Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 6x^{2} + 7x + 11 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70636 | −1.91369 | −0.956844 | − | 0.290604i | \(-0.906144\pi\) | ||||
−0.956844 | + | 0.290604i | \(0.906144\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.32440 | 2.66220 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.70636 | 1.10487 | ||||||||
\(7\) | −0.470294 | −0.177754 | −0.0888772 | − | 0.996043i | \(-0.528328\pi\) | ||||
−0.0888772 | + | 0.996043i | \(0.528328\pi\) | |||||||
\(8\) | −8.99702 | −3.18093 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.18148 | −0.959252 | −0.479626 | − | 0.877473i | \(-0.659228\pi\) | ||||
−0.479626 | + | 0.877473i | \(0.659228\pi\) | |||||||
\(12\) | −5.32440 | −1.53702 | ||||||||
\(13\) | −0.563444 | −0.156271 | −0.0781356 | − | 0.996943i | \(-0.524897\pi\) | ||||
−0.0781356 | + | 0.996943i | \(0.524897\pi\) | |||||||
\(14\) | 1.27279 | 0.340166 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.7004 | 3.42510 | ||||||||
\(17\) | 1.70636 | 0.413854 | 0.206927 | − | 0.978356i | \(-0.433654\pi\) | ||||
0.206927 | + | 0.978356i | \(0.433654\pi\) | |||||||
\(18\) | −2.70636 | −0.637896 | ||||||||
\(19\) | 3.74010 | 0.858038 | 0.429019 | − | 0.903295i | \(-0.358859\pi\) | ||||
0.429019 | + | 0.903295i | \(0.358859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.470294 | 0.102627 | ||||||||
\(22\) | 8.61023 | 1.83571 | ||||||||
\(23\) | 2.26981 | 0.473287 | 0.236644 | − | 0.971597i | \(-0.423953\pi\) | ||||
0.236644 | + | 0.971597i | \(0.423953\pi\) | |||||||
\(24\) | 8.99702 | 1.83651 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.52488 | 0.299054 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.50403 | −0.473218 | ||||||||
\(29\) | −8.32440 | −1.54580 | −0.772901 | − | 0.634527i | \(-0.781195\pi\) | ||||
−0.772901 | + | 0.634527i | \(0.781195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.43656 | 0.976434 | 0.488217 | − | 0.872722i | \(-0.337647\pi\) | ||||
0.488217 | + | 0.872722i | \(0.337647\pi\) | |||||||
\(32\) | −19.0842 | −3.37364 | ||||||||
\(33\) | 3.18148 | 0.553824 | ||||||||
\(34\) | −4.61803 | −0.791986 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.32440 | 0.887399 | ||||||||
\(37\) | −1.02085 | −0.167827 | −0.0839135 | − | 0.996473i | \(-0.526742\pi\) | ||||
−0.0839135 | + | 0.996473i | \(0.526742\pi\) | |||||||
\(38\) | −10.1221 | −1.64202 | ||||||||
\(39\) | 0.563444 | 0.0902233 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47214 | 0.229909 | 0.114955 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114955 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(42\) | −1.27279 | −0.196395 | ||||||||
\(43\) | −6.72721 | −1.02589 | −0.512945 | − | 0.858421i | \(-0.671446\pi\) | ||||
−0.512945 | + | 0.858421i | \(0.671446\pi\) | |||||||
\(44\) | −16.9395 | −2.55372 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.14292 | −0.905724 | ||||||||
\(47\) | 4.43358 | 0.646703 | 0.323352 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323352 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(48\) | −13.7004 | −1.97748 | ||||||||
\(49\) | −6.77882 | −0.968403 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70636 | −0.238938 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | 7.05161 | 0.968613 | 0.484307 | − | 0.874898i | \(-0.339072\pi\) | ||||
0.484307 | + | 0.874898i | \(0.339072\pi\) | |||||||
\(54\) | 2.70636 | 0.368289 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.23125 | 0.565424 | ||||||||
\(57\) | −3.74010 | −0.495388 | ||||||||
\(58\) | 22.5288 | 2.95818 | ||||||||
\(59\) | −12.8720 | −1.67579 | −0.837894 | − | 0.545833i | \(-0.816213\pi\) | ||||
−0.837894 | + | 0.545833i | \(0.816213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.126888 | 0.0162464 | 0.00812319 | − | 0.999967i | \(-0.497414\pi\) | ||||
0.00812319 | + | 0.999967i | \(0.497414\pi\) | |||||||
\(62\) | −14.7133 | −1.86859 | ||||||||
\(63\) | −0.470294 | −0.0592515 | ||||||||
\(64\) | 24.2480 | 3.03100 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.61023 | −1.05985 | ||||||||
\(67\) | 2.79469 | 0.341426 | 0.170713 | − | 0.985321i | \(-0.445393\pi\) | ||||
0.170713 | + | 0.985321i | \(0.445393\pi\) | |||||||
\(68\) | 9.08535 | 1.10176 | ||||||||
\(69\) | −2.26981 | −0.273253 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0456 | 1.90427 | 0.952134 | − | 0.305681i | \(-0.0988839\pi\) | ||||
0.952134 | + | 0.305681i | \(0.0988839\pi\) | |||||||
\(72\) | −8.99702 | −1.06031 | ||||||||
\(73\) | 9.78873 | 1.14568 | 0.572842 | − | 0.819666i | \(-0.305841\pi\) | ||||
0.572842 | + | 0.819666i | \(0.305841\pi\) | |||||||
\(74\) | 2.76279 | 0.321168 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.9138 | 2.28427 | ||||||||
\(77\) | 1.49623 | 0.170511 | ||||||||
\(78\) | −1.52488 | −0.172659 | ||||||||
\(79\) | −4.75499 | −0.534978 | −0.267489 | − | 0.963561i | \(-0.586194\pi\) | ||||
−0.267489 | + | 0.963561i | \(0.586194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.98413 | −0.439974 | ||||||||
\(83\) | −11.6905 | −1.28320 | −0.641599 | − | 0.767040i | \(-0.721729\pi\) | ||||
−0.641599 | + | 0.767040i | \(0.721729\pi\) | |||||||
\(84\) | 2.50403 | 0.273212 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.2063 | 1.96323 | ||||||||
\(87\) | 8.32440 | 0.892469 | ||||||||
\(88\) | 28.6238 | 3.05131 | ||||||||
\(89\) | −6.20049 | −0.657250 | −0.328625 | − | 0.944460i | \(-0.606585\pi\) | ||||
−0.328625 | + | 0.944460i | \(0.606585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.264985 | 0.0277779 | ||||||||
\(92\) | 12.0853 | 1.25998 | ||||||||
\(93\) | −5.43656 | −0.563745 | ||||||||
\(94\) | −11.9989 | −1.23759 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 19.0842 | 1.94777 | ||||||||
\(97\) | −8.45443 | −0.858417 | −0.429209 | − | 0.903205i | \(-0.641207\pi\) | ||||
−0.429209 | + | 0.903205i | \(0.641207\pi\) | |||||||
\(98\) | 18.3460 | 1.85322 | ||||||||
\(99\) | −3.18148 | −0.319751 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.83325 | −0.580430 | −0.290215 | − | 0.956961i | \(-0.593727\pi\) | ||||
−0.290215 | + | 0.956961i | \(0.593727\pi\) | |||||||
\(102\) | 4.61803 | 0.457254 | ||||||||
\(103\) | 14.0794 | 1.38728 | 0.693642 | − | 0.720320i | \(-0.256005\pi\) | ||||
0.693642 | + | 0.720320i | \(0.256005\pi\) | |||||||
\(104\) | 5.06932 | 0.497088 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.0842 | −1.85362 | ||||||||
\(107\) | 8.61207 | 0.832561 | 0.416280 | − | 0.909236i | \(-0.363334\pi\) | ||||
0.416280 | + | 0.909236i | \(0.363334\pi\) | |||||||
\(108\) | −5.32440 | −0.512340 | ||||||||
\(109\) | 16.6875 | 1.59837 | 0.799187 | − | 0.601082i | \(-0.205264\pi\) | ||||
0.799187 | + | 0.601082i | \(0.205264\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.02085 | 0.0968949 | ||||||||
\(112\) | −6.44322 | −0.608827 | ||||||||
\(113\) | −11.7758 | −1.10778 | −0.553889 | − | 0.832590i | \(-0.686857\pi\) | ||||
−0.553889 | + | 0.832590i | \(0.686857\pi\) | |||||||
