Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45990 | −1.73941 | −0.869707 | − | 0.493569i | \(-0.835692\pi\) | ||||
−0.869707 | + | 0.493569i | \(0.835692\pi\) | |||||||
\(3\) | 1.58815 | 0.916917 | 0.458458 | − | 0.888716i | \(-0.348402\pi\) | ||||
0.458458 | + | 0.888716i | \(0.348402\pi\) | |||||||
\(4\) | 4.05112 | 2.02556 | ||||||||
\(5\) | −3.55113 | −1.58811 | −0.794056 | − | 0.607845i | \(-0.792034\pi\) | ||||
−0.794056 | + | 0.607845i | \(0.792034\pi\) | |||||||
\(6\) | −3.90668 | −1.59490 | ||||||||
\(7\) | −1.72696 | −0.652730 | −0.326365 | − | 0.945244i | \(-0.605824\pi\) | ||||
−0.326365 | + | 0.945244i | \(0.605824\pi\) | |||||||
\(8\) | −5.04554 | −1.78387 | ||||||||
\(9\) | −0.477790 | −0.159263 | ||||||||
\(10\) | 8.73542 | 2.76238 | ||||||||
\(11\) | 0.521731 | 0.157308 | 0.0786539 | − | 0.996902i | \(-0.474938\pi\) | ||||
0.0786539 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(12\) | 6.43377 | 1.85727 | ||||||||
\(13\) | −6.48917 | −1.79977 | −0.899886 | − | 0.436126i | \(-0.856350\pi\) | ||||
−0.899886 | + | 0.436126i | \(0.856350\pi\) | |||||||
\(14\) | 4.24815 | 1.13537 | ||||||||
\(15\) | −5.63971 | −1.45617 | ||||||||
\(16\) | 4.30930 | 1.07733 | ||||||||
\(17\) | −0.0823109 | −0.0199633 | −0.00998166 | − | 0.999950i | \(-0.503177\pi\) | ||||
−0.00998166 | + | 0.999950i | \(0.503177\pi\) | |||||||
\(18\) | 1.17532 | 0.277025 | ||||||||
\(19\) | −1.33145 | −0.305455 | −0.152728 | − | 0.988268i | \(-0.548806\pi\) | ||||
−0.152728 | + | 0.988268i | \(0.548806\pi\) | |||||||
\(20\) | −14.3860 | −3.21681 | ||||||||
\(21\) | −2.74267 | −0.598499 | ||||||||
\(22\) | −1.28341 | −0.273623 | ||||||||
\(23\) | 1.60664 | 0.335008 | 0.167504 | − | 0.985871i | \(-0.446429\pi\) | ||||
0.167504 | + | 0.985871i | \(0.446429\pi\) | |||||||
\(24\) | −8.01306 | −1.63566 | ||||||||
\(25\) | 7.61050 | 1.52210 | ||||||||
\(26\) | 15.9627 | 3.13055 | ||||||||
\(27\) | −5.52324 | −1.06295 | ||||||||
\(28\) | −6.99612 | −1.32214 | ||||||||
\(29\) | −5.29778 | −0.983773 | −0.491886 | − | 0.870659i | \(-0.663692\pi\) | ||||
−0.491886 | + | 0.870659i | \(0.663692\pi\) | |||||||
\(30\) | 13.8731 | 2.53288 | ||||||||
\(31\) | −3.36137 | −0.603720 | −0.301860 | − | 0.953352i | \(-0.597607\pi\) | ||||
−0.301860 | + | 0.953352i | \(0.597607\pi\) | |||||||
\(32\) | −0.509382 | −0.0900469 | ||||||||
\(33\) | 0.828585 | 0.144238 | ||||||||
\(34\) | 0.202477 | 0.0347245 | ||||||||
\(35\) | 6.13265 | 1.03661 | ||||||||
\(36\) | −1.93558 | −0.322597 | ||||||||
\(37\) | 1.70361 | 0.280072 | 0.140036 | − | 0.990146i | \(-0.455278\pi\) | ||||
0.140036 | + | 0.990146i | \(0.455278\pi\) | |||||||
\(38\) | 3.27523 | 0.531313 | ||||||||
\(39\) | −10.3058 | −1.65024 | ||||||||
\(40\) | 17.9174 | 2.83298 | ||||||||
\(41\) | −6.24946 | −0.976001 | −0.488001 | − | 0.872843i | \(-0.662274\pi\) | ||||
−0.488001 | + | 0.872843i | \(0.662274\pi\) | |||||||
\(42\) | 6.74669 | 1.04104 | ||||||||
\(43\) | −11.5125 | −1.75564 | −0.877819 | − | 0.478992i | \(-0.841002\pi\) | ||||
−0.877819 | + | 0.478992i | \(0.841002\pi\) | |||||||
\(44\) | 2.11359 | 0.318636 | ||||||||
\(45\) | 1.69669 | 0.252928 | ||||||||
\(46\) | −3.95218 | −0.582717 | ||||||||
\(47\) | 0.681014 | 0.0993362 | 0.0496681 | − | 0.998766i | \(-0.484184\pi\) | ||||
0.0496681 | + | 0.998766i | \(0.484184\pi\) | |||||||
\(48\) | 6.84381 | 0.987819 | ||||||||
\(49\) | −4.01761 | −0.573944 | ||||||||
\(50\) | −18.7211 | −2.64756 | ||||||||
\(51\) | −0.130722 | −0.0183047 | ||||||||
\(52\) | −26.2884 | −3.64554 | ||||||||
\(53\) | −5.03721 | −0.691914 | −0.345957 | − | 0.938250i | \(-0.612446\pi\) | ||||
−0.345957 | + | 0.938250i | \(0.612446\pi\) | |||||||
\(54\) | 13.5866 | 1.84891 | ||||||||
\(55\) | −1.85273 | −0.249822 | ||||||||
\(56\) | 8.71345 | 1.16438 | ||||||||
\(57\) | −2.11454 | −0.280077 | ||||||||
\(58\) | 13.0320 | 1.71119 | ||||||||
\(59\) | 3.94334 | 0.513379 | 0.256690 | − | 0.966494i | \(-0.417368\pi\) | ||||
0.256690 | + | 0.966494i | \(0.417368\pi\) | |||||||
\(60\) | −22.8471 | −2.94955 | ||||||||
\(61\) | 4.73428 | 0.606162 | 0.303081 | − | 0.952965i | \(-0.401985\pi\) | ||||
0.303081 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(62\) | 8.26863 | 1.05012 | ||||||||
\(63\) | 0.825124 | 0.103956 | ||||||||
\(64\) | −7.36558 | −0.920698 | ||||||||
\(65\) | 23.0439 | 2.85824 | ||||||||
\(66\) | −2.03824 | −0.250890 | ||||||||
\(67\) | 11.5204 | 1.40744 | 0.703722 | − | 0.710475i | \(-0.251520\pi\) | ||||
0.703722 | + | 0.710475i | \(0.251520\pi\) | |||||||
\(68\) | −0.333451 | −0.0404369 | ||||||||
\(69\) | 2.55158 | 0.307174 | ||||||||
\(70\) | −15.0857 | −1.80309 | ||||||||
\(71\) | −3.21876 | −0.381996 | −0.190998 | − | 0.981590i | \(-0.561172\pi\) | ||||
−0.190998 | + | 0.981590i | \(0.561172\pi\) | |||||||
\(72\) | 2.41071 | 0.284105 | ||||||||
\(73\) | −13.0677 | −1.52946 | −0.764729 | − | 0.644352i | \(-0.777127\pi\) | ||||
−0.764729 | + | 0.644352i | \(0.777127\pi\) | |||||||
\(74\) | −4.19071 | −0.487161 | ||||||||
\(75\) | 12.0866 | 1.39564 | ||||||||
\(76\) | −5.39385 | −0.618718 | ||||||||
\(77\) | −0.901009 | −0.102679 | ||||||||
\(78\) | 25.3511 | 2.87045 | ||||||||
\(79\) | −15.5574 | −1.75034 | −0.875171 | − | 0.483814i | \(-0.839251\pi\) | ||||
−0.875171 | + | 0.483814i | \(0.839251\pi\) | |||||||
\(80\) | −15.3029 | −1.71091 | ||||||||
\(81\) | −7.33835 | −0.815372 | ||||||||
\(82\) | 15.3730 | 1.69767 | ||||||||
\(83\) | 8.37536 | 0.919315 | 0.459658 | − | 0.888096i | \(-0.347972\pi\) | ||||
0.459658 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(84\) | −11.1109 | −1.21229 | ||||||||
\(85\) | 0.292296 | 0.0317040 | ||||||||
\(86\) | 28.3196 | 3.05378 | ||||||||
\(87\) | −8.41365 | −0.902038 | ||||||||
\(88\) | −2.63242 | −0.280616 | ||||||||
\(89\) | 5.06939 | 0.537354 | 0.268677 | − | 0.963230i | \(-0.413414\pi\) | ||||
0.268677 | + | 0.963230i | \(0.413414\pi\) | |||||||
\(90\) | −4.17370 | −0.439946 | ||||||||
\(91\) | 11.2065 | 1.17476 | ||||||||
\(92\) | 6.50869 | 0.678577 | ||||||||
\(93\) | −5.33835 | −0.553561 | ||||||||
\(94\) | −1.67523 | −0.172787 | ||||||||
\(95\) | 4.72814 | 0.485097 | ||||||||
\(96\) | −0.808973 | −0.0825655 | ||||||||
\(97\) | −9.06329 | −0.920238 | −0.460119 | − | 0.887857i | \(-0.652193\pi\) | ||||
−0.460119 | + | 0.887857i | \(0.652193\pi\) | |||||||
\(98\) | 9.88292 | 0.998326 | ||||||||
\(99\) | −0.249278 | −0.0250534 | ||||||||
\(100\) | 30.8310 | 3.08310 | ||||||||
\(101\) | −19.1942 | −1.90990 | −0.954948 | − | 0.296772i | \(-0.904090\pi\) | ||||
−0.954948 | + | 0.296772i | \(0.904090\pi\) | |||||||
\(102\) | 0.321563 | 0.0318395 | ||||||||
\(103\) | −12.6345 | −1.24491 | −0.622456 | − | 0.782655i | \(-0.713865\pi\) | ||||
−0.622456 | + | 0.782655i | \(0.713865\pi\) | |||||||
\(104\) | 32.7414 | 3.21056 | ||||||||
\(105\) | 9.73955 | 0.950483 | ||||||||
\(106\) | 12.3910 | 1.20352 | ||||||||
\(107\) | −8.24556 | −0.797128 | −0.398564 | − | 0.917140i | \(-0.630491\pi\) | ||||
−0.398564 | + | 0.917140i | \(0.630491\pi\) | |||||||
\(108\) | −22.3753 | −2.15306 | ||||||||
\(109\) | −16.8635 | −1.61523 | −0.807617 | − | 0.589707i | \(-0.799243\pi\) | ||||
