Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.64474 | −0.949589 | −0.474794 | − | 0.880097i | \(-0.657478\pi\) | ||||
−0.474794 | + | 0.880097i | \(0.657478\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.535091 | −0.239300 | −0.119650 | − | 0.992816i | \(-0.538177\pi\) | ||||
−0.119650 | + | 0.992816i | \(0.538177\pi\) | |||||||
\(6\) | −1.64474 | −0.671461 | ||||||||
\(7\) | −1.74380 | −0.659095 | −0.329547 | − | 0.944139i | \(-0.606896\pi\) | ||||
−0.329547 | + | 0.944139i | \(0.606896\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.294845 | −0.0982815 | ||||||||
\(10\) | −0.535091 | −0.169211 | ||||||||
\(11\) | −1.93819 | −0.584386 | −0.292193 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292193 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(12\) | −1.64474 | −0.474794 | ||||||||
\(13\) | 3.27734 | 0.908970 | 0.454485 | − | 0.890754i | \(-0.349823\pi\) | ||||
0.454485 | + | 0.890754i | \(0.349823\pi\) | |||||||
\(14\) | −1.74380 | −0.466051 | ||||||||
\(15\) | 0.880083 | 0.227236 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.55193 | −0.376399 | −0.188200 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188200 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(18\) | −0.294845 | −0.0694955 | ||||||||
\(19\) | 0.183349 | 0.0420630 | 0.0210315 | − | 0.999779i | \(-0.493305\pi\) | ||||
0.0210315 | + | 0.999779i | \(0.493305\pi\) | |||||||
\(20\) | −0.535091 | −0.119650 | ||||||||
\(21\) | 2.86809 | 0.625869 | ||||||||
\(22\) | −1.93819 | −0.413224 | ||||||||
\(23\) | 8.78022 | 1.83080 | 0.915401 | − | 0.402543i | \(-0.131874\pi\) | ||||
0.915401 | + | 0.402543i | \(0.131874\pi\) | |||||||
\(24\) | −1.64474 | −0.335730 | ||||||||
\(25\) | −4.71368 | −0.942736 | ||||||||
\(26\) | 3.27734 | 0.642739 | ||||||||
\(27\) | 5.41915 | 1.04292 | ||||||||
\(28\) | −1.74380 | −0.329547 | ||||||||
\(29\) | −3.77491 | −0.700982 | −0.350491 | − | 0.936566i | \(-0.613985\pi\) | ||||
−0.350491 | + | 0.936566i | \(0.613985\pi\) | |||||||
\(30\) | 0.880083 | 0.160680 | ||||||||
\(31\) | −8.42757 | −1.51364 | −0.756818 | − | 0.653625i | \(-0.773247\pi\) | ||||
−0.756818 | + | 0.653625i | \(0.773247\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.18781 | 0.554927 | ||||||||
\(34\) | −1.55193 | −0.266154 | ||||||||
\(35\) | 0.933092 | 0.157721 | ||||||||
\(36\) | −0.294845 | −0.0491408 | ||||||||
\(37\) | −0.166018 | −0.0272931 | −0.0136466 | − | 0.999907i | \(-0.504344\pi\) | ||||
−0.0136466 | + | 0.999907i | \(0.504344\pi\) | |||||||
\(38\) | 0.183349 | 0.0297431 | ||||||||
\(39\) | −5.39035 | −0.863147 | ||||||||
\(40\) | −0.535091 | −0.0846053 | ||||||||
\(41\) | −2.70104 | −0.421832 | −0.210916 | − | 0.977504i | \(-0.567645\pi\) | ||||
−0.210916 | + | 0.977504i | \(0.567645\pi\) | |||||||
\(42\) | 2.86809 | 0.442556 | ||||||||
\(43\) | 4.36327 | 0.665393 | 0.332696 | − | 0.943034i | \(-0.392042\pi\) | ||||
0.332696 | + | 0.943034i | \(0.392042\pi\) | |||||||
\(44\) | −1.93819 | −0.292193 | ||||||||
\(45\) | 0.157769 | 0.0235188 | ||||||||
\(46\) | 8.78022 | 1.29457 | ||||||||
\(47\) | −12.8366 | −1.87241 | −0.936205 | − | 0.351454i | \(-0.885688\pi\) | ||||
−0.936205 | + | 0.351454i | \(0.885688\pi\) | |||||||
\(48\) | −1.64474 | −0.237397 | ||||||||
\(49\) | −3.95916 | −0.565594 | ||||||||
\(50\) | −4.71368 | −0.666615 | ||||||||
\(51\) | 2.55252 | 0.357424 | ||||||||
\(52\) | 3.27734 | 0.454485 | ||||||||
\(53\) | 8.19730 | 1.12599 | 0.562993 | − | 0.826462i | \(-0.309650\pi\) | ||||
0.562993 | + | 0.826462i | \(0.309650\pi\) | |||||||
\(54\) | 5.41915 | 0.737453 | ||||||||
\(55\) | 1.03711 | 0.139844 | ||||||||
\(56\) | −1.74380 | −0.233025 | ||||||||
\(57\) | −0.301560 | −0.0399426 | ||||||||
\(58\) | −3.77491 | −0.495669 | ||||||||
\(59\) | 12.9123 | 1.68103 | 0.840517 | − | 0.541784i | \(-0.182251\pi\) | ||||
0.840517 | + | 0.541784i | \(0.182251\pi\) | |||||||
\(60\) | 0.880083 | 0.113618 | ||||||||
\(61\) | 8.27695 | 1.05975 | 0.529877 | − | 0.848074i | \(-0.322238\pi\) | ||||
0.529877 | + | 0.848074i | \(0.322238\pi\) | |||||||
\(62\) | −8.42757 | −1.07030 | ||||||||
\(63\) | 0.514150 | 0.0647769 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.75367 | −0.217516 | ||||||||
\(66\) | 3.18781 | 0.392392 | ||||||||
\(67\) | 1.83260 | 0.223888 | 0.111944 | − | 0.993715i | \(-0.464292\pi\) | ||||
0.111944 | + | 0.993715i | \(0.464292\pi\) | |||||||
\(68\) | −1.55193 | −0.188200 | ||||||||
\(69\) | −14.4411 | −1.73851 | ||||||||
\(70\) | 0.933092 | 0.111526 | ||||||||
\(71\) | −2.99104 | −0.354972 | −0.177486 | − | 0.984123i | \(-0.556796\pi\) | ||||
−0.177486 | + | 0.984123i | \(0.556796\pi\) | |||||||
\(72\) | −0.294845 | −0.0347478 | ||||||||
\(73\) | 7.79312 | 0.912115 | 0.456058 | − | 0.889950i | \(-0.349261\pi\) | ||||
0.456058 | + | 0.889950i | \(0.349261\pi\) | |||||||
\(74\) | −0.166018 | −0.0192992 | ||||||||
\(75\) | 7.75275 | 0.895211 | ||||||||
\(76\) | 0.183349 | 0.0210315 | ||||||||
\(77\) | 3.37982 | 0.385166 | ||||||||
\(78\) | −5.39035 | −0.610337 | ||||||||
\(79\) | 7.03516 | 0.791517 | 0.395758 | − | 0.918355i | \(-0.370482\pi\) | ||||
0.395758 | + | 0.918355i | \(0.370482\pi\) | |||||||
\(80\) | −0.535091 | −0.0598250 | ||||||||
\(81\) | −8.02853 | −0.892059 | ||||||||
\(82\) | −2.70104 | −0.298280 | ||||||||
\(83\) | 11.9340 | 1.30993 | 0.654963 | − | 0.755661i | \(-0.272684\pi\) | ||||
0.654963 | + | 0.755661i | \(0.272684\pi\) | |||||||
\(84\) | 2.86809 | 0.312935 | ||||||||
\(85\) | 0.830425 | 0.0900723 | ||||||||
\(86\) | 4.36327 | 0.470504 | ||||||||
\(87\) | 6.20872 | 0.665645 | ||||||||
\(88\) | −1.93819 | −0.206612 | ||||||||
\(89\) | −1.25449 | −0.132976 | −0.0664879 | − | 0.997787i | \(-0.521179\pi\) | ||||
−0.0664879 | + | 0.997787i | \(0.521179\pi\) | |||||||
\(90\) | 0.157769 | 0.0166303 | ||||||||
\(91\) | −5.71503 | −0.599098 | ||||||||
\(92\) | 8.78022 | 0.915401 | ||||||||
\(93\) | 13.8611 | 1.43733 | ||||||||
\(94\) | −12.8366 | −1.32399 | ||||||||
\(95\) | −0.0981081 | −0.0100657 | ||||||||
\(96\) | −1.64474 | −0.167865 | ||||||||
\(97\) | 14.8335 | 1.50612 | 0.753059 | − | 0.657953i | \(-0.228577\pi\) | ||||
0.753059 | + | 0.657953i | \(0.228577\pi\) | |||||||
\(98\) | −3.95916 | −0.399935 | ||||||||
\(99\) | 0.571465 | 0.0574344 | ||||||||
\(100\) | −4.71368 | −0.471368 | ||||||||
\(101\) | 10.3409 | 1.02896 | 0.514481 | − | 0.857502i | \(-0.327985\pi\) | ||||
0.514481 | + | 0.857502i | \(0.327985\pi\) | |||||||
\(102\) | 2.55252 | 0.252737 | ||||||||
\(103\) | 13.0167 | 1.28257 | 0.641285 | − | 0.767303i | \(-0.278402\pi\) | ||||
0.641285 | + | 0.767303i | \(0.278402\pi\) | |||||||
\(104\) | 3.27734 | 0.321369 | ||||||||
\(105\) | −1.53469 | −0.149770 | ||||||||
\(106\) | 8.19730 | 0.796192 | ||||||||
\(107\) | −1.60704 | −0.155359 | −0.0776795 | − | 0.996978i | \(-0.524751\pi\) | ||||
−0.0776795 | + | 0.996978i | \(0.524751\pi\) | |||||||
\(108\) | 5.41915 | 0.521458 | ||||||||
\(109\) | 12.3196 | 1.18000 | 0.590002 | − | 0.807402i | \(-0.299127\pi\) | ||||
0.590002 | + | 0.807402i | \(0.299127\pi\) | |||||||
\(110\) | 1.03711 | 0.0988844 | ||||||||
\(111\) | 0.273055 | 0.0259173 | ||||||||
\(112\) | −1.74380 | −0.164774 | ||||||||
