Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65348 | −1.87629 | −0.938145 | − | 0.346242i | \(-0.887458\pi\) | ||||
−0.938145 | + | 0.346242i | \(0.887458\pi\) | |||||||
\(3\) | 3.32664 | 1.92064 | 0.960318 | − | 0.278907i | \(-0.0899722\pi\) | ||||
0.960318 | + | 0.278907i | \(0.0899722\pi\) | |||||||
\(4\) | 5.04093 | 2.52047 | ||||||||
\(5\) | −4.27882 | −1.91355 | −0.956773 | − | 0.290835i | \(-0.906067\pi\) | ||||
−0.956773 | + | 0.290835i | \(0.906067\pi\) | |||||||
\(6\) | −8.82716 | −3.60367 | ||||||||
\(7\) | −1.52713 | −0.577199 | −0.288600 | − | 0.957450i | \(-0.593190\pi\) | ||||
−0.288600 | + | 0.957450i | \(0.593190\pi\) | |||||||
\(8\) | −8.06904 | −2.85284 | ||||||||
\(9\) | 8.06653 | 2.68884 | ||||||||
\(10\) | 11.3537 | 3.59037 | ||||||||
\(11\) | 5.37053 | 1.61928 | 0.809638 | − | 0.586930i | \(-0.199664\pi\) | ||||
0.809638 | + | 0.586930i | \(0.199664\pi\) | |||||||
\(12\) | 16.7694 | 4.84090 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.05219 | 1.08299 | ||||||||
\(15\) | −14.2341 | −3.67523 | ||||||||
\(16\) | 11.3291 | 2.83229 | ||||||||
\(17\) | 2.47955 | 0.601380 | 0.300690 | − | 0.953722i | \(-0.402783\pi\) | ||||
0.300690 | + | 0.953722i | \(0.402783\pi\) | |||||||
\(18\) | −21.4043 | −5.04505 | ||||||||
\(19\) | 7.80572 | 1.79076 | 0.895378 | − | 0.445308i | \(-0.146906\pi\) | ||||
0.895378 | + | 0.445308i | \(0.146906\pi\) | |||||||
\(20\) | −21.5692 | −4.82303 | ||||||||
\(21\) | −5.08020 | −1.10859 | ||||||||
\(22\) | −14.2506 | −3.03823 | ||||||||
\(23\) | 7.04503 | 1.46899 | 0.734495 | − | 0.678614i | \(-0.237419\pi\) | ||||
0.734495 | + | 0.678614i | \(0.237419\pi\) | |||||||
\(24\) | −26.8428 | −5.47926 | ||||||||
\(25\) | 13.3083 | 2.66166 | ||||||||
\(26\) | −2.65348 | −0.520389 | ||||||||
\(27\) | 16.8545 | 3.24365 | ||||||||
\(28\) | −7.69814 | −1.45481 | ||||||||
\(29\) | −2.05919 | −0.382383 | −0.191191 | − | 0.981553i | \(-0.561235\pi\) | ||||
−0.191191 | + | 0.981553i | \(0.561235\pi\) | |||||||
\(30\) | 37.7698 | 6.89579 | ||||||||
\(31\) | 6.19956 | 1.11347 | 0.556737 | − | 0.830689i | \(-0.312053\pi\) | ||||
0.556737 | + | 0.830689i | \(0.312053\pi\) | |||||||
\(32\) | −13.9235 | −2.46136 | ||||||||
\(33\) | 17.8658 | 3.11004 | ||||||||
\(34\) | −6.57944 | −1.12836 | ||||||||
\(35\) | 6.53429 | 1.10450 | ||||||||
\(36\) | 40.6628 | 6.77714 | ||||||||
\(37\) | 6.31080 | 1.03749 | 0.518744 | − | 0.854929i | \(-0.326400\pi\) | ||||
0.518744 | + | 0.854929i | \(0.326400\pi\) | |||||||
\(38\) | −20.7123 | −3.35998 | ||||||||
\(39\) | 3.32664 | 0.532689 | ||||||||
\(40\) | 34.5260 | 5.45904 | ||||||||
\(41\) | −1.52181 | −0.237668 | −0.118834 | − | 0.992914i | \(-0.537916\pi\) | ||||
−0.118834 | + | 0.992914i | \(0.537916\pi\) | |||||||
\(42\) | 13.4802 | 2.08004 | ||||||||
\(43\) | 0.0379119 | 0.00578151 | 0.00289076 | − | 0.999996i | \(-0.499080\pi\) | ||||
0.00289076 | + | 0.999996i | \(0.499080\pi\) | |||||||
\(44\) | 27.0725 | 4.08133 | ||||||||
\(45\) | −34.5152 | −5.14523 | ||||||||
\(46\) | −18.6938 | −2.75625 | ||||||||
\(47\) | −11.0005 | −1.60459 | −0.802296 | − | 0.596926i | \(-0.796389\pi\) | ||||
−0.802296 | + | 0.596926i | \(0.796389\pi\) | |||||||
\(48\) | 37.6880 | 5.43979 | ||||||||
\(49\) | −4.66789 | −0.666841 | ||||||||
\(50\) | −35.3132 | −4.99405 | ||||||||
\(51\) | 8.24858 | 1.15503 | ||||||||
\(52\) | 5.04093 | 0.699052 | ||||||||
\(53\) | −6.78526 | −0.932027 | −0.466014 | − | 0.884778i | \(-0.654310\pi\) | ||||
−0.466014 | + | 0.884778i | \(0.654310\pi\) | |||||||
\(54\) | −44.7231 | −6.08604 | ||||||||
\(55\) | −22.9795 | −3.09856 | ||||||||
\(56\) | 12.3224 | 1.64666 | ||||||||
\(57\) | 25.9668 | 3.43939 | ||||||||
\(58\) | 5.46402 | 0.717461 | ||||||||
\(59\) | 0.352703 | 0.0459180 | 0.0229590 | − | 0.999736i | \(-0.492691\pi\) | ||||
0.0229590 | + | 0.999736i | \(0.492691\pi\) | |||||||
\(60\) | −71.7531 | −9.26329 | ||||||||
\(61\) | 2.36952 | 0.303386 | 0.151693 | − | 0.988428i | \(-0.451527\pi\) | ||||
0.151693 | + | 0.988428i | \(0.451527\pi\) | |||||||
\(62\) | −16.4504 | −2.08920 | ||||||||
\(63\) | −12.3186 | −1.55200 | ||||||||
\(64\) | 14.2875 | 1.78593 | ||||||||
\(65\) | −4.27882 | −0.530722 | ||||||||
\(66\) | −47.4065 | −5.83534 | ||||||||
\(67\) | 1.19322 | 0.145776 | 0.0728878 | − | 0.997340i | \(-0.476778\pi\) | ||||
0.0728878 | + | 0.997340i | \(0.476778\pi\) | |||||||
\(68\) | 12.4993 | 1.51576 | ||||||||
\(69\) | 23.4363 | 2.82140 | ||||||||
\(70\) | −17.3386 | −2.07236 | ||||||||
\(71\) | 11.6409 | 1.38152 | 0.690762 | − | 0.723082i | \(-0.257275\pi\) | ||||
0.690762 | + | 0.723082i | \(0.257275\pi\) | |||||||
\(72\) | −65.0892 | −7.67083 | ||||||||
\(73\) | −6.83565 | −0.800053 | −0.400026 | − | 0.916504i | \(-0.630999\pi\) | ||||
−0.400026 | + | 0.916504i | \(0.630999\pi\) | |||||||
\(74\) | −16.7455 | −1.94663 | ||||||||
\(75\) | 44.2719 | 5.11208 | ||||||||
\(76\) | 39.3481 | 4.51354 | ||||||||
\(77\) | −8.20147 | −0.934645 | ||||||||
\(78\) | −8.82716 | −0.999479 | ||||||||
\(79\) | 12.6509 | 1.42334 | 0.711670 | − | 0.702514i | \(-0.247939\pi\) | ||||
0.711670 | + | 0.702514i | \(0.247939\pi\) | |||||||
\(80\) | −48.4754 | −5.41971 | ||||||||
\(81\) | 31.8693 | 3.54103 | ||||||||
\(82\) | 4.03810 | 0.445933 | ||||||||
\(83\) | 6.57489 | 0.721688 | 0.360844 | − | 0.932626i | \(-0.382489\pi\) | ||||
0.360844 | + | 0.932626i | \(0.382489\pi\) | |||||||
\(84\) | −25.6089 | −2.79416 | ||||||||
\(85\) | −10.6096 | −1.15077 | ||||||||
\(86\) | −0.100598 | −0.0108478 | ||||||||
\(87\) | −6.85019 | −0.734418 | ||||||||
\(88\) | −43.3351 | −4.61953 | ||||||||
\(89\) | 3.55557 | 0.376890 | 0.188445 | − | 0.982084i | \(-0.439655\pi\) | ||||
0.188445 | + | 0.982084i | \(0.439655\pi\) | |||||||
\(90\) | 91.5853 | 9.65394 | ||||||||
\(91\) | −1.52713 | −0.160086 | ||||||||
\(92\) | 35.5135 | 3.70254 | ||||||||
\(93\) | 20.6237 | 2.13858 | ||||||||
\(94\) | 29.1897 | 3.01068 | ||||||||
\(95\) | −33.3993 | −3.42669 | ||||||||
\(96\) | −46.3186 | −4.72737 | ||||||||
\(97\) | −12.5527 | −1.27453 | −0.637265 | − | 0.770645i | \(-0.719934\pi\) | ||||
−0.637265 | + | 0.770645i | \(0.719934\pi\) | |||||||
\(98\) | 12.3861 | 1.25119 | ||||||||
\(99\) | 43.3215 | 4.35398 | ||||||||
\(100\) | 67.0862 | 6.70862 | ||||||||
\(101\) | −11.6624 | −1.16045 | −0.580226 | − | 0.814455i | \(-0.697036\pi\) | ||||
−0.580226 | + | 0.814455i | \(0.697036\pi\) | |||||||
\(102\) | −21.8874 | −2.16718 | ||||||||
\(103\) | 2.59646 | 0.255837 | 0.127919 | − | 0.991785i | \(-0.459170\pi\) | ||||
0.127919 | + | 0.991785i | \(0.459170\pi\) | |||||||
\(104\) | −8.06904 | −0.791235 | ||||||||
\(105\) | 21.7372 | 2.12134 | ||||||||
\(106\) | 18.0045 | 1.74875 | ||||||||
\(107\) | −6.63513 | −0.641443 | −0.320721 | − | 0.947174i | \(-0.603925\pi\) | ||||
−0.320721 | + | 0.947174i | \(0.603925\pi\) | |||||||
\(108\) | 84.9625 | 8.17552 | ||||||||
\(109\) | 0.189504 | 0.0181511 | 0.00907557 | − | 0.999959i | \(-0.497111\pi\) | ||||
0.00907557 | + | 0.999959i | \(0.497111\pi\) | |||||||
\(110\) | 60.9756 | 5.81380 | ||||||||
\(111\) | 20.9937 | 1.99264 | ||||||||
\(112\) | −17.3010 | −1.63479 | ||||||||