\(114\) | 10.1221 | 0.948018 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −44.3224 | −4.11523 | ||||||||
\(117\) | −0.563444 | −0.0520904 | ||||||||
\(118\) | 34.8362 | 3.20693 | ||||||||
\(119\) | −0.802492 | −0.0735643 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.878197 | −0.0798361 | ||||||||
\(122\) | −0.343406 | −0.0310905 | ||||||||
\(123\) | −1.47214 | −0.132738 | ||||||||
\(124\) | 28.9464 | 2.59946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.27279 | 0.113389 | ||||||||
\(127\) | −1.77882 | −0.157845 | −0.0789225 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789225 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(128\) | −27.4554 | −2.42674 | ||||||||
\(129\) | 6.72721 | 0.592298 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.91860 | −0.517110 | −0.258555 | − | 0.965996i | \(-0.583246\pi\) | ||||
−0.258555 | + | 0.965996i | \(0.583246\pi\) | |||||||
\(132\) | 16.9395 | 1.47439 | ||||||||
\(133\) | −1.75895 | −0.152520 | ||||||||
\(134\) | −7.56344 | −0.653382 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.3522 | −1.31644 | ||||||||
\(137\) | 5.11611 | 0.437098 | 0.218549 | − | 0.975826i | \(-0.429868\pi\) | ||||
0.218549 | + | 0.975826i | \(0.429868\pi\) | |||||||
\(138\) | 6.14292 | 0.522920 | ||||||||
\(139\) | −8.23817 | −0.698753 | −0.349376 | − | 0.936982i | \(-0.613607\pi\) | ||||
−0.349376 | + | 0.936982i | \(0.613607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.43358 | −0.373374 | ||||||||
\(142\) | −43.4253 | −3.64417 | ||||||||
\(143\) | 1.79259 | 0.149904 | ||||||||
\(144\) | 13.7004 | 1.14170 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26.4918 | −2.19248 | ||||||||
\(147\) | 6.77882 | 0.559108 | ||||||||
\(148\) | −5.43542 | −0.446789 | ||||||||
\(149\) | −10.0585 | −0.824027 | −0.412014 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412014 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9810 | −0.974999 | −0.487500 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487500 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(152\) | −33.6498 | −2.72936 | ||||||||
\(153\) | 1.70636 | 0.137951 | ||||||||
\(154\) | −4.04934 | −0.326305 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | −19.5960 | −1.56393 | −0.781967 | − | 0.623319i | \(-0.785784\pi\) | ||||
−0.781967 | + | 0.623319i | \(0.785784\pi\) | |||||||
\(158\) | 12.8687 | 1.02378 | ||||||||
\(159\) | −7.05161 | −0.559229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.06748 | −0.0841290 | ||||||||
\(162\) | −2.70636 | −0.212632 | ||||||||
\(163\) | −11.8927 | −0.931505 | −0.465753 | − | 0.884915i | \(-0.654216\pi\) | ||||
−0.465753 | + | 0.884915i | \(0.654216\pi\) | |||||||
\(164\) | 7.83824 | 0.612063 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 31.6387 | 2.45564 | ||||||||
\(167\) | 5.99378 | 0.463812 | 0.231906 | − | 0.972738i | \(-0.425504\pi\) | ||||
0.231906 | + | 0.972738i | \(0.425504\pi\) | |||||||
\(168\) | −4.23125 | −0.326448 | ||||||||
\(169\) | −12.6825 | −0.975579 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.74010 | 0.286013 | ||||||||
\(172\) | −35.8184 | −2.73112 | ||||||||
\(173\) | −17.3244 | −1.31715 | −0.658575 | − | 0.752515i | \(-0.728840\pi\) | ||||
−0.658575 | + | 0.752515i | \(0.728840\pi\) | |||||||
\(174\) | −22.5288 | −1.70791 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −43.5875 | −3.28553 | ||||||||
\(177\) | 12.8720 | 0.967517 | ||||||||
\(178\) | 16.7808 | 1.25777 | ||||||||
\(179\) | 10.5765 | 0.790524 | 0.395262 | − | 0.918568i | \(-0.370654\pi\) | ||||
0.395262 | + | 0.918568i | \(0.370654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9799 | 0.890455 | 0.445228 | − | 0.895417i | \(-0.353123\pi\) | ||||
0.445228 | + | 0.895417i | \(0.353123\pi\) | |||||||
\(182\) | −0.717144 | −0.0531583 | ||||||||
\(183\) | −0.126888 | −0.00937986 | ||||||||
\(184\) | −20.4215 | −1.50549 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.7133 | 1.07883 | ||||||||
\(187\) | −5.42875 | −0.396990 | ||||||||
\(188\) | 23.6061 | 1.72165 | ||||||||
\(189\) | 0.470294 | 0.0342089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2657 | 1.32166 | 0.660829 | − | 0.750536i | \(-0.270205\pi\) | ||||
0.660829 | + | 0.750536i | \(0.270205\pi\) | |||||||
\(192\) | −24.2480 | −1.74995 | ||||||||
\(193\) | −25.2063 | −1.81439 | −0.907194 | − | 0.420713i | \(-0.861780\pi\) | ||||
−0.907194 | + | 0.420713i | \(0.861780\pi\) | |||||||
\(194\) | 22.8807 | 1.64274 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −36.0931 | −2.57808 | ||||||||
\(197\) | −12.0923 | −0.861539 | −0.430769 | − | 0.902462i | \(-0.641758\pi\) | ||||
−0.430769 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(198\) | 8.61023 | 0.611903 | ||||||||
\(199\) | −0.544434 | −0.0385939 | −0.0192970 | − | 0.999814i | \(-0.506143\pi\) | ||||
−0.0192970 | + | 0.999814i | \(0.506143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.79469 | −0.197122 | ||||||||
\(202\) | 15.7869 | 1.11076 | ||||||||
\(203\) | 3.91492 | 0.274773 | ||||||||
\(204\) | −9.08535 | −0.636102 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −38.1039 | −2.65483 | ||||||||
\(207\) | 2.26981 | 0.157762 | ||||||||
\(208\) | −7.71941 | −0.535245 | ||||||||
\(209\) | −11.8990 | −0.823074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.12207 | −0.214932 | −0.107466 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107466 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(212\) | 37.5456 | 2.57864 | ||||||||
\(213\) | −16.0456 | −1.09943 | ||||||||
\(214\) | −23.3074 | −1.59326 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.99702 | 0.612170 | ||||||||
\(217\) | −2.55678 | −0.173566 | ||||||||
\(218\) | −45.1625 | −3.05879 | ||||||||
\(219\) | −9.78873 | −0.661461 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.961440 | −0.0646734 | ||||||||
\(222\) | −2.76279 | −0.185427 | ||||||||
\(223\) | −0.339125 | −0.0227095 | −0.0113547 | − | 0.999936i | \(-0.503614\pi\) | ||||
−0.0113547 | + | 0.999936i | \(0.503614\pi\) | |||||||
\(224\) | 8.97519 | 0.599680 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.8697 | 2.11994 | ||||||||
\(227\) | 1.78847 | 0.118705 | 0.0593524 | − | 0.998237i | \(-0.481096\pi\) | ||||
0.0593524 | + | 0.998237i | \(0.481096\pi\) | |||||||
\(228\) | −19.9138 | −1.31882 | ||||||||
\(229\) | −27.9833 | −1.84919 | −0.924593 | − | 0.380957i | \(-0.875595\pi\) | ||||
−0.924593 | + | 0.380957i | \(0.875595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.49623 | −0.0984448 | ||||||||
\(232\) | 74.8948 | 4.91708 | ||||||||
\(233\) | 6.77400 | 0.443780 | 0.221890 | − | 0.975072i | \(-0.428777\pi\) | ||||
0.221890 | + | 0.975072i | \(0.428777\pi\) | |||||||
\(234\) | 1.52488 | 0.0996848 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −68.5355 | −4.46128 | ||||||||
\(237\) | 4.75499 | 0.308870 | ||||||||
\(238\) | 2.17183 | 0.140779 | ||||||||
\(239\) | −6.48334 | −0.419373 | −0.209686 | − | 0.977769i | \(-0.567244\pi\) | ||||
