990984i | \(-0.542776\pi\) | ||||
−0.133982 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(642\) | −2.16992 | −0.0856401 | ||||||||
\(643\) | 7.64781 | 0.301600 | 0.150800 | − | 0.988564i | \(-0.451815\pi\) | ||||
0.150800 | + | 0.988564i | \(0.451815\pi\) | |||||||
\(644\) | 0.683067 | 0.0269166 | ||||||||
\(645\) | −2.01614 | −0.0793853 | ||||||||
\(646\) | −16.1543 | −0.635583 | ||||||||
\(647\) | 12.4504 | 0.489475 | 0.244737 | − | 0.969589i | \(-0.421298\pi\) | ||||
0.244737 | + | 0.969589i | \(0.421298\pi\) | |||||||
\(648\) | −8.60099 | −0.337879 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.384053 | −0.0150638 | ||||||||
\(651\) | 0.265479 | 0.0104049 | ||||||||
\(652\) | 20.9868 | 0.821905 | ||||||||
\(653\) | 32.5664 | 1.27442 | 0.637212 | − | 0.770689i | \(-0.280088\pi\) | ||||
0.637212 | + | 0.770689i | \(0.280088\pi\) | |||||||
\(654\) | 0.560478 | 0.0219164 | ||||||||
\(655\) | 12.9629 | 0.506503 | ||||||||
\(656\) | −9.62110 | −0.375641 | ||||||||
\(657\) | −30.5845 | −1.19322 | ||||||||
\(658\) | 7.55052 | 0.294350 | ||||||||
\(659\) | −13.3486 | −0.519990 | −0.259995 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259995 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.5491 | 1.46049 | 0.730246 | − | 0.683184i | \(-0.239405\pi\) | ||||
0.730246 | + | 0.683184i | \(0.239405\pi\) | |||||||
\(662\) | −17.3885 | −0.675823 | ||||||||
\(663\) | −0.271692 | −0.0105516 | ||||||||
\(664\) | −10.5195 | −0.408237 | ||||||||
\(665\) | −4.82002 | −0.186912 | ||||||||
\(666\) | 2.53249 | 0.0981320 | ||||||||
\(667\) | −1.09759 | −0.0424988 | ||||||||
\(668\) | −21.8752 | −0.846378 | ||||||||
\(669\) | −0.587617 | −0.0227186 | ||||||||
\(670\) | 4.97372 | 0.192152 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.211079 | 0.00814256 | ||||||||
\(673\) | 6.12768 | 0.236205 | 0.118102 | − | 0.993001i | \(-0.462319\pi\) | ||||
0.118102 | + | 0.993001i | \(0.462319\pi\) | |||||||
\(674\) | −16.4320 | −0.632938 | ||||||||
\(675\) | 1.25707 | 0.0483847 | ||||||||
\(676\) | −12.8525 | −0.494327 | ||||||||
\(677\) | −15.7476 | −0.605229 | −0.302615 | − | 0.953113i | \(-0.597859\pi\) | ||||
−0.302615 | + | 0.953113i | \(0.597859\pi\) | |||||||
\(678\) | 2.15858 | 0.0828996 | ||||||||
\(679\) | 11.2671 | 0.432392 | ||||||||
\(680\) | 3.35151 | 0.128524 | ||||||||
\(681\) | −3.31683 | −0.127101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0157 | −0.574559 | −0.287280 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287280 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(684\) | −14.2453 | −0.544683 | ||||||||
\(685\) | −12.4469 | −0.475570 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −3.60345 | −0.137480 | ||||||||
\(688\) | −9.55155 | −0.364150 | ||||||||
\(689\) | −5.19955 | −0.198087 | ||||||||
\(690\) | −0.144181 | −0.00548889 | ||||||||
