Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0300168158\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16689 | −1.53223 | −0.766113 | − | 0.642706i | \(-0.777812\pi\) | ||||
−0.766113 | + | 0.642706i | \(0.777812\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.69543 | 1.34772 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.16689 | 0.884631 | ||||||||
\(7\) | 0.00504296 | 0.00190606 | 0.000953030 | − | 1.00000i | \(-0.499697\pi\) | ||||
0.000953030 | 1.00000i | \(0.499697\pi\) | ||||||||
\(8\) | −1.50693 | −0.532779 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.16689 | 0.685232 | ||||||||
\(11\) | 1.76259 | 0.531440 | 0.265720 | − | 0.964050i | \(-0.414390\pi\) | ||||
0.265720 | + | 0.964050i | \(0.414390\pi\) | |||||||
\(12\) | −2.69543 | −0.778104 | ||||||||
\(13\) | 3.82887 | 1.06194 | 0.530969 | − | 0.847392i | \(-0.321828\pi\) | ||||
0.530969 | + | 0.847392i | \(0.321828\pi\) | |||||||
\(14\) | −0.0109276 | −0.00292051 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.12551 | −0.531378 | ||||||||
\(17\) | 4.15472 | 1.00767 | 0.503834 | − | 0.863801i | \(-0.331922\pi\) | ||||
0.503834 | + | 0.863801i | \(0.331922\pi\) | |||||||
\(18\) | −2.16689 | −0.510742 | ||||||||
\(19\) | 0.970934 | 0.222747 | 0.111374 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111374 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(20\) | −2.69543 | −0.602717 | ||||||||
\(21\) | −0.00504296 | −0.00110046 | ||||||||
\(22\) | −3.81934 | −0.814286 | ||||||||
\(23\) | −2.02549 | −0.422344 | −0.211172 | − | 0.977449i | \(-0.567728\pi\) | ||||
−0.211172 | + | 0.977449i | \(0.567728\pi\) | |||||||
\(24\) | 1.50693 | 0.307600 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.29675 | −1.62713 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.0135929 | 0.00256883 | ||||||||
\(29\) | 7.57134 | 1.40596 | 0.702981 | − | 0.711209i | \(-0.251852\pi\) | ||||
0.702981 | + | 0.711209i | \(0.251852\pi\) | |||||||
\(30\) | −2.16689 | −0.395619 | ||||||||
\(31\) | −2.56990 | −0.461568 | −0.230784 | − | 0.973005i | \(-0.574129\pi\) | ||||
−0.230784 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(32\) | 7.61961 | 1.34697 | ||||||||
\(33\) | −1.76259 | −0.306827 | ||||||||
\(34\) | −9.00284 | −1.54397 | ||||||||
\(35\) | −0.00504296 | −0.000852416 0 | ||||||||
\(36\) | 2.69543 | 0.449239 | ||||||||
\(37\) | −2.34651 | −0.385764 | −0.192882 | − | 0.981222i | \(-0.561784\pi\) | ||||
−0.192882 | + | 0.981222i | \(0.561784\pi\) | |||||||
\(38\) | −2.10391 | −0.341299 | ||||||||
\(39\) | −3.82887 | −0.613110 | ||||||||
\(40\) | 1.50693 | 0.238266 | ||||||||
\(41\) | 8.18663 | 1.27854 | 0.639269 | − | 0.768984i | \(-0.279237\pi\) | ||||
0.639269 | + | 0.768984i | \(0.279237\pi\) | |||||||
\(42\) | 0.0109276 | 0.00168616 | ||||||||
\(43\) | 10.0295 | 1.52948 | 0.764739 | − | 0.644340i | \(-0.222868\pi\) | ||||
0.764739 | + | 0.644340i | \(0.222868\pi\) | |||||||
\(44\) | 4.75093 | 0.716230 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 4.38903 | 0.647126 | ||||||||
\(47\) | 3.69280 | 0.538650 | 0.269325 | − | 0.963049i | \(-0.413199\pi\) | ||||
0.269325 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(48\) | 2.12551 | 0.306791 | ||||||||
\(49\) | −6.99997 | −0.999996 | ||||||||
\(50\) | −2.16689 | −0.306445 | ||||||||
\(51\) | −4.15472 | −0.581777 | ||||||||
\(52\) | 10.3205 | 1.43119 | ||||||||
\(53\) | 11.0767 | 1.52150 | 0.760750 | − | 0.649045i | \(-0.224831\pi\) | ||||
0.760750 | + | 0.649045i | \(0.224831\pi\) | |||||||
\(54\) | 2.16689 | 0.294877 | ||||||||
\(55\) | −1.76259 | −0.237667 | ||||||||
\(56\) | −0.00759937 | −0.00101551 | ||||||||
\(57\) | −0.970934 | −0.128603 | ||||||||
\(58\) | −16.4063 | −2.15425 | ||||||||
\(59\) | 3.40656 | 0.443497 | 0.221748 | − | 0.975104i | \(-0.428824\pi\) | ||||
0.221748 | + | 0.975104i | \(0.428824\pi\) | |||||||
\(60\) | 2.69543 | 0.347979 | ||||||||
\(61\) | 2.14095 | 0.274120 | 0.137060 | − | 0.990563i | \(-0.456235\pi\) | ||||
0.137060 | + | 0.990563i | \(0.456235\pi\) | |||||||
\(62\) | 5.56870 | 0.707226 | ||||||||
\(63\) | 0.00504296 | 0.000635353 0 | ||||||||
\(64\) | −12.2599 | −1.53248 | ||||||||
\(65\) | −3.82887 | −0.474913 | ||||||||
\(66\) | 3.81934 | 0.470128 | ||||||||
\(67\) | 15.4956 | 1.89309 | 0.946545 | − | 0.322570i | \(-0.104547\pi\) | ||||
0.946545 | + | 0.322570i | \(0.104547\pi\) | |||||||
\(68\) | 11.1988 | 1.35805 | ||||||||
\(69\) | 2.02549 | 0.243840 | ||||||||
\(70\) | 0.0109276 | 0.00130609 | ||||||||
\(71\) | 6.55114 | 0.777477 | 0.388738 | − | 0.921348i | \(-0.372911\pi\) | ||||
0.388738 | + | 0.921348i | \(0.372911\pi\) | |||||||
\(72\) | −1.50693 | −0.177593 | ||||||||
\(73\) | −2.90544 | −0.340056 | −0.170028 | − | 0.985439i | \(-0.554386\pi\) | ||||
−0.170028 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(74\) | 5.08465 | 0.591078 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.61709 | 0.300200 | ||||||||
\(77\) | 0.00888865 | 0.00101296 | ||||||||
\(78\) | 8.29675 | 0.939422 | ||||||||
\(79\) | −16.7124 | −1.88029 | −0.940145 | − | 0.340776i | \(-0.889310\pi\) | ||||
−0.940145 | + | 0.340776i | \(0.889310\pi\) | |||||||
\(80\) | 2.12551 | 0.237639 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.7396 | −1.95901 | ||||||||
\(83\) | 10.7751 | 1.18272 | 0.591361 | − | 0.806407i | \(-0.298591\pi\) | ||||
0.591361 | + | 0.806407i | \(0.298591\pi\) | |||||||
\(84\) | −0.0135929 | −0.00148311 | ||||||||
\(85\) | −4.15472 | −0.450643 | ||||||||
\(86\) | −21.7328 | −2.34351 | ||||||||
\(87\) | −7.57134 | −0.811733 | ||||||||
\(88\) | −2.65609 | −0.283140 | ||||||||
\(89\) | −10.0083 | −1.06087 | −0.530437 | − | 0.847725i | \(-0.677972\pi\) | ||||
−0.530437 | + | 0.847725i | \(0.677972\pi\) | |||||||
\(90\) | 2.16689 | 0.228411 | ||||||||
\(91\) | 0.0193088 | 0.00202411 | ||||||||
\(92\) | −5.45957 | −0.569200 | ||||||||
\(93\) | 2.56990 | 0.266486 | ||||||||
\(94\) | −8.00190 | −0.825333 | ||||||||
\(95\) | −0.970934 | −0.0996157 | ||||||||
\(96\) | −7.61961 | −0.777674 | ||||||||
\(97\) | 8.39573 | 0.852457 | 0.426229 | − | 0.904615i | \(-0.359842\pi\) | ||||
0.426229 | + | 0.904615i | \(0.359842\pi\) | |||||||
\(98\) | 15.1682 | 1.53222 | ||||||||
\(99\) | 1.76259 | 0.177147 | ||||||||
\(100\) | 2.69543 | 0.269543 | ||||||||
\(101\) | 0.662610 | 0.0659321 | 0.0329661 | − | 0.999456i | \(-0.489505\pi\) | ||||
0.0329661 | + | 0.999456i | \(0.489505\pi\) | |||||||
\(102\) | 9.00284 | 0.891414 | ||||||||
\(103\) | −8.12507 | −0.800587 | −0.400293 | − | 0.916387i | \(-0.631092\pi\) | ||||
−0.400293 | + | 0.916387i | \(0.631092\pi\) | |||||||
\(104\) | −5.76983 | −0.565778 | ||||||||
\(105\) | 0.00504296 | 0.000492142 0 | ||||||||
\(106\) | −24.0020 | −2.33128 | ||||||||
\(107\) | −11.8467 | −1.14527 | −0.572633 | − | 0.819812i | \(-0.694078\pi\) | ||||
−0.572633 | + | 0.819812i | \(0.694078\pi\) | |||||||
\(108\) | −2.69543 | −0.259368 | ||||||||
\(109\) | 10.1499 | 0.972188 | 0.486094 | − | 0.873906i | \(-0.338421\pi\) | ||||
0.486094 | + | 0.873906i | \(0.338421\pi\) | |||||||
\(110\) | 3.81934 | 0.364160 | ||||||||
\(111\) | 2.34651 | 0.222721 | ||||||||
\(112\) | −0.0107189 | −0.00101284 | ||||||||
\(113\) | 1.13141 | 0.106434 | 0.0532172 | − | 0.998583i | \(-0.483052\pi\) | ||||
