Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, 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("975.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(7.78541419707\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67513 | −1.89160 | −0.945802 | − | 0.324745i | \(-0.894721\pi\) | ||||
−0.945802 | + | 0.324745i | \(0.894721\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.15633 | 2.57816 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.67513 | 1.09212 | ||||||||
\(7\) | 2.28726 | 0.864502 | 0.432251 | − | 0.901753i | \(-0.357719\pi\) | ||||
0.432251 | + | 0.901753i | \(0.357719\pi\) | |||||||
\(8\) | −8.44358 | −2.98526 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.130933 | −0.0394777 | −0.0197388 | − | 0.999805i | \(-0.506283\pi\) | ||||
−0.0197388 | + | 0.999805i | \(0.506283\pi\) | |||||||
\(12\) | −5.15633 | −1.48850 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −6.11871 | −1.63530 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2750 | 3.06876 | ||||||||
\(17\) | −7.96239 | −1.93116 | −0.965581 | − | 0.260101i | \(-0.916244\pi\) | ||||
−0.965581 | + | 0.260101i | \(0.916244\pi\) | |||||||
\(18\) | −2.67513 | −0.630534 | ||||||||
\(19\) | −5.11871 | −1.17431 | −0.587157 | − | 0.809473i | \(-0.699753\pi\) | ||||
−0.587157 | + | 0.809473i | \(0.699753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.28726 | −0.499121 | ||||||||
\(22\) | 0.350262 | 0.0746761 | ||||||||
\(23\) | 5.50659 | 1.14820 | 0.574101 | − | 0.818784i | \(-0.305352\pi\) | ||||
0.574101 | + | 0.818784i | \(0.305352\pi\) | |||||||
\(24\) | 8.44358 | 1.72354 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.67513 | −0.524636 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 11.7938 | 2.22883 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.79384 | −1.39982 | −0.699908 | − | 0.714233i | \(-0.746776\pi\) | ||||
−0.699908 | + | 0.714233i | \(0.746776\pi\) | |||||||
\(32\) | −15.9502 | −2.81962 | ||||||||
\(33\) | 0.130933 | 0.0227924 | ||||||||
\(34\) | 21.3004 | 3.65299 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.15633 | 0.859388 | ||||||||
\(37\) | −4.80606 | −0.790112 | −0.395056 | − | 0.918657i | \(-0.629275\pi\) | ||||
−0.395056 | + | 0.918657i | \(0.629275\pi\) | |||||||
\(38\) | 13.6932 | 2.22134 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4314 | 1.78528 | 0.892640 | − | 0.450771i | \(-0.148851\pi\) | ||||
0.892640 | + | 0.450771i | \(0.148851\pi\) | |||||||
\(42\) | 6.11871 | 0.944138 | ||||||||
\(43\) | 2.93207 | 0.447137 | 0.223568 | − | 0.974688i | \(-0.428229\pi\) | ||||
0.223568 | + | 0.974688i | \(0.428229\pi\) | |||||||
\(44\) | −0.675131 | −0.101780 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.7308 | −2.17194 | ||||||||
\(47\) | −2.67513 | −0.390208 | −0.195104 | − | 0.980783i | \(-0.562504\pi\) | ||||
−0.195104 | + | 0.980783i | \(0.562504\pi\) | |||||||
\(48\) | −12.2750 | −1.77175 | ||||||||
\(49\) | −1.76845 | −0.252636 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.96239 | 1.11496 | ||||||||
\(52\) | 5.15633 | 0.715054 | ||||||||
\(53\) | 8.50659 | 1.16847 | 0.584235 | − | 0.811585i | \(-0.301395\pi\) | ||||
0.584235 | + | 0.811585i | \(0.301395\pi\) | |||||||
\(54\) | 2.67513 | 0.364039 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.3127 | −2.58076 | ||||||||
\(57\) | 5.11871 | 0.677990 | ||||||||
\(58\) | 8.02539 | 1.05379 | ||||||||
\(59\) | −10.4133 | −1.35569 | −0.677846 | − | 0.735204i | \(-0.737086\pi\) | ||||
−0.677846 | + | 0.735204i | \(0.737086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.18664 | 0.664082 | 0.332041 | − | 0.943265i | \(-0.392263\pi\) | ||||
0.332041 | + | 0.943265i | \(0.392263\pi\) | |||||||
\(62\) | 20.8496 | 2.64790 | ||||||||
\(63\) | 2.28726 | 0.288167 | ||||||||
\(64\) | 18.1187 | 2.26484 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.350262 | −0.0431142 | ||||||||
\(67\) | 6.05571 | 0.739823 | 0.369911 | − | 0.929067i | \(-0.379388\pi\) | ||||
0.369911 | + | 0.929067i | \(0.379388\pi\) | |||||||
\(68\) | −41.0567 | −4.97885 | ||||||||
\(69\) | −5.50659 | −0.662915 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0435 | −1.78533 | −0.892667 | − | 0.450717i | \(-0.851168\pi\) | ||||
−0.892667 | + | 0.450717i | \(0.851168\pi\) | |||||||
\(72\) | −8.44358 | −0.995086 | ||||||||
\(73\) | 0.932071 | 0.109091 | 0.0545454 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545454 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(74\) | 12.8568 | 1.49458 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.3938 | −3.02757 | ||||||||
\(77\) | −0.299477 | −0.0341285 | ||||||||
\(78\) | 2.67513 | 0.302899 | ||||||||
\(79\) | 8.85685 | 0.996473 | 0.498237 | − | 0.867041i | \(-0.333981\pi\) | ||||
0.498237 | + | 0.867041i | \(0.333981\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −30.5804 | −3.37704 | ||||||||
\(83\) | −6.80114 | −0.746522 | −0.373261 | − | 0.927726i | \(-0.621760\pi\) | ||||
−0.373261 | + | 0.927726i | \(0.621760\pi\) | |||||||
\(84\) | −11.7938 | −1.28681 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.84367 | −0.845805 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 1.10554 | 0.117851 | ||||||||
\(89\) | −8.12601 | −0.861355 | −0.430678 | − | 0.902506i | \(-0.641725\pi\) | ||||
−0.430678 | + | 0.902506i | \(0.641725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.28726 | 0.239770 | ||||||||
\(92\) | 28.3938 | 2.96025 | ||||||||
\(93\) | 7.79384 | 0.808184 | ||||||||
\(94\) | 7.15633 | 0.738119 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.9502 | 1.62791 | ||||||||
\(97\) | −18.9624 | −1.92534 | −0.962669 | − | 0.270680i | \(-0.912752\pi\) | ||||
−0.962669 | + | 0.270680i | \(0.912752\pi\) | |||||||
\(98\) | 4.73084 | 0.477887 | ||||||||
\(99\) | −0.130933 | −0.0131592 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.54420 | −0.352661 | −0.176330 | − | 0.984331i | \(-0.556423\pi\) | ||||
−0.176330 | + | 0.984331i | \(0.556423\pi\) | |||||||
\(102\) | −21.3004 | −2.10906 | ||||||||
\(103\) | −14.0811 | −1.38745 | −0.693726 | − | 0.720239i | \(-0.744032\pi\) | ||||
−0.693726 | + | 0.720239i | \(0.744032\pi\) | |||||||
\(104\) | −8.44358 | −0.827961 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.7562 | −2.21028 | ||||||||
\(107\) | 2.64974 | 0.256160 | 0.128080 | − | 0.991764i | \(-0.459119\pi\) | ||||
0.128080 | + | 0.991764i | \(0.459119\pi\) | |||||||
\(108\) | −5.15633 | −0.496168 | ||||||||
\(109\) | −9.31994 | −0.892689 | −0.446344 | − | 0.894861i | \(-0.647274\pi\) | ||||
−0.446344 | + | 0.894861i | \(0.647274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.80606 | 0.456171 | ||||||||
\(112\) | 28.0762 | 2.65295 | ||||||||
\(113\) | −13.3503 | −1.25589 | −0.627943 | − | 0.778259i | \(-0.716103\pi\) | ||||
−0.627943 | + | 0.778259i | \(0.716103\pi\) | |||||||
