Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, 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("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 | ||||||||
\(3\) | −2.16991 | −1.25280 | −0.626398 | − | 0.779504i | \(-0.715471\pi\) | ||||
−0.626398 | + | 0.779504i | \(0.715471\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.35323 | −1.05240 | −0.526199 | − | 0.850362i | \(-0.676383\pi\) | ||||
−0.526199 | + | 0.850362i | \(0.676383\pi\) | |||||||
\(6\) | −2.16991 | −0.885860 | ||||||||
\(7\) | −2.98482 | −1.12816 | −0.564078 | − | 0.825722i | \(-0.690768\pi\) | ||||
−0.564078 | + | 0.825722i | \(0.690768\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.70849 | 0.569496 | ||||||||
\(10\) | −2.35323 | −0.744157 | ||||||||
\(11\) | 3.26147 | 0.983371 | 0.491685 | − | 0.870773i | \(-0.336381\pi\) | ||||
0.491685 | + | 0.870773i | \(0.336381\pi\) | |||||||
\(12\) | −2.16991 | −0.626398 | ||||||||
\(13\) | −0.832404 | −0.230867 | −0.115434 | − | 0.993315i | \(-0.536826\pi\) | ||||
−0.115434 | + | 0.993315i | \(0.536826\pi\) | |||||||
\(14\) | −2.98482 | −0.797727 | ||||||||
\(15\) | 5.10629 | 1.31844 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.928806 | −0.225268 | −0.112634 | − | 0.993637i | \(-0.535929\pi\) | ||||
−0.112634 | + | 0.993637i | \(0.535929\pi\) | |||||||
\(18\) | 1.70849 | 0.402695 | ||||||||
\(19\) | 1.16473 | 0.267206 | 0.133603 | − | 0.991035i | \(-0.457345\pi\) | ||||
0.133603 | + | 0.991035i | \(0.457345\pi\) | |||||||
\(20\) | −2.35323 | −0.526199 | ||||||||
\(21\) | 6.47678 | 1.41335 | ||||||||
\(22\) | 3.26147 | 0.695348 | ||||||||
\(23\) | −3.48217 | −0.726082 | −0.363041 | − | 0.931773i | \(-0.618261\pi\) | ||||
−0.363041 | + | 0.931773i | \(0.618261\pi\) | |||||||
\(24\) | −2.16991 | −0.442930 | ||||||||
\(25\) | 0.537703 | 0.107541 | ||||||||
\(26\) | −0.832404 | −0.163248 | ||||||||
\(27\) | 2.80246 | 0.539333 | ||||||||
\(28\) | −2.98482 | −0.564078 | ||||||||
\(29\) | −3.05692 | −0.567656 | −0.283828 | − | 0.958875i | \(-0.591604\pi\) | ||||
−0.283828 | + | 0.958875i | \(0.591604\pi\) | |||||||
\(30\) | 5.10629 | 0.932277 | ||||||||
\(31\) | 5.74043 | 1.03101 | 0.515505 | − | 0.856886i | \(-0.327604\pi\) | ||||
0.515505 | + | 0.856886i | \(0.327604\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.07708 | −1.23196 | ||||||||
\(34\) | −0.928806 | −0.159289 | ||||||||
\(35\) | 7.02397 | 1.18727 | ||||||||
\(36\) | 1.70849 | 0.284748 | ||||||||
\(37\) | −0.186459 | −0.0306537 | −0.0153269 | − | 0.999883i | \(-0.504879\pi\) | ||||
−0.0153269 | + | 0.999883i | \(0.504879\pi\) | |||||||
\(38\) | 1.16473 | 0.188943 | ||||||||
\(39\) | 1.80624 | 0.289229 | ||||||||
\(40\) | −2.35323 | −0.372079 | ||||||||
\(41\) | −2.25855 | −0.352726 | −0.176363 | − | 0.984325i | \(-0.556433\pi\) | ||||
−0.176363 | + | 0.984325i | \(0.556433\pi\) | |||||||
\(42\) | 6.47678 | 0.999388 | ||||||||
\(43\) | 3.59422 | 0.548114 | 0.274057 | − | 0.961714i | \(-0.411634\pi\) | ||||
0.274057 | + | 0.961714i | \(0.411634\pi\) | |||||||
\(44\) | 3.26147 | 0.491685 | ||||||||
\(45\) | −4.02047 | −0.599337 | ||||||||
\(46\) | −3.48217 | −0.513417 | ||||||||
\(47\) | 9.11758 | 1.32994 | 0.664968 | − | 0.746872i | \(-0.268445\pi\) | ||||
0.664968 | + | 0.746872i | \(0.268445\pi\) | |||||||
\(48\) | −2.16991 | −0.313199 | ||||||||
\(49\) | 1.90915 | 0.272735 | ||||||||
\(50\) | 0.537703 | 0.0760426 | ||||||||
\(51\) | 2.01542 | 0.282215 | ||||||||
\(52\) | −0.832404 | −0.115434 | ||||||||
\(53\) | 6.06820 | 0.833531 | 0.416765 | − | 0.909014i | \(-0.363164\pi\) | ||||
0.416765 | + | 0.909014i | \(0.363164\pi\) | |||||||
\(54\) | 2.80246 | 0.381366 | ||||||||
\(55\) | −7.67500 | −1.03490 | ||||||||
\(56\) | −2.98482 | −0.398863 | ||||||||
\(57\) | −2.52734 | −0.334755 | ||||||||
\(58\) | −3.05692 | −0.401393 | ||||||||
\(59\) | −13.0104 | −1.69381 | −0.846907 | − | 0.531741i | \(-0.821538\pi\) | ||||
−0.846907 | + | 0.531741i | \(0.821538\pi\) | |||||||
\(60\) | 5.10629 | 0.659219 | ||||||||
\(61\) | 6.73229 | 0.861981 | 0.430991 | − | 0.902356i | \(-0.358164\pi\) | ||||
0.430991 | + | 0.902356i | \(0.358164\pi\) | |||||||
\(62\) | 5.74043 | 0.729035 | ||||||||
\(63\) | −5.09953 | −0.642481 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.95884 | 0.242964 | ||||||||
\(66\) | −7.07708 | −0.871129 | ||||||||
\(67\) | 2.28839 | 0.279571 | 0.139786 | − | 0.990182i | \(-0.455359\pi\) | ||||
0.139786 | + | 0.990182i | \(0.455359\pi\) | |||||||
\(68\) | −0.928806 | −0.112634 | ||||||||
\(69\) | 7.55597 | 0.909632 | ||||||||
\(70\) | 7.02397 | 0.839525 | ||||||||
\(71\) | 6.03999 | 0.716815 | 0.358408 | − | 0.933565i | \(-0.383320\pi\) | ||||
0.358408 | + | 0.933565i | \(0.383320\pi\) | |||||||
\(72\) | 1.70849 | 0.201347 | ||||||||
\(73\) | 3.41169 | 0.399308 | 0.199654 | − | 0.979866i | \(-0.436018\pi\) | ||||
0.199654 | + | 0.979866i | \(0.436018\pi\) | |||||||
\(74\) | −0.186459 | −0.0216755 | ||||||||
\(75\) | −1.16676 | −0.134726 | ||||||||
\(76\) | 1.16473 | 0.133603 | ||||||||
\(77\) | −9.73490 | −1.10940 | ||||||||
\(78\) | 1.80624 | 0.204516 | ||||||||
\(79\) | −2.81530 | −0.316746 | −0.158373 | − | 0.987379i | \(-0.550625\pi\) | ||||
−0.158373 | + | 0.987379i | \(0.550625\pi\) | |||||||
\(80\) | −2.35323 | −0.263099 | ||||||||
\(81\) | −11.2065 | −1.24517 | ||||||||
\(82\) | −2.25855 | −0.249415 | ||||||||
\(83\) | 10.5789 | 1.16118 | 0.580591 | − | 0.814195i | \(-0.302822\pi\) | ||||
0.580591 | + | 0.814195i | \(0.302822\pi\) | |||||||
\(84\) | 6.47678 | 0.706674 | ||||||||
\(85\) | 2.18570 | 0.237072 | ||||||||
\(86\) | 3.59422 | 0.387575 | ||||||||
\(87\) | 6.63323 | 0.711157 | ||||||||
\(88\) | 3.26147 | 0.347674 | ||||||||
\(89\) | 17.8579 | 1.89294 | 0.946469 | − | 0.322793i | \(-0.104622\pi\) | ||||
0.946469 | + | 0.322793i | \(0.104622\pi\) | |||||||
\(90\) | −4.02047 | −0.423795 | ||||||||
\(91\) | 2.48457 | 0.260454 | ||||||||
\(92\) | −3.48217 | −0.363041 | ||||||||
\(93\) | −12.4562 | −1.29165 | ||||||||
\(94\) | 9.11758 | 0.940407 | ||||||||
\(95\) | −2.74087 | −0.281207 | ||||||||
\(96\) | −2.16991 | −0.221465 | ||||||||
\(97\) | −5.59501 | −0.568087 | −0.284044 | − | 0.958811i | \(-0.591676\pi\) | ||||
−0.284044 | + | 0.958811i | \(0.591676\pi\) | |||||||
\(98\) | 1.90915 | 0.192853 | ||||||||
\(99\) | 5.57219 | 0.560026 | ||||||||
\(100\) | 0.537703 | 0.0537703 | ||||||||
\(101\) | −6.64581 | −0.661283 | −0.330641 | − | 0.943756i | \(-0.607265\pi\) | ||||
−0.330641 | + | 0.943756i | \(0.607265\pi\) | |||||||
\(102\) | 2.01542 | 0.199556 | ||||||||
\(103\) | 9.91051 | 0.976511 | 0.488256 | − | 0.872701i | \(-0.337633\pi\) | ||||
0.488256 | + | 0.872701i | \(0.337633\pi\) | |||||||
\(104\) | −0.832404 | −0.0816239 | ||||||||
\(105\) | −15.2414 | −1.48740 | ||||||||
\(106\) | 6.06820 | 0.589395 | ||||||||
\(107\) | 4.50760 | 0.435766 | 0.217883 | − | 0.975975i | \(-0.430085\pi\) | ||||
0.217883 | + | 0.975975i | \(0.430085\pi\) | |||||||
\(108\) | 2.80246 | 0.269666 | ||||||||
\(109\) | −2.92956 | −0.280601 | −0.140301 | − | 0.990109i | \(-0.544807\pi\) | ||||
−0.140301 | + | 0.990109i | \(0.544807\pi\) | |||||||
\(110\) | −7.67500 | −0.731783 | ||||||||
\(111\) | 0.404599 | 0.0384029 | ||||||||
