Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.53413\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53413 | 1.08480 | 0.542398 | − | 0.840122i | \(-0.317517\pi\) | ||||
0.542398 | + | 0.840122i | \(0.317517\pi\) | |||||||
\(3\) | 2.66039 | 1.53598 | 0.767989 | − | 0.640464i | \(-0.221258\pi\) | ||||
0.767989 | + | 0.640464i | \(0.221258\pi\) | |||||||
\(4\) | 0.353561 | 0.176780 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.08139 | 1.66622 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.52585 | −0.893025 | ||||||||
\(9\) | 4.07768 | 1.35923 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.84745 | −1.76307 | −0.881536 | − | 0.472117i | \(-0.843490\pi\) | ||||
−0.881536 | + | 0.472117i | \(0.843490\pi\) | |||||||
\(12\) | 0.940610 | 0.271531 | ||||||||
\(13\) | 0.0444244 | 0.0123211 | 0.00616055 | − | 0.999981i | \(-0.498039\pi\) | ||||
0.00616055 | + | 0.999981i | \(0.498039\pi\) | |||||||
\(14\) | −1.53413 | −0.410014 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.58212 | −1.14553 | ||||||||
\(17\) | −7.20179 | −1.74669 | −0.873345 | − | 0.487103i | \(-0.838054\pi\) | ||||
−0.873345 | + | 0.487103i | \(0.838054\pi\) | |||||||
\(18\) | 6.25569 | 1.47448 | ||||||||
\(19\) | −2.29291 | −0.526029 | −0.263015 | − | 0.964792i | \(-0.584717\pi\) | ||||
−0.263015 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.66039 | −0.580545 | ||||||||
\(22\) | −8.97076 | −1.91257 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −6.71976 | −1.37167 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0681529 | 0.0133659 | ||||||||
\(27\) | 2.86704 | 0.551762 | ||||||||
\(28\) | −0.353561 | −0.0668167 | ||||||||
\(29\) | 7.92658 | 1.47193 | 0.735965 | − | 0.677020i | \(-0.236729\pi\) | ||||
0.735965 | + | 0.677020i | \(0.236729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.44342 | −1.15727 | −0.578636 | − | 0.815586i | \(-0.696415\pi\) | ||||
−0.578636 | + | 0.815586i | \(0.696415\pi\) | |||||||
\(32\) | −1.97786 | −0.349640 | ||||||||
\(33\) | −15.5565 | −2.70804 | ||||||||
\(34\) | −11.0485 | −1.89480 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.44171 | 0.240285 | ||||||||
\(37\) | 0.590146 | 0.0970195 | 0.0485097 | − | 0.998823i | \(-0.484553\pi\) | ||||
0.0485097 | + | 0.998823i | \(0.484553\pi\) | |||||||
\(38\) | −3.51762 | −0.570634 | ||||||||
\(39\) | 0.118186 | 0.0189249 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0590 | −1.72712 | −0.863561 | − | 0.504244i | \(-0.831771\pi\) | ||||
−0.863561 | + | 0.504244i | \(0.831771\pi\) | |||||||
\(42\) | −4.08139 | −0.629772 | ||||||||
\(43\) | −3.01294 | −0.459468 | −0.229734 | − | 0.973253i | \(-0.573786\pi\) | ||||
−0.229734 | + | 0.973253i | \(0.573786\pi\) | |||||||
\(44\) | −2.06743 | −0.311677 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53413 | 0.226195 | ||||||||
\(47\) | 9.08931 | 1.32581 | 0.662906 | − | 0.748703i | \(-0.269323\pi\) | ||||
0.662906 | + | 0.748703i | \(0.269323\pi\) | |||||||
\(48\) | −12.1902 | −1.75951 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.1596 | −2.68287 | ||||||||
\(52\) | 0.0157067 | 0.00217813 | ||||||||
\(53\) | 5.31834 | 0.730530 | 0.365265 | − | 0.930904i | \(-0.380978\pi\) | ||||
0.365265 | + | 0.930904i | \(0.380978\pi\) | |||||||
\(54\) | 4.39842 | 0.598549 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.52585 | 0.337532 | ||||||||
\(57\) | −6.10003 | −0.807969 | ||||||||
\(58\) | 12.1604 | 1.59674 | ||||||||
\(59\) | −3.75523 | −0.488890 | −0.244445 | − | 0.969663i | \(-0.578606\pi\) | ||||
−0.244445 | + | 0.969663i | \(0.578606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6040 | 1.61377 | 0.806886 | − | 0.590707i | \(-0.201151\pi\) | ||||
0.806886 | + | 0.590707i | \(0.201151\pi\) | |||||||
\(62\) | −9.88506 | −1.25540 | ||||||||
\(63\) | −4.07768 | −0.513739 | ||||||||
\(64\) | 6.12993 | 0.766242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −23.8657 | −2.93767 | ||||||||
\(67\) | −1.58900 | −0.194127 | −0.0970637 | − | 0.995278i | \(-0.530945\pi\) | ||||
−0.0970637 | + | 0.995278i | \(0.530945\pi\) | |||||||
\(68\) | −2.54627 | −0.308781 | ||||||||
\(69\) | 2.66039 | 0.320273 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44237 | −0.289856 | −0.144928 | − | 0.989442i | \(-0.546295\pi\) | ||||
−0.144928 | + | 0.989442i | \(0.546295\pi\) | |||||||
\(72\) | −10.2996 | −1.21382 | ||||||||
\(73\) | −1.09091 | −0.127682 | −0.0638408 | − | 0.997960i | \(-0.520335\pi\) | ||||
−0.0638408 | + | 0.997960i | \(0.520335\pi\) | |||||||
\(74\) | 0.905362 | 0.105246 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.810682 | −0.0929916 | ||||||||
\(77\) | 5.84745 | 0.666379 | ||||||||
\(78\) | 0.181313 | 0.0205297 | ||||||||
\(79\) | 0.301216 | 0.0338894 | 0.0169447 | − | 0.999856i | \(-0.494606\pi\) | ||||
0.0169447 | + | 0.999856i | \(0.494606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.60558 | −0.511731 | ||||||||
\(82\) | −16.9659 | −1.87357 | ||||||||
\(83\) | −12.3450 | −1.35504 | −0.677519 | − | 0.735505i | \(-0.736945\pi\) | ||||
−0.677519 | + | 0.735505i | \(0.736945\pi\) | |||||||
\(84\) | −0.940610 | −0.102629 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.62224 | −0.498429 | ||||||||
\(87\) | 21.0878 | 2.26085 | ||||||||
\(88\) | 14.7698 | 1.57447 | ||||||||
\(89\) | 6.18893 | 0.656025 | 0.328012 | − | 0.944673i | \(-0.393621\pi\) | ||||
0.328012 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0444244 | −0.00465694 | ||||||||
\(92\) | 0.353561 | 0.0368613 | ||||||||
\(93\) | −17.1420 | −1.77754 | ||||||||
\(94\) | 13.9442 | 1.43823 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.26188 | −0.537039 | ||||||||
\(97\) | −15.4115 | −1.56480 | −0.782400 | − | 0.622777i | \(-0.786004\pi\) | ||||
−0.782400 | + | 0.622777i | \(0.786004\pi\) | |||||||
\(98\) | 1.53413 | 0.154971 | ||||||||
\(99\) | −23.8440 | −2.39641 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.6168 | 1.65343 | 0.826716 | − | 0.562620i | \(-0.190206\pi\) | ||||
0.826716 | + | 0.562620i | \(0.190206\pi\) | |||||||
\(102\) | −29.3933 | −2.91037 | ||||||||
\(103\) | 10.2458 | 1.00955 | 0.504776 | − | 0.863250i | \(-0.331575\pi\) | ||||
0.504776 | + | 0.863250i | \(0.331575\pi\) | |||||||
\(104\) | −0.112210 | −0.0110030 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.15904 | 0.792476 | ||||||||
\(107\) | −14.8612 | −1.43668 | −0.718342 | − | 0.695690i | \(-0.755099\pi\) | ||||
−0.718342 | + | 0.695690i | \(0.755099\pi\) | |||||||
\(108\) | 1.01367 | 0.0975408 | ||||||||
\(109\) | −6.48526 | −0.621175 | −0.310588 | − | 0.950545i | \(-0.600526\pi\) | ||||
−0.310588 | + | 0.950545i | \(0.600526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.57002 | 0.149020 | ||||||||
\(112\) | 4.58212 | 0.432969 | ||||||||
\(113\) | −6.08765 | −0.572678 | −0.286339 | − | 0.958128i | \(-0.592438\pi\) | ||||
−0.286339 | + | 0.958128i | \(0.592438\pi\) | |||||||
