Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(1\) |
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: | \( x^{7} - 41x^{5} - 7x^{4} + 484x^{3} + 63x^{2} - 1736x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.06012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.06012 | −1.08192 | −0.540958 | − | 0.841050i | \(-0.681938\pi\) | ||||
−0.540958 | + | 0.841050i | \(0.681938\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 1.36432 | 0.170540 | ||||||||
\(5\) | 0.675250 | 0.0603962 | 0.0301981 | − | 0.999544i | \(-0.490386\pi\) | ||||
0.0301981 | + | 0.999544i | \(0.490386\pi\) | |||||||
\(6\) | 9.18035 | 0.624644 | ||||||||
\(7\) | −3.38755 | −0.182910 | −0.0914552 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914552 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(8\) | 20.3060 | 0.897405 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −2.06635 | −0.0653436 | ||||||||
\(11\) | −8.79097 | −0.240962 | −0.120481 | − | 0.992716i | \(-0.538444\pi\) | ||||
−0.120481 | + | 0.992716i | \(0.538444\pi\) | |||||||
\(12\) | −4.09296 | −0.0984614 | ||||||||
\(13\) | 59.4118 | 1.26753 | 0.633764 | − | 0.773526i | \(-0.281509\pi\) | ||||
0.633764 | + | 0.773526i | \(0.281509\pi\) | |||||||
\(14\) | 10.3663 | 0.197894 | ||||||||
\(15\) | −2.02575 | −0.0348698 | ||||||||
\(16\) | −73.0532 | −1.14146 | ||||||||
\(17\) | 31.2380 | 0.445666 | 0.222833 | − | 0.974857i | \(-0.428469\pi\) | ||||
0.222833 | + | 0.974857i | \(0.428469\pi\) | |||||||
\(18\) | −27.5411 | −0.360638 | ||||||||
\(19\) | −77.5189 | −0.936003 | −0.468002 | − | 0.883728i | \(-0.655026\pi\) | ||||
−0.468002 | + | 0.883728i | \(0.655026\pi\) | |||||||
\(20\) | 0.921258 | 0.0103000 | ||||||||
\(21\) | 10.1626 | 0.105603 | ||||||||
\(22\) | 26.9014 | 0.260700 | ||||||||
\(23\) | 73.1225 | 0.662917 | 0.331458 | − | 0.943470i | \(-0.392459\pi\) | ||||
0.331458 | + | 0.943470i | \(0.392459\pi\) | |||||||
\(24\) | −60.9179 | −0.518117 | ||||||||
\(25\) | −124.544 | −0.996352 | ||||||||
\(26\) | −181.807 | −1.37136 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −4.62171 | −0.0311936 | ||||||||
\(29\) | −61.5678 | −0.394236 | −0.197118 | − | 0.980380i | \(-0.563158\pi\) | ||||
−0.197118 | + | 0.980380i | \(0.563158\pi\) | |||||||
\(30\) | 6.19904 | 0.0377261 | ||||||||
\(31\) | −278.253 | −1.61212 | −0.806059 | − | 0.591835i | \(-0.798404\pi\) | ||||
−0.806059 | + | 0.591835i | \(0.798404\pi\) | |||||||
\(32\) | 61.1037 | 0.337554 | ||||||||
\(33\) | 26.3729 | 0.139119 | ||||||||
\(34\) | −95.5920 | −0.482173 | ||||||||
\(35\) | −2.28744 | −0.0110471 | ||||||||
\(36\) | 12.2789 | 0.0568467 | ||||||||
\(37\) | −326.365 | −1.45011 | −0.725055 | − | 0.688691i | \(-0.758186\pi\) | ||||
−0.725055 | + | 0.688691i | \(0.758186\pi\) | |||||||
\(38\) | 237.217 | 1.01268 | ||||||||
\(39\) | −178.235 | −0.731808 | ||||||||
\(40\) | 13.7116 | 0.0541999 | ||||||||
\(41\) | 453.551 | 1.72763 | 0.863815 | − | 0.503809i | \(-0.168069\pi\) | ||||
0.863815 | + | 0.503809i | \(0.168069\pi\) | |||||||
\(42\) | −31.0989 | −0.114254 | ||||||||
\(43\) | −174.901 | −0.620282 | −0.310141 | − | 0.950691i | \(-0.600376\pi\) | ||||
−0.310141 | + | 0.950691i | \(0.600376\pi\) | |||||||
\(44\) | −11.9937 | −0.0410936 | ||||||||
\(45\) | 6.07725 | 0.0201321 | ||||||||
\(46\) | −223.763 | −0.717220 | ||||||||
\(47\) | −480.883 | −1.49243 | −0.746213 | − | 0.665707i | \(-0.768130\pi\) | ||||
−0.746213 | + | 0.665707i | \(0.768130\pi\) | |||||||
\(48\) | 219.160 | 0.659020 | ||||||||
\(49\) | −331.525 | −0.966544 | ||||||||
\(50\) | 381.119 | 1.07797 | ||||||||
\(51\) | −93.7140 | −0.257306 | ||||||||
\(52\) | 81.0568 | 0.216165 | ||||||||
\(53\) | −185.568 | −0.480938 | −0.240469 | − | 0.970657i | \(-0.577301\pi\) | ||||
−0.240469 | + | 0.970657i | \(0.577301\pi\) | |||||||
\(54\) | 82.6232 | 0.208215 | ||||||||
\(55\) | −5.93610 | −0.0145532 | ||||||||
\(56\) | −68.7874 | −0.164145 | ||||||||
\(57\) | 232.557 | 0.540402 | ||||||||
\(58\) | 188.405 | 0.426530 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | −2.76378 | −0.00594670 | ||||||||
\(61\) | 807.823 | 1.69559 | 0.847796 | − | 0.530322i | \(-0.177929\pi\) | ||||
0.847796 | + | 0.530322i | \(0.177929\pi\) | |||||||
\(62\) | 851.486 | 1.74417 | ||||||||
\(63\) | −30.4879 | −0.0609702 | ||||||||
\(64\) | 397.441 | 0.776252 | ||||||||
\(65\) | 40.1178 | 0.0765539 | ||||||||
\(66\) | −80.7042 | −0.150515 | ||||||||
\(67\) | −129.081 | −0.235369 | −0.117685 | − | 0.993051i | \(-0.537547\pi\) | ||||
−0.117685 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(68\) | 42.6187 | 0.0760040 | ||||||||
\(69\) | −219.367 | −0.382735 | ||||||||
\(70\) | 6.99985 | 0.0119520 | ||||||||
\(71\) | −272.032 | −0.454708 | −0.227354 | − | 0.973812i | \(-0.573007\pi\) | ||||
−0.227354 | + | 0.973812i | \(0.573007\pi\) | |||||||
\(72\) | 182.754 | 0.299135 | ||||||||
\(73\) | −610.054 | −0.978102 | −0.489051 | − | 0.872255i | \(-0.662657\pi\) | ||||
−0.489051 | + | 0.872255i | \(0.662657\pi\) | |||||||
\(74\) | 998.716 | 1.56890 | ||||||||
\(75\) | 373.632 | 0.575244 | ||||||||
\(76\) | −105.761 | −0.159626 | ||||||||
\(77\) | 29.7798 | 0.0440744 | ||||||||
\(78\) | 545.422 | 0.791754 | ||||||||
\(79\) | 886.175 | 1.26206 | 0.631028 | − | 0.775760i | \(-0.282633\pi\) | ||||
0.631028 | + | 0.775760i | \(0.282633\pi\) | |||||||
\(80\) | −49.3292 | −0.0689396 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1387.92 | −1.86915 | ||||||||
\(83\) | 51.4871 | 0.0680896 | 0.0340448 | − | 0.999420i | \(-0.489161\pi\) | ||||
0.0340448 | + | 0.999420i | \(0.489161\pi\) | |||||||
\(84\) | 13.8651 | 0.0180096 | ||||||||
\(85\) | 21.0935 | 0.0269166 | ||||||||
\(86\) | 535.217 | 0.671092 | ||||||||
\(87\) | 184.703 | 0.227612 | ||||||||
\(88\) | −178.509 | −0.216240 | ||||||||
\(89\) | 182.350 | 0.217180 | 0.108590 | − | 0.994087i | \(-0.465366\pi\) | ||||
0.108590 | + | 0.994087i | \(0.465366\pi\) | |||||||
\(90\) | −18.5971 | −0.0217812 | ||||||||
\(91\) | −201.261 | −0.231844 | ||||||||
\(92\) | 99.7625 | 0.113054 | ||||||||
\(93\) | 834.758 | 0.930757 | ||||||||
\(94\) | 1471.56 | 1.61468 | ||||||||
\(95\) | −52.3447 | −0.0565311 | ||||||||
\(96\) | −183.311 | −0.194887 | ||||||||
\(97\) | −1353.44 | −1.41671 | −0.708354 | − | 0.705857i | \(-0.750562\pi\) | ||||
−0.708354 | + | 0.705857i | \(0.750562\pi\) | |||||||
\(98\) | 1014.50 | 1.04572 | ||||||||
\(99\) | −79.1187 | −0.0803205 | ||||||||
\(100\) | −169.918 | −0.169918 | ||||||||
\(101\) | −406.406 | −0.400385 | −0.200192 | − | 0.979757i | \(-0.564157\pi\) | ||||
−0.200192 | + | 0.979757i | \(0.564157\pi\) | |||||||
\(102\) | 286.776 | 0.278383 | ||||||||
\(103\) | −304.606 | −0.291395 | −0.145697 | − | 0.989329i | \(-0.546543\pi\) | ||||
−0.145697 | + | 0.989329i | \(0.546543\pi\) | |||||||
\(104\) | 1206.41 | 1.13749 | ||||||||
\(105\) | 6.86233 | 0.00637805 | ||||||||
\(106\) | 567.859 | 0.520334 | ||||||||
\(107\) | −1515.70 | −1.36942 | −0.684711 | − | 0.728815i | \(-0.740071\pi\) | ||||
−0.684711 | + | 0.728815i | \(0.740071\pi\) | |||||||
\(108\) | −36.8367 | −0.0328205 | ||||||||
\(109\) | −1.57624 | −0.00138511 | −0.000692553 | − | 1.00000i | \(-0.500220\pi\) | ||||
−0.000692553 | 1.00000i | \(0.500220\pi\) | ||||||||
