Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48119 | 1.04736 | 0.523681 | − | 0.851914i | \(-0.324558\pi\) | ||||
0.523681 | + | 0.851914i | \(0.324558\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.193937 | 0.0969683 | ||||||||
\(5\) | −0.193937 | −0.0867311 | −0.0433655 | − | 0.999059i | \(-0.513808\pi\) | ||||
−0.0433655 | + | 0.999059i | \(0.513808\pi\) | |||||||
\(6\) | 1.48119 | 0.604695 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.67513 | −0.945802 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.287258 | −0.0908389 | ||||||||
\(11\) | −5.35026 | −1.61316 | −0.806582 | − | 0.591122i | \(-0.798685\pi\) | ||||
−0.806582 | + | 0.591122i | \(0.798685\pi\) | |||||||
\(12\) | 0.193937 | 0.0559847 | ||||||||
\(13\) | 3.86907 | 1.07309 | 0.536543 | − | 0.843873i | \(-0.319730\pi\) | ||||
0.536543 | + | 0.843873i | \(0.319730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.193937 | −0.0500742 | ||||||||
\(16\) | −4.35026 | −1.08757 | ||||||||
\(17\) | 0.156325 | 0.0379144 | 0.0189572 | − | 0.999820i | \(-0.493965\pi\) | ||||
0.0189572 | + | 0.999820i | \(0.493965\pi\) | |||||||
\(18\) | 1.48119 | 0.349121 | ||||||||
\(19\) | 1.84367 | 0.422968 | 0.211484 | − | 0.977381i | \(-0.432170\pi\) | ||||
0.211484 | + | 0.977381i | \(0.432170\pi\) | |||||||
\(20\) | −0.0376114 | −0.00841016 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.92478 | −1.68957 | ||||||||
\(23\) | 7.79384 | 1.62513 | 0.812564 | − | 0.582871i | \(-0.198071\pi\) | ||||
0.812564 | + | 0.582871i | \(0.198071\pi\) | |||||||
\(24\) | −2.67513 | −0.546059 | ||||||||
\(25\) | −4.96239 | −0.992478 | ||||||||
\(26\) | 5.73084 | 1.12391 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.28726 | −0.796124 | −0.398062 | − | 0.917359i | \(-0.630317\pi\) | ||||
−0.398062 | + | 0.917359i | \(0.630317\pi\) | |||||||
\(30\) | −0.287258 | −0.0524458 | ||||||||
\(31\) | −0.806063 | −0.144773 | −0.0723866 | − | 0.997377i | \(-0.523062\pi\) | ||||
−0.0723866 | + | 0.997377i | \(0.523062\pi\) | |||||||
\(32\) | −1.09332 | −0.193274 | ||||||||
\(33\) | −5.35026 | −0.931361 | ||||||||
\(34\) | 0.231548 | 0.0397101 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.193937 | 0.0323228 | ||||||||
\(37\) | −5.80606 | −0.954511 | −0.477255 | − | 0.878765i | \(-0.658368\pi\) | ||||
−0.477255 | + | 0.878765i | \(0.658368\pi\) | |||||||
\(38\) | 2.73084 | 0.443001 | ||||||||
\(39\) | 3.86907 | 0.619547 | ||||||||
\(40\) | 0.518806 | 0.0820304 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.41819 | −0.978765 | −0.489382 | − | 0.872069i | \(-0.662778\pi\) | ||||
−0.489382 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(44\) | −1.03761 | −0.156426 | ||||||||
\(45\) | −0.193937 | −0.0289104 | ||||||||
\(46\) | 11.5442 | 1.70210 | ||||||||
\(47\) | 3.15633 | 0.460397 | 0.230199 | − | 0.973144i | \(-0.426062\pi\) | ||||
0.230199 | + | 0.973144i | \(0.426062\pi\) | |||||||
\(48\) | −4.35026 | −0.627906 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.35026 | −1.03948 | ||||||||
\(51\) | 0.156325 | 0.0218899 | ||||||||
\(52\) | 0.750354 | 0.104055 | ||||||||
\(53\) | −1.86907 | −0.256736 | −0.128368 | − | 0.991727i | \(-0.540974\pi\) | ||||
−0.128368 | + | 0.991727i | \(0.540974\pi\) | |||||||
\(54\) | 1.48119 | 0.201565 | ||||||||
\(55\) | 1.03761 | 0.139911 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.84367 | 0.244201 | ||||||||
\(58\) | −6.35026 | −0.833830 | ||||||||
\(59\) | 1.96968 | 0.256431 | 0.128215 | − | 0.991746i | \(-0.459075\pi\) | ||||
0.128215 | + | 0.991746i | \(0.459075\pi\) | |||||||
\(60\) | −0.0376114 | −0.00485561 | ||||||||
\(61\) | −6.15633 | −0.788237 | −0.394118 | − | 0.919060i | \(-0.628950\pi\) | ||||
−0.394118 | + | 0.919060i | \(0.628950\pi\) | |||||||
\(62\) | −1.19394 | −0.151630 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.08110 | 0.885138 | ||||||||
\(65\) | −0.750354 | −0.0930699 | ||||||||
\(66\) | −7.92478 | −0.975473 | ||||||||
\(67\) | −10.8945 | −1.33097 | −0.665485 | − | 0.746411i | \(-0.731775\pi\) | ||||
−0.665485 | + | 0.746411i | \(0.731775\pi\) | |||||||
\(68\) | 0.0303172 | 0.00367650 | ||||||||
\(69\) | 7.79384 | 0.938269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3430 | −1.22748 | −0.613742 | − | 0.789506i | \(-0.710337\pi\) | ||||
−0.613742 | + | 0.789506i | \(0.710337\pi\) | |||||||
\(72\) | −2.67513 | −0.315267 | ||||||||
\(73\) | −11.8192 | −1.38334 | −0.691669 | − | 0.722215i | \(-0.743124\pi\) | ||||
−0.691669 | + | 0.722215i | \(0.743124\pi\) | |||||||
\(74\) | −8.59991 | −0.999719 | ||||||||
\(75\) | −4.96239 | −0.573007 | ||||||||
\(76\) | 0.357556 | 0.0410145 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.73084 | 0.648890 | ||||||||
\(79\) | −1.61942 | −0.182199 | −0.0910996 | − | 0.995842i | \(-0.529038\pi\) | ||||
−0.0910996 | + | 0.995842i | \(0.529038\pi\) | |||||||
\(80\) | 0.843675 | 0.0943257 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.48119 | −0.163571 | ||||||||
\(83\) | −6.12601 | −0.672417 | −0.336208 | − | 0.941788i | \(-0.609145\pi\) | ||||
−0.336208 | + | 0.941788i | \(0.609145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0303172 | −0.00328836 | ||||||||
\(86\) | −9.50659 | −1.02512 | ||||||||
\(87\) | −4.28726 | −0.459642 | ||||||||
\(88\) | 14.3127 | 1.52573 | ||||||||
\(89\) | −16.6253 | −1.76228 | −0.881139 | − | 0.472857i | \(-0.843223\pi\) | ||||
−0.881139 | + | 0.472857i | \(0.843223\pi\) | |||||||
\(90\) | −0.287258 | −0.0302796 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.51151 | 0.157586 | ||||||||
\(93\) | −0.806063 | −0.0835849 | ||||||||
\(94\) | 4.67513 | 0.482203 | ||||||||
\(95\) | −0.357556 | −0.0366845 | ||||||||
\(96\) | −1.09332 | −0.111587 | ||||||||
\(97\) | 2.28726 | 0.232236 | 0.116118 | − | 0.993235i | \(-0.462955\pi\) | ||||
0.116118 | + | 0.993235i | \(0.462955\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.35026 | −0.537722 | ||||||||
\(100\) | −0.962389 | −0.0962389 | ||||||||
\(101\) | −14.4993 | −1.44273 | −0.721367 | − | 0.692553i | \(-0.756486\pi\) | ||||
−0.721367 | + | 0.692553i | \(0.756486\pi\) | |||||||
\(102\) | 0.231548 | 0.0229267 | ||||||||
\(103\) | 5.63752 | 0.555481 | 0.277741 | − | 0.960656i | \(-0.410414\pi\) | ||||
0.277741 | + | 0.960656i | \(0.410414\pi\) | |||||||
\(104\) | −10.3503 | −1.01493 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.76845 | −0.268896 | ||||||||
\(107\) | −2.93700 | −0.283930 | −0.141965 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141965 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(108\) | 0.193937 | 0.0186616 | ||||||||
\(109\) | 5.89446 | 0.564587 | 0.282293 | − | 0.959328i | \(-0.408905\pi\) | ||||
0.282293 | + | 0.959328i | \(0.408905\pi\) | |||||||
\(110\) | 1.53690 | 0.146538 | ||||||||
\(111\) | −5.80606 | −0.551087 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5369 | 1.46159 | 0.730794 | − | 0.682598i | \(-0.239150\pi\) | ||||
0.730794 | + | 0.682598i | \(0.239150\pi\) | |||||||
