Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.35 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.49203 | 1.05502 | 0.527511 | − | 0.849548i | \(-0.323126\pi\) | ||||
0.527511 | + | 0.849548i | \(0.323126\pi\) | |||||||
\(3\) | −3.12646 | −1.80506 | −0.902531 | − | 0.430626i | \(-0.858293\pi\) | ||||
−0.902531 | + | 0.430626i | \(0.858293\pi\) | |||||||
\(4\) | 0.226139 | 0.113070 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.66475 | −1.90438 | ||||||||
\(7\) | −4.66024 | −1.76140 | −0.880702 | − | 0.473670i | \(-0.842929\pi\) | ||||
−0.880702 | + | 0.473670i | \(0.842929\pi\) | |||||||
\(8\) | −2.64665 | −0.935730 | ||||||||
\(9\) | 6.77474 | 2.25825 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.92431 | −1.78625 | −0.893123 | − | 0.449812i | \(-0.851491\pi\) | ||||
−0.893123 | + | 0.449812i | \(0.851491\pi\) | |||||||
\(12\) | −0.707014 | −0.204097 | ||||||||
\(13\) | 4.29102 | 1.19012 | 0.595058 | − | 0.803683i | \(-0.297129\pi\) | ||||
0.595058 | + | 0.803683i | \(0.297129\pi\) | |||||||
\(14\) | −6.95319 | −1.85832 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.40114 | −1.10028 | ||||||||
\(17\) | 5.72527 | 1.38858 | 0.694291 | − | 0.719694i | \(-0.255718\pi\) | ||||
0.694291 | + | 0.719694i | \(0.255718\pi\) | |||||||
\(18\) | 10.1081 | 2.38250 | ||||||||
\(19\) | −1.23168 | −0.282568 | −0.141284 | − | 0.989969i | \(-0.545123\pi\) | ||||
−0.141284 | + | 0.989969i | \(0.545123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.5700 | 3.17944 | ||||||||
\(22\) | −8.83922 | −1.88453 | ||||||||
\(23\) | 3.63376 | 0.757692 | 0.378846 | − | 0.925460i | \(-0.376321\pi\) | ||||
0.378846 | + | 0.925460i | \(0.376321\pi\) | |||||||
\(24\) | 8.27462 | 1.68905 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.40231 | 1.25560 | ||||||||
\(27\) | −11.8016 | −2.27121 | ||||||||
\(28\) | −1.05386 | −0.199161 | ||||||||
\(29\) | 1.81182 | 0.336447 | 0.168224 | − | 0.985749i | \(-0.446197\pi\) | ||||
0.168224 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.11419 | −0.200114 | −0.100057 | − | 0.994982i | \(-0.531902\pi\) | ||||
−0.100057 | + | 0.994982i | \(0.531902\pi\) | |||||||
\(32\) | −1.27332 | −0.225093 | ||||||||
\(33\) | 18.5221 | 3.22428 | ||||||||
\(34\) | 8.54225 | 1.46498 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.53203 | 0.255339 | ||||||||
\(37\) | 7.32690 | 1.20454 | 0.602268 | − | 0.798294i | \(-0.294264\pi\) | ||||
0.602268 | + | 0.798294i | \(0.294264\pi\) | |||||||
\(38\) | −1.83770 | −0.298115 | ||||||||
\(39\) | −13.4157 | −2.14823 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.45271 | −1.00774 | −0.503872 | − | 0.863778i | \(-0.668092\pi\) | ||||
−0.503872 | + | 0.863778i | \(0.668092\pi\) | |||||||
\(42\) | 21.7389 | 3.35438 | ||||||||
\(43\) | 4.57155 | 0.697155 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(44\) | −1.33972 | −0.201970 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.42167 | 0.799381 | ||||||||
\(47\) | 7.71296 | 1.12505 | 0.562525 | − | 0.826780i | \(-0.309830\pi\) | ||||
0.562525 | + | 0.826780i | \(0.309830\pi\) | |||||||
\(48\) | 13.7600 | 1.98608 | ||||||||
\(49\) | 14.7178 | 2.10255 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.8998 | −2.50648 | ||||||||
\(52\) | 0.970368 | 0.134566 | ||||||||
\(53\) | −10.1745 | −1.39758 | −0.698788 | − | 0.715329i | \(-0.746277\pi\) | ||||
−0.698788 | + | 0.715329i | \(0.746277\pi\) | |||||||
\(54\) | −17.6082 | −2.39618 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.3340 | 1.64820 | ||||||||
\(57\) | 3.85081 | 0.510052 | ||||||||
\(58\) | 2.70329 | 0.354959 | ||||||||
\(59\) | −5.66965 | −0.738126 | −0.369063 | − | 0.929404i | \(-0.620321\pi\) | ||||
−0.369063 | + | 0.929404i | \(0.620321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.76640 | 0.610275 | 0.305138 | − | 0.952308i | \(-0.401298\pi\) | ||||
0.305138 | + | 0.952308i | \(0.401298\pi\) | |||||||
\(62\) | −1.66239 | −0.211124 | ||||||||
\(63\) | −31.5719 | −3.97768 | ||||||||
\(64\) | 6.90245 | 0.862807 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 27.6354 | 3.40169 | ||||||||
\(67\) | 14.0103 | 1.71163 | 0.855814 | − | 0.517283i | \(-0.173057\pi\) | ||||
0.855814 | + | 0.517283i | \(0.173057\pi\) | |||||||
\(68\) | 1.29471 | 0.157006 | ||||||||
\(69\) | −11.3608 | −1.36768 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.96855 | −0.470980 | −0.235490 | − | 0.971877i | \(-0.575669\pi\) | ||||
−0.235490 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(72\) | −17.9303 | −2.11311 | ||||||||
\(73\) | −8.92040 | −1.04405 | −0.522027 | − | 0.852929i | \(-0.674824\pi\) | ||||
−0.522027 | + | 0.852929i | \(0.674824\pi\) | |||||||
\(74\) | 10.9319 | 1.27081 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.278532 | −0.0319498 | ||||||||
\(77\) | 27.6087 | 3.14630 | ||||||||
\(78\) | −20.0166 | −2.26643 | ||||||||
\(79\) | 1.77420 | 0.199614 | 0.0998068 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998068 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.5729 | 1.84143 | ||||||||
\(82\) | −9.62761 | −1.06319 | ||||||||
\(83\) | 9.93218 | 1.09020 | 0.545099 | − | 0.838372i | \(-0.316492\pi\) | ||||
0.545099 | + | 0.838372i | \(0.316492\pi\) | |||||||
\(84\) | 3.29485 | 0.359498 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.82087 | 0.735514 | ||||||||
\(87\) | −5.66459 | −0.607308 | ||||||||
\(88\) | 15.6795 | 1.67144 | ||||||||
\(89\) | −7.03898 | −0.746131 | −0.373065 | − | 0.927805i | \(-0.621693\pi\) | ||||
−0.373065 | + | 0.927805i | \(0.621693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.9972 | −2.09627 | ||||||||
\(92\) | 0.821736 | 0.0856719 | ||||||||
\(93\) | 3.48346 | 0.361217 | ||||||||
\(94\) | 11.5079 | 1.18695 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.98098 | 0.406307 | ||||||||
\(97\) | −5.03884 | −0.511617 | −0.255808 | − | 0.966727i | \(-0.582342\pi\) | ||||
−0.255808 | + | 0.966727i | \(0.582342\pi\) | |||||||
\(98\) | 21.9594 | 2.21823 | ||||||||
\(99\) | −40.1356 | −4.03378 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.87959 | −0.883552 | −0.441776 | − | 0.897125i | \(-0.645651\pi\) | ||||
−0.441776 | + | 0.897125i | \(0.645651\pi\) | |||||||
\(102\) | −26.7070 | −2.64438 | ||||||||
\(103\) | −3.12126 | −0.307547 | −0.153774 | − | 0.988106i | \(-0.549143\pi\) | ||||
−0.153774 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(104\) | −11.3568 | −1.11363 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.1806 | −1.47447 | ||||||||
\(107\) | 2.37926 | 0.230012 | 0.115006 | − | 0.993365i | \(-0.463311\pi\) | ||||
0.115006 | + | 0.993365i | \(0.463311\pi\) | |||||||
\(108\) | −2.66879 | −0.256805 | ||||||||
\(109\) | −10.9286 | −1.04677 | −0.523386 | − | 0.852096i | \(-0.675331\pi\) | ||||
−0.523386 | + | 0.852096i | \(0.675331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.9072 | −2.17426 | ||||||||