\(691\) | 30.5545 | 1.16235 | 0.581174 | − | 0.813779i | \(-0.302594\pi\) | ||||
0.581174 | + | 0.813779i | \(0.302594\pi\) | |||||||
\(692\) | −0.216594 | −0.00823366 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.0372 | 1.21612 | ||||||||
\(695\) | −12.0205 | −0.455965 | ||||||||
\(696\) | −0.339174 | −0.0128563 | ||||||||
\(697\) | −32.2452 | −1.22137 | ||||||||
\(698\) | 35.8054 | 1.35525 | ||||||||
\(699\) | −1.52315 | −0.0576109 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 3.92911 | 0.148400 | 0.0742002 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0742002 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(702\) | −0.482781 | −0.0182214 | ||||||||
\(703\) | 4.13022 | 0.155774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.59376 | −0.0600244 | ||||||||
\(706\) | 15.4312 | 0.580763 | ||||||||
\(707\) | −0.707992 | −0.0266268 | ||||||||
\(708\) | −1.53439 | −0.0576658 | ||||||||
\(709\) | 24.1255 | 0.906054 | 0.453027 | − | 0.891497i | \(-0.350344\pi\) | ||||
0.453027 | + | 0.891497i | \(0.350344\pi\) | |||||||
\(710\) | 0.840435 | 0.0315410 | ||||||||
\(711\) | 9.95310 | 0.373270 | ||||||||
\(712\) | −15.0365 | −0.563515 | ||||||||
\(713\) | −0.859107 | −0.0321738 | ||||||||
\(714\) | 0.707434 | 0.0264750 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.0592 | −0.637534 | ||||||||
\(717\) | −1.03549 | −0.0386712 | ||||||||
\(718\) | 16.8842 | 0.630114 | ||||||||
\(719\) | −43.8622 | −1.63578 | −0.817892 | − | 0.575371i | \(-0.804858\pi\) | ||||
−0.817892 | + | 0.575371i | \(0.804858\pi\) | |||||||
\(720\) | 2.95545 | 0.110143 | ||||||||
\(721\) | 0.602041 | 0.0224212 | ||||||||
\(722\) | −4.23260 | −0.157521 | ||||||||
\(723\) | 4.96169 | 0.184527 | ||||||||
\(724\) | 3.45754 | 0.128498 | ||||||||
\(725\) | −1.60685 | −0.0596771 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7183 | −0.768400 | −0.384200 | − | 0.923250i | \(-0.625523\pi\) | ||||
−0.384200 | + | 0.923250i | \(0.625523\pi\) | |||||||
\(728\) | −0.384053 | −0.0142339 | ||||||||
\(729\) | −24.6237 | −0.911991 | ||||||||
\(730\) | 10.3485 | 0.383016 | ||||||||
\(731\) | −32.0121 | −1.18401 | ||||||||
\(732\) | 0.821376 | 0.0303589 | ||||||||
\(733\) | 33.0173 | 1.21952 | 0.609761 | − | 0.792585i | \(-0.291265\pi\) | ||||
0.609761 | + | 0.792585i | \(0.291265\pi\) | |||||||
\(734\) | 8.94654 | 0.330223 | ||||||||
\(735\) | 0.211079 | 0.00778578 | ||||||||
\(736\) | −0.683067 | −0.0251782 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −28.4346 | −1.04669 | ||||||||
\(739\) | −5.21925 | −0.191993 | −0.0959967 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959967 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(740\) | −0.856889 | −0.0314999 | ||||||||
\(741\) | −0.390738 | −0.0143541 | ||||||||
\(742\) | 13.5386 | 0.497019 | ||||||||
\(743\) | −32.5419 | −1.19385 | −0.596923 | − | 0.802299i | \(-0.703610\pi\) | ||||