−0.209686 | + | 0.977769i | \(0.567244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.44857 | −0.479804 | −0.239902 | − | 0.970797i | \(-0.577115\pi\) | ||||
−0.239902 | + | 0.970797i | \(0.577115\pi\) | |||||||
\(242\) | 2.37672 | 0.152781 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.675604 | 0.0432511 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.98413 | 0.254019 | ||||||||
\(247\) | −2.10734 | −0.134087 | ||||||||
\(248\) | −48.9128 | −3.10597 | ||||||||
\(249\) | 11.6905 | 0.740855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.60217 | −0.290486 | −0.145243 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145243 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(252\) | −2.50403 | −0.157739 | ||||||||
\(253\) | −7.22134 | −0.454002 | ||||||||
\(254\) | 4.81414 | 0.302066 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 25.8083 | 1.61302 | ||||||||
\(257\) | 5.79485 | 0.361473 | 0.180736 | − | 0.983532i | \(-0.442152\pi\) | ||||
0.180736 | + | 0.983532i | \(0.442152\pi\) | |||||||
\(258\) | −18.2063 | −1.13347 | ||||||||
\(259\) | 0.480101 | 0.0298320 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.32440 | −0.515267 | ||||||||
\(262\) | 16.0179 | 0.989587 | ||||||||
\(263\) | −14.2989 | −0.881707 | −0.440854 | − | 0.897579i | \(-0.645324\pi\) | ||||
−0.440854 | + | 0.897579i | \(0.645324\pi\) | |||||||
\(264\) | −28.6238 | −1.76167 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.76035 | 0.291876 | ||||||||
\(267\) | 6.20049 | 0.379464 | ||||||||
\(268\) | 14.8800 | 0.908943 | ||||||||
\(269\) | −19.2205 | −1.17189 | −0.585946 | − | 0.810350i | \(-0.699277\pi\) | ||||
−0.585946 | + | 0.810350i | \(0.699277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2433 | −1.41193 | −0.705964 | − | 0.708248i | \(-0.749486\pi\) | ||||
−0.705964 | + | 0.708248i | \(0.749486\pi\) | |||||||
\(272\) | 23.3778 | 1.41749 | ||||||||
\(273\) | −0.264985 | −0.0160376 | ||||||||
\(274\) | −13.8460 | −0.836470 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.0853 | −0.727452 | ||||||||
\(277\) | −21.8910 | −1.31530 | −0.657651 | − | 0.753323i | \(-0.728450\pi\) | ||||
−0.657651 | + | 0.753323i | \(0.728450\pi\) | |||||||
\(278\) | 22.2955 | 1.33719 | ||||||||
\(279\) | 5.43656 | 0.325478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1138 | 1.61748 | 0.808738 | − | 0.588169i | \(-0.200151\pi\) | ||||
0.808738 | + | 0.588169i | \(0.200151\pi\) | |||||||
\(282\) | 11.9989 | 0.714522 | ||||||||
\(283\) | −16.3074 | −0.969374 | −0.484687 | − | 0.874688i | \(-0.661066\pi\) | ||||
−0.484687 | + | 0.874688i | \(0.661066\pi\) | |||||||
\(284\) | 85.4334 | 5.06954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.85139 | −0.286868 | ||||||||
\(287\) | −0.692337 | −0.0408674 | ||||||||
\(288\) | −19.0842 | −1.12455 | ||||||||
\(289\) | −14.0883 | −0.828725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.45443 | 0.495607 | ||||||||
\(292\) | 52.1191 | 3.05004 | ||||||||
\(293\) | −5.46407 | −0.319214 | −0.159607 | − | 0.987181i | \(-0.551023\pi\) | ||||
−0.159607 | + | 0.987181i | \(0.551023\pi\) | |||||||
\(294\) | −18.3460 | −1.06996 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.18462 | 0.533845 | ||||||||
\(297\) | 3.18148 | 0.184608 | ||||||||
\(298\) | 27.2220 | 1.57693 | ||||||||
\(299\) | −1.27891 | −0.0739612 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.16377 | 0.182357 | ||||||||
\(302\) | 32.4249 | 1.86584 | ||||||||
\(303\) | 5.83325 | 0.335111 | ||||||||
\(304\) | 51.2409 | 2.93887 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.61803 | −0.263995 | ||||||||
\(307\) | 21.4194 | 1.22247 | 0.611235 | − | 0.791450i | \(-0.290673\pi\) | ||||
0.611235 | + | 0.791450i | \(0.290673\pi\) | |||||||
\(308\) | 7.96652 | 0.453935 | ||||||||
\(309\) | −14.0794 | −0.800948 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.85200 | −0.161722 | −0.0808610 | − | 0.996725i | \(-0.525767\pi\) | ||||
−0.0808610 | + | 0.996725i | \(0.525767\pi\) | |||||||
\(312\) | −5.06932 | −0.286994 | ||||||||
\(313\) | −14.4375 | −0.816057 | −0.408029 | − | 0.912969i | \(-0.633784\pi\) | ||||
−0.408029 | + | 0.912969i | \(0.633784\pi\) | |||||||
\(314\) | 53.0340 | 2.99288 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.3175 | −1.42422 | ||||||||
\(317\) | −22.6102 | −1.26992 | −0.634959 | − | 0.772546i | \(-0.718983\pi\) | ||||
−0.634959 | + | 0.772546i | \(0.718983\pi\) | |||||||
\(318\) | 19.0842 | 1.07019 | ||||||||
\(319\) | 26.4839 | 1.48281 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.61207 | −0.480679 | ||||||||
\(322\) | 2.88898 | 0.160996 | ||||||||
\(323\) | 6.38197 | 0.355102 | ||||||||
\(324\) | 5.32440 | 0.295800 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.1859 | 1.78261 | ||||||||
\(327\) | −16.6875 | −0.922822 | ||||||||
\(328\) | −13.2448 | −0.731324 | ||||||||
\(329\) | −2.08508 | −0.114954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.86645 | 0.212519 | 0.106260 | − | 0.994338i | \(-0.466113\pi\) | ||||
0.106260 | + | 0.994338i | \(0.466113\pi\) | |||||||
\(332\) | −62.2448 | −3.41613 | ||||||||
\(333\) | −1.02085 | −0.0559423 | ||||||||
\(334\) | −16.2213 | −0.887592 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.44322 | 0.351506 | ||||||||
\(337\) | −17.4853 | −0.952484 | −0.476242 | − | 0.879314i | \(-0.658001\pi\) | ||||
−0.476242 | + | 0.879314i | \(0.658001\pi\) | |||||||
\(338\) | 34.3235 | 1.86695 | ||||||||
\(339\) | 11.7758 | 0.639576 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2963 | −0.936646 | ||||||||
\(342\) | −10.1221 | −0.547339 | ||||||||
\(343\) | 6.48010 | 0.349893 | ||||||||
\(344\) | 60.5249 | 3.26328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 46.8861 | 2.52061 | ||||||||
\(347\) | 23.0941 | 1.23976 | 0.619879 | − | 0.784698i | \(-0.287182\pi\) | ||||
0.619879 | + | 0.784698i | \(0.287182\pi\) | |||||||
\(348\) | 44.3224 | 2.37593 | ||||||||
\(349\) | −9.32650 | −0.499236 | −0.249618 | − | 0.968344i | \(-0.580305\pi\) | ||||
−0.249618 | + | 0.968344i | \(0.580305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.563444 | 0.0300744 | ||||||||
\(352\) | 60.7160 | 3.23617 | ||||||||
\(353\) | −31.9471 | −1.70037 | −0.850186 | − | 0.526483i | \(-0.823510\pi\) | ||||
−0.850186 | + | 0.526483i | \(0.823510\pi\) | |||||||
\(354\) | −34.8362 | −1.85152 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −33.0139 | −1.74973 | ||||||||
\(357\) | 0.802492 | 0.0424724 | ||||||||
\(358\) | −28.6238 | −1.51282 | ||||||||
\(359\) | −9.58954 | −0.506117 | −0.253058 | − | 0.967451i | \(-0.581436\pi\) | ||||
−0.253058 | + | 0.967451i | \(0.581436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.01165 | −0.263771 | ||||||||
\(362\) | −32.4218 | −1.70405 | ||||||||
\(363\) | 0.878197 | 0.0460934 | ||||||||
\(364\) | 1.41088 | 0.0739503 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.343406 | 0.0179501 | ||||||||
\(367\) | −1.06423 | −0.0555525 | −0.0277763 | − | 0.999614i | \(-0.508843\pi\) | ||||
−0.0277763 | + | 0.999614i | \(0.508843\pi\) | |||||||