\(112\) | 20.5104 | 1.93805 | ||||||||
\(113\) | −12.3477 | −1.16157 | −0.580787 | − | 0.814055i | \(-0.697255\pi\) | ||||
−0.580787 | + | 0.814055i | \(0.697255\pi\) | |||||||
\(114\) | 5.74550 | 0.538116 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.409724 | 0.0380419 | ||||||||
\(117\) | 29.0706 | 2.68757 | ||||||||
\(118\) | −8.45926 | −0.778738 | ||||||||
\(119\) | −26.6811 | −2.44585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.0974 | 2.19068 | ||||||||
\(122\) | 7.11159 | 0.643853 | ||||||||
\(123\) | 20.1741 | 1.81904 | ||||||||
\(124\) | −0.251961 | −0.0226268 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −47.1061 | −4.19654 | ||||||||
\(127\) | 8.83493 | 0.783974 | 0.391987 | − | 0.919971i | \(-0.371788\pi\) | ||||
0.391987 | + | 0.919971i | \(0.371788\pi\) | |||||||
\(128\) | 12.8453 | 1.13537 | ||||||||
\(129\) | −14.2928 | −1.25841 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6930 | 0.934252 | 0.467126 | − | 0.884191i | \(-0.345289\pi\) | ||||
0.467126 | + | 0.884191i | \(0.345289\pi\) | |||||||
\(132\) | 4.18857 | 0.364568 | ||||||||
\(133\) | 5.73994 | 0.497716 | ||||||||
\(134\) | 20.9037 | 1.80580 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.1528 | −1.29934 | ||||||||
\(137\) | 6.53145 | 0.558020 | 0.279010 | − | 0.960288i | \(-0.409994\pi\) | ||||
0.279010 | + | 0.960288i | \(0.409994\pi\) | |||||||
\(138\) | −16.9506 | −1.44293 | ||||||||
\(139\) | −9.68333 | −0.821329 | −0.410664 | − | 0.911787i | \(-0.634703\pi\) | ||||
−0.410664 | + | 0.911787i | \(0.634703\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.1142 | −2.03079 | ||||||||
\(142\) | −5.92117 | −0.496893 | ||||||||
\(143\) | −25.4213 | −2.12584 | ||||||||
\(144\) | −29.8166 | −2.48471 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.3095 | −1.10150 | ||||||||
\(147\) | −46.0147 | −3.79522 | ||||||||
\(148\) | 1.65690 | 0.136196 | ||||||||
\(149\) | 14.7898 | 1.21163 | 0.605814 | − | 0.795606i | \(-0.292847\pi\) | ||||
0.605814 | + | 0.795606i | \(0.292847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.21804 | −0.0991228 | −0.0495614 | − | 0.998771i | \(-0.515782\pi\) | ||||
−0.0495614 | + | 0.998771i | \(0.515782\pi\) | |||||||
\(152\) | 3.25983 | 0.264407 | ||||||||
\(153\) | 38.7872 | 3.13576 | ||||||||
\(154\) | 41.1929 | 3.31942 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.03381 | −0.242899 | ||||||||
\(157\) | −9.48425 | −0.756926 | −0.378463 | − | 0.925616i | \(-0.623547\pi\) | ||||
−0.378463 | + | 0.925616i | \(0.623547\pi\) | |||||||
\(158\) | 2.64716 | 0.210597 | ||||||||
\(159\) | 31.8101 | 2.52271 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.9342 | −1.33460 | ||||||||
\(162\) | 24.7271 | 1.94275 | ||||||||
\(163\) | −2.02231 | −0.158400 | −0.0791999 | − | 0.996859i | \(-0.525237\pi\) | ||||
−0.0791999 | + | 0.996859i | \(0.525237\pi\) | |||||||
\(164\) | −1.45921 | −0.113945 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.8191 | 1.15018 | ||||||||
\(167\) | 12.0440 | 0.931992 | 0.465996 | − | 0.884787i | \(-0.345696\pi\) | ||||
0.465996 | + | 0.884787i | \(0.345696\pi\) | |||||||
\(168\) | −38.5617 | −2.97510 | ||||||||
\(169\) | 5.41287 | 0.416375 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.34434 | −0.638107 | ||||||||
\(172\) | 1.03381 | 0.0788270 | ||||||||
\(173\) | −10.6055 | −0.806322 | −0.403161 | − | 0.915129i | \(-0.632089\pi\) | ||||
−0.403161 | + | 0.915129i | \(0.632089\pi\) | |||||||
\(174\) | −8.45171 | −0.640723 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 26.0737 | 1.96538 | ||||||||
\(177\) | 17.7259 | 1.33236 | ||||||||
\(178\) | −10.5023 | −0.787184 | ||||||||
\(179\) | −15.6670 | −1.17101 | −0.585505 | − | 0.810669i | \(-0.699104\pi\) | ||||
−0.585505 | + | 0.810669i | \(0.699104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00433 | 0.446298 | 0.223149 | − | 0.974784i | \(-0.428366\pi\) | ||||
0.223149 | + | 0.974784i | \(0.428366\pi\) | |||||||
\(182\) | −29.8363 | −2.21161 | ||||||||
\(183\) | −14.9020 | −1.10158 | ||||||||
\(184\) | −9.61728 | −0.708995 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.19740 | 0.381092 | ||||||||
\(187\) | −33.9183 | −2.48035 | ||||||||
\(188\) | 1.74420 | 0.127209 | ||||||||
\(189\) | 54.9981 | 4.00052 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5050 | −1.04954 | −0.524772 | − | 0.851243i | \(-0.675849\pi\) | ||||
−0.524772 | + | 0.851243i | \(0.675849\pi\) | |||||||
\(192\) | −21.5802 | −1.55742 | ||||||||
\(193\) | −3.41996 | −0.246174 | −0.123087 | − | 0.992396i | \(-0.539279\pi\) | ||||
−0.123087 | + | 0.992396i | \(0.539279\pi\) | |||||||
\(194\) | −7.51808 | −0.539767 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.32827 | 0.237734 | ||||||||
\(197\) | −20.5076 | −1.46111 | −0.730554 | − | 0.682855i | \(-0.760738\pi\) | ||||
−0.730554 | + | 0.682855i | \(0.760738\pi\) | |||||||
\(198\) | −59.8834 | −4.25573 | ||||||||
\(199\) | −2.77785 | −0.196917 | −0.0984583 | − | 0.995141i | \(-0.531391\pi\) | ||||
−0.0984583 | + | 0.995141i | \(0.531391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43.8026 | −3.08959 | ||||||||
\(202\) | −13.2486 | −0.932166 | ||||||||
\(203\) | −8.44353 | −0.592620 | ||||||||
\(204\) | −4.04785 | −0.283406 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.65700 | −0.324469 | ||||||||
\(207\) | 24.6178 | 1.71105 | ||||||||
\(208\) | −18.8854 | −1.30947 | ||||||||
\(209\) | 7.29688 | 0.504735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.9148 | 1.57752 | 0.788760 | − | 0.614701i | \(-0.210723\pi\) | ||||
0.788760 | + | 0.614701i | \(0.210723\pi\) | |||||||
\(212\) | −2.30085 | −0.158023 | ||||||||
\(213\) | 12.4075 | 0.850147 | ||||||||
\(214\) | 3.54991 | 0.242667 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.2345 | 2.12524 | ||||||||
\(217\) | 5.19237 | 0.352481 | ||||||||
\(218\) | −16.3058 | −1.10437 | ||||||||
\(219\) | 27.8893 | 1.88458 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.5673 | 1.65257 | ||||||||
\(222\) | −34.1782 | −2.29389 | ||||||||
\(223\) | −7.52468 | −0.503890 | −0.251945 | − | 0.967742i | \(-0.581070\pi\) | ||||
−0.251945 | + | 0.967742i | \(0.581070\pi\) | |||||||
\(224\) | 5.93397 | 0.396480 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.4231 | −1.22549 | ||||||||
\(227\) | −0.950254 | −0.0630706 | −0.0315353 | − | 0.999503i | \(-0.510040\pi\) | ||||
−0.0315353 | + | 0.999503i | \(0.510040\pi\) | |||||||
\(228\) | 0.870818 | 0.0576713 | ||||||||
\(229\) | 14.6545 | 0.968396 | 0.484198 | − | 0.874958i | \(-0.339111\pi\) | ||||
0.484198 | + | 0.874958i | \(0.339111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −86.3174 | −5.67927 | ||||||||
\(232\) | −4.79526 | −0.314824 | ||||||||
\(233\) | 19.1614 | 1.25530 | 0.627651 | − | 0.778495i | \(-0.284016\pi\) | ||||
0.627651 | + | 0.778495i | \(0.284016\pi\) | |||||||
