Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.59 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.53772 | 1.79444 | 0.897219 | − | 0.441585i | \(-0.145584\pi\) | ||||
0.897219 | + | 0.441585i | \(0.145584\pi\) | |||||||
\(3\) | 0.285178 | 0.164647 | 0.0823237 | − | 0.996606i | \(-0.473766\pi\) | ||||
0.0823237 | + | 0.996606i | \(0.473766\pi\) | |||||||
\(4\) | 4.44002 | 2.22001 | ||||||||
\(5\) | 0.796665 | 0.356280 | 0.178140 | − | 0.984005i | \(-0.442992\pi\) | ||||
0.178140 | + | 0.984005i | \(0.442992\pi\) | |||||||
\(6\) | 0.723701 | 0.295450 | ||||||||
\(7\) | −4.79173 | −1.81110 | −0.905551 | − | 0.424237i | \(-0.860542\pi\) | ||||
−0.905551 | + | 0.424237i | \(0.860542\pi\) | |||||||
\(8\) | 6.19208 | 2.18923 | ||||||||
\(9\) | −2.91867 | −0.972891 | ||||||||
\(10\) | 2.02171 | 0.639322 | ||||||||
\(11\) | 1.54971 | 0.467255 | 0.233627 | − | 0.972326i | \(-0.424940\pi\) | ||||
0.233627 | + | 0.972326i | \(0.424940\pi\) | |||||||
\(12\) | 1.26619 | 0.365519 | ||||||||
\(13\) | −5.02316 | −1.39317 | −0.696587 | − | 0.717472i | \(-0.745299\pi\) | ||||
−0.696587 | + | 0.717472i | \(0.745299\pi\) | |||||||
\(14\) | −12.1601 | −3.24991 | ||||||||
\(15\) | 0.227191 | 0.0586605 | ||||||||
\(16\) | 6.83373 | 1.70843 | ||||||||
\(17\) | −1.17589 | −0.285194 | −0.142597 | − | 0.989781i | \(-0.545545\pi\) | ||||
−0.142597 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(18\) | −7.40677 | −1.74579 | ||||||||
\(19\) | −8.12663 | −1.86438 | −0.932188 | − | 0.361975i | \(-0.882103\pi\) | ||||
−0.932188 | + | 0.361975i | \(0.882103\pi\) | |||||||
\(20\) | 3.53721 | 0.790944 | ||||||||
\(21\) | −1.36649 | −0.298193 | ||||||||
\(22\) | 3.93273 | 0.838460 | ||||||||
\(23\) | 3.47312 | 0.724195 | 0.362098 | − | 0.932140i | \(-0.382061\pi\) | ||||
0.362098 | + | 0.932140i | \(0.382061\pi\) | |||||||
\(24\) | 1.76584 | 0.360451 | ||||||||
\(25\) | −4.36532 | −0.873065 | ||||||||
\(26\) | −12.7474 | −2.49997 | ||||||||
\(27\) | −1.68787 | −0.324831 | ||||||||
\(28\) | −21.2754 | −4.02066 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0.576547 | 0.105263 | ||||||||
\(31\) | 2.69512 | 0.484058 | 0.242029 | − | 0.970269i | \(-0.422187\pi\) | ||||
0.242029 | + | 0.970269i | \(0.422187\pi\) | |||||||
\(32\) | 4.95792 | 0.876445 | ||||||||
\(33\) | 0.441942 | 0.0769323 | ||||||||
\(34\) | −2.98407 | −0.511764 | ||||||||
\(35\) | −3.81740 | −0.645259 | ||||||||
\(36\) | −12.9590 | −2.15983 | ||||||||
\(37\) | −0.742083 | −0.121998 | −0.0609989 | − | 0.998138i | \(-0.519429\pi\) | ||||
−0.0609989 | + | 0.998138i | \(0.519429\pi\) | |||||||
\(38\) | −20.6231 | −3.34551 | ||||||||
\(39\) | −1.43249 | −0.229382 | ||||||||
\(40\) | 4.93302 | 0.779979 | ||||||||
\(41\) | 4.24308 | 0.662658 | 0.331329 | − | 0.943515i | \(-0.392503\pi\) | ||||
0.331329 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(42\) | −3.46778 | −0.535089 | ||||||||
\(43\) | −3.87094 | −0.590313 | −0.295156 | − | 0.955449i | \(-0.595372\pi\) | ||||
−0.295156 | + | 0.955449i | \(0.595372\pi\) | |||||||
\(44\) | 6.88074 | 1.03731 | ||||||||
\(45\) | −2.32521 | −0.346621 | ||||||||
\(46\) | 8.81380 | 1.29952 | ||||||||
\(47\) | 7.59056 | 1.10720 | 0.553598 | − | 0.832784i | \(-0.313254\pi\) | ||||
0.553598 | + | 0.832784i | \(0.313254\pi\) | |||||||
\(48\) | 1.94883 | 0.281289 | ||||||||
\(49\) | 15.9606 | 2.28009 | ||||||||
\(50\) | −11.0780 | −1.56666 | ||||||||
\(51\) | −0.335337 | −0.0469565 | ||||||||
\(52\) | −22.3029 | −3.09286 | ||||||||
\(53\) | 1.60143 | 0.219973 | 0.109986 | − | 0.993933i | \(-0.464919\pi\) | ||||
0.109986 | + | 0.993933i | \(0.464919\pi\) | |||||||
\(54\) | −4.28335 | −0.582890 | ||||||||
\(55\) | 1.23460 | 0.166473 | ||||||||
\(56\) | −29.6708 | −3.96492 | ||||||||
\(57\) | −2.31753 | −0.306965 | ||||||||
\(58\) | −2.53772 | −0.333219 | ||||||||
\(59\) | −7.23792 | −0.942296 | −0.471148 | − | 0.882054i | \(-0.656160\pi\) | ||||
−0.471148 | + | 0.882054i | \(0.656160\pi\) | |||||||
\(60\) | 1.00873 | 0.130227 | ||||||||
\(61\) | −12.2953 | −1.57426 | −0.787128 | − | 0.616789i | \(-0.788433\pi\) | ||||
−0.787128 | + | 0.616789i | \(0.788433\pi\) | |||||||
\(62\) | 6.83946 | 0.868612 | ||||||||
\(63\) | 13.9855 | 1.76201 | ||||||||
\(64\) | −1.08564 | −0.135705 | ||||||||
\(65\) | −4.00178 | −0.496359 | ||||||||
\(66\) | 1.12153 | 0.138050 | ||||||||
\(67\) | 6.44378 | 0.787233 | 0.393617 | − | 0.919275i | \(-0.371224\pi\) | ||||
0.393617 | + | 0.919275i | \(0.371224\pi\) | |||||||
\(68\) | −5.22096 | −0.633134 | ||||||||
\(69\) | 0.990455 | 0.119237 | ||||||||
\(70\) | −9.68750 | −1.15788 | ||||||||
\(71\) | −4.42671 | −0.525354 | −0.262677 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262677 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(72\) | −18.0727 | −2.12988 | ||||||||
\(73\) | 15.0871 | 1.76581 | 0.882904 | − | 0.469554i | \(-0.155585\pi\) | ||||
0.882904 | + | 0.469554i | \(0.155585\pi\) | |||||||
\(74\) | −1.88320 | −0.218917 | ||||||||
\(75\) | −1.24489 | −0.143748 | ||||||||
\(76\) | −36.0824 | −4.13893 | ||||||||
\(77\) | −7.42578 | −0.846246 | ||||||||
\(78\) | −3.63526 | −0.411613 | ||||||||
\(79\) | −2.60803 | −0.293426 | −0.146713 | − | 0.989179i | \(-0.546869\pi\) | ||||
−0.146713 | + | 0.989179i | \(0.546869\pi\) | |||||||
\(80\) | 5.44420 | 0.608680 | ||||||||
\(81\) | 8.27468 | 0.919409 | ||||||||
\(82\) | 10.7677 | 1.18910 | ||||||||
\(83\) | 10.4739 | 1.14966 | 0.574831 | − | 0.818272i | \(-0.305068\pi\) | ||||
0.574831 | + | 0.818272i | \(0.305068\pi\) | |||||||
\(84\) | −6.06725 | −0.661992 | ||||||||
\(85\) | −0.936788 | −0.101609 | ||||||||
\(86\) | −9.82336 | −1.05928 | ||||||||
\(87\) | −0.285178 | −0.0305742 | ||||||||
\(88\) | 9.59593 | 1.02293 | ||||||||
\(89\) | 3.80181 | 0.402991 | 0.201495 | − | 0.979489i | \(-0.435420\pi\) | ||||
0.201495 | + | 0.979489i | \(0.435420\pi\) | |||||||
\(90\) | −5.90072 | −0.621991 | ||||||||
\(91\) | 24.0696 | 2.52318 | ||||||||
\(92\) | 15.4207 | 1.60772 | ||||||||
\(93\) | 0.768588 | 0.0796989 | ||||||||
\(94\) | 19.2627 | 1.98680 | ||||||||
\(95\) | −6.47420 | −0.664239 | ||||||||
\(96\) | 1.41389 | 0.144304 | ||||||||
\(97\) | 2.33492 | 0.237075 | 0.118538 | − | 0.992950i | \(-0.462179\pi\) | ||||
0.118538 | + | 0.992950i | \(0.462179\pi\) | |||||||
\(98\) | 40.5036 | 4.09148 | ||||||||
\(99\) | −4.52309 | −0.454588 | ||||||||
\(100\) | −19.3821 | −1.93821 | ||||||||
\(101\) | 17.6804 | 1.75927 | 0.879635 | − | 0.475650i | \(-0.157787\pi\) | ||||
0.879635 | + | 0.475650i | \(0.157787\pi\) | |||||||
\(102\) | −0.850990 | −0.0842606 | ||||||||
\(103\) | −3.17646 | −0.312986 | −0.156493 | − | 0.987679i | \(-0.550019\pi\) | ||||
−0.156493 | + | 0.987679i | \(0.550019\pi\) | |||||||
\(104\) | −31.1038 | −3.04998 | ||||||||
\(105\) | −1.08864 | −0.106240 | ||||||||
\(106\) | 4.06397 | 0.394728 | ||||||||
\(107\) | −10.2925 | −0.995018 | −0.497509 | − | 0.867459i | \(-0.665752\pi\) | ||||
−0.497509 | + | 0.867459i | \(0.665752\pi\) | |||||||
\(108\) | −7.49419 | −0.721129 | ||||||||
\(109\) | −11.3574 | −1.08784 | −0.543921 | − | 0.839136i | \(-0.683061\pi\) | ||||
−0.543921 | + | 0.839136i | \(0.683061\pi\) | |||||||