\(113\) | 0.997434 | 0.0938307 | 0.0469153 | − | 0.998899i | \(-0.485061\pi\) | ||||
0.0469153 | + | 0.998899i | \(0.485061\pi\) | |||||||
\(114\) | −68.9023 | −6.45329 | ||||||||
\(115\) | −30.1444 | −2.81098 | ||||||||
\(116\) | −10.3803 | −0.963783 | ||||||||
\(117\) | 8.06653 | 0.745751 | ||||||||
\(118\) | −0.935889 | −0.0861555 | ||||||||
\(119\) | −3.78659 | −0.347116 | ||||||||
\(120\) | 114.856 | 10.4848 | ||||||||
\(121\) | 17.8426 | 1.62205 | ||||||||
\(122\) | −6.28747 | −0.569240 | ||||||||
\(123\) | −5.06253 | −0.456473 | ||||||||
\(124\) | 31.2516 | 2.80647 | ||||||||
\(125\) | −35.5497 | −3.17966 | ||||||||
\(126\) | 32.6871 | 2.91200 | ||||||||
\(127\) | 8.30924 | 0.737326 | 0.368663 | − | 0.929563i | \(-0.379816\pi\) | ||||
0.368663 | + | 0.929563i | \(0.379816\pi\) | |||||||
\(128\) | −10.0644 | −0.889572 | ||||||||
\(129\) | 0.126119 | 0.0111042 | ||||||||
\(130\) | 11.3537 | 0.995789 | ||||||||
\(131\) | −8.84089 | −0.772432 | −0.386216 | − | 0.922408i | \(-0.626218\pi\) | ||||
−0.386216 | + | 0.922408i | \(0.626218\pi\) | |||||||
\(132\) | 90.0604 | 7.83875 | ||||||||
\(133\) | −11.9203 | −1.03362 | ||||||||
\(134\) | −3.16619 | −0.273517 | ||||||||
\(135\) | −72.1174 | −6.20688 | ||||||||
\(136\) | −20.0076 | −1.71564 | ||||||||
\(137\) | 6.13309 | 0.523985 | 0.261993 | − | 0.965070i | \(-0.415620\pi\) | ||||
0.261993 | + | 0.965070i | \(0.415620\pi\) | |||||||
\(138\) | −62.1876 | −5.29376 | ||||||||
\(139\) | −14.6614 | −1.24357 | −0.621784 | − | 0.783189i | \(-0.713592\pi\) | ||||
−0.621784 | + | 0.783189i | \(0.713592\pi\) | |||||||
\(140\) | 32.9389 | 2.78385 | ||||||||
\(141\) | −36.5948 | −3.08184 | ||||||||
\(142\) | −30.8889 | −2.59214 | ||||||||
\(143\) | 5.37053 | 0.449106 | ||||||||
\(144\) | 91.3869 | 7.61558 | ||||||||
\(145\) | 8.81092 | 0.731707 | ||||||||
\(146\) | 18.1382 | 1.50113 | ||||||||
\(147\) | −15.5284 | −1.28076 | ||||||||
\(148\) | 31.8123 | 2.61496 | ||||||||
\(149\) | 18.9302 | 1.55082 | 0.775412 | − | 0.631456i | \(-0.217542\pi\) | ||||
0.775412 | + | 0.631456i | \(0.217542\pi\) | |||||||
\(150\) | −117.474 | −9.59175 | ||||||||
\(151\) | −11.0789 | −0.901590 | −0.450795 | − | 0.892628i | \(-0.648859\pi\) | ||||
−0.450795 | + | 0.892628i | \(0.648859\pi\) | |||||||
\(152\) | −62.9847 | −5.10873 | ||||||||
\(153\) | 20.0014 | 1.61702 | ||||||||
\(154\) | 21.7624 | 1.75366 | ||||||||
\(155\) | −26.5268 | −2.13068 | ||||||||
\(156\) | 16.7694 | 1.34262 | ||||||||
\(157\) | 4.72032 | 0.376723 | 0.188361 | − | 0.982100i | \(-0.439682\pi\) | ||||
0.188361 | + | 0.982100i | \(0.439682\pi\) | |||||||
\(158\) | −33.5689 | −2.67060 | ||||||||
\(159\) | −22.5721 | −1.79008 | ||||||||
\(160\) | 59.5763 | 4.70992 | ||||||||
\(161\) | −10.7586 | −0.847900 | ||||||||
\(162\) | −84.5644 | −6.64401 | ||||||||
\(163\) | 24.8824 | 1.94894 | 0.974472 | − | 0.224510i | \(-0.0720781\pi\) | ||||
0.974472 | + | 0.224510i | \(0.0720781\pi\) | |||||||
\(164\) | −7.67137 | −0.599033 | ||||||||
\(165\) | −76.4446 | −5.95120 | ||||||||
\(166\) | −17.4463 | −1.35410 | ||||||||
\(167\) | −23.7894 | −1.84088 | −0.920439 | − | 0.390887i | \(-0.872168\pi\) | ||||
−0.920439 | + | 0.390887i | \(0.872168\pi\) | |||||||
\(168\) | 40.9923 | 3.16263 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 28.1522 | 2.15918 | ||||||||
\(171\) | 62.9651 | 4.81506 | ||||||||
\(172\) | 0.191112 | 0.0145721 | ||||||||
\(173\) | −17.2713 | −1.31312 | −0.656558 | − | 0.754276i | \(-0.727988\pi\) | ||||
−0.656558 | + | 0.754276i | \(0.727988\pi\) | |||||||
\(174\) | 18.1768 | 1.37798 | ||||||||
\(175\) | −20.3234 | −1.53631 | ||||||||
\(176\) | 60.8435 | 4.58625 | ||||||||
\(177\) | 1.17332 | 0.0881918 | ||||||||
\(178\) | −9.43462 | −0.707155 | ||||||||
\(179\) | 2.16725 | 0.161988 | 0.0809938 | − | 0.996715i | \(-0.474191\pi\) | ||||
0.0809938 | + | 0.996715i | \(0.474191\pi\) | |||||||
\(180\) | −173.989 | −12.9684 | ||||||||
\(181\) | −11.0310 | −0.819931 | −0.409966 | − | 0.912101i | \(-0.634459\pi\) | ||||
−0.409966 | + | 0.912101i | \(0.634459\pi\) | |||||||
\(182\) | 4.05219 | 0.300368 | ||||||||
\(183\) | 7.88254 | 0.582694 | ||||||||
\(184\) | −56.8467 | −4.19079 | ||||||||
\(185\) | −27.0028 | −1.98528 | ||||||||
\(186\) | −54.7245 | −4.01259 | ||||||||
\(187\) | 13.3165 | 0.973801 | ||||||||
\(188\) | −55.4530 | −4.04432 | ||||||||
\(189\) | −25.7390 | −1.87223 | ||||||||
\(190\) | 88.6242 | 6.42947 | ||||||||
\(191\) | 2.50169 | 0.181016 | 0.0905079 | − | 0.995896i | \(-0.471151\pi\) | ||||
0.0905079 | + | 0.995896i | \(0.471151\pi\) | |||||||
\(192\) | 47.5292 | 3.43013 | ||||||||
\(193\) | −3.44930 | −0.248286 | −0.124143 | − | 0.992264i | \(-0.539618\pi\) | ||||
−0.124143 | + | 0.992264i | \(0.539618\pi\) | |||||||
\(194\) | 33.3082 | 2.39139 | ||||||||
\(195\) | −14.2341 | −1.01932 | ||||||||
\(196\) | −23.5305 | −1.68075 | ||||||||
\(197\) | −7.26576 | −0.517664 | −0.258832 | − | 0.965922i | \(-0.583338\pi\) | ||||
−0.258832 | + | 0.965922i | \(0.583338\pi\) | |||||||
\(198\) | −114.953 | −8.16933 | ||||||||
\(199\) | −11.0581 | −0.783887 | −0.391943 | − | 0.919989i | \(-0.628197\pi\) | ||||
−0.391943 | + | 0.919989i | \(0.628197\pi\) | |||||||
\(200\) | −107.385 | −7.59328 | ||||||||
\(201\) | 3.96943 | 0.279982 | ||||||||
\(202\) | 30.9459 | 2.17735 | ||||||||
\(203\) | 3.14465 | 0.220711 | ||||||||
\(204\) | 41.5806 | 2.91122 | ||||||||
\(205\) | 6.51157 | 0.454788 | ||||||||
\(206\) | −6.88965 | −0.480025 | ||||||||
\(207\) | 56.8290 | 3.94989 | ||||||||
\(208\) | 11.3291 | 0.785535 | ||||||||
\(209\) | 41.9209 | 2.89973 | ||||||||
\(210\) | −57.6792 | −3.98025 | ||||||||
\(211\) | 20.7836 | 1.43080 | 0.715402 | − | 0.698713i | \(-0.246244\pi\) | ||||
0.715402 | + | 0.698713i | \(0.246244\pi\) | |||||||
\(212\) | −34.2040 | −2.34914 | ||||||||
\(213\) | 38.7252 | 2.65340 | ||||||||
\(214\) | 17.6062 | 1.20353 | ||||||||
\(215\) | −0.162218 | −0.0110632 | ||||||||
\(216\) | −136.000 | −9.25362 | ||||||||
\(217\) | −9.46751 | −0.642696 | ||||||||
\(218\) | −0.502843 | −0.0340568 | ||||||||
\(219\) | −22.7398 | −1.53661 | ||||||||
\(220\) | −115.838 | −7.80982 | ||||||||
\(221\) | 2.47955 | 0.166793 | ||||||||
\(222\) | −55.7064 | −3.73877 | ||||||||
\(223\) | −19.4527 | −1.30265 | −0.651323 | − | 0.758800i | \(-0.725786\pi\) | ||||
−0.651323 | + | 0.758800i | \(0.725786\pi\) | |||||||
\(224\) | 21.2630 | 1.42069 | ||||||||
\(225\) | 107.352 | 7.15678 | ||||||||
\(226\) | −2.64667 | −0.176054 | ||||||||
\(227\) | −5.83001 | −0.386952 | −0.193476 | − | 0.981105i | \(-0.561976\pi\) | ||||
−0.193476 | + | 0.981105i | \(0.561976\pi\) | |||||||
\(228\) | 130.897 | 8.66887 | ||||||||
\(229\) | −7.54215 | −0.498399 | −0.249200 | − | 0.968452i | \(-0.580168\pi\) | ||||
−0.249200 | + | 0.968452i | \(0.580168\pi\) | |||||||
\(230\) | 79.9875 | 5.27422 | ||||||||
\(231\) | −27.2833 | −1.79511 | ||||||||
\(232\) | 16.6157 | 1.09088 | ||||||||
\(233\) | 1.55226 | 0.101692 | 0.0508459 | − | 0.998707i | \(-0.483808\pi\) | ||||
0.0508459 | + | 0.998707i | \(0.483808\pi\) | |||||||
\(234\) | −21.4043 | −1.39925 | ||||||||