\(234\) | 43.3740 | 2.83545 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.28213 | −0.0834595 | ||||||||
\(237\) | −5.54697 | −0.360315 | ||||||||
\(238\) | −39.8089 | −2.58043 | ||||||||
\(239\) | −3.88636 | −0.251388 | −0.125694 | − | 0.992069i | \(-0.540116\pi\) | ||||
−0.125694 | + | 0.992069i | \(0.540116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 35.9540 | 2.31121 | ||||||||
\(243\) | −16.4097 | −1.05268 | ||||||||
\(244\) | 1.07787 | 0.0690035 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.1003 | 1.91913 | ||||||||
\(247\) | −5.28518 | −0.336288 | ||||||||
\(248\) | 2.94885 | 0.187252 | ||||||||
\(249\) | −31.0525 | −1.96787 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.8452 | −0.873904 | −0.436952 | − | 0.899485i | \(-0.643942\pi\) | ||||
−0.436952 | + | 0.899485i | \(0.643942\pi\) | |||||||
\(252\) | −7.13964 | −0.449755 | ||||||||
\(253\) | −21.5275 | −1.35342 | ||||||||
\(254\) | 13.1819 | 0.827109 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.36056 | 0.335035 | ||||||||
\(257\) | −6.17221 | −0.385012 | −0.192506 | − | 0.981296i | \(-0.561662\pi\) | ||||
−0.192506 | + | 0.981296i | \(0.561662\pi\) | |||||||
\(258\) | −21.3252 | −1.32765 | ||||||||
\(259\) | −34.1451 | −2.12167 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2746 | 0.759781 | ||||||||
\(262\) | 15.9542 | 0.985656 | ||||||||
\(263\) | −14.8523 | −0.915835 | −0.457917 | − | 0.888995i | \(-0.651404\pi\) | ||||
−0.457917 | + | 0.888995i | \(0.651404\pi\) | |||||||
\(264\) | −49.0214 | −3.01706 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.56414 | 0.525101 | ||||||||
\(267\) | 22.0071 | 1.34681 | ||||||||
\(268\) | 3.16827 | 0.193533 | ||||||||
\(269\) | 24.7594 | 1.50960 | 0.754802 | − | 0.655952i | \(-0.227733\pi\) | ||||
0.754802 | + | 0.655952i | \(0.227733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9399 | 1.33275 | 0.666376 | − | 0.745616i | \(-0.267845\pi\) | ||||
0.666376 | + | 0.745616i | \(0.267845\pi\) | |||||||
\(272\) | −25.1977 | −1.52784 | ||||||||
\(273\) | 62.5204 | 3.78390 | ||||||||
\(274\) | 9.74509 | 0.588723 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.56912 | −0.154643 | ||||||||
\(277\) | −17.9537 | −1.07873 | −0.539367 | − | 0.842071i | \(-0.681336\pi\) | ||||
−0.539367 | + | 0.842071i | \(0.681336\pi\) | |||||||
\(278\) | −14.4478 | −0.866519 | ||||||||
\(279\) | −7.54832 | −0.451906 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9520 | 0.891960 | 0.445980 | − | 0.895043i | \(-0.352855\pi\) | ||||
0.445980 | + | 0.895043i | \(0.352855\pi\) | |||||||
\(282\) | −35.9791 | −2.14252 | ||||||||
\(283\) | 16.8819 | 1.00352 | 0.501761 | − | 0.865006i | \(-0.332686\pi\) | ||||
0.501761 | + | 0.865006i | \(0.332686\pi\) | |||||||
\(284\) | −0.897443 | −0.0532534 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −37.9293 | −2.24281 | ||||||||
\(287\) | 30.0712 | 1.77505 | ||||||||
\(288\) | −8.62641 | −0.508316 | ||||||||
\(289\) | 15.7787 | 0.928160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.7537 | 0.923500 | ||||||||
\(292\) | −2.01725 | −0.118051 | ||||||||
\(293\) | 16.3651 | 0.956061 | 0.478030 | − | 0.878343i | \(-0.341351\pi\) | ||||
0.478030 | + | 0.878343i | \(0.341351\pi\) | |||||||
\(294\) | −68.6550 | −4.00404 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −19.3917 | −1.12712 | ||||||||
\(297\) | 69.9161 | 4.05694 | ||||||||
\(298\) | 22.0668 | 1.27829 | ||||||||
\(299\) | 15.5926 | 0.901741 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.3045 | −1.22797 | ||||||||
\(302\) | −1.81735 | −0.104577 | ||||||||
\(303\) | 27.7617 | 1.59487 | ||||||||
\(304\) | 5.42081 | 0.310905 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 57.8715 | 3.30829 | ||||||||
\(307\) | −19.0297 | −1.08608 | −0.543041 | − | 0.839706i | \(-0.682727\pi\) | ||||
−0.543041 | + | 0.839706i | \(0.682727\pi\) | |||||||
\(308\) | 6.24340 | 0.355751 | ||||||||
\(309\) | 9.75850 | 0.555142 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3005 | −0.924318 | −0.462159 | − | 0.886797i | \(-0.652925\pi\) | ||||
−0.462159 | + | 0.886797i | \(0.652925\pi\) | |||||||
\(312\) | 35.5066 | 2.01017 | ||||||||
\(313\) | −1.71271 | −0.0968084 | −0.0484042 | − | 0.998828i | \(-0.515414\pi\) | ||||
−0.0484042 | + | 0.998828i | \(0.515414\pi\) | |||||||
\(314\) | −14.1507 | −0.798573 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.401217 | 0.0225702 | ||||||||
\(317\) | −9.33229 | −0.524154 | −0.262077 | − | 0.965047i | \(-0.584407\pi\) | ||||
−0.262077 | + | 0.965047i | \(0.584407\pi\) | |||||||
\(318\) | 47.4615 | 2.66151 | ||||||||
\(319\) | −10.7338 | −0.600978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.43865 | −0.415185 | ||||||||
\(322\) | −25.2663 | −1.40803 | ||||||||
\(323\) | −7.05172 | −0.392368 | ||||||||
\(324\) | 3.74777 | 0.208209 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.01734 | −0.167115 | ||||||||
\(327\) | 34.1678 | 1.88949 | ||||||||
\(328\) | 17.0780 | 0.942977 | ||||||||
\(329\) | −35.9442 | −1.98167 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2007 | 0.670613 | 0.335306 | − | 0.942109i | \(-0.391160\pi\) | ||||
0.335306 | + | 0.942109i | \(0.391160\pi\) | |||||||
\(332\) | 2.24605 | 0.123268 | ||||||||
\(333\) | 49.6378 | 2.72014 | ||||||||
\(334\) | 17.9699 | 0.983271 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −64.1248 | −3.49829 | ||||||||
\(337\) | −1.32894 | −0.0723920 | −0.0361960 | − | 0.999345i | \(-0.511524\pi\) | ||||
−0.0361960 | + | 0.999345i | \(0.511524\pi\) | |||||||
\(338\) | 8.07614 | 0.439284 | ||||||||
\(339\) | 38.6046 | 2.09671 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.60078 | 0.357452 | ||||||||
\(342\) | −12.4500 | −0.673217 | ||||||||
\(343\) | −35.9669 | −1.94203 | ||||||||
\(344\) | −12.0993 | −0.652350 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.8237 | −0.850687 | ||||||||
\(347\) | 2.21075 | 0.118679 | 0.0593396 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593396 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(348\) | −1.28099 | −0.0686680 | ||||||||
\(349\) | 17.8704 | 0.956580 | 0.478290 | − | 0.878202i | \(-0.341257\pi\) | ||||
0.478290 | + | 0.878202i | \(0.341257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −50.6407 | −2.70300 | ||||||||
\(352\) | 7.54354 | 0.402072 | ||||||||
\(353\) | −9.10115 | −0.484405 | −0.242203 | − | 0.970226i | \(-0.577870\pi\) | ||||
−0.242203 | + | 0.970226i | \(0.577870\pi\) | |||||||
\(354\) | 26.4475 | 1.40567 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.59179 | −0.0843647 | ||||||||
\(357\) | 83.4174 | 4.41492 | ||||||||
\(358\) | −23.3756 | −1.23544 | ||||||||
\(359\) | −23.0382 | −1.21591 | −0.607956 | − | 0.793971i | \(-0.708010\pi\) | ||||
−0.607956 | + | 0.793971i | \(0.708010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4830 | −0.920155 | ||||||||
