Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32736 | −1.64570 | −0.822848 | − | 0.568262i | \(-0.807616\pi\) | ||||
−0.822848 | + | 0.568262i | \(0.807616\pi\) | |||||||
\(3\) | −1.68164 | −0.970894 | −0.485447 | − | 0.874266i | \(-0.661343\pi\) | ||||
−0.485447 | + | 0.874266i | \(0.661343\pi\) | |||||||
\(4\) | 3.41663 | 1.70831 | ||||||||
\(5\) | 2.73432 | 1.22282 | 0.611412 | − | 0.791313i | \(-0.290602\pi\) | ||||
0.611412 | + | 0.791313i | \(0.290602\pi\) | |||||||
\(6\) | 3.91378 | 1.59780 | ||||||||
\(7\) | 2.98551 | 1.12842 | 0.564208 | − | 0.825632i | \(-0.309181\pi\) | ||||
0.564208 | + | 0.825632i | \(0.309181\pi\) | |||||||
\(8\) | −3.29700 | −1.16567 | ||||||||
\(9\) | −0.172094 | −0.0573647 | ||||||||
\(10\) | −6.36375 | −2.01239 | ||||||||
\(11\) | 5.81906 | 1.75451 | 0.877256 | − | 0.480022i | \(-0.159371\pi\) | ||||
0.877256 | + | 0.480022i | \(0.159371\pi\) | |||||||
\(12\) | −5.74553 | −1.65859 | ||||||||
\(13\) | 4.09184 | 1.13487 | 0.567436 | − | 0.823417i | \(-0.307935\pi\) | ||||
0.567436 | + | 0.823417i | \(0.307935\pi\) | |||||||
\(14\) | −6.94837 | −1.85703 | ||||||||
\(15\) | −4.59813 | −1.18723 | ||||||||
\(16\) | 0.840077 | 0.210019 | ||||||||
\(17\) | 1.41108 | 0.342238 | 0.171119 | − | 0.985250i | \(-0.445262\pi\) | ||||
0.171119 | + | 0.985250i | \(0.445262\pi\) | |||||||
\(18\) | 0.400526 | 0.0944048 | ||||||||
\(19\) | −0.843215 | −0.193447 | −0.0967234 | − | 0.995311i | \(-0.530836\pi\) | ||||
−0.0967234 | + | 0.995311i | \(0.530836\pi\) | |||||||
\(20\) | 9.34213 | 2.08896 | ||||||||
\(21\) | −5.02055 | −1.09557 | ||||||||
\(22\) | −13.5431 | −2.88739 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 5.54436 | 1.13174 | ||||||||
\(25\) | 2.47648 | 0.495296 | ||||||||
\(26\) | −9.52320 | −1.86765 | ||||||||
\(27\) | 5.33431 | 1.02659 | ||||||||
\(28\) | 10.2004 | 1.92769 | ||||||||
\(29\) | 7.07815 | 1.31438 | 0.657189 | − | 0.753726i | \(-0.271745\pi\) | ||||
0.657189 | + | 0.753726i | \(0.271745\pi\) | |||||||
\(30\) | 10.7015 | 1.95382 | ||||||||
\(31\) | −2.42137 | −0.434890 | −0.217445 | − | 0.976073i | \(-0.569772\pi\) | ||||
−0.217445 | + | 0.976073i | \(0.569772\pi\) | |||||||
\(32\) | 4.63884 | 0.820039 | ||||||||
\(33\) | −9.78555 | −1.70345 | ||||||||
\(34\) | −3.28410 | −0.563219 | ||||||||
\(35\) | 8.16333 | 1.37985 | ||||||||
\(36\) | −0.587981 | −0.0979968 | ||||||||
\(37\) | −5.17537 | −0.850825 | −0.425413 | − | 0.904999i | \(-0.639871\pi\) | ||||
−0.425413 | + | 0.904999i | \(0.639871\pi\) | |||||||
\(38\) | 1.96247 | 0.318355 | ||||||||
\(39\) | −6.88099 | −1.10184 | ||||||||
\(40\) | −9.01505 | −1.42540 | ||||||||
\(41\) | −1.45321 | −0.226953 | −0.113477 | − | 0.993541i | \(-0.536199\pi\) | ||||
−0.113477 | + | 0.993541i | \(0.536199\pi\) | |||||||
\(42\) | 11.6846 | 1.80298 | ||||||||
\(43\) | −8.03543 | −1.22539 | −0.612696 | − | 0.790319i | \(-0.709915\pi\) | ||||
−0.612696 | + | 0.790319i | \(0.709915\pi\) | |||||||
\(44\) | 19.8815 | 2.99726 | ||||||||
\(45\) | −0.470559 | −0.0701469 | ||||||||
\(46\) | −2.32736 | −0.343151 | ||||||||
\(47\) | −0.879671 | −0.128313 | −0.0641566 | − | 0.997940i | \(-0.520436\pi\) | ||||
−0.0641566 | + | 0.997940i | \(0.520436\pi\) | |||||||
\(48\) | −1.41271 | −0.203906 | ||||||||
\(49\) | 1.91327 | 0.273324 | ||||||||
\(50\) | −5.76368 | −0.815107 | ||||||||
\(51\) | −2.37293 | −0.332276 | ||||||||
\(52\) | 13.9803 | 1.93872 | ||||||||
\(53\) | 0.713413 | 0.0979948 | 0.0489974 | − | 0.998799i | \(-0.484397\pi\) | ||||
0.0489974 | + | 0.998799i | \(0.484397\pi\) | |||||||
\(54\) | −12.4149 | −1.68945 | ||||||||
\(55\) | 15.9111 | 2.14546 | ||||||||
\(56\) | −9.84324 | −1.31536 | ||||||||
\(57\) | 1.41798 | 0.187816 | ||||||||
\(58\) | −16.4734 | −2.16307 | ||||||||
\(59\) | −12.5029 | −1.62774 | −0.813869 | − | 0.581049i | \(-0.802643\pi\) | ||||
−0.813869 | + | 0.581049i | \(0.802643\pi\) | |||||||
\(60\) | −15.7101 | −2.02816 | ||||||||
\(61\) | 8.18803 | 1.04837 | 0.524185 | − | 0.851605i | \(-0.324370\pi\) | ||||
0.524185 | + | 0.851605i | \(0.324370\pi\) | |||||||
\(62\) | 5.63540 | 0.715696 | ||||||||
\(63\) | −0.513788 | −0.0647313 | ||||||||
\(64\) | −12.4764 | −1.55955 | ||||||||
\(65\) | 11.1884 | 1.38775 | ||||||||
\(66\) | 22.7745 | 2.80335 | ||||||||
\(67\) | 7.32236 | 0.894568 | 0.447284 | − | 0.894392i | \(-0.352391\pi\) | ||||
0.447284 | + | 0.894392i | \(0.352391\pi\) | |||||||
\(68\) | 4.82114 | 0.584649 | ||||||||
\(69\) | −1.68164 | −0.202445 | ||||||||
\(70\) | −18.9990 | −2.27082 | ||||||||
\(71\) | 3.98574 | 0.473020 | 0.236510 | − | 0.971629i | \(-0.423996\pi\) | ||||
0.236510 | + | 0.971629i | \(0.423996\pi\) | |||||||
\(72\) | 0.567395 | 0.0668681 | ||||||||
\(73\) | −12.0378 | −1.40891 | −0.704457 | − | 0.709747i | \(-0.748809\pi\) | ||||
−0.704457 | + | 0.709747i | \(0.748809\pi\) | |||||||
\(74\) | 12.0450 | 1.40020 | ||||||||
\(75\) | −4.16455 | −0.480880 | ||||||||
\(76\) | −2.88095 | −0.330468 | ||||||||
\(77\) | 17.3729 | 1.97982 | ||||||||
\(78\) | 16.0146 | 1.81329 | ||||||||
\(79\) | 6.86405 | 0.772266 | 0.386133 | − | 0.922443i | \(-0.373811\pi\) | ||||
0.386133 | + | 0.922443i | \(0.373811\pi\) | |||||||
\(80\) | 2.29704 | 0.256816 | ||||||||
\(81\) | −8.45410 | −0.939345 | ||||||||
\(82\) | 3.38215 | 0.373496 | ||||||||
\(83\) | 2.00548 | 0.220130 | 0.110065 | − | 0.993924i | \(-0.464894\pi\) | ||||
0.110065 | + | 0.993924i | \(0.464894\pi\) | |||||||
\(84\) | −17.1533 | −1.87158 | ||||||||
\(85\) | 3.85834 | 0.418496 | ||||||||
\(86\) | 18.7014 | 2.01662 | ||||||||
\(87\) | −11.9029 | −1.27612 | ||||||||
\(88\) | −19.1855 | −2.04518 | ||||||||
\(89\) | −6.63433 | −0.703238 | −0.351619 | − | 0.936143i | \(-0.614369\pi\) | ||||
−0.351619 | + | 0.936143i | \(0.614369\pi\) | |||||||
\(90\) | 1.09516 | 0.115440 | ||||||||
\(91\) | 12.2162 | 1.28061 | ||||||||
\(92\) | 3.41663 | 0.356208 | ||||||||
\(93\) | 4.07186 | 0.422232 | ||||||||
\(94\) | 2.04732 | 0.211165 | ||||||||
\(95\) | −2.30562 | −0.236551 | ||||||||
\(96\) | −7.80085 | −0.796171 | ||||||||
\(97\) | −7.59549 | −0.771205 | −0.385603 | − | 0.922665i | \(-0.626006\pi\) | ||||
−0.385603 | + | 0.922665i | \(0.626006\pi\) | |||||||
\(98\) | −4.45288 | −0.449809 | ||||||||
\(99\) | −1.00143 | −0.100647 | ||||||||
\(100\) | 8.46121 | 0.846121 | ||||||||
\(101\) | 17.5517 | 1.74646 | 0.873231 | − | 0.487307i | \(-0.162021\pi\) | ||||
0.873231 | + | 0.487307i | \(0.162021\pi\) | |||||||
\(102\) | 5.52267 | 0.546826 | ||||||||
\(103\) | 14.1752 | 1.39673 | 0.698363 | − | 0.715744i | \(-0.253912\pi\) | ||||
0.698363 | + | 0.715744i | \(0.253912\pi\) | |||||||
\(104\) | −13.4908 | −1.32288 | ||||||||
\(105\) | −13.7278 | −1.33969 | ||||||||
\(106\) | −1.66037 | −0.161270 | ||||||||
\(107\) | 1.14586 | 0.110775 | 0.0553874 | − | 0.998465i | \(-0.482361\pi\) | ||||
0.0553874 | + | 0.998465i | \(0.482361\pi\) | |||||||
\(108\) | 18.2253 | 1.75374 | ||||||||
\(109\) | 20.2886 | 1.94329 | 0.971646 | − | 0.236442i | \(-0.0759815\pi\) | ||||
0.971646 | + | 0.236442i | \(0.0759815\pi\) | |||||||
\(110\) | −37.0310 | −3.53077 | ||||||||
\(111\) | 8.70310 | 0.826061 | ||||||||