\(235\) | 47.0693 | 3.07046 | ||||||||
\(236\) | 1.77795 | 0.115735 | ||||||||
\(237\) | 42.0850 | 2.73372 | ||||||||
\(238\) | 10.0476 | 0.651291 | ||||||||
\(239\) | −2.20129 | −0.142390 | −0.0711949 | − | 0.997462i | \(-0.522681\pi\) | ||||
−0.0711949 | + | 0.997462i | \(0.522681\pi\) | |||||||
\(240\) | −161.260 | −10.4093 | ||||||||
\(241\) | −13.1510 | −0.847131 | −0.423565 | − | 0.905865i | \(-0.639222\pi\) | ||||
−0.423565 | + | 0.905865i | \(0.639222\pi\) | |||||||
\(242\) | −47.3449 | −3.04345 | ||||||||
\(243\) | 55.4541 | 3.55739 | ||||||||
\(244\) | 11.9446 | 0.764675 | ||||||||
\(245\) | 19.9731 | 1.27603 | ||||||||
\(246\) | 13.4333 | 0.856476 | ||||||||
\(247\) | 7.80572 | 0.496666 | ||||||||
\(248\) | −50.0245 | −3.17656 | ||||||||
\(249\) | 21.8723 | 1.38610 | ||||||||
\(250\) | 94.3303 | 5.96597 | ||||||||
\(251\) | −20.0408 | −1.26496 | −0.632481 | − | 0.774576i | \(-0.717963\pi\) | ||||
−0.632481 | + | 0.774576i | \(0.717963\pi\) | |||||||
\(252\) | −62.0973 | −3.91176 | ||||||||
\(253\) | 37.8356 | 2.37870 | ||||||||
\(254\) | −22.0484 | −1.38344 | ||||||||
\(255\) | −35.2942 | −2.21021 | ||||||||
\(256\) | −1.86938 | −0.116836 | ||||||||
\(257\) | −8.32458 | −0.519273 | −0.259637 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259637 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(258\) | −0.334655 | −0.0208347 | ||||||||
\(259\) | −9.63738 | −0.598837 | ||||||||
\(260\) | −21.5692 | −1.33767 | ||||||||
\(261\) | −16.6105 | −1.02817 | ||||||||
\(262\) | 23.4591 | 1.44931 | ||||||||
\(263\) | −10.0866 | −0.621968 | −0.310984 | − | 0.950415i | \(-0.600659\pi\) | ||||
−0.310984 | + | 0.950415i | \(0.600659\pi\) | |||||||
\(264\) | −144.160 | −8.87244 | ||||||||
\(265\) | 29.0329 | 1.78348 | ||||||||
\(266\) | 31.6303 | 1.93938 | ||||||||
\(267\) | 11.8281 | 0.723868 | ||||||||
\(268\) | 6.01497 | 0.367423 | ||||||||
\(269\) | 7.91603 | 0.482649 | 0.241324 | − | 0.970445i | \(-0.422418\pi\) | ||||
0.241324 | + | 0.970445i | \(0.422418\pi\) | |||||||
\(270\) | 191.362 | 11.6459 | ||||||||
\(271\) | 7.58461 | 0.460733 | 0.230366 | − | 0.973104i | \(-0.426008\pi\) | ||||
0.230366 | + | 0.973104i | \(0.426008\pi\) | |||||||
\(272\) | 28.0912 | 1.70328 | ||||||||
\(273\) | −5.08020 | −0.307467 | ||||||||
\(274\) | −16.2740 | −0.983149 | ||||||||
\(275\) | 71.4726 | 4.30996 | ||||||||
\(276\) | 118.141 | 7.11124 | ||||||||
\(277\) | −16.6113 | −0.998079 | −0.499040 | − | 0.866579i | \(-0.666314\pi\) | ||||
−0.499040 | + | 0.866579i | \(0.666314\pi\) | |||||||
\(278\) | 38.9038 | 2.33329 | ||||||||
\(279\) | 50.0089 | 2.99396 | ||||||||
\(280\) | −52.7255 | −3.15095 | ||||||||
\(281\) | −17.6871 | −1.05512 | −0.527562 | − | 0.849516i | \(-0.676894\pi\) | ||||
−0.527562 | + | 0.849516i | \(0.676894\pi\) | |||||||
\(282\) | 97.1034 | 5.78243 | ||||||||
\(283\) | 21.1046 | 1.25454 | 0.627268 | − | 0.778803i | \(-0.284173\pi\) | ||||
0.627268 | + | 0.778803i | \(0.284173\pi\) | |||||||
\(284\) | 58.6811 | 3.48208 | ||||||||
\(285\) | −111.107 | −6.58143 | ||||||||
\(286\) | −14.2506 | −0.842654 | ||||||||
\(287\) | 2.32400 | 0.137181 | ||||||||
\(288\) | −112.315 | −6.61820 | ||||||||
\(289\) | −10.8518 | −0.638342 | ||||||||
\(290\) | −23.3796 | −1.37289 | ||||||||
\(291\) | −41.7582 | −2.44791 | ||||||||
\(292\) | −34.4581 | −2.01651 | ||||||||
\(293\) | −5.52910 | −0.323013 | −0.161507 | − | 0.986872i | \(-0.551635\pi\) | ||||
−0.161507 | + | 0.986872i | \(0.551635\pi\) | |||||||
\(294\) | 41.2042 | 2.40308 | ||||||||
\(295\) | −1.50915 | −0.0878662 | ||||||||
\(296\) | −50.9221 | −2.95979 | ||||||||
\(297\) | 90.5177 | 5.25237 | ||||||||
\(298\) | −50.2308 | −2.90979 | ||||||||
\(299\) | 7.04503 | 0.407425 | ||||||||
\(300\) | 223.172 | 12.8848 | ||||||||
\(301\) | −0.0578963 | −0.00333708 | ||||||||
\(302\) | 29.3976 | 1.69164 | ||||||||
\(303\) | −38.7966 | −2.22881 | ||||||||
\(304\) | 88.4322 | 5.07193 | ||||||||
\(305\) | −10.1388 | −0.580543 | ||||||||
\(306\) | −53.0732 | −3.03399 | ||||||||
\(307\) | −17.9911 | −1.02681 | −0.513404 | − | 0.858147i | \(-0.671616\pi\) | ||||
−0.513404 | + | 0.858147i | \(0.671616\pi\) | |||||||
\(308\) | −41.3431 | −2.35574 | ||||||||
\(309\) | 8.63750 | 0.491370 | ||||||||
\(310\) | 70.3882 | 3.99778 | ||||||||
\(311\) | −11.4886 | −0.651458 | −0.325729 | − | 0.945463i | \(-0.605610\pi\) | ||||
−0.325729 | + | 0.945463i | \(0.605610\pi\) | |||||||
\(312\) | −26.8428 | −1.51967 | ||||||||
\(313\) | 30.8178 | 1.74193 | 0.870963 | − | 0.491348i | \(-0.163496\pi\) | ||||
0.870963 | + | 0.491348i | \(0.163496\pi\) | |||||||
\(314\) | −12.5253 | −0.706842 | ||||||||
\(315\) | 52.7091 | 2.96982 | ||||||||
\(316\) | 63.7725 | 3.58748 | ||||||||
\(317\) | 2.24243 | 0.125948 | 0.0629738 | − | 0.998015i | \(-0.479942\pi\) | ||||
0.0629738 | + | 0.998015i | \(0.479942\pi\) | |||||||
\(318\) | 59.8946 | 3.35872 | ||||||||
\(319\) | −11.0590 | −0.619183 | ||||||||
\(320\) | −61.1334 | −3.41746 | ||||||||
\(321\) | −22.0727 | −1.23198 | ||||||||
\(322\) | 28.5478 | 1.59091 | ||||||||
\(323\) | 19.3547 | 1.07692 | ||||||||
\(324\) | 160.651 | 8.92506 | ||||||||
\(325\) | 13.3083 | 0.738211 | ||||||||
\(326\) | −66.0250 | −3.65678 | ||||||||
\(327\) | 0.630410 | 0.0348617 | ||||||||
\(328\) | 12.2796 | 0.678027 | ||||||||
\(329\) | 16.7992 | 0.926169 | ||||||||
\(330\) | 202.844 | 11.1662 | ||||||||
\(331\) | −5.66581 | −0.311421 | −0.155711 | − | 0.987803i | \(-0.549767\pi\) | ||||
−0.155711 | + | 0.987803i | \(0.549767\pi\) | |||||||
\(332\) | 33.1436 | 1.81899 | ||||||||
\(333\) | 50.9062 | 2.78964 | ||||||||
\(334\) | 63.1246 | 3.45402 | ||||||||
\(335\) | −5.10559 | −0.278948 | ||||||||
\(336\) | −57.5543 | −3.13984 | ||||||||
\(337\) | −9.49515 | −0.517234 | −0.258617 | − | 0.965980i | \(-0.583267\pi\) | ||||
−0.258617 | + | 0.965980i | \(0.583267\pi\) | |||||||
\(338\) | −2.65348 | −0.144330 | ||||||||
\(339\) | 3.31810 | 0.180215 | ||||||||
\(340\) | −53.4821 | −2.90048 | ||||||||
\(341\) | 33.2949 | 1.80302 | ||||||||
\(342\) | −167.076 | −9.03445 | ||||||||
\(343\) | 17.8183 | 0.962099 | ||||||||
\(344\) | −0.305913 | −0.0164937 | ||||||||
\(345\) | −100.280 | −5.39887 | ||||||||
\(346\) | 45.8291 | 2.46379 | ||||||||
\(347\) | −4.44782 | −0.238771 | −0.119386 | − | 0.992848i | \(-0.538093\pi\) | ||||
−0.119386 | + | 0.992848i | \(0.538093\pi\) | |||||||
\(348\) | −34.5314 | −1.85108 | ||||||||
\(349\) | 25.9524 | 1.38920 | 0.694601 | − | 0.719395i | \(-0.255581\pi\) | ||||
0.694601 | + | 0.719395i | \(0.255581\pi\) | |||||||
\(350\) | 53.9277 | 2.88256 | ||||||||
\(351\) | 16.8545 | 0.899628 | ||||||||
\(352\) | −74.7767 | −3.98561 | ||||||||
\(353\) | 24.0489 | 1.27999 | 0.639996 | − | 0.768378i | \(-0.278936\pi\) | ||||
0.639996 | + | 0.768378i | \(0.278936\pi\) | |||||||
\(354\) | −3.11336 | −0.165473 | ||||||||
\(355\) | −49.8094 | −2.64361 | ||||||||
\(356\) | 17.9234 | 0.949938 | ||||||||
\(357\) | −12.5966 | −0.666684 | ||||||||
\(358\) | −5.75074 | −0.303936 | ||||||||
\(359\) | −3.62449 | −0.191293 | −0.0956466 | − | 0.995415i | \(-0.530492\pi\) | ||||
