Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, 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("75.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(4.42514325043\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70156 | 0.601593 | 0.300797 | − | 0.953688i | \(-0.402747\pi\) | ||||
0.300797 | + | 0.953688i | \(0.402747\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −5.10469 | −0.638086 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.10469 | −0.347330 | ||||||||
\(7\) | −22.2094 | −1.19919 | −0.599597 | − | 0.800302i | \(-0.704672\pi\) | ||||
−0.599597 | + | 0.800302i | \(0.704672\pi\) | |||||||
\(8\) | −22.2984 | −0.985461 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79063 | −0.0490813 | −0.0245407 | − | 0.999699i | \(-0.507812\pi\) | ||||
−0.0245407 | + | 0.999699i | \(0.507812\pi\) | |||||||
\(12\) | 15.3141 | 0.368399 | ||||||||
\(13\) | −58.2094 | −1.24188 | −0.620938 | − | 0.783860i | \(-0.713248\pi\) | ||||
−0.620938 | + | 0.783860i | \(0.713248\pi\) | |||||||
\(14\) | −37.7906 | −0.721426 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.89531 | 0.0452393 | ||||||||
\(17\) | −18.9844 | −0.270846 | −0.135423 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135423 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(18\) | 15.3141 | 0.200531 | ||||||||
\(19\) | 104.837 | 1.26586 | 0.632931 | − | 0.774208i | \(-0.281852\pi\) | ||||
0.632931 | + | 0.774208i | \(0.281852\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 66.6281 | 0.692355 | ||||||||
\(22\) | −3.04686 | −0.0295270 | ||||||||
\(23\) | 49.6125 | 0.449779 | 0.224890 | − | 0.974384i | \(-0.427798\pi\) | ||||
0.224890 | + | 0.974384i | \(0.427798\pi\) | |||||||
\(24\) | 66.8953 | 0.568956 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −99.0469 | −0.747103 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 113.372 | 0.765188 | ||||||||
\(29\) | −293.466 | −1.87914 | −0.939572 | − | 0.342350i | \(-0.888777\pi\) | ||||
−0.939572 | + | 0.342350i | \(0.888777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.4187 | 0.373224 | 0.186612 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186612 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(32\) | 183.314 | 1.01268 | ||||||||
\(33\) | 5.37188 | 0.0283371 | ||||||||
\(34\) | −32.3031 | −0.162939 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −45.9422 | −0.212695 | ||||||||
\(37\) | 19.8844 | 0.0883505 | 0.0441752 | − | 0.999024i | \(-0.485934\pi\) | ||||
0.0441752 | + | 0.999024i | \(0.485934\pi\) | |||||||
\(38\) | 178.388 | 0.761534 | ||||||||
\(39\) | 174.628 | 0.716997 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −165.581 | −0.630718 | −0.315359 | − | 0.948972i | \(-0.602125\pi\) | ||||
−0.315359 | + | 0.948972i | \(0.602125\pi\) | |||||||
\(42\) | 113.372 | 0.416516 | ||||||||
\(43\) | 247.350 | 0.877221 | 0.438611 | − | 0.898677i | \(-0.355471\pi\) | ||||
0.438611 | + | 0.898677i | \(0.355471\pi\) | |||||||
\(44\) | 9.14059 | 0.0313181 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 84.4187 | 0.270584 | ||||||||
\(47\) | −384.544 | −1.19344 | −0.596718 | − | 0.802451i | \(-0.703529\pi\) | ||||
−0.596718 | + | 0.802451i | \(0.703529\pi\) | |||||||
\(48\) | −8.68594 | −0.0261189 | ||||||||
\(49\) | 150.256 | 0.438065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 56.9531 | 0.156373 | ||||||||
\(52\) | 297.141 | 0.792423 | ||||||||
\(53\) | −463.528 | −1.20133 | −0.600665 | − | 0.799501i | \(-0.705097\pi\) | ||||
−0.600665 | + | 0.799501i | \(0.705097\pi\) | |||||||
\(54\) | −45.9422 | −0.115777 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 495.234 | 1.18176 | ||||||||
\(57\) | −314.512 | −0.730846 | ||||||||
\(58\) | −499.350 | −1.13048 | ||||||||
\(59\) | −73.7906 | −0.162826 | −0.0814129 | − | 0.996680i | \(-0.525943\pi\) | ||||
−0.0814129 | + | 0.996680i | \(0.525943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −137.350 | −0.288293 | −0.144146 | − | 0.989556i | \(-0.546044\pi\) | ||||
−0.144146 | + | 0.989556i | \(0.546044\pi\) | |||||||
\(62\) | 109.612 | 0.224529 | ||||||||
\(63\) | −199.884 | −0.399731 | ||||||||
\(64\) | 288.758 | 0.563980 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.14059 | 0.0170474 | ||||||||
\(67\) | −173.906 | −0.317105 | −0.158552 | − | 0.987351i | \(-0.550683\pi\) | ||||
−0.158552 | + | 0.987351i | \(0.550683\pi\) | |||||||
\(68\) | 96.9093 | 0.172823 | ||||||||
\(69\) | −148.837 | −0.259680 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −594.281 | −0.993355 | −0.496677 | − | 0.867935i | \(-0.665447\pi\) | ||||
−0.496677 | + | 0.867935i | \(0.665447\pi\) | |||||||
\(72\) | −200.686 | −0.328487 | ||||||||
\(73\) | −320.231 | −0.513428 | −0.256714 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(74\) | 33.8345 | 0.0531510 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −535.163 | −0.807728 | ||||||||
\(77\) | 39.7687 | 0.0588580 | ||||||||
\(78\) | 297.141 | 0.431340 | ||||||||
\(79\) | −770.469 | −1.09727 | −0.548636 | − | 0.836061i | \(-0.684853\pi\) | ||||
−0.548636 | + | 0.836061i | \(0.684853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −281.747 | −0.379436 | ||||||||
\(83\) | −173.925 | −0.230009 | −0.115004 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115004 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(84\) | −340.116 | −0.441782 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 420.881 | 0.527730 | ||||||||
\(87\) | 880.397 | 1.08492 | ||||||||
\(88\) | 39.9282 | 0.0483677 | ||||||||
\(89\) | 1019.02 | 1.21367 | 0.606834 | − | 0.794829i | \(-0.292439\pi\) | ||||
0.606834 | + | 0.794829i | \(0.292439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1292.79 | 1.48925 | ||||||||
\(92\) | −253.256 | −0.286998 | ||||||||
\(93\) | −193.256 | −0.215481 | ||||||||
\(94\) | −654.325 | −0.717962 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −549.942 | −0.584669 | ||||||||
\(97\) | −384.375 | −0.402344 | −0.201172 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201172 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(98\) | 255.670 | 0.263537 | ||||||||
\(99\) | −16.1156 | −0.0163604 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34.4906 | 0.0339796 | 0.0169898 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169898 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(102\) | 96.9093 | 0.0940730 | ||||||||
\(103\) | 1756.30 | 1.68013 | 0.840066 | − | 0.542484i | \(-0.182516\pi\) | ||||
0.840066 | + | 0.542484i | \(0.182516\pi\) | |||||||
\(104\) | 1297.98 | 1.22382 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −788.722 | −0.722712 | ||||||||
\(107\) | 1361.74 | 1.23032 | 0.615159 | − | 0.788403i | \(-0.289092\pi\) | ||||
0.615159 | + | 0.788403i | \(0.289092\pi\) | |||||||
\(108\) | 137.827 | 0.122800 | ||||||||
\(109\) | 321.119 | 0.282180 | 0.141090 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141090 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −59.6531 | −0.0510092 | ||||||||
\(112\) | −64.3031 | −0.0542506 | ||||||||
\(113\) | 1582.25 | 1.31721 | 0.658607 | − | 0.752487i | \(-0.271146\pi\) | ||||