\(110\) | 3.13307 | 0.298726 | ||||||||
\(111\) | −0.211626 | −0.0200866 | ||||||||
\(112\) | −32.7454 | −3.09415 | ||||||||
\(113\) | −11.9089 | −1.12030 | −0.560148 | − | 0.828393i | \(-0.689256\pi\) | ||||
−0.560148 | + | 0.828393i | \(0.689256\pi\) | |||||||
\(114\) | −5.88124 | −0.550829 | ||||||||
\(115\) | 2.76691 | 0.258016 | ||||||||
\(116\) | −4.44002 | −0.412245 | ||||||||
\(117\) | 14.6610 | 1.35541 | ||||||||
\(118\) | −18.3678 | −1.69089 | ||||||||
\(119\) | 5.63453 | 0.516516 | ||||||||
\(120\) | 1.40679 | 0.128421 | ||||||||
\(121\) | −8.59840 | −0.781673 | ||||||||
\(122\) | −31.2021 | −2.82491 | ||||||||
\(123\) | 1.21003 | 0.109105 | ||||||||
\(124\) | 11.9664 | 1.07461 | ||||||||
\(125\) | −7.46103 | −0.667335 | ||||||||
\(126\) | 35.4912 | 3.16181 | ||||||||
\(127\) | −9.67962 | −0.858928 | −0.429464 | − | 0.903084i | \(-0.641297\pi\) | ||||
−0.429464 | + | 0.903084i | \(0.641297\pi\) | |||||||
\(128\) | −12.6709 | −1.11996 | ||||||||
\(129\) | −1.10390 | −0.0971934 | ||||||||
\(130\) | −10.1554 | −0.890687 | ||||||||
\(131\) | 7.30840 | 0.638538 | 0.319269 | − | 0.947664i | \(-0.396563\pi\) | ||||
0.319269 | + | 0.947664i | \(0.396563\pi\) | |||||||
\(132\) | 1.96223 | 0.170790 | ||||||||
\(133\) | 38.9406 | 3.37658 | ||||||||
\(134\) | 16.3525 | 1.41264 | ||||||||
\(135\) | −1.34467 | −0.115731 | ||||||||
\(136\) | −7.28119 | −0.624357 | ||||||||
\(137\) | −15.6435 | −1.33651 | −0.668257 | − | 0.743930i | \(-0.732959\pi\) | ||||
−0.668257 | + | 0.743930i | \(0.732959\pi\) | |||||||
\(138\) | 2.51350 | 0.213963 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | −16.9493 | −1.43248 | ||||||||
\(141\) | 2.16466 | 0.182297 | ||||||||
\(142\) | −11.2337 | −0.942715 | ||||||||
\(143\) | −7.78444 | −0.650967 | ||||||||
\(144\) | −19.9454 | −1.66212 | ||||||||
\(145\) | −0.796665 | −0.0661595 | ||||||||
\(146\) | 38.2867 | 3.16863 | ||||||||
\(147\) | 4.55162 | 0.375411 | ||||||||
\(148\) | −3.29486 | −0.270836 | ||||||||
\(149\) | 10.4692 | 0.857667 | 0.428834 | − | 0.903384i | \(-0.358925\pi\) | ||||
0.428834 | + | 0.903384i | \(0.358925\pi\) | |||||||
\(150\) | −3.15919 | −0.257947 | ||||||||
\(151\) | −3.19515 | −0.260018 | −0.130009 | − | 0.991513i | \(-0.541501\pi\) | ||||
−0.130009 | + | 0.991513i | \(0.541501\pi\) | |||||||
\(152\) | −50.3207 | −4.08155 | ||||||||
\(153\) | 3.43203 | 0.277463 | ||||||||
\(154\) | −18.8445 | −1.51854 | ||||||||
\(155\) | 2.14711 | 0.172460 | ||||||||
\(156\) | −6.36030 | −0.509231 | ||||||||
\(157\) | 15.4995 | 1.23700 | 0.618499 | − | 0.785786i | \(-0.287741\pi\) | ||||
0.618499 | + | 0.785786i | \(0.287741\pi\) | |||||||
\(158\) | −6.61844 | −0.526535 | ||||||||
\(159\) | 0.456691 | 0.0362179 | ||||||||
\(160\) | 3.94981 | 0.312260 | ||||||||
\(161\) | −16.6422 | −1.31159 | ||||||||
\(162\) | 20.9988 | 1.64982 | ||||||||
\(163\) | 2.82163 | 0.221007 | 0.110504 | − | 0.993876i | \(-0.464754\pi\) | ||||
0.110504 | + | 0.993876i | \(0.464754\pi\) | |||||||
\(164\) | 18.8394 | 1.47111 | ||||||||
\(165\) | 0.352080 | 0.0274094 | ||||||||
\(166\) | 26.5798 | 2.06300 | ||||||||
\(167\) | −12.9137 | −0.999296 | −0.499648 | − | 0.866229i | \(-0.666537\pi\) | ||||
−0.499648 | + | 0.866229i | \(0.666537\pi\) | |||||||
\(168\) | −8.46144 | −0.652814 | ||||||||
\(169\) | 12.2321 | 0.940934 | ||||||||
\(170\) | −2.37731 | −0.182331 | ||||||||
\(171\) | 23.7190 | 1.81383 | ||||||||
\(172\) | −17.1870 | −1.31050 | ||||||||
\(173\) | −21.2376 | −1.61466 | −0.807332 | − | 0.590098i | \(-0.799089\pi\) | ||||
−0.807332 | + | 0.590098i | \(0.799089\pi\) | |||||||
\(174\) | −0.723701 | −0.0548636 | ||||||||
\(175\) | 20.9174 | 1.58121 | ||||||||
\(176\) | 10.5903 | 0.798273 | ||||||||
\(177\) | −2.06409 | −0.155147 | ||||||||
\(178\) | 9.64792 | 0.723142 | ||||||||
\(179\) | −13.2653 | −0.991498 | −0.495749 | − | 0.868466i | \(-0.665106\pi\) | ||||
−0.495749 | + | 0.868466i | \(0.665106\pi\) | |||||||
\(180\) | −10.3240 | −0.769503 | ||||||||
\(181\) | 18.9995 | 1.41222 | 0.706110 | − | 0.708102i | \(-0.250448\pi\) | ||||
0.706110 | + | 0.708102i | \(0.250448\pi\) | |||||||
\(182\) | 61.0819 | 4.52769 | ||||||||
\(183\) | −3.50636 | −0.259197 | ||||||||
\(184\) | 21.5058 | 1.58543 | ||||||||
\(185\) | −0.591192 | −0.0434653 | ||||||||
\(186\) | 1.95046 | 0.143015 | ||||||||
\(187\) | −1.82228 | −0.133259 | ||||||||
\(188\) | 33.7022 | 2.45799 | ||||||||
\(189\) | 8.08783 | 0.588303 | ||||||||
\(190\) | −16.4297 | −1.19194 | ||||||||
\(191\) | 1.90555 | 0.137881 | 0.0689405 | − | 0.997621i | \(-0.478038\pi\) | ||||
0.0689405 | + | 0.997621i | \(0.478038\pi\) | |||||||
\(192\) | −0.309601 | −0.0223435 | ||||||||
\(193\) | −14.8013 | −1.06542 | −0.532709 | − | 0.846299i | \(-0.678826\pi\) | ||||
−0.532709 | + | 0.846299i | \(0.678826\pi\) | |||||||
\(194\) | 5.92537 | 0.425417 | ||||||||
\(195\) | −1.14122 | −0.0817243 | ||||||||
\(196\) | 70.8655 | 5.06182 | ||||||||
\(197\) | −2.78404 | −0.198355 | −0.0991773 | − | 0.995070i | \(-0.531621\pi\) | ||||
−0.0991773 | + | 0.995070i | \(0.531621\pi\) | |||||||
\(198\) | −11.4783 | −0.815730 | ||||||||
\(199\) | −6.37861 | −0.452167 | −0.226084 | − | 0.974108i | \(-0.572592\pi\) | ||||
−0.226084 | + | 0.974108i | \(0.572592\pi\) | |||||||
\(200\) | −27.0305 | −1.91134 | ||||||||
\(201\) | 1.83762 | 0.129616 | ||||||||
\(202\) | 44.8680 | 3.15690 | ||||||||
\(203\) | 4.79173 | 0.336313 | ||||||||
\(204\) | −1.48890 | −0.104244 | ||||||||
\(205\) | 3.38031 | 0.236091 | ||||||||
\(206\) | −8.06097 | −0.561634 | ||||||||
\(207\) | −10.1369 | −0.704563 | ||||||||
\(208\) | −34.3269 | −2.38014 | ||||||||
\(209\) | −12.5939 | −0.871139 | ||||||||
\(210\) | −2.76266 | −0.190641 | ||||||||
\(211\) | −4.96941 | −0.342108 | −0.171054 | − | 0.985262i | \(-0.554717\pi\) | ||||
−0.171054 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(212\) | 7.11036 | 0.488342 | ||||||||
\(213\) | −1.26240 | −0.0864981 | ||||||||
\(214\) | −26.1196 | −1.78550 | ||||||||
\(215\) | −3.08384 | −0.210316 | ||||||||
\(216\) | −10.4515 | −0.711131 | ||||||||
\(217\) | −12.9143 | −0.876679 | ||||||||
\(218\) | −28.8219 | −1.95207 | ||||||||
\(219\) | 4.30249 | 0.290735 | ||||||||
\(220\) | 5.48164 | 0.369572 | ||||||||
\(221\) | 5.90667 | 0.397326 | ||||||||
\(222\) | −0.537046 | −0.0360442 | ||||||||
\(223\) | 18.4599 | 1.23617 | 0.618083 | − | 0.786113i | \(-0.287910\pi\) | ||||
0.618083 | + | 0.786113i | \(0.287910\pi\) | |||||||
\(224\) | −23.7570 | −1.58733 | ||||||||
\(225\) | 12.7410 | 0.849397 | ||||||||
\(226\) | −30.2215 | −2.01030 | ||||||||
\(227\) | −14.7954 | −0.982004 | −0.491002 | − | 0.871158i | \(-0.663369\pi\) | ||||
−0.491002 | + | 0.871158i | \(0.663369\pi\) | |||||||
\(228\) | −10.2899 | −0.681464 | ||||||||
\(229\) | −20.1165 | −1.32934 | −0.664669 | − | 0.747138i | \(-0.731427\pi\) | ||||
−0.664669 | + | 0.747138i | \(0.731427\pi\) | |||||||
\(230\) | 7.02165 | 0.462994 | ||||||||
\(231\) | −2.11767 | −0.139332 | ||||||||
\(232\) | −6.19208 | −0.406530 | ||||||||
\(233\) | 13.6728 | 0.895736 | 0.447868 | − | 0.894100i | \(-0.352184\pi\) | ||||
0.447868 | + | 0.894100i | \(0.352184\pi\) | |||||||