−0.0956466 | + | 0.995415i | \(0.530492\pi\) | |||||||
\(360\) | 278.505 | 14.6785 | ||||||||
\(361\) | 41.9293 | 2.20680 | ||||||||
\(362\) | 29.2706 | 1.53843 | ||||||||
\(363\) | 59.3559 | 3.11538 | ||||||||
\(364\) | −7.69814 | −0.403492 | ||||||||
\(365\) | 29.2485 | 1.53094 | ||||||||
\(366\) | −20.9161 | −1.09330 | ||||||||
\(367\) | 29.9799 | 1.56494 | 0.782469 | − | 0.622689i | \(-0.213960\pi\) | ||||
0.782469 | + | 0.622689i | \(0.213960\pi\) | |||||||
\(368\) | 79.8142 | 4.16060 | ||||||||
\(369\) | −12.2758 | −0.639051 | ||||||||
\(370\) | 71.6512 | 3.72497 | ||||||||
\(371\) | 10.3619 | 0.537965 | ||||||||
\(372\) | 103.963 | 5.39022 | ||||||||
\(373\) | −16.1864 | −0.838099 | −0.419049 | − | 0.907963i | \(-0.637637\pi\) | ||||
−0.419049 | + | 0.907963i | \(0.637637\pi\) | |||||||
\(374\) | −35.3351 | −1.82713 | ||||||||
\(375\) | −118.261 | −6.10697 | ||||||||
\(376\) | 88.7638 | 4.57764 | ||||||||
\(377\) | −2.05919 | −0.106054 | ||||||||
\(378\) | 68.2977 | 3.51285 | ||||||||
\(379\) | 17.9277 | 0.920886 | 0.460443 | − | 0.887689i | \(-0.347691\pi\) | ||||
0.460443 | + | 0.887689i | \(0.347691\pi\) | |||||||
\(380\) | −168.364 | −8.63687 | ||||||||
\(381\) | 27.6418 | 1.41613 | ||||||||
\(382\) | −6.63817 | −0.339638 | ||||||||
\(383\) | 2.48108 | 0.126777 | 0.0633887 | − | 0.997989i | \(-0.479809\pi\) | ||||
0.0633887 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(384\) | −33.4805 | −1.70854 | ||||||||
\(385\) | 35.0926 | 1.78849 | ||||||||
\(386\) | 9.15264 | 0.465857 | ||||||||
\(387\) | 0.305818 | 0.0155456 | ||||||||
\(388\) | −63.2771 | −3.21241 | ||||||||
\(389\) | 13.3669 | 0.677729 | 0.338865 | − | 0.940835i | \(-0.389957\pi\) | ||||
0.338865 | + | 0.940835i | \(0.389957\pi\) | |||||||
\(390\) | 37.7698 | 1.91255 | ||||||||
\(391\) | 17.4685 | 0.883422 | ||||||||
\(392\) | 37.6654 | 1.90239 | ||||||||
\(393\) | −29.4104 | −1.48356 | ||||||||
\(394\) | 19.2795 | 0.971289 | ||||||||
\(395\) | −54.1310 | −2.72363 | ||||||||
\(396\) | 218.381 | 10.9741 | ||||||||
\(397\) | −27.7489 | −1.39268 | −0.696339 | − | 0.717713i | \(-0.745189\pi\) | ||||
−0.696339 | + | 0.717713i | \(0.745189\pi\) | |||||||
\(398\) | 29.3423 | 1.47080 | ||||||||
\(399\) | −39.6546 | −1.98521 | ||||||||
\(400\) | 150.772 | 7.53858 | ||||||||
\(401\) | 4.86422 | 0.242908 | 0.121454 | − | 0.992597i | \(-0.461244\pi\) | ||||
0.121454 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(402\) | −10.5328 | −0.525328 | ||||||||
\(403\) | 6.19956 | 0.308822 | ||||||||
\(404\) | −58.7894 | −2.92488 | ||||||||
\(405\) | −136.363 | −6.77593 | ||||||||
\(406\) | −8.34424 | −0.414118 | ||||||||
\(407\) | 33.8923 | 1.67998 | ||||||||
\(408\) | −66.5582 | −3.29512 | ||||||||
\(409\) | −14.1580 | −0.700070 | −0.350035 | − | 0.936737i | \(-0.613830\pi\) | ||||
−0.350035 | + | 0.936737i | \(0.613830\pi\) | |||||||
\(410\) | −17.2783 | −0.853314 | ||||||||
\(411\) | 20.4026 | 1.00639 | ||||||||
\(412\) | 13.0886 | 0.644829 | ||||||||
\(413\) | −0.538621 | −0.0265038 | ||||||||
\(414\) | −150.794 | −7.41113 | ||||||||
\(415\) | −28.1328 | −1.38098 | ||||||||
\(416\) | −13.9235 | −0.682657 | ||||||||
\(417\) | −48.7733 | −2.38844 | ||||||||
\(418\) | −111.236 | −5.44073 | ||||||||
\(419\) | −6.06992 | −0.296535 | −0.148267 | − | 0.988947i | \(-0.547370\pi\) | ||||
−0.148267 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(420\) | 109.576 | 5.34676 | ||||||||
\(421\) | −18.0581 | −0.880100 | −0.440050 | − | 0.897973i | \(-0.645039\pi\) | ||||
−0.440050 | + | 0.897973i | \(0.645039\pi\) | |||||||
\(422\) | −55.1488 | −2.68460 | ||||||||
\(423\) | −88.7361 | −4.31450 | ||||||||
\(424\) | 54.7506 | 2.65892 | ||||||||
\(425\) | 32.9986 | 1.60067 | ||||||||
\(426\) | −102.756 | −4.97856 | ||||||||
\(427\) | −3.61856 | −0.175114 | ||||||||
\(428\) | −33.4473 | −1.61674 | ||||||||
\(429\) | 17.8658 | 0.862570 | ||||||||
\(430\) | 0.430442 | 0.0207578 | ||||||||
\(431\) | 36.8440 | 1.77471 | 0.887356 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887356 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(432\) | 190.947 | 9.18696 | ||||||||
\(433\) | −10.5847 | −0.508668 | −0.254334 | − | 0.967116i | \(-0.581856\pi\) | ||||
−0.254334 | + | 0.967116i | \(0.581856\pi\) | |||||||
\(434\) | 25.1218 | 1.20588 | ||||||||
\(435\) | 29.3107 | 1.40534 | ||||||||
\(436\) | 0.955275 | 0.0457494 | ||||||||
\(437\) | 54.9916 | 2.63060 | ||||||||
\(438\) | 60.3394 | 2.88313 | ||||||||
\(439\) | 13.4929 | 0.643980 | 0.321990 | − | 0.946743i | \(-0.395648\pi\) | ||||
0.321990 | + | 0.946743i | \(0.395648\pi\) | |||||||
\(440\) | 185.423 | 8.83969 | ||||||||
\(441\) | −37.6537 | −1.79303 | ||||||||
\(442\) | −6.57944 | −0.312952 | ||||||||
\(443\) | −28.3848 | −1.34860 | −0.674302 | − | 0.738456i | \(-0.735555\pi\) | ||||
−0.674302 | + | 0.738456i | \(0.735555\pi\) | |||||||
\(444\) | 105.828 | 5.02238 | ||||||||
\(445\) | −15.2136 | −0.721196 | ||||||||
\(446\) | 51.6172 | 2.44414 | ||||||||
\(447\) | 62.9740 | 2.97857 | ||||||||
\(448\) | −21.8187 | −1.03084 | ||||||||
\(449\) | 25.2885 | 1.19344 | 0.596719 | − | 0.802450i | \(-0.296471\pi\) | ||||
0.596719 | + | 0.802450i | \(0.296471\pi\) | |||||||
\(450\) | −284.855 | −13.4282 | ||||||||
\(451\) | −8.17295 | −0.384849 | ||||||||
\(452\) | 5.02800 | 0.236497 | ||||||||
\(453\) | −36.8556 | −1.73163 | ||||||||
\(454\) | 15.4698 | 0.726034 | ||||||||
\(455\) | 6.53429 | 0.306332 | ||||||||
\(456\) | −209.527 | −9.81202 | ||||||||
\(457\) | −18.0549 | −0.844571 | −0.422285 | − | 0.906463i | \(-0.638772\pi\) | ||||
−0.422285 | + | 0.906463i | \(0.638772\pi\) | |||||||
\(458\) | 20.0129 | 0.935142 | ||||||||
\(459\) | 41.7917 | 1.95067 | ||||||||
\(460\) | −151.956 | −7.08499 | ||||||||
\(461\) | −10.1268 | −0.471653 | −0.235826 | − | 0.971795i | \(-0.575780\pi\) | ||||
−0.235826 | + | 0.971795i | \(0.575780\pi\) | |||||||
\(462\) | 72.3957 | 3.36815 | ||||||||
\(463\) | 23.7908 | 1.10565 | 0.552825 | − | 0.833297i | \(-0.313550\pi\) | ||||
0.552825 | + | 0.833297i | \(0.313550\pi\) | |||||||
\(464\) | −23.3289 | −1.08302 | ||||||||
\(465\) | −88.2451 | −4.09227 | ||||||||
\(466\) | −4.11888 | −0.190803 | ||||||||
\(467\) | −15.8417 | −0.733067 | −0.366534 | − | 0.930405i | \(-0.619456\pi\) | ||||
−0.366534 | + | 0.930405i | \(0.619456\pi\) | |||||||
\(468\) | 40.6628 | 1.87964 | ||||||||
\(469\) | −1.82220 | −0.0841416 | ||||||||
\(470\) | −124.897 | −5.76108 | ||||||||
\(471\) | 15.7028 | 0.723547 | ||||||||
\(472\) | −2.84598 | −0.130997 | ||||||||
\(473\) | 0.203607 | 0.00936187 | ||||||||
\(474\) | −111.672 | −5.12925 | ||||||||
\(475\) | 103.881 | 4.76638 | ||||||||
\(476\) | −19.0880 | −0.874895 | ||||||||
\(477\) | −54.7335 | −2.50607 | ||||||||
\(478\) | 5.84108 | 0.267165 | ||||||||
\(479\) | 26.8047 | 1.22474 | 0.612370 | − | 0.790572i | \(-0.290216\pi\) | ||||
0.612370 | + | 0.790572i | \(0.290216\pi\) | |||||||
\(480\) | 198.189 | 9.04604 | ||||||||
\(481\) | 6.31080 | 0.287748 | ||||||||
\(482\) | 34.8959 | 1.58946 | ||||||||
\(483\) | −35.7901 | −1.62851 | ||||||||
\(484\) | 89.9433 | 4.08833 | ||||||||
\(485\) | 53.7106 | 2.43887 | ||||||||