−0.807617 | + | 0.589707i | \(0.799243\pi\) | |||||||
\(110\) | 4.55754 | 0.434544 | ||||||||
\(111\) | 2.70558 | 0.256803 | ||||||||
\(112\) | −7.44200 | −0.703203 | ||||||||
\(113\) | 15.7677 | 1.48330 | 0.741648 | − | 0.670789i | \(-0.234044\pi\) | ||||
0.741648 | + | 0.670789i | \(0.234044\pi\) | |||||||
\(114\) | 5.20155 | 0.487170 | ||||||||
\(115\) | −5.70538 | −0.532030 | ||||||||
\(116\) | −21.4619 | −1.99269 | ||||||||
\(117\) | 3.10046 | 0.286638 | ||||||||
\(118\) | −9.70023 | −0.892978 | ||||||||
\(119\) | 0.142148 | 0.0130307 | ||||||||
\(120\) | 28.4554 | 2.59761 | ||||||||
\(121\) | −10.7278 | −0.975254 | ||||||||
\(122\) | −11.6459 | −1.05437 | ||||||||
\(123\) | −9.92505 | −0.894912 | ||||||||
\(124\) | −13.6173 | −1.22287 | ||||||||
\(125\) | −9.27020 | −0.829152 | ||||||||
\(126\) | −2.02972 | −0.180822 | ||||||||
\(127\) | 1.11937 | 0.0993276 | 0.0496638 | − | 0.998766i | \(-0.484185\pi\) | ||||
0.0496638 | + | 0.998766i | \(0.484185\pi\) | |||||||
\(128\) | 19.1374 | 1.69152 | ||||||||
\(129\) | −18.2835 | −1.60977 | ||||||||
\(130\) | −56.6856 | −4.97166 | ||||||||
\(131\) | −2.29123 | −0.200186 | −0.100093 | − | 0.994978i | \(-0.531914\pi\) | ||||
−0.100093 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(132\) | 3.35669 | 0.292163 | ||||||||
\(133\) | 2.29936 | 0.199380 | ||||||||
\(134\) | −28.3391 | −2.44813 | ||||||||
\(135\) | 19.6137 | 1.68808 | ||||||||
\(136\) | 0.415303 | 0.0356120 | ||||||||
\(137\) | 5.67546 | 0.484887 | 0.242444 | − | 0.970166i | \(-0.422051\pi\) | ||||
0.242444 | + | 0.970166i | \(0.422051\pi\) | |||||||
\(138\) | −6.27664 | −0.534303 | ||||||||
\(139\) | 16.5980 | 1.40782 | 0.703912 | − | 0.710287i | \(-0.251435\pi\) | ||||
0.703912 | + | 0.710287i | \(0.251435\pi\) | |||||||
\(140\) | 24.8441 | 2.09971 | ||||||||
\(141\) | 1.08155 | 0.0910830 | ||||||||
\(142\) | 7.91783 | 0.664449 | ||||||||
\(143\) | −3.38560 | −0.283118 | ||||||||
\(144\) | −2.05894 | −0.171579 | ||||||||
\(145\) | 18.8131 | 1.56234 | ||||||||
\(146\) | 32.1452 | 2.66036 | ||||||||
\(147\) | −6.38055 | −0.526259 | ||||||||
\(148\) | 6.90152 | 0.567302 | ||||||||
\(149\) | 13.8639 | 1.13577 | 0.567887 | − | 0.823106i | \(-0.307761\pi\) | ||||
0.567887 | + | 0.823106i | \(0.307761\pi\) | |||||||
\(150\) | −29.7318 | −2.42759 | ||||||||
\(151\) | −3.97982 | −0.323873 | −0.161937 | − | 0.986801i | \(-0.551774\pi\) | ||||
−0.161937 | + | 0.986801i | \(0.551774\pi\) | |||||||
\(152\) | 6.71788 | 0.544892 | ||||||||
\(153\) | 0.0393273 | 0.00317943 | ||||||||
\(154\) | 2.21639 | 0.178602 | ||||||||
\(155\) | 11.9366 | 0.958774 | ||||||||
\(156\) | −41.7498 | −3.34266 | ||||||||
\(157\) | −2.80504 | −0.223867 | −0.111933 | − | 0.993716i | \(-0.535704\pi\) | ||||
−0.111933 | + | 0.993716i | \(0.535704\pi\) | |||||||
\(158\) | 38.2696 | 3.04457 | ||||||||
\(159\) | −7.99983 | −0.634428 | ||||||||
\(160\) | 1.80888 | 0.143005 | ||||||||
\(161\) | −2.77460 | −0.218669 | ||||||||
\(162\) | 18.0516 | 1.41827 | ||||||||
\(163\) | 18.0445 | 1.41335 | 0.706677 | − | 0.707536i | \(-0.250193\pi\) | ||||
0.706677 | + | 0.707536i | \(0.250193\pi\) | |||||||
\(164\) | −25.3173 | −1.97695 | ||||||||
\(165\) | −2.94241 | −0.229066 | ||||||||
\(166\) | −20.6026 | −1.59907 | ||||||||
\(167\) | 11.0705 | 0.856660 | 0.428330 | − | 0.903622i | \(-0.359102\pi\) | ||||
0.428330 | + | 0.903622i | \(0.359102\pi\) | |||||||
\(168\) | 13.8382 | 1.06764 | ||||||||
\(169\) | 29.1093 | 2.23918 | ||||||||
\(170\) | −0.719020 | −0.0551464 | ||||||||
\(171\) | 0.636153 | 0.0486478 | ||||||||
\(172\) | −46.6384 | −3.55615 | ||||||||
\(173\) | 22.7368 | 1.72865 | 0.864324 | − | 0.502936i | \(-0.167747\pi\) | ||||
0.864324 | + | 0.502936i | \(0.167747\pi\) | |||||||
\(174\) | 20.6968 | 1.56902 | ||||||||
\(175\) | −13.1430 | −0.993519 | ||||||||
\(176\) | 2.24830 | 0.169472 | ||||||||
\(177\) | 6.26260 | 0.470726 | ||||||||
\(178\) | −12.4702 | −0.934681 | ||||||||
\(179\) | −10.2359 | −0.765066 | −0.382533 | − | 0.923942i | \(-0.624948\pi\) | ||||
−0.382533 | + | 0.923942i | \(0.624948\pi\) | |||||||
\(180\) | 6.87350 | 0.512320 | ||||||||
\(181\) | 6.64223 | 0.493713 | 0.246857 | − | 0.969052i | \(-0.420602\pi\) | ||||
0.246857 | + | 0.969052i | \(0.420602\pi\) | |||||||
\(182\) | −27.5670 | −2.04340 | ||||||||
\(183\) | 7.51873 | 0.555801 | ||||||||
\(184\) | −8.10637 | −0.597610 | ||||||||
\(185\) | −6.04974 | −0.444786 | ||||||||
\(186\) | 13.1318 | 0.962871 | ||||||||
\(187\) | −0.0429441 | −0.00314039 | ||||||||
\(188\) | 2.75887 | 0.201211 | ||||||||
\(189\) | 9.53842 | 0.693818 | ||||||||
\(190\) | −11.6308 | −0.843785 | ||||||||
\(191\) | 11.2867 | 0.816678 | 0.408339 | − | 0.912830i | \(-0.366108\pi\) | ||||
0.408339 | + | 0.912830i | \(0.366108\pi\) | |||||||
\(192\) | −11.6976 | −0.844203 | ||||||||
\(193\) | 3.74238 | 0.269383 | 0.134691 | − | 0.990888i | \(-0.456996\pi\) | ||||
0.134691 | + | 0.990888i | \(0.456996\pi\) | |||||||
\(194\) | 22.2948 | 1.60067 | ||||||||
\(195\) | 36.5970 | 2.62077 | ||||||||
\(196\) | −16.2758 | −1.16256 | ||||||||
\(197\) | −10.3683 | −0.738713 | −0.369356 | − | 0.929288i | \(-0.620422\pi\) | ||||
−0.369356 | + | 0.929288i | \(0.620422\pi\) | |||||||
\(198\) | 0.613199 | 0.0435781 | ||||||||
\(199\) | 24.8886 | 1.76431 | 0.882154 | − | 0.470961i | \(-0.156093\pi\) | ||||
0.882154 | + | 0.470961i | \(0.156093\pi\) | |||||||
\(200\) | −38.3991 | −2.71522 | ||||||||
\(201\) | 18.2961 | 1.29051 | ||||||||
\(202\) | 47.2159 | 3.32210 | ||||||||
\(203\) | 9.14906 | 0.642138 | ||||||||
\(204\) | −0.529569 | −0.0370773 | ||||||||
\(205\) | 22.1926 | 1.55000 | ||||||||
\(206\) | 31.0795 | 2.16541 | ||||||||
\(207\) | −0.767637 | −0.0533544 | ||||||||
\(208\) | −27.9638 | −1.93894 | ||||||||
\(209\) | −0.694658 | −0.0480505 | ||||||||
\(210\) | −23.9583 | −1.65328 | ||||||||
\(211\) | −28.0208 | −1.92903 | −0.964516 | − | 0.264024i | \(-0.914950\pi\) | ||||
−0.964516 | + | 0.264024i | \(0.914950\pi\) | |||||||
\(212\) | −20.4063 | −1.40151 | ||||||||
\(213\) | −5.11186 | −0.350259 | ||||||||
\(214\) | 20.2833 | 1.38654 | ||||||||
\(215\) | 40.8823 | 2.78815 | ||||||||
\(216\) | 27.8677 | 1.89616 | ||||||||
\(217\) | 5.80495 | 0.394066 | ||||||||
\(218\) | 41.4827 | 2.80956 | ||||||||
\(219\) | −20.7534 | −1.40239 | ||||||||
\(220\) | −7.50563 | −0.506030 | ||||||||
\(221\) | 0.534129 | 0.0359294 | ||||||||
\(222\) | −6.65547 | −0.446686 | ||||||||
\(223\) | −3.74555 | −0.250820 | −0.125410 | − | 0.992105i | \(-0.540025\pi\) | ||||
−0.125410 | + | 0.992105i | \(0.540025\pi\) | |||||||
\(224\) | 0.879683 | 0.0587763 | ||||||||
\(225\) | −3.63622 | −0.242415 | ||||||||
\(226\) | −38.7869 | −2.58007 | ||||||||
\(227\) | 17.0030 | 1.12853 | 0.564264 | − | 0.825595i | \(-0.309160\pi\) | ||||
0.564264 | + | 0.825595i | \(0.309160\pi\) | |||||||
\(228\) | −8.56623 | −0.567313 | ||||||||
\(229\) | −10.2817 | −0.679434 | −0.339717 | − | 0.940528i | \(-0.610331\pi\) | ||||
−0.339717 | + | 0.940528i | \(0.610331\pi\) | |||||||
\(230\) | 14.0347 | 0.925419 | ||||||||
\(231\) | −1.43093 | −0.0941485 | ||||||||
\(232\) | 26.7302 | 1.75492 | ||||||||
\(233\) | −20.4752 | −1.34138 | −0.670688 | − | 0.741739i | \(-0.734001\pi\) | ||||
