Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.38197 | −0.522334 | −0.261167 | − | 0.965294i | \(-0.584107\pi\) | ||||
−0.261167 | + | 0.965294i | \(0.584107\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.85410 | −1.34629 | −0.673143 | − | 0.739512i | \(-0.735056\pi\) | ||||
−0.673143 | + | 0.739512i | \(0.735056\pi\) | |||||||
\(14\) | −1.38197 | −0.369346 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.47214 | 1.56972 | 0.784862 | − | 0.619671i | \(-0.212734\pi\) | ||||
0.784862 | + | 0.619671i | \(0.212734\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.85410 | −1.11361 | −0.556804 | − | 0.830644i | \(-0.687972\pi\) | ||||
−0.556804 | + | 0.830644i | \(0.687972\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.38197 | 0.301570 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.61803 | −1.79698 | −0.898492 | − | 0.438990i | \(-0.855336\pi\) | ||||
−0.898492 | + | 0.438990i | \(0.855336\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.85410 | −0.951968 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.38197 | −0.261167 | ||||||||
\(29\) | 7.23607 | 1.34370 | 0.671852 | − | 0.740685i | \(-0.265499\pi\) | ||||
0.671852 | + | 0.740685i | \(0.265499\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −7.23607 | −1.29964 | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||||
−0.649818 | + | 0.760090i | \(0.725155\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | −1.38197 | −0.233595 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.14590 | −0.517182 | −0.258591 | − | 0.965987i | \(-0.583258\pi\) | ||||
−0.258591 | + | 0.965987i | \(0.583258\pi\) | |||||||
\(38\) | −4.85410 | −0.787439 | ||||||||
\(39\) | 4.85410 | 0.777278 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.09017 | −0.170256 | −0.0851280 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851280 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(42\) | 1.38197 | 0.213242 | ||||||||
\(43\) | 1.23607 | 0.188499 | 0.0942493 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942493 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −8.61803 | −1.27066 | ||||||||
\(47\) | 11.7984 | 1.72097 | 0.860485 | − | 0.509476i | \(-0.170161\pi\) | ||||
0.860485 | + | 0.509476i | \(0.170161\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.09017 | −0.727167 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | −4.85410 | −0.673143 | ||||||||
\(53\) | −13.0902 | −1.79807 | −0.899037 | − | 0.437874i | \(-0.855732\pi\) | ||||
−0.899037 | + | 0.437874i | \(0.855732\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.38197 | −0.184673 | ||||||||
\(57\) | 4.85410 | 0.642942 | ||||||||
\(58\) | 7.23607 | 0.950142 | ||||||||
\(59\) | −9.32624 | −1.21417 | −0.607086 | − | 0.794636i | \(-0.707662\pi\) | ||||
−0.607086 | + | 0.794636i | \(0.707662\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −3.70820 | −0.474787 | −0.237393 | − | 0.971414i | \(-0.576293\pi\) | ||||
−0.237393 | + | 0.971414i | \(0.576293\pi\) | |||||||
\(62\) | −7.23607 | −0.918982 | ||||||||
\(63\) | −1.38197 | −0.174111 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.85410 | −0.602077 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.7082 | −1.91906 | −0.959531 | − | 0.281602i | \(-0.909134\pi\) | ||||
−0.959531 | + | 0.281602i | \(0.909134\pi\) | |||||||
\(68\) | 6.47214 | 0.784862 | ||||||||
\(69\) | 8.61803 | 1.03749 | ||||||||
\(70\) | −1.38197 | −0.165177 | ||||||||
\(71\) | 8.18034 | 0.970828 | 0.485414 | − | 0.874284i | \(-0.338669\pi\) | ||||
0.485414 | + | 0.874284i | \(0.338669\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −3.14590 | −0.365703 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −4.85410 | −0.556804 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.85410 | 0.549619 | ||||||||
\(79\) | −3.52786 | −0.396916 | −0.198458 | − | 0.980109i | \(-0.563593\pi\) | ||||
−0.198458 | + | 0.980109i | \(0.563593\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.09017 | −0.120389 | ||||||||
\(83\) | −6.47214 | −0.710409 | −0.355205 | − | 0.934789i | \(-0.615589\pi\) | ||||
−0.355205 | + | 0.934789i | \(0.615589\pi\) | |||||||
\(84\) | 1.38197 | 0.150785 | ||||||||
\(85\) | 6.47214 | 0.702002 | ||||||||
\(86\) | 1.23607 | 0.133289 | ||||||||
\(87\) | −7.23607 | −0.775788 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.5623 | 1.22560 | 0.612801 | − | 0.790237i | \(-0.290043\pi\) | ||||
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 6.70820 | 0.703211 | ||||||||
\(92\) | −8.61803 | −0.898492 | ||||||||
\(93\) | 7.23607 | 0.750345 | ||||||||
\(94\) | 11.7984 | 1.21691 | ||||||||
\(95\) | −4.85410 | −0.498020 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −5.09017 | −0.514185 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.41641 | 0.737960 | 0.368980 | − | 0.929437i | \(-0.379707\pi\) | ||||
0.368980 | + | 0.929437i | \(0.379707\pi\) | |||||||
\(102\) | −6.47214 | −0.640837 | ||||||||
\(103\) | −4.85410 | −0.478289 | −0.239144 | − | 0.970984i | \(-0.576867\pi\) | ||||
−0.239144 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(104\) | −4.85410 | −0.475984 | ||||||||
\(105\) | 1.38197 | 0.134866 | ||||||||
\(106\) | −13.0902 | −1.27143 | ||||||||
\(107\) | 1.52786 | 0.147704 | 0.0738521 | − | 0.997269i | \(-0.476471\pi\) | ||||
0.0738521 | + | 0.997269i | \(0.476471\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.41641 | 0.710363 | 0.355182 | − | 0.934797i | \(-0.384419\pi\) | ||||
0.355182 | + | 0.934797i | \(0.384419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.14590 | 0.298595 | ||||||||
\(112\) | −1.38197 | −0.130584 | ||||||||
\(113\) | −3.52786 | −0.331874 | −0.165937 | − | 0.986136i | \(-0.553065\pi\) | ||||
−0.165937 | + | 0.986136i | \(0.553065\pi\) | |||||||
\(114\) | 4.85410 | 0.454628 | ||||||||
\(115\) | −8.61803 | −0.803636 | ||||||||
\(116\) | 7.23607 | 0.671852 | ||||||||
\(117\) | −4.85410 | −0.448762 | ||||||||
\(118\) | −9.32624 | −0.858550 | ||||||||
\(119\) | −8.94427 | −0.819920 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.70820 | −0.335725 | ||||||||
\(123\) | 1.09017 | 0.0982973 | ||||||||
\(124\) | −7.23607 | −0.649818 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.38197 | −0.123115 | ||||||||
\(127\) | 10.5623 | 0.937253 | 0.468627 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468627 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.23607 | −0.108830 | ||||||||
\(130\) | −4.85410 | −0.425733 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.70820 | 0.581675 | ||||||||
\(134\) | −15.7082 | −1.35698 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 6.47214 | 0.554981 | ||||||||