\(114\) | −13.6932 | −1.28249 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.4690 | −1.43626 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 27.8568 | 2.56443 | ||||||||
\(119\) | −18.2120 | −1.66949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9829 | −0.998442 | ||||||||
\(122\) | −13.8749 | −1.25618 | ||||||||
\(123\) | −11.4314 | −1.03073 | ||||||||
\(124\) | −40.1876 | −3.60895 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.11871 | −0.545098 | ||||||||
\(127\) | −8.73084 | −0.774737 | −0.387368 | − | 0.921925i | \(-0.626616\pi\) | ||||
−0.387368 | + | 0.921925i | \(0.626616\pi\) | |||||||
\(128\) | −16.5696 | −1.46456 | ||||||||
\(129\) | −2.93207 | −0.258154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0435 | 1.66384 | 0.831919 | − | 0.554897i | \(-0.187243\pi\) | ||||
0.831919 | + | 0.554897i | \(0.187243\pi\) | |||||||
\(132\) | 0.675131 | 0.0587626 | ||||||||
\(133\) | −11.7078 | −1.01520 | ||||||||
\(134\) | −16.1998 | −1.39945 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 67.2311 | 5.76502 | ||||||||
\(137\) | −7.66291 | −0.654687 | −0.327343 | − | 0.944905i | \(-0.606153\pi\) | ||||
−0.327343 | + | 0.944905i | \(0.606153\pi\) | |||||||
\(138\) | 14.7308 | 1.25397 | ||||||||
\(139\) | 7.61213 | 0.645652 | 0.322826 | − | 0.946458i | \(-0.395367\pi\) | ||||
0.322826 | + | 0.946458i | \(0.395367\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.67513 | 0.225287 | ||||||||
\(142\) | 40.2433 | 3.37714 | ||||||||
\(143\) | −0.130933 | −0.0109491 | ||||||||
\(144\) | 12.2750 | 1.02292 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.49341 | −0.206356 | ||||||||
\(147\) | 1.76845 | 0.145859 | ||||||||
\(148\) | −24.7816 | −2.03704 | ||||||||
\(149\) | 0.887166 | 0.0726795 | 0.0363397 | − | 0.999339i | \(-0.488430\pi\) | ||||
0.0363397 | + | 0.999339i | \(0.488430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.93700 | 0.239009 | 0.119505 | − | 0.992834i | \(-0.461869\pi\) | ||||
0.119505 | + | 0.992834i | \(0.461869\pi\) | |||||||
\(152\) | 43.2203 | 3.50563 | ||||||||
\(153\) | −7.96239 | −0.643721 | ||||||||
\(154\) | 0.801139 | 0.0645576 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.15633 | −0.412836 | ||||||||
\(157\) | −15.7816 | −1.25951 | −0.629755 | − | 0.776793i | \(-0.716845\pi\) | ||||
−0.629755 | + | 0.776793i | \(0.716845\pi\) | |||||||
\(158\) | −23.6932 | −1.88493 | ||||||||
\(159\) | −8.50659 | −0.674616 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.5950 | 0.992624 | ||||||||
\(162\) | −2.67513 | −0.210178 | ||||||||
\(163\) | 17.4314 | 1.36533 | 0.682665 | − | 0.730732i | \(-0.260821\pi\) | ||||
0.682665 | + | 0.730732i | \(0.260821\pi\) | |||||||
\(164\) | 58.9438 | 4.60274 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.1939 | 1.41212 | ||||||||
\(167\) | 1.91890 | 0.148489 | 0.0742444 | − | 0.997240i | \(-0.476346\pi\) | ||||
0.0742444 | + | 0.997240i | \(0.476346\pi\) | |||||||
\(168\) | 19.3127 | 1.49000 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.11871 | −0.391438 | ||||||||
\(172\) | 15.1187 | 1.15279 | ||||||||
\(173\) | 7.93207 | 0.603064 | 0.301532 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301532 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(174\) | −8.02539 | −0.608403 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.60720 | −0.121147 | ||||||||
\(177\) | 10.4133 | 0.782709 | ||||||||
\(178\) | 21.7381 | 1.62934 | ||||||||
\(179\) | 14.9175 | 1.11499 | 0.557493 | − | 0.830182i | \(-0.311764\pi\) | ||||
0.557493 | + | 0.830182i | \(0.311764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.5804 | −1.75272 | −0.876358 | − | 0.481659i | \(-0.840034\pi\) | ||||
−0.876358 | + | 0.481659i | \(0.840034\pi\) | |||||||
\(182\) | −6.11871 | −0.453549 | ||||||||
\(183\) | −5.18664 | −0.383408 | ||||||||
\(184\) | −46.4953 | −3.42768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.8496 | −1.52876 | ||||||||
\(187\) | 1.04254 | 0.0762378 | ||||||||
\(188\) | −13.7938 | −1.00602 | ||||||||
\(189\) | −2.28726 | −0.166374 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.38787 | 0.606925 | 0.303463 | − | 0.952843i | \(-0.401857\pi\) | ||||
0.303463 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(192\) | −18.1187 | −1.30761 | ||||||||
\(193\) | −18.1563 | −1.30692 | −0.653460 | − | 0.756961i | \(-0.726683\pi\) | ||||
−0.653460 | + | 0.756961i | \(0.726683\pi\) | |||||||
\(194\) | 50.7269 | 3.64198 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.11871 | −0.651337 | ||||||||
\(197\) | 1.19394 | 0.0850645 | 0.0425322 | − | 0.999095i | \(-0.486457\pi\) | ||||
0.0425322 | + | 0.999095i | \(0.486457\pi\) | |||||||
\(198\) | 0.350262 | 0.0248920 | ||||||||
\(199\) | 0.700523 | 0.0496588 | 0.0248294 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248294 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05571 | −0.427137 | ||||||||
\(202\) | 9.48119 | 0.667095 | ||||||||
\(203\) | −6.86177 | −0.481602 | ||||||||
\(204\) | 41.0567 | 2.87454 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 37.6688 | 2.62451 | ||||||||
\(207\) | 5.50659 | 0.382734 | ||||||||
\(208\) | 12.2750 | 0.851121 | ||||||||
\(209\) | 0.670206 | 0.0463591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9829 | 1.16915 | 0.584574 | − | 0.811340i | \(-0.301262\pi\) | ||||
0.584574 | + | 0.811340i | \(0.301262\pi\) | |||||||
\(212\) | 43.8627 | 3.01250 | ||||||||
\(213\) | 15.0435 | 1.03076 | ||||||||
\(214\) | −7.08840 | −0.484553 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.44358 | 0.574513 | ||||||||
\(217\) | −17.8265 | −1.21014 | ||||||||
\(218\) | 24.9321 | 1.68861 | ||||||||
\(219\) | −0.932071 | −0.0629836 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.96239 | −0.535608 | ||||||||
\(222\) | −12.8568 | −0.862895 | ||||||||
\(223\) | 0.806063 | 0.0539780 | 0.0269890 | − | 0.999636i | \(-0.491408\pi\) | ||||
0.0269890 | + | 0.999636i | \(0.491408\pi\) | |||||||
\(224\) | −36.4821 | −2.43757 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.7137 | 2.37564 | ||||||||
\(227\) | −7.68243 | −0.509900 | −0.254950 | − | 0.966954i | \(-0.582059\pi\) | ||||
−0.254950 | + | 0.966954i | \(0.582059\pi\) | |||||||
\(228\) | 26.3938 | 1.74797 | ||||||||
\(229\) | −4.44851 | −0.293966 | −0.146983 | − | 0.989139i | \(-0.546956\pi\) | ||||
−0.146983 | + | 0.989139i | \(0.546956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.299477 | 0.0197041 | ||||||||
\(232\) | 25.3307 | 1.66305 | ||||||||
\(233\) | 10.1260 | 0.663377 | 0.331688 | − | 0.943389i | \(-0.392382\pi\) | ||||
0.331688 | + | 0.943389i | \(0.392382\pi\) | |||||||
\(234\) | −2.67513 | −0.174879 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −53.6942 | −3.49519 | ||||||||
\(237\) | −8.85685 | −0.575314 | ||||||||
\(238\) | 48.7196 | 3.15802 | ||||||||
\(239\) | −19.4363 | −1.25723 | −0.628615 | − | 0.777717i | \(-0.716378\pi\) | ||||