\(112\) | 2.50806 | 0.236989 | ||||||||
\(113\) | 4.25824 | 0.400581 | 0.200291 | − | 0.979737i | \(-0.435811\pi\) | ||||
0.200291 | + | 0.979737i | \(0.435811\pi\) | |||||||
\(114\) | −3.30016 | −0.309089 | ||||||||
\(115\) | 2.73432 | 0.254976 | ||||||||
\(116\) | 24.1834 | 2.24537 | ||||||||
\(117\) | −0.704181 | −0.0651016 | ||||||||
\(118\) | 29.0988 | 2.67876 | ||||||||
\(119\) | 4.21280 | 0.386187 | ||||||||
\(120\) | 15.1600 | 1.38392 | ||||||||
\(121\) | 22.8615 | 2.07831 | ||||||||
\(122\) | −19.0565 | −1.72530 | ||||||||
\(123\) | 2.44377 | 0.220348 | ||||||||
\(124\) | −8.27290 | −0.742928 | ||||||||
\(125\) | −6.90010 | −0.617163 | ||||||||
\(126\) | 1.19577 | 0.106528 | ||||||||
\(127\) | 1.54916 | 0.137466 | 0.0687329 | − | 0.997635i | \(-0.478104\pi\) | ||||
0.0687329 | + | 0.997635i | \(0.478104\pi\) | |||||||
\(128\) | 19.7595 | 1.74651 | ||||||||
\(129\) | 13.5127 | 1.18973 | ||||||||
\(130\) | −26.0394 | −2.28381 | ||||||||
\(131\) | −14.8765 | −1.29977 | −0.649883 | − | 0.760034i | \(-0.725182\pi\) | ||||
−0.649883 | + | 0.760034i | \(0.725182\pi\) | |||||||
\(132\) | −33.4336 | −2.91002 | ||||||||
\(133\) | −2.51743 | −0.218289 | ||||||||
\(134\) | −17.0418 | −1.47219 | ||||||||
\(135\) | 14.5857 | 1.25534 | ||||||||
\(136\) | −4.65234 | −0.398935 | ||||||||
\(137\) | 15.3396 | 1.31055 | 0.655276 | − | 0.755390i | \(-0.272552\pi\) | ||||
0.655276 | + | 0.755390i | \(0.272552\pi\) | |||||||
\(138\) | 3.91378 | 0.333163 | ||||||||
\(139\) | 14.1749 | 1.20230 | 0.601151 | − | 0.799136i | \(-0.294709\pi\) | ||||
0.601151 | + | 0.799136i | \(0.294709\pi\) | |||||||
\(140\) | 27.8910 | 2.35722 | ||||||||
\(141\) | 1.47929 | 0.124579 | ||||||||
\(142\) | −9.27626 | −0.778446 | ||||||||
\(143\) | 23.8107 | 1.99115 | ||||||||
\(144\) | −0.144572 | −0.0120477 | ||||||||
\(145\) | 19.3539 | 1.60725 | ||||||||
\(146\) | 28.0163 | 2.31864 | ||||||||
\(147\) | −3.21743 | −0.265369 | ||||||||
\(148\) | −17.6823 | −1.45348 | ||||||||
\(149\) | −18.9209 | −1.55006 | −0.775028 | − | 0.631927i | \(-0.782264\pi\) | ||||
−0.775028 | + | 0.631927i | \(0.782264\pi\) | |||||||
\(150\) | 9.69242 | 0.791382 | ||||||||
\(151\) | 10.0386 | 0.816930 | 0.408465 | − | 0.912774i | \(-0.366064\pi\) | ||||
0.408465 | + | 0.912774i | \(0.366064\pi\) | |||||||
\(152\) | 2.78008 | 0.225495 | ||||||||
\(153\) | −0.242839 | −0.0196323 | ||||||||
\(154\) | −40.4330 | −3.25818 | ||||||||
\(155\) | −6.62078 | −0.531794 | ||||||||
\(156\) | −23.5098 | −1.88229 | ||||||||
\(157\) | −20.3741 | −1.62603 | −0.813014 | − | 0.582244i | \(-0.802175\pi\) | ||||
−0.813014 | + | 0.582244i | \(0.802175\pi\) | |||||||
\(158\) | −15.9752 | −1.27091 | ||||||||
\(159\) | −1.19970 | −0.0951426 | ||||||||
\(160\) | 12.6841 | 1.00276 | ||||||||
\(161\) | 2.98551 | 0.235291 | ||||||||
\(162\) | 19.6758 | 1.54587 | ||||||||
\(163\) | 10.2711 | 0.804495 | 0.402248 | − | 0.915531i | \(-0.368229\pi\) | ||||
0.402248 | + | 0.915531i | \(0.368229\pi\) | |||||||
\(164\) | −4.96507 | −0.387707 | ||||||||
\(165\) | −26.7568 | −2.08301 | ||||||||
\(166\) | −4.66747 | −0.362266 | ||||||||
\(167\) | 7.65655 | 0.592482 | 0.296241 | − | 0.955113i | \(-0.404267\pi\) | ||||
0.296241 | + | 0.955113i | \(0.404267\pi\) | |||||||
\(168\) | 16.5528 | 1.27707 | ||||||||
\(169\) | 3.74316 | 0.287935 | ||||||||
\(170\) | −8.97977 | −0.688717 | ||||||||
\(171\) | 0.145112 | 0.0110970 | ||||||||
\(172\) | −27.4540 | −2.09335 | ||||||||
\(173\) | −4.81599 | −0.366153 | −0.183076 | − | 0.983099i | \(-0.558606\pi\) | ||||
−0.183076 | + | 0.983099i | \(0.558606\pi\) | |||||||
\(174\) | 27.7023 | 2.10011 | ||||||||
\(175\) | 7.39356 | 0.558901 | ||||||||
\(176\) | 4.88846 | 0.368481 | ||||||||
\(177\) | 21.0253 | 1.58036 | ||||||||
\(178\) | 15.4405 | 1.15731 | ||||||||
\(179\) | 2.48395 | 0.185659 | 0.0928295 | − | 0.995682i | \(-0.470409\pi\) | ||||
0.0928295 | + | 0.995682i | \(0.470409\pi\) | |||||||
\(180\) | −1.60773 | −0.119833 | ||||||||
\(181\) | 10.7086 | 0.795964 | 0.397982 | − | 0.917393i | \(-0.369711\pi\) | ||||
0.397982 | + | 0.917393i | \(0.369711\pi\) | |||||||
\(182\) | −28.4316 | −2.10749 | ||||||||
\(183\) | −13.7693 | −1.01786 | ||||||||
\(184\) | −3.29700 | −0.243058 | ||||||||
\(185\) | −14.1511 | −1.04041 | ||||||||
\(186\) | −9.47670 | −0.694865 | ||||||||
\(187\) | 8.21117 | 0.600460 | ||||||||
\(188\) | −3.00551 | −0.219199 | ||||||||
\(189\) | 15.9256 | 1.15842 | ||||||||
\(190\) | 5.36601 | 0.389291 | ||||||||
\(191\) | 15.5937 | 1.12832 | 0.564160 | − | 0.825666i | \(-0.309200\pi\) | ||||
0.564160 | + | 0.825666i | \(0.309200\pi\) | |||||||
\(192\) | 20.9808 | 1.51416 | ||||||||
\(193\) | 16.5892 | 1.19411 | 0.597057 | − | 0.802199i | \(-0.296337\pi\) | ||||
0.597057 | + | 0.802199i | \(0.296337\pi\) | |||||||
\(194\) | 17.6775 | 1.26917 | ||||||||
\(195\) | −18.8148 | −1.34736 | ||||||||
\(196\) | 6.53693 | 0.466923 | ||||||||
\(197\) | 22.6011 | 1.61026 | 0.805132 | − | 0.593095i | \(-0.202094\pi\) | ||||
0.805132 | + | 0.593095i | \(0.202094\pi\) | |||||||
\(198\) | 2.33068 | 0.165634 | ||||||||
\(199\) | −11.0208 | −0.781244 | −0.390622 | − | 0.920551i | \(-0.627740\pi\) | ||||
−0.390622 | + | 0.920551i | \(0.627740\pi\) | |||||||
\(200\) | −8.16497 | −0.577350 | ||||||||
\(201\) | −12.3136 | −0.868531 | ||||||||
\(202\) | −40.8493 | −2.87414 | ||||||||
\(203\) | 21.1319 | 1.48317 | ||||||||
\(204\) | −8.10741 | −0.567632 | ||||||||
\(205\) | −3.97353 | −0.277524 | ||||||||
\(206\) | −32.9909 | −2.29859 | ||||||||
\(207\) | −0.172094 | −0.0119614 | ||||||||
\(208\) | 3.43746 | 0.238345 | ||||||||
\(209\) | −4.90672 | −0.339405 | ||||||||
\(210\) | 31.9495 | 2.20472 | ||||||||
\(211\) | −15.1655 | −1.04404 | −0.522018 | − | 0.852934i | \(-0.674821\pi\) | ||||
−0.522018 | + | 0.852934i | \(0.674821\pi\) | |||||||
\(212\) | 2.43746 | 0.167406 | ||||||||
\(213\) | −6.70256 | −0.459252 | ||||||||
\(214\) | −2.66684 | −0.182301 | ||||||||
\(215\) | −21.9714 | −1.49844 | ||||||||
\(216\) | −17.5872 | −1.19666 | ||||||||
\(217\) | −7.22901 | −0.490737 | ||||||||
\(218\) | −47.2189 | −3.19806 | ||||||||
\(219\) | 20.2432 | 1.36791 | ||||||||
\(220\) | 54.3624 | 3.66511 | ||||||||
\(221\) | 5.77392 | 0.388396 | ||||||||
\(222\) | −20.2553 | −1.35945 | ||||||||
\(223\) | −9.58028 | −0.641543 | −0.320772 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320772 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(224\) | 13.8493 | 0.925346 | ||||||||
\(225\) | −0.426188 | −0.0284125 | ||||||||
\(226\) | −9.91047 | −0.659234 | ||||||||
\(227\) | 3.21564 | 0.213430 | 0.106715 | − | 0.994290i | \(-0.465967\pi\) | ||||
0.106715 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(228\) | 4.84472 | 0.320849 | ||||||||
\(229\) | 14.8115 | 0.978772 | 0.489386 | − | 0.872067i | \(-0.337221\pi\) | ||||
0.489386 | + | 0.872067i | \(0.337221\pi\) | |||||||
\(230\) | −6.36375 | −0.419613 | ||||||||
\(231\) | −29.2149 | −1.92220 | ||||||||
\(232\) | −23.3367 | −1.53213 | ||||||||
\(233\) | 16.8961 | 1.10690 | 0.553451 | − | 0.832881i | \(-0.313310\pi\) | ||||
0.553451 | + | 0.832881i | \(0.313310\pi\) | |||||||
