Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1071,2,Mod(1,1071)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1071, 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("1071.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1071 = 3^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1071.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: | \(8.55197805648\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.453749.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 119) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.32183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1071.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.877834 | −0.620723 | −0.310361 | − | 0.950619i | \(-0.600450\pi\) | ||||
−0.310361 | + | 0.950619i | \(0.600450\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.22941 | −0.614704 | ||||||||
\(5\) | −3.03818 | −1.35872 | −0.679358 | − | 0.733807i | \(-0.737742\pi\) | ||||
−0.679358 | + | 0.733807i | \(0.737742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.83488 | 1.00228 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66702 | 0.843385 | ||||||||
\(11\) | −4.78178 | −1.44176 | −0.720880 | − | 0.693060i | \(-0.756262\pi\) | ||||
−0.720880 | + | 0.693060i | \(0.756262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.39933 | −1.22015 | −0.610077 | − | 0.792342i | \(-0.708861\pi\) | ||||
−0.610077 | + | 0.792342i | \(0.708861\pi\) | |||||||
\(14\) | 0.877834 | 0.234611 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0297440 | −0.00743600 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.64366 | −0.606497 | −0.303248 | − | 0.952912i | \(-0.598071\pi\) | ||||
−0.303248 | + | 0.952912i | \(0.598071\pi\) | |||||||
\(20\) | 3.73516 | 0.835207 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.19761 | 0.894933 | ||||||||
\(23\) | 8.45881 | 1.76378 | 0.881892 | − | 0.471451i | \(-0.156270\pi\) | ||||
0.881892 | + | 0.471451i | \(0.156270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.23054 | 0.846109 | ||||||||
\(26\) | 3.86188 | 0.757377 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22941 | 0.232336 | ||||||||
\(29\) | −7.04298 | −1.30785 | −0.653925 | − | 0.756560i | \(-0.726879\pi\) | ||||
−0.653925 | + | 0.756560i | \(0.726879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.42063 | −0.614364 | −0.307182 | − | 0.951651i | \(-0.599386\pi\) | ||||
−0.307182 | + | 0.951651i | \(0.599386\pi\) | |||||||
\(32\) | −5.64366 | −0.997667 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.877834 | 0.150547 | ||||||||
\(35\) | 3.03818 | 0.513546 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.66977 | 1.58970 | 0.794850 | − | 0.606806i | \(-0.207549\pi\) | ||||
0.794850 | + | 0.606806i | \(0.207549\pi\) | |||||||
\(38\) | 2.32069 | 0.376466 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.61289 | −1.36182 | ||||||||
\(41\) | −1.33675 | −0.208766 | −0.104383 | − | 0.994537i | \(-0.533287\pi\) | ||||
−0.104383 | + | 0.994537i | \(0.533287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.52513 | 0.385078 | 0.192539 | − | 0.981289i | \(-0.438328\pi\) | ||||
0.192539 | + | 0.981289i | \(0.438328\pi\) | |||||||
\(44\) | 5.87875 | 0.886255 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.42544 | −1.09482 | ||||||||
\(47\) | 5.57082 | 0.812588 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.71372 | −0.525199 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.40856 | 0.750033 | ||||||||
\(53\) | −5.17630 | −0.711020 | −0.355510 | − | 0.934673i | \(-0.615693\pi\) | ||||
−0.355510 | + | 0.934673i | \(0.615693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.5279 | 1.95894 | ||||||||
\(56\) | −2.83488 | −0.378827 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.18257 | 0.811812 | ||||||||
\(59\) | −9.28732 | −1.20911 | −0.604553 | − | 0.796565i | \(-0.706648\pi\) | ||||
−0.604553 | + | 0.796565i | \(0.706648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.66325 | 0.853141 | 0.426571 | − | 0.904454i | \(-0.359722\pi\) | ||||
0.426571 | + | 0.904454i | \(0.359722\pi\) | |||||||
\(62\) | 3.00275 | 0.381350 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.01368 | 0.626710 | ||||||||
\(65\) | 13.3659 | 1.65784 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28251 | 0.645362 | 0.322681 | − | 0.946508i | \(-0.395416\pi\) | ||||
0.322681 | + | 0.946508i | \(0.395416\pi\) | |||||||
\(68\) | 1.22941 | 0.149088 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.66702 | −0.318770 | ||||||||
\(71\) | 11.9310 | 1.41595 | 0.707973 | − | 0.706239i | \(-0.249610\pi\) | ||||
0.707973 | + | 0.706239i | \(0.249610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7155 | 1.48823 | 0.744116 | − | 0.668050i | \(-0.232871\pi\) | ||||
0.744116 | + | 0.668050i | \(0.232871\pi\) | |||||||
\(74\) | −8.48845 | −0.986763 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.25013 | 0.372816 | ||||||||
\(77\) | 4.78178 | 0.544934 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.94051 | 0.218325 | 0.109162 | − | 0.994024i | \(-0.465183\pi\) | ||||
0.109162 | + | 0.994024i | \(0.465183\pi\) | |||||||
\(80\) | 0.0903677 | 0.0101034 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.17345 | 0.129586 | ||||||||
\(83\) | 4.58417 | 0.503178 | 0.251589 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251589 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.03818 | 0.329537 | ||||||||
\(86\) | −2.21664 | −0.239027 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.5558 | −1.44505 | ||||||||
\(89\) | 13.3956 | 1.41993 | 0.709965 | − | 0.704237i | \(-0.248711\pi\) | ||||
0.709965 | + | 0.704237i | \(0.248711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.39933 | 0.461175 | ||||||||
\(92\) | −10.3993 | −1.08420 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.89026 | −0.504392 | ||||||||
\(95\) | 8.03191 | 0.824057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1668 | −1.53995 | −0.769976 | − | 0.638073i | \(-0.779732\pi\) | ||||
−0.769976 | + | 0.638073i | \(0.779732\pi\) | |||||||
\(98\) | −0.877834 | −0.0886746 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.20106 | −0.520106 | ||||||||
\(101\) | −3.24786 | −0.323174 | −0.161587 | − | 0.986858i | \(-0.551661\pi\) | ||||
−0.161587 | + | 0.986858i | \(0.551661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7031 | −1.25168 | −0.625839 | − | 0.779952i | \(-0.715243\pi\) | ||||
−0.625839 | + | 0.779952i | \(0.715243\pi\) | |||||||
\(104\) | −12.4716 | −1.22294 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.54393 | 0.441346 | ||||||||
\(107\) | −3.91410 | −0.378390 | −0.189195 | − | 0.981940i | \(-0.560588\pi\) | ||||
