Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(1\) |
Dimension: | \(159\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73932 | −1.93699 | −0.968495 | − | 0.249034i | \(-0.919887\pi\) | ||||
−0.968495 | + | 0.249034i | \(0.919887\pi\) | |||||||
\(3\) | −1.57093 | −0.906977 | −0.453489 | − | 0.891262i | \(-0.649821\pi\) | ||||
−0.453489 | + | 0.891262i | \(0.649821\pi\) | |||||||
\(4\) | 5.50386 | 2.75193 | ||||||||
\(5\) | 0.430202 | 0.192392 | 0.0961961 | − | 0.995362i | \(-0.469332\pi\) | ||||
0.0961961 | + | 0.995362i | \(0.469332\pi\) | |||||||
\(6\) | 4.30328 | 1.75681 | ||||||||
\(7\) | 4.35305 | 1.64530 | 0.822649 | − | 0.568550i | \(-0.192495\pi\) | ||||
0.822649 | + | 0.568550i | \(0.192495\pi\) | |||||||
\(8\) | −9.59817 | −3.39347 | ||||||||
\(9\) | −0.532177 | −0.177392 | ||||||||
\(10\) | −1.17846 | −0.372662 | ||||||||
\(11\) | 1.10131 | 0.332058 | 0.166029 | − | 0.986121i | \(-0.446905\pi\) | ||||
0.166029 | + | 0.986121i | \(0.446905\pi\) | |||||||
\(12\) | −8.64618 | −2.49594 | ||||||||
\(13\) | −0.711797 | −0.197417 | −0.0987085 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987085 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(14\) | −11.9244 | −3.18692 | ||||||||
\(15\) | −0.675817 | −0.174495 | ||||||||
\(16\) | 15.2847 | 3.82118 | ||||||||
\(17\) | −2.28135 | −0.553310 | −0.276655 | − | 0.960969i | \(-0.589226\pi\) | ||||
−0.276655 | + | 0.960969i | \(0.589226\pi\) | |||||||
\(18\) | 1.45780 | 0.343607 | ||||||||
\(19\) | 6.76417 | 1.55181 | 0.775903 | − | 0.630852i | \(-0.217295\pi\) | ||||
0.775903 | + | 0.630852i | \(0.217295\pi\) | |||||||
\(20\) | 2.36777 | 0.529449 | ||||||||
\(21\) | −6.83834 | −1.49225 | ||||||||
\(22\) | −3.01684 | −0.643193 | ||||||||
\(23\) | −5.24693 | −1.09406 | −0.547030 | − | 0.837113i | \(-0.684242\pi\) | ||||
−0.547030 | + | 0.837113i | \(0.684242\pi\) | |||||||
\(24\) | 15.0781 | 3.07780 | ||||||||
\(25\) | −4.81493 | −0.962985 | ||||||||
\(26\) | 1.94984 | 0.382395 | ||||||||
\(27\) | 5.54880 | 1.06787 | ||||||||
\(28\) | 23.9585 | 4.52774 | ||||||||
\(29\) | 1.04319 | 0.193716 | 0.0968581 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968581 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(30\) | 1.85128 | 0.337996 | ||||||||
\(31\) | −3.38421 | −0.607822 | −0.303911 | − | 0.952700i | \(-0.598293\pi\) | ||||
−0.303911 | + | 0.952700i | \(0.598293\pi\) | |||||||
\(32\) | −22.6734 | −4.00812 | ||||||||
\(33\) | −1.73008 | −0.301169 | ||||||||
\(34\) | 6.24935 | 1.07176 | ||||||||
\(35\) | 1.87269 | 0.316542 | ||||||||
\(36\) | −2.92902 | −0.488171 | ||||||||
\(37\) | 8.44952 | 1.38909 | 0.694546 | − | 0.719448i | \(-0.255605\pi\) | ||||
0.694546 | + | 0.719448i | \(0.255605\pi\) | |||||||
\(38\) | −18.5292 | −3.00583 | ||||||||
\(39\) | 1.11818 | 0.179053 | ||||||||
\(40\) | −4.12915 | −0.652876 | ||||||||
\(41\) | −2.20537 | −0.344421 | −0.172210 | − | 0.985060i | \(-0.555091\pi\) | ||||
−0.172210 | + | 0.985060i | \(0.555091\pi\) | |||||||
\(42\) | 18.7324 | 2.89047 | ||||||||
\(43\) | −9.09917 | −1.38761 | −0.693805 | − | 0.720163i | \(-0.744067\pi\) | ||||
−0.693805 | + | 0.720163i | \(0.744067\pi\) | |||||||
\(44\) | 6.06146 | 0.913799 | ||||||||
\(45\) | −0.228943 | −0.0341289 | ||||||||
\(46\) | 14.3730 | 2.11918 | ||||||||
\(47\) | −1.54488 | −0.225343 | −0.112672 | − | 0.993632i | \(-0.535941\pi\) | ||||
−0.112672 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(48\) | −24.0112 | −3.46572 | ||||||||
\(49\) | 11.9490 | 1.70700 | ||||||||
\(50\) | 13.1896 | 1.86529 | ||||||||
\(51\) | 3.58385 | 0.501839 | ||||||||
\(52\) | −3.91763 | −0.543277 | ||||||||
\(53\) | 4.98410 | 0.684619 | 0.342309 | − | 0.939587i | \(-0.388791\pi\) | ||||
0.342309 | + | 0.939587i | \(0.388791\pi\) | |||||||
\(54\) | −15.1999 | −2.06845 | ||||||||
\(55\) | 0.473786 | 0.0638853 | ||||||||
\(56\) | −41.7813 | −5.58326 | ||||||||
\(57\) | −10.6260 | −1.40745 | ||||||||
\(58\) | −2.85764 | −0.375226 | ||||||||
\(59\) | −0.799511 | −0.104087 | −0.0520437 | − | 0.998645i | \(-0.516574\pi\) | ||||
−0.0520437 | + | 0.998645i | \(0.516574\pi\) | |||||||
\(60\) | −3.71960 | −0.480199 | ||||||||
\(61\) | −4.02412 | −0.515236 | −0.257618 | − | 0.966247i | \(-0.582938\pi\) | ||||
−0.257618 | + | 0.966247i | \(0.582938\pi\) | |||||||
\(62\) | 9.27042 | 1.17734 | ||||||||
\(63\) | −2.31659 | −0.291863 | ||||||||
\(64\) | 31.5400 | 3.94251 | ||||||||
\(65\) | −0.306217 | −0.0379815 | ||||||||
\(66\) | 4.73925 | 0.583361 | ||||||||
\(67\) | −2.34621 | −0.286635 | −0.143317 | − | 0.989677i | \(-0.545777\pi\) | ||||
−0.143317 | + | 0.989677i | \(0.545777\pi\) | |||||||
\(68\) | −12.5562 | −1.52267 | ||||||||
\(69\) | 8.24256 | 0.992287 | ||||||||
\(70\) | −5.12989 | −0.613139 | ||||||||
\(71\) | −9.31516 | −1.10551 | −0.552753 | − | 0.833345i | \(-0.686423\pi\) | ||||
−0.552753 | + | 0.833345i | \(0.686423\pi\) | |||||||
\(72\) | 5.10792 | 0.601974 | ||||||||
\(73\) | −16.5615 | −1.93838 | −0.969190 | − | 0.246316i | \(-0.920780\pi\) | ||||
−0.969190 | + | 0.246316i | \(0.920780\pi\) | |||||||
\(74\) | −23.1459 | −2.69066 | ||||||||
\(75\) | 7.56392 | 0.873406 | ||||||||
\(76\) | 37.2290 | 4.27046 | ||||||||
\(77\) | 4.79406 | 0.546334 | ||||||||
\(78\) | −3.06306 | −0.346823 | ||||||||
\(79\) | −5.02560 | −0.565424 | −0.282712 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282712 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(80\) | 6.57552 | 0.735165 | ||||||||
\(81\) | −7.12026 | −0.791140 | ||||||||
\(82\) | 6.04121 | 0.667140 | ||||||||
\(83\) | −12.4468 | −1.36621 | −0.683107 | − | 0.730319i | \(-0.739372\pi\) | ||||
−0.683107 | + | 0.730319i | \(0.739372\pi\) | |||||||
\(84\) | −37.6372 | −4.10656 | ||||||||
\(85\) | −0.981443 | −0.106452 | ||||||||
\(86\) | 24.9255 | 2.68779 | ||||||||
\(87\) | −1.63879 | −0.175696 | ||||||||
\(88\) | −10.5706 | −1.12683 | ||||||||
\(89\) | −16.3078 | −1.72863 | −0.864314 | − | 0.502953i | \(-0.832247\pi\) | ||||
−0.864314 | + | 0.502953i | \(0.832247\pi\) | |||||||
\(90\) | 0.627149 | 0.0661073 | ||||||||
\(91\) | −3.09849 | −0.324810 | ||||||||
\(92\) | −28.8783 | −3.01077 | ||||||||
\(93\) | 5.31636 | 0.551281 | ||||||||
\(94\) | 4.23190 | 0.436488 | ||||||||
\(95\) | 2.90996 | 0.298555 | ||||||||
\(96\) | 35.6183 | 3.63527 | ||||||||
\(97\) | 8.41742 | 0.854660 | 0.427330 | − | 0.904096i | \(-0.359454\pi\) | ||||
0.427330 | + | 0.904096i | \(0.359454\pi\) | |||||||
\(98\) | −32.7321 | −3.30645 | ||||||||
\(99\) | −0.586092 | −0.0589045 | ||||||||
\(100\) | −26.5007 | −2.65007 | ||||||||
\(101\) | 10.1067 | 1.00565 | 0.502827 | − | 0.864387i | \(-0.332293\pi\) | ||||
0.502827 | + | 0.864387i | \(0.332293\pi\) | |||||||
\(102\) | −9.81730 | −0.972058 | ||||||||
\(103\) | −19.7910 | −1.95006 | −0.975030 | − | 0.222072i | \(-0.928718\pi\) | ||||
−0.975030 | + | 0.222072i | \(0.928718\pi\) | |||||||
\(104\) | 6.83195 | 0.669928 | ||||||||
\(105\) | −2.94187 | −0.287097 | ||||||||
\(106\) | −13.6530 | −1.32610 | ||||||||
\(107\) | −12.9540 | −1.25231 | −0.626154 | − | 0.779699i | \(-0.715372\pi\) | ||||
−0.626154 | + | 0.779699i | \(0.715372\pi\) | |||||||
\(108\) | 30.5398 | 2.93870 | ||||||||