\(112\) | −2.98482 | −0.282039 | ||||||||
\(113\) | 1.44266 | 0.135714 | 0.0678570 | − | 0.997695i | \(-0.478384\pi\) | ||||
0.0678570 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(114\) | −2.52734 | −0.236707 | ||||||||
\(115\) | 8.19434 | 0.764127 | ||||||||
\(116\) | −3.05692 | −0.283828 | ||||||||
\(117\) | −1.42215 | −0.131478 | ||||||||
\(118\) | −13.0104 | −1.19771 | ||||||||
\(119\) | 2.77232 | 0.254138 | ||||||||
\(120\) | 5.10629 | 0.466139 | ||||||||
\(121\) | −0.362804 | −0.0329822 | ||||||||
\(122\) | 6.73229 | 0.609513 | ||||||||
\(123\) | 4.90084 | 0.441894 | ||||||||
\(124\) | 5.74043 | 0.515505 | ||||||||
\(125\) | 10.5008 | 0.939222 | ||||||||
\(126\) | −5.09953 | −0.454302 | ||||||||
\(127\) | −18.3308 | −1.62660 | −0.813299 | − | 0.581847i | \(-0.802330\pi\) | ||||
−0.813299 | + | 0.581847i | \(0.802330\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.79912 | −0.686674 | ||||||||
\(130\) | 1.95884 | 0.171802 | ||||||||
\(131\) | −1.69597 | −0.148178 | −0.0740889 | − | 0.997252i | \(-0.523605\pi\) | ||||
−0.0740889 | + | 0.997252i | \(0.523605\pi\) | |||||||
\(132\) | −7.07708 | −0.615981 | ||||||||
\(133\) | −3.47649 | −0.301450 | ||||||||
\(134\) | 2.28839 | 0.197687 | ||||||||
\(135\) | −6.59483 | −0.567593 | ||||||||
\(136\) | −0.928806 | −0.0796444 | ||||||||
\(137\) | −16.6391 | −1.42158 | −0.710789 | − | 0.703406i | \(-0.751662\pi\) | ||||
−0.710789 | + | 0.703406i | \(0.751662\pi\) | |||||||
\(138\) | 7.55597 | 0.643207 | ||||||||
\(139\) | −22.2620 | −1.88824 | −0.944118 | − | 0.329608i | \(-0.893083\pi\) | ||||
−0.944118 | + | 0.329608i | \(0.893083\pi\) | |||||||
\(140\) | 7.02397 | 0.593634 | ||||||||
\(141\) | −19.7843 | −1.66614 | ||||||||
\(142\) | 6.03999 | 0.506865 | ||||||||
\(143\) | −2.71486 | −0.227028 | ||||||||
\(144\) | 1.70849 | 0.142374 | ||||||||
\(145\) | 7.19364 | 0.597400 | ||||||||
\(146\) | 3.41169 | 0.282354 | ||||||||
\(147\) | −4.14267 | −0.341682 | ||||||||
\(148\) | −0.186459 | −0.0153269 | ||||||||
\(149\) | −2.19544 | −0.179858 | −0.0899288 | − | 0.995948i | \(-0.528664\pi\) | ||||
−0.0899288 | + | 0.995948i | \(0.528664\pi\) | |||||||
\(150\) | −1.16676 | −0.0952658 | ||||||||
\(151\) | 21.6601 | 1.76267 | 0.881336 | − | 0.472490i | \(-0.156645\pi\) | ||||
0.881336 | + | 0.472490i | \(0.156645\pi\) | |||||||
\(152\) | 1.16473 | 0.0944717 | ||||||||
\(153\) | −1.58685 | −0.128290 | ||||||||
\(154\) | −9.73490 | −0.784461 | ||||||||
\(155\) | −13.5086 | −1.08503 | ||||||||
\(156\) | 1.80624 | 0.144615 | ||||||||
\(157\) | 8.58779 | 0.685380 | 0.342690 | − | 0.939448i | \(-0.388662\pi\) | ||||
0.342690 | + | 0.939448i | \(0.388662\pi\) | |||||||
\(158\) | −2.81530 | −0.223973 | ||||||||
\(159\) | −13.1674 | −1.04424 | ||||||||
\(160\) | −2.35323 | −0.186039 | ||||||||
\(161\) | 10.3936 | 0.819133 | ||||||||
\(162\) | −11.2065 | −0.880468 | ||||||||
\(163\) | −12.2050 | −0.955973 | −0.477987 | − | 0.878367i | \(-0.658633\pi\) | ||||
−0.477987 | + | 0.878367i | \(0.658633\pi\) | |||||||
\(164\) | −2.25855 | −0.176363 | ||||||||
\(165\) | 16.6540 | 1.29651 | ||||||||
\(166\) | 10.5789 | 0.821080 | ||||||||
\(167\) | 10.2158 | 0.790525 | 0.395263 | − | 0.918568i | \(-0.370654\pi\) | ||||
0.395263 | + | 0.918568i | \(0.370654\pi\) | |||||||
\(168\) | 6.47678 | 0.499694 | ||||||||
\(169\) | −12.3071 | −0.946700 | ||||||||
\(170\) | 2.18570 | 0.167635 | ||||||||
\(171\) | 1.98992 | 0.152173 | ||||||||
\(172\) | 3.59422 | 0.274057 | ||||||||
\(173\) | −5.95829 | −0.453000 | −0.226500 | − | 0.974011i | \(-0.572728\pi\) | ||||
−0.226500 | + | 0.974011i | \(0.572728\pi\) | |||||||
\(174\) | 6.63323 | 0.502864 | ||||||||
\(175\) | −1.60495 | −0.121322 | ||||||||
\(176\) | 3.26147 | 0.245843 | ||||||||
\(177\) | 28.2314 | 2.12200 | ||||||||
\(178\) | 17.8579 | 1.33851 | ||||||||
\(179\) | −25.5355 | −1.90861 | −0.954306 | − | 0.298830i | \(-0.903404\pi\) | ||||
−0.954306 | + | 0.298830i | \(0.903404\pi\) | |||||||
\(180\) | −4.02047 | −0.299668 | ||||||||
\(181\) | −0.390180 | −0.0290019 | −0.0145009 | − | 0.999895i | \(-0.504616\pi\) | ||||
−0.0145009 | + | 0.999895i | \(0.504616\pi\) | |||||||
\(182\) | 2.48457 | 0.184169 | ||||||||
\(183\) | −14.6084 | −1.07989 | ||||||||
\(184\) | −3.48217 | −0.256709 | ||||||||
\(185\) | 0.438782 | 0.0322599 | ||||||||
\(186\) | −12.4562 | −0.913331 | ||||||||
\(187\) | −3.02927 | −0.221522 | ||||||||
\(188\) | 9.11758 | 0.664968 | ||||||||
\(189\) | −8.36483 | −0.608452 | ||||||||
\(190\) | −2.74087 | −0.198844 | ||||||||
\(191\) | −19.5953 | −1.41786 | −0.708932 | − | 0.705276i | \(-0.750823\pi\) | ||||
−0.708932 | + | 0.705276i | \(0.750823\pi\) | |||||||
\(192\) | −2.16991 | −0.156599 | ||||||||
\(193\) | 27.3634 | 1.96966 | 0.984831 | − | 0.173518i | \(-0.0555134\pi\) | ||||
0.984831 | + | 0.173518i | \(0.0555134\pi\) | |||||||
\(194\) | −5.59501 | −0.401698 | ||||||||
\(195\) | −4.25050 | −0.304384 | ||||||||
\(196\) | 1.90915 | 0.136368 | ||||||||
\(197\) | −4.92877 | −0.351160 | −0.175580 | − | 0.984465i | \(-0.556180\pi\) | ||||
−0.175580 | + | 0.984465i | \(0.556180\pi\) | |||||||
\(198\) | 5.57219 | 0.395998 | ||||||||
\(199\) | −4.46565 | −0.316561 | −0.158281 | − | 0.987394i | \(-0.550595\pi\) | ||||
−0.158281 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(200\) | 0.537703 | 0.0380213 | ||||||||
\(201\) | −4.96559 | −0.350246 | ||||||||
\(202\) | −6.64581 | −0.467598 | ||||||||
\(203\) | 9.12436 | 0.640404 | ||||||||
\(204\) | 2.01542 | 0.141108 | ||||||||
\(205\) | 5.31489 | 0.371208 | ||||||||
\(206\) | 9.91051 | 0.690498 | ||||||||
\(207\) | −5.94924 | −0.413501 | ||||||||
\(208\) | −0.832404 | −0.0577168 | ||||||||
\(209\) | 3.79872 | 0.262763 | ||||||||
\(210\) | −15.2414 | −1.05175 | ||||||||
\(211\) | −26.5620 | −1.82860 | −0.914300 | − | 0.405037i | \(-0.867259\pi\) | ||||
−0.914300 | + | 0.405037i | \(0.867259\pi\) | |||||||
\(212\) | 6.06820 | 0.416765 | ||||||||
\(213\) | −13.1062 | −0.898023 | ||||||||
\(214\) | 4.50760 | 0.308133 | ||||||||
\(215\) | −8.45804 | −0.576833 | ||||||||
\(216\) | 2.80246 | 0.190683 | ||||||||
\(217\) | −17.1341 | −1.16314 | ||||||||
\(218\) | −2.92956 | −0.198415 | ||||||||
\(219\) | −7.40305 | −0.500251 | ||||||||
\(220\) | −7.67500 | −0.517448 | ||||||||
\(221\) | 0.773141 | 0.0520071 | ||||||||
\(222\) | 0.404599 | 0.0271549 | ||||||||
\(223\) | 4.85876 | 0.325367 | 0.162683 | − | 0.986678i | \(-0.447985\pi\) | ||||
0.162683 | + | 0.986678i | \(0.447985\pi\) | |||||||
\(224\) | −2.98482 | −0.199432 | ||||||||
\(225\) | 0.918659 | 0.0612439 | ||||||||
\(226\) | 1.44266 | 0.0959642 | ||||||||
\(227\) | 11.9983 | 0.796356 | 0.398178 | − | 0.917308i | \(-0.369643\pi\) | ||||
0.398178 | + | 0.917308i | \(0.369643\pi\) | |||||||
\(228\) | −2.52734 | −0.167377 | ||||||||
\(229\) | −28.6718 | −1.89469 | −0.947344 | − | 0.320217i | \(-0.896244\pi\) | ||||
−0.947344 | + | 0.320217i | \(0.896244\pi\) | |||||||
\(230\) | 8.19434 | 0.540319 | ||||||||
\(231\) | 21.1238 | 1.38985 | ||||||||
\(232\) | −3.05692 | −0.200697 | ||||||||
\(233\) | 25.9732 | 1.70156 | 0.850780 | − | 0.525521i | \(-0.176130\pi\) | ||||
0.850780 | + | 0.525521i | \(0.176130\pi\) | |||||||