\(110\) | 18.1652 | 0.0157453 | ||||||||
\(111\) | 979.095 | 0.837222 | ||||||||
\(112\) | 247.471 | 0.208784 | ||||||||
\(113\) | −577.813 | −0.481027 | −0.240514 | − | 0.970646i | \(-0.577316\pi\) | ||||
−0.240514 | + | 0.970646i | \(0.577316\pi\) | |||||||
\(114\) | −711.651 | −0.584669 | ||||||||
\(115\) | 49.3760 | 0.0400377 | ||||||||
\(116\) | −83.9983 | −0.0672331 | ||||||||
\(117\) | 534.706 | 0.422510 | ||||||||
\(118\) | −180.547 | −0.140853 | ||||||||
\(119\) | −105.820 | −0.0815171 | ||||||||
\(120\) | −41.1348 | −0.0312923 | ||||||||
\(121\) | −1253.72 | −0.941938 | ||||||||
\(122\) | −2472.03 | −1.83449 | ||||||||
\(123\) | −1360.65 | −0.997448 | ||||||||
\(124\) | −379.626 | −0.274931 | ||||||||
\(125\) | −168.505 | −0.120572 | ||||||||
\(126\) | 93.2967 | 0.0659645 | ||||||||
\(127\) | 291.667 | 0.203789 | 0.101895 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101895 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(128\) | −1705.05 | −1.17739 | ||||||||
\(129\) | 524.702 | 0.358120 | ||||||||
\(130\) | −122.765 | −0.0828249 | ||||||||
\(131\) | −1160.30 | −0.773863 | −0.386932 | − | 0.922108i | \(-0.626465\pi\) | ||||
−0.386932 | + | 0.922108i | \(0.626465\pi\) | |||||||
\(132\) | 35.9811 | 0.0237254 | ||||||||
\(133\) | 262.599 | 0.171205 | ||||||||
\(134\) | 395.003 | 0.254649 | ||||||||
\(135\) | −18.2318 | −0.0116233 | ||||||||
\(136\) | 634.318 | 0.399943 | ||||||||
\(137\) | 571.419 | 0.356348 | 0.178174 | − | 0.983999i | \(-0.442981\pi\) | ||||
0.178174 | + | 0.983999i | \(0.442981\pi\) | |||||||
\(138\) | 671.290 | 0.414087 | ||||||||
\(139\) | −576.322 | −0.351677 | −0.175838 | − | 0.984419i | \(-0.556264\pi\) | ||||
−0.175838 | + | 0.984419i | \(0.556264\pi\) | |||||||
\(140\) | −3.12081 | −0.00188397 | ||||||||
\(141\) | 1442.65 | 0.861653 | ||||||||
\(142\) | 832.450 | 0.491956 | ||||||||
\(143\) | −522.287 | −0.305426 | ||||||||
\(144\) | −657.479 | −0.380485 | ||||||||
\(145\) | −41.5737 | −0.0238104 | ||||||||
\(146\) | 1866.84 | 1.05822 | ||||||||
\(147\) | 994.574 | 0.558034 | ||||||||
\(148\) | −445.267 | −0.247302 | ||||||||
\(149\) | −1845.62 | −1.01476 | −0.507380 | − | 0.861723i | \(-0.669386\pi\) | ||||
−0.507380 | + | 0.861723i | \(0.669386\pi\) | |||||||
\(150\) | −1143.36 | −0.622365 | ||||||||
\(151\) | −1957.64 | −1.05503 | −0.527517 | − | 0.849545i | \(-0.676877\pi\) | ||||
−0.527517 | + | 0.849545i | \(0.676877\pi\) | |||||||
\(152\) | −1574.10 | −0.839974 | ||||||||
\(153\) | 281.142 | 0.148555 | ||||||||
\(154\) | −91.1298 | −0.0476847 | ||||||||
\(155\) | −187.890 | −0.0973658 | ||||||||
\(156\) | −243.170 | −0.124803 | ||||||||
\(157\) | 791.623 | 0.402410 | 0.201205 | − | 0.979549i | \(-0.435514\pi\) | ||||
0.201205 | + | 0.979549i | \(0.435514\pi\) | |||||||
\(158\) | −2711.80 | −1.36544 | ||||||||
\(159\) | 556.703 | 0.277669 | ||||||||
\(160\) | 41.2603 | 0.0203870 | ||||||||
\(161\) | −247.706 | −0.121254 | ||||||||
\(162\) | −247.870 | −0.120213 | ||||||||
\(163\) | −3364.00 | −1.61650 | −0.808248 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(164\) | 618.790 | 0.294630 | ||||||||
\(165\) | 17.8083 | 0.00840227 | ||||||||
\(166\) | −157.556 | −0.0736672 | ||||||||
\(167\) | 514.992 | 0.238630 | 0.119315 | − | 0.992856i | \(-0.461930\pi\) | ||||
0.119315 | + | 0.992856i | \(0.461930\pi\) | |||||||
\(168\) | 206.362 | 0.0947690 | ||||||||
\(169\) | 1332.76 | 0.606629 | ||||||||
\(170\) | −64.5485 | −0.0291214 | ||||||||
\(171\) | −697.670 | −0.312001 | ||||||||
\(172\) | −238.621 | −0.105783 | ||||||||
\(173\) | 2625.47 | 1.15382 | 0.576910 | − | 0.816808i | \(-0.304258\pi\) | ||||
0.576910 | + | 0.816808i | \(0.304258\pi\) | |||||||
\(174\) | −565.214 | −0.246257 | ||||||||
\(175\) | 421.899 | 0.182243 | ||||||||
\(176\) | 642.208 | 0.275047 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −558.012 | −0.234971 | ||||||||
\(179\) | −165.711 | −0.0691947 | −0.0345973 | − | 0.999401i | \(-0.511015\pi\) | ||||
−0.0345973 | + | 0.999401i | \(0.511015\pi\) | |||||||
\(180\) | 8.29133 | 0.00343333 | ||||||||
\(181\) | 1680.47 | 0.690100 | 0.345050 | − | 0.938584i | \(-0.387862\pi\) | ||||
0.345050 | + | 0.938584i | \(0.387862\pi\) | |||||||
\(182\) | 615.881 | 0.250836 | ||||||||
\(183\) | −2423.47 | −0.978951 | ||||||||
\(184\) | 1484.82 | 0.594905 | ||||||||
\(185\) | −220.378 | −0.0875812 | ||||||||
\(186\) | −2554.46 | −1.00700 | ||||||||
\(187\) | −274.612 | −0.107388 | ||||||||
\(188\) | −656.079 | −0.254519 | ||||||||
\(189\) | 91.4638 | 0.0352011 | ||||||||
\(190\) | 160.181 | 0.0611618 | ||||||||
\(191\) | −825.467 | −0.312716 | −0.156358 | − | 0.987700i | \(-0.549975\pi\) | ||||
−0.156358 | + | 0.987700i | \(0.549975\pi\) | |||||||
\(192\) | −1192.32 | −0.448169 | ||||||||
\(193\) | 3110.12 | 1.15995 | 0.579977 | − | 0.814633i | \(-0.303061\pi\) | ||||
0.579977 | + | 0.814633i | \(0.303061\pi\) | |||||||
\(194\) | 4141.68 | 1.53276 | ||||||||
\(195\) | −120.354 | −0.0441984 | ||||||||
\(196\) | −452.306 | −0.164835 | ||||||||
\(197\) | −1252.31 | −0.452909 | −0.226455 | − | 0.974022i | \(-0.572713\pi\) | ||||
−0.226455 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(198\) | 242.113 | 0.0869000 | ||||||||
\(199\) | 854.395 | 0.304354 | 0.152177 | − | 0.988353i | \(-0.451372\pi\) | ||||
0.152177 | + | 0.988353i | \(0.451372\pi\) | |||||||
\(200\) | −2528.99 | −0.894132 | ||||||||
\(201\) | 387.242 | 0.135890 | ||||||||
\(202\) | 1243.65 | 0.433182 | ||||||||
\(203\) | 208.564 | 0.0721099 | ||||||||
\(204\) | −127.856 | −0.0438809 | ||||||||
\(205\) | 306.261 | 0.104342 | ||||||||
\(206\) | 932.129 | 0.315265 | ||||||||
\(207\) | 658.102 | 0.220972 | ||||||||
\(208\) | −4340.22 | −1.44683 | ||||||||
\(209\) | 681.466 | 0.225541 | ||||||||
\(210\) | −20.9995 | −0.00690051 | ||||||||
\(211\) | 5555.73 | 1.81266 | 0.906332 | − | 0.422566i | \(-0.138870\pi\) | ||||
0.906332 | + | 0.422566i | \(0.138870\pi\) | |||||||
\(212\) | −253.174 | −0.0820192 | ||||||||
\(213\) | 816.096 | 0.262526 | ||||||||
\(214\) | 4638.22 | 1.48160 | ||||||||
\(215\) | −118.102 | −0.0374627 | ||||||||
\(216\) | −548.261 | −0.172706 | ||||||||
\(217\) | 942.595 | 0.294873 | ||||||||
\(218\) | 4.82349 | 0.00149857 | ||||||||
\(219\) | 1830.16 | 0.564707 | ||||||||
\(220\) | −8.09875 | −0.00248190 | ||||||||
\(221\) | 1855.91 | 0.564895 | ||||||||
\(222\) | −2996.15 | −0.905803 | ||||||||
\(223\) | −2120.53 | −0.636776 | −0.318388 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318388 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(224\) | −206.992 | −0.0617421 | ||||||||
\(225\) | −1120.90 | −0.332117 | ||||||||
\(226\) | 1768.18 | 0.520431 | ||||||||
\(227\) | 3373.06 | 0.986247 | 0.493123 | − | 0.869959i | \(-0.335855\pi\) | ||||
0.493123 | + | 0.869959i | \(0.335855\pi\) | |||||||
\(228\) | 317.282 | 0.0921602 | ||||||||
\(229\) | 1545.12 | 0.445872 | 0.222936 | − | 0.974833i | \(-0.428436\pi\) | ||||
0.222936 | + | 0.974833i | \(0.428436\pi\) | |||||||
\(230\) | −151.096 | −0.0433173 | ||||||||
\(231\) | −89.3395 | −0.0254464 | ||||||||
\(232\) | −1250.19 | −0.353790 | ||||||||
\(233\) | 4860.03 | 1.36649 | 0.683243 | − | 0.730191i | \(-0.260569\pi\) | ||||
0.683243 | + | 0.730191i | \(0.260569\pi\) | |||||||