0.0532172 | + | 0.998583i | \(0.483052\pi\) | |||||||
\(114\) | 2.10391 | 0.197049 | ||||||||
\(115\) | 2.02549 | 0.188878 | ||||||||
\(116\) | 20.4080 | 1.89484 | ||||||||
\(117\) | 3.82887 | 0.353979 | ||||||||
\(118\) | −7.38166 | −0.679537 | ||||||||
\(119\) | 0.0209521 | 0.00192067 | ||||||||
\(120\) | −1.50693 | −0.137563 | ||||||||
\(121\) | −7.89329 | −0.717571 | ||||||||
\(122\) | −4.63921 | −0.420014 | ||||||||
\(123\) | −8.18663 | −0.738164 | ||||||||
\(124\) | −6.92699 | −0.622062 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.0109276 | −0.000973504 0 | ||||||||
\(127\) | −6.34172 | −0.562737 | −0.281369 | − | 0.959600i | \(-0.590788\pi\) | ||||
−0.281369 | + | 0.959600i | \(0.590788\pi\) | |||||||
\(128\) | 11.3266 | 1.00114 | ||||||||
\(129\) | −10.0295 | −0.883045 | ||||||||
\(130\) | 8.29675 | 0.727673 | ||||||||
\(131\) | 6.08939 | 0.532032 | 0.266016 | − | 0.963969i | \(-0.414293\pi\) | ||||
0.266016 | + | 0.963969i | \(0.414293\pi\) | |||||||
\(132\) | −4.75093 | −0.413516 | ||||||||
\(133\) | 0.00489638 | 0.000424570 0 | ||||||||
\(134\) | −33.5774 | −2.90064 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −6.26086 | −0.536864 | ||||||||
\(137\) | 2.67382 | 0.228440 | 0.114220 | − | 0.993455i | \(-0.463563\pi\) | ||||
0.114220 | + | 0.993455i | \(0.463563\pi\) | |||||||
\(138\) | −4.38903 | −0.373619 | ||||||||
\(139\) | 2.73592 | 0.232058 | 0.116029 | − | 0.993246i | \(-0.462983\pi\) | ||||
0.116029 | + | 0.993246i | \(0.462983\pi\) | |||||||
\(140\) | −0.0135929 | −0.00114881 | ||||||||
\(141\) | −3.69280 | −0.310990 | ||||||||
\(142\) | −14.1956 | −1.19127 | ||||||||
\(143\) | 6.74871 | 0.564356 | ||||||||
\(144\) | −2.12551 | −0.177126 | ||||||||
\(145\) | −7.57134 | −0.628765 | ||||||||
\(146\) | 6.29579 | 0.521043 | ||||||||
\(147\) | 6.99997 | 0.577348 | ||||||||
\(148\) | −6.32487 | −0.519901 | ||||||||
\(149\) | 5.25042 | 0.430131 | 0.215066 | − | 0.976600i | \(-0.431003\pi\) | ||||
0.215066 | + | 0.976600i | \(0.431003\pi\) | |||||||
\(150\) | 2.16689 | 0.176926 | ||||||||
\(151\) | −12.0736 | −0.982535 | −0.491268 | − | 0.871009i | \(-0.663466\pi\) | ||||
−0.491268 | + | 0.871009i | \(0.663466\pi\) | |||||||
\(152\) | −1.46313 | −0.118675 | ||||||||
\(153\) | 4.15472 | 0.335889 | ||||||||
\(154\) | −0.0192608 | −0.00155208 | ||||||||
\(155\) | 2.56990 | 0.206419 | ||||||||
\(156\) | −10.3205 | −0.826298 | ||||||||
\(157\) | 12.0714 | 0.963401 | 0.481701 | − | 0.876336i | \(-0.340019\pi\) | ||||
0.481701 | + | 0.876336i | \(0.340019\pi\) | |||||||
\(158\) | 36.2140 | 2.88103 | ||||||||
\(159\) | −11.0767 | −0.878439 | ||||||||
\(160\) | −7.61961 | −0.602383 | ||||||||
\(161\) | −0.0102145 | −0.000805013 0 | ||||||||
\(162\) | −2.16689 | −0.170247 | ||||||||
\(163\) | 1.17314 | 0.0918878 | 0.0459439 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459439 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(164\) | 22.0665 | 1.72310 | ||||||||
\(165\) | 1.76259 | 0.137217 | ||||||||
\(166\) | −23.3485 | −1.81220 | ||||||||
\(167\) | −14.6844 | −1.13631 | −0.568156 | − | 0.822921i | \(-0.692343\pi\) | ||||
−0.568156 | + | 0.822921i | \(0.692343\pi\) | |||||||
\(168\) | 0.00759937 | 0.000586304 0 | ||||||||
\(169\) | 1.66023 | 0.127710 | ||||||||
\(170\) | 9.00284 | 0.690486 | ||||||||
\(171\) | 0.970934 | 0.0742491 | ||||||||
\(172\) | 27.0337 | 2.06130 | ||||||||
\(173\) | 0.0371186 | 0.00282208 | 0.00141104 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00141104 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(174\) | 16.4063 | 1.24376 | ||||||||
\(175\) | 0.00504296 | 0.000381212 0 | ||||||||
\(176\) | −3.74640 | −0.282395 | ||||||||
\(177\) | −3.40656 | −0.256053 | ||||||||
\(178\) | 21.6868 | 1.62550 | ||||||||
\(179\) | −6.30136 | −0.470986 | −0.235493 | − | 0.971876i | \(-0.575670\pi\) | ||||
−0.235493 | + | 0.971876i | \(0.575670\pi\) | |||||||
\(180\) | −2.69543 | −0.200906 | ||||||||
\(181\) | −3.22464 | −0.239686 | −0.119843 | − | 0.992793i | \(-0.538239\pi\) | ||||
−0.119843 | + | 0.992793i | \(0.538239\pi\) | |||||||
\(182\) | −0.0418402 | −0.00310140 | ||||||||
\(183\) | −2.14095 | −0.158264 | ||||||||
\(184\) | 3.05227 | 0.225016 | ||||||||
\(185\) | 2.34651 | 0.172519 | ||||||||
\(186\) | −5.56870 | −0.408317 | ||||||||
\(187\) | 7.32306 | 0.535515 | ||||||||
\(188\) | 9.95368 | 0.725947 | ||||||||
\(189\) | −0.00504296 | −0.000366821 0 | ||||||||
\(190\) | 2.10391 | 0.152634 | ||||||||
\(191\) | −6.82580 | −0.493898 | −0.246949 | − | 0.969029i | \(-0.579428\pi\) | ||||
−0.246949 | + | 0.969029i | \(0.579428\pi\) | |||||||
\(192\) | 12.2599 | 0.884780 | ||||||||
\(193\) | 9.33805 | 0.672168 | 0.336084 | − | 0.941832i | \(-0.390897\pi\) | ||||
0.336084 | + | 0.941832i | \(0.390897\pi\) | |||||||
\(194\) | −18.1927 | −1.30616 | ||||||||
\(195\) | 3.82887 | 0.274191 | ||||||||
\(196\) | −18.8680 | −1.34771 | ||||||||
\(197\) | −12.3305 | −0.878514 | −0.439257 | − | 0.898362i | \(-0.644758\pi\) | ||||
−0.439257 | + | 0.898362i | \(0.644758\pi\) | |||||||
\(198\) | −3.81934 | −0.271429 | ||||||||
\(199\) | −6.80836 | −0.482632 | −0.241316 | − | 0.970447i | \(-0.577579\pi\) | ||||
−0.241316 | + | 0.970447i | \(0.577579\pi\) | |||||||
\(200\) | −1.50693 | −0.106556 | ||||||||
\(201\) | −15.4956 | −1.09298 | ||||||||
\(202\) | −1.43580 | −0.101023 | ||||||||
\(203\) | 0.0381819 | 0.00267985 | ||||||||
\(204\) | −11.1988 | −0.784070 | ||||||||
\(205\) | −8.18663 | −0.571779 | ||||||||
\(206\) | 17.6062 | 1.22668 | ||||||||
\(207\) | −2.02549 | −0.140781 | ||||||||
\(208\) | −8.13830 | −0.564290 | ||||||||
\(209\) | 1.71136 | 0.118377 | ||||||||
\(210\) | −0.0109276 | −0.000754073 0 | ||||||||
\(211\) | −14.4508 | −0.994835 | −0.497418 | − | 0.867511i | \(-0.665718\pi\) | ||||
−0.497418 | + | 0.867511i | \(0.665718\pi\) | |||||||
\(212\) | 29.8565 | 2.05055 | ||||||||
\(213\) | −6.55114 | −0.448877 | ||||||||
\(214\) | 25.6706 | 1.75481 | ||||||||
\(215\) | −10.0295 | −0.684004 | ||||||||
\(216\) | 1.50693 | 0.102533 | ||||||||
\(217\) | −0.0129599 | −0.000879775 0 | ||||||||
\(218\) | −21.9939 | −1.48961 | ||||||||
\(219\) | 2.90544 | 0.196332 | ||||||||
\(220\) | −4.75093 | −0.320308 | ||||||||
\(221\) | 15.9079 | 1.07008 | ||||||||
\(222\) | −5.08465 | −0.341259 | ||||||||
\(223\) | −4.76381 | −0.319008 | −0.159504 | − | 0.987197i | \(-0.550990\pi\) | ||||
−0.159504 | + | 0.987197i | \(0.550990\pi\) | |||||||
\(224\) | 0.0384254 | 0.00256740 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.45165 | −0.163082 | ||||||||
\(227\) | −4.42996 | −0.294027 | −0.147014 | − | 0.989134i | \(-0.546966\pi\) | ||||
−0.147014 | + | 0.989134i | \(0.546966\pi\) | |||||||
\(228\) | −2.61709 | −0.173321 | ||||||||
\(229\) | −5.80113 | −0.383349 | −0.191675 | − | 0.981459i | \(-0.561392\pi\) | ||||
−0.191675 | + | 0.981459i | \(0.561392\pi\) | |||||||
\(230\) | −4.38903 | −0.289404 | ||||||||
\(231\) | −0.00888865 | −0.000584830 0 | ||||||||
\(232\) | −11.4095 | −0.749067 | ||||||||
\(233\) | 18.4705 | 1.21004 | 0.605020 | − | 0.796210i | \(-0.293165\pi\) | ||||
0.605020 | + | 0.796210i | \(0.293165\pi\) | |||||||
\(234\) | −8.29675 | −0.542376 | ||||||||
\(235\) | −3.69280 | −0.240891 | ||||||||