\(137\) | −19.4164 | −1.65886 | −0.829428 | − | 0.558614i | \(-0.811333\pi\) | ||||
−0.829428 | + | 0.558614i | \(0.811333\pi\) | |||||||
\(138\) | 8.61803 | 0.733616 | ||||||||
\(139\) | −20.7984 | −1.76410 | −0.882048 | − | 0.471160i | \(-0.843835\pi\) | ||||
−0.882048 | + | 0.471160i | \(0.843835\pi\) | |||||||
\(140\) | −1.38197 | −0.116797 | ||||||||
\(141\) | −11.7984 | −0.993602 | ||||||||
\(142\) | 8.18034 | 0.686479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.23607 | 0.600923 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 5.09017 | 0.419830 | ||||||||
\(148\) | −3.14590 | −0.258591 | ||||||||
\(149\) | −2.47214 | −0.202525 | −0.101263 | − | 0.994860i | \(-0.532288\pi\) | ||||
−0.101263 | + | 0.994860i | \(0.532288\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −11.5279 | −0.938124 | −0.469062 | − | 0.883165i | \(-0.655408\pi\) | ||||
−0.469062 | + | 0.883165i | \(0.655408\pi\) | |||||||
\(152\) | −4.85410 | −0.393720 | ||||||||
\(153\) | 6.47214 | 0.523241 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.23607 | −0.581215 | ||||||||
\(156\) | 4.85410 | 0.388639 | ||||||||
\(157\) | −2.14590 | −0.171261 | −0.0856307 | − | 0.996327i | \(-0.527291\pi\) | ||||
−0.0856307 | + | 0.996327i | \(0.527291\pi\) | |||||||
\(158\) | −3.52786 | −0.280662 | ||||||||
\(159\) | 13.0902 | 1.03812 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.9098 | 0.938626 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −3.41641 | −0.267594 | −0.133797 | − | 0.991009i | \(-0.542717\pi\) | ||||
−0.133797 | + | 0.991009i | \(0.542717\pi\) | |||||||
\(164\) | −1.09017 | −0.0851280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.47214 | −0.502335 | ||||||||
\(167\) | −23.0344 | −1.78246 | −0.891229 | − | 0.453553i | \(-0.850156\pi\) | ||||
−0.891229 | + | 0.453553i | \(0.850156\pi\) | |||||||
\(168\) | 1.38197 | 0.106621 | ||||||||
\(169\) | 10.5623 | 0.812485 | ||||||||
\(170\) | 6.47214 | 0.496390 | ||||||||
\(171\) | −4.85410 | −0.371202 | ||||||||
\(172\) | 1.23607 | 0.0942493 | ||||||||
\(173\) | −14.6180 | −1.11139 | −0.555694 | − | 0.831387i | \(-0.687547\pi\) | ||||
−0.555694 | + | 0.831387i | \(0.687547\pi\) | |||||||
\(174\) | −7.23607 | −0.548565 | ||||||||
\(175\) | −1.38197 | −0.104467 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.32624 | 0.701003 | ||||||||
\(178\) | 11.5623 | 0.866631 | ||||||||
\(179\) | 11.0902 | 0.828918 | 0.414459 | − | 0.910068i | \(-0.363971\pi\) | ||||
0.414459 | + | 0.910068i | \(0.363971\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 6.70820 | 0.497245 | ||||||||
\(183\) | 3.70820 | 0.274118 | ||||||||
\(184\) | −8.61803 | −0.635330 | ||||||||
\(185\) | −3.14590 | −0.231291 | ||||||||
\(186\) | 7.23607 | 0.530574 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.7984 | 0.860485 | ||||||||
\(189\) | 1.38197 | 0.100523 | ||||||||
\(190\) | −4.85410 | −0.352154 | ||||||||
\(191\) | −6.18034 | −0.447194 | −0.223597 | − | 0.974682i | \(-0.571780\pi\) | ||||
−0.223597 | + | 0.974682i | \(0.571780\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −1.70820 | −0.122959 | −0.0614796 | − | 0.998108i | \(-0.519582\pi\) | ||||
−0.0614796 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 4.85410 | 0.347609 | ||||||||
\(196\) | −5.09017 | −0.363584 | ||||||||
\(197\) | 14.6180 | 1.04149 | 0.520746 | − | 0.853712i | \(-0.325654\pi\) | ||||
0.520746 | + | 0.853712i | \(0.325654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.47214 | 0.175245 | 0.0876225 | − | 0.996154i | \(-0.472073\pi\) | ||||
0.0876225 | + | 0.996154i | \(0.472073\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.7082 | 1.10797 | ||||||||
\(202\) | 7.41641 | 0.521817 | ||||||||
\(203\) | −10.0000 | −0.701862 | ||||||||
\(204\) | −6.47214 | −0.453140 | ||||||||
\(205\) | −1.09017 | −0.0761408 | ||||||||
\(206\) | −4.85410 | −0.338201 | ||||||||
\(207\) | −8.61803 | −0.598995 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.38197 | 0.0953647 | ||||||||
\(211\) | 14.4721 | 0.996303 | 0.498151 | − | 0.867090i | \(-0.334012\pi\) | ||||
0.498151 | + | 0.867090i | \(0.334012\pi\) | |||||||
\(212\) | −13.0902 | −0.899037 | ||||||||
\(213\) | −8.18034 | −0.560508 | ||||||||
\(214\) | 1.52786 | 0.104443 | ||||||||
\(215\) | 1.23607 | 0.0842991 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 7.41641 | 0.502303 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.4164 | −2.11330 | ||||||||
\(222\) | 3.14590 | 0.211139 | ||||||||
\(223\) | −8.43769 | −0.565030 | −0.282515 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282515 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(224\) | −1.38197 | −0.0923365 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.52786 | −0.234670 | ||||||||
\(227\) | 15.7082 | 1.04259 | 0.521295 | − | 0.853377i | \(-0.325449\pi\) | ||||
0.521295 | + | 0.853377i | \(0.325449\pi\) | |||||||
\(228\) | 4.85410 | 0.321471 | ||||||||
\(229\) | 5.05573 | 0.334092 | 0.167046 | − | 0.985949i | \(-0.446577\pi\) | ||||
0.167046 | + | 0.985949i | \(0.446577\pi\) | |||||||
\(230\) | −8.61803 | −0.568256 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.23607 | 0.475071 | ||||||||
\(233\) | −3.23607 | −0.212002 | −0.106001 | − | 0.994366i | \(-0.533805\pi\) | ||||
−0.106001 | + | 0.994366i | \(0.533805\pi\) | |||||||
\(234\) | −4.85410 | −0.317323 | ||||||||
\(235\) | 11.7984 | 0.769641 | ||||||||
\(236\) | −9.32624 | −0.607086 | ||||||||
\(237\) | 3.52786 | 0.229159 | ||||||||
\(238\) | −8.94427 | −0.579771 | ||||||||
\(239\) | 12.1803 | 0.787881 | 0.393940 | − | 0.919136i | \(-0.371112\pi\) | ||||
0.393940 | + | 0.919136i | \(0.371112\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 5.56231 | 0.358300 | 0.179150 | − | 0.983822i | \(-0.442665\pi\) | ||||
0.179150 | + | 0.983822i | \(0.442665\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.70820 | −0.237393 | ||||||||
\(245\) | −5.09017 | −0.325199 | ||||||||
\(246\) | 1.09017 | 0.0695067 | ||||||||
\(247\) | 23.5623 | 1.49923 | ||||||||
\(248\) | −7.23607 | −0.459491 | ||||||||
\(249\) | 6.47214 | 0.410155 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −3.67376 | −0.231886 | −0.115943 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115943 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(252\) | −1.38197 | −0.0870557 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.5623 | 0.662738 | ||||||||
\(255\) | −6.47214 | −0.405301 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5279 | −1.21811 | −0.609057 | − | 0.793126i | \(-0.708452\pi\) | ||||
−0.609057 | + | 0.793126i | \(0.708452\pi\) | |||||||
\(258\) | −1.23607 | −0.0769542 | ||||||||