−0.628615 | + | 0.777717i | \(0.716378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.46898 | −0.416703 | −0.208352 | − | 0.978054i | \(-0.566810\pi\) | ||||
−0.208352 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(242\) | 29.3806 | 1.88866 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 26.7440 | 1.71211 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.5804 | 1.94973 | ||||||||
\(247\) | −5.11871 | −0.325696 | ||||||||
\(248\) | 65.8080 | 4.17881 | ||||||||
\(249\) | 6.80114 | 0.431005 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.7685 | −1.12153 | −0.560767 | − | 0.827973i | \(-0.689494\pi\) | ||||
−0.560767 | + | 0.827973i | \(0.689494\pi\) | |||||||
\(252\) | 11.7938 | 0.742942 | ||||||||
\(253\) | −0.720992 | −0.0453283 | ||||||||
\(254\) | 23.3561 | 1.46549 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.08840 | 0.505525 | ||||||||
\(257\) | 4.81924 | 0.300616 | 0.150308 | − | 0.988639i | \(-0.451974\pi\) | ||||
0.150308 | + | 0.988639i | \(0.451974\pi\) | |||||||
\(258\) | 7.84367 | 0.488326 | ||||||||
\(259\) | −10.9927 | −0.683054 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | −50.9438 | −3.14732 | ||||||||
\(263\) | 1.30536 | 0.0804917 | 0.0402459 | − | 0.999190i | \(-0.487186\pi\) | ||||
0.0402459 | + | 0.999190i | \(0.487186\pi\) | |||||||
\(264\) | −1.10554 | −0.0680413 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 31.3199 | 1.92035 | ||||||||
\(267\) | 8.12601 | 0.497304 | ||||||||
\(268\) | 31.2252 | 1.90738 | ||||||||
\(269\) | −8.79877 | −0.536470 | −0.268235 | − | 0.963353i | \(-0.586440\pi\) | ||||
−0.268235 | + | 0.963353i | \(0.586440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4264 | 1.05858 | 0.529290 | − | 0.848441i | \(-0.322458\pi\) | ||||
0.529290 | + | 0.848441i | \(0.322458\pi\) | |||||||
\(272\) | −97.7386 | −5.92627 | ||||||||
\(273\) | −2.28726 | −0.138431 | ||||||||
\(274\) | 20.4993 | 1.23841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −28.3938 | −1.70910 | ||||||||
\(277\) | −11.7381 | −0.705276 | −0.352638 | − | 0.935760i | \(-0.614715\pi\) | ||||
−0.352638 | + | 0.935760i | \(0.614715\pi\) | |||||||
\(278\) | −20.3634 | −1.22132 | ||||||||
\(279\) | −7.79384 | −0.466605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5647 | −0.868855 | −0.434428 | − | 0.900707i | \(-0.643049\pi\) | ||||
−0.434428 | + | 0.900707i | \(0.643049\pi\) | |||||||
\(282\) | −7.15633 | −0.426153 | ||||||||
\(283\) | −26.1016 | −1.55158 | −0.775789 | − | 0.630993i | \(-0.782648\pi\) | ||||
−0.775789 | + | 0.630993i | \(0.782648\pi\) | |||||||
\(284\) | −77.5691 | −4.60288 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.350262 | 0.0207114 | ||||||||
\(287\) | 26.1465 | 1.54338 | ||||||||
\(288\) | −15.9502 | −0.939873 | ||||||||
\(289\) | 46.3996 | 2.72939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.9624 | 1.11159 | ||||||||
\(292\) | 4.80606 | 0.281254 | ||||||||
\(293\) | −9.07381 | −0.530098 | −0.265049 | − | 0.964235i | \(-0.585388\pi\) | ||||
−0.265049 | + | 0.964235i | \(0.585388\pi\) | |||||||
\(294\) | −4.73084 | −0.275908 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 40.5804 | 2.35869 | ||||||||
\(297\) | 0.130933 | 0.00759748 | ||||||||
\(298\) | −2.37328 | −0.137481 | ||||||||
\(299\) | 5.50659 | 0.318454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.70640 | 0.386551 | ||||||||
\(302\) | −7.85685 | −0.452111 | ||||||||
\(303\) | 3.54420 | 0.203609 | ||||||||
\(304\) | −62.8324 | −3.60369 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 21.3004 | 1.21766 | ||||||||
\(307\) | 11.3806 | 0.649524 | 0.324762 | − | 0.945796i | \(-0.394716\pi\) | ||||
0.324762 | + | 0.945796i | \(0.394716\pi\) | |||||||
\(308\) | −1.54420 | −0.0879889 | ||||||||
\(309\) | 14.0811 | 0.801046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.22425 | 0.523059 | 0.261530 | − | 0.965195i | \(-0.415773\pi\) | ||||
0.261530 | + | 0.965195i | \(0.415773\pi\) | |||||||
\(312\) | 8.44358 | 0.478024 | ||||||||
\(313\) | −18.7685 | −1.06086 | −0.530428 | − | 0.847730i | \(-0.677969\pi\) | ||||
−0.530428 | + | 0.847730i | \(0.677969\pi\) | |||||||
\(314\) | 42.2179 | 2.38249 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45.6688 | 2.56907 | ||||||||
\(317\) | −10.5442 | −0.592221 | −0.296111 | − | 0.955154i | \(-0.595690\pi\) | ||||
−0.296111 | + | 0.955154i | \(0.595690\pi\) | |||||||
\(318\) | 22.7562 | 1.27611 | ||||||||
\(319\) | 0.392798 | 0.0219924 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.64974 | −0.147894 | ||||||||
\(322\) | −33.6932 | −1.87765 | ||||||||
\(323\) | 40.7572 | 2.26779 | ||||||||
\(324\) | 5.15633 | 0.286463 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −46.6312 | −2.58266 | ||||||||
\(327\) | 9.31994 | 0.515394 | ||||||||
\(328\) | −96.5217 | −5.32952 | ||||||||
\(329\) | −6.11871 | −0.337336 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.95651 | 0.272434 | 0.136217 | − | 0.990679i | \(-0.456506\pi\) | ||||
0.136217 | + | 0.990679i | \(0.456506\pi\) | |||||||
\(332\) | −35.0689 | −1.92466 | ||||||||
\(333\) | −4.80606 | −0.263371 | ||||||||
\(334\) | −5.13330 | −0.280882 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −28.0762 | −1.53168 | ||||||||
\(337\) | 32.6082 | 1.77628 | 0.888140 | − | 0.459573i | \(-0.151998\pi\) | ||||
0.888140 | + | 0.459573i | \(0.151998\pi\) | |||||||
\(338\) | −2.67513 | −0.145508 | ||||||||
\(339\) | 13.3503 | 0.725087 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02047 | 0.0552614 | ||||||||
\(342\) | 13.6932 | 0.740445 | ||||||||
\(343\) | −20.0557 | −1.08291 | ||||||||
\(344\) | −24.7572 | −1.33482 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2193 | −1.14076 | ||||||||
\(347\) | 22.1622 | 1.18973 | 0.594865 | − | 0.803826i | \(-0.297206\pi\) | ||||
0.594865 | + | 0.803826i | \(0.297206\pi\) | |||||||
\(348\) | 15.4690 | 0.829224 | ||||||||
\(349\) | −4.34297 | −0.232474 | −0.116237 | − | 0.993222i | \(-0.537083\pi\) | ||||
−0.116237 | + | 0.993222i | \(0.537083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.08840 | 0.111312 | ||||||||
\(353\) | 6.96827 | 0.370883 | 0.185442 | − | 0.982655i | \(-0.440628\pi\) | ||||
0.185442 | + | 0.982655i | \(0.440628\pi\) | |||||||
\(354\) | −27.8568 | −1.48057 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −41.9003 | −2.22071 | ||||||||
\(357\) | 18.2120 | 0.963883 | ||||||||
\(358\) | −39.9062 | −2.10911 | ||||||||
\(359\) | −15.0122 | −0.792315 | −0.396157 | − | 0.918183i | \(-0.629657\pi\) | ||||
−0.396157 | + | 0.918183i | \(0.629657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.20123 | 0.379012 | ||||||||
\(362\) | 63.0806 | 3.31544 | ||||||||
\(363\) | 10.9829 | 0.576450 | ||||||||
\(364\) | 11.7938 | 0.618165 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.8749 | 0.725255 | ||||||||
\(367\) | −27.0738 | −1.41324 | −0.706621 | − | 0.707593i | \(-0.749781\pi\) | ||||
−0.706621 | + | 0.707593i | \(0.749781\pi\) | |||||||