\(234\) | −1636.26 | −0.457120 | ||||||||
\(235\) | −324.717 | −0.0901369 | ||||||||
\(236\) | 80.4950 | 0.0222024 | ||||||||
\(237\) | −2658.52 | −0.728648 | ||||||||
\(238\) | 323.823 | 0.0881945 | ||||||||
\(239\) | 6957.12 | 1.88292 | 0.941462 | − | 0.337119i | \(-0.109452\pi\) | ||||
0.941462 | + | 0.337119i | \(0.109452\pi\) | |||||||
\(240\) | 147.988 | 0.0398023 | ||||||||
\(241\) | −463.881 | −0.123988 | −0.0619942 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619942 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(242\) | 3836.53 | 1.01910 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1102.13 | 0.289167 | ||||||||
\(245\) | −223.862 | −0.0583756 | ||||||||
\(246\) | 4163.76 | 1.07915 | ||||||||
\(247\) | −4605.54 | −1.18641 | ||||||||
\(248\) | −5650.19 | −1.44672 | ||||||||
\(249\) | −154.461 | −0.0393116 | ||||||||
\(250\) | 515.644 | 0.130449 | ||||||||
\(251\) | −7550.40 | −1.89871 | −0.949356 | − | 0.314202i | \(-0.898263\pi\) | ||||
−0.949356 | + | 0.314202i | \(0.898263\pi\) | |||||||
\(252\) | −41.5954 | −0.0103979 | ||||||||
\(253\) | −642.817 | −0.159737 | ||||||||
\(254\) | −892.534 | −0.220483 | ||||||||
\(255\) | −63.2804 | −0.0155403 | ||||||||
\(256\) | 2038.11 | 0.497586 | ||||||||
\(257\) | 69.0755 | 0.0167658 | 0.00838290 | − | 0.999965i | \(-0.497332\pi\) | ||||
0.00838290 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(258\) | −1605.65 | −0.387455 | ||||||||
\(259\) | 1105.58 | 0.265240 | ||||||||
\(260\) | 54.7336 | 0.0130555 | ||||||||
\(261\) | −554.110 | −0.131412 | ||||||||
\(262\) | 3550.66 | 0.837254 | ||||||||
\(263\) | −6387.24 | −1.49754 | −0.748772 | − | 0.662828i | \(-0.769356\pi\) | ||||
−0.748772 | + | 0.662828i | \(0.769356\pi\) | |||||||
\(264\) | 535.527 | 0.124846 | ||||||||
\(265\) | −125.305 | −0.0290468 | ||||||||
\(266\) | −803.585 | −0.185229 | ||||||||
\(267\) | −547.049 | −0.125389 | ||||||||
\(268\) | −176.108 | −0.0401399 | ||||||||
\(269\) | −1359.76 | −0.308201 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(270\) | 55.7913 | 0.0125754 | ||||||||
\(271\) | −3184.33 | −0.713780 | −0.356890 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356890 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(272\) | −2282.04 | −0.508709 | ||||||||
\(273\) | 603.782 | 0.133855 | ||||||||
\(274\) | −1748.61 | −0.385538 | ||||||||
\(275\) | 1094.86 | 0.240083 | ||||||||
\(276\) | −299.288 | −0.0652717 | ||||||||
\(277\) | 2086.69 | 0.452626 | 0.226313 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226313 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(278\) | 1763.61 | 0.380484 | ||||||||
\(279\) | −2504.27 | −0.537373 | ||||||||
\(280\) | −46.4487 | −0.00991372 | ||||||||
\(281\) | 6730.70 | 1.42890 | 0.714448 | − | 0.699688i | \(-0.246678\pi\) | ||||
0.714448 | + | 0.699688i | \(0.246678\pi\) | |||||||
\(282\) | −4414.68 | −0.932235 | ||||||||
\(283\) | 6977.08 | 1.46553 | 0.732764 | − | 0.680483i | \(-0.238230\pi\) | ||||
0.732764 | + | 0.680483i | \(0.238230\pi\) | |||||||
\(284\) | −371.139 | −0.0775460 | ||||||||
\(285\) | 157.034 | 0.0326382 | ||||||||
\(286\) | 1598.26 | 0.330445 | ||||||||
\(287\) | −1536.43 | −0.316002 | ||||||||
\(288\) | 549.934 | 0.112518 | ||||||||
\(289\) | −3937.19 | −0.801382 | ||||||||
\(290\) | 127.220 | 0.0257608 | ||||||||
\(291\) | 4060.31 | 0.817937 | ||||||||
\(292\) | −832.310 | −0.166806 | ||||||||
\(293\) | 1173.58 | 0.233999 | 0.116999 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.116999 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(294\) | −3043.51 | −0.603746 | ||||||||
\(295\) | 39.8398 | 0.00786292 | ||||||||
\(296\) | −6627.16 | −1.30134 | ||||||||
\(297\) | 237.356 | 0.0463731 | ||||||||
\(298\) | 5647.82 | 1.09788 | ||||||||
\(299\) | 4344.34 | 0.840266 | ||||||||
\(300\) | 509.754 | 0.0981023 | ||||||||
\(301\) | 592.485 | 0.113456 | ||||||||
\(302\) | 5990.60 | 1.14146 | ||||||||
\(303\) | 1219.22 | 0.231162 | ||||||||
\(304\) | 5663.01 | 1.06841 | ||||||||
\(305\) | 545.483 | 0.102407 | ||||||||
\(306\) | −860.328 | −0.160724 | ||||||||
\(307\) | −6437.77 | −1.19682 | −0.598409 | − | 0.801191i | \(-0.704200\pi\) | ||||
−0.598409 | + | 0.801191i | \(0.704200\pi\) | |||||||
\(308\) | 40.6293 | 0.00751646 | ||||||||
\(309\) | 913.817 | 0.168237 | ||||||||
\(310\) | 574.966 | 0.105342 | ||||||||
\(311\) | −3665.91 | −0.668407 | −0.334204 | − | 0.942501i | \(-0.608467\pi\) | ||||
−0.334204 | + | 0.942501i | \(0.608467\pi\) | |||||||
\(312\) | −3619.24 | −0.656728 | ||||||||
\(313\) | −1795.66 | −0.324270 | −0.162135 | − | 0.986769i | \(-0.551838\pi\) | ||||
−0.162135 | + | 0.986769i | \(0.551838\pi\) | |||||||
\(314\) | −2422.46 | −0.435373 | ||||||||
\(315\) | −20.5870 | −0.00368237 | ||||||||
\(316\) | 1209.03 | 0.215231 | ||||||||
\(317\) | 793.810 | 0.140646 | 0.0703230 | − | 0.997524i | \(-0.477597\pi\) | ||||
0.0703230 | + | 0.997524i | \(0.477597\pi\) | |||||||
\(318\) | −1703.58 | −0.300415 | ||||||||
\(319\) | 541.240 | 0.0949958 | ||||||||
\(320\) | 268.372 | 0.0468827 | ||||||||
\(321\) | 4547.09 | 0.790636 | ||||||||
\(322\) | 758.009 | 0.131187 | ||||||||
\(323\) | −2421.54 | −0.417145 | ||||||||
\(324\) | 110.510 | 0.0189489 | ||||||||
\(325\) | −7399.39 | −1.26291 | ||||||||
\(326\) | 10294.2 | 1.74891 | ||||||||
\(327\) | 4.72873 | 0.000799692 0 | ||||||||
\(328\) | 9209.80 | 1.55038 | ||||||||
\(329\) | 1629.02 | 0.272980 | ||||||||
\(330\) | −54.4955 | −0.00909055 | ||||||||
\(331\) | 3322.57 | 0.551737 | 0.275868 | − | 0.961195i | \(-0.411035\pi\) | ||||
0.275868 | + | 0.961195i | \(0.411035\pi\) | |||||||
\(332\) | 70.2449 | 0.0116120 | ||||||||
\(333\) | −2937.29 | −0.483370 | ||||||||
\(334\) | −1575.94 | −0.258178 | ||||||||
\(335\) | −87.1619 | −0.0142154 | ||||||||
\(336\) | −742.414 | −0.120542 | ||||||||
\(337\) | 2092.35 | 0.338213 | 0.169106 | − | 0.985598i | \(-0.445912\pi\) | ||||
0.169106 | + | 0.985598i | \(0.445912\pi\) | |||||||
\(338\) | −4078.42 | −0.656322 | ||||||||
\(339\) | 1733.44 | 0.277721 | ||||||||
\(340\) | 28.7783 | 0.00459036 | ||||||||
\(341\) | 2446.11 | 0.388458 | ||||||||
\(342\) | 2134.95 | 0.337559 | ||||||||
\(343\) | 2284.99 | 0.359701 | ||||||||
\(344\) | −3551.53 | −0.556644 | ||||||||
\(345\) | −148.128 | −0.0231158 | ||||||||
\(346\) | −8034.25 | −1.24834 | ||||||||
\(347\) | −9919.25 | −1.53456 | −0.767281 | − | 0.641311i | \(-0.778391\pi\) | ||||
−0.767281 | + | 0.641311i | \(0.778391\pi\) | |||||||
\(348\) | 251.995 | 0.0388171 | ||||||||
\(349\) | 1359.74 | 0.208554 | 0.104277 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104277 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(350\) | −1291.06 | −0.197172 | ||||||||
\(351\) | −1604.12 | −0.243936 | ||||||||
\(352\) | −537.161 | −0.0813374 | ||||||||
\(353\) | −1123.35 | −0.169376 | −0.0846880 | − | 0.996408i | \(-0.526989\pi\) | ||||
−0.0846880 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(354\) | 541.641 | 0.0813217 | ||||||||
\(355\) | −183.690 | −0.0274626 | ||||||||
\(356\) | 248.784 | 0.0370380 | ||||||||
\(357\) | 317.461 | 0.0470639 | ||||||||
\(358\) | 507.096 | 0.0748628 | ||||||||
\(359\) | 4438.64 | 0.652541 | 0.326271 | − | 0.945276i | \(-0.394208\pi\) | ||||
0.326271 | + | 0.945276i | \(0.394208\pi\) | |||||||