\(234\) | 37.2054 | 2.43219 | ||||||||
\(235\) | 6.04713 | 0.394471 | ||||||||
\(236\) | −32.1365 | −2.09191 | ||||||||
\(237\) | −0.743751 | −0.0483118 | ||||||||
\(238\) | 14.2989 | 0.926857 | ||||||||
\(239\) | −3.37243 | −0.218144 | −0.109072 | − | 0.994034i | \(-0.534788\pi\) | ||||
−0.109072 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(240\) | 1.55256 | 0.100218 | ||||||||
\(241\) | −16.2913 | −1.04941 | −0.524706 | − | 0.851283i | \(-0.675825\pi\) | ||||
−0.524706 | + | 0.851283i | \(0.675825\pi\) | |||||||
\(242\) | −21.8203 | −1.40266 | ||||||||
\(243\) | 7.42337 | 0.476210 | ||||||||
\(244\) | −54.5915 | −3.49487 | ||||||||
\(245\) | 12.7153 | 0.812350 | ||||||||
\(246\) | 3.07072 | 0.195782 | ||||||||
\(247\) | 40.8213 | 2.59740 | ||||||||
\(248\) | 16.6884 | 1.05972 | ||||||||
\(249\) | 2.98693 | 0.189289 | ||||||||
\(250\) | −18.9340 | −1.19749 | ||||||||
\(251\) | 23.3630 | 1.47466 | 0.737330 | − | 0.675533i | \(-0.236086\pi\) | ||||
0.737330 | + | 0.675533i | \(0.236086\pi\) | |||||||
\(252\) | 62.0958 | 3.91167 | ||||||||
\(253\) | 5.38232 | 0.338384 | ||||||||
\(254\) | −24.5642 | −1.54129 | ||||||||
\(255\) | −0.267151 | −0.0167296 | ||||||||
\(256\) | −29.9839 | −1.87399 | ||||||||
\(257\) | 18.4379 | 1.15013 | 0.575063 | − | 0.818109i | \(-0.304977\pi\) | ||||
0.575063 | + | 0.818109i | \(0.304977\pi\) | |||||||
\(258\) | −2.80140 | −0.174408 | ||||||||
\(259\) | 3.55586 | 0.220950 | ||||||||
\(260\) | −17.7680 | −1.10192 | ||||||||
\(261\) | 2.91867 | 0.180661 | ||||||||
\(262\) | 18.5467 | 1.14582 | ||||||||
\(263\) | −18.7904 | −1.15867 | −0.579334 | − | 0.815090i | \(-0.696687\pi\) | ||||
−0.579334 | + | 0.815090i | \(0.696687\pi\) | |||||||
\(264\) | 2.73654 | 0.168423 | ||||||||
\(265\) | 1.27580 | 0.0783718 | ||||||||
\(266\) | 98.8202 | 6.05906 | ||||||||
\(267\) | 1.08419 | 0.0663513 | ||||||||
\(268\) | 28.6105 | 1.74767 | ||||||||
\(269\) | −4.77448 | −0.291105 | −0.145553 | − | 0.989351i | \(-0.546496\pi\) | ||||
−0.145553 | + | 0.989351i | \(0.546496\pi\) | |||||||
\(270\) | −3.41240 | −0.207672 | ||||||||
\(271\) | 19.7178 | 1.19777 | 0.598886 | − | 0.800834i | \(-0.295610\pi\) | ||||
0.598886 | + | 0.800834i | \(0.295610\pi\) | |||||||
\(272\) | −8.03570 | −0.487236 | ||||||||
\(273\) | 6.86411 | 0.415435 | ||||||||
\(274\) | −39.6988 | −2.39829 | ||||||||
\(275\) | −6.76498 | −0.407944 | ||||||||
\(276\) | 4.39764 | 0.264707 | ||||||||
\(277\) | −19.8208 | −1.19092 | −0.595459 | − | 0.803386i | \(-0.703030\pi\) | ||||
−0.595459 | + | 0.803386i | \(0.703030\pi\) | |||||||
\(278\) | −2.53772 | −0.152202 | ||||||||
\(279\) | −7.86618 | −0.470936 | ||||||||
\(280\) | −23.6377 | −1.41262 | ||||||||
\(281\) | −4.91402 | −0.293146 | −0.146573 | − | 0.989200i | \(-0.546824\pi\) | ||||
−0.146573 | + | 0.989200i | \(0.546824\pi\) | |||||||
\(282\) | 5.49329 | 0.327121 | ||||||||
\(283\) | 24.2398 | 1.44091 | 0.720453 | − | 0.693504i | \(-0.243934\pi\) | ||||
0.720453 | + | 0.693504i | \(0.243934\pi\) | |||||||
\(284\) | −19.6547 | −1.16629 | ||||||||
\(285\) | −1.84630 | −0.109365 | ||||||||
\(286\) | −19.7547 | −1.16812 | ||||||||
\(287\) | −20.3317 | −1.20014 | ||||||||
\(288\) | −14.4706 | −0.852686 | ||||||||
\(289\) | −15.6173 | −0.918664 | ||||||||
\(290\) | −2.02171 | −0.118719 | ||||||||
\(291\) | 0.665867 | 0.0390338 | ||||||||
\(292\) | 66.9868 | 3.92011 | ||||||||
\(293\) | −18.0032 | −1.05176 | −0.525878 | − | 0.850560i | \(-0.676263\pi\) | ||||
−0.525878 | + | 0.850560i | \(0.676263\pi\) | |||||||
\(294\) | 11.5507 | 0.673652 | ||||||||
\(295\) | −5.76620 | −0.335721 | ||||||||
\(296\) | −4.59504 | −0.267081 | ||||||||
\(297\) | −2.61571 | −0.151779 | ||||||||
\(298\) | 26.5678 | 1.53903 | ||||||||
\(299\) | −17.4460 | −1.00893 | ||||||||
\(300\) | −5.52735 | −0.319122 | ||||||||
\(301\) | 18.5485 | 1.06912 | ||||||||
\(302\) | −8.10839 | −0.466585 | ||||||||
\(303\) | 5.04206 | 0.289659 | ||||||||
\(304\) | −55.5352 | −3.18516 | ||||||||
\(305\) | −9.79527 | −0.560876 | ||||||||
\(306\) | 8.70953 | 0.497891 | ||||||||
\(307\) | −13.3837 | −0.763851 | −0.381925 | − | 0.924193i | \(-0.624739\pi\) | ||||
−0.381925 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(308\) | −32.9706 | −1.87867 | ||||||||
\(309\) | −0.905856 | −0.0515323 | ||||||||
\(310\) | 5.44876 | 0.309469 | ||||||||
\(311\) | −14.3619 | −0.814391 | −0.407195 | − | 0.913341i | \(-0.633493\pi\) | ||||
−0.407195 | + | 0.913341i | \(0.633493\pi\) | |||||||
\(312\) | −8.87011 | −0.502171 | ||||||||
\(313\) | −25.1419 | −1.42111 | −0.710553 | − | 0.703644i | \(-0.751555\pi\) | ||||
−0.710553 | + | 0.703644i | \(0.751555\pi\) | |||||||
\(314\) | 39.3335 | 2.21972 | ||||||||
\(315\) | 11.1418 | 0.627767 | ||||||||
\(316\) | −11.5797 | −0.651409 | ||||||||
\(317\) | −4.54696 | −0.255382 | −0.127691 | − | 0.991814i | \(-0.540757\pi\) | ||||
−0.127691 | + | 0.991814i | \(0.540757\pi\) | |||||||
\(318\) | 1.15895 | 0.0649909 | ||||||||
\(319\) | −1.54971 | −0.0867670 | ||||||||
\(320\) | −0.864894 | −0.0483491 | ||||||||
\(321\) | −2.93520 | −0.163827 | ||||||||
\(322\) | −42.2333 | −2.35357 | ||||||||
\(323\) | 9.55599 | 0.531710 | ||||||||
\(324\) | 36.7397 | 2.04110 | ||||||||
\(325\) | 21.9277 | 1.21633 | ||||||||
\(326\) | 7.16051 | 0.396584 | ||||||||
\(327\) | −3.23888 | −0.179110 | ||||||||
\(328\) | 26.2735 | 1.45071 | ||||||||
\(329\) | −36.3719 | −2.00525 | ||||||||
\(330\) | 0.893480 | 0.0491845 | ||||||||
\(331\) | 1.69402 | 0.0931119 | 0.0465559 | − | 0.998916i | \(-0.485175\pi\) | ||||
0.0465559 | + | 0.998916i | \(0.485175\pi\) | |||||||
\(332\) | 46.5044 | 2.55226 | ||||||||
\(333\) | 2.16590 | 0.118691 | ||||||||
\(334\) | −32.7715 | −1.79317 | ||||||||
\(335\) | 5.13354 | 0.280475 | ||||||||
\(336\) | −9.33824 | −0.509443 | ||||||||
\(337\) | −18.9476 | −1.03214 | −0.516070 | − | 0.856547i | \(-0.672605\pi\) | ||||
−0.516070 | + | 0.856547i | \(0.672605\pi\) | |||||||
\(338\) | 31.0417 | 1.68845 | ||||||||
\(339\) | −3.39615 | −0.184454 | ||||||||
\(340\) | −4.15936 | −0.225573 | ||||||||
\(341\) | 4.17665 | 0.226178 | ||||||||
\(342\) | 60.1921 | 3.25482 | ||||||||
\(343\) | −42.9369 | −2.31838 | ||||||||
\(344\) | −23.9692 | −1.29233 | ||||||||
\(345\) | 0.789061 | 0.0424816 | ||||||||
\(346\) | −53.8950 | −2.89741 | ||||||||
\(347\) | 15.2909 | 0.820860 | 0.410430 | − | 0.911892i | \(-0.365379\pi\) | ||||
0.410430 | + | 0.911892i | \(0.365379\pi\) | |||||||
\(348\) | −1.26619 | −0.0678751 | ||||||||
\(349\) | 21.9159 | 1.17313 | 0.586566 | − | 0.809901i | \(-0.300479\pi\) | ||||
0.586566 | + | 0.809901i | \(0.300479\pi\) | |||||||
\(350\) | 53.0826 | 2.83738 | ||||||||
\(351\) | 8.47846 | 0.452547 | ||||||||
\(352\) | 7.68334 | 0.409523 | ||||||||
\(353\) | −3.17192 | −0.168824 | −0.0844121 | − | 0.996431i | \(-0.526901\pi\) | ||||
−0.0844121 | + | 0.996431i | \(0.526901\pi\) | |||||||
\(354\) | −5.23809 | −0.278401 | ||||||||
\(355\) | −3.52661 | −0.187173 | ||||||||
\(356\) | 16.8801 | 0.894643 | ||||||||
\(357\) | 1.60684 | 0.0850431 | ||||||||
\(358\) | −33.6637 | −1.77918 | ||||||||
\(359\) | −27.4520 | −1.44886 | −0.724431 | − | 0.689347i | \(-0.757898\pi\) | ||||