\(234\) | −1.42215 | −0.0929690 | ||||||||
\(235\) | −21.4558 | −1.39962 | ||||||||
\(236\) | −13.0104 | −0.846907 | ||||||||
\(237\) | 6.10894 | 0.396818 | ||||||||
\(238\) | 2.77232 | 0.179703 | ||||||||
\(239\) | −7.37644 | −0.477142 | −0.238571 | − | 0.971125i | \(-0.576679\pi\) | ||||
−0.238571 | + | 0.971125i | \(0.576679\pi\) | |||||||
\(240\) | 5.10629 | 0.329610 | ||||||||
\(241\) | 3.64527 | 0.234813 | 0.117406 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117406 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(242\) | −0.362804 | −0.0233219 | ||||||||
\(243\) | 15.9097 | 1.02061 | ||||||||
\(244\) | 6.73229 | 0.430991 | ||||||||
\(245\) | −4.49267 | −0.287026 | ||||||||
\(246\) | 4.90084 | 0.312466 | ||||||||
\(247\) | −0.969522 | −0.0616892 | ||||||||
\(248\) | 5.74043 | 0.364517 | ||||||||
\(249\) | −22.9551 | −1.45472 | ||||||||
\(250\) | 10.5008 | 0.664130 | ||||||||
\(251\) | −11.4270 | −0.721266 | −0.360633 | − | 0.932708i | \(-0.617439\pi\) | ||||
−0.360633 | + | 0.932708i | \(0.617439\pi\) | |||||||
\(252\) | −5.09953 | −0.321240 | ||||||||
\(253\) | −11.3570 | −0.714007 | ||||||||
\(254\) | −18.3308 | −1.15018 | ||||||||
\(255\) | −4.74275 | −0.297003 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.00591 | −0.0627468 | −0.0313734 | − | 0.999508i | \(-0.509988\pi\) | ||||
−0.0313734 | + | 0.999508i | \(0.509988\pi\) | |||||||
\(258\) | −7.79912 | −0.485552 | ||||||||
\(259\) | 0.556548 | 0.0345822 | ||||||||
\(260\) | 1.95884 | 0.121482 | ||||||||
\(261\) | −5.22272 | −0.323278 | ||||||||
\(262\) | −1.69597 | −0.104777 | ||||||||
\(263\) | −26.2139 | −1.61642 | −0.808209 | − | 0.588896i | \(-0.799563\pi\) | ||||
−0.808209 | + | 0.588896i | \(0.799563\pi\) | |||||||
\(264\) | −7.07708 | −0.435564 | ||||||||
\(265\) | −14.2799 | −0.877206 | ||||||||
\(266\) | −3.47649 | −0.213158 | ||||||||
\(267\) | −38.7501 | −2.37147 | ||||||||
\(268\) | 2.28839 | 0.139786 | ||||||||
\(269\) | 12.8463 | 0.783251 | 0.391626 | − | 0.920125i | \(-0.371913\pi\) | ||||
0.391626 | + | 0.920125i | \(0.371913\pi\) | |||||||
\(270\) | −6.59483 | −0.401349 | ||||||||
\(271\) | −11.0513 | −0.671318 | −0.335659 | − | 0.941984i | \(-0.608959\pi\) | ||||
−0.335659 | + | 0.941984i | \(0.608959\pi\) | |||||||
\(272\) | −0.928806 | −0.0563171 | ||||||||
\(273\) | −5.39129 | −0.326296 | ||||||||
\(274\) | −16.6391 | −1.00521 | ||||||||
\(275\) | 1.75370 | 0.105752 | ||||||||
\(276\) | 7.55597 | 0.454816 | ||||||||
\(277\) | −6.45607 | −0.387907 | −0.193954 | − | 0.981011i | \(-0.562131\pi\) | ||||
−0.193954 | + | 0.981011i | \(0.562131\pi\) | |||||||
\(278\) | −22.2620 | −1.33518 | ||||||||
\(279\) | 9.80745 | 0.587157 | ||||||||
\(280\) | 7.02397 | 0.419763 | ||||||||
\(281\) | −12.1267 | −0.723417 | −0.361708 | − | 0.932291i | \(-0.617806\pi\) | ||||
−0.361708 | + | 0.932291i | \(0.617806\pi\) | |||||||
\(282\) | −19.7843 | −1.17814 | ||||||||
\(283\) | 25.0839 | 1.49108 | 0.745541 | − | 0.666459i | \(-0.232191\pi\) | ||||
0.745541 | + | 0.666459i | \(0.232191\pi\) | |||||||
\(284\) | 6.03999 | 0.358408 | ||||||||
\(285\) | 5.94743 | 0.352295 | ||||||||
\(286\) | −2.71486 | −0.160533 | ||||||||
\(287\) | 6.74136 | 0.397930 | ||||||||
\(288\) | 1.70849 | 0.100674 | ||||||||
\(289\) | −16.1373 | −0.949254 | ||||||||
\(290\) | 7.19364 | 0.422425 | ||||||||
\(291\) | 12.1406 | 0.711697 | ||||||||
\(292\) | 3.41169 | 0.199654 | ||||||||
\(293\) | 1.76172 | 0.102921 | 0.0514604 | − | 0.998675i | \(-0.483612\pi\) | ||||
0.0514604 | + | 0.998675i | \(0.483612\pi\) | |||||||
\(294\) | −4.14267 | −0.241605 | ||||||||
\(295\) | 30.6166 | 1.78257 | ||||||||
\(296\) | −0.186459 | −0.0108377 | ||||||||
\(297\) | 9.14013 | 0.530364 | ||||||||
\(298\) | −2.19544 | −0.127178 | ||||||||
\(299\) | 2.89857 | 0.167628 | ||||||||
\(300\) | −1.16676 | −0.0673631 | ||||||||
\(301\) | −10.7281 | −0.618358 | ||||||||
\(302\) | 21.6601 | 1.24640 | ||||||||
\(303\) | 14.4208 | 0.828452 | ||||||||
\(304\) | 1.16473 | 0.0668016 | ||||||||
\(305\) | −15.8426 | −0.907147 | ||||||||
\(306\) | −1.58685 | −0.0907144 | ||||||||
\(307\) | 17.7922 | 1.01546 | 0.507729 | − | 0.861517i | \(-0.330485\pi\) | ||||
0.507729 | + | 0.861517i | \(0.330485\pi\) | |||||||
\(308\) | −9.73490 | −0.554698 | ||||||||
\(309\) | −21.5049 | −1.22337 | ||||||||
\(310\) | −13.5086 | −0.767234 | ||||||||
\(311\) | −11.1608 | −0.632868 | −0.316434 | − | 0.948614i | \(-0.602486\pi\) | ||||
−0.316434 | + | 0.948614i | \(0.602486\pi\) | |||||||
\(312\) | 1.80624 | 0.102258 | ||||||||
\(313\) | −22.1853 | −1.25399 | −0.626995 | − | 0.779023i | \(-0.715715\pi\) | ||||
−0.626995 | + | 0.779023i | \(0.715715\pi\) | |||||||
\(314\) | 8.58779 | 0.484637 | ||||||||
\(315\) | 12.0004 | 0.676145 | ||||||||
\(316\) | −2.81530 | −0.158373 | ||||||||
\(317\) | −8.19846 | −0.460472 | −0.230236 | − | 0.973135i | \(-0.573950\pi\) | ||||
−0.230236 | + | 0.973135i | \(0.573950\pi\) | |||||||
\(318\) | −13.1674 | −0.738392 | ||||||||
\(319\) | −9.97006 | −0.558216 | ||||||||
\(320\) | −2.35323 | −0.131550 | ||||||||
\(321\) | −9.78106 | −0.545925 | ||||||||
\(322\) | 10.3936 | 0.579215 | ||||||||
\(323\) | −1.08180 | −0.0601931 | ||||||||
\(324\) | −11.2065 | −0.622585 | ||||||||
\(325\) | −0.447586 | −0.0248276 | ||||||||
\(326\) | −12.2050 | −0.675975 | ||||||||
\(327\) | 6.35687 | 0.351536 | ||||||||
\(328\) | −2.25855 | −0.124707 | ||||||||
\(329\) | −27.2143 | −1.50038 | ||||||||
\(330\) | 16.6540 | 0.916774 | ||||||||
\(331\) | −32.7930 | −1.80247 | −0.901234 | − | 0.433333i | \(-0.857338\pi\) | ||||
−0.901234 | + | 0.433333i | \(0.857338\pi\) | |||||||
\(332\) | 10.5789 | 0.580591 | ||||||||
\(333\) | −0.318564 | −0.0174572 | ||||||||
\(334\) | 10.2158 | 0.558986 | ||||||||
\(335\) | −5.38512 | −0.294220 | ||||||||
\(336\) | 6.47678 | 0.353337 | ||||||||
\(337\) | 17.8495 | 0.972325 | 0.486163 | − | 0.873868i | \(-0.338396\pi\) | ||||
0.486163 | + | 0.873868i | \(0.338396\pi\) | |||||||
\(338\) | −12.3071 | −0.669418 | ||||||||
\(339\) | −3.13043 | −0.170022 | ||||||||
\(340\) | 2.18570 | 0.118536 | ||||||||
\(341\) | 18.7222 | 1.01387 | ||||||||
\(342\) | 1.98992 | 0.107603 | ||||||||
\(343\) | 15.1953 | 0.820468 | ||||||||
\(344\) | 3.59422 | 0.193787 | ||||||||
\(345\) | −17.7810 | −0.957294 | ||||||||
\(346\) | −5.95829 | −0.320320 | ||||||||
\(347\) | −23.4732 | −1.26011 | −0.630053 | − | 0.776552i | \(-0.716967\pi\) | ||||
−0.630053 | + | 0.776552i | \(0.716967\pi\) | |||||||
\(348\) | 6.63323 | 0.355578 | ||||||||
\(349\) | −5.79132 | −0.310002 | −0.155001 | − | 0.987914i | \(-0.549538\pi\) | ||||
−0.155001 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(350\) | −1.60495 | −0.0857879 | ||||||||
\(351\) | −2.33277 | −0.124514 | ||||||||
\(352\) | 3.26147 | 0.173837 | ||||||||
\(353\) | −3.57572 | −0.190316 | −0.0951581 | − | 0.995462i | \(-0.530336\pi\) | ||||
−0.0951581 | + | 0.995462i | \(0.530336\pi\) | |||||||
\(354\) | 28.2314 | 1.50048 | ||||||||
\(355\) | −14.2135 | −0.754375 | ||||||||
\(356\) | 17.8579 | 0.946469 | ||||||||
\(357\) | −6.01567 | −0.318383 | ||||||||
\(358\) | −25.5355 | −1.34959 | ||||||||
\(359\) | −10.1988 | −0.538271 | −0.269136 | − | 0.963102i | \(-0.586738\pi\) | ||||