\(360\) | 123.404 | 0.0180666 | ||||||||
\(361\) | −849.815 | −0.123898 | ||||||||
\(362\) | −5142.43 | −0.746630 | ||||||||
\(363\) | 3761.16 | 0.543828 | ||||||||
\(364\) | −274.584 | −0.0395388 | ||||||||
\(365\) | −411.939 | −0.0590736 | ||||||||
\(366\) | 7416.10 | 1.05914 | ||||||||
\(367\) | −12343.3 | −1.75563 | −0.877817 | − | 0.478996i | \(-0.841001\pi\) | ||||
−0.877817 | + | 0.478996i | \(0.841001\pi\) | |||||||
\(368\) | −5341.83 | −0.756690 | ||||||||
\(369\) | 4081.96 | 0.575877 | ||||||||
\(370\) | 674.383 | 0.0947554 | ||||||||
\(371\) | 628.620 | 0.0879685 | ||||||||
\(372\) | 1138.88 | 0.158731 | ||||||||
\(373\) | 8458.96 | 1.17423 | 0.587116 | − | 0.809503i | \(-0.300263\pi\) | ||||
0.587116 | + | 0.809503i | \(0.300263\pi\) | |||||||
\(374\) | 840.346 | 0.116185 | ||||||||
\(375\) | 505.514 | 0.0696123 | ||||||||
\(376\) | −9764.79 | −1.33931 | ||||||||
\(377\) | −3657.85 | −0.499706 | ||||||||
\(378\) | −279.890 | −0.0380846 | ||||||||
\(379\) | −7901.32 | −1.07088 | −0.535440 | − | 0.844573i | \(-0.679854\pi\) | ||||
−0.535440 | + | 0.844573i | \(0.679854\pi\) | |||||||
\(380\) | −71.4150 | −0.00964082 | ||||||||
\(381\) | −875.000 | −0.117658 | ||||||||
\(382\) | 2526.03 | 0.338332 | ||||||||
\(383\) | 1775.56 | 0.236885 | 0.118443 | − | 0.992961i | \(-0.462210\pi\) | ||||
0.118443 | + | 0.992961i | \(0.462210\pi\) | |||||||
\(384\) | 5115.14 | 0.679768 | ||||||||
\(385\) | 20.1088 | 0.00266193 | ||||||||
\(386\) | −9517.33 | −1.25497 | ||||||||
\(387\) | −1574.11 | −0.206761 | ||||||||
\(388\) | −1846.52 | −0.241606 | ||||||||
\(389\) | 12845.2 | 1.67423 | 0.837115 | − | 0.547027i | \(-0.184241\pi\) | ||||
0.837115 | + | 0.547027i | \(0.184241\pi\) | |||||||
\(390\) | 368.296 | 0.0478190 | ||||||||
\(391\) | 2284.20 | 0.295440 | ||||||||
\(392\) | −6731.92 | −0.867381 | ||||||||
\(393\) | 3480.91 | 0.446790 | ||||||||
\(394\) | 3832.20 | 0.490009 | ||||||||
\(395\) | 598.390 | 0.0762234 | ||||||||
\(396\) | −107.943 | −0.0136979 | ||||||||
\(397\) | 3824.54 | 0.483497 | 0.241749 | − | 0.970339i | \(-0.422279\pi\) | ||||
0.241749 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(398\) | −2614.55 | −0.329285 | ||||||||
\(399\) | −787.798 | −0.0988452 | ||||||||
\(400\) | 9098.34 | 1.13729 | ||||||||
\(401\) | −10107.1 | −1.25867 | −0.629334 | − | 0.777135i | \(-0.716672\pi\) | ||||
−0.629334 | + | 0.777135i | \(0.716672\pi\) | |||||||
\(402\) | −1185.01 | −0.147022 | ||||||||
\(403\) | −16531.5 | −2.04341 | ||||||||
\(404\) | −554.468 | −0.0682817 | ||||||||
\(405\) | 54.6953 | 0.00671069 | ||||||||
\(406\) | −638.230 | −0.0780168 | ||||||||
\(407\) | 2869.07 | 0.349421 | ||||||||
\(408\) | −1902.95 | −0.230907 | ||||||||
\(409\) | −863.888 | −0.104441 | −0.0522207 | − | 0.998636i | \(-0.516630\pi\) | ||||
−0.0522207 | + | 0.998636i | \(0.516630\pi\) | |||||||
\(410\) | −937.194 | −0.112890 | ||||||||
\(411\) | −1714.26 | −0.205737 | ||||||||
\(412\) | −415.580 | −0.0496945 | ||||||||
\(413\) | −199.865 | −0.0238129 | ||||||||
\(414\) | −2013.87 | −0.239073 | ||||||||
\(415\) | 34.7666 | 0.00411235 | ||||||||
\(416\) | 3630.28 | 0.427859 | ||||||||
\(417\) | 1728.97 | 0.203041 | ||||||||
\(418\) | −2085.37 | −0.244016 | ||||||||
\(419\) | 10373.1 | 1.20945 | 0.604725 | − | 0.796434i | \(-0.293283\pi\) | ||||
0.604725 | + | 0.796434i | \(0.293283\pi\) | |||||||
\(420\) | 9.36243 | 0.00108771 | ||||||||
\(421\) | 4058.69 | 0.469853 | 0.234927 | − | 0.972013i | \(-0.424515\pi\) | ||||
0.234927 | + | 0.972013i | \(0.424515\pi\) | |||||||
\(422\) | −17001.2 | −1.96115 | ||||||||
\(423\) | −4327.95 | −0.497475 | ||||||||
\(424\) | −3768.13 | −0.431596 | ||||||||
\(425\) | −3890.51 | −0.444041 | ||||||||
\(426\) | −2497.35 | −0.284031 | ||||||||
\(427\) | −2736.54 | −0.310142 | ||||||||
\(428\) | −2067.90 | −0.233541 | ||||||||
\(429\) | 1566.86 | 0.176338 | ||||||||
\(430\) | 361.405 | 0.0405314 | ||||||||
\(431\) | −13813.1 | −1.54375 | −0.771873 | − | 0.635777i | \(-0.780680\pi\) | ||||
−0.771873 | + | 0.635777i | \(0.780680\pi\) | |||||||
\(432\) | 1972.44 | 0.219673 | ||||||||
\(433\) | −14065.7 | −1.56110 | −0.780551 | − | 0.625093i | \(-0.785061\pi\) | ||||
−0.780551 | + | 0.625093i | \(0.785061\pi\) | |||||||
\(434\) | −2884.45 | −0.319028 | ||||||||
\(435\) | 124.721 | 0.0137469 | ||||||||
\(436\) | −2.15050 | −0.000236216 0 | ||||||||
\(437\) | −5668.37 | −0.620492 | ||||||||
\(438\) | −5600.51 | −0.610965 | ||||||||
\(439\) | 15470.0 | 1.68187 | 0.840937 | − | 0.541133i | \(-0.182004\pi\) | ||||
0.840937 | + | 0.541133i | \(0.182004\pi\) | |||||||
\(440\) | −120.538 | −0.0130601 | ||||||||
\(441\) | −2983.72 | −0.322181 | ||||||||
\(442\) | −5679.29 | −0.611168 | ||||||||
\(443\) | 805.886 | 0.0864307 | 0.0432153 | − | 0.999066i | \(-0.486240\pi\) | ||||
0.0432153 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(444\) | 1335.80 | 0.142780 | ||||||||
\(445\) | 123.132 | 0.0131169 | ||||||||
\(446\) | 6489.06 | 0.688937 | ||||||||
\(447\) | 5536.86 | 0.585871 | ||||||||
\(448\) | −1346.35 | −0.141985 | ||||||||
\(449\) | 15047.6 | 1.58160 | 0.790800 | − | 0.612074i | \(-0.209665\pi\) | ||||
0.790800 | + | 0.612074i | \(0.209665\pi\) | |||||||
\(450\) | 3430.07 | 0.359323 | ||||||||
\(451\) | −3987.16 | −0.416292 | ||||||||
\(452\) | −788.323 | −0.0820345 | ||||||||
\(453\) | 5872.91 | 0.609124 | ||||||||
\(454\) | −10322.0 | −1.06704 | ||||||||
\(455\) | −135.901 | −0.0140025 | ||||||||
\(456\) | 4722.29 | 0.484959 | ||||||||
\(457\) | 2132.43 | 0.218273 | 0.109137 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109137 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(458\) | −4728.26 | −0.482395 | ||||||||
\(459\) | −843.426 | −0.0857685 | ||||||||
\(460\) | 67.3647 | 0.00682803 | ||||||||
\(461\) | −7140.37 | −0.721389 | −0.360695 | − | 0.932684i | \(-0.617460\pi\) | ||||
−0.360695 | + | 0.932684i | \(0.617460\pi\) | |||||||
\(462\) | 273.390 | 0.0275308 | ||||||||
\(463\) | 10919.2 | 1.09602 | 0.548011 | − | 0.836471i | \(-0.315385\pi\) | ||||
0.548011 | + | 0.836471i | \(0.315385\pi\) | |||||||
\(464\) | 4497.72 | 0.450003 | ||||||||
\(465\) | 563.671 | 0.0562142 | ||||||||
\(466\) | −14872.3 | −1.47842 | ||||||||
\(467\) | 13946.8 | 1.38197 | 0.690987 | − | 0.722867i | \(-0.257176\pi\) | ||||
0.690987 | + | 0.722867i | \(0.257176\pi\) | |||||||
\(468\) | 729.511 | 0.0720549 | ||||||||
\(469\) | 437.268 | 0.0430515 | ||||||||
\(470\) | 993.671 | 0.0975205 | ||||||||
\(471\) | −2374.87 | −0.232332 | ||||||||
\(472\) | 1198.05 | 0.116832 | ||||||||
\(473\) | 1537.55 | 0.149464 | ||||||||
\(474\) | 8135.40 | 0.788336 | ||||||||
\(475\) | 9654.52 | 0.932589 | ||||||||
\(476\) | −144.373 | −0.0139019 | ||||||||
\(477\) | −1670.11 | −0.160313 | ||||||||
\(478\) | −21289.6 | −2.03716 | ||||||||
\(479\) | 18107.2 | 1.72723 | 0.863613 | − | 0.504155i | \(-0.168196\pi\) | ||||
0.863613 | + | 0.504155i | \(0.168196\pi\) | |||||||
\(480\) | −123.781 | −0.0117704 | ||||||||
\(481\) | −19389.9 | −1.83806 | ||||||||
\(482\) | 1419.53 | 0.134145 | ||||||||
\(483\) | 743.118 | 0.0700063 | ||||||||
\(484\) | −1710.48 | −0.160638 | ||||||||
\(485\) | −913.908 | −0.0855638 | ||||||||
\(486\) | 743.609 | 0.0694049 | ||||||||