\(114\) | 2.73084 | 0.255767 | ||||||||
\(115\) | −1.51151 | −0.140949 | ||||||||
\(116\) | −0.831456 | −0.0771988 | ||||||||
\(117\) | 3.86907 | 0.357695 | ||||||||
\(118\) | 2.91748 | 0.268576 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.518806 | 0.0473603 | ||||||||
\(121\) | 17.6253 | 1.60230 | ||||||||
\(122\) | −9.11871 | −0.825570 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −0.156325 | −0.0140384 | ||||||||
\(125\) | 1.93207 | 0.172810 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4993 | −1.46408 | −0.732038 | − | 0.681264i | \(-0.761431\pi\) | ||||
−0.732038 | + | 0.681264i | \(0.761431\pi\) | |||||||
\(128\) | 12.6751 | 1.12033 | ||||||||
\(129\) | −6.41819 | −0.565090 | ||||||||
\(130\) | −1.11142 | −0.0974779 | ||||||||
\(131\) | −4.46898 | −0.390456 | −0.195228 | − | 0.980758i | \(-0.562545\pi\) | ||||
−0.195228 | + | 0.980758i | \(0.562545\pi\) | |||||||
\(132\) | −1.03761 | −0.0903125 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16.1368 | −1.39401 | ||||||||
\(135\) | −0.193937 | −0.0166914 | ||||||||
\(136\) | −0.418190 | −0.0358595 | ||||||||
\(137\) | −5.56230 | −0.475219 | −0.237610 | − | 0.971361i | \(-0.576364\pi\) | ||||
−0.237610 | + | 0.971361i | \(0.576364\pi\) | |||||||
\(138\) | 11.5442 | 0.982707 | ||||||||
\(139\) | 1.55642 | 0.132014 | 0.0660068 | − | 0.997819i | \(-0.478974\pi\) | ||||
0.0660068 | + | 0.997819i | \(0.478974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.15633 | 0.265811 | ||||||||
\(142\) | −15.3199 | −1.28562 | ||||||||
\(143\) | −20.7005 | −1.73106 | ||||||||
\(144\) | −4.35026 | −0.362522 | ||||||||
\(145\) | 0.831456 | 0.0690487 | ||||||||
\(146\) | −17.5066 | −1.44886 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.12601 | −0.0925573 | ||||||||
\(149\) | 5.69323 | 0.466408 | 0.233204 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233204 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(150\) | −7.35026 | −0.600146 | ||||||||
\(151\) | 9.58769 | 0.780235 | 0.390118 | − | 0.920765i | \(-0.372434\pi\) | ||||
0.390118 | + | 0.920765i | \(0.372434\pi\) | |||||||
\(152\) | −4.93207 | −0.400044 | ||||||||
\(153\) | 0.156325 | 0.0126381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.156325 | 0.0125563 | ||||||||
\(156\) | 0.750354 | 0.0600764 | ||||||||
\(157\) | 2.68006 | 0.213892 | 0.106946 | − | 0.994265i | \(-0.465893\pi\) | ||||
0.106946 | + | 0.994265i | \(0.465893\pi\) | |||||||
\(158\) | −2.39868 | −0.190829 | ||||||||
\(159\) | −1.86907 | −0.148227 | ||||||||
\(160\) | 0.212035 | 0.0167628 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.48119 | 0.116374 | ||||||||
\(163\) | −11.9551 | −0.936395 | −0.468198 | − | 0.883624i | \(-0.655096\pi\) | ||||
−0.468198 | + | 0.883624i | \(0.655096\pi\) | |||||||
\(164\) | −0.193937 | −0.0151439 | ||||||||
\(165\) | 1.03761 | 0.0807779 | ||||||||
\(166\) | −9.07381 | −0.704264 | ||||||||
\(167\) | −18.6121 | −1.44025 | −0.720125 | − | 0.693845i | \(-0.755915\pi\) | ||||
−0.720125 | + | 0.693845i | \(0.755915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.96968 | 0.151514 | ||||||||
\(170\) | −0.0449056 | −0.00344410 | ||||||||
\(171\) | 1.84367 | 0.140989 | ||||||||
\(172\) | −1.24472 | −0.0949091 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | −6.35026 | −0.481412 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.2750 | 1.75442 | ||||||||
\(177\) | 1.96968 | 0.148050 | ||||||||
\(178\) | −24.6253 | −1.84574 | ||||||||
\(179\) | −17.5066 | −1.30850 | −0.654252 | − | 0.756277i | \(-0.727016\pi\) | ||||
−0.654252 | + | 0.756277i | \(0.727016\pi\) | |||||||
\(180\) | −0.0376114 | −0.00280339 | ||||||||
\(181\) | 11.2447 | 0.835814 | 0.417907 | − | 0.908490i | \(-0.362764\pi\) | ||||
0.417907 | + | 0.908490i | \(0.362764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.15633 | −0.455089 | ||||||||
\(184\) | −20.8496 | −1.53705 | ||||||||
\(185\) | 1.12601 | 0.0827858 | ||||||||
\(186\) | −1.19394 | −0.0875437 | ||||||||
\(187\) | −0.836381 | −0.0611622 | ||||||||
\(188\) | 0.612127 | 0.0446439 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.529610 | −0.0384219 | ||||||||
\(191\) | −16.3938 | −1.18621 | −0.593105 | − | 0.805125i | \(-0.702098\pi\) | ||||
−0.593105 | + | 0.805125i | \(0.702098\pi\) | |||||||
\(192\) | 7.08110 | 0.511035 | ||||||||
\(193\) | 16.6556 | 1.19890 | 0.599449 | − | 0.800413i | \(-0.295386\pi\) | ||||
0.599449 | + | 0.800413i | \(0.295386\pi\) | |||||||
\(194\) | 3.38787 | 0.243235 | ||||||||
\(195\) | −0.750354 | −0.0537339 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.41090 | −0.670499 | −0.335249 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335249 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(198\) | −7.92478 | −0.563189 | ||||||||
\(199\) | 21.2301 | 1.50496 | 0.752482 | − | 0.658613i | \(-0.228856\pi\) | ||||
0.752482 | + | 0.658613i | \(0.228856\pi\) | |||||||
\(200\) | 13.2750 | 0.938687 | ||||||||
\(201\) | −10.8945 | −0.768436 | ||||||||
\(202\) | −21.4763 | −1.51107 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0303172 | 0.00212263 | ||||||||
\(205\) | 0.193937 | 0.0135451 | ||||||||
\(206\) | 8.35026 | 0.581790 | ||||||||
\(207\) | 7.79384 | 0.541710 | ||||||||
\(208\) | −16.8315 | −1.16705 | ||||||||
\(209\) | −9.86414 | −0.682317 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.380579 | 0.0262001 | 0.0131001 | − | 0.999914i | \(-0.495830\pi\) | ||||
0.0131001 | + | 0.999914i | \(0.495830\pi\) | |||||||
\(212\) | −0.362481 | −0.0248953 | ||||||||
\(213\) | −10.3430 | −0.708688 | ||||||||
\(214\) | −4.35026 | −0.297378 | ||||||||
\(215\) | 1.24472 | 0.0848893 | ||||||||
\(216\) | −2.67513 | −0.182020 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.73084 | 0.591327 | ||||||||
\(219\) | −11.8192 | −0.798670 | ||||||||
\(220\) | 0.201231 | 0.0135670 | ||||||||
\(221\) | 0.604833 | 0.0406854 | ||||||||
\(222\) | −8.59991 | −0.577188 | ||||||||
\(223\) | 14.8070 | 0.991551 | 0.495776 | − | 0.868451i | \(-0.334884\pi\) | ||||
0.495776 | + | 0.868451i | \(0.334884\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.96239 | −0.330826 | ||||||||
\(226\) | 23.0132 | 1.53081 | ||||||||
\(227\) | −9.39375 | −0.623485 | −0.311743 | − | 0.950167i | \(-0.600913\pi\) | ||||
−0.311743 | + | 0.950167i | \(0.600913\pi\) | |||||||
\(228\) | 0.357556 | 0.0236797 | ||||||||
\(229\) | 25.2252 | 1.66693 | 0.833464 | − | 0.552573i | \(-0.186354\pi\) | ||||
0.833464 | + | 0.552573i | \(0.186354\pi\) | |||||||
\(230\) | −2.23884 | −0.147625 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.4690 | 0.752975 | ||||||||
\(233\) | 1.06793 | 0.0699623 | 0.0349812 | − | 0.999388i | \(-0.488863\pi\) | ||||
0.0349812 | + | 0.999388i | \(0.488863\pi\) | |||||||
\(234\) | 5.73084 | 0.374637 | ||||||||
\(235\) | −0.612127 | −0.0399308 | ||||||||
\(236\) | 0.381994 | 0.0248657 | ||||||||
\(237\) | −1.61942 | −0.105193 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.21440 | −0.596030 | −0.298015 | − | 0.954561i | \(-0.596325\pi\) | ||||