−0.670688 | + | 0.741739i | \(0.734001\pi\) | |||||||
\(234\) | −7.62682 | −0.498581 | ||||||||
\(235\) | −2.41837 | −0.157757 | ||||||||
\(236\) | 15.9749 | 1.03988 | ||||||||
\(237\) | −24.7074 | −1.60492 | ||||||||
\(238\) | −0.349669 | −0.0226657 | ||||||||
\(239\) | −9.55740 | −0.618217 | −0.309109 | − | 0.951027i | \(-0.600031\pi\) | ||||
−0.309109 | + | 0.951027i | \(0.600031\pi\) | |||||||
\(240\) | −24.3032 | −1.56877 | ||||||||
\(241\) | 24.5206 | 1.57951 | 0.789755 | − | 0.613423i | \(-0.210208\pi\) | ||||
0.789755 | + | 0.613423i | \(0.210208\pi\) | |||||||
\(242\) | 26.3893 | 1.69637 | ||||||||
\(243\) | 4.91535 | 0.315320 | ||||||||
\(244\) | 19.1791 | 1.22782 | ||||||||
\(245\) | 14.2670 | 0.911487 | ||||||||
\(246\) | 24.4147 | 1.55662 | ||||||||
\(247\) | 8.64000 | 0.549750 | ||||||||
\(248\) | 16.9599 | 1.07696 | ||||||||
\(249\) | 13.3013 | 0.842936 | ||||||||
\(250\) | 22.8038 | 1.44224 | ||||||||
\(251\) | 5.98919 | 0.378034 | 0.189017 | − | 0.981974i | \(-0.439470\pi\) | ||||
0.189017 | + | 0.981974i | \(0.439470\pi\) | |||||||
\(252\) | 3.34267 | 0.210569 | ||||||||
\(253\) | 0.838234 | 0.0526993 | ||||||||
\(254\) | −2.75353 | −0.172772 | ||||||||
\(255\) | 0.464210 | 0.0290699 | ||||||||
\(256\) | −32.3449 | −2.02155 | ||||||||
\(257\) | −6.32166 | −0.394334 | −0.197167 | − | 0.980370i | \(-0.563174\pi\) | ||||
−0.197167 | + | 0.980370i | \(0.563174\pi\) | |||||||
\(258\) | 44.9757 | 2.80006 | ||||||||
\(259\) | −2.94207 | −0.182811 | ||||||||
\(260\) | 93.3533 | 5.78953 | ||||||||
\(261\) | 2.53123 | 0.156679 | ||||||||
\(262\) | 5.63621 | 0.348206 | ||||||||
\(263\) | 3.38587 | 0.208782 | 0.104391 | − | 0.994536i | \(-0.466711\pi\) | ||||
0.104391 | + | 0.994536i | \(0.466711\pi\) | |||||||
\(264\) | −4.18066 | −0.257302 | ||||||||
\(265\) | 17.8878 | 1.09884 | ||||||||
\(266\) | −5.65620 | −0.346804 | ||||||||
\(267\) | 8.05093 | 0.492709 | ||||||||
\(268\) | 46.6706 | 2.85086 | ||||||||
\(269\) | −30.8170 | −1.87895 | −0.939473 | − | 0.342623i | \(-0.888685\pi\) | ||||
−0.939473 | + | 0.342623i | \(0.888685\pi\) | |||||||
\(270\) | −48.2478 | −2.93627 | ||||||||
\(271\) | −24.7506 | −1.50349 | −0.751745 | − | 0.659454i | \(-0.770788\pi\) | ||||
−0.751745 | + | 0.659454i | \(0.770788\pi\) | |||||||
\(272\) | −0.354703 | −0.0215070 | ||||||||
\(273\) | 17.7976 | 1.07716 | ||||||||
\(274\) | −13.9611 | −0.843419 | ||||||||
\(275\) | 3.97063 | 0.239438 | ||||||||
\(276\) | 10.3367 | 0.622199 | ||||||||
\(277\) | 15.2327 | 0.915243 | 0.457621 | − | 0.889147i | \(-0.348702\pi\) | ||||
0.457621 | + | 0.889147i | \(0.348702\pi\) | |||||||
\(278\) | −40.8294 | −2.44879 | ||||||||
\(279\) | 1.60603 | 0.0961504 | ||||||||
\(280\) | −30.9426 | −1.84917 | ||||||||
\(281\) | 18.4994 | 1.10358 | 0.551792 | − | 0.833982i | \(-0.313944\pi\) | ||||
0.551792 | + | 0.833982i | \(0.313944\pi\) | |||||||
\(282\) | −2.66051 | −0.158431 | ||||||||
\(283\) | −4.00257 | −0.237928 | −0.118964 | − | 0.992899i | \(-0.537957\pi\) | ||||
−0.118964 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(284\) | −13.0396 | −0.773755 | ||||||||
\(285\) | 7.50899 | 0.444794 | ||||||||
\(286\) | 8.32824 | 0.492459 | ||||||||
\(287\) | 10.7926 | 0.637065 | ||||||||
\(288\) | 0.243378 | 0.0143412 | ||||||||
\(289\) | −16.9932 | −0.999601 | ||||||||
\(290\) | −46.2783 | −2.71756 | ||||||||
\(291\) | −14.3938 | −0.843782 | ||||||||
\(292\) | −52.9387 | −3.09800 | ||||||||
\(293\) | 19.9352 | 1.16462 | 0.582312 | − | 0.812965i | \(-0.302148\pi\) | ||||
0.582312 | + | 0.812965i | \(0.302148\pi\) | |||||||
\(294\) | 15.6955 | 0.915382 | ||||||||
\(295\) | −14.0033 | −0.815303 | ||||||||
\(296\) | −8.59564 | −0.499611 | ||||||||
\(297\) | −2.88165 | −0.167210 | ||||||||
\(298\) | −34.1038 | −1.97558 | ||||||||
\(299\) | −10.4258 | −0.602937 | ||||||||
\(300\) | 48.9642 | 2.82695 | ||||||||
\(301\) | 19.8816 | 1.14596 | ||||||||
\(302\) | 9.78997 | 0.563350 | ||||||||
\(303\) | −30.4832 | −1.75122 | ||||||||
\(304\) | −5.73762 | −0.329075 | ||||||||
\(305\) | −16.8120 | −0.962654 | ||||||||
\(306\) | −0.0967414 | −0.00553034 | ||||||||
\(307\) | −23.8579 | −1.36164 | −0.680822 | − | 0.732449i | \(-0.738377\pi\) | ||||
−0.680822 | + | 0.732449i | \(0.738377\pi\) | |||||||
\(308\) | −3.65009 | −0.207983 | ||||||||
\(309\) | −20.0654 | −1.14148 | ||||||||
\(310\) | −29.3630 | −1.66770 | ||||||||
\(311\) | 5.55638 | 0.315073 | 0.157537 | − | 0.987513i | \(-0.449645\pi\) | ||||
0.157537 | + | 0.987513i | \(0.449645\pi\) | |||||||
\(312\) | 51.9981 | 2.94381 | ||||||||
\(313\) | −4.89132 | −0.276474 | −0.138237 | − | 0.990399i | \(-0.544144\pi\) | ||||
−0.138237 | + | 0.990399i | \(0.544144\pi\) | |||||||
\(314\) | 6.90013 | 0.389397 | ||||||||
\(315\) | −2.93012 | −0.165094 | ||||||||
\(316\) | −63.0247 | −3.54542 | ||||||||
\(317\) | −25.7739 | −1.44761 | −0.723803 | − | 0.690007i | \(-0.757608\pi\) | ||||
−0.723803 | + | 0.690007i | \(0.757608\pi\) | |||||||
\(318\) | 19.6788 | 1.10353 | ||||||||
\(319\) | −2.76402 | −0.154755 | ||||||||
\(320\) | 26.1561 | 1.46217 | ||||||||
\(321\) | −13.0952 | −0.730901 | ||||||||
\(322\) | 6.82525 | 0.380357 | ||||||||
\(323\) | 0.109593 | 0.00609791 | ||||||||
\(324\) | −29.7285 | −1.65158 | ||||||||
\(325\) | −49.3858 | −2.73943 | ||||||||
\(326\) | −44.3877 | −2.45841 | ||||||||
\(327\) | −26.7818 | −1.48104 | ||||||||
\(328\) | 31.5319 | 1.74106 | ||||||||
\(329\) | −1.17608 | −0.0648397 | ||||||||
\(330\) | 7.23804 | 0.398441 | ||||||||
\(331\) | 21.8664 | 1.20189 | 0.600944 | − | 0.799291i | \(-0.294792\pi\) | ||||
0.600944 | + | 0.799291i | \(0.294792\pi\) | |||||||
\(332\) | 33.9296 | 1.86213 | ||||||||
\(333\) | −0.813968 | −0.0446052 | ||||||||
\(334\) | −27.2323 | −1.49009 | ||||||||
\(335\) | −40.9105 | −2.23518 | ||||||||
\(336\) | −11.8190 | −0.644779 | ||||||||
\(337\) | 13.8352 | 0.753651 | 0.376826 | − | 0.926284i | \(-0.377016\pi\) | ||||
0.376826 | + | 0.926284i | \(0.377016\pi\) | |||||||
\(338\) | −71.6060 | −3.89485 | ||||||||
\(339\) | 25.0414 | 1.36006 | ||||||||
\(340\) | 1.18413 | 0.0642183 | ||||||||
\(341\) | −1.75373 | −0.0949698 | ||||||||
\(342\) | −1.56487 | −0.0846187 | ||||||||
\(343\) | 19.0270 | 1.02736 | ||||||||
\(344\) | 58.0867 | 3.13183 | ||||||||
\(345\) | −9.06099 | −0.487827 | ||||||||
\(346\) | −55.9303 | −3.00683 | ||||||||
\(347\) | 16.5307 | 0.887415 | 0.443707 | − | 0.896172i | \(-0.353663\pi\) | ||||
0.443707 | + | 0.896172i | \(0.353663\pi\) | |||||||
\(348\) | −34.0847 | −1.82713 | ||||||||
\(349\) | 3.96726 | 0.212362 | 0.106181 | − | 0.994347i | \(-0.466138\pi\) | ||||
0.106181 | + | 0.994347i | \(0.466138\pi\) | |||||||
\(350\) | 32.3306 | 1.72814 | ||||||||
\(351\) | 35.8412 | 1.91306 | ||||||||
\(352\) | −0.265760 | −0.0141651 | ||||||||
\(353\) | 23.0752 | 1.22817 | 0.614085 | − | 0.789240i | \(-0.289525\pi\) | ||||
0.614085 | + | 0.789240i | \(0.289525\pi\) | |||||||
\(354\) | −15.4054 | −0.818787 | ||||||||
\(355\) | 11.4302 | 0.606653 | ||||||||
\(356\) | 20.5367 | 1.08844 | ||||||||
\(357\) | 0.225751 | 0.0119480 | ||||||||
\(358\) | 25.1793 | 1.33077 | ||||||||