\(259\) | 4.34752 | 0.270142 | ||||||||
\(260\) | −4.85410 | −0.301039 | ||||||||
\(261\) | 7.23607 | 0.447901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.381966 | 0.0235530 | 0.0117765 | − | 0.999931i | \(-0.496251\pi\) | ||||
0.0117765 | + | 0.999931i | \(0.496251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.0902 | −0.804123 | ||||||||
\(266\) | 6.70820 | 0.411306 | ||||||||
\(267\) | −11.5623 | −0.707602 | ||||||||
\(268\) | −15.7082 | −0.959531 | ||||||||
\(269\) | −21.5967 | −1.31678 | −0.658388 | − | 0.752678i | \(-0.728762\pi\) | ||||
−0.658388 | + | 0.752678i | \(0.728762\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −6.29180 | −0.382199 | −0.191100 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191100 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(272\) | 6.47214 | 0.392431 | ||||||||
\(273\) | −6.70820 | −0.405999 | ||||||||
\(274\) | −19.4164 | −1.17299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.61803 | 0.518745 | ||||||||
\(277\) | −11.7426 | −0.705547 | −0.352774 | − | 0.935709i | \(-0.614761\pi\) | ||||
−0.352774 | + | 0.935709i | \(0.614761\pi\) | |||||||
\(278\) | −20.7984 | −1.24740 | ||||||||
\(279\) | −7.23607 | −0.433212 | ||||||||
\(280\) | −1.38197 | −0.0825883 | ||||||||
\(281\) | 26.9443 | 1.60736 | 0.803680 | − | 0.595061i | \(-0.202872\pi\) | ||||
0.803680 | + | 0.595061i | \(0.202872\pi\) | |||||||
\(282\) | −11.7984 | −0.702583 | ||||||||
\(283\) | −17.1246 | −1.01795 | −0.508976 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508976 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(284\) | 8.18034 | 0.485414 | ||||||||
\(285\) | 4.85410 | 0.287532 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50658 | 0.0889305 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 7.23607 | 0.424917 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | −10.9098 | −0.637359 | −0.318680 | − | 0.947863i | \(-0.603239\pi\) | ||||
−0.318680 | + | 0.947863i | \(0.603239\pi\) | |||||||
\(294\) | 5.09017 | 0.296865 | ||||||||
\(295\) | −9.32624 | −0.542995 | ||||||||
\(296\) | −3.14590 | −0.182852 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.47214 | −0.143207 | ||||||||
\(299\) | 41.8328 | 2.41925 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −1.70820 | −0.0984592 | ||||||||
\(302\) | −11.5279 | −0.663354 | ||||||||
\(303\) | −7.41641 | −0.426061 | ||||||||
\(304\) | −4.85410 | −0.278402 | ||||||||
\(305\) | −3.70820 | −0.212331 | ||||||||
\(306\) | 6.47214 | 0.369987 | ||||||||
\(307\) | 26.8328 | 1.53143 | 0.765715 | − | 0.643180i | \(-0.222385\pi\) | ||||
0.765715 | + | 0.643180i | \(0.222385\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.85410 | 0.276140 | ||||||||
\(310\) | −7.23607 | −0.410981 | ||||||||
\(311\) | 11.8885 | 0.674137 | 0.337069 | − | 0.941480i | \(-0.390565\pi\) | ||||
0.337069 | + | 0.941480i | \(0.390565\pi\) | |||||||
\(312\) | 4.85410 | 0.274809 | ||||||||
\(313\) | −7.70820 | −0.435693 | −0.217847 | − | 0.975983i | \(-0.569903\pi\) | ||||
−0.217847 | + | 0.975983i | \(0.569903\pi\) | |||||||
\(314\) | −2.14590 | −0.121100 | ||||||||
\(315\) | −1.38197 | −0.0778650 | ||||||||
\(316\) | −3.52786 | −0.198458 | ||||||||
\(317\) | −22.0902 | −1.24071 | −0.620354 | − | 0.784322i | \(-0.713011\pi\) | ||||
−0.620354 | + | 0.784322i | \(0.713011\pi\) | |||||||
\(318\) | 13.0902 | 0.734060 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.52786 | −0.0852771 | ||||||||
\(322\) | 11.9098 | 0.663709 | ||||||||
\(323\) | −31.4164 | −1.74806 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.85410 | −0.269257 | ||||||||
\(326\) | −3.41641 | −0.189217 | ||||||||
\(327\) | −7.41641 | −0.410128 | ||||||||
\(328\) | −1.09017 | −0.0601946 | ||||||||
\(329\) | −16.3050 | −0.898921 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8541 | 0.926385 | 0.463193 | − | 0.886258i | \(-0.346704\pi\) | ||||
0.463193 | + | 0.886258i | \(0.346704\pi\) | |||||||
\(332\) | −6.47214 | −0.355205 | ||||||||
\(333\) | −3.14590 | −0.172394 | ||||||||
\(334\) | −23.0344 | −1.26039 | ||||||||
\(335\) | −15.7082 | −0.858231 | ||||||||
\(336\) | 1.38197 | 0.0753924 | ||||||||
\(337\) | −3.41641 | −0.186104 | −0.0930518 | − | 0.995661i | \(-0.529662\pi\) | ||||
−0.0930518 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(338\) | 10.5623 | 0.574514 | ||||||||
\(339\) | 3.52786 | 0.191607 | ||||||||
\(340\) | 6.47214 | 0.351001 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.85410 | −0.262480 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 1.23607 | 0.0666443 | ||||||||
\(345\) | 8.61803 | 0.463979 | ||||||||
\(346\) | −14.6180 | −0.785870 | ||||||||
\(347\) | 3.70820 | 0.199067 | 0.0995334 | − | 0.995034i | \(-0.468265\pi\) | ||||
0.0995334 | + | 0.995034i | \(0.468265\pi\) | |||||||
\(348\) | −7.23607 | −0.387894 | ||||||||
\(349\) | −13.4164 | −0.718164 | −0.359082 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359082 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(350\) | −1.38197 | −0.0738692 | ||||||||
\(351\) | 4.85410 | 0.259093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.23607 | 0.172239 | 0.0861193 | − | 0.996285i | \(-0.472553\pi\) | ||||
0.0861193 | + | 0.996285i | \(0.472553\pi\) | |||||||
\(354\) | 9.32624 | 0.495684 | ||||||||
\(355\) | 8.18034 | 0.434167 | ||||||||
\(356\) | 11.5623 | 0.612801 | ||||||||
\(357\) | 8.94427 | 0.473381 | ||||||||
\(358\) | 11.0902 | 0.586134 | ||||||||
\(359\) | 24.7639 | 1.30699 | 0.653495 | − | 0.756931i | \(-0.273302\pi\) | ||||
0.653495 | + | 0.756931i | \(0.273302\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 4.56231 | 0.240121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.70820 | 0.351605 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 3.70820 | 0.193831 | ||||||||
\(367\) | 8.58359 | 0.448060 | 0.224030 | − | 0.974582i | \(-0.428079\pi\) | ||||
0.224030 | + | 0.974582i | \(0.428079\pi\) | |||||||
\(368\) | −8.61803 | −0.449246 | ||||||||
\(369\) | −1.09017 | −0.0567520 | ||||||||
\(370\) | −3.14590 | −0.163547 | ||||||||
\(371\) | 18.0902 | 0.939195 | ||||||||
\(372\) | 7.23607 | 0.375173 | ||||||||
\(373\) | 34.5623 | 1.78957 | 0.894784 | − | 0.446499i | \(-0.147329\pi\) | ||||
0.894784 | + | 0.446499i | \(0.147329\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 11.7984 | 0.608455 | ||||||||
\(377\) | −35.1246 | −1.80901 | ||||||||
\(378\) | 1.38197 | 0.0710807 | ||||||||
\(379\) | −4.50658 | −0.231487 | −0.115744 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115744 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(380\) | −4.85410 | −0.249010 | ||||||||
