Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39333 | 1.69234 | 0.846170 | − | 0.532913i | \(-0.178903\pi\) | ||||
0.846170 | + | 0.532913i | \(0.178903\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.72803 | 1.86402 | ||||||||
\(5\) | −1.40202 | −0.627001 | −0.313501 | − | 0.949588i | \(-0.601502\pi\) | ||||
−0.313501 | + | 0.949588i | \(0.601502\pi\) | |||||||
\(6\) | 2.39333 | 0.977073 | ||||||||
\(7\) | 1.96997 | 0.744579 | 0.372289 | − | 0.928117i | \(-0.378573\pi\) | ||||
0.372289 | + | 0.928117i | \(0.378573\pi\) | |||||||
\(8\) | 4.13575 | 1.46221 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.35549 | −1.06110 | ||||||||
\(11\) | 6.57798 | 1.98334 | 0.991668 | − | 0.128818i | \(-0.0411184\pi\) | ||||
0.991668 | + | 0.128818i | \(0.0411184\pi\) | |||||||
\(12\) | 3.72803 | 1.07619 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.71479 | 1.26008 | ||||||||
\(15\) | −1.40202 | −0.361999 | ||||||||
\(16\) | 2.44215 | 0.610539 | ||||||||
\(17\) | −1.72068 | −0.417326 | −0.208663 | − | 0.977988i | \(-0.566911\pi\) | ||||
−0.208663 | + | 0.977988i | \(0.566911\pi\) | |||||||
\(18\) | 2.39333 | 0.564113 | ||||||||
\(19\) | 2.07272 | 0.475514 | 0.237757 | − | 0.971325i | \(-0.423588\pi\) | ||||
0.237757 | + | 0.971325i | \(0.423588\pi\) | |||||||
\(20\) | −5.22676 | −1.16874 | ||||||||
\(21\) | 1.96997 | 0.429883 | ||||||||
\(22\) | 15.7433 | 3.35648 | ||||||||
\(23\) | 6.57879 | 1.37177 | 0.685886 | − | 0.727709i | \(-0.259415\pi\) | ||||
0.685886 | + | 0.727709i | \(0.259415\pi\) | |||||||
\(24\) | 4.13575 | 0.844206 | ||||||||
\(25\) | −3.03435 | −0.606869 | ||||||||
\(26\) | −2.39333 | −0.469371 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.34411 | 1.38791 | ||||||||
\(29\) | 0.697292 | 0.129484 | 0.0647419 | − | 0.997902i | \(-0.479378\pi\) | ||||
0.0647419 | + | 0.997902i | \(0.479378\pi\) | |||||||
\(30\) | −3.35549 | −0.612626 | ||||||||
\(31\) | 1.51915 | 0.272848 | 0.136424 | − | 0.990651i | \(-0.456439\pi\) | ||||
0.136424 | + | 0.990651i | \(0.456439\pi\) | |||||||
\(32\) | −2.42662 | −0.428969 | ||||||||
\(33\) | 6.57798 | 1.14508 | ||||||||
\(34\) | −4.11816 | −0.706258 | ||||||||
\(35\) | −2.76193 | −0.466852 | ||||||||
\(36\) | 3.72803 | 0.621339 | ||||||||
\(37\) | −8.95694 | −1.47251 | −0.736256 | − | 0.676704i | \(-0.763408\pi\) | ||||
−0.736256 | + | 0.676704i | \(0.763408\pi\) | |||||||
\(38\) | 4.96070 | 0.804731 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −5.79839 | −0.916807 | ||||||||
\(41\) | −10.0180 | −1.56454 | −0.782272 | − | 0.622937i | \(-0.785939\pi\) | ||||
−0.782272 | + | 0.622937i | \(0.785939\pi\) | |||||||