\(114\) | −9.35825 | −0.876480 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.80253 | 0.260208 | ||||||||
\(117\) | 0.181148 | 0.0167472 | ||||||||
\(118\) | −5.76103 | −0.530345 | ||||||||
\(119\) | 7.20179 | 0.660187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.1926 | 2.10842 | ||||||||
\(122\) | 19.3361 | 1.75061 | ||||||||
\(123\) | −29.4212 | −2.65282 | ||||||||
\(124\) | −2.27814 | −0.204583 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.25569 | −0.557302 | ||||||||
\(127\) | 3.41982 | 0.303460 | 0.151730 | − | 0.988422i | \(-0.451516\pi\) | ||||
0.151730 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(128\) | 13.3598 | 1.18085 | ||||||||
\(129\) | −8.01558 | −0.705733 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2790 | 1.07282 | 0.536412 | − | 0.843956i | \(-0.319779\pi\) | ||||
0.536412 | + | 0.843956i | \(0.319779\pi\) | |||||||
\(132\) | −5.50017 | −0.478728 | ||||||||
\(133\) | 2.29291 | 0.198820 | ||||||||
\(134\) | −2.43774 | −0.210588 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.1907 | 1.55984 | ||||||||
\(137\) | 1.21300 | 0.103634 | 0.0518168 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518168 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(138\) | 4.08139 | 0.347431 | ||||||||
\(139\) | 7.53216 | 0.638870 | 0.319435 | − | 0.947608i | \(-0.396507\pi\) | ||||
0.319435 | + | 0.947608i | \(0.396507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.1811 | 2.03642 | ||||||||
\(142\) | −3.74692 | −0.314435 | ||||||||
\(143\) | −0.259769 | −0.0217230 | ||||||||
\(144\) | −18.6844 | −1.55703 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.67360 | −0.138508 | ||||||||
\(147\) | 2.66039 | 0.219425 | ||||||||
\(148\) | 0.208653 | 0.0171511 | ||||||||
\(149\) | −2.24652 | −0.184042 | −0.0920210 | − | 0.995757i | \(-0.529333\pi\) | ||||
−0.0920210 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9643 | −1.13640 | −0.568198 | − | 0.822892i | \(-0.692359\pi\) | ||||
−0.568198 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(152\) | 5.79155 | 0.469757 | ||||||||
\(153\) | −29.3666 | −2.37414 | ||||||||
\(154\) | 8.97076 | 0.722884 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0417860 | 0.00334556 | ||||||||
\(157\) | −0.0899912 | −0.00718208 | −0.00359104 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359104 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(158\) | 0.462104 | 0.0367631 | ||||||||
\(159\) | 14.1489 | 1.12208 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −7.06557 | −0.555124 | ||||||||
\(163\) | −7.53351 | −0.590070 | −0.295035 | − | 0.955486i | \(-0.595331\pi\) | ||||
−0.295035 | + | 0.955486i | \(0.595331\pi\) | |||||||
\(164\) | −3.91002 | −0.305321 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.9388 | −1.46994 | ||||||||
\(167\) | 7.56740 | 0.585583 | 0.292792 | − | 0.956176i | \(-0.405416\pi\) | ||||
0.292792 | + | 0.956176i | \(0.405416\pi\) | |||||||
\(168\) | 6.71976 | 0.518441 | ||||||||
\(169\) | −12.9980 | −0.999848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.34973 | −0.714992 | ||||||||
\(172\) | −1.06526 | −0.0812250 | ||||||||
\(173\) | 6.89548 | 0.524254 | 0.262127 | − | 0.965033i | \(-0.415576\pi\) | ||||
0.262127 | + | 0.965033i | \(0.415576\pi\) | |||||||
\(174\) | 32.3515 | 2.45256 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 26.7937 | 2.01965 | ||||||||
\(177\) | −9.99039 | −0.750924 | ||||||||
\(178\) | 9.49463 | 0.711653 | ||||||||
\(179\) | 22.7833 | 1.70290 | 0.851451 | − | 0.524434i | \(-0.175723\pi\) | ||||
0.851451 | + | 0.524434i | \(0.175723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.93003 | −0.738093 | −0.369047 | − | 0.929411i | \(-0.620316\pi\) | ||||
−0.369047 | + | 0.929411i | \(0.620316\pi\) | |||||||
\(182\) | −0.0681529 | −0.00505183 | ||||||||
\(183\) | 33.5315 | 2.47872 | ||||||||
\(184\) | −2.52585 | −0.186208 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −26.2981 | −1.92827 | ||||||||
\(187\) | 42.1121 | 3.07954 | ||||||||
\(188\) | 3.21362 | 0.234378 | ||||||||
\(189\) | −2.86704 | −0.208547 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.39126 | −0.462455 | −0.231228 | − | 0.972900i | \(-0.574274\pi\) | ||||
−0.231228 | + | 0.972900i | \(0.574274\pi\) | |||||||
\(192\) | 16.3080 | 1.17693 | ||||||||
\(193\) | 7.98914 | 0.575071 | 0.287535 | − | 0.957770i | \(-0.407164\pi\) | ||||
0.287535 | + | 0.957770i | \(0.407164\pi\) | |||||||
\(194\) | −23.6433 | −1.69749 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.353561 | 0.0252543 | ||||||||
\(197\) | −18.2321 | −1.29898 | −0.649492 | − | 0.760369i | \(-0.725018\pi\) | ||||
−0.649492 | + | 0.760369i | \(0.725018\pi\) | |||||||
\(198\) | −36.5798 | −2.59962 | ||||||||
\(199\) | −12.7332 | −0.902632 | −0.451316 | − | 0.892364i | \(-0.649045\pi\) | ||||
−0.451316 | + | 0.892364i | \(0.649045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.22736 | −0.298175 | ||||||||
\(202\) | 25.4923 | 1.79363 | ||||||||
\(203\) | −7.92658 | −0.556337 | ||||||||
\(204\) | −6.77407 | −0.474280 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.7185 | 1.09516 | ||||||||
\(207\) | 4.07768 | 0.283418 | ||||||||
\(208\) | −0.203558 | −0.0141142 | ||||||||
\(209\) | 13.4077 | 0.927427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.75457 | −0.327318 | −0.163659 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163659 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(212\) | 1.88036 | 0.129143 | ||||||||
\(213\) | −6.49766 | −0.445213 | ||||||||
\(214\) | −22.7990 | −1.55851 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.24173 | −0.492737 | ||||||||
\(217\) | 6.44342 | 0.437408 | ||||||||
\(218\) | −9.94925 | −0.673848 | ||||||||
\(219\) | −2.90225 | −0.196116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.319935 | −0.0215211 | ||||||||
\(222\) | 2.40862 | 0.161656 | ||||||||
\(223\) | −26.5866 | −1.78037 | −0.890184 | − | 0.455602i | \(-0.849424\pi\) | ||||
−0.890184 | + | 0.455602i | \(0.849424\pi\) | |||||||
\(224\) | 1.97786 | 0.132151 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.33926 | −0.621238 | ||||||||
\(227\) | 3.76751 | 0.250059 | 0.125029 | − | 0.992153i | \(-0.460098\pi\) | ||||
0.125029 | + | 0.992153i | \(0.460098\pi\) | |||||||
\(228\) | −2.15673 | −0.142833 | ||||||||
\(229\) | −13.5176 | −0.893270 | −0.446635 | − | 0.894716i | \(-0.647378\pi\) | ||||
−0.446635 | + | 0.894716i | \(0.647378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.5565 | 1.02354 | ||||||||
\(232\) | −20.0214 | −1.31447 | ||||||||
\(233\) | 6.81789 | 0.446655 | 0.223327 | − | 0.974743i | \(-0.428308\pi\) | ||||
0.223327 | + | 0.974743i | \(0.428308\pi\) | |||||||
\(234\) | 0.277905 | 0.0181672 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.32770 | −0.0864262 | ||||||||
\(237\) | 0.801351 | 0.0520533 | ||||||||
\(238\) | 11.0485 | 0.716167 | ||||||||