−0.189195 | + | 0.981940i | \(0.560588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.56356 | −0.341327 | −0.170663 | − | 0.985329i | \(-0.554591\pi\) | ||||
−0.170663 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(110\) | −12.7531 | −1.21596 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0297440 | 0.00281054 | ||||||||
\(113\) | −0.966622 | −0.0909322 | −0.0454661 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454661 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.6994 | −2.39648 | ||||||||
\(116\) | 8.65869 | 0.803940 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.15272 | 0.750519 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8654 | 1.07867 | ||||||||
\(122\) | −5.84923 | −0.529564 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.20535 | 0.377652 | ||||||||
\(125\) | 2.33775 | 0.209095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.55875 | −0.493260 | −0.246630 | − | 0.969110i | \(-0.579323\pi\) | ||||
−0.246630 | + | 0.969110i | \(0.579323\pi\) | |||||||
\(128\) | 6.88613 | 0.608654 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.7331 | −1.02906 | ||||||||
\(131\) | 3.51134 | 0.306787 | 0.153393 | − | 0.988165i | \(-0.450980\pi\) | ||||
0.153393 | + | 0.988165i | \(0.450980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64366 | 0.229234 | ||||||||
\(134\) | −4.63717 | −0.400590 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.83488 | −0.243089 | ||||||||
\(137\) | 1.93780 | 0.165557 | 0.0827786 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827786 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.69834 | 0.398508 | 0.199254 | − | 0.979948i | \(-0.436148\pi\) | ||||
0.199254 | + | 0.979948i | \(0.436148\pi\) | |||||||
\(140\) | −3.73516 | −0.315679 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4734 | −0.878910 | ||||||||
\(143\) | 21.0366 | 1.75917 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.3979 | 1.77700 | ||||||||
\(146\) | −11.1621 | −0.923780 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.8881 | −0.977194 | ||||||||
\(149\) | −4.24162 | −0.347487 | −0.173743 | − | 0.984791i | \(-0.555586\pi\) | ||||
−0.173743 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4584 | 1.01385 | 0.506924 | − | 0.861991i | \(-0.330783\pi\) | ||||
0.506924 | + | 0.861991i | \(0.330783\pi\) | |||||||
\(152\) | −7.49446 | −0.607881 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.19761 | −0.338253 | ||||||||
\(155\) | 10.3925 | 0.834746 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6472 | −1.40840 | −0.704199 | − | 0.710002i | \(-0.748694\pi\) | ||||
−0.704199 | + | 0.710002i | \(0.748694\pi\) | |||||||
\(158\) | −1.70345 | −0.135519 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.1465 | 1.35555 | ||||||||
\(161\) | −8.45881 | −0.666648 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.67557 | −0.209567 | −0.104783 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104783 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(164\) | 1.64341 | 0.128329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.02414 | −0.312334 | ||||||||
\(167\) | 1.95783 | 0.151501 | 0.0757507 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757507 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.35407 | 0.488775 | ||||||||
\(170\) | −2.66702 | −0.204551 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.10441 | −0.236709 | ||||||||
\(173\) | −6.01732 | −0.457488 | −0.228744 | − | 0.973487i | \(-0.573462\pi\) | ||||
−0.228744 | + | 0.973487i | \(0.573462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.23054 | −0.319799 | ||||||||
\(176\) | 0.142229 | 0.0107209 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.7591 | −0.881382 | ||||||||
\(179\) | −1.75112 | −0.130885 | −0.0654423 | − | 0.997856i | \(-0.520846\pi\) | ||||
−0.0654423 | + | 0.997856i | \(0.520846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.76491 | 0.205514 | 0.102757 | − | 0.994707i | \(-0.467234\pi\) | ||||
0.102757 | + | 0.994707i | \(0.467234\pi\) | |||||||
\(182\) | −3.86188 | −0.286262 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.9798 | 1.76781 | ||||||||
\(185\) | −29.3785 | −2.15995 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.78178 | 0.349678 | ||||||||
\(188\) | −6.84881 | −0.499501 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.05069 | −0.511511 | ||||||||
\(191\) | −18.8461 | −1.36365 | −0.681827 | − | 0.731514i | \(-0.738814\pi\) | ||||
−0.681827 | + | 0.731514i | \(0.738814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9107 | 0.857348 | 0.428674 | − | 0.903459i | \(-0.358981\pi\) | ||||
0.428674 | + | 0.903459i | \(0.358981\pi\) | |||||||
\(194\) | 13.3139 | 0.955883 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.22941 | −0.0878148 | ||||||||
\(197\) | 17.2682 | 1.23031 | 0.615153 | − | 0.788408i | \(-0.289094\pi\) | ||||
0.615153 | + | 0.788408i | \(0.289094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.2451 | −1.08070 | −0.540350 | − | 0.841440i | \(-0.681708\pi\) | ||||
−0.540350 | + | 0.841440i | \(0.681708\pi\) | |||||||
\(200\) | 11.9931 | 0.848040 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.85108 | 0.200601 | ||||||||
\(203\) | 7.04298 | 0.494321 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.06130 | 0.283653 | ||||||||
\(206\) | 11.1513 | 0.776945 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.130854 | 0.00907306 | ||||||||
\(209\) | 12.6414 | 0.874423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.51331 | 0.586080 | 0.293040 | − | 0.956100i | \(-0.405333\pi\) | ||||
0.293040 | + | 0.956100i | \(0.405333\pi\) | |||||||
\(212\) | 6.36378 | 0.437066 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.43593 | 0.234875 | ||||||||
\(215\) | −7.67179 | −0.523212 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.42063 | 0.232208 | ||||||||
\(218\) | 3.12821 | 0.211869 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.8607 | −1.20417 | ||||||||
\(221\) | 4.39933 | 0.295931 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.49093 | −0.166805 | −0.0834027 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834027 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(224\) | 5.64366 | 0.377083 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.848534 | 0.0564437 | ||||||||
\(227\) | 16.9842 | 1.12728 | 0.563640 | − | 0.826020i | \(-0.309400\pi\) | ||||
0.563640 | + | 0.826020i | \(0.309400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3303 | −1.07914 | −0.539568 | − | 0.841942i | \(-0.681413\pi\) | ||||
−0.539568 | + | 0.841942i | \(0.681413\pi\) | |||||||
\(230\) | 22.5598 | 1.48755 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.9660 | −1.31083 | ||||||||
\(233\) | 5.77825 | 0.378546 | 0.189273 | − | 0.981925i | \(-0.439387\pi\) | ||||
