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: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | 1.2 | ||
Root | \(1.61803\) 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 | ||||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 5.61803 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.61803 | 0.417775 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.61803 | 1.12004 | 0.560019 | − | 0.828480i | \(-0.310794\pi\) | ||||
0.560019 | + | 0.828480i | \(0.310794\pi\) | |||||||
\(18\) | −0.381966 | −0.0900303 | ||||||||
\(19\) | −5.23607 | −1.20124 | −0.600618 | − | 0.799536i | \(-0.705079\pi\) | ||||
−0.600618 | + | 0.799536i | \(0.705079\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.47214 | 1.76656 | 0.883281 | − | 0.468844i | \(-0.155329\pi\) | ||||
0.883281 | + | 0.468844i | \(0.155329\pi\) | |||||||
\(24\) | 1.61803 | 0.330280 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.61803 | 1.10179 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −5.85410 | −1.08708 | −0.543540 | − | 0.839383i | \(-0.682916\pi\) | ||||
−0.543540 | + | 0.839383i | \(0.682916\pi\) | |||||||
\(30\) | 1.61803 | 0.295411 | ||||||||
\(31\) | 5.23607 | 0.940426 | 0.470213 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470213 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.61803 | 0.791986 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | −3.70820 | −0.609625 | −0.304812 | − | 0.952412i | \(-0.598594\pi\) | ||||
−0.304812 | + | 0.952412i | \(0.598594\pi\) | |||||||
\(38\) | −5.23607 | −0.849402 | ||||||||
\(39\) | 9.09017 | 1.45559 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.94427 | 1.39686 | 0.698430 | − | 0.715678i | \(-0.253882\pi\) | ||||
0.698430 | + | 0.715678i | \(0.253882\pi\) | |||||||
\(42\) | 1.61803 | 0.249668 | ||||||||
\(43\) | 3.23607 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | 8.47214 | 1.24915 | ||||||||
\(47\) | −13.0902 | −1.90940 | −0.954699 | − | 0.297574i | \(-0.903823\pi\) | ||||
−0.954699 | + | 0.297574i | \(0.903823\pi\) | |||||||
\(48\) | 1.61803 | 0.233543 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 7.47214 | 1.04631 | ||||||||
\(52\) | 5.61803 | 0.779081 | ||||||||
\(53\) | 6.47214 | 0.889016 | 0.444508 | − | 0.895775i | \(-0.353378\pi\) | ||||
0.444508 | + | 0.895775i | \(0.353378\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −8.47214 | −1.12216 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | 4.76393 | 0.620211 | 0.310106 | − | 0.950702i | \(-0.399636\pi\) | ||||
0.310106 | + | 0.950702i | \(0.399636\pi\) | |||||||
\(60\) | 1.61803 | 0.208887 | ||||||||
\(61\) | −11.7082 | −1.49908 | −0.749541 | − | 0.661958i | \(-0.769726\pi\) | ||||
−0.749541 | + | 0.661958i | \(0.769726\pi\) | |||||||
\(62\) | 5.23607 | 0.664981 | ||||||||
\(63\) | −0.381966 | −0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.61803 | 0.696831 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.23607 | −0.151010 | −0.0755049 | − | 0.997145i | \(-0.524057\pi\) | ||||
−0.0755049 | + | 0.997145i | \(0.524057\pi\) | |||||||
\(68\) | 4.61803 | 0.560019 | ||||||||
\(69\) | 13.7082 | 1.65027 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −7.32624 | −0.869464 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(72\) | −0.381966 | −0.0450151 | ||||||||
\(73\) | 4.32624 | 0.506348 | 0.253174 | − | 0.967421i | \(-0.418526\pi\) | ||||
0.253174 | + | 0.967421i | \(0.418526\pi\) | |||||||
\(74\) | −3.70820 | −0.431070 | ||||||||
\(75\) | 1.61803 | 0.186834 | ||||||||
\(76\) | −5.23607 | −0.600618 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.09017 | 1.02926 | ||||||||
\(79\) | −0.854102 | −0.0960940 | −0.0480470 | − | 0.998845i | \(-0.515300\pi\) | ||||
−0.0480470 | + | 0.998845i | \(0.515300\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 8.94427 | 0.987730 | ||||||||
\(83\) | 13.6180 | 1.49477 | 0.747387 | − | 0.664389i | \(-0.231308\pi\) | ||||
0.747387 | + | 0.664389i | \(0.231308\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | 4.61803 | 0.500896 | ||||||||
\(86\) | 3.23607 | 0.348954 | ||||||||
\(87\) | −9.47214 | −1.01552 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.291796 | 0.0309303 | 0.0154652 | − | 0.999880i | \(-0.495077\pi\) | ||||
0.0154652 | + | 0.999880i | \(0.495077\pi\) | |||||||
\(90\) | −0.381966 | −0.0402628 | ||||||||
\(91\) | 5.61803 | 0.588930 | ||||||||
\(92\) | 8.47214 | 0.883281 | ||||||||
\(93\) | 8.47214 | 0.878520 | ||||||||
\(94\) | −13.0902 | −1.35015 | ||||||||
\(95\) | −5.23607 | −0.537209 | ||||||||
\(96\) | 1.61803 | 0.165140 | ||||||||
\(97\) | −3.38197 | −0.343387 | −0.171693 | − | 0.985150i | \(-0.554924\pi\) | ||||
−0.171693 | + | 0.985150i | \(0.554924\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.23607 | −0.521008 | −0.260504 | − | 0.965473i | \(-0.583889\pi\) | ||||
−0.260504 | + | 0.965473i | \(0.583889\pi\) | |||||||
\(102\) | 7.47214 | 0.739852 | ||||||||
\(103\) | 3.56231 | 0.351004 | 0.175502 | − | 0.984479i | \(-0.443845\pi\) | ||||
0.175502 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(104\) | 5.61803 | 0.550894 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | 6.47214 | 0.628629 | ||||||||
\(107\) | −10.7639 | −1.04059 | −0.520294 | − | 0.853987i | \(-0.674178\pi\) | ||||
−0.520294 | + | 0.853987i | \(0.674178\pi\) | |||||||
\(108\) | −5.47214 | −0.526557 | ||||||||
\(109\) | 3.52786 | 0.337908 | 0.168954 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168954 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.52786 | −0.143729 | −0.0718647 | − | 0.997414i | \(-0.522895\pi\) | ||||
−0.0718647 | + | 0.997414i | \(0.522895\pi\) | |||||||
\(114\) | −8.47214 | −0.793488 | ||||||||
\(115\) | 8.47214 | 0.790031 | ||||||||
\(116\) | −5.85410 | −0.543540 | ||||||||
\(117\) | −2.14590 | −0.198388 | ||||||||
\(118\) | 4.76393 | 0.438555 | ||||||||
\(119\) | 4.61803 | 0.423334 | ||||||||
\(120\) | 1.61803 | 0.147706 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.7082 | −1.06001 | ||||||||
\(123\) | 14.4721 | 1.30491 | ||||||||
\(124\) | 5.23607 | 0.470213 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.381966 | −0.0340282 | ||||||||
\(127\) | 20.1803 | 1.79072 | 0.895358 | − | 0.445348i | \(-0.146920\pi\) | ||||
0.895358 | + | 0.445348i | \(0.146920\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.23607 | 0.461010 | ||||||||
\(130\) | 5.61803 | 0.492734 | ||||||||
\(131\) | −11.4164 | −0.997456 | −0.498728 | − | 0.866758i | \(-0.666199\pi\) | ||||
−0.498728 | + | 0.866758i | \(0.666199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.23607 | −0.454025 | ||||||||
\(134\) | −1.23607 | −0.106780 | ||||||||