\(109\) | 8.18618 | 0.784093 | 0.392047 | − | 0.919945i | \(-0.371767\pi\) | ||||
0.392047 | + | 0.919945i | \(0.371767\pi\) | |||||||
\(110\) | −1.29785 | −0.123745 | ||||||||
\(111\) | −13.2736 | −1.25988 | ||||||||
\(112\) | 66.5351 | 6.28698 | ||||||||
\(113\) | −2.93722 | −0.276311 | −0.138155 | − | 0.990411i | \(-0.544117\pi\) | ||||
−0.138155 | + | 0.990411i | \(0.544117\pi\) | |||||||
\(114\) | 29.1081 | 2.72622 | ||||||||
\(115\) | −2.25724 | −0.210488 | ||||||||
\(116\) | 5.74159 | 0.533093 | ||||||||
\(117\) | 0.378802 | 0.0350202 | ||||||||
\(118\) | 2.19011 | 0.201616 | ||||||||
\(119\) | −9.93085 | −0.910359 | ||||||||
\(120\) | 6.48661 | 0.592144 | ||||||||
\(121\) | −9.78711 | −0.889738 | ||||||||
\(122\) | 11.0233 | 0.998007 | ||||||||
\(123\) | 3.46448 | 0.312382 | ||||||||
\(124\) | −18.6262 | −1.67268 | ||||||||
\(125\) | −4.22240 | −0.377663 | ||||||||
\(126\) | 6.34587 | 0.565335 | ||||||||
\(127\) | 4.46387 | 0.396105 | 0.198052 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198052 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(128\) | −41.0515 | −3.62847 | ||||||||
\(129\) | 14.2942 | 1.25853 | ||||||||
\(130\) | 0.838824 | 0.0735697 | ||||||||
\(131\) | 11.4012 | 0.996130 | 0.498065 | − | 0.867140i | \(-0.334044\pi\) | ||||
0.498065 | + | 0.867140i | \(0.334044\pi\) | |||||||
\(132\) | −9.52213 | −0.828795 | ||||||||
\(133\) | 29.4447 | 2.55318 | ||||||||
\(134\) | 6.42700 | 0.555209 | ||||||||
\(135\) | 2.38711 | 0.205449 | ||||||||
\(136\) | 21.8968 | 1.87764 | ||||||||
\(137\) | 18.5527 | 1.58506 | 0.792532 | − | 0.609831i | \(-0.208763\pi\) | ||||
0.792532 | + | 0.609831i | \(0.208763\pi\) | |||||||
\(138\) | −22.5790 | −1.92205 | ||||||||
\(139\) | 11.9184 | 1.01090 | 0.505451 | − | 0.862855i | \(-0.331326\pi\) | ||||
0.505451 | + | 0.862855i | \(0.331326\pi\) | |||||||
\(140\) | 10.3070 | 0.871102 | ||||||||
\(141\) | 2.42689 | 0.204381 | ||||||||
\(142\) | 25.5172 | 2.14135 | ||||||||
\(143\) | −0.783910 | −0.0655539 | ||||||||
\(144\) | −8.13417 | −0.677848 | ||||||||
\(145\) | 0.448784 | 0.0372695 | ||||||||
\(146\) | 45.3672 | 3.75462 | ||||||||
\(147\) | −18.7711 | −1.54821 | ||||||||
\(148\) | 46.5049 | 3.82268 | ||||||||
\(149\) | 13.6681 | 1.11973 | 0.559867 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559867 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(150\) | −20.7200 | −1.69178 | ||||||||
\(151\) | 14.2697 | 1.16125 | 0.580626 | − | 0.814171i | \(-0.302808\pi\) | ||||
0.580626 | + | 0.814171i | \(0.302808\pi\) | |||||||
\(152\) | −64.9236 | −5.26600 | ||||||||
\(153\) | 1.21408 | 0.0981528 | ||||||||
\(154\) | −13.1324 | −1.05824 | ||||||||
\(155\) | −1.45589 | −0.116940 | ||||||||
\(156\) | 6.15433 | 0.492740 | ||||||||
\(157\) | −12.4181 | −0.991069 | −0.495534 | − | 0.868588i | \(-0.665028\pi\) | ||||
−0.495534 | + | 0.868588i | \(0.665028\pi\) | |||||||
\(158\) | 13.7667 | 1.09522 | ||||||||
\(159\) | −7.82968 | −0.620934 | ||||||||
\(160\) | −9.75412 | −0.771131 | ||||||||
\(161\) | −22.8401 | −1.80005 | ||||||||
\(162\) | 19.5046 | 1.53243 | ||||||||
\(163\) | −20.3342 | −1.59269 | −0.796347 | − | 0.604840i | \(-0.793237\pi\) | ||||
−0.796347 | + | 0.604840i | \(0.793237\pi\) | |||||||
\(164\) | −12.1380 | −0.947822 | ||||||||
\(165\) | −0.744285 | −0.0579425 | ||||||||
\(166\) | 34.0957 | 2.64634 | ||||||||
\(167\) | 18.0819 | 1.39922 | 0.699611 | − | 0.714524i | \(-0.253357\pi\) | ||||
0.699611 | + | 0.714524i | \(0.253357\pi\) | |||||||
\(168\) | 65.6355 | 5.06389 | ||||||||
\(169\) | −12.4933 | −0.961027 | ||||||||
\(170\) | 2.68848 | 0.206197 | ||||||||
\(171\) | −3.59973 | −0.275278 | ||||||||
\(172\) | −50.0805 | −3.81860 | ||||||||
\(173\) | 2.87626 | 0.218678 | 0.109339 | − | 0.994005i | \(-0.465127\pi\) | ||||
0.109339 | + | 0.994005i | \(0.465127\pi\) | |||||||
\(174\) | 4.48915 | 0.340322 | ||||||||
\(175\) | −20.9596 | −1.58440 | ||||||||
\(176\) | 16.8332 | 1.26885 | ||||||||
\(177\) | 1.25598 | 0.0944050 | ||||||||
\(178\) | 44.6724 | 3.34833 | ||||||||
\(179\) | 2.46145 | 0.183978 | 0.0919889 | − | 0.995760i | \(-0.470678\pi\) | ||||
0.0919889 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(180\) | −1.26007 | −0.0939202 | ||||||||
\(181\) | 16.0714 | 1.19458 | 0.597289 | − | 0.802026i | \(-0.296245\pi\) | ||||
0.597289 | + | 0.802026i | \(0.296245\pi\) | |||||||
\(182\) | 8.48774 | 0.629153 | ||||||||
\(183\) | 6.32162 | 0.467307 | ||||||||
\(184\) | 50.3609 | 3.71265 | ||||||||
\(185\) | 3.63500 | 0.267250 | ||||||||
\(186\) | −14.5632 | −1.06782 | ||||||||
\(187\) | −2.51248 | −0.183731 | ||||||||
\(188\) | −8.50277 | −0.620129 | ||||||||
\(189\) | 24.1542 | 1.75696 | ||||||||
\(190\) | −7.97130 | −0.578299 | ||||||||
\(191\) | −15.0024 | −1.08553 | −0.542767 | − | 0.839884i | \(-0.682623\pi\) | ||||
−0.542767 | + | 0.839884i | \(0.682623\pi\) | |||||||
\(192\) | −49.5472 | −3.57576 | ||||||||
\(193\) | 4.59085 | 0.330457 | 0.165228 | − | 0.986255i | \(-0.447164\pi\) | ||||
0.165228 | + | 0.986255i | \(0.447164\pi\) | |||||||
\(194\) | −23.0580 | −1.65547 | ||||||||
\(195\) | 0.481045 | 0.0344483 | ||||||||
\(196\) | 65.7657 | 4.69755 | ||||||||
\(197\) | −23.8359 | −1.69824 | −0.849119 | − | 0.528201i | \(-0.822867\pi\) | ||||
−0.849119 | + | 0.528201i | \(0.822867\pi\) | |||||||
\(198\) | 1.60549 | 0.114097 | ||||||||
\(199\) | 20.6228 | 1.46191 | 0.730957 | − | 0.682423i | \(-0.239074\pi\) | ||||
0.730957 | + | 0.682423i | \(0.239074\pi\) | |||||||
\(200\) | 46.2145 | 3.26786 | ||||||||
\(201\) | 3.68573 | 0.259971 | ||||||||
\(202\) | −27.6854 | −1.94794 | ||||||||
\(203\) | 4.54107 | 0.318721 | ||||||||
\(204\) | 19.7250 | 1.38103 | ||||||||
\(205\) | −0.948755 | −0.0662639 | ||||||||
\(206\) | 54.2137 | 3.77725 | ||||||||
\(207\) | 2.79229 | 0.194078 | ||||||||
\(208\) | −10.8796 | −0.754366 | ||||||||
\(209\) | 7.44945 | 0.515289 | ||||||||
\(210\) | 8.05870 | 0.556103 | ||||||||
\(211\) | 0.585315 | 0.0402948 | 0.0201474 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201474 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(212\) | 27.4318 | 1.88402 | ||||||||
\(213\) | 14.6335 | 1.00267 | ||||||||
\(214\) | 35.4851 | 2.42571 | ||||||||
\(215\) | −3.91448 | −0.266965 | ||||||||
\(216\) | −53.2584 | −3.62377 | ||||||||
\(217\) | −14.7316 | −1.00005 | ||||||||
\(218\) | −22.4245 | −1.51878 | ||||||||
\(219\) | 26.0170 | 1.75807 | ||||||||
\(220\) | 2.60765 | 0.175808 | ||||||||
\(221\) | 1.62386 | 0.109233 | ||||||||
\(222\) | 36.3606 | 2.44036 | ||||||||
\(223\) | −6.48849 | −0.434502 | −0.217251 | − | 0.976116i | \(-0.569709\pi\) | ||||
−0.217251 | + | 0.976116i | \(0.569709\pi\) | |||||||
\(224\) | −98.6982 | −6.59455 | ||||||||
\(225\) | 2.56239 | 0.170826 | ||||||||
\(226\) | 8.04598 | 0.535211 | ||||||||
\(227\) | 0.510980 | 0.0339149 | 0.0169575 | − | 0.999856i | \(-0.494602\pi\) | ||||
0.0169575 | + | 0.999856i | \(0.494602\pi\) | |||||||
\(228\) | −58.4842 | −3.87321 | ||||||||
\(229\) | 12.0994 | 0.799551 | 0.399776 | − | 0.916613i | \(-0.369088\pi\) | ||||
0.399776 | + | 0.916613i | \(0.369088\pi\) | |||||||
\(230\) | 6.18329 | 0.407714 | ||||||||
\(231\) | −7.53114 | −0.495512 | ||||||||