0.189273 | + | 0.981925i | \(0.439387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9252 | −1.10408 | ||||||||
\(236\) | 11.4179 | 0.743241 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.877834 | −0.0569015 | ||||||||
\(239\) | −7.44275 | −0.481432 | −0.240716 | − | 0.970596i | \(-0.577382\pi\) | ||||
−0.240716 | + | 0.970596i | \(0.577382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9036 | 1.41093 | 0.705467 | − | 0.708743i | \(-0.250737\pi\) | ||||
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(242\) | −10.4159 | −0.669557 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.19184 | −0.524429 | ||||||||
\(245\) | −3.03818 | −0.194102 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.6303 | 0.740019 | ||||||||
\(248\) | −9.69710 | −0.615766 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.05216 | −0.129790 | ||||||||
\(251\) | −16.5769 | −1.04632 | −0.523162 | − | 0.852233i | \(-0.675248\pi\) | ||||
−0.523162 | + | 0.852233i | \(0.675248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.4482 | −2.54296 | ||||||||
\(254\) | 4.87966 | 0.306177 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0723 | −1.00452 | ||||||||
\(257\) | −12.1158 | −0.755764 | −0.377882 | − | 0.925854i | \(-0.623347\pi\) | ||||
−0.377882 | + | 0.925854i | \(0.623347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.66977 | −0.600850 | ||||||||
\(260\) | −16.4322 | −1.01908 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.08237 | −0.190430 | ||||||||
\(263\) | −3.20135 | −0.197404 | −0.0987018 | − | 0.995117i | \(-0.531469\pi\) | ||||
−0.0987018 | + | 0.995117i | \(0.531469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7265 | 0.966074 | ||||||||
\(266\) | −2.32069 | −0.142291 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.49436 | −0.396706 | ||||||||
\(269\) | −15.4400 | −0.941396 | −0.470698 | − | 0.882294i | \(-0.655998\pi\) | ||||
−0.470698 | + | 0.882294i | \(0.655998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8878 | −1.51182 | −0.755912 | − | 0.654673i | \(-0.772806\pi\) | ||||
−0.755912 | + | 0.654673i | \(0.772806\pi\) | |||||||
\(272\) | 0.0297440 | 0.00180349 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.70106 | −0.102765 | ||||||||
\(275\) | −20.2295 | −1.21989 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2870 | −0.678172 | −0.339086 | − | 0.940755i | \(-0.610118\pi\) | ||||
−0.339086 | + | 0.940755i | \(0.610118\pi\) | |||||||
\(278\) | −4.12437 | −0.247363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.61289 | 0.514719 | ||||||||
\(281\) | −13.0332 | −0.777495 | −0.388747 | − | 0.921344i | \(-0.627092\pi\) | ||||
−0.388747 | + | 0.921344i | \(0.627092\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7190 | 1.29106 | 0.645531 | − | 0.763734i | \(-0.276636\pi\) | ||||
0.645531 | + | 0.763734i | \(0.276636\pi\) | |||||||
\(284\) | −14.6680 | −0.870387 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.4667 | −1.09196 | ||||||||
\(287\) | 1.33675 | 0.0789061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −18.7838 | −1.10302 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.6325 | −0.914822 | ||||||||
\(293\) | 28.9400 | 1.69069 | 0.845346 | − | 0.534219i | \(-0.179394\pi\) | ||||
0.845346 | + | 0.534219i | \(0.179394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2165 | 1.64283 | ||||||||
\(296\) | 27.4127 | 1.59333 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.72344 | 0.215693 | ||||||||
\(299\) | −37.2131 | −2.15209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.52513 | −0.145546 | ||||||||
\(302\) | −10.9364 | −0.629318 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.0786330 | 0.00450991 | ||||||||
\(305\) | −20.2441 | −1.15918 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5836 | −0.661110 | −0.330555 | − | 0.943787i | \(-0.607236\pi\) | ||||
−0.330555 | + | 0.943787i | \(0.607236\pi\) | |||||||
\(308\) | −5.87875 | −0.334973 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.12289 | −0.518146 | ||||||||
\(311\) | 15.7999 | 0.895932 | 0.447966 | − | 0.894051i | \(-0.352149\pi\) | ||||
0.447966 | + | 0.894051i | \(0.352149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2658 | 1.14549 | 0.572745 | − | 0.819733i | \(-0.305878\pi\) | ||||
0.572745 | + | 0.819733i | \(0.305878\pi\) | |||||||
\(314\) | 15.4913 | 0.874225 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.38568 | −0.134205 | ||||||||
\(317\) | −6.36537 | −0.357515 | −0.178757 | − | 0.983893i | \(-0.557208\pi\) | ||||
−0.178757 | + | 0.983893i | \(0.557208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.6780 | 1.88561 | ||||||||
\(320\) | −15.2325 | −0.851521 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.42544 | 0.413803 | ||||||||
\(323\) | 2.64366 | 0.147097 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.6115 | −1.03238 | ||||||||
\(326\) | 2.34871 | 0.130083 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.78954 | −0.209242 | ||||||||
\(329\) | −5.57082 | −0.307130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5910 | 1.35165 | 0.675823 | − | 0.737064i | \(-0.263788\pi\) | ||||
0.675823 | + | 0.737064i | \(0.263788\pi\) | |||||||
\(332\) | −5.63581 | −0.309305 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.71865 | −0.0940403 | ||||||||
\(335\) | −16.0492 | −0.876863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.11956 | 0.387827 | 0.193913 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193913 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(338\) | −5.57782 | −0.303393 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.73516 | −0.202568 | ||||||||
\(341\) | 16.3567 | 0.885766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.15844 | 0.385957 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.28221 | 0.283973 | ||||||||
\(347\) | −1.51477 | −0.0813173 | −0.0406586 | − | 0.999173i | \(-0.512946\pi\) | ||||
−0.0406586 | + | 0.999173i | \(0.512946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7937 | 1.32717 | 0.663587 | − | 0.748099i | \(-0.269033\pi\) | ||||
0.663587 | + | 0.748099i | \(0.269033\pi\) | |||||||
\(350\) | 3.71372 | 0.198506 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.9867 | 1.43840 | ||||||||
\(353\) | 11.8416 | 0.630267 | 0.315133 | − | 0.949047i | \(-0.397951\pi\) | ||||
0.315133 | + | 0.949047i | \(0.397951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.2485 | −1.92387 | ||||||||
\(356\) | −16.4686 | −0.872836 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.53719 | 0.0812430 | ||||||||
\(359\) | 26.6743 | 1.40781 | 0.703907 | − | 0.710292i | \(-0.251437\pi\) | ||||
0.703907 | + | 0.710292i | \(0.251437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0111 | −0.632162 | ||||||||
