Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48734 | −1.75882 | −0.879408 | − | 0.476069i | \(-0.842061\pi\) | ||||
−0.879408 | + | 0.476069i | \(0.842061\pi\) | |||||||
\(3\) | −0.305991 | −0.176664 | −0.0883319 | − | 0.996091i | \(-0.528154\pi\) | ||||
−0.0883319 | + | 0.996091i | \(0.528154\pi\) | |||||||
\(4\) | 4.18686 | 2.09343 | ||||||||
\(5\) | −0.333485 | −0.149139 | −0.0745695 | − | 0.997216i | \(-0.523758\pi\) | ||||
−0.0745695 | + | 0.997216i | \(0.523758\pi\) | |||||||
\(6\) | 0.761103 | 0.310719 | ||||||||
\(7\) | 2.33440 | 0.882319 | 0.441159 | − | 0.897429i | \(-0.354567\pi\) | ||||
0.441159 | + | 0.897429i | \(0.354567\pi\) | |||||||
\(8\) | −5.43948 | −1.92315 | ||||||||
\(9\) | −2.90637 | −0.968790 | ||||||||
\(10\) | 0.829491 | 0.262308 | ||||||||
\(11\) | 5.64108 | 1.70085 | 0.850425 | − | 0.526097i | \(-0.176345\pi\) | ||||
0.850425 | + | 0.526097i | \(0.176345\pi\) | |||||||
\(12\) | −1.28114 | −0.369834 | ||||||||
\(13\) | −5.88144 | −1.63122 | −0.815610 | − | 0.578603i | \(-0.803598\pi\) | ||||
−0.815610 | + | 0.578603i | \(0.803598\pi\) | |||||||
\(14\) | −5.80644 | −1.55184 | ||||||||
\(15\) | 0.102043 | 0.0263475 | ||||||||
\(16\) | 5.15610 | 1.28903 | ||||||||
\(17\) | −4.23276 | −1.02660 | −0.513298 | − | 0.858210i | \(-0.671576\pi\) | ||||
−0.513298 | + | 0.858210i | \(0.671576\pi\) | |||||||
\(18\) | 7.22913 | 1.70392 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.39626 | −0.312212 | ||||||||
\(21\) | −0.714303 | −0.155874 | ||||||||
\(22\) | −14.0313 | −2.99148 | ||||||||
\(23\) | −5.07913 | −1.05907 | −0.529536 | − | 0.848288i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848288i | \(0.677634\pi\) | |||||||
\(24\) | 1.66443 | 0.339750 | ||||||||
\(25\) | −4.88879 | −0.977758 | ||||||||
\(26\) | 14.6292 | 2.86901 | ||||||||
\(27\) | 1.80729 | 0.347814 | ||||||||
\(28\) | 9.77380 | 1.84707 | ||||||||
\(29\) | 3.03815 | 0.564171 | 0.282085 | − | 0.959389i | \(-0.408974\pi\) | ||||
0.282085 | + | 0.959389i | \(0.408974\pi\) | |||||||
\(30\) | −0.253816 | −0.0463403 | ||||||||
\(31\) | 5.90976 | 1.06142 | 0.530712 | − | 0.847552i | \(-0.321925\pi\) | ||||
0.530712 | + | 0.847552i | \(0.321925\pi\) | |||||||
\(32\) | −1.94603 | −0.344013 | ||||||||
\(33\) | −1.72612 | −0.300478 | ||||||||
\(34\) | 10.5283 | 1.80559 | ||||||||
\(35\) | −0.778486 | −0.131588 | ||||||||
\(36\) | −12.1686 | −2.02810 | ||||||||
\(37\) | 9.27079 | 1.52411 | 0.762054 | − | 0.647513i | \(-0.224191\pi\) | ||||
0.762054 | + | 0.647513i | \(0.224191\pi\) | |||||||
\(38\) | 2.48734 | 0.403500 | ||||||||
\(39\) | 1.79967 | 0.288177 | ||||||||
\(40\) | 1.81398 | 0.286816 | ||||||||
\(41\) | 7.13705 | 1.11462 | 0.557310 | − | 0.830305i | \(-0.311834\pi\) | ||||
0.557310 | + | 0.830305i | \(0.311834\pi\) | |||||||
\(42\) | 1.77672 | 0.274153 | ||||||||
\(43\) | 10.5909 | 1.61509 | 0.807547 | − | 0.589803i | \(-0.200794\pi\) | ||||
0.807547 | + | 0.589803i | \(0.200794\pi\) | |||||||
\(44\) | 23.6184 | 3.56061 | ||||||||
\(45\) | 0.969231 | 0.144484 | ||||||||
\(46\) | 12.6335 | 1.86271 | ||||||||
\(47\) | −0.0898896 | −0.0131117 | −0.00655587 | − | 0.999979i | \(-0.502087\pi\) | ||||
−0.00655587 | + | 0.999979i | \(0.502087\pi\) | |||||||
\(48\) | −1.57772 | −0.227724 | ||||||||
\(49\) | −1.55060 | −0.221514 | ||||||||
\(50\) | 12.1601 | 1.71970 | ||||||||
\(51\) | 1.29519 | 0.181362 | ||||||||
\(52\) | −24.6248 | −3.41485 | ||||||||
\(53\) | −8.17447 | −1.12285 | −0.561425 | − | 0.827528i | \(-0.689747\pi\) | ||||
−0.561425 | + | 0.827528i | \(0.689747\pi\) | |||||||
\(54\) | −4.49536 | −0.611740 | ||||||||
\(55\) | −1.88122 | −0.253663 | ||||||||
\(56\) | −12.6979 | −1.69683 | ||||||||
\(57\) | 0.305991 | 0.0405294 | ||||||||
\(58\) | −7.55692 | −0.992272 | ||||||||
\(59\) | 0.903345 | 0.117605 | 0.0588027 | − | 0.998270i | \(-0.481272\pi\) | ||||
0.0588027 | + | 0.998270i | \(0.481272\pi\) | |||||||
\(60\) | 0.427241 | 0.0551566 | ||||||||
\(61\) | −1.56508 | −0.200388 | −0.100194 | − | 0.994968i | \(-0.531946\pi\) | ||||
−0.100194 | + | 0.994968i | \(0.531946\pi\) | |||||||
\(62\) | −14.6996 | −1.86685 | ||||||||
\(63\) | −6.78462 | −0.854781 | ||||||||
\(64\) | −5.47176 | −0.683970 | ||||||||
\(65\) | 1.96137 | 0.243278 | ||||||||
\(66\) | 4.29344 | 0.528486 | ||||||||
\(67\) | −7.39866 | −0.903890 | −0.451945 | − | 0.892046i | \(-0.649270\pi\) | ||||
−0.451945 | + | 0.892046i | \(0.649270\pi\) | |||||||
\(68\) | −17.7220 | −2.14911 | ||||||||
\(69\) | 1.55417 | 0.187100 | ||||||||
\(70\) | 1.93636 | 0.231439 | ||||||||
\(71\) | 9.00344 | 1.06851 | 0.534256 | − | 0.845323i | \(-0.320592\pi\) | ||||
0.534256 | + | 0.845323i | \(0.320592\pi\) | |||||||
\(72\) | 15.8091 | 1.86312 | ||||||||
\(73\) | −10.4696 | −1.22537 | −0.612684 | − | 0.790328i | \(-0.709910\pi\) | ||||
−0.612684 | + | 0.790328i | \(0.709910\pi\) | |||||||
\(74\) | −23.0596 | −2.68063 | ||||||||
\(75\) | 1.49592 | 0.172734 | ||||||||
\(76\) | −4.18686 | −0.480266 | ||||||||
\(77\) | 13.1685 | 1.50069 | ||||||||
\(78\) | −4.47638 | −0.506851 | ||||||||
\(79\) | 5.95569 | 0.670067 | 0.335034 | − | 0.942206i | \(-0.391252\pi\) | ||||
0.335034 | + | 0.942206i | \(0.391252\pi\) | |||||||
\(80\) | −1.71948 | −0.192244 | ||||||||
\(81\) | 8.16609 | 0.907344 | ||||||||
\(82\) | −17.7523 | −1.96041 | ||||||||
\(83\) | 2.13433 | 0.234273 | 0.117137 | − | 0.993116i | \(-0.462628\pi\) | ||||
0.117137 | + | 0.993116i | \(0.462628\pi\) | |||||||
\(84\) | −2.99069 | −0.326311 | ||||||||
\(85\) | 1.41156 | 0.153106 | ||||||||
\(86\) | −26.3431 | −2.84065 | ||||||||
\(87\) | −0.929646 | −0.0996685 | ||||||||
\(88\) | −30.6845 | −3.27098 | ||||||||
\(89\) | 9.25404 | 0.980927 | 0.490463 | − | 0.871462i | \(-0.336828\pi\) | ||||
0.490463 | + | 0.871462i | \(0.336828\pi\) | |||||||
\(90\) | −2.41081 | −0.254121 | ||||||||
\(91\) | −13.7296 | −1.43926 | ||||||||
\(92\) | −21.2656 | −2.21709 | ||||||||
\(93\) | −1.80833 | −0.187515 | ||||||||
\(94\) | 0.223586 | 0.0230611 | ||||||||
\(95\) | 0.333485 | 0.0342148 | ||||||||
\(96\) | 0.595468 | 0.0607747 | ||||||||
\(97\) | −15.2436 | −1.54775 | −0.773875 | − | 0.633338i | \(-0.781684\pi\) | ||||
−0.773875 | + | 0.633338i | \(0.781684\pi\) | |||||||
\(98\) | 3.85686 | 0.389602 | ||||||||
\(99\) | −16.3951 | −1.64777 | ||||||||
\(100\) | −20.4687 | −2.04687 | ||||||||
\(101\) | −0.203196 | −0.0202188 | −0.0101094 | − | 0.999949i | \(-0.503218\pi\) | ||||
−0.0101094 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(102\) | −3.22157 | −0.318983 | ||||||||
\(103\) | −7.89007 | −0.777432 | −0.388716 | − | 0.921358i | \(-0.627081\pi\) | ||||
−0.388716 | + | 0.921358i | \(0.627081\pi\) | |||||||
\(104\) | 31.9920 | 3.13707 | ||||||||
\(105\) | 0.238209 | 0.0232469 | ||||||||
\(106\) | 20.3327 | 1.97489 | ||||||||
\(107\) | 15.9432 | 1.54129 | 0.770644 | − | 0.637266i | \(-0.219935\pi\) | ||||
0.770644 | + | 0.637266i | \(0.219935\pi\) | |||||||
\(108\) | 7.56689 | 0.728125 | ||||||||
\(109\) | −1.06672 | −0.102173 | −0.0510867 | − | 0.998694i | \(-0.516268\pi\) | ||||
−0.0510867 | + | 0.998694i | \(0.516268\pi\) | |||||||
\(110\) | 4.67922 | 0.446146 | ||||||||
\(111\) | −2.83678 | −0.269255 | ||||||||