−0.596923 | + | 0.802299i | \(0.703610\pi\) | |||||||
\(744\) | −0.265479 | −0.00973292 | ||||||||
\(745\) | 12.1628 | 0.445612 | ||||||||
\(746\) | 13.2408 | 0.484781 | ||||||||
\(747\) | −31.0899 | −1.13752 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2801 | −0.375628 | ||||||||
\(750\) | −0.211079 | −0.00770753 | ||||||||
\(751\) | 47.1955 | 1.72219 | 0.861094 | − | 0.508446i | \(-0.169780\pi\) | ||||
0.861094 | + | 0.508446i | \(0.169780\pi\) | |||||||
\(752\) | −7.55052 | −0.275339 | ||||||||
\(753\) | 1.28471 | 0.0468175 | ||||||||
\(754\) | 0.617117 | 0.0224741 | ||||||||
\(755\) | −20.2628 | −0.737438 | ||||||||
\(756\) | 1.25707 | 0.0457192 | ||||||||
\(757\) | −36.8265 | −1.33848 | −0.669241 | − | 0.743045i | \(-0.733381\pi\) | ||||
−0.669241 | + | 0.743045i | \(0.733381\pi\) | |||||||
\(758\) | 15.8412 | 0.575378 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.82002 | 0.174841 | ||||||||
\(761\) | −6.08704 | −0.220655 | −0.110328 | − | 0.993895i | \(-0.535190\pi\) | ||||
−0.110328 | + | 0.993895i | \(0.535190\pi\) | |||||||
\(762\) | −4.44320 | −0.160960 | ||||||||
\(763\) | 2.65530 | 0.0961282 | ||||||||
\(764\) | 2.95839 | 0.107031 | ||||||||
\(765\) | 9.90519 | 0.358123 | ||||||||
\(766\) | 0.127136 | 0.00459363 | ||||||||
\(767\) | 2.79177 | 0.100805 | ||||||||
\(768\) | −0.211079 | −0.00761667 | ||||||||
\(769\) | 42.1342 | 1.51940 | 0.759700 | − | 0.650274i | \(-0.225346\pi\) | ||||
0.759700 | + | 0.650274i | \(0.225346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.373450 | −0.0134495 | ||||||||
\(772\) | 9.47612 | 0.341053 | ||||||||
\(773\) | −16.3152 | −0.586818 | −0.293409 | − | 0.955987i | \(-0.594790\pi\) | ||||
−0.293409 | + | 0.955987i | \(0.594790\pi\) | |||||||
\(774\) | −28.2291 | −1.01467 | ||||||||
\(775\) | −1.25772 | −0.0451786 | ||||||||
\(776\) | −11.2671 | −0.404466 | ||||||||
\(777\) | −0.180872 | −0.00648873 | ||||||||
\(778\) | −10.0764 | −0.361255 | ||||||||
\(779\) | −46.3739 | −1.66152 | ||||||||
\(780\) | 0.0810656 | 0.00290261 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.28930 | −0.0818653 | ||||||||
\(783\) | −2.01993 | −0.0721864 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.0988 | 0.360442 | ||||||||
\(786\) | −2.73620 | −0.0975970 | ||||||||
\(787\) | 0.381541 | 0.0136005 | 0.00680023 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680023 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(788\) | −5.06389 | −0.180394 | ||||||||
\(789\) | 4.42097 | 0.157391 | ||||||||
\(790\) | −3.36771 | −0.119818 | ||||||||
\(791\) | 10.2264 | 0.363608 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.49447 | −0.0530702 | ||||||||
\(794\) | −8.42050 | −0.298832 | ||||||||
\(795\) | −2.85773 | −0.101353 | ||||||||
\(796\) | −21.7104 | −0.769506 | ||||||||
