Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −2.28825 | −1.02333 | −0.511667 | − | 0.859184i | \(-0.670972\pi\) | ||||
−0.511667 | + | 0.859184i | \(0.670972\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.41421 | 0.447214 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.57649 | −1.26929 | −0.634645 | − | 0.772804i | \(-0.718854\pi\) | ||||
−0.634645 | + | 0.772804i | \(0.718854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.03631 | 0.925993 | 0.462996 | − | 0.886360i | \(-0.346774\pi\) | ||||
0.462996 | + | 0.886360i | \(0.346774\pi\) | |||||||
\(20\) | 3.70246 | 0.827895 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.618034 | −0.131765 | ||||||||
\(23\) | −7.23607 | −1.50882 | −0.754412 | − | 0.656401i | \(-0.772078\pi\) | ||||
−0.754412 | + | 0.656401i | \(0.772078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.236068 | 0.0472136 | ||||||||
\(26\) | 2.82843 | 0.554700 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.23607 | 0.229532 | 0.114766 | − | 0.993393i | \(-0.463388\pi\) | ||||
0.114766 | + | 0.993393i | \(0.463388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.99070 | 1.07596 | 0.537981 | − | 0.842957i | \(-0.319187\pi\) | ||||
0.537981 | + | 0.842957i | \(0.319187\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.95440 | −0.335176 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7082 | −1.76042 | −0.880209 | − | 0.474586i | \(-0.842598\pi\) | ||||
−0.880209 | + | 0.474586i | \(0.842598\pi\) | |||||||
\(38\) | −2.49458 | −0.404674 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.11667 | −0.809017 | ||||||||
\(41\) | 5.78437 | 0.903367 | 0.451684 | − | 0.892178i | \(-0.350824\pi\) | ||||
0.451684 | + | 0.892178i | \(0.350824\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.94427 | 0.906493 | 0.453246 | − | 0.891385i | \(-0.350266\pi\) | ||||
0.453246 | + | 0.891385i | \(0.350266\pi\) | |||||||
\(44\) | −1.61803 | −0.243928 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.47214 | 0.659380 | ||||||||
\(47\) | 3.03476 | 0.442665 | 0.221332 | − | 0.975198i | \(-0.428959\pi\) | ||||
0.221332 | + | 0.975198i | \(0.428959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.145898 | −0.0206331 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.40492 | 1.02688 | ||||||||
\(53\) | 10.7082 | 1.47088 | 0.735442 | − | 0.677587i | \(-0.236974\pi\) | ||||
0.735442 | + | 0.677587i | \(0.236974\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28825 | −0.308547 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.763932 | −0.100309 | ||||||||
\(59\) | 14.4760 | 1.88461 | 0.942306 | − | 0.334752i | \(-0.108652\pi\) | ||||
0.942306 | + | 0.334752i | \(0.108652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.94665 | −1.14550 | −0.572751 | − | 0.819730i | \(-0.694124\pi\) | ||||
−0.572751 | + | 0.819730i | \(0.694124\pi\) | |||||||
\(62\) | −3.70246 | −0.470213 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 10.4721 | 1.29891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47214 | 0.179850 | 0.0899250 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899250 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(68\) | −5.11667 | −0.620488 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.47214 | 0.649423 | 0.324712 | − | 0.945813i | \(-0.394733\pi\) | ||||
0.324712 | + | 0.945813i | \(0.394733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.73722 | 0.788532 | 0.394266 | − | 0.918996i | \(-0.370999\pi\) | ||||
0.394266 | + | 0.918996i | \(0.370999\pi\) | |||||||
\(74\) | 6.61803 | 0.769331 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.53089 | −0.749144 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.76393 | −0.873511 | −0.436755 | − | 0.899580i | \(-0.643872\pi\) | ||||
−0.436755 | + | 0.899580i | \(0.643872\pi\) | |||||||
\(80\) | −4.24264 | −0.474342 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.57494 | −0.394786 | ||||||||
\(83\) | 8.61280 | 0.945378 | 0.472689 | − | 0.881229i | \(-0.343283\pi\) | ||||
0.472689 | + | 0.881229i | \(0.343283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.23607 | −0.784862 | ||||||||
\(86\) | −3.67376 | −0.396152 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | −6.32456 | −0.670402 | −0.335201 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335201 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.7082 | 1.22066 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.87558 | −0.193452 | ||||||||
\(95\) | −9.23607 | −0.947601 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.19704 | −0.629214 | −0.314607 | − | 0.949222i | \(-0.601873\pi\) | ||||
−0.314607 | + | 0.949222i | \(0.601873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.381966 | −0.0381966 | ||||||||
\(101\) | −18.7186 | −1.86257 | −0.931286 | − | 0.364288i | \(-0.881313\pi\) | ||||
−0.931286 | + | 0.364288i | \(0.881313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.78437 | 0.569951 | 0.284976 | − | 0.958535i | \(-0.408014\pi\) | ||||
0.284976 | + | 0.958535i | \(0.408014\pi\) | |||||||
\(104\) | −10.2333 | −1.00346 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.61803 | −0.642800 | ||||||||
\(107\) | 11.9443 | 1.15470 | 0.577348 | − | 0.816498i | \(-0.304088\pi\) | ||||
0.577348 | + | 0.816498i | \(0.304088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 1.41421 | 0.134840 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.76393 | −0.354081 | −0.177040 | − | 0.984204i | \(-0.556652\pi\) | ||||
−0.177040 | + | 0.984204i | \(0.556652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.5579 | 1.54403 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.94665 | −0.823606 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 5.52933 | 0.500602 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.69316 | −0.870472 | ||||||||
\(125\) | 10.9010 | 0.975019 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6525 | −1.56640 | −0.783202 | − | 0.621767i | \(-0.786415\pi\) | ||||