\(234\) | 1.63889 | 0.107137 | ||||||||
\(235\) | −2.40530 | −0.156904 | ||||||||
\(236\) | −42.7177 | −2.78069 | ||||||||
\(237\) | −11.5428 | −0.749789 | ||||||||
\(238\) | −9.80472 | −0.635545 | ||||||||
\(239\) | −18.1942 | −1.17689 | −0.588444 | − | 0.808538i | \(-0.700259\pi\) | ||||
−0.588444 | + | 0.808538i | \(0.700259\pi\) | |||||||
\(240\) | −3.86278 | −0.249341 | ||||||||
\(241\) | 30.7883 | 1.98325 | 0.991625 | − | 0.129153i | \(-0.0412258\pi\) | ||||
0.991625 | + | 0.129153i | \(0.0412258\pi\) | |||||||
\(242\) | −53.2069 | −3.42027 | ||||||||
\(243\) | −1.78620 | −0.114585 | ||||||||
\(244\) | 27.9754 | 1.79094 | ||||||||
\(245\) | 5.23149 | 0.334227 | ||||||||
\(246\) | −5.68755 | −0.362625 | ||||||||
\(247\) | −3.45030 | −0.219538 | ||||||||
\(248\) | 7.98325 | 0.506937 | ||||||||
\(249\) | −3.37248 | −0.213722 | ||||||||
\(250\) | 16.0590 | 1.01566 | ||||||||
\(251\) | −7.59537 | −0.479416 | −0.239708 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239708 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(252\) | −1.75542 | −0.110581 | ||||||||
\(253\) | 5.81906 | 0.365841 | ||||||||
\(254\) | −3.60546 | −0.226227 | ||||||||
\(255\) | −6.48833 | −0.406315 | ||||||||
\(256\) | −21.0347 | −1.31467 | ||||||||
\(257\) | −24.6502 | −1.53764 | −0.768819 | − | 0.639467i | \(-0.779155\pi\) | ||||
−0.768819 | + | 0.639467i | \(0.779155\pi\) | |||||||
\(258\) | −31.4489 | −1.95792 | ||||||||
\(259\) | −15.4511 | −0.960086 | ||||||||
\(260\) | 38.2265 | 2.37071 | ||||||||
\(261\) | −1.21811 | −0.0753989 | ||||||||
\(262\) | 34.6230 | 2.13902 | ||||||||
\(263\) | 8.21180 | 0.506361 | 0.253181 | − | 0.967419i | \(-0.418523\pi\) | ||||
0.253181 | + | 0.967419i | \(0.418523\pi\) | |||||||
\(264\) | 32.2630 | 1.98565 | ||||||||
\(265\) | 1.95070 | 0.119830 | ||||||||
\(266\) | 5.85897 | 0.359237 | ||||||||
\(267\) | 11.1565 | 0.682769 | ||||||||
\(268\) | 25.0177 | 1.52820 | ||||||||
\(269\) | −28.6451 | −1.74652 | −0.873262 | − | 0.487251i | \(-0.838000\pi\) | ||||
−0.873262 | + | 0.487251i | \(0.838000\pi\) | |||||||
\(270\) | −33.9462 | −2.06590 | ||||||||
\(271\) | 2.23336 | 0.135667 | 0.0678333 | − | 0.997697i | \(-0.478391\pi\) | ||||
0.0678333 | + | 0.997697i | \(0.478391\pi\) | |||||||
\(272\) | 1.18542 | 0.0718765 | ||||||||
\(273\) | −20.5433 | −1.24334 | ||||||||
\(274\) | −35.7009 | −2.15677 | ||||||||
\(275\) | 14.4108 | 0.869004 | ||||||||
\(276\) | −5.74553 | −0.345840 | ||||||||
\(277\) | −2.57497 | −0.154715 | −0.0773574 | − | 0.997003i | \(-0.524648\pi\) | ||||
−0.0773574 | + | 0.997003i | \(0.524648\pi\) | |||||||
\(278\) | −32.9902 | −1.97862 | ||||||||
\(279\) | 0.416703 | 0.0249473 | ||||||||
\(280\) | −26.9145 | −1.60845 | ||||||||
\(281\) | −15.4368 | −0.920883 | −0.460442 | − | 0.887690i | \(-0.652309\pi\) | ||||
−0.460442 | + | 0.887690i | \(0.652309\pi\) | |||||||
\(282\) | −3.44284 | −0.205018 | ||||||||
\(283\) | 13.1430 | 0.781269 | 0.390634 | − | 0.920546i | \(-0.372256\pi\) | ||||
0.390634 | + | 0.920546i | \(0.372256\pi\) | |||||||
\(284\) | 13.6178 | 0.808066 | ||||||||
\(285\) | 3.87721 | 0.229666 | ||||||||
\(286\) | −55.4161 | −3.27682 | ||||||||
\(287\) | −4.33857 | −0.256098 | ||||||||
\(288\) | −0.798317 | −0.0470413 | ||||||||
\(289\) | −15.0088 | −0.882873 | ||||||||
\(290\) | −45.0435 | −2.64505 | ||||||||
\(291\) | 12.7729 | 0.748759 | ||||||||
\(292\) | −41.1285 | −2.40686 | ||||||||
\(293\) | 2.65975 | 0.155384 | 0.0776920 | − | 0.996977i | \(-0.475245\pi\) | ||||
0.0776920 | + | 0.996977i | \(0.475245\pi\) | |||||||
\(294\) | 7.48813 | 0.436717 | ||||||||
\(295\) | −34.1869 | −1.99044 | ||||||||
\(296\) | 17.0632 | 0.991779 | ||||||||
\(297\) | 31.0407 | 1.80116 | ||||||||
\(298\) | 44.0357 | 2.55092 | ||||||||
\(299\) | 4.09184 | 0.236637 | ||||||||
\(300\) | −14.2287 | −0.821494 | ||||||||
\(301\) | −23.9899 | −1.38275 | ||||||||
\(302\) | −23.3635 | −1.34442 | ||||||||
\(303\) | −29.5156 | −1.69563 | ||||||||
\(304\) | −0.708366 | −0.0406276 | ||||||||
\(305\) | 22.3887 | 1.28197 | ||||||||
\(306\) | 0.565174 | 0.0323089 | ||||||||
\(307\) | 19.4171 | 1.10819 | 0.554097 | − | 0.832452i | \(-0.313064\pi\) | ||||
0.554097 | + | 0.832452i | \(0.313064\pi\) | |||||||
\(308\) | 59.3566 | 3.38215 | ||||||||
\(309\) | −23.8376 | −1.35607 | ||||||||
\(310\) | 15.4090 | 0.875170 | ||||||||
\(311\) | −31.2179 | −1.77021 | −0.885104 | − | 0.465394i | \(-0.845913\pi\) | ||||
−0.885104 | + | 0.465394i | \(0.845913\pi\) | |||||||
\(312\) | 22.6867 | 1.28438 | ||||||||
\(313\) | 15.7129 | 0.888144 | 0.444072 | − | 0.895991i | \(-0.353534\pi\) | ||||
0.444072 | + | 0.895991i | \(0.353534\pi\) | |||||||
\(314\) | 47.4179 | 2.67595 | ||||||||
\(315\) | −1.40486 | −0.0791549 | ||||||||
\(316\) | 23.4519 | 1.31927 | ||||||||
\(317\) | 10.2980 | 0.578394 | 0.289197 | − | 0.957270i | \(-0.406612\pi\) | ||||
0.289197 | + | 0.957270i | \(0.406612\pi\) | |||||||
\(318\) | 2.79214 | 0.156576 | ||||||||
\(319\) | 41.1882 | 2.30609 | ||||||||
\(320\) | −34.1145 | −1.90706 | ||||||||
\(321\) | −1.92693 | −0.107551 | ||||||||
\(322\) | −6.94837 | −0.387218 | ||||||||
\(323\) | −1.18985 | −0.0662048 | ||||||||
\(324\) | −28.8845 | −1.60469 | ||||||||
\(325\) | 10.1334 | 0.562098 | ||||||||
\(326\) | −23.9046 | −1.32395 | ||||||||
\(327\) | −34.1180 | −1.88673 | ||||||||
\(328\) | 4.79124 | 0.264552 | ||||||||
\(329\) | −2.62627 | −0.144791 | ||||||||
\(330\) | 62.2728 | 3.42800 | ||||||||
\(331\) | −8.49775 | −0.467079 | −0.233539 | − | 0.972347i | \(-0.575031\pi\) | ||||
−0.233539 | + | 0.972347i | \(0.575031\pi\) | |||||||
\(332\) | 6.85196 | 0.376050 | ||||||||
\(333\) | 0.890650 | 0.0488073 | ||||||||
\(334\) | −17.8196 | −0.975044 | ||||||||
\(335\) | 20.0216 | 1.09390 | ||||||||
\(336\) | −4.21765 | −0.230091 | ||||||||
\(337\) | 24.2853 | 1.32290 | 0.661452 | − | 0.749987i | \(-0.269940\pi\) | ||||
0.661452 | + | 0.749987i | \(0.269940\pi\) | |||||||
\(338\) | −8.71169 | −0.473853 | ||||||||
\(339\) | −7.16081 | −0.388922 | ||||||||
\(340\) | 13.1825 | 0.714922 | ||||||||
\(341\) | −14.0901 | −0.763020 | ||||||||
\(342\) | −0.337729 | −0.0182623 | ||||||||
\(343\) | −15.1865 | −0.819993 | ||||||||
\(344\) | 26.4928 | 1.42840 | ||||||||
\(345\) | −4.59813 | −0.247555 | ||||||||
\(346\) | 11.2086 | 0.602576 | ||||||||
\(347\) | 1.91315 | 0.102703 | 0.0513516 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513516 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(348\) | −40.6677 | −2.18002 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −17.2075 | −0.919780 | ||||||||
\(351\) | 21.8272 | 1.16505 | ||||||||
\(352\) | 26.9937 | 1.43877 | ||||||||
\(353\) | 29.5738 | 1.57405 | 0.787027 | − | 0.616919i | \(-0.211619\pi\) | ||||
0.787027 | + | 0.616919i | \(0.211619\pi\) | |||||||
\(354\) | −48.9336 | −2.60079 | ||||||||
\(355\) | 10.8983 | 0.578419 | ||||||||
\(356\) | −22.6670 | −1.20135 | ||||||||
\(357\) | −7.08440 | −0.374946 | ||||||||
\(358\) | −5.78105 | −0.305538 | ||||||||
\(359\) | −12.7981 | −0.675460 | −0.337730 | − | 0.941243i | \(-0.609659\pi\) | ||||
−0.337730 | + | 0.941243i | \(0.609659\pi\) | |||||||