\(797\) | −20.6764 | −0.732397 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(798\) | 1.01741 | 0.0360158 | ||||||||
\(799\) | −25.3056 | −0.895248 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −44.4394 | −1.57019 | ||||||||
\(802\) | 18.9810 | 0.670242 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.04985 | −0.0370253 | ||||||||
\(805\) | −0.683067 | −0.0240749 | ||||||||
\(806\) | 0.483031 | 0.0170140 | ||||||||
\(807\) | 6.06358 | 0.213448 | ||||||||
\(808\) | 0.707992 | 0.0249071 | ||||||||
\(809\) | −0.587236 | −0.0206461 | −0.0103231 | − | 0.999947i | \(-0.503286\pi\) | ||||
−0.0103231 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(810\) | 8.60099 | 0.302208 | ||||||||
\(811\) | 13.5752 | 0.476691 | 0.238345 | − | 0.971180i | \(-0.423395\pi\) | ||||
0.238345 | + | 0.971180i | \(0.423395\pi\) | |||||||
\(812\) | −1.60685 | −0.0563895 | ||||||||
\(813\) | −0.970821 | −0.0340482 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.9868 | −0.735134 | ||||||||
\(816\) | −0.707434 | −0.0247651 | ||||||||
\(817\) | −46.0387 | −1.61069 | ||||||||
\(818\) | 23.6931 | 0.828411 | ||||||||
\(819\) | −1.13505 | −0.0396617 | ||||||||
\(820\) | 9.62110 | 0.335983 | ||||||||
\(821\) | 0.584317 | 0.0203928 | 0.0101964 | − | 0.999948i | \(-0.496754\pi\) | ||||
0.0101964 | + | 0.999948i | \(0.496754\pi\) | |||||||
\(822\) | 2.62728 | 0.0916368 | ||||||||
\(823\) | 26.6347 | 0.928428 | 0.464214 | − | 0.885723i | \(-0.346337\pi\) | ||||
0.464214 | + | 0.885723i | \(0.346337\pi\) | |||||||
\(824\) | −0.602041 | −0.0209731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.26925 | −0.252929 | ||||||||
\(827\) | 13.1807 | 0.458339 | 0.229170 | − | 0.973386i | \(-0.426399\pi\) | ||||
0.229170 | + | 0.973386i | \(0.426399\pi\) | |||||||
\(828\) | −2.01877 | −0.0701570 | ||||||||
\(829\) | −20.0631 | −0.696820 | −0.348410 | − | 0.937342i | \(-0.613278\pi\) | ||||
−0.348410 | + | 0.937342i | \(0.613278\pi\) | |||||||
\(830\) | 10.5195 | 0.365138 | ||||||||
\(831\) | 5.04850 | 0.175130 | ||||||||
\(832\) | 0.384053 | 0.0133146 | ||||||||
\(833\) | 3.35151 | 0.116123 | ||||||||
\(834\) | 2.53729 | 0.0878590 | ||||||||
\(835\) | 21.8752 | 0.757024 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.58104 | −0.0546489 | ||||||||
\(838\) | 2.81468 | 0.0972316 | ||||||||
\(839\) | 9.70087 | 0.334911 | 0.167456 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167456 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(840\) | −0.211079 | −0.00728293 | ||||||||
\(841\) | −26.4180 | −0.910966 | ||||||||
\(842\) | 2.78939 | 0.0961287 | ||||||||
\(843\) | 5.11683 | 0.176233 | ||||||||
\(844\) | −15.9979 | −0.550671 | ||||||||
\(845\) | 12.8525 | 0.442140 | ||||||||
\(846\) | −22.3151 | −0.767210 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.5386 | −0.464919 | ||||||||
\(849\) | 0.466137 | 0.0159978 | ||||||||