−0.783202 | + | 0.621767i | \(0.786415\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.47214 | −0.567644 | ||||||||
\(131\) | −20.2604 | −1.77016 | −0.885078 | − | 0.465443i | \(-0.845895\pi\) | ||||
−0.885078 | + | 0.465443i | \(0.845895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.909830 | −0.0785973 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.07107 | 0.606339 | ||||||||
\(137\) | 8.23607 | 0.703655 | 0.351827 | − | 0.936065i | \(-0.385560\pi\) | ||||
0.351827 | + | 0.936065i | \(0.385560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.69316 | 0.822163 | 0.411082 | − | 0.911598i | \(-0.365151\pi\) | ||||
0.411082 | + | 0.911598i | \(0.365151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.38197 | −0.283808 | ||||||||
\(143\) | −4.57649 | −0.382705 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.82843 | −0.234888 | ||||||||
\(146\) | −4.16383 | −0.344601 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.3262 | 1.42421 | ||||||||
\(149\) | −10.5279 | −0.862476 | −0.431238 | − | 0.902238i | \(-0.641923\pi\) | ||||
−0.431238 | + | 0.902238i | \(0.641923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7082 | −1.52245 | −0.761226 | − | 0.648487i | \(-0.775402\pi\) | ||||
−0.761226 | + | 0.648487i | \(0.775402\pi\) | |||||||
\(152\) | 9.02546 | 0.732062 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.7082 | −1.10107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8098 | 1.18195 | 0.590977 | − | 0.806689i | \(-0.298742\pi\) | ||||
0.590977 | + | 0.806689i | \(0.298742\pi\) | |||||||
\(158\) | 4.79837 | 0.381738 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.8554 | 1.01631 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.76393 | −0.294814 | −0.147407 | − | 0.989076i | \(-0.547093\pi\) | ||||
−0.147407 | + | 0.989076i | \(0.547093\pi\) | |||||||
\(164\) | −9.35931 | −0.730840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.32300 | −0.413145 | ||||||||
\(167\) | −18.1784 | −1.40669 | −0.703345 | − | 0.710848i | \(-0.748311\pi\) | ||||
−0.703345 | + | 0.710848i | \(0.748311\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.94427 | 0.611098 | ||||||||
\(170\) | 4.47214 | 0.342997 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.61803 | −0.733368 | ||||||||
\(173\) | 16.0965 | 1.22380 | 0.611898 | − | 0.790936i | \(-0.290406\pi\) | ||||
0.611898 | + | 0.790936i | \(0.290406\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.85410 | 0.139758 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.90879 | 0.292976 | ||||||||
\(179\) | −24.3607 | −1.82080 | −0.910401 | − | 0.413726i | \(-0.864227\pi\) | ||||
−0.910401 | + | 0.413726i | \(0.864227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.6367 | −1.23660 | −0.618299 | − | 0.785943i | \(-0.712178\pi\) | ||||
−0.618299 | + | 0.785943i | \(0.712178\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.1803 | −1.19283 | ||||||||
\(185\) | 24.5030 | 1.80150 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16228 | 0.231249 | ||||||||
\(188\) | −4.91034 | −0.358123 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.70820 | 0.414117 | ||||||||
\(191\) | 22.4164 | 1.62199 | 0.810997 | − | 0.585050i | \(-0.198925\pi\) | ||||
0.810997 | + | 0.585050i | \(0.198925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.52786 | −0.541868 | −0.270934 | − | 0.962598i | \(-0.587332\pi\) | ||||
−0.270934 | + | 0.962598i | \(0.587332\pi\) | |||||||
\(194\) | 3.82998 | 0.274976 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.41641 | −0.599644 | −0.299822 | − | 0.953995i | \(-0.596927\pi\) | ||||
−0.299822 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.37016 | −0.309792 | −0.154896 | − | 0.987931i | \(-0.549504\pi\) | ||||
−0.154896 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(200\) | 0.527864 | 0.0373256 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.5687 | 0.813974 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.2361 | −0.924447 | ||||||||
\(206\) | −3.57494 | −0.249078 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.48528 | −0.588348 | ||||||||
\(209\) | 4.03631 | 0.279197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7082 | −1.15024 | −0.575120 | − | 0.818069i | \(-0.695045\pi\) | ||||
−0.575120 | + | 0.818069i | \(0.695045\pi\) | |||||||
\(212\) | −17.3262 | −1.18997 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.38197 | −0.504621 | ||||||||
\(215\) | −13.6020 | −0.927646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.23607 | 0.625545 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.70246 | 0.249620 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.32300 | −0.356455 | −0.178227 | − | 0.983989i | \(-0.557036\pi\) | ||||
−0.178227 | + | 0.983989i | \(0.557036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.32624 | 0.154739 | ||||||||
\(227\) | −0.952843 | −0.0632424 | −0.0316212 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316212 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.78437 | −0.382242 | −0.191121 | − | 0.981566i | \(-0.561212\pi\) | ||||
−0.191121 | + | 0.981566i | \(0.561212\pi\) | |||||||
\(230\) | −10.2333 | −0.674767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.76393 | 0.181461 | ||||||||
\(233\) | 5.05573 | 0.331212 | 0.165606 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165606 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.94427 | −0.452994 | ||||||||
\(236\) | −23.4226 | −1.52468 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.94427 | −0.255134 | −0.127567 | − | 0.991830i | \(-0.540717\pi\) | ||||
−0.127567 | + | 0.991830i | \(0.540717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3516 | −1.05330 | −0.526649 | − | 0.850083i | \(-0.676552\pi\) | ||||
−0.526649 | + | 0.850083i | \(0.676552\pi\) | |||||||
\(242\) | 6.18034 | 0.397287 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.4760 | 0.926730 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4721 | −1.17535 | ||||||||