\(359\) | −17.8603 | −0.942632 | −0.471316 | − | 0.881965i | \(-0.656221\pi\) | ||||
−0.471316 | + | 0.881965i | \(0.656221\pi\) | |||||||
\(360\) | −8.56073 | −0.451190 | ||||||||
\(361\) | −17.2272 | −0.906697 | ||||||||
\(362\) | −16.3392 | −0.858772 | ||||||||
\(363\) | −17.0373 | −0.894227 | ||||||||
\(364\) | 45.3990 | 2.37955 | ||||||||
\(365\) | 46.4050 | 2.42895 | ||||||||
\(366\) | −18.4953 | −0.966767 | ||||||||
\(367\) | −6.24911 | −0.326201 | −0.163100 | − | 0.986609i | \(-0.552149\pi\) | ||||
−0.163100 | + | 0.986609i | \(0.552149\pi\) | |||||||
\(368\) | 6.92350 | 0.360913 | ||||||||
\(369\) | 2.98593 | 0.155441 | ||||||||
\(370\) | 14.8818 | 0.773666 | ||||||||
\(371\) | 8.69907 | 0.451633 | ||||||||
\(372\) | −21.6263 | −1.12127 | ||||||||
\(373\) | 5.43820 | 0.281579 | 0.140790 | − | 0.990040i | \(-0.455036\pi\) | ||||
0.140790 | + | 0.990040i | \(0.455036\pi\) | |||||||
\(374\) | 0.105638 | 0.00546243 | ||||||||
\(375\) | −14.7224 | −0.760264 | ||||||||
\(376\) | −3.43609 | −0.177203 | ||||||||
\(377\) | 34.3782 | 1.77057 | ||||||||
\(378\) | −23.4636 | −1.20684 | ||||||||
\(379\) | −30.0170 | −1.54187 | −0.770936 | − | 0.636913i | \(-0.780211\pi\) | ||||
−0.770936 | + | 0.636913i | \(0.780211\pi\) | |||||||
\(380\) | 19.1543 | 0.982593 | ||||||||
\(381\) | 1.77772 | 0.0910752 | ||||||||
\(382\) | −27.7642 | −1.42054 | ||||||||
\(383\) | −7.03107 | −0.359271 | −0.179635 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179635 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(384\) | 30.3929 | 1.55098 | ||||||||
\(385\) | 3.19960 | 0.163066 | ||||||||
\(386\) | −9.20589 | −0.468568 | ||||||||
\(387\) | 5.50055 | 0.279609 | ||||||||
\(388\) | −36.7164 | −1.86399 | ||||||||
\(389\) | −4.50037 | −0.228178 | −0.114089 | − | 0.993471i | \(-0.536395\pi\) | ||||
−0.114089 | + | 0.993471i | \(0.536395\pi\) | |||||||
\(390\) | −90.0251 | −4.55860 | ||||||||
\(391\) | −0.132244 | −0.00668787 | ||||||||
\(392\) | 20.2710 | 1.02384 | ||||||||
\(393\) | −3.63882 | −0.183554 | ||||||||
\(394\) | 25.5051 | 1.28493 | ||||||||
\(395\) | 55.2462 | 2.77974 | ||||||||
\(396\) | −1.00985 | −0.0507470 | ||||||||
\(397\) | −9.45105 | −0.474335 | −0.237167 | − | 0.971469i | \(-0.576219\pi\) | ||||
−0.237167 | + | 0.971469i | \(0.576219\pi\) | |||||||
\(398\) | −61.2236 | −3.06886 | ||||||||
\(399\) | 3.65172 | 0.182815 | ||||||||
\(400\) | 32.7959 | 1.63980 | ||||||||
\(401\) | 13.2693 | 0.662638 | 0.331319 | − | 0.943519i | \(-0.392506\pi\) | ||||
0.331319 | + | 0.943519i | \(0.392506\pi\) | |||||||
\(402\) | −45.0067 | −2.24473 | ||||||||
\(403\) | 21.8125 | 1.08656 | ||||||||
\(404\) | −77.7580 | −3.86861 | ||||||||
\(405\) | 26.0594 | 1.29490 | ||||||||
\(406\) | −22.5058 | −1.11694 | ||||||||
\(407\) | 0.888826 | 0.0440575 | ||||||||
\(408\) | 0.659562 | 0.0326532 | ||||||||
\(409\) | 31.4287 | 1.55405 | 0.777025 | − | 0.629470i | \(-0.216728\pi\) | ||||
0.777025 | + | 0.629470i | \(0.216728\pi\) | |||||||
\(410\) | −54.5916 | −2.69609 | ||||||||
\(411\) | 9.01346 | 0.444601 | ||||||||
\(412\) | −51.1837 | −2.52164 | ||||||||
\(413\) | −6.80999 | −0.335098 | ||||||||
\(414\) | 1.88831 | 0.0928054 | ||||||||
\(415\) | −29.7420 | −1.45998 | ||||||||
\(416\) | 3.30547 | 0.162064 | ||||||||
\(417\) | 26.3601 | 1.29086 | ||||||||
\(418\) | 1.70879 | 0.0835797 | ||||||||
\(419\) | −16.4010 | −0.801240 | −0.400620 | − | 0.916244i | \(-0.631205\pi\) | ||||
−0.400620 | + | 0.916244i | \(0.631205\pi\) | |||||||
\(420\) | 39.4561 | 1.92526 | ||||||||
\(421\) | −0.00764314 | −0.000372504 0 | −0.000186252 | − | 1.00000i | \(-0.500059\pi\) | ||||
−0.000186252 | 1.00000i | \(0.500059\pi\) | ||||||||
\(422\) | 68.9284 | 3.35538 | ||||||||
\(423\) | −0.325382 | −0.0158206 | ||||||||
\(424\) | 25.4155 | 1.23428 | ||||||||
\(425\) | −0.626427 | −0.0303862 | ||||||||
\(426\) | 12.5747 | 0.609245 | ||||||||
\(427\) | −8.17591 | −0.395660 | ||||||||
\(428\) | −33.4037 | −1.61463 | ||||||||
\(429\) | −5.37683 | −0.259596 | ||||||||
\(430\) | −100.566 | −4.84974 | ||||||||
\(431\) | −27.0587 | −1.30337 | −0.651685 | − | 0.758489i | \(-0.725938\pi\) | ||||
−0.651685 | + | 0.758489i | \(0.725938\pi\) | |||||||
\(432\) | −23.8013 | −1.14514 | ||||||||
\(433\) | 35.6967 | 1.71547 | 0.857737 | − | 0.514088i | \(-0.171870\pi\) | ||||
0.857737 | + | 0.514088i | \(0.171870\pi\) | |||||||
\(434\) | −14.2796 | −0.685443 | ||||||||
\(435\) | 29.8779 | 1.43254 | ||||||||
\(436\) | −68.3162 | −3.27175 | ||||||||
\(437\) | −2.13916 | −0.102330 | ||||||||
\(438\) | 51.0513 | 2.43933 | ||||||||
\(439\) | −0.366379 | −0.0174863 | −0.00874315 | − | 0.999962i | \(-0.502783\pi\) | ||||
−0.00874315 | + | 0.999962i | \(0.502783\pi\) | |||||||
\(440\) | 9.34804 | 0.445650 | ||||||||
\(441\) | 1.91957 | 0.0914082 | ||||||||
\(442\) | −1.31391 | −0.0624961 | ||||||||
\(443\) | 15.4416 | 0.733651 | 0.366826 | − | 0.930290i | \(-0.380445\pi\) | ||||
0.366826 | + | 0.930290i | \(0.380445\pi\) | |||||||
\(444\) | 10.9606 | 0.520169 | ||||||||
\(445\) | −18.0020 | −0.853379 | ||||||||
\(446\) | 9.21367 | 0.436280 | ||||||||
\(447\) | 22.0179 | 1.04141 | ||||||||
\(448\) | 12.7201 | 0.600967 | ||||||||
\(449\) | 5.18194 | 0.244551 | 0.122276 | − | 0.992496i | \(-0.460981\pi\) | ||||
0.122276 | + | 0.992496i | \(0.460981\pi\) | |||||||
\(450\) | 8.94474 | 0.421659 | ||||||||
\(451\) | −3.26053 | −0.153533 | ||||||||
\(452\) | 63.8766 | 3.00450 | ||||||||
\(453\) | −6.32054 | −0.296965 | ||||||||
\(454\) | −41.8257 | −1.96298 | ||||||||
\(455\) | −39.7958 | −1.86566 | ||||||||
\(456\) | 10.6690 | 0.499621 | ||||||||
\(457\) | 32.5937 | 1.52467 | 0.762335 | − | 0.647183i | \(-0.224053\pi\) | ||||
0.762335 | + | 0.647183i | \(0.224053\pi\) | |||||||
\(458\) | 25.2920 | 1.18182 | ||||||||
\(459\) | 0.454623 | 0.0212200 | ||||||||
\(460\) | −23.1132 | −1.07766 | ||||||||
\(461\) | −7.23003 | −0.336736 | −0.168368 | − | 0.985724i | \(-0.553850\pi\) | ||||
−0.168368 | + | 0.985724i | \(0.553850\pi\) | |||||||
\(462\) | 3.51996 | 0.163763 | ||||||||
\(463\) | −33.7004 | −1.56619 | −0.783094 | − | 0.621903i | \(-0.786360\pi\) | ||||
−0.783094 | + | 0.621903i | \(0.786360\pi\) | |||||||
\(464\) | −22.8297 | −1.05984 | ||||||||
\(465\) | 18.9571 | 0.879116 | ||||||||
\(466\) | 50.3670 | 2.33321 | ||||||||
\(467\) | 10.0468 | 0.464911 | 0.232456 | − | 0.972607i | \(-0.425324\pi\) | ||||
0.232456 | + | 0.972607i | \(0.425324\pi\) | |||||||
\(468\) | 12.5603 | 0.580601 | ||||||||
\(469\) | −19.8953 | −0.918681 | ||||||||
\(470\) | 5.94895 | 0.274404 | ||||||||
\(471\) | −4.45482 | −0.205267 | ||||||||
\(472\) | −19.8963 | −0.915801 | ||||||||
\(473\) | −6.00642 | −0.276176 | ||||||||
\(474\) | 60.7778 | 2.79162 | ||||||||
\(475\) | −10.1330 | −0.464933 | ||||||||
\(476\) | 0.575857 | 0.0263943 | ||||||||
\(477\) | 2.40673 | 0.110197 | ||||||||
\(478\) | 23.5103 | 1.07533 | ||||||||
\(479\) | −6.20194 | −0.283374 | −0.141687 | − | 0.989912i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989912i | \(0.545253\pi\) | |||||||
\(480\) | 2.87277 | 0.131123 | ||||||||
\(481\) | −11.0550 | −0.504065 | ||||||||
\(482\) | −60.3182 | −2.74742 | ||||||||
\(483\) | −4.40648 | −0.200502 | ||||||||