\(239\) | 7.35354 | 0.475661 | 0.237831 | − | 0.971307i | \(-0.423564\pi\) | ||||
0.237831 | + | 0.971307i | \(0.423564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.8543 | −1.27892 | −0.639462 | − | 0.768822i | \(-0.720843\pi\) | ||||
−0.639462 | + | 0.768822i | \(0.720843\pi\) | |||||||
\(242\) | 35.5806 | 2.28721 | ||||||||
\(243\) | −20.8538 | −1.33777 | ||||||||
\(244\) | 4.45627 | 0.285283 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −45.1360 | −2.87777 | ||||||||
\(247\) | −0.101861 | −0.00648126 | ||||||||
\(248\) | 16.2751 | 1.03347 | ||||||||
\(249\) | −32.8425 | −2.08131 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.7478 | −0.867755 | −0.433878 | − | 0.900972i | \(-0.642855\pi\) | ||||
−0.433878 | + | 0.900972i | \(0.642855\pi\) | |||||||
\(252\) | −1.44171 | −0.0908190 | ||||||||
\(253\) | −5.84745 | −0.367626 | ||||||||
\(254\) | 5.24646 | 0.329192 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.23591 | 0.514744 | ||||||||
\(257\) | −1.04042 | −0.0648997 | −0.0324499 | − | 0.999473i | \(-0.510331\pi\) | ||||
−0.0324499 | + | 0.999473i | \(0.510331\pi\) | |||||||
\(258\) | −12.2970 | −0.765575 | ||||||||
\(259\) | −0.590146 | −0.0366699 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.3220 | 2.00068 | ||||||||
\(262\) | 18.8376 | 1.16379 | ||||||||
\(263\) | 12.7175 | 0.784192 | 0.392096 | − | 0.919924i | \(-0.371750\pi\) | ||||
0.392096 | + | 0.919924i | \(0.371750\pi\) | |||||||
\(264\) | 39.2934 | 2.41834 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.51762 | 0.215679 | ||||||||
\(267\) | 16.4650 | 1.00764 | ||||||||
\(268\) | −0.561809 | −0.0343179 | ||||||||
\(269\) | −18.4312 | −1.12377 | −0.561885 | − | 0.827216i | \(-0.689924\pi\) | ||||
−0.561885 | + | 0.827216i | \(0.689924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.2816 | −1.35351 | −0.676755 | − | 0.736209i | \(-0.736614\pi\) | ||||
−0.676755 | + | 0.736209i | \(0.736614\pi\) | |||||||
\(272\) | 32.9994 | 2.00088 | ||||||||
\(273\) | −0.118186 | −0.00715295 | ||||||||
\(274\) | 1.86090 | 0.112421 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.940610 | 0.0566181 | ||||||||
\(277\) | 22.6500 | 1.36091 | 0.680453 | − | 0.732791i | \(-0.261783\pi\) | ||||
0.680453 | + | 0.732791i | \(0.261783\pi\) | |||||||
\(278\) | 11.5553 | 0.693043 | ||||||||
\(279\) | −26.2742 | −1.57299 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7126 | 1.11630 | 0.558151 | − | 0.829739i | \(-0.311511\pi\) | ||||
0.558151 | + | 0.829739i | \(0.311511\pi\) | |||||||
\(282\) | 37.0970 | 2.20909 | ||||||||
\(283\) | −5.98802 | −0.355951 | −0.177975 | − | 0.984035i | \(-0.556955\pi\) | ||||
−0.177975 | + | 0.984035i | \(0.556955\pi\) | |||||||
\(284\) | −0.863527 | −0.0512409 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.398520 | −0.0235650 | ||||||||
\(287\) | 11.0590 | 0.652791 | ||||||||
\(288\) | −8.06508 | −0.475239 | ||||||||
\(289\) | 34.8657 | 2.05092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.0006 | −2.40350 | ||||||||
\(292\) | −0.385704 | −0.0225716 | ||||||||
\(293\) | 23.5579 | 1.37627 | 0.688133 | − | 0.725585i | \(-0.258431\pi\) | ||||
0.688133 | + | 0.725585i | \(0.258431\pi\) | |||||||
\(294\) | 4.08139 | 0.238031 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.49062 | −0.0866408 | ||||||||
\(297\) | −16.7649 | −0.972796 | ||||||||
\(298\) | −3.44646 | −0.199648 | ||||||||
\(299\) | 0.0444244 | 0.00256913 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.01294 | 0.173663 | ||||||||
\(302\) | −21.4230 | −1.23276 | ||||||||
\(303\) | 44.2071 | 2.53963 | ||||||||
\(304\) | 10.5064 | 0.602582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −45.0522 | −2.57546 | ||||||||
\(307\) | −30.5545 | −1.74384 | −0.871918 | − | 0.489653i | \(-0.837124\pi\) | ||||
−0.871918 | + | 0.489653i | \(0.837124\pi\) | |||||||
\(308\) | 2.06743 | 0.117803 | ||||||||
\(309\) | 27.2579 | 1.55065 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8768 | 0.730176 | 0.365088 | − | 0.930973i | \(-0.381039\pi\) | ||||
0.365088 | + | 0.930973i | \(0.381039\pi\) | |||||||
\(312\) | −0.298521 | −0.0169004 | ||||||||
\(313\) | 25.9654 | 1.46765 | 0.733824 | − | 0.679339i | \(-0.237733\pi\) | ||||
0.733824 | + | 0.679339i | \(0.237733\pi\) | |||||||
\(314\) | −0.138058 | −0.00779109 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.106498 | 0.00599098 | ||||||||
\(317\) | 5.00852 | 0.281307 | 0.140653 | − | 0.990059i | \(-0.455080\pi\) | ||||
0.140653 | + | 0.990059i | \(0.455080\pi\) | |||||||
\(318\) | 21.7062 | 1.21722 | ||||||||
\(319\) | −46.3503 | −2.59512 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.5365 | −2.20671 | ||||||||
\(322\) | −1.53413 | −0.0854938 | ||||||||
\(323\) | 16.5130 | 0.918809 | ||||||||
\(324\) | −1.62835 | −0.0904641 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.5574 | −0.640105 | ||||||||
\(327\) | −17.2533 | −0.954111 | ||||||||
\(328\) | 27.9334 | 1.54236 | ||||||||
\(329\) | −9.08931 | −0.501110 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.6122 | −1.62763 | −0.813816 | − | 0.581123i | \(-0.802614\pi\) | ||||
−0.813816 | + | 0.581123i | \(0.802614\pi\) | |||||||
\(332\) | −4.36470 | −0.239544 | ||||||||
\(333\) | 2.40643 | 0.131871 | ||||||||
\(334\) | 11.6094 | 0.635238 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.1902 | 0.665031 | ||||||||
\(337\) | 18.2156 | 0.992269 | 0.496135 | − | 0.868246i | \(-0.334752\pi\) | ||||
0.496135 | + | 0.868246i | \(0.334752\pi\) | |||||||
\(338\) | −19.9407 | −1.08463 | ||||||||
\(339\) | −16.1955 | −0.879620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.6776 | 2.04035 | ||||||||
\(342\) | −14.3437 | −0.775620 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.61024 | 0.410316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5786 | 0.568708 | ||||||||
\(347\) | −5.01092 | −0.269000 | −0.134500 | − | 0.990914i | \(-0.542943\pi\) | ||||
−0.134500 | + | 0.990914i | \(0.542943\pi\) | |||||||
\(348\) | 7.45582 | 0.399674 | ||||||||
\(349\) | −4.42081 | −0.236641 | −0.118320 | − | 0.992975i | \(-0.537751\pi\) | ||||
−0.118320 | + | 0.992975i | \(0.537751\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.127366 | 0.00679832 | ||||||||
\(352\) | 11.5654 | 0.616440 | ||||||||
\(353\) | −10.7456 | −0.571931 | −0.285965 | − | 0.958240i | \(-0.592314\pi\) | ||||
−0.285965 | + | 0.958240i | \(0.592314\pi\) | |||||||
\(354\) | −15.3266 | −0.814598 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.18816 | 0.115972 | ||||||||
\(357\) | 19.1596 | 1.01403 | ||||||||
\(358\) | 34.9526 | 1.84730 | ||||||||
\(359\) | −11.5145 | −0.607711 | −0.303855 | − | 0.952718i | \(-0.598274\pi\) | ||||
−0.303855 | + | 0.952718i | \(0.598274\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7426 | −0.723293 | ||||||||
\(362\) | −15.2340 | −0.800680 | ||||||||
\(363\) | 61.7015 | 3.23849 | ||||||||