\(850\) | −3.35151 | −0.114956 | ||||||||
\(851\) | 0.585313 | 0.0200643 | ||||||||
\(852\) | −0.177399 | −0.00607757 | ||||||||
\(853\) | 5.16515 | 0.176851 | 0.0884256 | − | 0.996083i | \(-0.471816\pi\) | ||||
0.0884256 | + | 0.996083i | \(0.471816\pi\) | |||||||
\(854\) | 3.89131 | 0.133158 | ||||||||
\(855\) | 14.2453 | 0.487179 | ||||||||
\(856\) | 10.2801 | 0.351368 | ||||||||
\(857\) | −5.43985 | −0.185822 | −0.0929109 | − | 0.995674i | \(-0.529617\pi\) | ||||
−0.0929109 | + | 0.995674i | \(0.529617\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5615 | 0.838028 | 0.419014 | − | 0.907980i | \(-0.362376\pi\) | ||||
0.419014 | + | 0.907980i | \(0.362376\pi\) | |||||||
\(860\) | 9.55155 | 0.325705 | ||||||||
\(861\) | 2.03081 | 0.0692100 | ||||||||
\(862\) | −6.27580 | −0.213755 | ||||||||
\(863\) | −18.2185 | −0.620166 | −0.310083 | − | 0.950710i | \(-0.600357\pi\) | ||||
−0.310083 | + | 0.950710i | \(0.600357\pi\) | |||||||
\(864\) | −1.25707 | −0.0427664 | ||||||||
\(865\) | 0.216594 | 0.00736441 | ||||||||
\(866\) | −25.3703 | −0.862118 | ||||||||
\(867\) | 1.21738 | 0.0413444 | ||||||||
\(868\) | −1.25772 | −0.0426898 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.339174 | 0.0114991 | ||||||||
\(871\) | 1.91017 | 0.0647237 | ||||||||
\(872\) | −2.65530 | −0.0899197 | ||||||||
\(873\) | −33.2993 | −1.12701 | ||||||||
\(874\) | −3.29240 | −0.111367 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −2.18436 | −0.0738027 | ||||||||
\(877\) | 10.5936 | 0.357722 | 0.178861 | − | 0.983874i | \(-0.442759\pi\) | ||||
0.178861 | + | 0.983874i | \(0.442759\pi\) | |||||||
\(878\) | 14.4302 | 0.486995 | ||||||||
\(879\) | −4.61718 | −0.155733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.7215 | 1.91100 | 0.955498 | − | 0.294996i | \(-0.0953185\pi\) | ||||
0.955498 | + | 0.294996i | \(0.0953185\pi\) | |||||||
\(882\) | 2.95545 | 0.0995150 | ||||||||
\(883\) | 41.7759 | 1.40587 | 0.702935 | − | 0.711254i | \(-0.251873\pi\) | ||||
0.702935 | + | 0.711254i | \(0.251873\pi\) | |||||||
\(884\) | 1.28715 | 0.0432917 | ||||||||
\(885\) | 1.53439 | 0.0515779 | ||||||||
\(886\) | −23.5142 | −0.789975 | ||||||||
\(887\) | −0.460010 | −0.0154456 | −0.00772282 | − | 0.999970i | \(-0.502458\pi\) | ||||
−0.00772282 | + | 0.999970i | \(0.502458\pi\) | |||||||
\(888\) | 0.180872 | 0.00606965 | ||||||||
\(889\) | −21.0499 | −0.705991 | ||||||||
\(890\) | 15.0365 | 0.504023 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.78387 | 0.0932109 | ||||||||
\(893\) | −36.3936 | −1.21787 | ||||||||
\(894\) | −2.56732 | −0.0858642 | ||||||||
\(895\) | 17.0592 | 0.570228 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.0553732 | −0.00184886 | ||||||||
\(898\) | 6.33865 | 0.211524 | ||||||||
\(899\) | 2.02097 | 0.0674032 | ||||||||
\(900\) | −2.95545 | −0.0985149 | ||||||||