−0.724431 | + | 0.689347i | \(0.757898\pi\) | |||||||
\(360\) | −14.3979 | −0.758834 | ||||||||
\(361\) | 47.0420 | 2.47590 | ||||||||
\(362\) | 48.2154 | 2.53414 | ||||||||
\(363\) | −2.45207 | −0.128700 | ||||||||
\(364\) | 106.870 | 5.60149 | ||||||||
\(365\) | 12.0193 | 0.629121 | ||||||||
\(366\) | −8.89815 | −0.465114 | ||||||||
\(367\) | 28.3318 | 1.47891 | 0.739454 | − | 0.673207i | \(-0.235084\pi\) | ||||
0.739454 | + | 0.673207i | \(0.235084\pi\) | |||||||
\(368\) | 23.7343 | 1.23724 | ||||||||
\(369\) | −12.3842 | −0.644694 | ||||||||
\(370\) | −1.50028 | −0.0779958 | ||||||||
\(371\) | −7.67360 | −0.398393 | ||||||||
\(372\) | 3.41255 | 0.176932 | ||||||||
\(373\) | 25.6096 | 1.32602 | 0.663009 | − | 0.748612i | \(-0.269279\pi\) | ||||
0.663009 | + | 0.748612i | \(0.269279\pi\) | |||||||
\(374\) | −4.62444 | −0.239124 | ||||||||
\(375\) | −2.12772 | −0.109875 | ||||||||
\(376\) | 47.0014 | 2.42391 | ||||||||
\(377\) | 5.02316 | 0.258706 | ||||||||
\(378\) | 20.5246 | 1.05567 | ||||||||
\(379\) | 2.89663 | 0.148790 | 0.0743949 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743949 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(380\) | −28.7456 | −1.47462 | ||||||||
\(381\) | −2.76041 | −0.141420 | ||||||||
\(382\) | 4.83576 | 0.247419 | ||||||||
\(383\) | −5.79718 | −0.296222 | −0.148111 | − | 0.988971i | \(-0.547319\pi\) | ||||
−0.148111 | + | 0.988971i | \(0.547319\pi\) | |||||||
\(384\) | −3.61346 | −0.184399 | ||||||||
\(385\) | −5.91586 | −0.301500 | ||||||||
\(386\) | −37.5614 | −1.91183 | ||||||||
\(387\) | 11.2980 | 0.574310 | ||||||||
\(388\) | 10.3671 | 0.526309 | ||||||||
\(389\) | 25.0477 | 1.26997 | 0.634983 | − | 0.772526i | \(-0.281007\pi\) | ||||
0.634983 | + | 0.772526i | \(0.281007\pi\) | |||||||
\(390\) | −2.89609 | −0.146649 | ||||||||
\(391\) | −4.08399 | −0.206536 | ||||||||
\(392\) | 98.8296 | 4.99165 | ||||||||
\(393\) | 2.08419 | 0.105134 | ||||||||
\(394\) | −7.06511 | −0.355935 | ||||||||
\(395\) | −2.07773 | −0.104542 | ||||||||
\(396\) | −20.0826 | −1.00919 | ||||||||
\(397\) | 14.5316 | 0.729323 | 0.364661 | − | 0.931140i | \(-0.381185\pi\) | ||||
0.364661 | + | 0.931140i | \(0.381185\pi\) | |||||||
\(398\) | −16.1871 | −0.811387 | ||||||||
\(399\) | 11.1050 | 0.555944 | ||||||||
\(400\) | −29.8315 | −1.49157 | ||||||||
\(401\) | −20.6903 | −1.03323 | −0.516613 | − | 0.856219i | \(-0.672807\pi\) | ||||
−0.516613 | + | 0.856219i | \(0.672807\pi\) | |||||||
\(402\) | 4.66337 | 0.232588 | ||||||||
\(403\) | −13.5380 | −0.674377 | ||||||||
\(404\) | 78.5015 | 3.90559 | ||||||||
\(405\) | 6.59215 | 0.327567 | ||||||||
\(406\) | 12.1601 | 0.603493 | ||||||||
\(407\) | −1.15001 | −0.0570040 | ||||||||
\(408\) | −2.07643 | −0.102799 | ||||||||
\(409\) | 11.8991 | 0.588372 | 0.294186 | − | 0.955748i | \(-0.404951\pi\) | ||||
0.294186 | + | 0.955748i | \(0.404951\pi\) | |||||||
\(410\) | 8.57829 | 0.423651 | ||||||||
\(411\) | −4.46118 | −0.220054 | ||||||||
\(412\) | −14.1036 | −0.694832 | ||||||||
\(413\) | 34.6821 | 1.70660 | ||||||||
\(414\) | −25.7246 | −1.26429 | ||||||||
\(415\) | 8.34420 | 0.409601 | ||||||||
\(416\) | −24.9044 | −1.22104 | ||||||||
\(417\) | −0.285178 | −0.0139652 | ||||||||
\(418\) | −31.9598 | −1.56320 | ||||||||
\(419\) | −8.87022 | −0.433339 | −0.216669 | − | 0.976245i | \(-0.569519\pi\) | ||||
−0.216669 | + | 0.976245i | \(0.569519\pi\) | |||||||
\(420\) | −4.83357 | −0.235854 | ||||||||
\(421\) | −23.6182 | −1.15108 | −0.575540 | − | 0.817774i | \(-0.695208\pi\) | ||||
−0.575540 | + | 0.817774i | \(0.695208\pi\) | |||||||
\(422\) | −12.6110 | −0.613892 | ||||||||
\(423\) | −22.1544 | −1.07718 | ||||||||
\(424\) | 9.91616 | 0.481571 | ||||||||
\(425\) | 5.13313 | 0.248993 | ||||||||
\(426\) | −3.20361 | −0.155216 | ||||||||
\(427\) | 58.9159 | 2.85114 | ||||||||
\(428\) | −45.6991 | −2.20895 | ||||||||
\(429\) | −2.21995 | −0.107180 | ||||||||
\(430\) | −7.82593 | −0.377400 | ||||||||
\(431\) | 17.0125 | 0.819463 | 0.409731 | − | 0.912206i | \(-0.365622\pi\) | ||||
0.409731 | + | 0.912206i | \(0.365622\pi\) | |||||||
\(432\) | −11.5345 | −0.554952 | ||||||||
\(433\) | 19.1772 | 0.921596 | 0.460798 | − | 0.887505i | \(-0.347563\pi\) | ||||
0.460798 | + | 0.887505i | \(0.347563\pi\) | |||||||
\(434\) | −32.7728 | −1.57315 | ||||||||
\(435\) | −0.227191 | −0.0108930 | ||||||||
\(436\) | −50.4271 | −2.41502 | ||||||||
\(437\) | −28.2247 | −1.35017 | ||||||||
\(438\) | 10.9185 | 0.521707 | ||||||||
\(439\) | −19.2404 | −0.918294 | −0.459147 | − | 0.888360i | \(-0.651845\pi\) | ||||
−0.459147 | + | 0.888360i | \(0.651845\pi\) | |||||||
\(440\) | 7.64474 | 0.364449 | ||||||||
\(441\) | −46.5839 | −2.21828 | ||||||||
\(442\) | 14.9895 | 0.712976 | ||||||||
\(443\) | −22.5443 | −1.07111 | −0.535557 | − | 0.844499i | \(-0.679898\pi\) | ||||
−0.535557 | + | 0.844499i | \(0.679898\pi\) | |||||||
\(444\) | −0.939621 | −0.0445925 | ||||||||
\(445\) | 3.02877 | 0.143577 | ||||||||
\(446\) | 46.8460 | 2.21822 | ||||||||
\(447\) | 2.98557 | 0.141213 | ||||||||
\(448\) | 5.20211 | 0.245776 | ||||||||
\(449\) | 21.6798 | 1.02313 | 0.511566 | − | 0.859244i | \(-0.329066\pi\) | ||||
0.511566 | + | 0.859244i | \(0.329066\pi\) | |||||||
\(450\) | 32.3330 | 1.52419 | ||||||||
\(451\) | 6.57554 | 0.309630 | ||||||||
\(452\) | −52.8758 | −2.48707 | ||||||||
\(453\) | −0.911185 | −0.0428112 | ||||||||
\(454\) | −37.5465 | −1.76215 | ||||||||
\(455\) | 19.1754 | 0.898958 | ||||||||
\(456\) | −14.3503 | −0.672017 | ||||||||
\(457\) | −23.7798 | −1.11237 | −0.556187 | − | 0.831057i | \(-0.687736\pi\) | ||||
−0.556187 | + | 0.831057i | \(0.687736\pi\) | |||||||
\(458\) | −51.0501 | −2.38541 | ||||||||
\(459\) | 1.98475 | 0.0926401 | ||||||||
\(460\) | 12.2851 | 0.572798 | ||||||||
\(461\) | −18.2163 | −0.848420 | −0.424210 | − | 0.905564i | \(-0.639448\pi\) | ||||
−0.424210 | + | 0.905564i | \(0.639448\pi\) | |||||||
\(462\) | −5.37404 | −0.250023 | ||||||||
\(463\) | 3.50654 | 0.162963 | 0.0814813 | − | 0.996675i | \(-0.474035\pi\) | ||||
0.0814813 | + | 0.996675i | \(0.474035\pi\) | |||||||
\(464\) | −6.83373 | −0.317248 | ||||||||
\(465\) | 0.612308 | 0.0283951 | ||||||||
\(466\) | 34.6978 | 1.60734 | ||||||||
\(467\) | −5.00400 | −0.231557 | −0.115779 | − | 0.993275i | \(-0.536936\pi\) | ||||
−0.115779 | + | 0.993275i | \(0.536936\pi\) | |||||||
\(468\) | 65.0950 | 3.00902 | ||||||||
\(469\) | −30.8768 | −1.42576 | ||||||||
\(470\) | 15.3459 | 0.707855 | ||||||||
\(471\) | 4.42012 | 0.203668 | ||||||||
\(472\) | −44.8178 | −2.06291 | ||||||||
\(473\) | −5.99883 | −0.275826 | ||||||||
\(474\) | −1.88743 | −0.0866926 | ||||||||
\(475\) | 35.4754 | 1.62772 | ||||||||
\(476\) | 25.0174 | 1.14667 | ||||||||
\(477\) | −4.67404 | −0.214010 | ||||||||
\(478\) | −8.55829 | −0.391447 | ||||||||
\(479\) | −5.29017 | −0.241714 | −0.120857 | − | 0.992670i | \(-0.538564\pi\) | ||||
−0.120857 | + | 0.992670i | \(0.538564\pi\) | |||||||
\(480\) | 1.12640 | 0.0514127 | ||||||||
\(481\) | 3.72760 | 0.169964 | ||||||||
\(482\) | −41.3426 | −1.88311 | ||||||||
\(483\) | −4.74599 | −0.215950 | ||||||||
\(484\) | −38.1771 | −1.73532 | ||||||||
\(485\) | 1.86015 | 0.0844651 | ||||||||