\(135\) | −5.47214 | −0.470966 | ||||||||
\(136\) | 4.61803 | 0.395993 | ||||||||
\(137\) | −16.0000 | −1.36697 | −0.683486 | − | 0.729964i | \(-0.739537\pi\) | ||||
−0.683486 | + | 0.729964i | \(0.739537\pi\) | |||||||
\(138\) | 13.7082 | 1.16692 | ||||||||
\(139\) | 8.94427 | 0.758643 | 0.379322 | − | 0.925265i | \(-0.376157\pi\) | ||||
0.379322 | + | 0.925265i | \(0.376157\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −21.1803 | −1.78371 | ||||||||
\(142\) | −7.32624 | −0.614804 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | −5.85410 | −0.486157 | ||||||||
\(146\) | 4.32624 | 0.358042 | ||||||||
\(147\) | 1.61803 | 0.133453 | ||||||||
\(148\) | −3.70820 | −0.304812 | ||||||||
\(149\) | 20.8541 | 1.70843 | 0.854217 | − | 0.519916i | \(-0.174037\pi\) | ||||
0.854217 | + | 0.519916i | \(0.174037\pi\) | |||||||
\(150\) | 1.61803 | 0.132112 | ||||||||
\(151\) | 21.3820 | 1.74004 | 0.870020 | − | 0.493017i | \(-0.164106\pi\) | ||||
0.870020 | + | 0.493017i | \(0.164106\pi\) | |||||||
\(152\) | −5.23607 | −0.424701 | ||||||||
\(153\) | −1.76393 | −0.142605 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.23607 | 0.420571 | ||||||||
\(156\) | 9.09017 | 0.727796 | ||||||||
\(157\) | −11.0902 | −0.885092 | −0.442546 | − | 0.896746i | \(-0.645925\pi\) | ||||
−0.442546 | + | 0.896746i | \(0.645925\pi\) | |||||||
\(158\) | −0.854102 | −0.0679487 | ||||||||
\(159\) | 10.4721 | 0.830494 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 8.47214 | 0.667698 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | −14.6525 | −1.14767 | −0.573835 | − | 0.818971i | \(-0.694545\pi\) | ||||
−0.573835 | + | 0.818971i | \(0.694545\pi\) | |||||||
\(164\) | 8.94427 | 0.698430 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6180 | 1.05696 | ||||||||
\(167\) | 20.0000 | 1.54765 | 0.773823 | − | 0.633402i | \(-0.218342\pi\) | ||||
0.773823 | + | 0.633402i | \(0.218342\pi\) | |||||||
\(168\) | 1.61803 | 0.124834 | ||||||||
\(169\) | 18.5623 | 1.42787 | ||||||||
\(170\) | 4.61803 | 0.354187 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 3.23607 | 0.246748 | ||||||||
\(173\) | −15.5066 | −1.17894 | −0.589472 | − | 0.807789i | \(-0.700664\pi\) | ||||
−0.589472 | + | 0.807789i | \(0.700664\pi\) | |||||||
\(174\) | −9.47214 | −0.718081 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.70820 | 0.579384 | ||||||||
\(178\) | 0.291796 | 0.0218710 | ||||||||
\(179\) | −19.5623 | −1.46216 | −0.731078 | − | 0.682294i | \(-0.760982\pi\) | ||||
−0.731078 | + | 0.682294i | \(0.760982\pi\) | |||||||
\(180\) | −0.381966 | −0.0284701 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 5.61803 | 0.416436 | ||||||||
\(183\) | −18.9443 | −1.40040 | ||||||||
\(184\) | 8.47214 | 0.624574 | ||||||||
\(185\) | −3.70820 | −0.272633 | ||||||||
\(186\) | 8.47214 | 0.621207 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.0902 | −0.954699 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | −5.23607 | −0.379864 | ||||||||
\(191\) | 0.854102 | 0.0618006 | 0.0309003 | − | 0.999522i | \(-0.490163\pi\) | ||||
0.0309003 | + | 0.999522i | \(0.490163\pi\) | |||||||
\(192\) | 1.61803 | 0.116772 | ||||||||
\(193\) | 12.9443 | 0.931749 | 0.465875 | − | 0.884851i | \(-0.345740\pi\) | ||||
0.465875 | + | 0.884851i | \(0.345740\pi\) | |||||||
\(194\) | −3.38197 | −0.242811 | ||||||||
\(195\) | 9.09017 | 0.650961 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −15.4164 | −1.09837 | −0.549187 | − | 0.835700i | \(-0.685062\pi\) | ||||
−0.549187 | + | 0.835700i | \(0.685062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9443 | −0.775819 | −0.387909 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387909 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | −5.23607 | −0.368408 | ||||||||
\(203\) | −5.85410 | −0.410877 | ||||||||
\(204\) | 7.47214 | 0.523154 | ||||||||
\(205\) | 8.94427 | 0.624695 | ||||||||
\(206\) | 3.56231 | 0.248198 | ||||||||
\(207\) | −3.23607 | −0.224922 | ||||||||
\(208\) | 5.61803 | 0.389541 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.61803 | 0.111655 | ||||||||
\(211\) | 15.3262 | 1.05510 | 0.527551 | − | 0.849523i | \(-0.323110\pi\) | ||||
0.527551 | + | 0.849523i | \(0.323110\pi\) | |||||||
\(212\) | 6.47214 | 0.444508 | ||||||||
\(213\) | −11.8541 | −0.812230 | ||||||||
\(214\) | −10.7639 | −0.735807 | ||||||||
\(215\) | 3.23607 | 0.220698 | ||||||||
\(216\) | −5.47214 | −0.372332 | ||||||||
\(217\) | 5.23607 | 0.355447 | ||||||||
\(218\) | 3.52786 | 0.238937 | ||||||||
\(219\) | 7.00000 | 0.473016 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.9443 | 1.74520 | ||||||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | −18.4721 | −1.23699 | −0.618493 | − | 0.785790i | \(-0.712256\pi\) | ||||
−0.618493 | + | 0.785790i | \(0.712256\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −0.381966 | −0.0254644 | ||||||||
\(226\) | −1.52786 | −0.101632 | ||||||||
\(227\) | 7.14590 | 0.474290 | 0.237145 | − | 0.971474i | \(-0.423788\pi\) | ||||
0.237145 | + | 0.971474i | \(0.423788\pi\) | |||||||
\(228\) | −8.47214 | −0.561081 | ||||||||
\(229\) | 7.70820 | 0.509372 | 0.254686 | − | 0.967024i | \(-0.418028\pi\) | ||||
0.254686 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(230\) | 8.47214 | 0.558636 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.85410 | −0.384341 | ||||||||
\(233\) | −16.6525 | −1.09094 | −0.545470 | − | 0.838130i | \(-0.683649\pi\) | ||||
−0.545470 | + | 0.838130i | \(0.683649\pi\) | |||||||
\(234\) | −2.14590 | −0.140282 | ||||||||
\(235\) | −13.0902 | −0.853909 | ||||||||
\(236\) | 4.76393 | 0.310106 | ||||||||
\(237\) | −1.38197 | −0.0897683 | ||||||||
\(238\) | 4.61803 | 0.299343 | ||||||||
\(239\) | 8.85410 | 0.572724 | 0.286362 | − | 0.958121i | \(-0.407554\pi\) | ||||
0.286362 | + | 0.958121i | \(0.407554\pi\) | |||||||
\(240\) | 1.61803 | 0.104444 | ||||||||
\(241\) | −3.70820 | −0.238866 | −0.119433 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119433 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | −11.7082 | −0.749541 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 14.4721 | 0.922710 | ||||||||
\(247\) | −29.4164 | −1.87172 | ||||||||
\(248\) | 5.23607 | 0.332491 | ||||||||
\(249\) | 22.0344 | 1.39638 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 0.763932 | 0.0482190 | 0.0241095 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241095 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 20.1803 | 1.26623 | ||||||||
\(255\) | 7.47214 | 0.467923 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.2705 | −0.827792 | −0.413896 | − | 0.910324i | \(-0.635832\pi\) | ||||