\(112\) | 12.0364 | 1.13733 | ||||||||
\(113\) | 13.1327 | 1.23542 | 0.617712 | − | 0.786405i | \(-0.288060\pi\) | ||||
0.617712 | + | 0.786405i | \(0.288060\pi\) | |||||||
\(114\) | −0.761103 | −0.0712838 | ||||||||
\(115\) | 1.69381 | 0.157949 | ||||||||
\(116\) | 12.7203 | 1.18105 | ||||||||
\(117\) | 17.0937 | 1.58031 | ||||||||
\(118\) | −2.24693 | −0.206846 | ||||||||
\(119\) | −9.88094 | −0.905785 | ||||||||
\(120\) | −0.555062 | −0.0506700 | ||||||||
\(121\) | 20.8218 | 1.89289 | ||||||||
\(122\) | 3.89289 | 0.352446 | ||||||||
\(123\) | −2.18387 | −0.196913 | ||||||||
\(124\) | 24.7434 | 2.22202 | ||||||||
\(125\) | 3.29776 | 0.294961 | ||||||||
\(126\) | 16.8757 | 1.50340 | ||||||||
\(127\) | −4.66947 | −0.414348 | −0.207174 | − | 0.978304i | \(-0.566427\pi\) | ||||
−0.207174 | + | 0.978304i | \(0.566427\pi\) | |||||||
\(128\) | 17.5022 | 1.54699 | ||||||||
\(129\) | −3.24071 | −0.285329 | ||||||||
\(130\) | −4.87860 | −0.427882 | ||||||||
\(131\) | −12.8980 | −1.12691 | −0.563454 | − | 0.826148i | \(-0.690528\pi\) | ||||
−0.563454 | + | 0.826148i | \(0.690528\pi\) | |||||||
\(132\) | −7.22702 | −0.629031 | ||||||||
\(133\) | −2.33440 | −0.202418 | ||||||||
\(134\) | 18.4030 | 1.58978 | ||||||||
\(135\) | −0.602705 | −0.0518726 | ||||||||
\(136\) | 23.0240 | 1.97429 | ||||||||
\(137\) | 0.164002 | 0.0140116 | 0.00700581 | − | 0.999975i | \(-0.497770\pi\) | ||||
0.00700581 | + | 0.999975i | \(0.497770\pi\) | |||||||
\(138\) | −3.86574 | −0.329074 | ||||||||
\(139\) | −19.3645 | −1.64247 | −0.821237 | − | 0.570587i | \(-0.806716\pi\) | ||||
−0.821237 | + | 0.570587i | \(0.806716\pi\) | |||||||
\(140\) | −3.25942 | −0.275471 | ||||||||
\(141\) | 0.0275054 | 0.00231637 | ||||||||
\(142\) | −22.3946 | −1.87932 | ||||||||
\(143\) | −33.1777 | −2.77446 | ||||||||
\(144\) | −14.9855 | −1.24880 | ||||||||
\(145\) | −1.01318 | −0.0841399 | ||||||||
\(146\) | 26.0413 | 2.15520 | ||||||||
\(147\) | 0.474468 | 0.0391334 | ||||||||
\(148\) | 38.8156 | 3.19062 | ||||||||
\(149\) | −10.2177 | −0.837064 | −0.418532 | − | 0.908202i | \(-0.637455\pi\) | ||||
−0.418532 | + | 0.908202i | \(0.637455\pi\) | |||||||
\(150\) | −3.72087 | −0.303808 | ||||||||
\(151\) | −21.2493 | −1.72924 | −0.864620 | − | 0.502426i | \(-0.832441\pi\) | ||||
−0.864620 | + | 0.502426i | \(0.832441\pi\) | |||||||
\(152\) | 5.43948 | 0.441200 | ||||||||
\(153\) | 12.3020 | 0.994556 | ||||||||
\(154\) | −32.7546 | −2.63944 | ||||||||
\(155\) | −1.97082 | −0.158300 | ||||||||
\(156\) | 7.53496 | 0.603280 | ||||||||
\(157\) | 5.44540 | 0.434590 | 0.217295 | − | 0.976106i | \(-0.430277\pi\) | ||||
0.217295 | + | 0.976106i | \(0.430277\pi\) | |||||||
\(158\) | −14.8138 | −1.17852 | ||||||||
\(159\) | 2.50131 | 0.198367 | ||||||||
\(160\) | 0.648973 | 0.0513058 | ||||||||
\(161\) | −11.8567 | −0.934439 | ||||||||
\(162\) | −20.3119 | −1.59585 | ||||||||
\(163\) | −21.4071 | −1.67674 | −0.838368 | − | 0.545105i | \(-0.816490\pi\) | ||||
−0.838368 | + | 0.545105i | \(0.816490\pi\) | |||||||
\(164\) | 29.8819 | 2.33338 | ||||||||
\(165\) | 0.575634 | 0.0448131 | ||||||||
\(166\) | −5.30881 | −0.412044 | ||||||||
\(167\) | −6.71767 | −0.519829 | −0.259914 | − | 0.965632i | \(-0.583694\pi\) | ||||
−0.259914 | + | 0.965632i | \(0.583694\pi\) | |||||||
\(168\) | 3.88544 | 0.299768 | ||||||||
\(169\) | 21.5914 | 1.66088 | ||||||||
\(170\) | −3.51104 | −0.269284 | ||||||||
\(171\) | 2.90637 | 0.222256 | ||||||||
\(172\) | 44.3426 | 3.38109 | ||||||||
\(173\) | −3.74493 | −0.284722 | −0.142361 | − | 0.989815i | \(-0.545469\pi\) | ||||
−0.142361 | + | 0.989815i | \(0.545469\pi\) | |||||||
\(174\) | 2.31235 | 0.175299 | ||||||||
\(175\) | −11.4124 | −0.862694 | ||||||||
\(176\) | 29.0860 | 2.19244 | ||||||||
\(177\) | −0.276415 | −0.0207766 | ||||||||
\(178\) | −23.0180 | −1.72527 | ||||||||
\(179\) | −11.7883 | −0.881097 | −0.440549 | − | 0.897729i | \(-0.645216\pi\) | ||||
−0.440549 | + | 0.897729i | \(0.645216\pi\) | |||||||
\(180\) | 4.05804 | 0.302468 | ||||||||
\(181\) | 23.5490 | 1.75038 | 0.875192 | − | 0.483775i | \(-0.160735\pi\) | ||||
0.875192 | + | 0.483775i | \(0.160735\pi\) | |||||||
\(182\) | 34.1502 | 2.53138 | ||||||||
\(183\) | 0.478900 | 0.0354013 | ||||||||
\(184\) | 27.6278 | 2.03675 | ||||||||
\(185\) | −3.09167 | −0.227304 | ||||||||
\(186\) | 4.49794 | 0.329805 | ||||||||
\(187\) | −23.8774 | −1.74609 | ||||||||
\(188\) | −0.376356 | −0.0274485 | ||||||||
\(189\) | 4.21894 | 0.306883 | ||||||||
\(190\) | −0.829491 | −0.0601776 | ||||||||
\(191\) | −19.8495 | −1.43626 | −0.718128 | − | 0.695911i | \(-0.755001\pi\) | ||||
−0.718128 | + | 0.695911i | \(0.755001\pi\) | |||||||
\(192\) | 1.67431 | 0.120833 | ||||||||
\(193\) | −16.5428 | −1.19077 | −0.595387 | − | 0.803439i | \(-0.703001\pi\) | ||||
−0.595387 | + | 0.803439i | \(0.703001\pi\) | |||||||
\(194\) | 37.9160 | 2.72221 | ||||||||
\(195\) | −0.600162 | −0.0429785 | ||||||||
\(196\) | −6.49214 | −0.463724 | ||||||||
\(197\) | −4.34082 | −0.309271 | −0.154635 | − | 0.987972i | \(-0.549420\pi\) | ||||
−0.154635 | + | 0.987972i | \(0.549420\pi\) | |||||||
\(198\) | 40.7801 | 2.89812 | ||||||||
\(199\) | 27.4020 | 1.94247 | 0.971237 | − | 0.238114i | \(-0.0765292\pi\) | ||||
0.971237 | + | 0.238114i | \(0.0765292\pi\) | |||||||
\(200\) | 26.5924 | 1.88037 | ||||||||
\(201\) | 2.26392 | 0.159685 | ||||||||
\(202\) | 0.505419 | 0.0355611 | ||||||||
\(203\) | 7.09225 | 0.497778 | ||||||||
\(204\) | 5.42277 | 0.379670 | ||||||||
\(205\) | −2.38010 | −0.166233 | ||||||||
\(206\) | 19.6253 | 1.36736 | ||||||||
\(207\) | 14.7618 | 1.02602 | ||||||||
\(208\) | −30.3253 | −2.10268 | ||||||||
\(209\) | −5.64108 | −0.390202 | ||||||||
\(210\) | −0.592508 | −0.0408869 | ||||||||
\(211\) | −17.7844 | −1.22433 | −0.612163 | − | 0.790731i | \(-0.709701\pi\) | ||||
−0.612163 | + | 0.790731i | \(0.709701\pi\) | |||||||
\(212\) | −34.2254 | −2.35061 | ||||||||
\(213\) | −2.75497 | −0.188767 | ||||||||
\(214\) | −39.6562 | −2.71084 | ||||||||
\(215\) | −3.53190 | −0.240874 | ||||||||
\(216\) | −9.83073 | −0.668897 | ||||||||
\(217\) | 13.7957 | 0.936515 | ||||||||
\(218\) | 2.65330 | 0.179704 | ||||||||
\(219\) | 3.20358 | 0.216478 | ||||||||
\(220\) | −7.87639 | −0.531026 | ||||||||
\(221\) | 24.8948 | 1.67460 | ||||||||
\(222\) | 7.05603 | 0.473570 | ||||||||
\(223\) | 4.06392 | 0.272140 | 0.136070 | − | 0.990699i | \(-0.456553\pi\) | ||||
0.136070 | + | 0.990699i | \(0.456553\pi\) | |||||||
\(224\) | −4.54281 | −0.303529 | ||||||||
\(225\) | 14.2086 | 0.947242 | ||||||||
\(226\) | −32.6656 | −2.17288 | ||||||||
\(227\) | 11.3929 | 0.756171 | 0.378085 | − | 0.925771i | \(-0.376583\pi\) | ||||
0.378085 | + | 0.925771i | \(0.376583\pi\) | |||||||
\(228\) | 1.28114 | 0.0848456 | ||||||||
\(229\) | −23.0907 | −1.52587 | −0.762937 | − | 0.646473i | \(-0.776243\pi\) | ||||
−0.762937 | + | 0.646473i | \(0.776243\pi\) | |||||||
\(230\) | −4.21309 | −0.277803 | ||||||||
\(231\) | −4.02944 | −0.265118 | ||||||||
\(232\) | −16.5260 | −1.08498 | ||||||||
\(233\) | 9.67528 | 0.633849 | 0.316924 | − | 0.948451i | \(-0.397350\pi\) | ||||
0.316924 | + | 0.948451i | \(0.397350\pi\) | |||||||