\(248\) | 13.3956 | 0.850623 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.73722 | −0.426099 | ||||||||
\(251\) | 18.5123 | 1.16849 | 0.584243 | − | 0.811579i | \(-0.301392\pi\) | ||||
0.584243 | + | 0.811579i | \(0.301392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.23607 | −0.454928 | ||||||||
\(254\) | 10.9098 | 0.684544 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −9.56564 | −0.596689 | −0.298344 | − | 0.954458i | \(-0.596434\pi\) | ||||
−0.298344 | + | 0.954458i | \(0.596434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.9443 | −1.05084 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.5216 | 0.773586 | ||||||||
\(263\) | 9.76393 | 0.602070 | 0.301035 | − | 0.953613i | \(-0.402668\pi\) | ||||
0.301035 | + | 0.953613i | \(0.402668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.5030 | −1.50521 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.38197 | −0.145502 | ||||||||
\(269\) | −4.16383 | −0.253873 | −0.126937 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126937 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1723 | −1.58985 | −0.794926 | − | 0.606707i | \(-0.792490\pi\) | ||||
−0.794926 | + | 0.606707i | \(0.792490\pi\) | |||||||
\(272\) | 5.86319 | 0.355508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.09017 | −0.307508 | ||||||||
\(275\) | 0.236068 | 0.0142354 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2361 | 0.615026 | 0.307513 | − | 0.951544i | \(-0.400503\pi\) | ||||
0.307513 | + | 0.951544i | \(0.400503\pi\) | |||||||
\(278\) | −5.99070 | −0.359299 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.00000 | −0.298275 | −0.149137 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149137 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.3516 | 0.972000 | 0.486000 | − | 0.873959i | \(-0.338456\pi\) | ||||
0.486000 | + | 0.873959i | \(0.338456\pi\) | |||||||
\(284\) | −8.85410 | −0.525394 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82843 | 0.167248 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 1.74806 | 0.102650 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.9010 | −0.637935 | ||||||||
\(293\) | −13.5231 | −0.790030 | −0.395015 | − | 0.918675i | \(-0.629261\pi\) | ||||
−0.395015 | + | 0.918675i | \(0.629261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.1246 | −1.92859 | ||||||||
\(296\) | −23.9443 | −1.39173 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.50658 | 0.376916 | ||||||||
\(299\) | 33.1158 | 1.91514 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.5623 | 0.665336 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.48373 | 0.429221 | ||||||||
\(305\) | 20.4721 | 1.17223 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9830 | 0.740977 | 0.370488 | − | 0.928837i | \(-0.379190\pi\) | ||||
0.370488 | + | 0.928837i | \(0.379190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.47214 | 0.481185 | ||||||||
\(311\) | 12.6004 | 0.714503 | 0.357252 | − | 0.934008i | \(-0.383714\pi\) | ||||
0.357252 | + | 0.934008i | \(0.383714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.746512 | −0.0421954 | −0.0210977 | − | 0.999777i | \(-0.506716\pi\) | ||||
−0.0210977 | + | 0.999777i | \(0.506716\pi\) | |||||||
\(314\) | −9.15298 | −0.516533 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.5623 | 0.706685 | ||||||||
\(317\) | −34.8328 | −1.95641 | −0.978203 | − | 0.207651i | \(-0.933418\pi\) | ||||
−0.978203 | + | 0.207651i | \(0.933418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23607 | 0.0692065 | ||||||||
\(320\) | 0.540182 | 0.0301971 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.7639 | 0.710204 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.08036 | −0.0599278 | ||||||||
\(326\) | 2.32624 | 0.128838 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.9343 | 0.714175 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | −13.9358 | −0.764827 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.2349 | 0.614746 | ||||||||
\(335\) | −3.36861 | −0.184047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.18034 | 0.282191 | 0.141096 | − | 0.989996i | \(-0.454938\pi\) | ||||
0.141096 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(338\) | −4.90983 | −0.267060 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.7082 | 0.634967 | ||||||||
\(341\) | 5.99070 | 0.324415 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.2918 | 0.716646 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.94820 | −0.534819 | ||||||||
\(347\) | 4.05573 | 0.217723 | 0.108861 | − | 0.994057i | \(-0.465280\pi\) | ||||
0.108861 | + | 0.994057i | \(0.465280\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.7673 | −1.00459 | −0.502296 | − | 0.864696i | \(-0.667511\pi\) | ||||
−0.502296 | + | 0.864696i | \(0.667511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.61803 | −0.299442 | ||||||||
\(353\) | −33.2433 | −1.76936 | −0.884682 | − | 0.466195i | \(-0.845624\pi\) | ||||
−0.884682 | + | 0.466195i | \(0.845624\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.5216 | −0.664577 | ||||||||
\(356\) | 10.2333 | 0.542366 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0557 | 0.795720 | ||||||||
\(359\) | −5.18034 | −0.273408 | −0.136704 | − | 0.990612i | \(-0.543651\pi\) | ||||
−0.136704 | + | 0.990612i | \(0.543651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.70820 | −0.142537 | ||||||||
\(362\) | 10.2821 | 0.540413 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.4164 | −0.806932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.57649 | 0.238891 | 0.119445 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119445 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(368\) | −13.4164 | −0.699379 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.1437 | −0.787283 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1803 | 0.682452 | 0.341226 | − | 0.939981i | \(-0.389158\pi\) | ||||
0.341226 | + | 0.939981i | \(0.389158\pi\) | |||||||
\(374\) | −1.95440 | −0.101059 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.78593 | 0.349957 | ||||||||
