Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8049,2,Mod(1,8049)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8049, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8049.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8049 = 3 \cdot 2683 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8049.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: | \(64.2715885869\) |
Analytic rank: | \(0\) |
Dimension: | \(129\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8049.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30919 | −1.63285 | −0.816423 | − | 0.577454i | \(-0.804046\pi\) | ||||
−0.816423 | + | 0.577454i | \(0.804046\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.33237 | 1.66619 | ||||||||
\(5\) | −0.223778 | −0.100076 | −0.0500382 | − | 0.998747i | \(-0.515934\pi\) | ||||
−0.0500382 | + | 0.998747i | \(0.515934\pi\) | |||||||
\(6\) | −2.30919 | −0.942724 | ||||||||
\(7\) | 3.94364 | 1.49056 | 0.745279 | − | 0.666753i | \(-0.232316\pi\) | ||||
0.745279 | + | 0.666753i | \(0.232316\pi\) | |||||||
\(8\) | −3.07670 | −1.08778 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.516746 | 0.163409 | ||||||||
\(11\) | −4.65249 | −1.40278 | −0.701389 | − | 0.712779i | \(-0.747436\pi\) | ||||
−0.701389 | + | 0.712779i | \(0.747436\pi\) | |||||||
\(12\) | 3.33237 | 0.961973 | ||||||||
\(13\) | −0.868261 | −0.240812 | −0.120406 | − | 0.992725i | \(-0.538420\pi\) | ||||
−0.120406 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(14\) | −9.10664 | −2.43385 | ||||||||
\(15\) | −0.223778 | −0.0577792 | ||||||||
\(16\) | 0.439960 | 0.109990 | ||||||||
\(17\) | −2.19008 | −0.531172 | −0.265586 | − | 0.964087i | \(-0.585565\pi\) | ||||
−0.265586 | + | 0.964087i | \(0.585565\pi\) | |||||||
\(18\) | −2.30919 | −0.544282 | ||||||||
\(19\) | 8.29060 | 1.90199 | 0.950997 | − | 0.309200i | \(-0.100061\pi\) | ||||
0.950997 | + | 0.309200i | \(0.100061\pi\) | |||||||
\(20\) | −0.745711 | −0.166746 | ||||||||
\(21\) | 3.94364 | 0.860574 | ||||||||
\(22\) | 10.7435 | 2.29052 | ||||||||
\(23\) | −2.92422 | −0.609743 | −0.304871 | − | 0.952394i | \(-0.598613\pi\) | ||||
−0.304871 | + | 0.952394i | \(0.598613\pi\) | |||||||
\(24\) | −3.07670 | −0.628030 | ||||||||
\(25\) | −4.94992 | −0.989985 | ||||||||
\(26\) | 2.00498 | 0.393210 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 13.1417 | 2.48355 | ||||||||
\(29\) | −1.95710 | −0.363424 | −0.181712 | − | 0.983352i | \(-0.558164\pi\) | ||||
−0.181712 | + | 0.983352i | \(0.558164\pi\) | |||||||
\(30\) | 0.516746 | 0.0943445 | ||||||||
\(31\) | −8.87044 | −1.59318 | −0.796589 | − | 0.604521i | \(-0.793365\pi\) | ||||
−0.796589 | + | 0.604521i | \(0.793365\pi\) | |||||||
\(32\) | 5.13746 | 0.908183 | ||||||||
\(33\) | −4.65249 | −0.809894 | ||||||||
\(34\) | 5.05731 | 0.867322 | ||||||||
\(35\) | −0.882500 | −0.149170 | ||||||||
\(36\) | 3.33237 | 0.555395 | ||||||||
\(37\) | 2.47861 | 0.407481 | 0.203740 | − | 0.979025i | \(-0.434690\pi\) | ||||
0.203740 | + | 0.979025i | \(0.434690\pi\) | |||||||
\(38\) | −19.1446 | −3.10566 | ||||||||
\(39\) | −0.868261 | −0.139033 | ||||||||
\(40\) | 0.688498 | 0.108861 | ||||||||
\(41\) | −4.80549 | −0.750492 | −0.375246 | − | 0.926925i | \(-0.622442\pi\) | ||||
−0.375246 | + | 0.926925i | \(0.622442\pi\) | |||||||
\(42\) | −9.10664 | −1.40518 | ||||||||
\(43\) | 3.31798 | 0.505987 | 0.252994 | − | 0.967468i | \(-0.418585\pi\) | ||||
0.252994 | + | 0.967468i | \(0.418585\pi\) | |||||||
\(44\) | −15.5038 | −2.33729 | ||||||||
\(45\) | −0.223778 | −0.0333588 | ||||||||
\(46\) | 6.75259 | 0.995616 | ||||||||
\(47\) | −0.547298 | −0.0798317 | −0.0399158 | − | 0.999203i | \(-0.512709\pi\) | ||||
−0.0399158 | + | 0.999203i | \(0.512709\pi\) | |||||||
\(48\) | 0.439960 | 0.0635027 | ||||||||
\(49\) | 8.55234 | 1.22176 | ||||||||
\(50\) | 11.4303 | 1.61649 | ||||||||
\(51\) | −2.19008 | −0.306672 | ||||||||
\(52\) | −2.89337 | −0.401238 | ||||||||
\(53\) | −0.651506 | −0.0894912 | −0.0447456 | − | 0.998998i | \(-0.514248\pi\) | ||||
−0.0447456 | + | 0.998998i | \(0.514248\pi\) | |||||||
\(54\) | −2.30919 | −0.314241 | ||||||||
\(55\) | 1.04112 | 0.140385 | ||||||||
\(56\) | −12.1334 | −1.62140 | ||||||||
\(57\) | 8.29060 | 1.09812 | ||||||||
\(58\) | 4.51932 | 0.593415 | ||||||||
\(59\) | 9.59738 | 1.24947 | 0.624736 | − | 0.780836i | \(-0.285207\pi\) | ||||
0.624736 | + | 0.780836i | \(0.285207\pi\) | |||||||
\(60\) | −0.745711 | −0.0962708 | ||||||||
\(61\) | 12.5445 | 1.60616 | 0.803078 | − | 0.595873i | \(-0.203194\pi\) | ||||
0.803078 | + | 0.595873i | \(0.203194\pi\) | |||||||
\(62\) | 20.4836 | 2.60142 | ||||||||
\(63\) | 3.94364 | 0.496853 | ||||||||
\(64\) | −12.7433 | −1.59291 | ||||||||
\(65\) | 0.194298 | 0.0240996 | ||||||||
\(66\) | 10.7435 | 1.32243 | ||||||||
\(67\) | −4.05863 | −0.495841 | −0.247920 | − | 0.968780i | \(-0.579747\pi\) | ||||
−0.247920 | + | 0.968780i | \(0.579747\pi\) | |||||||
\(68\) | −7.29815 | −0.885031 | ||||||||
\(69\) | −2.92422 | −0.352035 | ||||||||
\(70\) | 2.03786 | 0.243571 | ||||||||
\(71\) | −4.25409 | −0.504868 | −0.252434 | − | 0.967614i | \(-0.581231\pi\) | ||||
−0.252434 | + | 0.967614i | \(0.581231\pi\) | |||||||
\(72\) | −3.07670 | −0.362593 | ||||||||
\(73\) | 2.99090 | 0.350058 | 0.175029 | − | 0.984563i | \(-0.443998\pi\) | ||||
0.175029 | + | 0.984563i | \(0.443998\pi\) | |||||||
\(74\) | −5.72359 | −0.665353 | ||||||||
\(75\) | −4.94992 | −0.571568 | ||||||||
\(76\) | 27.6274 | 3.16908 | ||||||||
\(77\) | −18.3478 | −2.09092 | ||||||||
\(78\) | 2.00498 | 0.227020 | ||||||||
\(79\) | −9.51405 | −1.07041 | −0.535207 | − | 0.844721i | \(-0.679766\pi\) | ||||
−0.535207 | + | 0.844721i | \(0.679766\pi\) | |||||||
\(80\) | −0.0984531 | −0.0110074 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.0968 | 1.22544 | ||||||||
\(83\) | 5.74416 | 0.630504 | 0.315252 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315252 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(84\) | 13.1417 | 1.43388 | ||||||||
\(85\) | 0.490091 | 0.0531578 | ||||||||
\(86\) | −7.66186 | −0.826199 | ||||||||
\(87\) | −1.95710 | −0.209823 | ||||||||
\(88\) | 14.3143 | 1.52591 | ||||||||
\(89\) | 2.16881 | 0.229893 | 0.114947 | − | 0.993372i | \(-0.463330\pi\) | ||||
0.114947 | + | 0.993372i | \(0.463330\pi\) | |||||||
\(90\) | 0.516746 | 0.0544698 | ||||||||
\(91\) | −3.42411 | −0.358945 | ||||||||
\(92\) | −9.74460 | −1.01594 | ||||||||
\(93\) | −8.87044 | −0.919822 | ||||||||
\(94\) | 1.26382 | 0.130353 | ||||||||
\(95\) | −1.85525 | −0.190345 | ||||||||
\(96\) | 5.13746 | 0.524340 | ||||||||
\(97\) | 2.50946 | 0.254798 | 0.127399 | − | 0.991852i | \(-0.459337\pi\) | ||||
0.127399 | + | 0.991852i | \(0.459337\pi\) | |||||||
\(98\) | −19.7490 | −1.99495 | ||||||||
\(99\) | −4.65249 | −0.467592 | ||||||||
\(100\) | −16.4950 | −1.64950 | ||||||||
\(101\) | −8.39236 | −0.835071 | −0.417536 | − | 0.908661i | \(-0.637106\pi\) | ||||
−0.417536 | + | 0.908661i | \(0.637106\pi\) | |||||||
\(102\) | 5.05731 | 0.500749 | ||||||||
\(103\) | 3.24018 | 0.319264 | 0.159632 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159632 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(104\) | 2.67138 | 0.261951 | ||||||||
\(105\) | −0.882500 | −0.0861232 | ||||||||