−0.269136 | + | 0.963102i | \(0.586738\pi\) | |||||||
\(360\) | −4.02047 | −0.211897 | ||||||||
\(361\) | −17.6434 | −0.928601 | ||||||||
\(362\) | −0.390180 | −0.0205074 | ||||||||
\(363\) | 0.787251 | 0.0413200 | ||||||||
\(364\) | 2.48457 | 0.130227 | ||||||||
\(365\) | −8.02850 | −0.420231 | ||||||||
\(366\) | −14.6084 | −0.763595 | ||||||||
\(367\) | −13.0245 | −0.679876 | −0.339938 | − | 0.940448i | \(-0.610406\pi\) | ||||
−0.339938 | + | 0.940448i | \(0.610406\pi\) | |||||||
\(368\) | −3.48217 | −0.181520 | ||||||||
\(369\) | −3.85871 | −0.200876 | ||||||||
\(370\) | 0.438782 | 0.0228112 | ||||||||
\(371\) | −18.1125 | −0.940353 | ||||||||
\(372\) | −12.4562 | −0.645823 | ||||||||
\(373\) | −10.3512 | −0.535965 | −0.267983 | − | 0.963424i | \(-0.586357\pi\) | ||||
−0.267983 | + | 0.963424i | \(0.586357\pi\) | |||||||
\(374\) | −3.02927 | −0.156640 | ||||||||
\(375\) | −22.7858 | −1.17665 | ||||||||
\(376\) | 9.11758 | 0.470204 | ||||||||
\(377\) | 2.54459 | 0.131053 | ||||||||
\(378\) | −8.36483 | −0.430240 | ||||||||
\(379\) | 13.3344 | 0.684943 | 0.342472 | − | 0.939528i | \(-0.388736\pi\) | ||||
0.342472 | + | 0.939528i | \(0.388736\pi\) | |||||||
\(380\) | −2.74087 | −0.140604 | ||||||||
\(381\) | 39.7761 | 2.03779 | ||||||||
\(382\) | −19.5953 | −1.00258 | ||||||||
\(383\) | −15.1494 | −0.774098 | −0.387049 | − | 0.922059i | \(-0.626506\pi\) | ||||
−0.387049 | + | 0.922059i | \(0.626506\pi\) | |||||||
\(384\) | −2.16991 | −0.110733 | ||||||||
\(385\) | 22.9085 | 1.16752 | ||||||||
\(386\) | 27.3634 | 1.39276 | ||||||||
\(387\) | 6.14069 | 0.312149 | ||||||||
\(388\) | −5.59501 | −0.284044 | ||||||||
\(389\) | −12.4338 | −0.630420 | −0.315210 | − | 0.949022i | \(-0.602075\pi\) | ||||
−0.315210 | + | 0.949022i | \(0.602075\pi\) | |||||||
\(390\) | −4.25050 | −0.215232 | ||||||||
\(391\) | 3.23425 | 0.163563 | ||||||||
\(392\) | 1.90915 | 0.0964266 | ||||||||
\(393\) | 3.68010 | 0.185636 | ||||||||
\(394\) | −4.92877 | −0.248308 | ||||||||
\(395\) | 6.62506 | 0.333343 | ||||||||
\(396\) | 5.57219 | 0.280013 | ||||||||
\(397\) | −22.5317 | −1.13083 | −0.565417 | − | 0.824805i | \(-0.691285\pi\) | ||||
−0.565417 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(398\) | −4.46565 | −0.223843 | ||||||||
\(399\) | 7.54366 | 0.377656 | ||||||||
\(400\) | 0.537703 | 0.0268851 | ||||||||
\(401\) | 33.7936 | 1.68757 | 0.843786 | − | 0.536679i | \(-0.180322\pi\) | ||||
0.843786 | + | 0.536679i | \(0.180322\pi\) | |||||||
\(402\) | −4.96559 | −0.247661 | ||||||||
\(403\) | −4.77835 | −0.238027 | ||||||||
\(404\) | −6.64581 | −0.330641 | ||||||||
\(405\) | 26.3716 | 1.31041 | ||||||||
\(406\) | 9.12436 | 0.452834 | ||||||||
\(407\) | −0.608132 | −0.0301440 | ||||||||
\(408\) | 2.01542 | 0.0997782 | ||||||||
\(409\) | −30.0250 | −1.48464 | −0.742319 | − | 0.670046i | \(-0.766274\pi\) | ||||
−0.742319 | + | 0.670046i | \(0.766274\pi\) | |||||||
\(410\) | 5.31489 | 0.262484 | ||||||||
\(411\) | 36.1054 | 1.78095 | ||||||||
\(412\) | 9.91051 | 0.488256 | ||||||||
\(413\) | 38.8338 | 1.91089 | ||||||||
\(414\) | −5.94924 | −0.292389 | ||||||||
\(415\) | −24.8945 | −1.22202 | ||||||||
\(416\) | −0.832404 | −0.0408119 | ||||||||
\(417\) | 48.3064 | 2.36557 | ||||||||
\(418\) | 3.79872 | 0.185801 | ||||||||
\(419\) | 22.2807 | 1.08849 | 0.544243 | − | 0.838928i | \(-0.316817\pi\) | ||||
0.544243 | + | 0.838928i | \(0.316817\pi\) | |||||||
\(420\) | −15.2414 | −0.743702 | ||||||||
\(421\) | 27.1606 | 1.32373 | 0.661864 | − | 0.749624i | \(-0.269765\pi\) | ||||
0.661864 | + | 0.749624i | \(0.269765\pi\) | |||||||
\(422\) | −26.5620 | −1.29302 | ||||||||
\(423\) | 15.5773 | 0.757394 | ||||||||
\(424\) | 6.06820 | 0.294698 | ||||||||
\(425\) | −0.499421 | −0.0242255 | ||||||||
\(426\) | −13.1062 | −0.634998 | ||||||||
\(427\) | −20.0947 | −0.972449 | ||||||||
\(428\) | 4.50760 | 0.217883 | ||||||||
\(429\) | 5.89099 | 0.284420 | ||||||||
\(430\) | −8.45804 | −0.407883 | ||||||||
\(431\) | 8.37480 | 0.403400 | 0.201700 | − | 0.979447i | \(-0.435353\pi\) | ||||
0.201700 | + | 0.979447i | \(0.435353\pi\) | |||||||
\(432\) | 2.80246 | 0.134833 | ||||||||
\(433\) | 33.4393 | 1.60699 | 0.803496 | − | 0.595310i | \(-0.202971\pi\) | ||||
0.803496 | + | 0.595310i | \(0.202971\pi\) | |||||||
\(434\) | −17.1341 | −0.822465 | ||||||||
\(435\) | −15.6095 | −0.748420 | ||||||||
\(436\) | −2.92956 | −0.140301 | ||||||||
\(437\) | −4.05577 | −0.194014 | ||||||||
\(438\) | −7.40305 | −0.353731 | ||||||||
\(439\) | 13.8872 | 0.662799 | 0.331400 | − | 0.943490i | \(-0.392479\pi\) | ||||
0.331400 | + | 0.943490i | \(0.392479\pi\) | |||||||
\(440\) | −7.67500 | −0.365891 | ||||||||
\(441\) | 3.26176 | 0.155322 | ||||||||
\(442\) | 0.773141 | 0.0367746 | ||||||||
\(443\) | −13.5757 | −0.645002 | −0.322501 | − | 0.946569i | \(-0.604524\pi\) | ||||
−0.322501 | + | 0.946569i | \(0.604524\pi\) | |||||||
\(444\) | 0.404599 | 0.0192014 | ||||||||
\(445\) | −42.0239 | −1.99212 | ||||||||
\(446\) | 4.85876 | 0.230069 | ||||||||
\(447\) | 4.76390 | 0.225325 | ||||||||
\(448\) | −2.98482 | −0.141019 | ||||||||
\(449\) | −25.2855 | −1.19329 | −0.596647 | − | 0.802504i | \(-0.703501\pi\) | ||||
−0.596647 | + | 0.802504i | \(0.703501\pi\) | |||||||
\(450\) | 0.918659 | 0.0433060 | ||||||||
\(451\) | −7.36619 | −0.346860 | ||||||||
\(452\) | 1.44266 | 0.0678570 | ||||||||
\(453\) | −47.0003 | −2.20827 | ||||||||
\(454\) | 11.9983 | 0.563109 | ||||||||
\(455\) | −5.84678 | −0.274101 | ||||||||
\(456\) | −2.52734 | −0.118354 | ||||||||
\(457\) | 28.0984 | 1.31439 | 0.657193 | − | 0.753722i | \(-0.271744\pi\) | ||||
0.657193 | + | 0.753722i | \(0.271744\pi\) | |||||||
\(458\) | −28.6718 | −1.33975 | ||||||||
\(459\) | −2.60294 | −0.121495 | ||||||||
\(460\) | 8.19434 | 0.382063 | ||||||||
\(461\) | 7.28760 | 0.339418 | 0.169709 | − | 0.985494i | \(-0.445717\pi\) | ||||
0.169709 | + | 0.985494i | \(0.445717\pi\) | |||||||
\(462\) | 21.1238 | 0.982769 | ||||||||
\(463\) | −24.3859 | −1.13331 | −0.566654 | − | 0.823956i | \(-0.691762\pi\) | ||||
−0.566654 | + | 0.823956i | \(0.691762\pi\) | |||||||
\(464\) | −3.05692 | −0.141914 | ||||||||
\(465\) | 29.3123 | 1.35932 | ||||||||
\(466\) | 25.9732 | 1.20319 | ||||||||
\(467\) | −29.9631 | −1.38653 | −0.693263 | − | 0.720684i | \(-0.743828\pi\) | ||||
−0.693263 | + | 0.720684i | \(0.743828\pi\) | |||||||
\(468\) | −1.42215 | −0.0657390 | ||||||||
\(469\) | −6.83043 | −0.315400 | ||||||||
\(470\) | −21.4558 | −0.989682 | ||||||||
\(471\) | −18.6347 | −0.858642 | ||||||||
\(472\) | −13.0104 | −0.598854 | ||||||||
\(473\) | 11.7225 | 0.538999 | ||||||||
\(474\) | 6.10894 | 0.280593 | ||||||||
\(475\) | 0.626276 | 0.0287355 | ||||||||
\(476\) | 2.77232 | 0.127069 | ||||||||
\(477\) | 10.3674 | 0.474693 | ||||||||
\(478\) | −7.37644 | −0.337391 | ||||||||
\(479\) | 14.9194 | 0.681686 | 0.340843 | − | 0.940120i | \(-0.389288\pi\) | ||||
0.340843 | + | 0.940120i | \(0.389288\pi\) | |||||||
\(480\) | 5.10629 | 0.233069 | ||||||||
\(481\) | 0.155209 | 0.00707694 | ||||||||
\(482\) | 3.64527 | 0.166038 | ||||||||
\(483\) | −22.5532 | −1.02621 | ||||||||
\(484\) | −0.362804 | −0.0164911 | ||||||||
\(485\) | 13.1664 | 0.597854 | ||||||||