\(368\) | 67.5936 | 3.52356 | ||||||||
\(369\) | 11.4314 | 0.595093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4568 | 1.01014 | ||||||||
\(372\) | 40.1876 | 2.08363 | ||||||||
\(373\) | −3.49341 | −0.180882 | −0.0904410 | − | 0.995902i | \(-0.528828\pi\) | ||||
−0.0904410 | + | 0.995902i | \(0.528828\pi\) | |||||||
\(374\) | −2.78892 | −0.144212 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.5877 | 1.16487 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 6.11871 | 0.314713 | ||||||||
\(379\) | 26.9937 | 1.38657 | 0.693286 | − | 0.720663i | \(-0.256162\pi\) | ||||
0.693286 | + | 0.720663i | \(0.256162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.73084 | 0.447295 | ||||||||
\(382\) | −22.4387 | −1.14806 | ||||||||
\(383\) | −5.52118 | −0.282119 | −0.141059 | − | 0.990001i | \(-0.545051\pi\) | ||||
−0.141059 | + | 0.990001i | \(0.545051\pi\) | |||||||
\(384\) | 16.5696 | 0.845563 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 48.5705 | 2.47218 | ||||||||
\(387\) | 2.93207 | 0.149046 | ||||||||
\(388\) | −97.7762 | −4.96384 | ||||||||
\(389\) | −15.9003 | −0.806179 | −0.403090 | − | 0.915161i | \(-0.632064\pi\) | ||||
−0.403090 | + | 0.915161i | \(0.632064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.8456 | −2.21737 | ||||||||
\(392\) | 14.9321 | 0.754183 | ||||||||
\(393\) | −19.0435 | −0.960617 | ||||||||
\(394\) | −3.19394 | −0.160908 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.675131 | −0.0339266 | ||||||||
\(397\) | 17.1998 | 0.863234 | 0.431617 | − | 0.902057i | \(-0.357943\pi\) | ||||
0.431617 | + | 0.902057i | \(0.357943\pi\) | |||||||
\(398\) | −1.87399 | −0.0939347 | ||||||||
\(399\) | 11.7078 | 0.586124 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0435 | 0.950987 | 0.475493 | − | 0.879719i | \(-0.342270\pi\) | ||||
0.475493 | + | 0.879719i | \(0.342270\pi\) | |||||||
\(402\) | 16.1998 | 0.807973 | ||||||||
\(403\) | −7.79384 | −0.388239 | ||||||||
\(404\) | −18.2750 | −0.909217 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.3561 | 0.911000 | ||||||||
\(407\) | 0.629270 | 0.0311918 | ||||||||
\(408\) | −67.2311 | −3.32843 | ||||||||
\(409\) | 12.4182 | 0.614040 | 0.307020 | − | 0.951703i | \(-0.400668\pi\) | ||||
0.307020 | + | 0.951703i | \(0.400668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.66291 | 0.377984 | ||||||||
\(412\) | −72.6067 | −3.57708 | ||||||||
\(413\) | −23.8178 | −1.17200 | ||||||||
\(414\) | −14.7308 | −0.723981 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.9502 | −0.782021 | ||||||||
\(417\) | −7.61213 | −0.372767 | ||||||||
\(418\) | −1.79289 | −0.0876931 | ||||||||
\(419\) | 6.14174 | 0.300043 | 0.150022 | − | 0.988683i | \(-0.452066\pi\) | ||||
0.150022 | + | 0.988683i | \(0.452066\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6121 | −0.858363 | −0.429181 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429181 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(422\) | −45.4314 | −2.21156 | ||||||||
\(423\) | −2.67513 | −0.130069 | ||||||||
\(424\) | −71.8261 | −3.48818 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −40.2433 | −1.94979 | ||||||||
\(427\) | 11.8632 | 0.574100 | ||||||||
\(428\) | 13.6629 | 0.660422 | ||||||||
\(429\) | 0.130933 | 0.00632148 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.65703 | −0.176153 | −0.0880765 | − | 0.996114i | \(-0.528072\pi\) | ||||
−0.0880765 | + | 0.996114i | \(0.528072\pi\) | |||||||
\(432\) | −12.2750 | −0.590583 | ||||||||
\(433\) | −9.28963 | −0.446431 | −0.223216 | − | 0.974769i | \(-0.571655\pi\) | ||||
−0.223216 | + | 0.974769i | \(0.571655\pi\) | |||||||
\(434\) | 47.6883 | 2.28911 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.0567 | −2.30150 | ||||||||
\(437\) | −28.1866 | −1.34835 | ||||||||
\(438\) | 2.49341 | 0.119140 | ||||||||
\(439\) | 27.0581 | 1.29141 | 0.645706 | − | 0.763586i | \(-0.276563\pi\) | ||||
0.645706 | + | 0.763586i | \(0.276563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76845 | −0.0842120 | ||||||||
\(442\) | 21.3004 | 1.01316 | ||||||||
\(443\) | −7.09428 | −0.337059 | −0.168530 | − | 0.985697i | \(-0.553902\pi\) | ||||
−0.168530 | + | 0.985697i | \(0.553902\pi\) | |||||||
\(444\) | 24.7816 | 1.17608 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.15633 | −0.102105 | ||||||||
\(447\) | −0.887166 | −0.0419615 | ||||||||
\(448\) | 41.4422 | 1.95796 | ||||||||
\(449\) | −14.7612 | −0.696622 | −0.348311 | − | 0.937379i | \(-0.613245\pi\) | ||||
−0.348311 | + | 0.937379i | \(0.613245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.49674 | −0.0704786 | ||||||||
\(452\) | −68.8383 | −3.23788 | ||||||||
\(453\) | −2.93700 | −0.137992 | ||||||||
\(454\) | 20.5515 | 0.964529 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −43.2203 | −2.02398 | ||||||||
\(457\) | −2.28233 | −0.106763 | −0.0533815 | − | 0.998574i | \(-0.517000\pi\) | ||||
−0.0533815 | + | 0.998574i | \(0.517000\pi\) | |||||||
\(458\) | 11.9003 | 0.556066 | ||||||||
\(459\) | 7.96239 | 0.371652 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5647 | −0.492046 | −0.246023 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246023 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(462\) | −0.801139 | −0.0372724 | ||||||||
\(463\) | 6.18172 | 0.287289 | 0.143644 | − | 0.989629i | \(-0.454118\pi\) | ||||
0.143644 | + | 0.989629i | \(0.454118\pi\) | |||||||
\(464\) | −36.8251 | −1.70956 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.0884 | −1.25485 | ||||||||
\(467\) | −6.32250 | −0.292570 | −0.146285 | − | 0.989242i | \(-0.546732\pi\) | ||||
−0.146285 | + | 0.989242i | \(0.546732\pi\) | |||||||
\(468\) | 5.15633 | 0.238351 | ||||||||
\(469\) | 13.8510 | 0.639578 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7816 | 0.727179 | ||||||||
\(472\) | 87.9253 | 4.04709 | ||||||||
\(473\) | −0.383904 | −0.0176519 | ||||||||
\(474\) | 23.6932 | 1.08827 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −93.9072 | −4.30423 | ||||||||
\(477\) | 8.50659 | 0.389490 | ||||||||
\(478\) | 51.9946 | 2.37818 | ||||||||
\(479\) | 3.33075 | 0.152186 | 0.0760929 | − | 0.997101i | \(-0.475755\pi\) | ||||
0.0760929 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.80606 | −0.219138 | ||||||||
\(482\) | 17.3054 | 0.788237 | ||||||||
\(483\) | −12.5950 | −0.573092 | ||||||||
\(484\) | −56.6312 | −2.57414 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.67513 | 0.121346 | ||||||||
\(487\) | −8.44358 | −0.382615 | −0.191308 | − | 0.981530i | \(-0.561273\pi\) | ||||
−0.191308 | + | 0.981530i | \(0.561273\pi\) | |||||||
\(488\) | −43.7938 | −1.98245 | ||||||||
\(489\) | −17.4314 | −0.788274 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3112 | −1.05202 | −0.526011 | − | 0.850478i | \(-0.676313\pi\) | ||||
−0.526011 | + | 0.850478i | \(0.676313\pi\) | |||||||
\(492\) | −58.9438 | −2.65739 | ||||||||