\(234\) | −42.5177 | −2.77947 | ||||||||
\(235\) | 0.0299768 | 0.00195547 | ||||||||
\(236\) | 3.78218 | 0.246199 | ||||||||
\(237\) | −1.82238 | −0.118377 | ||||||||
\(238\) | 24.5773 | 1.59311 | ||||||||
\(239\) | −20.1259 | −1.30184 | −0.650919 | − | 0.759147i | \(-0.725616\pi\) | ||||
−0.650919 | + | 0.759147i | \(0.725616\pi\) | |||||||
\(240\) | 0.526146 | 0.0339626 | ||||||||
\(241\) | 24.4920 | 1.57767 | 0.788834 | − | 0.614606i | \(-0.210685\pi\) | ||||
0.788834 | + | 0.614606i | \(0.210685\pi\) | |||||||
\(242\) | −51.7909 | −3.32924 | ||||||||
\(243\) | −7.92063 | −0.508109 | ||||||||
\(244\) | −6.55279 | −0.419499 | ||||||||
\(245\) | 0.517101 | 0.0330363 | ||||||||
\(246\) | 5.43203 | 0.346334 | ||||||||
\(247\) | 5.88144 | 0.374227 | ||||||||
\(248\) | −32.1460 | −2.04127 | ||||||||
\(249\) | −0.653086 | −0.0413876 | ||||||||
\(250\) | −8.20266 | −0.518782 | ||||||||
\(251\) | 11.1112 | 0.701336 | 0.350668 | − | 0.936500i | \(-0.385955\pi\) | ||||
0.350668 | + | 0.936500i | \(0.385955\pi\) | |||||||
\(252\) | −28.4063 | −1.78943 | ||||||||
\(253\) | −28.6518 | −1.80132 | ||||||||
\(254\) | 11.6146 | 0.728762 | ||||||||
\(255\) | −0.431925 | −0.0270482 | ||||||||
\(256\) | −32.5904 | −2.03690 | ||||||||
\(257\) | −10.5583 | −0.658608 | −0.329304 | − | 0.944224i | \(-0.606814\pi\) | ||||
−0.329304 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(258\) | 8.06075 | 0.501841 | ||||||||
\(259\) | 21.6417 | 1.34475 | ||||||||
\(260\) | 8.21200 | 0.509287 | ||||||||
\(261\) | −8.83000 | −0.546563 | ||||||||
\(262\) | 32.0818 | 1.98202 | ||||||||
\(263\) | 8.47745 | 0.522742 | 0.261371 | − | 0.965238i | \(-0.415825\pi\) | ||||
0.261371 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(264\) | 9.38917 | 0.577864 | ||||||||
\(265\) | 2.72606 | 0.167461 | ||||||||
\(266\) | 5.80644 | 0.356016 | ||||||||
\(267\) | −2.83165 | −0.173294 | ||||||||
\(268\) | −30.9772 | −1.89223 | ||||||||
\(269\) | 1.08324 | 0.0660466 | 0.0330233 | − | 0.999455i | \(-0.489486\pi\) | ||||
0.0330233 | + | 0.999455i | \(0.489486\pi\) | |||||||
\(270\) | 1.49913 | 0.0912344 | ||||||||
\(271\) | 8.68000 | 0.527273 | 0.263636 | − | 0.964622i | \(-0.415078\pi\) | ||||
0.263636 | + | 0.964622i | \(0.415078\pi\) | |||||||
\(272\) | −21.8246 | −1.32331 | ||||||||
\(273\) | 4.20113 | 0.254264 | ||||||||
\(274\) | −0.407928 | −0.0246438 | ||||||||
\(275\) | −27.5780 | −1.66302 | ||||||||
\(276\) | 6.50708 | 0.391680 | ||||||||
\(277\) | −21.8149 | −1.31073 | −0.655365 | − | 0.755312i | \(-0.727485\pi\) | ||||
−0.655365 | + | 0.755312i | \(0.727485\pi\) | |||||||
\(278\) | 48.1661 | 2.88881 | ||||||||
\(279\) | −17.1759 | −1.02830 | ||||||||
\(280\) | 4.23456 | 0.253063 | ||||||||
\(281\) | 25.5444 | 1.52385 | 0.761926 | − | 0.647664i | \(-0.224254\pi\) | ||||
0.761926 | + | 0.647664i | \(0.224254\pi\) | |||||||
\(282\) | −0.0684152 | −0.00407407 | ||||||||
\(283\) | −25.3017 | −1.50403 | −0.752016 | − | 0.659144i | \(-0.770919\pi\) | ||||
−0.752016 | + | 0.659144i | \(0.770919\pi\) | |||||||
\(284\) | 37.6962 | 2.23686 | ||||||||
\(285\) | −0.102043 | −0.00604452 | ||||||||
\(286\) | 82.5242 | 4.87976 | ||||||||
\(287\) | 16.6607 | 0.983450 | ||||||||
\(288\) | 5.65589 | 0.333277 | ||||||||
\(289\) | 0.916284 | 0.0538991 | ||||||||
\(290\) | 2.52012 | 0.147987 | ||||||||
\(291\) | 4.66439 | 0.273431 | ||||||||
\(292\) | −43.8346 | −2.56523 | ||||||||
\(293\) | −16.1594 | −0.944041 | −0.472021 | − | 0.881587i | \(-0.656475\pi\) | ||||
−0.472021 | + | 0.881587i | \(0.656475\pi\) | |||||||
\(294\) | −1.18016 | −0.0688285 | ||||||||
\(295\) | −0.301252 | −0.0175396 | ||||||||
\(296\) | −50.4283 | −2.93108 | ||||||||
\(297\) | 10.1951 | 0.591579 | ||||||||
\(298\) | 25.4148 | 1.47224 | ||||||||
\(299\) | 29.8726 | 1.72758 | ||||||||
\(300\) | 6.26323 | 0.361608 | ||||||||
\(301\) | 24.7233 | 1.42503 | ||||||||
\(302\) | 52.8542 | 3.04142 | ||||||||
\(303\) | 0.0621762 | 0.00357193 | ||||||||
\(304\) | −5.15610 | −0.295723 | ||||||||
\(305\) | 0.521932 | 0.0298857 | ||||||||
\(306\) | −30.5992 | −1.74924 | ||||||||
\(307\) | −2.65740 | −0.151666 | −0.0758330 | − | 0.997121i | \(-0.524162\pi\) | ||||
−0.0758330 | + | 0.997121i | \(0.524162\pi\) | |||||||
\(308\) | 55.1348 | 3.14160 | ||||||||
\(309\) | 2.41429 | 0.137344 | ||||||||
\(310\) | 4.90209 | 0.278420 | ||||||||
\(311\) | 22.4582 | 1.27349 | 0.636744 | − | 0.771075i | \(-0.280281\pi\) | ||||
0.636744 | + | 0.771075i | \(0.280281\pi\) | |||||||
\(312\) | −9.78924 | −0.554207 | ||||||||
\(313\) | −8.10086 | −0.457888 | −0.228944 | − | 0.973440i | \(-0.573527\pi\) | ||||
−0.228944 | + | 0.973440i | \(0.573527\pi\) | |||||||
\(314\) | −13.5446 | −0.764363 | ||||||||
\(315\) | 2.26257 | 0.127481 | ||||||||
\(316\) | 24.9357 | 1.40274 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | −6.22161 | −0.348891 | ||||||||
\(319\) | 17.1385 | 0.959570 | ||||||||
\(320\) | 1.82475 | 0.102007 | ||||||||
\(321\) | −4.87847 | −0.272290 | ||||||||
\(322\) | 29.4916 | 1.64351 | ||||||||
\(323\) | 4.23276 | 0.235517 | ||||||||
\(324\) | 34.1903 | 1.89946 | ||||||||
\(325\) | 28.7531 | 1.59494 | ||||||||
\(326\) | 53.2468 | 2.94907 | ||||||||
\(327\) | 0.326407 | 0.0180503 | ||||||||
\(328\) | −38.8218 | −2.14358 | ||||||||
\(329\) | −0.209838 | −0.0115687 | ||||||||
\(330\) | −1.43180 | −0.0788179 | ||||||||
\(331\) | 19.1862 | 1.05457 | 0.527283 | − | 0.849690i | \(-0.323211\pi\) | ||||
0.527283 | + | 0.849690i | \(0.323211\pi\) | |||||||
\(332\) | 8.93616 | 0.490436 | ||||||||
\(333\) | −26.9444 | −1.47654 | ||||||||
\(334\) | 16.7091 | 0.914283 | ||||||||
\(335\) | 2.46734 | 0.134805 | ||||||||
\(336\) | −3.68302 | −0.200925 | ||||||||
\(337\) | −15.3887 | −0.838276 | −0.419138 | − | 0.907922i | \(-0.637668\pi\) | ||||
−0.419138 | + | 0.907922i | \(0.637668\pi\) | |||||||
\(338\) | −53.7052 | −2.92118 | ||||||||
\(339\) | −4.01849 | −0.218255 | ||||||||
\(340\) | 5.91002 | 0.320516 | ||||||||
\(341\) | 33.3374 | 1.80532 | ||||||||
\(342\) | −7.22913 | −0.390907 | ||||||||
\(343\) | −19.9605 | −1.07776 | ||||||||
\(344\) | −57.6089 | −3.10606 | ||||||||
\(345\) | −0.518291 | −0.0279038 | ||||||||
\(346\) | 9.31492 | 0.500773 | ||||||||
\(347\) | 8.27371 | 0.444156 | 0.222078 | − | 0.975029i | \(-0.428716\pi\) | ||||
0.222078 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(348\) | −3.89230 | −0.208649 | ||||||||
\(349\) | 9.93165 | 0.531629 | 0.265814 | − | 0.964024i | \(-0.414359\pi\) | ||||
0.265814 | + | 0.964024i | \(0.414359\pi\) | |||||||
\(350\) | 28.3864 | 1.51732 | ||||||||
\(351\) | −10.6295 | −0.567361 | ||||||||
\(352\) | −10.9777 | −0.585115 | ||||||||
\(353\) | 11.2119 | 0.596749 | 0.298375 | − | 0.954449i | \(-0.403556\pi\) | ||||
0.298375 | + | 0.954449i | \(0.403556\pi\) | |||||||
\(354\) | 0.687538 | 0.0365423 | ||||||||
\(355\) | −3.00251 | −0.159357 | ||||||||
\(356\) | 38.7454 | 2.05350 | ||||||||
\(357\) | 3.02348 | 0.160019 | ||||||||
\(358\) | 29.3215 | 1.54969 | ||||||||
\(359\) | −3.23673 | −0.170828 | −0.0854140 | − | 0.996346i | \(-0.527221\pi\) | ||||
−0.0854140 | + | 0.996346i | \(0.527221\pi\) | |||||||
\(360\) | −5.27211 | −0.277864 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −58.5744 | −3.07860 | ||||||||
