Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 25x^{9} - 7x^{8} + 212x^{7} + 112x^{6} - 694x^{5} - 480x^{4} + 740x^{3} + 632x^{2} + 48x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1064) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.30652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-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 | 0 | ||||||||
\(3\) | −3.30652 | −1.90902 | −0.954510 | − | 0.298179i | \(-0.903621\pi\) | ||||
−0.954510 | + | 0.298179i | \(0.903621\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.89470 | −0.847336 | −0.423668 | − | 0.905817i | \(-0.639258\pi\) | ||||
−0.423668 | + | 0.905817i | \(0.639258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.93307 | 2.64436 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.04694 | −1.52171 | −0.760855 | − | 0.648922i | \(-0.775220\pi\) | ||||
−0.760855 | + | 0.648922i | \(0.775220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.48574 | −1.52147 | −0.760736 | − | 0.649062i | \(-0.775162\pi\) | ||||
−0.760736 | + | 0.649062i | \(0.775162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.26487 | 1.61758 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.64492 | 1.12656 | 0.563279 | − | 0.826267i | \(-0.309540\pi\) | ||||
0.563279 | + | 0.826267i | \(0.309540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.62087 | 0.337974 | 0.168987 | − | 0.985618i | \(-0.445950\pi\) | ||||
0.168987 | + | 0.985618i | \(0.445950\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.41010 | −0.282021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.3113 | −3.13911 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.36766 | 1.18245 | 0.591223 | − | 0.806508i | \(-0.298645\pi\) | ||||
0.591223 | + | 0.806508i | \(0.298645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.87764 | −1.77408 | −0.887038 | − | 0.461696i | \(-0.847241\pi\) | ||||
−0.887038 | + | 0.461696i | \(0.847241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.6878 | 2.90498 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.33543 | −0.383942 | −0.191971 | − | 0.981401i | \(-0.561488\pi\) | ||||
−0.191971 | + | 0.981401i | \(0.561488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.1387 | 2.90452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.07651 | −0.324297 | −0.162148 | − | 0.986766i | \(-0.551842\pi\) | ||||
−0.162148 | + | 0.986766i | \(0.551842\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.514880 | −0.0785185 | −0.0392592 | − | 0.999229i | \(-0.512500\pi\) | ||||
−0.0392592 | + | 0.999229i | \(0.512500\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.0308 | −2.24066 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.51172 | −0.949832 | −0.474916 | − | 0.880031i | \(-0.657522\pi\) | ||||
−0.474916 | + | 0.880031i | \(0.657522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.3585 | −2.15062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.23852 | −0.856926 | −0.428463 | − | 0.903559i | \(-0.640945\pi\) | ||||
−0.428463 | + | 0.903559i | \(0.640945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.56245 | 1.28940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.30652 | 0.437959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.59343 | 0.598014 | 0.299007 | − | 0.954251i | \(-0.403345\pi\) | ||||
0.299007 | + | 0.954251i | \(0.403345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.61446 | −1.10297 | −0.551484 | − | 0.834185i | \(-0.685938\pi\) | ||||
−0.551484 | + | 0.834185i | \(0.685938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.3938 | 1.28920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0521628 | −0.00637270 | −0.00318635 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318635 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.35943 | −0.645199 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.16475 | −0.968977 | −0.484489 | − | 0.874798i | \(-0.660994\pi\) | ||||
−0.484489 | + | 0.874798i | \(0.660994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0580 | 1.41128 | 0.705639 | − | 0.708571i | \(-0.250660\pi\) | ||||
0.705639 | + | 0.708571i | \(0.250660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.66254 | 0.538383 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9542 | −1.34495 | −0.672474 | − | 0.740121i | \(-0.734768\pi\) | ||||
−0.672474 | + | 0.740121i | \(0.734768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.1344 | 3.34827 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.80009 | 0.197585 | 0.0987927 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987927 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.80074 | −0.954574 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.0548 | −2.25731 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5858 | −1.12210 | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||||
−0.561048 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 32.6606 | 3.38675 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.89470 | 0.194392 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.9780 | −1.72386 | −0.861929 | − | 0.507030i | \(-0.830744\pi\) | ||||
−0.861929 | + | 0.507030i | \(0.830744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.0378 | −4.02395 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.65959 | −0.762157 | −0.381079 | − | 0.924543i | \(-0.624447\pi\) | ||||
−0.381079 | + | 0.924543i | \(0.624447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.794144 | −0.0782493 | −0.0391247 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391247 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.53622 | 0.438532 | 0.219266 | − | 0.975665i | \(-0.429634\pi\) | ||||