\(364\) | −0.0157067 | −0.000823256 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 51.4417 | 2.68890 | ||||||||
\(367\) | −3.15274 | −0.164572 | −0.0822859 | − | 0.996609i | \(-0.526222\pi\) | ||||
−0.0822859 | + | 0.996609i | \(0.526222\pi\) | |||||||
\(368\) | −4.58212 | −0.238859 | ||||||||
\(369\) | −45.0949 | −2.34755 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.31834 | −0.276114 | ||||||||
\(372\) | −6.06075 | −0.314235 | ||||||||
\(373\) | −9.25639 | −0.479278 | −0.239639 | − | 0.970862i | \(-0.577029\pi\) | ||||
−0.239639 | + | 0.970862i | \(0.577029\pi\) | |||||||
\(374\) | 64.6055 | 3.34067 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.9583 | −1.18398 | ||||||||
\(377\) | 0.352134 | 0.0181358 | ||||||||
\(378\) | −4.39842 | −0.226230 | ||||||||
\(379\) | −36.5965 | −1.87984 | −0.939919 | − | 0.341397i | \(-0.889100\pi\) | ||||
−0.939919 | + | 0.341397i | \(0.889100\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.09806 | 0.466108 | ||||||||
\(382\) | −9.80504 | −0.501669 | ||||||||
\(383\) | −18.3797 | −0.939156 | −0.469578 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469578 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(384\) | 35.5424 | 1.81377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.2564 | 0.623834 | ||||||||
\(387\) | −12.2858 | −0.624521 | ||||||||
\(388\) | −5.44890 | −0.276626 | ||||||||
\(389\) | −1.84084 | −0.0933344 | −0.0466672 | − | 0.998910i | \(-0.514860\pi\) | ||||
−0.0466672 | + | 0.998910i | \(0.514860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.20179 | −0.364210 | ||||||||
\(392\) | −2.52585 | −0.127575 | ||||||||
\(393\) | 32.6670 | 1.64783 | ||||||||
\(394\) | −27.9704 | −1.40913 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.43031 | −0.423639 | ||||||||
\(397\) | −30.9012 | −1.55089 | −0.775443 | − | 0.631418i | \(-0.782473\pi\) | ||||
−0.775443 | + | 0.631418i | \(0.782473\pi\) | |||||||
\(398\) | −19.5344 | −0.979171 | ||||||||
\(399\) | 6.10003 | 0.305383 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.04586 | −0.451728 | −0.225864 | − | 0.974159i | \(-0.572521\pi\) | ||||
−0.225864 | + | 0.974159i | \(0.572521\pi\) | |||||||
\(402\) | −6.48533 | −0.323459 | ||||||||
\(403\) | −0.286245 | −0.0142589 | ||||||||
\(404\) | 5.87504 | 0.292294 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.1604 | −0.603512 | ||||||||
\(407\) | −3.45085 | −0.171052 | ||||||||
\(408\) | 48.3943 | 2.39587 | ||||||||
\(409\) | 9.73025 | 0.481130 | 0.240565 | − | 0.970633i | \(-0.422667\pi\) | ||||
0.240565 | + | 0.970633i | \(0.422667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.22705 | 0.159179 | ||||||||
\(412\) | 3.62253 | 0.178469 | ||||||||
\(413\) | 3.75523 | 0.184783 | ||||||||
\(414\) | 6.25569 | 0.307451 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0878653 | −0.00430795 | ||||||||
\(417\) | 20.0385 | 0.981289 | ||||||||
\(418\) | 20.5691 | 1.00607 | ||||||||
\(419\) | −6.99729 | −0.341840 | −0.170920 | − | 0.985285i | \(-0.554674\pi\) | ||||
−0.170920 | + | 0.985285i | \(0.554674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.5420 | −0.806209 | −0.403104 | − | 0.915154i | \(-0.632069\pi\) | ||||
−0.403104 | + | 0.915154i | \(0.632069\pi\) | |||||||
\(422\) | −7.29413 | −0.355073 | ||||||||
\(423\) | 37.0633 | 1.80208 | ||||||||
\(424\) | −13.4334 | −0.652381 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.96828 | −0.482965 | ||||||||
\(427\) | −12.6040 | −0.609948 | ||||||||
\(428\) | −5.25433 | −0.253978 | ||||||||
\(429\) | −0.691088 | −0.0333660 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.03469 | 0.194344 | 0.0971721 | − | 0.995268i | \(-0.469020\pi\) | ||||
0.0971721 | + | 0.995268i | \(0.469020\pi\) | |||||||
\(432\) | −13.1371 | −0.632060 | ||||||||
\(433\) | 10.8719 | 0.522468 | 0.261234 | − | 0.965276i | \(-0.415871\pi\) | ||||
0.261234 | + | 0.965276i | \(0.415871\pi\) | |||||||
\(434\) | 9.88506 | 0.474498 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.29293 | −0.109812 | ||||||||
\(437\) | −2.29291 | −0.109685 | ||||||||
\(438\) | −4.45244 | −0.212746 | ||||||||
\(439\) | 22.5326 | 1.07542 | 0.537711 | − | 0.843129i | \(-0.319289\pi\) | ||||
0.537711 | + | 0.843129i | \(0.319289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.07768 | 0.194175 | ||||||||
\(442\) | −0.490822 | −0.0233460 | ||||||||
\(443\) | −40.8033 | −1.93862 | −0.969312 | − | 0.245834i | \(-0.920938\pi\) | ||||
−0.969312 | + | 0.245834i | \(0.920938\pi\) | |||||||
\(444\) | 0.555098 | 0.0263438 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −40.7873 | −1.93133 | ||||||||
\(447\) | −5.97662 | −0.282684 | ||||||||
\(448\) | −6.12993 | −0.289612 | ||||||||
\(449\) | 38.8789 | 1.83481 | 0.917404 | − | 0.397957i | \(-0.130281\pi\) | ||||
0.917404 | + | 0.397957i | \(0.130281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 64.6668 | 3.04504 | ||||||||
\(452\) | −2.15236 | −0.101238 | ||||||||
\(453\) | −37.1504 | −1.74548 | ||||||||
\(454\) | 5.77986 | 0.271262 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.4078 | 0.721536 | ||||||||
\(457\) | 23.5917 | 1.10357 | 0.551787 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551787 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(458\) | −20.7378 | −0.969015 | ||||||||
\(459\) | −20.6478 | −0.963757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4335 | 0.625659 | 0.312829 | − | 0.949809i | \(-0.398723\pi\) | ||||
0.312829 | + | 0.949809i | \(0.398723\pi\) | |||||||
\(462\) | 23.8657 | 1.11033 | ||||||||
\(463\) | 35.0951 | 1.63101 | 0.815505 | − | 0.578750i | \(-0.196459\pi\) | ||||
0.815505 | + | 0.578750i | \(0.196459\pi\) | |||||||
\(464\) | −36.3205 | −1.68614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.4595 | 0.484529 | ||||||||
\(467\) | −29.4556 | −1.36304 | −0.681521 | − | 0.731798i | \(-0.738681\pi\) | ||||
−0.681521 | + | 0.731798i | \(0.738681\pi\) | |||||||
\(468\) | 0.0640469 | 0.00296057 | ||||||||
\(469\) | 1.58900 | 0.0733733 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.239412 | −0.0110315 | ||||||||
\(472\) | 9.48518 | 0.436591 | ||||||||
\(473\) | 17.6180 | 0.810076 | ||||||||
\(474\) | 1.22938 | 0.0564672 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.54627 | 0.116708 | ||||||||
\(477\) | 21.6865 | 0.992955 | ||||||||
\(478\) | 11.2813 | 0.515995 | ||||||||
\(479\) | 27.6443 | 1.26310 | 0.631550 | − | 0.775335i | \(-0.282419\pi\) | ||||
0.631550 | + | 0.775335i | \(0.282419\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0262169 | 0.00119539 | ||||||||
\(482\) | −30.4590 | −1.38737 | ||||||||
\(483\) | −2.66039 | −0.121052 | ||||||||
\(484\) | 8.20001 | 0.372728 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −31.9924 | −1.45121 | ||||||||
\(487\) | 10.5707 | 0.479004 | 0.239502 | − | 0.970896i | \(-0.423016\pi\) | ||||
0.239502 | + | 0.970896i | \(0.423016\pi\) | |||||||
\(488\) | −31.8358 | −1.44114 | ||||||||