0.658607 | + | 0.752487i | \(0.271146\pi\) | |||||||
\(114\) | −535.163 | −0.439672 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1498.05 | 1.19906 | ||||||||
\(117\) | −523.884 | −0.413958 | ||||||||
\(118\) | −125.559 | −0.0979549 | ||||||||
\(119\) | 421.631 | 0.324797 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1327.79 | −0.997591 | ||||||||
\(122\) | −233.709 | −0.173435 | ||||||||
\(123\) | 496.744 | 0.364145 | ||||||||
\(124\) | −328.837 | −0.238149 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −340.116 | −0.240475 | ||||||||
\(127\) | 1197.14 | 0.836449 | 0.418225 | − | 0.908344i | \(-0.362652\pi\) | ||||
0.418225 | + | 0.908344i | \(0.362652\pi\) | |||||||
\(128\) | −975.173 | −0.673390 | ||||||||
\(129\) | −742.050 | −0.506464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −321.647 | −0.214522 | −0.107261 | − | 0.994231i | \(-0.534208\pi\) | ||||
−0.107261 | + | 0.994231i | \(0.534208\pi\) | |||||||
\(132\) | −27.4218 | −0.0180815 | ||||||||
\(133\) | −2328.37 | −1.51801 | ||||||||
\(134\) | −295.912 | −0.190768 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 423.322 | 0.266909 | ||||||||
\(137\) | −354.291 | −0.220942 | −0.110471 | − | 0.993879i | \(-0.535236\pi\) | ||||
−0.110471 | + | 0.993879i | \(0.535236\pi\) | |||||||
\(138\) | −253.256 | −0.156222 | ||||||||
\(139\) | 77.2562 | 0.0471424 | 0.0235712 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235712 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1153.63 | 0.689030 | ||||||||
\(142\) | −1011.21 | −0.597595 | ||||||||
\(143\) | 104.231 | 0.0609529 | ||||||||
\(144\) | 26.0578 | 0.0150798 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −544.893 | −0.308875 | ||||||||
\(147\) | −450.769 | −0.252917 | ||||||||
\(148\) | −101.503 | −0.0563752 | ||||||||
\(149\) | −1705.38 | −0.937651 | −0.468826 | − | 0.883291i | \(-0.655323\pi\) | ||||
−0.468826 | + | 0.883291i | \(0.655323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 758.281 | 0.408663 | 0.204331 | − | 0.978902i | \(-0.434498\pi\) | ||||
0.204331 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(152\) | −2337.71 | −1.24746 | ||||||||
\(153\) | −170.859 | −0.0902821 | ||||||||
\(154\) | 67.6689 | 0.0354086 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −891.422 | −0.457506 | ||||||||
\(157\) | 1769.05 | 0.899273 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(158\) | −1311.00 | −0.660111 | ||||||||
\(159\) | 1390.58 | 0.693588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1101.86 | −0.539372 | ||||||||
\(162\) | 137.827 | 0.0668437 | ||||||||
\(163\) | 881.719 | 0.423690 | 0.211845 | − | 0.977303i | \(-0.432053\pi\) | ||||
0.211845 | + | 0.977303i | \(0.432053\pi\) | |||||||
\(164\) | 845.240 | 0.402452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −295.944 | −0.138372 | ||||||||
\(167\) | 216.900 | 0.100504 | 0.0502522 | − | 0.998737i | \(-0.483997\pi\) | ||||
0.0502522 | + | 0.998737i | \(0.483997\pi\) | |||||||
\(168\) | −1485.70 | −0.682289 | ||||||||
\(169\) | 1191.33 | 0.542254 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 943.537 | 0.421954 | ||||||||
\(172\) | −1262.64 | −0.559742 | ||||||||
\(173\) | −4125.91 | −1.81322 | −0.906610 | − | 0.421970i | \(-0.861339\pi\) | ||||
−0.906610 | + | 0.421970i | \(0.861339\pi\) | |||||||
\(174\) | 1498.05 | 0.652683 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.18443 | −0.00222040 | ||||||||
\(177\) | 221.372 | 0.0940075 | ||||||||
\(178\) | 1733.93 | 0.730134 | ||||||||
\(179\) | −3213.14 | −1.34168 | −0.670842 | − | 0.741600i | \(-0.734067\pi\) | ||||
−0.670842 | + | 0.741600i | \(0.734067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3394.42 | 1.39395 | 0.696976 | − | 0.717095i | \(-0.254529\pi\) | ||||
0.696976 | + | 0.717095i | \(0.254529\pi\) | |||||||
\(182\) | 2199.77 | 0.895921 | ||||||||
\(183\) | 412.050 | 0.166446 | ||||||||
\(184\) | −1106.28 | −0.443240 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −328.837 | −0.129632 | ||||||||
\(187\) | 33.9939 | 0.0132935 | ||||||||
\(188\) | 1962.98 | 0.761514 | ||||||||
\(189\) | 599.653 | 0.230785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3467.49 | −1.31361 | −0.656804 | − | 0.754062i | \(-0.728092\pi\) | ||||
−0.656804 | + | 0.754062i | \(0.728092\pi\) | |||||||
\(192\) | −866.273 | −0.325614 | ||||||||
\(193\) | −1792.14 | −0.668401 | −0.334200 | − | 0.942502i | \(-0.608466\pi\) | ||||
−0.334200 | + | 0.942502i | \(0.608466\pi\) | |||||||
\(194\) | −654.038 | −0.242047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −767.011 | −0.279523 | ||||||||
\(197\) | −1678.19 | −0.606935 | −0.303467 | − | 0.952842i | \(-0.598144\pi\) | ||||
−0.303467 | + | 0.952842i | \(0.598144\pi\) | |||||||
\(198\) | −27.4218 | −0.00984233 | ||||||||
\(199\) | 3108.23 | 1.10722 | 0.553610 | − | 0.832776i | \(-0.313250\pi\) | ||||
0.553610 | + | 0.832776i | \(0.313250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 521.719 | 0.183081 | ||||||||
\(202\) | 58.6878 | 0.0204419 | ||||||||
\(203\) | 6517.69 | 2.25346 | ||||||||
\(204\) | −290.728 | −0.0997795 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2988.46 | 1.01076 | ||||||||
\(207\) | 446.512 | 0.149926 | ||||||||
\(208\) | −168.534 | −0.0561815 | ||||||||
\(209\) | −187.725 | −0.0621301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4473.27 | −1.45949 | −0.729745 | − | 0.683719i | \(-0.760361\pi\) | ||||
−0.729745 | + | 0.683719i | \(0.760361\pi\) | |||||||
\(212\) | 2366.17 | 0.766551 | ||||||||
\(213\) | 1782.84 | 0.573514 | ||||||||
\(214\) | 2317.08 | 0.740151 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 602.058 | 0.189652 | ||||||||
\(217\) | −1430.70 | −0.447568 | ||||||||
\(218\) | 546.403 | 0.169757 | ||||||||
\(219\) | 960.694 | 0.296428 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1105.07 | 0.336357 | ||||||||
\(222\) | −101.503 | −0.0306868 | ||||||||
\(223\) | 1753.42 | 0.526535 | 0.263268 | − | 0.964723i | \(-0.415200\pi\) | ||||
0.263268 | + | 0.964723i | \(0.415200\pi\) | |||||||
\(224\) | −4071.29 | −1.21440 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2692.29 | 0.792427 | ||||||||
\(227\) | 936.900 | 0.273939 | 0.136970 | − | 0.990575i | \(-0.456264\pi\) | ||||
0.136970 | + | 0.990575i | \(0.456264\pi\) | |||||||
\(228\) | 1605.49 | 0.466342 | ||||||||
\(229\) | −2582.06 | −0.745096 | −0.372548 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372548 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −119.306 | −0.0339817 | ||||||||
\(232\) | 6543.82 | 1.85182 | ||||||||
\(233\) | −2295.01 | −0.645284 | −0.322642 | − | 0.946521i | \(-0.604571\pi\) | ||||
−0.322642 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(234\) | −891.422 | −0.249034 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 376.678 | 0.103897 | ||||||||
\(237\) | 2311.41 | 0.633510 | ||||||||
\(238\) | 717.432 | 0.195396 | ||||||||
\(239\) | −2294.01 | −0.620866 | −0.310433 | − | 0.950595i | \(-0.600474\pi\) | ||||