\(901\) | −45.3748 | −1.51165 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.01614 | 0.0670928 | ||||||||
\(904\) | −10.2264 | −0.340124 | ||||||||
\(905\) | −3.45754 | −0.114932 | ||||||||
\(906\) | 4.27706 | 0.142096 | ||||||||
\(907\) | −36.2499 | −1.20366 | −0.601829 | − | 0.798625i | \(-0.705561\pi\) | ||||
−0.601829 | + | 0.798625i | \(0.705561\pi\) | |||||||
\(908\) | 15.7137 | 0.521476 | ||||||||
\(909\) | 2.09243 | 0.0694016 | ||||||||
\(910\) | 0.384053 | 0.0127312 | ||||||||
\(911\) | 54.8407 | 1.81695 | 0.908477 | − | 0.417935i | \(-0.137246\pi\) | ||||
0.908477 | + | 0.417935i | \(0.137246\pi\) | |||||||
\(912\) | −1.01741 | −0.0336897 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.08335 | −0.135065 | ||||||||
\(915\) | −0.821376 | −0.0271538 | ||||||||
\(916\) | 17.0716 | 0.564060 | ||||||||
\(917\) | −12.9629 | −0.428073 | ||||||||
\(918\) | −4.21308 | −0.139052 | ||||||||
\(919\) | −17.7239 | −0.584658 | −0.292329 | − | 0.956318i | \(-0.594430\pi\) | ||||
−0.292329 | + | 0.956318i | \(0.594430\pi\) | |||||||
\(920\) | 0.683067 | 0.0225201 | ||||||||
\(921\) | −0.193669 | −0.00638162 | ||||||||
\(922\) | 27.7053 | 0.912426 | ||||||||
\(923\) | 0.322771 | 0.0106241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.856889 | 0.0281743 | ||||||||
\(926\) | 30.6895 | 1.00852 | ||||||||
\(927\) | −1.77930 | −0.0584399 | ||||||||
\(928\) | 1.60685 | 0.0527476 | ||||||||
\(929\) | −8.59746 | −0.282074 | −0.141037 | − | 0.990004i | \(-0.545044\pi\) | ||||
−0.141037 | + | 0.990004i | \(0.545044\pi\) | |||||||
\(930\) | 0.265479 | 0.00870539 | ||||||||
\(931\) | 4.82002 | 0.157970 | ||||||||
\(932\) | 7.21602 | 0.236369 | ||||||||
\(933\) | −0.626818 | −0.0205211 | ||||||||
\(934\) | 5.78418 | 0.189264 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.13505 | 0.0371002 | ||||||||
\(937\) | 54.1754 | 1.76983 | 0.884916 | − | 0.465751i | \(-0.154216\pi\) | ||||
0.884916 | + | 0.465751i | \(0.154216\pi\) | |||||||
\(938\) | −4.97372 | −0.162398 | ||||||||
\(939\) | 0.212768 | 0.00694343 | ||||||||
\(940\) | 7.55052 | 0.246271 | ||||||||
\(941\) | −42.0976 | −1.37234 | −0.686171 | − | 0.727440i | \(-0.740710\pi\) | ||||
−0.686171 | + | 0.727440i | \(0.740710\pi\) | |||||||
\(942\) | −2.13165 | −0.0694528 | ||||||||
\(943\) | −6.57185 | −0.214009 | ||||||||
\(944\) | 7.26925 | 0.236594 | ||||||||
\(945\) | −1.25707 | −0.0408925 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.3240 | 1.05039 | 0.525194 | − | 0.850982i | \(-0.323993\pi\) | ||||
0.525194 | + | 0.850982i | \(0.323993\pi\) | |||||||
\(948\) | 0.710855 | 0.0230875 | ||||||||
\(949\) | 3.97438 | 0.129014 | ||||||||
\(950\) | −4.82002 | −0.156382 | ||||||||
\(951\) | 0.733825 | 0.0237959 | ||||||||
\(952\) | −3.35151 | −0.108623 | ||||||||
\(953\) | −40.3551 | −1.30723 | −0.653615 | − | 0.756827i | \(-0.726748\pi\) | ||||
−0.653615 | + | 0.756827i | \(0.726748\pi\) | |||||||