\(489\) | −20.0421 | −0.906334 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7758 | −0.531434 | −0.265717 | − | 0.964051i | \(-0.585609\pi\) | ||||
−0.265717 | + | 0.964051i | \(0.585609\pi\) | |||||||
\(492\) | −10.4022 | −0.468967 | ||||||||
\(493\) | −57.0856 | −2.57100 | ||||||||
\(494\) | −0.156268 | −0.00703084 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.5245 | 1.32569 | ||||||||
\(497\) | 2.44237 | 0.109555 | ||||||||
\(498\) | −50.3847 | −2.25779 | ||||||||
\(499\) | 19.8327 | 0.887831 | 0.443916 | − | 0.896069i | \(-0.353589\pi\) | ||||
0.443916 | + | 0.896069i | \(0.353589\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1322 | 0.899442 | ||||||||
\(502\) | −21.0910 | −0.941337 | ||||||||
\(503\) | 39.7040 | 1.77032 | 0.885158 | − | 0.465291i | \(-0.154050\pi\) | ||||
0.885158 | + | 0.465291i | \(0.154050\pi\) | |||||||
\(504\) | 10.2996 | 0.458782 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.97076 | −0.398799 | ||||||||
\(507\) | −34.5798 | −1.53574 | ||||||||
\(508\) | 1.20912 | 0.0536458 | ||||||||
\(509\) | −35.5293 | −1.57481 | −0.787404 | − | 0.616437i | \(-0.788576\pi\) | ||||
−0.787404 | + | 0.616437i | \(0.788576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09091 | 0.0482591 | ||||||||
\(512\) | −14.0847 | −0.622463 | ||||||||
\(513\) | −6.57386 | −0.290243 | ||||||||
\(514\) | −1.59614 | −0.0704029 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.83400 | −0.124760 | ||||||||
\(517\) | −53.1492 | −2.33750 | ||||||||
\(518\) | −0.905362 | −0.0397793 | ||||||||
\(519\) | 18.3447 | 0.805241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0961 | −0.573753 | −0.286876 | − | 0.957968i | \(-0.592617\pi\) | ||||
−0.286876 | + | 0.957968i | \(0.592617\pi\) | |||||||
\(522\) | 49.5863 | 2.17033 | ||||||||
\(523\) | 15.4915 | 0.677395 | 0.338698 | − | 0.940895i | \(-0.390014\pi\) | ||||
0.338698 | + | 0.940895i | \(0.390014\pi\) | |||||||
\(524\) | 4.34138 | 0.189654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.5102 | 0.850687 | ||||||||
\(527\) | 46.4041 | 2.02140 | ||||||||
\(528\) | 71.2817 | 3.10214 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.3126 | −0.664512 | ||||||||
\(532\) | 0.810682 | 0.0351475 | ||||||||
\(533\) | −0.491288 | −0.0212801 | ||||||||
\(534\) | 25.2594 | 1.09308 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.01359 | 0.173361 | ||||||||
\(537\) | 60.6124 | 2.61562 | ||||||||
\(538\) | −28.2759 | −1.21906 | ||||||||
\(539\) | −5.84745 | −0.251867 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6655 | −1.31841 | −0.659205 | − | 0.751963i | \(-0.729107\pi\) | ||||
−0.659205 | + | 0.751963i | \(0.729107\pi\) | |||||||
\(542\) | −34.1829 | −1.46828 | ||||||||
\(543\) | −26.4178 | −1.13369 | ||||||||
\(544\) | 14.2441 | 0.610712 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.181313 | −0.00775949 | ||||||||
\(547\) | 13.4001 | 0.572946 | 0.286473 | − | 0.958088i | \(-0.407517\pi\) | ||||
0.286473 | + | 0.958088i | \(0.407517\pi\) | |||||||
\(548\) | 0.428869 | 0.0183204 | ||||||||
\(549\) | 51.3949 | 2.19348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.1749 | −0.774278 | ||||||||
\(552\) | −6.71976 | −0.286012 | ||||||||
\(553\) | −0.301216 | −0.0128090 | ||||||||
\(554\) | 34.7481 | 1.47630 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.66308 | 0.112940 | ||||||||
\(557\) | 29.5160 | 1.25063 | 0.625316 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(558\) | −40.3081 | −1.70638 | ||||||||
\(559\) | −0.133848 | −0.00566116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 112.035 | 4.73010 | ||||||||
\(562\) | 28.7077 | 1.21096 | ||||||||
\(563\) | −16.7153 | −0.704464 | −0.352232 | − | 0.935913i | \(-0.614577\pi\) | ||||
−0.352232 | + | 0.935913i | \(0.614577\pi\) | |||||||
\(564\) | 8.54949 | 0.359999 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.18641 | −0.386134 | ||||||||
\(567\) | 4.60558 | 0.193416 | ||||||||
\(568\) | 6.16908 | 0.258849 | ||||||||
\(569\) | −0.879898 | −0.0368872 | −0.0184436 | − | 0.999830i | \(-0.505871\pi\) | ||||
−0.0184436 | + | 0.999830i | \(0.505871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4017 | −1.14672 | −0.573362 | − | 0.819302i | \(-0.694361\pi\) | ||||
−0.573362 | + | 0.819302i | \(0.694361\pi\) | |||||||
\(572\) | −0.0918442 | −0.00384020 | ||||||||
\(573\) | −17.0032 | −0.710321 | ||||||||
\(574\) | 16.9659 | 0.708144 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.9959 | 1.04150 | ||||||||
\(577\) | −6.85040 | −0.285186 | −0.142593 | − | 0.989781i | \(-0.545544\pi\) | ||||
−0.142593 | + | 0.989781i | \(0.545544\pi\) | |||||||
\(578\) | 53.4886 | 2.22483 | ||||||||
\(579\) | 21.2542 | 0.883295 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3450 | 0.512156 | ||||||||
\(582\) | −62.9003 | −2.60730 | ||||||||
\(583\) | −31.0987 | −1.28798 | ||||||||
\(584\) | 2.75548 | 0.114023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.1409 | 1.49297 | ||||||||
\(587\) | 7.19749 | 0.297072 | 0.148536 | − | 0.988907i | \(-0.452544\pi\) | ||||
0.148536 | + | 0.988907i | \(0.452544\pi\) | |||||||
\(588\) | 0.940610 | 0.0387901 | ||||||||
\(589\) | 14.7742 | 0.608759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −48.5045 | −1.99521 | ||||||||
\(592\) | −2.70412 | −0.111139 | ||||||||
\(593\) | 5.50071 | 0.225887 | 0.112944 | − | 0.993601i | \(-0.463972\pi\) | ||||
0.112944 | + | 0.993601i | \(0.463972\pi\) | |||||||
\(594\) | −25.7195 | −1.05528 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.794281 | −0.0325350 | ||||||||
\(597\) | −33.8753 | −1.38642 | ||||||||
\(598\) | 0.0681529 | 0.00278698 | ||||||||
\(599\) | −21.3379 | −0.871845 | −0.435922 | − | 0.899984i | \(-0.643578\pi\) | ||||
−0.435922 | + | 0.899984i | \(0.643578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.76359 | −0.153520 | −0.0767599 | − | 0.997050i | \(-0.524458\pi\) | ||||
−0.0767599 | + | 0.997050i | \(0.524458\pi\) | |||||||
\(602\) | 4.62224 | 0.188388 | ||||||||
\(603\) | −6.47943 | −0.263863 | ||||||||
\(604\) | −4.93722 | −0.200893 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 67.8196 | 2.75498 | ||||||||
\(607\) | 27.7160 | 1.12496 | 0.562479 | − | 0.826812i | \(-0.309848\pi\) | ||||
0.562479 | + | 0.826812i | \(0.309848\pi\) | |||||||
\(608\) | 4.53505 | 0.183921 | ||||||||
\(609\) | −21.0878 | −0.854521 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.403787 | 0.0163355 | ||||||||
\(612\) | −10.3829 | −0.419702 | ||||||||
\(613\) | 23.4433 | 0.946866 | 0.473433 | − | 0.880830i | \(-0.343015\pi\) | ||||
0.473433 | + | 0.880830i | \(0.343015\pi\) | |||||||
\(614\) | −46.8746 | −1.89170 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.7698 | −0.595092 | ||||||||
\(617\) | 19.6379 | 0.790594 | 0.395297 | − | 0.918553i | \(-0.370642\pi\) | ||||
0.395297 | + | 0.918553i | \(0.370642\pi\) | |||||||
\(618\) | 41.8172 | 1.68214 | ||||||||