\(360\) | 1.55144 | 0.0817678 | ||||||||
\(361\) | −18.2890 | −0.962578 | ||||||||
\(362\) | −24.9228 | −1.30991 | ||||||||
\(363\) | −38.4447 | −2.01782 | ||||||||
\(364\) | 41.7383 | 2.18768 | ||||||||
\(365\) | −32.9150 | −1.72285 | ||||||||
\(366\) | 32.0462 | 1.67508 | ||||||||
\(367\) | 3.44465 | 0.179809 | 0.0899047 | − | 0.995950i | \(-0.471344\pi\) | ||||
0.0899047 | + | 0.995950i | \(0.471344\pi\) | |||||||
\(368\) | 0.840077 | 0.0437920 | ||||||||
\(369\) | 0.250089 | 0.0130191 | ||||||||
\(370\) | 32.9347 | 1.71220 | ||||||||
\(371\) | 2.12990 | 0.110579 | ||||||||
\(372\) | 13.9120 | 0.721305 | ||||||||
\(373\) | 0.144165 | 0.00746457 | 0.00373228 | − | 0.999993i | \(-0.498812\pi\) | ||||
0.00373228 | + | 0.999993i | \(0.498812\pi\) | |||||||
\(374\) | −19.1104 | −0.988174 | ||||||||
\(375\) | 11.6035 | 0.599200 | ||||||||
\(376\) | 2.90028 | 0.149570 | ||||||||
\(377\) | 28.9626 | 1.49165 | ||||||||
\(378\) | −37.0648 | −1.90641 | ||||||||
\(379\) | 2.99289 | 0.153735 | 0.0768673 | − | 0.997041i | \(-0.475508\pi\) | ||||
0.0768673 | + | 0.997041i | \(0.475508\pi\) | |||||||
\(380\) | −7.87743 | −0.404104 | ||||||||
\(381\) | −2.60513 | −0.133465 | ||||||||
\(382\) | −36.2922 | −1.85687 | ||||||||
\(383\) | −35.1189 | −1.79449 | −0.897245 | − | 0.441533i | \(-0.854435\pi\) | ||||
−0.897245 | + | 0.441533i | \(0.854435\pi\) | |||||||
\(384\) | −33.2283 | −1.69568 | ||||||||
\(385\) | 47.5029 | 2.42097 | ||||||||
\(386\) | −38.6090 | −1.96515 | ||||||||
\(387\) | 1.38285 | 0.0702942 | ||||||||
\(388\) | −25.9510 | −1.31746 | ||||||||
\(389\) | −7.35037 | −0.372678 | −0.186339 | − | 0.982485i | \(-0.559662\pi\) | ||||
−0.186339 | + | 0.982485i | \(0.559662\pi\) | |||||||
\(390\) | 43.7889 | 2.21734 | ||||||||
\(391\) | 1.41108 | 0.0713615 | ||||||||
\(392\) | −6.30806 | −0.318605 | ||||||||
\(393\) | 25.0169 | 1.26194 | ||||||||
\(394\) | −52.6011 | −2.65000 | ||||||||
\(395\) | 18.7685 | 0.944345 | ||||||||
\(396\) | −3.42150 | −0.171937 | ||||||||
\(397\) | −24.4397 | −1.22659 | −0.613295 | − | 0.789854i | \(-0.710156\pi\) | ||||
−0.613295 | + | 0.789854i | \(0.710156\pi\) | |||||||
\(398\) | 25.6494 | 1.28569 | ||||||||
\(399\) | 4.23340 | 0.211935 | ||||||||
\(400\) | 2.08044 | 0.104022 | ||||||||
\(401\) | −26.9732 | −1.34698 | −0.673488 | − | 0.739198i | \(-0.735205\pi\) | ||||
−0.673488 | + | 0.739198i | \(0.735205\pi\) | |||||||
\(402\) | 28.6581 | 1.42934 | ||||||||
\(403\) | −9.90784 | −0.493545 | ||||||||
\(404\) | 59.9677 | 2.98350 | ||||||||
\(405\) | −23.1162 | −1.14865 | ||||||||
\(406\) | −49.1816 | −2.44084 | ||||||||
\(407\) | −30.1158 | −1.49278 | ||||||||
\(408\) | 7.82355 | 0.387323 | ||||||||
\(409\) | −11.1449 | −0.551078 | −0.275539 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275539 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(410\) | 9.24786 | 0.456719 | ||||||||
\(411\) | −25.7957 | −1.27241 | ||||||||
\(412\) | 48.4314 | 2.38605 | ||||||||
\(413\) | −37.3275 | −1.83677 | ||||||||
\(414\) | 0.400526 | 0.0196848 | ||||||||
\(415\) | 5.48360 | 0.269179 | ||||||||
\(416\) | 18.9814 | 0.930639 | ||||||||
\(417\) | −23.8371 | −1.16731 | ||||||||
\(418\) | 11.4197 | 0.558557 | ||||||||
\(419\) | −22.2672 | −1.08783 | −0.543913 | − | 0.839142i | \(-0.683058\pi\) | ||||
−0.543913 | + | 0.839142i | \(0.683058\pi\) | |||||||
\(420\) | −46.9026 | −2.28861 | ||||||||
\(421\) | 9.66366 | 0.470978 | 0.235489 | − | 0.971877i | \(-0.424331\pi\) | ||||
0.235489 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(422\) | 35.2956 | 1.71816 | ||||||||
\(423\) | 0.151386 | 0.00736065 | ||||||||
\(424\) | −2.35212 | −0.114229 | ||||||||
\(425\) | 3.49452 | 0.169509 | ||||||||
\(426\) | 15.5993 | 0.755789 | ||||||||
\(427\) | 24.4454 | 1.18300 | ||||||||
\(428\) | 3.91498 | 0.189238 | ||||||||
\(429\) | −40.0409 | −1.93319 | ||||||||
\(430\) | 51.1354 | 2.46597 | ||||||||
\(431\) | 23.3189 | 1.12323 | 0.561616 | − | 0.827398i | \(-0.310180\pi\) | ||||
0.561616 | + | 0.827398i | \(0.310180\pi\) | |||||||
\(432\) | 4.48123 | 0.215603 | ||||||||
\(433\) | −3.76269 | −0.180824 | −0.0904118 | − | 0.995904i | \(-0.528818\pi\) | ||||
−0.0904118 | + | 0.995904i | \(0.528818\pi\) | |||||||
\(434\) | 16.8245 | 0.807604 | ||||||||
\(435\) | −32.5462 | −1.56047 | ||||||||
\(436\) | 69.3184 | 3.31975 | ||||||||
\(437\) | −0.843215 | −0.0403365 | ||||||||
\(438\) | −47.1132 | −2.25116 | ||||||||
\(439\) | 37.5563 | 1.79246 | 0.896232 | − | 0.443585i | \(-0.146294\pi\) | ||||
0.896232 | + | 0.443585i | \(0.146294\pi\) | |||||||
\(440\) | −52.4591 | −2.50089 | ||||||||
\(441\) | −0.329262 | −0.0156792 | ||||||||
\(442\) | −13.4380 | −0.639181 | ||||||||
\(443\) | 25.1894 | 1.19679 | 0.598393 | − | 0.801203i | \(-0.295806\pi\) | ||||
0.598393 | + | 0.801203i | \(0.295806\pi\) | |||||||
\(444\) | 29.7352 | 1.41117 | ||||||||
\(445\) | −18.1404 | −0.859935 | ||||||||
\(446\) | 22.2968 | 1.05578 | ||||||||
\(447\) | 31.8180 | 1.50494 | ||||||||
\(448\) | −37.2485 | −1.75983 | ||||||||
\(449\) | 21.2411 | 1.00243 | 0.501215 | − | 0.865323i | \(-0.332886\pi\) | ||||
0.501215 | + | 0.865323i | \(0.332886\pi\) | |||||||
\(450\) | 0.991894 | 0.0467583 | ||||||||
\(451\) | −8.45632 | −0.398192 | ||||||||
\(452\) | 14.5488 | 0.684318 | ||||||||
\(453\) | −16.8813 | −0.793152 | ||||||||
\(454\) | −7.48398 | −0.351240 | ||||||||
\(455\) | 33.4030 | 1.56596 | ||||||||
\(456\) | −4.67509 | −0.218931 | ||||||||
\(457\) | −18.5327 | −0.866924 | −0.433462 | − | 0.901172i | \(-0.642708\pi\) | ||||
−0.433462 | + | 0.901172i | \(0.642708\pi\) | |||||||
\(458\) | −34.4718 | −1.61076 | ||||||||
\(459\) | 7.52715 | 0.351337 | ||||||||
\(460\) | 9.34213 | 0.435579 | ||||||||
\(461\) | 23.3608 | 1.08802 | 0.544011 | − | 0.839078i | \(-0.316905\pi\) | ||||
0.544011 | + | 0.839078i | \(0.316905\pi\) | |||||||
\(462\) | 67.9936 | 3.16335 | ||||||||
\(463\) | 6.62455 | 0.307869 | 0.153935 | − | 0.988081i | \(-0.450806\pi\) | ||||
0.153935 | + | 0.988081i | \(0.450806\pi\) | |||||||
\(464\) | 5.94619 | 0.276045 | ||||||||
\(465\) | 11.1337 | 0.516315 | ||||||||
\(466\) | −39.3235 | −1.82162 | ||||||||
\(467\) | −40.4788 | −1.87314 | −0.936568 | − | 0.350487i | \(-0.886016\pi\) | ||||
−0.936568 | + | 0.350487i | \(0.886016\pi\) | |||||||
\(468\) | −2.40592 | −0.111214 | ||||||||
\(469\) | 21.8610 | 1.00945 | ||||||||
\(470\) | 5.59801 | 0.258217 | ||||||||
\(471\) | 34.2618 | 1.57870 | ||||||||
\(472\) | 41.2221 | 1.89740 | ||||||||
\(473\) | −46.7586 | −2.14996 | ||||||||
\(474\) | 26.8644 | 1.23392 | ||||||||
\(475\) | −2.08821 | −0.0958135 | ||||||||
\(476\) | 14.3936 | 0.659727 | ||||||||
\(477\) | −0.122774 | −0.00562144 | ||||||||
\(478\) | 42.3446 | 1.93680 | ||||||||
\(479\) | −38.5423 | −1.76104 | −0.880521 | − | 0.474007i | \(-0.842807\pi\) | ||||
−0.880521 | + | 0.474007i | \(0.842807\pi\) | |||||||
\(480\) | −21.3300 | −0.973576 | ||||||||
\(481\) | −21.1768 | −0.965578 | ||||||||
\(482\) | −71.6556 | −3.26382 | ||||||||
\(483\) | −5.02055 | −0.228443 | ||||||||
\(484\) | 78.1090 | 3.55041 | ||||||||
\(485\) | −20.7685 | −0.943048 | ||||||||