\(493\) | 23.8872 | 1.07582 | ||||||||
\(494\) | 13.6932 | 0.616088 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −95.6697 | −4.29570 | ||||||||
\(497\) | −34.4083 | −1.54343 | ||||||||
\(498\) | −18.1939 | −0.815290 | ||||||||
\(499\) | −31.8651 | −1.42648 | −0.713239 | − | 0.700921i | \(-0.752773\pi\) | ||||
−0.713239 | + | 0.700921i | \(0.752773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.91890 | −0.0857300 | ||||||||
\(502\) | 47.5329 | 2.12150 | ||||||||
\(503\) | 9.43136 | 0.420524 | 0.210262 | − | 0.977645i | \(-0.432568\pi\) | ||||
0.210262 | + | 0.977645i | \(0.432568\pi\) | |||||||
\(504\) | −19.3127 | −0.860254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.92875 | 0.0857433 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −45.0191 | −1.99740 | ||||||||
\(509\) | 37.4821 | 1.66137 | 0.830684 | − | 0.556745i | \(-0.187950\pi\) | ||||
0.830684 | + | 0.556745i | \(0.187950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.13189 | 0.0943092 | ||||||||
\(512\) | 11.5017 | 0.508306 | ||||||||
\(513\) | 5.11871 | 0.225997 | ||||||||
\(514\) | −12.8921 | −0.568646 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.1187 | −0.665564 | ||||||||
\(517\) | 0.350262 | 0.0154045 | ||||||||
\(518\) | 29.4069 | 1.29207 | ||||||||
\(519\) | −7.93207 | −0.348179 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9248 | 0.697677 | 0.348839 | − | 0.937183i | \(-0.386576\pi\) | ||||
0.348839 | + | 0.937183i | \(0.386576\pi\) | |||||||
\(522\) | 8.02539 | 0.351262 | ||||||||
\(523\) | −2.27645 | −0.0995424 | −0.0497712 | − | 0.998761i | \(-0.515849\pi\) | ||||
−0.0497712 | + | 0.998761i | \(0.515849\pi\) | |||||||
\(524\) | 98.1944 | 4.28964 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.49200 | −0.152258 | ||||||||
\(527\) | 62.0576 | 2.70327 | ||||||||
\(528\) | 1.60720 | 0.0699445 | ||||||||
\(529\) | 7.32250 | 0.318370 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.4133 | −0.451897 | ||||||||
\(532\) | −60.3693 | −2.61734 | ||||||||
\(533\) | 11.4314 | 0.495147 | ||||||||
\(534\) | −21.7381 | −0.940701 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −51.1319 | −2.20856 | ||||||||
\(537\) | −14.9175 | −0.643737 | ||||||||
\(538\) | 23.5379 | 1.01479 | ||||||||
\(539\) | 0.231548 | 0.00997348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.3317 | 0.831135 | 0.415567 | − | 0.909562i | \(-0.363583\pi\) | ||||
0.415567 | + | 0.909562i | \(0.363583\pi\) | |||||||
\(542\) | −46.6180 | −2.00241 | ||||||||
\(543\) | 23.5804 | 1.01193 | ||||||||
\(544\) | 127.001 | 5.44514 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.11871 | 0.261857 | ||||||||
\(547\) | 40.9438 | 1.75063 | 0.875316 | − | 0.483552i | \(-0.160653\pi\) | ||||
0.875316 | + | 0.483552i | \(0.160653\pi\) | |||||||
\(548\) | −39.5125 | −1.68789 | ||||||||
\(549\) | 5.18664 | 0.221361 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.3561 | 0.654194 | ||||||||
\(552\) | 46.4953 | 1.97897 | ||||||||
\(553\) | 20.2579 | 0.861453 | ||||||||
\(554\) | 31.4010 | 1.33410 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.2506 | 1.66460 | ||||||||
\(557\) | 36.4953 | 1.54636 | 0.773178 | − | 0.634189i | \(-0.218666\pi\) | ||||
0.773178 | + | 0.634189i | \(0.218666\pi\) | |||||||
\(558\) | 20.8496 | 0.882632 | ||||||||
\(559\) | 2.93207 | 0.124013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.04254 | −0.0440159 | ||||||||
\(562\) | 38.9624 | 1.64353 | ||||||||
\(563\) | −1.04349 | −0.0439779 | −0.0219890 | − | 0.999758i | \(-0.507000\pi\) | ||||
−0.0219890 | + | 0.999758i | \(0.507000\pi\) | |||||||
\(564\) | 13.7938 | 0.580826 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 69.8251 | 2.93497 | ||||||||
\(567\) | 2.28726 | 0.0960558 | ||||||||
\(568\) | 127.021 | 5.32968 | ||||||||
\(569\) | −39.4807 | −1.65512 | −0.827559 | − | 0.561378i | \(-0.810271\pi\) | ||||
−0.827559 | + | 0.561378i | \(0.810271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.4920 | 1.48529 | 0.742647 | − | 0.669683i | \(-0.233570\pi\) | ||||
0.742647 | + | 0.669683i | \(0.233570\pi\) | |||||||
\(572\) | −0.675131 | −0.0282286 | ||||||||
\(573\) | −8.38787 | −0.350408 | ||||||||
\(574\) | −69.9452 | −2.91946 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.1187 | 0.754946 | ||||||||
\(577\) | 36.0625 | 1.50130 | 0.750652 | − | 0.660698i | \(-0.229740\pi\) | ||||
0.750652 | + | 0.660698i | \(0.229740\pi\) | |||||||
\(578\) | −124.125 | −5.16292 | ||||||||
\(579\) | 18.1563 | 0.754551 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.5560 | −0.645370 | ||||||||
\(582\) | −50.7269 | −2.10270 | ||||||||
\(583\) | −1.11379 | −0.0461284 | ||||||||
\(584\) | −7.87002 | −0.325664 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.2736 | 1.00273 | ||||||||
\(587\) | 22.4944 | 0.928442 | 0.464221 | − | 0.885719i | \(-0.346334\pi\) | ||||
0.464221 | + | 0.885719i | \(0.346334\pi\) | |||||||
\(588\) | 9.11871 | 0.376049 | ||||||||
\(589\) | 39.8945 | 1.64382 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.19394 | −0.0491120 | ||||||||
\(592\) | −58.9946 | −2.42466 | ||||||||
\(593\) | 28.8627 | 1.18525 | 0.592625 | − | 0.805478i | \(-0.298092\pi\) | ||||
0.592625 | + | 0.805478i | \(0.298092\pi\) | |||||||
\(594\) | −0.350262 | −0.0143714 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.57452 | 0.187379 | ||||||||
\(597\) | −0.700523 | −0.0286705 | ||||||||
\(598\) | −14.7308 | −0.602389 | ||||||||
\(599\) | 2.62927 | 0.107429 | 0.0537145 | − | 0.998556i | \(-0.482894\pi\) | ||||
0.0537145 | + | 0.998556i | \(0.482894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.6048 | −1.28919 | −0.644594 | − | 0.764525i | \(-0.722974\pi\) | ||||
−0.644594 | + | 0.764525i | \(0.722974\pi\) | |||||||
\(602\) | −17.9405 | −0.731200 | ||||||||
\(603\) | 6.05571 | 0.246608 | ||||||||
\(604\) | 15.1441 | 0.616205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.48119 | −0.385147 | ||||||||
\(607\) | −13.9149 | −0.564790 | −0.282395 | − | 0.959298i | \(-0.591129\pi\) | ||||
−0.282395 | + | 0.959298i | \(0.591129\pi\) | |||||||
\(608\) | 81.6444 | 3.31112 | ||||||||
\(609\) | 6.86177 | 0.278053 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.67513 | −0.108224 | ||||||||
\(612\) | −41.0567 | −1.65962 | ||||||||
\(613\) | −25.4471 | −1.02780 | −0.513899 | − | 0.857851i | \(-0.671799\pi\) | ||||
−0.513899 | + | 0.857851i | \(0.671799\pi\) | |||||||
\(614\) | −30.4445 | −1.22864 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.52865 | 0.101882 | ||||||||
\(617\) | −30.6497 | −1.23391 | −0.616956 | − | 0.786998i | \(-0.711634\pi\) | ||||
−0.616956 | + | 0.786998i | \(0.711634\pi\) | |||||||
\(618\) | −37.6688 | −1.51526 | ||||||||
\(619\) | −7.99412 | −0.321311 | −0.160655 | − | 0.987011i | \(-0.551361\pi\) | ||||
−0.160655 | + | 0.987011i | \(0.551361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.50659 | −0.220972 | ||||||||