\(113\) | −7.06350 | −0.664478 | −0.332239 | − | 0.943195i | \(-0.607804\pi\) | ||||
−0.332239 | + | 0.943195i | \(0.607804\pi\) | |||||||
\(114\) | −0.301560 | −0.0282437 | ||||||||
\(115\) | −4.69821 | −0.438111 | ||||||||
\(116\) | −3.77491 | −0.350491 | ||||||||
\(117\) | −0.966305 | −0.0893350 | ||||||||
\(118\) | 12.9123 | 1.18867 | ||||||||
\(119\) | 2.70626 | 0.248083 | ||||||||
\(120\) | 0.880083 | 0.0803402 | ||||||||
\(121\) | −7.24342 | −0.658492 | ||||||||
\(122\) | 8.27695 | 0.749360 | ||||||||
\(123\) | 4.44250 | 0.400567 | ||||||||
\(124\) | −8.42757 | −0.756818 | ||||||||
\(125\) | 5.19770 | 0.464896 | ||||||||
\(126\) | 0.514150 | 0.0458042 | ||||||||
\(127\) | −0.412758 | −0.0366263 | −0.0183132 | − | 0.999832i | \(-0.505830\pi\) | ||||
−0.0183132 | + | 0.999832i | \(0.505830\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.17643 | −0.631849 | ||||||||
\(130\) | −1.75367 | −0.153807 | ||||||||
\(131\) | 15.3237 | 1.33884 | 0.669419 | − | 0.742885i | \(-0.266543\pi\) | ||||
0.669419 | + | 0.742885i | \(0.266543\pi\) | |||||||
\(132\) | 3.18781 | 0.277463 | ||||||||
\(133\) | −0.319723 | −0.0277235 | ||||||||
\(134\) | 1.83260 | 0.158313 | ||||||||
\(135\) | −2.89974 | −0.249570 | ||||||||
\(136\) | −1.55193 | −0.133077 | ||||||||
\(137\) | −0.194785 | −0.0166416 | −0.00832080 | − | 0.999965i | \(-0.502649\pi\) | ||||
−0.00832080 | + | 0.999965i | \(0.502649\pi\) | |||||||
\(138\) | −14.4411 | −1.22931 | ||||||||
\(139\) | 11.1840 | 0.948613 | 0.474306 | − | 0.880360i | \(-0.342699\pi\) | ||||
0.474306 | + | 0.880360i | \(0.342699\pi\) | |||||||
\(140\) | 0.933092 | 0.0788607 | ||||||||
\(141\) | 21.1128 | 1.77802 | ||||||||
\(142\) | −2.99104 | −0.251003 | ||||||||
\(143\) | −6.35210 | −0.531190 | ||||||||
\(144\) | −0.294845 | −0.0245704 | ||||||||
\(145\) | 2.01992 | 0.167745 | ||||||||
\(146\) | 7.79312 | 0.644963 | ||||||||
\(147\) | 6.51177 | 0.537081 | ||||||||
\(148\) | −0.166018 | −0.0136466 | ||||||||
\(149\) | −11.9277 | −0.977153 | −0.488577 | − | 0.872521i | \(-0.662484\pi\) | ||||
−0.488577 | + | 0.872521i | \(0.662484\pi\) | |||||||
\(150\) | 7.75275 | 0.633010 | ||||||||
\(151\) | 10.4538 | 0.850720 | 0.425360 | − | 0.905024i | \(-0.360147\pi\) | ||||
0.425360 | + | 0.905024i | \(0.360147\pi\) | |||||||
\(152\) | 0.183349 | 0.0148715 | ||||||||
\(153\) | 0.457579 | 0.0369931 | ||||||||
\(154\) | 3.37982 | 0.272354 | ||||||||
\(155\) | 4.50952 | 0.362213 | ||||||||
\(156\) | −5.39035 | −0.431574 | ||||||||
\(157\) | −15.6334 | −1.24768 | −0.623841 | − | 0.781551i | \(-0.714429\pi\) | ||||
−0.623841 | + | 0.781551i | \(0.714429\pi\) | |||||||
\(158\) | 7.03516 | 0.559687 | ||||||||
\(159\) | −13.4824 | −1.06922 | ||||||||
\(160\) | −0.535091 | −0.0423026 | ||||||||
\(161\) | −15.3110 | −1.20667 | ||||||||
\(162\) | −8.02853 | −0.630781 | ||||||||
\(163\) | 3.44930 | 0.270170 | 0.135085 | − | 0.990834i | \(-0.456869\pi\) | ||||
0.135085 | + | 0.990834i | \(0.456869\pi\) | |||||||
\(164\) | −2.70104 | −0.210916 | ||||||||
\(165\) | −1.70577 | −0.132794 | ||||||||
\(166\) | 11.9340 | 0.926257 | ||||||||
\(167\) | 3.38984 | 0.262313 | 0.131157 | − | 0.991362i | \(-0.458131\pi\) | ||||
0.131157 | + | 0.991362i | \(0.458131\pi\) | |||||||
\(168\) | 2.86809 | 0.221278 | ||||||||
\(169\) | −2.25906 | −0.173774 | ||||||||
\(170\) | 0.830425 | 0.0636907 | ||||||||
\(171\) | −0.0540593 | −0.00413402 | ||||||||
\(172\) | 4.36327 | 0.332696 | ||||||||
\(173\) | 14.0345 | 1.06702 | 0.533511 | − | 0.845793i | \(-0.320872\pi\) | ||||
0.533511 | + | 0.845793i | \(0.320872\pi\) | |||||||
\(174\) | 6.20872 | 0.470682 | ||||||||
\(175\) | 8.21972 | 0.621352 | ||||||||
\(176\) | −1.93819 | −0.146097 | ||||||||
\(177\) | −21.2373 | −1.59629 | ||||||||
\(178\) | −1.25449 | −0.0940280 | ||||||||
\(179\) | −8.40342 | −0.628101 | −0.314051 | − | 0.949406i | \(-0.601686\pi\) | ||||
−0.314051 | + | 0.949406i | \(0.601686\pi\) | |||||||
\(180\) | 0.157769 | 0.0117594 | ||||||||
\(181\) | −24.6257 | −1.83042 | −0.915209 | − | 0.402980i | \(-0.867974\pi\) | ||||
−0.915209 | + | 0.402980i | \(0.867974\pi\) | |||||||
\(182\) | −5.71503 | −0.423626 | ||||||||
\(183\) | −13.6134 | −1.00633 | ||||||||
\(184\) | 8.78022 | 0.647286 | ||||||||
\(185\) | 0.0888345 | 0.00653125 | ||||||||
\(186\) | 13.8611 | 1.01635 | ||||||||
\(187\) | 3.00794 | 0.219963 | ||||||||
\(188\) | −12.8366 | −0.936205 | ||||||||
\(189\) | −9.44992 | −0.687380 | ||||||||
\(190\) | −0.0981081 | −0.00711751 | ||||||||
\(191\) | −9.53239 | −0.689740 | −0.344870 | − | 0.938651i | \(-0.612077\pi\) | ||||
−0.344870 | + | 0.938651i | \(0.612077\pi\) | |||||||
\(192\) | −1.64474 | −0.118699 | ||||||||
\(193\) | 16.9460 | 1.21980 | 0.609900 | − | 0.792478i | \(-0.291209\pi\) | ||||
0.609900 | + | 0.792478i | \(0.291209\pi\) | |||||||
\(194\) | 14.8335 | 1.06499 | ||||||||
\(195\) | 2.88433 | 0.206551 | ||||||||
\(196\) | −3.95916 | −0.282797 | ||||||||
\(197\) | 22.0413 | 1.57038 | 0.785188 | − | 0.619258i | \(-0.212566\pi\) | ||||
0.785188 | + | 0.619258i | \(0.212566\pi\) | |||||||
\(198\) | 0.571465 | 0.0406123 | ||||||||
\(199\) | 27.4022 | 1.94249 | 0.971244 | − | 0.238088i | \(-0.0765208\pi\) | ||||
0.971244 | + | 0.238088i | \(0.0765208\pi\) | |||||||
\(200\) | −4.71368 | −0.333307 | ||||||||
\(201\) | −3.01414 | −0.212601 | ||||||||
\(202\) | 10.3409 | 0.727586 | ||||||||
\(203\) | 6.58269 | 0.462014 | ||||||||
\(204\) | 2.55252 | 0.178712 | ||||||||
\(205\) | 1.44530 | 0.100944 | ||||||||
\(206\) | 13.0167 | 0.906914 | ||||||||
\(207\) | −2.58880 | −0.179934 | ||||||||
\(208\) | 3.27734 | 0.227242 | ||||||||
\(209\) | −0.355364 | −0.0245811 | ||||||||
\(210\) | −1.53469 | −0.105904 | ||||||||
\(211\) | 14.5885 | 1.00431 | 0.502155 | − | 0.864777i | \(-0.332541\pi\) | ||||
0.502155 | + | 0.864777i | \(0.332541\pi\) | |||||||
\(212\) | 8.19730 | 0.562993 | ||||||||
\(213\) | 4.91948 | 0.337077 | ||||||||
\(214\) | −1.60704 | −0.109855 | ||||||||
\(215\) | −2.33475 | −0.159228 | ||||||||
\(216\) | 5.41915 | 0.368726 | ||||||||
\(217\) | 14.6960 | 0.997630 | ||||||||
\(218\) | 12.3196 | 0.834389 | ||||||||
\(219\) | −12.8176 | −0.866134 | ||||||||
\(220\) | 1.03711 | 0.0699218 | ||||||||
\(221\) | −5.08621 | −0.342136 | ||||||||
\(222\) | 0.273055 | 0.0183263 | ||||||||
\(223\) | −1.37324 | −0.0919592 | −0.0459796 | − | 0.998942i | \(-0.514641\pi\) | ||||
−0.0459796 | + | 0.998942i | \(0.514641\pi\) | |||||||
\(224\) | −1.74380 | −0.116513 | ||||||||
\(225\) | 1.38980 | 0.0926535 | ||||||||
\(226\) | −7.06350 | −0.469857 | ||||||||
\(227\) | −24.7682 | −1.64392 | −0.821962 | − | 0.569543i | \(-0.807120\pi\) | ||||
−0.821962 | + | 0.569543i | \(0.807120\pi\) | |||||||
\(228\) | −0.301560 | −0.0199713 | ||||||||
\(229\) | −29.1508 | −1.92634 | −0.963169 | − | 0.268898i | \(-0.913341\pi\) | ||||
−0.963169 | + | 0.268898i | \(0.913341\pi\) | |||||||
\(230\) | −4.69821 | −0.309791 | ||||||||
\(231\) | −5.55891 | −0.365749 | ||||||||
\(232\) | −3.77491 | −0.247835 | ||||||||
\(233\) | 16.9061 | 1.10756 | 0.553779 | − | 0.832664i | \(-0.313185\pi\) | ||||
0.553779 | + | 0.832664i | \(0.313185\pi\) | |||||||
\(234\) | −0.966305 | −0.0631694 | ||||||||
\(235\) | 6.86875 | 0.448068 | ||||||||
\(236\) | 12.9123 | 0.840517 | ||||||||