−0.413896 | + | 0.910324i | \(0.635832\pi\) | |||||||
\(258\) | 5.23607 | 0.325983 | ||||||||
\(259\) | −3.70820 | −0.230417 | ||||||||
\(260\) | 5.61803 | 0.348416 | ||||||||
\(261\) | 2.23607 | 0.138409 | ||||||||
\(262\) | −11.4164 | −0.705308 | ||||||||
\(263\) | 14.2918 | 0.881270 | 0.440635 | − | 0.897686i | \(-0.354753\pi\) | ||||
0.440635 | + | 0.897686i | \(0.354753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.47214 | 0.397580 | ||||||||
\(266\) | −5.23607 | −0.321044 | ||||||||
\(267\) | 0.472136 | 0.0288943 | ||||||||
\(268\) | −1.23607 | −0.0755049 | ||||||||
\(269\) | 19.7082 | 1.20163 | 0.600815 | − | 0.799388i | \(-0.294843\pi\) | ||||
0.600815 | + | 0.799388i | \(0.294843\pi\) | |||||||
\(270\) | −5.47214 | −0.333024 | ||||||||
\(271\) | 15.1246 | 0.918755 | 0.459377 | − | 0.888241i | \(-0.348073\pi\) | ||||
0.459377 | + | 0.888241i | \(0.348073\pi\) | |||||||
\(272\) | 4.61803 | 0.280009 | ||||||||
\(273\) | 9.09017 | 0.550162 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.7082 | 0.825137 | ||||||||
\(277\) | 13.4164 | 0.806114 | 0.403057 | − | 0.915175i | \(-0.367948\pi\) | ||||
0.403057 | + | 0.915175i | \(0.367948\pi\) | |||||||
\(278\) | 8.94427 | 0.536442 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 18.3607 | 1.09531 | 0.547653 | − | 0.836705i | \(-0.315521\pi\) | ||||
0.547653 | + | 0.836705i | \(0.315521\pi\) | |||||||
\(282\) | −21.1803 | −1.26127 | ||||||||
\(283\) | −14.3262 | −0.851606 | −0.425803 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425803 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(284\) | −7.32624 | −0.434732 | ||||||||
\(285\) | −8.47214 | −0.501846 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94427 | 0.527964 | ||||||||
\(288\) | −0.381966 | −0.0225076 | ||||||||
\(289\) | 4.32624 | 0.254485 | ||||||||
\(290\) | −5.85410 | −0.343765 | ||||||||
\(291\) | −5.47214 | −0.320782 | ||||||||
\(292\) | 4.32624 | 0.253174 | ||||||||
\(293\) | −25.4164 | −1.48484 | −0.742421 | − | 0.669933i | \(-0.766323\pi\) | ||||
−0.742421 | + | 0.669933i | \(0.766323\pi\) | |||||||
\(294\) | 1.61803 | 0.0943657 | ||||||||
\(295\) | 4.76393 | 0.277367 | ||||||||
\(296\) | −3.70820 | −0.215535 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.8541 | 1.20805 | ||||||||
\(299\) | 47.5967 | 2.75259 | ||||||||
\(300\) | 1.61803 | 0.0934172 | ||||||||
\(301\) | 3.23607 | 0.186524 | ||||||||
\(302\) | 21.3820 | 1.23039 | ||||||||
\(303\) | −8.47214 | −0.486711 | ||||||||
\(304\) | −5.23607 | −0.300309 | ||||||||
\(305\) | −11.7082 | −0.670410 | ||||||||
\(306\) | −1.76393 | −0.100837 | ||||||||
\(307\) | −33.4508 | −1.90914 | −0.954570 | − | 0.297985i | \(-0.903685\pi\) | ||||
−0.954570 | + | 0.297985i | \(0.903685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.76393 | 0.327899 | ||||||||
\(310\) | 5.23607 | 0.297389 | ||||||||
\(311\) | 10.1803 | 0.577274 | 0.288637 | − | 0.957439i | \(-0.406798\pi\) | ||||
0.288637 | + | 0.957439i | \(0.406798\pi\) | |||||||
\(312\) | 9.09017 | 0.514630 | ||||||||
\(313\) | 11.8885 | 0.671980 | 0.335990 | − | 0.941866i | \(-0.390929\pi\) | ||||
0.335990 | + | 0.941866i | \(0.390929\pi\) | |||||||
\(314\) | −11.0902 | −0.625854 | ||||||||
\(315\) | −0.381966 | −0.0215213 | ||||||||
\(316\) | −0.854102 | −0.0480470 | ||||||||
\(317\) | 17.8885 | 1.00472 | 0.502360 | − | 0.864658i | \(-0.332465\pi\) | ||||
0.502360 | + | 0.864658i | \(0.332465\pi\) | |||||||
\(318\) | 10.4721 | 0.587248 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −17.4164 | −0.972089 | ||||||||
\(322\) | 8.47214 | 0.472134 | ||||||||
\(323\) | −24.1803 | −1.34543 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | 5.61803 | 0.311632 | ||||||||
\(326\) | −14.6525 | −0.811526 | ||||||||
\(327\) | 5.70820 | 0.315664 | ||||||||
\(328\) | 8.94427 | 0.493865 | ||||||||
\(329\) | −13.0902 | −0.721684 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.38197 | −0.350785 | −0.175392 | − | 0.984499i | \(-0.556119\pi\) | ||||
−0.175392 | + | 0.984499i | \(0.556119\pi\) | |||||||
\(332\) | 13.6180 | 0.747387 | ||||||||
\(333\) | 1.41641 | 0.0776187 | ||||||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | −1.23607 | −0.0675336 | ||||||||
\(336\) | 1.61803 | 0.0882710 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 18.5623 | 1.00966 | ||||||||
\(339\) | −2.47214 | −0.134268 | ||||||||
\(340\) | 4.61803 | 0.250448 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.23607 | 0.174477 | ||||||||
\(345\) | 13.7082 | 0.738025 | ||||||||
\(346\) | −15.5066 | −0.833639 | ||||||||
\(347\) | 25.8885 | 1.38977 | 0.694885 | − | 0.719121i | \(-0.255455\pi\) | ||||
0.694885 | + | 0.719121i | \(0.255455\pi\) | |||||||
\(348\) | −9.47214 | −0.507760 | ||||||||
\(349\) | −26.9443 | −1.44229 | −0.721147 | − | 0.692782i | \(-0.756385\pi\) | ||||
−0.721147 | + | 0.692782i | \(0.756385\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −30.7426 | −1.64092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4508 | −1.30139 | −0.650694 | − | 0.759340i | \(-0.725522\pi\) | ||||
−0.650694 | + | 0.759340i | \(0.725522\pi\) | |||||||
\(354\) | 7.70820 | 0.409686 | ||||||||
\(355\) | −7.32624 | −0.388836 | ||||||||
\(356\) | 0.291796 | 0.0154652 | ||||||||
\(357\) | 7.47214 | 0.395467 | ||||||||
\(358\) | −19.5623 | −1.03390 | ||||||||
\(359\) | 17.9787 | 0.948880 | 0.474440 | − | 0.880288i | \(-0.342651\pi\) | ||||
0.474440 | + | 0.880288i | \(0.342651\pi\) | |||||||
\(360\) | −0.381966 | −0.0201314 | ||||||||
\(361\) | 8.41641 | 0.442969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.61803 | 0.294465 | ||||||||
\(365\) | 4.32624 | 0.226446 | ||||||||
\(366\) | −18.9443 | −0.990233 | ||||||||
\(367\) | 35.3262 | 1.84401 | 0.922007 | − | 0.387172i | \(-0.126548\pi\) | ||||
0.922007 | + | 0.387172i | \(0.126548\pi\) | |||||||
\(368\) | 8.47214 | 0.441641 | ||||||||
\(369\) | −3.41641 | −0.177851 | ||||||||
\(370\) | −3.70820 | −0.192780 | ||||||||
\(371\) | 6.47214 | 0.336017 | ||||||||
\(372\) | 8.47214 | 0.439260 | ||||||||
\(373\) | −2.65248 | −0.137340 | −0.0686700 | − | 0.997639i | \(-0.521876\pi\) | ||||
−0.0686700 | + | 0.997639i | \(0.521876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.61803 | 0.0835549 | ||||||||
\(376\) | −13.0902 | −0.675074 | ||||||||
\(377\) | −32.8885 | −1.69385 | ||||||||
\(378\) | −5.47214 | −0.281456 | ||||||||
\(379\) | 16.1459 | 0.829359 | 0.414680 | − | 0.909968i | \(-0.363894\pi\) | ||||
0.414680 | + | 0.909968i | \(0.363894\pi\) | |||||||
\(380\) | −5.23607 | −0.268605 | ||||||||
\(381\) | 32.6525 | 1.67284 | ||||||||
\(382\) | 0.854102 | 0.0436997 | ||||||||