\(486\) | −147.146 | −6.67469 | ||||||||
\(487\) | −10.3326 | −0.468217 | −0.234108 | − | 0.972210i | \(-0.575217\pi\) | ||||
−0.234108 | + | 0.972210i | \(0.575217\pi\) | |||||||
\(488\) | −19.1198 | −0.865511 | ||||||||
\(489\) | 82.7749 | 3.74321 | ||||||||
\(490\) | −52.9980 | −2.39421 | ||||||||
\(491\) | 25.7638 | 1.16270 | 0.581352 | − | 0.813653i | \(-0.302524\pi\) | ||||
0.581352 | + | 0.813653i | \(0.302524\pi\) | |||||||
\(492\) | −25.5199 | −1.15052 | ||||||||
\(493\) | −5.10588 | −0.229957 | ||||||||
\(494\) | −20.7123 | −0.931890 | ||||||||
\(495\) | −185.365 | −8.33154 | ||||||||
\(496\) | 70.2357 | 3.15368 | ||||||||
\(497\) | −17.7771 | −0.797414 | ||||||||
\(498\) | −58.0376 | −2.60073 | ||||||||
\(499\) | 27.7424 | 1.24192 | 0.620960 | − | 0.783842i | \(-0.286743\pi\) | ||||
0.620960 | + | 0.783842i | \(0.286743\pi\) | |||||||
\(500\) | −179.204 | −8.01423 | ||||||||
\(501\) | −79.1387 | −3.53566 | ||||||||
\(502\) | 53.1777 | 2.37344 | ||||||||
\(503\) | −35.2198 | −1.57037 | −0.785187 | − | 0.619259i | \(-0.787433\pi\) | ||||
−0.785187 | + | 0.619259i | \(0.787433\pi\) | |||||||
\(504\) | 99.3993 | 4.42760 | ||||||||
\(505\) | 49.9013 | 2.22058 | ||||||||
\(506\) | −100.396 | −4.46313 | ||||||||
\(507\) | 3.32664 | 0.147741 | ||||||||
\(508\) | 41.8863 | 1.85840 | ||||||||
\(509\) | 36.2071 | 1.60485 | 0.802425 | − | 0.596753i | \(-0.203543\pi\) | ||||
0.802425 | + | 0.596753i | \(0.203543\pi\) | |||||||
\(510\) | 93.6523 | 4.14699 | ||||||||
\(511\) | 10.4389 | 0.461790 | ||||||||
\(512\) | 25.0891 | 1.10879 | ||||||||
\(513\) | 131.562 | 5.80859 | ||||||||
\(514\) | 22.0891 | 0.974307 | ||||||||
\(515\) | −11.1098 | −0.489556 | ||||||||
\(516\) | 0.635759 | 0.0279877 | ||||||||
\(517\) | −59.0787 | −2.59828 | ||||||||
\(518\) | 25.5725 | 1.12359 | ||||||||
\(519\) | −57.4555 | −2.52202 | ||||||||
\(520\) | 34.5260 | 1.51406 | ||||||||
\(521\) | 6.98027 | 0.305811 | 0.152906 | − | 0.988241i | \(-0.451137\pi\) | ||||
0.152906 | + | 0.988241i | \(0.451137\pi\) | |||||||
\(522\) | 44.0757 | 1.92914 | ||||||||
\(523\) | 26.4952 | 1.15856 | 0.579278 | − | 0.815130i | \(-0.303335\pi\) | ||||
0.579278 | + | 0.815130i | \(0.303335\pi\) | |||||||
\(524\) | −44.5663 | −1.94689 | ||||||||
\(525\) | −67.6087 | −2.95069 | ||||||||
\(526\) | 26.7646 | 1.16699 | ||||||||
\(527\) | 15.3721 | 0.669621 | ||||||||
\(528\) | 202.404 | 8.80852 | ||||||||
\(529\) | 26.6325 | 1.15793 | ||||||||
\(530\) | −77.0381 | −3.34632 | ||||||||
\(531\) | 2.84509 | 0.123466 | ||||||||
\(532\) | −60.0895 | −2.60521 | ||||||||
\(533\) | −1.52181 | −0.0659171 | ||||||||
\(534\) | −31.3856 | −1.35819 | ||||||||
\(535\) | 28.3905 | 1.22743 | ||||||||
\(536\) | −9.62819 | −0.415874 | ||||||||
\(537\) | 7.20965 | 0.311119 | ||||||||
\(538\) | −21.0050 | −0.905589 | ||||||||
\(539\) | −25.0690 | −1.07980 | ||||||||
\(540\) | −363.539 | −15.6442 | ||||||||
\(541\) | 27.2417 | 1.17121 | 0.585606 | − | 0.810596i | \(-0.300857\pi\) | ||||
0.585606 | + | 0.810596i | \(0.300857\pi\) | |||||||
\(542\) | −20.1256 | −0.864468 | ||||||||
\(543\) | −36.6963 | −1.57479 | ||||||||
\(544\) | −34.5242 | −1.48021 | ||||||||
\(545\) | −0.810851 | −0.0347331 | ||||||||
\(546\) | 13.4802 | 0.576898 | ||||||||
\(547\) | 16.1414 | 0.690156 | 0.345078 | − | 0.938574i | \(-0.387852\pi\) | ||||
0.345078 | + | 0.938574i | \(0.387852\pi\) | |||||||
\(548\) | 30.9165 | 1.32069 | ||||||||
\(549\) | 19.1138 | 0.815757 | ||||||||
\(550\) | −189.651 | −8.08674 | ||||||||
\(551\) | −16.0735 | −0.684754 | ||||||||
\(552\) | −189.108 | −8.04899 | ||||||||
\(553\) | −19.3195 | −0.821550 | ||||||||
\(554\) | 44.0778 | 1.87269 | ||||||||
\(555\) | −89.8284 | −3.81300 | ||||||||
\(556\) | −73.9074 | −3.13437 | ||||||||
\(557\) | 2.76570 | 0.117187 | 0.0585933 | − | 0.998282i | \(-0.481338\pi\) | ||||
0.0585933 | + | 0.998282i | \(0.481338\pi\) | |||||||
\(558\) | −132.697 | −5.61753 | ||||||||
\(559\) | 0.0379119 | 0.00160350 | ||||||||
\(560\) | 74.0280 | 3.12825 | ||||||||
\(561\) | 44.2993 | 1.87032 | ||||||||
\(562\) | 46.9323 | 1.97972 | ||||||||
\(563\) | 4.90073 | 0.206541 | 0.103271 | − | 0.994653i | \(-0.467069\pi\) | ||||
0.103271 | + | 0.994653i | \(0.467069\pi\) | |||||||
\(564\) | −184.472 | −7.76767 | ||||||||
\(565\) | −4.26784 | −0.179549 | ||||||||
\(566\) | −56.0005 | −2.35388 | ||||||||
\(567\) | −48.6684 | −2.04388 | ||||||||
\(568\) | −93.9311 | −3.94126 | ||||||||
\(569\) | 2.89045 | 0.121174 | 0.0605870 | − | 0.998163i | \(-0.480703\pi\) | ||||
0.0605870 | + | 0.998163i | \(0.480703\pi\) | |||||||
\(570\) | 294.821 | 12.3487 | ||||||||
\(571\) | −21.2154 | −0.887835 | −0.443918 | − | 0.896068i | \(-0.646412\pi\) | ||||
−0.443918 | + | 0.896068i | \(0.646412\pi\) | |||||||
\(572\) | 27.0725 | 1.13196 | ||||||||
\(573\) | 8.32222 | 0.347666 | ||||||||
\(574\) | −6.16668 | −0.257392 | ||||||||
\(575\) | 93.7574 | 3.90995 | ||||||||
\(576\) | 115.250 | 4.80209 | ||||||||
\(577\) | 15.7081 | 0.653937 | 0.326969 | − | 0.945035i | \(-0.393973\pi\) | ||||
0.326969 | + | 0.945035i | \(0.393973\pi\) | |||||||
\(578\) | 28.7950 | 1.19771 | ||||||||
\(579\) | −11.4746 | −0.476868 | ||||||||
\(580\) | 44.4152 | 1.84424 | ||||||||
\(581\) | −10.0407 | −0.416558 | ||||||||
\(582\) | 110.804 | 4.59299 | ||||||||
\(583\) | −36.4404 | −1.50921 | ||||||||
\(584\) | 55.1572 | 2.28242 | ||||||||
\(585\) | −34.5152 | −1.42703 | ||||||||
\(586\) | 14.6713 | 0.606067 | ||||||||
\(587\) | −12.9568 | −0.534785 | −0.267393 | − | 0.963588i | \(-0.586162\pi\) | ||||
−0.267393 | + | 0.963588i | \(0.586162\pi\) | |||||||
\(588\) | −78.2775 | −3.22811 | ||||||||
\(589\) | 48.3920 | 1.99396 | ||||||||
\(590\) | 4.00450 | 0.164863 | ||||||||
\(591\) | −24.1706 | −0.994245 | ||||||||
\(592\) | 71.4959 | 2.93847 | ||||||||
\(593\) | −27.3272 | −1.12219 | −0.561097 | − | 0.827750i | \(-0.689620\pi\) | ||||
−0.561097 | + | 0.827750i | \(0.689620\pi\) | |||||||
\(594\) | −240.187 | −9.85497 | ||||||||
\(595\) | 16.2021 | 0.664223 | ||||||||
\(596\) | 95.4259 | 3.90880 | ||||||||
\(597\) | −36.7862 | −1.50556 | ||||||||
\(598\) | −18.6938 | −0.764447 | ||||||||
\(599\) | −7.69601 | −0.314450 | −0.157225 | − | 0.987563i | \(-0.550255\pi\) | ||||
−0.157225 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(600\) | −357.232 | −14.5839 | ||||||||
\(601\) | −43.4407 | −1.77198 | −0.885992 | − | 0.463701i | \(-0.846521\pi\) | ||||
−0.885992 | + | 0.463701i | \(0.846521\pi\) | |||||||
\(602\) | 0.153626 | 0.00626134 | ||||||||
\(603\) | 9.62518 | 0.391968 | ||||||||
\(604\) | −55.8481 | −2.27243 | ||||||||
\(605\) | −76.3452 | −3.10388 | ||||||||
\(606\) | 102.946 | 4.18189 | ||||||||
\(607\) | 27.9835 | 1.13581 | 0.567907 | − | 0.823093i | \(-0.307753\pi\) | ||||
0.567907 | + | 0.823093i | \(0.307753\pi\) | |||||||
\(608\) | −108.683 | −4.40769 | ||||||||
\(609\) | 10.4611 | 0.423905 | ||||||||
\(610\) | 26.9029 | 1.08927 | ||||||||
\(611\) | −11.0005 | −0.445034 | ||||||||
\(612\) | 100.826 | 4.07564 | ||||||||
\(613\) | −31.1620 | −1.25862 | −0.629311 | − | 0.777153i | \(-0.716663\pi\) | ||||
