Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.218728\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.218728 | 0.0773321 | 0.0386660 | − | 0.999252i | \(-0.487689\pi\) | ||||
0.0386660 | + | 0.999252i | \(0.487689\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.95216 | −0.994020 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −0.656184 | −0.0446477 | ||||||||
\(7\) | −21.0000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −3.48919 | −0.154202 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 1.09364 | 0.0345840 | ||||||||
\(11\) | −1.46553 | −0.0401704 | −0.0200852 | − | 0.999798i | \(-0.506394\pi\) | ||||
−0.0200852 | + | 0.999798i | \(0.506394\pi\) | |||||||
\(12\) | 23.8565 | 0.573898 | ||||||||
\(13\) | −79.4367 | −1.69475 | −0.847376 | − | 0.530994i | \(-0.821819\pi\) | ||||
−0.847376 | + | 0.530994i | \(0.821819\pi\) | |||||||
\(14\) | −4.59329 | −0.0876863 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 62.8541 | 0.982095 | ||||||||
\(17\) | −65.4406 | −0.933628 | −0.466814 | − | 0.884355i | \(-0.654598\pi\) | ||||
−0.466814 | + | 0.884355i | \(0.654598\pi\) | |||||||
\(18\) | 1.96855 | 0.0257774 | ||||||||
\(19\) | 116.908 | 1.41160 | 0.705802 | − | 0.708409i | \(-0.250587\pi\) | ||||
0.705802 | + | 0.708409i | \(0.250587\pi\) | |||||||
\(20\) | −39.7608 | −0.444539 | ||||||||
\(21\) | 63.0000 | 0.654654 | ||||||||
\(22\) | −0.320553 | −0.00310646 | ||||||||
\(23\) | −177.448 | −1.60871 | −0.804356 | − | 0.594148i | \(-0.797489\pi\) | ||||
−0.804356 | + | 0.594148i | \(0.797489\pi\) | |||||||
\(24\) | 10.4676 | 0.0890284 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −17.3750 | −0.131059 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 166.995 | 1.12711 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −3.28092 | −0.0199671 | ||||||||
\(31\) | 77.7850 | 0.450664 | 0.225332 | − | 0.974282i | \(-0.427653\pi\) | ||||
0.225332 | + | 0.974282i | \(0.427653\pi\) | |||||||
\(32\) | 41.6614 | 0.230149 | ||||||||
\(33\) | 4.39659 | 0.0231924 | ||||||||
\(34\) | −14.3137 | −0.0721994 | ||||||||
\(35\) | −105.000 | −0.507093 | ||||||||
\(36\) | −71.5694 | −0.331340 | ||||||||
\(37\) | 175.767 | 0.780973 | 0.390486 | − | 0.920609i | \(-0.372307\pi\) | ||||
0.390486 | + | 0.920609i | \(0.372307\pi\) | |||||||
\(38\) | 25.5710 | 0.109162 | ||||||||
\(39\) | 238.310 | 0.978465 | ||||||||
\(40\) | −17.4459 | −0.0689611 | ||||||||
\(41\) | 62.4580 | 0.237910 | 0.118955 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118955 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(42\) | 13.7799 | 0.0506257 | ||||||||
\(43\) | 66.0473 | 0.234235 | 0.117118 | − | 0.993118i | \(-0.462635\pi\) | ||||
0.117118 | + | 0.993118i | \(0.462635\pi\) | |||||||
\(44\) | 11.6541 | 0.0399301 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −38.8128 | −0.124405 | ||||||||
\(47\) | 179.320 | 0.556521 | 0.278260 | − | 0.960506i | \(-0.410242\pi\) | ||||
0.278260 | + | 0.960506i | \(0.410242\pi\) | |||||||
\(48\) | −188.562 | −0.567013 | ||||||||
\(49\) | 98.0000 | 0.285714 | ||||||||
\(50\) | 5.46820 | 0.0154664 | ||||||||
\(51\) | 196.322 | 0.539031 | ||||||||
\(52\) | 631.693 | 1.68462 | ||||||||
\(53\) | 676.773 | 1.75400 | 0.876999 | − | 0.480492i | \(-0.159542\pi\) | ||||
0.876999 | + | 0.480492i | \(0.159542\pi\) | |||||||
\(54\) | −5.90566 | −0.0148826 | ||||||||
\(55\) | −7.32765 | −0.0179647 | ||||||||
\(56\) | 73.2729 | 0.174848 | ||||||||
\(57\) | −350.723 | −0.814990 | ||||||||
\(58\) | 6.34312 | 0.0143602 | ||||||||
\(59\) | 415.156 | 0.916080 | 0.458040 | − | 0.888932i | \(-0.348552\pi\) | ||||
0.458040 | + | 0.888932i | \(0.348552\pi\) | |||||||
\(60\) | 119.282 | 0.256655 | ||||||||
\(61\) | −426.377 | −0.894951 | −0.447475 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447475 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(62\) | 17.0138 | 0.0348508 | ||||||||
\(63\) | −189.000 | −0.377964 | ||||||||
\(64\) | −493.720 | −0.964297 | ||||||||
\(65\) | −397.183 | −0.757916 | ||||||||
\(66\) | 0.961658 | 0.00179351 | ||||||||
\(67\) | 79.1909 | 0.144399 | 0.0721993 | − | 0.997390i | \(-0.476998\pi\) | ||||
0.0721993 | + | 0.997390i | \(0.476998\pi\) | |||||||
\(68\) | 520.394 | 0.928045 | ||||||||
\(69\) | 532.343 | 0.928790 | ||||||||
\(70\) | −22.9665 | −0.0392145 | ||||||||
\(71\) | 218.606 | 0.365404 | 0.182702 | − | 0.983168i | \(-0.441516\pi\) | ||||
0.182702 | + | 0.983168i | \(0.441516\pi\) | |||||||
\(72\) | −31.4027 | −0.0514006 | ||||||||
\(73\) | 1024.13 | 1.64199 | 0.820996 | − | 0.570933i | \(-0.193419\pi\) | ||||
0.820996 | + | 0.570933i | \(0.193419\pi\) | |||||||
\(74\) | 38.4453 | 0.0603943 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −929.669 | −1.40316 | ||||||||
\(77\) | 30.7761 | 0.0455489 | ||||||||
\(78\) | 52.1251 | 0.0756667 | ||||||||
\(79\) | 1053.21 | 1.49994 | 0.749972 | − | 0.661470i | \(-0.230067\pi\) | ||||
0.749972 | + | 0.661470i | \(0.230067\pi\) | |||||||
\(80\) | 314.270 | 0.439206 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 13.6613 | 0.0183981 | ||||||||
\(83\) | −1179.75 | −1.56017 | −0.780084 | − | 0.625675i | \(-0.784824\pi\) | ||||
−0.780084 | + | 0.625675i | \(0.784824\pi\) | |||||||
\(84\) | −500.986 | −0.650739 | ||||||||
\(85\) | −327.203 | −0.417531 | ||||||||
\(86\) | 14.4464 | 0.0181139 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | 5.11351 | 0.00619434 | ||||||||
\(89\) | 1411.60 | 1.68123 | 0.840613 | − | 0.541637i | \(-0.182195\pi\) | ||||
0.840613 | + | 0.541637i | \(0.182195\pi\) | |||||||
\(90\) | 9.84277 | 0.0115280 | ||||||||
\(91\) | 1668.17 | 1.92167 | ||||||||
\(92\) | 1411.09 | 1.59909 | ||||||||
\(93\) | −233.355 | −0.260191 | ||||||||
\(94\) | 39.2223 | 0.0430369 | ||||||||
\(95\) | 584.539 | 0.631288 | ||||||||
\(96\) | −124.984 | −0.132877 | ||||||||
\(97\) | 884.714 | 0.926073 | 0.463037 | − | 0.886339i | \(-0.346760\pi\) | ||||
0.463037 | + | 0.886339i | \(0.346760\pi\) | |||||||
\(98\) | 21.4353 | 0.0220949 | ||||||||
\(99\) | −13.1898 | −0.0133901 | ||||||||
\(100\) | −198.804 | −0.198804 | ||||||||
\(101\) | −647.242 | −0.637654 | −0.318827 | − | 0.947813i | \(-0.603289\pi\) | ||||
−0.318827 | + | 0.947813i | \(0.603289\pi\) | |||||||
\(102\) | 42.9411 | 0.0416844 | ||||||||
\(103\) | −1550.51 | −1.48326 | −0.741631 | − | 0.670808i | \(-0.765947\pi\) | ||||
−0.741631 | + | 0.670808i | \(0.765947\pi\) | |||||||
\(104\) | 277.169 | 0.261334 | ||||||||
\(105\) | 315.000 | 0.292770 | ||||||||
\(106\) | 148.029 | 0.135640 | ||||||||
\(107\) | −1212.45 | −1.09544 | −0.547718 | − | 0.836663i | \(-0.684503\pi\) | ||||
−0.547718 | + | 0.836663i | \(0.684503\pi\) | |||||||
\(108\) | 214.708 | 0.191299 | ||||||||
\(109\) | −1128.35 | −0.991528 | −0.495764 | − | 0.868457i | \(-0.665112\pi\) | ||||
−0.495764 | + | 0.868457i | \(0.665112\pi\) | |||||||
\(110\) | −1.60276 | −0.00138925 | ||||||||
\(111\) | −527.302 | −0.450895 | ||||||||
\(112\) | −1319.94 | −1.11359 | ||||||||
\(113\) | −825.104 | −0.686896 | −0.343448 | − | 0.939172i | \(-0.611595\pi\) | ||||
−0.343448 | + | 0.939172i | \(0.611595\pi\) | |||||||
\(114\) | −76.7130 | −0.0630249 | ||||||||
\(115\) | −887.238 | −0.719438 | ||||||||