0.219266 | + | 0.975665i | \(0.429634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31875 | 0.222096 | 0.111048 | − | 0.993815i | \(-0.464579\pi\) | ||||
0.111048 | + | 0.993815i | \(0.464579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.72214 | 0.732953 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.48718 | −0.610262 | −0.305131 | − | 0.952310i | \(-0.598700\pi\) | ||||
−0.305131 | + | 0.952310i | \(0.598700\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.07106 | −0.286378 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −43.5188 | −4.02331 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.4716 | 1.31560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.86603 | 0.619089 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1452 | 1.08630 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1971 | −0.904845 | −0.452423 | − | 0.891804i | \(-0.649440\pi\) | ||||
−0.452423 | + | 0.891804i | \(0.649440\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.70246 | 0.149893 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4185 | −1.08501 | −0.542503 | − | 0.840054i | \(-0.682523\pi\) | ||||
−0.542503 | + | 0.840054i | \(0.682523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30.9050 | 2.65988 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7915 | −1.00742 | −0.503709 | − | 0.863873i | \(-0.668032\pi\) | ||||
−0.503709 | + | 0.863873i | \(0.668032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2774 | −1.12617 | −0.563085 | − | 0.826399i | \(-0.690386\pi\) | ||||
−0.563085 | + | 0.826399i | \(0.690386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.5311 | 1.81325 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.6862 | 2.31524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0648 | −1.00193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5942 | −1.03176 | −0.515880 | − | 0.856661i | \(-0.672535\pi\) | ||||
−0.515880 | + | 0.856661i | \(0.672535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.51717 | 0.367602 | 0.183801 | − | 0.982963i | \(-0.441160\pi\) | ||||
0.183801 | + | 0.982963i | \(0.441160\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.8485 | 2.97902 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7152 | 1.50324 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.60949 | −0.527495 | −0.263747 | − | 0.964592i | \(-0.584959\pi\) | ||||
−0.263747 | + | 0.964592i | \(0.584959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.6278 | 1.63589 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5029 | −1.21428 | −0.607140 | − | 0.794595i | \(-0.707683\pi\) | ||||
−0.607140 | + | 0.794595i | \(0.707683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −31.6184 | −2.46149 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.76414 | 0.523425 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.0934 | 1.31487 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.93307 | −0.606657 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.2291 | −1.61401 | −0.807007 | − | 0.590541i | \(-0.798914\pi\) | ||||
−0.807007 | + | 0.590541i | \(0.798914\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.1883 | −1.14162 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0404 | −1.49789 | −0.748945 | − | 0.662632i | \(-0.769440\pi\) | ||||
−0.748945 | + | 0.662632i | \(0.769440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.20042 | 0.163556 | 0.0817780 | − | 0.996651i | \(-0.473940\pi\) | ||||
0.0817780 | + | 0.996651i | \(0.473940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.4839 | 2.10559 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.42494 | 0.325328 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.4426 | −1.71430 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3726 | −0.967607 | −0.483803 | − | 0.875177i | \(-0.660745\pi\) | ||||
−0.483803 | + | 0.875177i | \(0.660745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.0992 | 1.59074 | 0.795369 | − | 0.606125i | \(-0.207277\pi\) | ||||
0.795369 | + | 0.606125i | \(0.207277\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −34.3675 | −2.46110 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.46613 | −0.531940 | −0.265970 | − | 0.963981i | \(-0.585692\pi\) | ||||
−0.265970 | + | 0.963981i | \(0.585692\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.64006 | 0.399813 | 0.199907 | − | 0.979815i | \(-0.435936\pi\) | ||||
0.199907 | + | 0.979815i | \(0.435936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.172477 | 0.0121656 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.93437 | 0.274789 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8584 | 0.893724 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.04694 | 0.349104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.98185 | −0.274122 | −0.137061 | − | 0.990563i | \(-0.543766\pi\) | ||||
−0.137061 | + | 0.990563i | \(0.543766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.9969 | 1.84980 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.975544 | 0.0665316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39.8699 | −2.69416 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.4808 | −1.71403 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3902 | −1.23150 | −0.615750 | − | 0.787941i | \(-0.711147\pi\) | ||||
−0.615750 | + | 0.787941i | \(0.711147\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.1865 | −0.745764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4451 | −0.892382 | −0.446191 | − | 0.894938i | \(-0.647220\pi\) | ||||
−0.446191 | + | 0.894938i | \(0.647220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.62234 | 0.635862 | 0.317931 | − | 0.948114i | \(-0.397012\pi\) | ||||
0.317931 | + | 0.948114i | \(0.397012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8329 | 1.29930 | 0.649649 | − | 0.760234i | \(-0.274916\pi\) | ||||