−0.629311 | + | 0.777153i | \(0.716663\pi\) | |||||||
\(614\) | 47.7390 | 1.92659 | ||||||||
\(615\) | 21.6616 | 0.873482 | ||||||||
\(616\) | 66.1781 | 2.66639 | ||||||||
\(617\) | −1.00000 | −0.0402585 | ||||||||
\(618\) | −22.9194 | −0.921953 | ||||||||
\(619\) | 10.2091 | 0.410339 | 0.205170 | − | 0.978726i | \(-0.434225\pi\) | ||||
0.205170 | + | 0.978726i | \(0.434225\pi\) | |||||||
\(620\) | −133.720 | −5.37032 | ||||||||
\(621\) | 118.741 | 4.76490 | ||||||||
\(622\) | 30.4847 | 1.22233 | ||||||||
\(623\) | −5.42980 | −0.217540 | ||||||||
\(624\) | 37.6880 | 1.50873 | ||||||||
\(625\) | 85.5693 | 3.42277 | ||||||||
\(626\) | −81.7744 | −3.26836 | ||||||||
\(627\) | 139.456 | 5.56932 | ||||||||
\(628\) | 23.7948 | 0.949517 | ||||||||
\(629\) | 15.6480 | 0.623925 | ||||||||
\(630\) | −139.862 | −5.57225 | ||||||||
\(631\) | −31.8454 | −1.26774 | −0.633872 | − | 0.773438i | \(-0.718536\pi\) | ||||
−0.633872 | + | 0.773438i | \(0.718536\pi\) | |||||||
\(632\) | −102.081 | −4.06056 | ||||||||
\(633\) | 69.1396 | 2.74805 | ||||||||
\(634\) | −5.95025 | −0.236314 | ||||||||
\(635\) | −35.5537 | −1.41091 | ||||||||
\(636\) | −113.785 | −4.51185 | ||||||||
\(637\) | −4.66789 | −0.184948 | ||||||||
\(638\) | 29.3447 | 1.16177 | ||||||||
\(639\) | 93.9018 | 3.71470 | ||||||||
\(640\) | 43.0636 | 1.70224 | ||||||||
\(641\) | −23.1373 | −0.913868 | −0.456934 | − | 0.889501i | \(-0.651052\pi\) | ||||
−0.456934 | + | 0.889501i | \(0.651052\pi\) | |||||||
\(642\) | 58.5694 | 2.31155 | ||||||||
\(643\) | 28.9898 | 1.14325 | 0.571624 | − | 0.820516i | \(-0.306314\pi\) | ||||
0.571624 | + | 0.820516i | \(0.306314\pi\) | |||||||
\(644\) | −54.2336 | −2.13710 | ||||||||
\(645\) | −0.539642 | −0.0212484 | ||||||||
\(646\) | −51.3573 | −2.02062 | ||||||||
\(647\) | 34.0168 | 1.33734 | 0.668670 | − | 0.743559i | \(-0.266864\pi\) | ||||
0.668670 | + | 0.743559i | \(0.266864\pi\) | |||||||
\(648\) | −257.155 | −10.1020 | ||||||||
\(649\) | 1.89420 | 0.0743539 | ||||||||
\(650\) | −35.3132 | −1.38510 | ||||||||
\(651\) | −31.4950 | −1.23439 | ||||||||
\(652\) | 125.431 | 4.91225 | ||||||||
\(653\) | 33.6326 | 1.31615 | 0.658073 | − | 0.752955i | \(-0.271372\pi\) | ||||
0.658073 | + | 0.752955i | \(0.271372\pi\) | |||||||
\(654\) | −1.67278 | −0.0654108 | ||||||||
\(655\) | 37.8286 | 1.47808 | ||||||||
\(656\) | −17.2409 | −0.673143 | ||||||||
\(657\) | −55.1400 | −2.15122 | ||||||||
\(658\) | −44.5763 | −1.73776 | ||||||||
\(659\) | −7.19719 | −0.280363 | −0.140181 | − | 0.990126i | \(-0.544769\pi\) | ||||
−0.140181 | + | 0.990126i | \(0.544769\pi\) | |||||||
\(660\) | −385.352 | −14.9998 | ||||||||
\(661\) | 13.3075 | 0.517600 | 0.258800 | − | 0.965931i | \(-0.416673\pi\) | ||||
0.258800 | + | 0.965931i | \(0.416673\pi\) | |||||||
\(662\) | 15.0341 | 0.584317 | ||||||||
\(663\) | 8.24858 | 0.320348 | ||||||||
\(664\) | −53.0531 | −2.05886 | ||||||||
\(665\) | 51.0049 | 1.97788 | ||||||||
\(666\) | −135.078 | −5.23418 | ||||||||
\(667\) | −14.5071 | −0.561716 | ||||||||
\(668\) | −119.921 | −4.63987 | ||||||||
\(669\) | −64.7120 | −2.50191 | ||||||||
\(670\) | 13.5476 | 0.523388 | ||||||||
\(671\) | 12.7256 | 0.491266 | ||||||||
\(672\) | 70.7342 | 2.72863 | ||||||||
\(673\) | −31.7762 | −1.22488 | −0.612441 | − | 0.790516i | \(-0.709812\pi\) | ||||
−0.612441 | + | 0.790516i | \(0.709812\pi\) | |||||||
\(674\) | 25.1951 | 0.970481 | ||||||||
\(675\) | 224.305 | 8.63350 | ||||||||
\(676\) | 5.04093 | 0.193882 | ||||||||
\(677\) | −49.6854 | −1.90957 | −0.954783 | − | 0.297303i | \(-0.903913\pi\) | ||||
−0.954783 | + | 0.297303i | \(0.903913\pi\) | |||||||
\(678\) | −8.80451 | −0.338135 | ||||||||
\(679\) | 19.1695 | 0.735657 | ||||||||
\(680\) | 85.6091 | 3.28296 | ||||||||
\(681\) | −19.3944 | −0.743193 | ||||||||
\(682\) | −88.3473 | −3.38299 | ||||||||
\(683\) | −34.6843 | −1.32716 | −0.663579 | − | 0.748107i | \(-0.730963\pi\) | ||||
−0.663579 | + | 0.748107i | \(0.730963\pi\) | |||||||
\(684\) | 317.403 | 12.1362 | ||||||||
\(685\) | −26.2424 | −1.00267 | ||||||||
\(686\) | −47.2805 | −1.80518 | ||||||||
\(687\) | −25.0900 | −0.957243 | ||||||||
\(688\) | 0.429510 | 0.0163749 | ||||||||
\(689\) | −6.78526 | −0.258498 | ||||||||
\(690\) | 266.090 | 10.1299 | ||||||||
\(691\) | −16.8921 | −0.642604 | −0.321302 | − | 0.946977i | \(-0.604121\pi\) | ||||
−0.321302 | + | 0.946977i | \(0.604121\pi\) | |||||||
\(692\) | −87.0637 | −3.30967 | ||||||||
\(693\) | −66.1574 | −2.51311 | ||||||||
\(694\) | 11.8022 | 0.448005 | ||||||||
\(695\) | 62.7337 | 2.37962 | ||||||||
\(696\) | 55.2745 | 2.09517 | ||||||||
\(697\) | −3.77342 | −0.142929 | ||||||||
\(698\) | −68.8641 | −2.60655 | ||||||||
\(699\) | 5.16380 | 0.195313 | ||||||||
\(700\) | −102.449 | −3.87221 | ||||||||
\(701\) | 43.1872 | 1.63116 | 0.815579 | − | 0.578646i | \(-0.196419\pi\) | ||||
0.815579 | + | 0.578646i | \(0.196419\pi\) | |||||||
\(702\) | −44.7231 | −1.68796 | ||||||||
\(703\) | 49.2603 | 1.85789 | ||||||||
\(704\) | 76.7312 | 2.89192 | ||||||||
\(705\) | 156.583 | 5.89724 | ||||||||
\(706\) | −63.8131 | −2.40164 | ||||||||
\(707\) | 17.8099 | 0.669812 | ||||||||
\(708\) | 5.91460 | 0.222284 | ||||||||
\(709\) | 31.1556 | 1.17007 | 0.585037 | − | 0.811006i | \(-0.301080\pi\) | ||||
0.585037 | + | 0.811006i | \(0.301080\pi\) | |||||||
\(710\) | 132.168 | 4.96018 | ||||||||
\(711\) | 102.049 | 3.82714 | ||||||||
\(712\) | −28.6901 | −1.07521 | ||||||||
\(713\) | 43.6761 | 1.63568 | ||||||||
\(714\) | 33.4248 | 1.25089 | ||||||||
\(715\) | −22.9795 | −0.859386 | ||||||||
\(716\) | 10.9249 | 0.408284 | ||||||||
\(717\) | −7.32291 | −0.273479 | ||||||||
\(718\) | 9.61750 | 0.358922 | ||||||||
\(719\) | −4.62775 | −0.172586 | −0.0862929 | − | 0.996270i | \(-0.527502\pi\) | ||||
−0.0862929 | + | 0.996270i | \(0.527502\pi\) | |||||||
\(720\) | −391.028 | −14.5728 | ||||||||
\(721\) | −3.96513 | −0.147669 | ||||||||
\(722\) | −111.258 | −4.14061 | ||||||||
\(723\) | −43.7487 | −1.62703 | ||||||||
\(724\) | −55.6068 | −2.06661 | ||||||||
\(725\) | −27.4043 | −1.01777 | ||||||||
\(726\) | −157.499 | −5.84535 | ||||||||
\(727\) | −25.7202 | −0.953910 | −0.476955 | − | 0.878928i | \(-0.658260\pi\) | ||||
−0.476955 | + | 0.878928i | \(0.658260\pi\) | |||||||
\(728\) | 12.3224 | 0.456700 | ||||||||
\(729\) | 88.8680 | 3.29141 | ||||||||
\(730\) | −77.6103 | −2.87248 | ||||||||
\(731\) | 0.0940047 | 0.00347689 | ||||||||
\(732\) | 39.7354 | 1.46866 | ||||||||
\(733\) | 10.4136 | 0.384635 | 0.192318 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192318 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(734\) | −79.5510 | −2.93628 | ||||||||
\(735\) | 66.4431 | 2.45079 | ||||||||
\(736\) | −98.0917 | −3.61571 | ||||||||
\(737\) | 6.40825 | 0.236051 | ||||||||
\(738\) | 32.5734 | 1.19904 | ||||||||
\(739\) | 16.9981 | 0.625284 | 0.312642 | − | 0.949871i | \(-0.398786\pi\) | ||||
0.312642 | + | 0.949871i | \(0.398786\pi\) | |||||||
\(740\) | −136.119 | −5.00384 | ||||||||
\(741\) | 25.9668 | 0.953915 | ||||||||
\(742\) | −27.4952 | −1.00938 | ||||||||
\(743\) | 5.45640 | 0.200176 | 0.100088 | − | 0.994979i | \(-0.468088\pi\) | ||||