\(116\) | −230.613 | −0.184585 | ||||||||
\(117\) | −714.930 | −0.564917 | ||||||||
\(118\) | 90.8063 | 0.0708424 | ||||||||
\(119\) | 1374.25 | 1.05864 | ||||||||
\(120\) | 52.3378 | 0.0398147 | ||||||||
\(121\) | −1328.85 | −0.998386 | ||||||||
\(122\) | −93.2607 | −0.0692084 | ||||||||
\(123\) | −187.374 | −0.137357 | ||||||||
\(124\) | −618.558 | −0.447969 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −41.3396 | −0.0292288 | ||||||||
\(127\) | 2020.56 | 1.41178 | 0.705889 | − | 0.708322i | \(-0.250548\pi\) | ||||
0.705889 | + | 0.708322i | \(0.250548\pi\) | |||||||
\(128\) | −441.282 | −0.304720 | ||||||||
\(129\) | −198.142 | −0.135236 | ||||||||
\(130\) | −86.8752 | −0.0586112 | ||||||||
\(131\) | 286.621 | 0.191162 | 0.0955809 | − | 0.995422i | \(-0.469529\pi\) | ||||
0.0955809 | + | 0.995422i | \(0.469529\pi\) | |||||||
\(132\) | −34.9624 | −0.0230537 | ||||||||
\(133\) | −2455.06 | −1.60061 | ||||||||
\(134\) | 17.3213 | 0.0111666 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 228.335 | 0.143967 | ||||||||
\(137\) | 1903.55 | 1.18709 | 0.593545 | − | 0.804801i | \(-0.297728\pi\) | ||||
0.593545 | + | 0.804801i | \(0.297728\pi\) | |||||||
\(138\) | 116.438 | 0.0718253 | ||||||||
\(139\) | −1439.13 | −0.878167 | −0.439083 | − | 0.898446i | \(-0.644697\pi\) | ||||
−0.439083 | + | 0.898446i | \(0.644697\pi\) | |||||||
\(140\) | 834.977 | 0.504060 | ||||||||
\(141\) | −537.959 | −0.321307 | ||||||||
\(142\) | 47.8152 | 0.0282575 | ||||||||
\(143\) | 116.417 | 0.0680788 | ||||||||
\(144\) | 565.687 | 0.327365 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | 224.006 | 0.126979 | ||||||||
\(147\) | −294.000 | −0.164957 | ||||||||
\(148\) | −1397.73 | −0.776302 | ||||||||
\(149\) | 1733.83 | 0.953295 | 0.476647 | − | 0.879095i | \(-0.341852\pi\) | ||||
0.476647 | + | 0.879095i | \(0.341852\pi\) | |||||||
\(150\) | −16.4046 | −0.00892954 | ||||||||
\(151\) | −2585.20 | −1.39325 | −0.696623 | − | 0.717437i | \(-0.745315\pi\) | ||||
−0.696623 | + | 0.717437i | \(0.745315\pi\) | |||||||
\(152\) | −407.913 | −0.217672 | ||||||||
\(153\) | −588.966 | −0.311209 | ||||||||
\(154\) | 6.73161 | 0.00352239 | ||||||||
\(155\) | 388.925 | 0.201543 | ||||||||
\(156\) | −1895.08 | −0.972614 | ||||||||
\(157\) | 2911.36 | 1.47995 | 0.739975 | − | 0.672635i | \(-0.234837\pi\) | ||||
0.739975 | + | 0.672635i | \(0.234837\pi\) | |||||||
\(158\) | 230.367 | 0.115994 | ||||||||
\(159\) | −2030.32 | −1.01267 | ||||||||
\(160\) | 208.307 | 0.102926 | ||||||||
\(161\) | 3726.40 | 1.82411 | ||||||||
\(162\) | 17.7170 | 0.00859245 | ||||||||
\(163\) | −2877.35 | −1.38265 | −0.691323 | − | 0.722546i | \(-0.742972\pi\) | ||||
−0.691323 | + | 0.722546i | \(0.742972\pi\) | |||||||
\(164\) | −496.676 | −0.236487 | ||||||||
\(165\) | 21.9830 | 0.0103719 | ||||||||
\(166\) | −258.044 | −0.120651 | ||||||||
\(167\) | 1135.80 | 0.526292 | 0.263146 | − | 0.964756i | \(-0.415240\pi\) | ||||
0.263146 | + | 0.964756i | \(0.415240\pi\) | |||||||
\(168\) | −219.819 | −0.100949 | ||||||||
\(169\) | 4113.18 | 1.87218 | ||||||||
\(170\) | −71.5685 | −0.0322886 | ||||||||
\(171\) | 1052.17 | 0.470535 | ||||||||
\(172\) | −525.219 | −0.232835 | ||||||||
\(173\) | 3337.04 | 1.46653 | 0.733267 | − | 0.679941i | \(-0.237995\pi\) | ||||
0.733267 | + | 0.679941i | \(0.237995\pi\) | |||||||
\(174\) | −19.0294 | −0.00829087 | ||||||||
\(175\) | −525.000 | −0.226779 | ||||||||
\(176\) | −92.1145 | −0.0394511 | ||||||||
\(177\) | −1245.47 | −0.528899 | ||||||||
\(178\) | 308.756 | 0.130013 | ||||||||
\(179\) | −4693.70 | −1.95991 | −0.979955 | − | 0.199220i | \(-0.936159\pi\) | ||||
−0.979955 | + | 0.199220i | \(0.936159\pi\) | |||||||
\(180\) | −357.847 | −0.148180 | ||||||||
\(181\) | 1068.75 | 0.438892 | 0.219446 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219446 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(182\) | 364.876 | 0.148607 | ||||||||
\(183\) | 1279.13 | 0.516700 | ||||||||
\(184\) | 619.147 | 0.248066 | ||||||||
\(185\) | 878.837 | 0.349262 | ||||||||
\(186\) | −51.0413 | −0.0201211 | ||||||||
\(187\) | 95.9052 | 0.0375042 | ||||||||
\(188\) | −1425.98 | −0.553192 | ||||||||
\(189\) | 567.000 | 0.218218 | ||||||||
\(190\) | 127.855 | 0.0488188 | ||||||||
\(191\) | −1082.04 | −0.409913 | −0.204956 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204956 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(192\) | 1481.16 | 0.556737 | ||||||||
\(193\) | −4044.87 | −1.50858 | −0.754290 | − | 0.656541i | \(-0.772019\pi\) | ||||
−0.754290 | + | 0.656541i | \(0.772019\pi\) | |||||||
\(194\) | 193.512 | 0.0716152 | ||||||||
\(195\) | 1191.55 | 0.437583 | ||||||||
\(196\) | −779.311 | −0.284006 | ||||||||
\(197\) | 1433.82 | 0.518556 | 0.259278 | − | 0.965803i | \(-0.416515\pi\) | ||||
0.259278 | + | 0.965803i | \(0.416515\pi\) | |||||||
\(198\) | −2.88497 | −0.00103549 | ||||||||
\(199\) | 3460.17 | 1.23259 | 0.616293 | − | 0.787517i | \(-0.288634\pi\) | ||||
0.616293 | + | 0.787517i | \(0.288634\pi\) | |||||||
\(200\) | −87.2297 | −0.0308403 | ||||||||
\(201\) | −237.573 | −0.0833686 | ||||||||
\(202\) | −141.570 | −0.0493111 | ||||||||
\(203\) | −609.000 | −0.210559 | ||||||||
\(204\) | −1561.18 | −0.535807 | ||||||||
\(205\) | 312.290 | 0.106397 | ||||||||
\(206\) | −339.139 | −0.114704 | ||||||||
\(207\) | −1597.03 | −0.536237 | ||||||||
\(208\) | −4992.92 | −1.66441 | ||||||||
\(209\) | −171.332 | −0.0567046 | ||||||||
\(210\) | 68.8994 | 0.0226405 | ||||||||
\(211\) | 2044.61 | 0.667093 | 0.333547 | − | 0.942734i | \(-0.391755\pi\) | ||||
0.333547 | + | 0.942734i | \(0.391755\pi\) | |||||||
\(212\) | −5381.81 | −1.74351 | ||||||||
\(213\) | −655.817 | −0.210966 | ||||||||
\(214\) | −265.196 | −0.0847123 | ||||||||
\(215\) | 330.237 | 0.104753 | ||||||||
\(216\) | 94.2080 | 0.0296761 | ||||||||
\(217\) | −1633.48 | −0.511005 | ||||||||
\(218\) | −246.802 | −0.0766769 | ||||||||
\(219\) | −3072.39 | −0.948005 | ||||||||
\(220\) | 58.2706 | 0.0178573 | ||||||||
\(221\) | 5198.39 | 1.58227 | ||||||||
\(222\) | −115.336 | −0.0348686 | ||||||||
\(223\) | −2296.00 | −0.689470 | −0.344735 | − | 0.938700i | \(-0.612031\pi\) | ||||
−0.344735 | + | 0.938700i | \(0.612031\pi\) | |||||||
\(224\) | −874.890 | −0.260965 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −180.473 | −0.0531191 | ||||||||
\(227\) | −5953.92 | −1.74086 | −0.870431 | − | 0.492290i | \(-0.836160\pi\) | ||||
−0.870431 | + | 0.492290i | \(0.836160\pi\) | |||||||
\(228\) | 2789.01 | 0.810116 | ||||||||
\(229\) | 1286.19 | 0.371151 | 0.185576 | − | 0.982630i | \(-0.440585\pi\) | ||||
0.185576 | + | 0.982630i | \(0.440585\pi\) | |||||||
\(230\) | −194.064 | −0.0556356 | ||||||||
\(231\) | −92.3284 | −0.0262977 | ||||||||
\(232\) | −101.186 | −0.0286345 | ||||||||
\(233\) | 203.636 | 0.0572559 | 0.0286280 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286280 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(234\) | −156.375 | −0.0436862 | ||||||||
\(235\) | 896.599 | 0.248884 | ||||||||
\(236\) | −3301.39 | −0.910601 | ||||||||
\(237\) | −3159.63 | −0.865993 | ||||||||
\(238\) | 300.588 | 0.0818665 | ||||||||
\(239\) | 2264.94 | 0.612998 | 0.306499 | − | 0.951871i | \(-0.400842\pi\) | ||||