\(377\) | −5.65685 | −0.291343 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.347524 | −0.0178511 | −0.00892556 | − | 0.999960i | \(-0.502841\pi\) | ||||
−0.00892556 | + | 0.999960i | \(0.502841\pi\) | |||||||
\(380\) | 14.9443 | 0.766625 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.8541 | −0.708838 | ||||||||
\(383\) | 24.6305 | 1.25856 | 0.629280 | − | 0.777178i | \(-0.283350\pi\) | ||||
0.629280 | + | 0.777178i | \(0.283350\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.65248 | 0.236805 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0270 | 0.509045 | ||||||||
\(389\) | −6.94427 | −0.352089 | −0.176044 | − | 0.984382i | \(-0.556330\pi\) | ||||
−0.176044 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8825 | −1.15722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.20163 | 0.262054 | ||||||||
\(395\) | 17.7658 | 0.893894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.9867 | 1.60537 | 0.802684 | − | 0.596405i | \(-0.203405\pi\) | ||||
0.802684 | + | 0.596405i | \(0.203405\pi\) | |||||||
\(398\) | 2.70091 | 0.135384 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.437694 | 0.0218847 | ||||||||
\(401\) | −21.0689 | −1.05213 | −0.526065 | − | 0.850444i | \(-0.676333\pi\) | ||||
−0.526065 | + | 0.850444i | \(0.676333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.4164 | −1.36571 | ||||||||
\(404\) | 30.2874 | 1.50685 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.7082 | −0.530786 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.9265 | −0.985302 | −0.492651 | − | 0.870227i | \(-0.663972\pi\) | ||||
−0.492651 | + | 0.870227i | \(0.663972\pi\) | |||||||
\(410\) | 8.18034 | 0.403998 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.35931 | −0.461100 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.7082 | −0.967438 | ||||||||
\(416\) | 25.7109 | 1.26058 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.49458 | −0.122014 | ||||||||
\(419\) | 23.0100 | 1.12411 | 0.562055 | − | 0.827100i | \(-0.310011\pi\) | ||||
0.562055 | + | 0.827100i | \(0.310011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8885 | −1.01805 | −0.509023 | − | 0.860753i | \(-0.669993\pi\) | ||||
−0.509023 | + | 0.860753i | \(0.669993\pi\) | |||||||
\(422\) | 10.3262 | 0.502673 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.9443 | 1.16284 | ||||||||
\(425\) | 0.746512 | 0.0362112 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −19.3262 | −0.934169 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.40647 | 0.405396 | ||||||||
\(431\) | 3.41641 | 0.164563 | 0.0822813 | − | 0.996609i | \(-0.473779\pi\) | ||||
0.0822813 | + | 0.996609i | \(0.473779\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.2433 | 1.59757 | 0.798786 | − | 0.601615i | \(-0.205476\pi\) | ||||
0.798786 | + | 0.601615i | \(0.205476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.1803 | 1.15803 | ||||||||
\(437\) | −29.2070 | −1.39716 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7379 | 1.70568 | 0.852838 | − | 0.522175i | \(-0.174879\pi\) | ||||
0.852838 | + | 0.522175i | \(0.174879\pi\) | |||||||
\(440\) | −5.11667 | −0.243928 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.94427 | 0.425436 | ||||||||
\(443\) | −15.7082 | −0.746319 | −0.373160 | − | 0.927767i | \(-0.621726\pi\) | ||||
−0.373160 | + | 0.927767i | \(0.621726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4721 | 0.686045 | ||||||||
\(446\) | 3.28980 | 0.155776 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5279 | 1.06316 | 0.531578 | − | 0.847009i | \(-0.321599\pi\) | ||||
0.531578 | + | 0.847009i | \(0.321599\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.78437 | 0.272376 | ||||||||
\(452\) | 6.09017 | 0.286457 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.588890 | 0.0276380 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.8328 | −1.39552 | −0.697760 | − | 0.716331i | \(-0.745820\pi\) | ||||
−0.697760 | + | 0.716331i | \(0.745820\pi\) | |||||||
\(458\) | 3.57494 | 0.167046 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.7912 | −1.24915 | ||||||||
\(461\) | −8.69161 | −0.404809 | −0.202404 | − | 0.979302i | \(-0.564876\pi\) | ||||
−0.202404 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.11146 | −0.0516537 | −0.0258269 | − | 0.999666i | \(-0.508222\pi\) | ||||
−0.0258269 | + | 0.999666i | \(0.508222\pi\) | |||||||
\(464\) | 2.29180 | 0.106394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.12461 | −0.144745 | ||||||||
\(467\) | 13.4443 | 0.622129 | 0.311065 | − | 0.950389i | \(-0.399314\pi\) | ||||
0.311065 | + | 0.950389i | \(0.399314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.29180 | 0.197966 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.3693 | 1.48992 | ||||||||
\(473\) | 5.94427 | 0.273318 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.952843 | 0.0437195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.43769 | 0.111498 | ||||||||
\(479\) | −14.0633 | −0.642570 | −0.321285 | − | 0.946983i | \(-0.604115\pi\) | ||||
−0.321285 | + | 0.946983i | \(0.604115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.0060 | 2.23448 | ||||||||
\(482\) | 10.1058 | 0.460308 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.1803 | 0.735470 | ||||||||
\(485\) | 14.1803 | 0.643896 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.94427 | 0.178732 | 0.0893660 | − | 0.995999i | \(-0.471516\pi\) | ||||
0.0893660 | + | 0.995999i | \(0.471516\pi\) | |||||||
\(488\) | −20.0053 | −0.905598 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0000 | 0.992846 | 0.496423 | − | 0.868081i | \(-0.334646\pi\) | ||||
0.496423 | + | 0.868081i | \(0.334646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.90879 | 0.176043 | ||||||||
\(494\) | 11.4164 | 0.513648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.1074 | 0.498736 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.8885 | 0.979866 | 0.489933 | − | 0.871760i | \(-0.337021\pi\) | ||||