\(622\) | −24.6761 | −0.989421 | ||||||||
\(623\) | −18.5863 | −0.744643 | ||||||||
\(624\) | −12.2750 | −0.491395 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 50.2081 | 2.00672 | ||||||||
\(627\) | −0.670206 | −0.0267655 | ||||||||
\(628\) | −81.3752 | −3.24722 | ||||||||
\(629\) | 38.2677 | 1.52583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.3463 | 1.64597 | 0.822985 | − | 0.568063i | \(-0.192307\pi\) | ||||
0.822985 | + | 0.568063i | \(0.192307\pi\) | |||||||
\(632\) | −74.7835 | −2.97473 | ||||||||
\(633\) | −16.9829 | −0.675008 | ||||||||
\(634\) | 28.2071 | 1.12025 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −43.8627 | −1.73927 | ||||||||
\(637\) | −1.76845 | −0.0700686 | ||||||||
\(638\) | −1.05079 | −0.0416010 | ||||||||
\(639\) | −15.0435 | −0.595111 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.26187 | 0.128836 | 0.0644180 | − | 0.997923i | \(-0.479481\pi\) | ||||
0.0644180 | + | 0.997923i | \(0.479481\pi\) | |||||||
\(642\) | 7.08840 | 0.279757 | ||||||||
\(643\) | 6.82065 | 0.268980 | 0.134490 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134490 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(644\) | 64.9438 | 2.55915 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −109.031 | −4.28976 | ||||||||
\(647\) | 30.9478 | 1.21668 | 0.608342 | − | 0.793675i | \(-0.291835\pi\) | ||||
0.608342 | + | 0.793675i | \(0.291835\pi\) | |||||||
\(648\) | −8.44358 | −0.331695 | ||||||||
\(649\) | 1.36344 | 0.0535195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.8265 | 0.698677 | ||||||||
\(652\) | 89.8818 | 3.52004 | ||||||||
\(653\) | −16.9003 | −0.661361 | −0.330681 | − | 0.943743i | \(-0.607278\pi\) | ||||
−0.330681 | + | 0.943743i | \(0.607278\pi\) | |||||||
\(654\) | −24.9321 | −0.974921 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 140.320 | 5.47859 | ||||||||
\(657\) | 0.932071 | 0.0363636 | ||||||||
\(658\) | 16.3684 | 0.638105 | ||||||||
\(659\) | 4.79621 | 0.186834 | 0.0934170 | − | 0.995627i | \(-0.470221\pi\) | ||||
0.0934170 | + | 0.995627i | \(0.470221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.105540 | −0.00410503 | −0.00205251 | − | 0.999998i | \(-0.500653\pi\) | ||||
−0.00205251 | + | 0.999998i | \(0.500653\pi\) | |||||||
\(662\) | −13.2593 | −0.515338 | ||||||||
\(663\) | 7.96239 | 0.309234 | ||||||||
\(664\) | 57.4260 | 2.22856 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.8568 | 0.498193 | ||||||||
\(667\) | −16.5198 | −0.639648 | ||||||||
\(668\) | 9.89446 | 0.382828 | ||||||||
\(669\) | −0.806063 | −0.0311642 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.679100 | −0.0262164 | ||||||||
\(672\) | 36.4821 | 1.40733 | ||||||||
\(673\) | −3.86670 | −0.149050 | −0.0745251 | − | 0.997219i | \(-0.523744\pi\) | ||||
−0.0745251 | + | 0.997219i | \(0.523744\pi\) | |||||||
\(674\) | −87.2311 | −3.36002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.15633 | 0.198320 | ||||||||
\(677\) | −30.1622 | −1.15923 | −0.579614 | − | 0.814891i | \(-0.696797\pi\) | ||||
−0.579614 | + | 0.814891i | \(0.696797\pi\) | |||||||
\(678\) | −35.7137 | −1.37158 | ||||||||
\(679\) | −43.3719 | −1.66446 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.68243 | 0.294391 | ||||||||
\(682\) | −2.72989 | −0.104533 | ||||||||
\(683\) | 17.9805 | 0.688004 | 0.344002 | − | 0.938969i | \(-0.388217\pi\) | ||||
0.344002 | + | 0.938969i | \(0.388217\pi\) | |||||||
\(684\) | −26.3938 | −1.00919 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 53.6516 | 2.04843 | ||||||||
\(687\) | 4.44851 | 0.169721 | ||||||||
\(688\) | 35.9913 | 1.37216 | ||||||||
\(689\) | 8.50659 | 0.324075 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.4363 | 1.19589 | 0.597946 | − | 0.801536i | \(-0.295984\pi\) | ||||
0.597946 | + | 0.801536i | \(0.295984\pi\) | |||||||
\(692\) | 40.9003 | 1.55480 | ||||||||
\(693\) | −0.299477 | −0.0113762 | ||||||||
\(694\) | −59.2868 | −2.25050 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.3307 | −0.960160 | ||||||||
\(697\) | −91.0210 | −3.44766 | ||||||||
\(698\) | 11.6180 | 0.439748 | ||||||||
\(699\) | −10.1260 | −0.383001 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.32724 | 0.201207 | 0.100604 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100604 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(702\) | 2.67513 | 0.100966 | ||||||||
\(703\) | 24.6009 | 0.927839 | ||||||||
\(704\) | −2.37233 | −0.0894105 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.6410 | −0.701564 | ||||||||
\(707\) | −8.10650 | −0.304876 | ||||||||
\(708\) | 53.6942 | 2.01795 | ||||||||
\(709\) | 27.8046 | 1.04423 | 0.522113 | − | 0.852876i | \(-0.325144\pi\) | ||||
0.522113 | + | 0.852876i | \(0.325144\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.85685 | 0.332158 | ||||||||
\(712\) | 68.6126 | 2.57137 | ||||||||
\(713\) | −42.9175 | −1.60727 | ||||||||
\(714\) | −48.7196 | −1.82328 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 76.9194 | 2.87461 | ||||||||
\(717\) | 19.4363 | 0.725862 | ||||||||
\(718\) | 40.1596 | 1.49874 | ||||||||
\(719\) | −0.992706 | −0.0370217 | −0.0185108 | − | 0.999829i | \(-0.505893\pi\) | ||||
−0.0185108 | + | 0.999829i | \(0.505893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.2071 | −1.19946 | ||||||||
\(722\) | −19.2642 | −0.716941 | ||||||||
\(723\) | 6.46898 | 0.240584 | ||||||||
\(724\) | −121.588 | −4.51879 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −29.3806 | −1.09042 | ||||||||
\(727\) | 40.0468 | 1.48525 | 0.742627 | − | 0.669705i | \(-0.233580\pi\) | ||||
0.742627 | + | 0.669705i | \(0.233580\pi\) | |||||||
\(728\) | −19.3127 | −0.715774 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.3463 | −0.863494 | ||||||||
\(732\) | −26.7440 | −0.988487 | ||||||||
\(733\) | 30.8627 | 1.13994 | 0.569970 | − | 0.821665i | \(-0.306955\pi\) | ||||
0.569970 | + | 0.821665i | \(0.306955\pi\) | |||||||
\(734\) | 72.4260 | 2.67329 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −87.8310 | −3.23749 | ||||||||
\(737\) | −0.792890 | −0.0292065 | ||||||||
\(738\) | −30.5804 | −1.12568 | ||||||||
\(739\) | 34.1309 | 1.25553 | 0.627763 | − | 0.778404i | \(-0.283971\pi\) | ||||
0.627763 | + | 0.778404i | \(0.283971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.11871 | 0.188041 | ||||||||
\(742\) | −52.0494 | −1.91079 | ||||||||
\(743\) | 14.1916 | 0.520638 | 0.260319 | − | 0.965523i | \(-0.416172\pi\) | ||||
0.260319 | + | 0.965523i | \(0.416172\pi\) | |||||||
\(744\) | −65.8080 | −2.41264 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.34534 | 0.342157 | ||||||||
\(747\) | −6.80114 | −0.248841 | ||||||||
\(748\) | 5.37565 | 0.196553 | ||||||||
\(749\) | 6.06063 | 0.221451 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.4050 | 0.489156 | 0.244578 | − | 0.969630i | \(-0.421351\pi\) | ||||
0.244578 | + | 0.969630i | \(0.421351\pi\) | |||||||