−0.310433 | + | 0.950595i | \(0.600474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 382.287 | 0.102180 | 0.0510898 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510898 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(242\) | −2259.32 | −0.600144 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 701.128 | 0.183956 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 845.240 | 0.219067 | ||||||||
\(247\) | −6102.52 | −1.57204 | ||||||||
\(248\) | −1436.44 | −0.367798 | ||||||||
\(249\) | 521.775 | 0.132796 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2259.98 | −0.568322 | −0.284161 | − | 0.958777i | \(-0.591715\pi\) | ||||
−0.284161 | + | 0.958777i | \(0.591715\pi\) | |||||||
\(252\) | 1020.35 | 0.255063 | ||||||||
\(253\) | −88.8375 | −0.0220758 | ||||||||
\(254\) | 2037.01 | 0.503202 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3969.38 | −0.969087 | ||||||||
\(257\) | 92.7843 | 0.0225203 | 0.0112602 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112602 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(258\) | −1262.64 | −0.304685 | ||||||||
\(259\) | −441.619 | −0.105949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2641.19 | −0.626382 | ||||||||
\(262\) | −547.302 | −0.129055 | ||||||||
\(263\) | 568.312 | 0.133246 | 0.0666229 | − | 0.997778i | \(-0.478778\pi\) | ||||
0.0666229 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(264\) | −119.785 | −0.0279251 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3961.87 | −0.913226 | ||||||||
\(267\) | −3057.07 | −0.700711 | ||||||||
\(268\) | 887.737 | 0.202340 | ||||||||
\(269\) | 7582.41 | 1.71862 | 0.859309 | − | 0.511458i | \(-0.170894\pi\) | ||||
0.859309 | + | 0.511458i | \(0.170894\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7943.69 | 1.78061 | 0.890304 | − | 0.455366i | \(-0.150492\pi\) | ||||
0.890304 | + | 0.455366i | \(0.150492\pi\) | |||||||
\(272\) | −54.9657 | −0.0122529 | ||||||||
\(273\) | −3878.38 | −0.859818 | ||||||||
\(274\) | −602.847 | −0.132917 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 759.769 | 0.165698 | ||||||||
\(277\) | −6823.00 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(278\) | 131.456 | 0.0283605 | ||||||||
\(279\) | 579.769 | 0.124408 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3315.86 | 0.703942 | 0.351971 | − | 0.936011i | \(-0.385512\pi\) | ||||
0.351971 | + | 0.936011i | \(0.385512\pi\) | |||||||
\(282\) | 1962.98 | 0.414516 | ||||||||
\(283\) | −6602.76 | −1.38690 | −0.693451 | − | 0.720504i | \(-0.743910\pi\) | ||||
−0.693451 | + | 0.720504i | \(0.743910\pi\) | |||||||
\(284\) | 3033.62 | 0.633846 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 177.356 | 0.0366688 | ||||||||
\(287\) | 3677.46 | 0.756353 | ||||||||
\(288\) | 1649.83 | 0.337559 | ||||||||
\(289\) | −4552.59 | −0.926642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1153.12 | 0.232293 | ||||||||
\(292\) | 1634.68 | 0.327611 | ||||||||
\(293\) | −5814.14 | −1.15927 | −0.579634 | − | 0.814877i | \(-0.696805\pi\) | ||||
−0.579634 | + | 0.814877i | \(0.696805\pi\) | |||||||
\(294\) | −767.011 | −0.152153 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −443.390 | −0.0870660 | ||||||||
\(297\) | 48.3469 | 0.00944570 | ||||||||
\(298\) | −2901.81 | −0.564084 | ||||||||
\(299\) | −2887.91 | −0.558570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5493.49 | −1.05196 | ||||||||
\(302\) | 1290.26 | 0.245849 | ||||||||
\(303\) | −103.472 | −0.0196181 | ||||||||
\(304\) | 303.537 | 0.0572667 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −290.728 | −0.0543131 | ||||||||
\(307\) | 8124.86 | 1.51046 | 0.755229 | − | 0.655462i | \(-0.227526\pi\) | ||||
0.755229 | + | 0.655462i | \(0.227526\pi\) | |||||||
\(308\) | −203.007 | −0.0375564 | ||||||||
\(309\) | −5268.91 | −0.970025 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7336.26 | 1.33762 | 0.668812 | − | 0.743432i | \(-0.266803\pi\) | ||||
0.668812 | + | 0.743432i | \(0.266803\pi\) | |||||||
\(312\) | −3893.93 | −0.706572 | ||||||||
\(313\) | 2202.66 | 0.397768 | 0.198884 | − | 0.980023i | \(-0.436268\pi\) | ||||
0.198884 | + | 0.980023i | \(0.436268\pi\) | |||||||
\(314\) | 3010.15 | 0.540996 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3933.00 | 0.700154 | ||||||||
\(317\) | −10008.9 | −1.77336 | −0.886679 | − | 0.462386i | \(-0.846993\pi\) | ||||
−0.886679 | + | 0.462386i | \(0.846993\pi\) | |||||||
\(318\) | 2366.17 | 0.417258 | ||||||||
\(319\) | 525.488 | 0.0922309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4085.21 | −0.710325 | ||||||||
\(322\) | −1874.89 | −0.324483 | ||||||||
\(323\) | −1990.27 | −0.342854 | ||||||||
\(324\) | −413.480 | −0.0708984 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1500.30 | 0.254889 | ||||||||
\(327\) | −963.356 | −0.162917 | ||||||||
\(328\) | 3692.20 | 0.621548 | ||||||||
\(329\) | 8540.47 | 1.43116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8695.94 | −1.44402 | −0.722012 | − | 0.691881i | \(-0.756782\pi\) | ||||
−0.722012 | + | 0.691881i | \(0.756782\pi\) | |||||||
\(332\) | 887.832 | 0.146765 | ||||||||
\(333\) | 178.959 | 0.0294502 | ||||||||
\(334\) | 369.069 | 0.0604627 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 192.909 | 0.0313216 | ||||||||
\(337\) | 7400.61 | 1.19625 | 0.598126 | − | 0.801402i | \(-0.295912\pi\) | ||||
0.598126 | + | 0.801402i | \(0.295912\pi\) | |||||||
\(338\) | 2027.12 | 0.326216 | ||||||||
\(339\) | −4746.74 | −0.760494 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −115.350 | −0.0183183 | ||||||||
\(342\) | 1605.49 | 0.253845 | ||||||||
\(343\) | 4280.72 | 0.673869 | ||||||||
\(344\) | −5515.52 | −0.864467 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7020.49 | −1.09082 | ||||||||
\(347\) | −7841.44 | −1.21311 | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||||
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(348\) | −4494.15 | −0.692275 | ||||||||
\(349\) | −4961.26 | −0.760946 | −0.380473 | − | 0.924792i | \(-0.624239\pi\) | ||||
−0.380473 | + | 0.924792i | \(0.624239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1571.65 | 0.238999 | ||||||||
\(352\) | −328.247 | −0.0497035 | ||||||||
\(353\) | 12163.0 | 1.83392 | 0.916959 | − | 0.398981i | \(-0.130636\pi\) | ||||
0.916959 | + | 0.398981i | \(0.130636\pi\) | |||||||
\(354\) | 376.678 | 0.0565543 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5201.80 | −0.774424 | ||||||||
\(357\) | −1264.89 | −0.187522 | ||||||||
\(358\) | −5467.36 | −0.807148 | ||||||||
\(359\) | 5193.79 | 0.763559 | 0.381779 | − | 0.924253i | \(-0.375311\pi\) | ||||
0.381779 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4131.90 | 0.602406 | ||||||||
\(362\) | 5775.81 | 0.838591 | ||||||||
\(363\) | 3983.38 | 0.575959 | ||||||||
\(364\) | −6599.31 | −0.950268 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 701.128 | 0.100133 | ||||||||
\(367\) | 6086.09 | 0.865644 | 0.432822 | − | 0.901479i | \(-0.357518\pi\) | ||||
0.432822 | + | 0.901479i | \(0.357518\pi\) | |||||||
\(368\) | 143.644 | 0.0203477 | ||||||||
\(369\) | −1490.23 | −0.210239 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10294.7 | 1.44063 | ||||||||
\(372\) | 986.512 | 0.137495 | ||||||||