0.306499 | + | 0.951871i | \(0.400842\pi\) | |||||||
\(240\) | −942.811 | −0.253576 | ||||||||
\(241\) | −3584.42 | −0.958060 | −0.479030 | − | 0.877799i | \(-0.659012\pi\) | ||||
−0.479030 | + | 0.877799i | \(0.659012\pi\) | |||||||
\(242\) | −290.657 | −0.0772073 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 3390.62 | 0.889599 | ||||||||
\(245\) | 490.000 | 0.127775 | ||||||||
\(246\) | −40.9840 | −0.0106221 | ||||||||
\(247\) | −9286.76 | −2.39232 | ||||||||
\(248\) | −271.406 | −0.0694932 | ||||||||
\(249\) | 3539.24 | 0.900763 | ||||||||
\(250\) | 27.3410 | 0.00691679 | ||||||||
\(251\) | −4549.43 | −1.14405 | −0.572027 | − | 0.820235i | \(-0.693843\pi\) | ||||
−0.572027 | + | 0.820235i | \(0.693843\pi\) | |||||||
\(252\) | 1502.96 | 0.375704 | ||||||||
\(253\) | 260.055 | 0.0646225 | ||||||||
\(254\) | 441.954 | 0.109176 | ||||||||
\(255\) | 981.609 | 0.241062 | ||||||||
\(256\) | 3853.24 | 0.940732 | ||||||||
\(257\) | 1342.72 | 0.325901 | 0.162951 | − | 0.986634i | \(-0.447899\pi\) | ||||
0.162951 | + | 0.986634i | \(0.447899\pi\) | |||||||
\(258\) | −43.3392 | −0.0104581 | ||||||||
\(259\) | −3691.12 | −0.885540 | ||||||||
\(260\) | 3158.46 | 0.753383 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | 62.6921 | 0.0147829 | ||||||||
\(263\) | 6631.18 | 1.55474 | 0.777369 | − | 0.629045i | \(-0.216554\pi\) | ||||
0.777369 | + | 0.629045i | \(0.216554\pi\) | |||||||
\(264\) | −15.3405 | −0.00357630 | ||||||||
\(265\) | 3383.86 | 0.784412 | ||||||||
\(266\) | −536.991 | −0.123778 | ||||||||
\(267\) | −4234.79 | −0.970656 | ||||||||
\(268\) | −629.739 | −0.143535 | ||||||||
\(269\) | 5563.54 | 1.26102 | 0.630511 | − | 0.776180i | \(-0.282845\pi\) | ||||
0.630511 | + | 0.776180i | \(0.282845\pi\) | |||||||
\(270\) | −29.5283 | −0.00665569 | ||||||||
\(271\) | −3556.15 | −0.797125 | −0.398562 | − | 0.917141i | \(-0.630491\pi\) | ||||
−0.398562 | + | 0.917141i | \(0.630491\pi\) | |||||||
\(272\) | −4113.21 | −0.916912 | ||||||||
\(273\) | −5004.51 | −1.10948 | ||||||||
\(274\) | 416.360 | 0.0918002 | ||||||||
\(275\) | −36.6383 | −0.00803407 | ||||||||
\(276\) | −4233.27 | −0.923236 | ||||||||
\(277\) | 7099.67 | 1.53999 | 0.769996 | − | 0.638049i | \(-0.220258\pi\) | ||||
0.769996 | + | 0.638049i | \(0.220258\pi\) | |||||||
\(278\) | −314.778 | −0.0679105 | ||||||||
\(279\) | 700.065 | 0.150221 | ||||||||
\(280\) | 366.365 | 0.0781945 | ||||||||
\(281\) | 1382.11 | 0.293415 | 0.146708 | − | 0.989180i | \(-0.453132\pi\) | ||||
0.146708 | + | 0.989180i | \(0.453132\pi\) | |||||||
\(282\) | −117.667 | −0.0248474 | ||||||||
\(283\) | −1867.69 | −0.392305 | −0.196153 | − | 0.980573i | \(-0.562845\pi\) | ||||
−0.196153 | + | 0.980573i | \(0.562845\pi\) | |||||||
\(284\) | −1738.39 | −0.363219 | ||||||||
\(285\) | −1753.62 | −0.364475 | ||||||||
\(286\) | 25.4636 | 0.00526467 | ||||||||
\(287\) | −1311.62 | −0.269764 | ||||||||
\(288\) | 374.953 | 0.0767164 | ||||||||
\(289\) | −630.524 | −0.128338 | ||||||||
\(290\) | 31.7156 | 0.00642208 | ||||||||
\(291\) | −2654.14 | −0.534669 | ||||||||
\(292\) | −8144.05 | −1.63217 | ||||||||
\(293\) | 4914.25 | 0.979842 | 0.489921 | − | 0.871767i | \(-0.337026\pi\) | ||||
0.489921 | + | 0.871767i | \(0.337026\pi\) | |||||||
\(294\) | −64.3060 | −0.0127565 | ||||||||
\(295\) | 2075.78 | 0.409683 | ||||||||
\(296\) | −613.285 | −0.120427 | ||||||||
\(297\) | 39.5693 | 0.00773079 | ||||||||
\(298\) | 379.237 | 0.0737203 | ||||||||
\(299\) | 14095.8 | 2.72637 | ||||||||
\(300\) | 596.412 | 0.114780 | ||||||||
\(301\) | −1386.99 | −0.265598 | ||||||||
\(302\) | −565.455 | −0.107743 | ||||||||
\(303\) | 1941.73 | 0.368150 | ||||||||
\(304\) | 7348.13 | 1.38633 | ||||||||
\(305\) | −2131.89 | −0.400234 | ||||||||
\(306\) | −128.823 | −0.0240665 | ||||||||
\(307\) | −2357.55 | −0.438282 | −0.219141 | − | 0.975693i | \(-0.570326\pi\) | ||||
−0.219141 | + | 0.975693i | \(0.570326\pi\) | |||||||
\(308\) | −244.737 | −0.0452765 | ||||||||
\(309\) | 4651.52 | 0.856361 | ||||||||
\(310\) | 85.0688 | 0.0155858 | ||||||||
\(311\) | 9821.76 | 1.79081 | 0.895404 | − | 0.445255i | \(-0.146887\pi\) | ||||
0.895404 | + | 0.445255i | \(0.146887\pi\) | |||||||
\(312\) | −831.508 | −0.150881 | ||||||||
\(313\) | −823.712 | −0.148751 | −0.0743753 | − | 0.997230i | \(-0.523696\pi\) | ||||
−0.0743753 | + | 0.997230i | \(0.523696\pi\) | |||||||
\(314\) | 636.797 | 0.114448 | ||||||||
\(315\) | −945.000 | −0.169031 | ||||||||
\(316\) | −8375.30 | −1.49097 | ||||||||
\(317\) | −657.982 | −0.116580 | −0.0582901 | − | 0.998300i | \(-0.518565\pi\) | ||||
−0.0582901 | + | 0.998300i | \(0.518565\pi\) | |||||||
\(318\) | −444.088 | −0.0783120 | ||||||||
\(319\) | −42.5004 | −0.00745945 | ||||||||
\(320\) | −2468.60 | −0.431247 | ||||||||
\(321\) | 3637.34 | 0.632450 | ||||||||
\(322\) | 815.068 | 0.141062 | ||||||||
\(323\) | −7650.51 | −1.31791 | ||||||||
\(324\) | −644.125 | −0.110447 | ||||||||
\(325\) | −1985.92 | −0.338950 | ||||||||
\(326\) | −629.357 | −0.106923 | ||||||||
\(327\) | 3385.06 | 0.572459 | ||||||||
\(328\) | −217.928 | −0.0366861 | ||||||||
\(329\) | −3765.71 | −0.631035 | ||||||||
\(330\) | 4.80829 | 0.000802084 0 | ||||||||
\(331\) | 8443.16 | 1.40205 | 0.701024 | − | 0.713138i | \(-0.252727\pi\) | ||||
0.701024 | + | 0.713138i | \(0.252727\pi\) | |||||||
\(332\) | 9381.53 | 1.55084 | ||||||||
\(333\) | 1581.91 | 0.260324 | ||||||||
\(334\) | 248.431 | 0.0406993 | ||||||||
\(335\) | 395.955 | 0.0645770 | ||||||||
\(336\) | 3959.81 | 0.642932 | ||||||||
\(337\) | 6836.82 | 1.10512 | 0.552560 | − | 0.833473i | \(-0.313651\pi\) | ||||
0.552560 | + | 0.833473i | \(0.313651\pi\) | |||||||
\(338\) | 899.669 | 0.144780 | ||||||||
\(339\) | 2475.31 | 0.396580 | ||||||||
\(340\) | 2601.97 | 0.415034 | ||||||||
\(341\) | −113.996 | −0.0181033 | ||||||||
\(342\) | 230.139 | 0.0363874 | ||||||||
\(343\) | 5145.00 | 0.809924 | ||||||||
\(344\) | −230.451 | −0.0361195 | ||||||||
\(345\) | 2661.71 | 0.415368 | ||||||||
\(346\) | 729.904 | 0.113410 | ||||||||
\(347\) | 7797.57 | 1.20633 | 0.603164 | − | 0.797617i | \(-0.293907\pi\) | ||||
0.603164 | + | 0.797617i | \(0.293907\pi\) | |||||||
\(348\) | 691.838 | 0.106570 | ||||||||
\(349\) | 7869.23 | 1.20696 | 0.603482 | − | 0.797377i | \(-0.293780\pi\) | ||||
0.603482 | + | 0.797377i | \(0.293780\pi\) | |||||||
\(350\) | −114.832 | −0.0175373 | ||||||||
\(351\) | 2144.79 | 0.326155 | ||||||||
\(352\) | −61.0561 | −0.00924517 | ||||||||
\(353\) | 943.862 | 0.142314 | 0.0711568 | − | 0.997465i | \(-0.477331\pi\) | ||||
0.0711568 | + | 0.997465i | \(0.477331\pi\) | |||||||
\(354\) | −272.419 | −0.0409009 | ||||||||
\(355\) | 1093.03 | 0.163414 | ||||||||
\(356\) | −11225.2 | −1.67117 | ||||||||
\(357\) | −4122.76 | −0.611203 | ||||||||
\(358\) | −1026.64 | −0.151564 | ||||||||
\(359\) | 5181.28 | 0.761720 | 0.380860 | − | 0.924633i | \(-0.375628\pi\) | ||||
0.380860 | + | 0.924633i | \(0.375628\pi\) | |||||||
\(360\) | −157.013 | −0.0229870 | ||||||||
\(361\) | 6808.42 | 0.992625 | ||||||||
\(362\) | 233.766 | 0.0339405 | ||||||||
\(363\) | 3986.56 | 0.576419 | ||||||||
\(364\) | −13265.5 | −1.91018 | ||||||||
\(365\) | 5120.66 | 0.734321 | ||||||||