\(232\) | −10.0128 | −0.657370 | ||||||||
\(233\) | 1.95030 | 0.127768 | 0.0638842 | − | 0.997957i | \(-0.479651\pi\) | ||||
0.0638842 | + | 0.997957i | \(0.479651\pi\) | |||||||
\(234\) | −1.03766 | −0.0678338 | ||||||||
\(235\) | −0.664609 | −0.0433543 | ||||||||
\(236\) | −4.40039 | −0.286441 | ||||||||
\(237\) | 7.89487 | 0.512827 | ||||||||
\(238\) | 27.2037 | 1.76336 | ||||||||
\(239\) | 2.42607 | 0.156930 | 0.0784649 | − | 0.996917i | \(-0.474998\pi\) | ||||
0.0784649 | + | 0.996917i | \(0.474998\pi\) | |||||||
\(240\) | −10.3297 | −0.666778 | ||||||||
\(241\) | −20.4109 | −1.31478 | −0.657392 | − | 0.753549i | \(-0.728340\pi\) | ||||
−0.657392 | + | 0.753549i | \(0.728340\pi\) | |||||||
\(242\) | 26.8100 | 1.72341 | ||||||||
\(243\) | −5.46098 | −0.350322 | ||||||||
\(244\) | −22.1482 | −1.41789 | ||||||||
\(245\) | 5.14049 | 0.328414 | ||||||||
\(246\) | −9.49032 | −0.605081 | ||||||||
\(247\) | −4.81472 | −0.306353 | ||||||||
\(248\) | 32.4822 | 2.06262 | ||||||||
\(249\) | 19.5531 | 1.23912 | ||||||||
\(250\) | 11.5665 | 0.731529 | ||||||||
\(251\) | −5.25827 | −0.331899 | −0.165950 | − | 0.986134i | \(-0.553069\pi\) | ||||
−0.165950 | + | 0.986134i | \(0.553069\pi\) | |||||||
\(252\) | −12.7502 | −0.803186 | ||||||||
\(253\) | −5.77850 | −0.363291 | ||||||||
\(254\) | −12.2280 | −0.767251 | ||||||||
\(255\) | 1.54178 | 0.0965500 | ||||||||
\(256\) | 49.3729 | 3.08581 | ||||||||
\(257\) | 25.7458 | 1.60598 | 0.802988 | − | 0.595995i | \(-0.203242\pi\) | ||||
0.802988 | + | 0.595995i | \(0.203242\pi\) | |||||||
\(258\) | −39.1563 | −2.43776 | ||||||||
\(259\) | 36.7811 | 2.28547 | ||||||||
\(260\) | −1.68537 | −0.104522 | ||||||||
\(261\) | −0.555163 | −0.0343638 | ||||||||
\(262\) | −31.2316 | −1.92949 | ||||||||
\(263\) | 1.28290 | 0.0791073 | 0.0395536 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395536 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(264\) | 16.6056 | 1.02201 | ||||||||
\(265\) | 2.14417 | 0.131715 | ||||||||
\(266\) | −80.6585 | −4.94549 | ||||||||
\(267\) | 25.6185 | 1.56783 | ||||||||
\(268\) | −12.9132 | −0.788798 | ||||||||
\(269\) | −10.2217 | −0.623230 | −0.311615 | − | 0.950209i | \(-0.600870\pi\) | ||||
−0.311615 | + | 0.950209i | \(0.600870\pi\) | |||||||
\(270\) | −6.53904 | −0.397953 | ||||||||
\(271\) | −7.25588 | −0.440763 | −0.220382 | − | 0.975414i | \(-0.570730\pi\) | ||||
−0.220382 | + | 0.975414i | \(0.570730\pi\) | |||||||
\(272\) | −34.8699 | −2.11430 | ||||||||
\(273\) | 4.86751 | 0.294595 | ||||||||
\(274\) | −50.8217 | −3.07025 | ||||||||
\(275\) | −5.30273 | −0.319767 | ||||||||
\(276\) | 45.3658 | 2.73070 | ||||||||
\(277\) | −30.4520 | −1.82969 | −0.914843 | − | 0.403809i | \(-0.867686\pi\) | ||||
−0.914843 | + | 0.403809i | \(0.867686\pi\) | |||||||
\(278\) | −32.6482 | −1.95811 | ||||||||
\(279\) | 1.80100 | 0.107823 | ||||||||
\(280\) | −17.9744 | −1.07418 | ||||||||
\(281\) | −2.75494 | −0.164346 | −0.0821728 | − | 0.996618i | \(-0.526186\pi\) | ||||
−0.0821728 | + | 0.996618i | \(0.526186\pi\) | |||||||
\(282\) | −6.64803 | −0.395884 | ||||||||
\(283\) | 1.32039 | 0.0784889 | 0.0392444 | − | 0.999230i | \(-0.487505\pi\) | ||||
0.0392444 | + | 0.999230i | \(0.487505\pi\) | |||||||
\(284\) | −51.2693 | −3.04227 | ||||||||
\(285\) | −4.57134 | −0.270783 | ||||||||
\(286\) | 2.14738 | 0.126977 | ||||||||
\(287\) | −9.60008 | −0.566675 | ||||||||
\(288\) | 12.0662 | 0.711009 | ||||||||
\(289\) | −11.7954 | −0.693848 | ||||||||
\(290\) | −1.22936 | −0.0721906 | ||||||||
\(291\) | −13.2232 | −0.775157 | ||||||||
\(292\) | −91.1522 | −5.33428 | ||||||||
\(293\) | −3.60676 | −0.210709 | −0.105355 | − | 0.994435i | \(-0.533598\pi\) | ||||
−0.105355 | + | 0.994435i | \(0.533598\pi\) | |||||||
\(294\) | 51.4199 | 2.99887 | ||||||||
\(295\) | −0.343951 | −0.0200256 | ||||||||
\(296\) | −81.0999 | −4.71384 | ||||||||
\(297\) | 6.11096 | 0.354594 | ||||||||
\(298\) | −37.4413 | −2.16891 | ||||||||
\(299\) | 3.73475 | 0.215986 | ||||||||
\(300\) | 41.6307 | 2.40355 | ||||||||
\(301\) | −39.6091 | −2.28303 | ||||||||
\(302\) | −39.0892 | −2.24933 | ||||||||
\(303\) | −15.8769 | −0.912105 | ||||||||
\(304\) | 103.388 | 5.92973 | ||||||||
\(305\) | −1.73119 | −0.0991274 | ||||||||
\(306\) | −3.32576 | −0.190121 | ||||||||
\(307\) | 16.2312 | 0.926361 | 0.463180 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463180 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(308\) | 26.3858 | 1.50347 | ||||||||
\(309\) | 31.0902 | 1.76866 | ||||||||
\(310\) | 3.98815 | 0.226512 | ||||||||
\(311\) | −2.66711 | −0.151238 | −0.0756190 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756190 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(312\) | −10.7325 | −0.607610 | ||||||||
\(313\) | 2.85219 | 0.161215 | 0.0806076 | − | 0.996746i | \(-0.474314\pi\) | ||||
0.0806076 | + | 0.996746i | \(0.474314\pi\) | |||||||
\(314\) | 34.0170 | 1.91969 | ||||||||
\(315\) | −0.996601 | −0.0561521 | ||||||||
\(316\) | −27.6602 | −1.55601 | ||||||||
\(317\) | 14.2887 | 0.802533 | 0.401267 | − | 0.915961i | \(-0.368570\pi\) | ||||
0.401267 | + | 0.915961i | \(0.368570\pi\) | |||||||
\(318\) | 21.4480 | 1.20274 | ||||||||
\(319\) | 1.14888 | 0.0643250 | ||||||||
\(320\) | 13.5686 | 0.758507 | ||||||||
\(321\) | 20.3498 | 1.13582 | ||||||||
\(322\) | 62.5663 | 3.48668 | ||||||||
\(323\) | −15.4315 | −0.858630 | ||||||||
\(324\) | −39.1889 | −2.17716 | ||||||||
\(325\) | 3.42725 | 0.190110 | ||||||||
\(326\) | 55.7017 | 3.08503 | ||||||||
\(327\) | −12.8599 | −0.711155 | ||||||||
\(328\) | 21.1675 | 1.16878 | ||||||||
\(329\) | −6.72492 | −0.370757 | ||||||||
\(330\) | 2.03883 | 0.112234 | ||||||||
\(331\) | −1.20663 | −0.0663224 | −0.0331612 | − | 0.999450i | \(-0.510557\pi\) | ||||
−0.0331612 | + | 0.999450i | \(0.510557\pi\) | |||||||
\(332\) | −68.5054 | −3.75972 | ||||||||
\(333\) | −4.49664 | −0.246414 | ||||||||
\(334\) | −49.5321 | −2.71028 | ||||||||
\(335\) | −1.00934 | −0.0551463 | ||||||||
\(336\) | −104.522 | −5.70215 | ||||||||
\(337\) | 8.43996 | 0.459754 | 0.229877 | − | 0.973220i | \(-0.426168\pi\) | ||||
0.229877 | + | 0.973220i | \(0.426168\pi\) | |||||||
\(338\) | 34.2232 | 1.86150 | ||||||||
\(339\) | 4.61417 | 0.250607 | ||||||||
\(340\) | −5.40172 | −0.292950 | ||||||||
\(341\) | −3.72707 | −0.201832 | ||||||||
\(342\) | 9.86080 | 0.533211 | ||||||||
\(343\) | 21.5433 | 1.16323 | ||||||||
\(344\) | 87.3354 | 4.70881 | ||||||||
\(345\) | 3.54596 | 0.190908 | ||||||||
\(346\) | −7.87899 | −0.423577 | ||||||||
\(347\) | −31.5412 | −1.69322 | −0.846611 | − | 0.532212i | \(-0.821361\pi\) | ||||
−0.846611 | + | 0.532212i | \(0.821361\pi\) | |||||||
\(348\) | −9.01964 | −0.483503 | ||||||||
\(349\) | −17.2006 | −0.920728 | −0.460364 | − | 0.887730i | \(-0.652281\pi\) | ||||
−0.460364 | + | 0.887730i | \(0.652281\pi\) | |||||||
\(350\) | 57.4150 | 3.06896 | ||||||||
\(351\) | −3.94962 | −0.210815 | ||||||||
\(352\) | −24.9704 | −1.33093 | ||||||||
\(353\) | −28.2117 | −1.50156 | −0.750778 | − | 0.660555i | \(-0.770321\pi\) | ||||
−0.750778 | + | 0.660555i | \(0.770321\pi\) | |||||||
\(354\) | −3.44052 | −0.182861 | ||||||||
\(355\) | −4.00740 | −0.212691 | ||||||||