\(373\) | 10581.9 | 1.46893 | 0.734466 | − | 0.678646i | \(-0.237433\pi\) | ||||
0.734466 | + | 0.678646i | \(0.237433\pi\) | |||||||
\(374\) | 57.8428 | 0.00799727 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8574.72 | 1.17608 | ||||||||
\(377\) | 17082.4 | 2.33366 | ||||||||
\(378\) | 1020.35 | 0.138839 | ||||||||
\(379\) | 11655.2 | 1.57964 | 0.789822 | − | 0.613336i | \(-0.210173\pi\) | ||||
0.789822 | + | 0.613336i | \(0.210173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3591.42 | −0.482924 | ||||||||
\(382\) | −5900.16 | −0.790257 | ||||||||
\(383\) | −6364.97 | −0.849177 | −0.424588 | − | 0.905387i | \(-0.639581\pi\) | ||||
−0.424588 | + | 0.905387i | \(0.639581\pi\) | |||||||
\(384\) | 2925.52 | 0.388782 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3049.44 | −0.402105 | ||||||||
\(387\) | 2226.15 | 0.292407 | ||||||||
\(388\) | 1962.11 | 0.256730 | ||||||||
\(389\) | 6134.33 | 0.799545 | 0.399773 | − | 0.916614i | \(-0.369089\pi\) | ||||
0.399773 | + | 0.916614i | \(0.369089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −941.862 | −0.121821 | ||||||||
\(392\) | −3350.48 | −0.431696 | ||||||||
\(393\) | 964.941 | 0.123855 | ||||||||
\(394\) | −2855.55 | −0.365128 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 82.2653 | 0.0104394 | ||||||||
\(397\) | −9746.46 | −1.23214 | −0.616072 | − | 0.787690i | \(-0.711277\pi\) | ||||
−0.616072 | + | 0.787690i | \(0.711277\pi\) | |||||||
\(398\) | 5288.85 | 0.666096 | ||||||||
\(399\) | 6985.12 | 0.876425 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1306.44 | −0.162695 | −0.0813474 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813474 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(402\) | 887.737 | 0.110140 | ||||||||
\(403\) | −3749.77 | −0.463498 | ||||||||
\(404\) | −176.063 | −0.0216819 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11090.2 | 1.35566 | ||||||||
\(407\) | −35.6055 | −0.00433636 | ||||||||
\(408\) | −1269.97 | −0.154100 | ||||||||
\(409\) | −3876.93 | −0.468709 | −0.234354 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234354 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1062.87 | 0.127561 | ||||||||
\(412\) | −8965.38 | −1.07207 | ||||||||
\(413\) | 1638.84 | 0.195260 | ||||||||
\(414\) | 759.769 | 0.0901947 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10670.6 | −1.25762 | ||||||||
\(417\) | −231.769 | −0.0272177 | ||||||||
\(418\) | −319.426 | −0.0373771 | ||||||||
\(419\) | −16022.5 | −1.86814 | −0.934071 | − | 0.357088i | \(-0.883770\pi\) | ||||
−0.934071 | + | 0.357088i | \(0.883770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8119.73 | −0.939980 | −0.469990 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469990 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(422\) | −7611.54 | −0.878019 | ||||||||
\(423\) | −3460.89 | −0.397812 | ||||||||
\(424\) | 10336.0 | 1.18386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3033.62 | 0.345022 | ||||||||
\(427\) | 3050.46 | 0.345719 | ||||||||
\(428\) | −6951.24 | −0.785049 | ||||||||
\(429\) | −312.694 | −0.0351911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5713.99 | −0.638592 | −0.319296 | − | 0.947655i | \(-0.603446\pi\) | ||||
−0.319296 | + | 0.947655i | \(0.603446\pi\) | |||||||
\(432\) | −78.1735 | −0.00870630 | ||||||||
\(433\) | −6251.34 | −0.693811 | −0.346906 | − | 0.937900i | \(-0.612768\pi\) | ||||
−0.346906 | + | 0.937900i | \(0.612768\pi\) | |||||||
\(434\) | −2434.42 | −0.269254 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1639.21 | −0.180055 | ||||||||
\(437\) | 5201.25 | 0.569358 | ||||||||
\(438\) | 1634.68 | 0.178329 | ||||||||
\(439\) | −4230.97 | −0.459984 | −0.229992 | − | 0.973192i | \(-0.573870\pi\) | ||||
−0.229992 | + | 0.973192i | \(0.573870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1352.31 | 0.146022 | ||||||||
\(442\) | 1880.34 | 0.202350 | ||||||||
\(443\) | −6314.29 | −0.677203 | −0.338601 | − | 0.940930i | \(-0.609954\pi\) | ||||
−0.338601 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(444\) | 304.510 | 0.0325482 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2983.55 | 0.316760 | ||||||||
\(447\) | 5116.13 | 0.541353 | ||||||||
\(448\) | −6413.13 | −0.676321 | ||||||||
\(449\) | −9349.71 | −0.982717 | −0.491358 | − | 0.870957i | \(-0.663499\pi\) | ||||
−0.491358 | + | 0.870957i | \(0.663499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 296.494 | 0.0309565 | ||||||||
\(452\) | −8076.87 | −0.840496 | ||||||||
\(453\) | −2274.84 | −0.235941 | ||||||||
\(454\) | 1594.19 | 0.164800 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7013.14 | 0.720220 | ||||||||
\(457\) | 9547.46 | 0.977268 | 0.488634 | − | 0.872489i | \(-0.337495\pi\) | ||||
0.488634 | + | 0.872489i | \(0.337495\pi\) | |||||||
\(458\) | −4393.53 | −0.448245 | ||||||||
\(459\) | 512.578 | 0.0521244 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6237.23 | 0.630145 | 0.315073 | − | 0.949068i | \(-0.397971\pi\) | ||||
0.315073 | + | 0.949068i | \(0.397971\pi\) | |||||||
\(462\) | −203.007 | −0.0204431 | ||||||||
\(463\) | −6469.98 | −0.649428 | −0.324714 | − | 0.945812i | \(-0.605268\pi\) | ||||
−0.324714 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(464\) | −849.675 | −0.0850111 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3905.10 | −0.388198 | ||||||||
\(467\) | −7206.64 | −0.714097 | −0.357049 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357049 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(468\) | 2674.27 | 0.264141 | ||||||||
\(469\) | 3862.35 | 0.380270 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5307.16 | −0.519195 | ||||||||
\(472\) | 1645.42 | 0.160458 | ||||||||
\(473\) | −442.912 | −0.0430552 | ||||||||
\(474\) | 3933.00 | 0.381115 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2152.29 | −0.207248 | ||||||||
\(477\) | −4171.75 | −0.400443 | ||||||||
\(478\) | −3903.39 | −0.373509 | ||||||||
\(479\) | −10851.8 | −1.03514 | −0.517571 | − | 0.855640i | \(-0.673164\pi\) | ||||
−0.517571 | + | 0.855640i | \(0.673164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1157.46 | −0.109720 | ||||||||
\(482\) | 650.485 | 0.0614705 | ||||||||
\(483\) | 3305.59 | 0.311407 | ||||||||
\(484\) | 6777.97 | 0.636549 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −413.480 | −0.0385922 | ||||||||
\(487\) | −12757.1 | −1.18702 | −0.593510 | − | 0.804827i | \(-0.702258\pi\) | ||||
−0.593510 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(488\) | 3062.69 | 0.284101 | ||||||||
\(489\) | −2645.16 | −0.244618 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7016.52 | −0.644911 | −0.322455 | − | 0.946585i | \(-0.604508\pi\) | ||||
−0.322455 | + | 0.946585i | \(0.604508\pi\) | |||||||
\(492\) | −2535.72 | −0.232356 | ||||||||
\(493\) | 5571.26 | 0.508960 | ||||||||
\(494\) | −10383.8 | −0.945729 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 186.512 | 0.0168844 | ||||||||
\(497\) | 13198.6 | 1.19122 | ||||||||
\(498\) | 887.832 | 0.0798890 | ||||||||
\(499\) | 11372.3 | 1.02023 | 0.510113 | − | 0.860107i | \(-0.329604\pi\) | ||||