\(619\) | 20.6941 | 0.831766 | 0.415883 | − | 0.909418i | \(-0.363473\pi\) | ||||
0.415883 | + | 0.909418i | \(0.363473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.86704 | 0.115050 | ||||||||
\(622\) | 19.7547 | 0.792091 | ||||||||
\(623\) | −6.18893 | −0.247954 | ||||||||
\(624\) | −0.541543 | −0.0216791 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.8343 | 1.59210 | ||||||||
\(627\) | 35.6696 | 1.42451 | ||||||||
\(628\) | −0.0318174 | −0.00126965 | ||||||||
\(629\) | −4.25011 | −0.169463 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1580 | −0.484002 | −0.242001 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242001 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(632\) | −0.760827 | −0.0302641 | ||||||||
\(633\) | −12.6490 | −0.502753 | ||||||||
\(634\) | 7.68373 | 0.305160 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.00248 | 0.198361 | ||||||||
\(637\) | 0.0444244 | 0.00176016 | ||||||||
\(638\) | −71.1075 | −2.81517 | ||||||||
\(639\) | −9.95921 | −0.393980 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.520035 | 0.0205402 | 0.0102701 | − | 0.999947i | \(-0.496731\pi\) | ||||
0.0102701 | + | 0.999947i | \(0.496731\pi\) | |||||||
\(642\) | −60.6542 | −2.39383 | ||||||||
\(643\) | 4.35842 | 0.171879 | 0.0859396 | − | 0.996300i | \(-0.472611\pi\) | ||||
0.0859396 | + | 0.996300i | \(0.472611\pi\) | |||||||
\(644\) | −0.353561 | −0.0139323 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.3332 | 0.996720 | ||||||||
\(647\) | −25.7828 | −1.01363 | −0.506814 | − | 0.862056i | \(-0.669177\pi\) | ||||
−0.506814 | + | 0.862056i | \(0.669177\pi\) | |||||||
\(648\) | 11.6330 | 0.456989 | ||||||||
\(649\) | 21.9585 | 0.861948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.1420 | 0.671849 | ||||||||
\(652\) | −2.66355 | −0.104313 | ||||||||
\(653\) | −5.42222 | −0.212188 | −0.106094 | − | 0.994356i | \(-0.533834\pi\) | ||||
−0.106094 | + | 0.994356i | \(0.533834\pi\) | |||||||
\(654\) | −26.4689 | −1.03502 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 50.6735 | 1.97847 | ||||||||
\(657\) | −4.44838 | −0.173548 | ||||||||
\(658\) | −13.9442 | −0.543601 | ||||||||
\(659\) | −0.588596 | −0.0229284 | −0.0114642 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114642 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2075 | −0.397025 | −0.198512 | − | 0.980098i | \(-0.563611\pi\) | ||||
−0.198512 | + | 0.980098i | \(0.563611\pi\) | |||||||
\(662\) | −45.4290 | −1.76565 | ||||||||
\(663\) | −0.851151 | −0.0330560 | ||||||||
\(664\) | 31.1816 | 1.21008 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.69178 | 0.143053 | ||||||||
\(667\) | 7.92658 | 0.306919 | ||||||||
\(668\) | 2.67554 | 0.103520 | ||||||||
\(669\) | −70.7306 | −2.73460 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −73.7010 | −2.84520 | ||||||||
\(672\) | 5.26188 | 0.202982 | ||||||||
\(673\) | 10.5029 | 0.404858 | 0.202429 | − | 0.979297i | \(-0.435117\pi\) | ||||
0.202429 | + | 0.979297i | \(0.435117\pi\) | |||||||
\(674\) | 27.9452 | 1.07641 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.59559 | −0.176754 | ||||||||
\(677\) | −45.6656 | −1.75507 | −0.877536 | − | 0.479512i | \(-0.840814\pi\) | ||||
−0.877536 | + | 0.479512i | \(0.840814\pi\) | |||||||
\(678\) | −24.8461 | −0.954208 | ||||||||
\(679\) | 15.4115 | 0.591438 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0231 | 0.384084 | ||||||||
\(682\) | 57.8024 | 2.21337 | ||||||||
\(683\) | 44.5094 | 1.70310 | 0.851552 | − | 0.524271i | \(-0.175662\pi\) | ||||
0.851552 | + | 0.524271i | \(0.175662\pi\) | |||||||
\(684\) | −3.30570 | −0.126397 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.53413 | −0.0585734 | ||||||||
\(687\) | −35.9622 | −1.37204 | ||||||||
\(688\) | 13.8056 | 0.526334 | ||||||||
\(689\) | 0.236264 | 0.00900094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.7437 | 1.85430 | 0.927148 | − | 0.374694i | \(-0.122252\pi\) | ||||
0.927148 | + | 0.374694i | \(0.122252\pi\) | |||||||
\(692\) | 2.43797 | 0.0926778 | ||||||||
\(693\) | 23.8440 | 0.905759 | ||||||||
\(694\) | −7.68741 | −0.291810 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −53.2647 | −2.01899 | ||||||||
\(697\) | 79.6444 | 3.01675 | ||||||||
\(698\) | −6.78211 | −0.256707 | ||||||||
\(699\) | 18.1383 | 0.686052 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.8750 | −0.826207 | −0.413103 | − | 0.910684i | \(-0.635555\pi\) | ||||
−0.413103 | + | 0.910684i | \(0.635555\pi\) | |||||||
\(702\) | 0.195397 | 0.00737478 | ||||||||
\(703\) | −1.35315 | −0.0510351 | ||||||||
\(704\) | −35.8445 | −1.35094 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.4852 | −0.620428 | ||||||||
\(707\) | −16.6168 | −0.624938 | ||||||||
\(708\) | −3.53221 | −0.132749 | ||||||||
\(709\) | −24.7697 | −0.930246 | −0.465123 | − | 0.885246i | \(-0.653990\pi\) | ||||
−0.465123 | + | 0.885246i | \(0.653990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.22826 | 0.0460633 | ||||||||
\(712\) | −15.6323 | −0.585846 | ||||||||
\(713\) | −6.44342 | −0.241308 | ||||||||
\(714\) | 29.3933 | 1.10002 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.05528 | 0.301040 | ||||||||
\(717\) | 19.5633 | 0.730605 | ||||||||
\(718\) | −17.6647 | −0.659242 | ||||||||
\(719\) | −34.4980 | −1.28656 | −0.643278 | − | 0.765632i | \(-0.722426\pi\) | ||||
−0.643278 | + | 0.765632i | \(0.722426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2458 | −0.381575 | ||||||||
\(722\) | −21.0829 | −0.784625 | ||||||||
\(723\) | −52.8201 | −1.96440 | ||||||||
\(724\) | −3.51087 | −0.130480 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 94.6582 | 3.51310 | ||||||||
\(727\) | 8.46738 | 0.314038 | 0.157019 | − | 0.987596i | \(-0.449812\pi\) | ||||
0.157019 | + | 0.987596i | \(0.449812\pi\) | |||||||
\(728\) | 0.112210 | 0.00415876 | ||||||||
\(729\) | −41.6624 | −1.54305 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.6985 | 0.802548 | ||||||||
\(732\) | 11.8554 | 0.438189 | ||||||||
\(733\) | 8.25993 | 0.305087 | 0.152544 | − | 0.988297i | \(-0.451254\pi\) | ||||
0.152544 | + | 0.988297i | \(0.451254\pi\) | |||||||
\(734\) | −4.83672 | −0.178527 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.97786 | −0.0729049 | ||||||||
\(737\) | 9.29160 | 0.342261 | ||||||||
\(738\) | −69.1816 | −2.54661 | ||||||||
\(739\) | 10.5936 | 0.389690 | 0.194845 | − | 0.980834i | \(-0.437580\pi\) | ||||
0.194845 | + | 0.980834i | \(0.437580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.270990 | −0.00995506 | ||||||||
\(742\) | −8.15904 | −0.299528 | ||||||||
\(743\) | 22.9817 | 0.843117 | 0.421559 | − | 0.906801i | \(-0.361483\pi\) | ||||
0.421559 | + | 0.906801i | \(0.361483\pi\) | |||||||
\(744\) | 43.2982 | 1.58739 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.2005 | −0.519918 | ||||||||
\(747\) | −50.3388 | −1.84180 | ||||||||
\(748\) | 14.8892 | 0.544402 | ||||||||