\(752\) | −32.8373 | −1.19745 | ||||||||
\(753\) | 17.7685 | 0.647518 | ||||||||
\(754\) | 8.02539 | 0.292268 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.7938 | −0.428938 | ||||||||
\(757\) | −5.76116 | −0.209393 | −0.104696 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104696 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(758\) | −72.2116 | −2.62284 | ||||||||
\(759\) | 0.720992 | 0.0261703 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.05334 | −0.328183 | −0.164092 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164092 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(762\) | −23.3561 | −0.846104 | ||||||||
\(763\) | −21.3171 | −0.771731 | ||||||||
\(764\) | 43.2506 | 1.56475 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.7699 | 0.533657 | ||||||||
\(767\) | −10.4133 | −0.376001 | ||||||||
\(768\) | −8.08840 | −0.291865 | ||||||||
\(769\) | −38.8383 | −1.40054 | −0.700272 | − | 0.713876i | \(-0.746938\pi\) | ||||
−0.700272 | + | 0.713876i | \(0.746938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.81924 | −0.173561 | ||||||||
\(772\) | −93.6199 | −3.36945 | ||||||||
\(773\) | 23.7381 | 0.853801 | 0.426901 | − | 0.904299i | \(-0.359605\pi\) | ||||
0.426901 | + | 0.904299i | \(0.359605\pi\) | |||||||
\(774\) | −7.84367 | −0.281935 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 160.111 | 5.74763 | ||||||||
\(777\) | 10.9927 | 0.394361 | ||||||||
\(778\) | 42.5355 | 1.52497 | ||||||||
\(779\) | −58.5139 | −2.09648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.96968 | 0.0704808 | ||||||||
\(782\) | 117.293 | 4.19438 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | −21.7078 | −0.775279 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 50.9438 | 1.81711 | ||||||||
\(787\) | −19.1803 | −0.683704 | −0.341852 | − | 0.939754i | \(-0.611054\pi\) | ||||
−0.341852 | + | 0.939754i | \(0.611054\pi\) | |||||||
\(788\) | 6.15633 | 0.219310 | ||||||||
\(789\) | −1.30536 | −0.0464719 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.5355 | −1.08572 | ||||||||
\(792\) | 1.10554 | 0.0392837 | ||||||||
\(793\) | 5.18664 | 0.184183 | ||||||||
\(794\) | −46.0118 | −1.63290 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.61213 | 0.128028 | ||||||||
\(797\) | −51.8627 | −1.83707 | −0.918536 | − | 0.395337i | \(-0.870628\pi\) | ||||
−0.918536 | + | 0.395337i | \(0.870628\pi\) | |||||||
\(798\) | −31.3199 | −1.10871 | ||||||||
\(799\) | 21.3004 | 0.753555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.12601 | −0.287118 | ||||||||
\(802\) | −50.9438 | −1.79889 | ||||||||
\(803\) | −0.122039 | −0.00430665 | ||||||||
\(804\) | −31.2252 | −1.10123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.8496 | 0.734394 | ||||||||
\(807\) | 8.79877 | 0.309731 | ||||||||
\(808\) | 29.9257 | 1.05278 | ||||||||
\(809\) | −18.1866 | −0.639408 | −0.319704 | − | 0.947517i | \(-0.603584\pi\) | ||||
−0.319704 | + | 0.947517i | \(0.603584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.71133 | 0.165437 | 0.0827185 | − | 0.996573i | \(-0.473640\pi\) | ||||
0.0827185 | + | 0.996573i | \(0.473640\pi\) | |||||||
\(812\) | −35.3815 | −1.24165 | ||||||||
\(813\) | −17.4264 | −0.611172 | ||||||||
\(814\) | −1.68338 | −0.0590024 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 97.7386 | 3.42154 | ||||||||
\(817\) | −15.0084 | −0.525079 | ||||||||
\(818\) | −33.2203 | −1.16152 | ||||||||
\(819\) | 2.28726 | 0.0799233 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.8046 | −1.17979 | −0.589895 | − | 0.807480i | \(-0.700831\pi\) | ||||
−0.589895 | + | 0.807480i | \(0.700831\pi\) | |||||||
\(822\) | −20.4993 | −0.714995 | ||||||||
\(823\) | 2.82653 | 0.0985267 | 0.0492633 | − | 0.998786i | \(-0.484313\pi\) | ||||
0.0492633 | + | 0.998786i | \(0.484313\pi\) | |||||||
\(824\) | 118.895 | 4.14190 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 63.7158 | 2.21696 | ||||||||
\(827\) | −39.9560 | −1.38941 | −0.694704 | − | 0.719296i | \(-0.744465\pi\) | ||||
−0.694704 | + | 0.719296i | \(0.744465\pi\) | |||||||
\(828\) | 28.3938 | 0.986751 | ||||||||
\(829\) | 1.30280 | 0.0452482 | 0.0226241 | − | 0.999744i | \(-0.492798\pi\) | ||||
0.0226241 | + | 0.999744i | \(0.492798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.7381 | 0.407191 | ||||||||
\(832\) | 18.1187 | 0.628153 | ||||||||
\(833\) | 14.0811 | 0.487881 | ||||||||
\(834\) | 20.3634 | 0.705128 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.45580 | 0.119521 | ||||||||
\(837\) | 7.79384 | 0.269395 | ||||||||
\(838\) | −16.4299 | −0.567563 | ||||||||
\(839\) | −17.9551 | −0.619879 | −0.309939 | − | 0.950756i | \(-0.600309\pi\) | ||||
−0.309939 | + | 0.950756i | \(0.600309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 47.1147 | 1.62368 | ||||||||
\(843\) | 14.5647 | 0.501634 | ||||||||
\(844\) | 87.5691 | 3.01425 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.15633 | 0.246040 | ||||||||
\(847\) | −25.1206 | −0.863155 | ||||||||
\(848\) | 104.419 | 3.58575 | ||||||||
\(849\) | 26.1016 | 0.895804 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.4650 | −0.907209 | ||||||||
\(852\) | 77.5691 | 2.65747 | ||||||||
\(853\) | 43.3258 | 1.48345 | 0.741724 | − | 0.670705i | \(-0.234008\pi\) | ||||
0.741724 | + | 0.670705i | \(0.234008\pi\) | |||||||
\(854\) | −31.7356 | −1.08597 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.3733 | −0.764703 | ||||||||
\(857\) | 15.5223 | 0.530232 | 0.265116 | − | 0.964216i | \(-0.414590\pi\) | ||||
0.265116 | + | 0.964216i | \(0.414590\pi\) | |||||||
\(858\) | −0.350262 | −0.0119577 | ||||||||
\(859\) | 14.0957 | 0.480939 | 0.240469 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240469 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.1465 | −0.891070 | ||||||||
\(862\) | 9.78304 | 0.333212 | ||||||||
\(863\) | 46.6105 | 1.58664 | 0.793320 | − | 0.608804i | \(-0.208351\pi\) | ||||
0.793320 | + | 0.608804i | \(0.208351\pi\) | |||||||
\(864\) | 15.9502 | 0.542636 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.8510 | 0.844470 | ||||||||
\(867\) | −46.3996 | −1.57581 | ||||||||
\(868\) | −91.9194 | −3.11995 | ||||||||
\(869\) | −1.15965 | −0.0393384 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.05571 | 0.205190 | ||||||||
\(872\) | 78.6937 | 2.66491 | ||||||||
\(873\) | −18.9624 | −0.641780 | ||||||||
\(874\) | 75.4030 | 2.55054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.80606 | −0.162382 | ||||||||
\(877\) | 33.3357 | 1.12567 | 0.562833 | − | 0.826571i | \(-0.309711\pi\) | ||||
0.562833 | + | 0.826571i | \(0.309711\pi\) | |||||||
\(878\) | −72.3839 | −2.44284 | ||||||||
\(879\) | 9.07381 | 0.306052 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1793 | 0.747241 | 0.373621 | − | 0.927582i | \(-0.378116\pi\) | ||||
0.373621 | + | 0.927582i | \(0.378116\pi\) | |||||||
\(882\) | 4.73084 | 0.159296 | ||||||||