0.489933 | + | 0.871760i | \(0.337021\pi\) | |||||||
\(500\) | −17.6383 | −0.788807 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.4412 | −0.510647 | ||||||||
\(503\) | 6.48218 | 0.289026 | 0.144513 | − | 0.989503i | \(-0.453838\pi\) | ||||
0.144513 | + | 0.989503i | \(0.453838\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.8328 | 1.90604 | ||||||||
\(506\) | 4.47214 | 0.198811 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.5623 | 1.26725 | ||||||||
\(509\) | −21.4682 | −0.951563 | −0.475782 | − | 0.879563i | \(-0.657835\pi\) | ||||
−0.475782 | + | 0.879563i | \(0.657835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.91189 | 0.260762 | ||||||||
\(515\) | −13.2361 | −0.583251 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.03476 | 0.133469 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.4164 | 1.02688 | ||||||||
\(521\) | 9.23179 | 0.404452 | 0.202226 | − | 0.979339i | \(-0.435182\pi\) | ||||
0.202226 | + | 0.979339i | \(0.435182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.28669 | 0.0562632 | 0.0281316 | − | 0.999604i | \(-0.491044\pi\) | ||||
0.0281316 | + | 0.999604i | \(0.491044\pi\) | |||||||
\(524\) | 32.7820 | 1.43209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.03444 | −0.263114 | ||||||||
\(527\) | 18.9443 | 0.825225 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.3607 | 1.27655 | ||||||||
\(530\) | 15.1437 | 0.657800 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.4721 | −1.14664 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.3314 | −1.18164 | ||||||||
\(536\) | 3.29180 | 0.142184 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.57339 | 0.110947 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5967 | 1.31546 | 0.657728 | − | 0.753255i | \(-0.271517\pi\) | ||||
0.657728 | + | 0.753255i | \(0.271517\pi\) | |||||||
\(542\) | 16.1753 | 0.694790 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.7658 | −0.761702 | ||||||||
\(545\) | 34.1962 | 1.46480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7082 | 0.457850 | 0.228925 | − | 0.973444i | \(-0.426479\pi\) | ||||
0.228925 | + | 0.973444i | \(0.426479\pi\) | |||||||
\(548\) | −13.3262 | −0.569269 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.145898 | −0.00622111 | ||||||||
\(551\) | 4.98915 | 0.212545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.32624 | −0.268776 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.6839 | −0.665144 | ||||||||
\(557\) | 7.29180 | 0.308963 | 0.154482 | − | 0.987996i | \(-0.450629\pi\) | ||||
0.154482 | + | 0.987996i | \(0.450629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.2039 | −1.15060 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.09017 | 0.130351 | ||||||||
\(563\) | −27.9504 | −1.17797 | −0.588985 | − | 0.808144i | \(-0.700472\pi\) | ||||
−0.588985 | + | 0.808144i | \(0.700472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.61280 | 0.362343 | ||||||||
\(566\) | −10.1058 | −0.424780 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.2361 | 0.513414 | ||||||||
\(569\) | −15.5836 | −0.653298 | −0.326649 | − | 0.945146i | \(-0.605920\pi\) | ||||
−0.326649 | + | 0.945146i | \(0.605920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.8197 | −0.745730 | −0.372865 | − | 0.927886i | \(-0.621624\pi\) | ||||
−0.372865 | + | 0.927886i | \(0.621624\pi\) | |||||||
\(572\) | 7.40492 | 0.309615 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.70820 | −0.0712370 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.03476 | −0.126339 | −0.0631693 | − | 0.998003i | \(-0.520121\pi\) | ||||
−0.0631693 | + | 0.998003i | \(0.520121\pi\) | |||||||
\(578\) | 4.32624 | 0.179948 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.57649 | 0.190028 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.7082 | 0.443488 | ||||||||
\(584\) | 15.0649 | 0.623389 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.35776 | 0.345256 | ||||||||
\(587\) | −28.2055 | −1.16416 | −0.582082 | − | 0.813130i | \(-0.697762\pi\) | ||||
−0.582082 | + | 0.813130i | \(0.697762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.1803 | 0.996334 | ||||||||
\(590\) | 20.4721 | 0.842824 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.8541 | −0.815999 | ||||||||
\(593\) | −34.2750 | −1.40750 | −0.703752 | − | 0.710445i | \(-0.748494\pi\) | ||||
−0.703752 | + | 0.710445i | \(0.748494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.0344 | 0.697758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.4667 | −0.836945 | ||||||||
\(599\) | −13.8328 | −0.565194 | −0.282597 | − | 0.959239i | \(-0.591196\pi\) | ||||
−0.282597 | + | 0.959239i | \(0.591196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.8245 | −1.17577 | −0.587887 | − | 0.808943i | \(-0.700040\pi\) | ||||
−0.587887 | + | 0.808943i | \(0.700040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.2705 | 1.23169 | ||||||||
\(605\) | 22.8825 | 0.930304 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.20943 | −0.0896782 | −0.0448391 | − | 0.998994i | \(-0.514278\pi\) | ||||
−0.0448391 | + | 0.998994i | \(0.514278\pi\) | |||||||
\(608\) | −22.6761 | −0.919638 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6525 | −0.512284 | ||||||||
\(611\) | −13.8885 | −0.561870 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8197 | 0.679340 | 0.339670 | − | 0.940545i | \(-0.389685\pi\) | ||||
0.339670 | + | 0.940545i | \(0.389685\pi\) | |||||||
\(614\) | −8.02391 | −0.323819 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.41641 | −0.218056 | −0.109028 | − | 0.994039i | \(-0.534774\pi\) | ||||
−0.109028 | + | 0.994039i | \(0.534774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.0485 | −1.81065 | −0.905326 | − | 0.424717i | \(-0.860374\pi\) | ||||
−0.905326 | + | 0.424717i | \(0.860374\pi\) | |||||||
\(620\) | 22.1803 | 0.890784 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.78748 | −0.312249 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.1246 | −1.04498 | ||||||||