\(363\) | −6.37127 | −0.334405 | ||||||||
\(364\) | −57.4841 | −3.01298 | ||||||||
\(365\) | 3.49144 | 0.182750 | ||||||||
\(366\) | −1.19119 | −0.0622644 | ||||||||
\(367\) | 3.04889 | 0.159151 | 0.0795754 | − | 0.996829i | \(-0.474644\pi\) | ||||
0.0795754 | + | 0.996829i | \(0.474644\pi\) | |||||||
\(368\) | −26.1885 | −1.36517 | ||||||||
\(369\) | −20.7429 | −1.07983 | ||||||||
\(370\) | 7.69004 | 0.399786 | ||||||||
\(371\) | −19.0824 | −0.990711 | ||||||||
\(372\) | −7.57124 | −0.392550 | ||||||||
\(373\) | −14.4516 | −0.748277 | −0.374139 | − | 0.927373i | \(-0.622062\pi\) | ||||
−0.374139 | + | 0.927373i | \(0.622062\pi\) | |||||||
\(374\) | 59.3911 | 3.07104 | ||||||||
\(375\) | −1.00908 | −0.0521089 | ||||||||
\(376\) | 0.488952 | 0.0252158 | ||||||||
\(377\) | −17.8687 | −0.920286 | ||||||||
\(378\) | −10.4939 | −0.539750 | ||||||||
\(379\) | −0.281718 | −0.0144709 | −0.00723545 | − | 0.999974i | \(-0.502303\pi\) | ||||
−0.00723545 | + | 0.999974i | \(0.502303\pi\) | |||||||
\(380\) | 1.39626 | 0.0716264 | ||||||||
\(381\) | 1.42881 | 0.0732003 | ||||||||
\(382\) | 49.3724 | 2.52611 | ||||||||
\(383\) | 25.5536 | 1.30573 | 0.652863 | − | 0.757476i | \(-0.273568\pi\) | ||||
0.652863 | + | 0.757476i | \(0.273568\pi\) | |||||||
\(384\) | −5.35551 | −0.273297 | ||||||||
\(385\) | −4.39150 | −0.223812 | ||||||||
\(386\) | 41.1475 | 2.09435 | ||||||||
\(387\) | −30.7810 | −1.56469 | ||||||||
\(388\) | −63.8228 | −3.24011 | ||||||||
\(389\) | −27.5950 | −1.39912 | −0.699560 | − | 0.714574i | \(-0.746621\pi\) | ||||
−0.699560 | + | 0.714574i | \(0.746621\pi\) | |||||||
\(390\) | 1.49281 | 0.0755912 | ||||||||
\(391\) | 21.4988 | 1.08724 | ||||||||
\(392\) | 8.43443 | 0.426003 | ||||||||
\(393\) | 3.94668 | 0.199084 | ||||||||
\(394\) | 10.7971 | 0.543950 | ||||||||
\(395\) | −1.98613 | −0.0999332 | ||||||||
\(396\) | −68.6439 | −3.44949 | ||||||||
\(397\) | 9.83774 | 0.493742 | 0.246871 | − | 0.969048i | \(-0.420598\pi\) | ||||
0.246871 | + | 0.969048i | \(0.420598\pi\) | |||||||
\(398\) | −68.1580 | −3.41645 | ||||||||
\(399\) | 0.714303 | 0.0357599 | ||||||||
\(400\) | −25.2071 | −1.26035 | ||||||||
\(401\) | −30.7020 | −1.53318 | −0.766592 | − | 0.642135i | \(-0.778049\pi\) | ||||
−0.766592 | + | 0.642135i | \(0.778049\pi\) | |||||||
\(402\) | −5.63114 | −0.280856 | ||||||||
\(403\) | −34.7579 | −1.73142 | ||||||||
\(404\) | −0.850756 | −0.0423267 | ||||||||
\(405\) | −2.72327 | −0.135320 | ||||||||
\(406\) | −17.6408 | −0.875500 | ||||||||
\(407\) | 52.2973 | 2.59228 | ||||||||
\(408\) | −7.04513 | −0.348786 | ||||||||
\(409\) | 1.06693 | 0.0527565 | 0.0263782 | − | 0.999652i | \(-0.491603\pi\) | ||||
0.0263782 | + | 0.999652i | \(0.491603\pi\) | |||||||
\(410\) | 5.92012 | 0.292374 | ||||||||
\(411\) | −0.0501830 | −0.00247534 | ||||||||
\(412\) | −33.0347 | −1.62750 | ||||||||
\(413\) | 2.10876 | 0.103766 | ||||||||
\(414\) | −36.7177 | −1.80458 | ||||||||
\(415\) | −0.711768 | −0.0349393 | ||||||||
\(416\) | 11.4455 | 0.561161 | ||||||||
\(417\) | 5.92535 | 0.290166 | ||||||||
\(418\) | 14.0313 | 0.686293 | ||||||||
\(419\) | −34.2091 | −1.67122 | −0.835611 | − | 0.549321i | \(-0.814886\pi\) | ||||
−0.835611 | + | 0.549321i | \(0.814886\pi\) | |||||||
\(420\) | 0.997350 | 0.0486657 | ||||||||
\(421\) | −32.1152 | −1.56520 | −0.782600 | − | 0.622524i | \(-0.786107\pi\) | ||||
−0.782600 | + | 0.622524i | \(0.786107\pi\) | |||||||
\(422\) | 44.2358 | 2.15337 | ||||||||
\(423\) | 0.261252 | 0.0127025 | ||||||||
\(424\) | 44.4648 | 2.15940 | ||||||||
\(425\) | 20.6931 | 1.00376 | ||||||||
\(426\) | 6.85255 | 0.332007 | ||||||||
\(427\) | −3.65352 | −0.176806 | ||||||||
\(428\) | 66.7520 | 3.22658 | ||||||||
\(429\) | 10.1521 | 0.490146 | ||||||||
\(430\) | 8.78504 | 0.423652 | ||||||||
\(431\) | −27.5683 | −1.32792 | −0.663960 | − | 0.747768i | \(-0.731125\pi\) | ||||
−0.663960 | + | 0.747768i | \(0.731125\pi\) | |||||||
\(432\) | 9.31859 | 0.448341 | ||||||||
\(433\) | 19.2270 | 0.923991 | 0.461996 | − | 0.886882i | \(-0.347134\pi\) | ||||
0.461996 | + | 0.886882i | \(0.347134\pi\) | |||||||
\(434\) | −34.3147 | −1.64716 | ||||||||
\(435\) | 0.310023 | 0.0148645 | ||||||||
\(436\) | −4.46622 | −0.213893 | ||||||||
\(437\) | 5.07913 | 0.242968 | ||||||||
\(438\) | −7.96841 | −0.380745 | ||||||||
\(439\) | −7.91050 | −0.377547 | −0.188774 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188774 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(440\) | 10.2328 | 0.487831 | ||||||||
\(441\) | 4.50661 | 0.214600 | ||||||||
\(442\) | −61.9218 | −2.94532 | ||||||||
\(443\) | −40.5112 | −1.92474 | −0.962372 | − | 0.271734i | \(-0.912403\pi\) | ||||
−0.962372 | + | 0.271734i | \(0.912403\pi\) | |||||||
\(444\) | −11.8772 | −0.563667 | ||||||||
\(445\) | −3.08609 | −0.146294 | ||||||||
\(446\) | −10.1084 | −0.478644 | ||||||||
\(447\) | 3.12651 | 0.147879 | ||||||||
\(448\) | −12.7733 | −0.603479 | ||||||||
\(449\) | −15.9096 | −0.750820 | −0.375410 | − | 0.926859i | \(-0.622498\pi\) | ||||
−0.375410 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(450\) | −35.3417 | −1.66602 | ||||||||
\(451\) | 40.2607 | 1.89580 | ||||||||
\(452\) | 54.9850 | 2.58628 | ||||||||
\(453\) | 6.50208 | 0.305494 | ||||||||
\(454\) | −28.3379 | −1.32996 | ||||||||
\(455\) | 4.57862 | 0.214649 | ||||||||
\(456\) | −1.66443 | −0.0779440 | ||||||||
\(457\) | −3.99061 | −0.186673 | −0.0933364 | − | 0.995635i | \(-0.529753\pi\) | ||||
−0.0933364 | + | 0.995635i | \(0.529753\pi\) | |||||||
\(458\) | 57.4343 | 2.68373 | ||||||||
\(459\) | −7.64985 | −0.357064 | ||||||||
\(460\) | 7.09177 | 0.330655 | ||||||||
\(461\) | −3.34960 | −0.156006 | −0.0780031 | − | 0.996953i | \(-0.524854\pi\) | ||||
−0.0780031 | + | 0.996953i | \(0.524854\pi\) | |||||||
\(462\) | 10.0226 | 0.466293 | ||||||||
\(463\) | −18.4875 | −0.859189 | −0.429594 | − | 0.903022i | \(-0.641343\pi\) | ||||
−0.429594 | + | 0.903022i | \(0.641343\pi\) | |||||||
\(464\) | 15.6650 | 0.727231 | ||||||||
\(465\) | 0.603051 | 0.0279658 | ||||||||
\(466\) | −24.0657 | −1.11482 | ||||||||
\(467\) | 10.4444 | 0.483310 | 0.241655 | − | 0.970362i | \(-0.422310\pi\) | ||||
0.241655 | + | 0.970362i | \(0.422310\pi\) | |||||||
\(468\) | 71.5688 | 3.30827 | ||||||||
\(469\) | −17.2714 | −0.797519 | ||||||||
\(470\) | −0.0745626 | −0.00343932 | ||||||||
\(471\) | −1.66624 | −0.0767763 | ||||||||
\(472\) | −4.91372 | −0.226172 | ||||||||
\(473\) | 59.7440 | 2.74703 | ||||||||
\(474\) | 4.53289 | 0.208203 | ||||||||
\(475\) | 4.88879 | 0.224313 | ||||||||
\(476\) | −41.3702 | −1.89620 | ||||||||
\(477\) | 23.7580 | 1.08781 | ||||||||
\(478\) | 50.0601 | 2.28969 | ||||||||
\(479\) | −34.8390 | −1.59183 | −0.795917 | − | 0.605406i | \(-0.793011\pi\) | ||||
−0.795917 | + | 0.605406i | \(0.793011\pi\) | |||||||
\(480\) | −0.198580 | −0.00906388 | ||||||||
\(481\) | −54.5257 | −2.48616 | ||||||||
\(482\) | −60.9200 | −2.77483 | ||||||||
\(483\) | 3.62804 | 0.165081 | ||||||||
\(484\) | 87.1780 | 3.96263 | ||||||||
\(485\) | 5.08350 | 0.230830 | ||||||||
\(486\) | 19.7013 | 0.893669 | ||||||||