0.100088 | + | 0.994979i | \(0.468088\pi\) | |||||||
\(744\) | −166.414 | −6.10102 | ||||||||
\(745\) | −80.9989 | −2.96757 | ||||||||
\(746\) | 42.9502 | 1.57252 | ||||||||
\(747\) | 53.0366 | 1.94051 | ||||||||
\(748\) | 67.1277 | 2.45443 | ||||||||
\(749\) | 10.1327 | 0.370240 | ||||||||
\(750\) | 313.803 | 11.4585 | ||||||||
\(751\) | 34.7121 | 1.26666 | 0.633332 | − | 0.773880i | \(-0.281687\pi\) | ||||
0.633332 | + | 0.773880i | \(0.281687\pi\) | |||||||
\(752\) | −124.627 | −4.54467 | ||||||||
\(753\) | −66.6684 | −2.42953 | ||||||||
\(754\) | 5.46402 | 0.198988 | ||||||||
\(755\) | 47.4047 | 1.72523 | ||||||||
\(756\) | −129.748 | −4.71890 | ||||||||
\(757\) | 8.83092 | 0.320965 | 0.160483 | − | 0.987039i | \(-0.448695\pi\) | ||||
0.160483 | + | 0.987039i | \(0.448695\pi\) | |||||||
\(758\) | −47.5708 | −1.72785 | ||||||||
\(759\) | 125.865 | 4.56862 | ||||||||
\(760\) | 269.500 | 9.77580 | ||||||||
\(761\) | −27.0388 | −0.980156 | −0.490078 | − | 0.871679i | \(-0.663032\pi\) | ||||
−0.490078 | + | 0.871679i | \(0.663032\pi\) | |||||||
\(762\) | −73.3469 | −2.65708 | ||||||||
\(763\) | −0.289396 | −0.0104768 | ||||||||
\(764\) | 12.6108 | 0.456244 | ||||||||
\(765\) | −85.5824 | −3.09424 | ||||||||
\(766\) | −6.58349 | −0.237871 | ||||||||
\(767\) | 0.352703 | 0.0127354 | ||||||||
\(768\) | −6.21876 | −0.224400 | ||||||||
\(769\) | −26.6802 | −0.962114 | −0.481057 | − | 0.876689i | \(-0.659747\pi\) | ||||
−0.481057 | + | 0.876689i | \(0.659747\pi\) | |||||||
\(770\) | −93.1174 | −3.35572 | ||||||||
\(771\) | −27.6929 | −0.997335 | ||||||||
\(772\) | −17.3877 | −0.625797 | ||||||||
\(773\) | 31.5628 | 1.13524 | 0.567618 | − | 0.823292i | \(-0.307865\pi\) | ||||
0.567618 | + | 0.823292i | \(0.307865\pi\) | |||||||
\(774\) | −0.811480 | −0.0291680 | ||||||||
\(775\) | 82.5056 | 2.96369 | ||||||||
\(776\) | 101.288 | 3.63603 | ||||||||
\(777\) | −32.0601 | −1.15015 | ||||||||
\(778\) | −35.4688 | −1.27162 | ||||||||
\(779\) | −11.8789 | −0.425604 | ||||||||
\(780\) | −71.7531 | −2.56917 | ||||||||
\(781\) | 62.5179 | 2.23707 | ||||||||
\(782\) | −46.3523 | −1.65756 | ||||||||
\(783\) | −34.7067 | −1.24032 | ||||||||
\(784\) | −52.8832 | −1.88869 | ||||||||
\(785\) | −20.1974 | −0.720877 | ||||||||
\(786\) | 78.0399 | 2.78359 | ||||||||
\(787\) | −36.0311 | −1.28437 | −0.642185 | − | 0.766549i | \(-0.721972\pi\) | ||||
−0.642185 | + | 0.766549i | \(0.721972\pi\) | |||||||
\(788\) | −36.6262 | −1.30476 | ||||||||
\(789\) | −33.5546 | −1.19457 | ||||||||
\(790\) | 143.635 | 5.11031 | ||||||||
\(791\) | −1.52321 | −0.0541590 | ||||||||
\(792\) | −349.563 | −12.4212 | ||||||||
\(793\) | 2.36952 | 0.0841441 | ||||||||
\(794\) | 73.6310 | 2.61307 | ||||||||
\(795\) | 96.5820 | 3.42541 | ||||||||
\(796\) | −55.7431 | −1.97576 | ||||||||
\(797\) | 13.4603 | 0.476787 | 0.238393 | − | 0.971169i | \(-0.423379\pi\) | ||||
0.238393 | + | 0.971169i | \(0.423379\pi\) | |||||||
\(798\) | 105.222 | 3.72484 | ||||||||
\(799\) | −27.2764 | −0.964970 | ||||||||
\(800\) | −185.298 | −6.55129 | ||||||||
\(801\) | 28.6811 | 1.01340 | ||||||||
\(802\) | −12.9071 | −0.455766 | ||||||||
\(803\) | −36.7111 | −1.29551 | ||||||||
\(804\) | 20.0096 | 0.705685 | ||||||||
\(805\) | 46.0343 | 1.62250 | ||||||||
\(806\) | −16.4504 | −0.579440 | ||||||||
\(807\) | 26.3338 | 0.926993 | ||||||||
\(808\) | 94.1044 | 3.31058 | ||||||||
\(809\) | 22.2872 | 0.783575 | 0.391787 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391787 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(810\) | 361.836 | 12.7136 | ||||||||
\(811\) | −21.0924 | −0.740656 | −0.370328 | − | 0.928901i | \(-0.620755\pi\) | ||||
−0.370328 | + | 0.928901i | \(0.620755\pi\) | |||||||
\(812\) | 15.8520 | 0.556294 | ||||||||
\(813\) | 25.2313 | 0.884900 | ||||||||
\(814\) | −89.9325 | −3.15213 | ||||||||
\(815\) | −106.467 | −3.72939 | ||||||||
\(816\) | 93.4494 | 3.27138 | ||||||||
\(817\) | 0.295930 | 0.0103533 | ||||||||
\(818\) | 37.5680 | 1.31353 | ||||||||
\(819\) | −12.3186 | −0.430447 | ||||||||
\(820\) | 32.8244 | 1.14628 | ||||||||
\(821\) | 6.88340 | 0.240232 | 0.120116 | − | 0.992760i | \(-0.461673\pi\) | ||||
0.120116 | + | 0.992760i | \(0.461673\pi\) | |||||||
\(822\) | −54.1378 | −1.88827 | ||||||||
\(823\) | 20.2016 | 0.704185 | 0.352093 | − | 0.935965i | \(-0.385470\pi\) | ||||
0.352093 | + | 0.935965i | \(0.385470\pi\) | |||||||
\(824\) | −20.9510 | −0.729862 | ||||||||
\(825\) | 237.764 | 8.27787 | ||||||||
\(826\) | 1.42922 | 0.0497289 | ||||||||
\(827\) | −44.7625 | −1.55655 | −0.778273 | − | 0.627926i | \(-0.783904\pi\) | ||||
−0.778273 | + | 0.627926i | \(0.783904\pi\) | |||||||
\(828\) | 286.471 | 9.95556 | ||||||||
\(829\) | −16.2514 | −0.564433 | −0.282217 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282217 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(830\) | 74.6496 | 2.59113 | ||||||||
\(831\) | −55.2600 | −1.91695 | ||||||||
\(832\) | 14.2875 | 0.495328 | ||||||||
\(833\) | −11.5743 | −0.401025 | ||||||||
\(834\) | 129.419 | 4.48141 | ||||||||
\(835\) | 101.790 | 3.52260 | ||||||||
\(836\) | 211.320 | 7.30867 | ||||||||
\(837\) | 104.491 | 3.61172 | ||||||||
\(838\) | 16.1064 | 0.556386 | ||||||||
\(839\) | −5.69727 | −0.196692 | −0.0983458 | − | 0.995152i | \(-0.531355\pi\) | ||||
−0.0983458 | + | 0.995152i | \(0.531355\pi\) | |||||||
\(840\) | −175.399 | −6.05183 | ||||||||
\(841\) | −24.7597 | −0.853784 | ||||||||
\(842\) | 47.9169 | 1.65132 | ||||||||
\(843\) | −58.8386 | −2.02651 | ||||||||
\(844\) | 104.769 | 3.60629 | ||||||||
\(845\) | −4.27882 | −0.147196 | ||||||||
\(846\) | 235.459 | 8.09525 | ||||||||
\(847\) | −27.2479 | −0.936248 | ||||||||
\(848\) | −76.8712 | −2.63977 | ||||||||
\(849\) | 70.2073 | 2.40951 | ||||||||
\(850\) | −87.5611 | −3.00332 | ||||||||
\(851\) | 44.4598 | 1.52406 | ||||||||
\(852\) | 195.211 | 6.68782 | ||||||||
\(853\) | −25.8944 | −0.886607 | −0.443304 | − | 0.896371i | \(-0.646194\pi\) | ||||
−0.443304 | + | 0.896371i | \(0.646194\pi\) | |||||||
\(854\) | 9.60175 | 0.328565 | ||||||||
\(855\) | −269.416 | −9.21384 | ||||||||
\(856\) | 53.5392 | 1.82993 | ||||||||
\(857\) | 15.6042 | 0.533029 | 0.266514 | − | 0.963831i | \(-0.414128\pi\) | ||||
0.266514 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(858\) | −47.4065 | −1.61843 | ||||||||
\(859\) | −42.1368 | −1.43769 | −0.718845 | − | 0.695170i | \(-0.755329\pi\) | ||||
−0.718845 | + | 0.695170i | \(0.755329\pi\) | |||||||
\(860\) | −0.817732 | −0.0278844 | ||||||||
\(861\) | 7.73111 | 0.263476 | ||||||||
\(862\) | −97.7647 | −3.32988 | ||||||||
\(863\) | 28.2564 | 0.961860 | 0.480930 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480930 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(864\) | −234.674 | −7.98378 | ||||||||
\(865\) | 73.9010 | 2.51271 | ||||||||
\(866\) | 28.0862 | 0.954409 | ||||||||
\(867\) | −36.1001 | −1.22602 | ||||||||
\(868\) | −47.7251 | −1.61989 | ||||||||
\(869\) | 67.9421 | 2.30478 | ||||||||
\(870\) | −77.7753 | −2.63683 | ||||||||
\(871\) | 1.19322 | 0.0404309 | ||||||||
\(872\) | −1.52911 | −0.0517823 | ||||||||