\(486\) | 18.8384 | 0.854529 | ||||||||
\(487\) | 39.4915 | 1.78953 | 0.894766 | − | 0.446536i | \(-0.147342\pi\) | ||||
0.894766 | + | 0.446536i | \(0.147342\pi\) | |||||||
\(488\) | −76.1338 | −3.44641 | ||||||||
\(489\) | 0.804666 | 0.0363883 | ||||||||
\(490\) | 32.2678 | 1.45771 | ||||||||
\(491\) | 5.22939 | 0.235999 | 0.118000 | − | 0.993014i | \(-0.462352\pi\) | ||||
0.118000 | + | 0.993014i | \(0.462352\pi\) | |||||||
\(492\) | 5.37256 | 0.242214 | ||||||||
\(493\) | 1.17589 | 0.0529593 | ||||||||
\(494\) | 103.593 | 4.66087 | ||||||||
\(495\) | −3.60339 | −0.161960 | ||||||||
\(496\) | 18.4177 | 0.826981 | ||||||||
\(497\) | 21.2116 | 0.951470 | ||||||||
\(498\) | 7.57998 | 0.339667 | ||||||||
\(499\) | 9.84913 | 0.440908 | 0.220454 | − | 0.975397i | \(-0.429246\pi\) | ||||
0.220454 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(500\) | −33.1271 | −1.48149 | ||||||||
\(501\) | −3.68271 | −0.164531 | ||||||||
\(502\) | 59.2887 | 2.64619 | ||||||||
\(503\) | −36.0985 | −1.60955 | −0.804776 | − | 0.593578i | \(-0.797715\pi\) | ||||
−0.804776 | + | 0.593578i | \(0.797715\pi\) | |||||||
\(504\) | 86.5993 | 3.85744 | ||||||||
\(505\) | 14.0854 | 0.626792 | ||||||||
\(506\) | 13.6588 | 0.607209 | ||||||||
\(507\) | 3.48833 | 0.154922 | ||||||||
\(508\) | −42.9777 | −1.90683 | ||||||||
\(509\) | −30.9886 | −1.37355 | −0.686773 | − | 0.726872i | \(-0.740973\pi\) | ||||
−0.686773 | + | 0.726872i | \(0.740973\pi\) | |||||||
\(510\) | −0.677954 | −0.0300203 | ||||||||
\(511\) | −72.2931 | −3.19806 | ||||||||
\(512\) | −50.7489 | −2.24281 | ||||||||
\(513\) | 13.7167 | 0.605608 | ||||||||
\(514\) | 46.7903 | 2.06383 | ||||||||
\(515\) | −2.53058 | −0.111511 | ||||||||
\(516\) | −4.90136 | −0.215770 | ||||||||
\(517\) | 11.7632 | 0.517343 | ||||||||
\(518\) | 9.02377 | 0.396482 | ||||||||
\(519\) | −6.05648 | −0.265850 | ||||||||
\(520\) | −24.7793 | −1.08665 | ||||||||
\(521\) | 25.5141 | 1.11779 | 0.558897 | − | 0.829237i | \(-0.311225\pi\) | ||||
0.558897 | + | 0.829237i | \(0.311225\pi\) | |||||||
\(522\) | 7.40677 | 0.324186 | ||||||||
\(523\) | −30.9044 | −1.35135 | −0.675676 | − | 0.737198i | \(-0.736148\pi\) | ||||
−0.675676 | + | 0.737198i | \(0.736148\pi\) | |||||||
\(524\) | 32.4494 | 1.41756 | ||||||||
\(525\) | 5.96518 | 0.260342 | ||||||||
\(526\) | −47.6849 | −2.07916 | ||||||||
\(527\) | −3.16916 | −0.138051 | ||||||||
\(528\) | 3.02011 | 0.131434 | ||||||||
\(529\) | −10.9375 | −0.475542 | ||||||||
\(530\) | 3.23762 | 0.140633 | ||||||||
\(531\) | 21.1251 | 0.916752 | ||||||||
\(532\) | 172.897 | 7.49603 | ||||||||
\(533\) | −21.3137 | −0.923197 | ||||||||
\(534\) | 2.75137 | 0.119063 | ||||||||
\(535\) | −8.19971 | −0.354504 | ||||||||
\(536\) | 39.9004 | 1.72344 | ||||||||
\(537\) | −3.78298 | −0.163248 | ||||||||
\(538\) | −12.1163 | −0.522370 | ||||||||
\(539\) | 24.7343 | 1.06538 | ||||||||
\(540\) | −5.97036 | −0.256923 | ||||||||
\(541\) | 33.5001 | 1.44028 | 0.720140 | − | 0.693829i | \(-0.244078\pi\) | ||||
0.720140 | + | 0.693829i | \(0.244078\pi\) | |||||||
\(542\) | 50.0383 | 2.14933 | ||||||||
\(543\) | 5.41823 | 0.232518 | ||||||||
\(544\) | −5.82996 | −0.249957 | ||||||||
\(545\) | −9.04806 | −0.387576 | ||||||||
\(546\) | 17.4192 | 0.745473 | ||||||||
\(547\) | −14.9992 | −0.641321 | −0.320661 | − | 0.947194i | \(-0.603905\pi\) | ||||
−0.320661 | + | 0.947194i | \(0.603905\pi\) | |||||||
\(548\) | −69.4574 | −2.96707 | ||||||||
\(549\) | 35.8861 | 1.53158 | ||||||||
\(550\) | −17.1676 | −0.732030 | ||||||||
\(551\) | 8.12663 | 0.346206 | ||||||||
\(552\) | 6.13298 | 0.261037 | ||||||||
\(553\) | 12.4970 | 0.531425 | ||||||||
\(554\) | −50.2997 | −2.13703 | ||||||||
\(555\) | −0.168595 | −0.00715645 | ||||||||
\(556\) | −4.44002 | −0.188299 | ||||||||
\(557\) | −15.2914 | −0.647918 | −0.323959 | − | 0.946071i | \(-0.605014\pi\) | ||||
−0.323959 | + | 0.946071i | \(0.605014\pi\) | |||||||
\(558\) | −19.9622 | −0.845065 | ||||||||
\(559\) | 19.4443 | 0.822408 | ||||||||
\(560\) | −26.0871 | −1.10238 | ||||||||
\(561\) | −0.519674 | −0.0219407 | ||||||||
\(562\) | −12.4704 | −0.526033 | ||||||||
\(563\) | 10.8072 | 0.455470 | 0.227735 | − | 0.973723i | \(-0.426868\pi\) | ||||
0.227735 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(564\) | 9.61112 | 0.404701 | ||||||||
\(565\) | −9.48741 | −0.399138 | ||||||||
\(566\) | 61.5138 | 2.58562 | ||||||||
\(567\) | −39.6500 | −1.66514 | ||||||||
\(568\) | −27.4106 | −1.15012 | ||||||||
\(569\) | −21.3874 | −0.896608 | −0.448304 | − | 0.893881i | \(-0.647972\pi\) | ||||
−0.448304 | + | 0.893881i | \(0.647972\pi\) | |||||||
\(570\) | −4.68538 | −0.196249 | ||||||||
\(571\) | 17.3643 | 0.726674 | 0.363337 | − | 0.931658i | \(-0.381637\pi\) | ||||
0.363337 | + | 0.931658i | \(0.381637\pi\) | |||||||
\(572\) | −34.5630 | −1.44515 | ||||||||
\(573\) | 0.543421 | 0.0227018 | ||||||||
\(574\) | −51.5961 | −2.15358 | ||||||||
\(575\) | −15.1613 | −0.632269 | ||||||||
\(576\) | 3.16864 | 0.132027 | ||||||||
\(577\) | −32.1823 | −1.33977 | −0.669884 | − | 0.742465i | \(-0.733656\pi\) | ||||
−0.669884 | + | 0.742465i | \(0.733656\pi\) | |||||||
\(578\) | −39.6323 | −1.64849 | ||||||||
\(579\) | −4.22099 | −0.175418 | ||||||||
\(580\) | −3.53721 | −0.146875 | ||||||||
\(581\) | −50.1881 | −2.08215 | ||||||||
\(582\) | 1.68978 | 0.0700438 | ||||||||
\(583\) | 2.48174 | 0.102783 | ||||||||
\(584\) | 93.4203 | 3.86576 | ||||||||
\(585\) | 11.6799 | 0.482904 | ||||||||
\(586\) | −45.6870 | −1.88731 | ||||||||
\(587\) | 16.7695 | 0.692153 | 0.346077 | − | 0.938206i | \(-0.387514\pi\) | ||||
0.346077 | + | 0.938206i | \(0.387514\pi\) | |||||||
\(588\) | 20.2093 | 0.833416 | ||||||||
\(589\) | −21.9022 | −0.902466 | ||||||||
\(590\) | −14.6330 | −0.602431 | ||||||||
\(591\) | −0.793946 | −0.0326586 | ||||||||
\(592\) | −5.07120 | −0.208425 | ||||||||
\(593\) | −19.3815 | −0.795903 | −0.397952 | − | 0.917406i | \(-0.630279\pi\) | ||||
−0.397952 | + | 0.917406i | \(0.630279\pi\) | |||||||
\(594\) | −6.63794 | −0.272358 | ||||||||
\(595\) | 4.48883 | 0.184024 | ||||||||
\(596\) | 46.4833 | 1.90403 | ||||||||
\(597\) | −1.81904 | −0.0744482 | ||||||||
\(598\) | −44.2731 | −1.81046 | ||||||||
\(599\) | 23.7607 | 0.970838 | 0.485419 | − | 0.874282i | \(-0.338667\pi\) | ||||
0.485419 | + | 0.874282i | \(0.338667\pi\) | |||||||
\(600\) | −7.70848 | −0.314697 | ||||||||
\(601\) | −36.3121 | −1.48120 | −0.740600 | − | 0.671946i | \(-0.765459\pi\) | ||||
−0.740600 | + | 0.671946i | \(0.765459\pi\) | |||||||
\(602\) | 47.0708 | 1.91846 | ||||||||
\(603\) | −18.8073 | −0.765892 | ||||||||
\(604\) | −14.1865 | −0.577241 | ||||||||
\(605\) | −6.85005 | −0.278494 | ||||||||
\(606\) | 12.7953 | 0.519775 | ||||||||
\(607\) | 30.8715 | 1.25303 | 0.626517 | − | 0.779408i | \(-0.284480\pi\) | ||||
0.626517 | + | 0.779408i | \(0.284480\pi\) | |||||||
\(608\) | −40.2912 | −1.63402 | ||||||||
\(609\) | 1.36649 | 0.0553731 | ||||||||
\(610\) | −24.8576 | −1.00646 | ||||||||
\(611\) | −38.1286 | −1.54252 | ||||||||
\(612\) | 15.2383 | 0.615971 | ||||||||
\(613\) | 35.0427 | 1.41536 | 0.707681 | − | 0.706532i | \(-0.249742\pi\) | ||||