\(487\) | −15930.5 | −1.48230 | −0.741150 | − | 0.671340i | \(-0.765719\pi\) | ||||
−0.741150 | + | 0.671340i | \(0.765719\pi\) | |||||||
\(488\) | 16403.6 | 1.52163 | ||||||||
\(489\) | 10092.0 | 0.933284 | ||||||||
\(490\) | 685.044 | 0.0631574 | ||||||||
\(491\) | 2619.27 | 0.240745 | 0.120373 | − | 0.992729i | \(-0.461591\pi\) | ||||
0.120373 | + | 0.992729i | \(0.461591\pi\) | |||||||
\(492\) | −1856.37 | −0.170105 | ||||||||
\(493\) | −1923.25 | −0.175698 | ||||||||
\(494\) | 14093.5 | 1.28360 | ||||||||
\(495\) | −53.4249 | −0.00485105 | ||||||||
\(496\) | 20327.2 | 1.84016 | ||||||||
\(497\) | 921.522 | 0.0831709 | ||||||||
\(498\) | 472.669 | 0.0425318 | ||||||||
\(499\) | −9350.73 | −0.838870 | −0.419435 | − | 0.907785i | \(-0.637772\pi\) | ||||
−0.419435 | + | 0.907785i | \(0.637772\pi\) | |||||||
\(500\) | −229.895 | −0.0205624 | ||||||||
\(501\) | −1544.98 | −0.137773 | ||||||||
\(502\) | 23105.1 | 2.05425 | ||||||||
\(503\) | −7300.43 | −0.647137 | −0.323568 | − | 0.946205i | \(-0.604883\pi\) | ||||
−0.323568 | + | 0.946205i | \(0.604883\pi\) | |||||||
\(504\) | −619.087 | −0.0547149 | ||||||||
\(505\) | −274.426 | −0.0241817 | ||||||||
\(506\) | 1967.10 | 0.172822 | ||||||||
\(507\) | −3998.29 | −0.350238 | ||||||||
\(508\) | 397.927 | 0.0347542 | ||||||||
\(509\) | 16241.5 | 1.41432 | 0.707162 | − | 0.707052i | \(-0.249975\pi\) | ||||
0.707162 | + | 0.707052i | \(0.249975\pi\) | |||||||
\(510\) | 193.645 | 0.0168133 | ||||||||
\(511\) | 2066.59 | 0.178905 | ||||||||
\(512\) | 7403.50 | 0.639046 | ||||||||
\(513\) | 2093.01 | 0.180134 | ||||||||
\(514\) | −211.379 | −0.0181392 | ||||||||
\(515\) | −205.685 | −0.0175991 | ||||||||
\(516\) | 715.862 | 0.0610738 | ||||||||
\(517\) | 4227.43 | 0.359617 | ||||||||
\(518\) | −3383.20 | −0.286968 | ||||||||
\(519\) | −7876.41 | −0.666158 | ||||||||
\(520\) | 814.631 | 0.0686999 | ||||||||
\(521\) | 21182.1 | 1.78120 | 0.890598 | − | 0.454792i | \(-0.150286\pi\) | ||||
0.890598 | + | 0.454792i | \(0.150286\pi\) | |||||||
\(522\) | 1695.64 | 0.142177 | ||||||||
\(523\) | 19761.6 | 1.65222 | 0.826112 | − | 0.563505i | \(-0.190548\pi\) | ||||
0.826112 | + | 0.563505i | \(0.190548\pi\) | |||||||
\(524\) | −1583.03 | −0.131975 | ||||||||
\(525\) | −1265.70 | −0.105218 | ||||||||
\(526\) | 19545.7 | 1.62022 | ||||||||
\(527\) | −8692.06 | −0.718467 | ||||||||
\(528\) | −1926.63 | −0.158798 | ||||||||
\(529\) | −6820.11 | −0.560541 | ||||||||
\(530\) | 383.447 | 0.0314262 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | 358.270 | 0.0291973 | ||||||||
\(533\) | 26946.3 | 2.18982 | ||||||||
\(534\) | 1674.04 | 0.135660 | ||||||||
\(535\) | −1023.48 | −0.0827079 | ||||||||
\(536\) | −2621.11 | −0.211221 | ||||||||
\(537\) | 497.134 | 0.0399496 | ||||||||
\(538\) | 4161.02 | 0.333447 | ||||||||
\(539\) | 2914.42 | 0.232900 | ||||||||
\(540\) | −24.8740 | −0.00198223 | ||||||||
\(541\) | 1805.49 | 0.143482 | 0.0717412 | − | 0.997423i | \(-0.477144\pi\) | ||||
0.0717412 | + | 0.997423i | \(0.477144\pi\) | |||||||
\(542\) | 9744.44 | 0.772250 | ||||||||
\(543\) | −5041.40 | −0.398429 | ||||||||
\(544\) | 1908.76 | 0.150436 | ||||||||
\(545\) | −1.06436 | −8.36552e−5 0 | ||||||||
\(546\) | −1847.64 | −0.144820 | ||||||||
\(547\) | −2017.11 | −0.157670 | −0.0788349 | − | 0.996888i | \(-0.525120\pi\) | ||||
−0.0788349 | + | 0.996888i | \(0.525120\pi\) | |||||||
\(548\) | 779.599 | 0.0607716 | ||||||||
\(549\) | 7270.41 | 0.565198 | ||||||||
\(550\) | −3350.41 | −0.259749 | ||||||||
\(551\) | 4772.67 | 0.369006 | ||||||||
\(552\) | −4454.46 | −0.343468 | ||||||||
\(553\) | −3001.96 | −0.230843 | ||||||||
\(554\) | −6385.53 | −0.489703 | ||||||||
\(555\) | 661.134 | 0.0505650 | ||||||||
\(556\) | −786.289 | −0.0599750 | ||||||||
\(557\) | 22836.9 | 1.73722 | 0.868611 | − | 0.495495i | \(-0.165013\pi\) | ||||
0.868611 | + | 0.495495i | \(0.165013\pi\) | |||||||
\(558\) | 7663.37 | 0.581392 | ||||||||
\(559\) | −10391.2 | −0.786225 | ||||||||
\(560\) | 167.105 | 0.0126098 | ||||||||
\(561\) | 823.837 | 0.0620007 | ||||||||
\(562\) | −20596.7 | −1.54594 | ||||||||
\(563\) | −11521.8 | −0.862494 | −0.431247 | − | 0.902234i | \(-0.641926\pi\) | ||||
−0.431247 | + | 0.902234i | \(0.641926\pi\) | |||||||
\(564\) | 1968.24 | 0.146946 | ||||||||
\(565\) | −390.168 | −0.0290522 | ||||||||
\(566\) | −21350.7 | −1.58558 | ||||||||
\(567\) | −274.392 | −0.0203234 | ||||||||
\(568\) | −5523.87 | −0.408057 | ||||||||
\(569\) | −431.235 | −0.0317721 | −0.0158860 | − | 0.999874i | \(-0.505057\pi\) | ||||
−0.0158860 | + | 0.999874i | \(0.505057\pi\) | |||||||
\(570\) | −480.543 | −0.0353118 | ||||||||
\(571\) | 7544.48 | 0.552937 | 0.276468 | − | 0.961023i | \(-0.410836\pi\) | ||||
0.276468 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(572\) | −712.568 | −0.0520874 | ||||||||
\(573\) | 2476.40 | 0.180547 | ||||||||
\(574\) | 4701.65 | 0.341887 | ||||||||
\(575\) | −9106.97 | −0.660499 | ||||||||
\(576\) | 3576.97 | 0.258751 | ||||||||
\(577\) | −12507.5 | −0.902416 | −0.451208 | − | 0.892419i | \(-0.649007\pi\) | ||||
−0.451208 | + | 0.892419i | \(0.649007\pi\) | |||||||
\(578\) | 12048.3 | 0.867027 | ||||||||
\(579\) | −9330.36 | −0.669700 | ||||||||
\(580\) | −56.7198 | −0.00406063 | ||||||||
\(581\) | −174.415 | −0.0124543 | ||||||||
\(582\) | −12425.0 | −0.884938 | ||||||||
\(583\) | 1631.32 | 0.115887 | ||||||||
\(584\) | −12387.7 | −0.877753 | ||||||||
\(585\) | 361.061 | 0.0255180 | ||||||||
\(586\) | −3591.31 | −0.253167 | ||||||||
\(587\) | 12553.1 | 0.882659 | 0.441330 | − | 0.897345i | \(-0.354507\pi\) | ||||
0.441330 | + | 0.897345i | \(0.354507\pi\) | |||||||
\(588\) | 1356.92 | 0.0951673 | ||||||||
\(589\) | 21569.9 | 1.50895 | ||||||||
\(590\) | −121.914 | −0.00850701 | ||||||||
\(591\) | 3756.92 | 0.261487 | ||||||||
\(592\) | 23842.0 | 1.65524 | ||||||||
\(593\) | −4198.56 | −0.290749 | −0.145374 | − | 0.989377i | \(-0.546439\pi\) | ||||
−0.145374 | + | 0.989377i | \(0.546439\pi\) | |||||||
\(594\) | −726.338 | −0.0501717 | ||||||||
\(595\) | −71.4552 | −0.00492332 | ||||||||
\(596\) | −2518.02 | −0.173057 | ||||||||
\(597\) | −2563.18 | −0.175719 | ||||||||
\(598\) | −13294.2 | −0.909097 | ||||||||
\(599\) | −4991.05 | −0.340449 | −0.170224 | − | 0.985405i | \(-0.554449\pi\) | ||||
−0.170224 | + | 0.985405i | \(0.554449\pi\) | |||||||
\(600\) | 7586.96 | 0.516227 | ||||||||
\(601\) | −8600.34 | −0.583719 | −0.291859 | − | 0.956461i | \(-0.594274\pi\) | ||||
−0.291859 | + | 0.956461i | \(0.594274\pi\) | |||||||
\(602\) | −1813.07 | −0.122750 | ||||||||
\(603\) | −1161.73 | −0.0784564 | ||||||||
\(604\) | −2670.84 | −0.179926 | ||||||||
\(605\) | −846.574 | −0.0568895 | ||||||||
\(606\) | −3730.95 | −0.250098 | ||||||||
\(607\) | −17833.1 | −1.19246 | −0.596230 | − | 0.802814i | \(-0.703335\pi\) | ||||
−0.596230 | + | 0.802814i | \(0.703335\pi\) | |||||||
\(608\) | −4736.70 | −0.315951 | ||||||||
\(609\) | −625.692 | −0.0416327 | ||||||||
\(610\) | −1669.24 | −0.110796 | ||||||||
\(611\) | −28570.2 | −1.89169 | ||||||||
\(612\) | 383.568 | 0.0253347 | ||||||||
\(613\) | −22215.0 | −1.46371 | −0.731856 | − | 0.681459i | \(-0.761346\pi\) | ||||
−0.731856 | + | 0.681459i | \(0.761346\pi\) | |||||||
\(614\) | 19700.3 | 1.29485 | ||||||||