\(356\) | −89.7560 | −4.75706 | ||||||||
\(357\) | 15.6007 | 0.825675 | ||||||||
\(358\) | −6.74270 | −0.356363 | ||||||||
\(359\) | 28.2751 | 1.49230 | 0.746151 | − | 0.665777i | \(-0.231900\pi\) | ||||
0.746151 | + | 0.665777i | \(0.231900\pi\) | |||||||
\(360\) | 2.19744 | 0.115815 | ||||||||
\(361\) | 26.7540 | 1.40810 | ||||||||
\(362\) | −44.0246 | −2.31388 | ||||||||
\(363\) | 15.3749 | 0.806972 | ||||||||
\(364\) | −17.0536 | −0.893853 | ||||||||
\(365\) | −7.12480 | −0.372929 | ||||||||
\(366\) | −17.3169 | −0.905170 | ||||||||
\(367\) | −4.18012 | −0.218201 | −0.109100 | − | 0.994031i | \(-0.534797\pi\) | ||||
−0.109100 | + | 0.994031i | \(0.534797\pi\) | |||||||
\(368\) | −80.1978 | −4.18060 | ||||||||
\(369\) | 1.17365 | 0.0610976 | ||||||||
\(370\) | −9.95741 | −0.517661 | ||||||||
\(371\) | 21.6960 | 1.12640 | ||||||||
\(372\) | 29.2605 | 1.51708 | ||||||||
\(373\) | −9.98754 | −0.517135 | −0.258568 | − | 0.965993i | \(-0.583250\pi\) | ||||
−0.258568 | + | 0.965993i | \(0.583250\pi\) | |||||||
\(374\) | 6.88248 | 0.355885 | ||||||||
\(375\) | 6.63310 | 0.342532 | ||||||||
\(376\) | 14.8280 | 0.764695 | ||||||||
\(377\) | −0.742543 | −0.0382429 | ||||||||
\(378\) | −66.1660 | −3.40321 | ||||||||
\(379\) | −21.0027 | −1.07884 | −0.539419 | − | 0.842037i | \(-0.681356\pi\) | ||||
−0.539419 | + | 0.842037i | \(0.681356\pi\) | |||||||
\(380\) | 16.0160 | 0.821603 | ||||||||
\(381\) | −7.01244 | −0.359258 | ||||||||
\(382\) | 41.0962 | 2.10267 | ||||||||
\(383\) | 2.59558 | 0.132628 | 0.0663141 | − | 0.997799i | \(-0.478876\pi\) | ||||
0.0663141 | + | 0.997799i | \(0.478876\pi\) | |||||||
\(384\) | 64.4890 | 3.29094 | ||||||||
\(385\) | 2.06241 | 0.105110 | ||||||||
\(386\) | −12.5758 | −0.640091 | ||||||||
\(387\) | 4.84237 | 0.246151 | ||||||||
\(388\) | 46.3283 | 2.35196 | ||||||||
\(389\) | 33.3513 | 1.69098 | 0.845488 | − | 0.533994i | \(-0.179310\pi\) | ||||
0.845488 | + | 0.533994i | \(0.179310\pi\) | |||||||
\(390\) | −1.31773 | −0.0667261 | ||||||||
\(391\) | 11.9701 | 0.605354 | ||||||||
\(392\) | −114.689 | −5.79266 | ||||||||
\(393\) | −17.9105 | −0.903468 | ||||||||
\(394\) | 65.2941 | 3.28947 | ||||||||
\(395\) | −2.16202 | −0.108783 | ||||||||
\(396\) | −3.22577 | −0.162101 | ||||||||
\(397\) | 7.55922 | 0.379387 | 0.189693 | − | 0.981843i | \(-0.439251\pi\) | ||||
0.189693 | + | 0.981843i | \(0.439251\pi\) | |||||||
\(398\) | −56.4925 | −2.83171 | ||||||||
\(399\) | −46.2556 | −2.31568 | ||||||||
\(400\) | −73.5948 | −3.67974 | ||||||||
\(401\) | 5.13373 | 0.256366 | 0.128183 | − | 0.991751i | \(-0.459085\pi\) | ||||
0.128183 | + | 0.991751i | \(0.459085\pi\) | |||||||
\(402\) | −10.0964 | −0.503562 | ||||||||
\(403\) | 2.40887 | 0.119994 | ||||||||
\(404\) | 55.6258 | 2.76749 | ||||||||
\(405\) | −3.06315 | −0.152209 | ||||||||
\(406\) | −12.4394 | −0.617359 | ||||||||
\(407\) | 9.30555 | 0.461259 | ||||||||
\(408\) | −34.3984 | −1.70298 | ||||||||
\(409\) | −35.7090 | −1.76570 | −0.882848 | − | 0.469660i | \(-0.844377\pi\) | ||||
−0.882848 | + | 0.469660i | \(0.844377\pi\) | |||||||
\(410\) | 2.59894 | 0.128352 | ||||||||
\(411\) | −29.1450 | −1.43762 | ||||||||
\(412\) | −108.927 | −5.36643 | ||||||||
\(413\) | −3.48031 | −0.171255 | ||||||||
\(414\) | −7.64897 | −0.375926 | ||||||||
\(415\) | −5.35464 | −0.262849 | ||||||||
\(416\) | 16.1388 | 0.791271 | ||||||||
\(417\) | −18.7229 | −0.916865 | ||||||||
\(418\) | −20.4064 | −0.998110 | ||||||||
\(419\) | 1.51590 | 0.0740563 | 0.0370282 | − | 0.999314i | \(-0.488211\pi\) | ||||
0.0370282 | + | 0.999314i | \(0.488211\pi\) | |||||||
\(420\) | −16.1916 | −0.790069 | ||||||||
\(421\) | 18.9741 | 0.924743 | 0.462371 | − | 0.886686i | \(-0.346999\pi\) | ||||
0.462371 | + | 0.886686i | \(0.346999\pi\) | |||||||
\(422\) | −1.60336 | −0.0780505 | ||||||||
\(423\) | 0.822147 | 0.0399741 | ||||||||
\(424\) | −47.8383 | −2.32323 | ||||||||
\(425\) | 10.9846 | 0.532829 | ||||||||
\(426\) | −40.0857 | −1.94216 | ||||||||
\(427\) | −17.5172 | −0.847716 | ||||||||
\(428\) | −71.2968 | −3.44626 | ||||||||
\(429\) | 1.23147 | 0.0594559 | ||||||||
\(430\) | 10.7230 | 0.517109 | ||||||||
\(431\) | −2.71318 | −0.130689 | −0.0653445 | − | 0.997863i | \(-0.520815\pi\) | ||||
−0.0653445 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(432\) | 84.8119 | 4.08052 | ||||||||
\(433\) | 11.9090 | 0.572308 | 0.286154 | − | 0.958184i | \(-0.407623\pi\) | ||||
0.286154 | + | 0.958184i | \(0.407623\pi\) | |||||||
\(434\) | 40.3546 | 1.93708 | ||||||||
\(435\) | −0.705009 | −0.0338026 | ||||||||
\(436\) | 45.0555 | 2.15777 | ||||||||
\(437\) | −35.4911 | −1.69777 | ||||||||
\(438\) | −71.2688 | −3.40536 | ||||||||
\(439\) | −1.35003 | −0.0644336 | −0.0322168 | − | 0.999481i | \(-0.510257\pi\) | ||||
−0.0322168 | + | 0.999481i | \(0.510257\pi\) | |||||||
\(440\) | −4.54748 | −0.216793 | ||||||||
\(441\) | −6.35899 | −0.302809 | ||||||||
\(442\) | −4.44827 | −0.211583 | ||||||||
\(443\) | −31.7093 | −1.50656 | −0.753278 | − | 0.657702i | \(-0.771529\pi\) | ||||
−0.753278 | + | 0.657702i | \(0.771529\pi\) | |||||||
\(444\) | −73.0560 | −3.46709 | ||||||||
\(445\) | −7.01567 | −0.332574 | ||||||||
\(446\) | 17.7740 | 0.841625 | ||||||||
\(447\) | −21.4716 | −1.01557 | ||||||||
\(448\) | 137.295 | 6.48659 | ||||||||
\(449\) | −35.7223 | −1.68584 | −0.842920 | − | 0.538038i | \(-0.819166\pi\) | ||||
−0.842920 | + | 0.538038i | \(0.819166\pi\) | |||||||
\(450\) | −7.01920 | −0.330888 | ||||||||
\(451\) | −2.42880 | −0.114368 | ||||||||
\(452\) | −16.1660 | −0.760387 | ||||||||
\(453\) | −22.4167 | −1.05323 | ||||||||
\(454\) | −1.39974 | −0.0656929 | ||||||||
\(455\) | −1.33298 | −0.0624908 | ||||||||
\(456\) | 101.991 | 4.77614 | ||||||||
\(457\) | 27.6878 | 1.29518 | 0.647591 | − | 0.761988i | \(-0.275776\pi\) | ||||
0.647591 | + | 0.761988i | \(0.275776\pi\) | |||||||
\(458\) | −33.1441 | −1.54872 | ||||||||
\(459\) | −12.6588 | −0.590862 | ||||||||
\(460\) | −12.4235 | −0.579249 | ||||||||
\(461\) | −13.2647 | −0.617800 | −0.308900 | − | 0.951095i | \(-0.599961\pi\) | ||||
−0.308900 | + | 0.951095i | \(0.599961\pi\) | |||||||
\(462\) | 20.6302 | 0.959802 | ||||||||
\(463\) | −36.8778 | −1.71386 | −0.856929 | − | 0.515434i | \(-0.827631\pi\) | ||||
−0.856929 | + | 0.515434i | \(0.827631\pi\) | |||||||
\(464\) | 15.9449 | 0.740225 | ||||||||
\(465\) | 2.28711 | 0.106062 | ||||||||
\(466\) | −5.34249 | −0.247486 | ||||||||
\(467\) | 15.5228 | 0.718311 | 0.359156 | − | 0.933278i | \(-0.383065\pi\) | ||||
0.359156 | + | 0.933278i | \(0.383065\pi\) | |||||||
\(468\) | 2.08487 | 0.0963732 | ||||||||
\(469\) | −10.2131 | −0.471599 | ||||||||
\(470\) | 1.82057 | 0.0839768 | ||||||||
\(471\) | 19.5079 | 0.898877 | ||||||||
\(472\) | 7.67384 | 0.353217 | ||||||||
\(473\) | −10.0210 | −0.460767 | ||||||||
\(474\) | −21.6265 | −0.993340 | ||||||||
\(475\) | −32.5690 | −1.49437 | ||||||||
\(476\) | −54.6579 | −2.50524 | ||||||||
\(477\) | −2.65242 | −0.121446 | ||||||||
\(478\) | −6.64579 | −0.303971 | ||||||||
\(479\) | −13.1582 | −0.601216 | −0.300608 | − | 0.953748i | \(-0.597190\pi\) | ||||
−0.300608 | + | 0.953748i | \(0.597190\pi\) | |||||||
\(480\) | 15.3230 | 0.699398 | ||||||||