0.649649 | + | 0.760234i | \(0.274916\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3378 | 0.804828 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39.5266 | 2.56753 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.92198 | −0.124323 | −0.0621614 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621614 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.47923 | −0.288532 | −0.144266 | − | 0.989539i | \(-0.546082\pi\) | ||||
−0.144266 | + | 0.989539i | \(0.546082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −50.7061 | −3.25280 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.48574 | 0.349049 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.95203 | −0.377195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.6386 | 1.87077 | 0.935385 | − | 0.353631i | \(-0.115053\pi\) | ||||
0.935385 | + | 0.353631i | \(0.115053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.18042 | −0.514299 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 29.0998 | 1.82230 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.2978 | 1.82755 | 0.913773 | − | 0.406225i | \(-0.133155\pi\) | ||||
0.913773 | + | 0.406225i | \(0.133155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 50.5151 | 3.12681 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.1598 | −1.05812 | −0.529058 | − | 0.848586i | \(-0.677455\pi\) | ||||
−0.529058 | + | 0.848586i | \(0.677455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.8201 | 0.726105 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.0022 | 2.14210 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.70864 | 0.348062 | 0.174031 | − | 0.984740i | \(-0.444321\pi\) | ||||
0.174031 | + | 0.984740i | \(0.444321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.46920 | −0.453722 | −0.226861 | − | 0.973927i | \(-0.572846\pi\) | ||||
−0.226861 | + | 0.973927i | \(0.572846\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.11672 | 0.429154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3196 | 1.22088 | 0.610442 | − | 0.792061i | \(-0.290992\pi\) | ||||
0.610442 | + | 0.792061i | \(0.290992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −78.3600 | −4.69129 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8087 | 0.704451 | 0.352225 | − | 0.935915i | \(-0.385425\pi\) | ||||
0.352225 | + | 0.935915i | \(0.385425\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.49546 | −0.267228 | −0.133614 | − | 0.991033i | \(-0.542658\pi\) | ||||
−0.133614 | + | 0.991033i | \(0.542658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.26487 | −0.371099 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.57528 | 0.269134 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 56.1382 | 3.29088 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.163384 | −0.00954498 | −0.00477249 | − | 0.999989i | \(-0.501519\pi\) | ||||
−0.00477249 | + | 0.999989i | \(0.501519\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.70319 | −0.506719 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 82.3222 | 4.77682 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.89166 | −0.514218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.3266 | 1.45497 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.3218 | 0.934586 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0828 | 1.48862 | 0.744312 | − | 0.667832i | \(-0.232778\pi\) | ||||
0.744312 | + | 0.667832i | \(0.232778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.62585 | 0.149380 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.14375 | 0.0648563 | 0.0324281 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324281 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.40393 | 0.0793551 | 0.0396775 | − | 0.999213i | \(-0.487367\pi\) | ||||
0.0396775 | + | 0.999213i | \(0.487367\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.2674 | −1.47532 | −0.737662 | − | 0.675171i | \(-0.764070\pi\) | ||||
−0.737662 | + | 0.675171i | \(0.764070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.1372 | −1.79934 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9991 | −0.837167 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.64492 | −0.258450 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.73547 | 0.429087 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.66700 | −0.423986 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.93736 | −0.381312 | −0.190656 | − | 0.981657i | \(-0.561061\pi\) | ||||
−0.190656 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.5271 | −1.01528 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0988329 | 0.00539982 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6914 | −0.854762 | −0.427381 | − | 0.904072i | \(-0.640564\pi\) | ||||
−0.427381 | + | 0.904072i | \(0.640564\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.4500 | 1.16500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 49.8519 | 2.69963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.1545 | 0.546701 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3227 | 0.607833 | 0.303917 | − | 0.952699i | \(-0.401706\pi\) | ||||
0.303917 | + | 0.952699i | \(0.401706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.6771 | 0.946232 | 0.473116 | − | 0.881000i | \(-0.343129\pi\) | ||||
0.473116 | + | 0.881000i | \(0.343129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 89.4796 | 4.77607 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.09677 | −0.271273 | −0.135637 | − | 0.990759i | \(-0.543308\pi\) | ||||
−0.135637 | + | 0.990759i | \(0.543308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4698 | 0.821050 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0524 | −0.688880 | −0.344440 | − | 0.938808i | \(-0.611931\pi\) | ||||