\(237\) | −11.5710 | −0.751615 | ||||||||
\(238\) | 2.70626 | 0.175421 | ||||||||
\(239\) | 20.5110 | 1.32675 | 0.663374 | − | 0.748288i | \(-0.269124\pi\) | ||||
0.663374 | + | 0.748288i | \(0.269124\pi\) | |||||||
\(240\) | 0.880083 | 0.0568091 | ||||||||
\(241\) | −14.6757 | −0.945344 | −0.472672 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472672 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(242\) | −7.24342 | −0.465625 | ||||||||
\(243\) | −3.05263 | −0.195826 | ||||||||
\(244\) | 8.27695 | 0.529877 | ||||||||
\(245\) | 2.11851 | 0.135347 | ||||||||
\(246\) | 4.44250 | 0.283243 | ||||||||
\(247\) | 0.600895 | 0.0382340 | ||||||||
\(248\) | −8.42757 | −0.535151 | ||||||||
\(249\) | −19.6283 | −1.24389 | ||||||||
\(250\) | 5.19770 | 0.328731 | ||||||||
\(251\) | 10.7043 | 0.675647 | 0.337823 | − | 0.941209i | \(-0.390309\pi\) | ||||
0.337823 | + | 0.941209i | \(0.390309\pi\) | |||||||
\(252\) | 0.514150 | 0.0323884 | ||||||||
\(253\) | −17.0177 | −1.06990 | ||||||||
\(254\) | −0.412758 | −0.0258987 | ||||||||
\(255\) | −1.36583 | −0.0855316 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0649 | 1.37637 | 0.688186 | − | 0.725534i | \(-0.258407\pi\) | ||||
0.688186 | + | 0.725534i | \(0.258407\pi\) | |||||||
\(258\) | −7.17643 | −0.446785 | ||||||||
\(259\) | 0.289502 | 0.0179888 | ||||||||
\(260\) | −1.75367 | −0.108758 | ||||||||
\(261\) | 1.11301 | 0.0688936 | ||||||||
\(262\) | 15.3237 | 0.946701 | ||||||||
\(263\) | 16.7320 | 1.03174 | 0.515870 | − | 0.856667i | \(-0.327469\pi\) | ||||
0.515870 | + | 0.856667i | \(0.327469\pi\) | |||||||
\(264\) | 3.18781 | 0.196196 | ||||||||
\(265\) | −4.38630 | −0.269448 | ||||||||
\(266\) | −0.319723 | −0.0196035 | ||||||||
\(267\) | 2.06331 | 0.126272 | ||||||||
\(268\) | 1.83260 | 0.111944 | ||||||||
\(269\) | −9.70358 | −0.591638 | −0.295819 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295819 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(270\) | −2.89974 | −0.176472 | ||||||||
\(271\) | 20.9871 | 1.27487 | 0.637437 | − | 0.770502i | \(-0.279995\pi\) | ||||
0.637437 | + | 0.770502i | \(0.279995\pi\) | |||||||
\(272\) | −1.55193 | −0.0940998 | ||||||||
\(273\) | 9.39971 | 0.568896 | ||||||||
\(274\) | −0.194785 | −0.0117674 | ||||||||
\(275\) | 9.13601 | 0.550922 | ||||||||
\(276\) | −14.4411 | −0.869254 | ||||||||
\(277\) | −29.8619 | −1.79423 | −0.897115 | − | 0.441797i | \(-0.854341\pi\) | ||||
−0.897115 | + | 0.441797i | \(0.854341\pi\) | |||||||
\(278\) | 11.1840 | 0.670770 | ||||||||
\(279\) | 2.48482 | 0.148763 | ||||||||
\(280\) | 0.933092 | 0.0557629 | ||||||||
\(281\) | 30.3835 | 1.81253 | 0.906265 | − | 0.422711i | \(-0.138921\pi\) | ||||
0.906265 | + | 0.422711i | \(0.138921\pi\) | |||||||
\(282\) | 21.1128 | 1.25725 | ||||||||
\(283\) | −25.3062 | −1.50430 | −0.752148 | − | 0.658994i | \(-0.770982\pi\) | ||||
−0.752148 | + | 0.658994i | \(0.770982\pi\) | |||||||
\(284\) | −2.99104 | −0.177486 | ||||||||
\(285\) | 0.161362 | 0.00955826 | ||||||||
\(286\) | −6.35210 | −0.375608 | ||||||||
\(287\) | 4.71008 | 0.278027 | ||||||||
\(288\) | −0.294845 | −0.0173739 | ||||||||
\(289\) | −14.5915 | −0.858324 | ||||||||
\(290\) | 2.01992 | 0.118614 | ||||||||
\(291\) | −24.3973 | −1.43019 | ||||||||
\(292\) | 7.79312 | 0.456058 | ||||||||
\(293\) | 15.4568 | 0.902994 | 0.451497 | − | 0.892273i | \(-0.350890\pi\) | ||||
0.451497 | + | 0.892273i | \(0.350890\pi\) | |||||||
\(294\) | 6.51177 | 0.379774 | ||||||||
\(295\) | −6.90924 | −0.402271 | ||||||||
\(296\) | −0.166018 | −0.00964958 | ||||||||
\(297\) | −10.5033 | −0.609466 | ||||||||
\(298\) | −11.9277 | −0.690952 | ||||||||
\(299\) | 28.7757 | 1.66414 | ||||||||
\(300\) | 7.75275 | 0.447605 | ||||||||
\(301\) | −7.60868 | −0.438557 | ||||||||
\(302\) | 10.4538 | 0.601550 | ||||||||
\(303\) | −17.0081 | −0.977091 | ||||||||
\(304\) | 0.183349 | 0.0105158 | ||||||||
\(305\) | −4.42892 | −0.253599 | ||||||||
\(306\) | 0.457579 | 0.0261581 | ||||||||
\(307\) | 15.0136 | 0.856873 | 0.428436 | − | 0.903572i | \(-0.359065\pi\) | ||||
0.428436 | + | 0.903572i | \(0.359065\pi\) | |||||||
\(308\) | 3.37982 | 0.192583 | ||||||||
\(309\) | −21.4090 | −1.21791 | ||||||||
\(310\) | 4.50952 | 0.256123 | ||||||||
\(311\) | −15.4281 | −0.874849 | −0.437425 | − | 0.899255i | \(-0.644109\pi\) | ||||
−0.437425 | + | 0.899255i | \(0.644109\pi\) | |||||||
\(312\) | −5.39035 | −0.305169 | ||||||||
\(313\) | 13.7594 | 0.777728 | 0.388864 | − | 0.921295i | \(-0.372868\pi\) | ||||
0.388864 | + | 0.921295i | \(0.372868\pi\) | |||||||
\(314\) | −15.6334 | −0.882244 | ||||||||
\(315\) | −0.275117 | −0.0155011 | ||||||||
\(316\) | 7.03516 | 0.395758 | ||||||||
\(317\) | 9.64703 | 0.541831 | 0.270915 | − | 0.962603i | \(-0.412674\pi\) | ||||
0.270915 | + | 0.962603i | \(0.412674\pi\) | |||||||
\(318\) | −13.4824 | −0.756055 | ||||||||
\(319\) | 7.31649 | 0.409645 | ||||||||
\(320\) | −0.535091 | −0.0299125 | ||||||||
\(321\) | 2.64316 | 0.147527 | ||||||||
\(322\) | −15.3110 | −0.853246 | ||||||||
\(323\) | −0.284545 | −0.0158325 | ||||||||
\(324\) | −8.02853 | −0.446030 | ||||||||
\(325\) | −15.4483 | −0.856918 | ||||||||
\(326\) | 3.44930 | 0.191039 | ||||||||
\(327\) | −20.2625 | −1.12052 | ||||||||
\(328\) | −2.70104 | −0.149140 | ||||||||
\(329\) | 22.3845 | 1.23410 | ||||||||
\(330\) | −1.70577 | −0.0938995 | ||||||||
\(331\) | 8.02708 | 0.441208 | 0.220604 | − | 0.975363i | \(-0.429197\pi\) | ||||
0.220604 | + | 0.975363i | \(0.429197\pi\) | |||||||
\(332\) | 11.9340 | 0.654963 | ||||||||
\(333\) | 0.0489494 | 0.00268241 | ||||||||
\(334\) | 3.38984 | 0.185484 | ||||||||
\(335\) | −0.980608 | −0.0535763 | ||||||||
\(336\) | 2.86809 | 0.156467 | ||||||||
\(337\) | −22.2909 | −1.21426 | −0.607131 | − | 0.794602i | \(-0.707680\pi\) | ||||
−0.607131 | + | 0.794602i | \(0.707680\pi\) | |||||||
\(338\) | −2.25906 | −0.122877 | ||||||||
\(339\) | 11.6176 | 0.630981 | ||||||||
\(340\) | 0.830425 | 0.0450361 | ||||||||
\(341\) | 16.3342 | 0.884549 | ||||||||
\(342\) | −0.0540593 | −0.00292319 | ||||||||
\(343\) | 19.1106 | 1.03188 | ||||||||
\(344\) | 4.36327 | 0.235252 | ||||||||
\(345\) | 7.72732 | 0.416025 | ||||||||
\(346\) | 14.0345 | 0.754499 | ||||||||
\(347\) | −5.97388 | −0.320695 | −0.160347 | − | 0.987061i | \(-0.551261\pi\) | ||||
−0.160347 | + | 0.987061i | \(0.551261\pi\) | |||||||
\(348\) | 6.20872 | 0.332822 | ||||||||
\(349\) | −2.97557 | −0.159279 | −0.0796394 | − | 0.996824i | \(-0.525377\pi\) | ||||
−0.0796394 | + | 0.996824i | \(0.525377\pi\) | |||||||
\(350\) | 8.21972 | 0.439362 | ||||||||
\(351\) | 17.7604 | 0.947979 | ||||||||
\(352\) | −1.93819 | −0.103306 | ||||||||
\(353\) | −12.1499 | −0.646674 | −0.323337 | − | 0.946284i | \(-0.604805\pi\) | ||||
−0.323337 | + | 0.946284i | \(0.604805\pi\) | |||||||
\(354\) | −21.2373 | −1.12875 | ||||||||
\(355\) | 1.60048 | 0.0849447 | ||||||||
\(356\) | −1.25449 | −0.0664879 | ||||||||
\(357\) | −4.45109 | −0.235577 | ||||||||
\(358\) | −8.40342 | −0.444135 | ||||||||
\(359\) | 9.90806 | 0.522927 | 0.261464 | − | 0.965213i | \(-0.415795\pi\) | ||||
0.261464 | + | 0.965213i | \(0.415795\pi\) | |||||||
\(360\) | 0.157769 | 0.00831514 | ||||||||