\(486\) | 15.9097 | 0.721681 | ||||||||
\(487\) | 22.0249 | 0.998045 | 0.499023 | − | 0.866589i | \(-0.333692\pi\) | ||||
0.499023 | + | 0.866589i | \(0.333692\pi\) | |||||||
\(488\) | 6.73229 | 0.304756 | ||||||||
\(489\) | 26.4838 | 1.19764 | ||||||||
\(490\) | −4.49267 | −0.202958 | ||||||||
\(491\) | −18.9968 | −0.857313 | −0.428656 | − | 0.903468i | \(-0.641013\pi\) | ||||
−0.428656 | + | 0.903468i | \(0.641013\pi\) | |||||||
\(492\) | 4.90084 | 0.220947 | ||||||||
\(493\) | 2.83928 | 0.127875 | ||||||||
\(494\) | −0.969522 | −0.0436208 | ||||||||
\(495\) | −13.1127 | −0.589370 | ||||||||
\(496\) | 5.74043 | 0.257753 | ||||||||
\(497\) | −18.0283 | −0.808679 | ||||||||
\(498\) | −22.9551 | −1.02864 | ||||||||
\(499\) | −14.1049 | −0.631422 | −0.315711 | − | 0.948855i | \(-0.602243\pi\) | ||||
−0.315711 | + | 0.948855i | \(0.602243\pi\) | |||||||
\(500\) | 10.5008 | 0.469611 | ||||||||
\(501\) | −22.1674 | −0.990367 | ||||||||
\(502\) | −11.4270 | −0.510012 | ||||||||
\(503\) | −24.6559 | −1.09935 | −0.549676 | − | 0.835378i | \(-0.685249\pi\) | ||||
−0.549676 | + | 0.835378i | \(0.685249\pi\) | |||||||
\(504\) | −5.09953 | −0.227151 | ||||||||
\(505\) | 15.6391 | 0.695933 | ||||||||
\(506\) | −11.3570 | −0.504879 | ||||||||
\(507\) | 26.7053 | 1.18602 | ||||||||
\(508\) | −18.3308 | −0.813299 | ||||||||
\(509\) | 12.2854 | 0.544540 | 0.272270 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272270 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(510\) | −4.74275 | −0.210013 | ||||||||
\(511\) | −10.1833 | −0.450482 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.26409 | 0.144113 | ||||||||
\(514\) | −1.00591 | −0.0443687 | ||||||||
\(515\) | −23.3217 | −1.02768 | ||||||||
\(516\) | −7.79912 | −0.343337 | ||||||||
\(517\) | 29.7367 | 1.30782 | ||||||||
\(518\) | 0.556548 | 0.0244533 | ||||||||
\(519\) | 12.9289 | 0.567517 | ||||||||
\(520\) | 1.95884 | 0.0859008 | ||||||||
\(521\) | 19.7011 | 0.863123 | 0.431561 | − | 0.902084i | \(-0.357963\pi\) | ||||
0.431561 | + | 0.902084i | \(0.357963\pi\) | |||||||
\(522\) | −5.22272 | −0.228592 | ||||||||
\(523\) | 20.6282 | 0.902007 | 0.451004 | − | 0.892522i | \(-0.351066\pi\) | ||||
0.451004 | + | 0.892522i | \(0.351066\pi\) | |||||||
\(524\) | −1.69597 | −0.0740889 | ||||||||
\(525\) | 3.48258 | 0.151992 | ||||||||
\(526\) | −26.2139 | −1.14298 | ||||||||
\(527\) | −5.33174 | −0.232254 | ||||||||
\(528\) | −7.07708 | −0.307991 | ||||||||
\(529\) | −10.8745 | −0.472805 | ||||||||
\(530\) | −14.2799 | −0.620278 | ||||||||
\(531\) | −22.2282 | −0.964621 | ||||||||
\(532\) | −3.47649 | −0.150725 | ||||||||
\(533\) | 1.88002 | 0.0814329 | ||||||||
\(534\) | −38.7501 | −1.67688 | ||||||||
\(535\) | −10.6074 | −0.458599 | ||||||||
\(536\) | 2.28839 | 0.0988434 | ||||||||
\(537\) | 55.4096 | 2.39110 | ||||||||
\(538\) | 12.8463 | 0.553842 | ||||||||
\(539\) | 6.22663 | 0.268200 | ||||||||
\(540\) | −6.59483 | −0.283796 | ||||||||
\(541\) | 21.1184 | 0.907949 | 0.453975 | − | 0.891015i | \(-0.350006\pi\) | ||||
0.453975 | + | 0.891015i | \(0.350006\pi\) | |||||||
\(542\) | −11.0513 | −0.474694 | ||||||||
\(543\) | 0.846654 | 0.0363334 | ||||||||
\(544\) | −0.928806 | −0.0398222 | ||||||||
\(545\) | 6.89394 | 0.295304 | ||||||||
\(546\) | −5.39129 | −0.230726 | ||||||||
\(547\) | 3.00351 | 0.128421 | 0.0642104 | − | 0.997936i | \(-0.479547\pi\) | ||||
0.0642104 | + | 0.997936i | \(0.479547\pi\) | |||||||
\(548\) | −16.6391 | −0.710789 | ||||||||
\(549\) | 11.5020 | 0.490895 | ||||||||
\(550\) | 1.75370 | 0.0747781 | ||||||||
\(551\) | −3.56047 | −0.151681 | ||||||||
\(552\) | 7.55597 | 0.321603 | ||||||||
\(553\) | 8.40317 | 0.357339 | ||||||||
\(554\) | −6.45607 | −0.274292 | ||||||||
\(555\) | −0.952116 | −0.0404151 | ||||||||
\(556\) | −22.2620 | −0.944118 | ||||||||
\(557\) | 15.8627 | 0.672125 | 0.336063 | − | 0.941840i | \(-0.390905\pi\) | ||||
0.336063 | + | 0.941840i | \(0.390905\pi\) | |||||||
\(558\) | 9.80745 | 0.415183 | ||||||||
\(559\) | −2.99184 | −0.126541 | ||||||||
\(560\) | 7.02397 | 0.296817 | ||||||||
\(561\) | 6.57323 | 0.277522 | ||||||||
\(562\) | −12.1267 | −0.511533 | ||||||||
\(563\) | −39.4995 | −1.66470 | −0.832352 | − | 0.554247i | \(-0.813006\pi\) | ||||
−0.832352 | + | 0.554247i | \(0.813006\pi\) | |||||||
\(564\) | −19.7843 | −0.833069 | ||||||||
\(565\) | −3.39491 | −0.142825 | ||||||||
\(566\) | 25.0839 | 1.05435 | ||||||||
\(567\) | 33.4495 | 1.40475 | ||||||||
\(568\) | 6.03999 | 0.253432 | ||||||||
\(569\) | 45.4813 | 1.90668 | 0.953338 | − | 0.301906i | \(-0.0976229\pi\) | ||||
0.953338 | + | 0.301906i | \(0.0976229\pi\) | |||||||
\(570\) | 5.94743 | 0.249110 | ||||||||
\(571\) | −0.956957 | −0.0400474 | −0.0200237 | − | 0.999800i | \(-0.506374\pi\) | ||||
−0.0200237 | + | 0.999800i | \(0.506374\pi\) | |||||||
\(572\) | −2.71486 | −0.113514 | ||||||||
\(573\) | 42.5199 | 1.77629 | ||||||||
\(574\) | 6.74136 | 0.281379 | ||||||||
\(575\) | −1.87237 | −0.0780832 | ||||||||
\(576\) | 1.70849 | 0.0711870 | ||||||||
\(577\) | −38.7347 | −1.61255 | −0.806273 | − | 0.591544i | \(-0.798519\pi\) | ||||
−0.806273 | + | 0.591544i | \(0.798519\pi\) | |||||||
\(578\) | −16.1373 | −0.671224 | ||||||||
\(579\) | −59.3760 | −2.46758 | ||||||||
\(580\) | 7.19364 | 0.298700 | ||||||||
\(581\) | −31.5760 | −1.30999 | ||||||||
\(582\) | 12.1406 | 0.503246 | ||||||||
\(583\) | 19.7912 | 0.819670 | ||||||||
\(584\) | 3.41169 | 0.141177 | ||||||||
\(585\) | 3.34666 | 0.138367 | ||||||||
\(586\) | 1.76172 | 0.0727760 | ||||||||
\(587\) | 43.3425 | 1.78893 | 0.894467 | − | 0.447133i | \(-0.147555\pi\) | ||||
0.894467 | + | 0.447133i | \(0.147555\pi\) | |||||||
\(588\) | −4.14267 | −0.170841 | ||||||||
\(589\) | 6.68602 | 0.275493 | ||||||||
\(590\) | 30.6166 | 1.26046 | ||||||||
\(591\) | 10.6950 | 0.439932 | ||||||||
\(592\) | −0.186459 | −0.00766343 | ||||||||
\(593\) | −7.45527 | −0.306151 | −0.153076 | − | 0.988214i | \(-0.548918\pi\) | ||||
−0.153076 | + | 0.988214i | \(0.548918\pi\) | |||||||
\(594\) | 9.14013 | 0.375024 | ||||||||
\(595\) | −6.52391 | −0.267454 | ||||||||
\(596\) | −2.19544 | −0.0899288 | ||||||||
\(597\) | 9.69003 | 0.396587 | ||||||||
\(598\) | 2.89857 | 0.118531 | ||||||||
\(599\) | −44.8807 | −1.83378 | −0.916888 | − | 0.399144i | \(-0.869307\pi\) | ||||
−0.916888 | + | 0.399144i | \(0.869307\pi\) | |||||||
\(600\) | −1.16676 | −0.0476329 | ||||||||
\(601\) | 12.3336 | 0.503097 | 0.251549 | − | 0.967845i | \(-0.419060\pi\) | ||||
0.251549 | + | 0.967845i | \(0.419060\pi\) | |||||||
\(602\) | −10.7281 | −0.437245 | ||||||||
\(603\) | 3.90969 | 0.159215 | ||||||||
\(604\) | 21.6601 | 0.881336 | ||||||||
\(605\) | 0.853763 | 0.0347104 | ||||||||
\(606\) | 14.4208 | 0.585804 | ||||||||
\(607\) | −30.5734 | −1.24094 | −0.620468 | − | 0.784232i | \(-0.713057\pi\) | ||||
−0.620468 | + | 0.784232i | \(0.713057\pi\) | |||||||
\(608\) | 1.16473 | 0.0472358 | ||||||||
\(609\) | −19.7990 | −0.802296 | ||||||||
\(610\) | −15.8426 | −0.641450 | ||||||||
\(611\) | −7.58951 | −0.307039 | ||||||||
\(612\) | −1.58685 | −0.0641448 | ||||||||
\(613\) | 28.6355 | 1.15658 | 0.578289 | − | 0.815832i | \(-0.303721\pi\) | ||||
0.578289 | + | 0.815832i | \(0.303721\pi\) | |||||||