\(383\) | 8.85410 | 0.452423 | 0.226212 | − | 0.974078i | \(-0.427366\pi\) | ||||
0.226212 | + | 0.974078i | \(0.427366\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9443 | 0.658846 | ||||||||
\(387\) | −1.23607 | −0.0628329 | ||||||||
\(388\) | −3.38197 | −0.171693 | ||||||||
\(389\) | −20.2705 | −1.02776 | −0.513878 | − | 0.857863i | \(-0.671792\pi\) | ||||
−0.513878 | + | 0.857863i | \(0.671792\pi\) | |||||||
\(390\) | 9.09017 | 0.460299 | ||||||||
\(391\) | 39.1246 | 1.97862 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −18.4721 | −0.931796 | ||||||||
\(394\) | −15.4164 | −0.776667 | ||||||||
\(395\) | −0.854102 | −0.0429745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.5623 | −1.53388 | −0.766939 | − | 0.641720i | \(-0.778221\pi\) | ||||
−0.766939 | + | 0.641720i | \(0.778221\pi\) | |||||||
\(398\) | −10.9443 | −0.548587 | ||||||||
\(399\) | −8.47214 | −0.424137 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −36.6180 | −1.82862 | −0.914309 | − | 0.405018i | \(-0.867265\pi\) | ||||
−0.914309 | + | 0.405018i | \(0.867265\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | 29.4164 | 1.46534 | ||||||||
\(404\) | −5.23607 | −0.260504 | ||||||||
\(405\) | −7.70820 | −0.383024 | ||||||||
\(406\) | −5.85410 | −0.290534 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.47214 | 0.369926 | ||||||||
\(409\) | 5.23607 | 0.258907 | 0.129453 | − | 0.991586i | \(-0.458678\pi\) | ||||
0.129453 | + | 0.991586i | \(0.458678\pi\) | |||||||
\(410\) | 8.94427 | 0.441726 | ||||||||
\(411\) | −25.8885 | −1.27699 | ||||||||
\(412\) | 3.56231 | 0.175502 | ||||||||
\(413\) | 4.76393 | 0.234418 | ||||||||
\(414\) | −3.23607 | −0.159044 | ||||||||
\(415\) | 13.6180 | 0.668483 | ||||||||
\(416\) | 5.61803 | 0.275447 | ||||||||
\(417\) | 14.4721 | 0.708704 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.94427 | 0.339250 | 0.169625 | − | 0.985509i | \(-0.445744\pi\) | ||||
0.169625 | + | 0.985509i | \(0.445744\pi\) | |||||||
\(420\) | 1.61803 | 0.0789520 | ||||||||
\(421\) | −11.3262 | −0.552007 | −0.276004 | − | 0.961157i | \(-0.589010\pi\) | ||||
−0.276004 | + | 0.961157i | \(0.589010\pi\) | |||||||
\(422\) | 15.3262 | 0.746070 | ||||||||
\(423\) | 5.00000 | 0.243108 | ||||||||
\(424\) | 6.47214 | 0.314315 | ||||||||
\(425\) | 4.61803 | 0.224008 | ||||||||
\(426\) | −11.8541 | −0.574333 | ||||||||
\(427\) | −11.7082 | −0.566600 | ||||||||
\(428\) | −10.7639 | −0.520294 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.23607 | 0.156057 | ||||||||
\(431\) | −15.5623 | −0.749610 | −0.374805 | − | 0.927104i | \(-0.622290\pi\) | ||||
−0.374805 | + | 0.927104i | \(0.622290\pi\) | |||||||
\(432\) | −5.47214 | −0.263278 | ||||||||
\(433\) | 4.09017 | 0.196561 | 0.0982805 | − | 0.995159i | \(-0.468666\pi\) | ||||
0.0982805 | + | 0.995159i | \(0.468666\pi\) | |||||||
\(434\) | 5.23607 | 0.251339 | ||||||||
\(435\) | −9.47214 | −0.454154 | ||||||||
\(436\) | 3.52786 | 0.168954 | ||||||||
\(437\) | −44.3607 | −2.12206 | ||||||||
\(438\) | 7.00000 | 0.334473 | ||||||||
\(439\) | −10.6525 | −0.508415 | −0.254207 | − | 0.967150i | \(-0.581815\pi\) | ||||
−0.254207 | + | 0.967150i | \(0.581815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 25.9443 | 1.23404 | ||||||||
\(443\) | −15.2361 | −0.723887 | −0.361944 | − | 0.932200i | \(-0.617887\pi\) | ||||
−0.361944 | + | 0.932200i | \(0.617887\pi\) | |||||||
\(444\) | −6.00000 | −0.284747 | ||||||||
\(445\) | 0.291796 | 0.0138325 | ||||||||
\(446\) | −18.4721 | −0.874681 | ||||||||
\(447\) | 33.7426 | 1.59597 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −19.5066 | −0.920572 | −0.460286 | − | 0.887771i | \(-0.652253\pi\) | ||||
−0.460286 | + | 0.887771i | \(0.652253\pi\) | |||||||
\(450\) | −0.381966 | −0.0180061 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.52786 | −0.0718647 | ||||||||
\(453\) | 34.5967 | 1.62550 | ||||||||
\(454\) | 7.14590 | 0.335374 | ||||||||
\(455\) | 5.61803 | 0.263377 | ||||||||
\(456\) | −8.47214 | −0.396744 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 7.70820 | 0.360181 | ||||||||
\(459\) | −25.2705 | −1.17953 | ||||||||
\(460\) | 8.47214 | 0.395015 | ||||||||
\(461\) | 25.1246 | 1.17017 | 0.585085 | − | 0.810972i | \(-0.301061\pi\) | ||||
0.585085 | + | 0.810972i | \(0.301061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1803 | −0.659016 | −0.329508 | − | 0.944153i | \(-0.606883\pi\) | ||||
−0.329508 | + | 0.944153i | \(0.606883\pi\) | |||||||
\(464\) | −5.85410 | −0.271770 | ||||||||
\(465\) | 8.47214 | 0.392886 | ||||||||
\(466\) | −16.6525 | −0.771411 | ||||||||
\(467\) | 21.6180 | 1.00036 | 0.500182 | − | 0.865920i | \(-0.333267\pi\) | ||||
0.500182 | + | 0.865920i | \(0.333267\pi\) | |||||||
\(468\) | −2.14590 | −0.0991942 | ||||||||
\(469\) | −1.23607 | −0.0570763 | ||||||||
\(470\) | −13.0902 | −0.603805 | ||||||||
\(471\) | −17.9443 | −0.826828 | ||||||||
\(472\) | 4.76393 | 0.219278 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.38197 | −0.0634758 | ||||||||
\(475\) | −5.23607 | −0.240247 | ||||||||
\(476\) | 4.61803 | 0.211667 | ||||||||
\(477\) | −2.47214 | −0.113191 | ||||||||
\(478\) | 8.85410 | 0.404977 | ||||||||
\(479\) | −35.1246 | −1.60488 | −0.802442 | − | 0.596730i | \(-0.796466\pi\) | ||||
−0.802442 | + | 0.596730i | \(0.796466\pi\) | |||||||
\(480\) | 1.61803 | 0.0738528 | ||||||||
\(481\) | −20.8328 | −0.949895 | ||||||||
\(482\) | −3.70820 | −0.168904 | ||||||||
\(483\) | 13.7082 | 0.623745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.38197 | −0.153567 | ||||||||
\(486\) | 3.94427 | 0.178916 | ||||||||
\(487\) | 11.8197 | 0.535600 | 0.267800 | − | 0.963475i | \(-0.413703\pi\) | ||||
0.267800 | + | 0.963475i | \(0.413703\pi\) | |||||||
\(488\) | −11.7082 | −0.530005 | ||||||||
\(489\) | −23.7082 | −1.07212 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 0.944272 | 0.0426144 | 0.0213072 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213072 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(492\) | 14.4721 | 0.652454 | ||||||||
\(493\) | −27.0344 | −1.21757 | ||||||||
\(494\) | −29.4164 | −1.32351 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.23607 | 0.235106 | ||||||||
\(497\) | −7.32624 | −0.328627 | ||||||||
\(498\) | 22.0344 | 0.987387 | ||||||||
\(499\) | −24.7984 | −1.11013 | −0.555064 | − | 0.831808i | \(-0.687306\pi\) | ||||
−0.555064 | + | 0.831808i | \(0.687306\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 32.3607 | 1.44577 | ||||||||
\(502\) | 0.763932 | 0.0340960 | ||||||||
\(503\) | 25.9787 | 1.15833 | 0.579167 | − | 0.815209i | \(-0.303378\pi\) | ||||
0.579167 | + | 0.815209i | \(0.303378\pi\) | |||||||
\(504\) | −0.381966 | −0.0170141 | ||||||||