\(361\) | −18.9664 | −0.998231 | ||||||||
\(362\) | −24.6257 | −1.29430 | ||||||||
\(363\) | 11.9135 | 0.625297 | ||||||||
\(364\) | −5.71503 | −0.299549 | ||||||||
\(365\) | −4.17003 | −0.218269 | ||||||||
\(366\) | −13.6134 | −0.711584 | ||||||||
\(367\) | 31.9933 | 1.67004 | 0.835018 | − | 0.550223i | \(-0.185457\pi\) | ||||
0.835018 | + | 0.550223i | \(0.185457\pi\) | |||||||
\(368\) | 8.78022 | 0.457700 | ||||||||
\(369\) | 0.796387 | 0.0414583 | ||||||||
\(370\) | 0.0888345 | 0.00461829 | ||||||||
\(371\) | −14.2945 | −0.742132 | ||||||||
\(372\) | 13.8611 | 0.718666 | ||||||||
\(373\) | 8.48716 | 0.439449 | 0.219724 | − | 0.975562i | \(-0.429484\pi\) | ||||
0.219724 | + | 0.975562i | \(0.429484\pi\) | |||||||
\(374\) | 3.00794 | 0.155537 | ||||||||
\(375\) | −8.54884 | −0.441460 | ||||||||
\(376\) | −12.8366 | −0.661997 | ||||||||
\(377\) | −12.3716 | −0.637172 | ||||||||
\(378\) | −9.44992 | −0.486051 | ||||||||
\(379\) | 3.11422 | 0.159967 | 0.0799835 | − | 0.996796i | \(-0.474513\pi\) | ||||
0.0799835 | + | 0.996796i | \(0.474513\pi\) | |||||||
\(380\) | −0.0981081 | −0.00503284 | ||||||||
\(381\) | 0.678877 | 0.0347799 | ||||||||
\(382\) | −9.53239 | −0.487720 | ||||||||
\(383\) | −6.12086 | −0.312761 | −0.156381 | − | 0.987697i | \(-0.549983\pi\) | ||||
−0.156381 | + | 0.987697i | \(0.549983\pi\) | |||||||
\(384\) | −1.64474 | −0.0839326 | ||||||||
\(385\) | −1.80851 | −0.0921702 | ||||||||
\(386\) | 16.9460 | 0.862529 | ||||||||
\(387\) | −1.28649 | −0.0653958 | ||||||||
\(388\) | 14.8335 | 0.753059 | ||||||||
\(389\) | 0.488904 | 0.0247884 | 0.0123942 | − | 0.999923i | \(-0.496055\pi\) | ||||
0.0123942 | + | 0.999923i | \(0.496055\pi\) | |||||||
\(390\) | 2.88433 | 0.146054 | ||||||||
\(391\) | −13.6263 | −0.689112 | ||||||||
\(392\) | −3.95916 | −0.199968 | ||||||||
\(393\) | −25.2034 | −1.27135 | ||||||||
\(394\) | 22.0413 | 1.11042 | ||||||||
\(395\) | −3.76445 | −0.189410 | ||||||||
\(396\) | 0.571465 | 0.0287172 | ||||||||
\(397\) | 20.3480 | 1.02124 | 0.510618 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510618 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(398\) | 27.4022 | 1.37355 | ||||||||
\(399\) | 0.525861 | 0.0263260 | ||||||||
\(400\) | −4.71368 | −0.235684 | ||||||||
\(401\) | −32.4212 | −1.61904 | −0.809519 | − | 0.587094i | \(-0.800272\pi\) | ||||
−0.809519 | + | 0.587094i | \(0.800272\pi\) | |||||||
\(402\) | −3.01414 | −0.150332 | ||||||||
\(403\) | −27.6200 | −1.37585 | ||||||||
\(404\) | 10.3409 | 0.514481 | ||||||||
\(405\) | 4.29599 | 0.213470 | ||||||||
\(406\) | 6.58269 | 0.326693 | ||||||||
\(407\) | 0.321774 | 0.0159497 | ||||||||
\(408\) | 2.55252 | 0.126369 | ||||||||
\(409\) | −18.4173 | −0.910675 | −0.455338 | − | 0.890319i | \(-0.650481\pi\) | ||||
−0.455338 | + | 0.890319i | \(0.650481\pi\) | |||||||
\(410\) | 1.44530 | 0.0713784 | ||||||||
\(411\) | 0.320370 | 0.0158027 | ||||||||
\(412\) | 13.0167 | 0.641285 | ||||||||
\(413\) | −22.5164 | −1.10796 | ||||||||
\(414\) | −2.58880 | −0.127233 | ||||||||
\(415\) | −6.38577 | −0.313465 | ||||||||
\(416\) | 3.27734 | 0.160685 | ||||||||
\(417\) | −18.3947 | −0.900792 | ||||||||
\(418\) | −0.355364 | −0.0173814 | ||||||||
\(419\) | −36.7509 | −1.79540 | −0.897700 | − | 0.440607i | \(-0.854763\pi\) | ||||
−0.897700 | + | 0.440607i | \(0.854763\pi\) | |||||||
\(420\) | −1.53469 | −0.0748852 | ||||||||
\(421\) | −24.9153 | −1.21430 | −0.607148 | − | 0.794588i | \(-0.707687\pi\) | ||||
−0.607148 | + | 0.794588i | \(0.707687\pi\) | |||||||
\(422\) | 14.5885 | 0.710155 | ||||||||
\(423\) | 3.78480 | 0.184023 | ||||||||
\(424\) | 8.19730 | 0.398096 | ||||||||
\(425\) | 7.31531 | 0.354845 | ||||||||
\(426\) | 4.91948 | 0.238349 | ||||||||
\(427\) | −14.4334 | −0.698479 | ||||||||
\(428\) | −1.60704 | −0.0776795 | ||||||||
\(429\) | 10.4475 | 0.504412 | ||||||||
\(430\) | −2.33475 | −0.112591 | ||||||||
\(431\) | 9.14506 | 0.440502 | 0.220251 | − | 0.975443i | \(-0.429312\pi\) | ||||
0.220251 | + | 0.975443i | \(0.429312\pi\) | |||||||
\(432\) | 5.41915 | 0.260729 | ||||||||
\(433\) | 3.73613 | 0.179547 | 0.0897735 | − | 0.995962i | \(-0.471386\pi\) | ||||
0.0897735 | + | 0.995962i | \(0.471386\pi\) | |||||||
\(434\) | 14.6960 | 0.705431 | ||||||||
\(435\) | −3.32223 | −0.159289 | ||||||||
\(436\) | 12.3196 | 0.590002 | ||||||||
\(437\) | 1.60984 | 0.0770091 | ||||||||
\(438\) | −12.8176 | −0.612449 | ||||||||
\(439\) | 39.0826 | 1.86531 | 0.932656 | − | 0.360768i | \(-0.117485\pi\) | ||||
0.932656 | + | 0.360768i | \(0.117485\pi\) | |||||||
\(440\) | 1.03711 | 0.0494422 | ||||||||
\(441\) | 1.16734 | 0.0555874 | ||||||||
\(442\) | −5.08621 | −0.241926 | ||||||||
\(443\) | 32.9595 | 1.56595 | 0.782977 | − | 0.622051i | \(-0.213700\pi\) | ||||
0.782977 | + | 0.622051i | \(0.213700\pi\) | |||||||
\(444\) | 0.273055 | 0.0129586 | ||||||||
\(445\) | 0.671266 | 0.0318211 | ||||||||
\(446\) | −1.37324 | −0.0650250 | ||||||||
\(447\) | 19.6179 | 0.927894 | ||||||||
\(448\) | −1.74380 | −0.0823869 | ||||||||
\(449\) | −36.3922 | −1.71745 | −0.858726 | − | 0.512434i | \(-0.828744\pi\) | ||||
−0.858726 | + | 0.512434i | \(0.828744\pi\) | |||||||
\(450\) | 1.38980 | 0.0655159 | ||||||||
\(451\) | 5.23513 | 0.246513 | ||||||||
\(452\) | −7.06350 | −0.332239 | ||||||||
\(453\) | −17.1938 | −0.807834 | ||||||||
\(454\) | −24.7682 | −1.16243 | ||||||||
\(455\) | 3.05806 | 0.143364 | ||||||||
\(456\) | −0.301560 | −0.0141218 | ||||||||
\(457\) | −22.8886 | −1.07068 | −0.535342 | − | 0.844635i | \(-0.679817\pi\) | ||||
−0.535342 | + | 0.844635i | \(0.679817\pi\) | |||||||
\(458\) | −29.1508 | −1.36213 | ||||||||
\(459\) | −8.41016 | −0.392553 | ||||||||
\(460\) | −4.69821 | −0.219055 | ||||||||
\(461\) | 5.22632 | 0.243414 | 0.121707 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121707 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(462\) | −5.55891 | −0.258624 | ||||||||
\(463\) | −33.9321 | −1.57696 | −0.788480 | − | 0.615060i | \(-0.789132\pi\) | ||||
−0.788480 | + | 0.615060i | \(0.789132\pi\) | |||||||
\(464\) | −3.77491 | −0.175246 | ||||||||
\(465\) | −7.41696 | −0.343953 | ||||||||
\(466\) | 16.9061 | 0.783161 | ||||||||
\(467\) | −2.48794 | −0.115128 | −0.0575641 | − | 0.998342i | \(-0.518333\pi\) | ||||
−0.0575641 | + | 0.998342i | \(0.518333\pi\) | |||||||
\(468\) | −0.966305 | −0.0446675 | ||||||||
\(469\) | −3.19569 | −0.147563 | ||||||||
\(470\) | 6.86875 | 0.316832 | ||||||||
\(471\) | 25.7128 | 1.18478 | ||||||||
\(472\) | 12.9123 | 0.594336 | ||||||||
\(473\) | −8.45685 | −0.388846 | ||||||||
\(474\) | −11.5710 | −0.531472 | ||||||||
\(475\) | −0.864246 | −0.0396543 | ||||||||
\(476\) | 2.70626 | 0.124041 | ||||||||
\(477\) | −2.41693 | −0.110664 | ||||||||
\(478\) | 20.5110 | 0.938152 | ||||||||
\(479\) | 8.97749 | 0.410192 | 0.205096 | − | 0.978742i | \(-0.434249\pi\) | ||||
0.205096 | + | 0.978742i | \(0.434249\pi\) | |||||||
\(480\) | 0.880083 | 0.0401701 | ||||||||
\(481\) | −0.544096 | −0.0248086 | ||||||||
\(482\) | −14.6757 | −0.668459 | ||||||||
\(483\) | 25.1825 | 1.14584 | ||||||||
\(484\) | −7.24342 | −0.329246 | ||||||||
\(485\) | −7.93730 | −0.360414 | ||||||||
\(486\) | −3.05263 | −0.138470 | ||||||||