\(366\) | 279.782 | 0.0399575 | ||||||||
\(367\) | 7016.17 | 0.997933 | 0.498966 | − | 0.866621i | \(-0.333713\pi\) | ||||
0.498966 | + | 0.866621i | \(0.333713\pi\) | |||||||
\(368\) | −11153.3 | −1.57991 | ||||||||
\(369\) | 562.122 | 0.0793033 | ||||||||
\(370\) | 192.226 | 0.0270091 | ||||||||
\(371\) | −14212.2 | −1.98885 | ||||||||
\(372\) | 1855.68 | 0.258635 | ||||||||
\(373\) | −4322.19 | −0.599985 | −0.299993 | − | 0.953942i | \(-0.596984\pi\) | ||||
−0.299993 | + | 0.953942i | \(0.596984\pi\) | |||||||
\(374\) | 20.9772 | 0.00290028 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −625.680 | −0.0858164 | ||||||||
\(377\) | −2303.66 | −0.314707 | ||||||||
\(378\) | 124.019 | 0.0168752 | ||||||||
\(379\) | −6955.45 | −0.942684 | −0.471342 | − | 0.881951i | \(-0.656230\pi\) | ||||
−0.471342 | + | 0.881951i | \(0.656230\pi\) | |||||||
\(380\) | −4648.34 | −0.627513 | ||||||||
\(381\) | −6061.68 | −0.815090 | ||||||||
\(382\) | −236.672 | −0.0316994 | ||||||||
\(383\) | −8543.13 | −1.13977 | −0.569887 | − | 0.821723i | \(-0.693013\pi\) | ||||
−0.569887 | + | 0.821723i | \(0.693013\pi\) | |||||||
\(384\) | 1323.85 | 0.175930 | ||||||||
\(385\) | 153.881 | 0.0203701 | ||||||||
\(386\) | −884.727 | −0.116662 | ||||||||
\(387\) | 594.426 | 0.0780785 | ||||||||
\(388\) | −7035.38 | −0.920535 | ||||||||
\(389\) | 5928.65 | 0.772736 | 0.386368 | − | 0.922345i | \(-0.373729\pi\) | ||||
0.386368 | + | 0.922345i | \(0.373729\pi\) | |||||||
\(390\) | 260.626 | 0.0338392 | ||||||||
\(391\) | 11612.3 | 1.50194 | ||||||||
\(392\) | −341.940 | −0.0440576 | ||||||||
\(393\) | −859.863 | −0.110367 | ||||||||
\(394\) | 313.617 | 0.0401010 | ||||||||
\(395\) | 5266.06 | 0.670795 | ||||||||
\(396\) | 104.887 | 0.0133100 | ||||||||
\(397\) | 10989.4 | 1.38927 | 0.694637 | − | 0.719360i | \(-0.255565\pi\) | ||||
0.694637 | + | 0.719360i | \(0.255565\pi\) | |||||||
\(398\) | 756.836 | 0.0953185 | ||||||||
\(399\) | 7365.19 | 0.924112 | ||||||||
\(400\) | 1571.35 | 0.196419 | ||||||||
\(401\) | 797.168 | 0.0992735 | 0.0496368 | − | 0.998767i | \(-0.484194\pi\) | ||||
0.0496368 | + | 0.998767i | \(0.484194\pi\) | |||||||
\(402\) | −51.9639 | −0.00644707 | ||||||||
\(403\) | −6178.98 | −0.763764 | ||||||||
\(404\) | 5146.97 | 0.633840 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −133.205 | −0.0162829 | ||||||||
\(407\) | −257.592 | −0.0313720 | ||||||||
\(408\) | −685.004 | −0.0831194 | ||||||||
\(409\) | −7879.82 | −0.952645 | −0.476323 | − | 0.879271i | \(-0.658031\pi\) | ||||
−0.476323 | + | 0.879271i | \(0.658031\pi\) | |||||||
\(410\) | 68.3067 | 0.00822787 | ||||||||
\(411\) | −5710.66 | −0.685367 | ||||||||
\(412\) | 12329.9 | 1.47439 | ||||||||
\(413\) | −8718.27 | −1.03874 | ||||||||
\(414\) | −349.315 | −0.0414683 | ||||||||
\(415\) | −5898.73 | −0.697728 | ||||||||
\(416\) | −3309.45 | −0.390046 | ||||||||
\(417\) | 4317.38 | 0.507010 | ||||||||
\(418\) | −37.4751 | −0.00438509 | ||||||||
\(419\) | 9358.61 | 1.09116 | 0.545582 | − | 0.838057i | \(-0.316309\pi\) | ||||
0.545582 | + | 0.838057i | \(0.316309\pi\) | |||||||
\(420\) | −2504.93 | −0.291019 | ||||||||
\(421\) | −3252.50 | −0.376525 | −0.188263 | − | 0.982119i | \(-0.560286\pi\) | ||||
−0.188263 | + | 0.982119i | \(0.560286\pi\) | |||||||
\(422\) | 447.213 | 0.0515877 | ||||||||
\(423\) | 1613.88 | 0.185507 | ||||||||
\(424\) | −2361.39 | −0.270470 | ||||||||
\(425\) | −1636.02 | −0.186726 | ||||||||
\(426\) | −143.446 | −0.0163145 | ||||||||
\(427\) | 8953.92 | 1.01478 | ||||||||
\(428\) | 9641.57 | 1.08888 | ||||||||
\(429\) | −349.250 | −0.0393053 | ||||||||
\(430\) | 72.2321 | 0.00810079 | ||||||||
\(431\) | 4340.20 | 0.485058 | 0.242529 | − | 0.970144i | \(-0.422023\pi\) | ||||
0.242529 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(432\) | −1697.06 | −0.189004 | ||||||||
\(433\) | 2983.79 | 0.331159 | 0.165579 | − | 0.986196i | \(-0.447051\pi\) | ||||
0.165579 | + | 0.986196i | \(0.447051\pi\) | |||||||
\(434\) | −357.289 | −0.0395171 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | 8972.84 | 0.985598 | ||||||||
\(437\) | −20745.0 | −2.27086 | ||||||||
\(438\) | −672.019 | −0.0733112 | ||||||||
\(439\) | −6943.69 | −0.754907 | −0.377454 | − | 0.926028i | \(-0.623200\pi\) | ||||
−0.377454 | + | 0.926028i | \(0.623200\pi\) | |||||||
\(440\) | 25.5675 | 0.00277019 | ||||||||
\(441\) | 882.000 | 0.0952380 | ||||||||
\(442\) | 1137.03 | 0.122360 | ||||||||
\(443\) | 13772.2 | 1.47706 | 0.738528 | − | 0.674223i | \(-0.235521\pi\) | ||||
0.738528 | + | 0.674223i | \(0.235521\pi\) | |||||||
\(444\) | 4193.19 | 0.448198 | ||||||||
\(445\) | 7057.99 | 0.751867 | ||||||||
\(446\) | −502.201 | −0.0533182 | ||||||||
\(447\) | −5201.49 | −0.550385 | ||||||||
\(448\) | 10368.1 | 1.09341 | ||||||||
\(449\) | 6057.15 | 0.636648 | 0.318324 | − | 0.947982i | \(-0.396880\pi\) | ||||
0.318324 | + | 0.947982i | \(0.396880\pi\) | |||||||
\(450\) | 49.2138 | 0.00515547 | ||||||||
\(451\) | −91.5341 | −0.00955693 | ||||||||
\(452\) | 6561.36 | 0.682788 | ||||||||
\(453\) | 7755.59 | 0.804391 | ||||||||
\(454\) | −1302.29 | −0.134624 | ||||||||
\(455\) | 8340.85 | 0.859396 | ||||||||
\(456\) | 1223.74 | 0.125673 | ||||||||
\(457\) | −18653.8 | −1.90938 | −0.954690 | − | 0.297603i | \(-0.903813\pi\) | ||||
−0.954690 | + | 0.297603i | \(0.903813\pi\) | |||||||
\(458\) | 281.325 | 0.0287019 | ||||||||
\(459\) | 1766.90 | 0.179677 | ||||||||
\(460\) | 7055.45 | 0.715135 | ||||||||
\(461\) | −2879.46 | −0.290910 | −0.145455 | − | 0.989365i | \(-0.546465\pi\) | ||||
−0.145455 | + | 0.989365i | \(0.546465\pi\) | |||||||
\(462\) | −20.1948 | −0.00203365 | ||||||||
\(463\) | 7645.28 | 0.767400 | 0.383700 | − | 0.923458i | \(-0.374650\pi\) | ||||
0.383700 | + | 0.923458i | \(0.374650\pi\) | |||||||
\(464\) | 1822.77 | 0.182370 | ||||||||
\(465\) | −1166.77 | −0.116361 | ||||||||
\(466\) | 44.5409 | 0.00442772 | ||||||||
\(467\) | 7486.58 | 0.741837 | 0.370918 | − | 0.928665i | \(-0.379043\pi\) | ||||
0.370918 | + | 0.928665i | \(0.379043\pi\) | |||||||
\(468\) | 5685.24 | 0.561539 | ||||||||
\(469\) | −1663.01 | −0.163733 | ||||||||
\(470\) | 196.111 | 0.0192467 | ||||||||
\(471\) | −8734.09 | −0.854449 | ||||||||
\(472\) | −1448.56 | −0.141261 | ||||||||
\(473\) | −96.7944 | −0.00940932 | ||||||||
\(474\) | −691.101 | −0.0669690 | ||||||||
\(475\) | 2922.69 | 0.282321 | ||||||||
\(476\) | −10928.3 | −1.05230 | ||||||||
\(477\) | 6090.96 | 0.584666 | ||||||||
\(478\) | 495.405 | 0.0474044 | ||||||||
\(479\) | 13351.7 | 1.27361 | 0.636803 | − | 0.771027i | \(-0.280257\pi\) | ||||
0.636803 | + | 0.771027i | \(0.280257\pi\) | |||||||
\(480\) | −624.922 | −0.0594243 | ||||||||
\(481\) | −13962.4 | −1.32355 | ||||||||
\(482\) | −784.013 | −0.0740888 | ||||||||
\(483\) | −11179.2 | −1.05315 | ||||||||
\(484\) | 10567.2 | 0.992416 | ||||||||
\(485\) | 4423.57 | 0.414152 | ||||||||
\(486\) | −53.1509 | −0.00496086 | ||||||||
\(487\) | −3228.98 | −0.300450 | −0.150225 | − | 0.988652i | \(-0.548000\pi\) | ||||
−0.150225 | + | 0.988652i | \(0.548000\pi\) | |||||||
\(488\) | 1487.71 | 0.138003 | ||||||||
\(489\) | 8632.05 | 0.798271 | ||||||||
\(490\) | 107.177 | 0.00988113 | ||||||||