\(484\) | −43.4595 | −1.97543 | ||||||||
\(485\) | 32.1849 | 1.46144 | ||||||||
\(486\) | −12.0913 | −0.548472 | ||||||||
\(487\) | −21.8945 | −0.992135 | −0.496067 | − | 0.868284i | \(-0.665223\pi\) | ||||
−0.496067 | + | 0.868284i | \(0.665223\pi\) | |||||||
\(488\) | −23.8870 | −1.08131 | ||||||||
\(489\) | 28.6573 | 1.29593 | ||||||||
\(490\) | −35.0955 | −1.58545 | ||||||||
\(491\) | −9.16110 | −0.413435 | −0.206717 | − | 0.978401i | \(-0.566278\pi\) | ||||
−0.206717 | + | 0.978401i | \(0.566278\pi\) | |||||||
\(492\) | −40.2075 | −1.81270 | ||||||||
\(493\) | 0.436065 | 0.0196394 | ||||||||
\(494\) | −21.2535 | −0.956242 | ||||||||
\(495\) | 0.885217 | 0.0397875 | ||||||||
\(496\) | −14.4852 | −0.650403 | ||||||||
\(497\) | 5.55867 | 0.249340 | ||||||||
\(498\) | −32.7199 | −1.46621 | ||||||||
\(499\) | 8.39825 | 0.375957 | 0.187979 | − | 0.982173i | \(-0.439806\pi\) | ||||
0.187979 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(500\) | −37.5547 | −1.67950 | ||||||||
\(501\) | 17.5816 | 0.785486 | ||||||||
\(502\) | −14.7328 | −0.657558 | ||||||||
\(503\) | 6.13750 | 0.273658 | 0.136829 | − | 0.990595i | \(-0.456309\pi\) | ||||
0.136829 | + | 0.990595i | \(0.456309\pi\) | |||||||
\(504\) | −4.16320 | −0.185444 | ||||||||
\(505\) | 68.1611 | 3.03313 | ||||||||
\(506\) | −2.06197 | −0.0916659 | ||||||||
\(507\) | 46.2298 | 2.05314 | ||||||||
\(508\) | 4.53468 | 0.201194 | ||||||||
\(509\) | 27.4079 | 1.21483 | 0.607416 | − | 0.794384i | \(-0.292206\pi\) | ||||
0.607416 | + | 0.794384i | \(0.292206\pi\) | |||||||
\(510\) | −1.14191 | −0.0505646 | ||||||||
\(511\) | 22.5674 | 0.998322 | ||||||||
\(512\) | 41.2905 | 1.82480 | ||||||||
\(513\) | 7.35391 | 0.324683 | ||||||||
\(514\) | 15.5506 | 0.685910 | ||||||||
\(515\) | 44.8666 | 1.97706 | ||||||||
\(516\) | −74.0687 | −3.26069 | ||||||||
\(517\) | 0.355306 | 0.0156264 | ||||||||
\(518\) | 7.23720 | 0.317984 | ||||||||
\(519\) | 36.1094 | 1.58503 | ||||||||
\(520\) | −116.269 | −5.09872 | ||||||||
\(521\) | 8.25760 | 0.361772 | 0.180886 | − | 0.983504i | \(-0.442104\pi\) | ||||
0.180886 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(522\) | −6.22657 | −0.272529 | ||||||||
\(523\) | −10.1348 | −0.443164 | −0.221582 | − | 0.975142i | \(-0.571122\pi\) | ||||
−0.221582 | + | 0.975142i | \(0.571122\pi\) | |||||||
\(524\) | −9.28205 | −0.405488 | ||||||||
\(525\) | −20.8731 | −0.910975 | ||||||||
\(526\) | −8.32890 | −0.363157 | ||||||||
\(527\) | 0.276677 | 0.0120523 | ||||||||
\(528\) | 3.57063 | 0.155392 | ||||||||
\(529\) | −20.4187 | −0.887770 | ||||||||
\(530\) | −44.0022 | −1.91133 | ||||||||
\(531\) | −1.88409 | −0.0817625 | ||||||||
\(532\) | 9.31497 | 0.403855 | ||||||||
\(533\) | 40.5538 | 1.75658 | ||||||||
\(534\) | −19.8045 | −0.857025 | ||||||||
\(535\) | 29.2810 | 1.26593 | ||||||||
\(536\) | −58.1268 | −2.51070 | ||||||||
\(537\) | −16.2561 | −0.701502 | ||||||||
\(538\) | 75.8068 | 3.26826 | ||||||||
\(539\) | −2.09611 | −0.0902859 | ||||||||
\(540\) | 79.4575 | 3.41930 | ||||||||
\(541\) | 24.8963 | 1.07037 | 0.535187 | − | 0.844734i | \(-0.320241\pi\) | ||||
0.535187 | + | 0.844734i | \(0.320241\pi\) | |||||||
\(542\) | 60.8840 | 2.61519 | ||||||||
\(543\) | 10.5488 | 0.452694 | ||||||||
\(544\) | 0.0419277 | 0.00179764 | ||||||||
\(545\) | 59.8846 | 2.56517 | ||||||||
\(546\) | −43.7804 | −1.87363 | ||||||||
\(547\) | 9.35363 | 0.399933 | 0.199966 | − | 0.979803i | \(-0.435917\pi\) | ||||
0.199966 | + | 0.979803i | \(0.435917\pi\) | |||||||
\(548\) | 22.9919 | 0.982167 | ||||||||
\(549\) | −2.26199 | −0.0965394 | ||||||||
\(550\) | −9.76736 | −0.416482 | ||||||||
\(551\) | 7.05372 | 0.300499 | ||||||||
\(552\) | −12.8741 | −0.547958 | ||||||||
\(553\) | 26.8670 | 1.14250 | ||||||||
\(554\) | −37.4709 | −1.59199 | ||||||||
\(555\) | −9.60787 | −0.407831 | ||||||||
\(556\) | 67.2404 | 2.85163 | ||||||||
\(557\) | −14.8190 | −0.627900 | −0.313950 | − | 0.949439i | \(-0.601652\pi\) | ||||
−0.313950 | + | 0.949439i | \(0.601652\pi\) | |||||||
\(558\) | −3.95067 | −0.167245 | ||||||||
\(559\) | 74.7065 | 3.15975 | ||||||||
\(560\) | 26.4275 | 1.11676 | ||||||||
\(561\) | −0.0682016 | −0.00287947 | ||||||||
\(562\) | −45.5068 | −1.91959 | ||||||||
\(563\) | −28.3788 | −1.19603 | −0.598013 | − | 0.801487i | \(-0.704043\pi\) | ||||
−0.598013 | + | 0.801487i | \(0.704043\pi\) | |||||||
\(564\) | 4.38149 | 0.184494 | ||||||||
\(565\) | −55.9929 | −2.35564 | ||||||||
\(566\) | 9.84592 | 0.413855 | ||||||||
\(567\) | 12.6730 | 0.532217 | ||||||||
\(568\) | 16.2404 | 0.681431 | ||||||||
\(569\) | 22.1033 | 0.926617 | 0.463309 | − | 0.886197i | \(-0.346662\pi\) | ||||
0.463309 | + | 0.886197i | \(0.346662\pi\) | |||||||
\(570\) | −18.4714 | −0.773680 | ||||||||
\(571\) | −17.1566 | −0.717980 | −0.358990 | − | 0.933341i | \(-0.616879\pi\) | ||||
−0.358990 | + | 0.933341i | \(0.616879\pi\) | |||||||
\(572\) | −13.7155 | −0.573472 | ||||||||
\(573\) | 17.9250 | 0.748826 | ||||||||
\(574\) | −26.5486 | −1.10812 | ||||||||
\(575\) | 12.2273 | 0.509915 | ||||||||
\(576\) | 3.51920 | 0.146633 | ||||||||
\(577\) | −0.0330496 | −0.00137587 | −0.000687936 | − | 1.00000i | \(-0.500219\pi\) | ||||
−0.000687936 | 1.00000i | \(0.500219\pi\) | ||||||||
\(578\) | 41.8017 | 1.73872 | ||||||||
\(579\) | 5.94345 | 0.247001 | ||||||||
\(580\) | 76.2140 | 3.16461 | ||||||||
\(581\) | −14.4639 | −0.600064 | ||||||||
\(582\) | 35.4074 | 1.46768 | ||||||||
\(583\) | −2.62807 | −0.108844 | ||||||||
\(584\) | 65.9336 | 2.72835 | ||||||||
\(585\) | −11.0101 | −0.455213 | ||||||||
\(586\) | −49.0385 | −2.02576 | ||||||||
\(587\) | 3.65229 | 0.150746 | 0.0753731 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753731 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(588\) | −25.8483 | −1.06597 | ||||||||
\(589\) | 4.47549 | 0.184409 | ||||||||
\(590\) | 34.4467 | 1.41815 | ||||||||
\(591\) | −16.4664 | −0.677338 | ||||||||
\(592\) | 7.34138 | 0.301729 | ||||||||
\(593\) | −36.3894 | −1.49433 | −0.747167 | − | 0.664637i | \(-0.768586\pi\) | ||||
−0.747167 | + | 0.664637i | \(0.768586\pi\) | |||||||
\(594\) | 7.08856 | 0.290847 | ||||||||
\(595\) | −0.504784 | −0.0206941 | ||||||||
\(596\) | 56.1642 | 2.30058 | ||||||||
\(597\) | 39.5268 | 1.61772 | ||||||||
\(598\) | 25.6463 | 1.04876 | ||||||||
\(599\) | 0.140841 | 0.00575460 | 0.00287730 | − | 0.999996i | \(-0.499084\pi\) | ||||
0.00287730 | + | 0.999996i | \(0.499084\pi\) | |||||||
\(600\) | −60.9834 | −2.48964 | ||||||||
\(601\) | −45.5881 | −1.85958 | −0.929789 | − | 0.368093i | \(-0.880011\pi\) | ||||
−0.929789 | + | 0.368093i | \(0.880011\pi\) | |||||||
\(602\) | −48.9068 | −1.99329 | ||||||||
\(603\) | −5.50435 | −0.224154 | ||||||||
\(604\) | −16.1227 | −0.656024 | ||||||||
\(605\) | 38.0958 | 1.54881 | ||||||||
\(606\) | 74.9858 | 3.04609 | ||||||||
\(607\) | −31.2698 | −1.26920 | −0.634600 | − | 0.772841i | \(-0.718835\pi\) | ||||
−0.634600 | + | 0.772841i | \(0.718835\pi\) | |||||||
\(608\) | 0.678216 | 0.0275053 | ||||||||
\(609\) | 14.5300 | 0.588787 | ||||||||
\(610\) | 41.3559 | 1.67445 | ||||||||
\(611\) | −4.41922 | −0.178782 | ||||||||
\(612\) | 0.159320 | 0.00644011 | ||||||||
