Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62103 | −1.85335 | −0.926673 | − | 0.375868i | \(-0.877345\pi\) | ||||
−0.926673 | + | 0.375868i | \(0.877345\pi\) | |||||||
\(3\) | −1.46003 | −0.842951 | −0.421476 | − | 0.906840i | \(-0.638488\pi\) | ||||
−0.421476 | + | 0.906840i | \(0.638488\pi\) | |||||||
\(4\) | 4.86979 | 2.43489 | ||||||||
\(5\) | 3.30025 | 1.47592 | 0.737958 | − | 0.674846i | \(-0.235790\pi\) | ||||
0.737958 | + | 0.674846i | \(0.235790\pi\) | |||||||
\(6\) | 3.82679 | 1.56228 | ||||||||
\(7\) | −2.17387 | −0.821647 | −0.410824 | − | 0.911715i | \(-0.634759\pi\) | ||||
−0.410824 | + | 0.911715i | \(0.634759\pi\) | |||||||
\(8\) | −7.52179 | −2.65936 | ||||||||
\(9\) | −0.868300 | −0.289433 | ||||||||
\(10\) | −8.65005 | −2.73539 | ||||||||
\(11\) | 5.62863 | 1.69709 | 0.848547 | − | 0.529119i | \(-0.177478\pi\) | ||||
0.848547 | + | 0.529119i | \(0.177478\pi\) | |||||||
\(12\) | −7.11006 | −2.05250 | ||||||||
\(13\) | 0.817330 | 0.226686 | 0.113343 | − | 0.993556i | \(-0.463844\pi\) | ||||
0.113343 | + | 0.993556i | \(0.463844\pi\) | |||||||
\(14\) | 5.69779 | 1.52280 | ||||||||
\(15\) | −4.81848 | −1.24413 | ||||||||
\(16\) | 9.97526 | 2.49381 | ||||||||
\(17\) | −3.22739 | −0.782757 | −0.391378 | − | 0.920230i | \(-0.628002\pi\) | ||||
−0.391378 | + | 0.920230i | \(0.628002\pi\) | |||||||
\(18\) | 2.27584 | 0.536420 | ||||||||
\(19\) | 1.28467 | 0.294723 | 0.147361 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147361 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(20\) | 16.0715 | 3.59370 | ||||||||
\(21\) | 3.17393 | 0.692609 | ||||||||
\(22\) | −14.7528 | −3.14530 | ||||||||
\(23\) | −0.920221 | −0.191879 | −0.0959396 | − | 0.995387i | \(-0.530586\pi\) | ||||
−0.0959396 | + | 0.995387i | \(0.530586\pi\) | |||||||
\(24\) | 10.9821 | 2.24171 | ||||||||
\(25\) | 5.89165 | 1.17833 | ||||||||
\(26\) | −2.14224 | −0.420129 | ||||||||
\(27\) | 5.64785 | 1.08693 | ||||||||
\(28\) | −10.5863 | −2.00062 | ||||||||
\(29\) | 0.512809 | 0.0952262 | 0.0476131 | − | 0.998866i | \(-0.484839\pi\) | ||||
0.0476131 | + | 0.998866i | \(0.484839\pi\) | |||||||
\(30\) | 12.6294 | 2.30580 | ||||||||
\(31\) | 7.33288 | 1.31702 | 0.658512 | − | 0.752570i | \(-0.271186\pi\) | ||||
0.658512 | + | 0.752570i | \(0.271186\pi\) | |||||||
\(32\) | −11.1018 | −1.96255 | ||||||||
\(33\) | −8.21799 | −1.43057 | ||||||||
\(34\) | 8.45907 | 1.45072 | ||||||||
\(35\) | −7.17433 | −1.21268 | ||||||||
\(36\) | −4.22844 | −0.704739 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −3.36715 | −0.546223 | ||||||||
\(39\) | −1.19333 | −0.191086 | ||||||||
\(40\) | −24.8238 | −3.92499 | ||||||||
\(41\) | 4.14353 | 0.647111 | 0.323556 | − | 0.946209i | \(-0.395122\pi\) | ||||
0.323556 | + | 0.946209i | \(0.395122\pi\) | |||||||
\(42\) | −8.31896 | −1.28364 | ||||||||
\(43\) | 3.69945 | 0.564161 | 0.282081 | − | 0.959391i | \(-0.408975\pi\) | ||||
0.282081 | + | 0.959391i | \(0.408975\pi\) | |||||||
\(44\) | 27.4102 | 4.13225 | ||||||||
\(45\) | −2.86561 | −0.427179 | ||||||||
\(46\) | 2.41192 | 0.355619 | ||||||||
\(47\) | 2.26760 | 0.330764 | 0.165382 | − | 0.986230i | \(-0.447114\pi\) | ||||
0.165382 | + | 0.986230i | \(0.447114\pi\) | |||||||
\(48\) | −14.5642 | −2.10216 | ||||||||
\(49\) | −2.27427 | −0.324896 | ||||||||
\(50\) | −15.4422 | −2.18386 | ||||||||
\(51\) | 4.71210 | 0.659826 | ||||||||
\(52\) | 3.98022 | 0.551957 | ||||||||
\(53\) | −2.68882 | −0.369338 | −0.184669 | − | 0.982801i | \(-0.559121\pi\) | ||||
−0.184669 | + | 0.982801i | \(0.559121\pi\) | |||||||
\(54\) | −14.8032 | −2.01446 | ||||||||
\(55\) | 18.5759 | 2.50477 | ||||||||
\(56\) | 16.3514 | 2.18505 | ||||||||
\(57\) | −1.87566 | −0.248437 | ||||||||
\(58\) | −1.34409 | −0.176487 | ||||||||
\(59\) | −8.75742 | −1.14012 | −0.570060 | − | 0.821603i | \(-0.693080\pi\) | ||||
−0.570060 | + | 0.821603i | \(0.693080\pi\) | |||||||
\(60\) | −23.4650 | −3.02931 | ||||||||
\(61\) | 3.88375 | 0.497263 | 0.248632 | − | 0.968598i | \(-0.420019\pi\) | ||||
0.248632 | + | 0.968598i | \(0.420019\pi\) | |||||||
\(62\) | −19.2197 | −2.44090 | ||||||||
\(63\) | 1.88757 | 0.237812 | ||||||||
\(64\) | 9.14772 | 1.14347 | ||||||||
\(65\) | 2.69739 | 0.334570 | ||||||||
\(66\) | 21.5396 | 2.65134 | ||||||||
\(67\) | −15.1747 | −1.85388 | −0.926941 | − | 0.375206i | \(-0.877572\pi\) | ||||
−0.926941 | + | 0.375206i | \(0.877572\pi\) | |||||||
\(68\) | −15.7167 | −1.90593 | ||||||||
\(69\) | 1.34355 | 0.161745 | ||||||||
\(70\) | 18.8041 | 2.24752 | ||||||||
\(71\) | 3.51248 | 0.416854 | 0.208427 | − | 0.978038i | \(-0.433166\pi\) | ||||
0.208427 | + | 0.978038i | \(0.433166\pi\) | |||||||
\(72\) | 6.53117 | 0.769706 | ||||||||
\(73\) | 2.24653 | 0.262936 | 0.131468 | − | 0.991320i | \(-0.458031\pi\) | ||||
0.131468 | + | 0.991320i | \(0.458031\pi\) | |||||||
\(74\) | −2.62103 | −0.304688 | ||||||||
\(75\) | −8.60202 | −0.993275 | ||||||||
\(76\) | 6.25605 | 0.717619 | ||||||||
\(77\) | −12.2359 | −1.39441 | ||||||||
\(78\) | 3.12775 | 0.354148 | ||||||||
\(79\) | 1.34886 | 0.151758 | 0.0758792 | − | 0.997117i | \(-0.475824\pi\) | ||||
0.0758792 | + | 0.997117i | \(0.475824\pi\) | |||||||
\(80\) | 32.9208 | 3.68066 | ||||||||
\(81\) | −5.64116 | −0.626795 | ||||||||
\(82\) | −10.8603 | −1.19932 | ||||||||
\(83\) | 4.42760 | 0.485992 | 0.242996 | − | 0.970027i | \(-0.421870\pi\) | ||||
0.242996 | + | 0.970027i | \(0.421870\pi\) | |||||||
\(84\) | 15.4564 | 1.68643 | ||||||||
\(85\) | −10.6512 | −1.15528 | ||||||||
\(86\) | −9.69637 | −1.04559 | ||||||||
\(87\) | −0.748718 | −0.0802710 | ||||||||
\(88\) | −42.3374 | −4.51318 | ||||||||
\(89\) | −6.63108 | −0.702893 | −0.351446 | − | 0.936208i | \(-0.614310\pi\) | ||||
−0.351446 | + | 0.936208i | \(0.614310\pi\) | |||||||
\(90\) | 7.51083 | 0.791711 | ||||||||
\(91\) | −1.77677 | −0.186256 | ||||||||
\(92\) | −4.48128 | −0.467206 | ||||||||
\(93\) | −10.7063 | −1.11019 | ||||||||
\(94\) | −5.94345 | −0.613020 | ||||||||
\(95\) | 4.23972 | 0.434986 | ||||||||
\(96\) | 16.2091 | 1.65433 | ||||||||
\(97\) | 16.1174 | 1.63647 | 0.818235 | − | 0.574884i | \(-0.194953\pi\) | ||||
0.818235 | + | 0.574884i | \(0.194953\pi\) | |||||||
\(98\) | 5.96093 | 0.602145 | ||||||||
\(99\) | −4.88733 | −0.491196 | ||||||||
\(100\) | 28.6911 | 2.86911 | ||||||||
\(101\) | 15.1330 | 1.50579 | 0.752894 | − | 0.658142i | \(-0.228657\pi\) | ||||
0.752894 | + | 0.658142i | \(0.228657\pi\) | |||||||
\(102\) | −12.3505 | −1.22289 | ||||||||
\(103\) | −4.93266 | −0.486030 | −0.243015 | − | 0.970023i | \(-0.578136\pi\) | ||||
−0.243015 | + | 0.970023i | \(0.578136\pi\) | |||||||
\(104\) | −6.14778 | −0.602840 | ||||||||
\(105\) | 10.4748 | 1.02223 | ||||||||
\(106\) | 7.04747 | 0.684511 | ||||||||
\(107\) | −9.51550 | −0.919898 | −0.459949 | − | 0.887945i | \(-0.652132\pi\) | ||||
−0.459949 | + | 0.887945i | \(0.652132\pi\) | |||||||
\(108\) | 27.5038 | 2.64656 | ||||||||
\(109\) | 12.7355 | 1.21984 | 0.609921 | − | 0.792462i | \(-0.291201\pi\) | ||||
0.609921 | + | 0.792462i | \(0.291201\pi\) | |||||||
\(110\) | −48.6879 | −4.64221 | ||||||||
\(111\) | −1.46003 | −0.138580 | ||||||||