\(486\) | 4.15715 | 0.188572 | ||||||||
\(487\) | 37.0798 | 1.68025 | 0.840124 | − | 0.542395i | \(-0.182482\pi\) | ||||
0.840124 | + | 0.542395i | \(0.182482\pi\) | |||||||
\(488\) | −26.9959 | −1.22205 | ||||||||
\(489\) | −17.2723 | −0.781080 | ||||||||
\(490\) | −12.1756 | −0.550036 | ||||||||
\(491\) | −16.6178 | −0.749952 | −0.374976 | − | 0.927034i | \(-0.622349\pi\) | ||||
−0.374976 | + | 0.927034i | \(0.622349\pi\) | |||||||
\(492\) | 8.34946 | 0.376423 | ||||||||
\(493\) | 9.98784 | 0.449830 | ||||||||
\(494\) | 8.03011 | 0.361292 | ||||||||
\(495\) | −2.73821 | −0.123074 | ||||||||
\(496\) | −2.03413 | −0.0913353 | ||||||||
\(497\) | 11.8995 | 0.533763 | ||||||||
\(498\) | 7.84900 | 0.351722 | ||||||||
\(499\) | 3.04495 | 0.136311 | 0.0681553 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681553 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(500\) | −23.5750 | −1.05431 | ||||||||
\(501\) | −12.8755 | −0.575237 | ||||||||
\(502\) | 17.6772 | 0.788972 | ||||||||
\(503\) | −12.3013 | −0.548487 | −0.274244 | − | 0.961660i | \(-0.588427\pi\) | ||||
−0.274244 | + | 0.961660i | \(0.588427\pi\) | |||||||
\(504\) | 1.69396 | 0.0754551 | ||||||||
\(505\) | 47.9919 | 2.13561 | ||||||||
\(506\) | −13.5431 | −0.602063 | ||||||||
\(507\) | −6.29463 | −0.279554 | ||||||||
\(508\) | 5.29290 | 0.234835 | ||||||||
\(509\) | −6.68287 | −0.296213 | −0.148106 | − | 0.988971i | \(-0.547318\pi\) | ||||
−0.148106 | + | 0.988971i | \(0.547318\pi\) | |||||||
\(510\) | 15.1007 | 0.668671 | ||||||||
\(511\) | −35.9389 | −1.58984 | ||||||||
\(512\) | 9.43645 | 0.417036 | ||||||||
\(513\) | −4.49798 | −0.198590 | ||||||||
\(514\) | 57.3700 | 2.53048 | ||||||||
\(515\) | 38.7595 | 1.70795 | ||||||||
\(516\) | 46.1678 | 2.03242 | ||||||||
\(517\) | −5.11886 | −0.225127 | ||||||||
\(518\) | 35.9604 | 1.58001 | ||||||||
\(519\) | 8.09875 | 0.355496 | ||||||||
\(520\) | −36.8881 | −1.61765 | ||||||||
\(521\) | −12.6902 | −0.555966 | −0.277983 | − | 0.960586i | \(-0.589666\pi\) | ||||
−0.277983 | + | 0.960586i | \(0.589666\pi\) | |||||||
\(522\) | 2.83498 | 0.124084 | ||||||||
\(523\) | −23.9052 | −1.04530 | −0.522650 | − | 0.852548i | \(-0.675056\pi\) | ||||
−0.522650 | + | 0.852548i | \(0.675056\pi\) | |||||||
\(524\) | −50.8274 | −2.22041 | ||||||||
\(525\) | −12.4333 | −0.542633 | ||||||||
\(526\) | −19.1119 | −0.833316 | ||||||||
\(527\) | −3.41674 | −0.148836 | ||||||||
\(528\) | −8.22062 | −0.357756 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.53998 | −0.197204 | ||||||||
\(531\) | 2.15167 | 0.0933747 | ||||||||
\(532\) | −8.60111 | −0.372905 | ||||||||
\(533\) | −5.94630 | −0.257563 | ||||||||
\(534\) | −25.9653 | −1.12363 | ||||||||
\(535\) | 3.13315 | 0.135458 | ||||||||
\(536\) | −24.1418 | −1.04277 | ||||||||
\(537\) | −4.17710 | −0.180255 | ||||||||
\(538\) | 66.6677 | 2.87425 | ||||||||
\(539\) | 11.1334 | 0.479551 | ||||||||
\(540\) | 49.8339 | 2.14451 | ||||||||
\(541\) | −28.9264 | −1.24364 | −0.621821 | − | 0.783159i | \(-0.713607\pi\) | ||||
−0.621821 | + | 0.783159i | \(0.713607\pi\) | |||||||
\(542\) | −5.19783 | −0.223266 | ||||||||
\(543\) | −18.0080 | −0.772797 | ||||||||
\(544\) | 6.54578 | 0.280648 | ||||||||
\(545\) | 55.4753 | 2.37630 | ||||||||
\(546\) | 47.8117 | 2.04615 | ||||||||
\(547\) | 2.80933 | 0.120118 | 0.0600592 | − | 0.998195i | \(-0.480871\pi\) | ||||
0.0600592 | + | 0.998195i | \(0.480871\pi\) | |||||||
\(548\) | 52.4097 | 2.23883 | ||||||||
\(549\) | −1.40911 | −0.0601394 | ||||||||
\(550\) | −33.5392 | −1.43012 | ||||||||
\(551\) | −5.96840 | −0.254262 | ||||||||
\(552\) | 5.54436 | 0.235984 | ||||||||
\(553\) | 20.4927 | 0.871438 | ||||||||
\(554\) | 5.99289 | 0.254613 | ||||||||
\(555\) | 23.7970 | 1.01013 | ||||||||
\(556\) | 48.4304 | 2.05391 | ||||||||
\(557\) | 30.3427 | 1.28566 | 0.642830 | − | 0.766009i | \(-0.277760\pi\) | ||||
0.642830 | + | 0.766009i | \(0.277760\pi\) | |||||||
\(558\) | −0.969819 | −0.0410557 | ||||||||
\(559\) | −32.8797 | −1.39066 | ||||||||
\(560\) | 6.85782 | 0.289796 | ||||||||
\(561\) | −13.8082 | −0.582983 | ||||||||
\(562\) | 35.9271 | 1.51549 | ||||||||
\(563\) | −1.18456 | −0.0499232 | −0.0249616 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249616 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(564\) | 5.05418 | 0.212819 | ||||||||
\(565\) | 11.6434 | 0.489840 | ||||||||
\(566\) | −30.5885 | −1.28573 | ||||||||
\(567\) | −25.2398 | −1.05997 | ||||||||
\(568\) | −13.1410 | −0.551383 | ||||||||
\(569\) | 38.9487 | 1.63282 | 0.816408 | − | 0.577475i | \(-0.195962\pi\) | ||||
0.816408 | + | 0.577475i | \(0.195962\pi\) | |||||||
\(570\) | −9.02369 | −0.377961 | ||||||||
\(571\) | −13.6586 | −0.571594 | −0.285797 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285797 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(572\) | 81.3521 | 3.40150 | ||||||||
\(573\) | −26.2229 | −1.09548 | ||||||||
\(574\) | 10.0974 | 0.421459 | ||||||||
\(575\) | 2.47648 | 0.103276 | ||||||||
\(576\) | 2.14712 | 0.0894633 | ||||||||
\(577\) | −4.23214 | −0.176186 | −0.0880931 | − | 0.996112i | \(-0.528077\pi\) | ||||
−0.0880931 | + | 0.996112i | \(0.528077\pi\) | |||||||
\(578\) | 34.9311 | 1.45294 | ||||||||
\(579\) | −27.8970 | −1.15936 | ||||||||
\(580\) | 66.1250 | 2.74569 | ||||||||
\(581\) | 5.98737 | 0.248398 | ||||||||
\(582\) | −29.7271 | −1.23223 | ||||||||
\(583\) | 4.15139 | 0.171933 | ||||||||
\(584\) | 39.6885 | 1.64232 | ||||||||
\(585\) | −1.92545 | −0.0796077 | ||||||||
\(586\) | −6.19020 | −0.255715 | ||||||||
\(587\) | −31.4840 | −1.29948 | −0.649742 | − | 0.760155i | \(-0.725123\pi\) | ||||
−0.649742 | + | 0.760155i | \(0.725123\pi\) | |||||||
\(588\) | −10.9927 | −0.453333 | ||||||||
\(589\) | 2.04173 | 0.0841281 | ||||||||
\(590\) | 79.5653 | 3.27565 | ||||||||
\(591\) | −38.0069 | −1.56340 | ||||||||
\(592\) | −4.34771 | −0.178690 | ||||||||
\(593\) | 4.69966 | 0.192992 | 0.0964959 | − | 0.995333i | \(-0.469237\pi\) | ||||
0.0964959 | + | 0.995333i | \(0.469237\pi\) | |||||||
\(594\) | −72.2430 | −2.96417 | ||||||||
\(595\) | 11.5191 | 0.472238 | ||||||||
\(596\) | −64.6455 | −2.64798 | ||||||||
\(597\) | 18.5330 | 0.758505 | ||||||||
\(598\) | −9.52320 | −0.389433 | ||||||||
\(599\) | 11.1541 | 0.455744 | 0.227872 | − | 0.973691i | \(-0.426823\pi\) | ||||
0.227872 | + | 0.973691i | \(0.426823\pi\) | |||||||
\(600\) | 13.7305 | 0.560546 | ||||||||
\(601\) | −35.5308 | −1.44933 | −0.724667 | − | 0.689100i | \(-0.758006\pi\) | ||||
−0.724667 | + | 0.689100i | \(0.758006\pi\) | |||||||
\(602\) | 55.8331 | 2.27559 | ||||||||
\(603\) | −1.26013 | −0.0513166 | ||||||||
\(604\) | 34.2981 | 1.39557 | ||||||||
\(605\) | 62.5104 | 2.54141 | ||||||||
\(606\) | 68.6936 | 2.79049 | ||||||||
\(607\) | 44.2640 | 1.79662 | 0.898310 | − | 0.439363i | \(-0.144796\pi\) | ||||
0.898310 | + | 0.439363i | \(0.144796\pi\) | |||||||
\(608\) | −3.91154 | −0.158634 | ||||||||
\(609\) | −35.5362 | −1.44000 | ||||||||
\(610\) | −52.1065 | −2.10973 | ||||||||
\(611\) | −3.59947 | −0.145619 | ||||||||
\(612\) | −0.829689 | −0.0335382 | ||||||||
\(613\) | −5.50730 | −0.222438 | −0.111219 | − | 0.993796i | \(-0.535475\pi\) | ||||