\(362\) | −2.42713 | −0.127567 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.40856 | −0.283486 | ||||||||
\(365\) | −38.6319 | −2.02209 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.6897 | −1.49759 | −0.748796 | − | 0.662801i | \(-0.769368\pi\) | ||||
−0.748796 | + | 0.662801i | \(0.769368\pi\) | |||||||
\(368\) | −0.251599 | −0.0131155 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.7895 | 1.34073 | ||||||||
\(371\) | 5.17630 | 0.268740 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.8946 | −1.39255 | −0.696275 | − | 0.717775i | \(-0.745161\pi\) | ||||
−0.696275 | + | 0.717775i | \(0.745161\pi\) | |||||||
\(374\) | −4.19761 | −0.217053 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7926 | 0.814443 | ||||||||
\(377\) | 30.9844 | 1.59578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.960453 | 0.0493351 | 0.0246676 | − | 0.999696i | \(-0.492147\pi\) | ||||
0.0246676 | + | 0.999696i | \(0.492147\pi\) | |||||||
\(380\) | −9.87449 | −0.506551 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.5437 | 0.846451 | ||||||||
\(383\) | 10.9913 | 0.561627 | 0.280814 | − | 0.959762i | \(-0.409396\pi\) | ||||
0.280814 | + | 0.959762i | \(0.409396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.5279 | −0.740411 | ||||||||
\(386\) | −10.4556 | −0.532175 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.6461 | 0.946614 | ||||||||
\(389\) | 25.4239 | 1.28904 | 0.644520 | − | 0.764587i | \(-0.277057\pi\) | ||||
0.644520 | + | 0.764587i | \(0.277057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.45881 | −0.427781 | ||||||||
\(392\) | 2.83488 | 0.143183 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.1586 | −0.763679 | ||||||||
\(395\) | −5.89563 | −0.296641 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0140 | −0.753533 | −0.376767 | − | 0.926308i | \(-0.622964\pi\) | ||||
−0.376767 | + | 0.926308i | \(0.622964\pi\) | |||||||
\(398\) | 13.3827 | 0.670815 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.125833 | −0.00629166 | ||||||||
\(401\) | 11.0656 | 0.552588 | 0.276294 | − | 0.961073i | \(-0.410894\pi\) | ||||
0.276294 | + | 0.961073i | \(0.410894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0485 | 0.749618 | ||||||||
\(404\) | 3.99294 | 0.198656 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.18257 | −0.306836 | ||||||||
\(407\) | −46.2387 | −2.29197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5650 | 1.41245 | 0.706225 | − | 0.707988i | \(-0.250397\pi\) | ||||
0.706225 | + | 0.707988i | \(0.250397\pi\) | |||||||
\(410\) | −3.56515 | −0.176070 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.6173 | 0.769411 | ||||||||
\(413\) | 9.28732 | 0.456999 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.9275 | −0.683676 | ||||||||
\(416\) | 24.8283 | 1.21731 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0970 | −0.542774 | ||||||||
\(419\) | 1.98566 | 0.0970057 | 0.0485029 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485029 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1984 | 1.22810 | 0.614048 | − | 0.789269i | \(-0.289540\pi\) | ||||
0.614048 | + | 0.789269i | \(0.289540\pi\) | |||||||
\(422\) | −7.47327 | −0.363793 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.6742 | −0.712643 | ||||||||
\(425\) | −4.23054 | −0.205211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.66325 | −0.322457 | ||||||||
\(428\) | 4.81202 | 0.232598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.73456 | 0.324769 | ||||||||
\(431\) | 27.4984 | 1.32455 | 0.662275 | − | 0.749261i | \(-0.269591\pi\) | ||||
0.662275 | + | 0.749261i | \(0.269591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.1977 | 1.35509 | 0.677547 | − | 0.735480i | \(-0.263043\pi\) | ||||
0.677547 | + | 0.735480i | \(0.263043\pi\) | |||||||
\(434\) | −3.00275 | −0.144137 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.38106 | 0.209815 | ||||||||
\(437\) | −22.3622 | −1.06973 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.31298 | 0.301302 | 0.150651 | − | 0.988587i | \(-0.451863\pi\) | ||||
0.150651 | + | 0.988587i | \(0.451863\pi\) | |||||||
\(440\) | 41.1849 | 1.96341 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.86188 | −0.183691 | ||||||||
\(443\) | −26.4557 | −1.25695 | −0.628473 | − | 0.777831i | \(-0.716320\pi\) | ||||
−0.628473 | + | 0.777831i | \(0.716320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.6982 | −1.92928 | ||||||||
\(446\) | 2.18663 | 0.103540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.01368 | −0.236874 | ||||||||
\(449\) | 34.5555 | 1.63077 | 0.815387 | − | 0.578916i | \(-0.196524\pi\) | ||||
0.815387 | + | 0.578916i | \(0.196524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.39206 | 0.300990 | ||||||||
\(452\) | 1.18837 | 0.0558963 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.9093 | −0.699728 | ||||||||
\(455\) | −13.3659 | −0.626605 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5922 | 1.24393 | 0.621965 | − | 0.783045i | \(-0.286334\pi\) | ||||
0.621965 | + | 0.783045i | \(0.286334\pi\) | |||||||
\(458\) | 14.3353 | 0.669844 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 31.5950 | 1.47313 | ||||||||
\(461\) | 0.310199 | 0.0144474 | 0.00722371 | − | 0.999974i | \(-0.497701\pi\) | ||||
0.00722371 | + | 0.999974i | \(0.497701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4654 | 1.04406 | 0.522028 | − | 0.852928i | \(-0.325175\pi\) | ||||
0.522028 | + | 0.852928i | \(0.325175\pi\) | |||||||
\(464\) | 0.209487 | 0.00972517 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.07235 | −0.234972 | ||||||||
\(467\) | 11.6126 | 0.537365 | 0.268682 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268682 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.28251 | −0.243924 | ||||||||
\(470\) | 14.8575 | 0.685325 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −26.3285 | −1.21187 | ||||||||
\(473\) | −12.0746 | −0.555190 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.1841 | −0.513162 | ||||||||
\(476\) | −1.22941 | −0.0563498 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.53350 | 0.298836 | ||||||||
\(479\) | −31.7976 | −1.45287 | −0.726435 | − | 0.687235i | \(-0.758824\pi\) | ||||
−0.726435 | + | 0.687235i | \(0.758824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.5405 | −1.93968 | ||||||||
\(482\) | −19.2277 | −0.875799 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.5874 | −0.663064 | ||||||||
\(485\) | 46.0794 | 2.09236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.0166 | −1.04298 | −0.521490 | − | 0.853257i | \(-0.674624\pi\) | ||||
−0.521490 | + | 0.853257i | \(0.674624\pi\) | |||||||
\(488\) | 18.8895 | 0.855089 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.66702 | 0.120484 | ||||||||
\(491\) | 33.3176 | 1.50360 | 0.751802 | − | 0.659389i | \(-0.229185\pi\) | ||||