\(481\) | −6.01434 | −0.274230 | ||||||||
\(482\) | 55.9120 | 2.54672 | ||||||||
\(483\) | 35.8802 | 1.63261 | ||||||||
\(484\) | −53.8669 | −2.44849 | ||||||||
\(485\) | 3.62119 | 0.164430 | ||||||||
\(486\) | 14.9594 | 0.678570 | ||||||||
\(487\) | 41.1922 | 1.86660 | 0.933298 | − | 0.359104i | \(-0.116918\pi\) | ||||
0.933298 | + | 0.359104i | \(0.116918\pi\) | |||||||
\(488\) | 38.6242 | 1.74844 | ||||||||
\(489\) | 31.9435 | 1.44454 | ||||||||
\(490\) | −14.0814 | −0.636134 | ||||||||
\(491\) | 28.4144 | 1.28232 | 0.641162 | − | 0.767406i | \(-0.278453\pi\) | ||||
0.641162 | + | 0.767406i | \(0.278453\pi\) | |||||||
\(492\) | 19.0680 | 0.859653 | ||||||||
\(493\) | −2.37990 | −0.107185 | ||||||||
\(494\) | 13.1890 | 0.593403 | ||||||||
\(495\) | −0.252138 | −0.0113328 | ||||||||
\(496\) | −51.7267 | −2.32260 | ||||||||
\(497\) | −40.5493 | −1.81889 | ||||||||
\(498\) | −53.5620 | −2.40017 | ||||||||
\(499\) | 21.2498 | 0.951271 | 0.475635 | − | 0.879643i | \(-0.342218\pi\) | ||||
0.475635 | + | 0.879643i | \(0.342218\pi\) | |||||||
\(500\) | −23.2395 | −1.03930 | ||||||||
\(501\) | −28.4055 | −1.26906 | ||||||||
\(502\) | 14.4041 | 0.642885 | ||||||||
\(503\) | 19.0667 | 0.850141 | 0.425070 | − | 0.905160i | \(-0.360249\pi\) | ||||
0.425070 | + | 0.905160i | \(0.360249\pi\) | |||||||
\(504\) | 22.2350 | 0.990427 | ||||||||
\(505\) | 4.34792 | 0.193480 | ||||||||
\(506\) | 15.8291 | 0.703691 | ||||||||
\(507\) | 19.6262 | 0.871629 | ||||||||
\(508\) | 24.5685 | 1.09005 | ||||||||
\(509\) | −25.3309 | −1.12277 | −0.561386 | − | 0.827554i | \(-0.689732\pi\) | ||||
−0.561386 | + | 0.827554i | \(0.689732\pi\) | |||||||
\(510\) | −4.22342 | −0.187016 | ||||||||
\(511\) | −72.0931 | −3.18921 | ||||||||
\(512\) | −53.1451 | −2.34870 | ||||||||
\(513\) | 37.5330 | 1.65712 | ||||||||
\(514\) | −70.5258 | −3.11076 | ||||||||
\(515\) | −8.51411 | −0.375176 | ||||||||
\(516\) | 78.6730 | 3.46339 | ||||||||
\(517\) | −1.70139 | −0.0748270 | ||||||||
\(518\) | −100.755 | −4.42693 | ||||||||
\(519\) | −4.51841 | −0.198336 | ||||||||
\(520\) | 2.93912 | 0.128889 | ||||||||
\(521\) | −9.81039 | −0.429801 | −0.214900 | − | 0.976636i | \(-0.568943\pi\) | ||||
−0.214900 | + | 0.976636i | \(0.568943\pi\) | |||||||
\(522\) | 1.52077 | 0.0665622 | ||||||||
\(523\) | −2.00874 | −0.0878359 | −0.0439180 | − | 0.999035i | \(-0.513984\pi\) | ||||
−0.0439180 | + | 0.999035i | \(0.513984\pi\) | |||||||
\(524\) | 62.7507 | 2.74128 | ||||||||
\(525\) | 32.9261 | 1.43701 | ||||||||
\(526\) | −3.51428 | −0.153230 | ||||||||
\(527\) | 7.72058 | 0.336314 | ||||||||
\(528\) | −26.4438 | −1.15082 | ||||||||
\(529\) | 4.53022 | 0.196966 | ||||||||
\(530\) | −5.87356 | −0.255131 | ||||||||
\(531\) | 0.425481 | 0.0184643 | ||||||||
\(532\) | 162.060 | 7.02618 | ||||||||
\(533\) | 1.56978 | 0.0679946 | ||||||||
\(534\) | −70.1772 | −3.03686 | ||||||||
\(535\) | −5.57283 | −0.240934 | ||||||||
\(536\) | 22.5193 | 0.972685 | ||||||||
\(537\) | −3.86677 | −0.166864 | ||||||||
\(538\) | 28.0005 | 1.20719 | ||||||||
\(539\) | 13.1596 | 0.566824 | ||||||||
\(540\) | 13.1383 | 0.565382 | ||||||||
\(541\) | 2.94807 | 0.126747 | 0.0633737 | − | 0.997990i | \(-0.479814\pi\) | ||||
0.0633737 | + | 0.997990i | \(0.479814\pi\) | |||||||
\(542\) | 19.8761 | 0.853754 | ||||||||
\(543\) | −25.2470 | −1.08345 | ||||||||
\(544\) | 51.7260 | 2.21773 | ||||||||
\(545\) | 3.52171 | 0.150853 | ||||||||
\(546\) | −13.3336 | −0.570627 | ||||||||
\(547\) | 9.87470 | 0.422212 | 0.211106 | − | 0.977463i | \(-0.432294\pi\) | ||||
0.211106 | + | 0.977463i | \(0.432294\pi\) | |||||||
\(548\) | 102.111 | 4.36198 | ||||||||
\(549\) | 2.14154 | 0.0913989 | ||||||||
\(550\) | 14.5259 | 0.619385 | ||||||||
\(551\) | 7.05634 | 0.300610 | ||||||||
\(552\) | −79.1135 | −3.36729 | ||||||||
\(553\) | −21.8767 | −0.930291 | ||||||||
\(554\) | 83.4178 | 3.54408 | ||||||||
\(555\) | −5.71033 | −0.242390 | ||||||||
\(556\) | 65.5969 | 2.78193 | ||||||||
\(557\) | −3.66922 | −0.155470 | −0.0777350 | − | 0.996974i | \(-0.524769\pi\) | ||||
−0.0777350 | + | 0.996974i | \(0.524769\pi\) | |||||||
\(558\) | −4.93350 | −0.208852 | ||||||||
\(559\) | 6.47676 | 0.273938 | ||||||||
\(560\) | 28.6235 | 1.20957 | ||||||||
\(561\) | 3.94694 | 0.166640 | ||||||||
\(562\) | 7.54664 | 0.318336 | ||||||||
\(563\) | 21.0158 | 0.885710 | 0.442855 | − | 0.896593i | \(-0.353966\pi\) | ||||
0.442855 | + | 0.896593i | \(0.353966\pi\) | |||||||
\(564\) | 13.3573 | 0.562443 | ||||||||
\(565\) | −1.26360 | −0.0531600 | ||||||||
\(566\) | −3.61696 | −0.152032 | ||||||||
\(567\) | −30.9948 | −1.30166 | ||||||||
\(568\) | 89.4085 | 3.75150 | ||||||||
\(569\) | 19.4728 | 0.816342 | 0.408171 | − | 0.912905i | \(-0.366167\pi\) | ||||
0.408171 | + | 0.912905i | \(0.366167\pi\) | |||||||
\(570\) | 12.5224 | 0.524504 | ||||||||
\(571\) | −21.6355 | −0.905417 | −0.452709 | − | 0.891658i | \(-0.649542\pi\) | ||||
−0.452709 | + | 0.891658i | \(0.649542\pi\) | |||||||
\(572\) | −4.31453 | −0.180400 | ||||||||
\(573\) | 23.5677 | 0.984554 | ||||||||
\(574\) | 26.2977 | 1.09764 | ||||||||
\(575\) | 25.2636 | 1.05356 | ||||||||
\(576\) | −16.7849 | −0.699370 | ||||||||
\(577\) | −21.7021 | −0.903471 | −0.451736 | − | 0.892152i | \(-0.649195\pi\) | ||||
−0.451736 | + | 0.892152i | \(0.649195\pi\) | |||||||
\(578\) | 32.3114 | 1.34398 | ||||||||
\(579\) | −7.21191 | −0.299717 | ||||||||
\(580\) | 2.47004 | 0.102563 | ||||||||
\(581\) | −54.1815 | −2.24783 | ||||||||
\(582\) | 36.2225 | 1.50147 | ||||||||
\(583\) | 5.48905 | 0.227333 | ||||||||
\(584\) | 158.960 | 6.57782 | ||||||||
\(585\) | 0.162961 | 0.00673762 | ||||||||
\(586\) | 9.88007 | 0.408142 | ||||||||
\(587\) | −16.3050 | −0.672978 | −0.336489 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336489 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(588\) | −103.313 | −4.26057 | ||||||||
\(589\) | −22.8914 | −0.943222 | ||||||||
\(590\) | 0.942191 | 0.0387894 | ||||||||
\(591\) | 37.4446 | 1.54026 | ||||||||
\(592\) | 129.149 | 5.30797 | ||||||||
\(593\) | −40.9852 | −1.68306 | −0.841531 | − | 0.540209i | \(-0.818345\pi\) | ||||
−0.841531 | + | 0.540209i | \(0.818345\pi\) | |||||||
\(594\) | −16.7399 | −0.686845 | ||||||||
\(595\) | −4.27227 | −0.175146 | ||||||||
\(596\) | 75.2273 | 3.08143 | ||||||||
\(597\) | −32.3970 | −1.32592 | ||||||||
\(598\) | −10.2307 | −0.418363 | ||||||||
\(599\) | 2.48186 | 0.101406 | 0.0507031 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507031 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(600\) | −72.5998 | −2.96387 | ||||||||
\(601\) | 15.5682 | 0.635038 | 0.317519 | − | 0.948252i | \(-0.397150\pi\) | ||||
0.317519 | + | 0.948252i | \(0.397150\pi\) | |||||||
\(602\) | 108.502 | 4.42221 | ||||||||
\(603\) | 1.24860 | 0.0508468 | ||||||||
\(604\) | 78.5384 | 3.19568 | ||||||||
\(605\) | −4.21044 | −0.171179 | ||||||||
\(606\) | 43.4919 | 1.76674 | ||||||||
\(607\) | 23.9444 | 0.971872 | 0.485936 | − | 0.873994i | \(-0.338479\pi\) | ||||
0.485936 | + | 0.873994i | \(0.338479\pi\) | |||||||
\(608\) | −153.366 | −6.21983 | ||||||||
\(609\) | −7.13371 | −0.289073 | ||||||||
\(610\) | 4.74227 | 0.192009 | ||||||||
\(611\) | 1.09964 | 0.0444866 | ||||||||