\(362\) | 8.95861 | 0.470854 | ||||||||
\(363\) | −75.3396 | −3.95430 | ||||||||
\(364\) | −4.52214 | −0.237025 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.2341 | −1.16219 | ||||||||
\(367\) | −32.4970 | −1.69633 | −0.848164 | − | 0.529734i | \(-0.822292\pi\) | ||||
−0.848164 | + | 0.529734i | \(0.822292\pi\) | |||||||
\(368\) | −15.9927 | −0.833677 | ||||||||
\(369\) | −43.7154 | −2.27573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.4156 | 2.46170 | ||||||||
\(372\) | 0.787745 | 0.0408427 | ||||||||
\(373\) | −35.2363 | −1.82447 | −0.912234 | − | 0.409671i | \(-0.865644\pi\) | ||||
−0.912234 | + | 0.409671i | \(0.865644\pi\) | |||||||
\(374\) | −50.6069 | −2.61682 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.4135 | −1.05274 | ||||||||
\(377\) | 7.77458 | 0.400411 | ||||||||
\(378\) | 82.0585 | 4.22063 | ||||||||
\(379\) | −5.18922 | −0.266553 | −0.133276 | − | 0.991079i | \(-0.542550\pi\) | ||||
−0.133276 | + | 0.991079i | \(0.542550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.6221 | −1.41512 | ||||||||
\(382\) | −21.6418 | −1.10729 | ||||||||
\(383\) | 5.72356 | 0.292460 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(384\) | −40.1602 | −2.04942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.10267 | −0.259719 | ||||||||
\(387\) | 30.9711 | 1.57435 | ||||||||
\(388\) | −1.13948 | −0.0578483 | ||||||||
\(389\) | 24.8562 | 1.26026 | 0.630130 | − | 0.776490i | \(-0.283002\pi\) | ||||
0.630130 | + | 0.776490i | \(0.283002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8043 | 1.05212 | ||||||||
\(392\) | −38.9529 | −1.96742 | ||||||||
\(393\) | −33.4312 | −1.68638 | ||||||||
\(394\) | −30.5979 | −1.54150 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.07623 | −0.456098 | ||||||||
\(397\) | 34.8213 | 1.74763 | 0.873815 | − | 0.486259i | \(-0.161639\pi\) | ||||
0.873815 | + | 0.486259i | \(0.161639\pi\) | |||||||
\(398\) | −4.14462 | −0.207751 | ||||||||
\(399\) | −17.9457 | −0.898408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.1370 | −1.60484 | −0.802422 | − | 0.596757i | \(-0.796456\pi\) | ||||
−0.802422 | + | 0.596757i | \(0.796456\pi\) | |||||||
\(402\) | −65.3545 | −3.25959 | ||||||||
\(403\) | −4.78100 | −0.238158 | ||||||||
\(404\) | −2.00802 | −0.0999028 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.5980 | −0.625227 | ||||||||
\(407\) | −43.4068 | −2.15160 | ||||||||
\(408\) | 47.3745 | 2.34539 | ||||||||
\(409\) | −30.4791 | −1.50709 | −0.753547 | − | 0.657395i | \(-0.771659\pi\) | ||||
−0.753547 | + | 0.657395i | \(0.771659\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.4203 | −1.00726 | ||||||||
\(412\) | −0.705839 | −0.0347742 | ||||||||
\(413\) | 26.4219 | 1.30014 | ||||||||
\(414\) | 36.7304 | 1.80520 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.46384 | −0.267887 | ||||||||
\(417\) | 30.2745 | 1.48255 | ||||||||
\(418\) | 10.8871 | 0.532507 | ||||||||
\(419\) | −14.0542 | −0.686592 | −0.343296 | − | 0.939227i | \(-0.611543\pi\) | ||||
−0.343296 | + | 0.939227i | \(0.611543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.96690 | 0.388283 | 0.194141 | − | 0.980974i | \(-0.437808\pi\) | ||||
0.194141 | + | 0.980974i | \(0.437808\pi\) | |||||||
\(422\) | 34.1895 | 1.66432 | ||||||||
\(423\) | 52.2533 | 2.54064 | ||||||||
\(424\) | 26.9283 | 1.30775 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.5123 | 0.896923 | ||||||||
\(427\) | −22.2126 | −1.07494 | ||||||||
\(428\) | 0.538043 | 0.0260073 | ||||||||
\(429\) | 79.4787 | 3.83727 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.6560 | −1.91016 | −0.955080 | − | 0.296348i | \(-0.904231\pi\) | ||||
−0.955080 | + | 0.296348i | \(0.904231\pi\) | |||||||
\(432\) | 51.9403 | 2.49898 | ||||||||
\(433\) | −3.27667 | −0.157467 | −0.0787333 | − | 0.996896i | \(-0.525088\pi\) | ||||
−0.0787333 | + | 0.996896i | \(0.525088\pi\) | |||||||
\(434\) | 7.74715 | 0.371875 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.47139 | −0.118358 | ||||||||
\(437\) | −4.47565 | −0.214099 | ||||||||
\(438\) | 41.6115 | 1.98827 | ||||||||
\(439\) | −14.5064 | −0.692355 | −0.346177 | − | 0.938169i | \(-0.612520\pi\) | ||||
−0.346177 | + | 0.938169i | \(0.612520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 99.7094 | 4.74807 | ||||||||
\(442\) | 36.6550 | 1.74350 | ||||||||
\(443\) | 19.5267 | 0.927742 | 0.463871 | − | 0.885903i | \(-0.346460\pi\) | ||||
0.463871 | + | 0.885903i | \(0.346460\pi\) | |||||||
\(444\) | −5.18022 | −0.245842 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.2270 | −0.531614 | ||||||||
\(447\) | −46.2397 | −2.18706 | ||||||||
\(448\) | −32.1671 | −1.51975 | ||||||||
\(449\) | −2.85475 | −0.134724 | −0.0673621 | − | 0.997729i | \(-0.521458\pi\) | ||||
−0.0673621 | + | 0.997729i | \(0.521458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.2279 | 1.80008 | ||||||||
\(452\) | −2.79230 | −0.131339 | ||||||||
\(453\) | 3.80815 | 0.178923 | ||||||||
\(454\) | −1.41780 | −0.0665408 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.1917 | −0.477271 | ||||||||
\(457\) | 11.7309 | 0.548749 | 0.274375 | − | 0.961623i | \(-0.411529\pi\) | ||||
0.274375 | + | 0.961623i | \(0.411529\pi\) | |||||||
\(458\) | 21.8649 | 1.02168 | ||||||||
\(459\) | −67.5671 | −3.15376 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41285 | 0.0658028 | 0.0329014 | − | 0.999459i | \(-0.489525\pi\) | ||||
0.0329014 | + | 0.999459i | \(0.489525\pi\) | |||||||
\(462\) | −128.788 | −5.99175 | ||||||||
\(463\) | 30.3025 | 1.40827 | 0.704137 | − | 0.710064i | \(-0.251334\pi\) | ||||
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(464\) | −7.97409 | −0.370188 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.5892 | 1.32437 | ||||||||
\(467\) | −10.2416 | −0.473927 | −0.236963 | − | 0.971519i | \(-0.576152\pi\) | ||||
−0.236963 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(468\) | 6.57399 | 0.303883 | ||||||||
\(469\) | −65.2913 | −3.01487 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.6521 | 1.36630 | ||||||||
\(472\) | 15.0056 | 0.690687 | ||||||||
\(473\) | −27.0833 | −1.24529 | ||||||||
\(474\) | −8.27623 | −0.380140 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.03364 | −0.276552 | ||||||||
\(477\) | −68.9296 | −3.15607 | ||||||||
\(478\) | −5.79855 | −0.265219 | ||||||||
\(479\) | −16.8364 | −0.769275 | −0.384638 | − | 0.923068i | \(-0.625674\pi\) | ||||
−0.384638 | + | 0.923068i | \(0.625674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.4399 | 1.43354 | ||||||||
\(482\) | 1.49203 | 0.0679599 | ||||||||
\(483\) | 52.9441 | 2.40904 | ||||||||
\(484\) | 5.44937 | 0.247699 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −24.4836 | −1.11060 | ||||||||
\(487\) | 19.1209 | 0.866452 | 0.433226 | − | 0.901285i | \(-0.357375\pi\) | ||||
0.433226 | + | 0.901285i | \(0.357375\pi\) | |||||||
\(488\) | −12.6150 | −0.571053 | ||||||||