0.707681 | + | 0.706532i | \(0.249742\pi\) | |||||||
\(614\) | −33.9642 | −1.37068 | ||||||||
\(615\) | 0.963990 | 0.0388718 | ||||||||
\(616\) | −45.9811 | −1.85263 | ||||||||
\(617\) | −31.6013 | −1.27222 | −0.636111 | − | 0.771598i | \(-0.719458\pi\) | ||||
−0.636111 | + | 0.771598i | \(0.719458\pi\) | |||||||
\(618\) | −2.29881 | −0.0924716 | ||||||||
\(619\) | 35.7655 | 1.43754 | 0.718769 | − | 0.695249i | \(-0.244706\pi\) | ||||
0.718769 | + | 0.695249i | \(0.244706\pi\) | |||||||
\(620\) | 9.53321 | 0.382863 | ||||||||
\(621\) | −5.86218 | −0.235241 | ||||||||
\(622\) | −36.4466 | −1.46137 | ||||||||
\(623\) | −18.2172 | −0.729857 | ||||||||
\(624\) | −9.78927 | −0.391884 | ||||||||
\(625\) | 15.8827 | 0.635307 | ||||||||
\(626\) | −63.8031 | −2.55009 | ||||||||
\(627\) | −3.59150 | −0.143431 | ||||||||
\(628\) | 68.8182 | 2.74615 | ||||||||
\(629\) | 0.872606 | 0.0347931 | ||||||||
\(630\) | 28.2746 | 1.12649 | ||||||||
\(631\) | 12.6991 | 0.505542 | 0.252771 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252771 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(632\) | −16.1491 | −0.642378 | ||||||||
\(633\) | −1.41716 | −0.0563272 | ||||||||
\(634\) | −11.5389 | −0.458268 | ||||||||
\(635\) | −7.71142 | −0.306018 | ||||||||
\(636\) | 2.02772 | 0.0804042 | ||||||||
\(637\) | −80.1729 | −3.17656 | ||||||||
\(638\) | −3.93273 | −0.155698 | ||||||||
\(639\) | 12.9201 | 0.511112 | ||||||||
\(640\) | −10.0945 | −0.399019 | ||||||||
\(641\) | 8.81038 | 0.347989 | 0.173995 | − | 0.984747i | \(-0.444332\pi\) | ||||
0.173995 | + | 0.984747i | \(0.444332\pi\) | |||||||
\(642\) | −7.44872 | −0.293977 | ||||||||
\(643\) | −42.1082 | −1.66059 | −0.830293 | − | 0.557328i | \(-0.811827\pi\) | ||||
−0.830293 | + | 0.557328i | \(0.811827\pi\) | |||||||
\(644\) | −73.8918 | −2.91175 | ||||||||
\(645\) | −0.879443 | −0.0346280 | ||||||||
\(646\) | 24.2504 | 0.954120 | ||||||||
\(647\) | −19.1129 | −0.751406 | −0.375703 | − | 0.926740i | \(-0.622599\pi\) | ||||
−0.375703 | + | 0.926740i | \(0.622599\pi\) | |||||||
\(648\) | 51.2375 | 2.01280 | ||||||||
\(649\) | −11.2167 | −0.440293 | ||||||||
\(650\) | 55.6464 | 2.18263 | ||||||||
\(651\) | −3.68286 | −0.144343 | ||||||||
\(652\) | 12.5281 | 0.490638 | ||||||||
\(653\) | −25.3308 | −0.991271 | −0.495635 | − | 0.868531i | \(-0.665065\pi\) | ||||
−0.495635 | + | 0.868531i | \(0.665065\pi\) | |||||||
\(654\) | −8.21937 | −0.321403 | ||||||||
\(655\) | 5.82235 | 0.227498 | ||||||||
\(656\) | 28.9961 | 1.13211 | ||||||||
\(657\) | −44.0342 | −1.71794 | ||||||||
\(658\) | −92.3016 | −3.59829 | ||||||||
\(659\) | 42.0640 | 1.63858 | 0.819291 | − | 0.573378i | \(-0.194367\pi\) | ||||
0.819291 | + | 0.573378i | \(0.194367\pi\) | |||||||
\(660\) | 1.56324 | 0.0608491 | ||||||||
\(661\) | −38.9926 | −1.51664 | −0.758318 | − | 0.651885i | \(-0.773979\pi\) | ||||
−0.758318 | + | 0.651885i | \(0.773979\pi\) | |||||||
\(662\) | 4.29895 | 0.167084 | ||||||||
\(663\) | 1.68445 | 0.0654186 | ||||||||
\(664\) | 64.8553 | 2.51688 | ||||||||
\(665\) | 31.0226 | 1.20300 | ||||||||
\(666\) | 5.49644 | 0.212983 | ||||||||
\(667\) | −3.47312 | −0.134480 | ||||||||
\(668\) | −57.3373 | −2.21845 | ||||||||
\(669\) | 5.26435 | 0.203532 | ||||||||
\(670\) | 13.0275 | 0.503295 | ||||||||
\(671\) | −19.0542 | −0.735579 | ||||||||
\(672\) | −6.77497 | −0.261350 | ||||||||
\(673\) | −19.4113 | −0.748252 | −0.374126 | − | 0.927378i | \(-0.622057\pi\) | ||||
−0.374126 | + | 0.927378i | \(0.622057\pi\) | |||||||
\(674\) | −48.0836 | −1.85211 | ||||||||
\(675\) | 7.36811 | 0.283599 | ||||||||
\(676\) | 54.3109 | 2.08888 | ||||||||
\(677\) | 30.4024 | 1.16846 | 0.584230 | − | 0.811588i | \(-0.301396\pi\) | ||||
0.584230 | + | 0.811588i | \(0.301396\pi\) | |||||||
\(678\) | −8.61848 | −0.330991 | ||||||||
\(679\) | −11.1883 | −0.429367 | ||||||||
\(680\) | −5.80067 | −0.222446 | ||||||||
\(681\) | −4.21931 | −0.161684 | ||||||||
\(682\) | 10.5992 | 0.405863 | ||||||||
\(683\) | 24.8688 | 0.951577 | 0.475788 | − | 0.879560i | \(-0.342163\pi\) | ||||
0.475788 | + | 0.879560i | \(0.342163\pi\) | |||||||
\(684\) | 105.313 | 4.02673 | ||||||||
\(685\) | −12.4626 | −0.476173 | ||||||||
\(686\) | −108.962 | −4.16018 | ||||||||
\(687\) | −5.73678 | −0.218872 | ||||||||
\(688\) | −26.4530 | −1.00851 | ||||||||
\(689\) | −8.04422 | −0.306460 | ||||||||
\(690\) | 2.00242 | 0.0762307 | ||||||||
\(691\) | −11.2010 | −0.426107 | −0.213054 | − | 0.977040i | \(-0.568341\pi\) | ||||
−0.213054 | + | 0.977040i | \(0.568341\pi\) | |||||||
\(692\) | −94.2952 | −3.58457 | ||||||||
\(693\) | 21.6734 | 0.823306 | ||||||||
\(694\) | 38.8041 | 1.47298 | ||||||||
\(695\) | −0.796665 | −0.0302192 | ||||||||
\(696\) | −1.76584 | −0.0669341 | ||||||||
\(697\) | −4.98938 | −0.188986 | ||||||||
\(698\) | 55.6165 | 2.10511 | ||||||||
\(699\) | 3.89918 | 0.147480 | ||||||||
\(700\) | 92.8738 | 3.51030 | ||||||||
\(701\) | 13.0843 | 0.494185 | 0.247093 | − | 0.968992i | \(-0.420525\pi\) | ||||
0.247093 | + | 0.968992i | \(0.420525\pi\) | |||||||
\(702\) | 21.5159 | 0.812067 | ||||||||
\(703\) | 6.03063 | 0.227450 | ||||||||
\(704\) | −1.68243 | −0.0634090 | ||||||||
\(705\) | 1.72451 | 0.0649487 | ||||||||
\(706\) | −8.04943 | −0.302944 | ||||||||
\(707\) | −84.7198 | −3.18622 | ||||||||
\(708\) | −9.16461 | −0.344427 | ||||||||
\(709\) | −19.3395 | −0.726310 | −0.363155 | − | 0.931729i | \(-0.618300\pi\) | ||||
−0.363155 | + | 0.931729i | \(0.618300\pi\) | |||||||
\(710\) | −8.94954 | −0.335870 | ||||||||
\(711\) | 7.61198 | 0.285472 | ||||||||
\(712\) | 23.5411 | 0.882240 | ||||||||
\(713\) | 9.36047 | 0.350552 | ||||||||
\(714\) | 4.07771 | 0.152605 | ||||||||
\(715\) | −6.20159 | −0.231926 | ||||||||
\(716\) | −58.8984 | −2.20114 | ||||||||
\(717\) | −0.961742 | −0.0359169 | ||||||||
\(718\) | −69.6656 | −2.59990 | ||||||||
\(719\) | 25.3379 | 0.944944 | 0.472472 | − | 0.881346i | \(-0.343362\pi\) | ||||
0.472472 | + | 0.881346i | \(0.343362\pi\) | |||||||
\(720\) | −15.8898 | −0.592179 | ||||||||
\(721\) | 15.2207 | 0.566850 | ||||||||
\(722\) | 119.379 | 4.44284 | ||||||||
\(723\) | −4.64590 | −0.172783 | ||||||||
\(724\) | 84.3581 | 3.13514 | ||||||||
\(725\) | 4.36532 | 0.162124 | ||||||||
\(726\) | −6.22267 | −0.230945 | ||||||||
\(727\) | −16.9623 | −0.629096 | −0.314548 | − | 0.949242i | \(-0.601853\pi\) | ||||
−0.314548 | + | 0.949242i | \(0.601853\pi\) | |||||||
\(728\) | 149.041 | 5.52383 | ||||||||
\(729\) | −22.7071 | −0.841002 | ||||||||
\(730\) | 30.5017 | 1.12892 | ||||||||
\(731\) | 4.55179 | 0.168354 | ||||||||
\(732\) | −15.5683 | −0.575420 | ||||||||
\(733\) | 27.4412 | 1.01356 | 0.506782 | − | 0.862074i | \(-0.330835\pi\) | ||||
0.506782 | + | 0.862074i | \(0.330835\pi\) | |||||||
\(734\) | 71.8981 | 2.65381 | ||||||||
\(735\) | 3.62612 | 0.133751 | ||||||||
\(736\) | 17.2195 | 0.634717 | ||||||||
\(737\) | 9.98599 | 0.367839 | ||||||||
\(738\) | −31.4275 | −1.15686 | ||||||||
\(739\) | 27.5380 | 1.01300 | 0.506502 | − | 0.862239i | \(-0.330938\pi\) | ||||
0.506502 | + | 0.862239i | \(0.330938\pi\) | |||||||
\(740\) | −2.62490 | −0.0964934 | ||||||||
\(741\) | 11.6413 | 0.427655 | ||||||||