\(368\) | 31.0973 | 1.62106 | ||||||||
\(369\) | 1.47214 | 0.0766363 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.31633 | −0.172175 | ||||||||
\(372\) | −28.9464 | −1.50080 | ||||||||
\(373\) | 4.12022 | 0.213337 | 0.106669 | − | 0.994295i | \(-0.465982\pi\) | ||||
0.106669 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(374\) | 14.6922 | 0.759714 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −39.8890 | −2.05712 | ||||||||
\(377\) | 4.69033 | 0.241564 | ||||||||
\(378\) | −1.27279 | −0.0654651 | ||||||||
\(379\) | 10.3563 | 0.531967 | 0.265984 | − | 0.963978i | \(-0.414303\pi\) | ||||
0.265984 | + | 0.963978i | \(0.414303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.77882 | 0.0911319 | ||||||||
\(382\) | −49.4336 | −2.52924 | ||||||||
\(383\) | −1.19935 | −0.0612839 | −0.0306420 | − | 0.999530i | \(-0.509755\pi\) | ||||
−0.0306420 | + | 0.999530i | \(0.509755\pi\) | |||||||
\(384\) | 27.4554 | 1.40108 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 68.2173 | 3.47217 | ||||||||
\(387\) | −6.72721 | −0.341963 | ||||||||
\(388\) | −45.0147 | −2.28528 | ||||||||
\(389\) | 12.6043 | 0.639062 | 0.319531 | − | 0.947576i | \(-0.396475\pi\) | ||||
0.319531 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.87311 | 0.195872 | ||||||||
\(392\) | 60.9892 | 3.08042 | ||||||||
\(393\) | 5.91860 | 0.298554 | ||||||||
\(394\) | 32.7261 | 1.64872 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.9395 | −0.851239 | ||||||||
\(397\) | 1.31335 | 0.0659152 | 0.0329576 | − | 0.999457i | \(-0.489507\pi\) | ||||
0.0329576 | + | 0.999457i | \(0.489507\pi\) | |||||||
\(398\) | 1.47344 | 0.0738567 | ||||||||
\(399\) | 1.75895 | 0.0880575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.1042 | 0.804205 | 0.402102 | − | 0.915595i | \(-0.368280\pi\) | ||||
0.402102 | + | 0.915595i | \(0.368280\pi\) | |||||||
\(402\) | 7.56344 | 0.377230 | ||||||||
\(403\) | −3.06320 | −0.152589 | ||||||||
\(404\) | −31.0585 | −1.54522 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.5952 | −0.525830 | ||||||||
\(407\) | 3.24782 | 0.160988 | ||||||||
\(408\) | 15.3522 | 0.760046 | ||||||||
\(409\) | 21.1600 | 1.04630 | 0.523148 | − | 0.852242i | \(-0.324758\pi\) | ||||
0.523148 | + | 0.852242i | \(0.324758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.11611 | −0.252359 | ||||||||
\(412\) | 74.9642 | 3.69322 | ||||||||
\(413\) | 6.05361 | 0.297879 | ||||||||
\(414\) | −6.14292 | −0.301908 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.7529 | 0.527204 | ||||||||
\(417\) | 8.23817 | 0.403425 | ||||||||
\(418\) | 32.2031 | 1.57511 | ||||||||
\(419\) | −6.67094 | −0.325897 | −0.162948 | − | 0.986635i | \(-0.552100\pi\) | ||||
−0.162948 | + | 0.986635i | \(0.552100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2980 | 1.33042 | 0.665212 | − | 0.746655i | \(-0.268341\pi\) | ||||
0.665212 | + | 0.746655i | \(0.268341\pi\) | |||||||
\(422\) | 8.44944 | 0.411312 | ||||||||
\(423\) | 4.43358 | 0.215568 | ||||||||
\(424\) | −63.4435 | −3.08109 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 43.4253 | 2.10396 | ||||||||
\(427\) | −0.0596749 | −0.00288787 | ||||||||
\(428\) | 45.8541 | 2.21644 | ||||||||
\(429\) | −1.79259 | −0.0865468 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2974 | 0.592346 | 0.296173 | − | 0.955134i | \(-0.404290\pi\) | ||||
0.296173 | + | 0.955134i | \(0.404290\pi\) | |||||||
\(432\) | −13.7004 | −0.659161 | ||||||||
\(433\) | 33.8452 | 1.62649 | 0.813247 | − | 0.581918i | \(-0.197698\pi\) | ||||
0.813247 | + | 0.581918i | \(0.197698\pi\) | |||||||
\(434\) | 6.91957 | 0.332150 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 88.8509 | 4.25519 | ||||||||
\(437\) | 8.48930 | 0.406098 | ||||||||
\(438\) | 26.4918 | 1.26583 | ||||||||
\(439\) | −20.9654 | −1.00062 | −0.500312 | − | 0.865845i | \(-0.666781\pi\) | ||||
−0.500312 | + | 0.865845i | \(0.666781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.77882 | −0.322801 | ||||||||
\(442\) | 2.60200 | 0.123765 | ||||||||
\(443\) | −6.04847 | −0.287371 | −0.143686 | − | 0.989623i | \(-0.545895\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(444\) | 5.43542 | 0.257954 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.917795 | 0.0434588 | ||||||||
\(447\) | 10.0585 | 0.475752 | ||||||||
\(448\) | −11.4037 | −0.538773 | ||||||||
\(449\) | 15.5896 | 0.735721 | 0.367860 | − | 0.929881i | \(-0.380090\pi\) | ||||
0.367860 | + | 0.929881i | \(0.380090\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68357 | −0.220541 | ||||||||
\(452\) | −62.6993 | −2.94912 | ||||||||
\(453\) | 11.9810 | 0.562916 | ||||||||
\(454\) | −4.84024 | −0.227164 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 33.6498 | 1.57579 | ||||||||
\(457\) | 2.50193 | 0.117035 | 0.0585176 | − | 0.998286i | \(-0.481363\pi\) | ||||
0.0585176 | + | 0.998286i | \(0.481363\pi\) | |||||||
\(458\) | 75.7328 | 3.53876 | ||||||||
\(459\) | −1.70636 | −0.0796462 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.153963 | −0.00717078 | −0.00358539 | − | 0.999994i | \(-0.501141\pi\) | ||||
−0.00358539 | + | 0.999994i | \(0.501141\pi\) | |||||||
\(462\) | 4.04934 | 0.188392 | ||||||||
\(463\) | 11.6327 | 0.540616 | 0.270308 | − | 0.962774i | \(-0.412875\pi\) | ||||
0.270308 | + | 0.962774i | \(0.412875\pi\) | |||||||
\(464\) | −114.048 | −5.29453 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.3329 | −0.849255 | ||||||||
\(467\) | −0.470294 | −0.0217626 | −0.0108813 | − | 0.999941i | \(-0.503464\pi\) | ||||
−0.0108813 | + | 0.999941i | \(0.503464\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −1.31433 | −0.0606900 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5960 | 0.902938 | ||||||||
\(472\) | 115.809 | 5.33056 | ||||||||
\(473\) | 21.4025 | 0.984087 | ||||||||
\(474\) | −12.8687 | −0.591080 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.27279 | −0.195843 | ||||||||
\(477\) | 7.05161 | 0.322871 | ||||||||
\(478\) | 17.5463 | 0.802548 | ||||||||
\(479\) | 12.4114 | 0.567092 | 0.283546 | − | 0.958959i | \(-0.408489\pi\) | ||||
0.283546 | + | 0.958959i | \(0.408489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.575193 | 0.0262265 | ||||||||
\(482\) | 20.1585 | 0.918196 | ||||||||
\(483\) | 1.06748 | 0.0485719 | ||||||||
\(484\) | −4.67587 | −0.212539 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.70636 | 0.122763 | ||||||||
\(487\) | −34.5646 | −1.56627 | −0.783135 | − | 0.621852i | \(-0.786381\pi\) | ||||
−0.783135 | + | 0.621852i | \(0.786381\pi\) | |||||||
\(488\) | −1.14162 | −0.0516786 | ||||||||
\(489\) | 11.8927 | 0.537805 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8658 | −1.12218 | −0.561088 | − | 0.827756i | \(-0.689617\pi\) | ||||
−0.561088 | + | 0.827756i | \(0.689617\pi\) | |||||||
\(492\) | −7.83824 | −0.353375 | ||||||||
\(493\) | −14.2044 | −0.639736 | ||||||||
\(494\) | 5.70322 | 0.256600 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 74.4830 | 3.34439 | ||||||||
\(497\) | −7.54618 | −0.338492 | ||||||||