\(613\) | 14.1771 | 0.572609 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(614\) | 58.6881 | 2.36846 | ||||||||
\(615\) | 35.2451 | 1.42122 | ||||||||
\(616\) | 4.54608 | 0.183167 | ||||||||
\(617\) | −14.4874 | −0.583243 | −0.291621 | − | 0.956534i | \(-0.594195\pi\) | ||||
−0.291621 | + | 0.956534i | \(0.594195\pi\) | |||||||
\(618\) | 49.3589 | 1.98551 | ||||||||
\(619\) | 11.1855 | 0.449583 | 0.224791 | − | 0.974407i | \(-0.427830\pi\) | ||||
0.224791 | + | 0.974407i | \(0.427830\pi\) | |||||||
\(620\) | 48.3567 | 1.94205 | ||||||||
\(621\) | −8.87386 | −0.356096 | ||||||||
\(622\) | −13.6681 | −0.548043 | ||||||||
\(623\) | −8.75464 | −0.350747 | ||||||||
\(624\) | −44.4106 | −1.77785 | ||||||||
\(625\) | −5.13283 | −0.205313 | ||||||||
\(626\) | 12.0322 | 0.480902 | ||||||||
\(627\) | −1.10322 | −0.0440583 | ||||||||
\(628\) | −11.3636 | −0.453455 | ||||||||
\(629\) | −0.140226 | −0.00559117 | ||||||||
\(630\) | 7.20781 | 0.287166 | ||||||||
\(631\) | −47.8932 | −1.90660 | −0.953299 | − | 0.302028i | \(-0.902337\pi\) | ||||
−0.953299 | + | 0.302028i | \(0.902337\pi\) | |||||||
\(632\) | 78.4954 | 3.12238 | ||||||||
\(633\) | −44.5012 | −1.76876 | ||||||||
\(634\) | 63.4012 | 2.51798 | ||||||||
\(635\) | −3.97501 | −0.157743 | ||||||||
\(636\) | −32.4082 | −1.28507 | ||||||||
\(637\) | 26.0709 | 1.03297 | ||||||||
\(638\) | 6.79920 | 0.269183 | ||||||||
\(639\) | 1.53789 | 0.0608380 | ||||||||
\(640\) | −67.9592 | −2.68632 | ||||||||
\(641\) | 14.6770 | 0.579705 | 0.289853 | − | 0.957071i | \(-0.406394\pi\) | ||||
0.289853 | + | 0.957071i | \(0.406394\pi\) | |||||||
\(642\) | 32.2128 | 1.27134 | ||||||||
\(643\) | −11.8705 | −0.468128 | −0.234064 | − | 0.972221i | \(-0.575203\pi\) | ||||
−0.234064 | + | 0.972221i | \(0.575203\pi\) | |||||||
\(644\) | −11.2402 | −0.442928 | ||||||||
\(645\) | 64.9271 | 2.55650 | ||||||||
\(646\) | −0.269588 | −0.0106068 | ||||||||
\(647\) | 26.1304 | 1.02729 | 0.513645 | − | 0.858003i | \(-0.328295\pi\) | ||||
0.513645 | + | 0.858003i | \(0.328295\pi\) | |||||||
\(648\) | 37.0259 | 1.45452 | ||||||||
\(649\) | 2.05736 | 0.0807585 | ||||||||
\(650\) | 121.484 | 4.76500 | ||||||||
\(651\) | 9.21911 | 0.361325 | ||||||||
\(652\) | 73.1004 | 2.86283 | ||||||||
\(653\) | 38.5577 | 1.50888 | 0.754440 | − | 0.656369i | \(-0.227909\pi\) | ||||
0.754440 | + | 0.656369i | \(0.227909\pi\) | |||||||
\(654\) | 65.8805 | 2.57613 | ||||||||
\(655\) | 8.13646 | 0.317918 | ||||||||
\(656\) | −26.9308 | −1.05147 | ||||||||
\(657\) | 6.24361 | 0.243586 | ||||||||
\(658\) | 2.89305 | 0.112783 | ||||||||
\(659\) | 10.0132 | 0.390059 | 0.195029 | − | 0.980797i | \(-0.437520\pi\) | ||||
0.195029 | + | 0.980797i | \(0.437520\pi\) | |||||||
\(660\) | −11.9200 | −0.463987 | ||||||||
\(661\) | −12.0432 | −0.468425 | −0.234212 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234212 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(662\) | −53.7893 | −2.09058 | ||||||||
\(663\) | 0.848276 | 0.0329443 | ||||||||
\(664\) | −42.2582 | −1.63994 | ||||||||
\(665\) | −8.16532 | −0.316637 | ||||||||
\(666\) | 2.00228 | 0.0775868 | ||||||||
\(667\) | −8.51163 | −0.329572 | ||||||||
\(668\) | 44.8478 | 1.73521 | ||||||||
\(669\) | −5.94848 | −0.229981 | ||||||||
\(670\) | 100.636 | 3.88790 | ||||||||
\(671\) | 2.47002 | 0.0953541 | ||||||||
\(672\) | 1.39707 | 0.0538930 | ||||||||
\(673\) | −28.2075 | −1.08732 | −0.543659 | − | 0.839306i | \(-0.682961\pi\) | ||||
−0.543659 | + | 0.839306i | \(0.682961\pi\) | |||||||
\(674\) | −34.0332 | −1.31091 | ||||||||
\(675\) | −42.0346 | −1.61791 | ||||||||
\(676\) | 117.925 | 4.53558 | ||||||||
\(677\) | −23.8767 | −0.917657 | −0.458829 | − | 0.888525i | \(-0.651731\pi\) | ||||
−0.458829 | + | 0.888525i | \(0.651731\pi\) | |||||||
\(678\) | −61.5993 | −2.36571 | ||||||||
\(679\) | 15.6519 | 0.600667 | ||||||||
\(680\) | −1.47479 | −0.0565558 | ||||||||
\(681\) | 27.0032 | 1.03477 | ||||||||
\(682\) | 4.31400 | 0.165192 | ||||||||
\(683\) | −20.7517 | −0.794043 | −0.397022 | − | 0.917809i | \(-0.629956\pi\) | ||||
−0.397022 | + | 0.917809i | \(0.629956\pi\) | |||||||
\(684\) | 2.57713 | 0.0985390 | ||||||||
\(685\) | −20.1543 | −0.770055 | ||||||||
\(686\) | −46.8045 | −1.78700 | ||||||||
\(687\) | −16.3289 | −0.622985 | ||||||||
\(688\) | −49.6108 | −1.89140 | ||||||||
\(689\) | 32.6873 | 1.24529 | ||||||||
\(690\) | 22.2891 | 0.848533 | ||||||||
\(691\) | 34.4125 | 1.30911 | 0.654556 | − | 0.756014i | \(-0.272856\pi\) | ||||
0.654556 | + | 0.756014i | \(0.272856\pi\) | |||||||
\(692\) | 92.1094 | 3.50147 | ||||||||
\(693\) | 0.430493 | 0.0163531 | ||||||||
\(694\) | −40.6639 | −1.54358 | ||||||||
\(695\) | −58.9416 | −2.23578 | ||||||||
\(696\) | 42.4514 | 1.60912 | ||||||||
\(697\) | 0.514398 | 0.0194842 | ||||||||
\(698\) | −9.75907 | −0.369386 | ||||||||
\(699\) | −32.5177 | −1.22993 | ||||||||
\(700\) | −53.2439 | −2.01243 | ||||||||
\(701\) | −19.9660 | −0.754106 | −0.377053 | − | 0.926192i | \(-0.623063\pi\) | ||||
−0.377053 | + | 0.926192i | \(0.623063\pi\) | |||||||
\(702\) | −88.1659 | −3.32761 | ||||||||
\(703\) | −2.26827 | −0.0855495 | ||||||||
\(704\) | −3.84285 | −0.144833 | ||||||||
\(705\) | −3.84072 | −0.144650 | ||||||||
\(706\) | −56.7628 | −2.13630 | ||||||||
\(707\) | 33.1477 | 1.24665 | ||||||||
\(708\) | 25.3705 | 0.953483 | ||||||||
\(709\) | 34.9806 | 1.31372 | 0.656862 | − | 0.754011i | \(-0.271883\pi\) | ||||
0.656862 | + | 0.754011i | \(0.271883\pi\) | |||||||
\(710\) | −28.1172 | −1.05522 | ||||||||
\(711\) | 7.43316 | 0.278765 | ||||||||
\(712\) | −25.5778 | −0.958569 | ||||||||
\(713\) | −5.40051 | −0.202251 | ||||||||
\(714\) | −0.555326 | −0.0207826 | ||||||||
\(715\) | 12.0227 | 0.449623 | ||||||||
\(716\) | −41.4668 | −1.54969 | ||||||||
\(717\) | −15.1786 | −0.566854 | ||||||||
\(718\) | 43.9346 | 1.63963 | ||||||||
\(719\) | 10.4400 | 0.389347 | 0.194674 | − | 0.980868i | \(-0.437635\pi\) | ||||
0.194674 | + | 0.980868i | \(0.437635\pi\) | |||||||
\(720\) | 7.31156 | 0.272486 | ||||||||
\(721\) | 21.8192 | 0.812591 | ||||||||
\(722\) | 42.3773 | 1.57712 | ||||||||
\(723\) | 38.9423 | 1.44828 | ||||||||
\(724\) | 26.9085 | 1.00005 | ||||||||
\(725\) | −40.3187 | −1.49740 | ||||||||
\(726\) | 41.9101 | 1.55543 | ||||||||
\(727\) | −34.0466 | −1.26272 | −0.631360 | − | 0.775490i | \(-0.717503\pi\) | ||||
−0.631360 | + | 0.775490i | \(0.717503\pi\) | |||||||
\(728\) | −56.5430 | −2.09562 | ||||||||
\(729\) | 29.8213 | 1.10449 | ||||||||
\(730\) | −114.152 | −4.22495 | ||||||||
\(731\) | 0.947604 | 0.0350484 | ||||||||
\(732\) | 30.4592 | 1.12581 | ||||||||
\(733\) | 46.3189 | 1.71083 | 0.855413 | − | 0.517947i | \(-0.173303\pi\) | ||||
0.855413 | + | 0.517947i | \(0.173303\pi\) | |||||||
\(734\) | 15.3722 | 0.567398 | ||||||||
\(735\) | 22.6581 | 0.835758 | ||||||||
\(736\) | −0.818394 | −0.0301664 | ||||||||
\(737\) | 6.01057 | 0.221402 | ||||||||
\(738\) | −7.34509 | −0.270376 | ||||||||
\(739\) | −32.5051 | −1.19572 | −0.597859 | − | 0.801601i | \(-0.703982\pi\) | ||||
−0.597859 | + | 0.801601i | \(0.703982\pi\) | |||||||
\(740\) | −24.5082 | −0.900939 | ||||||||
\(741\) | 13.7216 | 0.504075 | ||||||||