\(106\) | 1.50445 | 0.146125 | ||||||||
\(107\) | 19.7559 | 1.90988 | 0.954938 | − | 0.296804i | \(-0.0959208\pi\) | ||||
0.954938 | + | 0.296804i | \(0.0959208\pi\) | |||||||
\(108\) | 3.33237 | 0.320658 | ||||||||
\(109\) | 16.2859 | 1.55990 | 0.779951 | − | 0.625840i | \(-0.215244\pi\) | ||||
0.779951 | + | 0.625840i | \(0.215244\pi\) | |||||||
\(110\) | −2.40415 | −0.229227 | ||||||||
\(111\) | 2.47861 | 0.235259 | ||||||||
\(112\) | 1.73504 | 0.163946 | ||||||||
\(113\) | −6.70705 | −0.630946 | −0.315473 | − | 0.948935i | \(-0.602163\pi\) | ||||
−0.315473 | + | 0.948935i | \(0.602163\pi\) | |||||||
\(114\) | −19.1446 | −1.79306 | ||||||||
\(115\) | 0.654376 | 0.0610209 | ||||||||
\(116\) | −6.52178 | −0.605532 | ||||||||
\(117\) | −0.868261 | −0.0802708 | ||||||||
\(118\) | −22.1622 | −2.04020 | ||||||||
\(119\) | −8.63689 | −0.791742 | ||||||||
\(120\) | 0.688498 | 0.0628510 | ||||||||
\(121\) | 10.6456 | 0.967784 | ||||||||
\(122\) | −28.9676 | −2.62261 | ||||||||
\(123\) | −4.80549 | −0.433297 | ||||||||
\(124\) | −29.5596 | −2.65453 | ||||||||
\(125\) | 2.22657 | 0.199151 | ||||||||
\(126\) | −9.10664 | −0.811284 | ||||||||
\(127\) | 12.7044 | 1.12733 | 0.563666 | − | 0.826003i | \(-0.309390\pi\) | ||||
0.563666 | + | 0.826003i | \(0.309390\pi\) | |||||||
\(128\) | 19.1518 | 1.69280 | ||||||||
\(129\) | 3.31798 | 0.292132 | ||||||||
\(130\) | −0.448671 | −0.0393510 | ||||||||
\(131\) | 13.7546 | 1.20175 | 0.600874 | − | 0.799343i | \(-0.294819\pi\) | ||||
0.600874 | + | 0.799343i | \(0.294819\pi\) | |||||||
\(132\) | −15.5038 | −1.34943 | ||||||||
\(133\) | 32.6952 | 2.83503 | ||||||||
\(134\) | 9.37217 | 0.809632 | ||||||||
\(135\) | −0.223778 | −0.0192597 | ||||||||
\(136\) | 6.73822 | 0.577798 | ||||||||
\(137\) | 8.65141 | 0.739140 | 0.369570 | − | 0.929203i | \(-0.379505\pi\) | ||||
0.369570 | + | 0.929203i | \(0.379505\pi\) | |||||||
\(138\) | 6.75259 | 0.574819 | ||||||||
\(139\) | 6.89645 | 0.584949 | 0.292474 | − | 0.956273i | \(-0.405521\pi\) | ||||
0.292474 | + | 0.956273i | \(0.405521\pi\) | |||||||
\(140\) | −2.94082 | −0.248544 | ||||||||
\(141\) | −0.547298 | −0.0460908 | ||||||||
\(142\) | 9.82351 | 0.824371 | ||||||||
\(143\) | 4.03957 | 0.337806 | ||||||||
\(144\) | 0.439960 | 0.0366633 | ||||||||
\(145\) | 0.437955 | 0.0363702 | ||||||||
\(146\) | −6.90656 | −0.571591 | ||||||||
\(147\) | 8.55234 | 0.705385 | ||||||||
\(148\) | 8.25965 | 0.678939 | ||||||||
\(149\) | 7.88506 | 0.645969 | 0.322985 | − | 0.946404i | \(-0.395314\pi\) | ||||
0.322985 | + | 0.946404i | \(0.395314\pi\) | |||||||
\(150\) | 11.4303 | 0.933282 | ||||||||
\(151\) | 7.16906 | 0.583410 | 0.291705 | − | 0.956508i | \(-0.405777\pi\) | ||||
0.291705 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(152\) | −25.5077 | −2.06895 | ||||||||
\(153\) | −2.19008 | −0.177057 | ||||||||
\(154\) | 42.3685 | 3.41415 | ||||||||
\(155\) | 1.98501 | 0.159440 | ||||||||
\(156\) | −2.89337 | −0.231655 | ||||||||
\(157\) | −0.499226 | −0.0398426 | −0.0199213 | − | 0.999802i | \(-0.506342\pi\) | ||||
−0.0199213 | + | 0.999802i | \(0.506342\pi\) | |||||||
\(158\) | 21.9698 | 1.74782 | ||||||||
\(159\) | −0.651506 | −0.0516678 | ||||||||
\(160\) | −1.14965 | −0.0908877 | ||||||||
\(161\) | −11.5321 | −0.908856 | ||||||||
\(162\) | −2.30919 | −0.181427 | ||||||||
\(163\) | 5.37514 | 0.421013 | 0.210507 | − | 0.977592i | \(-0.432489\pi\) | ||||
0.210507 | + | 0.977592i | \(0.432489\pi\) | |||||||
\(164\) | −16.0137 | −1.25046 | ||||||||
\(165\) | 1.04112 | 0.0810513 | ||||||||
\(166\) | −13.2644 | −1.02952 | ||||||||
\(167\) | 11.7716 | 0.910910 | 0.455455 | − | 0.890259i | \(-0.349477\pi\) | ||||
0.455455 | + | 0.890259i | \(0.349477\pi\) | |||||||
\(168\) | −12.1334 | −0.936114 | ||||||||
\(169\) | −12.2461 | −0.942009 | ||||||||
\(170\) | −1.13171 | −0.0867985 | ||||||||
\(171\) | 8.29060 | 0.633998 | ||||||||
\(172\) | 11.0567 | 0.843069 | ||||||||
\(173\) | 24.9254 | 1.89504 | 0.947522 | − | 0.319691i | \(-0.103579\pi\) | ||||
0.947522 | + | 0.319691i | \(0.103579\pi\) | |||||||
\(174\) | 4.51932 | 0.342609 | ||||||||
\(175\) | −19.5207 | −1.47563 | ||||||||
\(176\) | −2.04691 | −0.154291 | ||||||||
\(177\) | 9.59738 | 0.721383 | ||||||||
\(178\) | −5.00820 | −0.375381 | ||||||||
\(179\) | −6.84478 | −0.511603 | −0.255801 | − | 0.966729i | \(-0.582339\pi\) | ||||
−0.255801 | + | 0.966729i | \(0.582339\pi\) | |||||||
\(180\) | −0.745711 | −0.0555820 | ||||||||
\(181\) | 21.2839 | 1.58202 | 0.791009 | − | 0.611804i | \(-0.209556\pi\) | ||||
0.791009 | + | 0.611804i | \(0.209556\pi\) | |||||||
\(182\) | 7.90694 | 0.586101 | ||||||||
\(183\) | 12.5445 | 0.927315 | ||||||||
\(184\) | 8.99697 | 0.663265 | ||||||||
\(185\) | −0.554657 | −0.0407792 | ||||||||
\(186\) | 20.4836 | 1.50193 | ||||||||
\(187\) | 10.1893 | 0.745116 | ||||||||
\(188\) | −1.82380 | −0.133014 | ||||||||
\(189\) | 3.94364 | 0.286858 | ||||||||
\(190\) | 4.28413 | 0.310804 | ||||||||
\(191\) | 22.6969 | 1.64229 | 0.821147 | − | 0.570717i | \(-0.193335\pi\) | ||||
0.821147 | + | 0.570717i | \(0.193335\pi\) | |||||||
\(192\) | −12.7433 | −0.919668 | ||||||||
\(193\) | −1.86094 | −0.133953 | −0.0669765 | − | 0.997755i | \(-0.521335\pi\) | ||||
−0.0669765 | + | 0.997755i | \(0.521335\pi\) | |||||||
\(194\) | −5.79484 | −0.416045 | ||||||||
\(195\) | 0.194298 | 0.0139139 | ||||||||
\(196\) | 28.4996 | 2.03568 | ||||||||
\(197\) | 8.82171 | 0.628521 | 0.314261 | − | 0.949337i | \(-0.398243\pi\) | ||||
0.314261 | + | 0.949337i | \(0.398243\pi\) | |||||||
\(198\) | 10.7435 | 0.763506 | ||||||||
\(199\) | −5.84192 | −0.414123 | −0.207061 | − | 0.978328i | \(-0.566390\pi\) | ||||
−0.207061 | + | 0.978328i | \(0.566390\pi\) | |||||||
\(200\) | 15.2295 | 1.07688 | ||||||||
\(201\) | −4.05863 | −0.286274 | ||||||||
\(202\) | 19.3796 | 1.36354 | ||||||||
\(203\) | −7.71810 | −0.541704 | ||||||||
\(204\) | −7.29815 | −0.510973 | ||||||||
\(205\) | 1.07536 | 0.0751065 | ||||||||
\(206\) | −7.48220 | −0.521309 | ||||||||
\(207\) | −2.92422 | −0.203248 | ||||||||
\(208\) | −0.382000 | −0.0264869 | ||||||||
\(209\) | −38.5719 | −2.66807 | ||||||||
\(210\) | 2.03786 | 0.140626 | ||||||||
\(211\) | 15.1432 | 1.04250 | 0.521250 | − | 0.853404i | \(-0.325466\pi\) | ||||
0.521250 | + | 0.853404i | \(0.325466\pi\) | |||||||
\(212\) | −2.17106 | −0.149109 | ||||||||
\(213\) | −4.25409 | −0.291485 | ||||||||
\(214\) | −45.6202 | −3.11853 | ||||||||
\(215\) | −0.742490 | −0.0506374 | ||||||||
\(216\) | −3.07670 | −0.209343 | ||||||||
\(217\) | −34.9819 | −2.37472 | ||||||||
\(218\) | −37.6072 | −2.54708 | ||||||||
\(219\) | 2.99090 | 0.202106 | ||||||||
\(220\) | 3.46941 | 0.233907 | ||||||||
\(221\) | 1.90156 | 0.127913 | ||||||||
\(222\) | −5.72359 | −0.384142 | ||||||||
\(223\) | 0.556387 | 0.0372584 | 0.0186292 | − | 0.999826i | \(-0.494070\pi\) | ||||
0.0186292 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(224\) | 20.2603 | 1.35370 | ||||||||
\(225\) | −4.94992 | −0.329995 | ||||||||
\(226\) | 15.4879 | 1.03024 | ||||||||
\(227\) | −18.4884 | −1.22712 | −0.613560 | − | 0.789648i | \(-0.710263\pi\) | ||||
−0.613560 | + | 0.789648i | \(0.710263\pi\) | |||||||
\(228\) | 27.6274 | 1.82967 | ||||||||
\(229\) | −8.71380 | −0.575824 | −0.287912 | − | 0.957657i | \(-0.592961\pi\) | ||||