\(487\) | −18.8956 | −0.856241 | −0.428121 | − | 0.903722i | \(-0.640824\pi\) | ||||
−0.428121 | + | 0.903722i | \(0.640824\pi\) | |||||||
\(488\) | 8.51323 | 0.385376 | ||||||||
\(489\) | 6.55038 | 0.296219 | ||||||||
\(490\) | −1.28621 | −0.0581048 | ||||||||
\(491\) | 38.5124 | 1.73804 | 0.869021 | − | 0.494776i | \(-0.164750\pi\) | ||||
0.869021 | + | 0.494776i | \(0.164750\pi\) | |||||||
\(492\) | −9.14357 | −0.412224 | ||||||||
\(493\) | −12.8598 | −0.579175 | ||||||||
\(494\) | −14.6292 | −0.658197 | ||||||||
\(495\) | 5.46751 | 0.245746 | ||||||||
\(496\) | 30.4713 | 1.36820 | ||||||||
\(497\) | 21.0176 | 0.942768 | ||||||||
\(498\) | 1.62445 | 0.0727932 | ||||||||
\(499\) | −43.0291 | −1.92625 | −0.963123 | − | 0.269063i | \(-0.913286\pi\) | ||||
−0.963123 | + | 0.269063i | \(0.913286\pi\) | |||||||
\(500\) | 13.8073 | 0.617480 | ||||||||
\(501\) | 2.05554 | 0.0918349 | ||||||||
\(502\) | −27.6375 | −1.23352 | ||||||||
\(503\) | 19.1013 | 0.851687 | 0.425843 | − | 0.904797i | \(-0.359977\pi\) | ||||
0.425843 | + | 0.904797i | \(0.359977\pi\) | |||||||
\(504\) | 36.9048 | 1.64387 | ||||||||
\(505\) | 0.0677629 | 0.00301541 | ||||||||
\(506\) | 71.2667 | 3.16819 | ||||||||
\(507\) | −6.60676 | −0.293417 | ||||||||
\(508\) | −19.5504 | −0.867410 | ||||||||
\(509\) | −4.95437 | −0.219598 | −0.109799 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109799 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(510\) | 1.07434 | 0.0475728 | ||||||||
\(511\) | −24.4401 | −1.08117 | ||||||||
\(512\) | 46.0591 | 2.03554 | ||||||||
\(513\) | −1.80729 | −0.0797940 | ||||||||
\(514\) | 26.2621 | 1.15837 | ||||||||
\(515\) | 2.63122 | 0.115945 | ||||||||
\(516\) | −13.5684 | −0.597316 | ||||||||
\(517\) | −0.507074 | −0.0223011 | ||||||||
\(518\) | −53.8303 | −2.36517 | ||||||||
\(519\) | 1.14591 | 0.0503000 | ||||||||
\(520\) | −10.6688 | −0.467860 | ||||||||
\(521\) | 9.66090 | 0.423252 | 0.211626 | − | 0.977351i | \(-0.432124\pi\) | ||||
0.211626 | + | 0.977351i | \(0.432124\pi\) | |||||||
\(522\) | 21.9632 | 0.961304 | ||||||||
\(523\) | 20.5205 | 0.897297 | 0.448649 | − | 0.893708i | \(-0.351906\pi\) | ||||
0.448649 | + | 0.893708i | \(0.351906\pi\) | |||||||
\(524\) | −54.0024 | −2.35910 | ||||||||
\(525\) | 3.49208 | 0.152407 | ||||||||
\(526\) | −21.0863 | −0.919406 | ||||||||
\(527\) | −25.0146 | −1.08965 | ||||||||
\(528\) | −8.90004 | −0.387324 | ||||||||
\(529\) | 2.79756 | 0.121633 | ||||||||
\(530\) | −6.78065 | −0.294533 | ||||||||
\(531\) | −2.62545 | −0.113935 | ||||||||
\(532\) | −9.77380 | −0.423748 | ||||||||
\(533\) | −41.9762 | −1.81819 | ||||||||
\(534\) | 7.04328 | 0.304793 | ||||||||
\(535\) | −5.31682 | −0.229866 | ||||||||
\(536\) | 40.2448 | 1.73831 | ||||||||
\(537\) | 3.60710 | 0.155658 | ||||||||
\(538\) | −2.69440 | −0.116164 | ||||||||
\(539\) | −8.74704 | −0.376762 | ||||||||
\(540\) | −2.52345 | −0.108592 | ||||||||
\(541\) | −10.6340 | −0.457193 | −0.228597 | − | 0.973521i | \(-0.573414\pi\) | ||||
−0.228597 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(542\) | −21.5901 | −0.927375 | ||||||||
\(543\) | −7.20578 | −0.309230 | ||||||||
\(544\) | 8.23710 | 0.353163 | ||||||||
\(545\) | 0.355735 | 0.0152380 | ||||||||
\(546\) | −10.4497 | −0.447204 | ||||||||
\(547\) | 1.19449 | 0.0510726 | 0.0255363 | − | 0.999674i | \(-0.491871\pi\) | ||||
0.0255363 | + | 0.999674i | \(0.491871\pi\) | |||||||
\(548\) | 0.686653 | 0.0293324 | ||||||||
\(549\) | 4.54871 | 0.194134 | ||||||||
\(550\) | 68.5960 | 2.92494 | ||||||||
\(551\) | −3.03815 | −0.129430 | ||||||||
\(552\) | −8.45385 | −0.359820 | ||||||||
\(553\) | 13.9029 | 0.591213 | ||||||||
\(554\) | 54.2611 | 2.30533 | ||||||||
\(555\) | 0.946022 | 0.0401564 | ||||||||
\(556\) | −81.0765 | −3.43841 | ||||||||
\(557\) | 41.6099 | 1.76307 | 0.881535 | − | 0.472120i | \(-0.156511\pi\) | ||||
0.881535 | + | 0.472120i | \(0.156511\pi\) | |||||||
\(558\) | 42.7224 | 1.80859 | ||||||||
\(559\) | −62.2897 | −2.63457 | ||||||||
\(560\) | −4.01395 | −0.169621 | ||||||||
\(561\) | 7.30625 | 0.308470 | ||||||||
\(562\) | −63.5377 | −2.68018 | ||||||||
\(563\) | 13.7132 | 0.577941 | 0.288971 | − | 0.957338i | \(-0.406687\pi\) | ||||
0.288971 | + | 0.957338i | \(0.406687\pi\) | |||||||
\(564\) | 0.115161 | 0.00484916 | ||||||||
\(565\) | −4.37957 | −0.184250 | ||||||||
\(566\) | 62.9341 | 2.64532 | ||||||||
\(567\) | 19.0629 | 0.800566 | ||||||||
\(568\) | −48.9740 | −2.05490 | ||||||||
\(569\) | −42.8511 | −1.79641 | −0.898206 | − | 0.439575i | \(-0.855129\pi\) | ||||
−0.898206 | + | 0.439575i | \(0.855129\pi\) | |||||||
\(570\) | 0.253816 | 0.0106312 | ||||||||
\(571\) | −41.1484 | −1.72201 | −0.861003 | − | 0.508599i | \(-0.830164\pi\) | ||||
−0.861003 | + | 0.508599i | \(0.830164\pi\) | |||||||
\(572\) | −138.911 | −5.80814 | ||||||||
\(573\) | 6.07375 | 0.253735 | ||||||||
\(574\) | −41.4408 | −1.72971 | ||||||||
\(575\) | 24.8308 | 1.03552 | ||||||||
\(576\) | 15.9030 | 0.662623 | ||||||||
\(577\) | −18.5775 | −0.773391 | −0.386696 | − | 0.922207i | \(-0.626384\pi\) | ||||
−0.386696 | + | 0.922207i | \(0.626384\pi\) | |||||||
\(578\) | −2.27911 | −0.0947985 | ||||||||
\(579\) | 5.06193 | 0.210367 | ||||||||
\(580\) | −4.24204 | −0.176141 | ||||||||
\(581\) | 4.98238 | 0.206704 | ||||||||
\(582\) | −11.6019 | −0.480916 | ||||||||
\(583\) | −46.1128 | −1.90980 | ||||||||
\(584\) | 56.9489 | 2.35656 | ||||||||
\(585\) | −5.70048 | −0.235686 | ||||||||
\(586\) | 40.1939 | 1.66039 | ||||||||
\(587\) | −7.35887 | −0.303733 | −0.151867 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151867 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(588\) | 1.98653 | 0.0819232 | ||||||||
\(589\) | −5.90976 | −0.243507 | ||||||||
\(590\) | 0.749316 | 0.0308489 | ||||||||
\(591\) | 1.32825 | 0.0546369 | ||||||||
\(592\) | 47.8012 | 1.96462 | ||||||||
\(593\) | 47.0838 | 1.93350 | 0.966750 | − | 0.255722i | \(-0.0823132\pi\) | ||||
0.966750 | + | 0.255722i | \(0.0823132\pi\) | |||||||
\(594\) | −25.3587 | −1.04048 | ||||||||
\(595\) | 3.29515 | 0.135088 | ||||||||
\(596\) | −42.7800 | −1.75234 | ||||||||
\(597\) | −8.38475 | −0.343165 | ||||||||
\(598\) | −74.3034 | −3.03849 | ||||||||
\(599\) | 21.0559 | 0.860322 | 0.430161 | − | 0.902752i | \(-0.358457\pi\) | ||||
0.430161 | + | 0.902752i | \(0.358457\pi\) | |||||||
\(600\) | −8.13704 | −0.332193 | ||||||||
\(601\) | 7.28573 | 0.297191 | 0.148596 | − | 0.988898i | \(-0.452525\pi\) | ||||
0.148596 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(602\) | −61.4953 | −2.50636 | ||||||||
\(603\) | 21.5032 | 0.875680 | ||||||||
\(604\) | −88.9678 | −3.62005 | ||||||||
\(605\) | −6.94375 | −0.282304 | ||||||||
\(606\) | −0.154653 | −0.00628236 | ||||||||
\(607\) | −39.2974 | −1.59503 | −0.797517 | − | 0.603296i | \(-0.793854\pi\) | ||||
−0.797517 | + | 0.603296i | \(0.793854\pi\) | |||||||
\(608\) | 1.94603 | 0.0789221 | ||||||||
\(609\) | −2.17016 | −0.0879394 | ||||||||
\(610\) | −1.29822 | −0.0525635 | ||||||||
\(611\) | 0.528681 | 0.0213881 | ||||||||
\(612\) | 51.5067 | 2.08203 | ||||||||
\(613\) | −10.4053 | −0.420266 | −0.210133 | − | 0.977673i | \(-0.567390\pi\) | ||||
−0.210133 | + | 0.977673i | \(0.567390\pi\) | |||||||