\(381\) | −10.5623 | −0.541123 | ||||||||
\(382\) | −6.18034 | −0.316214 | ||||||||
\(383\) | 15.7426 | 0.804412 | 0.402206 | − | 0.915549i | \(-0.368244\pi\) | ||||
0.402206 | + | 0.915549i | \(0.368244\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.70820 | −0.0869453 | ||||||||
\(387\) | 1.23607 | 0.0628329 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 4.85410 | 0.245797 | ||||||||
\(391\) | −55.7771 | −2.82077 | ||||||||
\(392\) | −5.09017 | −0.257092 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.6180 | 0.736446 | ||||||||
\(395\) | −3.52786 | −0.177506 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.7426 | −1.79387 | −0.896936 | − | 0.442160i | \(-0.854212\pi\) | ||||
−0.896936 | + | 0.442160i | \(0.854212\pi\) | |||||||
\(398\) | 2.47214 | 0.123917 | ||||||||
\(399\) | −6.70820 | −0.335830 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 10.0902 | 0.503879 | 0.251940 | − | 0.967743i | \(-0.418932\pi\) | ||||
0.251940 | + | 0.967743i | \(0.418932\pi\) | |||||||
\(402\) | 15.7082 | 0.783454 | ||||||||
\(403\) | 35.1246 | 1.74968 | ||||||||
\(404\) | 7.41641 | 0.368980 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.47214 | −0.320418 | ||||||||
\(409\) | 22.5623 | 1.11563 | 0.557817 | − | 0.829964i | \(-0.311639\pi\) | ||||
0.557817 | + | 0.829964i | \(0.311639\pi\) | |||||||
\(410\) | −1.09017 | −0.0538397 | ||||||||
\(411\) | 19.4164 | 0.957741 | ||||||||
\(412\) | −4.85410 | −0.239144 | ||||||||
\(413\) | 12.8885 | 0.634204 | ||||||||
\(414\) | −8.61803 | −0.423553 | ||||||||
\(415\) | −6.47214 | −0.317705 | ||||||||
\(416\) | −4.85410 | −0.237992 | ||||||||
\(417\) | 20.7984 | 1.01850 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.79837 | −0.185563 | −0.0927814 | − | 0.995687i | \(-0.529576\pi\) | ||||
−0.0927814 | + | 0.995687i | \(0.529576\pi\) | |||||||
\(420\) | 1.38197 | 0.0674330 | ||||||||
\(421\) | −39.8885 | −1.94405 | −0.972024 | − | 0.234880i | \(-0.924530\pi\) | ||||
−0.972024 | + | 0.234880i | \(0.924530\pi\) | |||||||
\(422\) | 14.4721 | 0.704493 | ||||||||
\(423\) | 11.7984 | 0.573657 | ||||||||
\(424\) | −13.0902 | −0.635715 | ||||||||
\(425\) | 6.47214 | 0.313945 | ||||||||
\(426\) | −8.18034 | −0.396339 | ||||||||
\(427\) | 5.12461 | 0.247997 | ||||||||
\(428\) | 1.52786 | 0.0738521 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.23607 | 0.0596085 | ||||||||
\(431\) | −34.6525 | −1.66915 | −0.834576 | − | 0.550894i | \(-0.814287\pi\) | ||||
−0.834576 | + | 0.550894i | \(0.814287\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 27.1246 | 1.30353 | 0.651763 | − | 0.758423i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758423i | \(0.274030\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | −7.23607 | −0.346943 | ||||||||
\(436\) | 7.41641 | 0.355182 | ||||||||
\(437\) | 41.8328 | 2.00113 | ||||||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | 20.2918 | 0.968475 | 0.484237 | − | 0.874937i | \(-0.339097\pi\) | ||||
0.484237 | + | 0.874937i | \(0.339097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.09017 | −0.242389 | ||||||||
\(442\) | −31.4164 | −1.49433 | ||||||||
\(443\) | 8.47214 | 0.402523 | 0.201262 | − | 0.979538i | \(-0.435496\pi\) | ||||
0.201262 | + | 0.979538i | \(0.435496\pi\) | |||||||
\(444\) | 3.14590 | 0.149298 | ||||||||
\(445\) | 11.5623 | 0.548106 | ||||||||
\(446\) | −8.43769 | −0.399536 | ||||||||
\(447\) | 2.47214 | 0.116928 | ||||||||
\(448\) | −1.38197 | −0.0652918 | ||||||||
\(449\) | 38.0902 | 1.79759 | 0.898793 | − | 0.438373i | \(-0.144445\pi\) | ||||
0.898793 | + | 0.438373i | \(0.144445\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.52786 | −0.165937 | ||||||||
\(453\) | 11.5279 | 0.541626 | ||||||||
\(454\) | 15.7082 | 0.737223 | ||||||||
\(455\) | 6.70820 | 0.314485 | ||||||||
\(456\) | 4.85410 | 0.227314 | ||||||||
\(457\) | 34.8328 | 1.62941 | 0.814705 | − | 0.579875i | \(-0.196899\pi\) | ||||
0.814705 | + | 0.579875i | \(0.196899\pi\) | |||||||
\(458\) | 5.05573 | 0.236239 | ||||||||
\(459\) | −6.47214 | −0.302093 | ||||||||
\(460\) | −8.61803 | −0.401818 | ||||||||
\(461\) | −15.7082 | −0.731604 | −0.365802 | − | 0.930693i | \(-0.619205\pi\) | ||||
−0.365802 | + | 0.930693i | \(0.619205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.27051 | −0.198467 | −0.0992337 | − | 0.995064i | \(-0.531639\pi\) | ||||
−0.0992337 | + | 0.995064i | \(0.531639\pi\) | |||||||
\(464\) | 7.23607 | 0.335926 | ||||||||
\(465\) | 7.23607 | 0.335565 | ||||||||
\(466\) | −3.23607 | −0.149908 | ||||||||
\(467\) | −9.52786 | −0.440897 | −0.220448 | − | 0.975399i | \(-0.570752\pi\) | ||||
−0.220448 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(468\) | −4.85410 | −0.224381 | ||||||||
\(469\) | 21.7082 | 1.00239 | ||||||||
\(470\) | 11.7984 | 0.544218 | ||||||||
\(471\) | 2.14590 | 0.0988778 | ||||||||
\(472\) | −9.32624 | −0.429275 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.52786 | 0.162040 | ||||||||
\(475\) | −4.85410 | −0.222721 | ||||||||
\(476\) | −8.94427 | −0.409960 | ||||||||
\(477\) | −13.0902 | −0.599358 | ||||||||
\(478\) | 12.1803 | 0.557116 | ||||||||
\(479\) | −2.76393 | −0.126287 | −0.0631436 | − | 0.998004i | \(-0.520113\pi\) | ||||
−0.0631436 | + | 0.998004i | \(0.520113\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 15.2705 | 0.696275 | ||||||||
\(482\) | 5.56231 | 0.253356 | ||||||||
\(483\) | −11.9098 | −0.541916 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.4164 | −1.06110 | −0.530549 | − | 0.847654i | \(-0.678014\pi\) | ||||
−0.530549 | + | 0.847654i | \(0.678014\pi\) | |||||||
\(488\) | −3.70820 | −0.167863 | ||||||||
\(489\) | 3.41641 | 0.154495 | ||||||||
\(490\) | −5.09017 | −0.229950 | ||||||||
\(491\) | −10.6738 | −0.481700 | −0.240850 | − | 0.970562i | \(-0.577426\pi\) | ||||
−0.240850 | + | 0.970562i | \(0.577426\pi\) | |||||||
\(492\) | 1.09017 | 0.0491487 | ||||||||
\(493\) | 46.8328 | 2.10924 | ||||||||
\(494\) | 23.5623 | 1.06012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.23607 | −0.324909 | ||||||||
\(497\) | −11.3050 | −0.507096 | ||||||||
\(498\) | 6.47214 | 0.290023 | ||||||||
\(499\) | 12.4377 | 0.556788 | 0.278394 | − | 0.960467i | \(-0.410198\pi\) | ||||
0.278394 | + | 0.960467i | \(0.410198\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 23.0344 | 1.02910 | ||||||||
\(502\) | −3.67376 | −0.163968 | ||||||||
\(503\) | 14.4508 | 0.644332 | 0.322166 | − | 0.946683i | \(-0.395589\pi\) | ||||
0.322166 | + | 0.946683i | \(0.395589\pi\) | |||||||
\(504\) | −1.38197 | −0.0615577 | ||||||||
\(505\) | 7.41641 | 0.330026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5623 | −0.469088 | ||||||||