\(112\) | −21.6850 | −2.04904 | ||||||||
\(113\) | 0.226430 | 0.0213007 | 0.0106504 | − | 0.999943i | \(-0.496610\pi\) | ||||
0.0106504 | + | 0.999943i | \(0.496610\pi\) | |||||||
\(114\) | 4.91615 | 0.460440 | ||||||||
\(115\) | −3.03696 | −0.283198 | ||||||||
\(116\) | 2.49727 | 0.231866 | ||||||||
\(117\) | −0.709687 | −0.0656106 | ||||||||
\(118\) | 22.9534 | 2.11304 | ||||||||
\(119\) | 7.01594 | 0.643150 | ||||||||
\(120\) | 36.2436 | 3.30857 | ||||||||
\(121\) | 20.6814 | 1.88013 | ||||||||
\(122\) | −10.1794 | −0.921601 | ||||||||
\(123\) | −6.04970 | −0.545483 | ||||||||
\(124\) | 35.7096 | 3.20681 | ||||||||
\(125\) | 2.94268 | 0.263201 | ||||||||
\(126\) | −4.94738 | −0.440748 | ||||||||
\(127\) | 11.8938 | 1.05540 | 0.527702 | − | 0.849429i | \(-0.323054\pi\) | ||||
0.527702 | + | 0.849429i | \(0.323054\pi\) | |||||||
\(128\) | −1.77275 | −0.156691 | ||||||||
\(129\) | −5.40133 | −0.475560 | ||||||||
\(130\) | −7.06994 | −0.620075 | ||||||||
\(131\) | −4.73913 | −0.414060 | −0.207030 | − | 0.978335i | \(-0.566380\pi\) | ||||
−0.207030 | + | 0.978335i | \(0.566380\pi\) | |||||||
\(132\) | −40.0199 | −3.48328 | ||||||||
\(133\) | −2.79270 | −0.242158 | ||||||||
\(134\) | 39.7733 | 3.43589 | ||||||||
\(135\) | 18.6393 | 1.60422 | ||||||||
\(136\) | 24.2757 | 2.08163 | ||||||||
\(137\) | 19.0911 | 1.63107 | 0.815533 | − | 0.578711i | \(-0.196444\pi\) | ||||
0.815533 | + | 0.578711i | \(0.196444\pi\) | |||||||
\(138\) | −3.52149 | −0.299769 | ||||||||
\(139\) | 3.97473 | 0.337133 | 0.168566 | − | 0.985690i | \(-0.446086\pi\) | ||||
0.168566 | + | 0.985690i | \(0.446086\pi\) | |||||||
\(140\) | −34.9375 | −2.95275 | ||||||||
\(141\) | −3.31078 | −0.278818 | ||||||||
\(142\) | −9.20630 | −0.772576 | ||||||||
\(143\) | 4.60044 | 0.384708 | ||||||||
\(144\) | −8.66151 | −0.721793 | ||||||||
\(145\) | 1.69240 | 0.140546 | ||||||||
\(146\) | −5.88822 | −0.487312 | ||||||||
\(147\) | 3.32051 | 0.273871 | ||||||||
\(148\) | 4.86979 | 0.400294 | ||||||||
\(149\) | 10.3780 | 0.850202 | 0.425101 | − | 0.905146i | \(-0.360239\pi\) | ||||
0.425101 | + | 0.905146i | \(0.360239\pi\) | |||||||
\(150\) | 22.5461 | 1.84088 | ||||||||
\(151\) | 4.47409 | 0.364097 | 0.182048 | − | 0.983290i | \(-0.441727\pi\) | ||||
0.182048 | + | 0.983290i | \(0.441727\pi\) | |||||||
\(152\) | −9.66300 | −0.783773 | ||||||||
\(153\) | 2.80234 | 0.226556 | ||||||||
\(154\) | 32.0707 | 2.58433 | ||||||||
\(155\) | 24.2003 | 1.94382 | ||||||||
\(156\) | −5.81126 | −0.465273 | ||||||||
\(157\) | −6.71841 | −0.536187 | −0.268094 | − | 0.963393i | \(-0.586394\pi\) | ||||
−0.268094 | + | 0.963393i | \(0.586394\pi\) | |||||||
\(158\) | −3.53539 | −0.281261 | ||||||||
\(159\) | 3.92577 | 0.311334 | ||||||||
\(160\) | −36.6389 | −2.89656 | ||||||||
\(161\) | 2.00044 | 0.157657 | ||||||||
\(162\) | 14.7856 | 1.16167 | ||||||||
\(163\) | −1.00000 | −0.0783260 | ||||||||
\(164\) | 20.1781 | 1.57565 | ||||||||
\(165\) | −27.1214 | −2.11140 | ||||||||
\(166\) | −11.6049 | −0.900712 | ||||||||
\(167\) | 11.1665 | 0.864089 | 0.432044 | − | 0.901852i | \(-0.357792\pi\) | ||||
0.432044 | + | 0.901852i | \(0.357792\pi\) | |||||||
\(168\) | −23.8737 | −1.84189 | ||||||||
\(169\) | −12.3320 | −0.948613 | ||||||||
\(170\) | 27.9171 | 2.14114 | ||||||||
\(171\) | −1.11548 | −0.0853026 | ||||||||
\(172\) | 18.0156 | 1.37367 | ||||||||
\(173\) | 3.28535 | 0.249781 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(174\) | 1.96241 | 0.148770 | ||||||||
\(175\) | −12.8077 | −0.968172 | ||||||||
\(176\) | 56.1470 | 4.23224 | ||||||||
\(177\) | 12.7861 | 0.961065 | ||||||||
\(178\) | 17.3802 | 1.30270 | ||||||||
\(179\) | −18.7965 | −1.40492 | −0.702460 | − | 0.711723i | \(-0.747915\pi\) | ||||
−0.702460 | + | 0.711723i | \(0.747915\pi\) | |||||||
\(180\) | −13.9549 | −1.04014 | ||||||||
\(181\) | −1.04912 | −0.0779803 | −0.0389901 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389901 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(182\) | 4.65697 | 0.345197 | ||||||||
\(183\) | −5.67041 | −0.419169 | ||||||||
\(184\) | 6.92171 | 0.510275 | ||||||||
\(185\) | 3.30025 | 0.242639 | ||||||||
\(186\) | 28.0614 | 2.05756 | ||||||||
\(187\) | −18.1658 | −1.32841 | ||||||||
\(188\) | 11.0427 | 0.805375 | ||||||||
\(189\) | −12.2777 | −0.893072 | ||||||||
\(190\) | −11.1124 | −0.806180 | ||||||||
\(191\) | 10.2687 | 0.743015 | 0.371508 | − | 0.928430i | \(-0.378841\pi\) | ||||
0.371508 | + | 0.928430i | \(0.378841\pi\) | |||||||
\(192\) | −13.3560 | −0.963886 | ||||||||
\(193\) | −14.7945 | −1.06493 | −0.532466 | − | 0.846451i | \(-0.678735\pi\) | ||||
−0.532466 | + | 0.846451i | \(0.678735\pi\) | |||||||
\(194\) | −42.2441 | −3.03295 | ||||||||
\(195\) | −3.93829 | −0.282026 | ||||||||
\(196\) | −11.0752 | −0.791087 | ||||||||
\(197\) | −16.7798 | −1.19551 | −0.597757 | − | 0.801677i | \(-0.703941\pi\) | ||||
−0.597757 | + | 0.801677i | \(0.703941\pi\) | |||||||
\(198\) | 12.8098 | 0.910356 | ||||||||
\(199\) | −13.3054 | −0.943197 | −0.471599 | − | 0.881813i | \(-0.656323\pi\) | ||||
−0.471599 | + | 0.881813i | \(0.656323\pi\) | |||||||
\(200\) | −44.3158 | −3.13360 | ||||||||
\(201\) | 22.1556 | 1.56273 | ||||||||
\(202\) | −39.6640 | −2.79075 | ||||||||
\(203\) | −1.11478 | −0.0782423 | ||||||||
\(204\) | 22.9469 | 1.60661 | ||||||||
\(205\) | 13.6747 | 0.955082 | ||||||||
\(206\) | 12.9286 | 0.900782 | ||||||||
\(207\) | 0.799027 | 0.0555362 | ||||||||
\(208\) | 8.15307 | 0.565314 | ||||||||
\(209\) | 7.23091 | 0.500172 | ||||||||
\(210\) | −27.4547 | −1.89455 | ||||||||
\(211\) | −6.73316 | −0.463530 | −0.231765 | − | 0.972772i | \(-0.574450\pi\) | ||||
−0.231765 | + | 0.972772i | \(0.574450\pi\) | |||||||
\(212\) | −13.0940 | −0.899298 | ||||||||
\(213\) | −5.12834 | −0.351388 | ||||||||
\(214\) | 24.9404 | 1.70489 | ||||||||
\(215\) | 12.2091 | 0.832655 | ||||||||
\(216\) | −42.4820 | −2.89053 | ||||||||
\(217\) | −15.9408 | −1.08213 | ||||||||
\(218\) | −33.3802 | −2.26079 | ||||||||
\(219\) | −3.28001 | −0.221643 | ||||||||
\(220\) | 90.4606 | 6.09885 | ||||||||
\(221\) | −2.63784 | −0.177440 | ||||||||
\(222\) | 3.82679 | 0.256837 | ||||||||
\(223\) | −2.34828 | −0.157252 | −0.0786262 | − | 0.996904i | \(-0.525053\pi\) | ||||
−0.0786262 | + | 0.996904i | \(0.525053\pi\) | |||||||
\(224\) | 24.1340 | 1.61252 | ||||||||
\(225\) | −5.11572 | −0.341048 | ||||||||
\(226\) | −0.593479 | −0.0394776 | ||||||||
\(227\) | −9.36369 | −0.621490 | −0.310745 | − | 0.950493i | \(-0.600579\pi\) | ||||
−0.310745 | + | 0.950493i | \(0.600579\pi\) | |||||||
\(228\) | −9.13406 | −0.604918 | ||||||||
\(229\) | 0.134441 | 0.00888411 | 0.00444205 | − | 0.999990i | \(-0.498586\pi\) | ||||
0.00444205 | + | 0.999990i | \(0.498586\pi\) | |||||||
\(230\) | 7.95995 | 0.524864 | ||||||||
\(231\) | 17.8649 | 1.17542 | ||||||||
\(232\) | −3.85724 | −0.253240 | ||||||||
\(233\) | 2.75353 | 0.180390 | 0.0901948 | − | 0.995924i | \(-0.471251\pi\) | ||||
0.0901948 | + | 0.995924i | \(0.471251\pi\) | |||||||
\(234\) | 1.86011 | 0.121599 | ||||||||
\(235\) | 7.48366 | 0.488180 | ||||||||
\(236\) | −42.6468 | −2.77607 | ||||||||