\(626\) | 0.461370 | 0.0184401 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.9628 | −0.956221 | ||||||||
\(629\) | −33.8623 | −1.35018 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6525 | −1.69797 | −0.848984 | − | 0.528418i | \(-0.822785\pi\) | ||||
−0.848984 | + | 0.528418i | \(0.822785\pi\) | |||||||
\(632\) | −17.3607 | −0.690571 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.5279 | 0.854981 | ||||||||
\(635\) | 40.3932 | 1.60296 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.763932 | −0.0302444 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.0447 | −1.02951 | ||||||||
\(641\) | −21.4721 | −0.848098 | −0.424049 | − | 0.905639i | \(-0.639392\pi\) | ||||
−0.424049 | + | 0.905639i | \(0.639392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.08347 | −0.121600 | −0.0608000 | − | 0.998150i | \(-0.519365\pi\) | ||||
−0.0608000 | + | 0.998150i | \(0.519365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.88854 | −0.310371 | ||||||||
\(647\) | −36.7394 | −1.44438 | −0.722188 | − | 0.691696i | \(-0.756864\pi\) | ||||
−0.722188 | + | 0.691696i | \(0.756864\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.4760 | 0.568232 | ||||||||
\(650\) | 0.667701 | 0.0261894 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.09017 | 0.238509 | ||||||||
\(653\) | 16.7082 | 0.653843 | 0.326921 | − | 0.945052i | \(-0.393989\pi\) | ||||
0.326921 | + | 0.945052i | \(0.393989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.3607 | 1.81146 | ||||||||
\(656\) | 10.7248 | 0.418734 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2361 | −0.632467 | −0.316234 | − | 0.948681i | \(-0.602418\pi\) | ||||
−0.316234 | + | 0.948681i | \(0.602418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.98915 | −0.194056 | −0.0970278 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970278 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(662\) | −1.23607 | −0.0480411 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.2588 | 0.747387 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.94427 | −0.346324 | ||||||||
\(668\) | 29.4133 | 1.13804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.08191 | 0.0804314 | ||||||||
\(671\) | −8.94665 | −0.345382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6525 | −0.834642 | −0.417321 | − | 0.908759i | \(-0.637031\pi\) | ||||
−0.417321 | + | 0.908759i | \(0.637031\pi\) | |||||||
\(674\) | −3.20163 | −0.123322 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8541 | −0.494389 | ||||||||
\(677\) | −7.07107 | −0.271763 | −0.135882 | − | 0.990725i | \(-0.543387\pi\) | ||||
−0.135882 | + | 0.990725i | \(0.543387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.1803 | −0.620488 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.70246 | −0.141774 | ||||||||
\(683\) | −22.2361 | −0.850839 | −0.425420 | − | 0.904996i | \(-0.639874\pi\) | ||||
−0.425420 | + | 0.904996i | \(0.639874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.8461 | −0.720074 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.0213 | 0.420183 | ||||||||
\(689\) | −49.0060 | −1.86698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.7711 | 1.43688 | 0.718440 | − | 0.695589i | \(-0.244856\pi\) | ||||
0.718440 | + | 0.695589i | \(0.244856\pi\) | |||||||
\(692\) | −26.0447 | −0.990072 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.50658 | −0.0951484 | ||||||||
\(695\) | −22.1803 | −0.841348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.2918 | 0.692851 | ||||||||
\(698\) | 11.5989 | 0.439023 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.18034 | 0.346737 | 0.173368 | − | 0.984857i | \(-0.444535\pi\) | ||||
0.173368 | + | 0.984857i | \(0.444535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.2216 | −1.63013 | ||||||||
\(704\) | −0.236068 | −0.00889715 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.5455 | 0.773240 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.6525 | 0.963399 | 0.481699 | − | 0.876336i | \(-0.340020\pi\) | ||||
0.481699 | + | 0.876336i | \(0.340020\pi\) | |||||||
\(710\) | 7.73877 | 0.290431 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.1421 | −0.529999 | ||||||||
\(713\) | −43.3491 | −1.62344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4721 | 0.391636 | ||||||||
\(716\) | 39.4164 | 1.47306 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.20163 | 0.119484 | ||||||||
\(719\) | −51.7556 | −1.93016 | −0.965079 | − | 0.261958i | \(-0.915632\pi\) | ||||
−0.965079 | + | 0.261958i | \(0.915632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.67376 | 0.0622910 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.9188 | 1.00043 | ||||||||
\(725\) | 0.291796 | 0.0108370 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.1320 | 1.78512 | 0.892558 | − | 0.450933i | \(-0.148909\pi\) | ||||
0.892558 | + | 0.450933i | \(0.148909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.52786 | 0.352642 | ||||||||
\(731\) | 18.7974 | 0.695248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.78437 | 0.213651 | 0.106825 | − | 0.994278i | \(-0.465931\pi\) | ||||
0.106825 | + | 0.994278i | \(0.465931\pi\) | |||||||
\(734\) | −2.82843 | −0.104399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.6525 | 1.49847 | ||||||||
\(737\) | 1.47214 | 0.0542268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3607 | 0.417909 | 0.208955 | − | 0.977925i | \(-0.432994\pi\) | ||||
0.208955 | + | 0.977925i | \(0.432994\pi\) | |||||||
\(740\) | −39.6467 | −1.45744 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.2492 | 1.43991 | 0.719957 | − | 0.694018i | \(-0.244161\pi\) | ||||
0.719957 | + | 0.694018i | \(0.244161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.0903 | 0.882602 | ||||||||
\(746\) | −8.14590 | −0.298243 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.11667 | −0.187084 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3050 | −1.17882 | −0.589412 | − | 0.807832i | \(-0.700641\pi\) | ||||
−0.589412 | + | 0.807832i | \(0.700641\pi\) | |||||||