\(614\) | 6.60987 | 0.266753 | ||||||||
\(615\) | 0.728288 | 0.0293674 | ||||||||
\(616\) | −71.6298 | −2.88605 | ||||||||
\(617\) | −0.907254 | −0.0365247 | −0.0182623 | − | 0.999833i | \(-0.505813\pi\) | ||||
−0.0182623 | + | 0.999833i | \(0.505813\pi\) | |||||||
\(618\) | −6.00516 | −0.241563 | ||||||||
\(619\) | 45.4027 | 1.82489 | 0.912444 | − | 0.409202i | \(-0.134193\pi\) | ||||
0.912444 | + | 0.409202i | \(0.134193\pi\) | |||||||
\(620\) | −8.25154 | −0.331390 | ||||||||
\(621\) | −9.17948 | −0.368360 | ||||||||
\(622\) | −55.8612 | −2.23983 | ||||||||
\(623\) | 21.6026 | 0.865490 | ||||||||
\(624\) | 9.27927 | 0.371468 | ||||||||
\(625\) | 23.3442 | 0.933767 | ||||||||
\(626\) | 20.1496 | 0.805340 | ||||||||
\(627\) | 1.72612 | 0.0689345 | ||||||||
\(628\) | 22.7991 | 0.909784 | ||||||||
\(629\) | −39.2411 | −1.56464 | ||||||||
\(630\) | −5.62778 | −0.224216 | ||||||||
\(631\) | −29.2003 | −1.16245 | −0.581224 | − | 0.813744i | \(-0.697426\pi\) | ||||
−0.581224 | + | 0.813744i | \(0.697426\pi\) | |||||||
\(632\) | −32.3958 | −1.28864 | ||||||||
\(633\) | 5.44185 | 0.216294 | ||||||||
\(634\) | 2.48734 | 0.0987849 | ||||||||
\(635\) | 1.55720 | 0.0617955 | ||||||||
\(636\) | 10.4726 | 0.415268 | ||||||||
\(637\) | 9.11975 | 0.361337 | ||||||||
\(638\) | −42.6292 | −1.68771 | ||||||||
\(639\) | −26.1673 | −1.03516 | ||||||||
\(640\) | −5.83672 | −0.230717 | ||||||||
\(641\) | −12.1126 | −0.478419 | −0.239210 | − | 0.970968i | \(-0.576888\pi\) | ||||
−0.239210 | + | 0.970968i | \(0.576888\pi\) | |||||||
\(642\) | 12.1344 | 0.478907 | ||||||||
\(643\) | 18.1936 | 0.717485 | 0.358742 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358742 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(644\) | −49.6424 | −1.95618 | ||||||||
\(645\) | 1.08073 | 0.0425536 | ||||||||
\(646\) | −10.5283 | −0.414231 | ||||||||
\(647\) | 17.1035 | 0.672406 | 0.336203 | − | 0.941789i | \(-0.390857\pi\) | ||||
0.336203 | + | 0.941789i | \(0.390857\pi\) | |||||||
\(648\) | −44.4193 | −1.74495 | ||||||||
\(649\) | 5.09584 | 0.200029 | ||||||||
\(650\) | −71.5188 | −2.80520 | ||||||||
\(651\) | −4.22136 | −0.165448 | ||||||||
\(652\) | −89.6288 | −3.51013 | ||||||||
\(653\) | −22.2528 | −0.870821 | −0.435411 | − | 0.900232i | \(-0.643397\pi\) | ||||
−0.435411 | + | 0.900232i | \(0.643397\pi\) | |||||||
\(654\) | −0.811884 | −0.0317472 | ||||||||
\(655\) | 4.30131 | 0.168066 | ||||||||
\(656\) | 36.7994 | 1.43677 | ||||||||
\(657\) | 30.4284 | 1.18712 | ||||||||
\(658\) | 0.521938 | 0.0203473 | ||||||||
\(659\) | −30.7589 | −1.19820 | −0.599098 | − | 0.800676i | \(-0.704474\pi\) | ||||
−0.599098 | + | 0.800676i | \(0.704474\pi\) | |||||||
\(660\) | 2.41010 | 0.0938131 | ||||||||
\(661\) | 34.9010 | 1.35749 | 0.678746 | − | 0.734373i | \(-0.262524\pi\) | ||||
0.678746 | + | 0.734373i | \(0.262524\pi\) | |||||||
\(662\) | −47.7225 | −1.85479 | ||||||||
\(663\) | −7.61756 | −0.295842 | ||||||||
\(664\) | −11.6097 | −0.450542 | ||||||||
\(665\) | 0.778486 | 0.0301884 | ||||||||
\(666\) | 67.0198 | 2.59696 | ||||||||
\(667\) | −15.4312 | −0.597497 | ||||||||
\(668\) | −28.1260 | −1.08823 | ||||||||
\(669\) | −1.24352 | −0.0480773 | ||||||||
\(670\) | −6.13712 | −0.237098 | ||||||||
\(671\) | −8.82875 | −0.340830 | ||||||||
\(672\) | 1.39006 | 0.0536226 | ||||||||
\(673\) | 23.5766 | 0.908810 | 0.454405 | − | 0.890795i | \(-0.349852\pi\) | ||||
0.454405 | + | 0.890795i | \(0.349852\pi\) | |||||||
\(674\) | 38.2770 | 1.47437 | ||||||||
\(675\) | −8.83547 | −0.340078 | ||||||||
\(676\) | 90.4002 | 3.47693 | ||||||||
\(677\) | 40.5000 | 1.55654 | 0.778271 | − | 0.627929i | \(-0.216097\pi\) | ||||
0.778271 | + | 0.627929i | \(0.216097\pi\) | |||||||
\(678\) | 9.99536 | 0.383869 | ||||||||
\(679\) | −35.5845 | −1.36561 | ||||||||
\(680\) | −7.67816 | −0.294444 | ||||||||
\(681\) | −3.48611 | −0.133588 | ||||||||
\(682\) | −82.9216 | −3.17523 | ||||||||
\(683\) | −15.6052 | −0.597116 | −0.298558 | − | 0.954392i | \(-0.596506\pi\) | ||||
−0.298558 | + | 0.954392i | \(0.596506\pi\) | |||||||
\(684\) | 12.1686 | 0.465277 | ||||||||
\(685\) | −0.0546921 | −0.00208968 | ||||||||
\(686\) | 49.6485 | 1.89559 | ||||||||
\(687\) | 7.06552 | 0.269567 | ||||||||
\(688\) | 54.6077 | 2.08190 | ||||||||
\(689\) | 48.0777 | 1.83161 | ||||||||
\(690\) | 1.28917 | 0.0490777 | ||||||||
\(691\) | −3.94273 | −0.149988 | −0.0749942 | − | 0.997184i | \(-0.523894\pi\) | ||||
−0.0749942 | + | 0.997184i | \(0.523894\pi\) | |||||||
\(692\) | −15.6795 | −0.596046 | ||||||||
\(693\) | −38.2726 | −1.45385 | ||||||||
\(694\) | −20.5795 | −0.781189 | ||||||||
\(695\) | 6.45777 | 0.244957 | ||||||||
\(696\) | 5.05679 | 0.191677 | ||||||||
\(697\) | −30.2094 | −1.14426 | ||||||||
\(698\) | −24.7034 | −0.935037 | ||||||||
\(699\) | −2.96055 | −0.111978 | ||||||||
\(700\) | −47.7820 | −1.80599 | ||||||||
\(701\) | 34.6640 | 1.30924 | 0.654621 | − | 0.755957i | \(-0.272828\pi\) | ||||
0.654621 | + | 0.755957i | \(0.272828\pi\) | |||||||
\(702\) | 26.4392 | 0.997883 | ||||||||
\(703\) | −9.27079 | −0.349655 | ||||||||
\(704\) | −30.8666 | −1.16333 | ||||||||
\(705\) | −0.00917263 | −0.000345461 0 | ||||||||
\(706\) | −27.8878 | −1.04957 | ||||||||
\(707\) | −0.474341 | −0.0178394 | ||||||||
\(708\) | −1.15731 | −0.0434945 | ||||||||
\(709\) | −30.8405 | −1.15824 | −0.579120 | − | 0.815242i | \(-0.696604\pi\) | ||||
−0.579120 | + | 0.815242i | \(0.696604\pi\) | |||||||
\(710\) | 7.46828 | 0.280279 | ||||||||
\(711\) | −17.3094 | −0.649154 | ||||||||
\(712\) | −50.3372 | −1.88646 | ||||||||
\(713\) | −30.0164 | −1.12412 | ||||||||
\(714\) | −7.52042 | −0.281444 | ||||||||
\(715\) | 11.0643 | 0.413780 | ||||||||
\(716\) | −49.3559 | −1.84452 | ||||||||
\(717\) | 6.15835 | 0.229988 | ||||||||
\(718\) | 8.05084 | 0.300455 | ||||||||
\(719\) | 32.0397 | 1.19488 | 0.597439 | − | 0.801915i | \(-0.296185\pi\) | ||||
0.597439 | + | 0.801915i | \(0.296185\pi\) | |||||||
\(720\) | 4.99745 | 0.186244 | ||||||||
\(721\) | −18.4185 | −0.685943 | ||||||||
\(722\) | −2.48734 | −0.0925692 | ||||||||
\(723\) | −7.49432 | −0.278717 | ||||||||
\(724\) | 98.5965 | 3.66431 | ||||||||
\(725\) | −14.8529 | −0.551622 | ||||||||
\(726\) | 15.8475 | 0.588156 | ||||||||
\(727\) | −29.7727 | −1.10421 | −0.552104 | − | 0.833775i | \(-0.686175\pi\) | ||||
−0.552104 | + | 0.833775i | \(0.686175\pi\) | |||||||
\(728\) | 74.6819 | 2.76790 | ||||||||
\(729\) | −22.0746 | −0.817579 | ||||||||
\(730\) | −8.68440 | −0.321424 | ||||||||
\(731\) | −44.8287 | −1.65805 | ||||||||
\(732\) | 2.00509 | 0.0741103 | ||||||||
\(733\) | −54.0820 | −1.99756 | −0.998782 | − | 0.0493439i | \(-0.984287\pi\) | ||||
−0.998782 | + | 0.0493439i | \(0.984287\pi\) | |||||||
\(734\) | −7.58363 | −0.279917 | ||||||||
\(735\) | −0.158228 | −0.00583632 | ||||||||
\(736\) | 9.88415 | 0.364335 | ||||||||
\(737\) | −41.7364 | −1.53738 | ||||||||
\(738\) | 51.5947 | 1.89923 | ||||||||
\(739\) | 52.7803 | 1.94155 | 0.970777 | − | 0.239983i | \(-0.0771418\pi\) | ||||
0.970777 | + | 0.239983i | \(0.0771418\pi\) | |||||||
\(740\) | −12.9444 | −0.475846 | ||||||||
\(741\) | −1.79967 | −0.0661124 | ||||||||
\(742\) | 47.4645 | 1.74248 | ||||||||