\(236\) | 9.18216 | 0.597707 | ||||||||
\(237\) | 16.7124 | 1.08559 | ||||||||
\(238\) | −0.0454009 | −0.00294291 | ||||||||
\(239\) | 9.36356 | 0.605678 | 0.302839 | − | 0.953042i | \(-0.402066\pi\) | ||||
0.302839 | + | 0.953042i | \(0.402066\pi\) | |||||||
\(240\) | −2.12551 | −0.137201 | ||||||||
\(241\) | −5.55603 | −0.357895 | −0.178948 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178948 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(242\) | 17.1039 | 1.09948 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.77078 | 0.369436 | ||||||||
\(245\) | 6.99997 | 0.447212 | ||||||||
\(246\) | 17.7396 | 1.13103 | ||||||||
\(247\) | 3.71758 | 0.236544 | ||||||||
\(248\) | 3.87265 | 0.245914 | ||||||||
\(249\) | −10.7751 | −0.682845 | ||||||||
\(250\) | 2.16689 | 0.137046 | ||||||||
\(251\) | 2.48181 | 0.156650 | 0.0783252 | − | 0.996928i | \(-0.475043\pi\) | ||||
0.0783252 | + | 0.996928i | \(0.475043\pi\) | |||||||
\(252\) | 0.0135929 | 0.000856275 0 | ||||||||
\(253\) | −3.57010 | −0.224451 | ||||||||
\(254\) | 13.7418 | 0.862240 | ||||||||
\(255\) | 4.15472 | 0.260179 | ||||||||
\(256\) | −0.0238591 | −0.00149119 | ||||||||
\(257\) | 17.5860 | 1.09698 | 0.548491 | − | 0.836157i | \(-0.315203\pi\) | ||||
0.548491 | + | 0.836157i | \(0.315203\pi\) | |||||||
\(258\) | 21.7328 | 1.35302 | ||||||||
\(259\) | −0.0118334 | −0.000735290 0 | ||||||||
\(260\) | −10.3205 | −0.640047 | ||||||||
\(261\) | 7.57134 | 0.468654 | ||||||||
\(262\) | −13.1951 | −0.815194 | ||||||||
\(263\) | −13.2922 | −0.819633 | −0.409816 | − | 0.912168i | \(-0.634407\pi\) | ||||
−0.409816 | + | 0.912168i | \(0.634407\pi\) | |||||||
\(264\) | 2.65609 | 0.163471 | ||||||||
\(265\) | −11.0767 | −0.680436 | ||||||||
\(266\) | −0.0106099 | −0.000650537 0 | ||||||||
\(267\) | 10.0083 | 0.612495 | ||||||||
\(268\) | 41.7674 | 2.55135 | ||||||||
\(269\) | 15.1862 | 0.925921 | 0.462960 | − | 0.886379i | \(-0.346787\pi\) | ||||
0.462960 | + | 0.886379i | \(0.346787\pi\) | |||||||
\(270\) | −2.16689 | −0.131873 | ||||||||
\(271\) | 0.0501761 | 0.00304798 | 0.00152399 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152399 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(272\) | −8.83091 | −0.535452 | ||||||||
\(273\) | −0.0193088 | −0.00116862 | ||||||||
\(274\) | −5.79388 | −0.350021 | ||||||||
\(275\) | 1.76259 | 0.106288 | ||||||||
\(276\) | 5.45957 | 0.328628 | ||||||||
\(277\) | −6.76742 | −0.406615 | −0.203307 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203307 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(278\) | −5.92846 | −0.355565 | ||||||||
\(279\) | −2.56990 | −0.153856 | ||||||||
\(280\) | 0.00759937 | 0.000454149 0 | ||||||||
\(281\) | 0.611028 | 0.0364509 | 0.0182254 | − | 0.999834i | \(-0.494198\pi\) | ||||
0.0182254 | + | 0.999834i | \(0.494198\pi\) | |||||||
\(282\) | 8.00190 | 0.476506 | ||||||||
\(283\) | 0.373208 | 0.0221849 | 0.0110925 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110925 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(284\) | 17.6581 | 1.04782 | ||||||||
\(285\) | 0.970934 | 0.0575131 | ||||||||
\(286\) | −14.6238 | −0.864721 | ||||||||
\(287\) | 0.0412848 | 0.00243697 | ||||||||
\(288\) | 7.61961 | 0.448990 | ||||||||
\(289\) | 0.261700 | 0.0153941 | ||||||||
\(290\) | 16.4063 | 0.963411 | ||||||||
\(291\) | −8.39573 | −0.492166 | ||||||||
\(292\) | −7.83142 | −0.458299 | ||||||||
\(293\) | 4.10295 | 0.239697 | 0.119849 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119849 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(294\) | −15.1682 | −0.884628 | ||||||||
\(295\) | −3.40656 | −0.198338 | ||||||||
\(296\) | 3.53602 | 0.205527 | ||||||||
\(297\) | −1.76259 | −0.102276 | ||||||||
\(298\) | −11.3771 | −0.659058 | ||||||||
\(299\) | −7.75534 | −0.448503 | ||||||||
\(300\) | −2.69543 | −0.155621 | ||||||||
\(301\) | 0.0505782 | 0.00291528 | ||||||||
\(302\) | 26.1622 | 1.50547 | ||||||||
\(303\) | −0.662610 | −0.0380659 | ||||||||
\(304\) | −2.06373 | −0.118363 | ||||||||
\(305\) | −2.14095 | −0.122590 | ||||||||
\(306\) | −9.00284 | −0.514658 | ||||||||
\(307\) | −14.6558 | −0.836452 | −0.418226 | − | 0.908343i | \(-0.637348\pi\) | ||||
−0.418226 | + | 0.908343i | \(0.637348\pi\) | |||||||
\(308\) | 0.0239588 | 0.00136518 | ||||||||
\(309\) | 8.12507 | 0.462219 | ||||||||
\(310\) | −5.56870 | −0.316281 | ||||||||
\(311\) | −25.1912 | −1.42846 | −0.714232 | − | 0.699909i | \(-0.753224\pi\) | ||||
−0.714232 | + | 0.699909i | \(0.753224\pi\) | |||||||
\(312\) | 5.76983 | 0.326652 | ||||||||
\(313\) | 7.25873 | 0.410288 | 0.205144 | − | 0.978732i | \(-0.434234\pi\) | ||||
0.205144 | + | 0.978732i | \(0.434234\pi\) | |||||||
\(314\) | −26.1574 | −1.47615 | ||||||||
\(315\) | −0.00504296 | −0.000284139 0 | ||||||||
\(316\) | −45.0471 | −2.53410 | ||||||||
\(317\) | −18.5700 | −1.04299 | −0.521497 | − | 0.853253i | \(-0.674626\pi\) | ||||
−0.521497 | + | 0.853253i | \(0.674626\pi\) | |||||||
\(318\) | 24.0020 | 1.34597 | ||||||||
\(319\) | 13.3451 | 0.747185 | ||||||||
\(320\) | 12.2599 | 0.685348 | ||||||||
\(321\) | 11.8467 | 0.661219 | ||||||||
\(322\) | 0.0221337 | 0.00123346 | ||||||||
\(323\) | 4.03396 | 0.224455 | ||||||||
\(324\) | 2.69543 | 0.149746 | ||||||||
\(325\) | 3.82887 | 0.212387 | ||||||||
\(326\) | −2.54208 | −0.140793 | ||||||||
\(327\) | −10.1499 | −0.561293 | ||||||||
\(328\) | −12.3367 | −0.681178 | ||||||||
\(329\) | 0.0186226 | 0.00102670 | ||||||||
\(330\) | −3.81934 | −0.210248 | ||||||||
\(331\) | −19.8133 | −1.08904 | −0.544519 | − | 0.838749i | \(-0.683288\pi\) | ||||
−0.544519 | + | 0.838749i | \(0.683288\pi\) | |||||||
\(332\) | 29.0436 | 1.59397 | ||||||||
\(333\) | −2.34651 | −0.128588 | ||||||||
\(334\) | 31.8195 | 1.74109 | ||||||||
\(335\) | −15.4956 | −0.846616 | ||||||||
\(336\) | 0.0107189 | 0.000584762 0 | ||||||||
\(337\) | 6.66980 | 0.363327 | 0.181664 | − | 0.983361i | \(-0.441852\pi\) | ||||
0.181664 | + | 0.983361i | \(0.441852\pi\) | |||||||
\(338\) | −3.59755 | −0.195681 | ||||||||
\(339\) | −1.13141 | −0.0614499 | ||||||||
\(340\) | −11.1988 | −0.607338 | ||||||||
\(341\) | −4.52967 | −0.245296 | ||||||||
\(342\) | −2.10391 | −0.113766 | ||||||||
\(343\) | −0.0706013 | −0.00381211 | ||||||||
\(344\) | −15.1137 | −0.814874 | ||||||||
\(345\) | −2.02549 | −0.109049 | ||||||||
\(346\) | −0.0804321 | −0.00432406 | ||||||||
\(347\) | 26.4112 | 1.41783 | 0.708915 | − | 0.705294i | \(-0.249185\pi\) | ||||
0.708915 | + | 0.705294i | \(0.249185\pi\) | |||||||
\(348\) | −20.4080 | −1.09398 | ||||||||
\(349\) | −16.5407 | −0.885405 | −0.442702 | − | 0.896669i | \(-0.645980\pi\) | ||||
−0.442702 | + | 0.896669i | \(0.645980\pi\) | |||||||
\(350\) | −0.0109276 | −0.000584103 0 | ||||||||
\(351\) | −3.82887 | −0.204370 | ||||||||
\(352\) | 13.4302 | 0.715834 | ||||||||
\(353\) | −12.4234 | −0.661231 | −0.330615 | − | 0.943766i | \(-0.607256\pi\) | ||||
−0.330615 | + | 0.943766i | \(0.607256\pi\) | |||||||
\(354\) | 7.38166 | 0.392331 | ||||||||
\(355\) | −6.55114 | −0.347698 | ||||||||
\(356\) | −26.9766 | −1.42976 | ||||||||
\(357\) | −0.0209521 | −0.00110890 | ||||||||
\(358\) | 13.6544 | 0.721657 | ||||||||
\(359\) | 22.1737 | 1.17028 | 0.585141 | − | 0.810932i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810932i | \(0.301039\pi\) | |||||||