\(237\) | −1.96938 | −0.127925 | ||||||||
\(238\) | −18.3890 | −1.19198 | ||||||||
\(239\) | 9.70374 | 0.627683 | 0.313841 | − | 0.949475i | \(-0.398384\pi\) | ||||
0.313841 | + | 0.949475i | \(0.398384\pi\) | |||||||
\(240\) | −48.0656 | −3.10262 | ||||||||
\(241\) | 11.3094 | 0.728502 | 0.364251 | − | 0.931301i | \(-0.381325\pi\) | ||||
0.364251 | + | 0.931301i | \(0.381325\pi\) | |||||||
\(242\) | −54.2066 | −3.48453 | ||||||||
\(243\) | −8.70727 | −0.558572 | ||||||||
\(244\) | 18.9130 | 1.21078 | ||||||||
\(245\) | −7.50566 | −0.479519 | ||||||||
\(246\) | 15.8564 | 1.01097 | ||||||||
\(247\) | 1.05000 | 0.0668097 | ||||||||
\(248\) | −55.1564 | −3.50244 | ||||||||
\(249\) | −6.46445 | −0.409668 | ||||||||
\(250\) | −7.71284 | −0.487803 | ||||||||
\(251\) | 15.9191 | 1.00480 | 0.502402 | − | 0.864634i | \(-0.332450\pi\) | ||||
0.502402 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(252\) | 9.19209 | 0.579047 | ||||||||
\(253\) | −5.17958 | −0.325637 | ||||||||
\(254\) | −31.1740 | −1.95603 | ||||||||
\(255\) | 15.5511 | 0.973848 | ||||||||
\(256\) | −13.6490 | −0.853063 | ||||||||
\(257\) | −7.49795 | −0.467709 | −0.233855 | − | 0.972272i | \(-0.575134\pi\) | ||||
−0.233855 | + | 0.972272i | \(0.575134\pi\) | |||||||
\(258\) | 14.1570 | 0.881378 | ||||||||
\(259\) | −2.17387 | −0.135078 | ||||||||
\(260\) | 13.1357 | 0.814643 | ||||||||
\(261\) | −0.445272 | −0.0275616 | ||||||||
\(262\) | 12.4214 | 0.767396 | ||||||||
\(263\) | 7.35883 | 0.453765 | 0.226882 | − | 0.973922i | \(-0.427147\pi\) | ||||
0.226882 | + | 0.973922i | \(0.427147\pi\) | |||||||
\(264\) | 61.8140 | 3.80439 | ||||||||
\(265\) | −8.87377 | −0.545112 | ||||||||
\(266\) | 7.31976 | 0.448803 | ||||||||
\(267\) | 9.68160 | 0.592504 | ||||||||
\(268\) | −73.8975 | −4.51401 | ||||||||
\(269\) | 28.8341 | 1.75804 | 0.879022 | − | 0.476781i | \(-0.158196\pi\) | ||||
0.879022 | + | 0.476781i | \(0.158196\pi\) | |||||||
\(270\) | −48.8542 | −2.97317 | ||||||||
\(271\) | 5.62339 | 0.341596 | 0.170798 | − | 0.985306i | \(-0.445365\pi\) | ||||
0.170798 | + | 0.985306i | \(0.445365\pi\) | |||||||
\(272\) | −32.1940 | −1.95205 | ||||||||
\(273\) | 2.59415 | 0.157005 | ||||||||
\(274\) | −50.0384 | −3.02293 | ||||||||
\(275\) | 33.1619 | 1.99974 | ||||||||
\(276\) | 6.54282 | 0.393832 | ||||||||
\(277\) | 3.23546 | 0.194400 | 0.0971999 | − | 0.995265i | \(-0.469011\pi\) | ||||
0.0971999 | + | 0.995265i | \(0.469011\pi\) | |||||||
\(278\) | −10.4179 | −0.624823 | ||||||||
\(279\) | −6.36714 | −0.381191 | ||||||||
\(280\) | 53.9638 | 3.22496 | ||||||||
\(281\) | 14.3038 | 0.853291 | 0.426645 | − | 0.904419i | \(-0.359695\pi\) | ||||
0.426645 | + | 0.904419i | \(0.359695\pi\) | |||||||
\(282\) | 8.67764 | 0.516746 | ||||||||
\(283\) | −4.23118 | −0.251517 | −0.125759 | − | 0.992061i | \(-0.540136\pi\) | ||||
−0.125759 | + | 0.992061i | \(0.540136\pi\) | |||||||
\(284\) | 17.1050 | 1.01500 | ||||||||
\(285\) | −6.19014 | −0.366672 | ||||||||
\(286\) | −12.0579 | −0.712998 | ||||||||
\(287\) | −9.00752 | −0.531697 | ||||||||
\(288\) | 9.63973 | 0.568026 | ||||||||
\(289\) | −6.58397 | −0.387292 | ||||||||
\(290\) | −4.43582 | −0.260480 | ||||||||
\(291\) | −23.5319 | −1.37946 | ||||||||
\(292\) | 10.9401 | 0.640222 | ||||||||
\(293\) | −17.0595 | −0.996626 | −0.498313 | − | 0.866997i | \(-0.666047\pi\) | ||||
−0.498313 | + | 0.866997i | \(0.666047\pi\) | |||||||
\(294\) | −8.70316 | −0.507579 | ||||||||
\(295\) | −28.9017 | −1.68272 | ||||||||
\(296\) | −7.52179 | −0.437195 | ||||||||
\(297\) | 31.7896 | 1.84462 | ||||||||
\(298\) | −27.2011 | −1.57572 | ||||||||
\(299\) | −0.752123 | −0.0434964 | ||||||||
\(300\) | −41.8900 | −2.41852 | ||||||||
\(301\) | −8.04215 | −0.463542 | ||||||||
\(302\) | −11.7267 | −0.674797 | ||||||||
\(303\) | −22.0947 | −1.26931 | ||||||||
\(304\) | 12.8149 | 0.734984 | ||||||||
\(305\) | 12.8173 | 0.733919 | ||||||||
\(306\) | −7.34501 | −0.419886 | ||||||||
\(307\) | −24.7356 | −1.41173 | −0.705867 | − | 0.708344i | \(-0.749443\pi\) | ||||
−0.705867 | + | 0.708344i | \(0.749443\pi\) | |||||||
\(308\) | −59.5864 | −3.39525 | ||||||||
\(309\) | 7.20186 | 0.409699 | ||||||||
\(310\) | −63.4298 | −3.60257 | ||||||||
\(311\) | −2.82690 | −0.160299 | −0.0801493 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801493 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(312\) | 8.97598 | 0.508165 | ||||||||
\(313\) | −27.8602 | −1.57475 | −0.787375 | − | 0.616474i | \(-0.788560\pi\) | ||||
−0.787375 | + | 0.616474i | \(0.788560\pi\) | |||||||
\(314\) | 17.6091 | 0.993741 | ||||||||
\(315\) | 6.22947 | 0.350991 | ||||||||
\(316\) | 6.56865 | 0.369516 | ||||||||
\(317\) | 26.9396 | 1.51308 | 0.756538 | − | 0.653950i | \(-0.226889\pi\) | ||||
0.756538 | + | 0.653950i | \(0.226889\pi\) | |||||||
\(318\) | −10.2895 | −0.577009 | ||||||||
\(319\) | 2.88641 | 0.161608 | ||||||||
\(320\) | 30.1898 | 1.68766 | ||||||||
\(321\) | 13.8930 | 0.775429 | ||||||||
\(322\) | −5.24322 | −0.292193 | ||||||||
\(323\) | −4.14612 | −0.230696 | ||||||||
\(324\) | −27.4712 | −1.52618 | ||||||||
\(325\) | 4.81542 | 0.267112 | ||||||||
\(326\) | 2.62103 | 0.145165 | ||||||||
\(327\) | −18.5943 | −1.02827 | ||||||||
\(328\) | −31.1668 | −1.72090 | ||||||||
\(329\) | −4.92948 | −0.271771 | ||||||||
\(330\) | 71.0860 | 3.91316 | ||||||||
\(331\) | 6.99012 | 0.384212 | 0.192106 | − | 0.981374i | \(-0.438468\pi\) | ||||
0.192106 | + | 0.981374i | \(0.438468\pi\) | |||||||
\(332\) | 21.5615 | 1.18334 | ||||||||
\(333\) | −0.868300 | −0.0475825 | ||||||||
\(334\) | −29.2677 | −1.60146 | ||||||||
\(335\) | −50.0803 | −2.73618 | ||||||||
\(336\) | 31.6608 | 1.72724 | ||||||||
\(337\) | −14.7790 | −0.805061 | −0.402531 | − | 0.915407i | \(-0.631869\pi\) | ||||
−0.402531 | + | 0.915407i | \(0.631869\pi\) | |||||||
\(338\) | 32.3224 | 1.75811 | ||||||||
\(339\) | −0.330595 | −0.0179555 | ||||||||
\(340\) | −51.8690 | −2.81299 | ||||||||
\(341\) | 41.2741 | 2.23512 | ||||||||
\(342\) | 2.92369 | 0.158095 | ||||||||
\(343\) | 20.1611 | 1.08860 | ||||||||
\(344\) | −27.8265 | −1.50031 | ||||||||
\(345\) | 4.43406 | 0.238722 | ||||||||
\(346\) | −8.61100 | −0.462930 | ||||||||
\(347\) | −0.569225 | −0.0305576 | −0.0152788 | − | 0.999883i | \(-0.504864\pi\) | ||||
−0.0152788 | + | 0.999883i | \(0.504864\pi\) | |||||||
\(348\) | −3.64610 | −0.195451 | ||||||||
\(349\) | 4.38665 | 0.234812 | 0.117406 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117406 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(350\) | 33.5694 | 1.79436 | ||||||||
\(351\) | 4.61615 | 0.246392 | ||||||||
\(352\) | −62.4881 | −3.33063 | ||||||||
\(353\) | 5.03369 | 0.267916 | 0.133958 | − | 0.990987i | \(-0.457231\pi\) | ||||
0.133958 | + | 0.990987i | \(0.457231\pi\) | |||||||
\(354\) | −33.5128 | −1.78119 | ||||||||
\(355\) | 11.5921 | 0.615243 | ||||||||
\(356\) | −32.2919 | −1.71147 | ||||||||
\(357\) | −10.2435 | −0.542144 | ||||||||
\(358\) | 49.2663 | 2.60380 | ||||||||
\(359\) | 14.0137 | 0.739613 | 0.369806 | − | 0.929109i | \(-0.379424\pi\) | ||||
0.369806 | + | 0.929109i | \(0.379424\pi\) | |||||||
\(360\) | 21.5545 | 1.13602 | ||||||||