\(612\) | 6.68214 | 0.270110 | ||||||||
\(613\) | −39.7024 | −1.60356 | −0.801782 | − | 0.597617i | \(-0.796114\pi\) | ||||
−0.801782 | + | 0.597617i | \(0.796114\pi\) | |||||||
\(614\) | −44.4623 | −1.79435 | ||||||||
\(615\) | 1.49043 | 0.0600998 | ||||||||
\(616\) | −46.0142 | −1.85397 | ||||||||
\(617\) | 30.3608 | 1.22228 | 0.611140 | − | 0.791522i | \(-0.290711\pi\) | ||||
0.611140 | + | 0.791522i | \(0.290711\pi\) | |||||||
\(618\) | −85.1659 | −3.42588 | ||||||||
\(619\) | 14.7069 | 0.591122 | 0.295561 | − | 0.955324i | \(-0.404493\pi\) | ||||
0.295561 | + | 0.955324i | \(0.404493\pi\) | |||||||
\(620\) | −8.01303 | −0.321811 | ||||||||
\(621\) | −29.1142 | −1.16831 | ||||||||
\(622\) | 7.30607 | 0.292947 | ||||||||
\(623\) | −70.9888 | −2.84411 | ||||||||
\(624\) | 17.0911 | 0.684193 | ||||||||
\(625\) | 22.2581 | 0.890326 | ||||||||
\(626\) | −7.81304 | −0.312272 | ||||||||
\(627\) | −11.7026 | −0.467356 | ||||||||
\(628\) | −68.3472 | −2.72735 | ||||||||
\(629\) | −19.2763 | −0.768598 | ||||||||
\(630\) | 2.73001 | 0.108766 | ||||||||
\(631\) | −29.7467 | −1.18420 | −0.592099 | − | 0.805865i | \(-0.701701\pi\) | ||||
−0.592099 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(632\) | 48.2366 | 1.91875 | ||||||||
\(633\) | −0.919490 | −0.0365464 | ||||||||
\(634\) | −39.1413 | −1.55450 | ||||||||
\(635\) | 1.92037 | 0.0762074 | ||||||||
\(636\) | −43.0934 | −1.70876 | ||||||||
\(637\) | −8.50528 | −0.336991 | ||||||||
\(638\) | −3.14715 | −0.124597 | ||||||||
\(639\) | 4.95731 | 0.196108 | ||||||||
\(640\) | −17.6604 | −0.698090 | ||||||||
\(641\) | −8.06443 | −0.318526 | −0.159263 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159263 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(642\) | −55.7446 | −2.20006 | ||||||||
\(643\) | −50.3749 | −1.98659 | −0.993296 | − | 0.115602i | \(-0.963120\pi\) | ||||
−0.993296 | + | 0.115602i | \(0.963120\pi\) | |||||||
\(644\) | −125.709 | −4.95362 | ||||||||
\(645\) | 6.14938 | 0.242132 | ||||||||
\(646\) | 42.2717 | 1.66316 | ||||||||
\(647\) | −34.2659 | −1.34713 | −0.673566 | − | 0.739127i | \(-0.735238\pi\) | ||||
−0.673566 | + | 0.739127i | \(0.735238\pi\) | |||||||
\(648\) | 68.3415 | 2.68471 | ||||||||
\(649\) | −0.880510 | −0.0345631 | ||||||||
\(650\) | −9.38833 | −0.368240 | ||||||||
\(651\) | 23.1424 | 0.907021 | ||||||||
\(652\) | −111.916 | −4.38298 | ||||||||
\(653\) | −25.1970 | −0.986034 | −0.493017 | − | 0.870020i | \(-0.664106\pi\) | ||||
−0.493017 | + | 0.870020i | \(0.664106\pi\) | |||||||
\(654\) | 35.2274 | 1.37750 | ||||||||
\(655\) | 4.90483 | 0.191648 | ||||||||
\(656\) | −33.7085 | −1.31609 | ||||||||
\(657\) | 8.81365 | 0.343853 | ||||||||
\(658\) | 18.4217 | 0.718152 | ||||||||
\(659\) | 28.9505 | 1.12775 | 0.563875 | − | 0.825860i | \(-0.309310\pi\) | ||||
0.563875 | + | 0.825860i | \(0.309310\pi\) | |||||||
\(660\) | −4.09644 | −0.159454 | ||||||||
\(661\) | 0.913834 | 0.0355440 | 0.0177720 | − | 0.999842i | \(-0.494343\pi\) | ||||
0.0177720 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(662\) | 3.30534 | 0.128466 | ||||||||
\(663\) | −2.55097 | −0.0990717 | ||||||||
\(664\) | 119.467 | 4.63620 | ||||||||
\(665\) | 12.6672 | 0.491212 | ||||||||
\(666\) | 12.3177 | 0.477302 | ||||||||
\(667\) | −5.47356 | −0.211937 | ||||||||
\(668\) | 99.5203 | 3.85056 | ||||||||
\(669\) | 10.1930 | 0.394083 | ||||||||
\(670\) | 2.76491 | 0.106818 | ||||||||
\(671\) | −4.43181 | −0.171088 | ||||||||
\(672\) | 155.048 | 5.98111 | ||||||||
\(673\) | 12.9334 | 0.498548 | 0.249274 | − | 0.968433i | \(-0.419808\pi\) | ||||
0.249274 | + | 0.968433i | \(0.419808\pi\) | |||||||
\(674\) | −23.1197 | −0.890538 | ||||||||
\(675\) | −26.7171 | −1.02834 | ||||||||
\(676\) | −68.7616 | −2.64468 | ||||||||
\(677\) | −43.8551 | −1.68549 | −0.842745 | − | 0.538313i | \(-0.819062\pi\) | ||||
−0.842745 | + | 0.538313i | \(0.819062\pi\) | |||||||
\(678\) | −12.6397 | −0.485424 | ||||||||
\(679\) | 36.6414 | 1.40617 | ||||||||
\(680\) | 9.42006 | 0.361243 | ||||||||
\(681\) | −0.802714 | −0.0307601 | ||||||||
\(682\) | 10.2096 | 0.390947 | ||||||||
\(683\) | −40.7262 | −1.55834 | −0.779172 | − | 0.626811i | \(-0.784360\pi\) | ||||
−0.779172 | + | 0.626811i | \(0.784360\pi\) | |||||||
\(684\) | −19.8124 | −0.757546 | ||||||||
\(685\) | 7.98140 | 0.304954 | ||||||||
\(686\) | −59.0140 | −2.25316 | ||||||||
\(687\) | −19.0073 | −0.725175 | ||||||||
\(688\) | −139.078 | −5.30231 | ||||||||
\(689\) | −3.54767 | −0.135155 | ||||||||
\(690\) | −9.71352 | −0.369787 | ||||||||
\(691\) | 17.8614 | 0.679479 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(692\) | 15.8305 | 0.601786 | ||||||||
\(693\) | −2.55129 | −0.0969154 | ||||||||
\(694\) | 86.4014 | 3.27975 | ||||||||
\(695\) | 5.12730 | 0.194490 | ||||||||
\(696\) | 15.7293 | 0.596219 | ||||||||
\(697\) | 5.03123 | 0.190572 | ||||||||
\(698\) | 47.1179 | 1.78344 | ||||||||
\(699\) | −3.06379 | −0.115883 | ||||||||
\(700\) | −115.359 | −4.36015 | ||||||||
\(701\) | −6.57618 | −0.248379 | −0.124189 | − | 0.992259i | \(-0.539633\pi\) | ||||
−0.124189 | + | 0.992259i | \(0.539633\pi\) | |||||||
\(702\) | 10.8193 | 0.408347 | ||||||||
\(703\) | 57.1540 | 2.15560 | ||||||||
\(704\) | 34.7354 | 1.30914 | ||||||||
\(705\) | 1.04405 | 0.0393213 | ||||||||
\(706\) | 77.2807 | 2.90850 | ||||||||
\(707\) | 43.9949 | 1.65460 | ||||||||
\(708\) | 6.91271 | 0.259796 | ||||||||
\(709\) | −45.7366 | −1.71767 | −0.858836 | − | 0.512250i | \(-0.828812\pi\) | ||||
−0.858836 | + | 0.512250i | \(0.828812\pi\) | |||||||
\(710\) | 10.9775 | 0.411980 | ||||||||
\(711\) | 2.67451 | 0.100302 | ||||||||
\(712\) | 156.526 | 5.86604 | ||||||||
\(713\) | 17.7567 | 0.664993 | ||||||||
\(714\) | −42.7352 | −1.59932 | ||||||||
\(715\) | −0.337240 | −0.0126121 | ||||||||
\(716\) | 13.5475 | 0.506294 | ||||||||
\(717\) | −3.81120 | −0.142332 | ||||||||
\(718\) | −77.4544 | −2.89057 | ||||||||
\(719\) | 44.5029 | 1.65968 | 0.829839 | − | 0.558002i | \(-0.188432\pi\) | ||||
0.829839 | + | 0.558002i | \(0.188432\pi\) | |||||||
\(720\) | −3.49934 | −0.130413 | ||||||||
\(721\) | −86.1509 | −3.20843 | ||||||||
\(722\) | −73.2876 | −2.72748 | ||||||||
\(723\) | 32.0642 | 1.19248 | ||||||||
\(724\) | 88.4546 | 3.28739 | ||||||||
\(725\) | −5.02290 | −0.186546 | ||||||||
\(726\) | −42.1167 | −1.56310 | ||||||||
\(727\) | −21.1327 | −0.783767 | −0.391884 | − | 0.920015i | \(-0.628176\pi\) | ||||
−0.391884 | + | 0.920015i | \(0.628176\pi\) | |||||||
\(728\) | 29.7398 | 1.10223 | ||||||||
\(729\) | 29.9396 | 1.10887 | ||||||||
\(730\) | 19.5171 | 0.722359 | ||||||||
\(731\) | 20.7584 | 0.767779 | ||||||||
\(732\) | 34.7933 | 1.28600 | ||||||||
\(733\) | 31.1435 | 1.15031 | 0.575156 | − | 0.818044i | \(-0.304941\pi\) | ||||
0.575156 | + | 0.818044i | \(0.304941\pi\) | |||||||
\(734\) | 11.4507 | 0.422652 | ||||||||
\(735\) | −8.07536 | −0.297864 | ||||||||
\(736\) | 118.965 | 4.38512 | ||||||||
\(737\) | −2.58390 | −0.0951793 | ||||||||
\(738\) | −3.21499 | −0.118345 | ||||||||
\(739\) | −28.1585 | −1.03583 | −0.517914 | − | 0.855433i | \(-0.673291\pi\) | ||||
−0.517914 | + | 0.855433i | \(0.673291\pi\) | |||||||
\(740\) | 20.0065 | 0.735454 | ||||||||