\(487\) | −9.40078 | −0.425990 | −0.212995 | − | 0.977053i | \(-0.568322\pi\) | ||||
−0.212995 | + | 0.977053i | \(0.568322\pi\) | |||||||
\(488\) | 8.27695 | 0.374680 | ||||||||
\(489\) | −5.67318 | −0.256550 | ||||||||
\(490\) | 2.11851 | 0.0957044 | ||||||||
\(491\) | 11.4028 | 0.514601 | 0.257300 | − | 0.966332i | \(-0.417167\pi\) | ||||
0.257300 | + | 0.966332i | \(0.417167\pi\) | |||||||
\(492\) | 4.44250 | 0.200283 | ||||||||
\(493\) | 5.85840 | 0.263849 | ||||||||
\(494\) | 0.600895 | 0.0270355 | ||||||||
\(495\) | −0.305786 | −0.0137440 | ||||||||
\(496\) | −8.42757 | −0.378409 | ||||||||
\(497\) | 5.21579 | 0.233960 | ||||||||
\(498\) | −19.6283 | −0.879564 | ||||||||
\(499\) | −8.69850 | −0.389398 | −0.194699 | − | 0.980863i | \(-0.562373\pi\) | ||||
−0.194699 | + | 0.980863i | \(0.562373\pi\) | |||||||
\(500\) | 5.19770 | 0.232448 | ||||||||
\(501\) | −5.57538 | −0.249090 | ||||||||
\(502\) | 10.7043 | 0.477755 | ||||||||
\(503\) | 41.0139 | 1.82872 | 0.914360 | − | 0.404902i | \(-0.132694\pi\) | ||||
0.914360 | + | 0.404902i | \(0.132694\pi\) | |||||||
\(504\) | 0.514150 | 0.0229021 | ||||||||
\(505\) | −5.53334 | −0.246231 | ||||||||
\(506\) | −17.0177 | −0.756531 | ||||||||
\(507\) | 3.71555 | 0.165013 | ||||||||
\(508\) | −0.412758 | −0.0183132 | ||||||||
\(509\) | 30.3228 | 1.34404 | 0.672018 | − | 0.740535i | \(-0.265428\pi\) | ||||
0.672018 | + | 0.740535i | \(0.265428\pi\) | |||||||
\(510\) | −1.36583 | −0.0604800 | ||||||||
\(511\) | −13.5896 | −0.601171 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.993593 | 0.0438682 | ||||||||
\(514\) | 22.0649 | 0.973242 | ||||||||
\(515\) | −6.96510 | −0.306919 | ||||||||
\(516\) | −7.17643 | −0.315925 | ||||||||
\(517\) | 24.8798 | 1.09421 | ||||||||
\(518\) | 0.289502 | 0.0127200 | ||||||||
\(519\) | −23.0830 | −1.01323 | ||||||||
\(520\) | −1.75367 | −0.0769037 | ||||||||
\(521\) | −6.35833 | −0.278564 | −0.139282 | − | 0.990253i | \(-0.544479\pi\) | ||||
−0.139282 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(522\) | 1.11301 | 0.0487152 | ||||||||
\(523\) | −34.6341 | −1.51444 | −0.757221 | − | 0.653158i | \(-0.773444\pi\) | ||||
−0.757221 | + | 0.653158i | \(0.773444\pi\) | |||||||
\(524\) | 15.3237 | 0.669419 | ||||||||
\(525\) | −13.5193 | −0.590029 | ||||||||
\(526\) | 16.7320 | 0.729551 | ||||||||
\(527\) | 13.0790 | 0.569731 | ||||||||
\(528\) | 3.18781 | 0.138732 | ||||||||
\(529\) | 54.0922 | 2.35184 | ||||||||
\(530\) | −4.38630 | −0.190529 | ||||||||
\(531\) | −3.80711 | −0.165215 | ||||||||
\(532\) | −0.319723 | −0.0138618 | ||||||||
\(533\) | −8.85222 | −0.383432 | ||||||||
\(534\) | 2.06331 | 0.0892879 | ||||||||
\(535\) | 0.859915 | 0.0371774 | ||||||||
\(536\) | 1.83260 | 0.0791563 | ||||||||
\(537\) | 13.8214 | 0.596438 | ||||||||
\(538\) | −9.70358 | −0.418351 | ||||||||
\(539\) | 7.67360 | 0.330525 | ||||||||
\(540\) | −2.89974 | −0.124785 | ||||||||
\(541\) | 0.985205 | 0.0423573 | 0.0211786 | − | 0.999776i | \(-0.493258\pi\) | ||||
0.0211786 | + | 0.999776i | \(0.493258\pi\) | |||||||
\(542\) | 20.9871 | 0.901472 | ||||||||
\(543\) | 40.5028 | 1.73814 | ||||||||
\(544\) | −1.55193 | −0.0665386 | ||||||||
\(545\) | −6.59211 | −0.282375 | ||||||||
\(546\) | 9.39971 | 0.402270 | ||||||||
\(547\) | 4.56775 | 0.195303 | 0.0976513 | − | 0.995221i | \(-0.468867\pi\) | ||||
0.0976513 | + | 0.995221i | \(0.468867\pi\) | |||||||
\(548\) | −0.194785 | −0.00832080 | ||||||||
\(549\) | −2.44041 | −0.104154 | ||||||||
\(550\) | 9.13601 | 0.389561 | ||||||||
\(551\) | −0.692123 | −0.0294855 | ||||||||
\(552\) | −14.4411 | −0.614656 | ||||||||
\(553\) | −12.2679 | −0.521685 | ||||||||
\(554\) | −29.8619 | −1.26871 | ||||||||
\(555\) | −0.146109 | −0.00620200 | ||||||||
\(556\) | 11.1840 | 0.474306 | ||||||||
\(557\) | 21.4967 | 0.910844 | 0.455422 | − | 0.890276i | \(-0.349488\pi\) | ||||
0.455422 | + | 0.890276i | \(0.349488\pi\) | |||||||
\(558\) | 2.48482 | 0.105191 | ||||||||
\(559\) | 14.2999 | 0.604822 | ||||||||
\(560\) | 0.933092 | 0.0394303 | ||||||||
\(561\) | −4.94727 | −0.208874 | ||||||||
\(562\) | 30.3835 | 1.28165 | ||||||||
\(563\) | −18.5685 | −0.782569 | −0.391285 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391285 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(564\) | 21.1128 | 0.889010 | ||||||||
\(565\) | 3.77961 | 0.159010 | ||||||||
\(566\) | −25.3062 | −1.06370 | ||||||||
\(567\) | 14.0002 | 0.587952 | ||||||||
\(568\) | −2.99104 | −0.125501 | ||||||||
\(569\) | −23.9375 | −1.00351 | −0.501755 | − | 0.865010i | \(-0.667312\pi\) | ||||
−0.501755 | + | 0.865010i | \(0.667312\pi\) | |||||||
\(570\) | 0.161362 | 0.00675871 | ||||||||
\(571\) | −41.9227 | −1.75441 | −0.877206 | − | 0.480114i | \(-0.840595\pi\) | ||||
−0.877206 | + | 0.480114i | \(0.840595\pi\) | |||||||
\(572\) | −6.35210 | −0.265595 | ||||||||
\(573\) | 15.6783 | 0.654969 | ||||||||
\(574\) | 4.71008 | 0.196595 | ||||||||
\(575\) | −41.3871 | −1.72596 | ||||||||
\(576\) | −0.294845 | −0.0122852 | ||||||||
\(577\) | −40.5422 | −1.68779 | −0.843897 | − | 0.536505i | \(-0.819744\pi\) | ||||
−0.843897 | + | 0.536505i | \(0.819744\pi\) | |||||||
\(578\) | −14.5915 | −0.606926 | ||||||||
\(579\) | −27.8717 | −1.15831 | ||||||||
\(580\) | 2.01992 | 0.0838725 | ||||||||
\(581\) | −20.8105 | −0.863366 | ||||||||
\(582\) | −24.3973 | −1.01130 | ||||||||
\(583\) | −15.8879 | −0.658011 | ||||||||
\(584\) | 7.79312 | 0.322481 | ||||||||
\(585\) | 0.517061 | 0.0213778 | ||||||||
\(586\) | 15.4568 | 0.638513 | ||||||||
\(587\) | 17.5449 | 0.724155 | 0.362078 | − | 0.932148i | \(-0.382068\pi\) | ||||
0.362078 | + | 0.932148i | \(0.382068\pi\) | |||||||
\(588\) | 6.51177 | 0.268541 | ||||||||
\(589\) | −1.54518 | −0.0636681 | ||||||||
\(590\) | −6.90924 | −0.284449 | ||||||||
\(591\) | −36.2521 | −1.49121 | ||||||||
\(592\) | −0.166018 | −0.00682329 | ||||||||
\(593\) | −19.0693 | −0.783083 | −0.391542 | − | 0.920160i | \(-0.628058\pi\) | ||||
−0.391542 | + | 0.920160i | \(0.628058\pi\) | |||||||
\(594\) | −10.5033 | −0.430957 | ||||||||
\(595\) | −1.44810 | −0.0593662 | ||||||||
\(596\) | −11.9277 | −0.488577 | ||||||||
\(597\) | −45.0693 | −1.84456 | ||||||||
\(598\) | 28.7757 | 1.17673 | ||||||||
\(599\) | −15.1197 | −0.617772 | −0.308886 | − | 0.951099i | \(-0.599956\pi\) | ||||
−0.308886 | + | 0.951099i | \(0.599956\pi\) | |||||||
\(600\) | 7.75275 | 0.316505 | ||||||||
\(601\) | 26.3651 | 1.07546 | 0.537728 | − | 0.843118i | \(-0.319283\pi\) | ||||
0.537728 | + | 0.843118i | \(0.319283\pi\) | |||||||
\(602\) | −7.60868 | −0.310107 | ||||||||
\(603\) | −0.540333 | −0.0220040 | ||||||||
\(604\) | 10.4538 | 0.425360 | ||||||||
\(605\) | 3.87589 | 0.157577 | ||||||||
\(606\) | −17.0081 | −0.690907 | ||||||||
\(607\) | 11.2277 | 0.455719 | 0.227860 | − | 0.973694i | \(-0.426827\pi\) | ||||
0.227860 | + | 0.973694i | \(0.426827\pi\) | |||||||
\(608\) | 0.183349 | 0.00743577 | ||||||||
\(609\) | −10.8268 | −0.438723 | ||||||||
\(610\) | −4.42892 | −0.179322 | ||||||||
\(611\) | −42.0699 | −1.70196 | ||||||||
\(612\) | 0.457579 | 0.0184965 | ||||||||
\(613\) | −1.25138 | −0.0505426 | −0.0252713 | − | 0.999681i | \(-0.508045\pi\) | ||||
−0.0252713 | + | 0.999681i | \(0.508045\pi\) | |||||||
\(614\) | 15.0136 | 0.605901 | ||||||||