\(742\) | −21.3989 | −0.785577 | ||||||||
\(743\) | 10.9235 | 0.400743 | 0.200372 | − | 0.979720i | \(-0.435785\pi\) | ||||
0.200372 | + | 0.979720i | \(0.435785\pi\) | |||||||
\(744\) | 26.9348 | 0.987479 | ||||||||
\(745\) | −49.2324 | −1.80374 | ||||||||
\(746\) | −13.3774 | −0.489783 | ||||||||
\(747\) | −4.00166 | −0.146413 | ||||||||
\(748\) | −0.173972 | −0.00636104 | ||||||||
\(749\) | 14.2398 | 0.520309 | ||||||||
\(750\) | 36.2158 | 1.32241 | ||||||||
\(751\) | −20.4686 | −0.746909 | −0.373454 | − | 0.927649i | \(-0.621827\pi\) | ||||
−0.373454 | + | 0.927649i | \(0.621827\pi\) | |||||||
\(752\) | 2.93470 | 0.107017 | ||||||||
\(753\) | 9.51171 | 0.346626 | ||||||||
\(754\) | −84.5669 | −3.07975 | ||||||||
\(755\) | 14.1329 | 0.514347 | ||||||||
\(756\) | 38.6412 | 1.40537 | ||||||||
\(757\) | 14.1329 | 0.513668 | 0.256834 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256834 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(758\) | 73.8389 | 2.68195 | ||||||||
\(759\) | 1.33124 | 0.0483209 | ||||||||
\(760\) | −23.8560 | −0.865350 | ||||||||
\(761\) | −33.6811 | −1.22094 | −0.610470 | − | 0.792039i | \(-0.709019\pi\) | ||||
−0.610470 | + | 0.792039i | \(0.709019\pi\) | |||||||
\(762\) | −4.37301 | −0.158417 | ||||||||
\(763\) | 29.1227 | 1.05431 | ||||||||
\(764\) | 45.7238 | 1.65423 | ||||||||
\(765\) | −0.139656 | −0.00504928 | ||||||||
\(766\) | 17.2957 | 0.624921 | ||||||||
\(767\) | −25.5890 | −0.923965 | ||||||||
\(768\) | −51.3684 | −1.85360 | ||||||||
\(769\) | 9.33897 | 0.336772 | 0.168386 | − | 0.985721i | \(-0.446145\pi\) | ||||
0.168386 | + | 0.985721i | \(0.446145\pi\) | |||||||
\(770\) | −7.87069 | −0.283640 | ||||||||
\(771\) | −10.0397 | −0.361572 | ||||||||
\(772\) | 15.1608 | 0.545650 | ||||||||
\(773\) | 20.3730 | 0.732764 | 0.366382 | − | 0.930464i | \(-0.380596\pi\) | ||||
0.366382 | + | 0.930464i | \(0.380596\pi\) | |||||||
\(774\) | −13.5308 | −0.486355 | ||||||||
\(775\) | −25.5817 | −0.918921 | ||||||||
\(776\) | 45.7292 | 1.64158 | ||||||||
\(777\) | −4.67244 | −0.167623 | ||||||||
\(778\) | 11.0705 | 0.396895 | ||||||||
\(779\) | 8.32083 | 0.298125 | ||||||||
\(780\) | 148.259 | 5.30851 | ||||||||
\(781\) | −1.67933 | −0.0600910 | ||||||||
\(782\) | 0.325307 | 0.0116330 | ||||||||
\(783\) | 29.2609 | 1.04570 | ||||||||
\(784\) | −17.3131 | −0.618325 | ||||||||
\(785\) | 9.96106 | 0.355526 | ||||||||
\(786\) | 8.95113 | 0.319276 | ||||||||
\(787\) | −3.99657 | −0.142462 | −0.0712312 | − | 0.997460i | \(-0.522693\pi\) | ||||
−0.0712312 | + | 0.997460i | \(0.522693\pi\) | |||||||
\(788\) | −42.0033 | −1.49631 | ||||||||
\(789\) | 5.37726 | 0.191435 | ||||||||
\(790\) | −135.900 | −4.83511 | ||||||||
\(791\) | −27.2301 | −0.968192 | ||||||||
\(792\) | 1.25774 | 0.0446919 | ||||||||
\(793\) | −30.7215 | −1.09095 | ||||||||
\(794\) | 23.2487 | 0.825064 | ||||||||
\(795\) | 28.4084 | 1.00754 | ||||||||
\(796\) | 100.827 | 3.57371 | ||||||||
\(797\) | 43.2861 | 1.53327 | 0.766636 | − | 0.642082i | \(-0.221929\pi\) | ||||
0.766636 | + | 0.642082i | \(0.221929\pi\) | |||||||
\(798\) | −8.98287 | −0.317990 | ||||||||
\(799\) | −0.0560549 | −0.00198308 | ||||||||
\(800\) | −3.87665 | −0.137060 | ||||||||
\(801\) | −2.42210 | −0.0855808 | ||||||||
\(802\) | −32.6412 | −1.15260 | ||||||||
\(803\) | −6.81782 | −0.240596 | ||||||||
\(804\) | 74.1198 | 2.61400 | ||||||||
\(805\) | 9.85297 | 0.347272 | ||||||||
\(806\) | −53.6566 | −1.88997 | ||||||||
\(807\) | −48.9419 | −1.72284 | ||||||||
\(808\) | 96.8453 | 3.40700 | ||||||||
\(809\) | −46.5763 | −1.63753 | −0.818767 | − | 0.574126i | \(-0.805342\pi\) | ||||
−0.818767 | + | 0.574126i | \(0.805342\pi\) | |||||||
\(810\) | −64.1035 | −2.25237 | ||||||||
\(811\) | 44.4191 | 1.55977 | 0.779883 | − | 0.625926i | \(-0.215279\pi\) | ||||
0.779883 | + | 0.625926i | \(0.215279\pi\) | |||||||
\(812\) | 37.0639 | 1.30069 | ||||||||
\(813\) | −39.3075 | −1.37858 | ||||||||
\(814\) | −2.18643 | −0.0766342 | ||||||||
\(815\) | −64.0783 | −2.24457 | ||||||||
\(816\) | −0.563320 | −0.0197201 | ||||||||
\(817\) | 15.3283 | 0.536269 | ||||||||
\(818\) | −77.3115 | −2.70313 | ||||||||
\(819\) | −5.35437 | −0.187097 | ||||||||
\(820\) | 89.9048 | 3.13961 | ||||||||
\(821\) | 16.0131 | 0.558860 | 0.279430 | − | 0.960166i | \(-0.409854\pi\) | ||||
0.279430 | + | 0.960166i | \(0.409854\pi\) | |||||||
\(822\) | −22.1722 | −0.773345 | ||||||||
\(823\) | 26.1091 | 0.910105 | 0.455052 | − | 0.890465i | \(-0.349621\pi\) | ||||
0.455052 | + | 0.890465i | \(0.349621\pi\) | |||||||
\(824\) | 63.7477 | 2.22076 | ||||||||
\(825\) | 6.30595 | 0.219545 | ||||||||
\(826\) | 16.7519 | 0.582873 | ||||||||
\(827\) | 42.5792 | 1.48062 | 0.740312 | − | 0.672263i | \(-0.234678\pi\) | ||||
0.740312 | + | 0.672263i | \(0.234678\pi\) | |||||||
\(828\) | −3.10979 | −0.108073 | ||||||||
\(829\) | 2.34632 | 0.0814909 | 0.0407455 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407455 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(830\) | 73.1623 | 2.53950 | ||||||||
\(831\) | 24.1917 | 0.839202 | ||||||||
\(832\) | 47.7965 | 1.65704 | ||||||||
\(833\) | 0.330693 | 0.0114578 | ||||||||
\(834\) | −64.8431 | −2.24533 | ||||||||
\(835\) | −39.3127 | −1.36047 | ||||||||
\(836\) | −2.81414 | −0.0973291 | ||||||||
\(837\) | 18.5656 | 0.641723 | ||||||||
\(838\) | 40.3448 | 1.39369 | ||||||||
\(839\) | 48.0298 | 1.65817 | 0.829087 | − | 0.559120i | \(-0.188861\pi\) | ||||
0.829087 | + | 0.559120i | \(0.188861\pi\) | |||||||
\(840\) | −49.1413 | −1.69554 | ||||||||
\(841\) | −0.933537 | −0.0321909 | ||||||||
\(842\) | 0.0188014 | 0.000647938 0 | ||||||||
\(843\) | 29.3798 | 1.01190 | ||||||||
\(844\) | −113.516 | −3.90737 | ||||||||
\(845\) | −103.371 | −3.55606 | ||||||||
\(846\) | 0.800407 | 0.0275186 | ||||||||
\(847\) | 18.5265 | 0.636577 | ||||||||
\(848\) | −21.7069 | −0.745418 | ||||||||
\(849\) | −6.35667 | −0.218160 | ||||||||
\(850\) | 1.54095 | 0.0528541 | ||||||||
\(851\) | 2.73709 | 0.0938263 | ||||||||
\(852\) | −20.7087 | −0.709469 | ||||||||
\(853\) | 1.17879 | 0.0403609 | 0.0201805 | − | 0.999796i | \(-0.493576\pi\) | ||||
0.0201805 | + | 0.999796i | \(0.493576\pi\) | |||||||
\(854\) | 20.1119 | 0.688217 | ||||||||
\(855\) | −2.25906 | −0.0772582 | ||||||||
\(856\) | 41.6033 | 1.42197 | ||||||||
\(857\) | 12.6071 | 0.430651 | 0.215326 | − | 0.976542i | \(-0.430919\pi\) | ||||
0.215326 | + | 0.976542i | \(0.430919\pi\) | |||||||
\(858\) | 13.2265 | 0.451544 | ||||||||
\(859\) | 42.5968 | 1.45338 | 0.726692 | − | 0.686964i | \(-0.241057\pi\) | ||||
0.726692 | + | 0.686964i | \(0.241057\pi\) | |||||||
\(860\) | 165.619 | 5.64756 | ||||||||
\(861\) | 17.1402 | 0.584136 | ||||||||
\(862\) | 66.5617 | 2.26710 | ||||||||
\(863\) | 23.0189 | 0.783573 | 0.391787 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391787 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(864\) | 2.81344 | 0.0957152 | ||||||||
\(865\) | −80.7413 | −2.74529 | ||||||||
\(866\) | −87.8104 | −2.98392 | ||||||||
\(867\) | −26.9877 | −0.916552 | ||||||||
\(868\) | 23.5165 | 0.798203 | ||||||||
\(869\) | −8.11677 | −0.275342 | ||||||||
\(870\) | −73.4968 | −2.49177 | ||||||||