\(42\) | 4.71479 | 0.727508 | ||||||||
\(43\) | 7.65800 | 1.16783 | 0.583917 | − | 0.811813i | \(-0.301519\pi\) | ||||
0.583917 | + | 0.811813i | \(0.301519\pi\) | |||||||
\(44\) | 24.5229 | 3.69697 | ||||||||
\(45\) | −1.40202 | −0.209000 | ||||||||
\(46\) | 15.7452 | 2.32151 | ||||||||
\(47\) | −5.50250 | −0.802623 | −0.401311 | − | 0.915942i | \(-0.631445\pi\) | ||||
−0.401311 | + | 0.915942i | \(0.631445\pi\) | |||||||
\(48\) | 2.44215 | 0.352495 | ||||||||
\(49\) | −3.11922 | −0.445603 | ||||||||
\(50\) | −7.26220 | −1.02703 | ||||||||
\(51\) | −1.72068 | −0.240944 | ||||||||
\(52\) | −3.72803 | −0.516985 | ||||||||
\(53\) | 6.02052 | 0.826983 | 0.413491 | − | 0.910508i | \(-0.364309\pi\) | ||||
0.413491 | + | 0.910508i | \(0.364309\pi\) | |||||||
\(54\) | 2.39333 | 0.325691 | ||||||||
\(55\) | −9.22245 | −1.24355 | ||||||||
\(56\) | 8.14730 | 1.08873 | ||||||||
\(57\) | 2.07272 | 0.274538 | ||||||||
\(58\) | 1.66885 | 0.219131 | ||||||||
\(59\) | −11.8504 | −1.54279 | −0.771396 | − | 0.636355i | \(-0.780441\pi\) | ||||
−0.771396 | + | 0.636355i | \(0.780441\pi\) | |||||||
\(60\) | −5.22676 | −0.674772 | ||||||||
\(61\) | 5.39639 | 0.690936 | 0.345468 | − | 0.938430i | \(-0.387720\pi\) | ||||
0.345468 | + | 0.938430i | \(0.387720\pi\) | |||||||
\(62\) | 3.63583 | 0.461751 | ||||||||
\(63\) | 1.96997 | 0.248193 | ||||||||
\(64\) | −10.6920 | −1.33650 | ||||||||
\(65\) | 1.40202 | 0.173899 | ||||||||
\(66\) | 15.7433 | 1.93786 | ||||||||
\(67\) | 4.09403 | 0.500165 | 0.250082 | − | 0.968225i | \(-0.419542\pi\) | ||||
0.250082 | + | 0.968225i | \(0.419542\pi\) | |||||||
\(68\) | −6.41475 | −0.777903 | ||||||||
\(69\) | 6.57879 | 0.791993 | ||||||||
\(70\) | −6.61022 | −0.790072 | ||||||||
\(71\) | 15.6357 | 1.85562 | 0.927810 | − | 0.373053i | \(-0.121689\pi\) | ||||
0.927810 | + | 0.373053i | \(0.121689\pi\) | |||||||
\(72\) | 4.13575 | 0.487403 | ||||||||
\(73\) | 12.5085 | 1.46401 | 0.732003 | − | 0.681301i | \(-0.238586\pi\) | ||||
0.732003 | + | 0.681301i | \(0.238586\pi\) | |||||||
\(74\) | −21.4369 | −2.49199 | ||||||||
\(75\) | −3.03435 | −0.350376 | ||||||||
\(76\) | 7.72715 | 0.886365 | ||||||||
\(77\) | 12.9584 | 1.47675 | ||||||||
\(78\) | −2.39333 | −0.270991 | ||||||||
\(79\) | −7.11099 | −0.800049 | −0.400025 | − | 0.916504i | \(-0.630998\pi\) | ||||
−0.400025 | + | 0.916504i | \(0.630998\pi\) | |||||||
\(80\) | −3.42394 | −0.382809 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −23.9763 | −2.64774 | ||||||||
\(83\) | 4.05475 | 0.445066 | 0.222533 | − | 0.974925i | \(-0.428567\pi\) | ||||
0.222533 | + | 0.974925i | \(0.428567\pi\) | |||||||