\(615\) | −2.37714 | −0.0958555 | ||||||||
\(616\) | 3.37982 | 0.136177 | ||||||||
\(617\) | 33.9446 | 1.36656 | 0.683278 | − | 0.730158i | \(-0.260554\pi\) | ||||
0.683278 | + | 0.730158i | \(0.260554\pi\) | |||||||
\(618\) | −21.4090 | −0.861195 | ||||||||
\(619\) | 11.5161 | 0.462872 | 0.231436 | − | 0.972850i | \(-0.425658\pi\) | ||||
0.231436 | + | 0.972850i | \(0.425658\pi\) | |||||||
\(620\) | 4.50952 | 0.181106 | ||||||||
\(621\) | 47.5813 | 1.90937 | ||||||||
\(622\) | −15.4281 | −0.618612 | ||||||||
\(623\) | 2.18758 | 0.0876436 | ||||||||
\(624\) | −5.39035 | −0.215787 | ||||||||
\(625\) | 20.7871 | 0.831486 | ||||||||
\(626\) | 13.7594 | 0.549937 | ||||||||
\(627\) | 0.584481 | 0.0233419 | ||||||||
\(628\) | −15.6334 | −0.623841 | ||||||||
\(629\) | 0.257648 | 0.0102731 | ||||||||
\(630\) | −0.275117 | −0.0109609 | ||||||||
\(631\) | 4.51047 | 0.179559 | 0.0897794 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897794 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(632\) | 7.03516 | 0.279843 | ||||||||
\(633\) | −23.9942 | −0.953682 | ||||||||
\(634\) | 9.64703 | 0.383132 | ||||||||
\(635\) | 0.220863 | 0.00876468 | ||||||||
\(636\) | −13.4824 | −0.534612 | ||||||||
\(637\) | −12.9755 | −0.514108 | ||||||||
\(638\) | 7.31649 | 0.289662 | ||||||||
\(639\) | 0.881893 | 0.0348872 | ||||||||
\(640\) | −0.535091 | −0.0211513 | ||||||||
\(641\) | 32.2052 | 1.27203 | 0.636015 | − | 0.771677i | \(-0.280582\pi\) | ||||
0.636015 | + | 0.771677i | \(0.280582\pi\) | |||||||
\(642\) | 2.64316 | 0.104317 | ||||||||
\(643\) | −5.22458 | −0.206037 | −0.103019 | − | 0.994679i | \(-0.532850\pi\) | ||||
−0.103019 | + | 0.994679i | \(0.532850\pi\) | |||||||
\(644\) | −15.3110 | −0.603336 | ||||||||
\(645\) | 3.84004 | 0.151201 | ||||||||
\(646\) | −0.284545 | −0.0111953 | ||||||||
\(647\) | −25.7603 | −1.01274 | −0.506371 | − | 0.862316i | \(-0.669013\pi\) | ||||
−0.506371 | + | 0.862316i | \(0.669013\pi\) | |||||||
\(648\) | −8.02853 | −0.315391 | ||||||||
\(649\) | −25.0264 | −0.982374 | ||||||||
\(650\) | −15.4483 | −0.605933 | ||||||||
\(651\) | −24.1711 | −0.947338 | ||||||||
\(652\) | 3.44930 | 0.135085 | ||||||||
\(653\) | −48.7147 | −1.90636 | −0.953178 | − | 0.302411i | \(-0.902209\pi\) | ||||
−0.953178 | + | 0.302411i | \(0.902209\pi\) | |||||||
\(654\) | −20.2625 | −0.792326 | ||||||||
\(655\) | −8.19957 | −0.320384 | ||||||||
\(656\) | −2.70104 | −0.105458 | ||||||||
\(657\) | −2.29776 | −0.0896441 | ||||||||
\(658\) | 22.3845 | 0.872638 | ||||||||
\(659\) | 9.10766 | 0.354784 | 0.177392 | − | 0.984140i | \(-0.443234\pi\) | ||||
0.177392 | + | 0.984140i | \(0.443234\pi\) | |||||||
\(660\) | −1.70577 | −0.0663969 | ||||||||
\(661\) | −4.35433 | −0.169364 | −0.0846819 | − | 0.996408i | \(-0.526987\pi\) | ||||
−0.0846819 | + | 0.996408i | \(0.526987\pi\) | |||||||
\(662\) | 8.02708 | 0.311981 | ||||||||
\(663\) | 8.36547 | 0.324888 | ||||||||
\(664\) | 11.9340 | 0.463129 | ||||||||
\(665\) | 0.171081 | 0.00663424 | ||||||||
\(666\) | 0.0489494 | 0.00189675 | ||||||||
\(667\) | −33.1445 | −1.28336 | ||||||||
\(668\) | 3.38984 | 0.131157 | ||||||||
\(669\) | 2.25862 | 0.0873234 | ||||||||
\(670\) | −0.980608 | −0.0378842 | ||||||||
\(671\) | −16.0423 | −0.619306 | ||||||||
\(672\) | 2.86809 | 0.110639 | ||||||||
\(673\) | 34.8823 | 1.34461 | 0.672307 | − | 0.740272i | \(-0.265303\pi\) | ||||
0.672307 | + | 0.740272i | \(0.265303\pi\) | |||||||
\(674\) | −22.2909 | −0.858613 | ||||||||
\(675\) | −25.5441 | −0.983194 | ||||||||
\(676\) | −2.25906 | −0.0868868 | ||||||||
\(677\) | 1.43170 | 0.0550245 | 0.0275123 | − | 0.999621i | \(-0.491241\pi\) | ||||
0.0275123 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(678\) | 11.6176 | 0.446171 | ||||||||
\(679\) | −25.8668 | −0.992675 | ||||||||
\(680\) | 0.830425 | 0.0318454 | ||||||||
\(681\) | 40.7372 | 1.56105 | ||||||||
\(682\) | 16.3342 | 0.625470 | ||||||||
\(683\) | −36.8512 | −1.41007 | −0.705036 | − | 0.709172i | \(-0.749069\pi\) | ||||
−0.705036 | + | 0.709172i | \(0.749069\pi\) | |||||||
\(684\) | −0.0540593 | −0.00206701 | ||||||||
\(685\) | 0.104228 | 0.00398233 | ||||||||
\(686\) | 19.1106 | 0.729646 | ||||||||
\(687\) | 47.9453 | 1.82923 | ||||||||
\(688\) | 4.36327 | 0.166348 | ||||||||
\(689\) | 26.8653 | 1.02349 | ||||||||
\(690\) | 7.72732 | 0.294174 | ||||||||
\(691\) | 22.6630 | 0.862140 | 0.431070 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431070 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(692\) | 14.0345 | 0.533511 | ||||||||
\(693\) | −0.996522 | −0.0378547 | ||||||||
\(694\) | −5.97388 | −0.226765 | ||||||||
\(695\) | −5.98444 | −0.227003 | ||||||||
\(696\) | 6.20872 | 0.235341 | ||||||||
\(697\) | 4.19184 | 0.158777 | ||||||||
\(698\) | −2.97557 | −0.112627 | ||||||||
\(699\) | −27.8061 | −1.05172 | ||||||||
\(700\) | 8.21972 | 0.310676 | ||||||||
\(701\) | 3.18887 | 0.120442 | 0.0602210 | − | 0.998185i | \(-0.480819\pi\) | ||||
0.0602210 | + | 0.998185i | \(0.480819\pi\) | |||||||
\(702\) | 17.7604 | 0.670322 | ||||||||
\(703\) | −0.0304391 | −0.00114803 | ||||||||
\(704\) | −1.93819 | −0.0730483 | ||||||||
\(705\) | −11.2973 | −0.425480 | ||||||||
\(706\) | −12.1499 | −0.457268 | ||||||||
\(707\) | −18.0325 | −0.678184 | ||||||||
\(708\) | −21.2373 | −0.798146 | ||||||||
\(709\) | 5.34912 | 0.200891 | 0.100445 | − | 0.994943i | \(-0.467973\pi\) | ||||
0.100445 | + | 0.994943i | \(0.467973\pi\) | |||||||
\(710\) | 1.60048 | 0.0600650 | ||||||||
\(711\) | −2.07428 | −0.0777915 | ||||||||
\(712\) | −1.25449 | −0.0470140 | ||||||||
\(713\) | −73.9959 | −2.77117 | ||||||||
\(714\) | −4.45109 | −0.166578 | ||||||||
\(715\) | 3.39895 | 0.127114 | ||||||||
\(716\) | −8.40342 | −0.314051 | ||||||||
\(717\) | −33.7352 | −1.25986 | ||||||||
\(718\) | 9.90806 | 0.369765 | ||||||||
\(719\) | 6.60652 | 0.246382 | 0.123191 | − | 0.992383i | \(-0.460687\pi\) | ||||
0.123191 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(720\) | 0.157769 | 0.00587969 | ||||||||
\(721\) | −22.6985 | −0.845336 | ||||||||
\(722\) | −18.9664 | −0.705856 | ||||||||
\(723\) | 24.1376 | 0.897687 | ||||||||
\(724\) | −24.6257 | −0.915209 | ||||||||
\(725\) | 17.7937 | 0.660841 | ||||||||
\(726\) | 11.9135 | 0.442152 | ||||||||
\(727\) | 9.17929 | 0.340441 | 0.170221 | − | 0.985406i | \(-0.445552\pi\) | ||||
0.170221 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(728\) | −5.71503 | −0.211813 | ||||||||
\(729\) | 29.1064 | 1.07801 | ||||||||
\(730\) | −4.17003 | −0.154340 | ||||||||
\(731\) | −6.77151 | −0.250453 | ||||||||
\(732\) | −13.6134 | −0.503166 | ||||||||
\(733\) | 50.6904 | 1.87229 | 0.936145 | − | 0.351613i | \(-0.114367\pi\) | ||||
0.936145 | + | 0.351613i | \(0.114367\pi\) | |||||||
\(734\) | 31.9933 | 1.18089 | ||||||||
\(735\) | −3.48439 | −0.128524 | ||||||||
\(736\) | 8.78022 | 0.323643 | ||||||||
\(737\) | −3.55193 | −0.130837 | ||||||||
\(738\) | 0.796387 | 0.0293154 | ||||||||
\(739\) | 15.5996 | 0.573840 | 0.286920 | − | 0.957955i | \(-0.407369\pi\) | ||||
0.286920 | + | 0.957955i | \(0.407369\pi\) | |||||||
\(740\) | 0.0888345 | 0.00326562 | ||||||||
\(741\) | −0.988314 | −0.0363066 | ||||||||
\(742\) | −14.2945 | −0.524766 | ||||||||