\(871\) | −74.7580 | −2.53308 | ||||||||
\(872\) | 85.0857 | 2.88137 | ||||||||
\(873\) | 4.33035 | 0.146560 | ||||||||
\(874\) | 5.26212 | 0.177994 | ||||||||
\(875\) | 16.0093 | 0.541212 | ||||||||
\(876\) | −84.0745 | −2.84061 | ||||||||
\(877\) | 37.2894 | 1.25917 | 0.629587 | − | 0.776930i | \(-0.283224\pi\) | ||||
0.629587 | + | 0.776930i | \(0.283224\pi\) | |||||||
\(878\) | 0.901255 | 0.0304159 | ||||||||
\(879\) | 31.6600 | 1.06786 | ||||||||
\(880\) | −7.98399 | −0.269140 | ||||||||
\(881\) | 11.2948 | 0.380531 | 0.190266 | − | 0.981733i | \(-0.439065\pi\) | ||||
0.190266 | + | 0.981733i | \(0.439065\pi\) | |||||||
\(882\) | −4.72196 | −0.158997 | ||||||||
\(883\) | −11.1627 | −0.375655 | −0.187827 | − | 0.982202i | \(-0.560145\pi\) | ||||
−0.187827 | + | 0.982202i | \(0.560145\pi\) | |||||||
\(884\) | 2.16382 | 0.0727771 | ||||||||
\(885\) | −22.2393 | −0.747565 | ||||||||
\(886\) | −37.9847 | −1.27612 | ||||||||
\(887\) | 26.6576 | 0.895076 | 0.447538 | − | 0.894265i | \(-0.352301\pi\) | ||||
0.447538 | + | 0.894265i | \(0.352301\pi\) | |||||||
\(888\) | −13.6511 | −0.458102 | ||||||||
\(889\) | −1.93310 | −0.0648341 | ||||||||
\(890\) | 44.2832 | 1.48438 | ||||||||
\(891\) | −3.82864 | −0.128264 | ||||||||
\(892\) | −15.1736 | −0.508051 | ||||||||
\(893\) | −0.906736 | −0.0303428 | ||||||||
\(894\) | −54.1619 | −1.81144 | ||||||||
\(895\) | 36.3489 | 1.21501 | ||||||||
\(896\) | −33.0495 | −1.10411 | ||||||||
\(897\) | −16.5576 | −0.552843 | ||||||||
\(898\) | −12.7471 | −0.425375 | ||||||||
\(899\) | 17.8078 | 0.593923 | ||||||||
\(900\) | −14.7307 | −0.491025 | ||||||||
\(901\) | 0.414618 | 0.0138129 | ||||||||
\(902\) | 8.02059 | 0.267057 | ||||||||
\(903\) | 31.5749 | 1.05075 | ||||||||
\(904\) | −79.5564 | −2.64601 | ||||||||
\(905\) | −23.5874 | −0.784072 | ||||||||
\(906\) | 15.5479 | 0.516545 | ||||||||
\(907\) | 39.3531 | 1.30670 | 0.653349 | − | 0.757057i | \(-0.273363\pi\) | ||||
0.653349 | + | 0.757057i | \(0.273363\pi\) | |||||||
\(908\) | 68.8810 | 2.28590 | ||||||||
\(909\) | 9.17081 | 0.304177 | ||||||||
\(910\) | 97.8938 | 3.24515 | ||||||||
\(911\) | −37.8619 | −1.25442 | −0.627210 | − | 0.778850i | \(-0.715803\pi\) | ||||
−0.627210 | + | 0.778850i | \(0.715803\pi\) | |||||||
\(912\) | −9.11218 | −0.301735 | ||||||||
\(913\) | 4.36968 | 0.144615 | ||||||||
\(914\) | −80.1773 | −2.65203 | ||||||||
\(915\) | −26.7000 | −0.882674 | ||||||||
\(916\) | −41.6524 | −1.37623 | ||||||||
\(917\) | 3.95687 | 0.130667 | ||||||||
\(918\) | −1.11833 | −0.0369103 | ||||||||
\(919\) | 40.0561 | 1.32133 | 0.660665 | − | 0.750681i | \(-0.270275\pi\) | ||||
0.660665 | + | 0.750681i | \(0.270275\pi\) | |||||||
\(920\) | 28.7867 | 0.949071 | ||||||||
\(921\) | −37.8899 | −1.24851 | ||||||||
\(922\) | 17.7852 | 0.585723 | ||||||||
\(923\) | 20.8871 | 0.687506 | ||||||||
\(924\) | −5.79688 | −0.190703 | ||||||||
\(925\) | 12.9653 | 0.426297 | ||||||||
\(926\) | 82.8996 | 2.72425 | ||||||||
\(927\) | 6.03662 | 0.198269 | ||||||||
\(928\) | 2.69859 | 0.0885857 | ||||||||
\(929\) | −12.0221 | −0.394432 | −0.197216 | − | 0.980360i | \(-0.563190\pi\) | ||||
−0.197216 | + | 0.980360i | \(0.563190\pi\) | |||||||
\(930\) | −46.6327 | −1.52915 | ||||||||
\(931\) | 5.34924 | 0.175314 | ||||||||
\(932\) | −82.9475 | −2.71704 | ||||||||
\(933\) | 8.82434 | 0.288896 | ||||||||
\(934\) | −24.7142 | −0.808673 | ||||||||
\(935\) | 0.152500 | 0.00498729 | ||||||||
\(936\) | −15.6435 | −0.511324 | ||||||||
\(937\) | −23.3096 | −0.761490 | −0.380745 | − | 0.924680i | \(-0.624332\pi\) | ||||
−0.380745 | + | 0.924680i | \(0.624332\pi\) | |||||||
\(938\) | 48.9406 | 1.59797 | ||||||||
\(939\) | −7.76813 | −0.253503 | ||||||||
\(940\) | −9.79709 | −0.319546 | ||||||||
\(941\) | 7.61178 | 0.248137 | 0.124068 | − | 0.992274i | \(-0.460406\pi\) | ||||
0.124068 | + | 0.992274i | \(0.460406\pi\) | |||||||
\(942\) | 10.9584 | 0.357045 | ||||||||
\(943\) | −10.0406 | −0.326968 | ||||||||
\(944\) | 16.9931 | 0.553077 | ||||||||
\(945\) | −33.8721 | −1.10186 | ||||||||
\(946\) | 14.7752 | 0.480383 | ||||||||
\(947\) | −12.5574 | −0.408062 | −0.204031 | − | 0.978964i | \(-0.565404\pi\) | ||||
−0.204031 | + | 0.978964i | \(0.565404\pi\) | |||||||
\(948\) | −100.093 | −3.25085 | ||||||||
\(949\) | 84.7984 | 2.75267 | ||||||||
\(950\) | 24.9262 | 0.808711 | ||||||||
\(951\) | −40.9327 | −1.32733 | ||||||||
\(952\) | −0.717212 | −0.0232450 | ||||||||
\(953\) | 3.08729 | 0.100007 | 0.0500036 | − | 0.998749i | \(-0.484077\pi\) | ||||
0.0500036 | + | 0.998749i | \(0.484077\pi\) | |||||||
\(954\) | −5.92032 | −0.191677 | ||||||||
\(955\) | −40.0806 | −1.29698 | ||||||||
\(956\) | −38.7181 | −1.25223 | ||||||||
\(957\) | −4.38966 | −0.141898 | ||||||||
\(958\) | 15.2562 | 0.492904 | ||||||||
\(959\) | −9.80129 | −0.316500 | ||||||||
\(960\) | 41.5397 | 1.34069 | ||||||||
\(961\) | −19.7012 | −0.635523 | ||||||||
\(962\) | 27.1943 | 0.876778 | ||||||||
\(963\) | 3.93965 | 0.126953 | ||||||||
\(964\) | 99.3357 | 3.19939 | ||||||||
\(965\) | −13.2897 | −0.427810 | ||||||||
\(966\) | 10.8395 | 0.348755 | ||||||||
\(967\) | 11.6797 | 0.375592 | 0.187796 | − | 0.982208i | \(-0.439866\pi\) | ||||
0.187796 | + | 0.982208i | \(0.439866\pi\) | |||||||
\(968\) | 54.1275 | 1.73973 | ||||||||
\(969\) | 0.174049 | 0.00559127 | ||||||||
\(970\) | −79.1717 | −2.54205 | ||||||||
\(971\) | −29.6158 | −0.950416 | −0.475208 | − | 0.879874i | \(-0.657627\pi\) | ||||
−0.475208 | + | 0.879874i | \(0.657627\pi\) | |||||||
\(972\) | 19.9127 | 0.638699 | ||||||||
\(973\) | −28.6641 | −0.918928 | ||||||||
\(974\) | 53.8583 | 1.72573 | ||||||||
\(975\) | −78.4319 | −2.51183 | ||||||||
\(976\) | 20.4015 | 0.653035 | ||||||||
\(977\) | 19.9372 | 0.637848 | 0.318924 | − | 0.947780i | \(-0.396679\pi\) | ||||
0.318924 | + | 0.947780i | \(0.396679\pi\) | |||||||
\(978\) | −70.4942 | −2.25416 | ||||||||
\(979\) | 2.64486 | 0.0845300 | ||||||||
\(980\) | 57.7974 | 1.84627 | ||||||||
\(981\) | 8.05723 | 0.257248 | ||||||||
\(982\) | 22.5354 | 0.719134 | ||||||||
\(983\) | −19.2335 | −0.613452 | −0.306726 | − | 0.951798i | \(-0.599234\pi\) | ||||
−0.306726 | + | 0.951798i | \(0.599234\pi\) | |||||||
\(984\) | 50.0773 | 1.59641 | ||||||||
\(985\) | 36.8192 | 1.17316 | ||||||||
\(986\) | −1.07268 | −0.0341610 | ||||||||
\(987\) | −1.86780 | −0.0594526 | ||||||||
\(988\) | 35.0016 | 1.11355 | ||||||||
\(989\) | −18.4964 | −0.588152 | ||||||||
\(990\) | −2.17755 | −0.0692070 | ||||||||
\(991\) | −13.4861 | −0.428399 | −0.214199 | − | 0.976790i | \(-0.568714\pi\) | ||||
−0.214199 | + | 0.976790i | \(0.568714\pi\) | |||||||
\(992\) | 1.71222 | 0.0543631 | ||||||||
\(993\) | 34.7271 | 1.10203 | ||||||||
\(994\) | −13.6738 | −0.433706 | ||||||||
\(995\) | −88.3827 | −2.80192 | ||||||||
\(996\) | 53.8851 | 1.70742 | ||||||||
\(997\) | 42.8373 | 1.35667 | 0.678336 | − | 0.734752i | \(-0.262702\pi\) | ||||
0.678336 | + | 0.734752i | \(0.262702\pi\) | |||||||
\(998\) | −20.6589 | −0.653945 | ||||||||
\(999\) | −9.40945 | −0.297702 |
(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 | 5077.2.a.c.1.16 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.16 | ✓ | 216 | 1.1 | even | 1 | trivial |