\(360\) | 1.50693 | 0.0794220 | ||||||||
\(361\) | −18.0573 | −0.950384 | ||||||||
\(362\) | 6.98745 | 0.367252 | ||||||||
\(363\) | 7.89329 | 0.414290 | ||||||||
\(364\) | 0.0520456 | 0.00272793 | ||||||||
\(365\) | 2.90544 | 0.152078 | ||||||||
\(366\) | 4.63921 | 0.242495 | ||||||||
\(367\) | 5.21685 | 0.272317 | 0.136159 | − | 0.990687i | \(-0.456524\pi\) | ||||
0.136159 | + | 0.990687i | \(0.456524\pi\) | |||||||
\(368\) | 4.30520 | 0.224424 | ||||||||
\(369\) | 8.18663 | 0.426179 | ||||||||
\(370\) | −5.08465 | −0.264338 | ||||||||
\(371\) | 0.0558593 | 0.00290007 | ||||||||
\(372\) | 6.92699 | 0.359148 | ||||||||
\(373\) | 21.8700 | 1.13238 | 0.566192 | − | 0.824274i | \(-0.308416\pi\) | ||||
0.566192 | + | 0.824274i | \(0.308416\pi\) | |||||||
\(374\) | −15.8683 | −0.820530 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −5.56478 | −0.286981 | ||||||||
\(377\) | 28.9897 | 1.49304 | ||||||||
\(378\) | 0.0109276 | 0.000562053 0 | ||||||||
\(379\) | 9.16916 | 0.470988 | 0.235494 | − | 0.971876i | \(-0.424329\pi\) | ||||
0.235494 | + | 0.971876i | \(0.424329\pi\) | |||||||
\(380\) | −2.61709 | −0.134254 | ||||||||
\(381\) | 6.34172 | 0.324896 | ||||||||
\(382\) | 14.7908 | 0.756763 | ||||||||
\(383\) | −0.0369414 | −0.00188762 | −0.000943809 | − | 1.00000i | \(-0.500300\pi\) | ||||
−0.000943809 | 1.00000i | \(0.500300\pi\) | ||||||||
\(384\) | −11.3266 | −0.578010 | ||||||||
\(385\) | −0.00888865 | −0.000453008 0 | ||||||||
\(386\) | −20.2346 | −1.02991 | ||||||||
\(387\) | 10.0295 | 0.509826 | ||||||||
\(388\) | 22.6301 | 1.14887 | ||||||||
\(389\) | −22.3190 | −1.13162 | −0.565809 | − | 0.824536i | \(-0.691436\pi\) | ||||
−0.565809 | + | 0.824536i | \(0.691436\pi\) | |||||||
\(390\) | −8.29675 | −0.420122 | ||||||||
\(391\) | −8.41535 | −0.425582 | ||||||||
\(392\) | 10.5485 | 0.532777 | ||||||||
\(393\) | −6.08939 | −0.307169 | ||||||||
\(394\) | 26.7190 | 1.34608 | ||||||||
\(395\) | 16.7124 | 0.840891 | ||||||||
\(396\) | 4.75093 | 0.238743 | ||||||||
\(397\) | 7.32213 | 0.367487 | 0.183743 | − | 0.982974i | \(-0.441178\pi\) | ||||
0.183743 | + | 0.982974i | \(0.441178\pi\) | |||||||
\(398\) | 14.7530 | 0.739501 | ||||||||
\(399\) | −0.00489638 | −0.000245125 0 | ||||||||
\(400\) | −2.12551 | −0.106276 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 33.5774 | 1.67469 | ||||||||
\(403\) | −9.83981 | −0.490156 | ||||||||
\(404\) | 1.78602 | 0.0888577 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −0.0827362 | −0.00410613 | ||||||||
\(407\) | −4.13593 | −0.205011 | ||||||||
\(408\) | 6.26086 | 0.309959 | ||||||||
\(409\) | −15.2133 | −0.752250 | −0.376125 | − | 0.926569i | \(-0.622744\pi\) | ||||
−0.376125 | + | 0.926569i | \(0.622744\pi\) | |||||||
\(410\) | 17.7396 | 0.876095 | ||||||||
\(411\) | −2.67382 | −0.131890 | ||||||||
\(412\) | −21.9006 | −1.07896 | ||||||||
\(413\) | 0.0171792 | 0.000845331 0 | ||||||||
\(414\) | 4.38903 | 0.215709 | ||||||||
\(415\) | −10.7751 | −0.528929 | ||||||||
\(416\) | 29.1745 | 1.43040 | ||||||||
\(417\) | −2.73592 | −0.133979 | ||||||||
\(418\) | −3.70833 | −0.181380 | ||||||||
\(419\) | −18.7772 | −0.917326 | −0.458663 | − | 0.888610i | \(-0.651671\pi\) | ||||
−0.458663 | + | 0.888610i | \(0.651671\pi\) | |||||||
\(420\) | 0.0135929 | 0.000663268 0 | ||||||||
\(421\) | 20.4730 | 0.997791 | 0.498895 | − | 0.866662i | \(-0.333739\pi\) | ||||
0.498895 | + | 0.866662i | \(0.333739\pi\) | |||||||
\(422\) | 31.3134 | 1.52431 | ||||||||
\(423\) | 3.69280 | 0.179550 | ||||||||
\(424\) | −16.6918 | −0.810624 | ||||||||
\(425\) | 4.15472 | 0.201534 | ||||||||
\(426\) | 14.1956 | 0.687780 | ||||||||
\(427\) | 0.0107967 | 0.000522490 0 | ||||||||
\(428\) | −31.9320 | −1.54349 | ||||||||
\(429\) | −6.74871 | −0.325831 | ||||||||
\(430\) | 21.7328 | 1.04805 | ||||||||
\(431\) | −8.80104 | −0.423931 | −0.211966 | − | 0.977277i | \(-0.567987\pi\) | ||||
−0.211966 | + | 0.977277i | \(0.567987\pi\) | |||||||
\(432\) | 2.12551 | 0.102264 | ||||||||
\(433\) | 21.6902 | 1.04236 | 0.521182 | − | 0.853446i | \(-0.325491\pi\) | ||||
0.521182 | + | 0.853446i | \(0.325491\pi\) | |||||||
\(434\) | 0.0280827 | 0.00134801 | ||||||||
\(435\) | 7.57134 | 0.363018 | ||||||||
\(436\) | 27.3585 | 1.31023 | ||||||||
\(437\) | −1.96662 | −0.0940761 | ||||||||
\(438\) | −6.29579 | −0.300824 | ||||||||
\(439\) | −8.09050 | −0.386139 | −0.193069 | − | 0.981185i | \(-0.561844\pi\) | ||||
−0.193069 | + | 0.981185i | \(0.561844\pi\) | |||||||
\(440\) | 2.65609 | 0.126624 | ||||||||
\(441\) | −6.99997 | −0.333332 | ||||||||
\(442\) | −34.4707 | −1.63960 | ||||||||
\(443\) | 6.48024 | 0.307886 | 0.153943 | − | 0.988080i | \(-0.450803\pi\) | ||||
0.153943 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(444\) | 6.32487 | 0.300165 | ||||||||
\(445\) | 10.0083 | 0.474437 | ||||||||
\(446\) | 10.3227 | 0.488793 | ||||||||
\(447\) | −5.25042 | −0.248336 | ||||||||
\(448\) | −0.0618260 | −0.00292101 | ||||||||
\(449\) | 40.0075 | 1.88807 | 0.944035 | − | 0.329844i | \(-0.106996\pi\) | ||||
0.944035 | + | 0.329844i | \(0.106996\pi\) | |||||||
\(450\) | −2.16689 | −0.102148 | ||||||||
\(451\) | 14.4297 | 0.679466 | ||||||||
\(452\) | 3.04965 | 0.143443 | ||||||||
\(453\) | 12.0736 | 0.567267 | ||||||||
\(454\) | 9.59927 | 0.450516 | ||||||||
\(455\) | −0.0193088 | −0.000905212 0 | ||||||||
\(456\) | 1.46313 | 0.0685172 | ||||||||
\(457\) | −36.3259 | −1.69925 | −0.849626 | − | 0.527386i | \(-0.823172\pi\) | ||||
−0.849626 | + | 0.527386i | \(0.823172\pi\) | |||||||
\(458\) | 12.5704 | 0.587378 | ||||||||
\(459\) | −4.15472 | −0.193926 | ||||||||
\(460\) | 5.45957 | 0.254554 | ||||||||
\(461\) | 1.80384 | 0.0840132 | 0.0420066 | − | 0.999117i | \(-0.486625\pi\) | ||||
0.0420066 | + | 0.999117i | \(0.486625\pi\) | |||||||
\(462\) | 0.0192608 | 0.000896092 0 | ||||||||
\(463\) | 23.7101 | 1.10190 | 0.550950 | − | 0.834538i | \(-0.314265\pi\) | ||||
0.550950 | + | 0.834538i | \(0.314265\pi\) | |||||||
\(464\) | −16.0930 | −0.747097 | ||||||||
\(465\) | −2.56990 | −0.119176 | ||||||||
\(466\) | −40.0236 | −1.85406 | ||||||||
\(467\) | 3.87922 | 0.179509 | 0.0897545 | − | 0.995964i | \(-0.471392\pi\) | ||||
0.0897545 | + | 0.995964i | \(0.471392\pi\) | |||||||
\(468\) | 10.3205 | 0.477063 | ||||||||
\(469\) | 0.0781438 | 0.00360834 | ||||||||
\(470\) | 8.00190 | 0.369100 | ||||||||
\(471\) | −12.0714 | −0.556220 | ||||||||
\(472\) | −5.13344 | −0.236286 | ||||||||
\(473\) | 17.6778 | 0.812826 | ||||||||
\(474\) | −36.2140 | −1.66336 | ||||||||
\(475\) | 0.970934 | 0.0445495 | ||||||||
\(476\) | 0.0564749 | 0.00258852 | ||||||||
\(477\) | 11.0767 | 0.507167 | ||||||||
\(478\) | −20.2898 | −0.928036 | ||||||||
\(479\) | 8.29971 | 0.379224 | 0.189612 | − | 0.981859i | \(-0.439277\pi\) | ||||
0.189612 | + | 0.981859i | \(0.439277\pi\) | |||||||
\(480\) | 7.61961 | 0.347786 | ||||||||
\(481\) | −8.98449 | −0.409657 | ||||||||
\(482\) | 12.0393 | 0.548377 | ||||||||
\(483\) | 0.0102145 | 0.000464774 0 | ||||||||
\(484\) | −21.2758 | −0.967082 | ||||||||
\(485\) | −8.39573 | −0.381231 | ||||||||
\(486\) | 2.16689 | 0.0982923 | ||||||||
\(487\) | −13.7270 | −0.622028 | −0.311014 | − | 0.950405i | \(-0.600669\pi\) | ||||