−0.344440 | + | 0.938808i | \(0.611931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −47.8507 | −2.51151 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.8463 | −1.19583 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5717 | 1.33483 | 0.667416 | − | 0.744685i | \(-0.267400\pi\) | ||||
0.667416 | + | 0.744685i | \(0.267400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4731 | −0.857557 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.2019 | 1.66735 | 0.833675 | − | 0.552255i | \(-0.186233\pi\) | ||||
0.833675 | + | 0.552255i | \(0.186233\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −40.1585 | −2.07377 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.9314 | −1.79906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.1673 | −1.13866 | −0.569329 | − | 0.822110i | \(-0.692797\pi\) | ||||
−0.569329 | + | 0.822110i | \(0.692797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.7169 | 1.72737 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6612 | 0.698054 | 0.349027 | − | 0.937113i | \(-0.386512\pi\) | ||||
0.349027 | + | 0.937113i | \(0.386512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.08458 | −0.207631 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.6997 | −0.745303 | −0.372651 | − | 0.927971i | \(-0.621551\pi\) | ||||
−0.372651 | + | 0.927971i | \(0.621551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.52879 | 0.380747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.0619 | 2.07130 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.6496 | 1.13962 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.60542 | −0.331516 | −0.165758 | − | 0.986166i | \(-0.553007\pi\) | ||||
−0.165758 | + | 0.986166i | \(0.553007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.6425 | 1.03084 | 0.515419 | − | 0.856938i | \(-0.327636\pi\) | ||||
0.515419 | + | 0.856938i | \(0.327636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 54.1862 | 2.69921 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −57.0957 | −2.83711 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7868 | 0.584249 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6301 | −0.575070 | −0.287535 | − | 0.957770i | \(-0.592836\pi\) | ||||
−0.287535 | + | 0.957770i | \(0.592836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.9889 | 1.92318 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.41063 | −0.167421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 43.9018 | 2.14988 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.56954 | −0.467502 | −0.233751 | − | 0.972296i | \(-0.575100\pi\) | ||||
−0.233751 | + | 0.972296i | \(0.575100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8221 | −1.01481 | −0.507404 | − | 0.861708i | \(-0.669395\pi\) | ||||
−0.507404 | + | 0.861708i | \(0.669395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −51.6580 | −2.51170 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.54982 | −0.317713 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −91.5450 | −4.41984 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.9972 | −1.39675 | −0.698373 | − | 0.715734i | \(-0.746092\pi\) | ||||
−0.698373 | + | 0.715734i | \(0.746092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.17331 | −0.344727 | −0.172364 | − | 0.985033i | \(-0.555140\pi\) | ||||
−0.172364 | + | 0.985033i | \(0.555140\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.8926 | 1.91270 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.62087 | −0.0775366 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5561 | 1.21972 | 0.609862 | − | 0.792508i | \(-0.291225\pi\) | ||||
0.609862 | + | 0.792508i | \(0.291225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.05961 | 0.0978548 | 0.0489274 | − | 0.998802i | \(-0.484420\pi\) | ||||
0.0489274 | + | 0.998802i | \(0.484420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.0570 | 0.950792 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.6431 | 1.96965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.59734 | 0.452927 | 0.226463 | − | 0.974020i | \(-0.427284\pi\) | ||||
0.226463 | + | 0.974020i | \(0.427284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4800 | 0.493486 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.9361 | −0.701760 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4947 | 1.37971 | 0.689853 | − | 0.723950i | \(-0.257675\pi\) | ||||
0.689853 | + | 0.723950i | \(0.257675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −75.7647 | −3.53639 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.2005 | −1.22028 | −0.610139 | − | 0.792294i | \(-0.708886\pi\) | ||||
−0.610139 | + | 0.792294i | \(0.708886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4074 | 0.716042 | 0.358021 | − | 0.933714i | \(-0.383452\pi\) | ||||
0.358021 | + | 0.933714i | \(0.383452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −61.8821 | −2.86971 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2036 | −0.610990 | −0.305495 | − | 0.952194i | \(-0.598822\pi\) | ||||
−0.305495 | + | 0.952194i | \(0.598822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.8544 | 1.00700 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.59857 | 0.119482 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41010 | 0.0647000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −49.4906 | −2.26602 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.3604 | 0.793217 | 0.396609 | − | 0.917988i | \(-0.370187\pi\) | ||||
0.396609 | + | 0.917988i | \(0.370187\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8116 | 0.584157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.1683 | 1.46069 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.03125 | 0.227988 | 0.113994 | − | 0.993481i | \(-0.463636\pi\) | ||||