−0.298015 | + | 0.954561i | \(0.596325\pi\) | |||||||
\(240\) | 0.843675 | 0.0544590 | ||||||||
\(241\) | 7.79877 | 0.502363 | 0.251181 | − | 0.967940i | \(-0.419181\pi\) | ||||
0.251181 | + | 0.967940i | \(0.419181\pi\) | |||||||
\(242\) | 26.1065 | 1.67819 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.19394 | −0.0764340 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.48119 | −0.0944375 | ||||||||
\(247\) | 7.13330 | 0.453881 | ||||||||
\(248\) | 2.15633 | 0.136927 | ||||||||
\(249\) | −6.12601 | −0.388220 | ||||||||
\(250\) | 2.86177 | 0.180994 | ||||||||
\(251\) | −21.9756 | −1.38709 | −0.693543 | − | 0.720416i | \(-0.743951\pi\) | ||||
−0.693543 | + | 0.720416i | \(0.743951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −41.6991 | −2.62160 | ||||||||
\(254\) | −24.4387 | −1.53342 | ||||||||
\(255\) | −0.0303172 | −0.00189853 | ||||||||
\(256\) | 4.61213 | 0.288258 | ||||||||
\(257\) | 20.2882 | 1.26554 | 0.632772 | − | 0.774338i | \(-0.281917\pi\) | ||||
0.632772 | + | 0.774338i | \(0.281917\pi\) | |||||||
\(258\) | −9.50659 | −0.591854 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.145521 | −0.00902483 | ||||||||
\(261\) | −4.28726 | −0.265375 | ||||||||
\(262\) | −6.61942 | −0.408949 | ||||||||
\(263\) | 14.1622 | 0.873279 | 0.436639 | − | 0.899637i | \(-0.356169\pi\) | ||||
0.436639 | + | 0.899637i | \(0.356169\pi\) | |||||||
\(264\) | 14.3127 | 0.880883 | ||||||||
\(265\) | 0.362481 | 0.0222670 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.6253 | −1.01745 | ||||||||
\(268\) | −2.11283 | −0.129062 | ||||||||
\(269\) | 1.49929 | 0.0914135 | 0.0457067 | − | 0.998955i | \(-0.485446\pi\) | ||||
0.0457067 | + | 0.998955i | \(0.485446\pi\) | |||||||
\(270\) | −0.287258 | −0.0174819 | ||||||||
\(271\) | 23.6072 | 1.43404 | 0.717018 | − | 0.697055i | \(-0.245507\pi\) | ||||
0.717018 | + | 0.697055i | \(0.245507\pi\) | |||||||
\(272\) | −0.680055 | −0.0412344 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.23884 | −0.497727 | ||||||||
\(275\) | 26.5501 | 1.60103 | ||||||||
\(276\) | 1.51151 | 0.0909823 | ||||||||
\(277\) | 6.94921 | 0.417538 | 0.208769 | − | 0.977965i | \(-0.433054\pi\) | ||||
0.208769 | + | 0.977965i | \(0.433054\pi\) | |||||||
\(278\) | 2.30536 | 0.138266 | ||||||||
\(279\) | −0.806063 | −0.0482578 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8315 | −1.36201 | −0.681005 | − | 0.732279i | \(-0.738457\pi\) | ||||
−0.681005 | + | 0.732279i | \(0.738457\pi\) | |||||||
\(282\) | 4.67513 | 0.278400 | ||||||||
\(283\) | −0.992706 | −0.0590102 | −0.0295051 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295051 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(284\) | −2.00588 | −0.119027 | ||||||||
\(285\) | −0.357556 | −0.0211798 | ||||||||
\(286\) | −30.6615 | −1.81305 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.09332 | −0.0644246 | ||||||||
\(289\) | −16.9756 | −0.998562 | ||||||||
\(290\) | 1.23155 | 0.0723190 | ||||||||
\(291\) | 2.28726 | 0.134081 | ||||||||
\(292\) | −2.29218 | −0.134140 | ||||||||
\(293\) | 12.4083 | 0.724903 | 0.362452 | − | 0.932003i | \(-0.381940\pi\) | ||||
0.362452 | + | 0.932003i | \(0.381940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.381994 | −0.0222405 | ||||||||
\(296\) | 15.5320 | 0.902778 | ||||||||
\(297\) | −5.35026 | −0.310454 | ||||||||
\(298\) | 8.43278 | 0.488498 | ||||||||
\(299\) | 30.1549 | 1.74390 | ||||||||
\(300\) | −0.962389 | −0.0555635 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.2012 | 0.817189 | ||||||||
\(303\) | −14.4993 | −0.832963 | ||||||||
\(304\) | −8.02047 | −0.460005 | ||||||||
\(305\) | 1.19394 | 0.0683646 | ||||||||
\(306\) | 0.231548 | 0.0132367 | ||||||||
\(307\) | 33.4626 | 1.90981 | 0.954907 | − | 0.296906i | \(-0.0959547\pi\) | ||||
0.954907 | + | 0.296906i | \(0.0959547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.63752 | 0.320707 | ||||||||
\(310\) | 0.231548 | 0.0131510 | ||||||||
\(311\) | 17.3430 | 0.983429 | 0.491715 | − | 0.870756i | \(-0.336370\pi\) | ||||
0.491715 | + | 0.870756i | \(0.336370\pi\) | |||||||
\(312\) | −10.3503 | −0.585968 | ||||||||
\(313\) | −1.04254 | −0.0589276 | −0.0294638 | − | 0.999566i | \(-0.509380\pi\) | ||||
−0.0294638 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(314\) | 3.96968 | 0.224022 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.314065 | −0.0176675 | ||||||||
\(317\) | 3.92970 | 0.220714 | 0.110357 | − | 0.993892i | \(-0.464801\pi\) | ||||
0.110357 | + | 0.993892i | \(0.464801\pi\) | |||||||
\(318\) | −2.76845 | −0.155247 | ||||||||
\(319\) | 22.9380 | 1.28428 | ||||||||
\(320\) | −1.37328 | −0.0767689 | ||||||||
\(321\) | −2.93700 | −0.163927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.288213 | 0.0160366 | ||||||||
\(324\) | 0.193937 | 0.0107743 | ||||||||
\(325\) | −19.1998 | −1.06501 | ||||||||
\(326\) | −17.7078 | −0.980745 | ||||||||
\(327\) | 5.89446 | 0.325964 | ||||||||
\(328\) | 2.67513 | 0.147709 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.53690 | 0.0846038 | ||||||||
\(331\) | 17.4993 | 0.961848 | 0.480924 | − | 0.876762i | \(-0.340301\pi\) | ||||
0.480924 | + | 0.876762i | \(0.340301\pi\) | |||||||
\(332\) | −1.18806 | −0.0652031 | ||||||||
\(333\) | −5.80606 | −0.318170 | ||||||||
\(334\) | −27.5682 | −1.50846 | ||||||||
\(335\) | 2.11283 | 0.115436 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3199 | −0.562163 | −0.281082 | − | 0.959684i | \(-0.590693\pi\) | ||||
−0.281082 | + | 0.959684i | \(0.590693\pi\) | |||||||
\(338\) | 2.91748 | 0.158690 | ||||||||
\(339\) | 15.5369 | 0.843849 | ||||||||
\(340\) | −0.00587961 | −0.000318866 0 | ||||||||
\(341\) | 4.31265 | 0.233543 | ||||||||
\(342\) | 2.73084 | 0.147667 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 17.1695 | 0.925717 | ||||||||
\(345\) | −1.51151 | −0.0813770 | ||||||||
\(346\) | 13.3307 | 0.716665 | ||||||||
\(347\) | −3.32979 | −0.178753 | −0.0893763 | − | 0.995998i | \(-0.528487\pi\) | ||||
−0.0893763 | + | 0.995998i | \(0.528487\pi\) | |||||||
\(348\) | −0.831456 | −0.0445707 | ||||||||
\(349\) | −22.6702 | −1.21351 | −0.606754 | − | 0.794890i | \(-0.707529\pi\) | ||||
−0.606754 | + | 0.794890i | \(0.707529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.86907 | 0.206516 | ||||||||
\(352\) | 5.84955 | 0.311782 | ||||||||
\(353\) | −35.5271 | −1.89091 | −0.945457 | − | 0.325746i | \(-0.894384\pi\) | ||||
−0.945457 | + | 0.325746i | \(0.894384\pi\) | |||||||
\(354\) | 2.91748 | 0.155062 | ||||||||
\(355\) | 2.00588 | 0.106461 | ||||||||
\(356\) | −3.22425 | −0.170885 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.9307 | −1.37048 | ||||||||
\(359\) | 23.8505 | 1.25878 | 0.629391 | − | 0.777089i | \(-0.283304\pi\) | ||||
0.629391 | + | 0.777089i | \(0.283304\pi\) | |||||||
\(360\) | 0.518806 | 0.0273435 | ||||||||
\(361\) | −15.6009 | −0.821098 | ||||||||
\(362\) | 16.6556 | 0.875400 | ||||||||