0.510113 | + | 0.860107i | \(0.329604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −650.700 | −0.0580262 | ||||||||
\(502\) | −3845.50 | −0.341899 | ||||||||
\(503\) | 5587.37 | 0.495285 | 0.247643 | − | 0.968851i | \(-0.420344\pi\) | ||||
0.247643 | + | 0.968851i | \(0.420344\pi\) | |||||||
\(504\) | 4457.11 | 0.393919 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −151.163 | −0.0132806 | ||||||||
\(507\) | −3573.99 | −0.313070 | ||||||||
\(508\) | −6111.03 | −0.533726 | ||||||||
\(509\) | 16256.7 | 1.41565 | 0.707825 | − | 0.706388i | \(-0.249676\pi\) | ||||
0.707825 | + | 0.706388i | \(0.249676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7112.14 | 0.615699 | ||||||||
\(512\) | 1047.24 | 0.0903943 | ||||||||
\(513\) | −2830.61 | −0.243615 | ||||||||
\(514\) | 157.878 | 0.0135481 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3787.93 | 0.323167 | ||||||||
\(517\) | 688.574 | 0.0585754 | ||||||||
\(518\) | −751.442 | −0.0637384 | ||||||||
\(519\) | 12377.7 | 1.04686 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19748.4 | 1.66064 | 0.830320 | − | 0.557286i | \(-0.188157\pi\) | ||||
0.830320 | + | 0.557286i | \(0.188157\pi\) | |||||||
\(522\) | −4494.15 | −0.376827 | ||||||||
\(523\) | 7843.44 | 0.655774 | 0.327887 | − | 0.944717i | \(-0.393663\pi\) | ||||
0.327887 | + | 0.944717i | \(0.393663\pi\) | |||||||
\(524\) | 1641.91 | 0.136884 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 967.019 | 0.0801597 | ||||||||
\(527\) | −1222.95 | −0.101086 | ||||||||
\(528\) | 15.5533 | 0.00128195 | ||||||||
\(529\) | −9705.60 | −0.797699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −664.116 | −0.0542753 | ||||||||
\(532\) | 11885.6 | 0.968622 | ||||||||
\(533\) | 9638.38 | 0.783273 | ||||||||
\(534\) | −5201.80 | −0.421543 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3877.84 | 0.312495 | ||||||||
\(537\) | 9639.42 | 0.774622 | ||||||||
\(538\) | 12902.0 | 1.03391 | ||||||||
\(539\) | −269.053 | −0.0215008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7383.29 | 0.586751 | 0.293376 | − | 0.955997i | \(-0.405221\pi\) | ||||
0.293376 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(542\) | 13516.7 | 1.07120 | ||||||||
\(543\) | −10183.3 | −0.804798 | ||||||||
\(544\) | −3480.10 | −0.274280 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6599.31 | −0.517260 | ||||||||
\(547\) | 3354.90 | 0.262240 | 0.131120 | − | 0.991367i | \(-0.458143\pi\) | ||||
0.131120 | + | 0.991367i | \(0.458143\pi\) | |||||||
\(548\) | 1808.54 | 0.140980 | ||||||||
\(549\) | −1236.15 | −0.0960976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30766.2 | −2.37874 | ||||||||
\(552\) | 3318.84 | 0.255905 | ||||||||
\(553\) | 17111.6 | 1.31584 | ||||||||
\(554\) | −11609.8 | −0.890346 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −394.369 | −0.0300809 | ||||||||
\(557\) | −20771.8 | −1.58012 | −0.790061 | − | 0.613028i | \(-0.789951\pi\) | ||||
−0.790061 | + | 0.613028i | \(0.789951\pi\) | |||||||
\(558\) | 986.512 | 0.0748430 | ||||||||
\(559\) | −14398.1 | −1.08940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −101.982 | −0.00767500 | ||||||||
\(562\) | 5642.15 | 0.423487 | ||||||||
\(563\) | −7194.86 | −0.538592 | −0.269296 | − | 0.963057i | \(-0.586791\pi\) | ||||
−0.269296 | + | 0.963057i | \(0.586791\pi\) | |||||||
\(564\) | −5888.93 | −0.439660 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11235.0 | −0.834350 | ||||||||
\(567\) | −1798.96 | −0.133244 | ||||||||
\(568\) | 13251.5 | 0.978913 | ||||||||
\(569\) | 11549.5 | 0.850931 | 0.425466 | − | 0.904975i | \(-0.360110\pi\) | ||||
0.425466 | + | 0.904975i | \(0.360110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1482.54 | 0.108655 | 0.0543277 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543277 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(572\) | −532.068 | −0.0388932 | ||||||||
\(573\) | 10402.5 | 0.758412 | ||||||||
\(574\) | 6257.42 | 0.455017 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2598.82 | 0.187993 | ||||||||
\(577\) | 15264.0 | 1.10130 | 0.550649 | − | 0.834737i | \(-0.314380\pi\) | ||||
0.550649 | + | 0.834737i | \(0.314380\pi\) | |||||||
\(578\) | −7746.52 | −0.557462 | ||||||||
\(579\) | 5376.43 | 0.385901 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3862.76 | 0.275825 | ||||||||
\(582\) | 1962.11 | 0.139746 | ||||||||
\(583\) | 830.006 | 0.0589628 | ||||||||
\(584\) | 7140.66 | 0.505963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9893.12 | −0.697408 | ||||||||
\(587\) | −1736.89 | −0.122128 | −0.0610639 | − | 0.998134i | \(-0.519449\pi\) | ||||
−0.0610639 | + | 0.998134i | \(0.519449\pi\) | |||||||
\(588\) | 2301.03 | 0.161383 | ||||||||
\(589\) | 6753.50 | 0.472450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5034.57 | 0.350414 | ||||||||
\(592\) | 57.5714 | 0.00399691 | ||||||||
\(593\) | 11764.8 | 0.814707 | 0.407353 | − | 0.913271i | \(-0.366452\pi\) | ||||
0.407353 | + | 0.913271i | \(0.366452\pi\) | |||||||
\(594\) | 82.2653 | 0.00568247 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8705.42 | 0.598302 | ||||||||
\(597\) | −9324.69 | −0.639253 | ||||||||
\(598\) | −4913.96 | −0.336032 | ||||||||
\(599\) | −9451.99 | −0.644737 | −0.322369 | − | 0.946614i | \(-0.604479\pi\) | ||||
−0.322369 | + | 0.946614i | \(0.604479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3131.93 | −0.212569 | −0.106285 | − | 0.994336i | \(-0.533895\pi\) | ||||
−0.106285 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(602\) | −9347.51 | −0.632851 | ||||||||
\(603\) | −1565.16 | −0.105702 | ||||||||
\(604\) | −3870.79 | −0.260762 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −176.063 | −0.0118021 | ||||||||
\(607\) | −22700.8 | −1.51795 | −0.758975 | − | 0.651120i | \(-0.774300\pi\) | ||||
−0.758975 | + | 0.651120i | \(0.774300\pi\) | |||||||
\(608\) | 19218.2 | 1.28191 | ||||||||
\(609\) | −19553.1 | −1.30103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22384.0 | 1.48210 | ||||||||
\(612\) | 872.184 | 0.0576077 | ||||||||
\(613\) | −28911.6 | −1.90494 | −0.952471 | − | 0.304629i | \(-0.901468\pi\) | ||||
−0.952471 | + | 0.304629i | \(0.901468\pi\) | |||||||
\(614\) | 13825.0 | 0.908681 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −886.780 | −0.0580023 | ||||||||
\(617\) | 5566.87 | 0.363231 | 0.181616 | − | 0.983370i | \(-0.441867\pi\) | ||||
0.181616 | + | 0.983370i | \(0.441867\pi\) | |||||||
\(618\) | −8965.38 | −0.583560 | ||||||||
\(619\) | 4150.32 | 0.269492 | 0.134746 | − | 0.990880i | \(-0.456978\pi\) | ||||
0.134746 | + | 0.990880i | \(0.456978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1339.54 | −0.0865600 | ||||||||
\(622\) | 12483.1 | 0.804705 | ||||||||
\(623\) | −22631.9 | −1.45542 | ||||||||
\(624\) | 505.603 | 0.0324364 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3747.96 | 0.239295 | ||||||||
\(627\) | 563.175 | 0.0358709 | ||||||||
\(628\) | −9030.46 | −0.573813 | ||||||||
\(629\) | −377.492 | −0.0239294 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4090.09 | −0.258041 | −0.129021 | − | 0.991642i | \(-0.541183\pi\) | ||||