\(505\) | −5.23607 | −0.233002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.0344 | 1.33388 | ||||||||
\(508\) | 20.1803 | 0.895358 | ||||||||
\(509\) | −19.8885 | −0.881544 | −0.440772 | − | 0.897619i | \(-0.645295\pi\) | ||||
−0.440772 | + | 0.897619i | \(0.645295\pi\) | |||||||
\(510\) | 7.47214 | 0.330872 | ||||||||
\(511\) | 4.32624 | 0.191381 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 28.6525 | 1.26504 | ||||||||
\(514\) | −13.2705 | −0.585337 | ||||||||
\(515\) | 3.56231 | 0.156974 | ||||||||
\(516\) | 5.23607 | 0.230505 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.70820 | −0.162929 | ||||||||
\(519\) | −25.0902 | −1.10134 | ||||||||
\(520\) | 5.61803 | 0.246367 | ||||||||
\(521\) | −32.5410 | −1.42565 | −0.712824 | − | 0.701343i | \(-0.752584\pi\) | ||||
−0.712824 | + | 0.701343i | \(0.752584\pi\) | |||||||
\(522\) | 2.23607 | 0.0978700 | ||||||||
\(523\) | −9.74265 | −0.426016 | −0.213008 | − | 0.977050i | \(-0.568326\pi\) | ||||
−0.213008 | + | 0.977050i | \(0.568326\pi\) | |||||||
\(524\) | −11.4164 | −0.498728 | ||||||||
\(525\) | 1.61803 | 0.0706168 | ||||||||
\(526\) | 14.2918 | 0.623152 | ||||||||
\(527\) | 24.1803 | 1.05331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.7771 | 2.12074 | ||||||||
\(530\) | 6.47214 | 0.281132 | ||||||||
\(531\) | −1.81966 | −0.0789665 | ||||||||
\(532\) | −5.23607 | −0.227012 | ||||||||
\(533\) | 50.2492 | 2.17654 | ||||||||
\(534\) | 0.472136 | 0.0204313 | ||||||||
\(535\) | −10.7639 | −0.465365 | ||||||||
\(536\) | −1.23607 | −0.0533900 | ||||||||
\(537\) | −31.6525 | −1.36591 | ||||||||
\(538\) | 19.7082 | 0.849681 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.47214 | −0.235483 | ||||||||
\(541\) | −8.09017 | −0.347824 | −0.173912 | − | 0.984761i | \(-0.555641\pi\) | ||||
−0.173912 | + | 0.984761i | \(0.555641\pi\) | |||||||
\(542\) | 15.1246 | 0.649658 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.61803 | 0.197997 | ||||||||
\(545\) | 3.52786 | 0.151117 | ||||||||
\(546\) | 9.09017 | 0.389023 | ||||||||
\(547\) | −22.1803 | −0.948363 | −0.474181 | − | 0.880427i | \(-0.657256\pi\) | ||||
−0.474181 | + | 0.880427i | \(0.657256\pi\) | |||||||
\(548\) | −16.0000 | −0.683486 | ||||||||
\(549\) | 4.47214 | 0.190866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.6525 | 1.30584 | ||||||||
\(552\) | 13.7082 | 0.583460 | ||||||||
\(553\) | −0.854102 | −0.0363201 | ||||||||
\(554\) | 13.4164 | 0.570009 | ||||||||
\(555\) | −6.00000 | −0.254686 | ||||||||
\(556\) | 8.94427 | 0.379322 | ||||||||
\(557\) | −45.5967 | −1.93200 | −0.965998 | − | 0.258549i | \(-0.916756\pi\) | ||||
−0.965998 | + | 0.258549i | \(0.916756\pi\) | |||||||
\(558\) | −2.00000 | −0.0846668 | ||||||||
\(559\) | 18.1803 | 0.768946 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.3607 | 0.774499 | ||||||||
\(563\) | −23.5623 | −0.993033 | −0.496516 | − | 0.868027i | \(-0.665388\pi\) | ||||
−0.496516 | + | 0.868027i | \(0.665388\pi\) | |||||||
\(564\) | −21.1803 | −0.891853 | ||||||||
\(565\) | −1.52786 | −0.0642777 | ||||||||
\(566\) | −14.3262 | −0.602177 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −7.32624 | −0.307402 | ||||||||
\(569\) | 18.7984 | 0.788069 | 0.394034 | − | 0.919096i | \(-0.371079\pi\) | ||||
0.394034 | + | 0.919096i | \(0.371079\pi\) | |||||||
\(570\) | −8.47214 | −0.354859 | ||||||||
\(571\) | −43.8541 | −1.83524 | −0.917619 | − | 0.397462i | \(-0.869891\pi\) | ||||
−0.917619 | + | 0.397462i | \(0.869891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.38197 | 0.0577325 | ||||||||
\(574\) | 8.94427 | 0.373327 | ||||||||
\(575\) | 8.47214 | 0.353312 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | 42.2148 | 1.75742 | 0.878712 | − | 0.477352i | \(-0.158403\pi\) | ||||
0.878712 | + | 0.477352i | \(0.158403\pi\) | |||||||
\(578\) | 4.32624 | 0.179948 | ||||||||
\(579\) | 20.9443 | 0.870414 | ||||||||
\(580\) | −5.85410 | −0.243078 | ||||||||
\(581\) | 13.6180 | 0.564971 | ||||||||
\(582\) | −5.47214 | −0.226827 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.32624 | 0.179021 | ||||||||
\(585\) | −2.14590 | −0.0887220 | ||||||||
\(586\) | −25.4164 | −1.04994 | ||||||||
\(587\) | 19.5066 | 0.805123 | 0.402561 | − | 0.915393i | \(-0.368120\pi\) | ||||
0.402561 | + | 0.915393i | \(0.368120\pi\) | |||||||
\(588\) | 1.61803 | 0.0667266 | ||||||||
\(589\) | −27.4164 | −1.12967 | ||||||||
\(590\) | 4.76393 | 0.196128 | ||||||||
\(591\) | −24.9443 | −1.02607 | ||||||||
\(592\) | −3.70820 | −0.152406 | ||||||||
\(593\) | 14.7984 | 0.607696 | 0.303848 | − | 0.952720i | \(-0.401728\pi\) | ||||
0.303848 | + | 0.952720i | \(0.401728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.61803 | 0.189321 | ||||||||
\(596\) | 20.8541 | 0.854217 | ||||||||
\(597\) | −17.7082 | −0.724749 | ||||||||
\(598\) | 47.5967 | 1.94638 | ||||||||
\(599\) | 38.3951 | 1.56878 | 0.784391 | − | 0.620267i | \(-0.212976\pi\) | ||||
0.784391 | + | 0.620267i | \(0.212976\pi\) | |||||||
\(600\) | 1.61803 | 0.0660560 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 3.23607 | 0.131892 | ||||||||
\(603\) | 0.472136 | 0.0192269 | ||||||||
\(604\) | 21.3820 | 0.870020 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.47214 | −0.344157 | ||||||||
\(607\) | −38.6869 | −1.57025 | −0.785127 | − | 0.619335i | \(-0.787402\pi\) | ||||
−0.785127 | + | 0.619335i | \(0.787402\pi\) | |||||||
\(608\) | −5.23607 | −0.212351 | ||||||||
\(609\) | −9.47214 | −0.383830 | ||||||||
\(610\) | −11.7082 | −0.474051 | ||||||||
\(611\) | −73.5410 | −2.97515 | ||||||||
\(612\) | −1.76393 | −0.0713027 | ||||||||
\(613\) | −22.9443 | −0.926710 | −0.463355 | − | 0.886173i | \(-0.653355\pi\) | ||||
−0.463355 | + | 0.886173i | \(0.653355\pi\) | |||||||
\(614\) | −33.4508 | −1.34997 | ||||||||
\(615\) | 14.4721 | 0.583573 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.81966 | −0.153774 | −0.0768869 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768869 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(618\) | 5.76393 | 0.231859 | ||||||||
\(619\) | 0.583592 | 0.0234565 | 0.0117283 | − | 0.999931i | \(-0.496267\pi\) | ||||
0.0117283 | + | 0.999931i | \(0.496267\pi\) | |||||||
\(620\) | 5.23607 | 0.210286 | ||||||||
\(621\) | −46.3607 | −1.86039 | ||||||||
\(622\) | 10.1803 | 0.408194 | ||||||||
\(623\) | 0.291796 | 0.0116906 | ||||||||
\(624\) | 9.09017 | 0.363898 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.8885 | 0.475162 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0902 | −0.442546 | ||||||||
\(629\) | −17.1246 | −0.682803 | ||||||||
\(630\) | −0.381966 | −0.0152179 | ||||||||