\(498\) | −31.6387 | −1.41776 | ||||||||
\(499\) | 12.6037 | 0.564220 | 0.282110 | − | 0.959382i | \(-0.408966\pi\) | ||||
0.282110 | + | 0.959382i | \(0.408966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.99378 | −0.267782 | ||||||||
\(502\) | 12.4551 | 0.555900 | ||||||||
\(503\) | −29.9927 | −1.33731 | −0.668655 | − | 0.743573i | \(-0.733130\pi\) | ||||
−0.668655 | + | 0.743573i | \(0.733130\pi\) | |||||||
\(504\) | 4.23125 | 0.188475 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.5436 | 0.868817 | ||||||||
\(507\) | 12.6825 | 0.563251 | ||||||||
\(508\) | −9.47116 | −0.420215 | ||||||||
\(509\) | −0.466989 | −0.0206989 | −0.0103495 | − | 0.999946i | \(-0.503294\pi\) | ||||
−0.0103495 | + | 0.999946i | \(0.503294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.60358 | −0.203651 | ||||||||
\(512\) | −14.9358 | −0.660074 | ||||||||
\(513\) | −3.74010 | −0.165129 | ||||||||
\(514\) | −15.6830 | −0.691746 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 35.8184 | 1.57681 | ||||||||
\(517\) | −14.1053 | −0.620351 | ||||||||
\(518\) | −1.29933 | −0.0570891 | ||||||||
\(519\) | 17.3244 | 0.760457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2819 | −0.757133 | −0.378566 | − | 0.925574i | \(-0.623583\pi\) | ||||
−0.378566 | + | 0.925574i | \(0.623583\pi\) | |||||||
\(522\) | 22.5288 | 0.986060 | ||||||||
\(523\) | −40.6479 | −1.77741 | −0.888705 | − | 0.458480i | \(-0.848394\pi\) | ||||
−0.888705 | + | 0.458480i | \(0.848394\pi\) | |||||||
\(524\) | −31.5130 | −1.37665 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.6980 | 1.68731 | ||||||||
\(527\) | 9.27673 | 0.404101 | ||||||||
\(528\) | 43.5875 | 1.89690 | ||||||||
\(529\) | −17.8480 | −0.775999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8720 | −0.558596 | ||||||||
\(532\) | −9.36533 | −0.406039 | ||||||||
\(533\) | −0.829466 | −0.0359282 | ||||||||
\(534\) | −16.7808 | −0.726175 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.1439 | −1.08605 | ||||||||
\(537\) | −10.5765 | −0.456409 | ||||||||
\(538\) | 52.0175 | 2.24264 | ||||||||
\(539\) | 21.5667 | 0.928943 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.98099 | −0.0851694 | −0.0425847 | − | 0.999093i | \(-0.513559\pi\) | ||||
−0.0425847 | + | 0.999093i | \(0.513559\pi\) | |||||||
\(542\) | 62.9047 | 2.70199 | ||||||||
\(543\) | −11.9799 | −0.514105 | ||||||||
\(544\) | −32.5646 | −1.39619 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.717144 | 0.0306909 | ||||||||
\(547\) | −35.0543 | −1.49881 | −0.749406 | − | 0.662111i | \(-0.769661\pi\) | ||||
−0.749406 | + | 0.662111i | \(0.769661\pi\) | |||||||
\(548\) | 27.2402 | 1.16364 | ||||||||
\(549\) | 0.126888 | 0.00541546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.1341 | −1.32636 | ||||||||
\(552\) | 20.4215 | 0.869196 | ||||||||
\(553\) | 2.23625 | 0.0950948 | ||||||||
\(554\) | 59.2449 | 2.51708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −43.8633 | −1.86022 | ||||||||
\(557\) | −19.2383 | −0.815154 | −0.407577 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407577 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(558\) | −14.7133 | −0.622863 | ||||||||
\(559\) | 3.79041 | 0.160317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.42875 | 0.229202 | ||||||||
\(562\) | −73.3798 | −3.09534 | ||||||||
\(563\) | 29.1741 | 1.22954 | 0.614771 | − | 0.788706i | \(-0.289248\pi\) | ||||
0.614771 | + | 0.788706i | \(0.289248\pi\) | |||||||
\(564\) | −23.6061 | −0.993997 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 44.1337 | 1.85508 | ||||||||
\(567\) | −0.470294 | −0.0197505 | ||||||||
\(568\) | −144.363 | −6.05734 | ||||||||
\(569\) | −32.9112 | −1.37971 | −0.689855 | − | 0.723947i | \(-0.742326\pi\) | ||||
−0.689855 | + | 0.723947i | \(0.742326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6349 | 1.11464 | 0.557319 | − | 0.830299i | \(-0.311830\pi\) | ||||
0.557319 | + | 0.830299i | \(0.311830\pi\) | |||||||
\(572\) | 9.54443 | 0.399073 | ||||||||
\(573\) | −18.2657 | −0.763060 | ||||||||
\(574\) | 1.87371 | 0.0782073 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.2480 | 1.01033 | ||||||||
\(577\) | −34.5156 | −1.43690 | −0.718452 | − | 0.695577i | \(-0.755149\pi\) | ||||
−0.718452 | + | 0.695577i | \(0.755149\pi\) | |||||||
\(578\) | 38.1281 | 1.58592 | ||||||||
\(579\) | 25.2063 | 1.04754 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.49797 | 0.228094 | ||||||||
\(582\) | −22.8807 | −0.948437 | ||||||||
\(583\) | −22.4345 | −0.929144 | ||||||||
\(584\) | −88.0694 | −3.64434 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7878 | 0.610877 | ||||||||
\(587\) | 22.2755 | 0.919408 | 0.459704 | − | 0.888072i | \(-0.347955\pi\) | ||||
0.459704 | + | 0.888072i | \(0.347955\pi\) | |||||||
\(588\) | 36.0931 | 1.48846 | ||||||||
\(589\) | 20.3333 | 0.837818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.0923 | 0.497410 | ||||||||
\(592\) | −13.9861 | −0.574824 | ||||||||
\(593\) | 30.9158 | 1.26956 | 0.634779 | − | 0.772693i | \(-0.281091\pi\) | ||||
0.634779 | + | 0.772693i | \(0.281091\pi\) | |||||||
\(594\) | −8.61023 | −0.353282 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −53.5556 | −2.19372 | ||||||||
\(597\) | 0.544434 | 0.0222822 | ||||||||
\(598\) | 3.46119 | 0.141539 | ||||||||
\(599\) | −24.0276 | −0.981742 | −0.490871 | − | 0.871232i | \(-0.663321\pi\) | ||||
−0.490871 | + | 0.871232i | \(0.663321\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.0387 | −1.30688 | −0.653442 | − | 0.756977i | \(-0.726676\pi\) | ||||
−0.653442 | + | 0.756977i | \(0.726676\pi\) | |||||||
\(602\) | −8.56231 | −0.348974 | ||||||||
\(603\) | 2.79469 | 0.113809 | ||||||||
\(604\) | −63.7915 | −2.59564 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.7869 | −0.641299 | ||||||||
\(607\) | −45.5915 | −1.85050 | −0.925251 | − | 0.379356i | \(-0.876145\pi\) | ||||
−0.925251 | + | 0.379356i | \(0.876145\pi\) | |||||||
\(608\) | −71.3769 | −2.89471 | ||||||||
\(609\) | −3.91492 | −0.158640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.49807 | −0.101061 | ||||||||
\(612\) | 9.08535 | 0.367253 | ||||||||
\(613\) | 10.8564 | 0.438485 | 0.219242 | − | 0.975670i | \(-0.429641\pi\) | ||||
0.219242 | + | 0.975670i | \(0.429641\pi\) | |||||||
\(614\) | −57.9686 | −2.33942 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.4616 | −0.542384 | ||||||||
\(617\) | 16.1054 | 0.648380 | 0.324190 | − | 0.945992i | \(-0.394908\pi\) | ||||
0.324190 | + | 0.945992i | \(0.394908\pi\) | |||||||
\(618\) | 38.1039 | 1.53276 | ||||||||
\(619\) | 38.3581 | 1.54174 | 0.770872 | − | 0.636991i | \(-0.219821\pi\) | ||||
0.770872 | + | 0.636991i | \(0.219821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.26981 | −0.0910842 | ||||||||
\(622\) | 7.71854 | 0.309485 | ||||||||
\(623\) | 2.91605 | 0.116829 | ||||||||
\(624\) | 7.71941 | 0.309024 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.0732 | 1.56168 | ||||||||
\(627\) | 11.8990 | 0.475202 | ||||||||
\(628\) | −104.337 | −4.16350 | ||||||||