−0.129021 | + | 0.991642i | \(0.541183\pi\) | |||||||
\(632\) | 17180.2 | 1.08132 | ||||||||
\(633\) | 13419.8 | 0.842637 | ||||||||
\(634\) | −17030.7 | −1.06684 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7098.50 | −0.442569 | ||||||||
\(637\) | −8746.32 | −0.544022 | ||||||||
\(638\) | 894.150 | 0.0554855 | ||||||||
\(639\) | −5348.53 | −0.331118 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3909.35 | 0.240890 | 0.120445 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120445 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(642\) | −6951.24 | −0.427327 | ||||||||
\(643\) | −30539.5 | −1.87303 | −0.936516 | − | 0.350624i | \(-0.885969\pi\) | ||||
−0.936516 | + | 0.350624i | \(0.885969\pi\) | |||||||
\(644\) | 5624.66 | 0.344166 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3386.58 | −0.206259 | ||||||||
\(647\) | 12707.7 | 0.772167 | 0.386083 | − | 0.922464i | \(-0.373828\pi\) | ||||
0.386083 | + | 0.922464i | \(0.373828\pi\) | |||||||
\(648\) | −1806.17 | −0.109496 | ||||||||
\(649\) | 132.132 | 0.00799170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4292.10 | 0.258403 | ||||||||
\(652\) | −4500.90 | −0.270351 | ||||||||
\(653\) | −12777.6 | −0.765737 | −0.382869 | − | 0.923803i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923803i | \(0.625064\pi\) | |||||||
\(654\) | −1639.21 | −0.0980095 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −479.410 | −0.0285332 | ||||||||
\(657\) | −2882.08 | −0.171143 | ||||||||
\(658\) | 14532.1 | 0.860976 | ||||||||
\(659\) | 23563.5 | 1.39287 | 0.696435 | − | 0.717620i | \(-0.254768\pi\) | ||||
0.696435 | + | 0.717620i | \(0.254768\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4361.31 | −0.256634 | −0.128317 | − | 0.991733i | \(-0.540958\pi\) | ||||
−0.128317 | + | 0.991733i | \(0.540958\pi\) | |||||||
\(662\) | −14796.7 | −0.868715 | ||||||||
\(663\) | −3315.21 | −0.194196 | ||||||||
\(664\) | 3878.25 | 0.226665 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 304.510 | 0.0177170 | ||||||||
\(667\) | −14559.6 | −0.845200 | ||||||||
\(668\) | −1107.21 | −0.0641304 | ||||||||
\(669\) | −5260.25 | −0.303995 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 245.943 | 0.0141498 | ||||||||
\(672\) | 12213.9 | 0.701131 | ||||||||
\(673\) | 8203.52 | 0.469870 | 0.234935 | − | 0.972011i | \(-0.424512\pi\) | ||||
0.234935 | + | 0.972011i | \(0.424512\pi\) | |||||||
\(674\) | 12592.6 | 0.719657 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6081.37 | −0.346004 | ||||||||
\(677\) | −28057.1 | −1.59279 | −0.796397 | − | 0.604774i | \(-0.793263\pi\) | ||||
−0.796397 | + | 0.604774i | \(0.793263\pi\) | |||||||
\(678\) | −8076.87 | −0.457508 | ||||||||
\(679\) | 8536.73 | 0.482488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2810.70 | −0.158159 | ||||||||
\(682\) | −196.275 | −0.0110202 | ||||||||
\(683\) | 3344.62 | 0.187377 | 0.0936885 | − | 0.995602i | \(-0.470134\pi\) | ||||
0.0936885 | + | 0.995602i | \(0.470134\pi\) | |||||||
\(684\) | −4816.46 | −0.269243 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7283.91 | 0.405395 | ||||||||
\(687\) | 7746.17 | 0.430182 | ||||||||
\(688\) | 716.156 | 0.0396849 | ||||||||
\(689\) | 26981.7 | 1.49190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12964.8 | 0.713757 | 0.356879 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356879 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(692\) | 21061.5 | 1.15699 | ||||||||
\(693\) | 357.918 | 0.0196193 | ||||||||
\(694\) | −13342.7 | −0.729801 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −19631.5 | −1.06915 | ||||||||
\(697\) | 3143.46 | 0.170828 | ||||||||
\(698\) | −8441.90 | −0.457780 | ||||||||
\(699\) | 6885.03 | 0.372555 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16162.1 | −0.870806 | −0.435403 | − | 0.900236i | \(-0.643394\pi\) | ||||
−0.435403 | + | 0.900236i | \(0.643394\pi\) | |||||||
\(702\) | 2674.27 | 0.143780 | ||||||||
\(703\) | 2084.63 | 0.111839 | ||||||||
\(704\) | −517.058 | −0.0276809 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20696.2 | 1.10327 | ||||||||
\(707\) | −766.014 | −0.0407481 | ||||||||
\(708\) | −1130.03 | −0.0599849 | ||||||||
\(709\) | −14244.4 | −0.754529 | −0.377265 | − | 0.926105i | \(-0.623135\pi\) | ||||
−0.377265 | + | 0.926105i | \(0.623135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6934.22 | −0.365757 | ||||||||
\(712\) | −22722.7 | −1.19602 | ||||||||
\(713\) | 3195.97 | 0.167868 | ||||||||
\(714\) | −2152.29 | −0.112812 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16402.1 | 0.856109 | ||||||||
\(717\) | 6882.02 | 0.358457 | ||||||||
\(718\) | 8837.55 | 0.459352 | ||||||||
\(719\) | −27638.5 | −1.43358 | −0.716790 | − | 0.697289i | \(-0.754389\pi\) | ||||
−0.716790 | + | 0.697289i | \(0.754389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39006.4 | −2.01480 | ||||||||
\(722\) | 7030.68 | 0.362403 | ||||||||
\(723\) | −1146.86 | −0.0589934 | ||||||||
\(724\) | −17327.4 | −0.889460 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6777.97 | 0.346493 | ||||||||
\(727\) | 2525.52 | 0.128840 | 0.0644199 | − | 0.997923i | \(-0.479480\pi\) | ||||
0.0644199 | + | 0.997923i | \(0.479480\pi\) | |||||||
\(728\) | −28827.3 | −1.46760 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4695.79 | −0.237592 | ||||||||
\(732\) | −2103.39 | −0.106207 | ||||||||
\(733\) | 8400.27 | 0.423289 | 0.211645 | − | 0.977347i | \(-0.432118\pi\) | ||||
0.211645 | + | 0.977347i | \(0.432118\pi\) | |||||||
\(734\) | 10355.9 | 0.520765 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9094.67 | 0.455481 | ||||||||
\(737\) | 311.401 | 0.0155639 | ||||||||
\(738\) | −2535.72 | −0.126479 | ||||||||
\(739\) | −19689.1 | −0.980074 | −0.490037 | − | 0.871702i | \(-0.663017\pi\) | ||||
−0.490037 | + | 0.871702i | \(0.663017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18307.6 | 0.907619 | ||||||||
\(742\) | 17517.0 | 0.866671 | ||||||||
\(743\) | 22526.6 | 1.11227 | 0.556137 | − | 0.831091i | \(-0.312283\pi\) | ||||
0.556137 | + | 0.831091i | \(0.312283\pi\) | |||||||
\(744\) | 4309.31 | 0.212348 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18005.8 | 0.883699 | ||||||||
\(747\) | −1565.32 | −0.0766696 | ||||||||
\(748\) | −173.528 | −0.00848239 | ||||||||
\(749\) | −30243.3 | −1.47539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34691.1 | 1.68562 | 0.842808 | − | 0.538215i | \(-0.180901\pi\) | ||||
0.842808 | + | 0.538215i | \(0.180901\pi\) | |||||||
\(752\) | −1113.37 | −0.0539902 | ||||||||
\(753\) | 6779.95 | 0.328121 | ||||||||
\(754\) | 29066.8 | 1.40392 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3061.04 | −0.147261 | ||||||||
\(757\) | −6619.98 | −0.317843 | −0.158922 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158922 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(758\) | 19832.0 | 0.950303 | ||||||||
\(759\) | 266.512 | 0.0127454 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29368.7 | −1.39897 | −0.699483 | − | 0.714649i | \(-0.746586\pi\) | ||||
−0.699483 | + | 0.714649i | \(0.746586\pi\) | |||||||