−0.311014 | + | 0.950405i | \(0.600669\pi\) | |||||||
\(488\) | −3.22625 | −0.146046 | ||||||||
\(489\) | −1.17314 | −0.0530514 | ||||||||
\(490\) | −15.1682 | −0.685230 | ||||||||
\(491\) | −4.29842 | −0.193985 | −0.0969925 | − | 0.995285i | \(-0.530922\pi\) | ||||
−0.0969925 | + | 0.995285i | \(0.530922\pi\) | |||||||
\(492\) | −22.0665 | −0.994835 | ||||||||
\(493\) | 31.4568 | 1.41674 | ||||||||
\(494\) | −8.05560 | −0.362438 | ||||||||
\(495\) | −1.76259 | −0.0792224 | ||||||||
\(496\) | 5.46235 | 0.245267 | ||||||||
\(497\) | 0.0330371 | 0.00148192 | ||||||||
\(498\) | 23.3485 | 1.04627 | ||||||||
\(499\) | 12.9791 | 0.581024 | 0.290512 | − | 0.956871i | \(-0.406174\pi\) | ||||
0.290512 | + | 0.956871i | \(0.406174\pi\) | |||||||
\(500\) | −2.69543 | −0.120543 | ||||||||
\(501\) | 14.6844 | 0.656050 | ||||||||
\(502\) | −5.37782 | −0.240024 | ||||||||
\(503\) | 40.9671 | 1.82663 | 0.913316 | − | 0.407251i | \(-0.133513\pi\) | ||||
0.913316 | + | 0.407251i | \(0.133513\pi\) | |||||||
\(504\) | −0.00759937 | −0.000338503 0 | ||||||||
\(505\) | −0.662610 | −0.0294857 | ||||||||
\(506\) | 7.73604 | 0.343909 | ||||||||
\(507\) | −1.66023 | −0.0737336 | ||||||||
\(508\) | −17.0937 | −0.758410 | ||||||||
\(509\) | 30.8686 | 1.36823 | 0.684113 | − | 0.729376i | \(-0.260189\pi\) | ||||
0.684113 | + | 0.729376i | \(0.260189\pi\) | |||||||
\(510\) | −9.00284 | −0.398652 | ||||||||
\(511\) | −0.0146520 | −0.000648168 0 | ||||||||
\(512\) | −22.6016 | −0.998857 | ||||||||
\(513\) | −0.970934 | −0.0428678 | ||||||||
\(514\) | −38.1069 | −1.68082 | ||||||||
\(515\) | 8.12507 | 0.358033 | ||||||||
\(516\) | −27.0337 | −1.19009 | ||||||||
\(517\) | 6.50888 | 0.286260 | ||||||||
\(518\) | 0.0256417 | 0.00112663 | ||||||||
\(519\) | −0.0371186 | −0.00162933 | ||||||||
\(520\) | 5.76983 | 0.253024 | ||||||||
\(521\) | −7.91428 | −0.346731 | −0.173365 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173365 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(522\) | −16.4063 | −0.718084 | ||||||||
\(523\) | 0.783187 | 0.0342464 | 0.0171232 | − | 0.999853i | \(-0.494549\pi\) | ||||
0.0171232 | + | 0.999853i | \(0.494549\pi\) | |||||||
\(524\) | 16.4135 | 0.717029 | ||||||||
\(525\) | −0.00504296 | −0.000220093 0 | ||||||||
\(526\) | 28.8028 | 1.25586 | ||||||||
\(527\) | −10.6772 | −0.465107 | ||||||||
\(528\) | 3.74640 | 0.163041 | ||||||||
\(529\) | −18.8974 | −0.821625 | ||||||||
\(530\) | 24.0020 | 1.04258 | ||||||||
\(531\) | 3.40656 | 0.147832 | ||||||||
\(532\) | 0.0131979 | 0.000572199 0 | ||||||||
\(533\) | 31.3455 | 1.35773 | ||||||||
\(534\) | −21.6868 | −0.938481 | ||||||||
\(535\) | 11.8467 | 0.512178 | ||||||||
\(536\) | −23.3508 | −1.00860 | ||||||||
\(537\) | 6.30136 | 0.271924 | ||||||||
\(538\) | −32.9070 | −1.41872 | ||||||||
\(539\) | −12.3381 | −0.531438 | ||||||||
\(540\) | 2.69543 | 0.115993 | ||||||||
\(541\) | −5.28262 | −0.227117 | −0.113559 | − | 0.993531i | \(-0.536225\pi\) | ||||
−0.113559 | + | 0.993531i | \(0.536225\pi\) | |||||||
\(542\) | −0.108726 | −0.00467019 | ||||||||
\(543\) | 3.22464 | 0.138383 | ||||||||
\(544\) | 31.6574 | 1.35730 | ||||||||
\(545\) | −10.1499 | −0.434776 | ||||||||
\(546\) | 0.0418402 | 0.00179059 | ||||||||
\(547\) | −10.6008 | −0.453260 | −0.226630 | − | 0.973981i | \(-0.572771\pi\) | ||||
−0.226630 | + | 0.973981i | \(0.572771\pi\) | |||||||
\(548\) | 7.20710 | 0.307872 | ||||||||
\(549\) | 2.14095 | 0.0913735 | ||||||||
\(550\) | −3.81934 | −0.162857 | ||||||||
\(551\) | 7.35127 | 0.313174 | ||||||||
\(552\) | −3.05227 | −0.129913 | ||||||||
\(553\) | −0.0842798 | −0.00358394 | ||||||||
\(554\) | 14.6643 | 0.623025 | ||||||||
\(555\) | −2.34651 | −0.0996039 | ||||||||
\(556\) | 7.37450 | 0.312748 | ||||||||
\(557\) | −24.4387 | −1.03550 | −0.517750 | − | 0.855532i | \(-0.673230\pi\) | ||||
−0.517750 | + | 0.855532i | \(0.673230\pi\) | |||||||
\(558\) | 5.56870 | 0.235742 | ||||||||
\(559\) | 38.4015 | 1.62421 | ||||||||
\(560\) | 0.0107189 | 0.000452955 0 | ||||||||
\(561\) | −7.32306 | −0.309180 | ||||||||
\(562\) | −1.32403 | −0.0558510 | ||||||||
\(563\) | −24.3687 | −1.02702 | −0.513508 | − | 0.858085i | \(-0.671654\pi\) | ||||
−0.513508 | + | 0.858085i | \(0.671654\pi\) | |||||||
\(564\) | −9.95368 | −0.419126 | ||||||||
\(565\) | −1.13141 | −0.0475989 | ||||||||
\(566\) | −0.808703 | −0.0339923 | ||||||||
\(567\) | 0.00504296 | 0.000211784 0 | ||||||||
\(568\) | −9.87209 | −0.414224 | ||||||||
\(569\) | 20.1924 | 0.846509 | 0.423254 | − | 0.906011i | \(-0.360888\pi\) | ||||
0.423254 | + | 0.906011i | \(0.360888\pi\) | |||||||
\(570\) | −2.10391 | −0.0881231 | ||||||||
\(571\) | 38.5531 | 1.61340 | 0.806698 | − | 0.590963i | \(-0.201252\pi\) | ||||
0.806698 | + | 0.590963i | \(0.201252\pi\) | |||||||
\(572\) | 18.1907 | 0.760591 | ||||||||
\(573\) | 6.82580 | 0.285152 | ||||||||
\(574\) | −0.0894599 | −0.00373398 | ||||||||
\(575\) | −2.02549 | −0.0844688 | ||||||||
\(576\) | −12.2599 | −0.510828 | ||||||||
\(577\) | 16.2255 | 0.675477 | 0.337738 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337738 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(578\) | −0.567077 | −0.0235873 | ||||||||
\(579\) | −9.33805 | −0.388076 | ||||||||
\(580\) | −20.4080 | −0.847397 | ||||||||
\(581\) | 0.0543384 | 0.00225434 | ||||||||
\(582\) | 18.1927 | 0.754110 | ||||||||
\(583\) | 19.5236 | 0.808586 | ||||||||
\(584\) | 4.37829 | 0.181175 | ||||||||
\(585\) | −3.82887 | −0.158304 | ||||||||
\(586\) | −8.89066 | −0.367270 | ||||||||
\(587\) | 3.97374 | 0.164014 | 0.0820069 | − | 0.996632i | \(-0.473867\pi\) | ||||
0.0820069 | + | 0.996632i | \(0.473867\pi\) | |||||||
\(588\) | 18.8680 | 0.778101 | ||||||||
\(589\) | −2.49520 | −0.102813 | ||||||||
\(590\) | 7.38166 | 0.303898 | ||||||||
\(591\) | 12.3305 | 0.507210 | ||||||||
\(592\) | 4.98754 | 0.204987 | ||||||||
\(593\) | 33.5065 | 1.37595 | 0.687974 | − | 0.725736i | \(-0.258500\pi\) | ||||
0.687974 | + | 0.725736i | \(0.258500\pi\) | |||||||
\(594\) | 3.81934 | 0.156709 | ||||||||
\(595\) | −0.0209521 | −0.000858952 0 | ||||||||
\(596\) | 14.1522 | 0.579695 | ||||||||
\(597\) | 6.80836 | 0.278648 | ||||||||
\(598\) | 16.8050 | 0.687208 | ||||||||
\(599\) | −17.3766 | −0.709989 | −0.354994 | − | 0.934868i | \(-0.615517\pi\) | ||||
−0.354994 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(600\) | 1.50693 | 0.0615200 | ||||||||
\(601\) | −15.9888 | −0.652198 | −0.326099 | − | 0.945336i | \(-0.605734\pi\) | ||||
−0.326099 | + | 0.945336i | \(0.605734\pi\) | |||||||
\(602\) | −0.109598 | −0.00446686 | ||||||||
\(603\) | 15.4956 | 0.631030 | ||||||||
\(604\) | −32.5436 | −1.32418 | ||||||||
\(605\) | 7.89329 | 0.320908 | ||||||||
\(606\) | 1.43580 | 0.0583256 | ||||||||
\(607\) | 8.10826 | 0.329104 | 0.164552 | − | 0.986368i | \(-0.447382\pi\) | ||||
0.164552 | + | 0.986368i | \(0.447382\pi\) | |||||||
\(608\) | 7.39814 | 0.300034 | ||||||||
\(609\) | −0.0381819 | −0.00154721 | ||||||||
\(610\) | 4.63921 | 0.187836 | ||||||||
\(611\) | 14.1392 | 0.572012 | ||||||||
\(612\) | 11.1988 | 0.452683 | ||||||||
\(613\) | 7.67715 | 0.310077 | 0.155039 | − | 0.987908i | \(-0.450450\pi\) | ||||
0.155039 | + | 0.987908i | \(0.450450\pi\) | |||||||
\(614\) | 31.7576 | 1.28163 | ||||||||