\(749\) | 14.8612 | 0.543015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.2485 | −1.57816 | −0.789080 | − | 0.614291i | \(-0.789442\pi\) | ||||
−0.789080 | + | 0.614291i | \(0.789442\pi\) | |||||||
\(752\) | −41.6483 | −1.51876 | ||||||||
\(753\) | −36.5746 | −1.33285 | ||||||||
\(754\) | 0.540219 | 0.0196736 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.01367 | −0.0368669 | ||||||||
\(757\) | −2.26509 | −0.0823263 | −0.0411631 | − | 0.999152i | \(-0.513106\pi\) | ||||
−0.0411631 | + | 0.999152i | \(0.513106\pi\) | |||||||
\(758\) | −56.1439 | −2.03924 | ||||||||
\(759\) | −15.5565 | −0.564665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.6486 | −1.50976 | −0.754880 | − | 0.655863i | \(-0.772305\pi\) | ||||
−0.754880 | + | 0.655863i | \(0.772305\pi\) | |||||||
\(762\) | 13.9576 | 0.505631 | ||||||||
\(763\) | 6.48526 | 0.234782 | ||||||||
\(764\) | −2.25970 | −0.0817531 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.1968 | −1.01879 | ||||||||
\(767\) | −0.166824 | −0.00602366 | ||||||||
\(768\) | 21.9107 | 0.790635 | ||||||||
\(769\) | −1.75425 | −0.0632600 | −0.0316300 | − | 0.999500i | \(-0.510070\pi\) | ||||
−0.0316300 | + | 0.999500i | \(0.510070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.76793 | −0.0996845 | ||||||||
\(772\) | 2.82465 | 0.101661 | ||||||||
\(773\) | 51.5019 | 1.85239 | 0.926197 | − | 0.377040i | \(-0.123058\pi\) | ||||
0.926197 | + | 0.377040i | \(0.123058\pi\) | |||||||
\(774\) | −18.8480 | −0.677477 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 38.9272 | 1.39740 | ||||||||
\(777\) | −1.57002 | −0.0563241 | ||||||||
\(778\) | −2.82410 | −0.101249 | ||||||||
\(779\) | 25.3572 | 0.908516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.2816 | 0.511038 | ||||||||
\(782\) | −11.0485 | −0.395093 | ||||||||
\(783\) | 22.7258 | 0.812155 | ||||||||
\(784\) | −4.58212 | −0.163647 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 50.1155 | 1.78756 | ||||||||
\(787\) | −16.3938 | −0.584377 | −0.292189 | − | 0.956361i | \(-0.594383\pi\) | ||||
−0.292189 | + | 0.956361i | \(0.594383\pi\) | |||||||
\(788\) | −6.44616 | −0.229635 | ||||||||
\(789\) | 33.8334 | 1.20450 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.08765 | 0.216452 | ||||||||
\(792\) | 60.2265 | 2.14006 | ||||||||
\(793\) | 0.559923 | 0.0198834 | ||||||||
\(794\) | −47.4065 | −1.68239 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.50196 | −0.159568 | ||||||||
\(797\) | −9.76893 | −0.346033 | −0.173017 | − | 0.984919i | \(-0.555351\pi\) | ||||
−0.173017 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(798\) | 9.35825 | 0.331278 | ||||||||
\(799\) | −65.4592 | −2.31578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.2364 | 0.891686 | ||||||||
\(802\) | −13.8775 | −0.490033 | ||||||||
\(803\) | 6.37905 | 0.225112 | ||||||||
\(804\) | −1.49463 | −0.0527116 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.439138 | −0.0154680 | ||||||||
\(807\) | −49.0341 | −1.72608 | ||||||||
\(808\) | −41.9716 | −1.47655 | ||||||||
\(809\) | 18.1414 | 0.637819 | 0.318910 | − | 0.947785i | \(-0.396683\pi\) | ||||
0.318910 | + | 0.947785i | \(0.396683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.7279 | −0.833199 | −0.416600 | − | 0.909090i | \(-0.636778\pi\) | ||||
−0.416600 | + | 0.909090i | \(0.636778\pi\) | |||||||
\(812\) | −2.80253 | −0.0983495 | ||||||||
\(813\) | −59.2777 | −2.07896 | ||||||||
\(814\) | −5.29406 | −0.185557 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 87.7913 | 3.07331 | ||||||||
\(817\) | 6.90838 | 0.241694 | ||||||||
\(818\) | 14.9275 | 0.521927 | ||||||||
\(819\) | −0.181148 | −0.00632983 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.744129 | 0.0259703 | 0.0129851 | − | 0.999916i | \(-0.495867\pi\) | ||||
0.0129851 | + | 0.999916i | \(0.495867\pi\) | |||||||
\(822\) | 4.95073 | 0.172676 | ||||||||
\(823\) | 8.11920 | 0.283018 | 0.141509 | − | 0.989937i | \(-0.454805\pi\) | ||||
0.141509 | + | 0.989937i | \(0.454805\pi\) | |||||||
\(824\) | −25.8795 | −0.901554 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.76103 | 0.200452 | ||||||||
\(827\) | 37.5943 | 1.30728 | 0.653641 | − | 0.756805i | \(-0.273241\pi\) | ||||
0.653641 | + | 0.756805i | \(0.273241\pi\) | |||||||
\(828\) | 1.44171 | 0.0501028 | ||||||||
\(829\) | 3.27714 | 0.113820 | 0.0569099 | − | 0.998379i | \(-0.481875\pi\) | ||||
0.0569099 | + | 0.998379i | \(0.481875\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 60.2578 | 2.09032 | ||||||||
\(832\) | 0.272318 | 0.00944094 | ||||||||
\(833\) | −7.20179 | −0.249527 | ||||||||
\(834\) | 30.7417 | 1.06450 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.74042 | 0.163951 | ||||||||
\(837\) | −18.4736 | −0.638539 | ||||||||
\(838\) | −10.7348 | −0.370827 | ||||||||
\(839\) | 24.4843 | 0.845291 | 0.422645 | − | 0.906295i | \(-0.361102\pi\) | ||||
0.422645 | + | 0.906295i | \(0.361102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8307 | 1.16658 | ||||||||
\(842\) | −25.3776 | −0.874572 | ||||||||
\(843\) | 49.7829 | 1.71461 | ||||||||
\(844\) | −1.68103 | −0.0578634 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 56.8599 | 1.95488 | ||||||||
\(847\) | −23.1926 | −0.796909 | ||||||||
\(848\) | −24.3693 | −0.836844 | ||||||||
\(849\) | −15.9305 | −0.546732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.590146 | 0.0202300 | ||||||||
\(852\) | −2.29732 | −0.0787049 | ||||||||
\(853\) | 51.6274 | 1.76769 | 0.883844 | − | 0.467782i | \(-0.154947\pi\) | ||||
0.883844 | + | 0.467782i | \(0.154947\pi\) | |||||||
\(854\) | −19.3361 | −0.661669 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 37.5372 | 1.28299 | ||||||||
\(857\) | −12.7598 | −0.435867 | −0.217933 | − | 0.975964i | \(-0.569932\pi\) | ||||
−0.217933 | + | 0.975964i | \(0.569932\pi\) | |||||||
\(858\) | −1.06022 | −0.0361953 | ||||||||
\(859\) | −34.0681 | −1.16239 | −0.581194 | − | 0.813765i | \(-0.697414\pi\) | ||||
−0.581194 | + | 0.813765i | \(0.697414\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.4212 | 1.00267 | ||||||||
\(862\) | 6.18975 | 0.210824 | ||||||||
\(863\) | −0.0669072 | −0.00227755 | −0.00113877 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113877 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(864\) | −5.67061 | −0.192918 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.6789 | 0.566771 | ||||||||
\(867\) | 92.7564 | 3.15017 | ||||||||
\(868\) | 2.27814 | 0.0773252 | ||||||||
\(869\) | −1.76134 | −0.0597495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0705904 | −0.00239186 | ||||||||
\(872\) | 16.3808 | 0.554725 | ||||||||
\(873\) | −62.8431 | −2.12692 | ||||||||
\(874\) | −3.51762 | −0.118985 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.02612 | −0.0346695 | ||||||||
\(877\) | −14.1049 | −0.476289 | −0.238145 | − | 0.971230i | \(-0.576539\pi\) | ||||
−0.238145 | + | 0.971230i | \(0.576539\pi\) | |||||||