\(762\) | −6111.03 | −0.290524 | ||||||||
\(763\) | −7131.84 | −0.338388 | ||||||||
\(764\) | 17700.5 | 0.838194 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10830.4 | −0.510859 | ||||||||
\(767\) | 4295.31 | 0.202209 | ||||||||
\(768\) | 11908.1 | 0.559503 | ||||||||
\(769\) | 32677.4 | 1.53235 | 0.766174 | − | 0.642633i | \(-0.222158\pi\) | ||||
0.766174 | + | 0.642633i | \(0.222158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −278.353 | −0.0130021 | ||||||||
\(772\) | 9148.33 | 0.426497 | ||||||||
\(773\) | 28047.5 | 1.30504 | 0.652522 | − | 0.757770i | \(-0.273711\pi\) | ||||
0.652522 | + | 0.757770i | \(0.273711\pi\) | |||||||
\(774\) | 3787.93 | 0.175910 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8570.96 | 0.396494 | ||||||||
\(777\) | 1324.86 | 0.0611699 | ||||||||
\(778\) | 10438.0 | 0.481001 | ||||||||
\(779\) | −17359.1 | −0.798402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1064.14 | 0.0487552 | ||||||||
\(782\) | −1602.64 | −0.0732867 | ||||||||
\(783\) | 7923.57 | 0.361642 | ||||||||
\(784\) | 435.039 | 0.0198177 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1641.91 | 0.0745100 | ||||||||
\(787\) | 22172.1 | 1.00426 | 0.502128 | − | 0.864793i | \(-0.332551\pi\) | ||||
0.502128 | + | 0.864793i | \(0.332551\pi\) | |||||||
\(788\) | 8566.64 | 0.387276 | ||||||||
\(789\) | −1704.94 | −0.0769295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35140.7 | −1.57960 | ||||||||
\(792\) | 359.354 | 0.0161226 | ||||||||
\(793\) | 7995.06 | 0.358024 | ||||||||
\(794\) | −16584.2 | −0.741249 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15866.5 | −0.706501 | ||||||||
\(797\) | 24170.3 | 1.07422 | 0.537112 | − | 0.843511i | \(-0.319515\pi\) | ||||
0.537112 | + | 0.843511i | \(0.319515\pi\) | |||||||
\(798\) | 11885.6 | 0.527251 | ||||||||
\(799\) | 7300.32 | 0.323238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9171.22 | 0.404556 | ||||||||
\(802\) | −2222.99 | −0.0978761 | ||||||||
\(803\) | 573.415 | 0.0251997 | ||||||||
\(804\) | −2663.21 | −0.116821 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6380.47 | −0.278837 | ||||||||
\(807\) | −22747.2 | −0.992244 | ||||||||
\(808\) | −769.085 | −0.0334856 | ||||||||
\(809\) | 15304.2 | 0.665102 | 0.332551 | − | 0.943085i | \(-0.392091\pi\) | ||||
0.332551 | + | 0.943085i | \(0.392091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27002.2 | −1.16914 | −0.584572 | − | 0.811342i | \(-0.698738\pi\) | ||||
−0.584572 | + | 0.811342i | \(0.698738\pi\) | |||||||
\(812\) | −33270.7 | −1.43790 | ||||||||
\(813\) | −23831.1 | −1.02803 | ||||||||
\(814\) | −60.5849 | −0.00260872 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 164.897 | 0.00707421 | ||||||||
\(817\) | 25931.5 | 1.11044 | ||||||||
\(818\) | −6596.84 | −0.281972 | ||||||||
\(819\) | 11635.1 | 0.496416 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25061.4 | 1.06535 | 0.532673 | − | 0.846321i | \(-0.321188\pi\) | ||||
0.532673 | + | 0.846321i | \(0.321188\pi\) | |||||||
\(822\) | 1808.54 | 0.0767398 | ||||||||
\(823\) | 24896.4 | 1.05448 | 0.527238 | − | 0.849718i | \(-0.323228\pi\) | ||||
0.527238 | + | 0.849718i | \(0.323228\pi\) | |||||||
\(824\) | −39162.8 | −1.65571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2788.59 | 0.117467 | ||||||||
\(827\) | 20063.2 | 0.843612 | 0.421806 | − | 0.906686i | \(-0.361396\pi\) | ||||
0.421806 | + | 0.906686i | \(0.361396\pi\) | |||||||
\(828\) | −2279.31 | −0.0956659 | ||||||||
\(829\) | −13884.2 | −0.581687 | −0.290844 | − | 0.956771i | \(-0.593936\pi\) | ||||
−0.290844 | + | 0.956771i | \(0.593936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20469.0 | 0.854467 | ||||||||
\(832\) | −16808.4 | −0.700393 | ||||||||
\(833\) | −2852.52 | −0.118648 | ||||||||
\(834\) | −394.369 | −0.0163740 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 958.277 | 0.0396444 | ||||||||
\(837\) | −1739.31 | −0.0718270 | ||||||||
\(838\) | −27263.3 | −1.12386 | ||||||||
\(839\) | −13678.1 | −0.562838 | −0.281419 | − | 0.959585i | \(-0.590805\pi\) | ||||
−0.281419 | + | 0.959585i | \(0.590805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61733.1 | 2.53118 | ||||||||
\(842\) | −13816.2 | −0.565485 | ||||||||
\(843\) | −9947.59 | −0.406421 | ||||||||
\(844\) | 22834.6 | 0.931280 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5888.93 | −0.239321 | ||||||||
\(847\) | 29489.5 | 1.19630 | ||||||||
\(848\) | −1342.06 | −0.0543473 | ||||||||
\(849\) | 19808.3 | 0.800728 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 986.512 | 0.0397382 | ||||||||
\(852\) | −9100.86 | −0.365951 | ||||||||
\(853\) | −29802.9 | −1.19629 | −0.598143 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598143 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(854\) | 5190.54 | 0.207982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30364.6 | −1.21243 | ||||||||
\(857\) | −22045.2 | −0.878706 | −0.439353 | − | 0.898314i | \(-0.644792\pi\) | ||||
−0.439353 | + | 0.898314i | \(0.644792\pi\) | |||||||
\(858\) | −532.068 | −0.0211708 | ||||||||
\(859\) | 33609.5 | 1.33497 | 0.667487 | − | 0.744622i | \(-0.267370\pi\) | ||||
0.667487 | + | 0.744622i | \(0.267370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11032.4 | −0.436681 | ||||||||
\(862\) | −9722.70 | −0.384172 | ||||||||
\(863\) | −33775.6 | −1.33226 | −0.666128 | − | 0.745838i | \(-0.732049\pi\) | ||||
−0.666128 | + | 0.745838i | \(0.732049\pi\) | |||||||
\(864\) | −4949.48 | −0.194890 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10637.0 | −0.417392 | ||||||||
\(867\) | 13657.8 | 0.534997 | ||||||||
\(868\) | 7303.27 | 0.285587 | ||||||||
\(869\) | 1379.62 | 0.0538556 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10123.0 | 0.393805 | ||||||||
\(872\) | −7160.44 | −0.278077 | ||||||||
\(873\) | −3459.37 | −0.134115 | ||||||||
\(874\) | 8850.25 | 0.342522 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4904.04 | −0.189146 | ||||||||
\(877\) | −12637.0 | −0.486570 | −0.243285 | − | 0.969955i | \(-0.578225\pi\) | ||||
−0.243285 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(878\) | −7199.25 | −0.276723 | ||||||||
\(879\) | 17442.4 | 0.669304 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6579.45 | −0.251609 | −0.125804 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125804 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(882\) | 2301.03 | 0.0878456 | ||||||||
\(883\) | 50442.1 | 1.92244 | 0.961219 | − | 0.275786i | \(-0.0889382\pi\) | ||||
0.961219 | + | 0.275786i | \(0.0889382\pi\) | |||||||
\(884\) | −5641.03 | −0.214625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10744.2 | −0.407401 | ||||||||
\(887\) | −984.823 | −0.0372797 | −0.0186399 | − | 0.999826i | \(-0.505934\pi\) | ||||
−0.0186399 | + | 0.999826i | \(0.505934\pi\) | |||||||
\(888\) | 1330.17 | 0.0502676 | ||||||||
\(889\) | −26587.7 | −1.00306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −145.041 | −0.00545348 | ||||||||
\(892\) | −8950.64 | −0.335975 | ||||||||
\(893\) | −40314.6 | −1.51072 | ||||||||