\(615\) | 8.18663 | 0.330117 | ||||||||
\(616\) | −0.0133946 | −0.000539682 0 | ||||||||
\(617\) | 31.4420 | 1.26581 | 0.632904 | − | 0.774230i | \(-0.281863\pi\) | ||||
0.632904 | + | 0.774230i | \(0.281863\pi\) | |||||||
\(618\) | −17.6062 | −0.708224 | ||||||||
\(619\) | −22.2006 | −0.892318 | −0.446159 | − | 0.894954i | \(-0.647209\pi\) | ||||
−0.446159 | + | 0.894954i | \(0.647209\pi\) | |||||||
\(620\) | 6.92699 | 0.278195 | ||||||||
\(621\) | 2.02549 | 0.0812802 | ||||||||
\(622\) | 54.5868 | 2.18873 | ||||||||
\(623\) | −0.0504712 | −0.00202209 | ||||||||
\(624\) | 8.13830 | 0.325793 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.7289 | −0.628653 | ||||||||
\(627\) | −1.71136 | −0.0683449 | ||||||||
\(628\) | 32.5376 | 1.29839 | ||||||||
\(629\) | −9.74911 | −0.388722 | ||||||||
\(630\) | 0.0109276 | 0.000435364 0 | ||||||||
\(631\) | 37.4356 | 1.49029 | 0.745143 | − | 0.666905i | \(-0.232381\pi\) | ||||
0.745143 | + | 0.666905i | \(0.232381\pi\) | |||||||
\(632\) | 25.1843 | 1.00178 | ||||||||
\(633\) | 14.4508 | 0.574368 | ||||||||
\(634\) | 40.2392 | 1.59810 | ||||||||
\(635\) | 6.34172 | 0.251664 | ||||||||
\(636\) | −29.8565 | −1.18389 | ||||||||
\(637\) | −26.8020 | −1.06193 | ||||||||
\(638\) | −28.9175 | −1.14486 | ||||||||
\(639\) | 6.55114 | 0.259159 | ||||||||
\(640\) | −11.3266 | −0.447724 | ||||||||
\(641\) | 20.5587 | 0.812019 | 0.406010 | − | 0.913869i | \(-0.366920\pi\) | ||||
0.406010 | + | 0.913869i | \(0.366920\pi\) | |||||||
\(642\) | −25.6706 | −1.01314 | ||||||||
\(643\) | 35.6074 | 1.40422 | 0.702110 | − | 0.712068i | \(-0.252241\pi\) | ||||
0.702110 | + | 0.712068i | \(0.252241\pi\) | |||||||
\(644\) | −0.0275324 | −0.00108493 | ||||||||
\(645\) | 10.0295 | 0.394910 | ||||||||
\(646\) | −8.74116 | −0.343916 | ||||||||
\(647\) | 19.6236 | 0.771482 | 0.385741 | − | 0.922607i | \(-0.373946\pi\) | ||||
0.385741 | + | 0.922607i | \(0.373946\pi\) | |||||||
\(648\) | −1.50693 | −0.0591977 | ||||||||
\(649\) | 6.00436 | 0.235692 | ||||||||
\(650\) | −8.29675 | −0.325425 | ||||||||
\(651\) | 0.0129599 | 0.000507938 0 | ||||||||
\(652\) | 3.16213 | 0.123839 | ||||||||
\(653\) | 14.0953 | 0.551593 | 0.275797 | − | 0.961216i | \(-0.411058\pi\) | ||||
0.275797 | + | 0.961216i | \(0.411058\pi\) | |||||||
\(654\) | 21.9939 | 0.860028 | ||||||||
\(655\) | −6.08939 | −0.237932 | ||||||||
\(656\) | −17.4008 | −0.679386 | ||||||||
\(657\) | −2.90544 | −0.113352 | ||||||||
\(658\) | −0.0403532 | −0.00157313 | ||||||||
\(659\) | 6.89872 | 0.268736 | 0.134368 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134368 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(660\) | 4.75093 | 0.184930 | ||||||||
\(661\) | −4.74671 | −0.184626 | −0.0923129 | − | 0.995730i | \(-0.529426\pi\) | ||||
−0.0923129 | + | 0.995730i | \(0.529426\pi\) | |||||||
\(662\) | 42.9333 | 1.66865 | ||||||||
\(663\) | −15.9079 | −0.617811 | ||||||||
\(664\) | −16.2373 | −0.630130 | ||||||||
\(665\) | −0.00489638 | −0.000189873 0 | ||||||||
\(666\) | 5.08465 | 0.197026 | ||||||||
\(667\) | −15.3357 | −0.593800 | ||||||||
\(668\) | −39.5807 | −1.53142 | ||||||||
\(669\) | 4.76381 | 0.184179 | ||||||||
\(670\) | 33.5774 | 1.29721 | ||||||||
\(671\) | 3.77361 | 0.145679 | ||||||||
\(672\) | −0.0384254 | −0.00148229 | ||||||||
\(673\) | 16.5598 | 0.638334 | 0.319167 | − | 0.947699i | \(-0.396597\pi\) | ||||
0.319167 | + | 0.947699i | \(0.396597\pi\) | |||||||
\(674\) | −14.4528 | −0.556699 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 4.47505 | 0.172117 | ||||||||
\(677\) | −19.9707 | −0.767535 | −0.383767 | − | 0.923430i | \(-0.625374\pi\) | ||||
−0.383767 | + | 0.923430i | \(0.625374\pi\) | |||||||
\(678\) | 2.45165 | 0.0941552 | ||||||||
\(679\) | 0.0423393 | 0.00162483 | ||||||||
\(680\) | 6.26086 | 0.240093 | ||||||||
\(681\) | 4.42996 | 0.169757 | ||||||||
\(682\) | 9.81532 | 0.375848 | ||||||||
\(683\) | 38.4201 | 1.47011 | 0.735053 | − | 0.678010i | \(-0.237157\pi\) | ||||
0.735053 | + | 0.678010i | \(0.237157\pi\) | |||||||
\(684\) | 2.61709 | 0.100067 | ||||||||
\(685\) | −2.67382 | −0.102161 | ||||||||
\(686\) | 0.152986 | 0.00584101 | ||||||||
\(687\) | 5.80113 | 0.221327 | ||||||||
\(688\) | −21.3177 | −0.812731 | ||||||||
\(689\) | 42.4112 | 1.61574 | ||||||||
\(690\) | 4.38903 | 0.167087 | ||||||||
\(691\) | 13.0693 | 0.497179 | 0.248590 | − | 0.968609i | \(-0.420033\pi\) | ||||
0.248590 | + | 0.968609i | \(0.420033\pi\) | |||||||
\(692\) | 0.100051 | 0.00380336 | ||||||||
\(693\) | 0.00888865 | 0.000337652 0 | ||||||||
\(694\) | −57.2304 | −2.17243 | ||||||||
\(695\) | −2.73592 | −0.103780 | ||||||||
\(696\) | 11.4095 | 0.432474 | ||||||||
\(697\) | 34.0132 | 1.28834 | ||||||||
\(698\) | 35.8420 | 1.35664 | ||||||||
\(699\) | −18.4705 | −0.698617 | ||||||||
\(700\) | 0.0135929 | 0.000513765 0 | ||||||||
\(701\) | −33.9526 | −1.28237 | −0.641186 | − | 0.767386i | \(-0.721557\pi\) | ||||
−0.641186 | + | 0.767386i | \(0.721557\pi\) | |||||||
\(702\) | 8.29675 | 0.313141 | ||||||||
\(703\) | −2.27831 | −0.0859280 | ||||||||
\(704\) | −21.6091 | −0.814424 | ||||||||
\(705\) | 3.69280 | 0.139079 | ||||||||
\(706\) | 26.9202 | 1.01316 | ||||||||
\(707\) | 0.00334151 | 0.000125670 0 | ||||||||
\(708\) | −9.18216 | −0.345087 | ||||||||
\(709\) | 3.44067 | 0.129217 | 0.0646085 | − | 0.997911i | \(-0.479420\pi\) | ||||
0.0646085 | + | 0.997911i | \(0.479420\pi\) | |||||||
\(710\) | 14.1956 | 0.532752 | ||||||||
\(711\) | −16.7124 | −0.626763 | ||||||||
\(712\) | 15.0817 | 0.565211 | ||||||||
\(713\) | 5.20531 | 0.194940 | ||||||||
\(714\) | 0.0454009 | 0.00169909 | ||||||||
\(715\) | −6.74871 | −0.252388 | ||||||||
\(716\) | −16.9849 | −0.634755 | ||||||||
\(717\) | −9.36356 | −0.349688 | ||||||||
\(718\) | −48.0480 | −1.79314 | ||||||||
\(719\) | 26.7896 | 0.999084 | 0.499542 | − | 0.866290i | \(-0.333502\pi\) | ||||
0.499542 | + | 0.866290i | \(0.333502\pi\) | |||||||
\(720\) | 2.12551 | 0.0792131 | ||||||||
\(721\) | −0.0409744 | −0.00152597 | ||||||||
\(722\) | 39.1282 | 1.45620 | ||||||||
\(723\) | 5.55603 | 0.206631 | ||||||||
\(724\) | −8.69179 | −0.323028 | ||||||||
\(725\) | 7.57134 | 0.281192 | ||||||||
\(726\) | −17.1039 | −0.634786 | ||||||||
\(727\) | 4.36497 | 0.161888 | 0.0809439 | − | 0.996719i | \(-0.474207\pi\) | ||||
0.0809439 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(728\) | −0.0290970 | −0.00107841 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.29579 | −0.233018 | ||||||||
\(731\) | 41.6696 | 1.54121 | ||||||||
\(732\) | −5.77078 | −0.213294 | ||||||||
\(733\) | 10.4218 | 0.384939 | 0.192470 | − | 0.981303i | \(-0.438350\pi\) | ||||
0.192470 | + | 0.981303i | \(0.438350\pi\) | |||||||
\(734\) | −11.3044 | −0.417252 | ||||||||
\(735\) | −6.99997 | −0.258198 | ||||||||
\(736\) | −15.4335 | −0.568885 | ||||||||
\(737\) | 27.3124 | 1.00606 | ||||||||
\(738\) | −17.7396 | −0.653002 | ||||||||
\(739\) | 11.3457 | 0.417359 | 0.208680 | − | 0.977984i | \(-0.433083\pi\) | ||||
0.208680 | + | 0.977984i | \(0.433083\pi\) | |||||||
\(740\) | 6.32487 | 0.232507 | ||||||||
\(741\) | −3.71758 | −0.136569 | ||||||||
\(742\) | −0.121041 | −0.00444356 | ||||||||
\(743\) | −39.3912 | −1.44512 | −0.722561 | − | 0.691307i | \(-0.757035\pi\) | ||||