\(743\) | 22.2579 | 0.816564 | 0.408282 | − | 0.912856i | \(-0.366128\pi\) | ||||
0.408282 | + | 0.912856i | \(0.366128\pi\) | |||||||
\(744\) | 9.83637 | 0.360619 | ||||||||
\(745\) | 3.40744 | 0.124839 | ||||||||
\(746\) | 35.9461 | 1.31608 | ||||||||
\(747\) | −6.20316 | −0.226962 | ||||||||
\(748\) | −99.9712 | −3.65531 | ||||||||
\(749\) | 37.2177 | 1.35991 | ||||||||
\(750\) | 2.50994 | 0.0916499 | ||||||||
\(751\) | −46.6337 | −1.70169 | −0.850844 | − | 0.525419i | \(-0.823909\pi\) | ||||
−0.850844 | + | 0.525419i | \(0.823909\pi\) | |||||||
\(752\) | −0.463480 | −0.0169014 | ||||||||
\(753\) | −3.39994 | −0.123901 | ||||||||
\(754\) | 44.4456 | 1.61861 | ||||||||
\(755\) | 7.08631 | 0.257897 | ||||||||
\(756\) | 17.6641 | 0.642438 | ||||||||
\(757\) | −28.0542 | −1.01965 | −0.509823 | − | 0.860279i | \(-0.670289\pi\) | ||||
−0.509823 | + | 0.860279i | \(0.670289\pi\) | |||||||
\(758\) | 0.700729 | 0.0254516 | ||||||||
\(759\) | 8.76717 | 0.318228 | ||||||||
\(760\) | −1.81398 | −0.0658001 | ||||||||
\(761\) | 12.0870 | 0.438152 | 0.219076 | − | 0.975708i | \(-0.429696\pi\) | ||||
0.219076 | + | 0.975708i | \(0.429696\pi\) | |||||||
\(762\) | −3.55395 | −0.128746 | ||||||||
\(763\) | −2.49015 | −0.0901494 | ||||||||
\(764\) | −83.1070 | −3.00671 | ||||||||
\(765\) | −4.10252 | −0.148327 | ||||||||
\(766\) | −63.5604 | −2.29653 | ||||||||
\(767\) | −5.31297 | −0.191840 | ||||||||
\(768\) | 9.97236 | 0.359846 | ||||||||
\(769\) | 28.5387 | 1.02913 | 0.514565 | − | 0.857451i | \(-0.327953\pi\) | ||||
0.514565 | + | 0.857451i | \(0.327953\pi\) | |||||||
\(770\) | 10.9232 | 0.393643 | ||||||||
\(771\) | 3.23074 | 0.116352 | ||||||||
\(772\) | −69.2623 | −2.49281 | ||||||||
\(773\) | −14.4280 | −0.518940 | −0.259470 | − | 0.965751i | \(-0.583548\pi\) | ||||
−0.259470 | + | 0.965751i | \(0.583548\pi\) | |||||||
\(774\) | 76.5629 | 2.75200 | ||||||||
\(775\) | −28.8916 | −1.03782 | ||||||||
\(776\) | 82.9171 | 2.97655 | ||||||||
\(777\) | −6.62216 | −0.237569 | ||||||||
\(778\) | 68.6381 | 2.46079 | ||||||||
\(779\) | −7.13705 | −0.255711 | ||||||||
\(780\) | −2.51280 | −0.0899725 | ||||||||
\(781\) | 50.7891 | 1.81738 | ||||||||
\(782\) | −53.4747 | −1.91225 | ||||||||
\(783\) | 5.49083 | 0.196226 | ||||||||
\(784\) | −7.99503 | −0.285537 | ||||||||
\(785\) | −1.81596 | −0.0648143 | ||||||||
\(786\) | −9.81674 | −0.350152 | ||||||||
\(787\) | 9.95770 | 0.354954 | 0.177477 | − | 0.984125i | \(-0.443207\pi\) | ||||
0.177477 | + | 0.984125i | \(0.443207\pi\) | |||||||
\(788\) | −18.1744 | −0.647437 | ||||||||
\(789\) | −2.59402 | −0.0923495 | ||||||||
\(790\) | 4.94019 | 0.175764 | ||||||||
\(791\) | 30.6570 | 1.09004 | ||||||||
\(792\) | 89.1806 | 3.16889 | ||||||||
\(793\) | 9.20495 | 0.326877 | ||||||||
\(794\) | −24.4698 | −0.868401 | ||||||||
\(795\) | −0.834150 | −0.0295842 | ||||||||
\(796\) | 114.728 | 4.06644 | ||||||||
\(797\) | −10.5310 | −0.373028 | −0.186514 | − | 0.982452i | \(-0.559719\pi\) | ||||
−0.186514 | + | 0.982452i | \(0.559719\pi\) | |||||||
\(798\) | −1.77672 | −0.0628950 | ||||||||
\(799\) | 0.380481 | 0.0134605 | ||||||||
\(800\) | 9.51374 | 0.336362 | ||||||||
\(801\) | −26.8957 | −0.950312 | ||||||||
\(802\) | 76.3663 | 2.69659 | ||||||||
\(803\) | −59.0596 | −2.08417 | ||||||||
\(804\) | 9.47873 | 0.334289 | ||||||||
\(805\) | 3.95403 | 0.139361 | ||||||||
\(806\) | 86.4548 | 3.04524 | ||||||||
\(807\) | −0.331463 | −0.0116680 | ||||||||
\(808\) | 1.10528 | 0.0388837 | ||||||||
\(809\) | −13.9718 | −0.491223 | −0.245611 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245611 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(810\) | 6.77370 | 0.238004 | ||||||||
\(811\) | −49.9644 | −1.75449 | −0.877244 | − | 0.480044i | \(-0.840621\pi\) | ||||
−0.877244 | + | 0.480044i | \(0.840621\pi\) | |||||||
\(812\) | 29.6943 | 1.04207 | ||||||||
\(813\) | −2.65600 | −0.0931499 | ||||||||
\(814\) | −130.081 | −4.55934 | ||||||||
\(815\) | 7.13896 | 0.250067 | ||||||||
\(816\) | 6.67811 | 0.233781 | ||||||||
\(817\) | −10.5909 | −0.370528 | ||||||||
\(818\) | −2.65383 | −0.0927889 | ||||||||
\(819\) | 39.9034 | 1.39434 | ||||||||
\(820\) | −9.96515 | −0.347998 | ||||||||
\(821\) | 8.15054 | 0.284456 | 0.142228 | − | 0.989834i | \(-0.454573\pi\) | ||||
0.142228 | + | 0.989834i | \(0.454573\pi\) | |||||||
\(822\) | 0.124822 | 0.00435367 | ||||||||
\(823\) | 4.77565 | 0.166469 | 0.0832344 | − | 0.996530i | \(-0.473475\pi\) | ||||
0.0832344 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(824\) | 42.9179 | 1.49511 | ||||||||
\(825\) | 8.43862 | 0.293795 | ||||||||
\(826\) | −5.24522 | −0.182504 | ||||||||
\(827\) | −39.0985 | −1.35959 | −0.679794 | − | 0.733403i | \(-0.737931\pi\) | ||||
−0.679794 | + | 0.733403i | \(0.737931\pi\) | |||||||
\(828\) | 61.8058 | 2.14790 | ||||||||
\(829\) | 32.3495 | 1.12354 | 0.561771 | − | 0.827292i | \(-0.310120\pi\) | ||||
0.561771 | + | 0.827292i | \(0.310120\pi\) | |||||||
\(830\) | 1.77041 | 0.0614518 | ||||||||
\(831\) | 6.67516 | 0.231559 | ||||||||
\(832\) | 32.1818 | 1.11570 | ||||||||
\(833\) | 6.56331 | 0.227405 | ||||||||
\(834\) | −14.7384 | −0.510348 | ||||||||
\(835\) | 2.24024 | 0.0775268 | ||||||||
\(836\) | −23.6184 | −0.816861 | ||||||||
\(837\) | 10.6807 | 0.369178 | ||||||||
\(838\) | 85.0896 | 2.93937 | ||||||||
\(839\) | −18.8784 | −0.651753 | −0.325877 | − | 0.945412i | \(-0.605659\pi\) | ||||
−0.325877 | + | 0.945412i | \(0.605659\pi\) | |||||||
\(840\) | −1.29573 | −0.0447071 | ||||||||
\(841\) | −19.7696 | −0.681711 | ||||||||
\(842\) | 79.8815 | 2.75290 | ||||||||
\(843\) | −7.81635 | −0.269209 | ||||||||
\(844\) | −74.4608 | −2.56305 | ||||||||
\(845\) | −7.20041 | −0.247701 | ||||||||
\(846\) | −0.649824 | −0.0223414 | ||||||||
\(847\) | 48.6063 | 1.67013 | ||||||||
\(848\) | −42.1484 | −1.44738 | ||||||||
\(849\) | 7.74210 | 0.265708 | ||||||||
\(850\) | −51.4707 | −1.76543 | ||||||||
\(851\) | −47.0876 | −1.61414 | ||||||||
\(852\) | −11.5347 | −0.395172 | ||||||||
\(853\) | −46.9480 | −1.60747 | −0.803734 | − | 0.594989i | \(-0.797157\pi\) | ||||
−0.803734 | + | 0.594989i | \(0.797157\pi\) | |||||||
\(854\) | 9.08755 | 0.310970 | ||||||||
\(855\) | −0.969231 | −0.0331470 | ||||||||
\(856\) | −86.7226 | −2.96412 | ||||||||
\(857\) | −49.2629 | −1.68279 | −0.841394 | − | 0.540423i | \(-0.818264\pi\) | ||||
−0.841394 | + | 0.540423i | \(0.818264\pi\) | |||||||
\(858\) | −25.2516 | −0.862077 | ||||||||
\(859\) | −53.7341 | −1.83338 | −0.916692 | − | 0.399593i | \(-0.869151\pi\) | ||||
−0.916692 | + | 0.399593i | \(0.869151\pi\) | |||||||
\(860\) | −14.7876 | −0.504253 | ||||||||
\(861\) | −5.09802 | −0.173740 | ||||||||
\(862\) | 68.5718 | 2.33556 | ||||||||
\(863\) | −1.08113 | −0.0368022 | −0.0184011 | − | 0.999831i | \(-0.505858\pi\) | ||||
−0.0184011 | + | 0.999831i | \(0.505858\pi\) | |||||||
\(864\) | −3.51705 | −0.119653 | ||||||||
\(865\) | 1.24888 | 0.0424631 | ||||||||
\(866\) | −47.8241 | −1.62513 | ||||||||
\(867\) | −0.280374 | −0.00952201 | ||||||||
\(868\) | 57.7608 | 1.96053 | ||||||||
\(869\) | 33.5965 | 1.13968 | ||||||||
\(870\) | −0.771133 | −0.0261439 | ||||||||
\(871\) | 43.5148 | 1.47444 | ||||||||