\(615\) | −918.782 | −0.0602421 | ||||||||
\(616\) | 604.708 | 0.0395526 | ||||||||
\(617\) | 18251.1 | 1.19086 | 0.595432 | − | 0.803406i | \(-0.296981\pi\) | ||||
0.595432 | + | 0.803406i | \(0.296981\pi\) | |||||||
\(618\) | −2796.39 | −0.182018 | ||||||||
\(619\) | 9872.40 | 0.641042 | 0.320521 | − | 0.947241i | \(-0.396142\pi\) | ||||
0.320521 | + | 0.947241i | \(0.396142\pi\) | |||||||
\(620\) | −256.343 | −0.0166048 | ||||||||
\(621\) | −1974.31 | −0.127578 | ||||||||
\(622\) | 11218.1 | 0.723160 | ||||||||
\(623\) | −617.719 | −0.0397245 | ||||||||
\(624\) | 13020.7 | 0.835327 | ||||||||
\(625\) | 15454.2 | 0.989070 | ||||||||
\(626\) | 5494.92 | 0.350833 | ||||||||
\(627\) | −2044.40 | −0.130216 | ||||||||
\(628\) | 1080.03 | 0.0686271 | ||||||||
\(629\) | −10195.0 | −0.646265 | ||||||||
\(630\) | 62.9986 | 0.00398401 | ||||||||
\(631\) | −9843.54 | −0.621023 | −0.310511 | − | 0.950570i | \(-0.600500\pi\) | ||||
−0.310511 | + | 0.950570i | \(0.600500\pi\) | |||||||
\(632\) | 17994.6 | 1.13258 | ||||||||
\(633\) | −16667.2 | −1.04654 | ||||||||
\(634\) | −2429.15 | −0.152167 | ||||||||
\(635\) | 196.948 | 0.0123081 | ||||||||
\(636\) | 759.522 | 0.0473538 | ||||||||
\(637\) | −19696.5 | −1.22512 | ||||||||
\(638\) | −1656.26 | −0.102777 | ||||||||
\(639\) | −2448.29 | −0.151569 | ||||||||
\(640\) | −1151.33 | −0.0711100 | ||||||||
\(641\) | −16239.8 | −1.00068 | −0.500338 | − | 0.865830i | \(-0.666791\pi\) | ||||
−0.500338 | + | 0.865830i | \(0.666791\pi\) | |||||||
\(642\) | −13914.6 | −0.855401 | ||||||||
\(643\) | −4102.04 | −0.251584 | −0.125792 | − | 0.992057i | \(-0.540147\pi\) | ||||
−0.125792 | + | 0.992057i | \(0.540147\pi\) | |||||||
\(644\) | −337.951 | −0.0206788 | ||||||||
\(645\) | 354.305 | 0.0216291 | ||||||||
\(646\) | 7410.19 | 0.451316 | ||||||||
\(647\) | −29339.0 | −1.78274 | −0.891371 | − | 0.453274i | \(-0.850256\pi\) | ||||
−0.891371 | + | 0.453274i | \(0.850256\pi\) | |||||||
\(648\) | 1644.78 | 0.0997117 | ||||||||
\(649\) | −518.667 | −0.0313705 | ||||||||
\(650\) | 22643.0 | 1.36636 | ||||||||
\(651\) | −2827.78 | −0.170245 | ||||||||
\(652\) | −4589.58 | −0.275677 | ||||||||
\(653\) | −22467.1 | −1.34641 | −0.673206 | − | 0.739455i | \(-0.735083\pi\) | ||||
−0.673206 | + | 0.739455i | \(0.735083\pi\) | |||||||
\(654\) | −14.4705 | −0.000865198 0 | ||||||||
\(655\) | −783.494 | −0.0467384 | ||||||||
\(656\) | −33133.4 | −1.97201 | ||||||||
\(657\) | −5490.49 | −0.326034 | ||||||||
\(658\) | −4984.98 | −0.295342 | ||||||||
\(659\) | 14150.3 | 0.836447 | 0.418223 | − | 0.908344i | \(-0.362653\pi\) | ||||
0.418223 | + | 0.908344i | \(0.362653\pi\) | |||||||
\(660\) | 24.2963 | 0.00143293 | ||||||||
\(661\) | −10577.7 | −0.622428 | −0.311214 | − | 0.950340i | \(-0.600736\pi\) | ||||
−0.311214 | + | 0.950340i | \(0.600736\pi\) | |||||||
\(662\) | −10167.4 | −0.596932 | ||||||||
\(663\) | −5567.72 | −0.326142 | ||||||||
\(664\) | 1045.49 | 0.0611040 | ||||||||
\(665\) | 177.320 | 0.0103401 | ||||||||
\(666\) | 8988.44 | 0.522965 | ||||||||
\(667\) | −4501.99 | −0.261346 | ||||||||
\(668\) | 702.615 | 0.0406961 | ||||||||
\(669\) | 6361.58 | 0.367643 | ||||||||
\(670\) | 266.726 | 0.0153799 | ||||||||
\(671\) | −7101.55 | −0.408573 | ||||||||
\(672\) | 620.976 | 0.0356468 | ||||||||
\(673\) | −9785.95 | −0.560506 | −0.280253 | − | 0.959926i | \(-0.590418\pi\) | ||||
−0.280253 | + | 0.959926i | \(0.590418\pi\) | |||||||
\(674\) | −6402.85 | −0.365918 | ||||||||
\(675\) | 3362.69 | 0.191748 | ||||||||
\(676\) | 1818.32 | 0.103455 | ||||||||
\(677\) | −25327.9 | −1.43786 | −0.718929 | − | 0.695084i | \(-0.755367\pi\) | ||||
−0.718929 | + | 0.695084i | \(0.755367\pi\) | |||||||
\(678\) | −5304.53 | −0.300471 | ||||||||
\(679\) | 4584.83 | 0.259131 | ||||||||
\(680\) | 428.323 | 0.0241551 | ||||||||
\(681\) | −10119.2 | −0.569410 | ||||||||
\(682\) | −7485.39 | −0.420279 | ||||||||
\(683\) | 11813.3 | 0.661819 | 0.330909 | − | 0.943662i | \(-0.392645\pi\) | ||||
0.330909 | + | 0.943662i | \(0.392645\pi\) | |||||||
\(684\) | −951.847 | −0.0532087 | ||||||||
\(685\) | 385.851 | 0.0215220 | ||||||||
\(686\) | −6992.32 | −0.389166 | ||||||||
\(687\) | −4635.37 | −0.257424 | ||||||||
\(688\) | 12777.1 | 0.708024 | ||||||||
\(689\) | −11024.9 | −0.609602 | ||||||||
\(690\) | 453.289 | 0.0250093 | ||||||||
\(691\) | 10486.4 | 0.577309 | 0.288655 | − | 0.957433i | \(-0.406792\pi\) | ||||
0.288655 | + | 0.957433i | \(0.406792\pi\) | |||||||
\(692\) | 3581.99 | 0.196773 | ||||||||
\(693\) | 268.019 | 0.0146915 | ||||||||
\(694\) | 30354.1 | 1.66027 | ||||||||
\(695\) | −389.162 | −0.0212399 | ||||||||
\(696\) | 3750.58 | 0.204261 | ||||||||
\(697\) | 14168.0 | 0.769946 | ||||||||
\(698\) | −4160.97 | −0.225637 | ||||||||
\(699\) | −14580.1 | −0.788942 | ||||||||
\(700\) | 575.606 | 0.0310798 | ||||||||
\(701\) | 10841.7 | 0.584144 | 0.292072 | − | 0.956396i | \(-0.405655\pi\) | ||||
0.292072 | + | 0.956396i | \(0.405655\pi\) | |||||||
\(702\) | 4908.79 | 0.263918 | ||||||||
\(703\) | 25299.5 | 1.35731 | ||||||||
\(704\) | −3493.89 | −0.187047 | ||||||||
\(705\) | 974.150 | 0.0520406 | ||||||||
\(706\) | 3437.57 | 0.183250 | ||||||||
\(707\) | 1376.72 | 0.0732346 | ||||||||
\(708\) | −241.485 | −0.0128186 | ||||||||
\(709\) | −15139.3 | −0.801930 | −0.400965 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400965 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(710\) | 562.112 | 0.0297123 | ||||||||
\(711\) | 7975.57 | 0.420685 | ||||||||
\(712\) | 3702.79 | 0.194899 | ||||||||
\(713\) | −20346.5 | −1.06870 | ||||||||
\(714\) | −971.468 | −0.0509191 | ||||||||
\(715\) | −352.675 | −0.0184466 | ||||||||
\(716\) | −226.084 | −0.0118005 | ||||||||
\(717\) | −20871.4 | −1.08711 | ||||||||
\(718\) | −13582.8 | −0.705994 | ||||||||
\(719\) | −26507.9 | −1.37494 | −0.687468 | − | 0.726215i | \(-0.741278\pi\) | ||||
−0.687468 | + | 0.726215i | \(0.741278\pi\) | |||||||
\(720\) | −443.963 | −0.0229799 | ||||||||
\(721\) | 1031.87 | 0.0532992 | ||||||||
\(722\) | 2600.53 | 0.134047 | ||||||||
\(723\) | 1391.64 | 0.0715847 | ||||||||
\(724\) | 2292.70 | 0.117690 | ||||||||
\(725\) | 7667.90 | 0.392798 | ||||||||
\(726\) | −11509.6 | −0.588376 | ||||||||
\(727\) | −4196.55 | −0.214087 | −0.107044 | − | 0.994254i | \(-0.534138\pi\) | ||||
−0.107044 | + | 0.994254i | \(0.534138\pi\) | |||||||
\(728\) | −4086.79 | −0.208058 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1260.58 | 0.0639127 | ||||||||
\(731\) | −5463.55 | −0.276439 | ||||||||
\(732\) | −3306.39 | −0.166950 | ||||||||
\(733\) | 19609.3 | 0.988110 | 0.494055 | − | 0.869431i | \(-0.335514\pi\) | ||||
0.494055 | + | 0.869431i | \(0.335514\pi\) | |||||||
\(734\) | 37772.1 | 1.89945 | ||||||||
\(735\) | 671.586 | 0.0337032 | ||||||||
\(736\) | 4468.05 | 0.223770 | ||||||||
\(737\) | 1134.75 | 0.0567149 | ||||||||
\(738\) | −12491.3 | −0.623050 | ||||||||
\(739\) | 2865.95 | 0.142660 | 0.0713299 | − | 0.997453i | \(-0.477276\pi\) | ||||
0.0713299 | + | 0.997453i | \(0.477276\pi\) | |||||||
\(740\) | −300.667 | −0.0149361 | ||||||||
\(741\) | 13816.6 | 0.684975 | ||||||||
\(742\) | −1923.65 | −0.0951745 | ||||||||
\(743\) | 6771.12 | 0.334332 | 0.167166 | − | 0.985929i | \(-0.446538\pi\) | ||||