\(631\) | 9.45085 | 0.376232 | 0.188116 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188116 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(632\) | −0.854102 | −0.0339744 | ||||||||
\(633\) | 24.7984 | 0.985647 | ||||||||
\(634\) | 17.8885 | 0.710445 | ||||||||
\(635\) | 20.1803 | 0.800832 | ||||||||
\(636\) | 10.4721 | 0.415247 | ||||||||
\(637\) | 5.61803 | 0.222595 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.79837 | 0.110702 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 9.79837 | 0.387012 | 0.193506 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193506 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(642\) | −17.4164 | −0.687371 | ||||||||
\(643\) | −15.1459 | −0.597296 | −0.298648 | − | 0.954363i | \(-0.596536\pi\) | ||||
−0.298648 | + | 0.954363i | \(0.596536\pi\) | |||||||
\(644\) | 8.47214 | 0.333849 | ||||||||
\(645\) | 5.23607 | 0.206170 | ||||||||
\(646\) | −24.1803 | −0.951363 | ||||||||
\(647\) | −41.7426 | −1.64107 | −0.820536 | − | 0.571594i | \(-0.806325\pi\) | ||||
−0.820536 | + | 0.571594i | \(0.806325\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.61803 | 0.220357 | ||||||||
\(651\) | 8.47214 | 0.332049 | ||||||||
\(652\) | −14.6525 | −0.573835 | ||||||||
\(653\) | −14.2918 | −0.559281 | −0.279641 | − | 0.960105i | \(-0.590215\pi\) | ||||
−0.279641 | + | 0.960105i | \(0.590215\pi\) | |||||||
\(654\) | 5.70820 | 0.223208 | ||||||||
\(655\) | −11.4164 | −0.446076 | ||||||||
\(656\) | 8.94427 | 0.349215 | ||||||||
\(657\) | −1.65248 | −0.0644692 | ||||||||
\(658\) | −13.0902 | −0.510308 | ||||||||
\(659\) | 5.25735 | 0.204797 | 0.102399 | − | 0.994743i | \(-0.467348\pi\) | ||||
0.102399 | + | 0.994743i | \(0.467348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.9443 | −0.736847 | −0.368423 | − | 0.929658i | \(-0.620102\pi\) | ||||
−0.368423 | + | 0.929658i | \(0.620102\pi\) | |||||||
\(662\) | −6.38197 | −0.248042 | ||||||||
\(663\) | 41.9787 | 1.63032 | ||||||||
\(664\) | 13.6180 | 0.528482 | ||||||||
\(665\) | −5.23607 | −0.203046 | ||||||||
\(666\) | 1.41641 | 0.0548847 | ||||||||
\(667\) | −49.5967 | −1.92039 | ||||||||
\(668\) | 20.0000 | 0.773823 | ||||||||
\(669\) | −29.8885 | −1.15556 | ||||||||
\(670\) | −1.23607 | −0.0477535 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.61803 | 0.0624170 | ||||||||
\(673\) | −4.58359 | −0.176684 | −0.0883422 | − | 0.996090i | \(-0.528157\pi\) | ||||
−0.0883422 | + | 0.996090i | \(0.528157\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | −5.47214 | −0.210623 | ||||||||
\(676\) | 18.5623 | 0.713935 | ||||||||
\(677\) | −13.9230 | −0.535104 | −0.267552 | − | 0.963543i | \(-0.586215\pi\) | ||||
−0.267552 | + | 0.963543i | \(0.586215\pi\) | |||||||
\(678\) | −2.47214 | −0.0949418 | ||||||||
\(679\) | −3.38197 | −0.129788 | ||||||||
\(680\) | 4.61803 | 0.177094 | ||||||||
\(681\) | 11.5623 | 0.443069 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.5967 | −1.66818 | −0.834092 | − | 0.551626i | \(-0.814008\pi\) | ||||
−0.834092 | + | 0.551626i | \(0.814008\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 12.4721 | 0.475842 | ||||||||
\(688\) | 3.23607 | 0.123374 | ||||||||
\(689\) | 36.3607 | 1.38523 | ||||||||
\(690\) | 13.7082 | 0.521862 | ||||||||
\(691\) | 2.47214 | 0.0940445 | 0.0470222 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470222 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(692\) | −15.5066 | −0.589472 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.8885 | 0.982716 | ||||||||
\(695\) | 8.94427 | 0.339276 | ||||||||
\(696\) | −9.47214 | −0.359040 | ||||||||
\(697\) | 41.3050 | 1.56454 | ||||||||
\(698\) | −26.9443 | −1.01986 | ||||||||
\(699\) | −26.9443 | −1.01913 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 39.5279 | 1.49295 | 0.746473 | − | 0.665415i | \(-0.231745\pi\) | ||||
0.746473 | + | 0.665415i | \(0.231745\pi\) | |||||||
\(702\) | −30.7426 | −1.16031 | ||||||||
\(703\) | 19.4164 | 0.732304 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.1803 | −0.797698 | ||||||||
\(706\) | −24.4508 | −0.920220 | ||||||||
\(707\) | −5.23607 | −0.196923 | ||||||||
\(708\) | 7.70820 | 0.289692 | ||||||||
\(709\) | 6.96556 | 0.261597 | 0.130799 | − | 0.991409i | \(-0.458246\pi\) | ||||
0.130799 | + | 0.991409i | \(0.458246\pi\) | |||||||
\(710\) | −7.32624 | −0.274949 | ||||||||
\(711\) | 0.326238 | 0.0122349 | ||||||||
\(712\) | 0.291796 | 0.0109355 | ||||||||
\(713\) | 44.3607 | 1.66132 | ||||||||
\(714\) | 7.47214 | 0.279638 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.5623 | −0.731078 | ||||||||
\(717\) | 14.3262 | 0.535023 | ||||||||
\(718\) | 17.9787 | 0.670960 | ||||||||
\(719\) | −32.3607 | −1.20685 | −0.603425 | − | 0.797420i | \(-0.706198\pi\) | ||||
−0.603425 | + | 0.797420i | \(0.706198\pi\) | |||||||
\(720\) | −0.381966 | −0.0142350 | ||||||||
\(721\) | 3.56231 | 0.132667 | ||||||||
\(722\) | 8.41641 | 0.313226 | ||||||||
\(723\) | −6.00000 | −0.223142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.85410 | −0.217416 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.3262 | 1.45853 | 0.729265 | − | 0.684232i | \(-0.239862\pi\) | ||||
0.729265 | + | 0.684232i | \(0.239862\pi\) | |||||||
\(728\) | 5.61803 | 0.208218 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 4.32624 | 0.160121 | ||||||||
\(731\) | 14.9443 | 0.552734 | ||||||||
\(732\) | −18.9443 | −0.700200 | ||||||||
\(733\) | 5.25735 | 0.194185 | 0.0970924 | − | 0.995275i | \(-0.469046\pi\) | ||||
0.0970924 | + | 0.995275i | \(0.469046\pi\) | |||||||
\(734\) | 35.3262 | 1.30392 | ||||||||
\(735\) | 1.61803 | 0.0596821 | ||||||||
\(736\) | 8.47214 | 0.312287 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.41641 | −0.125760 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −3.70820 | −0.136316 | ||||||||
\(741\) | −47.5967 | −1.74851 | ||||||||
\(742\) | 6.47214 | 0.237600 | ||||||||
\(743\) | −19.1246 | −0.701614 | −0.350807 | − | 0.936448i | \(-0.614093\pi\) | ||||
−0.350807 | + | 0.936448i | \(0.614093\pi\) | |||||||
\(744\) | 8.47214 | 0.310604 | ||||||||
\(745\) | 20.8541 | 0.764035 | ||||||||
\(746\) | −2.65248 | −0.0971140 | ||||||||
\(747\) | −5.20163 | −0.190318 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.7639 | −0.393306 | ||||||||
\(750\) | 1.61803 | 0.0590822 | ||||||||
\(751\) | −15.2705 | −0.557229 | −0.278614 | − | 0.960403i | \(-0.589875\pi\) | ||||
−0.278614 | + | 0.960403i | \(0.589875\pi\) | |||||||
\(752\) | −13.0902 | −0.477349 | ||||||||
\(753\) | 1.23607 | 0.0450448 | ||||||||
\(754\) | −32.8885 | −1.19773 | ||||||||
\(755\) | 21.3820 | 0.778169 | ||||||||
\(756\) | −5.47214 | −0.199020 | ||||||||