\(361\) | −17.3496 | −0.913138 | ||||||||
\(362\) | 2.74977 | 0.144525 | ||||||||
\(363\) | −30.1956 | −1.58486 | ||||||||
\(364\) | −8.65250 | −0.453514 | ||||||||
\(365\) | 7.41411 | 0.388072 | ||||||||
\(366\) | 14.8623 | 0.776865 | ||||||||
\(367\) | −12.9983 | −0.678507 | −0.339253 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339253 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(368\) | −9.17944 | −0.478511 | ||||||||
\(369\) | −3.59783 | −0.187295 | ||||||||
\(370\) | −8.65005 | −0.449695 | ||||||||
\(371\) | 5.84515 | 0.303465 | ||||||||
\(372\) | −52.1372 | −2.70319 | ||||||||
\(373\) | 13.4590 | 0.696879 | 0.348440 | − | 0.937331i | \(-0.386712\pi\) | ||||
0.348440 | + | 0.937331i | \(0.386712\pi\) | |||||||
\(374\) | 47.6130 | 2.46201 | ||||||||
\(375\) | −4.29641 | −0.221866 | ||||||||
\(376\) | −17.0564 | −0.879619 | ||||||||
\(377\) | 0.419134 | 0.0215865 | ||||||||
\(378\) | 32.1802 | 1.65517 | ||||||||
\(379\) | −15.3522 | −0.788588 | −0.394294 | − | 0.918984i | \(-0.629011\pi\) | ||||
−0.394294 | + | 0.918984i | \(0.629011\pi\) | |||||||
\(380\) | 20.6465 | 1.05915 | ||||||||
\(381\) | −17.3654 | −0.889655 | ||||||||
\(382\) | −26.9145 | −1.37707 | ||||||||
\(383\) | 16.0048 | 0.817806 | 0.408903 | − | 0.912578i | \(-0.365911\pi\) | ||||
0.408903 | + | 0.912578i | \(0.365911\pi\) | |||||||
\(384\) | 2.58828 | 0.132083 | ||||||||
\(385\) | −40.3816 | −2.05804 | ||||||||
\(386\) | 38.7768 | 1.97369 | ||||||||
\(387\) | −3.21223 | −0.163287 | ||||||||
\(388\) | 78.4881 | 3.98463 | ||||||||
\(389\) | 8.76024 | 0.444162 | 0.222081 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222081 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(390\) | 10.3224 | 0.522693 | ||||||||
\(391\) | 2.96991 | 0.150195 | ||||||||
\(392\) | 17.1066 | 0.864014 | ||||||||
\(393\) | 6.91930 | 0.349032 | ||||||||
\(394\) | 43.9804 | 2.21570 | ||||||||
\(395\) | 4.45157 | 0.223983 | ||||||||
\(396\) | −23.8003 | −1.19601 | ||||||||
\(397\) | 29.4983 | 1.48048 | 0.740238 | − | 0.672344i | \(-0.234713\pi\) | ||||
0.740238 | + | 0.672344i | \(0.234713\pi\) | |||||||
\(398\) | 34.8739 | 1.74807 | ||||||||
\(399\) | 4.07744 | 0.204128 | ||||||||
\(400\) | 58.7708 | 2.93854 | ||||||||
\(401\) | −14.2018 | −0.709206 | −0.354603 | − | 0.935017i | \(-0.615384\pi\) | ||||
−0.354603 | + | 0.935017i | \(0.615384\pi\) | |||||||
\(402\) | −58.0703 | −2.89629 | ||||||||
\(403\) | 5.99338 | 0.298552 | ||||||||
\(404\) | 73.6944 | 3.66643 | ||||||||
\(405\) | −18.6172 | −0.925098 | ||||||||
\(406\) | 2.92187 | 0.145010 | ||||||||
\(407\) | 5.62863 | 0.279001 | ||||||||
\(408\) | −35.4434 | −1.75471 | ||||||||
\(409\) | −16.9959 | −0.840394 | −0.420197 | − | 0.907433i | \(-0.638039\pi\) | ||||
−0.420197 | + | 0.907433i | \(0.638039\pi\) | |||||||
\(410\) | −35.8418 | −1.77010 | ||||||||
\(411\) | −27.8737 | −1.37491 | ||||||||
\(412\) | −24.0210 | −1.18343 | ||||||||
\(413\) | 19.0375 | 0.936776 | ||||||||
\(414\) | −2.09427 | −0.102928 | ||||||||
\(415\) | 14.6122 | 0.717284 | ||||||||
\(416\) | −9.07386 | −0.444883 | ||||||||
\(417\) | −5.80325 | −0.284186 | ||||||||
\(418\) | −18.9524 | −0.926993 | ||||||||
\(419\) | −22.4549 | −1.09699 | −0.548496 | − | 0.836153i | \(-0.684799\pi\) | ||||
−0.548496 | + | 0.836153i | \(0.684799\pi\) | |||||||
\(420\) | 51.0099 | 2.48903 | ||||||||
\(421\) | 38.3914 | 1.87108 | 0.935542 | − | 0.353216i | \(-0.114912\pi\) | ||||
0.935542 | + | 0.353216i | \(0.114912\pi\) | |||||||
\(422\) | 17.6478 | 0.859082 | ||||||||
\(423\) | −1.96896 | −0.0957340 | ||||||||
\(424\) | 20.2247 | 0.982200 | ||||||||
\(425\) | −19.0146 | −0.922346 | ||||||||
\(426\) | 13.4415 | 0.651244 | ||||||||
\(427\) | −8.44278 | −0.408575 | ||||||||
\(428\) | −46.3385 | −2.23985 | ||||||||
\(429\) | −6.71680 | −0.324290 | ||||||||
\(430\) | −32.0004 | −1.54320 | ||||||||
\(431\) | −25.8940 | −1.24727 | −0.623636 | − | 0.781715i | \(-0.714345\pi\) | ||||
−0.623636 | + | 0.781715i | \(0.714345\pi\) | |||||||
\(432\) | 56.3388 | 2.71060 | ||||||||
\(433\) | −9.71837 | −0.467035 | −0.233518 | − | 0.972353i | \(-0.575024\pi\) | ||||
−0.233518 | + | 0.972353i | \(0.575024\pi\) | |||||||
\(434\) | 41.7812 | 2.00556 | ||||||||
\(435\) | −2.47096 | −0.118473 | ||||||||
\(436\) | 62.0193 | 2.97019 | ||||||||
\(437\) | −1.18218 | −0.0565512 | ||||||||
\(438\) | 8.59700 | 0.410781 | ||||||||
\(439\) | −15.5978 | −0.744444 | −0.372222 | − | 0.928144i | \(-0.621404\pi\) | ||||
−0.372222 | + | 0.928144i | \(0.621404\pi\) | |||||||
\(440\) | −139.724 | −6.66108 | ||||||||
\(441\) | 1.97475 | 0.0940356 | ||||||||
\(442\) | 6.91385 | 0.328858 | ||||||||
\(443\) | 25.3305 | 1.20349 | 0.601743 | − | 0.798690i | \(-0.294473\pi\) | ||||
0.601743 | + | 0.798690i | \(0.294473\pi\) | |||||||
\(444\) | −7.11006 | −0.337428 | ||||||||
\(445\) | −21.8842 | −1.03741 | ||||||||
\(446\) | 6.15490 | 0.291443 | ||||||||
\(447\) | −15.1523 | −0.716679 | ||||||||
\(448\) | −19.8860 | −0.939525 | ||||||||
\(449\) | 24.3338 | 1.14838 | 0.574191 | − | 0.818721i | \(-0.305317\pi\) | ||||
0.574191 | + | 0.818721i | \(0.305317\pi\) | |||||||
\(450\) | 13.4084 | 0.632080 | ||||||||
\(451\) | 23.3224 | 1.09821 | ||||||||
\(452\) | 1.10267 | 0.0518650 | ||||||||
\(453\) | −6.53233 | −0.306916 | ||||||||
\(454\) | 24.5425 | 1.15184 | ||||||||
\(455\) | −5.86379 | −0.274899 | ||||||||
\(456\) | 14.1083 | 0.660682 | ||||||||
\(457\) | 31.9899 | 1.49642 | 0.748211 | − | 0.663460i | \(-0.230913\pi\) | ||||
0.748211 | + | 0.663460i | \(0.230913\pi\) | |||||||
\(458\) | −0.352373 | −0.0164653 | ||||||||
\(459\) | −18.2278 | −0.850801 | ||||||||
\(460\) | −14.7893 | −0.689557 | ||||||||
\(461\) | 28.5225 | 1.32843 | 0.664213 | − | 0.747543i | \(-0.268767\pi\) | ||||
0.664213 | + | 0.747543i | \(0.268767\pi\) | |||||||
\(462\) | −46.8243 | −2.17847 | ||||||||
\(463\) | −37.1043 | −1.72438 | −0.862191 | − | 0.506583i | \(-0.830908\pi\) | ||||
−0.862191 | + | 0.506583i | \(0.830908\pi\) | |||||||
\(464\) | 5.11540 | 0.237476 | ||||||||
\(465\) | −35.3333 | −1.63854 | ||||||||
\(466\) | −7.21707 | −0.334324 | ||||||||
\(467\) | −11.0594 | −0.511767 | −0.255883 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255883 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(468\) | −3.45602 | −0.159755 | ||||||||
\(469\) | 32.9879 | 1.52324 | ||||||||
\(470\) | −19.6149 | −0.904767 | ||||||||
\(471\) | 9.80911 | 0.451980 | ||||||||
\(472\) | 65.8715 | 3.03198 | ||||||||
\(473\) | 20.8228 | 0.957435 | ||||||||
\(474\) | 5.16180 | 0.237089 | ||||||||
\(475\) | 7.56881 | 0.347281 | ||||||||
\(476\) | 34.1661 | 1.56600 | ||||||||
\(477\) | 2.33470 | 0.106899 | ||||||||
\(478\) | −25.4338 | −1.16331 | ||||||||
\(479\) | −32.2584 | −1.47392 | −0.736962 | − | 0.675934i | \(-0.763740\pi\) | ||||
−0.736962 | + | 0.675934i | \(0.763740\pi\) | |||||||
\(480\) | 53.4940 | 2.44166 | ||||||||
\(481\) | 0.817330 | 0.0372670 | ||||||||
\(482\) | −29.6422 | −1.35017 | ||||||||
\(483\) | −2.92072 | −0.132897 | ||||||||
\(484\) | 100.714 | 4.57792 | ||||||||
\(485\) | 53.1913 | 2.41529 | ||||||||
\(486\) | 22.8220 | 1.03523 | ||||||||