\(491\) | −7804.20 | −0.717309 | −0.358655 | − | 0.933470i | \(-0.616764\pi\) | ||||
−0.358655 | + | 0.933470i | \(0.616764\pi\) | |||||||
\(492\) | 1490.03 | 0.136536 | ||||||||
\(493\) | −1897.78 | −0.173370 | ||||||||
\(494\) | −2031.28 | −0.185003 | ||||||||
\(495\) | −65.9489 | −0.00598824 | ||||||||
\(496\) | 4889.10 | 0.442595 | ||||||||
\(497\) | −4590.72 | −0.414330 | ||||||||
\(498\) | 774.131 | 0.0696579 | ||||||||
\(499\) | −3990.42 | −0.357988 | −0.178994 | − | 0.983850i | \(-0.557284\pi\) | ||||
−0.178994 | + | 0.983850i | \(0.557284\pi\) | |||||||
\(500\) | −994.020 | −0.0889078 | ||||||||
\(501\) | −3407.40 | −0.303855 | ||||||||
\(502\) | −995.089 | −0.0884721 | ||||||||
\(503\) | 6235.12 | 0.552704 | 0.276352 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276352 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(504\) | 659.456 | 0.0582828 | ||||||||
\(505\) | −3236.21 | −0.285167 | ||||||||
\(506\) | 56.8813 | 0.00499739 | ||||||||
\(507\) | −12339.6 | −1.08090 | ||||||||
\(508\) | −16067.8 | −1.40334 | ||||||||
\(509\) | −13441.4 | −1.17049 | −0.585246 | − | 0.810856i | \(-0.699002\pi\) | ||||
−0.585246 | + | 0.810856i | \(0.699002\pi\) | |||||||
\(510\) | 214.706 | 0.0186418 | ||||||||
\(511\) | −21506.8 | −1.86184 | ||||||||
\(512\) | 4373.07 | 0.377469 | ||||||||
\(513\) | −3156.51 | −0.271663 | ||||||||
\(514\) | 293.691 | 0.0252026 | ||||||||
\(515\) | −7752.53 | −0.663335 | ||||||||
\(516\) | 1575.66 | 0.134427 | ||||||||
\(517\) | −262.798 | −0.0223556 | ||||||||
\(518\) | −807.351 | −0.0684806 | ||||||||
\(519\) | −10011.1 | −0.846703 | ||||||||
\(520\) | 1385.85 | 0.116872 | ||||||||
\(521\) | 11314.2 | 0.951407 | 0.475703 | − | 0.879606i | \(-0.342194\pi\) | ||||
0.475703 | + | 0.879606i | \(0.342194\pi\) | |||||||
\(522\) | 57.0881 | 0.00478674 | ||||||||
\(523\) | 12003.7 | 1.00361 | 0.501804 | − | 0.864982i | \(-0.332670\pi\) | ||||
0.501804 | + | 0.864982i | \(0.332670\pi\) | |||||||
\(524\) | −2279.26 | −0.190019 | ||||||||
\(525\) | 1575.00 | 0.130931 | ||||||||
\(526\) | 1450.43 | 0.120231 | ||||||||
\(527\) | −5090.30 | −0.420753 | ||||||||
\(528\) | 276.344 | 0.0227771 | ||||||||
\(529\) | 19320.6 | 1.58795 | ||||||||
\(530\) | 740.146 | 0.0606602 | ||||||||
\(531\) | 3736.40 | 0.305360 | ||||||||
\(532\) | 19523.0 | 1.59104 | ||||||||
\(533\) | −4961.46 | −0.403198 | ||||||||
\(534\) | −926.268 | −0.0750628 | ||||||||
\(535\) | −6062.23 | −0.489894 | ||||||||
\(536\) | −276.312 | −0.0222665 | ||||||||
\(537\) | 14081.1 | 1.13155 | ||||||||
\(538\) | 1216.90 | 0.0975174 | ||||||||
\(539\) | −143.622 | −0.0114772 | ||||||||
\(540\) | 1073.54 | 0.0855516 | ||||||||
\(541\) | 2058.05 | 0.163553 | 0.0817767 | − | 0.996651i | \(-0.473941\pi\) | ||||
0.0817767 | + | 0.996651i | \(0.473941\pi\) | |||||||
\(542\) | −777.830 | −0.0616433 | ||||||||
\(543\) | −3206.25 | −0.253395 | ||||||||
\(544\) | −2726.35 | −0.214874 | ||||||||
\(545\) | −5641.76 | −0.443425 | ||||||||
\(546\) | −1094.63 | −0.0857980 | ||||||||
\(547\) | −2919.73 | −0.228224 | −0.114112 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114112 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(548\) | −15137.3 | −1.17999 | ||||||||
\(549\) | −3837.39 | −0.298317 | ||||||||
\(550\) | −8.01382 | −0.000621292 0 | ||||||||
\(551\) | 3390.32 | 0.262128 | ||||||||
\(552\) | −1857.44 | −0.143221 | ||||||||
\(553\) | −22117.4 | −1.70078 | ||||||||
\(554\) | 1552.90 | 0.119091 | ||||||||
\(555\) | −2636.51 | −0.201646 | ||||||||
\(556\) | 11444.2 | 0.872915 | ||||||||
\(557\) | 3685.44 | 0.280354 | 0.140177 | − | 0.990126i | \(-0.455233\pi\) | ||||
0.140177 | + | 0.990126i | \(0.455233\pi\) | |||||||
\(558\) | 153.124 | 0.0116169 | ||||||||
\(559\) | −5246.58 | −0.396971 | ||||||||
\(560\) | −6599.68 | −0.498013 | ||||||||
\(561\) | −287.716 | −0.0216531 | ||||||||
\(562\) | 302.306 | 0.0226904 | ||||||||
\(563\) | −9449.71 | −0.707385 | −0.353693 | − | 0.935362i | \(-0.615074\pi\) | ||||
−0.353693 | + | 0.935362i | \(0.615074\pi\) | |||||||
\(564\) | 4277.94 | 0.319386 | ||||||||
\(565\) | −4125.52 | −0.307189 | ||||||||
\(566\) | −408.515 | −0.0303378 | ||||||||
\(567\) | −1701.00 | −0.125988 | ||||||||
\(568\) | −762.756 | −0.0563460 | ||||||||
\(569\) | 2727.43 | 0.200949 | 0.100474 | − | 0.994940i | \(-0.467964\pi\) | ||||
0.100474 | + | 0.994940i | \(0.467964\pi\) | |||||||
\(570\) | −383.565 | −0.0281856 | ||||||||
\(571\) | −9211.18 | −0.675089 | −0.337545 | − | 0.941310i | \(-0.609596\pi\) | ||||
−0.337545 | + | 0.941310i | \(0.609596\pi\) | |||||||
\(572\) | −925.765 | −0.0676716 | ||||||||
\(573\) | 3246.11 | 0.236663 | ||||||||
\(574\) | −286.888 | −0.0208614 | ||||||||
\(575\) | −4436.19 | −0.321742 | ||||||||
\(576\) | −4443.48 | −0.321432 | ||||||||
\(577\) | 18864.4 | 1.36107 | 0.680534 | − | 0.732717i | \(-0.261748\pi\) | ||||
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(578\) | −137.913 | −0.00992463 | ||||||||
\(579\) | 12134.6 | 0.870980 | ||||||||
\(580\) | −1153.06 | −0.0825488 | ||||||||
\(581\) | 24774.7 | 1.76906 | ||||||||
\(582\) | −580.536 | −0.0413470 | ||||||||
\(583\) | −991.831 | −0.0704587 | ||||||||
\(584\) | −3573.38 | −0.253198 | ||||||||
\(585\) | −3574.65 | −0.252639 | ||||||||
\(586\) | 1074.88 | 0.0757732 | ||||||||
\(587\) | −14024.1 | −0.986092 | −0.493046 | − | 0.870003i | \(-0.664117\pi\) | ||||
−0.493046 | + | 0.870003i | \(0.664117\pi\) | |||||||
\(588\) | 2337.93 | 0.163971 | ||||||||
\(589\) | 9093.66 | 0.636159 | ||||||||
\(590\) | 454.032 | 0.0316817 | ||||||||
\(591\) | −4301.46 | −0.299388 | ||||||||
\(592\) | 11047.7 | 0.766989 | ||||||||
\(593\) | −17324.6 | −1.19973 | −0.599863 | − | 0.800102i | \(-0.704778\pi\) | ||||
−0.599863 | + | 0.800102i | \(0.704778\pi\) | |||||||
\(594\) | 8.65492 | 0.000597838 0 | ||||||||
\(595\) | 6871.27 | 0.473436 | ||||||||
\(596\) | −13787.7 | −0.947594 | ||||||||
\(597\) | −10380.5 | −0.711634 | ||||||||
\(598\) | 3083.16 | 0.210836 | ||||||||
\(599\) | −8141.83 | −0.555369 | −0.277685 | − | 0.960672i | \(-0.589567\pi\) | ||||
−0.277685 | + | 0.960672i | \(0.589567\pi\) | |||||||
\(600\) | 261.689 | 0.0178057 | ||||||||
\(601\) | 400.990 | 0.0272158 | 0.0136079 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136079 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(602\) | −303.375 | −0.0205393 | ||||||||
\(603\) | 712.718 | 0.0481329 | ||||||||
\(604\) | 20557.9 | 1.38491 | ||||||||
\(605\) | −6644.26 | −0.446492 | ||||||||
\(606\) | 424.710 | 0.0284698 | ||||||||
\(607\) | −19203.1 | −1.28407 | −0.642034 | − | 0.766677i | \(-0.721909\pi\) | ||||
−0.642034 | + | 0.766677i | \(0.721909\pi\) | |||||||
\(608\) | 4870.54 | 0.324879 | ||||||||
\(609\) | 1827.00 | 0.121566 | ||||||||
\(610\) | −466.303 | −0.0309509 | ||||||||
\(611\) | −14244.6 | −0.943164 | ||||||||
\(612\) | 4683.55 | 0.309348 | ||||||||
\(613\) | 6903.39 | 0.454853 | 0.227427 | − | 0.973795i | \(-0.426969\pi\) | ||||
0.227427 | + | 0.973795i | \(0.426969\pi\) | |||||||
\(614\) | −515.663 | −0.0338933 | ||||||||
\(615\) | −936.871 | −0.0614281 | ||||||||
\(616\) | −107.384 | −0.00702372 | ||||||||
\(617\) | −18090.6 | −1.18039 | −0.590193 | − | 0.807262i | \(-0.700948\pi\) | ||||