\(894\) | 8705.42 | 0.325674 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21658.0 | 0.807525 | ||||||||
\(897\) | 8663.74 | 0.322490 | ||||||||
\(898\) | −15909.1 | −0.591196 | ||||||||
\(899\) | −18904.7 | −0.701342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8799.79 | 0.325376 | ||||||||
\(902\) | 504.503 | 0.0186232 | ||||||||
\(903\) | 16480.5 | 0.607348 | ||||||||
\(904\) | −35281.6 | −1.29806 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3870.79 | −0.141941 | ||||||||
\(907\) | −43679.9 | −1.59908 | −0.799541 | − | 0.600612i | \(-0.794924\pi\) | ||||
−0.799541 | + | 0.600612i | \(0.794924\pi\) | |||||||
\(908\) | −4782.58 | −0.174797 | ||||||||
\(909\) | 310.415 | 0.0113265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10364.3 | −0.376930 | −0.188465 | − | 0.982080i | \(-0.560351\pi\) | ||||
−0.188465 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(912\) | −910.612 | −0.0330629 | ||||||||
\(913\) | 311.435 | 0.0112891 | ||||||||
\(914\) | 16245.6 | 0.587918 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13180.6 | 0.475435 | ||||||||
\(917\) | 7143.58 | 0.257254 | ||||||||
\(918\) | 872.184 | 0.0313577 | ||||||||
\(919\) | 11451.9 | 0.411059 | 0.205530 | − | 0.978651i | \(-0.434108\pi\) | ||||
0.205530 | + | 0.978651i | \(0.434108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24374.6 | −0.872063 | ||||||||
\(922\) | 10613.0 | 0.379091 | ||||||||
\(923\) | 34592.7 | 1.23362 | ||||||||
\(924\) | 609.020 | 0.0216832 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11009.1 | −0.390692 | ||||||||
\(927\) | 15806.7 | 0.560044 | ||||||||
\(928\) | −53796.4 | −1.90297 | ||||||||
\(929\) | −27701.8 | −0.978326 | −0.489163 | − | 0.872192i | \(-0.662698\pi\) | ||||
−0.489163 | + | 0.872192i | \(0.662698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15752.5 | 0.554529 | ||||||||
\(932\) | 11715.3 | 0.411746 | ||||||||
\(933\) | −22008.8 | −0.772277 | ||||||||
\(934\) | −12262.5 | −0.429596 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11681.8 | 0.407940 | ||||||||
\(937\) | 5878.01 | 0.204937 | 0.102469 | − | 0.994736i | \(-0.467326\pi\) | ||||
0.102469 | + | 0.994736i | \(0.467326\pi\) | |||||||
\(938\) | 6572.03 | 0.228768 | ||||||||
\(939\) | −6607.97 | −0.229652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28786.0 | −0.997234 | −0.498617 | − | 0.866823i | \(-0.666159\pi\) | ||||
−0.498617 | + | 0.866823i | \(0.666159\pi\) | |||||||
\(942\) | −9030.46 | −0.312344 | ||||||||
\(943\) | −8214.90 | −0.283684 | ||||||||
\(944\) | −213.647 | −0.00736612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −753.642 | −0.0259017 | ||||||||
\(947\) | 1695.04 | 0.0581641 | 0.0290821 | − | 0.999577i | \(-0.490742\pi\) | ||||
0.0290821 | + | 0.999577i | \(0.490742\pi\) | |||||||
\(948\) | −11799.0 | −0.404234 | ||||||||
\(949\) | 18640.5 | 0.637613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30026.6 | 1.02385 | ||||||||
\(952\) | −9401.72 | −0.320075 | ||||||||
\(953\) | −31929.4 | −1.08530 | −0.542651 | − | 0.839958i | \(-0.682580\pi\) | ||||
−0.542651 | + | 0.839958i | \(0.682580\pi\) | |||||||
\(954\) | −7098.50 | −0.240904 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11710.2 | 0.396166 | ||||||||
\(957\) | −1576.46 | −0.0532495 | ||||||||
\(958\) | −18465.1 | −0.622735 | ||||||||
\(959\) | 7868.57 | 0.264952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25641.2 | −0.860704 | ||||||||
\(962\) | −1969.48 | −0.0660069 | ||||||||
\(963\) | 12255.6 | 0.410106 | ||||||||
\(964\) | −1951.46 | −0.0651994 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5624.66 | 0.187340 | ||||||||
\(967\) | 10897.1 | 0.362385 | 0.181193 | − | 0.983448i | \(-0.442004\pi\) | ||||
0.181193 | + | 0.983448i | \(0.442004\pi\) | |||||||
\(968\) | 29607.7 | 0.983087 | ||||||||
\(969\) | 5970.82 | 0.197947 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7041.97 | 0.232737 | 0.116368 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116368 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(972\) | 1240.44 | 0.0409332 | ||||||||
\(973\) | −1715.81 | −0.0565328 | ||||||||
\(974\) | −21707.0 | −0.714103 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −397.671 | −0.0130422 | ||||||||
\(977\) | 37607.6 | 1.23150 | 0.615749 | − | 0.787943i | \(-0.288854\pi\) | ||||
0.615749 | + | 0.787943i | \(0.288854\pi\) | |||||||
\(978\) | −4500.90 | −0.147160 | ||||||||
\(979\) | −1824.69 | −0.0595684 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2890.07 | 0.0940599 | ||||||||
\(982\) | −11939.0 | −0.387974 | ||||||||
\(983\) | 25297.7 | 0.820826 | 0.410413 | − | 0.911900i | \(-0.365385\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(984\) | −11076.6 | −0.358851 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9479.85 | 0.306187 | ||||||||
\(987\) | −25621.4 | −0.826281 | ||||||||
\(988\) | 31151.5 | 1.00310 | ||||||||
\(989\) | 12271.6 | 0.394556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41686.5 | −1.33624 | −0.668120 | − | 0.744053i | \(-0.732901\pi\) | ||||
−0.668120 | + | 0.744053i | \(0.732901\pi\) | |||||||
\(992\) | 11808.9 | 0.377955 | ||||||||
\(993\) | 26087.8 | 0.833708 | ||||||||
\(994\) | 22458.3 | 0.716633 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2663.50 | −0.0847351 | ||||||||
\(997\) | −25465.9 | −0.808939 | −0.404470 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404470 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(998\) | 19350.6 | 0.613761 | ||||||||
\(999\) | −536.878 | −0.0170031 |
(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 | 75.4.a.c.1.2 | 2 | ||
3.2 | odd | 2 | 225.4.a.o.1.1 | 2 | |||
4.3 | odd | 2 | 1200.4.a.bt.1.2 | 2 | |||
5.2 | odd | 4 | 15.4.b.a.4.3 | yes | 4 | ||
5.3 | odd | 4 | 15.4.b.a.4.2 | ✓ | 4 | ||
5.4 | even | 2 | 75.4.a.f.1.1 | 2 | |||
15.2 | even | 4 | 45.4.b.b.19.2 | 4 | |||
15.8 | even | 4 | 45.4.b.b.19.3 | 4 | |||
15.14 | odd | 2 | 225.4.a.i.1.2 | 2 | |||
20.3 | even | 4 | 240.4.f.f.49.3 | 4 | |||
20.7 | even | 4 | 240.4.f.f.49.1 | 4 | |||
20.19 | odd | 2 | 1200.4.a.bn.1.1 | 2 | |||
40.3 | even | 4 | 960.4.f.p.769.2 | 4 | |||
40.13 | odd | 4 | 960.4.f.q.769.4 | 4 | |||
40.27 | even | 4 | 960.4.f.p.769.4 | 4 | |||
40.37 | odd | 4 | 960.4.f.q.769.2 | 4 | |||
60.23 | odd | 4 | 720.4.f.j.289.3 | 4 | |||
60.47 | odd | 4 | 720.4.f.j.289.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.2 | ✓ | 4 | 5.3 | odd | 4 | ||
15.4.b.a.4.3 | yes | 4 | 5.2 | odd | 4 | ||
45.4.b.b.19.2 | 4 | 15.2 | even | 4 | |||
45.4.b.b.19.3 | 4 | 15.8 | even | 4 | |||
75.4.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
75.4.a.f.1.1 | 2 | 5.4 | even | 2 | |||
225.4.a.i.1.2 | 2 | 15.14 | odd | 2 | |||
225.4.a.o.1.1 | 2 | 3.2 | odd | 2 | |||
240.4.f.f.49.1 | 4 | 20.7 | even | 4 | |||
240.4.f.f.49.3 | 4 | 20.3 | even | 4 | |||
720.4.f.j.289.3 | 4 | 60.23 | odd | 4 | |||
720.4.f.j.289.4 | 4 | 60.47 | odd | 4 | |||
960.4.f.p.769.2 | 4 | 40.3 | even | 4 | |||
960.4.f.p.769.4 | 4 | 40.27 | even | 4 | |||
960.4.f.q.769.2 | 4 | 40.37 | odd | 4 | |||
960.4.f.q.769.4 | 4 | 40.13 | odd | 4 | |||
1200.4.a.bn.1.1 | 2 | 20.19 | odd | 2 | |||
1200.4.a.bt.1.2 | 2 | 4.3 | odd | 2 |