\(741\) | 7.56358 | 0.277855 | ||||||||
\(742\) | −59.4323 | −2.18183 | ||||||||
\(743\) | −32.2826 | −1.18433 | −0.592167 | − | 0.805815i | \(-0.701727\pi\) | ||||
−0.592167 | + | 0.805815i | \(0.701727\pi\) | |||||||
\(744\) | −51.0273 | −1.87075 | ||||||||
\(745\) | 5.88004 | 0.215428 | ||||||||
\(746\) | 27.3590 | 1.00169 | ||||||||
\(747\) | 6.62389 | 0.242356 | ||||||||
\(748\) | −13.8283 | −0.505614 | ||||||||
\(749\) | −56.3893 | −2.06042 | ||||||||
\(750\) | −18.1702 | −0.663480 | ||||||||
\(751\) | 49.4263 | 1.80359 | 0.901795 | − | 0.432164i | \(-0.142250\pi\) | ||||
0.901795 | + | 0.432164i | \(0.142250\pi\) | |||||||
\(752\) | −23.6130 | −0.861077 | ||||||||
\(753\) | 8.26038 | 0.301025 | ||||||||
\(754\) | 2.03406 | 0.0740761 | ||||||||
\(755\) | 6.13885 | 0.223416 | ||||||||
\(756\) | 132.941 | 4.83503 | ||||||||
\(757\) | −17.2618 | −0.627390 | −0.313695 | − | 0.949524i | \(-0.601567\pi\) | ||||
−0.313695 | + | 0.949524i | \(0.601567\pi\) | |||||||
\(758\) | 57.5331 | 2.08970 | ||||||||
\(759\) | 9.07762 | 0.329497 | ||||||||
\(760\) | −27.9303 | −1.01314 | ||||||||
\(761\) | −0.784523 | −0.0284389 | −0.0142195 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142195 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(762\) | 19.2093 | 0.695879 | ||||||||
\(763\) | 35.6348 | 1.29007 | ||||||||
\(764\) | −82.5709 | −2.98731 | ||||||||
\(765\) | 0.522301 | 0.0188838 | ||||||||
\(766\) | −7.11013 | −0.256899 | ||||||||
\(767\) | 0.569090 | 0.0205486 | ||||||||
\(768\) | −77.5614 | −2.79876 | ||||||||
\(769\) | −25.1028 | −0.905231 | −0.452616 | − | 0.891706i | \(-0.649509\pi\) | ||||
−0.452616 | + | 0.891706i | \(0.649509\pi\) | |||||||
\(770\) | −5.64961 | −0.203598 | ||||||||
\(771\) | −40.4448 | −1.45658 | ||||||||
\(772\) | 25.2674 | 0.909393 | ||||||||
\(773\) | 11.6787 | 0.420055 | 0.210028 | − | 0.977695i | \(-0.432645\pi\) | ||||
0.210028 | + | 0.977695i | \(0.432645\pi\) | |||||||
\(774\) | −13.2648 | −0.476792 | ||||||||
\(775\) | 16.2947 | 0.585324 | ||||||||
\(776\) | −80.7919 | −2.90026 | ||||||||
\(777\) | −57.7806 | −2.07287 | ||||||||
\(778\) | −91.3597 | −3.27540 | ||||||||
\(779\) | −14.9175 | −0.534475 | ||||||||
\(780\) | 2.64760 | 0.0947994 | ||||||||
\(781\) | −10.2589 | −0.367092 | ||||||||
\(782\) | −32.7899 | −1.17256 | ||||||||
\(783\) | 5.78848 | 0.206863 | ||||||||
\(784\) | 182.637 | 6.52277 | ||||||||
\(785\) | −5.34227 | −0.190674 | ||||||||
\(786\) | 49.0627 | 1.75001 | ||||||||
\(787\) | 3.90646 | 0.139250 | 0.0696251 | − | 0.997573i | \(-0.477820\pi\) | ||||
0.0696251 | + | 0.997573i | \(0.477820\pi\) | |||||||
\(788\) | −131.189 | −4.67343 | ||||||||
\(789\) | −2.01535 | −0.0717485 | ||||||||
\(790\) | 5.92246 | 0.210712 | ||||||||
\(791\) | −12.7859 | −0.454613 | ||||||||
\(792\) | 5.62541 | 0.199890 | ||||||||
\(793\) | 2.86436 | 0.101716 | ||||||||
\(794\) | −20.7071 | −0.734868 | ||||||||
\(795\) | −3.36834 | −0.119463 | ||||||||
\(796\) | 113.505 | 4.02308 | ||||||||
\(797\) | 9.40642 | 0.333193 | 0.166596 | − | 0.986025i | \(-0.446722\pi\) | ||||
0.166596 | + | 0.986025i | \(0.446722\pi\) | |||||||
\(798\) | 126.709 | 4.48545 | ||||||||
\(799\) | 3.52441 | 0.124685 | ||||||||
\(800\) | 109.171 | 3.85976 | ||||||||
\(801\) | 8.67865 | 0.306645 | ||||||||
\(802\) | −14.0629 | −0.496578 | ||||||||
\(803\) | −18.2394 | −0.643654 | ||||||||
\(804\) | 20.2857 | 0.715422 | ||||||||
\(805\) | −9.82586 | −0.346316 | ||||||||
\(806\) | −6.59866 | −0.232428 | ||||||||
\(807\) | 16.0576 | 0.565255 | ||||||||
\(808\) | −97.0058 | −3.41265 | ||||||||
\(809\) | −39.5379 | −1.39008 | −0.695039 | − | 0.718972i | \(-0.744613\pi\) | ||||
−0.695039 | + | 0.718972i | \(0.744613\pi\) | |||||||
\(810\) | 8.39094 | 0.294827 | ||||||||
\(811\) | −33.9718 | −1.19291 | −0.596455 | − | 0.802647i | \(-0.703425\pi\) | ||||
−0.596455 | + | 0.802647i | \(0.703425\pi\) | |||||||
\(812\) | 24.9934 | 0.877097 | ||||||||
\(813\) | 11.3985 | 0.399762 | ||||||||
\(814\) | −25.4908 | −0.893454 | ||||||||
\(815\) | −8.74779 | −0.306422 | ||||||||
\(816\) | 54.7782 | 1.91762 | ||||||||
\(817\) | −61.5483 | −2.15330 | ||||||||
\(818\) | 97.8182 | 3.42013 | ||||||||
\(819\) | 1.64894 | 0.0576187 | ||||||||
\(820\) | −5.22181 | −0.182353 | ||||||||
\(821\) | 4.80849 | 0.167818 | 0.0839088 | − | 0.996473i | \(-0.473260\pi\) | ||||
0.0839088 | + | 0.996473i | \(0.473260\pi\) | |||||||
\(822\) | 79.8374 | 2.78465 | ||||||||
\(823\) | −10.5173 | −0.366609 | −0.183305 | − | 0.983056i | \(-0.558679\pi\) | ||||
−0.183305 | + | 0.983056i | \(0.558679\pi\) | |||||||
\(824\) | 189.957 | 6.61746 | ||||||||
\(825\) | 8.33023 | 0.290021 | ||||||||
\(826\) | 9.53367 | 0.331719 | ||||||||
\(827\) | 46.3473 | 1.61165 | 0.805827 | − | 0.592151i | \(-0.201721\pi\) | ||||
0.805827 | + | 0.592151i | \(0.201721\pi\) | |||||||
\(828\) | 15.3684 | 0.534088 | ||||||||
\(829\) | 4.41143 | 0.153215 | 0.0766076 | − | 0.997061i | \(-0.475591\pi\) | ||||
0.0766076 | + | 0.997061i | \(0.475591\pi\) | |||||||
\(830\) | 14.6680 | 0.509135 | ||||||||
\(831\) | 47.8381 | 1.65948 | ||||||||
\(832\) | −22.4501 | −0.778318 | ||||||||
\(833\) | −27.2600 | −0.944501 | ||||||||
\(834\) | 51.2880 | 1.77596 | ||||||||
\(835\) | 7.77888 | 0.269199 | ||||||||
\(836\) | 41.0007 | 1.41804 | ||||||||
\(837\) | −18.7783 | −0.649074 | ||||||||
\(838\) | −4.15252 | −0.143446 | ||||||||
\(839\) | 13.7760 | 0.475600 | 0.237800 | − | 0.971314i | \(-0.423574\pi\) | ||||
0.237800 | + | 0.971314i | \(0.423574\pi\) | |||||||
\(840\) | 28.2365 | 0.974253 | ||||||||
\(841\) | −27.9117 | −0.962474 | ||||||||
\(842\) | −51.9762 | −1.79122 | ||||||||
\(843\) | 4.32781 | 0.149058 | ||||||||
\(844\) | 3.22149 | 0.110888 | ||||||||
\(845\) | −5.37466 | −0.184894 | ||||||||
\(846\) | −2.25212 | −0.0774295 | ||||||||
\(847\) | −42.6038 | −1.46388 | ||||||||
\(848\) | 76.1806 | 2.61605 | ||||||||
\(849\) | −2.07424 | −0.0711876 | ||||||||
\(850\) | −30.0902 | −1.03208 | ||||||||
\(851\) | −44.3340 | −1.51975 | ||||||||
\(852\) | 80.5405 | 2.75927 | ||||||||
\(853\) | 26.3565 | 0.902430 | 0.451215 | − | 0.892415i | \(-0.350991\pi\) | ||||
0.451215 | + | 0.892415i | \(0.350991\pi\) | |||||||
\(854\) | 47.9851 | 1.64202 | ||||||||
\(855\) | −1.54861 | −0.0529614 | ||||||||
\(856\) | 124.335 | 4.24967 | ||||||||
\(857\) | −34.8146 | −1.18924 | −0.594622 | − | 0.804005i | \(-0.702698\pi\) | ||||
−0.594622 | + | 0.804005i | \(0.702698\pi\) | |||||||
\(858\) | −3.37338 | −0.115165 | ||||||||
\(859\) | 37.7334 | 1.28745 | 0.643724 | − | 0.765258i | \(-0.277389\pi\) | ||||
0.643724 | + | 0.765258i | \(0.277389\pi\) | |||||||
\(860\) | −21.5447 | −0.734670 | ||||||||
\(861\) | 15.0811 | 0.513961 | ||||||||
\(862\) | 7.43225 | 0.253143 | ||||||||
\(863\) | −52.3045 | −1.78047 | −0.890233 | − | 0.455505i | \(-0.849459\pi\) | ||||
−0.890233 | + | 0.455505i | \(0.849459\pi\) | |||||||
\(864\) | −125.810 | −4.28014 | ||||||||
\(865\) | 1.23737 | 0.0420719 | ||||||||
\(866\) | −32.6224 | −1.10856 | ||||||||
\(867\) | 18.5298 | 0.629305 | ||||||||
\(868\) | −81.0807 | −2.75206 | ||||||||
\(869\) | −5.53475 | −0.187753 | ||||||||
\(870\) | 1.93124 | 0.0654752 | ||||||||