\(487\) | 16.5561 | 0.750227 | 0.375113 | − | 0.926979i | \(-0.377604\pi\) | ||||
0.375113 | + | 0.926979i | \(0.377604\pi\) | |||||||
\(488\) | −29.2128 | −1.32240 | ||||||||
\(489\) | 1.46003 | 0.0660250 | ||||||||
\(490\) | 19.6726 | 0.888715 | ||||||||
\(491\) | 35.3475 | 1.59521 | 0.797604 | − | 0.603181i | \(-0.206100\pi\) | ||||
0.797604 | + | 0.603181i | \(0.206100\pi\) | |||||||
\(492\) | −29.4608 | −1.32819 | ||||||||
\(493\) | −1.65503 | −0.0745389 | ||||||||
\(494\) | −2.75207 | −0.123821 | ||||||||
\(495\) | −16.1294 | −0.724964 | ||||||||
\(496\) | 73.1474 | 3.28441 | ||||||||
\(497\) | −7.63569 | −0.342507 | ||||||||
\(498\) | 16.9435 | 0.759257 | ||||||||
\(499\) | −4.02250 | −0.180072 | −0.0900358 | − | 0.995939i | \(-0.528698\pi\) | ||||
−0.0900358 | + | 0.995939i | \(0.528698\pi\) | |||||||
\(500\) | 14.3302 | 0.640867 | ||||||||
\(501\) | −16.3035 | −0.728385 | ||||||||
\(502\) | −41.7244 | −1.86225 | ||||||||
\(503\) | −7.32232 | −0.326486 | −0.163243 | − | 0.986586i | \(-0.552195\pi\) | ||||
−0.163243 | + | 0.986586i | \(0.552195\pi\) | |||||||
\(504\) | −14.1979 | −0.632427 | ||||||||
\(505\) | 49.9426 | 2.22242 | ||||||||
\(506\) | 13.5758 | 0.603519 | ||||||||
\(507\) | 18.0051 | 0.799635 | ||||||||
\(508\) | 57.9203 | 2.56980 | ||||||||
\(509\) | 29.7770 | 1.31984 | 0.659922 | − | 0.751334i | \(-0.270589\pi\) | ||||
0.659922 | + | 0.751334i | \(0.270589\pi\) | |||||||
\(510\) | −40.7599 | −1.80488 | ||||||||
\(511\) | −4.88367 | −0.216041 | ||||||||
\(512\) | 39.3199 | 1.73771 | ||||||||
\(513\) | 7.25561 | 0.320343 | ||||||||
\(514\) | 19.6523 | 0.866827 | ||||||||
\(515\) | −16.2790 | −0.717339 | ||||||||
\(516\) | −26.3033 | −1.15794 | ||||||||
\(517\) | 12.7635 | 0.561338 | ||||||||
\(518\) | 5.69779 | 0.250346 | ||||||||
\(519\) | −4.79673 | −0.210553 | ||||||||
\(520\) | −20.2892 | −0.889742 | ||||||||
\(521\) | −35.8449 | −1.57040 | −0.785198 | − | 0.619245i | \(-0.787439\pi\) | ||||
−0.785198 | + | 0.619245i | \(0.787439\pi\) | |||||||
\(522\) | 1.16707 | 0.0510813 | ||||||||
\(523\) | −13.2570 | −0.579686 | −0.289843 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289843 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(524\) | −23.0786 | −1.00819 | ||||||||
\(525\) | 18.6997 | 0.816122 | ||||||||
\(526\) | −19.2877 | −0.840984 | ||||||||
\(527\) | −23.6661 | −1.03091 | ||||||||
\(528\) | −81.9766 | −3.56757 | ||||||||
\(529\) | −22.1532 | −0.963182 | ||||||||
\(530\) | 23.2584 | 1.01028 | ||||||||
\(531\) | 7.60407 | 0.329988 | ||||||||
\(532\) | −13.5999 | −0.589629 | ||||||||
\(533\) | 3.38663 | 0.146691 | ||||||||
\(534\) | −25.3757 | −1.09812 | ||||||||
\(535\) | −31.4035 | −1.35769 | ||||||||
\(536\) | 114.141 | 4.93013 | ||||||||
\(537\) | 27.4436 | 1.18428 | ||||||||
\(538\) | −75.5749 | −3.25827 | ||||||||
\(539\) | −12.8010 | −0.551379 | ||||||||
\(540\) | 90.7695 | 3.90610 | ||||||||
\(541\) | −28.3408 | −1.21847 | −0.609234 | − | 0.792990i | \(-0.708523\pi\) | ||||
−0.609234 | + | 0.792990i | \(0.708523\pi\) | |||||||
\(542\) | −14.7391 | −0.633097 | ||||||||
\(543\) | 1.53175 | 0.0657336 | ||||||||
\(544\) | 35.8299 | 1.53620 | ||||||||
\(545\) | 42.0304 | 1.80039 | ||||||||
\(546\) | −6.79933 | −0.290985 | ||||||||
\(547\) | 16.2003 | 0.692676 | 0.346338 | − | 0.938110i | \(-0.387425\pi\) | ||||
0.346338 | + | 0.938110i | \(0.387425\pi\) | |||||||
\(548\) | 92.9697 | 3.97147 | ||||||||
\(549\) | −3.37226 | −0.143925 | ||||||||
\(550\) | −86.9183 | −3.70621 | ||||||||
\(551\) | 0.658788 | 0.0280653 | ||||||||
\(552\) | −10.1059 | −0.430137 | ||||||||
\(553\) | −2.93225 | −0.124692 | ||||||||
\(554\) | −8.48023 | −0.360290 | ||||||||
\(555\) | −4.81848 | −0.204533 | ||||||||
\(556\) | 19.3561 | 0.820882 | ||||||||
\(557\) | 24.9327 | 1.05643 | 0.528216 | − | 0.849110i | \(-0.322861\pi\) | ||||
0.528216 | + | 0.849110i | \(0.322861\pi\) | |||||||
\(558\) | 16.6884 | 0.706478 | ||||||||
\(559\) | 3.02367 | 0.127888 | ||||||||
\(560\) | −71.5658 | −3.02421 | ||||||||
\(561\) | 26.5226 | 1.11979 | ||||||||
\(562\) | −37.4906 | −1.58144 | ||||||||
\(563\) | 22.3564 | 0.942210 | 0.471105 | − | 0.882077i | \(-0.343855\pi\) | ||||
0.471105 | + | 0.882077i | \(0.343855\pi\) | |||||||
\(564\) | −16.1228 | −0.678892 | ||||||||
\(565\) | 0.747275 | 0.0314381 | ||||||||
\(566\) | 11.0900 | 0.466149 | ||||||||
\(567\) | 12.2632 | 0.515005 | ||||||||
\(568\) | −26.4201 | −1.10856 | ||||||||
\(569\) | −6.63494 | −0.278151 | −0.139076 | − | 0.990282i | \(-0.544413\pi\) | ||||
−0.139076 | + | 0.990282i | \(0.544413\pi\) | |||||||
\(570\) | 16.2245 | 0.679571 | ||||||||
\(571\) | 34.1090 | 1.42742 | 0.713709 | − | 0.700442i | \(-0.247014\pi\) | ||||
0.713709 | + | 0.700442i | \(0.247014\pi\) | |||||||
\(572\) | 22.4032 | 0.936724 | ||||||||
\(573\) | −14.9926 | −0.626326 | ||||||||
\(574\) | 23.6090 | 0.985419 | ||||||||
\(575\) | −5.42162 | −0.226097 | ||||||||
\(576\) | −7.94296 | −0.330957 | ||||||||
\(577\) | 16.5632 | 0.689535 | 0.344767 | − | 0.938688i | \(-0.387958\pi\) | ||||
0.344767 | + | 0.938688i | \(0.387958\pi\) | |||||||
\(578\) | 17.2568 | 0.717787 | ||||||||
\(579\) | 21.6005 | 0.897686 | ||||||||
\(580\) | 8.24162 | 0.342215 | ||||||||
\(581\) | −9.62505 | −0.399314 | ||||||||
\(582\) | 61.6778 | 2.55663 | ||||||||
\(583\) | −15.1344 | −0.626801 | ||||||||
\(584\) | −16.8979 | −0.699241 | ||||||||
\(585\) | −2.34214 | −0.0968358 | ||||||||
\(586\) | 44.7134 | 1.84709 | ||||||||
\(587\) | 32.4446 | 1.33913 | 0.669566 | − | 0.742752i | \(-0.266480\pi\) | ||||
0.669566 | + | 0.742752i | \(0.266480\pi\) | |||||||
\(588\) | 16.1702 | 0.666848 | ||||||||
\(589\) | 9.42031 | 0.388157 | ||||||||
\(590\) | 75.7521 | 3.11867 | ||||||||
\(591\) | 24.4991 | 1.00776 | ||||||||
\(592\) | 9.97526 | 0.409981 | ||||||||
\(593\) | 11.1792 | 0.459075 | 0.229538 | − | 0.973300i | \(-0.426279\pi\) | ||||
0.229538 | + | 0.973300i | \(0.426279\pi\) | |||||||
\(594\) | −83.3215 | −3.41872 | ||||||||
\(595\) | 23.1543 | 0.949236 | ||||||||
\(596\) | 50.5389 | 2.07015 | ||||||||
\(597\) | 19.4264 | 0.795069 | ||||||||
\(598\) | 1.97134 | 0.0806140 | ||||||||
\(599\) | −20.7370 | −0.847292 | −0.423646 | − | 0.905828i | \(-0.639250\pi\) | ||||
−0.423646 | + | 0.905828i | \(0.639250\pi\) | |||||||
\(600\) | 64.7026 | 2.64147 | ||||||||
\(601\) | 1.16058 | 0.0473410 | 0.0236705 | − | 0.999720i | \(-0.492465\pi\) | ||||
0.0236705 | + | 0.999720i | \(0.492465\pi\) | |||||||
\(602\) | 21.0787 | 0.859103 | ||||||||
\(603\) | 13.1762 | 0.536575 | ||||||||
\(604\) | 21.7879 | 0.886537 | ||||||||
\(605\) | 68.2539 | 2.77492 | ||||||||
\(606\) | 57.9107 | 2.35246 | ||||||||
\(607\) | 14.8697 | 0.603540 | 0.301770 | − | 0.953381i | \(-0.402422\pi\) | ||||
0.301770 | + | 0.953381i | \(0.402422\pi\) | |||||||
\(608\) | −14.2622 | −0.578407 | ||||||||
\(609\) | 1.62762 | 0.0659545 | ||||||||
\(610\) | −33.5946 | −1.36021 | ||||||||
\(611\) | 1.85338 | 0.0749797 | ||||||||
\(612\) | 13.6468 | 0.551639 | ||||||||
\(613\) | 28.7128 | 1.15970 | 0.579849 | − | 0.814724i | \(-0.303112\pi\) | ||||
0.579849 | + | 0.814724i | \(0.303112\pi\) | |||||||