\(84\) | 7.34411 | 0.801308 | ||||||||
\(85\) | 2.41242 | 0.261664 | ||||||||
\(86\) | 18.3281 | 1.97637 | ||||||||
\(87\) | 0.697292 | 0.0747575 | ||||||||
\(88\) | 27.2049 | 2.90005 | ||||||||
\(89\) | 3.74013 | 0.396453 | 0.198227 | − | 0.980156i | \(-0.436482\pi\) | ||||
0.198227 | + | 0.980156i | \(0.436482\pi\) | |||||||
\(90\) | −3.35549 | −0.353700 | ||||||||
\(91\) | −1.96997 | −0.206509 | ||||||||
\(92\) | 24.5259 | 2.55701 | ||||||||
\(93\) | 1.51915 | 0.157529 | ||||||||
\(94\) | −13.1693 | −1.35831 | ||||||||
\(95\) | −2.90599 | −0.298148 | ||||||||
\(96\) | −2.42662 | −0.247665 | ||||||||
\(97\) | 2.19386 | 0.222753 | 0.111377 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111377 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(98\) | −7.46532 | −0.754111 | ||||||||
\(99\) | 6.57798 | 0.661112 | ||||||||
\(100\) | −11.3121 | −1.13121 | ||||||||
\(101\) | 4.53311 | 0.451061 | 0.225530 | − | 0.974236i | \(-0.427588\pi\) | ||||
0.225530 | + | 0.974236i | \(0.427588\pi\) | |||||||
\(102\) | −4.11816 | −0.407758 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −4.13575 | −0.405544 | ||||||||
\(105\) | −2.76193 | −0.269537 | ||||||||
\(106\) | 14.4091 | 1.39954 | ||||||||
\(107\) | 0.309436 | 0.0299143 | 0.0149572 | − | 0.999888i | \(-0.495239\pi\) | ||||
0.0149572 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(108\) | 3.72803 | 0.358730 | ||||||||
\(109\) | 3.16102 | 0.302770 | 0.151385 | − | 0.988475i | \(-0.451627\pi\) | ||||
0.151385 | + | 0.988475i | \(0.451627\pi\) | |||||||
\(110\) | −22.0724 | −2.10452 | ||||||||
\(111\) | −8.95694 | −0.850155 | ||||||||
\(112\) | 4.81097 | 0.454594 | ||||||||
\(113\) | 9.15105 | 0.860859 | 0.430429 | − | 0.902624i | \(-0.358362\pi\) | ||||
0.430429 | + | 0.902624i | \(0.358362\pi\) | |||||||
\(114\) | 4.96070 | 0.464612 | ||||||||
\(115\) | −9.22358 | −0.860103 | ||||||||
\(116\) | 2.59953 | 0.241360 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −28.3619 | −2.61093 | ||||||||
\(119\) | −3.38969 | −0.310732 | ||||||||
\(120\) | −5.79839 | −0.529318 | ||||||||
\(121\) | 32.2699 | 2.93362 | ||||||||
\(122\) | 12.9153 | 1.16930 | ||||||||
\(123\) | −10.0180 | −0.903290 | ||||||||
\(124\) | 5.66345 | 0.508593 | ||||||||
\(125\) | 11.2643 | 1.00751 | ||||||||
\(126\) | 4.71479 | 0.420027 | ||||||||
\(127\) | 10.3919 | 0.922131 | 0.461066 | − | 0.887366i | \(-0.347467\pi\) | ||||
0.461066 | + | 0.887366i | \(0.347467\pi\) | |||||||
\(128\) | −20.7363 | −1.83284 | ||||||||
\(129\) | 7.65800 | 0.674249 | ||||||||
\(130\) | 3.35549 | 0.294296 | ||||||||