\(614\) | 17.7922 | 0.718037 | ||||||||
\(615\) | −11.5328 | −0.465048 | ||||||||
\(616\) | −9.73490 | −0.392230 | ||||||||
\(617\) | 12.6450 | 0.509069 | 0.254534 | − | 0.967064i | \(-0.418078\pi\) | ||||
0.254534 | + | 0.967064i | \(0.418078\pi\) | |||||||
\(618\) | −21.5049 | −0.865053 | ||||||||
\(619\) | 6.60021 | 0.265285 | 0.132642 | − | 0.991164i | \(-0.457654\pi\) | ||||
0.132642 | + | 0.991164i | \(0.457654\pi\) | |||||||
\(620\) | −13.5086 | −0.542517 | ||||||||
\(621\) | −9.75862 | −0.391600 | ||||||||
\(622\) | −11.1608 | −0.447505 | ||||||||
\(623\) | −53.3028 | −2.13553 | ||||||||
\(624\) | 1.80624 | 0.0723074 | ||||||||
\(625\) | −27.3994 | −1.09598 | ||||||||
\(626\) | −22.1853 | −0.886705 | ||||||||
\(627\) | −8.24286 | −0.329188 | ||||||||
\(628\) | 8.58779 | 0.342690 | ||||||||
\(629\) | 0.173185 | 0.00690532 | ||||||||
\(630\) | 12.0004 | 0.478107 | ||||||||
\(631\) | −25.2557 | −1.00541 | −0.502707 | − | 0.864457i | \(-0.667662\pi\) | ||||
−0.502707 | + | 0.864457i | \(0.667662\pi\) | |||||||
\(632\) | −2.81530 | −0.111987 | ||||||||
\(633\) | 57.6369 | 2.29086 | ||||||||
\(634\) | −8.19846 | −0.325603 | ||||||||
\(635\) | 43.1367 | 1.71183 | ||||||||
\(636\) | −13.1674 | −0.522122 | ||||||||
\(637\) | −1.58918 | −0.0629657 | ||||||||
\(638\) | −9.97006 | −0.394718 | ||||||||
\(639\) | 10.3193 | 0.408224 | ||||||||
\(640\) | −2.35323 | −0.0930197 | ||||||||
\(641\) | −38.2841 | −1.51213 | −0.756066 | − | 0.654496i | \(-0.772881\pi\) | ||||
−0.756066 | + | 0.654496i | \(0.772881\pi\) | |||||||
\(642\) | −9.78106 | −0.386028 | ||||||||
\(643\) | 17.6205 | 0.694884 | 0.347442 | − | 0.937701i | \(-0.387050\pi\) | ||||
0.347442 | + | 0.937701i | \(0.387050\pi\) | |||||||
\(644\) | 10.3936 | 0.409567 | ||||||||
\(645\) | 18.3531 | 0.722654 | ||||||||
\(646\) | −1.08180 | −0.0425630 | ||||||||
\(647\) | −47.2984 | −1.85949 | −0.929745 | − | 0.368203i | \(-0.879973\pi\) | ||||
−0.929745 | + | 0.368203i | \(0.879973\pi\) | |||||||
\(648\) | −11.2065 | −0.440234 | ||||||||
\(649\) | −42.4331 | −1.66565 | ||||||||
\(650\) | −0.447586 | −0.0175557 | ||||||||
\(651\) | 37.1795 | 1.45718 | ||||||||
\(652\) | −12.2050 | −0.477987 | ||||||||
\(653\) | 17.6773 | 0.691767 | 0.345883 | − | 0.938278i | \(-0.387579\pi\) | ||||
0.345883 | + | 0.938278i | \(0.387579\pi\) | |||||||
\(654\) | 6.35687 | 0.248573 | ||||||||
\(655\) | 3.99102 | 0.155942 | ||||||||
\(656\) | −2.25855 | −0.0881815 | ||||||||
\(657\) | 5.82884 | 0.227405 | ||||||||
\(658\) | −27.2143 | −1.06093 | ||||||||
\(659\) | 41.7114 | 1.62485 | 0.812424 | − | 0.583068i | \(-0.198148\pi\) | ||||
0.812424 | + | 0.583068i | \(0.198148\pi\) | |||||||
\(660\) | 16.6540 | 0.648257 | ||||||||
\(661\) | 47.3867 | 1.84313 | 0.921565 | − | 0.388224i | \(-0.126911\pi\) | ||||
0.921565 | + | 0.388224i | \(0.126911\pi\) | |||||||
\(662\) | −32.7930 | −1.27454 | ||||||||
\(663\) | −1.67764 | −0.0651543 | ||||||||
\(664\) | 10.5789 | 0.410540 | ||||||||
\(665\) | 8.18100 | 0.317246 | ||||||||
\(666\) | −0.318564 | −0.0123441 | ||||||||
\(667\) | 10.6447 | 0.412165 | ||||||||
\(668\) | 10.2158 | 0.395263 | ||||||||
\(669\) | −10.5430 | −0.407618 | ||||||||
\(670\) | −5.38512 | −0.208045 | ||||||||
\(671\) | 21.9572 | 0.847647 | ||||||||
\(672\) | 6.47678 | 0.249847 | ||||||||
\(673\) | −12.6966 | −0.489417 | −0.244708 | − | 0.969597i | \(-0.578692\pi\) | ||||
−0.244708 | + | 0.969597i | \(0.578692\pi\) | |||||||
\(674\) | 17.8495 | 0.687538 | ||||||||
\(675\) | 1.50689 | 0.0580001 | ||||||||
\(676\) | −12.3071 | −0.473350 | ||||||||
\(677\) | −24.3140 | −0.934463 | −0.467232 | − | 0.884135i | \(-0.654749\pi\) | ||||
−0.467232 | + | 0.884135i | \(0.654749\pi\) | |||||||
\(678\) | −3.13043 | −0.120224 | ||||||||
\(679\) | 16.7001 | 0.640891 | ||||||||
\(680\) | 2.18570 | 0.0838176 | ||||||||
\(681\) | −26.0352 | −0.997672 | ||||||||
\(682\) | 18.7222 | 0.716911 | ||||||||
\(683\) | 5.69273 | 0.217826 | 0.108913 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108913 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(684\) | 1.98992 | 0.0760865 | ||||||||
\(685\) | 39.1558 | 1.49606 | ||||||||
\(686\) | 15.1953 | 0.580158 | ||||||||
\(687\) | 62.2152 | 2.37366 | ||||||||
\(688\) | 3.59422 | 0.137028 | ||||||||
\(689\) | −5.05119 | −0.192435 | ||||||||
\(690\) | −17.7810 | −0.676909 | ||||||||
\(691\) | 26.6737 | 1.01472 | 0.507358 | − | 0.861735i | \(-0.330622\pi\) | ||||
0.507358 | + | 0.861735i | \(0.330622\pi\) | |||||||
\(692\) | −5.95829 | −0.226500 | ||||||||
\(693\) | −16.6320 | −0.631797 | ||||||||
\(694\) | −23.4732 | −0.891029 | ||||||||
\(695\) | 52.3876 | 1.98717 | ||||||||
\(696\) | 6.63323 | 0.251432 | ||||||||
\(697\) | 2.09775 | 0.0794580 | ||||||||
\(698\) | −5.79132 | −0.219205 | ||||||||
\(699\) | −56.3594 | −2.13171 | ||||||||
\(700\) | −1.60495 | −0.0606612 | ||||||||
\(701\) | 38.7652 | 1.46414 | 0.732072 | − | 0.681228i | \(-0.238554\pi\) | ||||
0.732072 | + | 0.681228i | \(0.238554\pi\) | |||||||
\(702\) | −2.33277 | −0.0880449 | ||||||||
\(703\) | −0.217174 | −0.00819087 | ||||||||
\(704\) | 3.26147 | 0.122921 | ||||||||
\(705\) | 46.5570 | 1.75344 | ||||||||
\(706\) | −3.57572 | −0.134574 | ||||||||
\(707\) | 19.8365 | 0.746030 | ||||||||
\(708\) | 28.2314 | 1.06100 | ||||||||
\(709\) | −24.4641 | −0.918769 | −0.459385 | − | 0.888238i | \(-0.651930\pi\) | ||||
−0.459385 | + | 0.888238i | \(0.651930\pi\) | |||||||
\(710\) | −14.2135 | −0.533423 | ||||||||
\(711\) | −4.80991 | −0.180386 | ||||||||
\(712\) | 17.8579 | 0.669255 | ||||||||
\(713\) | −19.9891 | −0.748598 | ||||||||
\(714\) | −6.01567 | −0.225131 | ||||||||
\(715\) | 6.38870 | 0.238924 | ||||||||
\(716\) | −25.5355 | −0.954306 | ||||||||
\(717\) | 16.0062 | 0.597762 | ||||||||
\(718\) | −10.1988 | −0.380615 | ||||||||
\(719\) | 20.9300 | 0.780557 | 0.390278 | − | 0.920697i | \(-0.372379\pi\) | ||||
0.390278 | + | 0.920697i | \(0.372379\pi\) | |||||||
\(720\) | −4.02047 | −0.149834 | ||||||||
\(721\) | −29.5811 | −1.10166 | ||||||||
\(722\) | −17.6434 | −0.656620 | ||||||||
\(723\) | −7.90990 | −0.294172 | ||||||||
\(724\) | −0.390180 | −0.0145009 | ||||||||
\(725\) | −1.64371 | −0.0610460 | ||||||||
\(726\) | 0.787251 | 0.0292176 | ||||||||
\(727\) | 41.2124 | 1.52848 | 0.764241 | − | 0.644930i | \(-0.223114\pi\) | ||||
0.764241 | + | 0.644930i | \(0.223114\pi\) | |||||||
\(728\) | 2.48457 | 0.0920845 | ||||||||
\(729\) | −0.903045 | −0.0334461 | ||||||||
\(730\) | −8.02850 | −0.297148 | ||||||||
\(731\) | −3.33833 | −0.123473 | ||||||||
\(732\) | −14.6084 | −0.539943 | ||||||||
\(733\) | −14.4327 | −0.533083 | −0.266542 | − | 0.963823i | \(-0.585881\pi\) | ||||
−0.266542 | + | 0.963823i | \(0.585881\pi\) | |||||||
\(734\) | −13.0245 | −0.480745 | ||||||||
\(735\) | 9.74867 | 0.359585 | ||||||||
\(736\) | −3.48217 | −0.128354 | ||||||||
\(737\) | 7.46352 | 0.274922 | ||||||||
\(738\) | −3.85871 | −0.142041 | ||||||||
\(739\) | −10.8270 | −0.398276 | −0.199138 | − | 0.979971i | \(-0.563814\pi\) | ||||
−0.199138 | + | 0.979971i | \(0.563814\pi\) | |||||||
\(740\) | 0.438782 | 0.0161300 | ||||||||
\(741\) | 2.10377 | 0.0772839 | ||||||||
\(742\) | −18.1125 | −0.664930 | ||||||||