\(871\) | 1.67002 | 0.0565866 | ||||||||
\(872\) | −78.5723 | −2.66079 | ||||||||
\(873\) | −4.47956 | −0.151610 | ||||||||
\(874\) | 97.2213 | 3.28856 | ||||||||
\(875\) | −18.3803 | −0.621368 | ||||||||
\(876\) | 143.194 | 4.83807 | ||||||||
\(877\) | −43.4308 | −1.46655 | −0.733277 | − | 0.679930i | \(-0.762010\pi\) | ||||
−0.733277 | + | 0.679930i | \(0.762010\pi\) | |||||||
\(878\) | 3.69817 | 0.124807 | ||||||||
\(879\) | 5.66598 | 0.191109 | ||||||||
\(880\) | 7.24169 | 0.244117 | ||||||||
\(881\) | −3.53318 | −0.119036 | −0.0595179 | − | 0.998227i | \(-0.518956\pi\) | ||||
−0.0595179 | + | 0.998227i | \(0.518956\pi\) | |||||||
\(882\) | 17.4193 | 0.586538 | ||||||||
\(883\) | −8.76642 | −0.295013 | −0.147507 | − | 0.989061i | \(-0.547125\pi\) | ||||
−0.147507 | + | 0.989061i | \(0.547125\pi\) | |||||||
\(884\) | 8.93750 | 0.300601 | ||||||||
\(885\) | 0.540324 | 0.0181628 | ||||||||
\(886\) | 86.8619 | 2.91818 | ||||||||
\(887\) | 10.7201 | 0.359945 | 0.179972 | − | 0.983672i | \(-0.442399\pi\) | ||||
0.179972 | + | 0.983672i | \(0.442399\pi\) | |||||||
\(888\) | 127.402 | 4.27534 | ||||||||
\(889\) | 19.4314 | 0.651710 | ||||||||
\(890\) | 19.2181 | 0.644193 | ||||||||
\(891\) | −7.84162 | −0.262704 | ||||||||
\(892\) | −35.7117 | −1.19572 | ||||||||
\(893\) | −10.4498 | −0.349689 | ||||||||
\(894\) | 58.8176 | 1.96716 | ||||||||
\(895\) | 1.05892 | 0.0353959 | ||||||||
\(896\) | −178.699 | −5.96991 | ||||||||
\(897\) | −5.86703 | −0.195894 | ||||||||
\(898\) | 97.8548 | 3.26546 | ||||||||
\(899\) | −3.53039 | −0.117745 | ||||||||
\(900\) | 14.1030 | 0.470101 | ||||||||
\(901\) | −11.3705 | −0.378806 | ||||||||
\(902\) | 6.65325 | 0.221529 | ||||||||
\(903\) | 62.2232 | 2.07066 | ||||||||
\(904\) | 28.1920 | 0.937651 | ||||||||
\(905\) | 6.91395 | 0.229827 | ||||||||
\(906\) | 61.4065 | 2.04009 | ||||||||
\(907\) | −4.66312 | −0.154836 | −0.0774182 | − | 0.996999i | \(-0.524668\pi\) | ||||
−0.0774182 | + | 0.996999i | \(0.524668\pi\) | |||||||
\(908\) | 2.81236 | 0.0933315 | ||||||||
\(909\) | −5.37854 | −0.178395 | ||||||||
\(910\) | 3.65144 | 0.121044 | ||||||||
\(911\) | 9.20159 | 0.304862 | 0.152431 | − | 0.988314i | \(-0.451290\pi\) | ||||
0.152431 | + | 0.988314i | \(0.451290\pi\) | |||||||
\(912\) | −162.416 | −5.37813 | ||||||||
\(913\) | −13.7078 | −0.453662 | ||||||||
\(914\) | −75.8458 | −2.50876 | ||||||||
\(915\) | 2.71957 | 0.0899063 | ||||||||
\(916\) | 66.5934 | 2.20031 | ||||||||
\(917\) | 49.6301 | 1.63893 | ||||||||
\(918\) | 34.6764 | 1.14449 | ||||||||
\(919\) | 23.8796 | 0.787715 | 0.393857 | − | 0.919172i | \(-0.371140\pi\) | ||||
0.393857 | + | 0.919172i | \(0.371140\pi\) | |||||||
\(920\) | 21.6654 | 0.714286 | ||||||||
\(921\) | −25.4980 | −0.840188 | ||||||||
\(922\) | 36.3363 | 1.19667 | ||||||||
\(923\) | 6.63051 | 0.218246 | ||||||||
\(924\) | −41.4503 | −1.36361 | ||||||||
\(925\) | −40.6838 | −1.33768 | ||||||||
\(926\) | 101.020 | 3.31973 | ||||||||
\(927\) | 10.5323 | 0.345925 | ||||||||
\(928\) | −23.6527 | −0.776438 | ||||||||
\(929\) | 22.7646 | 0.746881 | 0.373441 | − | 0.927654i | \(-0.378178\pi\) | ||||
0.373441 | + | 0.927654i | \(0.378178\pi\) | |||||||
\(930\) | −6.26511 | −0.205441 | ||||||||
\(931\) | 80.8252 | 2.64894 | ||||||||
\(932\) | 10.7342 | 0.351609 | ||||||||
\(933\) | 4.18985 | 0.137170 | ||||||||
\(934\) | −42.5220 | −1.39136 | ||||||||
\(935\) | −1.08087 | −0.0353484 | ||||||||
\(936\) | −3.63581 | −0.118840 | ||||||||
\(937\) | −5.94358 | −0.194168 | −0.0970842 | − | 0.995276i | \(-0.530952\pi\) | ||||
−0.0970842 | + | 0.995276i | \(0.530952\pi\) | |||||||
\(938\) | 27.9770 | 0.913483 | ||||||||
\(939\) | −4.48059 | −0.146218 | ||||||||
\(940\) | −3.65791 | −0.119308 | ||||||||
\(941\) | 51.8602 | 1.69060 | 0.845298 | − | 0.534296i | \(-0.179423\pi\) | ||||
0.845298 | + | 0.534296i | \(0.179423\pi\) | |||||||
\(942\) | −53.4383 | −1.74111 | ||||||||
\(943\) | 11.5714 | 0.376817 | ||||||||
\(944\) | −12.2203 | −0.397737 | ||||||||
\(945\) | 10.3912 | 0.338025 | ||||||||
\(946\) | 27.4507 | 0.892501 | ||||||||
\(947\) | 12.6954 | 0.412545 | 0.206272 | − | 0.978495i | \(-0.433867\pi\) | ||||
0.206272 | + | 0.978495i | \(0.433867\pi\) | |||||||
\(948\) | 43.4522 | 1.41126 | ||||||||
\(949\) | 11.7884 | 0.382669 | ||||||||
\(950\) | 89.2167 | 2.89457 | ||||||||
\(951\) | −22.4466 | −0.727879 | ||||||||
\(952\) | 95.3180 | 3.08927 | ||||||||
\(953\) | 5.42171 | 0.175626 | 0.0878132 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878132 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(954\) | 7.26582 | 0.235240 | ||||||||
\(955\) | −6.45405 | −0.208848 | ||||||||
\(956\) | 13.3528 | 0.431859 | ||||||||
\(957\) | −1.80481 | −0.0583413 | ||||||||
\(958\) | 36.0446 | 1.16455 | ||||||||
\(959\) | 80.7607 | 2.60790 | ||||||||
\(960\) | −21.3153 | −0.687949 | ||||||||
\(961\) | −19.5471 | −0.630552 | ||||||||
\(962\) | 16.4752 | 0.531182 | ||||||||
\(963\) | 6.89380 | 0.222150 | ||||||||
\(964\) | −112.339 | −3.61819 | ||||||||
\(965\) | 1.97499 | 0.0635773 | ||||||||
\(966\) | −98.2873 | −3.16234 | ||||||||
\(967\) | 24.0998 | 0.774997 | 0.387499 | − | 0.921870i | \(-0.373339\pi\) | ||||
0.387499 | + | 0.921870i | \(0.373339\pi\) | |||||||
\(968\) | 93.9384 | 3.01929 | ||||||||
\(969\) | 24.2418 | 0.778758 | ||||||||
\(970\) | −9.91959 | −0.318499 | ||||||||
\(971\) | 9.18241 | 0.294677 | 0.147339 | − | 0.989086i | \(-0.452929\pi\) | ||||
0.147339 | + | 0.989086i | \(0.452929\pi\) | |||||||
\(972\) | −30.0565 | −0.964061 | ||||||||
\(973\) | 51.8812 | 1.66323 | ||||||||
\(974\) | −112.838 | −3.61558 | ||||||||
\(975\) | −5.38397 | −0.172425 | ||||||||
\(976\) | −61.5076 | −1.96881 | ||||||||
\(977\) | −25.4682 | −0.814799 | −0.407399 | − | 0.913250i | \(-0.633564\pi\) | ||||
−0.407399 | + | 0.913250i | \(0.633564\pi\) | |||||||
\(978\) | −87.5035 | −2.79805 | ||||||||
\(979\) | −17.9600 | −0.574005 | ||||||||
\(980\) | 28.2925 | 0.903772 | ||||||||
\(981\) | −4.35649 | −0.139092 | ||||||||
\(982\) | −77.8360 | −2.48385 | ||||||||
\(983\) | −40.2857 | −1.28492 | −0.642458 | − | 0.766321i | \(-0.722085\pi\) | ||||
−0.642458 | + | 0.766321i | \(0.722085\pi\) | |||||||
\(984\) | −33.2527 | −1.06006 | ||||||||
\(985\) | −10.2543 | −0.326728 | ||||||||
\(986\) | 6.51929 | 0.207616 | ||||||||
\(987\) | 10.5644 | 0.336268 | ||||||||
\(988\) | −26.4995 | −0.843061 | ||||||||
\(989\) | 47.7427 | 1.51813 | ||||||||
\(990\) | 0.690686 | 0.0219514 | ||||||||
\(991\) | 10.8526 | 0.344745 | 0.172372 | − | 0.985032i | \(-0.444857\pi\) | ||||
0.172372 | + | 0.985032i | \(0.444857\pi\) | |||||||
\(992\) | 76.7314 | 2.43622 | ||||||||
\(993\) | 1.89553 | 0.0601529 | ||||||||
\(994\) | 111.077 | 3.52316 | ||||||||
\(995\) | 8.87198 | 0.281261 | ||||||||
\(996\) | 107.617 | 3.40998 | ||||||||
\(997\) | −22.4709 | −0.711660 | −0.355830 | − | 0.934551i | \(-0.615802\pi\) | ||||
−0.355830 | + | 0.934551i | \(0.615802\pi\) | |||||||
\(998\) | −58.2099 | −1.84260 | ||||||||
\(999\) | 46.8847 | 1.48337 |
(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 | 4027.2.a.b.1.3 | ✓ | 159 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.b.1.3 | ✓ | 159 | 1.1 | even | 1 | trivial |