−0.287912 | + | 0.957657i | \(0.592961\pi\) | |||||||
\(230\) | −1.51108 | −0.0996377 | ||||||||
\(231\) | −18.3478 | −1.20719 | ||||||||
\(232\) | 6.02141 | 0.395325 | ||||||||
\(233\) | 22.0312 | 1.44331 | 0.721656 | − | 0.692252i | \(-0.243381\pi\) | ||||
0.721656 | + | 0.692252i | \(0.243381\pi\) | |||||||
\(234\) | 2.00498 | 0.131070 | ||||||||
\(235\) | 0.122473 | 0.00798927 | ||||||||
\(236\) | 31.9820 | 2.08185 | ||||||||
\(237\) | −9.51405 | −0.618004 | ||||||||
\(238\) | 19.9442 | 1.29279 | ||||||||
\(239\) | 3.06543 | 0.198286 | 0.0991430 | − | 0.995073i | \(-0.468390\pi\) | ||||
0.0991430 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(240\) | −0.0984531 | −0.00635512 | ||||||||
\(241\) | −17.4603 | −1.12471 | −0.562357 | − | 0.826894i | \(-0.690105\pi\) | ||||
−0.562357 | + | 0.826894i | \(0.690105\pi\) | |||||||
\(242\) | −24.5828 | −1.58024 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 41.8029 | 2.67616 | ||||||||
\(245\) | −1.91382 | −0.122270 | ||||||||
\(246\) | 11.0968 | 0.707507 | ||||||||
\(247\) | −7.19841 | −0.458024 | ||||||||
\(248\) | 27.2917 | 1.73303 | ||||||||
\(249\) | 5.74416 | 0.364022 | ||||||||
\(250\) | −5.14158 | −0.325182 | ||||||||
\(251\) | 7.68374 | 0.484993 | 0.242497 | − | 0.970152i | \(-0.422034\pi\) | ||||
0.242497 | + | 0.970152i | \(0.422034\pi\) | |||||||
\(252\) | 13.1417 | 0.827849 | ||||||||
\(253\) | 13.6049 | 0.855333 | ||||||||
\(254\) | −29.3369 | −1.84076 | ||||||||
\(255\) | 0.490091 | 0.0306907 | ||||||||
\(256\) | −18.7387 | −1.17117 | ||||||||
\(257\) | 21.0624 | 1.31384 | 0.656919 | − | 0.753961i | \(-0.271859\pi\) | ||||
0.656919 | + | 0.753961i | \(0.271859\pi\) | |||||||
\(258\) | −7.66186 | −0.477006 | ||||||||
\(259\) | 9.77475 | 0.607374 | ||||||||
\(260\) | 0.647472 | 0.0401545 | ||||||||
\(261\) | −1.95710 | −0.121141 | ||||||||
\(262\) | −31.7621 | −1.96227 | ||||||||
\(263\) | −14.6359 | −0.902491 | −0.451245 | − | 0.892400i | \(-0.649020\pi\) | ||||
−0.451245 | + | 0.892400i | \(0.649020\pi\) | |||||||
\(264\) | 14.3143 | 0.880986 | ||||||||
\(265\) | 0.145793 | 0.00895596 | ||||||||
\(266\) | −75.4995 | −4.62917 | ||||||||
\(267\) | 2.16881 | 0.132729 | ||||||||
\(268\) | −13.5249 | −0.826163 | ||||||||
\(269\) | 9.26375 | 0.564821 | 0.282410 | − | 0.959294i | \(-0.408866\pi\) | ||||
0.282410 | + | 0.959294i | \(0.408866\pi\) | |||||||
\(270\) | 0.516746 | 0.0314482 | ||||||||
\(271\) | 12.8171 | 0.778584 | 0.389292 | − | 0.921114i | \(-0.372720\pi\) | ||||
0.389292 | + | 0.921114i | \(0.372720\pi\) | |||||||
\(272\) | −0.963546 | −0.0584235 | ||||||||
\(273\) | −3.42411 | −0.207237 | ||||||||
\(274\) | −19.9778 | −1.20690 | ||||||||
\(275\) | 23.0294 | 1.38873 | ||||||||
\(276\) | −9.74460 | −0.586556 | ||||||||
\(277\) | 18.6361 | 1.11974 | 0.559868 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559868 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(278\) | −15.9252 | −0.955131 | ||||||||
\(279\) | −8.87044 | −0.531059 | ||||||||
\(280\) | 2.71519 | 0.162264 | ||||||||
\(281\) | 6.31691 | 0.376835 | 0.188418 | − | 0.982089i | \(-0.439664\pi\) | ||||
0.188418 | + | 0.982089i | \(0.439664\pi\) | |||||||
\(282\) | 1.26382 | 0.0752592 | ||||||||
\(283\) | −23.8199 | −1.41595 | −0.707973 | − | 0.706239i | \(-0.750390\pi\) | ||||
−0.707973 | + | 0.706239i | \(0.750390\pi\) | |||||||
\(284\) | −14.1762 | −0.841203 | ||||||||
\(285\) | −1.85525 | −0.109896 | ||||||||
\(286\) | −9.32815 | −0.551585 | ||||||||
\(287\) | −18.9512 | −1.11865 | ||||||||
\(288\) | 5.13746 | 0.302728 | ||||||||
\(289\) | −12.2036 | −0.717856 | ||||||||
\(290\) | −1.01132 | −0.0593869 | ||||||||
\(291\) | 2.50946 | 0.147107 | ||||||||
\(292\) | 9.96678 | 0.583262 | ||||||||
\(293\) | 11.6479 | 0.680479 | 0.340239 | − | 0.940339i | \(-0.389492\pi\) | ||||
0.340239 | + | 0.940339i | \(0.389492\pi\) | |||||||
\(294\) | −19.7490 | −1.15178 | ||||||||
\(295\) | −2.14768 | −0.125043 | ||||||||
\(296\) | −7.62595 | −0.443249 | ||||||||
\(297\) | −4.65249 | −0.269965 | ||||||||
\(298\) | −18.2081 | −1.05477 | ||||||||
\(299\) | 2.53899 | 0.146834 | ||||||||
\(300\) | −16.4950 | −0.952339 | ||||||||
\(301\) | 13.0849 | 0.754203 | ||||||||
\(302\) | −16.5547 | −0.952618 | ||||||||
\(303\) | −8.39236 | −0.482129 | ||||||||
\(304\) | 3.64753 | 0.209200 | ||||||||
\(305\) | −2.80718 | −0.160738 | ||||||||
\(306\) | 5.05731 | 0.289107 | ||||||||
\(307\) | −6.97570 | −0.398124 | −0.199062 | − | 0.979987i | \(-0.563790\pi\) | ||||
−0.199062 | + | 0.979987i | \(0.563790\pi\) | |||||||
\(308\) | −61.1415 | −3.48386 | ||||||||
\(309\) | 3.24018 | 0.184327 | ||||||||
\(310\) | −4.58376 | −0.260340 | ||||||||
\(311\) | −2.58733 | −0.146714 | −0.0733571 | − | 0.997306i | \(-0.523371\pi\) | ||||
−0.0733571 | + | 0.997306i | \(0.523371\pi\) | |||||||
\(312\) | 2.67138 | 0.151237 | ||||||||
\(313\) | −0.196515 | −0.0111077 | −0.00555384 | − | 0.999985i | \(-0.501768\pi\) | ||||
−0.00555384 | + | 0.999985i | \(0.501768\pi\) | |||||||
\(314\) | 1.15281 | 0.0650568 | ||||||||
\(315\) | −0.882500 | −0.0497232 | ||||||||
\(316\) | −31.7043 | −1.78351 | ||||||||
\(317\) | −22.0936 | −1.24090 | −0.620450 | − | 0.784246i | \(-0.713050\pi\) | ||||
−0.620450 | + | 0.784246i | \(0.713050\pi\) | |||||||
\(318\) | 1.50445 | 0.0843655 | ||||||||
\(319\) | 9.10537 | 0.509803 | ||||||||
\(320\) | 2.85167 | 0.159413 | ||||||||
\(321\) | 19.7559 | 1.10267 | ||||||||
\(322\) | 26.6298 | 1.48402 | ||||||||
\(323\) | −18.1571 | −1.01029 | ||||||||
\(324\) | 3.33237 | 0.185132 | ||||||||
\(325\) | 4.29783 | 0.238401 | ||||||||
\(326\) | −12.4122 | −0.687450 | ||||||||
\(327\) | 16.2859 | 0.900610 | ||||||||
\(328\) | 14.7851 | 0.816369 | ||||||||
\(329\) | −2.15835 | −0.118994 | ||||||||
\(330\) | −2.40415 | −0.132344 | ||||||||
\(331\) | −0.551627 | −0.0303201 | −0.0151601 | − | 0.999885i | \(-0.504826\pi\) | ||||
−0.0151601 | + | 0.999885i | \(0.504826\pi\) | |||||||
\(332\) | 19.1417 | 1.05054 | ||||||||
\(333\) | 2.47861 | 0.135827 | ||||||||
\(334\) | −27.1828 | −1.48738 | ||||||||
\(335\) | 0.908232 | 0.0496220 | ||||||||
\(336\) | 1.73504 | 0.0946544 | ||||||||
\(337\) | 30.6111 | 1.66749 | 0.833747 | − | 0.552146i | \(-0.186191\pi\) | ||||
0.833747 | + | 0.552146i | \(0.186191\pi\) | |||||||
\(338\) | 28.2787 | 1.53816 | ||||||||
\(339\) | −6.70705 | −0.364277 | ||||||||
\(340\) | 1.63316 | 0.0885708 | ||||||||
\(341\) | 41.2696 | 2.23487 | ||||||||
\(342\) | −19.1446 | −1.03522 | ||||||||
\(343\) | 6.12186 | 0.330549 | ||||||||
\(344\) | −10.2084 | −0.550402 | ||||||||
\(345\) | 0.654376 | 0.0352304 | ||||||||
\(346\) | −57.5576 | −3.09431 | ||||||||
\(347\) | −0.682669 | −0.0366476 | −0.0183238 | − | 0.999832i | \(-0.505833\pi\) | ||||
−0.0183238 | + | 0.999832i | \(0.505833\pi\) | |||||||
\(348\) | −6.52178 | −0.349604 | ||||||||
\(349\) | −9.13117 | −0.488780 | −0.244390 | − | 0.969677i | \(-0.578588\pi\) | ||||
−0.244390 | + | 0.969677i | \(0.578588\pi\) | |||||||
\(350\) | 45.0772 | 2.40948 | ||||||||
\(351\) | −0.868261 | −0.0463444 | ||||||||
\(352\) | −23.9019 | −1.27398 | ||||||||
\(353\) | −29.5873 | −1.57477 | −0.787387 | − | 0.616459i | \(-0.788566\pi\) | ||||
−0.787387 | + | 0.616459i | \(0.788566\pi\) | |||||||