\(629\) | −1.74194 | −0.0694558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7292 | 0.904833 | 0.452417 | − | 0.891807i | \(-0.350562\pi\) | ||||
0.452417 | + | 0.891807i | \(0.350562\pi\) | |||||||
\(632\) | 42.7808 | 1.70173 | ||||||||
\(633\) | 3.12207 | 0.124091 | ||||||||
\(634\) | 61.1915 | 2.43022 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −37.5456 | −1.48878 | ||||||||
\(637\) | 3.81949 | 0.151334 | ||||||||
\(638\) | −71.6750 | −2.83764 | ||||||||
\(639\) | 16.0456 | 0.634756 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.9930 | 1.06616 | 0.533080 | − | 0.846065i | \(-0.321035\pi\) | ||||
0.533080 | + | 0.846065i | \(0.321035\pi\) | |||||||
\(642\) | 23.3074 | 0.919869 | ||||||||
\(643\) | 25.9062 | 1.02164 | 0.510821 | − | 0.859687i | \(-0.329341\pi\) | ||||
0.510821 | + | 0.859687i | \(0.329341\pi\) | |||||||
\(644\) | −5.68367 | −0.223968 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.2719 | −0.679554 | ||||||||
\(647\) | 21.6623 | 0.851632 | 0.425816 | − | 0.904810i | \(-0.359987\pi\) | ||||
0.425816 | + | 0.904810i | \(0.359987\pi\) | |||||||
\(648\) | −8.99702 | −0.353436 | ||||||||
\(649\) | 40.9519 | 1.60750 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.55678 | 0.100208 | ||||||||
\(652\) | −63.3212 | −2.47985 | ||||||||
\(653\) | −11.1775 | −0.437411 | −0.218705 | − | 0.975791i | \(-0.570183\pi\) | ||||
−0.218705 | + | 0.975791i | \(0.570183\pi\) | |||||||
\(654\) | 45.1625 | 1.76599 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.1689 | 0.787461 | ||||||||
\(657\) | 9.78873 | 0.381895 | ||||||||
\(658\) | 5.64299 | 0.219987 | ||||||||
\(659\) | 13.4744 | 0.524888 | 0.262444 | − | 0.964947i | \(-0.415471\pi\) | ||||
0.262444 | + | 0.964947i | \(0.415471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2622 | −0.904793 | −0.452397 | − | 0.891817i | \(-0.649431\pi\) | ||||
−0.452397 | + | 0.891817i | \(0.649431\pi\) | |||||||
\(662\) | −10.4640 | −0.406695 | ||||||||
\(663\) | 0.961440 | 0.0373392 | ||||||||
\(664\) | 105.180 | 4.08176 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.76279 | 0.107056 | ||||||||
\(667\) | −18.8948 | −0.731608 | ||||||||
\(668\) | 31.9132 | 1.23476 | ||||||||
\(669\) | 0.339125 | 0.0131113 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.403693 | −0.0155844 | ||||||||
\(672\) | −8.97519 | −0.346226 | ||||||||
\(673\) | −18.8392 | −0.726198 | −0.363099 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363099 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(674\) | 47.3215 | 1.82276 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −67.5268 | −2.59719 | ||||||||
\(677\) | 42.2440 | 1.62357 | 0.811785 | − | 0.583957i | \(-0.198496\pi\) | ||||
0.811785 | + | 0.583957i | \(0.198496\pi\) | |||||||
\(678\) | −31.8697 | −1.22395 | ||||||||
\(679\) | 3.97607 | 0.152587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.78847 | −0.0685342 | ||||||||
\(682\) | 46.8100 | 1.79245 | ||||||||
\(683\) | −48.9502 | −1.87303 | −0.936513 | − | 0.350633i | \(-0.885966\pi\) | ||||
−0.936513 | + | 0.350633i | \(0.885966\pi\) | |||||||
\(684\) | 19.9138 | 0.761422 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.5375 | −0.669585 | ||||||||
\(687\) | 27.9833 | 1.06763 | ||||||||
\(688\) | −92.1655 | −3.51378 | ||||||||
\(689\) | −3.97319 | −0.151366 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1917 | −0.539878 | −0.269939 | − | 0.962877i | \(-0.587004\pi\) | ||||
−0.269939 | + | 0.962877i | \(0.587004\pi\) | |||||||
\(692\) | −92.2419 | −3.50651 | ||||||||
\(693\) | 1.49623 | 0.0568371 | ||||||||
\(694\) | −62.5010 | −2.37251 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −74.8948 | −2.83888 | ||||||||
\(697\) | 2.51200 | 0.0951487 | ||||||||
\(698\) | 25.2409 | 0.955382 | ||||||||
\(699\) | −6.77400 | −0.256216 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.00786 | −0.340222 | −0.170111 | − | 0.985425i | \(-0.554413\pi\) | ||||
−0.170111 | + | 0.985425i | \(0.554413\pi\) | |||||||
\(702\) | −1.52488 | −0.0575530 | ||||||||
\(703\) | −3.81809 | −0.144002 | ||||||||
\(704\) | −77.1444 | −2.90749 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 86.4604 | 3.25398 | ||||||||
\(707\) | 2.74334 | 0.103174 | ||||||||
\(708\) | 68.5355 | 2.57572 | ||||||||
\(709\) | 49.6994 | 1.86650 | 0.933249 | − | 0.359229i | \(-0.116960\pi\) | ||||
0.933249 | + | 0.359229i | \(0.116960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.75499 | −0.178326 | ||||||||
\(712\) | 55.7859 | 2.09067 | ||||||||
\(713\) | 12.3399 | 0.462134 | ||||||||
\(714\) | −2.17183 | −0.0812789 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 56.3134 | 2.10453 | ||||||||
\(717\) | 6.48334 | 0.242125 | ||||||||
\(718\) | 25.9528 | 0.968549 | ||||||||
\(719\) | −2.13706 | −0.0796988 | −0.0398494 | − | 0.999206i | \(-0.512688\pi\) | ||||
−0.0398494 | + | 0.999206i | \(0.512688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.62145 | −0.246596 | ||||||||
\(722\) | 13.5633 | 0.504775 | ||||||||
\(723\) | 7.44857 | 0.277015 | ||||||||
\(724\) | 63.7855 | 2.37057 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.37672 | −0.0882083 | ||||||||
\(727\) | 41.4634 | 1.53779 | 0.768895 | − | 0.639375i | \(-0.220807\pi\) | ||||
0.768895 | + | 0.639375i | \(0.220807\pi\) | |||||||
\(728\) | −2.38407 | −0.0883596 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.4791 | −0.424568 | ||||||||
\(732\) | −0.675604 | −0.0249710 | ||||||||
\(733\) | −32.5210 | −1.20119 | −0.600596 | − | 0.799553i | \(-0.705070\pi\) | ||||
−0.600596 | + | 0.799553i | \(0.705070\pi\) | |||||||
\(734\) | 2.88020 | 0.106310 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.3175 | −1.59670 | ||||||||
\(737\) | −8.89125 | −0.327513 | ||||||||
\(738\) | −3.98413 | −0.146658 | ||||||||
\(739\) | −35.3175 | −1.29917 | −0.649587 | − | 0.760287i | \(-0.725058\pi\) | ||||
−0.649587 | + | 0.760287i | \(0.725058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.10734 | 0.0774150 | ||||||||
\(742\) | 8.97519 | 0.329490 | ||||||||
\(743\) | 36.0897 | 1.32400 | 0.662001 | − | 0.749503i | \(-0.269708\pi\) | ||||
0.662001 | + | 0.749503i | \(0.269708\pi\) | |||||||
\(744\) | 48.9128 | 1.79323 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.1508 | −0.408261 | ||||||||
\(747\) | −11.6905 | −0.427733 | ||||||||
\(748\) | −28.9048 | −1.05687 | ||||||||
\(749\) | −4.05021 | −0.147991 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.62810 | −0.168882 | −0.0844409 | − | 0.996428i | \(-0.526910\pi\) | ||||
−0.0844409 | + | 0.996428i | \(0.526910\pi\) | |||||||
\(752\) | 60.7418 | 2.21502 | ||||||||
\(753\) | 4.60217 | 0.167712 | ||||||||
\(754\) | −12.6937 | −0.462279 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.50403 | 0.0910708 | ||||||||
\(757\) | −14.6243 | −0.531530 | −0.265765 | − | 0.964038i | \(-0.585625\pi\) | ||||
−0.265765 | + | 0.964038i | \(0.585625\pi\) | |||||||
\(758\) | −28.0279 | −1.01802 | ||||||||
\(759\) | 7.22134 | 0.262118 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1893 | 0.441861 | 0.220930 | − | 0.975290i | \(-0.429091\pi\) | ||||