\(489\) | 6.32268 | 0.285921 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6920 | 0.617910 | 0.308955 | − | 0.951077i | \(-0.400021\pi\) | ||||
0.308955 | + | 0.951077i | \(0.400021\pi\) | |||||||
\(492\) | 4.56216 | 0.205678 | ||||||||
\(493\) | 10.3732 | 0.467185 | ||||||||
\(494\) | −7.88563 | −0.354791 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.90369 | 0.220182 | ||||||||
\(497\) | 18.4944 | 0.829586 | ||||||||
\(498\) | −46.3312 | −2.07615 | ||||||||
\(499\) | 41.2184 | 1.84519 | 0.922595 | − | 0.385770i | \(-0.126064\pi\) | ||||
0.922595 | + | 0.385770i | \(0.126064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.6550 | −1.68230 | ||||||||
\(502\) | −20.6575 | −0.921988 | ||||||||
\(503\) | −23.7713 | −1.05991 | −0.529956 | − | 0.848025i | \(-0.677791\pi\) | ||||
−0.529956 | + | 0.848025i | \(0.677791\pi\) | |||||||
\(504\) | 83.5596 | 3.72204 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −32.1196 | −1.42789 | ||||||||
\(507\) | −16.9231 | −0.751582 | ||||||||
\(508\) | 1.99792 | 0.0886435 | ||||||||
\(509\) | 0.527203 | 0.0233679 | 0.0116839 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116839 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.5712 | 1.83900 | ||||||||
\(512\) | −17.6924 | −0.781903 | ||||||||
\(513\) | 14.5358 | 0.641771 | ||||||||
\(514\) | −9.20910 | −0.406196 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.23215 | −0.142288 | ||||||||
\(517\) | −45.6939 | −2.00962 | ||||||||
\(518\) | −50.9454 | −2.23841 | ||||||||
\(519\) | 33.1577 | 1.45546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7412 | 0.864876 | 0.432438 | − | 0.901664i | \(-0.357654\pi\) | ||||
0.432438 | + | 0.901664i | \(0.357654\pi\) | |||||||
\(522\) | 18.3141 | 0.801585 | ||||||||
\(523\) | −22.0882 | −0.965849 | −0.482925 | − | 0.875662i | \(-0.660426\pi\) | ||||
−0.482925 | + | 0.875662i | \(0.660426\pi\) | |||||||
\(524\) | 2.41811 | 0.105635 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.1601 | −0.966225 | ||||||||
\(527\) | −6.37902 | −0.277874 | ||||||||
\(528\) | −81.5183 | −3.54763 | ||||||||
\(529\) | −9.79577 | −0.425903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38.4104 | −1.66687 | ||||||||
\(532\) | 1.29802 | 0.0562765 | ||||||||
\(533\) | −27.6887 | −1.19933 | ||||||||
\(534\) | 32.8351 | 1.42091 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −37.0802 | −1.60162 | ||||||||
\(537\) | 48.9823 | 2.11374 | ||||||||
\(538\) | 36.9416 | 1.59267 | ||||||||
\(539\) | −87.1929 | −3.75567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.32264 | −0.314825 | −0.157412 | − | 0.987533i | \(-0.550315\pi\) | ||||
−0.157412 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(542\) | 32.7348 | 1.40608 | ||||||||
\(543\) | −18.7723 | −0.805596 | ||||||||
\(544\) | −7.29010 | −0.312561 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 93.2820 | 3.99210 | ||||||||
\(547\) | 27.9274 | 1.19409 | 0.597045 | − | 0.802208i | \(-0.296342\pi\) | ||||
0.597045 | + | 0.802208i | \(0.296342\pi\) | |||||||
\(548\) | 1.47702 | 0.0630950 | ||||||||
\(549\) | 32.2911 | 1.37815 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.23160 | −0.0950692 | ||||||||
\(552\) | 30.0680 | 1.27978 | ||||||||
\(553\) | −8.26821 | −0.351600 | ||||||||
\(554\) | −26.7874 | −1.13809 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.18978 | −0.0928673 | ||||||||
\(557\) | −13.5066 | −0.572293 | −0.286146 | − | 0.958186i | \(-0.592374\pi\) | ||||
−0.286146 | + | 0.958186i | \(0.592374\pi\) | |||||||
\(558\) | −11.2623 | −0.476770 | ||||||||
\(559\) | 19.6166 | 0.829696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 106.044 | 4.47718 | ||||||||
\(562\) | 22.3087 | 0.941037 | ||||||||
\(563\) | −4.30396 | −0.181390 | −0.0906951 | − | 0.995879i | \(-0.528909\pi\) | ||||
−0.0906951 | + | 0.995879i | \(0.528909\pi\) | |||||||
\(564\) | −5.45317 | −0.229620 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.1882 | 1.05874 | ||||||||
\(567\) | −77.2335 | −3.24350 | ||||||||
\(568\) | 10.5033 | 0.440710 | ||||||||
\(569\) | 10.2392 | 0.429248 | 0.214624 | − | 0.976697i | \(-0.431147\pi\) | ||||
0.214624 | + | 0.976697i | \(0.431147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.4305 | −1.06423 | −0.532117 | − | 0.846671i | \(-0.678603\pi\) | ||||
−0.532117 | + | 0.846671i | \(0.678603\pi\) | |||||||
\(572\) | −5.74876 | −0.240368 | ||||||||
\(573\) | 45.3492 | 1.89449 | ||||||||
\(574\) | 44.8670 | 1.87271 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 46.7623 | 1.94843 | ||||||||
\(577\) | 12.6994 | 0.528684 | 0.264342 | − | 0.964429i | \(-0.414845\pi\) | ||||
0.264342 | + | 0.964429i | \(0.414845\pi\) | |||||||
\(578\) | 23.5423 | 0.979229 | ||||||||
\(579\) | 10.6924 | 0.444360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.2863 | −1.92028 | ||||||||
\(582\) | 23.5050 | 0.974312 | ||||||||
\(583\) | 60.2769 | 2.49641 | ||||||||
\(584\) | 23.6091 | 0.976953 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.4172 | 1.00866 | ||||||||
\(587\) | −37.3627 | −1.54212 | −0.771061 | − | 0.636761i | \(-0.780274\pi\) | ||||
−0.771061 | + | 0.636761i | \(0.780274\pi\) | |||||||
\(588\) | −10.4057 | −0.429124 | ||||||||
\(589\) | 1.37233 | 0.0565457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 64.1162 | 2.63739 | ||||||||
\(592\) | −32.2467 | −1.32533 | ||||||||
\(593\) | 20.9359 | 0.859736 | 0.429868 | − | 0.902892i | \(-0.358560\pi\) | ||||
0.429868 | + | 0.902892i | \(0.358560\pi\) | |||||||
\(594\) | 104.317 | 4.28016 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.34455 | 0.136998 | ||||||||
\(597\) | 8.68483 | 0.355447 | ||||||||
\(598\) | 23.2645 | 0.951356 | ||||||||
\(599\) | −40.5567 | −1.65710 | −0.828551 | − | 0.559914i | \(-0.810834\pi\) | ||||
−0.828551 | + | 0.559914i | \(0.810834\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.1739 | −0.863700 | −0.431850 | − | 0.901946i | \(-0.642139\pi\) | ||||
−0.431850 | + | 0.901946i | \(0.642139\pi\) | |||||||
\(602\) | −31.7869 | −1.29554 | ||||||||
\(603\) | 94.9160 | 3.86528 | ||||||||
\(604\) | −0.275447 | −0.0112078 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 41.4211 | 1.68262 | ||||||||
\(607\) | 27.6387 | 1.12182 | 0.560910 | − | 0.827877i | \(-0.310451\pi\) | ||||
0.560910 | + | 0.827877i | \(0.310451\pi\) | |||||||
\(608\) | 1.56833 | 0.0636041 | ||||||||
\(609\) | 26.3984 | 1.06972 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.0965 | 1.33894 | ||||||||
\(612\) | 8.77130 | 0.354559 | ||||||||
\(613\) | −36.9421 | −1.49208 | −0.746039 | − | 0.665902i | \(-0.768047\pi\) | ||||
−0.746039 | + | 0.665902i | \(0.768047\pi\) | |||||||
\(614\) | −28.3928 | −1.14584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −73.0704 | −2.94409 | ||||||||
\(617\) | −40.1279 | −1.61549 | −0.807744 | − | 0.589533i | \(-0.799312\pi\) | ||||