\(354\) | −22.1622 | −1.17791 | ||||||||
\(355\) | 0.951970 | 0.0505253 | ||||||||
\(356\) | 7.22728 | 0.383045 | ||||||||
\(357\) | −8.63689 | −0.457113 | ||||||||
\(358\) | 15.8059 | 0.835368 | ||||||||
\(359\) | 15.2420 | 0.804443 | 0.402221 | − | 0.915542i | \(-0.368238\pi\) | ||||
0.402221 | + | 0.915542i | \(0.368238\pi\) | |||||||
\(360\) | 0.688498 | 0.0362870 | ||||||||
\(361\) | 49.7341 | 2.61758 | ||||||||
\(362\) | −49.1486 | −2.58319 | ||||||||
\(363\) | 10.6456 | 0.558750 | ||||||||
\(364\) | −11.4104 | −0.598069 | ||||||||
\(365\) | −0.669296 | −0.0350325 | ||||||||
\(366\) | −28.9676 | −1.51416 | ||||||||
\(367\) | −4.86360 | −0.253878 | −0.126939 | − | 0.991911i | \(-0.540515\pi\) | ||||
−0.126939 | + | 0.991911i | \(0.540515\pi\) | |||||||
\(368\) | −1.28654 | −0.0670655 | ||||||||
\(369\) | −4.80549 | −0.250164 | ||||||||
\(370\) | 1.28081 | 0.0665862 | ||||||||
\(371\) | −2.56931 | −0.133392 | ||||||||
\(372\) | −29.5596 | −1.53259 | ||||||||
\(373\) | 9.87652 | 0.511387 | 0.255693 | − | 0.966758i | \(-0.417696\pi\) | ||||
0.255693 | + | 0.966758i | \(0.417696\pi\) | |||||||
\(374\) | −23.5291 | −1.21666 | ||||||||
\(375\) | 2.22657 | 0.114980 | ||||||||
\(376\) | 1.68388 | 0.0868392 | ||||||||
\(377\) | 1.69927 | 0.0875170 | ||||||||
\(378\) | −9.10664 | −0.468395 | ||||||||
\(379\) | −37.6086 | −1.93182 | −0.965912 | − | 0.258869i | \(-0.916650\pi\) | ||||
−0.965912 | + | 0.258869i | \(0.916650\pi\) | |||||||
\(380\) | −6.18239 | −0.317150 | ||||||||
\(381\) | 12.7044 | 0.650866 | ||||||||
\(382\) | −52.4116 | −2.68161 | ||||||||
\(383\) | −3.79669 | −0.194002 | −0.0970008 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0970008 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(384\) | 19.1518 | 0.977337 | ||||||||
\(385\) | 4.10582 | 0.209252 | ||||||||
\(386\) | 4.29726 | 0.218725 | ||||||||
\(387\) | 3.31798 | 0.168662 | ||||||||
\(388\) | 8.36247 | 0.424540 | ||||||||
\(389\) | −32.3551 | −1.64047 | −0.820234 | − | 0.572027i | \(-0.806157\pi\) | ||||
−0.820234 | + | 0.572027i | \(0.806157\pi\) | |||||||
\(390\) | −0.448671 | −0.0227193 | ||||||||
\(391\) | 6.40428 | 0.323878 | ||||||||
\(392\) | −26.3130 | −1.32901 | ||||||||
\(393\) | 13.7546 | 0.693830 | ||||||||
\(394\) | −20.3710 | −1.02628 | ||||||||
\(395\) | 2.12903 | 0.107123 | ||||||||
\(396\) | −15.5038 | −0.779096 | ||||||||
\(397\) | 15.9887 | 0.802448 | 0.401224 | − | 0.915980i | \(-0.368585\pi\) | ||||
0.401224 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(398\) | 13.4901 | 0.676199 | ||||||||
\(399\) | 32.6952 | 1.63681 | ||||||||
\(400\) | −2.17777 | −0.108888 | ||||||||
\(401\) | −20.3510 | −1.01628 | −0.508140 | − | 0.861275i | \(-0.669667\pi\) | ||||
−0.508140 | + | 0.861275i | \(0.669667\pi\) | |||||||
\(402\) | 9.37217 | 0.467441 | ||||||||
\(403\) | 7.70186 | 0.383657 | ||||||||
\(404\) | −27.9665 | −1.39138 | ||||||||
\(405\) | −0.223778 | −0.0111196 | ||||||||
\(406\) | 17.8226 | 0.884520 | ||||||||
\(407\) | −11.5317 | −0.571605 | ||||||||
\(408\) | 6.73822 | 0.333592 | ||||||||
\(409\) | 25.0573 | 1.23900 | 0.619502 | − | 0.784995i | \(-0.287334\pi\) | ||||
0.619502 | + | 0.784995i | \(0.287334\pi\) | |||||||
\(410\) | −2.48322 | −0.122637 | ||||||||
\(411\) | 8.65141 | 0.426742 | ||||||||
\(412\) | 10.7975 | 0.531954 | ||||||||
\(413\) | 37.8486 | 1.86241 | ||||||||
\(414\) | 6.75259 | 0.331872 | ||||||||
\(415\) | −1.28542 | −0.0630986 | ||||||||
\(416\) | −4.46066 | −0.218702 | ||||||||
\(417\) | 6.89645 | 0.337720 | ||||||||
\(418\) | 89.0700 | 4.35655 | ||||||||
\(419\) | −17.7321 | −0.866272 | −0.433136 | − | 0.901329i | \(-0.642593\pi\) | ||||
−0.433136 | + | 0.901329i | \(0.642593\pi\) | |||||||
\(420\) | −2.94082 | −0.143497 | ||||||||
\(421\) | −21.8440 | −1.06461 | −0.532305 | − | 0.846552i | \(-0.678674\pi\) | ||||
−0.532305 | + | 0.846552i | \(0.678674\pi\) | |||||||
\(422\) | −34.9685 | −1.70224 | ||||||||
\(423\) | −0.547298 | −0.0266106 | ||||||||
\(424\) | 2.00449 | 0.0973467 | ||||||||
\(425\) | 10.8407 | 0.525852 | ||||||||
\(426\) | 9.82351 | 0.475951 | ||||||||
\(427\) | 49.4710 | 2.39407 | ||||||||
\(428\) | 65.8341 | 3.18221 | ||||||||
\(429\) | 4.03957 | 0.195032 | ||||||||
\(430\) | 1.71455 | 0.0826831 | ||||||||
\(431\) | 6.86119 | 0.330492 | 0.165246 | − | 0.986252i | \(-0.447158\pi\) | ||||
0.165246 | + | 0.986252i | \(0.447158\pi\) | |||||||
\(432\) | 0.439960 | 0.0211676 | ||||||||
\(433\) | 28.7591 | 1.38207 | 0.691037 | − | 0.722819i | \(-0.257154\pi\) | ||||
0.691037 | + | 0.722819i | \(0.257154\pi\) | |||||||
\(434\) | 80.7799 | 3.87756 | ||||||||
\(435\) | 0.437955 | 0.0209983 | ||||||||
\(436\) | 54.2705 | 2.59909 | ||||||||
\(437\) | −24.2436 | −1.15973 | ||||||||
\(438\) | −6.90656 | −0.330008 | ||||||||
\(439\) | −10.2911 | −0.491165 | −0.245583 | − | 0.969376i | \(-0.578979\pi\) | ||||
−0.245583 | + | 0.969376i | \(0.578979\pi\) | |||||||
\(440\) | −3.20323 | −0.152708 | ||||||||
\(441\) | 8.55234 | 0.407254 | ||||||||
\(442\) | −4.39107 | −0.208862 | ||||||||
\(443\) | 6.34405 | 0.301415 | 0.150707 | − | 0.988578i | \(-0.451845\pi\) | ||||
0.150707 | + | 0.988578i | \(0.451845\pi\) | |||||||
\(444\) | 8.25965 | 0.391986 | ||||||||
\(445\) | −0.485332 | −0.0230069 | ||||||||
\(446\) | −1.28480 | −0.0608373 | ||||||||
\(447\) | 7.88506 | 0.372951 | ||||||||
\(448\) | −50.2550 | −2.37433 | ||||||||
\(449\) | −34.0688 | −1.60780 | −0.803902 | − | 0.594762i | \(-0.797246\pi\) | ||||
−0.803902 | + | 0.594762i | \(0.797246\pi\) | |||||||
\(450\) | 11.4303 | 0.538831 | ||||||||
\(451\) | 22.3575 | 1.05277 | ||||||||
\(452\) | −22.3504 | −1.05127 | ||||||||
\(453\) | 7.16906 | 0.336832 | ||||||||
\(454\) | 42.6933 | 2.00370 | ||||||||
\(455\) | 0.766241 | 0.0359219 | ||||||||
\(456\) | −25.5077 | −1.19451 | ||||||||
\(457\) | 28.8395 | 1.34905 | 0.674527 | − | 0.738250i | \(-0.264347\pi\) | ||||
0.674527 | + | 0.738250i | \(0.264347\pi\) | |||||||
\(458\) | 20.1218 | 0.940232 | ||||||||
\(459\) | −2.19008 | −0.102224 | ||||||||
\(460\) | 2.18062 | 0.101672 | ||||||||
\(461\) | 33.0622 | 1.53986 | 0.769931 | − | 0.638127i | \(-0.220291\pi\) | ||||
0.769931 | + | 0.638127i | \(0.220291\pi\) | |||||||
\(462\) | 42.3685 | 1.97116 | ||||||||
\(463\) | −25.8383 | −1.20081 | −0.600403 | − | 0.799698i | \(-0.704993\pi\) | ||||
−0.600403 | + | 0.799698i | \(0.704993\pi\) | |||||||
\(464\) | −0.861044 | −0.0399730 | ||||||||
\(465\) | 1.98501 | 0.0920525 | ||||||||
\(466\) | −50.8743 | −2.35671 | ||||||||
\(467\) | 16.7010 | 0.772831 | 0.386415 | − | 0.922325i | \(-0.373713\pi\) | ||||
0.386415 | + | 0.922325i | \(0.373713\pi\) | |||||||
\(468\) | −2.89337 | −0.133746 | ||||||||
\(469\) | −16.0058 | −0.739079 | ||||||||
\(470\) | −0.282814 | −0.0130452 | ||||||||
\(471\) | −0.499226 | −0.0230031 | ||||||||
\(472\) | −29.5283 | −1.35915 | ||||||||
\(473\) | −15.4369 | −0.709787 | ||||||||
\(474\) | 21.9698 | 1.00910 | ||||||||
\(475\) | −41.0378 | −1.88295 | ||||||||
\(476\) | −28.7813 | −1.31919 | ||||||||
\(477\) | −0.651506 | −0.0298304 | ||||||||
\(478\) | −7.07866 | −0.323770 | ||||||||
\(479\) | 32.7043 | 1.49430 | 0.747149 | − | 0.664657i | \(-0.231422\pi\) | ||||
0.747149 | + | 0.664657i | \(0.231422\pi\) | |||||||
\(480\) | −1.14965 | −0.0524740 | ||||||||