0.751802 | + | 0.659389i | \(0.229185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.04298 | 0.317200 | ||||||||
\(494\) | −10.2095 | −0.459347 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.101743 | 0.00456841 | ||||||||
\(497\) | −11.9310 | −0.535177 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0236 | 1.65741 | 0.828703 | − | 0.559689i | \(-0.189079\pi\) | ||||
0.828703 | + | 0.559689i | \(0.189079\pi\) | |||||||
\(500\) | −2.87405 | −0.128531 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.5518 | 0.649477 | ||||||||
\(503\) | 12.4172 | 0.553654 | 0.276827 | − | 0.960920i | \(-0.410717\pi\) | ||||
0.276827 | + | 0.960920i | \(0.410717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.86759 | 0.439102 | ||||||||
\(506\) | 35.5068 | 1.57847 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.83397 | 0.303208 | ||||||||
\(509\) | −11.9257 | −0.528597 | −0.264299 | − | 0.964441i | \(-0.585140\pi\) | ||||
−0.264299 | + | 0.964441i | \(0.585140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7155 | −0.562499 | ||||||||
\(512\) | 0.336507 | 0.0148716 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.6357 | 0.469120 | ||||||||
\(515\) | 38.5945 | 1.70067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.6385 | −1.17156 | ||||||||
\(518\) | 8.48845 | 0.372961 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 37.8909 | 1.66163 | ||||||||
\(521\) | −26.3980 | −1.15652 | −0.578259 | − | 0.815853i | \(-0.696268\pi\) | ||||
−0.578259 | + | 0.815853i | \(0.696268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.6272 | 0.595874 | 0.297937 | − | 0.954586i | \(-0.403701\pi\) | ||||
0.297937 | + | 0.954586i | \(0.403701\pi\) | |||||||
\(524\) | −4.31686 | −0.188583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.81025 | 0.122533 | ||||||||
\(527\) | 3.42063 | 0.149005 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.5515 | 2.11094 | ||||||||
\(530\) | −13.8053 | −0.599664 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.25013 | −0.140911 | ||||||||
\(533\) | 5.88081 | 0.254726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.8917 | 0.514125 | ||||||||
\(536\) | 14.9753 | 0.646835 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.5538 | 0.584346 | ||||||||
\(539\) | −4.78178 | −0.205966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3358 | 1.13226 | 0.566132 | − | 0.824314i | \(-0.308439\pi\) | ||||
0.566132 | + | 0.824314i | \(0.308439\pi\) | |||||||
\(542\) | 21.8473 | 0.938424 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.64366 | 0.241970 | ||||||||
\(545\) | 10.8267 | 0.463766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.25139 | −0.0962624 | −0.0481312 | − | 0.998841i | \(-0.515327\pi\) | ||||
−0.0481312 | + | 0.998841i | \(0.515327\pi\) | |||||||
\(548\) | −2.38234 | −0.101769 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.7582 | 0.757211 | ||||||||
\(551\) | 18.6192 | 0.793206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.94051 | −0.0825190 | ||||||||
\(554\) | 9.90815 | 0.420957 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.77618 | −0.244964 | ||||||||
\(557\) | −30.3355 | −1.28536 | −0.642679 | − | 0.766136i | \(-0.722177\pi\) | ||||
−0.642679 | + | 0.766136i | \(0.722177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1089 | −0.469854 | ||||||||
\(560\) | −0.0903677 | −0.00381873 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.4410 | 0.482608 | ||||||||
\(563\) | −10.9867 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.93677 | 0.123551 | ||||||||
\(566\) | −19.0657 | −0.801391 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.8229 | 1.41918 | ||||||||
\(569\) | 28.8479 | 1.20937 | 0.604684 | − | 0.796465i | \(-0.293299\pi\) | ||||
0.604684 | + | 0.796465i | \(0.293299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5165 | −0.440100 | −0.220050 | − | 0.975489i | \(-0.570622\pi\) | ||||
−0.220050 | + | 0.975489i | \(0.570622\pi\) | |||||||
\(572\) | −25.8626 | −1.08137 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.17345 | −0.0489788 | ||||||||
\(575\) | 35.7854 | 1.49235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.8288 | −1.53320 | −0.766601 | − | 0.642123i | \(-0.778054\pi\) | ||||
−0.766601 | + | 0.642123i | \(0.778054\pi\) | |||||||
\(578\) | −0.877834 | −0.0365131 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −26.3067 | −1.09233 | ||||||||
\(581\) | −4.58417 | −0.190183 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.7519 | 1.02512 | ||||||||
\(584\) | 36.0469 | 1.49163 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.4045 | −1.04945 | ||||||||
\(587\) | −30.1420 | −1.24409 | −0.622047 | − | 0.782980i | \(-0.713699\pi\) | ||||
−0.622047 | + | 0.782980i | \(0.713699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.04298 | 0.372610 | ||||||||
\(590\) | −24.7694 | −1.01974 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.287618 | −0.0118210 | ||||||||
\(593\) | 7.88925 | 0.323973 | 0.161986 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161986 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.03818 | −0.124553 | ||||||||
\(596\) | 5.21467 | 0.213601 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.6669 | 1.33585 | ||||||||
\(599\) | −29.8059 | −1.21783 | −0.608917 | − | 0.793234i | \(-0.708396\pi\) | ||||
−0.608917 | + | 0.793234i | \(0.708396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9432 | 0.487175 | 0.243587 | − | 0.969879i | \(-0.421676\pi\) | ||||
0.243587 | + | 0.969879i | \(0.421676\pi\) | |||||||
\(602\) | 2.21664 | 0.0903436 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.3164 | −0.623216 | ||||||||
\(605\) | −36.0493 | −1.46561 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.67281 | −0.189664 | −0.0948318 | − | 0.995493i | \(-0.530231\pi\) | ||||
−0.0948318 | + | 0.995493i | \(0.530231\pi\) | |||||||
\(608\) | 14.9199 | 0.605082 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.7710 | 0.719527 | ||||||||
\(611\) | −24.5079 | −0.991483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3894 | 1.71209 | 0.856046 | − | 0.516900i | \(-0.172914\pi\) | ||||
0.856046 | + | 0.516900i | \(0.172914\pi\) | |||||||
\(614\) | 10.1685 | 0.410366 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.5558 | 0.546178 | ||||||||
\(617\) | 23.2809 | 0.937255 | 0.468628 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468628 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.2201 | −1.73716 | −0.868582 | − | 0.495545i | \(-0.834968\pi\) | ||||
−0.868582 | + | 0.495545i | \(0.834968\pi\) | |||||||
\(620\) | −12.7766 | −0.513121 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.8697 | −0.556125 | ||||||||