\(363\) | 17.6253 | 0.925088 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.29218 | 0.119978 | ||||||||
\(366\) | −9.11871 | −0.476643 | ||||||||
\(367\) | −27.0240 | −1.41064 | −0.705320 | − | 0.708889i | \(-0.749197\pi\) | ||||
−0.705320 | + | 0.708889i | \(0.749197\pi\) | |||||||
\(368\) | −33.9053 | −1.76743 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 1.66784 | 0.0867067 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.156325 | −0.00810508 | ||||||||
\(373\) | 26.9452 | 1.39517 | 0.697586 | − | 0.716501i | \(-0.254258\pi\) | ||||
0.697586 | + | 0.716501i | \(0.254258\pi\) | |||||||
\(374\) | −1.23884 | −0.0640590 | ||||||||
\(375\) | 1.93207 | 0.0997717 | ||||||||
\(376\) | −8.44358 | −0.435445 | ||||||||
\(377\) | −16.5877 | −0.854309 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5804 | −1.15988 | −0.579938 | − | 0.814660i | \(-0.696923\pi\) | ||||
−0.579938 | + | 0.814660i | \(0.696923\pi\) | |||||||
\(380\) | −0.0693432 | −0.00355723 | ||||||||
\(381\) | −16.4993 | −0.845284 | ||||||||
\(382\) | −24.2823 | −1.24239 | ||||||||
\(383\) | 23.7308 | 1.21259 | 0.606295 | − | 0.795240i | \(-0.292655\pi\) | ||||
0.606295 | + | 0.795240i | \(0.292655\pi\) | |||||||
\(384\) | 12.6751 | 0.646825 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.6702 | 1.25568 | ||||||||
\(387\) | −6.41819 | −0.326255 | ||||||||
\(388\) | 0.443583 | 0.0225195 | ||||||||
\(389\) | 23.2447 | 1.17855 | 0.589277 | − | 0.807931i | \(-0.299413\pi\) | ||||
0.589277 | + | 0.807931i | \(0.299413\pi\) | |||||||
\(390\) | −1.11142 | −0.0562789 | ||||||||
\(391\) | 1.21837 | 0.0616158 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.46898 | −0.225430 | ||||||||
\(394\) | −13.9394 | −0.702255 | ||||||||
\(395\) | 0.314065 | 0.0158023 | ||||||||
\(396\) | −1.03761 | −0.0521419 | ||||||||
\(397\) | −10.1563 | −0.509731 | −0.254866 | − | 0.966976i | \(-0.582031\pi\) | ||||
−0.254866 | + | 0.966976i | \(0.582031\pi\) | |||||||
\(398\) | 31.4460 | 1.57624 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5877 | 1.07938 | ||||||||
\(401\) | 22.1768 | 1.10746 | 0.553728 | − | 0.832698i | \(-0.313205\pi\) | ||||
0.553728 | + | 0.832698i | \(0.313205\pi\) | |||||||
\(402\) | −16.1368 | −0.804831 | ||||||||
\(403\) | −3.11871 | −0.155354 | ||||||||
\(404\) | −2.81194 | −0.139899 | ||||||||
\(405\) | −0.193937 | −0.00963679 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.0640 | 1.53978 | ||||||||
\(408\) | −0.418190 | −0.0207035 | ||||||||
\(409\) | 36.2228 | 1.79110 | 0.895552 | − | 0.444957i | \(-0.146781\pi\) | ||||
0.895552 | + | 0.444957i | \(0.146781\pi\) | |||||||
\(410\) | 0.287258 | 0.0141866 | ||||||||
\(411\) | −5.56230 | −0.274368 | ||||||||
\(412\) | 1.09332 | 0.0538641 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.5442 | 0.567366 | ||||||||
\(415\) | 1.18806 | 0.0583194 | ||||||||
\(416\) | −4.23013 | −0.207399 | ||||||||
\(417\) | 1.55642 | 0.0762181 | ||||||||
\(418\) | −14.6107 | −0.714633 | ||||||||
\(419\) | −38.7064 | −1.89093 | −0.945466 | − | 0.325721i | \(-0.894393\pi\) | ||||
−0.945466 | + | 0.325721i | \(0.894393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.04491 | −0.0996626 | −0.0498313 | − | 0.998758i | \(-0.515868\pi\) | ||||
−0.0498313 | + | 0.998758i | \(0.515868\pi\) | |||||||
\(422\) | 0.563711 | 0.0274410 | ||||||||
\(423\) | 3.15633 | 0.153466 | ||||||||
\(424\) | 5.00000 | 0.242821 | ||||||||
\(425\) | −0.775746 | −0.0376292 | ||||||||
\(426\) | −15.3199 | −0.742254 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.569591 | −0.0275322 | ||||||||
\(429\) | −20.7005 | −0.999431 | ||||||||
\(430\) | 1.84367 | 0.0889099 | ||||||||
\(431\) | −27.8799 | −1.34293 | −0.671463 | − | 0.741038i | \(-0.734334\pi\) | ||||
−0.671463 | + | 0.741038i | \(0.734334\pi\) | |||||||
\(432\) | −4.35026 | −0.209302 | ||||||||
\(433\) | 15.5271 | 0.746183 | 0.373091 | − | 0.927795i | \(-0.378298\pi\) | ||||
0.373091 | + | 0.927795i | \(0.378298\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.831456 | 0.0398653 | ||||||||
\(436\) | 1.14315 | 0.0547470 | ||||||||
\(437\) | 14.3693 | 0.687378 | ||||||||
\(438\) | −17.5066 | −0.836497 | ||||||||
\(439\) | −1.74401 | −0.0832373 | −0.0416186 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416186 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(440\) | −2.77575 | −0.132329 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.895875 | 0.0426124 | ||||||||
\(443\) | 10.9829 | 0.521811 | 0.260906 | − | 0.965364i | \(-0.415979\pi\) | ||||
0.260906 | + | 0.965364i | \(0.415979\pi\) | |||||||
\(444\) | −1.12601 | −0.0534380 | ||||||||
\(445\) | 3.22425 | 0.152844 | ||||||||
\(446\) | 21.9321 | 1.03851 | ||||||||
\(447\) | 5.69323 | 0.269281 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.8568 | 1.07868 | 0.539341 | − | 0.842088i | \(-0.318674\pi\) | ||||
0.539341 | + | 0.842088i | \(0.318674\pi\) | |||||||
\(450\) | −7.35026 | −0.346495 | ||||||||
\(451\) | 5.35026 | 0.251934 | ||||||||
\(452\) | 3.01317 | 0.141728 | ||||||||
\(453\) | 9.58769 | 0.450469 | ||||||||
\(454\) | −13.9140 | −0.653015 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.93207 | −0.230965 | ||||||||
\(457\) | −0.252016 | −0.0117888 | −0.00589441 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589441 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(458\) | 37.3634 | 1.74588 | ||||||||
\(459\) | 0.156325 | 0.00729663 | ||||||||
\(460\) | −0.293137 | −0.0136676 | ||||||||
\(461\) | −2.56134 | −0.119294 | −0.0596468 | − | 0.998220i | \(-0.518997\pi\) | ||||
−0.0596468 | + | 0.998220i | \(0.518997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1465 | −0.518021 | −0.259010 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259010 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(464\) | 18.6507 | 0.865837 | ||||||||
\(465\) | 0.156325 | 0.00724941 | ||||||||
\(466\) | 1.58181 | 0.0732759 | ||||||||
\(467\) | 3.87987 | 0.179539 | 0.0897695 | − | 0.995963i | \(-0.471387\pi\) | ||||
0.0897695 | + | 0.995963i | \(0.471387\pi\) | |||||||
\(468\) | 0.750354 | 0.0346851 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.906679 | −0.0418220 | ||||||||
\(471\) | 2.68006 | 0.123490 | ||||||||
\(472\) | −5.26916 | −0.242533 | ||||||||
\(473\) | 34.3390 | 1.57891 | ||||||||
\(474\) | −2.39868 | −0.110175 | ||||||||
\(475\) | −9.14903 | −0.419786 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.86907 | −0.0855787 | ||||||||
\(478\) | −13.6483 | −0.624260 | ||||||||
\(479\) | 39.6747 | 1.81278 | 0.906391 | − | 0.422440i | \(-0.138826\pi\) | ||||
0.906391 | + | 0.422440i | \(0.138826\pi\) | |||||||
\(480\) | 0.212035 | 0.00967803 | ||||||||
\(481\) | −22.4641 | −1.02427 | ||||||||
\(482\) | 11.5515 | 0.526156 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.41819 | 0.155372 | ||||||||
\(485\) | −0.443583 | −0.0201421 | ||||||||
\(486\) | 1.48119 | 0.0671883 | ||||||||
\(487\) | 15.6385 | 0.708647 | 0.354323 | − | 0.935123i | \(-0.384711\pi\) | ||||
0.354323 | + | 0.935123i | \(0.384711\pi\) | |||||||