\(743\) | −45.9533 | −1.68586 | −0.842932 | − | 0.538021i | \(-0.819172\pi\) | ||||
−0.842932 | + | 0.538021i | \(0.819172\pi\) | |||||||
\(744\) | 13.8611 | 0.508174 | ||||||||
\(745\) | 6.38239 | 0.233833 | ||||||||
\(746\) | 8.48716 | 0.310737 | ||||||||
\(747\) | −3.51867 | −0.128742 | ||||||||
\(748\) | 3.00794 | 0.109981 | ||||||||
\(749\) | 2.80237 | 0.102396 | ||||||||
\(750\) | −8.54884 | −0.312160 | ||||||||
\(751\) | 24.3091 | 0.887050 | 0.443525 | − | 0.896262i | \(-0.353728\pi\) | ||||
0.443525 | + | 0.896262i | \(0.353728\pi\) | |||||||
\(752\) | −12.8366 | −0.468103 | ||||||||
\(753\) | −17.6057 | −0.641587 | ||||||||
\(754\) | −12.3716 | −0.450549 | ||||||||
\(755\) | −5.59374 | −0.203577 | ||||||||
\(756\) | −9.44992 | −0.343690 | ||||||||
\(757\) | −25.3950 | −0.922996 | −0.461498 | − | 0.887141i | \(-0.652688\pi\) | ||||
−0.461498 | + | 0.887141i | \(0.652688\pi\) | |||||||
\(758\) | 3.11422 | 0.113114 | ||||||||
\(759\) | 27.9897 | 1.01596 | ||||||||
\(760\) | −0.0981081 | −0.00355876 | ||||||||
\(761\) | 32.8269 | 1.18998 | 0.594988 | − | 0.803735i | \(-0.297157\pi\) | ||||
0.594988 | + | 0.803735i | \(0.297157\pi\) | |||||||
\(762\) | 0.678877 | 0.0245931 | ||||||||
\(763\) | −21.4829 | −0.777735 | ||||||||
\(764\) | −9.53239 | −0.344870 | ||||||||
\(765\) | −0.244846 | −0.00885244 | ||||||||
\(766\) | −6.12086 | −0.221155 | ||||||||
\(767\) | 42.3179 | 1.52801 | ||||||||
\(768\) | −1.64474 | −0.0593493 | ||||||||
\(769\) | 25.0222 | 0.902324 | 0.451162 | − | 0.892442i | \(-0.351010\pi\) | ||||
0.451162 | + | 0.892442i | \(0.351010\pi\) | |||||||
\(770\) | −1.80851 | −0.0651742 | ||||||||
\(771\) | −36.2910 | −1.30699 | ||||||||
\(772\) | 16.9460 | 0.609900 | ||||||||
\(773\) | −7.83331 | −0.281744 | −0.140872 | − | 0.990028i | \(-0.544991\pi\) | ||||
−0.140872 | + | 0.990028i | \(0.544991\pi\) | |||||||
\(774\) | −1.28649 | −0.0462418 | ||||||||
\(775\) | 39.7249 | 1.42696 | ||||||||
\(776\) | 14.8335 | 0.532493 | ||||||||
\(777\) | −0.476154 | −0.0170819 | ||||||||
\(778\) | 0.488904 | 0.0175280 | ||||||||
\(779\) | −0.495232 | −0.0177435 | ||||||||
\(780\) | 2.88433 | 0.103276 | ||||||||
\(781\) | 5.79721 | 0.207441 | ||||||||
\(782\) | −13.6263 | −0.487276 | ||||||||
\(783\) | −20.4568 | −0.731065 | ||||||||
\(784\) | −3.95916 | −0.141398 | ||||||||
\(785\) | 8.36529 | 0.298570 | ||||||||
\(786\) | −25.2034 | −0.898977 | ||||||||
\(787\) | 0.717460 | 0.0255747 | 0.0127874 | − | 0.999918i | \(-0.495930\pi\) | ||||
0.0127874 | + | 0.999918i | \(0.495930\pi\) | |||||||
\(788\) | 22.0413 | 0.785188 | ||||||||
\(789\) | −27.5198 | −0.979729 | ||||||||
\(790\) | −3.76445 | −0.133933 | ||||||||
\(791\) | 12.3173 | 0.437954 | ||||||||
\(792\) | 0.571465 | 0.0203061 | ||||||||
\(793\) | 27.1264 | 0.963285 | ||||||||
\(794\) | 20.3480 | 0.722123 | ||||||||
\(795\) | 7.21430 | 0.255865 | ||||||||
\(796\) | 27.4022 | 0.971244 | ||||||||
\(797\) | −23.6900 | −0.839144 | −0.419572 | − | 0.907722i | \(-0.637820\pi\) | ||||
−0.419572 | + | 0.907722i | \(0.637820\pi\) | |||||||
\(798\) | 0.525861 | 0.0186153 | ||||||||
\(799\) | 19.9216 | 0.704774 | ||||||||
\(800\) | −4.71368 | −0.166654 | ||||||||
\(801\) | 0.369880 | 0.0130691 | ||||||||
\(802\) | −32.4212 | −1.14483 | ||||||||
\(803\) | −15.1045 | −0.533028 | ||||||||
\(804\) | −3.01414 | −0.106301 | ||||||||
\(805\) | 8.19275 | 0.288757 | ||||||||
\(806\) | −27.6200 | −0.972873 | ||||||||
\(807\) | 15.9598 | 0.561812 | ||||||||
\(808\) | 10.3409 | 0.363793 | ||||||||
\(809\) | −15.1652 | −0.533180 | −0.266590 | − | 0.963810i | \(-0.585897\pi\) | ||||
−0.266590 | + | 0.963810i | \(0.585897\pi\) | |||||||
\(810\) | 4.29599 | 0.150946 | ||||||||
\(811\) | −1.82428 | −0.0640593 | −0.0320296 | − | 0.999487i | \(-0.510197\pi\) | ||||
−0.0320296 | + | 0.999487i | \(0.510197\pi\) | |||||||
\(812\) | 6.58269 | 0.231007 | ||||||||
\(813\) | −34.5182 | −1.21061 | ||||||||
\(814\) | 0.321774 | 0.0112782 | ||||||||
\(815\) | −1.84569 | −0.0646516 | ||||||||
\(816\) | 2.55252 | 0.0893561 | ||||||||
\(817\) | 0.799999 | 0.0279884 | ||||||||
\(818\) | −18.4173 | −0.643945 | ||||||||
\(819\) | 1.68504 | 0.0588802 | ||||||||
\(820\) | 1.44530 | 0.0504721 | ||||||||
\(821\) | 5.00871 | 0.174805 | 0.0874026 | − | 0.996173i | \(-0.472143\pi\) | ||||
0.0874026 | + | 0.996173i | \(0.472143\pi\) | |||||||
\(822\) | 0.320370 | 0.0111742 | ||||||||
\(823\) | −39.4462 | −1.37501 | −0.687504 | − | 0.726180i | \(-0.741294\pi\) | ||||
−0.687504 | + | 0.726180i | \(0.741294\pi\) | |||||||
\(824\) | 13.0167 | 0.453457 | ||||||||
\(825\) | −15.0263 | −0.523149 | ||||||||
\(826\) | −22.5164 | −0.783447 | ||||||||
\(827\) | 5.90966 | 0.205499 | 0.102749 | − | 0.994707i | \(-0.467236\pi\) | ||||
0.102749 | + | 0.994707i | \(0.467236\pi\) | |||||||
\(828\) | −2.58880 | −0.0899670 | ||||||||
\(829\) | −50.6004 | −1.75742 | −0.878712 | − | 0.477353i | \(-0.841596\pi\) | ||||
−0.878712 | + | 0.477353i | \(0.841596\pi\) | |||||||
\(830\) | −6.38577 | −0.221653 | ||||||||
\(831\) | 49.1150 | 1.70378 | ||||||||
\(832\) | 3.27734 | 0.113621 | ||||||||
\(833\) | 6.14435 | 0.212889 | ||||||||
\(834\) | −18.3947 | −0.636956 | ||||||||
\(835\) | −1.81387 | −0.0627715 | ||||||||
\(836\) | −0.355364 | −0.0122905 | ||||||||
\(837\) | −45.6703 | −1.57859 | ||||||||
\(838\) | −36.7509 | −1.26954 | ||||||||
\(839\) | −25.2327 | −0.871128 | −0.435564 | − | 0.900158i | \(-0.643451\pi\) | ||||
−0.435564 | + | 0.900158i | \(0.643451\pi\) | |||||||
\(840\) | −1.53469 | −0.0529518 | ||||||||
\(841\) | −14.7501 | −0.508624 | ||||||||
\(842\) | −24.9153 | −0.858638 | ||||||||
\(843\) | −49.9729 | −1.72116 | ||||||||
\(844\) | 14.5885 | 0.502155 | ||||||||
\(845\) | 1.20880 | 0.0415840 | ||||||||
\(846\) | 3.78480 | 0.130124 | ||||||||
\(847\) | 12.6311 | 0.434009 | ||||||||
\(848\) | 8.19730 | 0.281496 | ||||||||
\(849\) | 41.6220 | 1.42846 | ||||||||
\(850\) | 7.31531 | 0.250913 | ||||||||
\(851\) | −1.45767 | −0.0499683 | ||||||||
\(852\) | 4.91948 | 0.168539 | ||||||||
\(853\) | 0.945622 | 0.0323775 | 0.0161887 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161887 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(854\) | −14.4334 | −0.493899 | ||||||||
\(855\) | 0.0289267 | 0.000989271 0 | ||||||||
\(856\) | −1.60704 | −0.0549277 | ||||||||
\(857\) | 18.3184 | 0.625743 | 0.312872 | − | 0.949795i | \(-0.398709\pi\) | ||||
0.312872 | + | 0.949795i | \(0.398709\pi\) | |||||||
\(858\) | 10.4475 | 0.356673 | ||||||||
\(859\) | −21.1262 | −0.720817 | −0.360408 | − | 0.932795i | \(-0.617363\pi\) | ||||
−0.360408 | + | 0.932795i | \(0.617363\pi\) | |||||||
\(860\) | −2.33475 | −0.0796142 | ||||||||
\(861\) | −7.74684 | −0.264011 | ||||||||
\(862\) | 9.14506 | 0.311482 | ||||||||
\(863\) | 34.5413 | 1.17580 | 0.587899 | − | 0.808934i | \(-0.299955\pi\) | ||||
0.587899 | + | 0.808934i | \(0.299955\pi\) | |||||||
\(864\) | 5.41915 | 0.184363 | ||||||||
\(865\) | −7.50973 | −0.255338 | ||||||||
\(866\) | 3.73613 | 0.126959 | ||||||||
\(867\) | 23.9992 | 0.815054 | ||||||||
\(868\) | 14.6960 | 0.498815 | ||||||||
\(869\) | −13.6355 | −0.462552 | ||||||||
\(870\) | −3.32223 | −0.112634 | ||||||||
\(871\) | 6.00605 | 0.203507 | ||||||||