\(743\) | −18.9790 | −0.696272 | −0.348136 | − | 0.937444i | \(-0.613185\pi\) | ||||
−0.348136 | + | 0.937444i | \(0.613185\pi\) | |||||||
\(744\) | −12.4562 | −0.456666 | ||||||||
\(745\) | 5.16638 | 0.189282 | ||||||||
\(746\) | −10.3512 | −0.378985 | ||||||||
\(747\) | 18.0739 | 0.661289 | ||||||||
\(748\) | −3.02927 | −0.110761 | ||||||||
\(749\) | −13.4544 | −0.491612 | ||||||||
\(750\) | −22.7858 | −0.832019 | ||||||||
\(751\) | −33.1438 | −1.20943 | −0.604717 | − | 0.796441i | \(-0.706714\pi\) | ||||
−0.604717 | + | 0.796441i | \(0.706714\pi\) | |||||||
\(752\) | 9.11758 | 0.332484 | ||||||||
\(753\) | 24.7955 | 0.903599 | ||||||||
\(754\) | 2.54459 | 0.0926686 | ||||||||
\(755\) | −50.9712 | −1.85503 | ||||||||
\(756\) | −8.36483 | −0.304226 | ||||||||
\(757\) | 34.4302 | 1.25139 | 0.625693 | − | 0.780070i | \(-0.284816\pi\) | ||||
0.625693 | + | 0.780070i | \(0.284816\pi\) | |||||||
\(758\) | 13.3344 | 0.484328 | ||||||||
\(759\) | 24.6436 | 0.894505 | ||||||||
\(760\) | −2.74087 | −0.0994218 | ||||||||
\(761\) | 13.3847 | 0.485194 | 0.242597 | − | 0.970127i | \(-0.422001\pi\) | ||||
0.242597 | + | 0.970127i | \(0.422001\pi\) | |||||||
\(762\) | 39.7761 | 1.44094 | ||||||||
\(763\) | 8.74421 | 0.316562 | ||||||||
\(764\) | −19.5953 | −0.708932 | ||||||||
\(765\) | 3.73424 | 0.135012 | ||||||||
\(766\) | −15.1494 | −0.547370 | ||||||||
\(767\) | 10.8299 | 0.391046 | ||||||||
\(768\) | −2.16991 | −0.0782997 | ||||||||
\(769\) | −46.3553 | −1.67162 | −0.835808 | − | 0.549022i | \(-0.815000\pi\) | ||||
−0.835808 | + | 0.549022i | \(0.815000\pi\) | |||||||
\(770\) | 22.9085 | 0.825565 | ||||||||
\(771\) | 2.18273 | 0.0786089 | ||||||||
\(772\) | 27.3634 | 0.984831 | ||||||||
\(773\) | 15.7375 | 0.566037 | 0.283019 | − | 0.959114i | \(-0.408664\pi\) | ||||
0.283019 | + | 0.959114i | \(0.408664\pi\) | |||||||
\(774\) | 6.14069 | 0.220722 | ||||||||
\(775\) | 3.08664 | 0.110875 | ||||||||
\(776\) | −5.59501 | −0.200849 | ||||||||
\(777\) | −1.20766 | −0.0433244 | ||||||||
\(778\) | −12.4338 | −0.445775 | ||||||||
\(779\) | −2.63059 | −0.0942506 | ||||||||
\(780\) | −4.25050 | −0.152192 | ||||||||
\(781\) | 19.6993 | 0.704895 | ||||||||
\(782\) | 3.23425 | 0.115657 | ||||||||
\(783\) | −8.56689 | −0.306156 | ||||||||
\(784\) | 1.90915 | 0.0681839 | ||||||||
\(785\) | −20.2091 | −0.721293 | ||||||||
\(786\) | 3.68010 | 0.131265 | ||||||||
\(787\) | −1.78885 | −0.0637657 | −0.0318828 | − | 0.999492i | \(-0.510150\pi\) | ||||
−0.0318828 | + | 0.999492i | \(0.510150\pi\) | |||||||
\(788\) | −4.92877 | −0.175580 | ||||||||
\(789\) | 56.8817 | 2.02504 | ||||||||
\(790\) | 6.62506 | 0.235709 | ||||||||
\(791\) | −4.30608 | −0.153106 | ||||||||
\(792\) | 5.57219 | 0.197999 | ||||||||
\(793\) | −5.60398 | −0.199003 | ||||||||
\(794\) | −22.5317 | −0.799620 | ||||||||
\(795\) | 30.9860 | 1.09896 | ||||||||
\(796\) | −4.46565 | −0.158281 | ||||||||
\(797\) | 1.11191 | 0.0393857 | 0.0196929 | − | 0.999806i | \(-0.493731\pi\) | ||||
0.0196929 | + | 0.999806i | \(0.493731\pi\) | |||||||
\(798\) | 7.54366 | 0.267043 | ||||||||
\(799\) | −8.46846 | −0.299593 | ||||||||
\(800\) | 0.537703 | 0.0190107 | ||||||||
\(801\) | 30.5101 | 1.07802 | ||||||||
\(802\) | 33.7936 | 1.19329 | ||||||||
\(803\) | 11.1271 | 0.392668 | ||||||||
\(804\) | −4.96559 | −0.175123 | ||||||||
\(805\) | −24.4586 | −0.862054 | ||||||||
\(806\) | −4.77835 | −0.168310 | ||||||||
\(807\) | −27.8752 | −0.981254 | ||||||||
\(808\) | −6.64581 | −0.233799 | ||||||||
\(809\) | −55.6931 | −1.95806 | −0.979032 | − | 0.203706i | \(-0.934701\pi\) | ||||
−0.979032 | + | 0.203706i | \(0.934701\pi\) | |||||||
\(810\) | 26.3716 | 0.926603 | ||||||||
\(811\) | 9.26811 | 0.325447 | 0.162724 | − | 0.986672i | \(-0.447972\pi\) | ||||
0.162724 | + | 0.986672i | \(0.447972\pi\) | |||||||
\(812\) | 9.12436 | 0.320202 | ||||||||
\(813\) | 23.9803 | 0.841024 | ||||||||
\(814\) | −0.608132 | −0.0213150 | ||||||||
\(815\) | 28.7213 | 1.00606 | ||||||||
\(816\) | 2.01542 | 0.0705538 | ||||||||
\(817\) | 4.18628 | 0.146459 | ||||||||
\(818\) | −30.0250 | −1.04980 | ||||||||
\(819\) | 4.24487 | 0.148328 | ||||||||
\(820\) | 5.31489 | 0.185604 | ||||||||
\(821\) | 40.8524 | 1.42576 | 0.712879 | − | 0.701287i | \(-0.247391\pi\) | ||||
0.712879 | + | 0.701287i | \(0.247391\pi\) | |||||||
\(822\) | 36.1054 | 1.25932 | ||||||||
\(823\) | 17.2494 | 0.601276 | 0.300638 | − | 0.953738i | \(-0.402800\pi\) | ||||
0.300638 | + | 0.953738i | \(0.402800\pi\) | |||||||
\(824\) | 9.91051 | 0.345249 | ||||||||
\(825\) | −3.80537 | −0.132486 | ||||||||
\(826\) | 38.8338 | 1.35120 | ||||||||
\(827\) | 22.7270 | 0.790296 | 0.395148 | − | 0.918618i | \(-0.370693\pi\) | ||||
0.395148 | + | 0.918618i | \(0.370693\pi\) | |||||||
\(828\) | −5.94924 | −0.206750 | ||||||||
\(829\) | 51.0696 | 1.77372 | 0.886860 | − | 0.462039i | \(-0.152882\pi\) | ||||
0.886860 | + | 0.462039i | \(0.152882\pi\) | |||||||
\(830\) | −24.8945 | −0.864102 | ||||||||
\(831\) | 14.0091 | 0.485969 | ||||||||
\(832\) | −0.832404 | −0.0288584 | ||||||||
\(833\) | −1.77323 | −0.0614387 | ||||||||
\(834\) | 48.3064 | 1.67271 | ||||||||
\(835\) | −24.0402 | −0.831947 | ||||||||
\(836\) | 3.79872 | 0.131381 | ||||||||
\(837\) | 16.0873 | 0.556058 | ||||||||
\(838\) | 22.2807 | 0.769676 | ||||||||
\(839\) | −27.2821 | −0.941882 | −0.470941 | − | 0.882165i | \(-0.656086\pi\) | ||||
−0.470941 | + | 0.882165i | \(0.656086\pi\) | |||||||
\(840\) | −15.2414 | −0.525877 | ||||||||
\(841\) | −19.6552 | −0.677767 | ||||||||
\(842\) | 27.1606 | 0.936018 | ||||||||
\(843\) | 26.3137 | 0.906293 | ||||||||
\(844\) | −26.5620 | −0.914300 | ||||||||
\(845\) | 28.9615 | 0.996305 | ||||||||
\(846\) | 15.5773 | 0.535558 | ||||||||
\(847\) | 1.08291 | 0.0372091 | ||||||||
\(848\) | 6.06820 | 0.208383 | ||||||||
\(849\) | −54.4297 | −1.86802 | ||||||||
\(850\) | −0.499421 | −0.0171300 | ||||||||
\(851\) | 0.649282 | 0.0222571 | ||||||||
\(852\) | −13.1062 | −0.449011 | ||||||||
\(853\) | 39.8085 | 1.36302 | 0.681508 | − | 0.731811i | \(-0.261325\pi\) | ||||
0.681508 | + | 0.731811i | \(0.261325\pi\) | |||||||
\(854\) | −20.0947 | −0.687625 | ||||||||
\(855\) | −4.68275 | −0.160147 | ||||||||
\(856\) | 4.50760 | 0.154066 | ||||||||
\(857\) | −5.20800 | −0.177902 | −0.0889510 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889510 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(858\) | 5.89099 | 0.201115 | ||||||||
\(859\) | 24.7829 | 0.845583 | 0.422791 | − | 0.906227i | \(-0.361050\pi\) | ||||
0.422791 | + | 0.906227i | \(0.361050\pi\) | |||||||
\(860\) | −8.45804 | −0.288417 | ||||||||
\(861\) | −14.6281 | −0.498525 | ||||||||
\(862\) | 8.37480 | 0.285247 | ||||||||
\(863\) | −4.66071 | −0.158652 | −0.0793261 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793261 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(864\) | 2.80246 | 0.0953415 | ||||||||
\(865\) | 14.0212 | 0.476737 | ||||||||
\(866\) | 33.4393 | 1.13631 | ||||||||
\(867\) | 35.0165 | 1.18922 | ||||||||
\(868\) | −17.1341 | −0.581570 | ||||||||
\(869\) | −9.18203 | −0.311479 | ||||||||
\(870\) | −15.6095 | −0.529213 | ||||||||
\(871\) | −1.90486 | −0.0645439 | ||||||||