\(508\) | 10.5623 | 0.468627 | ||||||||
\(509\) | 26.3607 | 1.16842 | 0.584208 | − | 0.811604i | \(-0.301405\pi\) | ||||
0.584208 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(510\) | −6.47214 | −0.286591 | ||||||||
\(511\) | −2.76393 | −0.122269 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.85410 | 0.214314 | ||||||||
\(514\) | −19.5279 | −0.861337 | ||||||||
\(515\) | −4.85410 | −0.213897 | ||||||||
\(516\) | −1.23607 | −0.0544149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.34752 | 0.191019 | ||||||||
\(519\) | 14.6180 | 0.641660 | ||||||||
\(520\) | −4.85410 | −0.212866 | ||||||||
\(521\) | −12.7984 | −0.560707 | −0.280353 | − | 0.959897i | \(-0.590452\pi\) | ||||
−0.280353 | + | 0.959897i | \(0.590452\pi\) | |||||||
\(522\) | 7.23607 | 0.316714 | ||||||||
\(523\) | −29.5967 | −1.29418 | −0.647088 | − | 0.762416i | \(-0.724013\pi\) | ||||
−0.647088 | + | 0.762416i | \(0.724013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.38197 | 0.0603139 | ||||||||
\(526\) | 0.381966 | 0.0166545 | ||||||||
\(527\) | −46.8328 | −2.04007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.2705 | 2.22915 | ||||||||
\(530\) | −13.0902 | −0.568601 | ||||||||
\(531\) | −9.32624 | −0.404724 | ||||||||
\(532\) | 6.70820 | 0.290838 | ||||||||
\(533\) | 5.29180 | 0.229213 | ||||||||
\(534\) | −11.5623 | −0.500350 | ||||||||
\(535\) | 1.52786 | 0.0660553 | ||||||||
\(536\) | −15.7082 | −0.678491 | ||||||||
\(537\) | −11.0902 | −0.478576 | ||||||||
\(538\) | −21.5967 | −0.931102 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −15.4164 | −0.662803 | −0.331402 | − | 0.943490i | \(-0.607521\pi\) | ||||
−0.331402 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(542\) | −6.29180 | −0.270256 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.47214 | 0.277491 | ||||||||
\(545\) | 7.41641 | 0.317684 | ||||||||
\(546\) | −6.70820 | −0.287085 | ||||||||
\(547\) | 27.7082 | 1.18472 | 0.592359 | − | 0.805674i | \(-0.298197\pi\) | ||||
0.592359 | + | 0.805674i | \(0.298197\pi\) | |||||||
\(548\) | −19.4164 | −0.829428 | ||||||||
\(549\) | −3.70820 | −0.158262 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.1246 | −1.49636 | ||||||||
\(552\) | 8.61803 | 0.366808 | ||||||||
\(553\) | 4.87539 | 0.207323 | ||||||||
\(554\) | −11.7426 | −0.498897 | ||||||||
\(555\) | 3.14590 | 0.133536 | ||||||||
\(556\) | −20.7984 | −0.882048 | ||||||||
\(557\) | 41.5066 | 1.75869 | 0.879345 | − | 0.476185i | \(-0.157981\pi\) | ||||
0.879345 | + | 0.476185i | \(0.157981\pi\) | |||||||
\(558\) | −7.23607 | −0.306327 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | −1.38197 | −0.0583987 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.9443 | 1.13658 | ||||||||
\(563\) | −17.5279 | −0.738711 | −0.369356 | − | 0.929288i | \(-0.620422\pi\) | ||||
−0.369356 | + | 0.929288i | \(0.620422\pi\) | |||||||
\(564\) | −11.7984 | −0.496801 | ||||||||
\(565\) | −3.52786 | −0.148418 | ||||||||
\(566\) | −17.1246 | −0.719801 | ||||||||
\(567\) | −1.38197 | −0.0580371 | ||||||||
\(568\) | 8.18034 | 0.343239 | ||||||||
\(569\) | −2.32624 | −0.0975210 | −0.0487605 | − | 0.998811i | \(-0.515527\pi\) | ||||
−0.0487605 | + | 0.998811i | \(0.515527\pi\) | |||||||
\(570\) | 4.85410 | 0.203316 | ||||||||
\(571\) | 18.9787 | 0.794234 | 0.397117 | − | 0.917768i | \(-0.370011\pi\) | ||||
0.397117 | + | 0.917768i | \(0.370011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.18034 | 0.258187 | ||||||||
\(574\) | 1.50658 | 0.0628833 | ||||||||
\(575\) | −8.61803 | −0.359397 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.7082 | −0.737202 | −0.368601 | − | 0.929588i | \(-0.620163\pi\) | ||||
−0.368601 | + | 0.929588i | \(0.620163\pi\) | |||||||
\(578\) | 24.8885 | 1.03523 | ||||||||
\(579\) | 1.70820 | 0.0709905 | ||||||||
\(580\) | 7.23607 | 0.300461 | ||||||||
\(581\) | 8.94427 | 0.371071 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | −4.85410 | −0.200692 | ||||||||
\(586\) | −10.9098 | −0.450681 | ||||||||
\(587\) | −3.05573 | −0.126123 | −0.0630617 | − | 0.998010i | \(-0.520086\pi\) | ||||
−0.0630617 | + | 0.998010i | \(0.520086\pi\) | |||||||
\(588\) | 5.09017 | 0.209915 | ||||||||
\(589\) | 35.1246 | 1.44728 | ||||||||
\(590\) | −9.32624 | −0.383955 | ||||||||
\(591\) | −14.6180 | −0.601306 | ||||||||
\(592\) | −3.14590 | −0.129296 | ||||||||
\(593\) | −23.8885 | −0.980985 | −0.490492 | − | 0.871445i | \(-0.663183\pi\) | ||||
−0.490492 | + | 0.871445i | \(0.663183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.94427 | −0.366679 | ||||||||
\(596\) | −2.47214 | −0.101263 | ||||||||
\(597\) | −2.47214 | −0.101178 | ||||||||
\(598\) | 41.8328 | 1.71067 | ||||||||
\(599\) | 0.180340 | 0.00736849 | 0.00368424 | − | 0.999993i | \(-0.498827\pi\) | ||||
0.00368424 | + | 0.999993i | \(0.498827\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −17.7984 | −0.726011 | −0.363005 | − | 0.931787i | \(-0.618249\pi\) | ||||
−0.363005 | + | 0.931787i | \(0.618249\pi\) | |||||||
\(602\) | −1.70820 | −0.0696212 | ||||||||
\(603\) | −15.7082 | −0.639688 | ||||||||
\(604\) | −11.5279 | −0.469062 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.41641 | −0.301271 | ||||||||
\(607\) | −23.4164 | −0.950443 | −0.475221 | − | 0.879866i | \(-0.657632\pi\) | ||||
−0.475221 | + | 0.879866i | \(0.657632\pi\) | |||||||
\(608\) | −4.85410 | −0.196860 | ||||||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | −3.70820 | −0.150141 | ||||||||
\(611\) | −57.2705 | −2.31692 | ||||||||
\(612\) | 6.47214 | 0.261621 | ||||||||
\(613\) | 14.5836 | 0.589026 | 0.294513 | − | 0.955648i | \(-0.404843\pi\) | ||||
0.294513 | + | 0.955648i | \(0.404843\pi\) | |||||||
\(614\) | 26.8328 | 1.08288 | ||||||||
\(615\) | 1.09017 | 0.0439599 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0000 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(618\) | 4.85410 | 0.195261 | ||||||||
\(619\) | 26.5623 | 1.06763 | 0.533815 | − | 0.845602i | \(-0.320758\pi\) | ||||
0.533815 | + | 0.845602i | \(0.320758\pi\) | |||||||
\(620\) | −7.23607 | −0.290607 | ||||||||
\(621\) | 8.61803 | 0.345830 | ||||||||
\(622\) | 11.8885 | 0.476687 | ||||||||
\(623\) | −15.9787 | −0.640174 | ||||||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.70820 | −0.308082 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.14590 | −0.0856307 | ||||||||
\(629\) | −20.3607 | −0.811833 | ||||||||
\(630\) | −1.38197 | −0.0550588 | ||||||||
\(631\) | 13.2361 | 0.526920 | 0.263460 | − | 0.964670i | \(-0.415136\pi\) | ||||
0.263460 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(632\) | −3.52786 | −0.140331 | ||||||||