\(872\) | 5.80240 | 0.196494 | ||||||||
\(873\) | 44.3035 | 1.49945 | ||||||||
\(874\) | −12.6335 | −0.427335 | ||||||||
\(875\) | 7.69828 | 0.260249 | ||||||||
\(876\) | 13.4130 | 0.453182 | ||||||||
\(877\) | 12.5264 | 0.422988 | 0.211494 | − | 0.977379i | \(-0.432167\pi\) | ||||
0.211494 | + | 0.977379i | \(0.432167\pi\) | |||||||
\(878\) | 19.6761 | 0.664036 | ||||||||
\(879\) | 4.94462 | 0.166778 | ||||||||
\(880\) | −9.69974 | −0.326978 | ||||||||
\(881\) | 29.8243 | 1.00481 | 0.502403 | − | 0.864634i | \(-0.332450\pi\) | ||||
0.502403 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(882\) | −11.2095 | −0.377442 | ||||||||
\(883\) | 24.1749 | 0.813550 | 0.406775 | − | 0.913528i | \(-0.366653\pi\) | ||||
0.406775 | + | 0.913528i | \(0.366653\pi\) | |||||||
\(884\) | 104.231 | 3.50567 | ||||||||
\(885\) | 0.0921803 | 0.00309861 | ||||||||
\(886\) | 100.765 | 3.38527 | ||||||||
\(887\) | 9.65289 | 0.324112 | 0.162056 | − | 0.986782i | \(-0.448187\pi\) | ||||
0.162056 | + | 0.986782i | \(0.448187\pi\) | |||||||
\(888\) | 15.4306 | 0.517816 | ||||||||
\(889\) | −10.9004 | −0.365587 | ||||||||
\(890\) | 7.67615 | 0.257305 | ||||||||
\(891\) | 46.0656 | 1.54326 | ||||||||
\(892\) | 17.0151 | 0.569707 | ||||||||
\(893\) | 0.0898896 | 0.00300804 | ||||||||
\(894\) | −7.77670 | −0.260092 | ||||||||
\(895\) | 3.93121 | 0.131406 | ||||||||
\(896\) | 40.8571 | 1.36494 | ||||||||
\(897\) | −9.14074 | −0.305200 | ||||||||
\(898\) | 39.5726 | 1.32055 | ||||||||
\(899\) | 17.9548 | 0.598825 | ||||||||
\(900\) | 59.4896 | 1.98299 | ||||||||
\(901\) | 34.6006 | 1.15271 | ||||||||
\(902\) | −100.142 | −3.33436 | ||||||||
\(903\) | −7.56510 | −0.251751 | ||||||||
\(904\) | −71.4352 | −2.37590 | ||||||||
\(905\) | −7.85324 | −0.261051 | ||||||||
\(906\) | −16.1729 | −0.537308 | ||||||||
\(907\) | 14.1432 | 0.469616 | 0.234808 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234808 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(908\) | 47.7004 | 1.58299 | ||||||||
\(909\) | 0.590564 | 0.0195878 | ||||||||
\(910\) | −11.3886 | −0.377528 | ||||||||
\(911\) | 48.1626 | 1.59570 | 0.797848 | − | 0.602858i | \(-0.205971\pi\) | ||||
0.797848 | + | 0.602858i | \(0.205971\pi\) | |||||||
\(912\) | 1.57772 | 0.0522435 | ||||||||
\(913\) | 12.0399 | 0.398464 | ||||||||
\(914\) | 9.92600 | 0.328323 | ||||||||
\(915\) | −0.159706 | −0.00527972 | ||||||||
\(916\) | −96.6774 | −3.19431 | ||||||||
\(917\) | −30.1091 | −0.994292 | ||||||||
\(918\) | 19.0278 | 0.628010 | ||||||||
\(919\) | 22.3758 | 0.738109 | 0.369054 | − | 0.929408i | \(-0.379682\pi\) | ||||
0.369054 | + | 0.929408i | \(0.379682\pi\) | |||||||
\(920\) | −9.21346 | −0.303759 | ||||||||
\(921\) | 0.813140 | 0.0267939 | ||||||||
\(922\) | 8.33159 | 0.274386 | ||||||||
\(923\) | −52.9533 | −1.74298 | ||||||||
\(924\) | −16.8707 | −0.555006 | ||||||||
\(925\) | −45.3229 | −1.49021 | ||||||||
\(926\) | 45.9848 | 1.51115 | ||||||||
\(927\) | 22.9315 | 0.753168 | ||||||||
\(928\) | −5.91235 | −0.194082 | ||||||||
\(929\) | −42.4069 | −1.39133 | −0.695663 | − | 0.718369i | \(-0.744889\pi\) | ||||
−0.695663 | + | 0.718369i | \(0.744889\pi\) | |||||||
\(930\) | −1.49999 | −0.0491867 | ||||||||
\(931\) | 1.55060 | 0.0508187 | ||||||||
\(932\) | 40.5091 | 1.32692 | ||||||||
\(933\) | −6.87200 | −0.224979 | ||||||||
\(934\) | −25.9788 | −0.850053 | ||||||||
\(935\) | 7.96274 | 0.260409 | ||||||||
\(936\) | −92.9805 | −3.03916 | ||||||||
\(937\) | −51.4560 | −1.68099 | −0.840497 | − | 0.541816i | \(-0.817737\pi\) | ||||
−0.840497 | + | 0.541816i | \(0.817737\pi\) | |||||||
\(938\) | 42.9599 | 1.40269 | ||||||||
\(939\) | 2.47879 | 0.0808922 | ||||||||
\(940\) | 0.125509 | 0.00409365 | ||||||||
\(941\) | 8.18511 | 0.266827 | 0.133414 | − | 0.991060i | \(-0.457406\pi\) | ||||
0.133414 | + | 0.991060i | \(0.457406\pi\) | |||||||
\(942\) | 4.14451 | 0.135035 | ||||||||
\(943\) | −36.2500 | −1.18046 | ||||||||
\(944\) | 4.65774 | 0.151597 | ||||||||
\(945\) | −1.40695 | −0.0457682 | ||||||||
\(946\) | −148.604 | −4.83152 | ||||||||
\(947\) | 29.3625 | 0.954152 | 0.477076 | − | 0.878862i | \(-0.341697\pi\) | ||||
0.477076 | + | 0.878862i | \(0.341697\pi\) | |||||||
\(948\) | −7.63008 | −0.247813 | ||||||||
\(949\) | 61.5761 | 1.99884 | ||||||||
\(950\) | −12.1601 | −0.394525 | ||||||||
\(951\) | 0.305991 | 0.00992242 | ||||||||
\(952\) | 53.7472 | 1.74196 | ||||||||
\(953\) | −32.5726 | −1.05513 | −0.527565 | − | 0.849515i | \(-0.676895\pi\) | ||||
−0.527565 | + | 0.849515i | \(0.676895\pi\) | |||||||
\(954\) | −59.0943 | −1.91325 | ||||||||
\(955\) | 6.61950 | 0.214202 | ||||||||
\(956\) | −84.2645 | −2.72531 | ||||||||
\(957\) | −5.24421 | −0.169521 | ||||||||
\(958\) | 86.6564 | 2.79974 | ||||||||
\(959\) | 0.382845 | 0.0123627 | ||||||||
\(960\) | −0.558356 | −0.0180209 | ||||||||
\(961\) | 3.92527 | 0.126622 | ||||||||
\(962\) | 135.624 | 4.37269 | ||||||||
\(963\) | −46.3368 | −1.49318 | ||||||||
\(964\) | 102.545 | 3.30274 | ||||||||
\(965\) | 5.51677 | 0.177591 | ||||||||
\(966\) | −9.02417 | −0.290348 | ||||||||
\(967\) | 14.7453 | 0.474177 | 0.237088 | − | 0.971488i | \(-0.423807\pi\) | ||||
0.237088 | + | 0.971488i | \(0.423807\pi\) | |||||||
\(968\) | −113.260 | −3.64030 | ||||||||
\(969\) | −1.29519 | −0.0416074 | ||||||||
\(970\) | −12.6444 | −0.405987 | ||||||||
\(971\) | −19.3873 | −0.622169 | −0.311084 | − | 0.950382i | \(-0.600692\pi\) | ||||
−0.311084 | + | 0.950382i | \(0.600692\pi\) | |||||||
\(972\) | −33.1626 | −1.06369 | ||||||||
\(973\) | −45.2044 | −1.44919 | ||||||||
\(974\) | 46.9998 | 1.50597 | ||||||||
\(975\) | −8.79819 | −0.281768 | ||||||||
\(976\) | −8.06973 | −0.258306 | ||||||||
\(977\) | −38.6596 | −1.23683 | −0.618415 | − | 0.785851i | \(-0.712225\pi\) | ||||
−0.618415 | + | 0.785851i | \(0.712225\pi\) | |||||||
\(978\) | −16.2930 | −0.520994 | ||||||||
\(979\) | 52.2028 | 1.66841 | ||||||||
\(980\) | 2.16503 | 0.0691593 | ||||||||
\(981\) | 3.10029 | 0.0989845 | ||||||||
\(982\) | −95.7935 | −3.05689 | ||||||||
\(983\) | 8.31092 | 0.265077 | 0.132539 | − | 0.991178i | \(-0.457687\pi\) | ||||
0.132539 | + | 0.991178i | \(0.457687\pi\) | |||||||
\(984\) | 11.8791 | 0.378692 | ||||||||
\(985\) | 1.44760 | 0.0461243 | ||||||||
\(986\) | 31.9867 | 1.01866 | ||||||||
\(987\) | 0.0642084 | 0.00204378 | ||||||||
\(988\) | 24.6248 | 0.783420 | ||||||||
\(989\) | −53.7925 | −1.71050 | ||||||||
\(990\) | −13.5996 | −0.432222 | ||||||||
\(991\) | −24.5068 | −0.778483 | −0.389241 | − | 0.921136i | \(-0.627263\pi\) | ||||
−0.389241 | + | 0.921136i | \(0.627263\pi\) | |||||||
\(992\) | −11.5006 | −0.365144 | ||||||||
\(993\) | −5.87078 | −0.186304 | ||||||||
\(994\) | −52.2779 | −1.65816 | ||||||||
\(995\) | −9.13815 | −0.289699 | ||||||||
\(996\) | −2.73438 | −0.0866422 | ||||||||
\(997\) | 17.3337 | 0.548963 | 0.274481 | − | 0.961592i | \(-0.411494\pi\) | ||||
0.274481 | + | 0.961592i | \(0.411494\pi\) | |||||||
\(998\) | 107.028 | 3.38791 | ||||||||
\(999\) | 16.7550 | 0.530106 |
(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 | 6023.2.a.b.1.7 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.7 | ✓ | 99 | 1.1 | even | 1 | trivial |