−0.590193 | + | 0.807262i | \(0.700948\pi\) | |||||||
\(618\) | 1017.42 | 0.0662242 | ||||||||
\(619\) | −23420.2 | −1.52074 | −0.760369 | − | 0.649492i | \(-0.774982\pi\) | ||||
−0.760369 | + | 0.649492i | \(0.774982\pi\) | |||||||
\(620\) | −3092.79 | −0.200338 | ||||||||
\(621\) | 4791.08 | 0.309597 | ||||||||
\(622\) | 2148.30 | 0.138487 | ||||||||
\(623\) | −29643.5 | −1.90633 | ||||||||
\(624\) | 14978.8 | 0.960946 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −180.169 | −0.0115032 | ||||||||
\(627\) | 513.995 | 0.0327384 | ||||||||
\(628\) | −23151.6 | −1.47110 | ||||||||
\(629\) | −11502.3 | −0.729138 | ||||||||
\(630\) | −206.698 | −0.0130715 | ||||||||
\(631\) | 10835.5 | 0.683607 | 0.341803 | − | 0.939771i | \(-0.388962\pi\) | ||||
0.341803 | + | 0.939771i | \(0.388962\pi\) | |||||||
\(632\) | −3674.85 | −0.231294 | ||||||||
\(633\) | −6133.83 | −0.385146 | ||||||||
\(634\) | −143.919 | −0.00901539 | ||||||||
\(635\) | 10102.8 | 0.631366 | ||||||||
\(636\) | 16145.4 | 1.00662 | ||||||||
\(637\) | −7784.79 | −0.484214 | ||||||||
\(638\) | −9.29603 | −0.000576855 0 | ||||||||
\(639\) | 1967.45 | 0.121801 | ||||||||
\(640\) | −2206.41 | −0.136275 | ||||||||
\(641\) | −910.547 | −0.0561068 | −0.0280534 | − | 0.999606i | \(-0.508931\pi\) | ||||
−0.0280534 | + | 0.999606i | \(0.508931\pi\) | |||||||
\(642\) | 795.589 | 0.0489087 | ||||||||
\(643\) | −81.2497 | −0.00498316 | −0.00249158 | − | 0.999997i | \(-0.500793\pi\) | ||||
−0.00249158 | + | 0.999997i | \(0.500793\pi\) | |||||||
\(644\) | −29632.9 | −1.81320 | ||||||||
\(645\) | −990.710 | −0.0604793 | ||||||||
\(646\) | −1673.38 | −0.101917 | ||||||||
\(647\) | −29487.9 | −1.79179 | −0.895895 | − | 0.444266i | \(-0.853465\pi\) | ||||
−0.895895 | + | 0.444266i | \(0.853465\pi\) | |||||||
\(648\) | −282.624 | −0.0171335 | ||||||||
\(649\) | −608.424 | −0.0367993 | ||||||||
\(650\) | −434.376 | −0.0262117 | ||||||||
\(651\) | 4900.45 | 0.295029 | ||||||||
\(652\) | 22881.1 | 1.37438 | ||||||||
\(653\) | 28469.2 | 1.70610 | 0.853051 | − | 0.521827i | \(-0.174749\pi\) | ||||
0.853051 | + | 0.521827i | \(0.174749\pi\) | |||||||
\(654\) | 740.407 | 0.0442694 | ||||||||
\(655\) | 1433.11 | 0.0854902 | ||||||||
\(656\) | 3925.74 | 0.233650 | ||||||||
\(657\) | 9217.18 | 0.547331 | ||||||||
\(658\) | −823.668 | −0.0487993 | ||||||||
\(659\) | 1953.52 | 0.115476 | 0.0577378 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577378 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(660\) | −174.812 | −0.0103099 | ||||||||
\(661\) | −16092.8 | −0.946956 | −0.473478 | − | 0.880806i | \(-0.657002\pi\) | ||||
−0.473478 | + | 0.880806i | \(0.657002\pi\) | |||||||
\(662\) | 1846.76 | 0.108423 | ||||||||
\(663\) | −15595.2 | −0.913523 | ||||||||
\(664\) | 4116.35 | 0.240581 | ||||||||
\(665\) | −12275.3 | −0.715814 | ||||||||
\(666\) | 346.008 | 0.0201314 | ||||||||
\(667\) | −5145.98 | −0.298730 | ||||||||
\(668\) | −9032.06 | −0.523145 | ||||||||
\(669\) | 6888.01 | 0.398066 | ||||||||
\(670\) | 86.6064 | 0.00499388 | ||||||||
\(671\) | 624.868 | 0.0359505 | ||||||||
\(672\) | 2624.67 | 0.150668 | ||||||||
\(673\) | −843.429 | −0.0483088 | −0.0241544 | − | 0.999708i | \(-0.507689\pi\) | ||||
−0.0241544 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(674\) | 1495.40 | 0.0854612 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −32708.7 | −1.86099 | ||||||||
\(677\) | 11706.7 | 0.664588 | 0.332294 | − | 0.943176i | \(-0.392177\pi\) | ||||
0.332294 | + | 0.943176i | \(0.392177\pi\) | |||||||
\(678\) | 541.420 | 0.0306683 | ||||||||
\(679\) | −18579.0 | −1.05007 | ||||||||
\(680\) | 1141.67 | 0.0643840 | ||||||||
\(681\) | 17861.8 | 1.00509 | ||||||||
\(682\) | −24.9342 | −0.00139997 | ||||||||
\(683\) | 5775.22 | 0.323547 | 0.161774 | − | 0.986828i | \(-0.448279\pi\) | ||||
0.161774 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(684\) | −8367.02 | −0.467721 | ||||||||
\(685\) | 9517.76 | 0.530883 | ||||||||
\(686\) | 1125.36 | 0.0626331 | ||||||||
\(687\) | −3858.56 | −0.214284 | ||||||||
\(688\) | 4151.35 | 0.230042 | ||||||||
\(689\) | −53760.6 | −2.97259 | ||||||||
\(690\) | 582.192 | 0.0321212 | ||||||||
\(691\) | 20629.4 | 1.13571 | 0.567857 | − | 0.823127i | \(-0.307773\pi\) | ||||
0.567857 | + | 0.823127i | \(0.307773\pi\) | |||||||
\(692\) | −26536.6 | −1.45776 | ||||||||
\(693\) | 276.985 | 0.0151830 | ||||||||
\(694\) | 1705.55 | 0.0932878 | ||||||||
\(695\) | −7195.64 | −0.392728 | ||||||||
\(696\) | 303.559 | 0.0165322 | ||||||||
\(697\) | −4087.29 | −0.222119 | ||||||||
\(698\) | 1721.22 | 0.0933370 | ||||||||
\(699\) | −610.908 | −0.0330567 | ||||||||
\(700\) | 4174.88 | 0.225422 | ||||||||
\(701\) | −5797.19 | −0.312350 | −0.156175 | − | 0.987729i | \(-0.549916\pi\) | ||||
−0.156175 | + | 0.987729i | \(0.549916\pi\) | |||||||
\(702\) | 469.126 | 0.0252222 | ||||||||
\(703\) | 20548.6 | 1.10242 | ||||||||
\(704\) | 723.562 | 0.0387362 | ||||||||
\(705\) | −2689.80 | −0.143693 | ||||||||
\(706\) | 206.449 | 0.0110054 | ||||||||
\(707\) | 13592.1 | 0.723031 | ||||||||
\(708\) | 9904.16 | 0.525736 | ||||||||
\(709\) | −4622.24 | −0.244841 | −0.122420 | − | 0.992478i | \(-0.539066\pi\) | ||||
−0.122420 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(710\) | 239.076 | 0.0126371 | ||||||||
\(711\) | 9478.90 | 0.499981 | ||||||||
\(712\) | −4925.33 | −0.259248 | ||||||||
\(713\) | −13802.8 | −0.724989 | ||||||||
\(714\) | −901.764 | −0.0472656 | ||||||||
\(715\) | 582.084 | 0.0304457 | ||||||||
\(716\) | 37325.1 | 1.94819 | ||||||||
\(717\) | −6794.81 | −0.353915 | ||||||||
\(718\) | 1133.29 | 0.0589054 | ||||||||
\(719\) | 20648.1 | 1.07099 | 0.535497 | − | 0.844537i | \(-0.320124\pi\) | ||||
0.535497 | + | 0.844537i | \(0.320124\pi\) | |||||||
\(720\) | 2828.43 | 0.146402 | ||||||||
\(721\) | 32560.6 | 1.68186 | ||||||||
\(722\) | 1489.19 | 0.0767618 | ||||||||
\(723\) | 10753.2 | 0.553136 | ||||||||
\(724\) | −8498.87 | −0.436268 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | 871.972 | 0.0445757 | ||||||||
\(727\) | −17177.6 | −0.876314 | −0.438157 | − | 0.898898i | \(-0.644369\pi\) | ||||
−0.438157 | + | 0.898898i | \(0.644369\pi\) | |||||||
\(728\) | −5820.56 | −0.296324 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1120.03 | 0.0567866 | ||||||||
\(731\) | −4322.18 | −0.218689 | ||||||||
\(732\) | −10171.9 | −0.513610 | ||||||||
\(733\) | 23803.4 | 1.19945 | 0.599725 | − | 0.800206i | \(-0.295277\pi\) | ||||
0.599725 | + | 0.800206i | \(0.295277\pi\) | |||||||
\(734\) | 1534.63 | 0.0771722 | ||||||||
\(735\) | −1470.00 | −0.0737711 | ||||||||
\(736\) | −7392.72 | −0.370244 | ||||||||
\(737\) | −116.057 | −0.00580055 | ||||||||
\(738\) | 122.952 | 0.00613269 | ||||||||
\(739\) | −16294.6 | −0.811106 | −0.405553 | − | 0.914072i | \(-0.632921\pi\) | ||||
−0.405553 | + | 0.914072i | \(0.632921\pi\) | |||||||
\(740\) | −6988.65 | −0.347173 | ||||||||
\(741\) | 27860.3 | 1.38120 | ||||||||
\(742\) | −3108.62 | −0.153802 | ||||||||
\(743\) | 25122.4 | 1.24045 | 0.620223 | − | 0.784426i | \(-0.287042\pi\) | ||||
0.620223 | + | 0.784426i | \(0.287042\pi\) | |||||||
\(744\) | 814.219 | 0.0401219 | ||||||||