\(488\) | 16.4690 | 0.745515 | ||||||||
\(489\) | −11.9551 | −0.540628 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7539 | −0.891479 | −0.445740 | − | 0.895163i | \(-0.647059\pi\) | ||||
−0.445740 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(492\) | −0.193937 | −0.00874334 | ||||||||
\(493\) | −0.670206 | −0.0301846 | ||||||||
\(494\) | 10.5658 | 0.475378 | ||||||||
\(495\) | 1.03761 | 0.0466372 | ||||||||
\(496\) | 3.50659 | 0.157450 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.07381 | −0.406607 | ||||||||
\(499\) | −35.3620 | −1.58302 | −0.791511 | − | 0.611155i | \(-0.790705\pi\) | ||||
−0.791511 | + | 0.611155i | \(0.790705\pi\) | |||||||
\(500\) | 0.374699 | 0.0167571 | ||||||||
\(501\) | −18.6121 | −0.831529 | ||||||||
\(502\) | −32.5501 | −1.45278 | ||||||||
\(503\) | 1.68594 | 0.0751721 | 0.0375861 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375861 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.81194 | 0.125130 | ||||||||
\(506\) | −61.7645 | −2.74577 | ||||||||
\(507\) | 1.96968 | 0.0874767 | ||||||||
\(508\) | −3.19982 | −0.141969 | ||||||||
\(509\) | −24.2433 | −1.07457 | −0.537283 | − | 0.843402i | \(-0.680549\pi\) | ||||
−0.537283 | + | 0.843402i | \(0.680549\pi\) | |||||||
\(510\) | −0.0449056 | −0.00198845 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.5188 | −0.818423 | ||||||||
\(513\) | 1.84367 | 0.0814002 | ||||||||
\(514\) | 30.0508 | 1.32548 | ||||||||
\(515\) | −1.09332 | −0.0481775 | ||||||||
\(516\) | −1.24472 | −0.0547958 | ||||||||
\(517\) | −16.8872 | −0.742697 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 2.00729 | 0.0880257 | ||||||||
\(521\) | 1.32582 | 0.0580854 | 0.0290427 | − | 0.999578i | \(-0.490754\pi\) | ||||
0.0290427 | + | 0.999578i | \(0.490754\pi\) | |||||||
\(522\) | −6.35026 | −0.277943 | ||||||||
\(523\) | 18.1055 | 0.791700 | 0.395850 | − | 0.918315i | \(-0.370450\pi\) | ||||
0.395850 | + | 0.918315i | \(0.370450\pi\) | |||||||
\(524\) | −0.866698 | −0.0378619 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.9770 | 0.914640 | ||||||||
\(527\) | −0.126008 | −0.00548899 | ||||||||
\(528\) | 23.2750 | 1.01292 | ||||||||
\(529\) | 37.7440 | 1.64104 | ||||||||
\(530\) | 0.536904 | 0.0233216 | ||||||||
\(531\) | 1.96968 | 0.0854770 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.86907 | −0.167588 | ||||||||
\(534\) | −24.6253 | −1.06564 | ||||||||
\(535\) | 0.569591 | 0.0246256 | ||||||||
\(536\) | 29.1441 | 1.25883 | ||||||||
\(537\) | −17.5066 | −0.755465 | ||||||||
\(538\) | 2.22074 | 0.0957431 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.0376114 | −0.00161854 | ||||||||
\(541\) | −7.59498 | −0.326534 | −0.163267 | − | 0.986582i | \(-0.552203\pi\) | ||||
−0.163267 | + | 0.986582i | \(0.552203\pi\) | |||||||
\(542\) | 34.9669 | 1.50195 | ||||||||
\(543\) | 11.2447 | 0.482557 | ||||||||
\(544\) | −0.170914 | −0.00732786 | ||||||||
\(545\) | −1.14315 | −0.0489672 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1886 | 1.67558 | 0.837791 | − | 0.545991i | \(-0.183847\pi\) | ||||
0.837791 | + | 0.545991i | \(0.183847\pi\) | |||||||
\(548\) | −1.07873 | −0.0460812 | ||||||||
\(549\) | −6.15633 | −0.262746 | ||||||||
\(550\) | 39.3258 | 1.67686 | ||||||||
\(551\) | −7.90431 | −0.336735 | ||||||||
\(552\) | −20.8496 | −0.887416 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.2931 | 0.437314 | ||||||||
\(555\) | 1.12601 | 0.0477964 | ||||||||
\(556\) | 0.301846 | 0.0128011 | ||||||||
\(557\) | −20.3331 | −0.861542 | −0.430771 | − | 0.902461i | \(-0.641758\pi\) | ||||
−0.430771 | + | 0.902461i | \(0.641758\pi\) | |||||||
\(558\) | −1.19394 | −0.0505434 | ||||||||
\(559\) | −24.8324 | −1.05030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.836381 | −0.0353120 | ||||||||
\(562\) | −33.8178 | −1.42652 | ||||||||
\(563\) | 15.7367 | 0.663224 | 0.331612 | − | 0.943416i | \(-0.392408\pi\) | ||||
0.331612 | + | 0.943416i | \(0.392408\pi\) | |||||||
\(564\) | 0.612127 | 0.0257752 | ||||||||
\(565\) | −3.01317 | −0.126765 | ||||||||
\(566\) | −1.47039 | −0.0618051 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.6688 | 1.16096 | ||||||||
\(569\) | −36.2823 | −1.52103 | −0.760517 | − | 0.649318i | \(-0.775055\pi\) | ||||
−0.760517 | + | 0.649318i | \(0.775055\pi\) | |||||||
\(570\) | −0.529610 | −0.0221829 | ||||||||
\(571\) | −3.81336 | −0.159584 | −0.0797920 | − | 0.996812i | \(-0.525426\pi\) | ||||
−0.0797920 | + | 0.996812i | \(0.525426\pi\) | |||||||
\(572\) | −4.01459 | −0.167858 | ||||||||
\(573\) | −16.3938 | −0.684859 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.6761 | −1.61290 | ||||||||
\(576\) | 7.08110 | 0.295046 | ||||||||
\(577\) | −20.7064 | −0.862019 | −0.431009 | − | 0.902347i | \(-0.641842\pi\) | ||||
−0.431009 | + | 0.902347i | \(0.641842\pi\) | |||||||
\(578\) | −25.1441 | −1.04586 | ||||||||
\(579\) | 16.6556 | 0.692184 | ||||||||
\(580\) | 0.161250 | 0.00669553 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.38787 | 0.140432 | ||||||||
\(583\) | 10.0000 | 0.414158 | ||||||||
\(584\) | 31.6180 | 1.30836 | ||||||||
\(585\) | −0.750354 | −0.0310233 | ||||||||
\(586\) | 18.3792 | 0.759236 | ||||||||
\(587\) | −36.8773 | −1.52209 | −0.761045 | − | 0.648699i | \(-0.775313\pi\) | ||||
−0.761045 | + | 0.648699i | \(0.775313\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.48612 | −0.0612345 | ||||||||
\(590\) | −0.565807 | −0.0232939 | ||||||||
\(591\) | −9.41090 | −0.387113 | ||||||||
\(592\) | 25.2579 | 1.03809 | ||||||||
\(593\) | −18.6399 | −0.765449 | −0.382724 | − | 0.923863i | \(-0.625014\pi\) | ||||
−0.382724 | + | 0.923863i | \(0.625014\pi\) | |||||||
\(594\) | −7.92478 | −0.325158 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.10413 | 0.0452267 | ||||||||
\(597\) | 21.2301 | 0.868892 | ||||||||
\(598\) | 44.6653 | 1.82650 | ||||||||
\(599\) | −32.0167 | −1.30817 | −0.654083 | − | 0.756423i | \(-0.726945\pi\) | ||||
−0.654083 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(600\) | 13.2750 | 0.541951 | ||||||||
\(601\) | 14.0254 | 0.572108 | 0.286054 | − | 0.958214i | \(-0.407656\pi\) | ||||
0.286054 | + | 0.958214i | \(0.407656\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.8945 | −0.443657 | ||||||||
\(604\) | 1.85940 | 0.0756581 | ||||||||
\(605\) | −3.41819 | −0.138969 | ||||||||
\(606\) | −21.4763 | −0.872414 | ||||||||
\(607\) | 29.9062 | 1.21386 | 0.606928 | − | 0.794757i | \(-0.292402\pi\) | ||||
0.606928 | + | 0.794757i | \(0.292402\pi\) | |||||||
\(608\) | −2.01573 | −0.0817486 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.76845 | 0.0716025 | ||||||||
\(611\) | 12.2120 | 0.494046 | ||||||||
\(612\) | 0.0303172 | 0.00122550 | ||||||||
\(613\) | 11.3733 | 0.459363 | 0.229681 | − | 0.973266i | \(-0.426232\pi\) | ||||
0.229681 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(614\) | 49.5647 | 2.00027 | ||||||||
\(615\) | 0.193937 | 0.00782028 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4142 | −0.982880 | −0.491440 | − | 0.870912i | \(-0.663529\pi\) | ||||