\(614\) | 64.8327 | 2.61643 | ||||||||
\(615\) | −19.9655 | −0.805088 | ||||||||
\(616\) | 92.0361 | 3.70824 | ||||||||
\(617\) | 28.5590 | 1.14974 | 0.574870 | − | 0.818244i | \(-0.305052\pi\) | ||||
0.574870 | + | 0.818244i | \(0.305052\pi\) | |||||||
\(618\) | −18.8763 | −0.759315 | ||||||||
\(619\) | −46.0483 | −1.85084 | −0.925419 | − | 0.378944i | \(-0.876287\pi\) | ||||
−0.925419 | + | 0.378944i | \(0.876287\pi\) | |||||||
\(620\) | 117.851 | 4.73299 | ||||||||
\(621\) | −5.19727 | −0.208559 | ||||||||
\(622\) | 7.40938 | 0.297089 | ||||||||
\(623\) | 14.4151 | 0.577530 | ||||||||
\(624\) | −11.9038 | −0.476532 | ||||||||
\(625\) | −19.7467 | −0.789868 | ||||||||
\(626\) | 73.0223 | 2.91856 | ||||||||
\(627\) | −10.5574 | −0.421621 | ||||||||
\(628\) | −32.7172 | −1.30556 | ||||||||
\(629\) | −3.22739 | −0.128684 | ||||||||
\(630\) | −16.3276 | −0.650508 | ||||||||
\(631\) | 23.4598 | 0.933922 | 0.466961 | − | 0.884278i | \(-0.345349\pi\) | ||||
0.466961 | + | 0.884278i | \(0.345349\pi\) | |||||||
\(632\) | −10.1458 | −0.403579 | ||||||||
\(633\) | 9.83065 | 0.390733 | ||||||||
\(634\) | −70.6093 | −2.80425 | ||||||||
\(635\) | 39.2525 | 1.55769 | ||||||||
\(636\) | 19.1177 | 0.758064 | ||||||||
\(637\) | −1.85883 | −0.0736495 | ||||||||
\(638\) | −7.56536 | −0.299515 | ||||||||
\(639\) | −3.04988 | −0.120652 | ||||||||
\(640\) | −5.85053 | −0.231263 | ||||||||
\(641\) | −6.35476 | −0.250998 | −0.125499 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125499 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(642\) | −36.4138 | −1.43714 | ||||||||
\(643\) | 34.3452 | 1.35444 | 0.677221 | − | 0.735780i | \(-0.263184\pi\) | ||||
0.677221 | + | 0.735780i | \(0.263184\pi\) | |||||||
\(644\) | 9.74174 | 0.383878 | ||||||||
\(645\) | −17.8257 | −0.701888 | ||||||||
\(646\) | 10.8671 | 0.427560 | ||||||||
\(647\) | 36.8936 | 1.45044 | 0.725218 | − | 0.688519i | \(-0.241739\pi\) | ||||
0.725218 | + | 0.688519i | \(0.241739\pi\) | |||||||
\(648\) | 42.4316 | 1.66687 | ||||||||
\(649\) | −49.2923 | −1.93489 | ||||||||
\(650\) | −12.6214 | −0.495050 | ||||||||
\(651\) | 23.2741 | 0.912182 | ||||||||
\(652\) | −4.86979 | −0.190716 | ||||||||
\(653\) | 41.4575 | 1.62236 | 0.811180 | − | 0.584797i | \(-0.198826\pi\) | ||||
0.811180 | + | 0.584797i | \(0.198826\pi\) | |||||||
\(654\) | 48.7362 | 1.90574 | ||||||||
\(655\) | −15.6403 | −0.611118 | ||||||||
\(656\) | 41.3328 | 1.61377 | ||||||||
\(657\) | −1.95066 | −0.0761025 | ||||||||
\(658\) | 12.9203 | 0.503686 | ||||||||
\(659\) | −26.0760 | −1.01578 | −0.507888 | − | 0.861423i | \(-0.669574\pi\) | ||||
−0.507888 | + | 0.861423i | \(0.669574\pi\) | |||||||
\(660\) | −132.076 | −5.14103 | ||||||||
\(661\) | −27.3158 | −1.06246 | −0.531230 | − | 0.847227i | \(-0.678270\pi\) | ||||
−0.531230 | + | 0.847227i | \(0.678270\pi\) | |||||||
\(662\) | −18.3213 | −0.712077 | ||||||||
\(663\) | 3.85134 | 0.149573 | ||||||||
\(664\) | −33.3035 | −1.29243 | ||||||||
\(665\) | −9.21662 | −0.357405 | ||||||||
\(666\) | 2.27584 | 0.0881869 | ||||||||
\(667\) | −0.471897 | −0.0182719 | ||||||||
\(668\) | 54.3784 | 2.10396 | ||||||||
\(669\) | 3.42857 | 0.132556 | ||||||||
\(670\) | 131.262 | 5.07108 | ||||||||
\(671\) | 21.8602 | 0.843903 | ||||||||
\(672\) | −35.2365 | −1.35928 | ||||||||
\(673\) | 26.1960 | 1.00978 | 0.504891 | − | 0.863183i | \(-0.331533\pi\) | ||||
0.504891 | + | 0.863183i | \(0.331533\pi\) | |||||||
\(674\) | 38.7361 | 1.49206 | ||||||||
\(675\) | 33.2752 | 1.28076 | ||||||||
\(676\) | −60.0541 | −2.30977 | ||||||||
\(677\) | 4.55034 | 0.174884 | 0.0874419 | − | 0.996170i | \(-0.472131\pi\) | ||||
0.0874419 | + | 0.996170i | \(0.472131\pi\) | |||||||
\(678\) | 0.866500 | 0.0332777 | ||||||||
\(679\) | −35.0371 | −1.34460 | ||||||||
\(680\) | 80.1160 | 3.07231 | ||||||||
\(681\) | 13.6713 | 0.523886 | ||||||||
\(682\) | −108.180 | −4.14244 | ||||||||
\(683\) | 10.8077 | 0.413546 | 0.206773 | − | 0.978389i | \(-0.433704\pi\) | ||||
0.206773 | + | 0.978389i | \(0.433704\pi\) | |||||||
\(684\) | −5.43213 | −0.207703 | ||||||||
\(685\) | 63.0055 | 2.40732 | ||||||||
\(686\) | −52.8428 | −2.01755 | ||||||||
\(687\) | −0.196288 | −0.00748887 | ||||||||
\(688\) | 36.9030 | 1.40691 | ||||||||
\(689\) | −2.19765 | −0.0837238 | ||||||||
\(690\) | −11.6218 | −0.442435 | ||||||||
\(691\) | −22.6618 | −0.862095 | −0.431047 | − | 0.902329i | \(-0.641856\pi\) | ||||
−0.431047 | + | 0.902329i | \(0.641856\pi\) | |||||||
\(692\) | 15.9990 | 0.608189 | ||||||||
\(693\) | 10.6245 | 0.403590 | ||||||||
\(694\) | 1.49195 | 0.0566338 | ||||||||
\(695\) | 13.1176 | 0.497580 | ||||||||
\(696\) | 5.63171 | 0.213469 | ||||||||
\(697\) | −13.3728 | −0.506530 | ||||||||
\(698\) | −11.4975 | −0.435188 | ||||||||
\(699\) | −4.02025 | −0.152060 | ||||||||
\(700\) | −62.3708 | −2.35740 | ||||||||
\(701\) | 8.49659 | 0.320912 | 0.160456 | − | 0.987043i | \(-0.448704\pi\) | ||||
0.160456 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(702\) | −12.0991 | −0.456650 | ||||||||
\(703\) | 1.28467 | 0.0484521 | ||||||||
\(704\) | 51.4891 | 1.94057 | ||||||||
\(705\) | −10.9264 | −0.411512 | ||||||||
\(706\) | −13.1934 | −0.496542 | ||||||||
\(707\) | −32.8972 | −1.23723 | ||||||||
\(708\) | 62.2658 | 2.34009 | ||||||||
\(709\) | 44.4148 | 1.66803 | 0.834017 | − | 0.551738i | \(-0.186035\pi\) | ||||
0.834017 | + | 0.551738i | \(0.186035\pi\) | |||||||
\(710\) | −30.3831 | −1.14026 | ||||||||
\(711\) | −1.17121 | −0.0439239 | ||||||||
\(712\) | 49.8776 | 1.86924 | ||||||||
\(713\) | −6.74787 | −0.252710 | ||||||||
\(714\) | 26.8485 | 1.00478 | ||||||||
\(715\) | 15.1826 | 0.567798 | ||||||||
\(716\) | −91.5352 | −3.42083 | ||||||||
\(717\) | −14.1678 | −0.529106 | ||||||||
\(718\) | −36.7302 | −1.37076 | ||||||||
\(719\) | 39.5177 | 1.47376 | 0.736881 | − | 0.676023i | \(-0.236298\pi\) | ||||
0.736881 | + | 0.676023i | \(0.236298\pi\) | |||||||
\(720\) | −28.5852 | −1.06531 | ||||||||
\(721\) | 10.7230 | 0.399345 | ||||||||
\(722\) | 45.4739 | 1.69236 | ||||||||
\(723\) | −16.5121 | −0.614092 | ||||||||
\(724\) | −5.10898 | −0.189874 | ||||||||
\(725\) | 3.02129 | 0.112208 | ||||||||
\(726\) | 79.1435 | 2.93729 | ||||||||
\(727\) | −29.8683 | −1.10775 | −0.553877 | − | 0.832599i | \(-0.686852\pi\) | ||||
−0.553877 | + | 0.832599i | \(0.686852\pi\) | |||||||
\(728\) | 13.3645 | 0.495322 | ||||||||
\(729\) | 29.6364 | 1.09764 | ||||||||
\(730\) | −19.4326 | −0.719232 | ||||||||
\(731\) | −11.9396 | −0.441601 | ||||||||
\(732\) | −27.6137 | −1.02063 | ||||||||
\(733\) | 18.8344 | 0.695664 | 0.347832 | − | 0.937557i | \(-0.386918\pi\) | ||||
0.347832 | + | 0.937557i | \(0.386918\pi\) | |||||||
\(734\) | 34.0689 | 1.25751 | ||||||||
\(735\) | 10.9585 | 0.404211 | ||||||||
\(736\) | 10.2161 | 0.376572 | ||||||||
\(737\) | −85.4126 | −3.14621 | ||||||||
\(738\) | 9.43001 | 0.347123 | ||||||||
\(739\) | −2.74405 | −0.100942 | −0.0504708 | − | 0.998726i | \(-0.516072\pi\) | ||||
−0.0504708 | + | 0.998726i | \(0.516072\pi\) | |||||||
\(740\) | 16.0715 | 0.590801 | ||||||||
\(741\) | −1.53303 | −0.0563173 | ||||||||
\(742\) | −15.3203 | −0.562426 | ||||||||