\(954\) | −40.0127 | −1.29546 | ||||||||
\(955\) | −2.95839 | −0.0957314 | ||||||||
\(956\) | 4.90570 | 0.158662 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.65632 | 0.215056 | ||||||||
\(959\) | 12.4469 | 0.401930 | ||||||||
\(960\) | 0.211079 | 0.00681256 | ||||||||
\(961\) | −29.4181 | −0.948972 | ||||||||
\(962\) | −0.329091 | −0.0106103 | ||||||||
\(963\) | 30.3824 | 0.979059 | ||||||||
\(964\) | −23.5063 | −0.757086 | ||||||||
\(965\) | −9.47612 | −0.305047 | ||||||||
\(966\) | 0.144181 | 0.00463896 | ||||||||
\(967\) | −1.52424 | −0.0490161 | −0.0245081 | − | 0.999700i | \(-0.507802\pi\) | ||||
−0.0245081 | + | 0.999700i | \(0.507802\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.40984 | −0.109540 | ||||||||
\(970\) | 11.2671 | 0.361765 | ||||||||
\(971\) | 30.9119 | 0.992011 | 0.496006 | − | 0.868319i | \(-0.334800\pi\) | ||||
0.496006 | + | 0.868319i | \(0.334800\pi\) | |||||||
\(972\) | −5.58671 | −0.179194 | ||||||||
\(973\) | 12.0205 | 0.385361 | ||||||||
\(974\) | 3.19787 | 0.102466 | ||||||||
\(975\) | −0.0810656 | −0.00259618 | ||||||||
\(976\) | −3.89131 | −0.124558 | ||||||||
\(977\) | 57.1348 | 1.82790 | 0.913952 | − | 0.405823i | \(-0.133015\pi\) | ||||
0.913952 | + | 0.405823i | \(0.133015\pi\) | |||||||
\(978\) | 4.42987 | 0.141652 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −7.84759 | −0.250554 | ||||||||
\(982\) | 2.50327 | 0.0798825 | ||||||||
\(983\) | −17.0792 | −0.544741 | −0.272370 | − | 0.962193i | \(-0.587808\pi\) | ||||
−0.272370 | + | 0.962193i | \(0.587808\pi\) | |||||||
\(984\) | −2.03081 | −0.0647400 | ||||||||
\(985\) | 5.06389 | 0.161349 | ||||||||
\(986\) | 5.38538 | 0.171506 | ||||||||
\(987\) | 1.59376 | 0.0507299 | ||||||||
\(988\) | 1.85114 | 0.0588926 | ||||||||
\(989\) | −6.52435 | −0.207462 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.3798 | 1.79096 | 0.895482 | − | 0.445097i | \(-0.146831\pi\) | ||||
0.895482 | + | 0.445097i | \(0.146831\pi\) | |||||||
\(992\) | 1.25772 | 0.0399327 | ||||||||
\(993\) | −3.67035 | −0.116475 | ||||||||
\(994\) | −0.840435 | −0.0266570 | ||||||||
\(995\) | 21.7104 | 0.688267 | ||||||||
\(996\) | −2.22046 | −0.0703578 | ||||||||
\(997\) | −38.8679 | −1.23096 | −0.615479 | − | 0.788153i | \(-0.711038\pi\) | ||||
−0.615479 | + | 0.788153i | \(0.711038\pi\) | |||||||
\(998\) | −21.6925 | −0.686663 | ||||||||
\(999\) | 1.07717 | 0.0340802 |
(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 | 8470.2.a.dg.1.4 | 8 | ||
11.2 | odd | 10 | 770.2.n.k.631.3 | yes | 16 | ||
11.6 | odd | 10 | 770.2.n.k.421.3 | ✓ | 16 | ||
11.10 | odd | 2 | 8470.2.a.dh.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.421.3 | ✓ | 16 | 11.6 | odd | 10 | ||
770.2.n.k.631.3 | yes | 16 | 11.2 | odd | 10 | ||
8470.2.a.dg.1.4 | 8 | 1.1 | even | 1 | trivial | ||
8470.2.a.dh.1.4 | 8 | 11.10 | odd | 2 |