−0.491440 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(618\) | 8.35026 | 0.335897 | ||||||||
\(619\) | 28.0372 | 1.12691 | 0.563454 | − | 0.826147i | \(-0.309472\pi\) | ||||
0.563454 | + | 0.826147i | \(0.309472\pi\) | |||||||
\(620\) | 0.0303172 | 0.00121757 | ||||||||
\(621\) | 7.79384 | 0.312756 | ||||||||
\(622\) | 25.6883 | 1.03001 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.8315 | −0.673797 | ||||||||
\(625\) | 24.4372 | 0.977490 | ||||||||
\(626\) | −1.54420 | −0.0617186 | ||||||||
\(627\) | −9.86414 | −0.393936 | ||||||||
\(628\) | 0.519761 | 0.0207407 | ||||||||
\(629\) | −0.907634 | −0.0361897 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.5745 | 0.739440 | 0.369720 | − | 0.929143i | \(-0.379454\pi\) | ||||
0.369720 | + | 0.929143i | \(0.379454\pi\) | |||||||
\(632\) | 4.33216 | 0.172324 | ||||||||
\(633\) | 0.380579 | 0.0151267 | ||||||||
\(634\) | 5.82065 | 0.231168 | ||||||||
\(635\) | 3.19982 | 0.126981 | ||||||||
\(636\) | −0.362481 | −0.0143733 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 33.9756 | 1.34511 | ||||||||
\(639\) | −10.3430 | −0.409161 | ||||||||
\(640\) | −2.45817 | −0.0971678 | ||||||||
\(641\) | −43.7802 | −1.72921 | −0.864607 | − | 0.502448i | \(-0.832433\pi\) | ||||
−0.864607 | + | 0.502448i | \(0.832433\pi\) | |||||||
\(642\) | −4.35026 | −0.171691 | ||||||||
\(643\) | 22.2677 | 0.878154 | 0.439077 | − | 0.898449i | \(-0.355306\pi\) | ||||
0.439077 | + | 0.898449i | \(0.355306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.24472 | 0.0490109 | ||||||||
\(646\) | 0.426899 | 0.0167961 | ||||||||
\(647\) | 45.6589 | 1.79504 | 0.897519 | − | 0.440976i | \(-0.145367\pi\) | ||||
0.897519 | + | 0.440976i | \(0.145367\pi\) | |||||||
\(648\) | −2.67513 | −0.105089 | ||||||||
\(649\) | −10.5383 | −0.413665 | ||||||||
\(650\) | −28.4387 | −1.11546 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.31853 | −0.0908006 | ||||||||
\(653\) | 7.11871 | 0.278577 | 0.139288 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139288 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(654\) | 8.73084 | 0.341403 | ||||||||
\(655\) | 0.866698 | 0.0338647 | ||||||||
\(656\) | 4.35026 | 0.169849 | ||||||||
\(657\) | −11.8192 | −0.461112 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.6531 | −0.609757 | −0.304878 | − | 0.952391i | \(-0.598616\pi\) | ||||
−0.304878 | + | 0.952391i | \(0.598616\pi\) | |||||||
\(660\) | 0.201231 | 0.00783290 | ||||||||
\(661\) | −30.2981 | −1.17846 | −0.589229 | − | 0.807966i | \(-0.700568\pi\) | ||||
−0.589229 | + | 0.807966i | \(0.700568\pi\) | |||||||
\(662\) | 25.9199 | 1.00740 | ||||||||
\(663\) | 0.604833 | 0.0234898 | ||||||||
\(664\) | 16.3879 | 0.635973 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.59991 | −0.333240 | ||||||||
\(667\) | −33.4142 | −1.29380 | ||||||||
\(668\) | −3.60957 | −0.139659 | ||||||||
\(669\) | 14.8070 | 0.572472 | ||||||||
\(670\) | 3.12952 | 0.120904 | ||||||||
\(671\) | 32.9380 | 1.27156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.6688 | −1.52912 | −0.764560 | − | 0.644553i | \(-0.777044\pi\) | ||||
−0.764560 | + | 0.644553i | \(0.777044\pi\) | |||||||
\(674\) | −15.2858 | −0.588789 | ||||||||
\(675\) | −4.96239 | −0.191002 | ||||||||
\(676\) | 0.381994 | 0.0146921 | ||||||||
\(677\) | −29.3503 | −1.12802 | −0.564011 | − | 0.825767i | \(-0.690742\pi\) | ||||
−0.564011 | + | 0.825767i | \(0.690742\pi\) | |||||||
\(678\) | 23.0132 | 0.883816 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.0811024 | 0.00311013 | ||||||||
\(681\) | −9.39375 | −0.359969 | ||||||||
\(682\) | 6.38787 | 0.244604 | ||||||||
\(683\) | −13.7626 | −0.526610 | −0.263305 | − | 0.964713i | \(-0.584813\pi\) | ||||
−0.263305 | + | 0.964713i | \(0.584813\pi\) | |||||||
\(684\) | 0.357556 | 0.0136715 | ||||||||
\(685\) | 1.07873 | 0.0412163 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.2252 | 0.962402 | ||||||||
\(688\) | 27.9208 | 1.06447 | ||||||||
\(689\) | −7.23155 | −0.275500 | ||||||||
\(690\) | −2.23884 | −0.0852313 | ||||||||
\(691\) | −51.4274 | −1.95639 | −0.978195 | − | 0.207688i | \(-0.933406\pi\) | ||||
−0.978195 | + | 0.207688i | \(0.933406\pi\) | |||||||
\(692\) | 1.74543 | 0.0663513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.93207 | −0.187219 | ||||||||
\(695\) | −0.301846 | −0.0114497 | ||||||||
\(696\) | 11.4690 | 0.434730 | ||||||||
\(697\) | −0.156325 | −0.00592124 | ||||||||
\(698\) | −33.5790 | −1.27098 | ||||||||
\(699\) | 1.06793 | 0.0403928 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.9478 | −0.866726 | −0.433363 | − | 0.901219i | \(-0.642673\pi\) | ||||
−0.433363 | + | 0.901219i | \(0.642673\pi\) | |||||||
\(702\) | 5.73084 | 0.216297 | ||||||||
\(703\) | −10.7045 | −0.403728 | ||||||||
\(704\) | −37.8858 | −1.42787 | ||||||||
\(705\) | −0.612127 | −0.0230540 | ||||||||
\(706\) | −52.6225 | −1.98047 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.381994 | 0.0143562 | ||||||||
\(709\) | −41.9511 | −1.57551 | −0.787754 | − | 0.615990i | \(-0.788756\pi\) | ||||
−0.787754 | + | 0.615990i | \(0.788756\pi\) | |||||||
\(710\) | 2.97110 | 0.111503 | ||||||||
\(711\) | −1.61942 | −0.0607330 | ||||||||
\(712\) | 44.4749 | 1.66677 | ||||||||
\(713\) | −6.28233 | −0.235275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01459 | 0.150137 | ||||||||
\(716\) | −3.39517 | −0.126883 | ||||||||
\(717\) | −9.21440 | −0.344118 | ||||||||
\(718\) | 35.3272 | 1.31840 | ||||||||
\(719\) | 34.8265 | 1.29881 | 0.649405 | − | 0.760443i | \(-0.275018\pi\) | ||||
0.649405 | + | 0.760443i | \(0.275018\pi\) | |||||||
\(720\) | 0.843675 | 0.0314419 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23.1079 | −0.859987 | ||||||||
\(723\) | 7.79877 | 0.290039 | ||||||||
\(724\) | 2.18076 | 0.0810474 | ||||||||
\(725\) | 21.2750 | 0.790135 | ||||||||
\(726\) | 26.1065 | 0.968903 | ||||||||
\(727\) | −9.21440 | −0.341743 | −0.170872 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170872 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.39517 | 0.125661 | ||||||||
\(731\) | −1.00332 | −0.0371093 | ||||||||
\(732\) | −1.19394 | −0.0441292 | ||||||||
\(733\) | 22.2374 | 0.821358 | 0.410679 | − | 0.911780i | \(-0.365292\pi\) | ||||
0.410679 | + | 0.911780i | \(0.365292\pi\) | |||||||
\(734\) | −40.0278 | −1.47745 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.52118 | −0.314095 | ||||||||
\(737\) | 58.2882 | 2.14707 | ||||||||
\(738\) | −1.48119 | −0.0545235 | ||||||||
\(739\) | 20.0910 | 0.739058 | 0.369529 | − | 0.929219i | \(-0.379519\pi\) | ||||
0.369529 | + | 0.929219i | \(0.379519\pi\) | |||||||
\(740\) | 0.218374 | 0.00802759 | ||||||||
\(741\) | 7.13330 | 0.262048 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.3561 | 1.29709 | 0.648546 | − | 0.761176i | \(-0.275378\pi\) | ||||
0.648546 | + | 0.761176i | \(0.275378\pi\) | |||||||
\(744\) | 2.15633 | 0.0790547 | ||||||||
\(745\) | −1.10413 | −0.0404520 | ||||||||