0.113994 | + | 0.993481i | \(0.463636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 51.2606 | 2.31808 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.32735 | −0.0599025 | −0.0299512 | − | 0.999551i | \(-0.509535\pi\) | ||||
−0.0299512 | + | 0.999551i | \(0.509535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.5773 | 1.33209 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 75.8596 | 3.40964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9518 | 1.02746 | 0.513732 | − | 0.857951i | \(-0.328263\pi\) | ||||
0.513732 | + | 0.857951i | \(0.328263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.3658 | −0.999229 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.75027 | −0.300980 | −0.150490 | − | 0.988612i | \(-0.548085\pi\) | ||||
−0.150490 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.5126 | 0.645804 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −56.5196 | −2.51012 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.2539 | 1.20801 | 0.604005 | − | 0.796981i | \(-0.293571\pi\) | ||||
0.604005 | + | 0.796981i | \(0.293571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.3113 | 0.720161 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.50467 | 0.0663035 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.8643 | 1.44537 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 70.1943 | 3.08119 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.5511 | −0.812738 | −0.406369 | − | 0.913709i | \(-0.633205\pi\) | ||||
−0.406369 | + | 0.913709i | \(0.633205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7813 | 1.65206 | 0.826031 | − | 0.563625i | \(-0.190594\pi\) | ||||
0.826031 | + | 0.563625i | \(0.190594\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.8808 | −1.99860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3728 | −0.885774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.4400 | 1.58136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3912 | 0.493408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.59478 | −0.371585 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 66.2640 | 2.85950 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.22642 | −0.396675 | −0.198337 | − | 0.980134i | \(-0.563554\pi\) | ||||
−0.198337 | + | 0.980134i | \(0.563554\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.27573 | −0.312232 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.39335 | −0.188190 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3367 | 0.441966 | 0.220983 | − | 0.975278i | \(-0.429074\pi\) | ||||
0.220983 | + | 0.975278i | \(0.429074\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −68.3391 | −2.91664 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.36766 | −0.271272 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.6312 | −0.621058 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.22359 | 0.306073 | 0.153037 | − | 0.988220i | \(-0.451095\pi\) | ||||
0.153037 | + | 0.988220i | \(0.451095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.82450 | 0.119464 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 77.5135 | 3.27262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1769 | 1.06108 | 0.530539 | − | 0.847660i | \(-0.321989\pi\) | ||||
0.530539 | + | 0.847660i | \(0.321989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2913 | 0.517098 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5326 | −0.567315 | −0.283658 | − | 0.958926i | \(-0.591548\pi\) | ||||
−0.283658 | + | 0.958926i | \(0.591548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.5262 | 1.36118 | 0.680589 | − | 0.732666i | \(-0.261724\pi\) | ||||
0.680589 | + | 0.732666i | \(0.261724\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.2167 | 1.84718 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.28559 | −0.0953157 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.8021 | 1.57372 | 0.786860 | − | 0.617131i | \(-0.211705\pi\) | ||||
0.786860 | + | 0.617131i | \(0.211705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −73.0716 | −3.03675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.4854 | 1.30399 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 82.4551 | 3.40910 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.79306 | 0.156556 | 0.0782781 | − | 0.996932i | \(-0.475058\pi\) | ||||
0.0782781 | + | 0.996932i | \(0.475058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.87764 | 0.407001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.6869 | 1.01548 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.3752 | 1.98653 | 0.993267 | − | 0.115852i | \(-0.0369598\pi\) | ||||
0.993267 | + | 0.115852i | \(0.0369598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.6490 | −0.763251 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.6858 | −0.477470 | −0.238735 | − | 0.971085i | \(-0.576733\pi\) | ||||
−0.238735 | + | 0.971085i | \(0.576733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.06684 | −0.165890 | −0.0829449 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829449 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.413811 | −0.0168517 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.4194 | −1.11476 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.1037 | 1.54658 | 0.773290 | − | 0.634053i | \(-0.218610\pi\) | ||||
0.773290 | + | 0.634053i | \(0.218610\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7216 | 1.44514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.69020 | 0.108656 | 0.0543281 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543281 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.0091 | −0.524577 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.1862 | −1.33603 | −0.668013 | − | 0.744150i | \(-0.732855\pi\) | ||||