\(742\) | −19.4734 | −0.714892 | ||||||||
\(743\) | −22.0284 | −0.808143 | −0.404071 | − | 0.914727i | \(-0.632405\pi\) | ||||
−0.404071 | + | 0.914727i | \(0.632405\pi\) | |||||||
\(744\) | 4.75916 | 0.174479 | ||||||||
\(745\) | 8.34042 | 0.305569 | ||||||||
\(746\) | 64.9901 | 2.37946 | ||||||||
\(747\) | −30.5699 | −1.11850 | ||||||||
\(748\) | −8.09097 | −0.295835 | ||||||||
\(749\) | 49.3190 | 1.80208 | ||||||||
\(750\) | −5.39955 | −0.197164 | ||||||||
\(751\) | 29.3811 | 1.07213 | 0.536066 | − | 0.844176i | \(-0.319910\pi\) | ||||
0.536066 | + | 0.844176i | \(0.319910\pi\) | |||||||
\(752\) | 51.8718 | 1.89157 | ||||||||
\(753\) | 6.66260 | 0.242799 | ||||||||
\(754\) | 12.7474 | 0.464232 | ||||||||
\(755\) | −2.54546 | −0.0926389 | ||||||||
\(756\) | 35.9101 | 1.30604 | ||||||||
\(757\) | −27.3024 | −0.992321 | −0.496160 | − | 0.868231i | \(-0.665257\pi\) | ||||
−0.496160 | + | 0.868231i | \(0.665257\pi\) | |||||||
\(758\) | 7.35083 | 0.266994 | ||||||||
\(759\) | 1.53492 | 0.0557140 | ||||||||
\(760\) | −40.0888 | −1.45417 | ||||||||
\(761\) | 27.5381 | 0.998257 | 0.499128 | − | 0.866528i | \(-0.333654\pi\) | ||||
0.499128 | + | 0.866528i | \(0.333654\pi\) | |||||||
\(762\) | −7.00515 | −0.253770 | ||||||||
\(763\) | 54.4216 | 1.97019 | ||||||||
\(764\) | 8.46070 | 0.306097 | ||||||||
\(765\) | 2.73418 | 0.0988545 | ||||||||
\(766\) | −14.7116 | −0.531552 | ||||||||
\(767\) | 36.3572 | 1.31278 | ||||||||
\(768\) | −8.55074 | −0.308548 | ||||||||
\(769\) | −12.9940 | −0.468576 | −0.234288 | − | 0.972167i | \(-0.575276\pi\) | ||||
−0.234288 | + | 0.972167i | \(0.575276\pi\) | |||||||
\(770\) | −15.0128 | −0.541024 | ||||||||
\(771\) | 5.25808 | 0.189365 | ||||||||
\(772\) | −65.7178 | −2.36524 | ||||||||
\(773\) | 11.7387 | 0.422211 | 0.211105 | − | 0.977463i | \(-0.432294\pi\) | ||||
0.211105 | + | 0.977463i | \(0.432294\pi\) | |||||||
\(774\) | 28.6712 | 1.03056 | ||||||||
\(775\) | −11.7651 | −0.422614 | ||||||||
\(776\) | 14.4580 | 0.519013 | ||||||||
\(777\) | 1.01405 | 0.0363789 | ||||||||
\(778\) | 63.5639 | 2.27888 | ||||||||
\(779\) | −34.4819 | −1.23544 | ||||||||
\(780\) | −5.06703 | −0.181429 | ||||||||
\(781\) | −6.86011 | −0.245474 | ||||||||
\(782\) | −10.3640 | −0.370617 | ||||||||
\(783\) | 1.68787 | 0.0603197 | ||||||||
\(784\) | 109.071 | 3.89538 | ||||||||
\(785\) | 12.3479 | 0.440717 | ||||||||
\(786\) | 5.28909 | 0.188656 | ||||||||
\(787\) | 53.6141 | 1.91114 | 0.955568 | − | 0.294772i | \(-0.0952436\pi\) | ||||
0.955568 | + | 0.294772i | \(0.0952436\pi\) | |||||||
\(788\) | −12.3612 | −0.440349 | ||||||||
\(789\) | −5.35861 | −0.190772 | ||||||||
\(790\) | −5.27268 | −0.187594 | ||||||||
\(791\) | 57.0642 | 2.02897 | ||||||||
\(792\) | −28.0074 | −0.995199 | ||||||||
\(793\) | 61.7615 | 2.19321 | ||||||||
\(794\) | 36.8772 | 1.30872 | ||||||||
\(795\) | 0.363830 | 0.0129037 | ||||||||
\(796\) | −28.3211 | −1.00382 | ||||||||
\(797\) | −22.5292 | −0.798025 | −0.399012 | − | 0.916946i | \(-0.630647\pi\) | ||||
−0.399012 | + | 0.916946i | \(0.630647\pi\) | |||||||
\(798\) | 28.1813 | 0.997608 | ||||||||
\(799\) | −8.92564 | −0.315766 | ||||||||
\(800\) | −21.6429 | −0.765194 | ||||||||
\(801\) | −11.0962 | −0.392066 | ||||||||
\(802\) | −52.5062 | −1.85406 | ||||||||
\(803\) | 23.3806 | 0.825082 | ||||||||
\(804\) | 8.15908 | 0.287749 | ||||||||
\(805\) | −13.2583 | −0.467293 | ||||||||
\(806\) | −34.3557 | −1.21013 | ||||||||
\(807\) | −1.36157 | −0.0479297 | ||||||||
\(808\) | 109.479 | 3.85145 | ||||||||
\(809\) | −37.3781 | −1.31414 | −0.657072 | − | 0.753828i | \(-0.728205\pi\) | ||||
−0.657072 | + | 0.753828i | \(0.728205\pi\) | |||||||
\(810\) | 16.7290 | 0.587798 | ||||||||
\(811\) | 15.4022 | 0.540844 | 0.270422 | − | 0.962742i | \(-0.412837\pi\) | ||||
0.270422 | + | 0.962742i | \(0.412837\pi\) | |||||||
\(812\) | 21.2754 | 0.746619 | ||||||||
\(813\) | 5.62308 | 0.197210 | ||||||||
\(814\) | −2.91841 | −0.102290 | ||||||||
\(815\) | 2.24790 | 0.0787404 | ||||||||
\(816\) | −2.29160 | −0.0802221 | ||||||||
\(817\) | 31.4577 | 1.10056 | ||||||||
\(818\) | 30.1966 | 1.05580 | ||||||||
\(819\) | −70.2513 | −2.45478 | ||||||||
\(820\) | 15.0087 | 0.524125 | ||||||||
\(821\) | −21.4154 | −0.747401 | −0.373701 | − | 0.927549i | \(-0.621911\pi\) | ||||
−0.373701 | + | 0.927549i | \(0.621911\pi\) | |||||||
\(822\) | −11.3212 | −0.394873 | ||||||||
\(823\) | 4.06262 | 0.141614 | 0.0708071 | − | 0.997490i | \(-0.477443\pi\) | ||||
0.0708071 | + | 0.997490i | \(0.477443\pi\) | |||||||
\(824\) | −19.6689 | −0.685199 | ||||||||
\(825\) | −1.92922 | −0.0671669 | ||||||||
\(826\) | 88.0135 | 3.06238 | ||||||||
\(827\) | 2.78910 | 0.0969864 | 0.0484932 | − | 0.998824i | \(-0.484558\pi\) | ||||
0.0484932 | + | 0.998824i | \(0.484558\pi\) | |||||||
\(828\) | −45.0080 | −1.56414 | ||||||||
\(829\) | −48.2172 | −1.67465 | −0.837327 | − | 0.546702i | \(-0.815883\pi\) | ||||
−0.837327 | + | 0.546702i | \(0.815883\pi\) | |||||||
\(830\) | 21.1752 | 0.735003 | ||||||||
\(831\) | −5.65246 | −0.196082 | ||||||||
\(832\) | 5.45336 | 0.189061 | ||||||||
\(833\) | −18.7679 | −0.650270 | ||||||||
\(834\) | −0.723701 | −0.0250597 | ||||||||
\(835\) | −10.2879 | −0.356029 | ||||||||
\(836\) | −55.9172 | −1.93394 | ||||||||
\(837\) | −4.54902 | −0.157237 | ||||||||
\(838\) | −22.5101 | −0.777600 | ||||||||
\(839\) | 17.7255 | 0.611952 | 0.305976 | − | 0.952039i | \(-0.401017\pi\) | ||||
0.305976 | + | 0.952039i | \(0.401017\pi\) | |||||||
\(840\) | −6.74093 | −0.232584 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −59.9363 | −2.06554 | ||||||||
\(843\) | −1.40137 | −0.0482657 | ||||||||
\(844\) | −22.0643 | −0.759484 | ||||||||
\(845\) | 9.74492 | 0.335236 | ||||||||
\(846\) | −56.2215 | −1.93294 | ||||||||
\(847\) | 41.2012 | 1.41569 | ||||||||
\(848\) | 10.9437 | 0.375809 | ||||||||
\(849\) | 6.91265 | 0.237241 | ||||||||
\(850\) | 13.0264 | 0.446803 | ||||||||
\(851\) | −2.57734 | −0.0883502 | ||||||||
\(852\) | −5.60507 | −0.192027 | ||||||||
\(853\) | −14.3916 | −0.492760 | −0.246380 | − | 0.969173i | \(-0.579241\pi\) | ||||
−0.246380 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(854\) | 149.512 | 5.11620 | ||||||||
\(855\) | 18.8961 | 0.646232 | ||||||||
\(856\) | −63.7323 | −2.17832 | ||||||||
\(857\) | −13.0574 | −0.446031 | −0.223016 | − | 0.974815i | \(-0.571590\pi\) | ||||
−0.223016 | + | 0.974815i | \(0.571590\pi\) | |||||||
\(858\) | −5.63360 | −0.192328 | ||||||||
\(859\) | 40.9730 | 1.39798 | 0.698990 | − | 0.715132i | \(-0.253633\pi\) | ||||
0.698990 | + | 0.715132i | \(0.253633\pi\) | |||||||
\(860\) | −13.6923 | −0.466904 | ||||||||
\(861\) | −5.79814 | −0.197600 | ||||||||
\(862\) | 43.1729 | 1.47048 | ||||||||
\(863\) | 24.0975 | 0.820289 | 0.410145 | − | 0.912020i | \(-0.365478\pi\) | ||||
0.410145 | + | 0.912020i | \(0.365478\pi\) | |||||||
\(864\) | −8.36835 | −0.284697 | ||||||||
\(865\) | −16.9192 | −0.575271 | ||||||||
\(866\) | 48.6663 | 1.65375 | ||||||||
\(867\) | −4.45370 | −0.151256 | ||||||||
\(868\) | −57.3397 | −1.94624 | ||||||||
\(869\) | −4.04168 | −0.137105 | ||||||||
\(870\) | −0.576547 | −0.0195468 | ||||||||
\(871\) | −32.3682 | −1.09675 | ||||||||