\(883\) | 27.4109 | 0.922450 | 0.461225 | − | 0.887283i | \(-0.347410\pi\) | ||||
0.461225 | + | 0.887283i | \(0.347410\pi\) | |||||||
\(884\) | −41.0567 | −1.38089 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.9781 | 0.637582 | ||||||||
\(887\) | −1.33170 | −0.0447142 | −0.0223571 | − | 0.999750i | \(-0.507117\pi\) | ||||
−0.0223571 | + | 0.999750i | \(0.507117\pi\) | |||||||
\(888\) | −40.5804 | −1.36179 | ||||||||
\(889\) | −19.9697 | −0.669762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.130933 | −0.00438641 | ||||||||
\(892\) | 4.15633 | 0.139164 | ||||||||
\(893\) | 13.6932 | 0.458226 | ||||||||
\(894\) | 2.37328 | 0.0793745 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −37.8989 | −1.26611 | ||||||||
\(897\) | −5.50659 | −0.183860 | ||||||||
\(898\) | 39.4880 | 1.31773 | ||||||||
\(899\) | 23.3815 | 0.779818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −67.7328 | −2.25651 | ||||||||
\(902\) | 4.00397 | 0.133318 | ||||||||
\(903\) | −6.70640 | −0.223175 | ||||||||
\(904\) | 112.724 | 3.74915 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.85685 | 0.261026 | ||||||||
\(907\) | 31.1754 | 1.03516 | 0.517581 | − | 0.855634i | \(-0.326833\pi\) | ||||
0.517581 | + | 0.855634i | \(0.326833\pi\) | |||||||
\(908\) | −39.6131 | −1.31461 | ||||||||
\(909\) | −3.54420 | −0.117554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.56722 | 0.316976 | 0.158488 | − | 0.987361i | \(-0.449338\pi\) | ||||
0.158488 | + | 0.987361i | \(0.449338\pi\) | |||||||
\(912\) | 62.8324 | 2.08059 | ||||||||
\(913\) | 0.890491 | 0.0294709 | ||||||||
\(914\) | 6.10554 | 0.201953 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.9380 | −0.757891 | ||||||||
\(917\) | 43.5574 | 1.43839 | ||||||||
\(918\) | −21.3004 | −0.703019 | ||||||||
\(919\) | −35.8397 | −1.18224 | −0.591121 | − | 0.806583i | \(-0.701315\pi\) | ||||
−0.591121 | + | 0.806583i | \(0.701315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.3806 | −0.375003 | ||||||||
\(922\) | 28.2619 | 0.930755 | ||||||||
\(923\) | −15.0435 | −0.495163 | ||||||||
\(924\) | 1.54420 | 0.0508004 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.5369 | −0.543436 | ||||||||
\(927\) | −14.0811 | −0.462484 | ||||||||
\(928\) | 47.8505 | 1.57077 | ||||||||
\(929\) | 19.7137 | 0.646785 | 0.323393 | − | 0.946265i | \(-0.395177\pi\) | ||||
0.323393 | + | 0.946265i | \(0.395177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.05220 | 0.296674 | ||||||||
\(932\) | 52.2130 | 1.71029 | ||||||||
\(933\) | −9.22425 | −0.301989 | ||||||||
\(934\) | 16.9135 | 0.553427 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.44358 | −0.275987 | ||||||||
\(937\) | 57.2736 | 1.87105 | 0.935524 | − | 0.353263i | \(-0.114928\pi\) | ||||
0.935524 | + | 0.353263i | \(0.114928\pi\) | |||||||
\(938\) | −37.0532 | −1.20983 | ||||||||
\(939\) | 18.7685 | 0.612485 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2447 | −0.822954 | −0.411477 | − | 0.911420i | \(-0.634987\pi\) | ||||
−0.411477 | + | 0.911420i | \(0.634987\pi\) | |||||||
\(942\) | −42.2179 | −1.37553 | ||||||||
\(943\) | 62.9478 | 2.04986 | ||||||||
\(944\) | −127.823 | −4.16029 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.02699 | 0.0333904 | ||||||||
\(947\) | 5.04254 | 0.163860 | 0.0819302 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819302 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(948\) | −45.6688 | −1.48325 | ||||||||
\(949\) | 0.932071 | 0.0302563 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5442 | 0.341919 | ||||||||
\(952\) | 153.775 | 4.98387 | ||||||||
\(953\) | 15.4426 | 0.500236 | 0.250118 | − | 0.968215i | \(-0.419531\pi\) | ||||
0.250118 | + | 0.968215i | \(0.419531\pi\) | |||||||
\(954\) | −22.7562 | −0.736760 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −100.220 | −3.24134 | ||||||||
\(957\) | −0.392798 | −0.0126973 | ||||||||
\(958\) | −8.91019 | −0.287875 | ||||||||
\(959\) | −17.5271 | −0.565978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7440 | 0.959484 | ||||||||
\(962\) | 12.8568 | 0.414521 | ||||||||
\(963\) | 2.64974 | 0.0853866 | ||||||||
\(964\) | −33.3561 | −1.07433 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 33.6932 | 1.08406 | ||||||||
\(967\) | 30.2979 | 0.974314 | 0.487157 | − | 0.873314i | \(-0.338034\pi\) | ||||
0.487157 | + | 0.873314i | \(0.338034\pi\) | |||||||
\(968\) | 92.7347 | 2.98060 | ||||||||
\(969\) | −40.7572 | −1.30931 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.7367 | −1.30730 | −0.653652 | − | 0.756795i | \(-0.726764\pi\) | ||||
−0.653652 | + | 0.756795i | \(0.726764\pi\) | |||||||
\(972\) | −5.15633 | −0.165389 | ||||||||
\(973\) | 17.4109 | 0.558168 | ||||||||
\(974\) | 22.5877 | 0.723756 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 63.6662 | 2.03791 | ||||||||
\(977\) | −53.1608 | −1.70076 | −0.850382 | − | 0.526166i | \(-0.823629\pi\) | ||||
−0.850382 | + | 0.526166i | \(0.823629\pi\) | |||||||
\(978\) | 46.6312 | 1.49110 | ||||||||
\(979\) | 1.06396 | 0.0340043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.31994 | −0.297563 | ||||||||
\(982\) | 62.3606 | 1.99001 | ||||||||
\(983\) | −11.1831 | −0.356687 | −0.178343 | − | 0.983968i | \(-0.557074\pi\) | ||||
−0.178343 | + | 0.983968i | \(0.557074\pi\) | |||||||
\(984\) | 96.5217 | 3.07700 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −63.9013 | −2.03503 | ||||||||
\(987\) | 6.11871 | 0.194761 | ||||||||
\(988\) | −26.3938 | −0.839697 | ||||||||
\(989\) | 16.1457 | 0.513404 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9208 | −1.83992 | −0.919958 | − | 0.392018i | \(-0.871777\pi\) | ||||
−0.919958 | + | 0.392018i | \(0.871777\pi\) | |||||||
\(992\) | 124.313 | 3.94695 | ||||||||
\(993\) | −4.95651 | −0.157290 | ||||||||
\(994\) | 92.0468 | 2.91955 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 35.0689 | 1.11120 | ||||||||
\(997\) | 27.4241 | 0.868529 | 0.434265 | − | 0.900785i | \(-0.357008\pi\) | ||||
0.434265 | + | 0.900785i | \(0.357008\pi\) | |||||||
\(998\) | 85.2433 | 2.69833 | ||||||||
\(999\) | 4.80606 | 0.152057 |
(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 | 975.2.a.m.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 2925.2.a.bk.1.3 | 3 | |||
5.2 | odd | 4 | 975.2.c.k.274.1 | 6 | |||
5.3 | odd | 4 | 975.2.c.k.274.6 | 6 | |||
5.4 | even | 2 | 975.2.a.q.1.3 | yes | 3 | ||
15.2 | even | 4 | 2925.2.c.y.2224.6 | 6 | |||
15.8 | even | 4 | 2925.2.c.y.2224.1 | 6 | |||
15.14 | odd | 2 | 2925.2.a.be.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.a.m.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
975.2.a.q.1.3 | yes | 3 | 5.4 | even | 2 | ||
975.2.c.k.274.1 | 6 | 5.2 | odd | 4 | |||
975.2.c.k.274.6 | 6 | 5.3 | odd | 4 | |||
2925.2.a.be.1.1 | 3 | 15.14 | odd | 2 | |||
2925.2.a.bk.1.3 | 3 | 3.2 | odd | 2 | |||
2925.2.c.y.2224.1 | 6 | 15.8 | even | 4 | |||
2925.2.c.y.2224.6 | 6 | 15.2 | even | 4 |