\(872\) | −2.92956 | −0.0992075 | ||||||||
\(873\) | −9.55902 | −0.323524 | ||||||||
\(874\) | −4.05577 | −0.137188 | ||||||||
\(875\) | −31.3431 | −1.05959 | ||||||||
\(876\) | −7.40305 | −0.250126 | ||||||||
\(877\) | −23.7311 | −0.801342 | −0.400671 | − | 0.916222i | \(-0.631223\pi\) | ||||
−0.400671 | + | 0.916222i | \(0.631223\pi\) | |||||||
\(878\) | 13.8872 | 0.468670 | ||||||||
\(879\) | −3.82277 | −0.128939 | ||||||||
\(880\) | −7.67500 | −0.258724 | ||||||||
\(881\) | −37.2553 | −1.25516 | −0.627582 | − | 0.778551i | \(-0.715955\pi\) | ||||
−0.627582 | + | 0.778551i | \(0.715955\pi\) | |||||||
\(882\) | 3.26176 | 0.109829 | ||||||||
\(883\) | −40.1527 | −1.35125 | −0.675623 | − | 0.737248i | \(-0.736125\pi\) | ||||
−0.675623 | + | 0.737248i | \(0.736125\pi\) | |||||||
\(884\) | 0.773141 | 0.0260035 | ||||||||
\(885\) | −66.4351 | −2.23319 | ||||||||
\(886\) | −13.5757 | −0.456085 | ||||||||
\(887\) | −41.1548 | −1.38184 | −0.690921 | − | 0.722930i | \(-0.742795\pi\) | ||||
−0.690921 | + | 0.722930i | \(0.742795\pi\) | |||||||
\(888\) | 0.404599 | 0.0135775 | ||||||||
\(889\) | 54.7142 | 1.83505 | ||||||||
\(890\) | −42.0239 | −1.40864 | ||||||||
\(891\) | −36.5498 | −1.22446 | ||||||||
\(892\) | 4.85876 | 0.162683 | ||||||||
\(893\) | 10.6195 | 0.355367 | ||||||||
\(894\) | 4.76390 | 0.159329 | ||||||||
\(895\) | 60.0910 | 2.00862 | ||||||||
\(896\) | −2.98482 | −0.0997158 | ||||||||
\(897\) | −6.28962 | −0.210004 | ||||||||
\(898\) | −25.2855 | −0.843787 | ||||||||
\(899\) | −17.5480 | −0.585259 | ||||||||
\(900\) | 0.918659 | 0.0306220 | ||||||||
\(901\) | −5.63617 | −0.187768 | ||||||||
\(902\) | −7.36619 | −0.245267 | ||||||||
\(903\) | 23.2790 | 0.774676 | ||||||||
\(904\) | 1.44266 | 0.0479821 | ||||||||
\(905\) | 0.918184 | 0.0305215 | ||||||||
\(906\) | −47.0003 | −1.56148 | ||||||||
\(907\) | 12.9280 | 0.429267 | 0.214634 | − | 0.976695i | \(-0.431144\pi\) | ||||
0.214634 | + | 0.976695i | \(0.431144\pi\) | |||||||
\(908\) | 11.9983 | 0.398178 | ||||||||
\(909\) | −11.3543 | −0.376598 | ||||||||
\(910\) | −5.84678 | −0.193819 | ||||||||
\(911\) | −17.8206 | −0.590421 | −0.295211 | − | 0.955432i | \(-0.595390\pi\) | ||||
−0.295211 | + | 0.955432i | \(0.595390\pi\) | |||||||
\(912\) | −2.52734 | −0.0836887 | ||||||||
\(913\) | 34.5027 | 1.14187 | ||||||||
\(914\) | 28.0984 | 0.929412 | ||||||||
\(915\) | 34.3770 | 1.13647 | ||||||||
\(916\) | −28.6718 | −0.947344 | ||||||||
\(917\) | 5.06217 | 0.167168 | ||||||||
\(918\) | −2.60294 | −0.0859097 | ||||||||
\(919\) | −31.9855 | −1.05510 | −0.527551 | − | 0.849523i | \(-0.676890\pi\) | ||||
−0.527551 | + | 0.849523i | \(0.676890\pi\) | |||||||
\(920\) | 8.19434 | 0.270160 | ||||||||
\(921\) | −38.6075 | −1.27216 | ||||||||
\(922\) | 7.28760 | 0.240004 | ||||||||
\(923\) | −5.02771 | −0.165489 | ||||||||
\(924\) | 21.1238 | 0.694923 | ||||||||
\(925\) | −0.100260 | −0.00329652 | ||||||||
\(926\) | −24.3859 | −0.801370 | ||||||||
\(927\) | 16.9320 | 0.556120 | ||||||||
\(928\) | −3.05692 | −0.100348 | ||||||||
\(929\) | 0.249465 | 0.00818468 | 0.00409234 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409234 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(930\) | 29.3123 | 0.961188 | ||||||||
\(931\) | 2.22363 | 0.0728766 | ||||||||
\(932\) | 25.9732 | 0.850780 | ||||||||
\(933\) | 24.2178 | 0.792854 | ||||||||
\(934\) | −29.9631 | −0.980422 | ||||||||
\(935\) | 7.12858 | 0.233130 | ||||||||
\(936\) | −1.42215 | −0.0464845 | ||||||||
\(937\) | −36.1938 | −1.18240 | −0.591201 | − | 0.806525i | \(-0.701346\pi\) | ||||
−0.591201 | + | 0.806525i | \(0.701346\pi\) | |||||||
\(938\) | −6.83043 | −0.223022 | ||||||||
\(939\) | 48.1401 | 1.57099 | ||||||||
\(940\) | −21.4558 | −0.699811 | ||||||||
\(941\) | −37.3473 | −1.21749 | −0.608743 | − | 0.793367i | \(-0.708326\pi\) | ||||
−0.608743 | + | 0.793367i | \(0.708326\pi\) | |||||||
\(942\) | −18.6347 | −0.607151 | ||||||||
\(943\) | 7.86464 | 0.256108 | ||||||||
\(944\) | −13.0104 | −0.423453 | ||||||||
\(945\) | 19.6844 | 0.640333 | ||||||||
\(946\) | 11.7225 | 0.381130 | ||||||||
\(947\) | −17.7454 | −0.576649 | −0.288324 | − | 0.957533i | \(-0.593098\pi\) | ||||
−0.288324 | + | 0.957533i | \(0.593098\pi\) | |||||||
\(948\) | 6.10894 | 0.198409 | ||||||||
\(949\) | −2.83990 | −0.0921872 | ||||||||
\(950\) | 0.626276 | 0.0203191 | ||||||||
\(951\) | 17.7899 | 0.576877 | ||||||||
\(952\) | 2.77232 | 0.0898513 | ||||||||
\(953\) | 51.6298 | 1.67245 | 0.836226 | − | 0.548385i | \(-0.184757\pi\) | ||||
0.836226 | + | 0.548385i | \(0.184757\pi\) | |||||||
\(954\) | 10.3674 | 0.335659 | ||||||||
\(955\) | 46.1123 | 1.49216 | ||||||||
\(956\) | −7.37644 | −0.238571 | ||||||||
\(957\) | 21.6341 | 0.699331 | ||||||||
\(958\) | 14.9194 | 0.482025 | ||||||||
\(959\) | 49.6648 | 1.60376 | ||||||||
\(960\) | 5.10629 | 0.164805 | ||||||||
\(961\) | 1.95248 | 0.0629834 | ||||||||
\(962\) | 0.155209 | 0.00500415 | ||||||||
\(963\) | 7.70118 | 0.248167 | ||||||||
\(964\) | 3.64527 | 0.117406 | ||||||||
\(965\) | −64.3925 | −2.07287 | ||||||||
\(966\) | −22.5532 | −0.725637 | ||||||||
\(967\) | −27.0761 | −0.870708 | −0.435354 | − | 0.900259i | \(-0.643377\pi\) | ||||
−0.435354 | + | 0.900259i | \(0.643377\pi\) | |||||||
\(968\) | −0.362804 | −0.0116610 | ||||||||
\(969\) | 2.34741 | 0.0754097 | ||||||||
\(970\) | 13.1664 | 0.422746 | ||||||||
\(971\) | −32.7197 | −1.05003 | −0.525013 | − | 0.851094i | \(-0.675940\pi\) | ||||
−0.525013 | + | 0.851094i | \(0.675940\pi\) | |||||||
\(972\) | 15.9097 | 0.510305 | ||||||||
\(973\) | 66.4480 | 2.13022 | ||||||||
\(974\) | 22.0249 | 0.705724 | ||||||||
\(975\) | 0.971218 | 0.0311039 | ||||||||
\(976\) | 6.73229 | 0.215495 | ||||||||
\(977\) | −53.1152 | −1.69931 | −0.849653 | − | 0.527342i | \(-0.823189\pi\) | ||||
−0.849653 | + | 0.527342i | \(0.823189\pi\) | |||||||
\(978\) | 26.4838 | 0.846858 | ||||||||
\(979\) | 58.2432 | 1.86146 | ||||||||
\(980\) | −4.49267 | −0.143513 | ||||||||
\(981\) | −5.00512 | −0.159801 | ||||||||
\(982\) | −18.9968 | −0.606212 | ||||||||
\(983\) | 16.0977 | 0.513438 | 0.256719 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256719 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(984\) | 4.90084 | 0.156233 | ||||||||
\(985\) | 11.5985 | 0.369560 | ||||||||
\(986\) | 2.83928 | 0.0904212 | ||||||||
\(987\) | 59.0526 | 1.87966 | ||||||||
\(988\) | −0.969522 | −0.0308446 | ||||||||
\(989\) | −12.5157 | −0.397975 | ||||||||
\(990\) | −13.1127 | −0.416748 | ||||||||
\(991\) | 35.2799 | 1.12070 | 0.560352 | − | 0.828255i | \(-0.310666\pi\) | ||||
0.560352 | + | 0.828255i | \(0.310666\pi\) | |||||||
\(992\) | 5.74043 | 0.182259 | ||||||||
\(993\) | 71.1578 | 2.25812 | ||||||||
\(994\) | −18.0283 | −0.571823 | ||||||||
\(995\) | 10.5087 | 0.333148 | ||||||||
\(996\) | −22.9551 | −0.727362 | ||||||||
\(997\) | 36.7985 | 1.16542 | 0.582711 | − | 0.812680i | \(-0.301992\pi\) | ||||
0.582711 | + | 0.812680i | \(0.301992\pi\) | |||||||
\(998\) | −14.1049 | −0.446483 | ||||||||
\(999\) | −0.522544 | −0.0165326 |
(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 | 8006.2.a.a.1.14 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.a.1.14 | ✓ | 69 | 1.1 | even | 1 | trivial |