−0.668013 | + | 0.744150i | \(0.732855\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.3164 | 1.74104 | 0.870518 | − | 0.492137i | \(-0.163784\pi\) | ||||
0.870518 | + | 0.492137i | \(0.163784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.4384 | −1.06094 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.9611 | −0.638443 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.6878 | −0.666447 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8479 | −0.432533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.63473 | 0.224315 | 0.112158 | − | 0.993690i | \(-0.464224\pi\) | ||||
0.112158 | + | 0.993690i | \(0.464224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.1661 | 0.523304 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.3204 | 0.766708 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −64.7715 | −2.56232 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.5726 | −1.52353 | −0.761763 | − | 0.647855i | \(-0.775666\pi\) | ||||
−0.761763 | + | 0.647855i | \(0.775666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5746 | 0.732511 | 0.366255 | − | 0.930514i | \(-0.380640\pi\) | ||||
0.366255 | + | 0.930514i | \(0.380640\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.22566 | −0.127010 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.76936 | −0.148189 | −0.0740944 | − | 0.997251i | \(-0.523607\pi\) | ||||
−0.0740944 | + | 0.997251i | \(0.523607\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.1828 | −0.910004 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.9149 | 1.79679 | 0.898394 | − | 0.439190i | \(-0.144735\pi\) | ||||
0.898394 | + | 0.439190i | \(0.144735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.5293 | 0.919365 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 95.6567 | 3.73192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7263 | 0.456793 | 0.228397 | − | 0.973568i | \(-0.426652\pi\) | ||||
0.228397 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.2749 | 1.83878 | 0.919390 | − | 0.393346i | \(-0.128683\pi\) | ||||
0.919390 | + | 0.393346i | \(0.128683\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 84.2529 | 3.27211 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3211 | 0.399636 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.8076 | 2.35096 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.4767 | 1.67840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.1187 | −0.544237 | −0.272119 | − | 0.962264i | \(-0.587724\pi\) | ||||
−0.272119 | + | 0.962264i | \(0.587724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 23.0006 | 0.885295 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.4869 | −1.51760 | −0.758802 | − | 0.651322i | \(-0.774215\pi\) | ||||
−0.758802 | + | 0.651322i | \(0.774215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44.4565 | 1.70358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5447 | −0.747857 | −0.373929 | − | 0.927457i | \(-0.621989\pi\) | ||||
−0.373929 | + | 0.927457i | \(0.621989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.3414 | 0.853622 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.8164 | −1.21387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.2229 | 1.30379 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.4954 | −1.38835 | −0.694175 | − | 0.719806i | \(-0.744231\pi\) | ||||
−0.694175 | + | 0.719806i | \(0.744231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.1566 | 0.954246 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.64524 | −0.365339 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −65.5780 | −2.48039 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.462695 | 0.0174757 | 0.00873787 | − | 0.999962i | \(-0.497219\pi\) | ||||
0.00873787 | + | 0.999962i | \(0.497219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.33543 | 0.0880824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −40.7951 | −1.53643 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9319 | 0.560780 | 0.280390 | − | 0.959886i | \(-0.409536\pi\) | ||||
0.280390 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −94.8331 | −3.55652 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0103 | −0.599592 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.4571 | −1.96179 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.35507 | 0.237335 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5202 | −0.989038 | −0.494519 | − | 0.869167i | \(-0.664656\pi\) | ||||
−0.494519 | + | 0.869167i | \(0.664656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.8107 | 0.550814 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.97907 | −0.333474 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1545 | −0.932928 | −0.466464 | − | 0.884540i | \(-0.654472\pi\) | ||||
−0.466464 | + | 0.884540i | \(0.654472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 77.2575 | 2.86139 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.39158 | −0.0884556 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6157 | −0.465971 | −0.232986 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232986 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.263263 | 0.00969740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.2690 | −1.92275 | −0.961374 | − | 0.275246i | \(-0.911241\pi\) | ||||
−0.961374 | + | 0.275246i | \(0.911241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1387 | −0.666342 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3119 | −0.561739 | −0.280870 | − | 0.959746i | \(-0.590623\pi\) | ||||