\(743\) | −0.698995 | −0.0256436 | −0.0128218 | − | 0.999918i | \(-0.504081\pi\) | ||||
−0.0128218 | + | 0.999918i | \(0.504081\pi\) | |||||||
\(744\) | 80.5303 | 2.95238 | ||||||||
\(745\) | 34.2501 | 1.25483 | ||||||||
\(746\) | −35.2764 | −1.29156 | ||||||||
\(747\) | −3.84448 | −0.140662 | ||||||||
\(748\) | −88.4634 | −3.23454 | ||||||||
\(749\) | 20.6855 | 0.755832 | ||||||||
\(750\) | 11.2610 | 0.411194 | ||||||||
\(751\) | −14.3569 | −0.523893 | −0.261946 | − | 0.965082i | \(-0.584364\pi\) | ||||
−0.261946 | + | 0.965082i | \(0.584364\pi\) | |||||||
\(752\) | 22.6199 | 0.824864 | ||||||||
\(753\) | −23.2424 | −0.847000 | ||||||||
\(754\) | −1.09856 | −0.0400072 | ||||||||
\(755\) | 14.7656 | 0.537376 | ||||||||
\(756\) | −59.7899 | −2.17454 | ||||||||
\(757\) | −29.6858 | −1.07895 | −0.539475 | − | 0.842001i | \(-0.681377\pi\) | ||||
−0.539475 | + | 0.842001i | \(0.681377\pi\) | |||||||
\(758\) | 40.2385 | 1.46153 | ||||||||
\(759\) | 7.56236 | 0.274496 | ||||||||
\(760\) | −31.8903 | −1.15678 | ||||||||
\(761\) | 47.9582 | 1.73848 | 0.869242 | − | 0.494387i | \(-0.164607\pi\) | ||||
0.869242 | + | 0.494387i | \(0.164607\pi\) | |||||||
\(762\) | 45.5151 | 1.64884 | ||||||||
\(763\) | −27.6854 | −1.00228 | ||||||||
\(764\) | 50.0063 | 1.80916 | ||||||||
\(765\) | 9.24842 | 0.334377 | ||||||||
\(766\) | −41.9490 | −1.51568 | ||||||||
\(767\) | −7.15770 | −0.258450 | ||||||||
\(768\) | 19.9280 | 0.719090 | ||||||||
\(769\) | 16.1027 | 0.580677 | 0.290338 | − | 0.956924i | \(-0.406232\pi\) | ||||
0.290338 | + | 0.956924i | \(0.406232\pi\) | |||||||
\(770\) | 105.841 | 3.81426 | ||||||||
\(771\) | 10.9473 | 0.394256 | ||||||||
\(772\) | −72.0461 | −2.59300 | ||||||||
\(773\) | −14.2944 | −0.514134 | −0.257067 | − | 0.966394i | \(-0.582756\pi\) | ||||
−0.257067 | + | 0.966394i | \(0.582756\pi\) | |||||||
\(774\) | 8.41935 | 0.302627 | ||||||||
\(775\) | 43.2028 | 1.55189 | ||||||||
\(776\) | −121.231 | −4.35196 | ||||||||
\(777\) | 3.17393 | 0.113864 | ||||||||
\(778\) | −22.9608 | −0.823186 | ||||||||
\(779\) | 5.32306 | 0.190718 | ||||||||
\(780\) | −19.1786 | −0.686705 | ||||||||
\(781\) | 19.7704 | 0.707442 | ||||||||
\(782\) | −7.78421 | −0.278363 | ||||||||
\(783\) | 2.89627 | 0.103504 | ||||||||
\(784\) | −22.6864 | −0.810230 | ||||||||
\(785\) | −22.1724 | −0.791368 | ||||||||
\(786\) | −18.1357 | −0.646878 | ||||||||
\(787\) | 35.3593 | 1.26042 | 0.630211 | − | 0.776424i | \(-0.282968\pi\) | ||||
0.630211 | + | 0.776424i | \(0.282968\pi\) | |||||||
\(788\) | −81.7142 | −2.91095 | ||||||||
\(789\) | −10.7441 | −0.382502 | ||||||||
\(790\) | −11.6677 | −0.415118 | ||||||||
\(791\) | −0.492230 | −0.0175017 | ||||||||
\(792\) | 36.7615 | 1.30626 | ||||||||
\(793\) | 3.17430 | 0.112723 | ||||||||
\(794\) | −77.3159 | −2.74384 | ||||||||
\(795\) | 12.9560 | 0.459503 | ||||||||
\(796\) | −64.7946 | −2.29658 | ||||||||
\(797\) | −38.1353 | −1.35082 | −0.675411 | − | 0.737441i | \(-0.736034\pi\) | ||||
−0.675411 | + | 0.737441i | \(0.736034\pi\) | |||||||
\(798\) | −10.6871 | −0.378319 | ||||||||
\(799\) | −7.31843 | −0.258908 | ||||||||
\(800\) | −65.4082 | −2.31253 | ||||||||
\(801\) | 5.75776 | 0.203441 | ||||||||
\(802\) | 37.2234 | 1.31440 | ||||||||
\(803\) | 12.6449 | 0.446228 | ||||||||
\(804\) | 107.893 | 3.80509 | ||||||||
\(805\) | 6.60197 | 0.232689 | ||||||||
\(806\) | −15.7088 | −0.553320 | ||||||||
\(807\) | −42.0987 | −1.48195 | ||||||||
\(808\) | −113.827 | −4.00442 | ||||||||
\(809\) | 15.1448 | 0.532464 | 0.266232 | − | 0.963909i | \(-0.414221\pi\) | ||||
0.266232 | + | 0.963909i | \(0.414221\pi\) | |||||||
\(810\) | 48.7963 | 1.71453 | ||||||||
\(811\) | 15.3824 | 0.540151 | 0.270075 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270075 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(812\) | −5.42875 | −0.190512 | ||||||||
\(813\) | −8.21034 | −0.287949 | ||||||||
\(814\) | −14.7528 | −0.517085 | ||||||||
\(815\) | −3.30025 | −0.115603 | ||||||||
\(816\) | 47.0044 | 1.64548 | ||||||||
\(817\) | 4.75256 | 0.166271 | ||||||||
\(818\) | 44.5468 | 1.55754 | ||||||||
\(819\) | 1.54277 | 0.0539088 | ||||||||
\(820\) | 66.5929 | 2.32552 | ||||||||
\(821\) | 44.5002 | 1.55307 | 0.776535 | − | 0.630075i | \(-0.216976\pi\) | ||||
0.776535 | + | 0.630075i | \(0.216976\pi\) | |||||||
\(822\) | 73.0578 | 2.54818 | ||||||||
\(823\) | 27.5382 | 0.959921 | 0.479960 | − | 0.877290i | \(-0.340651\pi\) | ||||
0.479960 | + | 0.877290i | \(0.340651\pi\) | |||||||
\(824\) | 37.1025 | 1.29253 | ||||||||
\(825\) | −48.4175 | −1.68568 | ||||||||
\(826\) | −49.8979 | −1.73617 | ||||||||
\(827\) | −14.5409 | −0.505638 | −0.252819 | − | 0.967514i | \(-0.581358\pi\) | ||||
−0.252819 | + | 0.967514i | \(0.581358\pi\) | |||||||
\(828\) | 3.89109 | 0.135225 | ||||||||
\(829\) | 2.29849 | 0.0798297 | 0.0399149 | − | 0.999203i | \(-0.487291\pi\) | ||||
0.0399149 | + | 0.999203i | \(0.487291\pi\) | |||||||
\(830\) | −38.2990 | −1.32938 | ||||||||
\(831\) | −4.72388 | −0.163870 | ||||||||
\(832\) | 7.47670 | 0.259208 | ||||||||
\(833\) | 7.33995 | 0.254314 | ||||||||
\(834\) | 15.2105 | 0.526696 | ||||||||
\(835\) | 36.8522 | 1.27532 | ||||||||
\(836\) | 35.2130 | 1.21787 | ||||||||
\(837\) | 41.4150 | 1.43151 | ||||||||
\(838\) | 58.8548 | 2.03311 | ||||||||
\(839\) | 12.4061 | 0.428306 | 0.214153 | − | 0.976800i | \(-0.431301\pi\) | ||||
0.214153 | + | 0.976800i | \(0.431301\pi\) | |||||||
\(840\) | −78.7890 | −2.71848 | ||||||||
\(841\) | −28.7370 | −0.990932 | ||||||||
\(842\) | −100.625 | −3.46777 | ||||||||
\(843\) | −20.8840 | −0.719282 | ||||||||
\(844\) | −32.7891 | −1.12865 | ||||||||
\(845\) | −40.6986 | −1.40007 | ||||||||
\(846\) | 5.16070 | 0.177428 | ||||||||
\(847\) | −44.9588 | −1.54480 | ||||||||
\(848\) | −26.8217 | −0.921059 | ||||||||
\(849\) | 6.17766 | 0.212017 | ||||||||
\(850\) | 49.8379 | 1.70943 | ||||||||
\(851\) | −0.920221 | −0.0315448 | ||||||||
\(852\) | −24.9739 | −0.855593 | ||||||||
\(853\) | −28.3282 | −0.969938 | −0.484969 | − | 0.874531i | \(-0.661169\pi\) | ||||
−0.484969 | + | 0.874531i | \(0.661169\pi\) | |||||||
\(854\) | 22.1288 | 0.757231 | ||||||||
\(855\) | −3.68135 | −0.125899 | ||||||||
\(856\) | 71.5736 | 2.44634 | ||||||||
\(857\) | 20.3224 | 0.694201 | 0.347101 | − | 0.937828i | \(-0.387166\pi\) | ||||
0.347101 | + | 0.937828i | \(0.387166\pi\) | |||||||
\(858\) | 17.6049 | 0.601022 | ||||||||
\(859\) | 43.2434 | 1.47545 | 0.737723 | − | 0.675103i | \(-0.235901\pi\) | ||||
0.737723 | + | 0.675103i | \(0.235901\pi\) | |||||||
\(860\) | 59.4558 | 2.02743 | ||||||||
\(861\) | 13.1513 | 0.448195 | ||||||||
\(862\) | 67.8690 | 2.31163 | ||||||||
\(863\) | −3.35841 | −0.114322 | −0.0571608 | − | 0.998365i | \(-0.518205\pi\) | ||||
−0.0571608 | + | 0.998365i | \(0.518205\pi\) | |||||||
\(864\) | −62.7015 | −2.13315 | ||||||||
\(865\) | 10.8425 | 0.368655 | ||||||||
\(866\) | 25.4721 | 0.865578 | ||||||||
\(867\) | 9.61282 | 0.326468 | ||||||||
\(868\) | −77.6281 | −2.63487 | ||||||||
\(869\) | 7.59222 | 0.257548 | ||||||||
\(870\) | 6.47645 | 0.219572 | ||||||||
\(871\) | −12.4027 | −0.420250 | ||||||||