0.220930 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(762\) | −4.81414 | −0.174398 | ||||||||
\(763\) | −7.84804 | −0.284118 | ||||||||
\(764\) | 97.2538 | 3.51852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.24587 | 0.117278 | ||||||||
\(767\) | 7.25264 | 0.261878 | ||||||||
\(768\) | −25.8083 | −0.931276 | ||||||||
\(769\) | 13.7961 | 0.497500 | 0.248750 | − | 0.968568i | \(-0.419980\pi\) | ||||
0.248750 | + | 0.968568i | \(0.419980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.79485 | −0.208697 | ||||||||
\(772\) | −134.208 | −4.83026 | ||||||||
\(773\) | −22.6539 | −0.814803 | −0.407402 | − | 0.913249i | \(-0.633565\pi\) | ||||
−0.407402 | + | 0.913249i | \(0.633565\pi\) | |||||||
\(774\) | 18.2063 | 0.654411 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 76.0647 | 2.73056 | ||||||||
\(777\) | −0.480101 | −0.0172235 | ||||||||
\(778\) | −34.1117 | −1.22296 | ||||||||
\(779\) | 5.50594 | 0.197271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.0489 | −1.82667 | ||||||||
\(782\) | −10.4820 | −0.374837 | ||||||||
\(783\) | 8.32440 | 0.297490 | ||||||||
\(784\) | −92.8726 | −3.31688 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.0179 | −0.571339 | ||||||||
\(787\) | 47.6857 | 1.69981 | 0.849905 | − | 0.526936i | \(-0.176659\pi\) | ||||
0.849905 | + | 0.526936i | \(0.176659\pi\) | |||||||
\(788\) | −64.3841 | −2.29359 | ||||||||
\(789\) | 14.2989 | 0.509054 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.53811 | 0.196913 | ||||||||
\(792\) | 28.6238 | 1.01710 | ||||||||
\(793\) | −0.0714945 | −0.00253884 | ||||||||
\(794\) | −3.55440 | −0.126141 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.89878 | −0.102745 | ||||||||
\(797\) | −27.2131 | −0.963938 | −0.481969 | − | 0.876188i | \(-0.660078\pi\) | ||||
−0.481969 | + | 0.876188i | \(0.660078\pi\) | |||||||
\(798\) | −4.76035 | −0.168515 | ||||||||
\(799\) | 7.56529 | 0.267641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.20049 | −0.219083 | ||||||||
\(802\) | −43.5838 | −1.53900 | ||||||||
\(803\) | −31.1426 | −1.09900 | ||||||||
\(804\) | −14.8800 | −0.524778 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.29012 | 0.292007 | ||||||||
\(807\) | 19.2205 | 0.676592 | ||||||||
\(808\) | 52.4819 | 1.84631 | ||||||||
\(809\) | −19.6155 | −0.689644 | −0.344822 | − | 0.938668i | \(-0.612061\pi\) | ||||
−0.344822 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0710 | 0.739903 | 0.369951 | − | 0.929051i | \(-0.379374\pi\) | ||||
0.369951 | + | 0.929051i | \(0.379374\pi\) | |||||||
\(812\) | 20.8446 | 0.731501 | ||||||||
\(813\) | 23.2433 | 0.815177 | ||||||||
\(814\) | −8.78977 | −0.308081 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −23.3778 | −0.818388 | ||||||||
\(817\) | −25.1605 | −0.880253 | ||||||||
\(818\) | −57.2667 | −2.00228 | ||||||||
\(819\) | 0.264985 | 0.00925931 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.4342 | 1.44606 | 0.723031 | − | 0.690815i | \(-0.242748\pi\) | ||||
0.723031 | + | 0.690815i | \(0.242748\pi\) | |||||||
\(822\) | 13.8460 | 0.482936 | ||||||||
\(823\) | −6.04093 | −0.210574 | −0.105287 | − | 0.994442i | \(-0.533576\pi\) | ||||
−0.105287 | + | 0.994442i | \(0.533576\pi\) | |||||||
\(824\) | −126.673 | −4.41285 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3833 | −0.570047 | ||||||||
\(827\) | 2.99361 | 0.104098 | 0.0520491 | − | 0.998645i | \(-0.483425\pi\) | ||||
0.0520491 | + | 0.998645i | \(0.483425\pi\) | |||||||
\(828\) | 12.0853 | 0.419995 | ||||||||
\(829\) | 26.8530 | 0.932642 | 0.466321 | − | 0.884616i | \(-0.345579\pi\) | ||||
0.466321 | + | 0.884616i | \(0.345579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.8910 | 0.759390 | ||||||||
\(832\) | −13.6624 | −0.473658 | ||||||||
\(833\) | −11.5671 | −0.400777 | ||||||||
\(834\) | −22.2955 | −0.772029 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −63.3552 | −2.19119 | ||||||||
\(837\) | −5.43656 | −0.187915 | ||||||||
\(838\) | 18.0540 | 0.623665 | ||||||||
\(839\) | 12.4595 | 0.430150 | 0.215075 | − | 0.976598i | \(-0.431000\pi\) | ||||
0.215075 | + | 0.976598i | \(0.431000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.2956 | 1.38950 | ||||||||
\(842\) | −73.8783 | −2.54601 | ||||||||
\(843\) | −27.1138 | −0.933850 | ||||||||
\(844\) | −16.6231 | −0.572191 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.9989 | −0.412529 | ||||||||
\(847\) | 0.413011 | 0.0141912 | ||||||||
\(848\) | 96.6099 | 3.31760 | ||||||||
\(849\) | 16.3074 | 0.559668 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.31714 | −0.0794304 | ||||||||
\(852\) | −85.4334 | −2.92690 | ||||||||
\(853\) | 5.69736 | 0.195074 | 0.0975369 | − | 0.995232i | \(-0.468904\pi\) | ||||
0.0975369 | + | 0.995232i | \(0.468904\pi\) | |||||||
\(854\) | 0.161502 | 0.00552648 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −77.4830 | −2.64831 | ||||||||
\(857\) | 7.41982 | 0.253456 | 0.126728 | − | 0.991937i | \(-0.459552\pi\) | ||||
0.126728 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(858\) | 4.85139 | 0.165624 | ||||||||
\(859\) | −5.68253 | −0.193885 | −0.0969427 | − | 0.995290i | \(-0.530906\pi\) | ||||
−0.0969427 | + | 0.995290i | \(0.530906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.692337 | 0.0235948 | ||||||||
\(862\) | −33.2813 | −1.13356 | ||||||||
\(863\) | 34.5747 | 1.17693 | 0.588467 | − | 0.808521i | \(-0.299732\pi\) | ||||
0.588467 | + | 0.808521i | \(0.299732\pi\) | |||||||
\(864\) | 19.0842 | 0.649258 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −91.5973 | −3.11260 | ||||||||
\(867\) | 14.0883 | 0.478465 | ||||||||
\(868\) | −13.6133 | −0.462066 | ||||||||
\(869\) | 15.1279 | 0.513179 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.57465 | −0.0533550 | ||||||||
\(872\) | −150.138 | −5.08431 | ||||||||
\(873\) | −8.45443 | −0.286139 | ||||||||
\(874\) | −22.9751 | −0.777145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −52.1191 | −1.76094 | ||||||||
\(877\) | 5.30013 | 0.178973 | 0.0894863 | − | 0.995988i | \(-0.471477\pi\) | ||||
0.0894863 | + | 0.995988i | \(0.471477\pi\) | |||||||
\(878\) | 56.7399 | 1.91488 | ||||||||
\(879\) | 5.46407 | 0.184299 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.61288 | 0.256484 | 0.128242 | − | 0.991743i | \(-0.459067\pi\) | ||||
0.128242 | + | 0.991743i | \(0.459067\pi\) | |||||||
\(882\) | 18.3460 | 0.617740 | ||||||||
\(883\) | 52.8334 | 1.77799 | 0.888993 | − | 0.457921i | \(-0.151406\pi\) | ||||
0.888993 | + | 0.457921i | \(0.151406\pi\) | |||||||
\(884\) | −5.11909 | −0.172174 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.3693 | 0.549939 | ||||||||
\(887\) | −7.70778 | −0.258802 | −0.129401 | − | 0.991592i | \(-0.541305\pi\) | ||||
−0.129401 | + | 0.991592i | \(0.541305\pi\) | |||||||
\(888\) | −9.18462 | −0.308216 | ||||||||
\(889\) | 0.836570 | 0.0280577 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.18148 | −0.106584 | ||||||||