\(746\) | 39.9111 | 1.46125 | ||||||||
\(747\) | −6.12601 | −0.224139 | ||||||||
\(748\) | −0.162205 | −0.00593079 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.86177 | 0.104497 | ||||||||
\(751\) | 35.9829 | 1.31303 | 0.656517 | − | 0.754312i | \(-0.272029\pi\) | ||||
0.656517 | + | 0.754312i | \(0.272029\pi\) | |||||||
\(752\) | −13.7308 | −0.500712 | ||||||||
\(753\) | −21.9756 | −0.800834 | ||||||||
\(754\) | −24.5696 | −0.894772 | ||||||||
\(755\) | −1.85940 | −0.0676706 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.66291 | 0.0604396 | 0.0302198 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302198 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(758\) | −33.4460 | −1.21481 | ||||||||
\(759\) | −41.6991 | −1.51358 | ||||||||
\(760\) | 0.956509 | 0.0346962 | ||||||||
\(761\) | −39.0059 | −1.41396 | −0.706981 | − | 0.707233i | \(-0.749943\pi\) | ||||
−0.706981 | + | 0.707233i | \(0.749943\pi\) | |||||||
\(762\) | −24.4387 | −0.885319 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.17935 | −0.115025 | ||||||||
\(765\) | −0.0303172 | −0.00109612 | ||||||||
\(766\) | 35.1500 | 1.27002 | ||||||||
\(767\) | 7.62084 | 0.275172 | ||||||||
\(768\) | 4.61213 | 0.166426 | ||||||||
\(769\) | −41.5271 | −1.49750 | −0.748752 | − | 0.662850i | \(-0.769347\pi\) | ||||
−0.748752 | + | 0.662850i | \(0.769347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.2882 | 0.730662 | ||||||||
\(772\) | 3.23013 | 0.116255 | ||||||||
\(773\) | −46.4894 | −1.67211 | −0.836055 | − | 0.548646i | \(-0.815143\pi\) | ||||
−0.836055 | + | 0.548646i | \(0.815143\pi\) | |||||||
\(774\) | −9.50659 | −0.341707 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | −6.11871 | −0.219649 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.4299 | 1.23437 | ||||||||
\(779\) | −1.84367 | −0.0660565 | ||||||||
\(780\) | −0.145521 | −0.00521049 | ||||||||
\(781\) | 55.3376 | 1.98013 | ||||||||
\(782\) | 1.80465 | 0.0645341 | ||||||||
\(783\) | −4.28726 | −0.153214 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.519761 | −0.0185511 | ||||||||
\(786\) | −6.61942 | −0.236107 | ||||||||
\(787\) | −24.6058 | −0.877102 | −0.438551 | − | 0.898706i | \(-0.644508\pi\) | ||||
−0.438551 | + | 0.898706i | \(0.644508\pi\) | |||||||
\(788\) | −1.82512 | −0.0650171 | ||||||||
\(789\) | 14.1622 | 0.504188 | ||||||||
\(790\) | 0.465191 | 0.0165508 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.3127 | 0.508578 | ||||||||
\(793\) | −23.8192 | −0.845846 | ||||||||
\(794\) | −15.0435 | −0.533874 | ||||||||
\(795\) | 0.362481 | 0.0128559 | ||||||||
\(796\) | 4.11730 | 0.145934 | ||||||||
\(797\) | 40.7123 | 1.44210 | 0.721052 | − | 0.692881i | \(-0.243659\pi\) | ||||
0.721052 | + | 0.692881i | \(0.243659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.493413 | 0.0174557 | ||||||||
\(800\) | 5.42548 | 0.191820 | ||||||||
\(801\) | −16.6253 | −0.587426 | ||||||||
\(802\) | 32.8481 | 1.15991 | ||||||||
\(803\) | 63.2360 | 2.23155 | ||||||||
\(804\) | −2.11283 | −0.0745139 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.61942 | −0.162712 | ||||||||
\(807\) | 1.49929 | 0.0527776 | ||||||||
\(808\) | 38.7875 | 1.36454 | ||||||||
\(809\) | −12.1916 | −0.428633 | −0.214316 | − | 0.976764i | \(-0.568752\pi\) | ||||
−0.214316 | + | 0.976764i | \(0.568752\pi\) | |||||||
\(810\) | −0.287258 | −0.0100932 | ||||||||
\(811\) | 39.7997 | 1.39756 | 0.698779 | − | 0.715338i | \(-0.253727\pi\) | ||||
0.698779 | + | 0.715338i | \(0.253727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.6072 | 0.827941 | ||||||||
\(814\) | 46.0118 | 1.61271 | ||||||||
\(815\) | 2.31853 | 0.0812146 | ||||||||
\(816\) | −0.680055 | −0.0238067 | ||||||||
\(817\) | −11.8331 | −0.413986 | ||||||||
\(818\) | 53.6531 | 1.87594 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0376114 | 0.00131345 | ||||||||
\(821\) | 4.47882 | 0.156312 | 0.0781560 | − | 0.996941i | \(-0.475097\pi\) | ||||
0.0781560 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(822\) | −8.23884 | −0.287363 | ||||||||
\(823\) | 23.4471 | 0.817314 | 0.408657 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408657 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(824\) | −15.0811 | −0.525375 | ||||||||
\(825\) | 26.5501 | 0.924355 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.1524 | −0.631219 | −0.315610 | − | 0.948889i | \(-0.602209\pi\) | ||||
−0.315610 | + | 0.948889i | \(0.602209\pi\) | |||||||
\(828\) | 1.51151 | 0.0525287 | ||||||||
\(829\) | 6.37328 | 0.221353 | 0.110677 | − | 0.993856i | \(-0.464698\pi\) | ||||
0.110677 | + | 0.993856i | \(0.464698\pi\) | |||||||
\(830\) | 1.75974 | 0.0610816 | ||||||||
\(831\) | 6.94921 | 0.241066 | ||||||||
\(832\) | 27.3973 | 0.949829 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.30536 | 0.0798280 | ||||||||
\(835\) | 3.60957 | 0.124914 | ||||||||
\(836\) | −1.91302 | −0.0661631 | ||||||||
\(837\) | −0.806063 | −0.0278616 | ||||||||
\(838\) | −57.3317 | −1.98049 | ||||||||
\(839\) | 7.63515 | 0.263595 | 0.131797 | − | 0.991277i | \(-0.457925\pi\) | ||||
0.131797 | + | 0.991277i | \(0.457925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6194 | −0.366187 | ||||||||
\(842\) | −3.02890 | −0.104383 | ||||||||
\(843\) | −22.8315 | −0.786357 | ||||||||
\(844\) | 0.0738082 | 0.00254058 | ||||||||
\(845\) | −0.381994 | −0.0131410 | ||||||||
\(846\) | 4.67513 | 0.160734 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.13093 | 0.279217 | ||||||||
\(849\) | −0.992706 | −0.0340696 | ||||||||
\(850\) | −1.14903 | −0.0394114 | ||||||||
\(851\) | −45.2516 | −1.55120 | ||||||||
\(852\) | −2.00588 | −0.0687203 | ||||||||
\(853\) | 11.0884 | 0.379659 | 0.189830 | − | 0.981817i | \(-0.439206\pi\) | ||||
0.189830 | + | 0.981817i | \(0.439206\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.357556 | −0.0122282 | ||||||||
\(856\) | 7.85685 | 0.268542 | ||||||||
\(857\) | −10.1286 | −0.345985 | −0.172993 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172993 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(858\) | −30.6615 | −1.04677 | ||||||||
\(859\) | −47.5221 | −1.62143 | −0.810717 | − | 0.585438i | \(-0.800923\pi\) | ||||
−0.810717 | + | 0.585438i | \(0.800923\pi\) | |||||||
\(860\) | 0.241397 | 0.00823157 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.2955 | −1.40653 | ||||||||
\(863\) | 48.3498 | 1.64585 | 0.822923 | − | 0.568153i | \(-0.192342\pi\) | ||||
0.822923 | + | 0.568153i | \(0.192342\pi\) | |||||||
\(864\) | −1.09332 | −0.0371955 | ||||||||
\(865\) | −1.74543 | −0.0593464 | ||||||||
\(866\) | 22.9986 | 0.781524 | ||||||||
\(867\) | −16.9756 | −0.576520 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.66433 | 0.293917 | ||||||||
\(870\) | 1.23155 | 0.0417534 | ||||||||
\(871\) | −42.1514 | −1.42825 | ||||||||
\(872\) | −15.7685 | −0.533987 | ||||||||
\(873\) | 2.28726 | 0.0774119 | ||||||||
\(874\) | 21.2837 | 0.719934 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.29218 | −0.0774457 | ||||||||