−0.722561 | + | 0.691307i | \(0.757035\pi\) | |||||||
\(744\) | −3.87265 | −0.141978 | ||||||||
\(745\) | −5.25042 | −0.192361 | ||||||||
\(746\) | −47.3899 | −1.73507 | ||||||||
\(747\) | 10.7751 | 0.394241 | ||||||||
\(748\) | 19.7388 | 0.721722 | ||||||||
\(749\) | −0.0597425 | −0.00218294 | ||||||||
\(750\) | −2.16689 | −0.0791238 | ||||||||
\(751\) | 14.4578 | 0.527574 | 0.263787 | − | 0.964581i | \(-0.415028\pi\) | ||||
0.263787 | + | 0.964581i | \(0.415028\pi\) | |||||||
\(752\) | −7.84908 | −0.286227 | ||||||||
\(753\) | −2.48181 | −0.0904421 | ||||||||
\(754\) | −62.8175 | −2.28768 | ||||||||
\(755\) | 12.0736 | 0.439403 | ||||||||
\(756\) | −0.0135929 | −0.000494371 0 | ||||||||
\(757\) | 16.8295 | 0.611677 | 0.305839 | − | 0.952083i | \(-0.401063\pi\) | ||||
0.305839 | + | 0.952083i | \(0.401063\pi\) | |||||||
\(758\) | −19.8686 | −0.721660 | ||||||||
\(759\) | 3.57010 | 0.129587 | ||||||||
\(760\) | 1.46313 | 0.0530732 | ||||||||
\(761\) | −30.2009 | −1.09478 | −0.547390 | − | 0.836878i | \(-0.684379\pi\) | ||||
−0.547390 | + | 0.836878i | \(0.684379\pi\) | |||||||
\(762\) | −13.7418 | −0.497815 | ||||||||
\(763\) | 0.0511857 | 0.00185305 | ||||||||
\(764\) | −18.3985 | −0.665634 | ||||||||
\(765\) | −4.15472 | −0.150214 | ||||||||
\(766\) | 0.0800481 | 0.00289226 | ||||||||
\(767\) | 13.0433 | 0.470966 | ||||||||
\(768\) | 0.0238591 | 0.000860940 0 | ||||||||
\(769\) | −7.53603 | −0.271756 | −0.135878 | − | 0.990726i | \(-0.543386\pi\) | ||||
−0.135878 | + | 0.990726i | \(0.543386\pi\) | |||||||
\(770\) | 0.0192608 | 0.000694110 0 | ||||||||
\(771\) | −17.5860 | −0.633343 | ||||||||
\(772\) | 25.1701 | 0.905891 | ||||||||
\(773\) | −15.0483 | −0.541249 | −0.270625 | − | 0.962685i | \(-0.587230\pi\) | ||||
−0.270625 | + | 0.962685i | \(0.587230\pi\) | |||||||
\(774\) | −21.7328 | −0.781169 | ||||||||
\(775\) | −2.56990 | −0.0923135 | ||||||||
\(776\) | −12.6518 | −0.454172 | ||||||||
\(777\) | 0.0118334 | 0.000424520 0 | ||||||||
\(778\) | 48.3629 | 1.73390 | ||||||||
\(779\) | 7.94868 | 0.284791 | ||||||||
\(780\) | 10.3205 | 0.369532 | ||||||||
\(781\) | 11.5470 | 0.413182 | ||||||||
\(782\) | 18.2352 | 0.652088 | ||||||||
\(783\) | −7.57134 | −0.270578 | ||||||||
\(784\) | 14.8785 | 0.531376 | ||||||||
\(785\) | −12.0714 | −0.430846 | ||||||||
\(786\) | 13.1951 | 0.470652 | ||||||||
\(787\) | −26.7369 | −0.953066 | −0.476533 | − | 0.879157i | \(-0.658107\pi\) | ||||
−0.476533 | + | 0.879157i | \(0.658107\pi\) | |||||||
\(788\) | −33.2361 | −1.18399 | ||||||||
\(789\) | 13.2922 | 0.473215 | ||||||||
\(790\) | −36.2140 | −1.28843 | ||||||||
\(791\) | 0.00570567 | 0.000202870 0 | ||||||||
\(792\) | −2.65609 | −0.0943801 | ||||||||
\(793\) | 8.19741 | 0.291099 | ||||||||
\(794\) | −15.8663 | −0.563073 | ||||||||
\(795\) | 11.0767 | 0.392850 | ||||||||
\(796\) | −18.3515 | −0.650451 | ||||||||
\(797\) | −42.0180 | −1.48835 | −0.744177 | − | 0.667983i | \(-0.767158\pi\) | ||||
−0.744177 | + | 0.667983i | \(0.767158\pi\) | |||||||
\(798\) | 0.0106099 | 0.000375588 0 | ||||||||
\(799\) | 15.3425 | 0.542780 | ||||||||
\(800\) | 7.61961 | 0.269394 | ||||||||
\(801\) | −10.0083 | −0.353624 | ||||||||
\(802\) | −2.16689 | −0.0765157 | ||||||||
\(803\) | −5.12110 | −0.180720 | ||||||||
\(804\) | −41.7674 | −1.47302 | ||||||||
\(805\) | 0.0102145 | 0.000360013 0 | ||||||||
\(806\) | 21.3218 | 0.751029 | ||||||||
\(807\) | −15.1862 | −0.534581 | ||||||||
\(808\) | −0.998504 | −0.0351273 | ||||||||
\(809\) | 31.7848 | 1.11749 | 0.558747 | − | 0.829338i | \(-0.311282\pi\) | ||||
0.558747 | + | 0.829338i | \(0.311282\pi\) | |||||||
\(810\) | 2.16689 | 0.0761369 | ||||||||
\(811\) | 49.1303 | 1.72520 | 0.862599 | − | 0.505888i | \(-0.168835\pi\) | ||||
0.862599 | + | 0.505888i | \(0.168835\pi\) | |||||||
\(812\) | 0.102917 | 0.00361167 | ||||||||
\(813\) | −0.0501761 | −0.00175975 | ||||||||
\(814\) | 8.96213 | 0.314123 | ||||||||
\(815\) | −1.17314 | −0.0410935 | ||||||||
\(816\) | 8.83091 | 0.309144 | ||||||||
\(817\) | 9.73794 | 0.340687 | ||||||||
\(818\) | 32.9656 | 1.15262 | ||||||||
\(819\) | 0.0193088 | 0.000674705 0 | ||||||||
\(820\) | −22.0665 | −0.770596 | ||||||||
\(821\) | −26.6244 | −0.929197 | −0.464599 | − | 0.885521i | \(-0.653801\pi\) | ||||
−0.464599 | + | 0.885521i | \(0.653801\pi\) | |||||||
\(822\) | 5.79388 | 0.202085 | ||||||||
\(823\) | 40.0432 | 1.39582 | 0.697908 | − | 0.716187i | \(-0.254114\pi\) | ||||
0.697908 | + | 0.716187i | \(0.254114\pi\) | |||||||
\(824\) | 12.2439 | 0.426536 | ||||||||
\(825\) | −1.76259 | −0.0613654 | ||||||||
\(826\) | −0.0372254 | −0.00129524 | ||||||||
\(827\) | −38.0400 | −1.32278 | −0.661391 | − | 0.750042i | \(-0.730033\pi\) | ||||
−0.661391 | + | 0.750042i | \(0.730033\pi\) | |||||||
\(828\) | −5.45957 | −0.189733 | ||||||||
\(829\) | −20.5302 | −0.713044 | −0.356522 | − | 0.934287i | \(-0.616038\pi\) | ||||
−0.356522 | + | 0.934287i | \(0.616038\pi\) | |||||||
\(830\) | 23.3485 | 0.810439 | ||||||||
\(831\) | 6.76742 | 0.234759 | ||||||||
\(832\) | −46.9414 | −1.62740 | ||||||||
\(833\) | −29.0829 | −1.00766 | ||||||||
\(834\) | 5.92846 | 0.205286 | ||||||||
\(835\) | 14.6844 | 0.508174 | ||||||||
\(836\) | 4.61284 | 0.159538 | ||||||||
\(837\) | 2.56990 | 0.0888287 | ||||||||
\(838\) | 40.6882 | 1.40555 | ||||||||
\(839\) | 20.2718 | 0.699860 | 0.349930 | − | 0.936776i | \(-0.386205\pi\) | ||||
0.349930 | + | 0.936776i | \(0.386205\pi\) | |||||||
\(840\) | −0.00759937 | −0.000262203 0 | ||||||||
\(841\) | 28.3252 | 0.976730 | ||||||||
\(842\) | −44.3627 | −1.52884 | ||||||||
\(843\) | −0.611028 | −0.0210449 | ||||||||
\(844\) | −38.9512 | −1.34076 | ||||||||
\(845\) | −1.66023 | −0.0571138 | ||||||||
\(846\) | −8.00190 | −0.275111 | ||||||||
\(847\) | −0.0398055 | −0.00136773 | ||||||||
\(848\) | −23.5436 | −0.808492 | ||||||||
\(849\) | −0.373208 | −0.0128085 | ||||||||
\(850\) | −9.00284 | −0.308795 | ||||||||
\(851\) | 4.75284 | 0.162925 | ||||||||
\(852\) | −17.6581 | −0.604958 | ||||||||
\(853\) | −9.91138 | −0.339359 | −0.169680 | − | 0.985499i | \(-0.554273\pi\) | ||||
−0.169680 | + | 0.985499i | \(0.554273\pi\) | |||||||
\(854\) | −0.0233953 | −0.000800572 0 | ||||||||
\(855\) | −0.970934 | −0.0332052 | ||||||||
\(856\) | 17.8521 | 0.610174 | ||||||||
\(857\) | 19.2380 | 0.657156 | 0.328578 | − | 0.944477i | \(-0.393431\pi\) | ||||
0.328578 | + | 0.944477i | \(0.393431\pi\) | |||||||
\(858\) | 14.6238 | 0.499247 | ||||||||
\(859\) | 31.2756 | 1.06711 | 0.533554 | − | 0.845766i | \(-0.320856\pi\) | ||||
0.533554 | + | 0.845766i | \(0.320856\pi\) | |||||||
\(860\) | −27.0337 | −0.921842 | ||||||||
\(861\) | −0.0412848 | −0.00140698 | ||||||||
\(862\) | 19.0709 | 0.649559 | ||||||||
\(863\) | −9.59780 | −0.326713 | −0.163357 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163357 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(864\) | −7.61961 | −0.259225 | ||||||||
\(865\) | −0.0371186 | −0.00126207 | ||||||||
\(866\) | −47.0003 | −1.59714 | ||||||||
\(867\) | −0.261700 | −0.00888781 | ||||||||
\(868\) | −0.0349325 | −0.00118569 | ||||||||
\(869\) | −29.4570 | −0.999261 | ||||||||
\(870\) | −16.4063 | −0.556225 | ||||||||
\(871\) | 59.3307 | 2.01034 | ||||||||
\(872\) | −15.2952 | −0.517962 | ||||||||