\(872\) | −95.7940 | −3.24399 | ||||||||
\(873\) | −13.9947 | −0.473649 | ||||||||
\(874\) | 3.09852 | 0.104809 | ||||||||
\(875\) | −6.39701 | −0.216258 | ||||||||
\(876\) | −15.9730 | −0.539676 | ||||||||
\(877\) | −36.1661 | −1.22124 | −0.610621 | − | 0.791923i | \(-0.709080\pi\) | ||||
−0.610621 | + | 0.791923i | \(0.709080\pi\) | |||||||
\(878\) | 40.8823 | 1.37971 | ||||||||
\(879\) | 24.9074 | 0.840107 | ||||||||
\(880\) | 185.299 | 6.24643 | ||||||||
\(881\) | −46.3196 | −1.56055 | −0.780273 | − | 0.625439i | \(-0.784920\pi\) | ||||
−0.780273 | + | 0.625439i | \(0.784920\pi\) | |||||||
\(882\) | −5.17587 | −0.174281 | ||||||||
\(883\) | −23.6623 | −0.796301 | −0.398150 | − | 0.917320i | \(-0.630348\pi\) | ||||
−0.398150 | + | 0.917320i | \(0.630348\pi\) | |||||||
\(884\) | −12.8457 | −0.432048 | ||||||||
\(885\) | 42.1975 | 1.41845 | ||||||||
\(886\) | −66.3918 | −2.23048 | ||||||||
\(887\) | 35.2104 | 1.18225 | 0.591125 | − | 0.806580i | \(-0.298684\pi\) | ||||
0.591125 | + | 0.806580i | \(0.298684\pi\) | |||||||
\(888\) | 10.9821 | 0.368534 | ||||||||
\(889\) | −25.8556 | −0.867171 | ||||||||
\(890\) | 57.3591 | 1.92268 | ||||||||
\(891\) | −31.7520 | −1.06373 | ||||||||
\(892\) | −11.4356 | −0.382893 | ||||||||
\(893\) | 2.91311 | 0.0974836 | ||||||||
\(894\) | 39.7146 | 1.32825 | ||||||||
\(895\) | −62.0333 | −2.07354 | ||||||||
\(896\) | 3.85375 | 0.128745 | ||||||||
\(897\) | 1.09813 | 0.0366654 | ||||||||
\(898\) | −63.7796 | −2.12835 | ||||||||
\(899\) | 3.76037 | 0.125415 | ||||||||
\(900\) | −24.9125 | −0.830416 | ||||||||
\(901\) | 8.67786 | 0.289101 | ||||||||
\(902\) | −61.1287 | −2.03536 | ||||||||
\(903\) | 11.7418 | 0.390743 | ||||||||
\(904\) | −1.70316 | −0.0566462 | ||||||||
\(905\) | −3.46235 | −0.115092 | ||||||||
\(906\) | 17.1214 | 0.568821 | ||||||||
\(907\) | −25.4931 | −0.846486 | −0.423243 | − | 0.906016i | \(-0.639108\pi\) | ||||
−0.423243 | + | 0.906016i | \(0.639108\pi\) | |||||||
\(908\) | −45.5992 | −1.51326 | ||||||||
\(909\) | −13.1400 | −0.435825 | ||||||||
\(910\) | 15.3692 | 0.509483 | ||||||||
\(911\) | 32.9035 | 1.09014 | 0.545071 | − | 0.838390i | \(-0.316503\pi\) | ||||
0.545071 | + | 0.838390i | \(0.316503\pi\) | |||||||
\(912\) | −18.7102 | −0.619556 | ||||||||
\(913\) | 24.9213 | 0.824775 | ||||||||
\(914\) | −83.8463 | −2.77339 | ||||||||
\(915\) | −18.7138 | −0.618658 | ||||||||
\(916\) | 0.654699 | 0.0216319 | ||||||||
\(917\) | 10.3023 | 0.340211 | ||||||||
\(918\) | 47.7756 | 1.57683 | ||||||||
\(919\) | −29.6909 | −0.979414 | −0.489707 | − | 0.871887i | \(-0.662896\pi\) | ||||
−0.489707 | + | 0.871887i | \(0.662896\pi\) | |||||||
\(920\) | 22.8434 | 0.753124 | ||||||||
\(921\) | 36.1148 | 1.19002 | ||||||||
\(922\) | −74.7583 | −2.46203 | ||||||||
\(923\) | 2.87085 | 0.0944953 | ||||||||
\(924\) | 86.9981 | 2.86203 | ||||||||
\(925\) | 5.89165 | 0.193716 | ||||||||
\(926\) | 97.2514 | 3.19588 | ||||||||
\(927\) | 4.28303 | 0.140673 | ||||||||
\(928\) | −5.69312 | −0.186886 | ||||||||
\(929\) | 20.8585 | 0.684346 | 0.342173 | − | 0.939637i | \(-0.388837\pi\) | ||||
0.342173 | + | 0.939637i | \(0.388837\pi\) | |||||||
\(930\) | 92.6097 | 3.03679 | ||||||||
\(931\) | −2.92168 | −0.0957542 | ||||||||
\(932\) | 13.4091 | 0.439230 | ||||||||
\(933\) | 4.12737 | 0.135124 | ||||||||
\(934\) | 28.9869 | 0.948481 | ||||||||
\(935\) | −59.9516 | −1.96063 | ||||||||
\(936\) | 5.33812 | 0.174482 | ||||||||
\(937\) | 28.8313 | 0.941877 | 0.470938 | − | 0.882166i | \(-0.343915\pi\) | ||||
0.470938 | + | 0.882166i | \(0.343915\pi\) | |||||||
\(938\) | −86.4621 | −2.82309 | ||||||||
\(939\) | 40.6768 | 1.32744 | ||||||||
\(940\) | 36.4438 | 1.18867 | ||||||||
\(941\) | 49.6151 | 1.61741 | 0.808704 | − | 0.588216i | \(-0.200170\pi\) | ||||
0.808704 | + | 0.588216i | \(0.200170\pi\) | |||||||
\(942\) | −25.7099 | −0.837675 | ||||||||
\(943\) | −3.81296 | −0.124167 | ||||||||
\(944\) | −87.3575 | −2.84325 | ||||||||
\(945\) | −40.5195 | −1.31810 | ||||||||
\(946\) | −54.5772 | −1.77446 | ||||||||
\(947\) | 43.9608 | 1.42853 | 0.714267 | − | 0.699873i | \(-0.246760\pi\) | ||||
0.714267 | + | 0.699873i | \(0.246760\pi\) | |||||||
\(948\) | −9.59046 | −0.311484 | ||||||||
\(949\) | 1.83615 | 0.0596041 | ||||||||
\(950\) | −19.8381 | −0.643632 | ||||||||
\(951\) | −39.3327 | −1.27545 | ||||||||
\(952\) | −52.7724 | −1.71036 | ||||||||
\(953\) | −37.0086 | −1.19883 | −0.599414 | − | 0.800439i | \(-0.704600\pi\) | ||||
−0.599414 | + | 0.800439i | \(0.704600\pi\) | |||||||
\(954\) | −6.11931 | −0.198120 | ||||||||
\(955\) | 33.8892 | 1.09663 | ||||||||
\(956\) | 47.2552 | 1.52834 | ||||||||
\(957\) | −4.21426 | −0.136228 | ||||||||
\(958\) | 84.5502 | 2.73169 | ||||||||
\(959\) | −41.5017 | −1.34016 | ||||||||
\(960\) | −44.0781 | −1.42261 | ||||||||
\(961\) | 22.7711 | 0.734553 | ||||||||
\(962\) | −2.14224 | −0.0690687 | ||||||||
\(963\) | 8.26230 | 0.266249 | ||||||||
\(964\) | 55.0744 | 1.77383 | ||||||||
\(965\) | −48.8256 | −1.57175 | ||||||||
\(966\) | 7.65528 | 0.246305 | ||||||||
\(967\) | −9.46540 | −0.304387 | −0.152193 | − | 0.988351i | \(-0.548634\pi\) | ||||
−0.152193 | + | 0.988351i | \(0.548634\pi\) | |||||||
\(968\) | −155.562 | −4.99994 | ||||||||
\(969\) | 6.05347 | 0.194466 | ||||||||
\(970\) | −139.416 | −4.47638 | ||||||||
\(971\) | −44.5417 | −1.42941 | −0.714705 | − | 0.699426i | \(-0.753439\pi\) | ||||
−0.714705 | + | 0.699426i | \(0.753439\pi\) | |||||||
\(972\) | −42.4026 | −1.36006 | ||||||||
\(973\) | −8.64057 | −0.277004 | ||||||||
\(974\) | −43.3939 | −1.39043 | ||||||||
\(975\) | −7.03068 | −0.225162 | ||||||||
\(976\) | 38.7414 | 1.24008 | ||||||||
\(977\) | 39.7834 | 1.27278 | 0.636392 | − | 0.771366i | \(-0.280426\pi\) | ||||
0.636392 | + | 0.771366i | \(0.280426\pi\) | |||||||
\(978\) | −3.82679 | −0.122367 | ||||||||
\(979\) | −37.3239 | −1.19288 | ||||||||
\(980\) | −36.5510 | −1.16758 | ||||||||
\(981\) | −11.0582 | −0.353063 | ||||||||
\(982\) | −92.6467 | −2.95648 | ||||||||
\(983\) | −22.5075 | −0.717878 | −0.358939 | − | 0.933361i | \(-0.616861\pi\) | ||||
−0.358939 | + | 0.933361i | \(0.616861\pi\) | |||||||
\(984\) | 45.5046 | 1.45063 | ||||||||
\(985\) | −55.3777 | −1.76448 | ||||||||
\(986\) | 4.33789 | 0.138146 | ||||||||
\(987\) | 7.19721 | 0.229090 | ||||||||
\(988\) | 5.11326 | 0.162674 | ||||||||
\(989\) | −3.40431 | −0.108251 | ||||||||
\(990\) | 42.2757 | 1.34361 | ||||||||
\(991\) | −36.6954 | −1.16567 | −0.582834 | − | 0.812591i | \(-0.698056\pi\) | ||||
−0.582834 | + | 0.812591i | \(0.698056\pi\) | |||||||
\(992\) | −81.4085 | −2.58472 | ||||||||
\(993\) | −10.2058 | −0.323872 | ||||||||
\(994\) | 20.0133 | 0.634785 | ||||||||
\(995\) | −43.9113 | −1.39208 | ||||||||
\(996\) | −31.4805 | −0.997498 | ||||||||
\(997\) | −44.6114 | −1.41286 | −0.706429 | − | 0.707784i | \(-0.749695\pi\) | ||||
−0.706429 | + | 0.707784i | \(0.749695\pi\) | |||||||
\(998\) | 10.5431 | 0.333735 | ||||||||
\(999\) | 5.64785 | 0.178690 |
(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 | 6031.2.a.e.1.5 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.e.1.5 | ✓ | 134 | 1.1 | even | 1 | trivial |