−0.280870 | + | 0.959746i | \(0.590623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8623 | 0.874248 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.2802 | 0.522487 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.17115 | −0.152207 | −0.0761037 | − | 0.997100i | \(-0.524248\pi\) | ||||
−0.0761037 | + | 0.997100i | \(0.524248\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −98.0005 | −3.57134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.55870 | −0.311483 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.9386 | 1.16083 | 0.580414 | − | 0.814321i | \(-0.302891\pi\) | ||||
0.580414 | + | 0.814321i | \(0.302891\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.0487 | 0.981806 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.5252 | −1.32404 | −0.662019 | − | 0.749487i | \(-0.730300\pi\) | ||||
−0.662019 | + | 0.749487i | \(0.730300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −69.8169 | −2.52423 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.1984 | −0.909861 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.1274 | −1.80764 | −0.903820 | − | 0.427913i | \(-0.859249\pi\) | ||||
−0.903820 | + | 0.427913i | \(0.859249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −96.8737 | −3.48882 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.9071 | 0.392301 | 0.196150 | − | 0.980574i | \(-0.437156\pi\) | ||||
0.196150 | + | 0.980574i | \(0.437156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9285 | 0.500327 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.07651 | 0.0743988 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.2070 | 1.47450 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −103.865 | −3.71183 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5230 | 0.446966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.8247 | 0.706675 | 0.353338 | − | 0.935496i | \(-0.385047\pi\) | ||||
0.353338 | + | 0.935496i | \(0.385047\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 56.7391 | 2.01996 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.2567 | 1.67814 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −39.0835 | −1.38615 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.84489 | 0.277880 | 0.138940 | − | 0.990301i | \(-0.455630\pi\) | ||||
0.138940 | + | 0.990301i | \(0.455630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.2464 | −1.07004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −83.9781 | −2.96722 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −60.8559 | −2.14756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.8757 | −0.664457 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.9624 | −0.561209 | −0.280605 | − | 0.959823i | \(-0.590535\pi\) | ||||
−0.280605 | + | 0.959823i | \(0.590535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.3313 | −1.27576 | −0.637882 | − | 0.770134i | \(-0.720189\pi\) | ||||
−0.637882 | + | 0.770134i | \(0.720189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.6971 | 0.866164 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.3733 | 1.02890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.514880 | 0.0180134 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.3963 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.3173 | 1.02194 | 0.510968 | − | 0.859600i | \(-0.329287\pi\) | ||||
0.510968 | + | 0.859600i | \(0.329287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.5316 | −0.819264 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.76537 | −0.200482 | −0.100241 | − | 0.994963i | \(-0.531961\pi\) | ||||
−0.100241 | + | 0.994963i | \(0.531961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.9925 | −1.00695 | −0.503476 | − | 0.864009i | \(-0.667946\pi\) | ||||
−0.503476 | + | 0.864009i | \(0.667946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −67.1870 | −2.33069 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.8160 | −0.443517 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 161.117 | 5.56902 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.3629 | 0.703006 | 0.351503 | − | 0.936187i | \(-0.385671\pi\) | ||||
0.351503 | + | 0.936187i | \(0.385671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5471 | 0.398177 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.0458 | −1.34481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.3868 | −1.11414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.8643 | 0.510143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.78542 | −0.129762 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.28329 | 0.0781783 | 0.0390892 | − | 0.999236i | \(-0.487554\pi\) | ||||
0.0390892 | + | 0.999236i | \(0.487554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.0308 | 0.514043 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.08593 | 0.105413 | 0.0527067 | − | 0.998610i | \(-0.483215\pi\) | ||||
0.0527067 | + | 0.998610i | \(0.483215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.6801 | −0.842074 | −0.421037 | − | 0.907044i | \(-0.638334\pi\) | ||||
−0.421037 | + | 0.907044i | \(0.638334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.5213 | −0.766633 | −0.383316 | − | 0.923617i | \(-0.625218\pi\) | ||||
−0.383316 | + | 0.923617i | \(0.625218\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.2227 | 1.36761 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.1282 | −0.513782 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.3319 | 2.04662 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.286152 | 0.00969588 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −134.688 | −4.55849 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5225 | −0.591692 | −0.295846 | − | 0.955236i | \(-0.595601\pi\) | ||||