\(892\) | −1.80563 | −0.0604571 | ||||||||
\(893\) | 16.5820 | 0.554896 | ||||||||
\(894\) | −27.2220 | −0.910441 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.9121 | 0.431363 | ||||||||
\(897\) | 1.27891 | 0.0427015 | ||||||||
\(898\) | −42.1912 | −1.40794 | ||||||||
\(899\) | −45.2560 | −1.50937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0326 | 0.400864 | ||||||||
\(902\) | 12.6754 | 0.422046 | ||||||||
\(903\) | −3.16377 | −0.105284 | ||||||||
\(904\) | 105.947 | 3.52376 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −32.4249 | −1.07725 | ||||||||
\(907\) | 11.3735 | 0.377650 | 0.188825 | − | 0.982011i | \(-0.439532\pi\) | ||||
0.188825 | + | 0.982011i | \(0.439532\pi\) | |||||||
\(908\) | 9.52251 | 0.316015 | ||||||||
\(909\) | −5.83325 | −0.193477 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5896 | −0.615902 | −0.307951 | − | 0.951402i | \(-0.599643\pi\) | ||||
−0.307951 | + | 0.951402i | \(0.599643\pi\) | |||||||
\(912\) | −51.2409 | −1.69676 | ||||||||
\(913\) | 37.1931 | 1.23091 | ||||||||
\(914\) | −6.77112 | −0.223969 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −148.994 | −4.92290 | ||||||||
\(917\) | 2.78348 | 0.0919187 | ||||||||
\(918\) | 4.61803 | 0.152418 | ||||||||
\(919\) | 7.64799 | 0.252284 | 0.126142 | − | 0.992012i | \(-0.459741\pi\) | ||||
0.126142 | + | 0.992012i | \(0.459741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.4194 | −0.705793 | ||||||||
\(922\) | 0.416680 | 0.0137226 | ||||||||
\(923\) | −9.04083 | −0.297582 | ||||||||
\(924\) | −7.96652 | −0.262079 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.4822 | −1.03457 | ||||||||
\(927\) | 14.0794 | 0.462428 | ||||||||
\(928\) | 158.865 | 5.21498 | ||||||||
\(929\) | −30.9487 | −1.01539 | −0.507696 | − | 0.861536i | \(-0.669503\pi\) | ||||
−0.507696 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.3535 | −0.830927 | ||||||||
\(932\) | 36.0675 | 1.18143 | ||||||||
\(933\) | 2.85200 | 0.0933702 | ||||||||
\(934\) | 1.27279 | 0.0416468 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.06932 | 0.165696 | ||||||||
\(937\) | −31.3694 | −1.02480 | −0.512398 | − | 0.858748i | \(-0.671243\pi\) | ||||
−0.512398 | + | 0.858748i | \(0.671243\pi\) | |||||||
\(938\) | 3.55704 | 0.116142 | ||||||||
\(939\) | 14.4375 | 0.471151 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.61810 | −0.117947 | −0.0589733 | − | 0.998260i | \(-0.518783\pi\) | ||||
−0.0589733 | + | 0.998260i | \(0.518783\pi\) | |||||||
\(942\) | −53.0340 | −1.72794 | ||||||||
\(943\) | 3.34146 | 0.108813 | ||||||||
\(944\) | −176.351 | −5.73974 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −57.9229 | −1.88323 | ||||||||
\(947\) | 11.3216 | 0.367902 | 0.183951 | − | 0.982935i | \(-0.441111\pi\) | ||||
0.183951 | + | 0.982935i | \(0.441111\pi\) | |||||||
\(948\) | 25.3175 | 0.822273 | ||||||||
\(949\) | −5.51540 | −0.179038 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6102 | 0.733187 | ||||||||
\(952\) | 7.22004 | 0.234003 | ||||||||
\(953\) | 17.2182 | 0.557752 | 0.278876 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278876 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(954\) | −19.0842 | −0.617874 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.5199 | −1.11645 | ||||||||
\(957\) | −26.4839 | −0.856102 | ||||||||
\(958\) | −33.5898 | −1.08524 | ||||||||
\(959\) | −2.40608 | −0.0776962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.44386 | −0.0465762 | ||||||||
\(962\) | −1.55668 | −0.0501894 | ||||||||
\(963\) | 8.61207 | 0.277520 | ||||||||
\(964\) | −39.6591 | −1.27733 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.88898 | −0.0929514 | ||||||||
\(967\) | 29.9064 | 0.961723 | 0.480862 | − | 0.876796i | \(-0.340324\pi\) | ||||
0.480862 | + | 0.876796i | \(0.340324\pi\) | |||||||
\(968\) | 7.90115 | 0.253953 | ||||||||
\(969\) | −6.38197 | −0.205018 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.1927 | −0.808472 | −0.404236 | − | 0.914655i | \(-0.632463\pi\) | ||||
−0.404236 | + | 0.914655i | \(0.632463\pi\) | |||||||
\(972\) | −5.32440 | −0.170780 | ||||||||
\(973\) | 3.87436 | 0.124206 | ||||||||
\(974\) | 93.5443 | 2.99735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.73842 | 0.0556455 | ||||||||
\(977\) | −57.0948 | −1.82663 | −0.913313 | − | 0.407259i | \(-0.866485\pi\) | ||||
−0.913313 | + | 0.407259i | \(0.866485\pi\) | |||||||
\(978\) | −32.1859 | −1.02919 | ||||||||
\(979\) | 19.7267 | 0.630469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.6875 | 0.532791 | ||||||||
\(982\) | 67.2957 | 2.14749 | ||||||||
\(983\) | 26.4168 | 0.842566 | 0.421283 | − | 0.906929i | \(-0.361580\pi\) | ||||
0.421283 | + | 0.906929i | \(0.361580\pi\) | |||||||
\(984\) | 13.2448 | 0.422230 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.4423 | 1.22425 | ||||||||
\(987\) | 2.08508 | 0.0663690 | ||||||||
\(988\) | −11.2203 | −0.356965 | ||||||||
\(989\) | −15.2695 | −0.485541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.5276 | −0.715612 | −0.357806 | − | 0.933796i | \(-0.616475\pi\) | ||||
−0.357806 | + | 0.933796i | \(0.616475\pi\) | |||||||
\(992\) | −103.752 | −3.29414 | ||||||||
\(993\) | −3.86645 | −0.122698 | ||||||||
\(994\) | 20.4227 | 0.647768 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 62.2448 | 1.97230 | ||||||||
\(997\) | 24.1043 | 0.763392 | 0.381696 | − | 0.924288i | \(-0.375340\pi\) | ||||
0.381696 | + | 0.924288i | \(0.375340\pi\) | |||||||
\(998\) | −34.1103 | −1.07974 | ||||||||
\(999\) | 1.02085 | 0.0322983 |
(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 | 1875.2.a.e.1.1 | 4 | ||
3.2 | odd | 2 | 5625.2.a.n.1.4 | 4 | |||
5.2 | odd | 4 | 1875.2.b.c.1249.1 | 8 | |||
5.3 | odd | 4 | 1875.2.b.c.1249.8 | 8 | |||
5.4 | even | 2 | 1875.2.a.h.1.4 | 4 | |||
15.14 | odd | 2 | 5625.2.a.i.1.1 | 4 | |||
25.3 | odd | 20 | 375.2.i.b.49.4 | 16 | |||
25.4 | even | 10 | 75.2.g.b.16.1 | ✓ | 8 | ||
25.6 | even | 5 | 375.2.g.b.301.2 | 8 | |||
25.8 | odd | 20 | 375.2.i.b.199.1 | 16 | |||
25.17 | odd | 20 | 375.2.i.b.199.4 | 16 | |||
25.19 | even | 10 | 75.2.g.b.61.1 | yes | 8 | ||
25.21 | even | 5 | 375.2.g.b.76.2 | 8 | |||
25.22 | odd | 20 | 375.2.i.b.49.1 | 16 | |||
75.29 | odd | 10 | 225.2.h.c.91.2 | 8 | |||
75.44 | odd | 10 | 225.2.h.c.136.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.16.1 | ✓ | 8 | 25.4 | even | 10 | ||
75.2.g.b.61.1 | yes | 8 | 25.19 | even | 10 | ||
225.2.h.c.91.2 | 8 | 75.29 | odd | 10 | |||
225.2.h.c.136.2 | 8 | 75.44 | odd | 10 | |||
375.2.g.b.76.2 | 8 | 25.21 | even | 5 | |||
375.2.g.b.301.2 | 8 | 25.6 | even | 5 | |||
375.2.i.b.49.1 | 16 | 25.22 | odd | 20 | |||
375.2.i.b.49.4 | 16 | 25.3 | odd | 20 | |||
375.2.i.b.199.1 | 16 | 25.8 | odd | 20 | |||
375.2.i.b.199.4 | 16 | 25.17 | odd | 20 | |||
1875.2.a.e.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1875.2.a.h.1.4 | 4 | 5.4 | even | 2 | |||
1875.2.b.c.1249.1 | 8 | 5.2 | odd | 4 | |||
1875.2.b.c.1249.8 | 8 | 5.3 | odd | 4 | |||
5625.2.a.i.1.1 | 4 | 15.14 | odd | 2 | |||
5625.2.a.n.1.4 | 4 | 3.2 | odd | 2 |