\(752\) | 5.62675 | 0.205186 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.49613 | 0.127321 | ||||||||
\(755\) | 42.8090 | 1.55798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0689 | −1.52902 | −0.764510 | − | 0.644612i | \(-0.777019\pi\) | ||||
−0.764510 | + | 0.644612i | \(0.777019\pi\) | |||||||
\(758\) | 0.214782 | 0.00780122 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.6525 | −0.749144 | ||||||||
\(761\) | −20.2604 | −0.734437 | −0.367219 | − | 0.930135i | \(-0.619690\pi\) | ||||
−0.367219 | + | 0.930135i | \(0.619690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −36.2705 | −1.31222 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.2225 | −0.550011 | ||||||||
\(767\) | −66.2492 | −2.39212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.1120 | 0.508893 | 0.254446 | − | 0.967087i | \(-0.418107\pi\) | ||||
0.254446 | + | 0.967087i | \(0.418107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.1803 | 0.438380 | ||||||||
\(773\) | 42.6026 | 1.53231 | 0.766155 | − | 0.642656i | \(-0.222167\pi\) | ||||
0.766155 | + | 0.642656i | \(0.222167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.41421 | 0.0508001 | ||||||||
\(776\) | −13.8570 | −0.497437 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.29180 | 0.153868 | ||||||||
\(779\) | 23.3475 | 0.836512 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.47214 | 0.195808 | ||||||||
\(782\) | 14.1421 | 0.505722 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.8885 | −1.20953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.6343 | −1.55539 | −0.777697 | − | 0.628639i | \(-0.783612\pi\) | ||||
−0.777697 | + | 0.628639i | \(0.783612\pi\) | |||||||
\(788\) | 13.6180 | 0.485122 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.9799 | −0.390646 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.9443 | 1.45397 | ||||||||
\(794\) | −19.7689 | −0.701572 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.07107 | 0.250627 | ||||||||
\(797\) | 20.8794 | 0.739585 | 0.369792 | − | 0.929114i | \(-0.379429\pi\) | ||||
0.369792 | + | 0.929114i | \(0.379429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.59675 | 0.339509 | ||||||||
\(800\) | −1.32624 | −0.0468896 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.0213 | 0.459798 | ||||||||
\(803\) | 6.73722 | 0.237751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.9443 | 0.596837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −41.8561 | −1.47249 | ||||||||
\(809\) | −23.5410 | −0.827658 | −0.413829 | − | 0.910355i | \(-0.635809\pi\) | ||||
−0.413829 | + | 0.910355i | \(0.635809\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.4990 | 1.77326 | 0.886630 | − | 0.462479i | \(-0.153040\pi\) | ||||
0.886630 | + | 0.462479i | \(0.153040\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.61803 | 0.231962 | ||||||||
\(815\) | 8.61280 | 0.301693 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9929 | 0.839406 | ||||||||
\(818\) | 12.3153 | 0.430593 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.4164 | 0.747893 | ||||||||
\(821\) | −10.8197 | −0.377609 | −0.188804 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188804 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4164 | 0.607098 | 0.303549 | − | 0.952816i | \(-0.401828\pi\) | ||||
0.303549 | + | 0.952816i | \(0.401828\pi\) | |||||||
\(824\) | 12.9343 | 0.450586 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.65248 | 0.335649 | 0.167825 | − | 0.985817i | \(-0.446326\pi\) | ||||
0.167825 | + | 0.985817i | \(0.446326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.24109 | 0.112568 | 0.0562838 | − | 0.998415i | \(-0.482075\pi\) | ||||
0.0562838 | + | 0.998415i | \(0.482075\pi\) | |||||||
\(830\) | 12.1803 | 0.422786 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.08036 | 0.0374548 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.5967 | 1.43951 | ||||||||
\(836\) | −6.53089 | −0.225875 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.2209 | −0.491254 | ||||||||
\(839\) | −19.0038 | −0.656083 | −0.328041 | − | 0.944663i | \(-0.606389\pi\) | ||||
−0.328041 | + | 0.944663i | \(0.606389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4721 | −0.947315 | ||||||||
\(842\) | 12.9098 | 0.444902 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.0344 | 0.930564 | ||||||||
\(845\) | −18.1784 | −0.625358 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.8541 | 0.681793 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.461370 | −0.0158249 | ||||||||
\(851\) | 77.4853 | 2.65616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7410 | 1.29223 | 0.646114 | − | 0.763241i | \(-0.276393\pi\) | ||||
0.646114 | + | 0.763241i | \(0.276393\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.7082 | 0.912868 | ||||||||
\(857\) | 55.2517 | 1.88736 | 0.943682 | − | 0.330854i | \(-0.107337\pi\) | ||||
0.943682 | + | 0.330854i | \(0.107337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3460 | 1.41071 | 0.705354 | − | 0.708855i | \(-0.250788\pi\) | ||||
0.705354 | + | 0.708855i | \(0.250788\pi\) | |||||||
\(860\) | 22.0084 | 0.750481 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.11146 | −0.0719165 | ||||||||
\(863\) | 40.3050 | 1.37200 | 0.685998 | − | 0.727603i | \(-0.259366\pi\) | ||||
0.685998 | + | 0.727603i | \(0.259366\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.8328 | −1.25235 | ||||||||
\(866\) | −20.5455 | −0.698165 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.76393 | −0.263373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.73722 | −0.228282 | ||||||||
\(872\) | −33.4164 | −1.13162 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.0509 | 0.610582 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2361 | 0.480718 | 0.240359 | − | 0.970684i | \(-0.422735\pi\) | ||||
0.240359 | + | 0.970684i | \(0.422735\pi\) | |||||||
\(878\) | −22.0872 | −0.745408 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.24264 | −0.143019 | ||||||||