−0.295846 | + | 0.955236i | \(0.595601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.540231 | 0.0182216 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.0772 | −1.48500 | −0.742499 | − | 0.669847i | \(-0.766360\pi\) | ||||
−0.742499 | + | 0.669847i | \(0.766360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.84919 | 0.264146 | 0.132073 | − | 0.991240i | \(-0.457837\pi\) | ||||
0.132073 | + | 0.991240i | \(0.457837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.7773 | 0.967337 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.6933 | −1.19846 | −0.599232 | − | 0.800576i | \(-0.704527\pi\) | ||||
−0.599232 | + | 0.800576i | \(0.704527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −152.087 | −5.09509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.51172 | 0.217906 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9706 | 1.26922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.4004 | 0.981652 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.8975 | −2.09775 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.9774 | −0.965378 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.16914 | −0.138587 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.68931 | 0.122502 | 0.0612508 | − | 0.998122i | \(-0.480491\pi\) | ||||
0.0612508 | + | 0.998122i | \(0.480491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −60.7640 | −2.01542 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0410 | −0.796512 | −0.398256 | − | 0.917274i | \(-0.630385\pi\) | ||||
−0.398256 | + | 0.917274i | \(0.630385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.08495 | −0.300668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −53.9685 | −1.78414 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.6071 | 1.10859 | 0.554297 | − | 0.832319i | \(-0.312987\pi\) | ||||
0.554297 | + | 0.832319i | \(0.312987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −86.2433 | −2.84181 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.7897 | 1.47427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.29320 | 0.108280 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.30000 | −0.206919 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.4161 | 1.85095 | 0.925477 | − | 0.378804i | \(-0.123665\pi\) | ||||
0.925477 | + | 0.378804i | \(0.123665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.78184 | −0.123812 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 44.4168 | 1.45259 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.9970 | 0.718610 | 0.359305 | − | 0.933220i | \(-0.383014\pi\) | ||||
0.359305 | + | 0.933220i | \(0.383014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.64214 | −0.151490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.8094 | −1.36295 | −0.681473 | − | 0.731843i | \(-0.738660\pi\) | ||||
−0.681473 | + | 0.731843i | \(0.738660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.36575 | −0.109604 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.5469 | 1.12262 | 0.561311 | − | 0.827605i | \(-0.310297\pi\) | ||||
0.561311 | + | 0.827605i | \(0.310297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.1469 | −2.14722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 86.8536 | 2.81642 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.43332 | −0.176002 | −0.0880012 | − | 0.996120i | \(-0.528048\pi\) | ||||
−0.0880012 | + | 0.996120i | \(0.528048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.3371 | 0.819888 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 106.262 | 3.43497 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.5677 | 2.14735 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.9861 | 1.15964 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.8715 | −1.34789 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.65268 | −0.149620 | −0.0748101 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748101 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.3585 | 0.493387 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.9044 | 1.02386 | 0.511930 | − | 0.859027i | \(-0.328931\pi\) | ||||
0.511930 | + | 0.859027i | \(0.328931\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.5775 | −0.819135 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.58747 | −0.0827805 | −0.0413903 | − | 0.999143i | \(-0.513179\pi\) | ||||
−0.0413903 | + | 0.999143i | \(0.513179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.4261 | 1.70750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.3948 | 0.587302 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.9203 | −1.08189 | −0.540945 | − | 0.841058i | \(-0.681933\pi\) | ||||
−0.540945 | + | 0.841058i | \(0.681933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1461 | 0.450732 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.834552 | −0.0265372 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.2547 | −1.65993 | −0.829963 | − | 0.557818i | \(-0.811639\pi\) | ||||
−0.829963 | + | 0.557818i | \(0.811639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.9385 | 0.727932 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.6862 | −0.338776 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.3576 | −1.37315 | −0.686575 | − | 0.727059i | \(-0.740887\pi\) | ||||
−0.686575 | + | 0.727059i | \(0.740887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.0939 | 1.20524 |
(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 | 7448.2.a.bt.1.1 | 11 | ||
7.2 | even | 3 | 1064.2.q.o.305.11 | ✓ | 22 | ||
7.4 | even | 3 | 1064.2.q.o.457.11 | yes | 22 | ||
7.6 | odd | 2 | 7448.2.a.bs.1.11 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.o.305.11 | ✓ | 22 | 7.2 | even | 3 | ||
1064.2.q.o.457.11 | yes | 22 | 7.4 | even | 3 | ||
7448.2.a.bs.1.11 | 11 | 7.6 | odd | 2 | |||
7448.2.a.bt.1.1 | 11 | 1.1 | even | 1 | trivial |