\(481\) | −2.15208 | −0.0981264 | ||||||||
\(482\) | 40.3191 | 1.83649 | ||||||||
\(483\) | −11.5321 | −0.524729 | ||||||||
\(484\) | 35.4752 | 1.61251 | ||||||||
\(485\) | −0.561562 | −0.0254992 | ||||||||
\(486\) | −2.30919 | −0.104747 | ||||||||
\(487\) | 15.1562 | 0.686794 | 0.343397 | − | 0.939190i | \(-0.388422\pi\) | ||||
0.343397 | + | 0.939190i | \(0.388422\pi\) | |||||||
\(488\) | −38.5957 | −1.74714 | ||||||||
\(489\) | 5.37514 | 0.243072 | ||||||||
\(490\) | 4.41938 | 0.199647 | ||||||||
\(491\) | −14.3531 | −0.647745 | −0.323872 | − | 0.946101i | \(-0.604985\pi\) | ||||
−0.323872 | + | 0.946101i | \(0.604985\pi\) | |||||||
\(492\) | −16.0137 | −0.721953 | ||||||||
\(493\) | 4.28620 | 0.193041 | ||||||||
\(494\) | 16.6225 | 0.747882 | ||||||||
\(495\) | 1.04112 | 0.0467950 | ||||||||
\(496\) | −3.90264 | −0.175234 | ||||||||
\(497\) | −16.7766 | −0.752534 | ||||||||
\(498\) | −13.2644 | −0.594391 | ||||||||
\(499\) | −28.7162 | −1.28551 | −0.642756 | − | 0.766071i | \(-0.722209\pi\) | ||||
−0.642756 | + | 0.766071i | \(0.722209\pi\) | |||||||
\(500\) | 7.41976 | 0.331822 | ||||||||
\(501\) | 11.7716 | 0.525914 | ||||||||
\(502\) | −17.7432 | −0.791919 | ||||||||
\(503\) | −37.3063 | −1.66341 | −0.831703 | − | 0.555221i | \(-0.812634\pi\) | ||||
−0.831703 | + | 0.555221i | \(0.812634\pi\) | |||||||
\(504\) | −12.1334 | −0.540466 | ||||||||
\(505\) | 1.87802 | 0.0835709 | ||||||||
\(506\) | −31.4163 | −1.39663 | ||||||||
\(507\) | −12.2461 | −0.543869 | ||||||||
\(508\) | 42.3357 | 1.87835 | ||||||||
\(509\) | −2.32115 | −0.102883 | −0.0514417 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514417 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(510\) | −1.13171 | −0.0501131 | ||||||||
\(511\) | 11.7950 | 0.521781 | ||||||||
\(512\) | 4.96752 | 0.219536 | ||||||||
\(513\) | 8.29060 | 0.366039 | ||||||||
\(514\) | −48.6372 | −2.14530 | ||||||||
\(515\) | −0.725080 | −0.0319508 | ||||||||
\(516\) | 11.0567 | 0.486746 | ||||||||
\(517\) | 2.54630 | 0.111986 | ||||||||
\(518\) | −22.5718 | −0.991748 | ||||||||
\(519\) | 24.9254 | 1.09410 | ||||||||
\(520\) | −0.597796 | −0.0262151 | ||||||||
\(521\) | −21.3185 | −0.933980 | −0.466990 | − | 0.884262i | \(-0.654662\pi\) | ||||
−0.466990 | + | 0.884262i | \(0.654662\pi\) | |||||||
\(522\) | 4.51932 | 0.197805 | ||||||||
\(523\) | −33.0074 | −1.44331 | −0.721656 | − | 0.692251i | \(-0.756619\pi\) | ||||
−0.721656 | + | 0.692251i | \(0.756619\pi\) | |||||||
\(524\) | 45.8356 | 2.00234 | ||||||||
\(525\) | −19.5207 | −0.851955 | ||||||||
\(526\) | 33.7972 | 1.47363 | ||||||||
\(527\) | 19.4270 | 0.846252 | ||||||||
\(528\) | −2.04691 | −0.0890801 | ||||||||
\(529\) | −14.4489 | −0.628214 | ||||||||
\(530\) | −0.336663 | −0.0146237 | ||||||||
\(531\) | 9.59738 | 0.416491 | ||||||||
\(532\) | 108.953 | 4.72369 | ||||||||
\(533\) | 4.17242 | 0.180728 | ||||||||
\(534\) | −5.00820 | −0.216726 | ||||||||
\(535\) | −4.42093 | −0.191134 | ||||||||
\(536\) | 12.4872 | 0.539365 | ||||||||
\(537\) | −6.84478 | −0.295374 | ||||||||
\(538\) | −21.3918 | −0.922265 | ||||||||
\(539\) | −39.7896 | −1.71386 | ||||||||
\(540\) | −0.745711 | −0.0320903 | ||||||||
\(541\) | −40.7528 | −1.75210 | −0.876050 | − | 0.482219i | \(-0.839831\pi\) | ||||
−0.876050 | + | 0.482219i | \(0.839831\pi\) | |||||||
\(542\) | −29.5972 | −1.27131 | ||||||||
\(543\) | 21.2839 | 0.913379 | ||||||||
\(544\) | −11.2514 | −0.482401 | ||||||||
\(545\) | −3.64441 | −0.156109 | ||||||||
\(546\) | 7.90694 | 0.338386 | ||||||||
\(547\) | −4.75585 | −0.203345 | −0.101673 | − | 0.994818i | \(-0.532419\pi\) | ||||
−0.101673 | + | 0.994818i | \(0.532419\pi\) | |||||||
\(548\) | 28.8297 | 1.23154 | ||||||||
\(549\) | 12.5445 | 0.535386 | ||||||||
\(550\) | −53.1794 | −2.26758 | ||||||||
\(551\) | −16.2255 | −0.691230 | ||||||||
\(552\) | 8.99697 | 0.382936 | ||||||||
\(553\) | −37.5200 | −1.59551 | ||||||||
\(554\) | −43.0344 | −1.82836 | ||||||||
\(555\) | −0.554657 | −0.0235439 | ||||||||
\(556\) | 22.9815 | 0.974634 | ||||||||
\(557\) | −2.97886 | −0.126219 | −0.0631093 | − | 0.998007i | \(-0.520102\pi\) | ||||
−0.0631093 | + | 0.998007i | \(0.520102\pi\) | |||||||
\(558\) | 20.4836 | 0.867138 | ||||||||
\(559\) | −2.88087 | −0.121848 | ||||||||
\(560\) | −0.388264 | −0.0164072 | ||||||||
\(561\) | 10.1893 | 0.430193 | ||||||||
\(562\) | −14.5870 | −0.615314 | ||||||||
\(563\) | −15.1944 | −0.640367 | −0.320183 | − | 0.947356i | \(-0.603745\pi\) | ||||
−0.320183 | + | 0.947356i | \(0.603745\pi\) | |||||||
\(564\) | −1.82380 | −0.0767959 | ||||||||
\(565\) | 1.50089 | 0.0631428 | ||||||||
\(566\) | 55.0047 | 2.31202 | ||||||||
\(567\) | 3.94364 | 0.165618 | ||||||||
\(568\) | 13.0886 | 0.549184 | ||||||||
\(569\) | 5.16884 | 0.216689 | 0.108345 | − | 0.994113i | \(-0.465445\pi\) | ||||
0.108345 | + | 0.994113i | \(0.465445\pi\) | |||||||
\(570\) | 4.28413 | 0.179443 | ||||||||
\(571\) | −6.79866 | −0.284515 | −0.142257 | − | 0.989830i | \(-0.545436\pi\) | ||||
−0.142257 | + | 0.989830i | \(0.545436\pi\) | |||||||
\(572\) | 13.4614 | 0.562848 | ||||||||
\(573\) | 22.6969 | 0.948178 | ||||||||
\(574\) | 43.7619 | 1.82659 | ||||||||
\(575\) | 14.4747 | 0.603636 | ||||||||
\(576\) | −12.7433 | −0.530971 | ||||||||
\(577\) | 8.60525 | 0.358241 | 0.179121 | − | 0.983827i | \(-0.442675\pi\) | ||||
0.179121 | + | 0.983827i | \(0.442675\pi\) | |||||||
\(578\) | 28.1804 | 1.17215 | ||||||||
\(579\) | −1.86094 | −0.0773379 | ||||||||
\(580\) | 1.45943 | 0.0605995 | ||||||||
\(581\) | 22.6529 | 0.939802 | ||||||||
\(582\) | −5.79484 | −0.240204 | ||||||||
\(583\) | 3.03112 | 0.125536 | ||||||||
\(584\) | −9.20210 | −0.380786 | ||||||||
\(585\) | 0.194298 | 0.00803321 | ||||||||
\(586\) | −26.8973 | −1.11112 | ||||||||
\(587\) | 31.2044 | 1.28794 | 0.643972 | − | 0.765049i | \(-0.277285\pi\) | ||||
0.643972 | + | 0.765049i | \(0.277285\pi\) | |||||||
\(588\) | 28.4996 | 1.17530 | ||||||||
\(589\) | −73.5413 | −3.03022 | ||||||||
\(590\) | 4.95940 | 0.204175 | ||||||||
\(591\) | 8.82171 | 0.362877 | ||||||||
\(592\) | 1.09049 | 0.0448188 | ||||||||
\(593\) | −9.34742 | −0.383852 | −0.191926 | − | 0.981409i | \(-0.561473\pi\) | ||||
−0.191926 | + | 0.981409i | \(0.561473\pi\) | |||||||
\(594\) | 10.7435 | 0.440811 | ||||||||
\(595\) | 1.93274 | 0.0792348 | ||||||||
\(596\) | 26.2760 | 1.07631 | ||||||||
\(597\) | −5.84192 | −0.239094 | ||||||||
\(598\) | −5.86302 | −0.239757 | ||||||||
\(599\) | 2.83717 | 0.115924 | 0.0579619 | − | 0.998319i | \(-0.481540\pi\) | ||||
0.0579619 | + | 0.998319i | \(0.481540\pi\) | |||||||
\(600\) | 15.2295 | 0.621740 | ||||||||
\(601\) | 42.2604 | 1.72384 | 0.861919 | − | 0.507046i | \(-0.169262\pi\) | ||||
0.861919 | + | 0.507046i | \(0.169262\pi\) | |||||||
\(602\) | −30.2156 | −1.23150 | ||||||||
\(603\) | −4.05863 | −0.165280 | ||||||||
\(604\) | 23.8900 | 0.972069 | ||||||||
\(605\) | −2.38225 | −0.0968523 | ||||||||
\(606\) | 19.3796 | 0.787242 | ||||||||
\(607\) | −11.6474 | −0.472753 | −0.236377 | − | 0.971662i | \(-0.575960\pi\) | ||||
−0.236377 | + | 0.971662i | \(0.575960\pi\) | |||||||
\(608\) | 42.5926 | 1.72736 | ||||||||
\(609\) | −7.71810 | −0.312753 | ||||||||
\(610\) | 6.48231 | 0.262461 | ||||||||
\(611\) | 0.475198 | 0.0192245 | ||||||||