−0.111219 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(614\) | −45.1907 | −1.82375 | ||||||||
\(615\) | 6.68205 | 0.269446 | ||||||||
\(616\) | −57.2784 | −2.30781 | ||||||||
\(617\) | −10.7057 | −0.430995 | −0.215498 | − | 0.976504i | \(-0.569137\pi\) | ||||
−0.215498 | + | 0.976504i | \(0.569137\pi\) | |||||||
\(618\) | 55.4788 | 2.23168 | ||||||||
\(619\) | −6.23190 | −0.250481 | −0.125241 | − | 0.992126i | \(-0.539970\pi\) | ||||
−0.125241 | + | 0.992126i | \(0.539970\pi\) | |||||||
\(620\) | −22.6207 | −0.908470 | ||||||||
\(621\) | 5.33431 | 0.214059 | ||||||||
\(622\) | 72.6555 | 2.91322 | ||||||||
\(623\) | −19.8069 | −0.793545 | ||||||||
\(624\) | −5.78056 | −0.231408 | ||||||||
\(625\) | −31.2494 | −1.24998 | ||||||||
\(626\) | −36.5696 | −1.46161 | ||||||||
\(627\) | 8.25133 | 0.329526 | ||||||||
\(628\) | −69.6106 | −2.77777 | ||||||||
\(629\) | −7.30287 | −0.291184 | ||||||||
\(630\) | 3.26962 | 0.130265 | ||||||||
\(631\) | −18.1344 | −0.721919 | −0.360959 | − | 0.932582i | \(-0.617551\pi\) | ||||
−0.360959 | + | 0.932582i | \(0.617551\pi\) | |||||||
\(632\) | −22.6308 | −0.900205 | ||||||||
\(633\) | 25.5029 | 1.01365 | ||||||||
\(634\) | −23.9672 | −0.951861 | ||||||||
\(635\) | 4.23590 | 0.168096 | ||||||||
\(636\) | −4.09893 | −0.162533 | ||||||||
\(637\) | 7.82880 | 0.310188 | ||||||||
\(638\) | −95.8598 | −3.79513 | ||||||||
\(639\) | −0.685921 | −0.0271346 | ||||||||
\(640\) | 54.0287 | 2.13567 | ||||||||
\(641\) | 50.5887 | 1.99813 | 0.999066 | − | 0.0432072i | \(-0.0137575\pi\) | ||||
0.999066 | + | 0.0432072i | \(0.0137575\pi\) | |||||||
\(642\) | 4.48466 | 0.176995 | ||||||||
\(643\) | 6.78845 | 0.267710 | 0.133855 | − | 0.991001i | \(-0.457264\pi\) | ||||
0.133855 | + | 0.991001i | \(0.457264\pi\) | |||||||
\(644\) | 10.2004 | 0.401951 | ||||||||
\(645\) | 36.9479 | 1.45482 | ||||||||
\(646\) | 2.76920 | 0.108953 | ||||||||
\(647\) | 41.5726 | 1.63439 | 0.817193 | − | 0.576364i | \(-0.195529\pi\) | ||||
0.817193 | + | 0.576364i | \(0.195529\pi\) | |||||||
\(648\) | 27.8732 | 1.09496 | ||||||||
\(649\) | −72.7551 | −2.85589 | ||||||||
\(650\) | −23.5840 | −0.925042 | ||||||||
\(651\) | 12.1566 | 0.476454 | ||||||||
\(652\) | 35.0925 | 1.37433 | ||||||||
\(653\) | −27.1592 | −1.06282 | −0.531411 | − | 0.847114i | \(-0.678338\pi\) | ||||
−0.531411 | + | 0.847114i | \(0.678338\pi\) | |||||||
\(654\) | 79.4050 | 3.10498 | ||||||||
\(655\) | −40.6771 | −1.58938 | ||||||||
\(656\) | −1.22081 | −0.0476645 | ||||||||
\(657\) | 2.07163 | 0.0808219 | ||||||||
\(658\) | 6.11228 | 0.238282 | ||||||||
\(659\) | −28.8138 | −1.12242 | −0.561212 | − | 0.827672i | \(-0.689665\pi\) | ||||
−0.561212 | + | 0.827672i | \(0.689665\pi\) | |||||||
\(660\) | −91.4179 | −3.55844 | ||||||||
\(661\) | 4.26191 | 0.165769 | 0.0828846 | − | 0.996559i | \(-0.473587\pi\) | ||||
0.0828846 | + | 0.996559i | \(0.473587\pi\) | |||||||
\(662\) | 19.7774 | 0.768669 | ||||||||
\(663\) | −9.70964 | −0.377091 | ||||||||
\(664\) | −6.61206 | −0.256598 | ||||||||
\(665\) | −6.88344 | −0.266928 | ||||||||
\(666\) | −2.07287 | −0.0803220 | ||||||||
\(667\) | 7.07815 | 0.274067 | ||||||||
\(668\) | 26.1596 | 1.01214 | ||||||||
\(669\) | 16.1106 | 0.622870 | ||||||||
\(670\) | −46.5976 | −1.80022 | ||||||||
\(671\) | 47.6466 | 1.83938 | ||||||||
\(672\) | −23.2895 | −0.898413 | ||||||||
\(673\) | 39.6915 | 1.52999 | 0.764997 | − | 0.644034i | \(-0.222741\pi\) | ||||
0.764997 | + | 0.644034i | \(0.222741\pi\) | |||||||
\(674\) | −56.5207 | −2.17710 | ||||||||
\(675\) | 13.2103 | 0.508466 | ||||||||
\(676\) | 12.7890 | 0.491883 | ||||||||
\(677\) | −5.65899 | −0.217493 | −0.108746 | − | 0.994070i | \(-0.534684\pi\) | ||||
−0.108746 | + | 0.994070i | \(0.534684\pi\) | |||||||
\(678\) | 16.6658 | 0.640047 | ||||||||
\(679\) | −22.6764 | −0.870241 | ||||||||
\(680\) | −12.7210 | −0.487827 | ||||||||
\(681\) | −5.40755 | −0.207218 | ||||||||
\(682\) | 32.7927 | 1.25570 | ||||||||
\(683\) | 40.2392 | 1.53971 | 0.769855 | − | 0.638219i | \(-0.220329\pi\) | ||||
0.769855 | + | 0.638219i | \(0.220329\pi\) | |||||||
\(684\) | 0.495794 | 0.0189572 | ||||||||
\(685\) | 41.9434 | 1.60257 | ||||||||
\(686\) | 35.3445 | 1.34946 | ||||||||
\(687\) | −24.9076 | −0.950284 | ||||||||
\(688\) | −6.75038 | −0.257356 | ||||||||
\(689\) | 2.91917 | 0.111212 | ||||||||
\(690\) | 10.7015 | 0.407400 | ||||||||
\(691\) | −13.1813 | −0.501441 | −0.250720 | − | 0.968060i | \(-0.580667\pi\) | ||||
−0.250720 | + | 0.968060i | \(0.580667\pi\) | |||||||
\(692\) | −16.4544 | −0.625503 | ||||||||
\(693\) | −2.98977 | −0.113572 | ||||||||
\(694\) | −4.45260 | −0.169018 | ||||||||
\(695\) | 38.7587 | 1.47020 | ||||||||
\(696\) | 39.2438 | 1.48753 | ||||||||
\(697\) | −2.05060 | −0.0776719 | ||||||||
\(698\) | 2.32736 | 0.0880920 | ||||||||
\(699\) | −28.4132 | −1.07469 | ||||||||
\(700\) | 25.2610 | 0.954777 | ||||||||
\(701\) | 10.4621 | 0.395146 | 0.197573 | − | 0.980288i | \(-0.436694\pi\) | ||||
0.197573 | + | 0.980288i | \(0.436694\pi\) | |||||||
\(702\) | −50.7998 | −1.91731 | ||||||||
\(703\) | 4.36395 | 0.164590 | ||||||||
\(704\) | −72.6011 | −2.73626 | ||||||||
\(705\) | 4.04484 | 0.152338 | ||||||||
\(706\) | −68.8290 | −2.59041 | ||||||||
\(707\) | 52.4008 | 1.97074 | ||||||||
\(708\) | 71.8357 | 2.69975 | ||||||||
\(709\) | −26.0586 | −0.978650 | −0.489325 | − | 0.872101i | \(-0.662757\pi\) | ||||
−0.489325 | + | 0.872101i | \(0.662757\pi\) | |||||||
\(710\) | −25.3642 | −0.951902 | ||||||||
\(711\) | −1.18126 | −0.0443008 | ||||||||
\(712\) | 21.8734 | 0.819740 | ||||||||
\(713\) | −2.42137 | −0.0906808 | ||||||||
\(714\) | 16.4880 | 0.617047 | ||||||||
\(715\) | 65.1059 | 2.43482 | ||||||||
\(716\) | 8.48672 | 0.317164 | ||||||||
\(717\) | 30.5961 | 1.14263 | ||||||||
\(718\) | 29.7860 | 1.11160 | ||||||||
\(719\) | −20.7378 | −0.773391 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(720\) | −0.395306 | −0.0147322 | ||||||||
\(721\) | 42.3203 | 1.57609 | ||||||||
\(722\) | 42.5651 | 1.58411 | ||||||||
\(723\) | −51.7748 | −1.92553 | ||||||||
\(724\) | 36.5873 | 1.35976 | ||||||||
\(725\) | 17.5289 | 0.651007 | ||||||||
\(726\) | 89.4748 | 3.32072 | ||||||||
\(727\) | 9.92499 | 0.368098 | 0.184049 | − | 0.982917i | \(-0.441080\pi\) | ||||
0.184049 | + | 0.982917i | \(0.441080\pi\) | |||||||
\(728\) | −40.2769 | −1.49276 | ||||||||
\(729\) | 28.3661 | 1.05059 | ||||||||
\(730\) | 76.6053 | 2.83529 | ||||||||
\(731\) | −11.3386 | −0.419375 | ||||||||
\(732\) | −47.0445 | −1.73882 | ||||||||
\(733\) | 39.6999 | 1.46635 | 0.733175 | − | 0.680040i | \(-0.238038\pi\) | ||||
0.733175 | + | 0.680040i | \(0.238038\pi\) | |||||||
\(734\) | −8.01697 | −0.295912 | ||||||||
\(735\) | −8.79747 | −0.324499 | ||||||||
\(736\) | 4.63884 | 0.170990 | ||||||||
\(737\) | 42.6092 | 1.56953 | ||||||||
\(738\) | −0.582048 | −0.0214255 | ||||||||
\(739\) | −33.4660 | −1.23107 | −0.615534 | − | 0.788110i | \(-0.711060\pi\) | ||||
−0.615534 | + | 0.788110i | \(0.711060\pi\) | |||||||
\(740\) | −48.3490 | −1.77734 | ||||||||
\(741\) | 5.80216 | 0.213148 | ||||||||