\(633\) | −14.4721 | −0.575216 | ||||||||
\(634\) | −22.0902 | −0.877313 | ||||||||
\(635\) | 10.5623 | 0.419152 | ||||||||
\(636\) | 13.0902 | 0.519059 | ||||||||
\(637\) | 24.7082 | 0.978975 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.18034 | 0.323609 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 46.6312 | 1.84182 | 0.920911 | − | 0.389774i | \(-0.127447\pi\) | ||||
0.920911 | + | 0.389774i | \(0.127447\pi\) | |||||||
\(642\) | −1.52786 | −0.0603000 | ||||||||
\(643\) | 40.0000 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 11.9098 | 0.469313 | ||||||||
\(645\) | −1.23607 | −0.0486701 | ||||||||
\(646\) | −31.4164 | −1.23606 | ||||||||
\(647\) | −14.1115 | −0.554779 | −0.277389 | − | 0.960758i | \(-0.589469\pi\) | ||||
−0.277389 | + | 0.960758i | \(0.589469\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.85410 | −0.190394 | ||||||||
\(651\) | −10.0000 | −0.391931 | ||||||||
\(652\) | −3.41641 | −0.133797 | ||||||||
\(653\) | −13.6869 | −0.535610 | −0.267805 | − | 0.963473i | \(-0.586298\pi\) | ||||
−0.267805 | + | 0.963473i | \(0.586298\pi\) | |||||||
\(654\) | −7.41641 | −0.290004 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.09017 | −0.0425640 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | −16.3050 | −0.635633 | ||||||||
\(659\) | −24.3262 | −0.947616 | −0.473808 | − | 0.880628i | \(-0.657121\pi\) | ||||
−0.473808 | + | 0.880628i | \(0.657121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.6525 | 0.803288 | 0.401644 | − | 0.915796i | \(-0.368439\pi\) | ||||
0.401644 | + | 0.915796i | \(0.368439\pi\) | |||||||
\(662\) | 16.8541 | 0.655053 | ||||||||
\(663\) | 31.4164 | 1.22011 | ||||||||
\(664\) | −6.47214 | −0.251168 | ||||||||
\(665\) | 6.70820 | 0.260133 | ||||||||
\(666\) | −3.14590 | −0.121901 | ||||||||
\(667\) | −62.3607 | −2.41462 | ||||||||
\(668\) | −23.0344 | −0.891229 | ||||||||
\(669\) | 8.43769 | 0.326220 | ||||||||
\(670\) | −15.7082 | −0.606861 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.38197 | 0.0533105 | ||||||||
\(673\) | 20.7639 | 0.800391 | 0.400195 | − | 0.916430i | \(-0.368942\pi\) | ||||
0.400195 | + | 0.916430i | \(0.368942\pi\) | |||||||
\(674\) | −3.41641 | −0.131595 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 10.5623 | 0.406243 | ||||||||
\(677\) | −10.3607 | −0.398193 | −0.199097 | − | 0.979980i | \(-0.563801\pi\) | ||||
−0.199097 | + | 0.979980i | \(0.563801\pi\) | |||||||
\(678\) | 3.52786 | 0.135487 | ||||||||
\(679\) | 2.76393 | 0.106070 | ||||||||
\(680\) | 6.47214 | 0.248195 | ||||||||
\(681\) | −15.7082 | −0.601940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.0132 | 1.64585 | 0.822926 | − | 0.568148i | \(-0.192340\pi\) | ||||
0.822926 | + | 0.568148i | \(0.192340\pi\) | |||||||
\(684\) | −4.85410 | −0.185601 | ||||||||
\(685\) | −19.4164 | −0.741863 | ||||||||
\(686\) | 16.7082 | 0.637922 | ||||||||
\(687\) | −5.05573 | −0.192888 | ||||||||
\(688\) | 1.23607 | 0.0471246 | ||||||||
\(689\) | 63.5410 | 2.42072 | ||||||||
\(690\) | 8.61803 | 0.328083 | ||||||||
\(691\) | 11.2016 | 0.426130 | 0.213065 | − | 0.977038i | \(-0.431655\pi\) | ||||
0.213065 | + | 0.977038i | \(0.431655\pi\) | |||||||
\(692\) | −14.6180 | −0.555694 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.70820 | 0.140761 | ||||||||
\(695\) | −20.7984 | −0.788927 | ||||||||
\(696\) | −7.23607 | −0.274282 | ||||||||
\(697\) | −7.05573 | −0.267255 | ||||||||
\(698\) | −13.4164 | −0.507819 | ||||||||
\(699\) | 3.23607 | 0.122399 | ||||||||
\(700\) | −1.38197 | −0.0522334 | ||||||||
\(701\) | −10.0689 | −0.380296 | −0.190148 | − | 0.981755i | \(-0.560897\pi\) | ||||
−0.190148 | + | 0.981755i | \(0.560897\pi\) | |||||||
\(702\) | 4.85410 | 0.183206 | ||||||||
\(703\) | 15.2705 | 0.575938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.7984 | −0.444352 | ||||||||
\(706\) | 3.23607 | 0.121791 | ||||||||
\(707\) | −10.2492 | −0.385462 | ||||||||
\(708\) | 9.32624 | 0.350501 | ||||||||
\(709\) | 15.2361 | 0.572203 | 0.286101 | − | 0.958199i | \(-0.407641\pi\) | ||||
0.286101 | + | 0.958199i | \(0.407641\pi\) | |||||||
\(710\) | 8.18034 | 0.307003 | ||||||||
\(711\) | −3.52786 | −0.132305 | ||||||||
\(712\) | 11.5623 | 0.433316 | ||||||||
\(713\) | 62.3607 | 2.33543 | ||||||||
\(714\) | 8.94427 | 0.334731 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.0902 | 0.414459 | ||||||||
\(717\) | −12.1803 | −0.454883 | ||||||||
\(718\) | 24.7639 | 0.924182 | ||||||||
\(719\) | 32.4721 | 1.21101 | 0.605503 | − | 0.795843i | \(-0.292972\pi\) | ||||
0.605503 | + | 0.795843i | \(0.292972\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 6.70820 | 0.249827 | ||||||||
\(722\) | 4.56231 | 0.169791 | ||||||||
\(723\) | −5.56231 | −0.206864 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.23607 | 0.268741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.6869 | −0.396356 | −0.198178 | − | 0.980166i | \(-0.563502\pi\) | ||||
−0.198178 | + | 0.980166i | \(0.563502\pi\) | |||||||
\(728\) | 6.70820 | 0.248623 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 3.70820 | 0.137059 | ||||||||
\(733\) | −10.5836 | −0.390914 | −0.195457 | − | 0.980712i | \(-0.562619\pi\) | ||||
−0.195457 | + | 0.980712i | \(0.562619\pi\) | |||||||
\(734\) | 8.58359 | 0.316826 | ||||||||
\(735\) | 5.09017 | 0.187754 | ||||||||
\(736\) | −8.61803 | −0.317665 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.09017 | −0.0401297 | ||||||||
\(739\) | −4.14590 | −0.152509 | −0.0762547 | − | 0.997088i | \(-0.524296\pi\) | ||||
−0.0762547 | + | 0.997088i | \(0.524296\pi\) | |||||||
\(740\) | −3.14590 | −0.115646 | ||||||||
\(741\) | −23.5623 | −0.865583 | ||||||||
\(742\) | 18.0902 | 0.664111 | ||||||||
\(743\) | −12.6180 | −0.462911 | −0.231455 | − | 0.972846i | \(-0.574349\pi\) | ||||
−0.231455 | + | 0.972846i | \(0.574349\pi\) | |||||||
\(744\) | 7.23607 | 0.265287 | ||||||||
\(745\) | −2.47214 | −0.0905721 | ||||||||
\(746\) | 34.5623 | 1.26542 | ||||||||
\(747\) | −6.47214 | −0.236803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.11146 | −0.0771509 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 8.58359 | 0.313220 | 0.156610 | − | 0.987661i | \(-0.449943\pi\) | ||||
0.156610 | + | 0.987661i | \(0.449943\pi\) | |||||||
\(752\) | 11.7984 | 0.430242 | ||||||||
\(753\) | 3.67376 | 0.133879 | ||||||||
\(754\) | −35.1246 | −1.27916 | ||||||||
\(755\) | −11.5279 | −0.419542 | ||||||||
\(756\) | 1.38197 | 0.0502616 | ||||||||
\(757\) | 50.1591 | 1.82306 | 0.911531 | − | 0.411232i | \(-0.134901\pi\) | ||||
0.911531 | + | 0.411232i | \(0.134901\pi\) | |||||||
\(758\) | −4.50658 | −0.163686 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.85410 | −0.176077 | ||||||||