\(612\) | −7.29815 | −0.295010 | ||||||||
\(613\) | −1.57469 | −0.0636011 | −0.0318005 | − | 0.999494i | \(-0.510124\pi\) | ||||
−0.0318005 | + | 0.999494i | \(0.510124\pi\) | |||||||
\(614\) | 16.1082 | 0.650076 | ||||||||
\(615\) | 1.07536 | 0.0433628 | ||||||||
\(616\) | 56.4506 | 2.27446 | ||||||||
\(617\) | −9.63509 | −0.387894 | −0.193947 | − | 0.981012i | \(-0.562129\pi\) | ||||
−0.193947 | + | 0.981012i | \(0.562129\pi\) | |||||||
\(618\) | −7.48220 | −0.300978 | ||||||||
\(619\) | 13.0019 | 0.522589 | 0.261294 | − | 0.965259i | \(-0.415851\pi\) | ||||
0.261294 | + | 0.965259i | \(0.415851\pi\) | |||||||
\(620\) | 6.61478 | 0.265656 | ||||||||
\(621\) | −2.92422 | −0.117345 | ||||||||
\(622\) | 5.97465 | 0.239562 | ||||||||
\(623\) | 8.55302 | 0.342670 | ||||||||
\(624\) | −0.382000 | −0.0152922 | ||||||||
\(625\) | 24.2514 | 0.970054 | ||||||||
\(626\) | 0.453791 | 0.0181371 | ||||||||
\(627\) | −38.5719 | −1.54041 | ||||||||
\(628\) | −1.66361 | −0.0663851 | ||||||||
\(629\) | −5.42835 | −0.216442 | ||||||||
\(630\) | 2.03786 | 0.0811904 | ||||||||
\(631\) | 16.0331 | 0.638266 | 0.319133 | − | 0.947710i | \(-0.396608\pi\) | ||||
0.319133 | + | 0.947710i | \(0.396608\pi\) | |||||||
\(632\) | 29.2719 | 1.16437 | ||||||||
\(633\) | 15.1432 | 0.601887 | ||||||||
\(634\) | 51.0184 | 2.02620 | ||||||||
\(635\) | −2.84296 | −0.112819 | ||||||||
\(636\) | −2.17106 | −0.0860882 | ||||||||
\(637\) | −7.42566 | −0.294215 | ||||||||
\(638\) | −21.0261 | −0.832430 | ||||||||
\(639\) | −4.25409 | −0.168289 | ||||||||
\(640\) | −4.28575 | −0.169409 | ||||||||
\(641\) | −20.9742 | −0.828429 | −0.414215 | − | 0.910179i | \(-0.635944\pi\) | ||||
−0.414215 | + | 0.910179i | \(0.635944\pi\) | |||||||
\(642\) | −45.6202 | −1.80049 | ||||||||
\(643\) | 22.3851 | 0.882782 | 0.441391 | − | 0.897315i | \(-0.354485\pi\) | ||||
0.441391 | + | 0.897315i | \(0.354485\pi\) | |||||||
\(644\) | −38.4292 | −1.51432 | ||||||||
\(645\) | −0.742490 | −0.0292355 | ||||||||
\(646\) | 41.9282 | 1.64964 | ||||||||
\(647\) | 36.7408 | 1.44443 | 0.722216 | − | 0.691668i | \(-0.243124\pi\) | ||||
0.722216 | + | 0.691668i | \(0.243124\pi\) | |||||||
\(648\) | −3.07670 | −0.120864 | ||||||||
\(649\) | −44.6516 | −1.75273 | ||||||||
\(650\) | −9.92451 | −0.389271 | ||||||||
\(651\) | −34.9819 | −1.37105 | ||||||||
\(652\) | 17.9120 | 0.701486 | ||||||||
\(653\) | −18.7159 | −0.732409 | −0.366205 | − | 0.930534i | \(-0.619343\pi\) | ||||
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(654\) | −37.6072 | −1.47056 | ||||||||
\(655\) | −3.07798 | −0.120267 | ||||||||
\(656\) | −2.11422 | −0.0825465 | ||||||||
\(657\) | 2.99090 | 0.116686 | ||||||||
\(658\) | 4.98405 | 0.194298 | ||||||||
\(659\) | −8.26000 | −0.321764 | −0.160882 | − | 0.986974i | \(-0.551434\pi\) | ||||
−0.160882 | + | 0.986974i | \(0.551434\pi\) | |||||||
\(660\) | 3.46941 | 0.135047 | ||||||||
\(661\) | −7.46824 | −0.290481 | −0.145240 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145240 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(662\) | 1.27381 | 0.0495081 | ||||||||
\(663\) | 1.90156 | 0.0738505 | ||||||||
\(664\) | −17.6731 | −0.685849 | ||||||||
\(665\) | −7.31645 | −0.283720 | ||||||||
\(666\) | −5.72359 | −0.221784 | ||||||||
\(667\) | 5.72299 | 0.221595 | ||||||||
\(668\) | 39.2272 | 1.51775 | ||||||||
\(669\) | 0.556387 | 0.0215112 | ||||||||
\(670\) | −2.09728 | −0.0810251 | ||||||||
\(671\) | −58.3630 | −2.25308 | ||||||||
\(672\) | 20.2603 | 0.781558 | ||||||||
\(673\) | −10.6084 | −0.408924 | −0.204462 | − | 0.978874i | \(-0.565545\pi\) | ||||
−0.204462 | + | 0.978874i | \(0.565545\pi\) | |||||||
\(674\) | −70.6870 | −2.72276 | ||||||||
\(675\) | −4.94992 | −0.190523 | ||||||||
\(676\) | −40.8086 | −1.56956 | ||||||||
\(677\) | 30.8256 | 1.18472 | 0.592362 | − | 0.805672i | \(-0.298195\pi\) | ||||
0.592362 | + | 0.805672i | \(0.298195\pi\) | |||||||
\(678\) | 15.4879 | 0.594808 | ||||||||
\(679\) | 9.89644 | 0.379790 | ||||||||
\(680\) | −1.50786 | −0.0578239 | ||||||||
\(681\) | −18.4884 | −0.708478 | ||||||||
\(682\) | −95.2995 | −3.64921 | ||||||||
\(683\) | 16.6597 | 0.637465 | 0.318732 | − | 0.947845i | \(-0.396743\pi\) | ||||
0.318732 | + | 0.947845i | \(0.396743\pi\) | |||||||
\(684\) | 27.6274 | 1.05636 | ||||||||
\(685\) | −1.93599 | −0.0739704 | ||||||||
\(686\) | −14.1366 | −0.539736 | ||||||||
\(687\) | −8.71380 | −0.332452 | ||||||||
\(688\) | 1.45978 | 0.0556535 | ||||||||
\(689\) | 0.565678 | 0.0215506 | ||||||||
\(690\) | −1.51108 | −0.0575258 | ||||||||
\(691\) | −27.2864 | −1.03802 | −0.519011 | − | 0.854767i | \(-0.673700\pi\) | ||||
−0.519011 | + | 0.854767i | \(0.673700\pi\) | |||||||
\(692\) | 83.0607 | 3.15750 | ||||||||
\(693\) | −18.3478 | −0.696973 | ||||||||
\(694\) | 1.57641 | 0.0598398 | ||||||||
\(695\) | −1.54327 | −0.0585396 | ||||||||
\(696\) | 6.02141 | 0.228241 | ||||||||
\(697\) | 10.5244 | 0.398640 | ||||||||
\(698\) | 21.0856 | 0.798103 | ||||||||
\(699\) | 22.0312 | 0.833297 | ||||||||
\(700\) | −65.0504 | −2.45867 | ||||||||
\(701\) | 50.5627 | 1.90973 | 0.954863 | − | 0.297046i | \(-0.0960014\pi\) | ||||
0.954863 | + | 0.297046i | \(0.0960014\pi\) | |||||||
\(702\) | 2.00498 | 0.0756732 | ||||||||
\(703\) | 20.5492 | 0.775026 | ||||||||
\(704\) | 59.2880 | 2.23450 | ||||||||
\(705\) | 0.122473 | 0.00461261 | ||||||||
\(706\) | 68.3228 | 2.57136 | ||||||||
\(707\) | −33.0965 | −1.24472 | ||||||||
\(708\) | 31.9820 | 1.20196 | ||||||||
\(709\) | 2.32108 | 0.0871699 | 0.0435850 | − | 0.999050i | \(-0.486122\pi\) | ||||
0.0435850 | + | 0.999050i | \(0.486122\pi\) | |||||||
\(710\) | −2.19828 | −0.0825001 | ||||||||
\(711\) | −9.51405 | −0.356805 | ||||||||
\(712\) | −6.67279 | −0.250073 | ||||||||
\(713\) | 25.9391 | 0.971429 | ||||||||
\(714\) | 19.9442 | 0.746395 | ||||||||
\(715\) | −0.903966 | −0.0338064 | ||||||||
\(716\) | −22.8093 | −0.852425 | ||||||||
\(717\) | 3.06543 | 0.114480 | ||||||||
\(718\) | −35.1968 | −1.31353 | ||||||||
\(719\) | −49.1036 | −1.83126 | −0.915628 | − | 0.402026i | \(-0.868306\pi\) | ||||
−0.915628 | + | 0.402026i | \(0.868306\pi\) | |||||||
\(720\) | −0.0984531 | −0.00366913 | ||||||||
\(721\) | 12.7781 | 0.475882 | ||||||||
\(722\) | −114.846 | −4.27411 | ||||||||
\(723\) | −17.4603 | −0.649354 | ||||||||
\(724\) | 70.9258 | 2.63594 | ||||||||
\(725\) | 9.68749 | 0.359784 | ||||||||
\(726\) | −24.5828 | −0.912353 | ||||||||
\(727\) | 28.4757 | 1.05610 | 0.528052 | − | 0.849212i | \(-0.322922\pi\) | ||||
0.528052 | + | 0.849212i | \(0.322922\pi\) | |||||||
\(728\) | 10.5350 | 0.390453 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.54553 | 0.0572027 | ||||||||
\(731\) | −7.26664 | −0.268766 | ||||||||
\(732\) | 41.8029 | 1.54508 | ||||||||
\(733\) | −40.6325 | −1.50080 | −0.750399 | − | 0.660985i | \(-0.770138\pi\) | ||||
−0.750399 | + | 0.660985i | \(0.770138\pi\) | |||||||
\(734\) | 11.2310 | 0.414543 | ||||||||
\(735\) | −1.91382 | −0.0705924 | ||||||||
\(736\) | −15.0231 | −0.553758 | ||||||||
\(737\) | 18.8827 | 0.695554 | ||||||||
\(738\) | 11.0968 | 0.408479 | ||||||||
\(739\) | 39.9846 | 1.47086 | 0.735428 | − | 0.677603i | \(-0.236981\pi\) | ||||
0.735428 | + | 0.677603i | \(0.236981\pi\) | |||||||
\(740\) | −1.84833 | −0.0679458 | ||||||||