\(872\) | −70.3260 | −2.38154 | ||||||||
\(873\) | −6.81487 | −0.230648 | ||||||||
\(874\) | −71.6264 | −2.42280 | ||||||||
\(875\) | 35.7512 | 1.20861 | ||||||||
\(876\) | 19.1031 | 0.645436 | ||||||||
\(877\) | 5.67715 | 0.191704 | 0.0958518 | − | 0.995396i | \(-0.469443\pi\) | ||||
0.0958518 | + | 0.995396i | \(0.469443\pi\) | |||||||
\(878\) | −48.8267 | −1.64782 | ||||||||
\(879\) | −5.13410 | −0.173169 | ||||||||
\(880\) | 8.43692 | 0.284409 | ||||||||
\(881\) | −3.40518 | −0.114723 | −0.0573617 | − | 0.998353i | \(-0.518269\pi\) | ||||
−0.0573617 | + | 0.998353i | \(0.518269\pi\) | |||||||
\(882\) | −118.217 | −3.98057 | ||||||||
\(883\) | 52.0600 | 1.75196 | 0.875979 | − | 0.482349i | \(-0.160216\pi\) | ||||
0.875979 | + | 0.482349i | \(0.160216\pi\) | |||||||
\(884\) | 26.2257 | 0.882067 | ||||||||
\(885\) | −1.64439 | −0.0552756 | ||||||||
\(886\) | −57.2112 | −1.92205 | ||||||||
\(887\) | 26.9795 | 0.905885 | 0.452942 | − | 0.891540i | \(-0.350374\pi\) | ||||
0.452942 | + | 0.891540i | \(0.350374\pi\) | |||||||
\(888\) | −1.31040 | −0.0439742 | ||||||||
\(889\) | 46.3821 | 1.55561 | ||||||||
\(890\) | 7.68616 | 0.257641 | ||||||||
\(891\) | 12.8233 | 0.429598 | ||||||||
\(892\) | 81.9623 | 2.74430 | ||||||||
\(893\) | −61.6856 | −2.06423 | ||||||||
\(894\) | 7.57654 | 0.253397 | ||||||||
\(895\) | −10.5680 | −0.353251 | ||||||||
\(896\) | 60.7155 | 2.02836 | ||||||||
\(897\) | −4.97522 | −0.166118 | ||||||||
\(898\) | 55.0172 | 1.83595 | ||||||||
\(899\) | −2.69512 | −0.0898873 | ||||||||
\(900\) | 56.5701 | 1.88567 | ||||||||
\(901\) | −1.88310 | −0.0627350 | ||||||||
\(902\) | 16.6869 | 0.555612 | ||||||||
\(903\) | 5.28961 | 0.176027 | ||||||||
\(904\) | −73.7409 | −2.45259 | ||||||||
\(905\) | 15.1362 | 0.503145 | ||||||||
\(906\) | −2.31233 | −0.0768221 | ||||||||
\(907\) | 40.4906 | 1.34447 | 0.672235 | − | 0.740338i | \(-0.265335\pi\) | ||||
0.672235 | + | 0.740338i | \(0.265335\pi\) | |||||||
\(908\) | −65.6918 | −2.18006 | ||||||||
\(909\) | −51.6034 | −1.71158 | ||||||||
\(910\) | 48.6618 | 1.61312 | ||||||||
\(911\) | 10.0305 | 0.332325 | 0.166162 | − | 0.986098i | \(-0.446862\pi\) | ||||
0.166162 | + | 0.986098i | \(0.446862\pi\) | |||||||
\(912\) | −15.8374 | −0.524428 | ||||||||
\(913\) | 16.2315 | 0.537185 | ||||||||
\(914\) | −60.3466 | −1.99609 | ||||||||
\(915\) | −2.79339 | −0.0923467 | ||||||||
\(916\) | −89.3177 | −2.95114 | ||||||||
\(917\) | −35.0199 | −1.15646 | ||||||||
\(918\) | 5.03673 | 0.166237 | ||||||||
\(919\) | −50.0023 | −1.64942 | −0.824712 | − | 0.565553i | \(-0.808663\pi\) | ||||
−0.824712 | + | 0.565553i | \(0.808663\pi\) | |||||||
\(920\) | 17.1330 | 0.564857 | ||||||||
\(921\) | −3.81674 | −0.125766 | ||||||||
\(922\) | −46.2280 | −1.52244 | ||||||||
\(923\) | 22.2361 | 0.731909 | ||||||||
\(924\) | −9.40248 | −0.309319 | ||||||||
\(925\) | 3.23943 | 0.106512 | ||||||||
\(926\) | 8.89861 | 0.292426 | ||||||||
\(927\) | 9.27106 | 0.304501 | ||||||||
\(928\) | −4.95792 | −0.162752 | ||||||||
\(929\) | −40.1577 | −1.31753 | −0.658765 | − | 0.752349i | \(-0.728921\pi\) | ||||
−0.658765 | + | 0.752349i | \(0.728921\pi\) | |||||||
\(930\) | 1.55386 | 0.0509532 | ||||||||
\(931\) | −129.706 | −4.25095 | ||||||||
\(932\) | 60.7075 | 1.98854 | ||||||||
\(933\) | −4.09570 | −0.134087 | ||||||||
\(934\) | −12.6987 | −0.415516 | ||||||||
\(935\) | −1.45175 | −0.0474773 | ||||||||
\(936\) | 90.7819 | 2.96730 | ||||||||
\(937\) | −15.2280 | −0.497476 | −0.248738 | − | 0.968571i | \(-0.580016\pi\) | ||||
−0.248738 | + | 0.968571i | \(0.580016\pi\) | |||||||
\(938\) | −78.3568 | −2.55844 | ||||||||
\(939\) | −7.16991 | −0.233981 | ||||||||
\(940\) | 26.8494 | 0.875730 | ||||||||
\(941\) | −40.3162 | −1.31427 | −0.657135 | − | 0.753773i | \(-0.728232\pi\) | ||||
−0.657135 | + | 0.753773i | \(0.728232\pi\) | |||||||
\(942\) | 11.2170 | 0.365470 | ||||||||
\(943\) | 14.7367 | 0.479893 | ||||||||
\(944\) | −49.4620 | −1.60985 | ||||||||
\(945\) | 6.44329 | 0.209600 | ||||||||
\(946\) | −15.2233 | −0.494954 | ||||||||
\(947\) | −35.7960 | −1.16321 | −0.581607 | − | 0.813470i | \(-0.697576\pi\) | ||||
−0.581607 | + | 0.813470i | \(0.697576\pi\) | |||||||
\(948\) | −3.30227 | −0.107253 | ||||||||
\(949\) | −75.7847 | −2.46008 | ||||||||
\(950\) | 90.0265 | 2.92085 | ||||||||
\(951\) | −1.29669 | −0.0420480 | ||||||||
\(952\) | 34.8895 | 1.13077 | ||||||||
\(953\) | 28.1088 | 0.910534 | 0.455267 | − | 0.890355i | \(-0.349544\pi\) | ||||
0.455267 | + | 0.890355i | \(0.349544\pi\) | |||||||
\(954\) | −11.8614 | −0.384027 | ||||||||
\(955\) | 1.51809 | 0.0491242 | ||||||||
\(956\) | −14.9737 | −0.484283 | ||||||||
\(957\) | −0.441942 | −0.0142860 | ||||||||
\(958\) | −13.4250 | −0.433741 | ||||||||
\(959\) | 74.9594 | 2.42056 | ||||||||
\(960\) | −0.246649 | −0.00796055 | ||||||||
\(961\) | −23.7363 | −0.765688 | ||||||||
\(962\) | 9.45961 | 0.304990 | ||||||||
\(963\) | 30.0406 | 0.968044 | ||||||||
\(964\) | −72.3335 | −2.32971 | ||||||||
\(965\) | −11.7916 | −0.379586 | ||||||||
\(966\) | −12.0440 | −0.387509 | ||||||||
\(967\) | 7.92826 | 0.254956 | 0.127478 | − | 0.991841i | \(-0.459312\pi\) | ||||
0.127478 | + | 0.991841i | \(0.459312\pi\) | |||||||
\(968\) | −53.2420 | −1.71126 | ||||||||
\(969\) | 2.72516 | 0.0875446 | ||||||||
\(970\) | 4.72054 | 0.151567 | ||||||||
\(971\) | −26.3203 | −0.844659 | −0.422329 | − | 0.906442i | \(-0.638787\pi\) | ||||
−0.422329 | + | 0.906442i | \(0.638787\pi\) | |||||||
\(972\) | 32.9599 | 1.05719 | ||||||||
\(973\) | 4.79173 | 0.153616 | ||||||||
\(974\) | 100.218 | 3.21120 | ||||||||
\(975\) | 6.25330 | 0.200266 | ||||||||
\(976\) | −84.0230 | −2.68951 | ||||||||
\(977\) | 48.9090 | 1.56474 | 0.782369 | − | 0.622816i | \(-0.214011\pi\) | ||||
0.782369 | + | 0.622816i | \(0.214011\pi\) | |||||||
\(978\) | 2.04202 | 0.0652965 | ||||||||
\(979\) | 5.89169 | 0.188299 | ||||||||
\(980\) | 56.4561 | 1.80342 | ||||||||
\(981\) | 33.1486 | 1.05835 | ||||||||
\(982\) | 13.2707 | 0.423486 | ||||||||
\(983\) | 51.0295 | 1.62759 | 0.813793 | − | 0.581154i | \(-0.197399\pi\) | ||||
0.813793 | + | 0.581154i | \(0.197399\pi\) | |||||||
\(984\) | 7.49261 | 0.238856 | ||||||||
\(985\) | −2.21795 | −0.0706697 | ||||||||
\(986\) | 2.98407 | 0.0950322 | ||||||||
\(987\) | −10.3724 | −0.330158 | ||||||||
\(988\) | 181.248 | 5.76625 | ||||||||
\(989\) | −13.4442 | −0.427501 | ||||||||
\(990\) | −9.14440 | −0.290628 | ||||||||
\(991\) | −0.670377 | −0.0212952 | −0.0106476 | − | 0.999943i | \(-0.503389\pi\) | ||||
−0.0106476 | + | 0.999943i | \(0.503389\pi\) | |||||||
\(992\) | 13.3622 | 0.424250 | ||||||||
\(993\) | 0.483097 | 0.0153306 | ||||||||
\(994\) | 53.8291 | 1.70735 | ||||||||
\(995\) | −5.08161 | −0.161098 | ||||||||
\(996\) | 13.2620 | 0.420223 | ||||||||
\(997\) | 6.41044 | 0.203021 | 0.101510 | − | 0.994834i | \(-0.467632\pi\) | ||||
0.101510 | + | 0.994834i | \(0.467632\pi\) | |||||||
\(998\) | 24.9943 | 0.791182 | ||||||||
\(999\) | 1.25254 | 0.0396287 |
(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 | 4031.2.a.c.1.59 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.59 | ✓ | 61 | 1.1 | even | 1 | trivial |