\(623\) | −13.3956 | −0.536683 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.2552 | −1.13021 | ||||||||
\(626\) | −17.7900 | −0.711032 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.6956 | 0.865748 | ||||||||
\(629\) | −9.66977 | −0.385559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6825 | 1.22145 | 0.610725 | − | 0.791843i | \(-0.290878\pi\) | ||||
0.610725 | + | 0.791843i | \(0.290878\pi\) | |||||||
\(632\) | 5.50113 | 0.218823 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.58774 | 0.221917 | ||||||||
\(635\) | 16.8885 | 0.670200 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.39933 | −0.174308 | ||||||||
\(638\) | −29.5637 | −1.17044 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.9213 | −0.826988 | ||||||||
\(641\) | 21.3561 | 0.843517 | 0.421758 | − | 0.906708i | \(-0.361413\pi\) | ||||
0.421758 | + | 0.906708i | \(0.361413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.7013 | 0.895253 | 0.447626 | − | 0.894221i | \(-0.352269\pi\) | ||||
0.447626 | + | 0.894221i | \(0.352269\pi\) | |||||||
\(644\) | 10.3993 | 0.409791 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.32069 | −0.0913065 | ||||||||
\(647\) | −35.2630 | −1.38633 | −0.693165 | − | 0.720779i | \(-0.743784\pi\) | ||||
−0.693165 | + | 0.720779i | \(0.743784\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.4099 | 1.74324 | ||||||||
\(650\) | 16.3378 | 0.640823 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.28936 | 0.128821 | ||||||||
\(653\) | 30.0593 | 1.17631 | 0.588155 | − | 0.808748i | \(-0.299854\pi\) | ||||
0.588155 | + | 0.808748i | \(0.299854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6681 | −0.416836 | ||||||||
\(656\) | 0.0397604 | 0.00155238 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.89026 | 0.190642 | ||||||||
\(659\) | 18.9747 | 0.739148 | 0.369574 | − | 0.929201i | \(-0.379504\pi\) | ||||
0.369574 | + | 0.929201i | \(0.379504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8038 | 1.00365 | 0.501825 | − | 0.864969i | \(-0.332662\pi\) | ||||
0.501825 | + | 0.864969i | \(0.332662\pi\) | |||||||
\(662\) | −21.5869 | −0.838997 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.9956 | 0.504327 | ||||||||
\(665\) | −8.03191 | −0.311464 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −59.5753 | −2.30676 | ||||||||
\(668\) | −2.40697 | −0.0931284 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.0886 | 0.544289 | ||||||||
\(671\) | −31.8622 | −1.23003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.38401 | 0.168991 | 0.0844956 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844956 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(674\) | −6.24979 | −0.240733 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.81174 | −0.300452 | ||||||||
\(677\) | 32.1115 | 1.23415 | 0.617073 | − | 0.786906i | \(-0.288318\pi\) | ||||
0.617073 | + | 0.786906i | \(0.288318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1668 | 0.582047 | ||||||||
\(680\) | 8.61289 | 0.330289 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.3585 | −0.549815 | ||||||||
\(683\) | 18.7093 | 0.715892 | 0.357946 | − | 0.933742i | \(-0.383477\pi\) | ||||
0.357946 | + | 0.933742i | \(0.383477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.88738 | −0.224945 | ||||||||
\(686\) | 0.877834 | 0.0335159 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0751073 | −0.00286344 | ||||||||
\(689\) | 22.7722 | 0.867553 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.9131 | −1.55641 | −0.778205 | − | 0.628011i | \(-0.783869\pi\) | ||||
−0.778205 | + | 0.628011i | \(0.783869\pi\) | |||||||
\(692\) | 7.39773 | 0.281220 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.32972 | 0.0504755 | ||||||||
\(695\) | −14.2744 | −0.541459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.33675 | 0.0506331 | ||||||||
\(698\) | −21.7647 | −0.823807 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.20106 | 0.196582 | ||||||||
\(701\) | 17.6240 | 0.665649 | 0.332825 | − | 0.942989i | \(-0.391998\pi\) | ||||
0.332825 | + | 0.942989i | \(0.391998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.5636 | −0.964148 | ||||||||
\(704\) | −23.9743 | −0.903566 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.3950 | −0.391221 | ||||||||
\(707\) | 3.24786 | 0.122148 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.18690 | −0.307466 | −0.153733 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153733 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(710\) | 31.8201 | 1.19419 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37.9749 | 1.42317 | ||||||||
\(713\) | −28.9345 | −1.08361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63.9130 | −2.39021 | ||||||||
\(716\) | 2.15283 | 0.0804552 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.4156 | −0.873862 | ||||||||
\(719\) | −42.6093 | −1.58906 | −0.794530 | − | 0.607225i | \(-0.792283\pi\) | ||||
−0.794530 | + | 0.607225i | \(0.792283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.7031 | 0.473090 | ||||||||
\(722\) | 10.5437 | 0.392397 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.39919 | −0.126330 | ||||||||
\(725\) | −29.7956 | −1.10658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5470 | −0.391166 | −0.195583 | − | 0.980687i | \(-0.562660\pi\) | ||||
−0.195583 | + | 0.980687i | \(0.562660\pi\) | |||||||
\(728\) | 12.4716 | 0.462227 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33.9124 | 1.25515 | ||||||||
\(731\) | −2.52513 | −0.0933951 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.61491 | 0.244327 | 0.122164 | − | 0.992510i | \(-0.461017\pi\) | ||||
0.122164 | + | 0.992510i | \(0.461017\pi\) | |||||||
\(734\) | 25.1848 | 0.929589 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.7387 | −1.75967 | ||||||||
\(737\) | −25.2598 | −0.930457 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.834376 | −0.0306930 | −0.0153465 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153465 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(740\) | 36.1181 | 1.32773 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.54393 | −0.166813 | ||||||||
\(743\) | −52.9082 | −1.94101 | −0.970506 | − | 0.241077i | \(-0.922499\pi\) | ||||
−0.970506 | + | 0.241077i | \(0.922499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.8868 | 0.472136 | ||||||||
\(746\) | 23.6090 | 0.864387 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.87875 | −0.214948 | ||||||||
\(749\) | 3.91410 | 0.143018 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.3681 | 1.29060 | 0.645300 | − | 0.763929i | \(-0.276732\pi\) | ||||
0.645300 | + | 0.763929i | \(0.276732\pi\) | |||||||
\(752\) | −0.165699 | −0.00604241 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.1992 | −0.990535 | ||||||||