\(761\) | 35.8885 | 1.30096 | 0.650479 | − | 0.759524i | \(-0.274568\pi\) | ||||
0.650479 | + | 0.759524i | \(0.274568\pi\) | |||||||
\(762\) | −10.5623 | −0.382632 | ||||||||
\(763\) | −10.2492 | −0.371047 | ||||||||
\(764\) | −6.18034 | −0.223597 | ||||||||
\(765\) | 6.47214 | 0.234001 | ||||||||
\(766\) | 15.7426 | 0.568805 | ||||||||
\(767\) | 45.2705 | 1.63462 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 35.9098 | 1.29494 | 0.647471 | − | 0.762090i | \(-0.275827\pi\) | ||||
0.647471 | + | 0.762090i | \(0.275827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5279 | 0.703279 | ||||||||
\(772\) | −1.70820 | −0.0614796 | ||||||||
\(773\) | 10.9098 | 0.392399 | 0.196200 | − | 0.980564i | \(-0.437140\pi\) | ||||
0.196200 | + | 0.980564i | \(0.437140\pi\) | |||||||
\(774\) | 1.23607 | 0.0444295 | ||||||||
\(775\) | −7.23607 | −0.259927 | ||||||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | −4.34752 | −0.155967 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | 5.29180 | 0.189598 | ||||||||
\(780\) | 4.85410 | 0.173805 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −55.7771 | −1.99458 | ||||||||
\(783\) | −7.23607 | −0.258596 | ||||||||
\(784\) | −5.09017 | −0.181792 | ||||||||
\(785\) | −2.14590 | −0.0765904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.29180 | 0.224278 | 0.112139 | − | 0.993693i | \(-0.464230\pi\) | ||||
0.112139 | + | 0.993693i | \(0.464230\pi\) | |||||||
\(788\) | 14.6180 | 0.520746 | ||||||||
\(789\) | −0.381966 | −0.0135984 | ||||||||
\(790\) | −3.52786 | −0.125516 | ||||||||
\(791\) | 4.87539 | 0.173349 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | −35.7426 | −1.26846 | ||||||||
\(795\) | 13.0902 | 0.464260 | ||||||||
\(796\) | 2.47214 | 0.0876225 | ||||||||
\(797\) | 21.9098 | 0.776086 | 0.388043 | − | 0.921641i | \(-0.373151\pi\) | ||||
0.388043 | + | 0.921641i | \(0.373151\pi\) | |||||||
\(798\) | −6.70820 | −0.237468 | ||||||||
\(799\) | 76.3607 | 2.70145 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 11.5623 | 0.408534 | ||||||||
\(802\) | 10.0902 | 0.356296 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.7082 | 0.553986 | ||||||||
\(805\) | 11.9098 | 0.419766 | ||||||||
\(806\) | 35.1246 | 1.23721 | ||||||||
\(807\) | 21.5967 | 0.760242 | ||||||||
\(808\) | 7.41641 | 0.260908 | ||||||||
\(809\) | 16.7426 | 0.588640 | 0.294320 | − | 0.955707i | \(-0.404907\pi\) | ||||
0.294320 | + | 0.955707i | \(0.404907\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 35.9230 | 1.26143 | 0.630713 | − | 0.776016i | \(-0.282762\pi\) | ||||
0.630713 | + | 0.776016i | \(0.282762\pi\) | |||||||
\(812\) | −10.0000 | −0.350931 | ||||||||
\(813\) | 6.29180 | 0.220663 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.41641 | −0.119672 | ||||||||
\(816\) | −6.47214 | −0.226570 | ||||||||
\(817\) | −6.00000 | −0.209913 | ||||||||
\(818\) | 22.5623 | 0.788873 | ||||||||
\(819\) | 6.70820 | 0.234404 | ||||||||
\(820\) | −1.09017 | −0.0380704 | ||||||||
\(821\) | 45.0132 | 1.57097 | 0.785485 | − | 0.618881i | \(-0.212414\pi\) | ||||
0.785485 | + | 0.618881i | \(0.212414\pi\) | |||||||
\(822\) | 19.4164 | 0.677225 | ||||||||
\(823\) | −7.14590 | −0.249090 | −0.124545 | − | 0.992214i | \(-0.539747\pi\) | ||||
−0.124545 | + | 0.992214i | \(0.539747\pi\) | |||||||
\(824\) | −4.85410 | −0.169101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8885 | 0.448450 | ||||||||
\(827\) | 3.34752 | 0.116405 | 0.0582024 | − | 0.998305i | \(-0.481463\pi\) | ||||
0.0582024 | + | 0.998305i | \(0.481463\pi\) | |||||||
\(828\) | −8.61803 | −0.299497 | ||||||||
\(829\) | −30.9443 | −1.07474 | −0.537369 | − | 0.843347i | \(-0.680582\pi\) | ||||
−0.537369 | + | 0.843347i | \(0.680582\pi\) | |||||||
\(830\) | −6.47214 | −0.224651 | ||||||||
\(831\) | 11.7426 | 0.407348 | ||||||||
\(832\) | −4.85410 | −0.168286 | ||||||||
\(833\) | −32.9443 | −1.14145 | ||||||||
\(834\) | 20.7984 | 0.720189 | ||||||||
\(835\) | −23.0344 | −0.797140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.23607 | 0.250115 | ||||||||
\(838\) | −3.79837 | −0.131213 | ||||||||
\(839\) | −43.4853 | −1.50128 | −0.750639 | − | 0.660712i | \(-0.770254\pi\) | ||||
−0.750639 | + | 0.660712i | \(0.770254\pi\) | |||||||
\(840\) | 1.38197 | 0.0476824 | ||||||||
\(841\) | 23.3607 | 0.805541 | ||||||||
\(842\) | −39.8885 | −1.37465 | ||||||||
\(843\) | −26.9443 | −0.928010 | ||||||||
\(844\) | 14.4721 | 0.498151 | ||||||||
\(845\) | 10.5623 | 0.363354 | ||||||||
\(846\) | 11.7984 | 0.405636 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.0902 | −0.449518 | ||||||||
\(849\) | 17.1246 | 0.587715 | ||||||||
\(850\) | 6.47214 | 0.221992 | ||||||||
\(851\) | 27.1115 | 0.929369 | ||||||||
\(852\) | −8.18034 | −0.280254 | ||||||||
\(853\) | −31.3820 | −1.07450 | −0.537249 | − | 0.843424i | \(-0.680536\pi\) | ||||
−0.537249 | + | 0.843424i | \(0.680536\pi\) | |||||||
\(854\) | 5.12461 | 0.175361 | ||||||||
\(855\) | −4.85410 | −0.166007 | ||||||||
\(856\) | 1.52786 | 0.0522213 | ||||||||
\(857\) | 37.5967 | 1.28428 | 0.642140 | − | 0.766587i | \(-0.278047\pi\) | ||||
0.642140 | + | 0.766587i | \(0.278047\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5066 | −0.426719 | −0.213359 | − | 0.976974i | \(-0.568441\pi\) | ||||
−0.213359 | + | 0.976974i | \(0.568441\pi\) | |||||||
\(860\) | 1.23607 | 0.0421496 | ||||||||
\(861\) | −1.50658 | −0.0513440 | ||||||||
\(862\) | −34.6525 | −1.18027 | ||||||||
\(863\) | −35.3951 | −1.20486 | −0.602432 | − | 0.798170i | \(-0.705802\pi\) | ||||
−0.602432 | + | 0.798170i | \(0.705802\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −14.6180 | −0.497028 | ||||||||
\(866\) | 27.1246 | 0.921732 | ||||||||
\(867\) | −24.8885 | −0.845259 | ||||||||
\(868\) | 10.0000 | 0.339422 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −7.23607 | −0.245326 | ||||||||
\(871\) | 76.2492 | 2.58361 | ||||||||
\(872\) | 7.41641 | 0.251151 | ||||||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | 41.8328 | 1.41502 | ||||||||
\(875\) | −1.38197 | −0.0467190 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 11.1459 | 0.376370 | 0.188185 | − | 0.982134i | \(-0.439740\pi\) | ||||
0.188185 | + | 0.982134i | \(0.439740\pi\) | |||||||
\(878\) | 20.2918 | 0.684815 | ||||||||
\(879\) | 10.9098 | 0.367979 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.50658 | 0.286594 | 0.143297 | − | 0.989680i | \(-0.454230\pi\) | ||||
0.143297 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(882\) | −5.09017 | −0.171395 | ||||||||