\(873\) | −101.256 | −3.42701 | ||||||||
\(874\) | −145.919 | −4.93578 | ||||||||
\(875\) | 54.2888 | 1.83530 | ||||||||
\(876\) | −114.630 | −3.87298 | ||||||||
\(877\) | −45.9148 | −1.55043 | −0.775217 | − | 0.631696i | \(-0.782359\pi\) | ||||
−0.775217 | + | 0.631696i | \(0.782359\pi\) | |||||||
\(878\) | −35.8030 | −1.20829 | ||||||||
\(879\) | −18.3933 | −0.620391 | ||||||||
\(880\) | −260.338 | −8.77601 | ||||||||
\(881\) | −31.2335 | −1.05228 | −0.526142 | − | 0.850397i | \(-0.676362\pi\) | ||||
−0.526142 | + | 0.850397i | \(0.676362\pi\) | |||||||
\(882\) | 99.9131 | 3.36425 | ||||||||
\(883\) | 8.67210 | 0.291839 | 0.145920 | − | 0.989296i | \(-0.453386\pi\) | ||||
0.145920 | + | 0.989296i | \(0.453386\pi\) | |||||||
\(884\) | 12.4993 | 0.420396 | ||||||||
\(885\) | −5.02040 | −0.168759 | ||||||||
\(886\) | 75.3185 | 2.53037 | ||||||||
\(887\) | 9.56019 | 0.321000 | 0.160500 | − | 0.987036i | \(-0.448689\pi\) | ||||
0.160500 | + | 0.987036i | \(0.448689\pi\) | |||||||
\(888\) | −169.399 | −5.68467 | ||||||||
\(889\) | −12.6892 | −0.425584 | ||||||||
\(890\) | 40.3690 | 1.35317 | ||||||||
\(891\) | 171.155 | 5.73391 | ||||||||
\(892\) | −98.0596 | −3.28328 | ||||||||
\(893\) | −85.8671 | −2.87343 | ||||||||
\(894\) | −167.100 | −5.58866 | ||||||||
\(895\) | −9.27326 | −0.309971 | ||||||||
\(896\) | 15.3695 | 0.513460 | ||||||||
\(897\) | 23.4363 | 0.782515 | ||||||||
\(898\) | −67.1025 | −2.23924 | ||||||||
\(899\) | −12.7661 | −0.425773 | ||||||||
\(900\) | 541.153 | 18.0384 | ||||||||
\(901\) | −16.8244 | −0.560503 | ||||||||
\(902\) | 21.6867 | 0.722089 | ||||||||
\(903\) | −0.192600 | −0.00640933 | ||||||||
\(904\) | −8.04834 | −0.267684 | ||||||||
\(905\) | 47.1999 | 1.56898 | ||||||||
\(906\) | 97.7953 | 3.24903 | ||||||||
\(907\) | −5.52820 | −0.183561 | −0.0917804 | − | 0.995779i | \(-0.529256\pi\) | ||||
−0.0917804 | + | 0.995779i | \(0.529256\pi\) | |||||||
\(908\) | −29.3887 | −0.975299 | ||||||||
\(909\) | −94.0751 | −3.12027 | ||||||||
\(910\) | −17.3386 | −0.574769 | ||||||||
\(911\) | −4.96970 | −0.164653 | −0.0823267 | − | 0.996605i | \(-0.526235\pi\) | ||||
−0.0823267 | + | 0.996605i | \(0.526235\pi\) | |||||||
\(912\) | 294.182 | 9.74134 | ||||||||
\(913\) | 35.3107 | 1.16861 | ||||||||
\(914\) | 47.9081 | 1.58466 | ||||||||
\(915\) | −33.7280 | −1.11501 | ||||||||
\(916\) | −38.0195 | −1.25620 | ||||||||
\(917\) | 13.5011 | 0.445847 | ||||||||
\(918\) | −110.893 | −3.66002 | ||||||||
\(919\) | −21.9256 | −0.723260 | −0.361630 | − | 0.932322i | \(-0.617780\pi\) | ||||
−0.361630 | + | 0.932322i | \(0.617780\pi\) | |||||||
\(920\) | 243.237 | 8.01928 | ||||||||
\(921\) | −59.8499 | −1.97212 | ||||||||
\(922\) | 26.8713 | 0.884958 | ||||||||
\(923\) | 11.6409 | 0.383166 | ||||||||
\(924\) | −137.534 | −4.52452 | ||||||||
\(925\) | 83.9859 | 2.76144 | ||||||||
\(926\) | −63.1282 | −2.07452 | ||||||||
\(927\) | 20.9445 | 0.687906 | ||||||||
\(928\) | 28.6712 | 0.941179 | ||||||||
\(929\) | 20.7066 | 0.679362 | 0.339681 | − | 0.940541i | \(-0.389681\pi\) | ||||
0.339681 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(930\) | 234.156 | 7.67828 | ||||||||
\(931\) | −36.4362 | −1.19415 | ||||||||
\(932\) | 7.82483 | 0.256311 | ||||||||
\(933\) | −38.2184 | −1.25121 | ||||||||
\(934\) | 42.0356 | 1.37545 | ||||||||
\(935\) | −56.9790 | −1.86341 | ||||||||
\(936\) | −65.0892 | −2.12751 | ||||||||
\(937\) | 31.4930 | 1.02883 | 0.514415 | − | 0.857541i | \(-0.328009\pi\) | ||||
0.514415 | + | 0.857541i | \(0.328009\pi\) | |||||||
\(938\) | 4.83517 | 0.157874 | ||||||||
\(939\) | 102.520 | 3.34561 | ||||||||
\(940\) | 237.273 | 7.73900 | ||||||||
\(941\) | 25.1900 | 0.821170 | 0.410585 | − | 0.911822i | \(-0.365325\pi\) | ||||
0.410585 | + | 0.911822i | \(0.365325\pi\) | |||||||
\(942\) | −41.6670 | −1.35759 | ||||||||
\(943\) | −10.7212 | −0.349131 | ||||||||
\(944\) | 3.99582 | 0.130053 | ||||||||
\(945\) | 110.132 | 3.58261 | ||||||||
\(946\) | −0.540267 | −0.0175656 | ||||||||
\(947\) | −3.73345 | −0.121321 | −0.0606604 | − | 0.998158i | \(-0.519321\pi\) | ||||
−0.0606604 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(948\) | 212.148 | 6.89025 | ||||||||
\(949\) | −6.83565 | −0.221895 | ||||||||
\(950\) | −275.645 | −8.94311 | ||||||||
\(951\) | 7.45977 | 0.241900 | ||||||||
\(952\) | 30.5542 | 0.990266 | ||||||||
\(953\) | −41.8614 | −1.35602 | −0.678011 | − | 0.735052i | \(-0.737158\pi\) | ||||
−0.678011 | + | 0.735052i | \(0.737158\pi\) | |||||||
\(954\) | 145.234 | 4.70212 | ||||||||
\(955\) | −10.7043 | −0.346382 | ||||||||
\(956\) | −11.0966 | −0.358889 | ||||||||
\(957\) | −36.7892 | −1.18922 | ||||||||
\(958\) | −71.1257 | −2.29797 | ||||||||
\(959\) | −9.36600 | −0.302444 | ||||||||
\(960\) | −203.369 | −6.56370 | ||||||||
\(961\) | 7.43455 | 0.239824 | ||||||||
\(962\) | −16.7455 | −0.539898 | ||||||||
\(963\) | −53.5225 | −1.72474 | ||||||||
\(964\) | −66.2934 | −2.13517 | ||||||||
\(965\) | 14.7589 | 0.475107 | ||||||||
\(966\) | 94.9683 | 3.05555 | ||||||||
\(967\) | −55.5865 | −1.78754 | −0.893770 | − | 0.448525i | \(-0.851950\pi\) | ||||
−0.893770 | + | 0.448525i | \(0.851950\pi\) | |||||||
\(968\) | −143.973 | −4.62746 | ||||||||
\(969\) | 64.3861 | 2.06838 | ||||||||
\(970\) | −142.520 | −4.57603 | ||||||||
\(971\) | −11.6901 | −0.375155 | −0.187577 | − | 0.982250i | \(-0.560064\pi\) | ||||
−0.187577 | + | 0.982250i | \(0.560064\pi\) | |||||||
\(972\) | 279.541 | 8.96627 | ||||||||
\(973\) | 22.3899 | 0.717786 | ||||||||
\(974\) | 27.4174 | 0.878511 | ||||||||
\(975\) | 44.2719 | 1.41784 | ||||||||
\(976\) | 26.8447 | 0.859276 | ||||||||
\(977\) | 20.8728 | 0.667781 | 0.333890 | − | 0.942612i | \(-0.391638\pi\) | ||||
0.333890 | + | 0.942612i | \(0.391638\pi\) | |||||||
\(978\) | −219.641 | −7.02335 | ||||||||
\(979\) | 19.0953 | 0.610288 | ||||||||
\(980\) | 100.683 | 3.21620 | ||||||||
\(981\) | 1.52864 | 0.0488056 | ||||||||
\(982\) | −68.3636 | −2.18157 | ||||||||
\(983\) | −54.5768 | −1.74073 | −0.870365 | − | 0.492406i | \(-0.836117\pi\) | ||||
−0.870365 | + | 0.492406i | \(0.836117\pi\) | |||||||
\(984\) | 40.8498 | 1.30224 | ||||||||
\(985\) | 31.0889 | 0.990574 | ||||||||
\(986\) | 13.5483 | 0.431467 | ||||||||
\(987\) | 55.8849 | 1.77883 | ||||||||
\(988\) | 39.3481 | 1.25183 | ||||||||
\(989\) | 0.267091 | 0.00849299 | ||||||||
\(990\) | 491.862 | 15.6324 | ||||||||
\(991\) | −4.06928 | −0.129265 | −0.0646325 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646325 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(992\) | −86.3198 | −2.74066 | ||||||||
\(993\) | −18.8481 | −0.598127 | ||||||||
\(994\) | 47.1712 | 1.49618 | ||||||||
\(995\) | 47.3155 | 1.50000 | ||||||||
\(996\) | 110.257 | 3.49362 | ||||||||
\(997\) | 23.5213 | 0.744926 | 0.372463 | − | 0.928047i | \(-0.378513\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378513\pi\) | |||||||
\(998\) | −73.6138 | −2.33020 | ||||||||
\(999\) | 106.365 | 3.36525 |
(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 | 8021.2.a.d.1.9 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.d.1.9 | ✓ | 174 | 1.1 | even | 1 | trivial |