−0.807744 | + | 0.589533i | \(0.799312\pi\) | |||||||
\(618\) | 14.5599 | 0.585686 | ||||||||
\(619\) | −30.3391 | −1.21943 | −0.609716 | − | 0.792620i | \(-0.708716\pi\) | ||||
−0.609716 | + | 0.792620i | \(0.708716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −42.8841 | −1.72088 | ||||||||
\(622\) | −24.3208 | −0.975175 | ||||||||
\(623\) | 32.8033 | 1.31424 | ||||||||
\(624\) | 59.0444 | 2.36367 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.55541 | −0.102135 | ||||||||
\(627\) | −22.8134 | −0.911078 | ||||||||
\(628\) | −2.14476 | −0.0855852 | ||||||||
\(629\) | 41.9485 | 1.67260 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0636 | −1.43567 | −0.717835 | − | 0.696213i | \(-0.754867\pi\) | ||||
−0.717835 | + | 0.696213i | \(0.754867\pi\) | |||||||
\(632\) | −4.69569 | −0.186784 | ||||||||
\(633\) | −71.6422 | −2.84752 | ||||||||
\(634\) | −13.9240 | −0.552993 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.19352 | 0.285241 | ||||||||
\(637\) | 63.1545 | 2.50227 | ||||||||
\(638\) | −16.0151 | −0.634044 | ||||||||
\(639\) | −26.8859 | −1.06359 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.0078 | 1.58021 | 0.790106 | − | 0.612970i | \(-0.210025\pi\) | ||||
0.790106 | + | 0.612970i | \(0.210025\pi\) | |||||||
\(642\) | −11.0987 | −0.438029 | ||||||||
\(643\) | 23.3695 | 0.921604 | 0.460802 | − | 0.887503i | \(-0.347562\pi\) | ||||
0.460802 | + | 0.887503i | \(0.347562\pi\) | |||||||
\(644\) | −3.82948 | −0.150903 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5214 | −0.413957 | ||||||||
\(647\) | 43.5626 | 1.71262 | 0.856312 | − | 0.516459i | \(-0.172750\pi\) | ||||
0.856312 | + | 0.516459i | \(0.172750\pi\) | |||||||
\(648\) | −43.8625 | −1.72308 | ||||||||
\(649\) | 33.5888 | 1.31847 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.2337 | −0.636250 | ||||||||
\(652\) | −0.457324 | −0.0179102 | ||||||||
\(653\) | −11.8810 | −0.464939 | −0.232469 | − | 0.972604i | \(-0.574681\pi\) | ||||
−0.232469 | + | 0.972604i | \(0.574681\pi\) | |||||||
\(654\) | 50.9793 | 1.99345 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 28.3993 | 1.10881 | ||||||||
\(657\) | −60.4334 | −2.35773 | ||||||||
\(658\) | −53.6297 | −2.09070 | ||||||||
\(659\) | 22.2402 | 0.866357 | 0.433178 | − | 0.901308i | \(-0.357392\pi\) | ||||
0.433178 | + | 0.901308i | \(0.357392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7001 | 0.805140 | 0.402570 | − | 0.915389i | \(-0.368117\pi\) | ||||
0.402570 | + | 0.915389i | \(0.368117\pi\) | |||||||
\(662\) | 18.2038 | 0.707511 | ||||||||
\(663\) | −76.8085 | −2.98300 | ||||||||
\(664\) | −26.2870 | −1.02013 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 74.0609 | 2.86980 | ||||||||
\(667\) | 6.58374 | 0.254923 | ||||||||
\(668\) | 2.72362 | 0.105380 | ||||||||
\(669\) | 23.5256 | 0.909551 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.2376 | −1.09010 | ||||||||
\(672\) | −18.5523 | −0.715671 | ||||||||
\(673\) | 4.14046 | 0.159603 | 0.0798016 | − | 0.996811i | \(-0.474571\pi\) | ||||
0.0798016 | + | 0.996811i | \(0.474571\pi\) | |||||||
\(674\) | −1.98281 | −0.0763751 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.22406 | 0.0470793 | ||||||||
\(677\) | 38.9911 | 1.49855 | 0.749275 | − | 0.662259i | \(-0.230402\pi\) | ||||
0.749275 | + | 0.662259i | \(0.230402\pi\) | |||||||
\(678\) | 57.5990 | 2.21208 | ||||||||
\(679\) | 23.4822 | 0.901164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.97093 | 0.113846 | ||||||||
\(682\) | 9.84853 | 0.377120 | ||||||||
\(683\) | 20.2200 | 0.773696 | 0.386848 | − | 0.922144i | \(-0.373564\pi\) | ||||
0.386848 | + | 0.922144i | \(0.373564\pi\) | |||||||
\(684\) | −1.88698 | −0.0721505 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −53.6635 | −2.04888 | ||||||||
\(687\) | −45.8166 | −1.74801 | ||||||||
\(688\) | −20.1200 | −0.767070 | ||||||||
\(689\) | −43.6590 | −1.66328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4772 | −0.398570 | −0.199285 | − | 0.979942i | \(-0.563862\pi\) | ||||
−0.199285 | + | 0.979942i | \(0.563862\pi\) | |||||||
\(692\) | −2.39832 | −0.0911705 | ||||||||
\(693\) | 187.042 | 7.10512 | ||||||||
\(694\) | 3.29849 | 0.125209 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 14.9922 | 0.568277 | ||||||||
\(697\) | −36.9435 | −1.39934 | ||||||||
\(698\) | 26.6631 | 1.00921 | ||||||||
\(699\) | −59.9072 | −2.26590 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2337 | 0.877524 | 0.438762 | − | 0.898603i | \(-0.355417\pi\) | ||||
0.438762 | + | 0.898603i | \(0.355417\pi\) | |||||||
\(702\) | −75.5573 | −2.85173 | ||||||||
\(703\) | −9.02443 | −0.340363 | ||||||||
\(704\) | −40.8923 | −1.54118 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.5791 | −0.511058 | ||||||||
\(707\) | 41.3810 | 1.55629 | ||||||||
\(708\) | 4.00852 | 0.150650 | ||||||||
\(709\) | −28.6569 | −1.07623 | −0.538116 | − | 0.842871i | \(-0.680864\pi\) | ||||
−0.538116 | + | 0.842871i | \(0.680864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0198 | 0.450777 | ||||||||
\(712\) | 18.6297 | 0.698177 | ||||||||
\(713\) | −4.04869 | −0.151625 | ||||||||
\(714\) | 124.461 | 4.65783 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.54293 | −0.132405 | ||||||||
\(717\) | 12.1505 | 0.453770 | ||||||||
\(718\) | −34.3736 | −1.28281 | ||||||||
\(719\) | −5.87954 | −0.219270 | −0.109635 | − | 0.993972i | \(-0.534968\pi\) | ||||
−0.109635 | + | 0.993972i | \(0.534968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5458 | 0.541715 | ||||||||
\(722\) | −26.0850 | −0.970783 | ||||||||
\(723\) | −3.12646 | −0.116274 | ||||||||
\(724\) | 1.35781 | 0.0504627 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −112.409 | −4.17187 | ||||||||
\(727\) | 49.0096 | 1.81767 | 0.908833 | − | 0.417161i | \(-0.136975\pi\) | ||||
0.908833 | + | 0.417161i | \(0.136975\pi\) | |||||||
\(728\) | 52.9255 | 1.96155 | ||||||||
\(729\) | 1.58556 | 0.0587245 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.1734 | 0.968058 | ||||||||
\(732\) | −3.36991 | −0.124556 | ||||||||
\(733\) | −15.4332 | −0.570040 | −0.285020 | − | 0.958522i | \(-0.592000\pi\) | ||||
−0.285020 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(734\) | −48.4863 | −1.78966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.62694 | −0.170551 | ||||||||
\(737\) | −83.0012 | −3.05739 | ||||||||
\(738\) | −65.2245 | −2.40095 | ||||||||
\(739\) | −19.0798 | −0.701863 | −0.350931 | − | 0.936401i | \(-0.614135\pi\) | ||||
−0.350931 | + | 0.936401i | \(0.614135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5239 | 0.607021 | ||||||||
\(742\) | 70.7453 | 2.59714 | ||||||||
\(743\) | 28.2323 | 1.03574 | 0.517871 | − | 0.855459i | \(-0.326725\pi\) | ||||
0.517871 | + | 0.855459i | \(0.326725\pi\) | |||||||
\(744\) | −9.21947 | −0.338002 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −52.5735 | −1.92485 | ||||||||