\(755\) | −37.8508 | −1.37753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6550 | −0.714372 | −0.357186 | − | 0.934033i | \(-0.616264\pi\) | ||||
−0.357186 | + | 0.934033i | \(0.616264\pi\) | |||||||
\(758\) | −0.843118 | −0.0306234 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.7695 | 0.825938 | ||||||||
\(761\) | 6.80776 | 0.246781 | 0.123390 | − | 0.992358i | \(-0.460623\pi\) | ||||
0.123390 | + | 0.992358i | \(0.460623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.56356 | 0.129009 | ||||||||
\(764\) | 23.1695 | 0.838243 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.64851 | −0.348615 | ||||||||
\(767\) | 40.8579 | 1.47529 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.3645 | 1.59983 | 0.799913 | − | 0.600116i | \(-0.204879\pi\) | ||||
0.799913 | + | 0.600116i | \(0.204879\pi\) | |||||||
\(770\) | 12.7531 | 0.459590 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.6431 | −0.527015 | ||||||||
\(773\) | 25.6974 | 0.924270 | 0.462135 | − | 0.886810i | \(-0.347084\pi\) | ||||
0.462135 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.4711 | −0.519819 | ||||||||
\(776\) | −42.9960 | −1.54347 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.3179 | −0.800137 | ||||||||
\(779\) | 3.53392 | 0.126616 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.0513 | −2.04146 | ||||||||
\(782\) | 7.42544 | 0.265533 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.0297440 | −0.00106229 | ||||||||
\(785\) | 53.6153 | 1.91361 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.6566 | 0.914558 | 0.457279 | − | 0.889323i | \(-0.348824\pi\) | ||||
0.457279 | + | 0.889323i | \(0.348824\pi\) | |||||||
\(788\) | −21.2296 | −0.756274 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.17538 | 0.184132 | ||||||||
\(791\) | 0.966622 | 0.0343691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.3138 | −1.04096 | ||||||||
\(794\) | 13.1798 | 0.467735 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.7425 | 0.664310 | ||||||||
\(797\) | −20.3683 | −0.721483 | −0.360741 | − | 0.932666i | \(-0.617476\pi\) | ||||
−0.360741 | + | 0.932666i | \(0.617476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.57082 | −0.197082 | ||||||||
\(800\) | −23.8757 | −0.844135 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.71373 | −0.343004 | ||||||||
\(803\) | −60.8026 | −2.14568 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.6994 | 0.905785 | ||||||||
\(806\) | −13.2101 | −0.465305 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.20731 | −0.323912 | ||||||||
\(809\) | 36.5480 | 1.28496 | 0.642480 | − | 0.766303i | \(-0.277906\pi\) | ||||
0.642480 | + | 0.766303i | \(0.277906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.33037 | 0.257404 | 0.128702 | − | 0.991683i | \(-0.458919\pi\) | ||||
0.128702 | + | 0.991683i | \(0.458919\pi\) | |||||||
\(812\) | −8.65869 | −0.303861 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 40.5899 | 1.42268 | ||||||||
\(815\) | 8.12886 | 0.284742 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67557 | −0.233549 | ||||||||
\(818\) | −25.0754 | −0.876739 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.99299 | −0.174363 | ||||||||
\(821\) | −1.76321 | −0.0615366 | −0.0307683 | − | 0.999527i | \(-0.509795\pi\) | ||||
−0.0307683 | + | 0.999527i | \(0.509795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.636323 | 0.0221808 | 0.0110904 | − | 0.999938i | \(-0.496470\pi\) | ||||
0.0110904 | + | 0.999938i | \(0.496470\pi\) | |||||||
\(824\) | −36.0119 | −1.25454 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.15272 | −0.283670 | ||||||||
\(827\) | 6.81869 | 0.237109 | 0.118554 | − | 0.992948i | \(-0.462174\pi\) | ||||
0.118554 | + | 0.992948i | \(0.462174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.9480 | 1.76950 | 0.884749 | − | 0.466068i | \(-0.154330\pi\) | ||||
0.884749 | + | 0.466068i | \(0.154330\pi\) | |||||||
\(830\) | 12.2261 | 0.424373 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.0568 | −0.764683 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.94824 | −0.205847 | ||||||||
\(836\) | −15.5414 | −0.537511 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.74308 | −0.0602137 | ||||||||
\(839\) | −2.95064 | −0.101867 | −0.0509336 | − | 0.998702i | \(-0.516220\pi\) | ||||
−0.0509336 | + | 0.998702i | \(0.516220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6036 | 0.710470 | ||||||||
\(842\) | −22.1200 | −0.762307 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.4663 | −0.360266 | ||||||||
\(845\) | −19.3048 | −0.664106 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.8654 | −0.407700 | ||||||||
\(848\) | 0.153964 | 0.00528714 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.71372 | 0.127379 | ||||||||
\(851\) | 81.7948 | 2.80389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.8764 | −0.988709 | −0.494355 | − | 0.869260i | \(-0.664596\pi\) | ||||
−0.494355 | + | 0.869260i | \(0.664596\pi\) | |||||||
\(854\) | 5.84923 | 0.200156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.0960 | −0.379254 | ||||||||
\(857\) | 9.83977 | 0.336120 | 0.168060 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168060 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1344 | −0.379900 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(860\) | 9.43175 | 0.321620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.1390 | −0.822178 | ||||||||
\(863\) | −22.7030 | −0.772818 | −0.386409 | − | 0.922328i | \(-0.626285\pi\) | ||||
−0.386409 | + | 0.922328i | \(0.626285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.2817 | 0.621596 | ||||||||
\(866\) | −24.7529 | −0.841137 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.20535 | −0.142739 | ||||||||
\(869\) | −9.27910 | −0.314772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2395 | −0.787440 | ||||||||
\(872\) | −10.1023 | −0.342106 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.6303 | 0.664005 | ||||||||
\(875\) | −2.33775 | −0.0790304 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.55717 | 0.0525819 | 0.0262910 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262910 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(878\) | −5.54175 | −0.187025 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.432118 | −0.0145667 | ||||||||
\(881\) | 10.3326 | 0.348113 | 0.174056 | − | 0.984736i | \(-0.444313\pi\) | ||||
0.174056 | + | 0.984736i | \(0.444313\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.6160 | 0.794743 | 0.397371 | − | 0.917658i | \(-0.369922\pi\) | ||||
0.397371 | + | 0.917658i | \(0.369922\pi\) | |||||||
\(884\) | −5.40856 | −0.181910 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.2237 | 0.780215 | ||||||||
\(887\) | −13.9260 | −0.467588 | −0.233794 | − | 0.972286i | \(-0.575114\pi\) | ||||