0.167166 | + | 0.985929i | \(0.446538\pi\) | |||||||
\(744\) | 16950.6 | 0.835266 | ||||||||
\(745\) | −1246.26 | −0.0612876 | ||||||||
\(746\) | −25885.4 | −1.27042 | ||||||||
\(747\) | 463.383 | 0.0226965 | ||||||||
\(748\) | −374.659 | −0.0183140 | ||||||||
\(749\) | 5134.50 | 0.250482 | ||||||||
\(750\) | −1546.93 | −0.0753146 | ||||||||
\(751\) | −15205.4 | −0.738819 | −0.369409 | − | 0.929267i | \(-0.620440\pi\) | ||||
−0.369409 | + | 0.929267i | \(0.620440\pi\) | |||||||
\(752\) | 35130.1 | 1.70354 | ||||||||
\(753\) | 22651.2 | 1.09622 | ||||||||
\(754\) | 11193.5 | 0.540639 | ||||||||
\(755\) | −1321.89 | −0.0637201 | ||||||||
\(756\) | 124.786 | 0.00600321 | ||||||||
\(757\) | 11748.5 | 0.564077 | 0.282038 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282038 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(758\) | 24179.0 | 1.15860 | ||||||||
\(759\) | 1928.45 | 0.0922244 | ||||||||
\(760\) | −1062.91 | −0.0507313 | ||||||||
\(761\) | −33071.4 | −1.57535 | −0.787673 | − | 0.616094i | \(-0.788714\pi\) | ||||
−0.787673 | + | 0.616094i | \(0.788714\pi\) | |||||||
\(762\) | 2677.60 | 0.127296 | ||||||||
\(763\) | 5.33960 | 0.000253351 0 | ||||||||
\(764\) | −1126.20 | −0.0533306 | ||||||||
\(765\) | 189.841 | 0.00897219 | ||||||||
\(766\) | −5433.43 | −0.256290 | ||||||||
\(767\) | 3505.30 | 0.165018 | ||||||||
\(768\) | −6114.34 | −0.287282 | ||||||||
\(769\) | 32399.7 | 1.51933 | 0.759665 | − | 0.650315i | \(-0.225363\pi\) | ||||
0.759665 | + | 0.650315i | \(0.225363\pi\) | |||||||
\(770\) | −61.5354 | −0.00287998 | ||||||||
\(771\) | −207.227 | −0.00967974 | ||||||||
\(772\) | 4243.20 | 0.197819 | ||||||||
\(773\) | −35967.3 | −1.67355 | −0.836774 | − | 0.547548i | \(-0.815561\pi\) | ||||
−0.836774 | + | 0.547548i | \(0.815561\pi\) | |||||||
\(774\) | 4816.95 | 0.223697 | ||||||||
\(775\) | 34654.7 | 1.60624 | ||||||||
\(776\) | −27482.8 | −1.27136 | ||||||||
\(777\) | −3316.73 | −0.153137 | ||||||||
\(778\) | −39307.7 | −1.81137 | ||||||||
\(779\) | −35158.8 | −1.61707 | ||||||||
\(780\) | −164.201 | −0.00753761 | ||||||||
\(781\) | 2391.43 | 0.109567 | ||||||||
\(782\) | −6989.92 | −0.319641 | ||||||||
\(783\) | 1662.33 | 0.0758708 | ||||||||
\(784\) | 24218.9 | 1.10327 | ||||||||
\(785\) | 534.543 | 0.0243040 | ||||||||
\(786\) | −10652.0 | −0.483389 | ||||||||
\(787\) | −2130.77 | −0.0965106 | −0.0482553 | − | 0.998835i | \(-0.515366\pi\) | ||||
−0.0482553 | + | 0.998835i | \(0.515366\pi\) | |||||||
\(788\) | −1708.55 | −0.0772392 | ||||||||
\(789\) | 19161.7 | 0.864607 | ||||||||
\(790\) | −1831.14 | −0.0824673 | ||||||||
\(791\) | 1957.37 | 0.0879849 | ||||||||
\(792\) | −1606.58 | −0.0720800 | ||||||||
\(793\) | 47994.3 | 2.14921 | ||||||||
\(794\) | −11703.6 | −0.523103 | ||||||||
\(795\) | 375.914 | 0.0167702 | ||||||||
\(796\) | 1165.67 | 0.0519046 | ||||||||
\(797\) | 25863.7 | 1.14949 | 0.574743 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574743 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(798\) | 2410.75 | 0.106942 | ||||||||
\(799\) | −15021.8 | −0.665124 | ||||||||
\(800\) | −7610.11 | −0.336322 | ||||||||
\(801\) | 1641.15 | 0.0723934 | ||||||||
\(802\) | 30929.0 | 1.36177 | ||||||||
\(803\) | 5362.97 | 0.235685 | ||||||||
\(804\) | 528.323 | 0.0231748 | ||||||||
\(805\) | −167.263 | −0.00732331 | ||||||||
\(806\) | 50588.3 | 2.21079 | ||||||||
\(807\) | 4079.28 | 0.177940 | ||||||||
\(808\) | −8252.46 | −0.359307 | ||||||||
\(809\) | 26720.2 | 1.16123 | 0.580614 | − | 0.814179i | \(-0.302813\pi\) | ||||
0.580614 | + | 0.814179i | \(0.302813\pi\) | |||||||
\(810\) | −167.374 | −0.00726040 | ||||||||
\(811\) | 23248.5 | 1.00662 | 0.503308 | − | 0.864107i | \(-0.332116\pi\) | ||||
0.503308 | + | 0.864107i | \(0.332116\pi\) | |||||||
\(812\) | 284.548 | 0.0122976 | ||||||||
\(813\) | 9553.00 | 0.412101 | ||||||||
\(814\) | −8779.68 | −0.378044 | ||||||||
\(815\) | −2271.54 | −0.0976302 | ||||||||
\(816\) | 6846.11 | 0.293703 | ||||||||
\(817\) | 13558.1 | 0.580586 | ||||||||
\(818\) | 2643.60 | 0.112997 | ||||||||
\(819\) | −1811.34 | −0.0772814 | ||||||||
\(820\) | 417.838 | 0.0177946 | ||||||||
\(821\) | 7799.17 | 0.331538 | 0.165769 | − | 0.986165i | \(-0.446989\pi\) | ||||
0.165769 | + | 0.986165i | \(0.446989\pi\) | |||||||
\(822\) | 5245.83 | 0.222590 | ||||||||
\(823\) | 2499.10 | 0.105848 | 0.0529242 | − | 0.998599i | \(-0.483146\pi\) | ||||
0.0529242 | + | 0.998599i | \(0.483146\pi\) | |||||||
\(824\) | −6185.31 | −0.261499 | ||||||||
\(825\) | −3284.59 | −0.138612 | ||||||||
\(826\) | 611.612 | 0.0257636 | ||||||||
\(827\) | −39871.3 | −1.67649 | −0.838246 | − | 0.545292i | \(-0.816419\pi\) | ||||
−0.838246 | + | 0.545292i | \(0.816419\pi\) | |||||||
\(828\) | 897.863 | 0.0376846 | ||||||||
\(829\) | 8721.76 | 0.365403 | 0.182702 | − | 0.983168i | \(-0.441516\pi\) | ||||
0.182702 | + | 0.983168i | \(0.441516\pi\) | |||||||
\(830\) | −106.390 | −0.00444922 | ||||||||
\(831\) | −6260.08 | −0.261324 | ||||||||
\(832\) | 23612.7 | 0.983922 | ||||||||
\(833\) | −10356.2 | −0.430756 | ||||||||
\(834\) | −5290.84 | −0.219673 | ||||||||
\(835\) | 347.749 | 0.0144124 | ||||||||
\(836\) | 929.739 | 0.0384638 | ||||||||
\(837\) | 7512.82 | 0.310252 | ||||||||
\(838\) | −31742.9 | −1.30852 | ||||||||
\(839\) | −11850.6 | −0.487637 | −0.243818 | − | 0.969821i | \(-0.578400\pi\) | ||||
−0.243818 | + | 0.969821i | \(0.578400\pi\) | |||||||
\(840\) | 139.346 | 0.00572369 | ||||||||
\(841\) | −20598.4 | −0.844578 | ||||||||
\(842\) | −12420.1 | −0.508341 | ||||||||
\(843\) | −20192.1 | −0.824974 | ||||||||
\(844\) | 7579.80 | 0.309132 | ||||||||
\(845\) | 899.950 | 0.0366381 | ||||||||
\(846\) | 13244.0 | 0.538226 | ||||||||
\(847\) | 4247.04 | 0.172290 | ||||||||
\(848\) | 13556.3 | 0.548969 | ||||||||
\(849\) | −20931.2 | −0.846123 | ||||||||
\(850\) | 11905.4 | 0.480414 | ||||||||
\(851\) | −23864.6 | −0.961303 | ||||||||
\(852\) | 1113.42 | 0.0447712 | ||||||||
\(853\) | −25857.7 | −1.03793 | −0.518963 | − | 0.854797i | \(-0.673682\pi\) | ||||
−0.518963 | + | 0.854797i | \(0.673682\pi\) | |||||||
\(854\) | 8374.14 | 0.335547 | ||||||||
\(855\) | −471.102 | −0.0188437 | ||||||||
\(856\) | −30777.7 | −1.22893 | ||||||||
\(857\) | −13217.7 | −0.526847 | −0.263424 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263424 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(858\) | −4794.78 | −0.190782 | ||||||||
\(859\) | 45527.8 | 1.80837 | 0.904184 | − | 0.427142i | \(-0.140480\pi\) | ||||
0.904184 | + | 0.427142i | \(0.140480\pi\) | |||||||
\(860\) | −161.129 | −0.00638889 | ||||||||
\(861\) | 4609.28 | 0.182444 | ||||||||
\(862\) | 42269.8 | 1.67020 | ||||||||
\(863\) | 5044.12 | 0.198961 | 0.0994807 | − | 0.995039i | \(-0.468282\pi\) | ||||
0.0994807 | + | 0.995039i | \(0.468282\pi\) | |||||||
\(864\) | −1649.80 | −0.0649622 | ||||||||
\(865\) | 1772.85 | 0.0696864 | ||||||||
\(866\) | 43042.9 | 1.68898 | ||||||||
\(867\) | 11811.6 | 0.462678 | ||||||||
\(868\) | 1286.00 | 0.0502877 | ||||||||
\(869\) | −7790.33 | −0.304107 | ||||||||
\(870\) | −381.661 | −0.0148730 | ||||||||
\(871\) | −7668.93 | −0.298337 | ||||||||
\(872\) | −32.0071 | −0.00124300 | ||||||||
\(873\) | −12180.9 | −0.472236 | ||||||||
\(874\) | 17345.9 | 0.671320 | ||||||||