\(742\) | −4.95706 | −0.181979 | ||||||||
\(743\) | 1.61372 | 0.0592017 | 0.0296009 | − | 0.999562i | \(-0.490576\pi\) | ||||
0.0296009 | + | 0.999562i | \(0.490576\pi\) | |||||||
\(744\) | −13.4249 | −0.492182 | ||||||||
\(745\) | −51.7356 | −1.89544 | ||||||||
\(746\) | −0.335524 | −0.0122844 | ||||||||
\(747\) | −0.345130 | −0.0126277 | ||||||||
\(748\) | 28.0545 | 1.02577 | ||||||||
\(749\) | 3.42098 | 0.125000 | ||||||||
\(750\) | −27.0055 | −0.986101 | ||||||||
\(751\) | −11.3562 | −0.414395 | −0.207198 | − | 0.978299i | \(-0.566434\pi\) | ||||
−0.207198 | + | 0.978299i | \(0.566434\pi\) | |||||||
\(752\) | −0.738992 | −0.0269483 | ||||||||
\(753\) | 12.7727 | 0.465462 | ||||||||
\(754\) | −67.4066 | −2.45480 | ||||||||
\(755\) | 27.4487 | 0.998960 | ||||||||
\(756\) | 54.4120 | 1.97894 | ||||||||
\(757\) | 21.3892 | 0.777404 | 0.388702 | − | 0.921364i | \(-0.372924\pi\) | ||||
0.388702 | + | 0.921364i | \(0.372924\pi\) | |||||||
\(758\) | −6.96555 | −0.253000 | ||||||||
\(759\) | −9.78555 | −0.355193 | ||||||||
\(760\) | 7.60163 | 0.275740 | ||||||||
\(761\) | 42.2649 | 1.53210 | 0.766050 | − | 0.642781i | \(-0.222219\pi\) | ||||
0.766050 | + | 0.642781i | \(0.222219\pi\) | |||||||
\(762\) | 6.06308 | 0.219642 | ||||||||
\(763\) | 60.5717 | 2.19284 | ||||||||
\(764\) | 53.2778 | 1.92752 | ||||||||
\(765\) | −0.663998 | −0.0240069 | ||||||||
\(766\) | 81.7344 | 2.95318 | ||||||||
\(767\) | −51.1598 | −1.84727 | ||||||||
\(768\) | 35.3728 | 1.27641 | ||||||||
\(769\) | 7.99723 | 0.288388 | 0.144194 | − | 0.989549i | \(-0.453941\pi\) | ||||
0.144194 | + | 0.989549i | \(0.453941\pi\) | |||||||
\(770\) | −110.557 | −3.98418 | ||||||||
\(771\) | 41.4527 | 1.49288 | ||||||||
\(772\) | 56.6790 | 2.03992 | ||||||||
\(773\) | 19.4827 | 0.700744 | 0.350372 | − | 0.936611i | \(-0.386055\pi\) | ||||
0.350372 | + | 0.936611i | \(0.386055\pi\) | |||||||
\(774\) | −3.21839 | −0.115683 | ||||||||
\(775\) | −5.99647 | −0.215399 | ||||||||
\(776\) | 25.0424 | 0.898968 | ||||||||
\(777\) | 25.9832 | 0.932141 | ||||||||
\(778\) | 17.1070 | 0.613315 | ||||||||
\(779\) | 1.22537 | 0.0439034 | ||||||||
\(780\) | −64.2831 | −2.30171 | ||||||||
\(781\) | 23.1932 | 0.829919 | ||||||||
\(782\) | −3.28410 | −0.117439 | ||||||||
\(783\) | 37.7571 | 1.34933 | ||||||||
\(784\) | 1.60729 | 0.0574034 | ||||||||
\(785\) | −55.7092 | −1.98835 | ||||||||
\(786\) | −58.2234 | −2.07676 | ||||||||
\(787\) | 39.3136 | 1.40138 | 0.700690 | − | 0.713466i | \(-0.252876\pi\) | ||||
0.700690 | + | 0.713466i | \(0.252876\pi\) | |||||||
\(788\) | 77.2196 | 2.75083 | ||||||||
\(789\) | −13.8093 | −0.491623 | ||||||||
\(790\) | −43.6811 | −1.55410 | ||||||||
\(791\) | 12.7130 | 0.452022 | ||||||||
\(792\) | 3.30170 | 0.117321 | ||||||||
\(793\) | 33.5041 | 1.18977 | ||||||||
\(794\) | 56.8800 | 2.01859 | ||||||||
\(795\) | −3.28036 | −0.116343 | ||||||||
\(796\) | −37.6540 | −1.33461 | ||||||||
\(797\) | 19.0338 | 0.674213 | 0.337107 | − | 0.941466i | \(-0.390552\pi\) | ||||
0.337107 | + | 0.941466i | \(0.390552\pi\) | |||||||
\(798\) | −9.85267 | −0.348781 | ||||||||
\(799\) | −1.24129 | −0.0439136 | ||||||||
\(800\) | 11.4880 | 0.406162 | ||||||||
\(801\) | 1.14173 | 0.0403410 | ||||||||
\(802\) | 62.7764 | 2.21671 | ||||||||
\(803\) | −70.0485 | −2.47196 | ||||||||
\(804\) | −42.0708 | −1.48372 | ||||||||
\(805\) | 8.16333 | 0.287719 | ||||||||
\(806\) | 23.0592 | 0.812224 | ||||||||
\(807\) | 48.1707 | 1.69569 | ||||||||
\(808\) | −57.8681 | −2.03579 | ||||||||
\(809\) | 14.8212 | 0.521085 | 0.260542 | − | 0.965462i | \(-0.416099\pi\) | ||||
0.260542 | + | 0.965462i | \(0.416099\pi\) | |||||||
\(810\) | 53.7998 | 1.89033 | ||||||||
\(811\) | 45.1684 | 1.58608 | 0.793038 | − | 0.609172i | \(-0.208498\pi\) | ||||
0.793038 | + | 0.609172i | \(0.208498\pi\) | |||||||
\(812\) | 72.1997 | 2.53371 | ||||||||
\(813\) | −3.75569 | −0.131718 | ||||||||
\(814\) | 70.0904 | 2.45667 | ||||||||
\(815\) | 28.0845 | 0.983756 | ||||||||
\(816\) | −1.99344 | −0.0697844 | ||||||||
\(817\) | 6.77560 | 0.237048 | ||||||||
\(818\) | 25.9381 | 0.906906 | ||||||||
\(819\) | −2.10234 | −0.0734617 | ||||||||
\(820\) | −13.5761 | −0.474097 | ||||||||
\(821\) | 27.9727 | 0.976253 | 0.488126 | − | 0.872773i | \(-0.337680\pi\) | ||||
0.488126 | + | 0.872773i | \(0.337680\pi\) | |||||||
\(822\) | 60.0360 | 2.09399 | ||||||||
\(823\) | 1.30171 | 0.0453746 | 0.0226873 | − | 0.999743i | \(-0.492778\pi\) | ||||
0.0226873 | + | 0.999743i | \(0.492778\pi\) | |||||||
\(824\) | −46.7358 | −1.62812 | ||||||||
\(825\) | −24.2337 | −0.843711 | ||||||||
\(826\) | 86.8747 | 3.02276 | ||||||||
\(827\) | 2.97183 | 0.103341 | 0.0516703 | − | 0.998664i | \(-0.483546\pi\) | ||||
0.0516703 | + | 0.998664i | \(0.483546\pi\) | |||||||
\(828\) | −0.587981 | −0.0204337 | ||||||||
\(829\) | 6.79264 | 0.235918 | 0.117959 | − | 0.993018i | \(-0.462365\pi\) | ||||
0.117959 | + | 0.993018i | \(0.462365\pi\) | |||||||
\(830\) | −12.7623 | −0.442987 | ||||||||
\(831\) | 4.33016 | 0.150212 | ||||||||
\(832\) | −51.0515 | −1.76989 | ||||||||
\(833\) | 2.69978 | 0.0935419 | ||||||||
\(834\) | 55.4776 | 1.92103 | ||||||||
\(835\) | 20.9354 | 0.724500 | ||||||||
\(836\) | −16.7644 | −0.579810 | ||||||||
\(837\) | −12.9163 | −0.446453 | ||||||||
\(838\) | 51.8240 | 1.79023 | ||||||||
\(839\) | −18.5299 | −0.639723 | −0.319861 | − | 0.947464i | \(-0.603636\pi\) | ||||
−0.319861 | + | 0.947464i | \(0.603636\pi\) | |||||||
\(840\) | 45.2605 | 1.56163 | ||||||||
\(841\) | 21.1002 | 0.727591 | ||||||||
\(842\) | −22.4909 | −0.775086 | ||||||||
\(843\) | 25.9591 | 0.894080 | ||||||||
\(844\) | −51.8148 | −1.78354 | ||||||||
\(845\) | 10.2350 | 0.352094 | ||||||||
\(846\) | −0.352331 | −0.0121134 | ||||||||
\(847\) | 68.2531 | 2.34520 | ||||||||
\(848\) | 0.599322 | 0.0205808 | ||||||||
\(849\) | −22.1017 | −0.758529 | ||||||||
\(850\) | −8.13302 | −0.278960 | ||||||||
\(851\) | −5.17537 | −0.177409 | ||||||||
\(852\) | −22.9001 | −0.784546 | ||||||||
\(853\) | −12.9502 | −0.443407 | −0.221704 | − | 0.975114i | \(-0.571162\pi\) | ||||
−0.221704 | + | 0.975114i | \(0.571162\pi\) | |||||||
\(854\) | −56.8934 | −1.94685 | ||||||||
\(855\) | 0.396783 | 0.0135697 | ||||||||
\(856\) | −3.77791 | −0.129126 | ||||||||
\(857\) | 42.0953 | 1.43795 | 0.718973 | − | 0.695038i | \(-0.244612\pi\) | ||||
0.718973 | + | 0.695038i | \(0.244612\pi\) | |||||||
\(858\) | 93.1898 | 3.18145 | ||||||||
\(859\) | 20.9662 | 0.715356 | 0.357678 | − | 0.933845i | \(-0.383569\pi\) | ||||
0.357678 | + | 0.933845i | \(0.383569\pi\) | |||||||
\(860\) | −75.0680 | −2.55980 | ||||||||
\(861\) | 7.29591 | 0.248644 | ||||||||
\(862\) | −54.2716 | −1.84850 | ||||||||
\(863\) | 47.5313 | 1.61798 | 0.808991 | − | 0.587821i | \(-0.200014\pi\) | ||||
0.808991 | + | 0.587821i | \(0.200014\pi\) | |||||||
\(864\) | 24.7450 | 0.841843 | ||||||||
\(865\) | −13.1684 | −0.447740 | ||||||||
\(866\) | 8.75716 | 0.297580 | ||||||||
\(867\) | 25.2394 | 0.857177 | ||||||||
\(868\) | −24.6988 | −0.838333 | ||||||||
\(869\) | 39.9423 | 1.35495 | ||||||||
\(870\) | 75.7469 | 2.56806 | ||||||||
\(871\) | 29.9619 | 1.01522 | ||||||||