\(873\) | 8.39573 | 0.284152 | ||||||||
\(874\) | 4.26145 | 0.144146 | ||||||||
\(875\) | −0.00504296 | −0.000170483 0 | ||||||||
\(876\) | 7.83142 | 0.264599 | ||||||||
\(877\) | −23.1994 | −0.783390 | −0.391695 | − | 0.920095i | \(-0.628111\pi\) | ||||
−0.391695 | + | 0.920095i | \(0.628111\pi\) | |||||||
\(878\) | 17.5313 | 0.591652 | ||||||||
\(879\) | −4.10295 | −0.138389 | ||||||||
\(880\) | 3.74640 | 0.126291 | ||||||||
\(881\) | 23.6639 | 0.797258 | 0.398629 | − | 0.917112i | \(-0.369486\pi\) | ||||
0.398629 | + | 0.917112i | \(0.369486\pi\) | |||||||
\(882\) | 15.1682 | 0.510740 | ||||||||
\(883\) | 31.3497 | 1.05500 | 0.527500 | − | 0.849555i | \(-0.323129\pi\) | ||||
0.527500 | + | 0.849555i | \(0.323129\pi\) | |||||||
\(884\) | 42.8786 | 1.44216 | ||||||||
\(885\) | 3.40656 | 0.114510 | ||||||||
\(886\) | −14.0420 | −0.471750 | ||||||||
\(887\) | 48.8031 | 1.63865 | 0.819323 | − | 0.573332i | \(-0.194349\pi\) | ||||
0.819323 | + | 0.573332i | \(0.194349\pi\) | |||||||
\(888\) | −3.53602 | −0.118661 | ||||||||
\(889\) | −0.0319811 | −0.00107261 | ||||||||
\(890\) | −21.6868 | −0.726944 | ||||||||
\(891\) | 1.76259 | 0.0590489 | ||||||||
\(892\) | −12.8405 | −0.429932 | ||||||||
\(893\) | 3.58546 | 0.119983 | ||||||||
\(894\) | 11.3771 | 0.380508 | ||||||||
\(895\) | 6.30136 | 0.210631 | ||||||||
\(896\) | 0.0571197 | 0.00190824 | ||||||||
\(897\) | 7.75534 | 0.258943 | ||||||||
\(898\) | −86.6920 | −2.89295 | ||||||||
\(899\) | −19.4576 | −0.648947 | ||||||||
\(900\) | 2.69543 | 0.0898477 | ||||||||
\(901\) | 46.0205 | 1.53317 | ||||||||
\(902\) | −31.2675 | −1.04109 | ||||||||
\(903\) | −0.0505782 | −0.00168314 | ||||||||
\(904\) | −1.70496 | −0.0567060 | ||||||||
\(905\) | 3.22464 | 0.107191 | ||||||||
\(906\) | −26.1622 | −0.869181 | ||||||||
\(907\) | 15.3571 | 0.509925 | 0.254962 | − | 0.966951i | \(-0.417937\pi\) | ||||
0.254962 | + | 0.966951i | \(0.417937\pi\) | |||||||
\(908\) | −11.9407 | −0.396265 | ||||||||
\(909\) | 0.662610 | 0.0219774 | ||||||||
\(910\) | 0.0418402 | 0.00138699 | ||||||||
\(911\) | 10.8585 | 0.359759 | 0.179879 | − | 0.983689i | \(-0.442429\pi\) | ||||
0.179879 | + | 0.983689i | \(0.442429\pi\) | |||||||
\(912\) | 2.06373 | 0.0683369 | ||||||||
\(913\) | 18.9921 | 0.628546 | ||||||||
\(914\) | 78.7143 | 2.60364 | ||||||||
\(915\) | 2.14095 | 0.0707776 | ||||||||
\(916\) | −15.6365 | −0.516646 | ||||||||
\(917\) | 0.0307085 | 0.00101409 | ||||||||
\(918\) | 9.00284 | 0.297138 | ||||||||
\(919\) | −10.5753 | −0.348847 | −0.174424 | − | 0.984671i | \(-0.555806\pi\) | ||||
−0.174424 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(920\) | −3.05227 | −0.100630 | ||||||||
\(921\) | 14.6558 | 0.482926 | ||||||||
\(922\) | −3.90873 | −0.128727 | ||||||||
\(923\) | 25.0834 | 0.825632 | ||||||||
\(924\) | −0.0239588 | −0.000788185 0 | ||||||||
\(925\) | −2.34651 | −0.0771529 | ||||||||
\(926\) | −51.3772 | −1.68836 | ||||||||
\(927\) | −8.12507 | −0.266862 | ||||||||
\(928\) | 57.6907 | 1.89379 | ||||||||
\(929\) | 21.1469 | 0.693807 | 0.346903 | − | 0.937901i | \(-0.387233\pi\) | ||||
0.346903 | + | 0.937901i | \(0.387233\pi\) | |||||||
\(930\) | 5.56870 | 0.182605 | ||||||||
\(931\) | −6.79651 | −0.222747 | ||||||||
\(932\) | 49.7859 | 1.63079 | ||||||||
\(933\) | 25.1912 | 0.824724 | ||||||||
\(934\) | −8.40587 | −0.275048 | ||||||||
\(935\) | −7.32306 | −0.239490 | ||||||||
\(936\) | −5.76983 | −0.188593 | ||||||||
\(937\) | −39.3882 | −1.28676 | −0.643379 | − | 0.765548i | \(-0.722468\pi\) | ||||
−0.643379 | + | 0.765548i | \(0.722468\pi\) | |||||||
\(938\) | −0.169329 | −0.00552880 | ||||||||
\(939\) | −7.25873 | −0.236880 | ||||||||
\(940\) | −9.95368 | −0.324653 | ||||||||
\(941\) | 55.5735 | 1.81164 | 0.905821 | − | 0.423660i | \(-0.139255\pi\) | ||||
0.905821 | + | 0.423660i | \(0.139255\pi\) | |||||||
\(942\) | 26.1574 | 0.852254 | ||||||||
\(943\) | −16.5819 | −0.539983 | ||||||||
\(944\) | −7.24069 | −0.235664 | ||||||||
\(945\) | 0.00504296 | 0.000164047 0 | ||||||||
\(946\) | −38.3059 | −1.24543 | ||||||||
\(947\) | −45.6057 | −1.48199 | −0.740993 | − | 0.671513i | \(-0.765645\pi\) | ||||
−0.740993 | + | 0.671513i | \(0.765645\pi\) | |||||||
\(948\) | 45.0471 | 1.46306 | ||||||||
\(949\) | −11.1246 | −0.361118 | ||||||||
\(950\) | −2.10391 | −0.0682599 | ||||||||
\(951\) | 18.5700 | 0.602173 | ||||||||
\(952\) | −0.0315733 | −0.00102330 | ||||||||
\(953\) | −13.1788 | −0.426904 | −0.213452 | − | 0.976954i | \(-0.568471\pi\) | ||||
−0.213452 | + | 0.976954i | \(0.568471\pi\) | |||||||
\(954\) | −24.0020 | −0.777094 | ||||||||
\(955\) | 6.82580 | 0.220878 | ||||||||
\(956\) | 25.2388 | 0.816282 | ||||||||
\(957\) | −13.3451 | −0.431387 | ||||||||
\(958\) | −17.9846 | −0.581056 | ||||||||
\(959\) | 0.0134840 | 0.000435420 0 | ||||||||
\(960\) | −12.2599 | −0.395686 | ||||||||
\(961\) | −24.3956 | −0.786955 | ||||||||
\(962\) | 19.4684 | 0.627688 | ||||||||
\(963\) | −11.8467 | −0.381755 | ||||||||
\(964\) | −14.9759 | −0.482341 | ||||||||
\(965\) | −9.33805 | −0.300603 | ||||||||
\(966\) | −0.0221337 | −0.000712139 0 | ||||||||
\(967\) | −21.3582 | −0.686834 | −0.343417 | − | 0.939183i | \(-0.611584\pi\) | ||||
−0.343417 | + | 0.939183i | \(0.611584\pi\) | |||||||
\(968\) | 11.8946 | 0.382307 | ||||||||
\(969\) | −4.03396 | −0.129589 | ||||||||
\(970\) | 18.1927 | 0.584131 | ||||||||
\(971\) | −25.9007 | −0.831191 | −0.415596 | − | 0.909549i | \(-0.636427\pi\) | ||||
−0.415596 | + | 0.909549i | \(0.636427\pi\) | |||||||
\(972\) | −2.69543 | −0.0864560 | ||||||||
\(973\) | 0.0137972 | 0.000442316 0 | ||||||||
\(974\) | 29.7449 | 0.953087 | ||||||||
\(975\) | −3.82887 | −0.122622 | ||||||||
\(976\) | −4.55061 | −0.145662 | ||||||||
\(977\) | −47.7440 | −1.52747 | −0.763733 | − | 0.645533i | \(-0.776635\pi\) | ||||
−0.763733 | + | 0.645533i | \(0.776635\pi\) | |||||||
\(978\) | 2.54208 | 0.0812868 | ||||||||
\(979\) | −17.6404 | −0.563790 | ||||||||
\(980\) | 18.8680 | 0.602715 | ||||||||
\(981\) | 10.1499 | 0.324063 | ||||||||
\(982\) | 9.31422 | 0.297229 | ||||||||
\(983\) | 13.0238 | 0.415395 | 0.207698 | − | 0.978193i | \(-0.433403\pi\) | ||||
0.207698 | + | 0.978193i | \(0.433403\pi\) | |||||||
\(984\) | 12.3367 | 0.393278 | ||||||||
\(985\) | 12.3305 | 0.392883 | ||||||||
\(986\) | −68.1635 | −2.17077 | ||||||||
\(987\) | −0.0186226 | −0.000592764 0 | ||||||||
\(988\) | 10.0205 | 0.318794 | ||||||||
\(989\) | −20.3146 | −0.645966 | ||||||||
\(990\) | 3.81934 | 0.121387 | ||||||||
\(991\) | −13.6345 | −0.433113 | −0.216557 | − | 0.976270i | \(-0.569483\pi\) | ||||
−0.216557 | + | 0.976270i | \(0.569483\pi\) | |||||||
\(992\) | −19.5816 | −0.621718 | ||||||||
\(993\) | 19.8133 | 0.628756 | ||||||||
\(994\) | −0.0715879 | −0.00227063 | ||||||||
\(995\) | 6.80836 | 0.215840 | ||||||||
\(996\) | −29.0436 | −0.920281 | ||||||||
\(997\) | 17.0307 | 0.539367 | 0.269684 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269684 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(998\) | −28.1243 | −0.890260 | ||||||||
\(999\) | 2.34651 | 0.0742404 |
(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 | 6015.2.a.e.1.3 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.e.1.3 | ✓ | 31 | 1.1 | even | 1 | trivial |