\(757\) | −12.6525 | −0.459862 | −0.229931 | − | 0.973207i | \(-0.573850\pi\) | ||||
−0.229931 | + | 0.973207i | \(0.573850\pi\) | |||||||
\(758\) | 16.1459 | 0.586445 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.23607 | −0.189932 | ||||||||
\(761\) | 18.5836 | 0.673655 | 0.336827 | − | 0.941566i | \(-0.390646\pi\) | ||||
0.336827 | + | 0.941566i | \(0.390646\pi\) | |||||||
\(762\) | 32.6525 | 1.18287 | ||||||||
\(763\) | 3.52786 | 0.127717 | ||||||||
\(764\) | 0.854102 | 0.0309003 | ||||||||
\(765\) | −1.76393 | −0.0637751 | ||||||||
\(766\) | 8.85410 | 0.319912 | ||||||||
\(767\) | 26.7639 | 0.966390 | ||||||||
\(768\) | 1.61803 | 0.0583858 | ||||||||
\(769\) | −21.7082 | −0.782818 | −0.391409 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391409 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.4721 | −0.773300 | ||||||||
\(772\) | 12.9443 | 0.465875 | ||||||||
\(773\) | 39.5066 | 1.42095 | 0.710476 | − | 0.703721i | \(-0.248479\pi\) | ||||
0.710476 | + | 0.703721i | \(0.248479\pi\) | |||||||
\(774\) | −1.23607 | −0.0444295 | ||||||||
\(775\) | 5.23607 | 0.188085 | ||||||||
\(776\) | −3.38197 | −0.121406 | ||||||||
\(777\) | −6.00000 | −0.215249 | ||||||||
\(778\) | −20.2705 | −0.726733 | ||||||||
\(779\) | −46.8328 | −1.67796 | ||||||||
\(780\) | 9.09017 | 0.325480 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 39.1246 | 1.39909 | ||||||||
\(783\) | 32.0344 | 1.14482 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.0902 | −0.395825 | ||||||||
\(786\) | −18.4721 | −0.658879 | ||||||||
\(787\) | −15.9098 | −0.567124 | −0.283562 | − | 0.958954i | \(-0.591516\pi\) | ||||
−0.283562 | + | 0.958954i | \(0.591516\pi\) | |||||||
\(788\) | −15.4164 | −0.549187 | ||||||||
\(789\) | 23.1246 | 0.823258 | ||||||||
\(790\) | −0.854102 | −0.0303876 | ||||||||
\(791\) | −1.52786 | −0.0543246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.7771 | −2.33581 | ||||||||
\(794\) | −30.5623 | −1.08462 | ||||||||
\(795\) | 10.4721 | 0.371408 | ||||||||
\(796\) | −10.9443 | −0.387909 | ||||||||
\(797\) | −32.6738 | −1.15736 | −0.578682 | − | 0.815553i | \(-0.696433\pi\) | ||||
−0.578682 | + | 0.815553i | \(0.696433\pi\) | |||||||
\(798\) | −8.47214 | −0.299910 | ||||||||
\(799\) | −60.4508 | −2.13860 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −0.111456 | −0.00393811 | ||||||||
\(802\) | −36.6180 | −1.29303 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | 8.47214 | 0.298604 | ||||||||
\(806\) | 29.4164 | 1.03615 | ||||||||
\(807\) | 31.8885 | 1.12253 | ||||||||
\(808\) | −5.23607 | −0.184204 | ||||||||
\(809\) | −27.6869 | −0.973420 | −0.486710 | − | 0.873564i | \(-0.661803\pi\) | ||||
−0.486710 | + | 0.873564i | \(0.661803\pi\) | |||||||
\(810\) | −7.70820 | −0.270839 | ||||||||
\(811\) | −18.1115 | −0.635979 | −0.317990 | − | 0.948094i | \(-0.603008\pi\) | ||||
−0.317990 | + | 0.948094i | \(0.603008\pi\) | |||||||
\(812\) | −5.85410 | −0.205439 | ||||||||
\(813\) | 24.4721 | 0.858275 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.6525 | −0.513254 | ||||||||
\(816\) | 7.47214 | 0.261577 | ||||||||
\(817\) | −16.9443 | −0.592805 | ||||||||
\(818\) | 5.23607 | 0.183075 | ||||||||
\(819\) | −2.14590 | −0.0749837 | ||||||||
\(820\) | 8.94427 | 0.312348 | ||||||||
\(821\) | 14.2148 | 0.496099 | 0.248050 | − | 0.968747i | \(-0.420210\pi\) | ||||
0.248050 | + | 0.968747i | \(0.420210\pi\) | |||||||
\(822\) | −25.8885 | −0.902967 | ||||||||
\(823\) | −40.3607 | −1.40688 | −0.703442 | − | 0.710752i | \(-0.748355\pi\) | ||||
−0.703442 | + | 0.710752i | \(0.748355\pi\) | |||||||
\(824\) | 3.56231 | 0.124099 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.76393 | 0.165758 | ||||||||
\(827\) | −32.9443 | −1.14558 | −0.572792 | − | 0.819701i | \(-0.694140\pi\) | ||||
−0.572792 | + | 0.819701i | \(0.694140\pi\) | |||||||
\(828\) | −3.23607 | −0.112461 | ||||||||
\(829\) | 29.8885 | 1.03807 | 0.519036 | − | 0.854752i | \(-0.326291\pi\) | ||||
0.519036 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(830\) | 13.6180 | 0.472689 | ||||||||
\(831\) | 21.7082 | 0.753049 | ||||||||
\(832\) | 5.61803 | 0.194770 | ||||||||
\(833\) | 4.61803 | 0.160005 | ||||||||
\(834\) | 14.4721 | 0.501129 | ||||||||
\(835\) | 20.0000 | 0.692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.6525 | −0.990374 | ||||||||
\(838\) | 6.94427 | 0.239886 | ||||||||
\(839\) | −0.360680 | −0.0124520 | −0.00622602 | − | 0.999981i | \(-0.501982\pi\) | ||||
−0.00622602 | + | 0.999981i | \(0.501982\pi\) | |||||||
\(840\) | 1.61803 | 0.0558275 | ||||||||
\(841\) | 5.27051 | 0.181742 | ||||||||
\(842\) | −11.3262 | −0.390328 | ||||||||
\(843\) | 29.7082 | 1.02320 | ||||||||
\(844\) | 15.3262 | 0.527551 | ||||||||
\(845\) | 18.5623 | 0.638563 | ||||||||
\(846\) | 5.00000 | 0.171904 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.47214 | 0.222254 | ||||||||
\(849\) | −23.1803 | −0.795547 | ||||||||
\(850\) | 4.61803 | 0.158397 | ||||||||
\(851\) | −31.4164 | −1.07694 | ||||||||
\(852\) | −11.8541 | −0.406115 | ||||||||
\(853\) | 8.27051 | 0.283177 | 0.141588 | − | 0.989926i | \(-0.454779\pi\) | ||||
0.141588 | + | 0.989926i | \(0.454779\pi\) | |||||||
\(854\) | −11.7082 | −0.400646 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | −10.7639 | −0.367904 | ||||||||
\(857\) | 33.4164 | 1.14148 | 0.570741 | − | 0.821130i | \(-0.306656\pi\) | ||||
0.570741 | + | 0.821130i | \(0.306656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.4164 | 1.89078 | 0.945392 | − | 0.325936i | \(-0.105680\pi\) | ||||
0.945392 | + | 0.325936i | \(0.105680\pi\) | |||||||
\(860\) | 3.23607 | 0.110349 | ||||||||
\(861\) | 14.4721 | 0.493209 | ||||||||
\(862\) | −15.5623 | −0.530054 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −5.47214 | −0.186166 | ||||||||
\(865\) | −15.5066 | −0.527239 | ||||||||
\(866\) | 4.09017 | 0.138990 | ||||||||
\(867\) | 7.00000 | 0.237732 | ||||||||
\(868\) | 5.23607 | 0.177724 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9.47214 | −0.321135 | ||||||||
\(871\) | −6.94427 | −0.235298 | ||||||||
\(872\) | 3.52786 | 0.119469 | ||||||||
\(873\) | 1.29180 | 0.0437207 | ||||||||
\(874\) | −44.3607 | −1.50052 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 7.00000 | 0.236508 | ||||||||
\(877\) | 26.5410 | 0.896227 | 0.448113 | − | 0.893977i | \(-0.352096\pi\) | ||||
0.448113 | + | 0.893977i | \(0.352096\pi\) | |||||||
\(878\) | −10.6525 | −0.359504 | ||||||||
\(879\) | −41.1246 | −1.38710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4853 | 1.26291 | 0.631456 | − | 0.775412i | \(-0.282458\pi\) | ||||
0.631456 | + | 0.775412i | \(0.282458\pi\) | |||||||