\(872\) | 12.3196 | 0.417194 | ||||||||
\(873\) | −4.37359 | −0.148024 | ||||||||
\(874\) | 1.60984 | 0.0544537 | ||||||||
\(875\) | −9.06376 | −0.306411 | ||||||||
\(876\) | −12.8176 | −0.433067 | ||||||||
\(877\) | 35.2280 | 1.18957 | 0.594783 | − | 0.803886i | \(-0.297238\pi\) | ||||
0.594783 | + | 0.803886i | \(0.297238\pi\) | |||||||
\(878\) | 39.0826 | 1.31897 | ||||||||
\(879\) | −25.4223 | −0.857473 | ||||||||
\(880\) | 1.03711 | 0.0349609 | ||||||||
\(881\) | 23.0409 | 0.776267 | 0.388133 | − | 0.921603i | \(-0.373120\pi\) | ||||
0.388133 | + | 0.921603i | \(0.373120\pi\) | |||||||
\(882\) | 1.16734 | 0.0393062 | ||||||||
\(883\) | −4.67656 | −0.157379 | −0.0786894 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786894 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(884\) | −5.08621 | −0.171068 | ||||||||
\(885\) | 11.3639 | 0.381992 | ||||||||
\(886\) | 32.9595 | 1.10730 | ||||||||
\(887\) | 23.4326 | 0.786789 | 0.393395 | − | 0.919370i | \(-0.371301\pi\) | ||||
0.393395 | + | 0.919370i | \(0.371301\pi\) | |||||||
\(888\) | 0.273055 | 0.00916313 | ||||||||
\(889\) | 0.719768 | 0.0241402 | ||||||||
\(890\) | 0.671266 | 0.0225009 | ||||||||
\(891\) | 15.5608 | 0.521307 | ||||||||
\(892\) | −1.37324 | −0.0459796 | ||||||||
\(893\) | −2.35357 | −0.0787593 | ||||||||
\(894\) | 19.6179 | 0.656120 | ||||||||
\(895\) | 4.49659 | 0.150305 | ||||||||
\(896\) | −1.74380 | −0.0582563 | ||||||||
\(897\) | −47.3285 | −1.58025 | ||||||||
\(898\) | −36.3922 | −1.21442 | ||||||||
\(899\) | 31.8133 | 1.06103 | ||||||||
\(900\) | 1.38980 | 0.0463268 | ||||||||
\(901\) | −12.7217 | −0.423820 | ||||||||
\(902\) | 5.23513 | 0.174311 | ||||||||
\(903\) | 12.5143 | 0.416449 | ||||||||
\(904\) | −7.06350 | −0.234928 | ||||||||
\(905\) | 13.1770 | 0.438019 | ||||||||
\(906\) | −17.1938 | −0.571225 | ||||||||
\(907\) | 34.5699 | 1.14788 | 0.573938 | − | 0.818899i | \(-0.305415\pi\) | ||||
0.573938 | + | 0.818899i | \(0.305415\pi\) | |||||||
\(908\) | −24.7682 | −0.821962 | ||||||||
\(909\) | −3.04897 | −0.101128 | ||||||||
\(910\) | 3.05806 | 0.101374 | ||||||||
\(911\) | 24.8411 | 0.823021 | 0.411510 | − | 0.911405i | \(-0.365001\pi\) | ||||
0.411510 | + | 0.911405i | \(0.365001\pi\) | |||||||
\(912\) | −0.301560 | −0.00998565 | ||||||||
\(913\) | −23.1304 | −0.765503 | ||||||||
\(914\) | −22.8886 | −0.757088 | ||||||||
\(915\) | 7.28440 | 0.240815 | ||||||||
\(916\) | −29.1508 | −0.963169 | ||||||||
\(917\) | −26.7215 | −0.882421 | ||||||||
\(918\) | −8.41016 | −0.277577 | ||||||||
\(919\) | 17.9118 | 0.590857 | 0.295429 | − | 0.955365i | \(-0.404538\pi\) | ||||
0.295429 | + | 0.955365i | \(0.404538\pi\) | |||||||
\(920\) | −4.69821 | −0.154896 | ||||||||
\(921\) | −24.6934 | −0.813677 | ||||||||
\(922\) | 5.22632 | 0.172120 | ||||||||
\(923\) | −9.80266 | −0.322659 | ||||||||
\(924\) | −5.55891 | −0.182875 | ||||||||
\(925\) | 0.782554 | 0.0257302 | ||||||||
\(926\) | −33.9321 | −1.11508 | ||||||||
\(927\) | −3.83789 | −0.126053 | ||||||||
\(928\) | −3.77491 | −0.123917 | ||||||||
\(929\) | 58.6445 | 1.92406 | 0.962032 | − | 0.272937i | \(-0.0879950\pi\) | ||||
0.962032 | + | 0.272937i | \(0.0879950\pi\) | |||||||
\(930\) | −7.41696 | −0.243212 | ||||||||
\(931\) | −0.725906 | −0.0237906 | ||||||||
\(932\) | 16.9061 | 0.553779 | ||||||||
\(933\) | 25.3752 | 0.830747 | ||||||||
\(934\) | −2.48794 | −0.0814079 | ||||||||
\(935\) | −1.60952 | −0.0526370 | ||||||||
\(936\) | −0.966305 | −0.0315847 | ||||||||
\(937\) | −58.5693 | −1.91338 | −0.956688 | − | 0.291114i | \(-0.905974\pi\) | ||||
−0.956688 | + | 0.291114i | \(0.905974\pi\) | |||||||
\(938\) | −3.19569 | −0.104343 | ||||||||
\(939\) | −22.6306 | −0.738522 | ||||||||
\(940\) | 6.86875 | 0.224034 | ||||||||
\(941\) | 41.5663 | 1.35502 | 0.677512 | − | 0.735512i | \(-0.263058\pi\) | ||||
0.677512 | + | 0.735512i | \(0.263058\pi\) | |||||||
\(942\) | 25.7128 | 0.837769 | ||||||||
\(943\) | −23.7157 | −0.772290 | ||||||||
\(944\) | 12.9123 | 0.420259 | ||||||||
\(945\) | 5.05656 | 0.164490 | ||||||||
\(946\) | −8.45685 | −0.274956 | ||||||||
\(947\) | −39.8619 | −1.29534 | −0.647668 | − | 0.761922i | \(-0.724256\pi\) | ||||
−0.647668 | + | 0.761922i | \(0.724256\pi\) | |||||||
\(948\) | −11.5710 | −0.375808 | ||||||||
\(949\) | 25.5407 | 0.829085 | ||||||||
\(950\) | −0.864246 | −0.0280398 | ||||||||
\(951\) | −15.8668 | −0.514517 | ||||||||
\(952\) | 2.70626 | 0.0877105 | ||||||||
\(953\) | −30.5586 | −0.989890 | −0.494945 | − | 0.868924i | \(-0.664812\pi\) | ||||
−0.494945 | + | 0.868924i | \(0.664812\pi\) | |||||||
\(954\) | −2.41693 | −0.0782510 | ||||||||
\(955\) | 5.10069 | 0.165055 | ||||||||
\(956\) | 20.5110 | 0.663374 | ||||||||
\(957\) | −12.0337 | −0.388994 | ||||||||
\(958\) | 8.97749 | 0.290049 | ||||||||
\(959\) | 0.339666 | 0.0109684 | ||||||||
\(960\) | 0.880083 | 0.0284046 | ||||||||
\(961\) | 40.0239 | 1.29109 | ||||||||
\(962\) | −0.544096 | −0.0175424 | ||||||||
\(963\) | 0.473829 | 0.0152689 | ||||||||
\(964\) | −14.6757 | −0.472672 | ||||||||
\(965\) | −9.06765 | −0.291898 | ||||||||
\(966\) | 25.1825 | 0.810233 | ||||||||
\(967\) | −30.7685 | −0.989449 | −0.494725 | − | 0.869050i | \(-0.664731\pi\) | ||||
−0.494725 | + | 0.869050i | \(0.664731\pi\) | |||||||
\(968\) | −7.24342 | −0.232812 | ||||||||
\(969\) | 0.468001 | 0.0150344 | ||||||||
\(970\) | −7.93730 | −0.254851 | ||||||||
\(971\) | 18.7378 | 0.601323 | 0.300662 | − | 0.953731i | \(-0.402793\pi\) | ||||
0.300662 | + | 0.953731i | \(0.402793\pi\) | |||||||
\(972\) | −3.05263 | −0.0979132 | ||||||||
\(973\) | −19.5026 | −0.625226 | ||||||||
\(974\) | −9.40078 | −0.301220 | ||||||||
\(975\) | 25.4084 | 0.813720 | ||||||||
\(976\) | 8.27695 | 0.264939 | ||||||||
\(977\) | −37.0943 | −1.18675 | −0.593375 | − | 0.804926i | \(-0.702205\pi\) | ||||
−0.593375 | + | 0.804926i | \(0.702205\pi\) | |||||||
\(978\) | −5.67318 | −0.181408 | ||||||||
\(979\) | 2.43144 | 0.0777092 | ||||||||
\(980\) | 2.11851 | 0.0676733 | ||||||||
\(981\) | −3.63237 | −0.115973 | ||||||||
\(982\) | 11.4028 | 0.363878 | ||||||||
\(983\) | −31.7506 | −1.01269 | −0.506344 | − | 0.862332i | \(-0.669003\pi\) | ||||
−0.506344 | + | 0.862332i | \(0.669003\pi\) | |||||||
\(984\) | 4.44250 | 0.141622 | ||||||||
\(985\) | −11.7941 | −0.375791 | ||||||||
\(986\) | 5.85840 | 0.186570 | ||||||||
\(987\) | −36.8166 | −1.17188 | ||||||||
\(988\) | 0.600895 | 0.0191170 | ||||||||
\(989\) | 38.3105 | 1.21820 | ||||||||
\(990\) | −0.305786 | −0.00971851 | ||||||||
\(991\) | −42.7285 | −1.35731 | −0.678657 | − | 0.734455i | \(-0.737438\pi\) | ||||
−0.678657 | + | 0.734455i | \(0.737438\pi\) | |||||||
\(992\) | −8.42757 | −0.267576 | ||||||||
\(993\) | −13.2024 | −0.418966 | ||||||||
\(994\) | 5.21579 | 0.165435 | ||||||||
\(995\) | −14.6626 | −0.464837 | ||||||||
\(996\) | −19.6283 | −0.621945 | ||||||||
\(997\) | −11.1318 | −0.352547 | −0.176274 | − | 0.984341i | \(-0.556404\pi\) | ||||
−0.176274 | + | 0.984341i | \(0.556404\pi\) | |||||||
\(998\) | −8.69850 | −0.275346 | ||||||||
\(999\) | −0.899675 | −0.0284644 |
(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 | 4006.2.a.i.1.10 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.i.1.10 | ✓ | 46 | 1.1 | even | 1 | trivial |