\(741\) | −7.19841 | −0.264440 | ||||||||
\(742\) | 5.93303 | 0.217808 | ||||||||
\(743\) | −6.98238 | −0.256159 | −0.128079 | − | 0.991764i | \(-0.540881\pi\) | ||||
−0.128079 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(744\) | 27.2917 | 1.00056 | ||||||||
\(745\) | −1.76450 | −0.0646463 | ||||||||
\(746\) | −22.8068 | −0.835016 | ||||||||
\(747\) | 5.74416 | 0.210168 | ||||||||
\(748\) | 33.9546 | 1.24150 | ||||||||
\(749\) | 77.9103 | 2.84678 | ||||||||
\(750\) | −5.14158 | −0.187744 | ||||||||
\(751\) | 18.4358 | 0.672732 | 0.336366 | − | 0.941731i | \(-0.390802\pi\) | ||||
0.336366 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(752\) | −0.240789 | −0.00878068 | ||||||||
\(753\) | 7.68374 | 0.280011 | ||||||||
\(754\) | −3.92395 | −0.142902 | ||||||||
\(755\) | −1.60428 | −0.0583856 | ||||||||
\(756\) | 13.1417 | 0.477959 | ||||||||
\(757\) | −33.6474 | −1.22293 | −0.611467 | − | 0.791270i | \(-0.709420\pi\) | ||||
−0.611467 | + | 0.791270i | \(0.709420\pi\) | |||||||
\(758\) | 86.8455 | 3.15437 | ||||||||
\(759\) | 13.6049 | 0.493827 | ||||||||
\(760\) | 5.70806 | 0.207053 | ||||||||
\(761\) | −3.71822 | −0.134785 | −0.0673927 | − | 0.997727i | \(-0.521468\pi\) | ||||
−0.0673927 | + | 0.997727i | \(0.521468\pi\) | |||||||
\(762\) | −29.3369 | −1.06276 | ||||||||
\(763\) | 64.2257 | 2.32512 | ||||||||
\(764\) | 75.6347 | 2.73637 | ||||||||
\(765\) | 0.490091 | 0.0177193 | ||||||||
\(766\) | 8.76728 | 0.316775 | ||||||||
\(767\) | −8.33303 | −0.300888 | ||||||||
\(768\) | −18.7387 | −0.676173 | ||||||||
\(769\) | 14.1764 | 0.511214 | 0.255607 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255607 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(770\) | −9.48112 | −0.341676 | ||||||||
\(771\) | 21.0624 | 0.758545 | ||||||||
\(772\) | −6.20133 | −0.223191 | ||||||||
\(773\) | 43.3850 | 1.56045 | 0.780225 | − | 0.625499i | \(-0.215104\pi\) | ||||
0.780225 | + | 0.625499i | \(0.215104\pi\) | |||||||
\(774\) | −7.66186 | −0.275400 | ||||||||
\(775\) | 43.9080 | 1.57722 | ||||||||
\(776\) | −7.72088 | −0.277163 | ||||||||
\(777\) | 9.77475 | 0.350667 | ||||||||
\(778\) | 74.7142 | 2.67863 | ||||||||
\(779\) | −39.8404 | −1.42743 | ||||||||
\(780\) | 0.647472 | 0.0231832 | ||||||||
\(781\) | 19.7921 | 0.708217 | ||||||||
\(782\) | −14.7887 | −0.528843 | ||||||||
\(783\) | −1.95710 | −0.0699410 | ||||||||
\(784\) | 3.76268 | 0.134381 | ||||||||
\(785\) | 0.111716 | 0.00398730 | ||||||||
\(786\) | −31.7621 | −1.13292 | ||||||||
\(787\) | 29.6983 | 1.05863 | 0.529315 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529315 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(788\) | 29.3972 | 1.04723 | ||||||||
\(789\) | −14.6359 | −0.521053 | ||||||||
\(790\) | −4.91634 | −0.174916 | ||||||||
\(791\) | −26.4502 | −0.940461 | ||||||||
\(792\) | 14.3143 | 0.508637 | ||||||||
\(793\) | −10.8919 | −0.386782 | ||||||||
\(794\) | −36.9209 | −1.31027 | ||||||||
\(795\) | 0.145793 | 0.00517073 | ||||||||
\(796\) | −19.4675 | −0.690006 | ||||||||
\(797\) | −46.5653 | −1.64943 | −0.824713 | − | 0.565551i | \(-0.808663\pi\) | ||||
−0.824713 | + | 0.565551i | \(0.808663\pi\) | |||||||
\(798\) | −75.4995 | −2.67265 | ||||||||
\(799\) | 1.19863 | 0.0424043 | ||||||||
\(800\) | −25.4300 | −0.899087 | ||||||||
\(801\) | 2.16881 | 0.0766312 | ||||||||
\(802\) | 46.9943 | 1.65943 | ||||||||
\(803\) | −13.9151 | −0.491053 | ||||||||
\(804\) | −13.5249 | −0.476986 | ||||||||
\(805\) | 2.58063 | 0.0909551 | ||||||||
\(806\) | −17.7851 | −0.626453 | ||||||||
\(807\) | 9.26375 | 0.326099 | ||||||||
\(808\) | 25.8208 | 0.908373 | ||||||||
\(809\) | 34.9838 | 1.22997 | 0.614983 | − | 0.788540i | \(-0.289163\pi\) | ||||
0.614983 | + | 0.788540i | \(0.289163\pi\) | |||||||
\(810\) | 0.516746 | 0.0181566 | ||||||||
\(811\) | 25.1624 | 0.883573 | 0.441787 | − | 0.897120i | \(-0.354345\pi\) | ||||
0.441787 | + | 0.897120i | \(0.354345\pi\) | |||||||
\(812\) | −25.7196 | −0.902580 | ||||||||
\(813\) | 12.8171 | 0.449516 | ||||||||
\(814\) | 26.6289 | 0.933343 | ||||||||
\(815\) | −1.20284 | −0.0421335 | ||||||||
\(816\) | −0.963546 | −0.0337308 | ||||||||
\(817\) | 27.5080 | 0.962385 | ||||||||
\(818\) | −57.8622 | −2.02310 | ||||||||
\(819\) | −3.42411 | −0.119648 | ||||||||
\(820\) | 3.58351 | 0.125141 | ||||||||
\(821\) | 49.2886 | 1.72018 | 0.860092 | − | 0.510139i | \(-0.170406\pi\) | ||||
0.860092 | + | 0.510139i | \(0.170406\pi\) | |||||||
\(822\) | −19.9778 | −0.696805 | ||||||||
\(823\) | −10.3308 | −0.360109 | −0.180055 | − | 0.983657i | \(-0.557627\pi\) | ||||
−0.180055 | + | 0.983657i | \(0.557627\pi\) | |||||||
\(824\) | −9.96907 | −0.347289 | ||||||||
\(825\) | 23.0294 | 0.801782 | ||||||||
\(826\) | −87.3998 | −3.04103 | ||||||||
\(827\) | −7.70542 | −0.267944 | −0.133972 | − | 0.990985i | \(-0.542773\pi\) | ||||
−0.133972 | + | 0.990985i | \(0.542773\pi\) | |||||||
\(828\) | −9.74460 | −0.338648 | ||||||||
\(829\) | 46.4413 | 1.61297 | 0.806486 | − | 0.591253i | \(-0.201366\pi\) | ||||
0.806486 | + | 0.591253i | \(0.201366\pi\) | |||||||
\(830\) | 2.96827 | 0.103030 | ||||||||
\(831\) | 18.6361 | 0.646480 | ||||||||
\(832\) | 11.0645 | 0.383593 | ||||||||
\(833\) | −18.7303 | −0.648966 | ||||||||
\(834\) | −15.9252 | −0.551445 | ||||||||
\(835\) | −2.63421 | −0.0911606 | ||||||||
\(836\) | −128.536 | −4.44551 | ||||||||
\(837\) | −8.87044 | −0.306607 | ||||||||
\(838\) | 40.9469 | 1.41449 | ||||||||
\(839\) | −17.0035 | −0.587026 | −0.293513 | − | 0.955955i | \(-0.594824\pi\) | ||||
−0.293513 | + | 0.955955i | \(0.594824\pi\) | |||||||
\(840\) | 2.71519 | 0.0936830 | ||||||||
\(841\) | −25.1698 | −0.867923 | ||||||||
\(842\) | 50.4420 | 1.73835 | ||||||||
\(843\) | 6.31691 | 0.217566 | ||||||||
\(844\) | 50.4627 | 1.73700 | ||||||||
\(845\) | 2.74041 | 0.0942729 | ||||||||
\(846\) | 1.26382 | 0.0434509 | ||||||||
\(847\) | 41.9825 | 1.44254 | ||||||||
\(848\) | −0.286636 | −0.00984313 | ||||||||
\(849\) | −23.8199 | −0.817497 | ||||||||
\(850\) | −25.0333 | −0.858635 | ||||||||
\(851\) | −7.24801 | −0.248458 | ||||||||
\(852\) | −14.1762 | −0.485669 | ||||||||
\(853\) | 12.2993 | 0.421121 | 0.210561 | − | 0.977581i | \(-0.432471\pi\) | ||||
0.210561 | + | 0.977581i | \(0.432471\pi\) | |||||||
\(854\) | −114.238 | −3.90915 | ||||||||
\(855\) | −1.85525 | −0.0634483 | ||||||||
\(856\) | −60.7831 | −2.07752 | ||||||||
\(857\) | −11.7667 | −0.401941 | −0.200971 | − | 0.979597i | \(-0.564410\pi\) | ||||
−0.200971 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(858\) | −9.32815 | −0.318458 | ||||||||
\(859\) | 42.4042 | 1.44681 | 0.723406 | − | 0.690423i | \(-0.242576\pi\) | ||||
0.723406 | + | 0.690423i | \(0.242576\pi\) | |||||||
\(860\) | −2.47425 | −0.0843713 | ||||||||
\(861\) | −18.9512 | −0.645854 | ||||||||
\(862\) | −15.8438 | −0.539642 | ||||||||
\(863\) | −43.8008 | −1.49100 | −0.745499 | − | 0.666507i | \(-0.767789\pi\) | ||||
−0.745499 | + | 0.666507i | \(0.767789\pi\) | |||||||
\(864\) | 5.13746 | 0.174780 | ||||||||
\(865\) | −5.57775 | −0.189649 | ||||||||
\(866\) | −66.4103 | −2.25672 | ||||||||
\(867\) | −12.2036 | −0.414455 | ||||||||
\(868\) | −116.573 | −3.95673 | ||||||||
\(869\) | 44.2640 | 1.50155 | ||||||||
\(870\) | −1.01132 | −0.0342870 | ||||||||