\(883\) | 15.4164 | 0.518803 | 0.259402 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259402 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(884\) | −31.4164 | −1.05665 | ||||||||
\(885\) | 9.32624 | 0.313498 | ||||||||
\(886\) | 8.47214 | 0.284627 | ||||||||
\(887\) | −15.3820 | −0.516476 | −0.258238 | − | 0.966081i | \(-0.583142\pi\) | ||||
−0.258238 | + | 0.966081i | \(0.583142\pi\) | |||||||
\(888\) | 3.14590 | 0.105569 | ||||||||
\(889\) | −14.5967 | −0.489559 | ||||||||
\(890\) | 11.5623 | 0.387569 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.43769 | −0.282515 | ||||||||
\(893\) | −57.2705 | −1.91648 | ||||||||
\(894\) | 2.47214 | 0.0826806 | ||||||||
\(895\) | 11.0902 | 0.370703 | ||||||||
\(896\) | −1.38197 | −0.0461682 | ||||||||
\(897\) | −41.8328 | −1.39676 | ||||||||
\(898\) | 38.0902 | 1.27109 | ||||||||
\(899\) | −52.3607 | −1.74633 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −84.7214 | −2.82248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.70820 | 0.0568455 | ||||||||
\(904\) | −3.52786 | −0.117335 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.5279 | 0.382988 | ||||||||
\(907\) | 58.2492 | 1.93413 | 0.967067 | − | 0.254522i | \(-0.0819183\pi\) | ||||
0.967067 | + | 0.254522i | \(0.0819183\pi\) | |||||||
\(908\) | 15.7082 | 0.521295 | ||||||||
\(909\) | 7.41641 | 0.245987 | ||||||||
\(910\) | 6.70820 | 0.222375 | ||||||||
\(911\) | −41.0132 | −1.35883 | −0.679413 | − | 0.733756i | \(-0.737766\pi\) | ||||
−0.679413 | + | 0.733756i | \(0.737766\pi\) | |||||||
\(912\) | 4.85410 | 0.160735 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.8328 | 1.15217 | ||||||||
\(915\) | 3.70820 | 0.122589 | ||||||||
\(916\) | 5.05573 | 0.167046 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.47214 | −0.213612 | ||||||||
\(919\) | 8.65248 | 0.285419 | 0.142709 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142709 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(920\) | −8.61803 | −0.284128 | ||||||||
\(921\) | −26.8328 | −0.884171 | ||||||||
\(922\) | −15.7082 | −0.517322 | ||||||||
\(923\) | −39.7082 | −1.30701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.14590 | −0.103436 | ||||||||
\(926\) | −4.27051 | −0.140338 | ||||||||
\(927\) | −4.85410 | −0.159430 | ||||||||
\(928\) | 7.23607 | 0.237536 | ||||||||
\(929\) | −12.4377 | −0.408068 | −0.204034 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204034 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(930\) | 7.23607 | 0.237280 | ||||||||
\(931\) | 24.7082 | 0.809779 | ||||||||
\(932\) | −3.23607 | −0.106001 | ||||||||
\(933\) | −11.8885 | −0.389213 | ||||||||
\(934\) | −9.52786 | −0.311761 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.85410 | −0.158661 | ||||||||
\(937\) | −14.8328 | −0.484567 | −0.242283 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242283 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(938\) | 21.7082 | 0.708798 | ||||||||
\(939\) | 7.70820 | 0.251548 | ||||||||
\(940\) | 11.7984 | 0.384821 | ||||||||
\(941\) | −35.7771 | −1.16630 | −0.583150 | − | 0.812365i | \(-0.698180\pi\) | ||||
−0.583150 | + | 0.812365i | \(0.698180\pi\) | |||||||
\(942\) | 2.14590 | 0.0699171 | ||||||||
\(943\) | 9.39512 | 0.305947 | ||||||||
\(944\) | −9.32624 | −0.303543 | ||||||||
\(945\) | 1.38197 | 0.0449554 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.9443 | −0.875571 | −0.437786 | − | 0.899079i | \(-0.644237\pi\) | ||||
−0.437786 | + | 0.899079i | \(0.644237\pi\) | |||||||
\(948\) | 3.52786 | 0.114580 | ||||||||
\(949\) | −9.70820 | −0.315142 | ||||||||
\(950\) | −4.85410 | −0.157488 | ||||||||
\(951\) | 22.0902 | 0.716323 | ||||||||
\(952\) | −8.94427 | −0.289886 | ||||||||
\(953\) | 37.0132 | 1.19897 | 0.599487 | − | 0.800385i | \(-0.295371\pi\) | ||||
0.599487 | + | 0.800385i | \(0.295371\pi\) | |||||||
\(954\) | −13.0902 | −0.423810 | ||||||||
\(955\) | −6.18034 | −0.199991 | ||||||||
\(956\) | 12.1803 | 0.393940 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.76393 | −0.0892986 | ||||||||
\(959\) | 26.8328 | 0.866477 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | 15.2705 | 0.492341 | ||||||||
\(963\) | 1.52786 | 0.0492347 | ||||||||
\(964\) | 5.56231 | 0.179150 | ||||||||
\(965\) | −1.70820 | −0.0549890 | ||||||||
\(966\) | −11.9098 | −0.383193 | ||||||||
\(967\) | −57.9787 | −1.86447 | −0.932235 | − | 0.361854i | \(-0.882144\pi\) | ||||
−0.932235 | + | 0.361854i | \(0.882144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.4164 | 1.00924 | ||||||||
\(970\) | −2.00000 | −0.0642161 | ||||||||
\(971\) | 4.03444 | 0.129471 | 0.0647357 | − | 0.997902i | \(-0.479380\pi\) | ||||
0.0647357 | + | 0.997902i | \(0.479380\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 28.7426 | 0.921447 | ||||||||
\(974\) | −23.4164 | −0.750310 | ||||||||
\(975\) | 4.85410 | 0.155456 | ||||||||
\(976\) | −3.70820 | −0.118697 | ||||||||
\(977\) | 1.05573 | 0.0337757 | 0.0168879 | − | 0.999857i | \(-0.494624\pi\) | ||||
0.0168879 | + | 0.999857i | \(0.494624\pi\) | |||||||
\(978\) | 3.41641 | 0.109245 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.09017 | −0.162600 | ||||||||
\(981\) | 7.41641 | 0.236788 | ||||||||
\(982\) | −10.6738 | −0.340613 | ||||||||
\(983\) | 21.2705 | 0.678424 | 0.339212 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339212 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(984\) | 1.09017 | 0.0347533 | ||||||||
\(985\) | 14.6180 | 0.465769 | ||||||||
\(986\) | 46.8328 | 1.49146 | ||||||||
\(987\) | 16.3050 | 0.518992 | ||||||||
\(988\) | 23.5623 | 0.749617 | ||||||||
\(989\) | −10.6525 | −0.338729 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | −7.23607 | −0.229745 | ||||||||
\(993\) | −16.8541 | −0.534849 | ||||||||
\(994\) | −11.3050 | −0.358571 | ||||||||
\(995\) | 2.47214 | 0.0783720 | ||||||||
\(996\) | 6.47214 | 0.205077 | ||||||||
\(997\) | −22.0000 | −0.696747 | −0.348373 | − | 0.937356i | \(-0.613266\pi\) | ||||
−0.348373 | + | 0.937356i | \(0.613266\pi\) | |||||||
\(998\) | 12.4377 | 0.393708 | ||||||||
\(999\) | 3.14590 | 0.0995318 |
(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 | 3630.2.a.bl.1.2 | 2 | ||
11.5 | even | 5 | 330.2.m.a.91.1 | ✓ | 4 | ||
11.9 | even | 5 | 330.2.m.a.301.1 | yes | 4 | ||
11.10 | odd | 2 | 3630.2.a.bf.1.1 | 2 | |||
33.5 | odd | 10 | 990.2.n.h.91.1 | 4 | |||
33.20 | odd | 10 | 990.2.n.h.631.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.a.91.1 | ✓ | 4 | 11.5 | even | 5 | ||
330.2.m.a.301.1 | yes | 4 | 11.9 | even | 5 | ||
990.2.n.h.91.1 | 4 | 33.5 | odd | 10 | |||
990.2.n.h.631.1 | 4 | 33.20 | odd | 10 | |||
3630.2.a.bf.1.1 | 2 | 11.10 | odd | 2 | |||
3630.2.a.bl.1.2 | 2 | 1.1 | even | 1 | trivial |