\(747\) | 67.2879 | 2.46194 | ||||||||
\(748\) | −7.67024 | −0.280452 | ||||||||
\(749\) | −11.0879 | −0.405143 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2127 | 0.372667 | 0.186333 | − | 0.982487i | \(-0.440340\pi\) | ||||
0.186333 | + | 0.982487i | \(0.440340\pi\) | |||||||
\(752\) | −33.9458 | −1.23788 | ||||||||
\(753\) | 43.2866 | 1.57745 | ||||||||
\(754\) | 11.5999 | 0.422442 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.4372 | 0.452337 | ||||||||
\(757\) | 42.5055 | 1.54489 | 0.772445 | − | 0.635082i | \(-0.219034\pi\) | ||||
0.772445 | + | 0.635082i | \(0.219034\pi\) | |||||||
\(758\) | −7.74245 | −0.281219 | ||||||||
\(759\) | 67.3049 | 2.44301 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.2390 | −1.20491 | −0.602456 | − | 0.798152i | \(-0.705811\pi\) | ||||
−0.602456 | + | 0.798152i | \(0.705811\pi\) | |||||||
\(762\) | −41.2128 | −1.49298 | ||||||||
\(763\) | 50.9299 | 1.84379 | ||||||||
\(764\) | −3.28014 | −0.118671 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.53970 | 0.308552 | ||||||||
\(767\) | −24.3286 | −0.878455 | ||||||||
\(768\) | −16.7596 | −0.604759 | ||||||||
\(769\) | 24.0517 | 0.867328 | 0.433664 | − | 0.901075i | \(-0.357221\pi\) | ||||
0.433664 | + | 0.901075i | \(0.357221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.2972 | 0.694971 | ||||||||
\(772\) | −0.773387 | −0.0278348 | ||||||||
\(773\) | 19.5958 | 0.704813 | 0.352407 | − | 0.935847i | \(-0.385363\pi\) | ||||
0.352407 | + | 0.935847i | \(0.385363\pi\) | |||||||
\(774\) | 46.2096 | 1.66097 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.3360 | 0.478735 | ||||||||
\(777\) | 106.753 | 3.82975 | ||||||||
\(778\) | 37.0861 | 1.32960 | ||||||||
\(779\) | 7.94770 | 0.284756 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.5109 | 0.841286 | ||||||||
\(782\) | 31.0405 | 1.11001 | ||||||||
\(783\) | −21.3824 | −0.764143 | ||||||||
\(784\) | −64.7752 | −2.31340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −49.8802 | −1.77917 | ||||||||
\(787\) | −14.4340 | −0.514515 | −0.257257 | − | 0.966343i | \(-0.582819\pi\) | ||||
−0.257257 | + | 0.966343i | \(0.582819\pi\) | |||||||
\(788\) | −4.63757 | −0.165207 | ||||||||
\(789\) | 46.4352 | 1.65314 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.5432 | 2.04600 | ||||||||
\(792\) | 106.225 | 3.77453 | ||||||||
\(793\) | 20.4527 | 0.726298 | ||||||||
\(794\) | 51.9542 | 1.84379 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.628181 | −0.0222653 | ||||||||
\(797\) | 36.2235 | 1.28310 | 0.641551 | − | 0.767081i | \(-0.278291\pi\) | ||||
0.641551 | + | 0.767081i | \(0.278291\pi\) | |||||||
\(798\) | −26.7754 | −0.947839 | ||||||||
\(799\) | 44.1588 | 1.56223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.6873 | −1.68495 | ||||||||
\(802\) | −47.9492 | −1.69314 | ||||||||
\(803\) | 52.8472 | 1.86494 | ||||||||
\(804\) | −9.90547 | −0.349339 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.13337 | −0.251262 | ||||||||
\(807\) | −77.4091 | −2.72493 | ||||||||
\(808\) | 23.5011 | 0.826766 | ||||||||
\(809\) | −33.5485 | −1.17950 | −0.589751 | − | 0.807585i | \(-0.700774\pi\) | ||||
−0.589751 | + | 0.807585i | \(0.700774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.8458 | −1.46941 | −0.734703 | − | 0.678389i | \(-0.762678\pi\) | ||||
−0.734703 | + | 0.678389i | \(0.762678\pi\) | |||||||
\(812\) | −1.90941 | −0.0670072 | ||||||||
\(813\) | −68.5940 | −2.40570 | ||||||||
\(814\) | −64.7641 | −2.26998 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 78.7796 | 2.75784 | ||||||||
\(817\) | −5.63071 | −0.196994 | ||||||||
\(818\) | −45.4755 | −1.59002 | ||||||||
\(819\) | −135.476 | −4.73390 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.6138 | −1.03353 | −0.516765 | − | 0.856127i | \(-0.672864\pi\) | ||||
−0.516765 | + | 0.856127i | \(0.672864\pi\) | |||||||
\(822\) | −30.4676 | −1.06268 | ||||||||
\(823\) | −5.60965 | −0.195540 | −0.0977701 | − | 0.995209i | \(-0.531171\pi\) | ||||
−0.0977701 | + | 0.995209i | \(0.531171\pi\) | |||||||
\(824\) | 8.26088 | 0.287781 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39.4222 | 1.37167 | ||||||||
\(827\) | −13.9106 | −0.483720 | −0.241860 | − | 0.970311i | \(-0.577758\pi\) | ||||
−0.241860 | + | 0.970311i | \(0.577758\pi\) | |||||||
\(828\) | 5.56704 | 0.193468 | ||||||||
\(829\) | 22.9062 | 0.795567 | 0.397783 | − | 0.917479i | \(-0.369780\pi\) | ||||
0.397783 | + | 0.917479i | \(0.369780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.1315 | 1.94718 | ||||||||
\(832\) | 29.6186 | 1.02684 | ||||||||
\(833\) | 84.2635 | 2.91956 | ||||||||
\(834\) | 45.1703 | 1.56412 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.65011 | 0.0570702 | ||||||||
\(837\) | 13.1491 | 0.454500 | ||||||||
\(838\) | −20.9692 | −0.724369 | ||||||||
\(839\) | −5.57070 | −0.192322 | −0.0961609 | − | 0.995366i | \(-0.530656\pi\) | ||||
−0.0961609 | + | 0.995366i | \(0.530656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7173 | −0.886803 | ||||||||
\(842\) | 11.8868 | 0.409647 | ||||||||
\(843\) | −46.7467 | −1.61004 | ||||||||
\(844\) | 5.18193 | 0.178369 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 77.9632 | 2.68043 | ||||||||
\(847\) | −112.300 | −3.85867 | ||||||||
\(848\) | 44.7794 | 1.53773 | ||||||||
\(849\) | −52.7804 | −1.81142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.6242 | 0.912667 | ||||||||
\(852\) | 2.80582 | 0.0961257 | ||||||||
\(853\) | −35.8612 | −1.22786 | −0.613931 | − | 0.789359i | \(-0.710413\pi\) | ||||
−0.613931 | + | 0.789359i | \(0.710413\pi\) | |||||||
\(854\) | −33.1417 | −1.13409 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.29705 | −0.215229 | ||||||||
\(857\) | 0.654119 | 0.0223443 | 0.0111721 | − | 0.999938i | \(-0.496444\pi\) | ||||
0.0111721 | + | 0.999938i | \(0.496444\pi\) | |||||||
\(858\) | 118.584 | 4.04840 | ||||||||
\(859\) | 2.58305 | 0.0881324 | 0.0440662 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440662 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −94.0163 | −3.20407 | ||||||||
\(862\) | −59.1677 | −2.01526 | ||||||||
\(863\) | −52.4627 | −1.78585 | −0.892925 | − | 0.450206i | \(-0.851351\pi\) | ||||
−0.892925 | + | 0.450206i | \(0.851351\pi\) | |||||||
\(864\) | 15.0272 | 0.511234 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.88887 | −0.166130 | ||||||||
\(867\) | −49.3315 | −1.67539 | ||||||||
\(868\) | 1.17420 | 0.0398549 | ||||||||
\(869\) | −10.5109 | −0.356559 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.1184 | 2.03704 | ||||||||
\(872\) | 28.9242 | 0.979496 | ||||||||
\(873\) | −34.1368 | −1.15536 | ||||||||
\(874\) | −6.67778 | −0.225879 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.30685 | 0.213089 | ||||||||
\(877\) | −19.1481 | −0.646586 | −0.323293 | − | 0.946299i | \(-0.604790\pi\) | ||||
−0.323293 | + | 0.946299i | \(0.604790\pi\) | |||||||