\(882\) | −0.381966 | −0.0128615 | ||||||||
\(883\) | −43.2361 | −1.45501 | −0.727505 | − | 0.686103i | \(-0.759320\pi\) | ||||
−0.727505 | + | 0.686103i | \(0.759320\pi\) | |||||||
\(884\) | 25.9443 | 0.872600 | ||||||||
\(885\) | 7.70820 | 0.259108 | ||||||||
\(886\) | −15.2361 | −0.511866 | ||||||||
\(887\) | 35.8541 | 1.20386 | 0.601931 | − | 0.798548i | \(-0.294398\pi\) | ||||
0.601931 | + | 0.798548i | \(0.294398\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | 20.1803 | 0.676827 | ||||||||
\(890\) | 0.291796 | 0.00978103 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.4721 | −0.618493 | ||||||||
\(893\) | 68.5410 | 2.29364 | ||||||||
\(894\) | 33.7426 | 1.12852 | ||||||||
\(895\) | −19.5623 | −0.653896 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 77.0132 | 2.57139 | ||||||||
\(898\) | −19.5066 | −0.650943 | ||||||||
\(899\) | −30.6525 | −1.02232 | ||||||||
\(900\) | −0.381966 | −0.0127322 | ||||||||
\(901\) | 29.8885 | 0.995732 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.23607 | 0.174245 | ||||||||
\(904\) | −1.52786 | −0.0508160 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.5967 | 1.14940 | ||||||||
\(907\) | −30.3607 | −1.00811 | −0.504055 | − | 0.863672i | \(-0.668159\pi\) | ||||
−0.504055 | + | 0.863672i | \(0.668159\pi\) | |||||||
\(908\) | 7.14590 | 0.237145 | ||||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 5.61803 | 0.186236 | ||||||||
\(911\) | 17.4508 | 0.578172 | 0.289086 | − | 0.957303i | \(-0.406649\pi\) | ||||
0.289086 | + | 0.957303i | \(0.406649\pi\) | |||||||
\(912\) | −8.47214 | −0.280540 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −14.0000 | −0.463079 | ||||||||
\(915\) | −18.9443 | −0.626278 | ||||||||
\(916\) | 7.70820 | 0.254686 | ||||||||
\(917\) | −11.4164 | −0.377003 | ||||||||
\(918\) | −25.2705 | −0.834051 | ||||||||
\(919\) | 52.5066 | 1.73203 | 0.866016 | − | 0.500016i | \(-0.166673\pi\) | ||||
0.866016 | + | 0.500016i | \(0.166673\pi\) | |||||||
\(920\) | 8.47214 | 0.279318 | ||||||||
\(921\) | −54.1246 | −1.78347 | ||||||||
\(922\) | 25.1246 | 0.827435 | ||||||||
\(923\) | −41.1591 | −1.35477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.70820 | −0.121925 | ||||||||
\(926\) | −14.1803 | −0.465995 | ||||||||
\(927\) | −1.36068 | −0.0446906 | ||||||||
\(928\) | −5.85410 | −0.192170 | ||||||||
\(929\) | 27.7771 | 0.911337 | 0.455668 | − | 0.890150i | \(-0.349400\pi\) | ||||
0.455668 | + | 0.890150i | \(0.349400\pi\) | |||||||
\(930\) | 8.47214 | 0.277812 | ||||||||
\(931\) | −5.23607 | −0.171605 | ||||||||
\(932\) | −16.6525 | −0.545470 | ||||||||
\(933\) | 16.4721 | 0.539274 | ||||||||
\(934\) | 21.6180 | 0.707364 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.14590 | −0.0701409 | ||||||||
\(937\) | −37.3951 | −1.22165 | −0.610823 | − | 0.791767i | \(-0.709161\pi\) | ||||
−0.610823 | + | 0.791767i | \(0.709161\pi\) | |||||||
\(938\) | −1.23607 | −0.0403591 | ||||||||
\(939\) | 19.2361 | 0.627745 | ||||||||
\(940\) | −13.0902 | −0.426954 | ||||||||
\(941\) | 42.6525 | 1.39043 | 0.695215 | − | 0.718801i | \(-0.255309\pi\) | ||||
0.695215 | + | 0.718801i | \(0.255309\pi\) | |||||||
\(942\) | −17.9443 | −0.584656 | ||||||||
\(943\) | 75.7771 | 2.46764 | ||||||||
\(944\) | 4.76393 | 0.155053 | ||||||||
\(945\) | −5.47214 | −0.178009 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.6525 | 1.06106 | 0.530531 | − | 0.847665i | \(-0.321992\pi\) | ||||
0.530531 | + | 0.847665i | \(0.321992\pi\) | |||||||
\(948\) | −1.38197 | −0.0448842 | ||||||||
\(949\) | 24.3050 | 0.788972 | ||||||||
\(950\) | −5.23607 | −0.169880 | ||||||||
\(951\) | 28.9443 | 0.938582 | ||||||||
\(952\) | 4.61803 | 0.149671 | ||||||||
\(953\) | 2.58359 | 0.0836908 | 0.0418454 | − | 0.999124i | \(-0.486676\pi\) | ||||
0.0418454 | + | 0.999124i | \(0.486676\pi\) | |||||||
\(954\) | −2.47214 | −0.0800384 | ||||||||
\(955\) | 0.854102 | 0.0276381 | ||||||||
\(956\) | 8.85410 | 0.286362 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.1246 | −1.13482 | ||||||||
\(959\) | −16.0000 | −0.516667 | ||||||||
\(960\) | 1.61803 | 0.0522218 | ||||||||
\(961\) | −3.58359 | −0.115600 | ||||||||
\(962\) | −20.8328 | −0.671677 | ||||||||
\(963\) | 4.11146 | 0.132490 | ||||||||
\(964\) | −3.70820 | −0.119433 | ||||||||
\(965\) | 12.9443 | 0.416691 | ||||||||
\(966\) | 13.7082 | 0.441054 | ||||||||
\(967\) | −4.29180 | −0.138015 | −0.0690074 | − | 0.997616i | \(-0.521983\pi\) | ||||
−0.0690074 | + | 0.997616i | \(0.521983\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.1246 | −1.25686 | ||||||||
\(970\) | −3.38197 | −0.108588 | ||||||||
\(971\) | 42.3607 | 1.35942 | 0.679709 | − | 0.733481i | \(-0.262106\pi\) | ||||
0.679709 | + | 0.733481i | \(0.262106\pi\) | |||||||
\(972\) | 3.94427 | 0.126513 | ||||||||
\(973\) | 8.94427 | 0.286740 | ||||||||
\(974\) | 11.8197 | 0.378726 | ||||||||
\(975\) | 9.09017 | 0.291118 | ||||||||
\(976\) | −11.7082 | −0.374770 | ||||||||
\(977\) | 52.9017 | 1.69248 | 0.846238 | − | 0.532806i | \(-0.178862\pi\) | ||||
0.846238 | + | 0.532806i | \(0.178862\pi\) | |||||||
\(978\) | −23.7082 | −0.758105 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −1.34752 | −0.0430231 | ||||||||
\(982\) | 0.944272 | 0.0301329 | ||||||||
\(983\) | −30.0344 | −0.957950 | −0.478975 | − | 0.877829i | \(-0.658992\pi\) | ||||
−0.478975 | + | 0.877829i | \(0.658992\pi\) | |||||||
\(984\) | 14.4721 | 0.461355 | ||||||||
\(985\) | −15.4164 | −0.491208 | ||||||||
\(986\) | −27.0344 | −0.860952 | ||||||||
\(987\) | −21.1803 | −0.674178 | ||||||||
\(988\) | −29.4164 | −0.935861 | ||||||||
\(989\) | 27.4164 | 0.871791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9230 | 0.346980 | 0.173490 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173490 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(992\) | 5.23607 | 0.166245 | ||||||||
\(993\) | −10.3262 | −0.327693 | ||||||||
\(994\) | −7.32624 | −0.232374 | ||||||||
\(995\) | −10.9443 | −0.346957 | ||||||||
\(996\) | 22.0344 | 0.698188 | ||||||||
\(997\) | 17.5623 | 0.556204 | 0.278102 | − | 0.960552i | \(-0.410295\pi\) | ||||
0.278102 | + | 0.960552i | \(0.410295\pi\) | |||||||
\(998\) | −24.7984 | −0.784979 | ||||||||
\(999\) | 20.2918 | 0.642004 |
(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.cc.1.2 | 2 | ||
11.3 | even | 5 | 770.2.n.a.141.1 | yes | 4 | ||
11.4 | even | 5 | 770.2.n.a.71.1 | ✓ | 4 | ||
11.10 | odd | 2 | 8470.2.a.bq.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.a.71.1 | ✓ | 4 | 11.4 | even | 5 | ||
770.2.n.a.141.1 | yes | 4 | 11.3 | even | 5 | ||
8470.2.a.bq.1.2 | 2 | 11.10 | odd | 2 | |||
8470.2.a.cc.1.2 | 2 | 1.1 | even | 1 | trivial |