\(875\) | 570.818 | 0.0220539 | ||||||||
\(876\) | 2496.93 | 0.0963053 | ||||||||
\(877\) | −16427.0 | −0.632498 | −0.316249 | − | 0.948676i | \(-0.602424\pi\) | ||||
−0.316249 | + | 0.948676i | \(0.602424\pi\) | |||||||
\(878\) | −47340.0 | −1.81965 | ||||||||
\(879\) | −3520.75 | −0.135099 | ||||||||
\(880\) | 433.651 | 0.0166118 | ||||||||
\(881\) | 49555.6 | 1.89508 | 0.947542 | − | 0.319631i | \(-0.103559\pi\) | ||||
0.947542 | + | 0.319631i | \(0.103559\pi\) | |||||||
\(882\) | 9130.54 | 0.348573 | ||||||||
\(883\) | −10096.6 | −0.384798 | −0.192399 | − | 0.981317i | \(-0.561627\pi\) | ||||
−0.192399 | + | 0.981317i | \(0.561627\pi\) | |||||||
\(884\) | 2532.05 | 0.0963373 | ||||||||
\(885\) | −119.519 | −0.00453966 | ||||||||
\(886\) | −2466.11 | −0.0935106 | ||||||||
\(887\) | 17531.6 | 0.663647 | 0.331824 | − | 0.943341i | \(-0.392336\pi\) | ||||
0.331824 | + | 0.943341i | \(0.392336\pi\) | |||||||
\(888\) | 19881.5 | 0.751327 | ||||||||
\(889\) | −988.035 | −0.0372752 | ||||||||
\(890\) | −376.798 | −0.0141913 | ||||||||
\(891\) | −712.068 | −0.0267735 | ||||||||
\(892\) | −2893.08 | −0.108596 | ||||||||
\(893\) | 37277.6 | 1.39692 | ||||||||
\(894\) | −16943.4 | −0.633863 | ||||||||
\(895\) | −111.897 | −0.00417910 | ||||||||
\(896\) | 5775.93 | 0.215357 | ||||||||
\(897\) | −13033.0 | −0.485128 | ||||||||
\(898\) | −46047.3 | −1.71116 | ||||||||
\(899\) | 17131.4 | 0.635555 | ||||||||
\(900\) | −1529.26 | −0.0566394 | ||||||||
\(901\) | −5796.77 | −0.214338 | ||||||||
\(902\) | 12201.2 | 0.450393 | ||||||||
\(903\) | −1777.45 | −0.0655039 | ||||||||
\(904\) | −11733.0 | −0.431676 | ||||||||
\(905\) | 1134.74 | 0.0416794 | ||||||||
\(906\) | −17971.8 | −0.659021 | ||||||||
\(907\) | 14205.5 | 0.520052 | 0.260026 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260026 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(908\) | 4601.94 | 0.168195 | ||||||||
\(909\) | −3657.65 | −0.133462 | ||||||||
\(910\) | 415.874 | 0.0151495 | ||||||||
\(911\) | −6382.81 | −0.232132 | −0.116066 | − | 0.993242i | \(-0.537028\pi\) | ||||
−0.116066 | + | 0.993242i | \(0.537028\pi\) | |||||||
\(912\) | −16989.0 | −0.616845 | ||||||||
\(913\) | −452.621 | −0.0164070 | ||||||||
\(914\) | −6525.48 | −0.236153 | ||||||||
\(915\) | −1636.45 | −0.0591249 | ||||||||
\(916\) | 2108.04 | 0.0760390 | ||||||||
\(917\) | 3930.58 | 0.141548 | ||||||||
\(918\) | 2580.98 | 0.0927943 | ||||||||
\(919\) | −4515.26 | −0.162073 | −0.0810363 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810363 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(920\) | 1002.63 | 0.0359300 | ||||||||
\(921\) | 19313.3 | 0.690983 | ||||||||
\(922\) | 21850.4 | 0.780482 | ||||||||
\(923\) | −16161.9 | −0.576356 | ||||||||
\(924\) | −121.888 | −0.00433963 | ||||||||
\(925\) | 40646.8 | 1.44482 | ||||||||
\(926\) | −33414.0 | −1.18580 | ||||||||
\(927\) | −2741.45 | −0.0971316 | ||||||||
\(928\) | −3762.02 | −0.133076 | ||||||||
\(929\) | −33860.3 | −1.19583 | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||||
−0.597913 | + | 0.801561i | \(0.704003\pi\) | |||||||
\(930\) | −1724.90 | −0.0608190 | ||||||||
\(931\) | 25699.4 | 0.904688 | ||||||||
\(932\) | 6630.65 | 0.233041 | ||||||||
\(933\) | 10997.7 | 0.385905 | ||||||||
\(934\) | −42678.9 | −1.49518 | ||||||||
\(935\) | −185.432 | −0.00648586 | ||||||||
\(936\) | 10857.7 | 0.379162 | ||||||||
\(937\) | −22085.0 | −0.769996 | −0.384998 | − | 0.922917i | \(-0.625798\pi\) | ||||
−0.384998 | + | 0.922917i | \(0.625798\pi\) | |||||||
\(938\) | −1338.09 | −0.0465780 | ||||||||
\(939\) | 5386.97 | 0.187217 | ||||||||
\(940\) | −443.018 | −0.0153720 | ||||||||
\(941\) | −14767.9 | −0.511603 | −0.255801 | − | 0.966729i | \(-0.582339\pi\) | ||||
−0.255801 | + | 0.966729i | \(0.582339\pi\) | |||||||
\(942\) | 7267.38 | 0.251363 | ||||||||
\(943\) | 33164.8 | 1.14527 | ||||||||
\(944\) | −4310.14 | −0.148605 | ||||||||
\(945\) | 61.7610 | 0.00212602 | ||||||||
\(946\) | −4705.07 | −0.161707 | ||||||||
\(947\) | 39640.1 | 1.36022 | 0.680111 | − | 0.733109i | \(-0.261932\pi\) | ||||
0.680111 | + | 0.733109i | \(0.261932\pi\) | |||||||
\(948\) | −3627.08 | −0.124264 | ||||||||
\(949\) | −36244.4 | −1.23977 | ||||||||
\(950\) | −29544.0 | −1.00898 | ||||||||
\(951\) | −2381.43 | −0.0812020 | ||||||||
\(952\) | −2148.78 | −0.0731538 | ||||||||
\(953\) | −10159.5 | −0.345328 | −0.172664 | − | 0.984981i | \(-0.555237\pi\) | ||||
−0.172664 | + | 0.984981i | \(0.555237\pi\) | |||||||
\(954\) | 5110.73 | 0.173445 | ||||||||
\(955\) | −557.397 | −0.0188869 | ||||||||
\(956\) | 9491.75 | 0.321114 | ||||||||
\(957\) | −1623.72 | −0.0548458 | ||||||||
\(958\) | −55410.3 | −1.86871 | ||||||||
\(959\) | −1935.71 | −0.0651797 | ||||||||
\(960\) | −805.116 | −0.0270677 | ||||||||
\(961\) | 47633.6 | 1.59892 | ||||||||
\(962\) | 59335.5 | 1.98862 | ||||||||
\(963\) | −13641.3 | −0.456474 | ||||||||
\(964\) | −632.882 | −0.0211450 | ||||||||
\(965\) | 2100.11 | 0.0700569 | ||||||||
\(966\) | −2274.03 | −0.0757408 | ||||||||
\(967\) | 2430.67 | 0.0808325 | 0.0404163 | − | 0.999183i | \(-0.487132\pi\) | ||||
0.0404163 | + | 0.999183i | \(0.487132\pi\) | |||||||
\(968\) | −25458.0 | −0.845300 | ||||||||
\(969\) | 7264.61 | 0.240839 | ||||||||
\(970\) | 2796.67 | 0.0925728 | ||||||||
\(971\) | 7053.09 | 0.233105 | 0.116552 | − | 0.993185i | \(-0.462816\pi\) | ||||
0.116552 | + | 0.993185i | \(0.462816\pi\) | |||||||
\(972\) | −331.530 | −0.0109402 | ||||||||
\(973\) | 1952.32 | 0.0643253 | ||||||||
\(974\) | 48749.2 | 1.60372 | ||||||||
\(975\) | 22198.2 | 0.729139 | ||||||||
\(976\) | −59014.1 | −1.93545 | ||||||||
\(977\) | 36193.6 | 1.18519 | 0.592597 | − | 0.805499i | \(-0.298103\pi\) | ||||
0.592597 | + | 0.805499i | \(0.298103\pi\) | |||||||
\(978\) | −30882.7 | −1.00973 | ||||||||
\(979\) | −1603.03 | −0.0523321 | ||||||||
\(980\) | −305.420 | −0.00995538 | ||||||||
\(981\) | −14.1862 | −0.000461702 0 | ||||||||
\(982\) | −8015.27 | −0.260466 | ||||||||
\(983\) | −12172.1 | −0.394944 | −0.197472 | − | 0.980309i | \(-0.563273\pi\) | ||||
−0.197472 | + | 0.980309i | \(0.563273\pi\) | |||||||
\(984\) | −27629.4 | −0.895115 | ||||||||
\(985\) | −845.620 | −0.0273540 | ||||||||
\(986\) | 5885.39 | 0.190090 | ||||||||
\(987\) | −4887.05 | −0.157605 | ||||||||
\(988\) | −6283.44 | −0.202331 | ||||||||
\(989\) | −12789.2 | −0.411195 | ||||||||
\(990\) | 163.487 | 0.00524843 | ||||||||
\(991\) | 37357.4 | 1.19747 | 0.598737 | − | 0.800946i | \(-0.295670\pi\) | ||||
0.598737 | + | 0.800946i | \(0.295670\pi\) | |||||||
\(992\) | −17002.3 | −0.544176 | ||||||||
\(993\) | −9967.70 | −0.318545 | ||||||||
\(994\) | −2819.97 | −0.0899838 | ||||||||
\(995\) | 576.930 | 0.0183818 | ||||||||
\(996\) | −210.735 | −0.00670420 | ||||||||
\(997\) | −43827.1 | −1.39220 | −0.696098 | − | 0.717947i | \(-0.745082\pi\) | ||||
−0.696098 | + | 0.717947i | \(0.745082\pi\) | |||||||
\(998\) | 28614.3 | 0.907586 | ||||||||
\(999\) | 8811.86 | 0.279074 |
(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 | 177.4.a.b.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 531.4.a.c.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.b.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
531.4.a.c.1.6 | 7 | 3.2 | odd | 2 |