\(745\) | 8669.15 | 0.426326 | ||||||||
\(746\) | −945.385 | −0.0463981 | ||||||||
\(747\) | −10617.7 | −0.520056 | ||||||||
\(748\) | −762.653 | −0.0372799 | ||||||||
\(749\) | 25461.4 | 1.24211 | ||||||||
\(750\) | −82.0231 | −0.00399341 | ||||||||
\(751\) | −29871.6 | −1.45144 | −0.725719 | − | 0.687991i | \(-0.758493\pi\) | ||||
−0.725719 | + | 0.687991i | \(0.758493\pi\) | |||||||
\(752\) | 11271.0 | 0.546556 | ||||||||
\(753\) | 13648.3 | 0.660520 | ||||||||
\(754\) | −503.876 | −0.0243370 | ||||||||
\(755\) | −12926.0 | −0.623079 | ||||||||
\(756\) | −4508.87 | −0.216913 | ||||||||
\(757\) | 17699.3 | 0.849791 | 0.424896 | − | 0.905242i | \(-0.360311\pi\) | ||||
0.424896 | + | 0.905242i | \(0.360311\pi\) | |||||||
\(758\) | −1521.35 | −0.0728997 | ||||||||
\(759\) | −780.164 | −0.0373098 | ||||||||
\(760\) | −2039.56 | −0.0973457 | ||||||||
\(761\) | 10189.2 | 0.485360 | 0.242680 | − | 0.970106i | \(-0.421973\pi\) | ||||
0.242680 | + | 0.970106i | \(0.421973\pi\) | |||||||
\(762\) | −1325.86 | −0.0630326 | ||||||||
\(763\) | 23695.4 | 1.12429 | ||||||||
\(764\) | 8604.52 | 0.407462 | ||||||||
\(765\) | −2944.83 | −0.139177 | ||||||||
\(766\) | −1868.62 | −0.0881412 | ||||||||
\(767\) | −32978.6 | −1.55253 | ||||||||
\(768\) | −11559.7 | −0.543132 | ||||||||
\(769\) | −17537.6 | −0.822395 | −0.411197 | − | 0.911546i | \(-0.634889\pi\) | ||||
−0.411197 | + | 0.911546i | \(0.634889\pi\) | |||||||
\(770\) | 33.6580 | 0.00157526 | ||||||||
\(771\) | −4028.16 | −0.188159 | ||||||||
\(772\) | 32165.4 | 1.49956 | ||||||||
\(773\) | −18819.3 | −0.875659 | −0.437830 | − | 0.899058i | \(-0.644253\pi\) | ||||
−0.437830 | + | 0.899058i | \(0.644253\pi\) | |||||||
\(774\) | 130.018 | 0.00603797 | ||||||||
\(775\) | 1944.62 | 0.0901329 | ||||||||
\(776\) | −3086.93 | −0.142802 | ||||||||
\(777\) | 11073.3 | 0.511267 | ||||||||
\(778\) | 1296.76 | 0.0597573 | ||||||||
\(779\) | 7301.83 | 0.335835 | ||||||||
\(780\) | −9475.39 | −0.434966 | ||||||||
\(781\) | −320.373 | −0.0146784 | ||||||||
\(782\) | 2539.93 | 0.116148 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | 6159.70 | 0.280598 | ||||||||
\(785\) | 14556.8 | 0.661854 | ||||||||
\(786\) | −188.076 | −0.00853494 | ||||||||
\(787\) | −11434.2 | −0.517900 | −0.258950 | − | 0.965891i | \(-0.583376\pi\) | ||||
−0.258950 | + | 0.965891i | \(0.583376\pi\) | |||||||
\(788\) | −11402.0 | −0.515455 | ||||||||
\(789\) | −19893.5 | −0.897628 | ||||||||
\(790\) | 1151.84 | 0.0518740 | ||||||||
\(791\) | 17327.2 | 0.778867 | ||||||||
\(792\) | 46.0216 | 0.00206478 | ||||||||
\(793\) | 33870.0 | 1.51672 | ||||||||
\(794\) | 2403.69 | 0.107435 | ||||||||
\(795\) | −10151.6 | −0.452880 | ||||||||
\(796\) | −27515.8 | −1.22522 | ||||||||
\(797\) | −14273.6 | −0.634375 | −0.317187 | − | 0.948363i | \(-0.602738\pi\) | ||||
−0.317187 | + | 0.948363i | \(0.602738\pi\) | |||||||
\(798\) | 1610.97 | 0.0714635 | ||||||||
\(799\) | −11734.8 | −0.519583 | ||||||||
\(800\) | 1041.54 | 0.0460298 | ||||||||
\(801\) | 12704.4 | 0.560408 | ||||||||
\(802\) | 174.363 | 0.00767703 | ||||||||
\(803\) | −1500.89 | −0.0659594 | ||||||||
\(804\) | 1889.22 | 0.0828700 | ||||||||
\(805\) | 18632.0 | 0.815766 | ||||||||
\(806\) | −1351.52 | −0.0590635 | ||||||||
\(807\) | −16690.6 | −0.728051 | ||||||||
\(808\) | 2258.35 | 0.0983273 | ||||||||
\(809\) | −92.7049 | −0.00402884 | −0.00201442 | − | 0.999998i | \(-0.500641\pi\) | ||||
−0.00201442 | + | 0.999998i | \(0.500641\pi\) | |||||||
\(810\) | 88.5849 | 0.00384266 | ||||||||
\(811\) | 20484.6 | 0.886946 | 0.443473 | − | 0.896288i | \(-0.353746\pi\) | ||||
0.443473 | + | 0.896288i | \(0.353746\pi\) | |||||||
\(812\) | 4842.86 | 0.209300 | ||||||||
\(813\) | 10668.5 | 0.460220 | ||||||||
\(814\) | −56.3427 | −0.00242606 | ||||||||
\(815\) | −14386.7 | −0.618338 | ||||||||
\(816\) | 12339.6 | 0.529379 | ||||||||
\(817\) | 7721.45 | 0.330648 | ||||||||
\(818\) | −1723.54 | −0.0736700 | ||||||||
\(819\) | 15013.5 | 0.640556 | ||||||||
\(820\) | −2483.38 | −0.105760 | ||||||||
\(821\) | 12828.4 | 0.545328 | 0.272664 | − | 0.962109i | \(-0.412095\pi\) | ||||
0.272664 | + | 0.962109i | \(0.412095\pi\) | |||||||
\(822\) | −1249.08 | −0.0530009 | ||||||||
\(823\) | −7959.43 | −0.337118 | −0.168559 | − | 0.985692i | \(-0.553911\pi\) | ||||
−0.168559 | + | 0.985692i | \(0.553911\pi\) | |||||||
\(824\) | 5410.00 | 0.228721 | ||||||||
\(825\) | 109.915 | 0.00463847 | ||||||||
\(826\) | −1906.93 | −0.0803277 | ||||||||
\(827\) | 15961.5 | 0.671144 | 0.335572 | − | 0.942015i | \(-0.391070\pi\) | ||||
0.335572 | + | 0.942015i | \(0.391070\pi\) | |||||||
\(828\) | 12699.8 | 0.533030 | ||||||||
\(829\) | −6830.19 | −0.286155 | −0.143077 | − | 0.989712i | \(-0.545700\pi\) | ||||
−0.143077 | + | 0.989712i | \(0.545700\pi\) | |||||||
\(830\) | −1290.22 | −0.0539568 | ||||||||
\(831\) | −21299.0 | −0.889115 | ||||||||
\(832\) | 39219.5 | 1.63424 | ||||||||
\(833\) | −6413.18 | −0.266751 | ||||||||
\(834\) | 944.333 | 0.0392081 | ||||||||
\(835\) | 5679.00 | 0.235365 | ||||||||
\(836\) | 1362.46 | 0.0563655 | ||||||||
\(837\) | −2100.19 | −0.0867304 | ||||||||
\(838\) | 2046.99 | 0.0843820 | ||||||||
\(839\) | 14841.7 | 0.610720 | 0.305360 | − | 0.952237i | \(-0.401223\pi\) | ||||
0.305360 | + | 0.952237i | \(0.401223\pi\) | |||||||
\(840\) | −1099.09 | −0.0451456 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −711.413 | −0.0291175 | ||||||||
\(843\) | −4146.33 | −0.169404 | ||||||||
\(844\) | −16259.0 | −0.663104 | ||||||||
\(845\) | 20565.9 | 0.837265 | ||||||||
\(846\) | 353.000 | 0.0143456 | ||||||||
\(847\) | 27905.9 | 1.13206 | ||||||||
\(848\) | 42537.9 | 1.72259 | ||||||||
\(849\) | 5603.06 | 0.226498 | ||||||||
\(850\) | −357.843 | −0.0144399 | ||||||||
\(851\) | −31189.5 | −1.25636 | ||||||||
\(852\) | 5215.16 | 0.209705 | ||||||||
\(853\) | −46778.2 | −1.87767 | −0.938836 | − | 0.344365i | \(-0.888094\pi\) | ||||
−0.938836 | + | 0.344365i | \(0.888094\pi\) | |||||||
\(854\) | 1958.47 | 0.0784749 | ||||||||
\(855\) | 5260.85 | 0.210429 | ||||||||
\(856\) | 4230.45 | 0.168918 | ||||||||
\(857\) | 14402.4 | 0.574070 | 0.287035 | − | 0.957920i | \(-0.407330\pi\) | ||||
0.287035 | + | 0.957920i | \(0.407330\pi\) | |||||||
\(858\) | −76.3909 | −0.00303956 | ||||||||
\(859\) | 23353.0 | 0.927584 | 0.463792 | − | 0.885944i | \(-0.346488\pi\) | ||||
0.463792 | + | 0.885944i | \(0.346488\pi\) | |||||||
\(860\) | −2626.09 | −0.104127 | ||||||||
\(861\) | 3934.86 | 0.155749 | ||||||||
\(862\) | 949.324 | 0.0375106 | ||||||||
\(863\) | 27267.6 | 1.07555 | 0.537776 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537776 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(864\) | −1124.86 | −0.0442922 | ||||||||
\(865\) | 16685.2 | 0.655854 | ||||||||
\(866\) | 652.639 | 0.0256092 | ||||||||
\(867\) | 1891.57 | 0.0740959 | ||||||||
\(868\) | 12989.7 | 0.507949 | ||||||||
\(869\) | −1543.51 | −0.0602533 | ||||||||
\(870\) | −95.1468 | −0.00370779 | ||||||||
\(871\) | −6290.66 | −0.244720 | ||||||||
\(872\) | 3937.03 | 0.152895 | ||||||||
\(873\) | 7962.43 | 0.308691 | ||||||||
\(874\) | −4537.51 | −0.175611 | ||||||||
\(875\) | −2625.00 | −0.101419 | ||||||||
\(876\) | 24432.2 | 0.942336 | ||||||||