\(871\) | 3.52395 | 0.119405 | ||||||||
\(872\) | −50.1068 | −1.69683 | ||||||||
\(873\) | 2.50946 | 0.0849325 | ||||||||
\(874\) | 55.9831 | 1.89366 | ||||||||
\(875\) | 8.78081 | 0.296845 | ||||||||
\(876\) | 9.96678 | 0.336746 | ||||||||
\(877\) | 7.34368 | 0.247979 | 0.123989 | − | 0.992284i | \(-0.460431\pi\) | ||||
0.123989 | + | 0.992284i | \(0.460431\pi\) | |||||||
\(878\) | 23.7640 | 0.801997 | ||||||||
\(879\) | 11.6479 | 0.392875 | ||||||||
\(880\) | 0.458052 | 0.0154409 | ||||||||
\(881\) | 11.3578 | 0.382654 | 0.191327 | − | 0.981526i | \(-0.438721\pi\) | ||||
0.191327 | + | 0.981526i | \(0.438721\pi\) | |||||||
\(882\) | −19.7490 | −0.664983 | ||||||||
\(883\) | 38.4711 | 1.29466 | 0.647328 | − | 0.762211i | \(-0.275886\pi\) | ||||
0.647328 | + | 0.762211i | \(0.275886\pi\) | |||||||
\(884\) | 6.33671 | 0.213126 | ||||||||
\(885\) | −2.14768 | −0.0721934 | ||||||||
\(886\) | −14.6496 | −0.492164 | ||||||||
\(887\) | 6.88399 | 0.231142 | 0.115571 | − | 0.993299i | \(-0.463130\pi\) | ||||
0.115571 | + | 0.993299i | \(0.463130\pi\) | |||||||
\(888\) | −7.62595 | −0.255910 | ||||||||
\(889\) | 50.1016 | 1.68035 | ||||||||
\(890\) | 1.12072 | 0.0375668 | ||||||||
\(891\) | −4.65249 | −0.155864 | ||||||||
\(892\) | 1.85409 | 0.0620795 | ||||||||
\(893\) | −4.53743 | −0.151839 | ||||||||
\(894\) | −18.2081 | −0.608971 | ||||||||
\(895\) | 1.53171 | 0.0511994 | ||||||||
\(896\) | 75.5280 | 2.52321 | ||||||||
\(897\) | 2.53899 | 0.0847744 | ||||||||
\(898\) | 78.6713 | 2.62530 | ||||||||
\(899\) | 17.3603 | 0.578999 | ||||||||
\(900\) | −16.4950 | −0.549833 | ||||||||
\(901\) | 1.42685 | 0.0475352 | ||||||||
\(902\) | −51.6277 | −1.71902 | ||||||||
\(903\) | 13.0849 | 0.435439 | ||||||||
\(904\) | 20.6356 | 0.686330 | ||||||||
\(905\) | −4.76286 | −0.158323 | ||||||||
\(906\) | −16.5547 | −0.549995 | ||||||||
\(907\) | 28.8725 | 0.958696 | 0.479348 | − | 0.877625i | \(-0.340873\pi\) | ||||
0.479348 | + | 0.877625i | \(0.340873\pi\) | |||||||
\(908\) | −61.6103 | −2.04461 | ||||||||
\(909\) | −8.39236 | −0.278357 | ||||||||
\(910\) | −1.76940 | −0.0586549 | ||||||||
\(911\) | 29.6630 | 0.982778 | 0.491389 | − | 0.870940i | \(-0.336489\pi\) | ||||
0.491389 | + | 0.870940i | \(0.336489\pi\) | |||||||
\(912\) | 3.64753 | 0.120782 | ||||||||
\(913\) | −26.7246 | −0.884457 | ||||||||
\(914\) | −66.5960 | −2.20280 | ||||||||
\(915\) | −2.80718 | −0.0928024 | ||||||||
\(916\) | −29.0376 | −0.959430 | ||||||||
\(917\) | 54.2434 | 1.79128 | ||||||||
\(918\) | 5.05731 | 0.166916 | ||||||||
\(919\) | 4.45092 | 0.146822 | 0.0734112 | − | 0.997302i | \(-0.476611\pi\) | ||||
0.0734112 | + | 0.997302i | \(0.476611\pi\) | |||||||
\(920\) | −2.01332 | −0.0663772 | ||||||||
\(921\) | −6.97570 | −0.229857 | ||||||||
\(922\) | −76.3471 | −2.51436 | ||||||||
\(923\) | 3.69366 | 0.121578 | ||||||||
\(924\) | −61.1415 | −2.01141 | ||||||||
\(925\) | −12.2689 | −0.403400 | ||||||||
\(926\) | 59.6655 | 1.96073 | ||||||||
\(927\) | 3.24018 | 0.106421 | ||||||||
\(928\) | −10.0545 | −0.330055 | ||||||||
\(929\) | −8.06216 | −0.264511 | −0.132255 | − | 0.991216i | \(-0.542222\pi\) | ||||
−0.132255 | + | 0.991216i | \(0.542222\pi\) | |||||||
\(930\) | −4.58376 | −0.150308 | ||||||||
\(931\) | 70.9040 | 2.32378 | ||||||||
\(932\) | 73.4162 | 2.40483 | ||||||||
\(933\) | −2.58733 | −0.0847055 | ||||||||
\(934\) | −38.5659 | −1.26191 | ||||||||
\(935\) | −2.28014 | −0.0745685 | ||||||||
\(936\) | 2.67138 | 0.0873169 | ||||||||
\(937\) | −23.0363 | −0.752562 | −0.376281 | − | 0.926506i | \(-0.622797\pi\) | ||||
−0.376281 | + | 0.926506i | \(0.622797\pi\) | |||||||
\(938\) | 36.9605 | 1.20680 | ||||||||
\(939\) | −0.196515 | −0.00641302 | ||||||||
\(940\) | 0.408126 | 0.0133116 | ||||||||
\(941\) | 45.6609 | 1.48850 | 0.744252 | − | 0.667899i | \(-0.232806\pi\) | ||||
0.744252 | + | 0.667899i | \(0.232806\pi\) | |||||||
\(942\) | 1.15281 | 0.0375606 | ||||||||
\(943\) | 14.0523 | 0.457607 | ||||||||
\(944\) | 4.22246 | 0.137429 | ||||||||
\(945\) | −0.882500 | −0.0287077 | ||||||||
\(946\) | 35.6467 | 1.15897 | ||||||||
\(947\) | −33.1849 | −1.07836 | −0.539182 | − | 0.842189i | \(-0.681266\pi\) | ||||
−0.539182 | + | 0.842189i | \(0.681266\pi\) | |||||||
\(948\) | −31.7043 | −1.02971 | ||||||||
\(949\) | −2.59688 | −0.0842983 | ||||||||
\(950\) | 94.7643 | 3.07456 | ||||||||
\(951\) | −22.0936 | −0.716434 | ||||||||
\(952\) | 26.5732 | 0.861241 | ||||||||
\(953\) | −4.18617 | −0.135603 | −0.0678016 | − | 0.997699i | \(-0.521598\pi\) | ||||
−0.0678016 | + | 0.997699i | \(0.521598\pi\) | |||||||
\(954\) | 1.50445 | 0.0487085 | ||||||||
\(955\) | −5.07907 | −0.164355 | ||||||||
\(956\) | 10.2151 | 0.330381 | ||||||||
\(957\) | 9.10537 | 0.294335 | ||||||||
\(958\) | −75.5205 | −2.43996 | ||||||||
\(959\) | 34.1181 | 1.10173 | ||||||||
\(960\) | 2.85167 | 0.0920371 | ||||||||
\(961\) | 47.6847 | 1.53822 | ||||||||
\(962\) | 4.96957 | 0.160225 | ||||||||
\(963\) | 19.7559 | 0.636626 | ||||||||
\(964\) | −58.1841 | −1.87398 | ||||||||
\(965\) | 0.416436 | 0.0134055 | ||||||||
\(966\) | 26.6298 | 0.856801 | ||||||||
\(967\) | 30.8911 | 0.993391 | 0.496695 | − | 0.867925i | \(-0.334547\pi\) | ||||
0.496695 | + | 0.867925i | \(0.334547\pi\) | |||||||
\(968\) | −32.7534 | −1.05273 | ||||||||
\(969\) | −18.1571 | −0.583289 | ||||||||
\(970\) | 1.29676 | 0.0416363 | ||||||||
\(971\) | −2.64645 | −0.0849285 | −0.0424643 | − | 0.999098i | \(-0.513521\pi\) | ||||
−0.0424643 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(972\) | 3.33237 | 0.106886 | ||||||||
\(973\) | 27.1971 | 0.871900 | ||||||||
\(974\) | −34.9987 | −1.12143 | ||||||||
\(975\) | 4.29783 | 0.137641 | ||||||||
\(976\) | 5.51907 | 0.176661 | ||||||||
\(977\) | 36.9313 | 1.18154 | 0.590769 | − | 0.806841i | \(-0.298824\pi\) | ||||
0.590769 | + | 0.806841i | \(0.298824\pi\) | |||||||
\(978\) | −12.4122 | −0.396899 | ||||||||
\(979\) | −10.0904 | −0.322489 | ||||||||
\(980\) | −6.37757 | −0.203724 | ||||||||
\(981\) | 16.2859 | 0.519968 | ||||||||
\(982\) | 33.1440 | 1.05767 | ||||||||
\(983\) | −25.8869 | −0.825663 | −0.412831 | − | 0.910808i | \(-0.635460\pi\) | ||||
−0.412831 | + | 0.910808i | \(0.635460\pi\) | |||||||
\(984\) | 14.7851 | 0.471331 | ||||||||
\(985\) | −1.97410 | −0.0629001 | ||||||||
\(986\) | −9.89766 | −0.315206 | ||||||||
\(987\) | −2.15835 | −0.0687011 | ||||||||
\(988\) | −23.9878 | −0.763153 | ||||||||
\(989\) | −9.70251 | −0.308522 | ||||||||
\(990\) | −2.40415 | −0.0764090 | ||||||||
\(991\) | −58.6070 | −1.86171 | −0.930856 | − | 0.365386i | \(-0.880937\pi\) | ||||
−0.930856 | + | 0.365386i | \(0.880937\pi\) | |||||||
\(992\) | −45.5715 | −1.44690 | ||||||||
\(993\) | −0.551627 | −0.0175053 | ||||||||
\(994\) | 38.7405 | 1.22877 | ||||||||
\(995\) | 1.30729 | 0.0414439 | ||||||||
\(996\) | 19.1417 | 0.606528 | ||||||||
\(997\) | −12.2278 | −0.387258 | −0.193629 | − | 0.981075i | \(-0.562026\pi\) | ||||
−0.193629 | + | 0.981075i | \(0.562026\pi\) | |||||||
\(998\) | 66.3111 | 2.09904 | ||||||||
\(999\) | 2.47861 | 0.0784197 |
(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 | 8049.2.a.d.1.16 | ✓ | 129 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8049.2.a.d.1.16 | ✓ | 129 | 1.1 | even | 1 | trivial |