\(878\) | −21.6440 | −0.730449 | ||||||||
\(879\) | −51.1649 | −1.72575 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6243 | −1.30129 | −0.650643 | − | 0.759384i | \(-0.725501\pi\) | ||||
−0.650643 | + | 0.759384i | \(0.725501\pi\) | |||||||
\(882\) | 148.769 | 5.00931 | ||||||||
\(883\) | −40.7541 | −1.37149 | −0.685743 | − | 0.727844i | \(-0.740523\pi\) | ||||
−0.685743 | + | 0.727844i | \(0.740523\pi\) | |||||||
\(884\) | 5.55562 | 0.186856 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.1344 | 0.978788 | ||||||||
\(887\) | 44.2838 | 1.48690 | 0.743452 | − | 0.668789i | \(-0.233187\pi\) | ||||
0.743452 | + | 0.668789i | \(0.233187\pi\) | |||||||
\(888\) | 60.6274 | 2.03452 | ||||||||
\(889\) | −41.1729 | −1.38089 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −98.1827 | −3.28925 | ||||||||
\(892\) | −1.70162 | −0.0569745 | ||||||||
\(893\) | −9.49993 | −0.317903 | ||||||||
\(894\) | −68.9908 | −2.30740 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −59.8620 | −1.99985 | ||||||||
\(897\) | −48.7495 | −1.62770 | ||||||||
\(898\) | −4.25936 | −0.142137 | ||||||||
\(899\) | −2.01871 | −0.0673277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.2518 | −1.94065 | ||||||||
\(902\) | 57.0369 | 1.89912 | ||||||||
\(903\) | 66.6077 | 2.21657 | ||||||||
\(904\) | 32.6800 | 1.08692 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.68186 | 0.188767 | ||||||||
\(907\) | 0.773290 | 0.0256767 | 0.0128383 | − | 0.999918i | \(-0.495913\pi\) | ||||
0.0128383 | + | 0.999918i | \(0.495913\pi\) | |||||||
\(908\) | −0.214889 | −0.00713136 | ||||||||
\(909\) | −60.1569 | −1.99528 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.1307 | 1.29646 | 0.648228 | − | 0.761446i | \(-0.275510\pi\) | ||||
0.648228 | + | 0.761446i | \(0.275510\pi\) | |||||||
\(912\) | −16.9479 | −0.561202 | ||||||||
\(913\) | −58.8413 | −1.94736 | ||||||||
\(914\) | 17.5028 | 0.578942 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.31395 | 0.109496 | ||||||||
\(917\) | −49.8319 | −1.64560 | ||||||||
\(918\) | −100.812 | −3.32729 | ||||||||
\(919\) | 24.2527 | 0.800023 | 0.400011 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400011 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.4955 | 1.96044 | ||||||||
\(922\) | 2.10800 | 0.0694233 | ||||||||
\(923\) | −17.0291 | −0.560520 | ||||||||
\(924\) | −19.5197 | −0.642152 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 45.2120 | 1.48576 | ||||||||
\(927\) | −21.1457 | −0.694517 | ||||||||
\(928\) | −2.30703 | −0.0757320 | ||||||||
\(929\) | 4.12264 | 0.135260 | 0.0676298 | − | 0.997710i | \(-0.478456\pi\) | ||||
0.0676298 | + | 0.997710i | \(0.478456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1277 | −0.594112 | ||||||||
\(932\) | 4.33313 | 0.141936 | ||||||||
\(933\) | 50.9629 | 1.66845 | ||||||||
\(934\) | −15.2808 | −0.500003 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −76.9394 | −2.51484 | ||||||||
\(937\) | 8.27592 | 0.270362 | 0.135181 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135181 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(938\) | −97.4162 | −3.18075 | ||||||||
\(939\) | 5.35473 | 0.174745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.2610 | 0.367100 | 0.183550 | − | 0.983010i | \(-0.441241\pi\) | ||||
0.183550 | + | 0.983010i | \(0.441241\pi\) | |||||||
\(942\) | 44.2417 | 1.44147 | ||||||||
\(943\) | −23.4476 | −0.763560 | ||||||||
\(944\) | 24.9529 | 0.812148 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.4090 | −1.31381 | ||||||||
\(947\) | −28.2529 | −0.918096 | −0.459048 | − | 0.888411i | \(-0.651809\pi\) | ||||
−0.459048 | + | 0.888411i | \(0.651809\pi\) | |||||||
\(948\) | −1.25439 | −0.0407406 | ||||||||
\(949\) | −38.2776 | −1.24254 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.1770 | 0.946130 | ||||||||
\(952\) | 70.6155 | 2.28866 | ||||||||
\(953\) | −39.0186 | −1.26394 | −0.631968 | − | 0.774995i | \(-0.717752\pi\) | ||||
−0.631968 | + | 0.774995i | \(0.717752\pi\) | |||||||
\(954\) | −102.845 | −3.32972 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.878858 | −0.0284243 | ||||||||
\(957\) | 33.5588 | 1.08480 | ||||||||
\(958\) | −25.1203 | −0.811602 | ||||||||
\(959\) | −30.4381 | −0.982899 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7586 | −0.959955 | ||||||||
\(962\) | 46.9091 | 1.51241 | ||||||||
\(963\) | 16.1188 | 0.519423 | ||||||||
\(964\) | 0.226139 | 0.00728345 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 78.9939 | 2.54159 | ||||||||
\(967\) | −39.9098 | −1.28341 | −0.641707 | − | 0.766950i | \(-0.721773\pi\) | ||||
−0.641707 | + | 0.766950i | \(0.721773\pi\) | |||||||
\(968\) | −63.7773 | −2.04988 | ||||||||
\(969\) | 22.0469 | 0.708249 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.1082 | 1.60805 | 0.804024 | − | 0.594597i | \(-0.202688\pi\) | ||||
0.804024 | + | 0.594597i | \(0.202688\pi\) | |||||||
\(972\) | −3.71087 | −0.119026 | ||||||||
\(973\) | 45.1266 | 1.44669 | ||||||||
\(974\) | 28.5289 | 0.914126 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.9776 | −0.671477 | ||||||||
\(977\) | 42.4558 | 1.35828 | 0.679141 | − | 0.734008i | \(-0.262352\pi\) | ||||
0.679141 | + | 0.734008i | \(0.262352\pi\) | |||||||
\(978\) | 9.43359 | 0.301653 | ||||||||
\(979\) | 41.7011 | 1.33277 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −74.0385 | −2.36387 | ||||||||
\(982\) | 20.4288 | 0.651908 | ||||||||
\(983\) | −18.7770 | −0.598895 | −0.299447 | − | 0.954113i | \(-0.596802\pi\) | ||||
−0.299447 | + | 0.954113i | \(0.596802\pi\) | |||||||
\(984\) | −53.3938 | −1.70213 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.4771 | 0.492890 | ||||||||
\(987\) | 112.378 | 3.57703 | ||||||||
\(988\) | −1.19519 | −0.0380239 | ||||||||
\(989\) | 16.6119 | 0.528229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.86345 | −0.249791 | −0.124895 | − | 0.992170i | \(-0.539860\pi\) | ||||
−0.124895 | + | 0.992170i | \(0.539860\pi\) | |||||||
\(992\) | 1.41872 | 0.0450443 | ||||||||
\(993\) | −38.1451 | −1.21050 | ||||||||
\(994\) | 27.5941 | 0.875230 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.02219 | −0.222507 | ||||||||
\(997\) | −4.32111 | −0.136851 | −0.0684255 | − | 0.997656i | \(-0.521798\pi\) | ||||
−0.0684255 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(998\) | 61.4989 | 1.94671 | ||||||||
\(999\) | −86.4688 | −2.73575 |
(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 | 6025.2.a.p.1.35 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.35 | yes | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.12 | ✓ | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.12 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.12 | ✓ | 46 | 5.3 | odd | 4 | ||
1205.2.b.c.724.35 | yes | 46 | 5.2 | odd | 4 | ||
6025.2.a.p.1.12 | 46 | 5.4 | even | 2 | inner | ||
6025.2.a.p.1.35 | 46 | 1.1 | even | 1 | trivial |