\(878\) | 34.5680 | 1.16661 | ||||||||
\(879\) | 62.6731 | 2.11391 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.314739 | 0.0106038 | 0.00530191 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530191 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(882\) | 6.25569 | 0.210640 | ||||||||
\(883\) | −29.6381 | −0.997400 | −0.498700 | − | 0.866775i | \(-0.666189\pi\) | ||||
−0.498700 | + | 0.866775i | \(0.666189\pi\) | |||||||
\(884\) | −0.113116 | −0.00380452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −62.5977 | −2.10301 | ||||||||
\(887\) | −12.9347 | −0.434305 | −0.217153 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217153 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(888\) | −3.96564 | −0.133078 | ||||||||
\(889\) | −3.41982 | −0.114697 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.9309 | 0.902219 | ||||||||
\(892\) | −9.39997 | −0.314734 | ||||||||
\(893\) | −20.8409 | −0.697415 | ||||||||
\(894\) | −9.16892 | −0.306655 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.3598 | −0.446321 | ||||||||
\(897\) | 0.118186 | 0.00394612 | ||||||||
\(898\) | 59.6453 | 1.99039 | ||||||||
\(899\) | −51.0743 | −1.70342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.3015 | −1.27601 | ||||||||
\(902\) | 99.2074 | 3.30325 | ||||||||
\(903\) | 8.01558 | 0.266742 | ||||||||
\(904\) | 15.3765 | 0.511416 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −56.9936 | −1.89349 | ||||||||
\(907\) | −39.6205 | −1.31558 | −0.657789 | − | 0.753203i | \(-0.728508\pi\) | ||||
−0.657789 | + | 0.753203i | \(0.728508\pi\) | |||||||
\(908\) | 1.33204 | 0.0442055 | ||||||||
\(909\) | 67.7579 | 2.24739 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.9218 | −1.05762 | −0.528809 | − | 0.848741i | \(-0.677361\pi\) | ||||
−0.528809 | + | 0.848741i | \(0.677361\pi\) | |||||||
\(912\) | 27.9510 | 0.925551 | ||||||||
\(913\) | 72.1866 | 2.38903 | ||||||||
\(914\) | 36.1928 | 1.19715 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.77930 | −0.157913 | ||||||||
\(917\) | −12.2790 | −0.405489 | ||||||||
\(918\) | −31.6765 | −1.04548 | ||||||||
\(919\) | 8.96185 | 0.295624 | 0.147812 | − | 0.989015i | \(-0.452777\pi\) | ||||
0.147812 | + | 0.989015i | \(0.452777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −81.2868 | −2.67849 | ||||||||
\(922\) | 20.6087 | 0.678712 | ||||||||
\(923\) | −0.108501 | −0.00357135 | ||||||||
\(924\) | 5.50017 | 0.180942 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 53.8406 | 1.76931 | ||||||||
\(927\) | 41.7792 | 1.37221 | ||||||||
\(928\) | −15.6777 | −0.514645 | ||||||||
\(929\) | −22.5482 | −0.739782 | −0.369891 | − | 0.929075i | \(-0.620605\pi\) | ||||
−0.369891 | + | 0.929075i | \(0.620605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.29291 | −0.0751470 | ||||||||
\(932\) | 2.41054 | 0.0789599 | ||||||||
\(933\) | 34.2573 | 1.12153 | ||||||||
\(934\) | −45.1888 | −1.47862 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.457554 | −0.0149556 | ||||||||
\(937\) | 15.5669 | 0.508547 | 0.254274 | − | 0.967132i | \(-0.418164\pi\) | ||||
0.254274 | + | 0.967132i | \(0.418164\pi\) | |||||||
\(938\) | 2.43774 | 0.0795950 | ||||||||
\(939\) | 69.0780 | 2.25428 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.7677 | −0.742207 | −0.371103 | − | 0.928592i | \(-0.621020\pi\) | ||||
−0.371103 | + | 0.928592i | \(0.621020\pi\) | |||||||
\(942\) | −0.367289 | −0.0119669 | ||||||||
\(943\) | −11.0590 | −0.360130 | ||||||||
\(944\) | 17.2069 | 0.560038 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.0283 | 0.878766 | ||||||||
\(947\) | 31.4177 | 1.02094 | 0.510469 | − | 0.859896i | \(-0.329472\pi\) | ||||
0.510469 | + | 0.859896i | \(0.329472\pi\) | |||||||
\(948\) | 0.283326 | 0.00920201 | ||||||||
\(949\) | −0.0484631 | −0.00157318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.3246 | 0.432080 | ||||||||
\(952\) | −18.1907 | −0.589563 | ||||||||
\(953\) | 26.8729 | 0.870499 | 0.435249 | − | 0.900310i | \(-0.356660\pi\) | ||||
0.435249 | + | 0.900310i | \(0.356660\pi\) | |||||||
\(954\) | 33.2699 | 1.07715 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.59993 | 0.0840876 | ||||||||
\(957\) | −123.310 | −3.98604 | ||||||||
\(958\) | 42.4100 | 1.37021 | ||||||||
\(959\) | −1.21300 | −0.0391698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5177 | 0.339280 | ||||||||
\(962\) | 0.0402202 | 0.00129675 | ||||||||
\(963\) | −60.5990 | −1.95278 | ||||||||
\(964\) | −7.01969 | −0.226089 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.08139 | −0.131317 | ||||||||
\(967\) | −17.7697 | −0.571436 | −0.285718 | − | 0.958314i | \(-0.592232\pi\) | ||||
−0.285718 | + | 0.958314i | \(0.592232\pi\) | |||||||
\(968\) | −58.5813 | −1.88287 | ||||||||
\(969\) | 43.9311 | 1.41127 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.7925 | 1.72628 | 0.863141 | − | 0.504962i | \(-0.168494\pi\) | ||||
0.863141 | + | 0.504962i | \(0.168494\pi\) | |||||||
\(972\) | −7.37308 | −0.236492 | ||||||||
\(973\) | −7.53216 | −0.241470 | ||||||||
\(974\) | 16.2168 | 0.519621 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.7528 | −1.84862 | ||||||||
\(977\) | −57.8020 | −1.84925 | −0.924625 | − | 0.380878i | \(-0.875622\pi\) | ||||
−0.924625 | + | 0.380878i | \(0.875622\pi\) | |||||||
\(978\) | −30.7472 | −0.983187 | ||||||||
\(979\) | −36.1894 | −1.15662 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.4448 | −0.844317 | ||||||||
\(982\) | −18.0656 | −0.576497 | ||||||||
\(983\) | −11.4133 | −0.364027 | −0.182014 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182014 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(984\) | 74.3137 | 2.36903 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −87.5768 | −2.78901 | ||||||||
\(987\) | −24.1811 | −0.769693 | ||||||||
\(988\) | −0.0360141 | −0.00114576 | ||||||||
\(989\) | −3.01294 | −0.0958058 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8328 | −0.725307 | −0.362654 | − | 0.931924i | \(-0.618129\pi\) | ||||
−0.362654 | + | 0.931924i | \(0.618129\pi\) | |||||||
\(992\) | 12.7442 | 0.404629 | ||||||||
\(993\) | −78.7799 | −2.50001 | ||||||||
\(994\) | 3.74692 | 0.118845 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.6118 | −0.367934 | ||||||||
\(997\) | 4.70495 | 0.149007 | 0.0745037 | − | 0.997221i | \(-0.476263\pi\) | ||||
0.0745037 | + | 0.997221i | \(0.476263\pi\) | |||||||
\(998\) | 30.4259 | 0.963115 | ||||||||
\(999\) | 1.69197 | 0.0535317 |
(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 | 4025.2.a.y.1.10 | 12 | ||
5.2 | odd | 4 | 805.2.c.b.484.19 | yes | 24 | ||
5.3 | odd | 4 | 805.2.c.b.484.6 | ✓ | 24 | ||
5.4 | even | 2 | 4025.2.a.x.1.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.b.484.6 | ✓ | 24 | 5.3 | odd | 4 | ||
805.2.c.b.484.19 | yes | 24 | 5.2 | odd | 4 | ||
4025.2.a.x.1.3 | 12 | 5.4 | even | 2 | |||
4025.2.a.y.1.10 | 12 | 1.1 | even | 1 | trivial |