−0.233794 | + | 0.972286i | \(0.575114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.55875 | 0.186435 | ||||||||
\(890\) | 35.7263 | 1.19755 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.06237 | 0.102536 | ||||||||
\(893\) | −14.7274 | −0.492832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.32021 | 0.177835 | ||||||||
\(896\) | −6.88613 | −0.230050 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.3340 | −1.01226 | ||||||||
\(899\) | 24.0915 | 0.803495 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.17630 | 0.172448 | ||||||||
\(902\) | −5.61117 | −0.186831 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.74026 | −0.0911398 | ||||||||
\(905\) | −8.40028 | −0.279235 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3628 | 0.377295 | 0.188648 | − | 0.982045i | \(-0.439590\pi\) | ||||
0.188648 | + | 0.982045i | \(0.439590\pi\) | |||||||
\(908\) | −20.8805 | −0.692943 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.7331 | 0.388948 | ||||||||
\(911\) | −4.75507 | −0.157543 | −0.0787713 | − | 0.996893i | \(-0.525100\pi\) | ||||
−0.0787713 | + | 0.996893i | \(0.525100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9205 | −0.725462 | ||||||||
\(914\) | −23.3435 | −0.772136 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0766 | 0.663349 | ||||||||
\(917\) | −3.51134 | −0.115955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.6303 | −1.07637 | −0.538187 | − | 0.842825i | \(-0.680891\pi\) | ||||
−0.538187 | + | 0.842825i | \(0.680891\pi\) | |||||||
\(920\) | −72.8548 | −2.40195 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.272303 | −0.00896784 | ||||||||
\(923\) | −52.4882 | −1.72767 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.9084 | 1.34506 | ||||||||
\(926\) | −19.7209 | −0.648070 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39.7482 | 1.30480 | ||||||||
\(929\) | 47.3546 | 1.55365 | 0.776827 | − | 0.629714i | \(-0.216828\pi\) | ||||
0.776827 | + | 0.629714i | \(0.216828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.64366 | −0.0866424 | ||||||||
\(932\) | −7.10382 | −0.232693 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.1939 | −0.333554 | ||||||||
\(935\) | −14.5279 | −0.475113 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.6525 | −1.68741 | −0.843707 | − | 0.536803i | \(-0.819632\pi\) | ||||
−0.843707 | + | 0.536803i | \(0.819632\pi\) | |||||||
\(938\) | 4.63717 | 0.151409 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.8079 | 0.678680 | ||||||||
\(941\) | 54.7240 | 1.78395 | 0.891975 | − | 0.452084i | \(-0.149319\pi\) | ||||
0.891975 | + | 0.452084i | \(0.149319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3073 | −0.368218 | ||||||||
\(944\) | 0.276242 | 0.00899091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.5995 | 0.344619 | ||||||||
\(947\) | 36.9728 | 1.20145 | 0.600727 | − | 0.799454i | \(-0.294878\pi\) | ||||
0.600727 | + | 0.799454i | \(0.294878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.9395 | −1.81587 | ||||||||
\(950\) | 9.81779 | 0.318531 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.83488 | 0.0918791 | ||||||||
\(953\) | 7.91313 | 0.256331 | 0.128166 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128166 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.2578 | 1.85282 | ||||||||
\(956\) | 9.15017 | 0.295938 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.9130 | 0.901830 | ||||||||
\(959\) | −1.93780 | −0.0625747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2993 | −0.622557 | ||||||||
\(962\) | 37.3435 | 1.20400 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.9284 | −0.867306 | ||||||||
\(965\) | −36.1867 | −1.16489 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.05906 | 0.259162 | 0.129581 | − | 0.991569i | \(-0.458637\pi\) | ||||
0.129581 | + | 0.991569i | \(0.458637\pi\) | |||||||
\(968\) | 33.6371 | 1.08114 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.4500 | −1.29877 | ||||||||
\(971\) | 1.81193 | 0.0581476 | 0.0290738 | − | 0.999577i | \(-0.490744\pi\) | ||||
0.0290738 | + | 0.999577i | \(0.490744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.69834 | −0.150622 | ||||||||
\(974\) | 20.2047 | 0.647401 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.198192 | −0.00634396 | ||||||||
\(977\) | −15.1934 | −0.486079 | −0.243040 | − | 0.970016i | \(-0.578145\pi\) | ||||
−0.243040 | + | 0.970016i | \(0.578145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.0547 | −2.04720 | ||||||||
\(980\) | 3.73516 | 0.119315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29.2474 | −0.933321 | ||||||||
\(983\) | −11.6472 | −0.371488 | −0.185744 | − | 0.982598i | \(-0.559470\pi\) | ||||
−0.185744 | + | 0.982598i | \(0.559470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.4638 | −1.67164 | ||||||||
\(986\) | −6.18257 | −0.196893 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.2984 | −0.454892 | ||||||||
\(989\) | 21.3596 | 0.679195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.1759 | −1.49859 | −0.749296 | − | 0.662235i | \(-0.769608\pi\) | ||||
−0.749296 | + | 0.662235i | \(0.769608\pi\) | |||||||
\(992\) | 19.3049 | 0.612931 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.4734 | 0.332197 | ||||||||
\(995\) | 46.3175 | 1.46836 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7574 | 1.25913 | 0.629564 | − | 0.776949i | \(-0.283234\pi\) | ||||
0.629564 | + | 0.776949i | \(0.283234\pi\) | |||||||
\(998\) | −32.5006 | −1.02879 | ||||||||
\(999\) | 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 | 1071.2.a.m.1.3 | 5 | ||
3.2 | odd | 2 | 119.2.a.b.1.3 | ✓ | 5 | ||
7.6 | odd | 2 | 7497.2.a.br.1.3 | 5 | |||
12.11 | even | 2 | 1904.2.a.t.1.2 | 5 | |||
15.14 | odd | 2 | 2975.2.a.m.1.3 | 5 | |||
21.2 | odd | 6 | 833.2.e.i.18.3 | 10 | |||
21.5 | even | 6 | 833.2.e.h.18.3 | 10 | |||
21.11 | odd | 6 | 833.2.e.i.324.3 | 10 | |||
21.17 | even | 6 | 833.2.e.h.324.3 | 10 | |||
21.20 | even | 2 | 833.2.a.g.1.3 | 5 | |||
24.5 | odd | 2 | 7616.2.a.bt.1.2 | 5 | |||
24.11 | even | 2 | 7616.2.a.bq.1.4 | 5 | |||
51.50 | odd | 2 | 2023.2.a.j.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
119.2.a.b.1.3 | ✓ | 5 | 3.2 | odd | 2 | ||
833.2.a.g.1.3 | 5 | 21.20 | even | 2 | |||
833.2.e.h.18.3 | 10 | 21.5 | even | 6 | |||
833.2.e.h.324.3 | 10 | 21.17 | even | 6 | |||
833.2.e.i.18.3 | 10 | 21.2 | odd | 6 | |||
833.2.e.i.324.3 | 10 | 21.11 | odd | 6 | |||
1071.2.a.m.1.3 | 5 | 1.1 | even | 1 | trivial | ||
1904.2.a.t.1.2 | 5 | 12.11 | even | 2 | |||
2023.2.a.j.1.3 | 5 | 51.50 | odd | 2 | |||
2975.2.a.m.1.3 | 5 | 15.14 | odd | 2 | |||
7497.2.a.br.1.3 | 5 | 7.6 | odd | 2 | |||
7616.2.a.bq.1.4 | 5 | 24.11 | even | 2 | |||
7616.2.a.bt.1.2 | 5 | 24.5 | odd | 2 |