\(881\) | −24.9157 | −0.839430 | −0.419715 | − | 0.907656i | \(-0.637870\pi\) | ||||
−0.419715 | + | 0.907656i | \(0.637870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3475 | 0.348222 | 0.174111 | − | 0.984726i | \(-0.444295\pi\) | ||||
0.174111 | + | 0.984726i | \(0.444295\pi\) | |||||||
\(884\) | 23.4164 | 0.787579 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.70820 | 0.326153 | ||||||||
\(887\) | 14.1421 | 0.474846 | 0.237423 | − | 0.971406i | \(-0.423697\pi\) | ||||
0.237423 | + | 0.971406i | \(0.423697\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.94427 | −0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.61280 | 0.288378 | ||||||||
\(893\) | 12.2492 | 0.409905 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.7432 | 1.86329 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.9230 | −0.464616 | ||||||||
\(899\) | 7.40492 | 0.246968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.8623 | 1.12812 | ||||||||
\(902\) | −3.57494 | −0.119032 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.41641 | −0.279926 | ||||||||
\(905\) | 38.0689 | 1.26545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.5410 | −1.84421 | −0.922105 | − | 0.386941i | \(-0.873532\pi\) | ||||
−0.922105 | + | 0.386941i | \(0.873532\pi\) | |||||||
\(908\) | 1.54173 | 0.0511642 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2492 | 1.33352 | 0.666758 | − | 0.745274i | \(-0.267681\pi\) | ||||
0.666758 | + | 0.745274i | \(0.267681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.61280 | 0.285042 | ||||||||
\(914\) | 18.4377 | 0.609865 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.35931 | 0.309240 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.18034 | −0.104910 | −0.0524549 | − | 0.998623i | \(-0.516705\pi\) | ||||
−0.0524549 | + | 0.998623i | \(0.516705\pi\) | |||||||
\(920\) | 37.0246 | 1.22066 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.37171 | 0.176908 | ||||||||
\(923\) | −25.0432 | −0.824306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.52786 | −0.0831157 | ||||||||
\(926\) | 0.686918 | 0.0225735 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.94427 | −0.227957 | ||||||||
\(929\) | −32.0841 | −1.05265 | −0.526323 | − | 0.850284i | \(-0.676430\pi\) | ||||
−0.526323 | + | 0.850284i | \(0.676430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.18034 | −0.267956 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.30905 | −0.271881 | ||||||||
\(935\) | −7.23607 | −0.236645 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.1667 | −1.67154 | −0.835772 | − | 0.549077i | \(-0.814980\pi\) | ||||
−0.835772 | + | 0.549077i | \(0.814980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.2361 | 0.366480 | ||||||||
\(941\) | −21.2920 | −0.694100 | −0.347050 | − | 0.937847i | \(-0.612817\pi\) | ||||
−0.347050 | + | 0.937847i | \(0.612817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.8561 | −1.36302 | ||||||||
\(944\) | 26.8400 | 0.873566 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.67376 | −0.119444 | ||||||||
\(947\) | −42.7639 | −1.38964 | −0.694821 | − | 0.719183i | \(-0.744516\pi\) | ||||
−0.694821 | + | 0.719183i | \(0.744516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8328 | −1.00088 | ||||||||
\(950\) | −0.588890 | −0.0191061 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.4164 | 1.85990 | 0.929950 | − | 0.367686i | \(-0.119850\pi\) | ||||
0.929950 | + | 0.367686i | \(0.119850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51.2942 | −1.65984 | ||||||||
\(956\) | 6.38197 | 0.206408 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.69161 | 0.280813 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.88854 | 0.157695 | ||||||||
\(962\) | −30.2874 | −0.976504 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.4574 | 0.852135 | ||||||||
\(965\) | 17.2256 | 0.554512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.472136 | −0.0151829 | −0.00759143 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00759143 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(968\) | −22.3607 | −0.718699 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.76393 | −0.281393 | ||||||||
\(971\) | 5.99070 | 0.192251 | 0.0961254 | − | 0.995369i | \(-0.469355\pi\) | ||||
0.0961254 | + | 0.995369i | \(0.469355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.43769 | −0.0781088 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.5880 | −0.530969 | ||||||||
\(977\) | 31.3050 | 1.00153 | 0.500767 | − | 0.865582i | \(-0.333051\pi\) | ||||
0.500767 | + | 0.865582i | \(0.333051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.32456 | −0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5967 | −0.433890 | ||||||||
\(983\) | −2.36706 | −0.0754974 | −0.0377487 | − | 0.999287i | \(-0.512019\pi\) | ||||
−0.0377487 | + | 0.999287i | \(0.512019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2588 | 0.613637 | ||||||||
\(986\) | −2.41577 | −0.0769336 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.8885 | 0.950881 | ||||||||
\(989\) | −43.0132 | −1.36774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4164 | 0.648549 | 0.324274 | − | 0.945963i | \(-0.394880\pi\) | ||||
0.324274 | + | 0.945963i | \(0.394880\pi\) | |||||||
\(992\) | −33.6560 | −1.06858 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.8778 | −0.629536 | −0.314768 | − | 0.949169i | \(-0.601927\pi\) | ||||
−0.314768 | + | 0.949169i | \(0.601927\pi\) | |||||||
\(998\) | −13.5279 | −0.428217 | ||||||||
\(999\) | 0 | 0 |
(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 | 3969.2.a.y.1.1 | yes | 4 | |
3.2 | odd | 2 | 3969.2.a.r.1.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 3969.2.a.y.1.2 | yes | 4 | |
21.20 | even | 2 | 3969.2.a.r.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3969.2.a.r.1.3 | ✓ | 4 | 21.20 | even | 2 | ||
3969.2.a.r.1.4 | yes | 4 | 3.2 | odd | 2 | ||
3969.2.a.y.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
3969.2.a.y.1.2 | yes | 4 | 7.6 | odd | 2 | inner |