\(877\) | 47.7137 | 1.61118 | 0.805589 | − | 0.592475i | \(-0.201849\pi\) | ||||
0.805589 | + | 0.592475i | \(0.201849\pi\) | |||||||
\(878\) | −2.58322 | −0.0871796 | ||||||||
\(879\) | 12.4083 | 0.418523 | ||||||||
\(880\) | −4.51388 | −0.152163 | ||||||||
\(881\) | −38.3660 | −1.29258 | −0.646292 | − | 0.763091i | \(-0.723681\pi\) | ||||
−0.646292 | + | 0.763091i | \(0.723681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.4372 | 1.22621 | 0.613105 | − | 0.790001i | \(-0.289920\pi\) | ||||
0.613105 | + | 0.790001i | \(0.289920\pi\) | |||||||
\(884\) | 0.117299 | 0.00394520 | ||||||||
\(885\) | −0.381994 | −0.0128406 | ||||||||
\(886\) | 16.2677 | 0.546526 | ||||||||
\(887\) | 10.9149 | 0.366487 | 0.183244 | − | 0.983068i | \(-0.441340\pi\) | ||||
0.183244 | + | 0.983068i | \(0.441340\pi\) | |||||||
\(888\) | 15.5320 | 0.521219 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.77575 | 0.160083 | ||||||||
\(891\) | −5.35026 | −0.179241 | ||||||||
\(892\) | 2.87162 | 0.0961490 | ||||||||
\(893\) | 5.81924 | 0.194733 | ||||||||
\(894\) | 8.43278 | 0.282034 | ||||||||
\(895\) | 3.39517 | 0.113488 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.1549 | 1.00684 | ||||||||
\(898\) | 33.8554 | 1.12977 | ||||||||
\(899\) | 3.45580 | 0.115257 | ||||||||
\(900\) | −0.962389 | −0.0320796 | ||||||||
\(901\) | −0.292182 | −0.00973400 | ||||||||
\(902\) | 7.92478 | 0.263866 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.5633 | −1.38237 | ||||||||
\(905\) | −2.18076 | −0.0724910 | ||||||||
\(906\) | 14.2012 | 0.471804 | ||||||||
\(907\) | 42.4993 | 1.41117 | 0.705583 | − | 0.708627i | \(-0.250685\pi\) | ||||
0.705583 | + | 0.708627i | \(0.250685\pi\) | |||||||
\(908\) | −1.82179 | −0.0604583 | ||||||||
\(909\) | −14.4993 | −0.480911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.93207 | −0.163407 | −0.0817034 | − | 0.996657i | \(-0.526036\pi\) | ||||
−0.0817034 | + | 0.996657i | \(0.526036\pi\) | |||||||
\(912\) | −8.02047 | −0.265584 | ||||||||
\(913\) | 32.7757 | 1.08472 | ||||||||
\(914\) | −0.373285 | −0.0123472 | ||||||||
\(915\) | 1.19394 | 0.0394703 | ||||||||
\(916\) | 4.89209 | 0.161639 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.231548 | 0.00764222 | ||||||||
\(919\) | −4.02776 | −0.132864 | −0.0664318 | − | 0.997791i | \(-0.521161\pi\) | ||||
−0.0664318 | + | 0.997791i | \(0.521161\pi\) | |||||||
\(920\) | 4.04349 | 0.133310 | ||||||||
\(921\) | 33.4626 | 1.10263 | ||||||||
\(922\) | −3.79384 | −0.124944 | ||||||||
\(923\) | −40.0176 | −1.31720 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8119 | 0.947331 | ||||||||
\(926\) | −16.5101 | −0.542555 | ||||||||
\(927\) | 5.63752 | 0.185160 | ||||||||
\(928\) | 4.68735 | 0.153870 | ||||||||
\(929\) | −14.9076 | −0.489104 | −0.244552 | − | 0.969636i | \(-0.578641\pi\) | ||||
−0.244552 | + | 0.969636i | \(0.578641\pi\) | |||||||
\(930\) | 0.231548 | 0.00759276 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.207110 | 0.00678413 | ||||||||
\(933\) | 17.3430 | 0.567783 | ||||||||
\(934\) | 5.74684 | 0.188042 | ||||||||
\(935\) | 0.162205 | 0.00530466 | ||||||||
\(936\) | −10.3503 | −0.338309 | ||||||||
\(937\) | 22.0957 | 0.721835 | 0.360917 | − | 0.932598i | \(-0.382464\pi\) | ||||
0.360917 | + | 0.932598i | \(0.382464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.04254 | −0.0340219 | ||||||||
\(940\) | −0.118714 | −0.00387202 | ||||||||
\(941\) | −34.0395 | −1.10966 | −0.554828 | − | 0.831965i | \(-0.687216\pi\) | ||||
−0.554828 | + | 0.831965i | \(0.687216\pi\) | |||||||
\(942\) | 3.96968 | 0.129339 | ||||||||
\(943\) | −7.79384 | −0.253803 | ||||||||
\(944\) | −8.56864 | −0.278885 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50.8627 | 1.65369 | ||||||||
\(947\) | 27.4363 | 0.891560 | 0.445780 | − | 0.895143i | \(-0.352926\pi\) | ||||
0.445780 | + | 0.895143i | \(0.352926\pi\) | |||||||
\(948\) | −0.314065 | −0.0102004 | ||||||||
\(949\) | −45.7294 | −1.48444 | ||||||||
\(950\) | −13.5515 | −0.439668 | ||||||||
\(951\) | 3.92970 | 0.127429 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4676 | 1.40805 | 0.704026 | − | 0.710174i | \(-0.251384\pi\) | ||||
0.704026 | + | 0.710174i | \(0.251384\pi\) | |||||||
\(954\) | −2.76845 | −0.0896319 | ||||||||
\(955\) | 3.17935 | 0.102881 | ||||||||
\(956\) | −1.78701 | −0.0577960 | ||||||||
\(957\) | 22.9380 | 0.741479 | ||||||||
\(958\) | 58.7659 | 1.89864 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.37328 | −0.0443226 | ||||||||
\(961\) | −30.3503 | −0.979041 | ||||||||
\(962\) | −33.2736 | −1.07278 | ||||||||
\(963\) | −2.93700 | −0.0946434 | ||||||||
\(964\) | 1.51247 | 0.0487133 | ||||||||
\(965\) | −3.23013 | −0.103982 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.5026 | 0.787951 | 0.393976 | − | 0.919121i | \(-0.371099\pi\) | ||||
0.393976 | + | 0.919121i | \(0.371099\pi\) | |||||||
\(968\) | −47.1500 | −1.51546 | ||||||||
\(969\) | 0.288213 | 0.00925873 | ||||||||
\(970\) | −0.657032 | −0.0210960 | ||||||||
\(971\) | 14.2184 | 0.456289 | 0.228145 | − | 0.973627i | \(-0.426734\pi\) | ||||
0.228145 | + | 0.973627i | \(0.426734\pi\) | |||||||
\(972\) | 0.193937 | 0.00622052 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.1636 | 0.742210 | ||||||||
\(975\) | −19.1998 | −0.614886 | ||||||||
\(976\) | 26.7816 | 0.857259 | ||||||||
\(977\) | 42.4201 | 1.35714 | 0.678570 | − | 0.734536i | \(-0.262600\pi\) | ||||
0.678570 | + | 0.734536i | \(0.262600\pi\) | |||||||
\(978\) | −17.7078 | −0.566234 | ||||||||
\(979\) | 88.9497 | 2.84285 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.89446 | 0.188196 | ||||||||
\(982\) | −29.2593 | −0.933702 | ||||||||
\(983\) | −9.16950 | −0.292462 | −0.146231 | − | 0.989251i | \(-0.546714\pi\) | ||||
−0.146231 | + | 0.989251i | \(0.546714\pi\) | |||||||
\(984\) | 2.67513 | 0.0852801 | ||||||||
\(985\) | 1.82512 | 0.0581531 | ||||||||
\(986\) | −0.992706 | −0.0316142 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.38341 | 0.0440121 | ||||||||
\(989\) | −50.0224 | −1.59062 | ||||||||
\(990\) | 1.53690 | 0.0488460 | ||||||||
\(991\) | 13.0870 | 0.415722 | 0.207861 | − | 0.978158i | \(-0.433350\pi\) | ||||
0.207861 | + | 0.978158i | \(0.433350\pi\) | |||||||
\(992\) | 0.881286 | 0.0279809 | ||||||||
\(993\) | 17.4993 | 0.555323 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.11730 | −0.130527 | ||||||||
\(996\) | −1.18806 | −0.0376450 | ||||||||
\(997\) | 49.5280 | 1.56857 | 0.784284 | − | 0.620402i | \(-0.213031\pi\) | ||||
0.784284 | + | 0.620402i | \(0.213031\pi\) | |||||||
\(998\) | −52.3780 | −1.65800 | ||||||||
\(999\) | −5.80606 | −0.183696 |
(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 | 6027.2.a.o.1.3 | 3 | ||
7.6 | odd | 2 | 861.2.a.h.1.3 | ✓ | 3 | ||
21.20 | even | 2 | 2583.2.a.n.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.h.1.3 | ✓ | 3 | 7.6 | odd | 2 | ||
2583.2.a.n.1.1 | 3 | 21.20 | even | 2 | |||
6027.2.a.o.1.3 | 3 | 1.1 | even | 1 | trivial |