\(877\) | −10549.3 | −0.406185 | −0.203092 | − | 0.979160i | \(-0.565099\pi\) | ||||
−0.203092 | + | 0.979160i | \(0.565099\pi\) | |||||||
\(878\) | −1518.78 | −0.0583786 | ||||||||
\(879\) | −14742.8 | −0.565712 | ||||||||
\(880\) | −460.573 | −0.0176431 | ||||||||
\(881\) | 25397.8 | 0.971251 | 0.485625 | − | 0.874167i | \(-0.338592\pi\) | ||||
0.485625 | + | 0.874167i | \(0.338592\pi\) | |||||||
\(882\) | 192.918 | 0.00736496 | ||||||||
\(883\) | −33416.7 | −1.27357 | −0.636785 | − | 0.771041i | \(-0.719736\pi\) | ||||
−0.636785 | + | 0.771041i | \(0.719736\pi\) | |||||||
\(884\) | −41338.4 | −1.57281 | ||||||||
\(885\) | −6227.34 | −0.236531 | ||||||||
\(886\) | 3012.36 | 0.114224 | ||||||||
\(887\) | −33336.9 | −1.26194 | −0.630971 | − | 0.775806i | \(-0.717343\pi\) | ||||
−0.630971 | + | 0.775806i | \(0.717343\pi\) | |||||||
\(888\) | 1839.86 | 0.0695288 | ||||||||
\(889\) | −42431.8 | −1.60081 | ||||||||
\(890\) | 1543.78 | 0.0581434 | ||||||||
\(891\) | −118.708 | −0.00446337 | ||||||||
\(892\) | 18258.2 | 0.685347 | ||||||||
\(893\) | 20963.9 | 0.785587 | ||||||||
\(894\) | −1137.71 | −0.0425624 | ||||||||
\(895\) | −23468.5 | −0.876498 | ||||||||
\(896\) | 9266.92 | 0.345520 | ||||||||
\(897\) | −42287.5 | −1.57407 | ||||||||
\(898\) | 1324.87 | 0.0492333 | ||||||||
\(899\) | 2255.76 | 0.0836863 | ||||||||
\(900\) | −1789.24 | −0.0662680 | ||||||||
\(901\) | −44288.4 | −1.63758 | ||||||||
\(902\) | −20.0211 | −0.000739057 0 | ||||||||
\(903\) | 4160.98 | 0.153343 | ||||||||
\(904\) | 2878.94 | 0.105921 | ||||||||
\(905\) | 5343.75 | 0.196279 | ||||||||
\(906\) | 1696.36 | 0.0622052 | ||||||||
\(907\) | 48386.2 | 1.77138 | 0.885688 | − | 0.464280i | \(-0.153687\pi\) | ||||
0.885688 | + | 0.464280i | \(0.153687\pi\) | |||||||
\(908\) | 47346.5 | 1.73045 | ||||||||
\(909\) | −5825.18 | −0.212551 | ||||||||
\(910\) | 1824.38 | 0.0664589 | ||||||||
\(911\) | 44095.4 | 1.60367 | 0.801836 | − | 0.597545i | \(-0.203857\pi\) | ||||
0.801836 | + | 0.597545i | \(0.203857\pi\) | |||||||
\(912\) | −22044.4 | −0.800397 | ||||||||
\(913\) | 1728.95 | 0.0626725 | ||||||||
\(914\) | −4080.10 | −0.147656 | ||||||||
\(915\) | 6395.66 | 0.231075 | ||||||||
\(916\) | −10228.0 | −0.368932 | ||||||||
\(917\) | −6019.04 | −0.216757 | ||||||||
\(918\) | 386.470 | 0.0138948 | ||||||||
\(919\) | −27520.1 | −0.987816 | −0.493908 | − | 0.869514i | \(-0.664432\pi\) | ||||
−0.493908 | + | 0.869514i | \(0.664432\pi\) | |||||||
\(920\) | 3095.74 | 0.110939 | ||||||||
\(921\) | 7072.66 | 0.253043 | ||||||||
\(922\) | −629.818 | −0.0224967 | ||||||||
\(923\) | −17365.3 | −0.619270 | ||||||||
\(924\) | 734.210 | 0.0261404 | ||||||||
\(925\) | 4394.19 | 0.156195 | ||||||||
\(926\) | 1672.24 | 0.0593447 | ||||||||
\(927\) | −13954.6 | −0.494420 | ||||||||
\(928\) | 1208.18 | 0.0427376 | ||||||||
\(929\) | 13243.5 | 0.467712 | 0.233856 | − | 0.972271i | \(-0.424866\pi\) | ||||
0.233856 | + | 0.972271i | \(0.424866\pi\) | |||||||
\(930\) | −255.206 | −0.00899844 | ||||||||
\(931\) | 11457.0 | 0.403315 | ||||||||
\(932\) | −1619.34 | −0.0569135 | ||||||||
\(933\) | −29465.3 | −1.03392 | ||||||||
\(934\) | 1637.53 | 0.0573678 | ||||||||
\(935\) | 479.526 | 0.0167724 | ||||||||
\(936\) | 2494.52 | 0.0871112 | ||||||||
\(937\) | 48606.1 | 1.69466 | 0.847329 | − | 0.531069i | \(-0.178210\pi\) | ||||
0.847329 | + | 0.531069i | \(0.178210\pi\) | |||||||
\(938\) | −363.747 | −0.0126618 | ||||||||
\(939\) | 2471.13 | 0.0858812 | ||||||||
\(940\) | −7129.89 | −0.247395 | ||||||||
\(941\) | 38178.2 | 1.32261 | 0.661303 | − | 0.750118i | \(-0.270004\pi\) | ||||
0.661303 | + | 0.750118i | \(0.270004\pi\) | |||||||
\(942\) | −1910.39 | −0.0660763 | ||||||||
\(943\) | −11083.0 | −0.382728 | ||||||||
\(944\) | 26094.2 | 0.899677 | ||||||||
\(945\) | 2835.00 | 0.0975900 | ||||||||
\(946\) | −21.1717 | −0.000727643 0 | ||||||||
\(947\) | −21472.2 | −0.736803 | −0.368402 | − | 0.929667i | \(-0.620095\pi\) | ||||
−0.368402 | + | 0.929667i | \(0.620095\pi\) | |||||||
\(948\) | 25125.9 | 0.860814 | ||||||||
\(949\) | −81353.6 | −2.78277 | ||||||||
\(950\) | 639.275 | 0.0218325 | ||||||||
\(951\) | 1973.95 | 0.0673076 | ||||||||
\(952\) | −4795.03 | −0.163243 | ||||||||
\(953\) | 5335.21 | 0.181348 | 0.0906739 | − | 0.995881i | \(-0.471098\pi\) | ||||
0.0906739 | + | 0.995881i | \(0.471098\pi\) | |||||||
\(954\) | 1332.26 | 0.0452134 | ||||||||
\(955\) | −5410.18 | −0.183319 | ||||||||
\(956\) | −18011.1 | −0.609332 | ||||||||
\(957\) | 127.501 | 0.00430671 | ||||||||
\(958\) | 2920.40 | 0.0984906 | ||||||||
\(959\) | −39974.6 | −1.34603 | ||||||||
\(960\) | 7405.80 | 0.248980 | ||||||||
\(961\) | −23740.5 | −0.796902 | ||||||||
\(962\) | −3053.97 | −0.102353 | ||||||||
\(963\) | −10912.0 | −0.365145 | ||||||||
\(964\) | 28503.8 | 0.952331 | ||||||||
\(965\) | −20224.3 | −0.674658 | ||||||||
\(966\) | −2445.20 | −0.0814422 | ||||||||
\(967\) | −4578.60 | −0.152263 | −0.0761313 | − | 0.997098i | \(-0.524257\pi\) | ||||
−0.0761313 | + | 0.997098i | \(0.524257\pi\) | |||||||
\(968\) | 4636.61 | 0.153953 | ||||||||
\(969\) | 22951.5 | 0.760898 | ||||||||
\(970\) | 967.559 | 0.0320273 | ||||||||
\(971\) | −13641.3 | −0.450846 | −0.225423 | − | 0.974261i | \(-0.572376\pi\) | ||||
−0.225423 | + | 0.974261i | \(0.572376\pi\) | |||||||
\(972\) | 1932.37 | 0.0637664 | ||||||||
\(973\) | 30221.7 | 0.995748 | ||||||||
\(974\) | −706.269 | −0.0232344 | ||||||||
\(975\) | 5957.75 | 0.195693 | ||||||||
\(976\) | −26799.5 | −0.878926 | ||||||||
\(977\) | 51144.7 | 1.67478 | 0.837391 | − | 0.546604i | \(-0.184080\pi\) | ||||
0.837391 | + | 0.546604i | \(0.184080\pi\) | |||||||
\(978\) | 1888.07 | 0.0617320 | ||||||||
\(979\) | −2068.74 | −0.0675354 | ||||||||
\(980\) | −3896.56 | −0.127011 | ||||||||
\(981\) | −10155.2 | −0.330509 | ||||||||
\(982\) | −1707.00 | −0.0554710 | ||||||||
\(983\) | 56699.8 | 1.83972 | 0.919859 | − | 0.392249i | \(-0.128303\pi\) | ||||
0.919859 | + | 0.392249i | \(0.128303\pi\) | |||||||
\(984\) | 653.783 | 0.0211807 | ||||||||
\(985\) | 7169.10 | 0.231905 | ||||||||
\(986\) | −415.098 | −0.0134071 | ||||||||
\(987\) | 11297.1 | 0.364328 | ||||||||
\(988\) | 73849.8 | 2.37801 | ||||||||
\(989\) | −11719.9 | −0.376817 | ||||||||
\(990\) | −14.4249 | −0.000463083 0 | ||||||||
\(991\) | 52946.3 | 1.69717 | 0.848585 | − | 0.529059i | \(-0.177455\pi\) | ||||
0.848585 | + | 0.529059i | \(0.177455\pi\) | |||||||
\(992\) | 3240.63 | 0.103720 | ||||||||
\(993\) | −25329.5 | −0.809473 | ||||||||
\(994\) | −1004.12 | −0.0320410 | ||||||||
\(995\) | 17300.8 | 0.551229 | ||||||||
\(996\) | −28144.6 | −0.895377 | ||||||||
\(997\) | −2112.74 | −0.0671126 | −0.0335563 | − | 0.999437i | \(-0.510683\pi\) | ||||
−0.0335563 | + | 0.999437i | \(0.510683\pi\) | |||||||
\(998\) | −872.818 | −0.0276839 | ||||||||
\(999\) | −4745.72 | −0.150298 |
(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 | 435.4.a.i.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.n.1.4 | 7 | |||
5.4 | even | 2 | 2175.4.a.n.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.i.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.n.1.4 | 7 | 3.2 | odd | 2 | |||
2175.4.a.n.1.4 | 7 | 5.4 | even | 2 |