\(872\) | −66.8914 | −2.26523 | ||||||||
\(873\) | 1.30714 | 0.0442400 | ||||||||
\(874\) | 1.96247 | 0.0663815 | ||||||||
\(875\) | −20.6003 | −0.696417 | ||||||||
\(876\) | 69.1633 | 2.33681 | ||||||||
\(877\) | 14.3308 | 0.483915 | 0.241958 | − | 0.970287i | \(-0.422210\pi\) | ||||
0.241958 | + | 0.970287i | \(0.422210\pi\) | |||||||
\(878\) | −87.4072 | −2.94985 | ||||||||
\(879\) | −4.47273 | −0.150861 | ||||||||
\(880\) | 13.3666 | 0.450588 | ||||||||
\(881\) | 38.5566 | 1.29900 | 0.649502 | − | 0.760360i | \(-0.274977\pi\) | ||||
0.649502 | + | 0.760360i | \(0.274977\pi\) | |||||||
\(882\) | 0.766314 | 0.0258031 | ||||||||
\(883\) | −18.3587 | −0.617818 | −0.308909 | − | 0.951092i | \(-0.599964\pi\) | ||||
−0.308909 | + | 0.951092i | \(0.599964\pi\) | |||||||
\(884\) | 19.7273 | 0.663502 | ||||||||
\(885\) | 57.4899 | 1.93250 | ||||||||
\(886\) | −58.6250 | −1.96955 | ||||||||
\(887\) | −22.2031 | −0.745509 | −0.372754 | − | 0.927930i | \(-0.621587\pi\) | ||||
−0.372754 | + | 0.927930i | \(0.621587\pi\) | |||||||
\(888\) | −28.6941 | −0.962912 | ||||||||
\(889\) | 4.62504 | 0.155119 | ||||||||
\(890\) | 42.2192 | 1.41519 | ||||||||
\(891\) | −49.1949 | −1.64809 | ||||||||
\(892\) | −32.7322 | −1.09596 | ||||||||
\(893\) | 0.741752 | 0.0248218 | ||||||||
\(894\) | −74.0521 | −2.47667 | ||||||||
\(895\) | 6.79190 | 0.227028 | ||||||||
\(896\) | 58.9922 | 1.97079 | ||||||||
\(897\) | −6.88099 | −0.229750 | ||||||||
\(898\) | −49.4358 | −1.64970 | ||||||||
\(899\) | −17.1388 | −0.571610 | ||||||||
\(900\) | −1.45612 | −0.0485375 | ||||||||
\(901\) | 1.00668 | 0.0335375 | ||||||||
\(902\) | 19.6809 | 0.655303 | ||||||||
\(903\) | 40.3422 | 1.34251 | ||||||||
\(904\) | −14.0394 | −0.466944 | ||||||||
\(905\) | 29.2807 | 0.973324 | ||||||||
\(906\) | 39.2889 | 1.30529 | ||||||||
\(907\) | −52.4764 | −1.74245 | −0.871225 | − | 0.490884i | \(-0.836674\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(908\) | 10.9867 | 0.364605 | ||||||||
\(909\) | −3.02055 | −0.100185 | ||||||||
\(910\) | −77.7410 | −2.57709 | ||||||||
\(911\) | 17.4259 | 0.577347 | 0.288674 | − | 0.957428i | \(-0.406786\pi\) | ||||
0.288674 | + | 0.957428i | \(0.406786\pi\) | |||||||
\(912\) | 1.19121 | 0.0394451 | ||||||||
\(913\) | 11.6700 | 0.386220 | ||||||||
\(914\) | 43.1324 | 1.42669 | ||||||||
\(915\) | −37.6496 | −1.24466 | ||||||||
\(916\) | 50.6054 | 1.67205 | ||||||||
\(917\) | −44.4139 | −1.46668 | ||||||||
\(918\) | −17.5184 | −0.578194 | ||||||||
\(919\) | −30.2110 | −0.996569 | −0.498284 | − | 0.867014i | \(-0.666036\pi\) | ||||
−0.498284 | + | 0.867014i | \(0.666036\pi\) | |||||||
\(920\) | −9.01505 | −0.297217 | ||||||||
\(921\) | −32.6526 | −1.07594 | ||||||||
\(922\) | −54.3691 | −1.79055 | ||||||||
\(923\) | 16.3090 | 0.536817 | ||||||||
\(924\) | −99.8162 | −3.28371 | ||||||||
\(925\) | −12.8167 | −0.421411 | ||||||||
\(926\) | −15.4177 | −0.506659 | ||||||||
\(927\) | −2.43947 | −0.0801228 | ||||||||
\(928\) | 32.8344 | 1.07784 | ||||||||
\(929\) | −39.8728 | −1.30818 | −0.654092 | − | 0.756415i | \(-0.726949\pi\) | ||||
−0.654092 | + | 0.756415i | \(0.726949\pi\) | |||||||
\(930\) | −25.9123 | −0.849698 | ||||||||
\(931\) | −1.61330 | −0.0528738 | ||||||||
\(932\) | 57.7278 | 1.89094 | ||||||||
\(933\) | 52.4973 | 1.71868 | ||||||||
\(934\) | 94.2089 | 3.08261 | ||||||||
\(935\) | 22.4519 | 0.734256 | ||||||||
\(936\) | 2.32169 | 0.0758867 | ||||||||
\(937\) | 41.9966 | 1.37197 | 0.685985 | − | 0.727616i | \(-0.259372\pi\) | ||||
0.685985 | + | 0.727616i | \(0.259372\pi\) | |||||||
\(938\) | −50.8784 | −1.66124 | ||||||||
\(939\) | −26.4233 | −0.862293 | ||||||||
\(940\) | −8.21801 | −0.268042 | ||||||||
\(941\) | 36.2933 | 1.18313 | 0.591564 | − | 0.806258i | \(-0.298511\pi\) | ||||
0.591564 | + | 0.806258i | \(0.298511\pi\) | |||||||
\(942\) | −79.7398 | −2.59806 | ||||||||
\(943\) | −1.45321 | −0.0473230 | ||||||||
\(944\) | −10.5034 | −0.341856 | ||||||||
\(945\) | 43.5457 | 1.41654 | ||||||||
\(946\) | 108.824 | 3.53819 | ||||||||
\(947\) | −29.4432 | −0.956774 | −0.478387 | − | 0.878149i | \(-0.658778\pi\) | ||||
−0.478387 | + | 0.878149i | \(0.658778\pi\) | |||||||
\(948\) | −39.4376 | −1.28087 | ||||||||
\(949\) | −49.2566 | −1.59894 | ||||||||
\(950\) | 4.86002 | 0.157680 | ||||||||
\(951\) | −17.3175 | −0.561560 | ||||||||
\(952\) | −13.8896 | −0.450165 | ||||||||
\(953\) | −25.0974 | −0.812986 | −0.406493 | − | 0.913654i | \(-0.633248\pi\) | ||||
−0.406493 | + | 0.913654i | \(0.633248\pi\) | |||||||
\(954\) | 0.285740 | 0.00925118 | ||||||||
\(955\) | 42.6381 | 1.37974 | ||||||||
\(956\) | −62.1629 | −2.01049 | ||||||||
\(957\) | −69.2636 | −2.23897 | ||||||||
\(958\) | 89.7019 | 2.89814 | ||||||||
\(959\) | 45.7966 | 1.47885 | ||||||||
\(960\) | 57.3682 | 1.85155 | ||||||||
\(961\) | −25.1370 | −0.810871 | ||||||||
\(962\) | 49.2861 | 1.58905 | ||||||||
\(963\) | −0.197196 | −0.00635456 | ||||||||
\(964\) | 105.192 | 3.38801 | ||||||||
\(965\) | 45.3600 | 1.46019 | ||||||||
\(966\) | 11.6846 | 0.375947 | ||||||||
\(967\) | 47.8759 | 1.53958 | 0.769792 | − | 0.638294i | \(-0.220360\pi\) | ||||
0.769792 | + | 0.638294i | \(0.220360\pi\) | |||||||
\(968\) | −75.3743 | −2.42262 | ||||||||
\(969\) | 2.00089 | 0.0642778 | ||||||||
\(970\) | 48.3358 | 1.55197 | ||||||||
\(971\) | −21.6509 | −0.694811 | −0.347406 | − | 0.937715i | \(-0.612937\pi\) | ||||
−0.347406 | + | 0.937715i | \(0.612937\pi\) | |||||||
\(972\) | −6.10279 | −0.195747 | ||||||||
\(973\) | 42.3194 | 1.35670 | ||||||||
\(974\) | −86.2983 | −2.76517 | ||||||||
\(975\) | −17.0407 | −0.545738 | ||||||||
\(976\) | 6.87857 | 0.220178 | ||||||||
\(977\) | −21.1515 | −0.676696 | −0.338348 | − | 0.941021i | \(-0.609868\pi\) | ||||
−0.338348 | + | 0.941021i | \(0.609868\pi\) | |||||||
\(978\) | 40.1989 | 1.28542 | ||||||||
\(979\) | −38.6056 | −1.23384 | ||||||||
\(980\) | 17.8740 | 0.570965 | ||||||||
\(981\) | −3.49154 | −0.111476 | ||||||||
\(982\) | 38.6758 | 1.23419 | ||||||||
\(983\) | −28.6150 | −0.912676 | −0.456338 | − | 0.889806i | \(-0.650839\pi\) | ||||
−0.456338 | + | 0.889806i | \(0.650839\pi\) | |||||||
\(984\) | −8.05713 | −0.256852 | ||||||||
\(985\) | 61.7986 | 1.96907 | ||||||||
\(986\) | −23.2453 | −0.740283 | ||||||||
\(987\) | 4.41643 | 0.140577 | ||||||||
\(988\) | −11.7884 | −0.375039 | ||||||||
\(989\) | −8.03543 | −0.255512 | ||||||||
\(990\) | 6.37282 | 0.202542 | ||||||||
\(991\) | 33.9697 | 1.07908 | 0.539541 | − | 0.841959i | \(-0.318598\pi\) | ||||
0.539541 | + | 0.841959i | \(0.318598\pi\) | |||||||
\(992\) | −11.2323 | −0.356627 | ||||||||
\(993\) | 14.2901 | 0.453484 | ||||||||
\(994\) | −27.6944 | −0.878412 | ||||||||
\(995\) | −30.1344 | −0.955324 | ||||||||
\(996\) | −11.5225 | −0.365105 | ||||||||
\(997\) | 47.1250 | 1.49246 | 0.746232 | − | 0.665686i | \(-0.231861\pi\) | ||||
0.746232 | + | 0.665686i | \(0.231861\pi\) | |||||||
\(998\) | −7.08670 | −0.224326 | ||||||||
\(999\) | −27.6070 | −0.873448 |
(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 | 8027.2.a.f.1.19 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.19 | ✓ | 176 | 1.1 | even | 1 | trivial |