\(131\) | −16.7622 | −1.46452 | −0.732260 | − | 0.681025i | \(-0.761534\pi\) | ||||
−0.732260 | + | 0.681025i | \(0.761534\pi\) | |||||||
\(132\) | 24.5229 | 2.13445 | ||||||||
\(133\) | 4.08319 | 0.354057 | ||||||||
\(134\) | 9.79836 | 0.846449 | ||||||||
\(135\) | −1.40202 | −0.120666 | ||||||||
\(136\) | −7.11631 | −0.610218 | ||||||||
\(137\) | 0.847367 | 0.0723954 | 0.0361977 | − | 0.999345i | \(-0.488475\pi\) | ||||
0.0361977 | + | 0.999345i | \(0.488475\pi\) | |||||||
\(138\) | 15.7452 | 1.34032 | ||||||||
\(139\) | −15.6706 | −1.32916 | −0.664579 | − | 0.747218i | \(-0.731389\pi\) | ||||
−0.664579 | + | 0.747218i | \(0.731389\pi\) | |||||||
\(140\) | −10.2966 | −0.870219 | ||||||||
\(141\) | −5.50250 | −0.463394 | ||||||||
\(142\) | 37.4215 | 3.14034 | ||||||||
\(143\) | −6.57798 | −0.550079 | ||||||||
\(144\) | 2.44215 | 0.203513 | ||||||||
\(145\) | −0.977615 | −0.0811865 | ||||||||
\(146\) | 29.9369 | 2.47760 | ||||||||
\(147\) | −3.11922 | −0.257269 | ||||||||
\(148\) | −33.3917 | −2.74478 | ||||||||
\(149\) | 22.1349 | 1.81336 | 0.906679 | − | 0.421820i | \(-0.138609\pi\) | ||||
0.906679 | + | 0.421820i | \(0.138609\pi\) | |||||||
\(150\) | −7.26220 | −0.592956 | ||||||||
\(151\) | −19.2801 | −1.56899 | −0.784496 | − | 0.620134i | \(-0.787078\pi\) | ||||
−0.784496 | + | 0.620134i | \(0.787078\pi\) | |||||||
\(152\) | 8.57224 | 0.695301 | ||||||||
\(153\) | −1.72068 | −0.139109 | ||||||||
\(154\) | 31.0138 | 2.49916 | ||||||||
\(155\) | −2.12988 | −0.171076 | ||||||||
\(156\) | −3.72803 | −0.298481 | ||||||||
\(157\) | −20.6178 | −1.64548 | −0.822741 | − | 0.568416i | \(-0.807557\pi\) | ||||
−0.822741 | + | 0.568416i | \(0.807557\pi\) | |||||||
\(158\) | −17.0190 | −1.35396 | ||||||||
\(159\) | 6.02052 | 0.477459 | ||||||||
\(160\) | 3.40216 | 0.268964 | ||||||||
\(161\) | 12.9600 | 1.02139 | ||||||||
\(162\) | 2.39333 | 0.188038 | ||||||||
\(163\) | −20.6759 | −1.61947 | −0.809733 | − | 0.586799i | \(-0.800388\pi\) | ||||
−0.809733 | + | 0.586799i | \(0.800388\pi\) | |||||||
\(164\) | −37.3473 | −2.91633 | ||||||||
\(165\) | −9.22245 | −0.717966 | ||||||||
\(166\) | 9.70435 | 0.753204 | ||||||||
\(167\) | −9.91149 | −0.766974 | −0.383487 | − | 0.923546i | \(-0.625277\pi\) | ||||
−0.383487 | + | 0.923546i | \(0.625277\pi\) | |||||||
\(168\) | 8.14730 | 0.628578 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.77373 | 0.442825 | ||||||||
\(171\) | 2.07272 | 0.158505 | ||||||||
\(172\) | 28.5493 | 2.17686 | ||||||||
\(173\) | −17.7226 | −1.34742 | −0.673711 | − | 0.738995i | \(-0.735301\pi\) | ||||
−0.673711 | + | 0.738995i | \(0.735301\pi\) | |||||||
\(174\) | 1.66885 | 0.126515 | ||||||||
\(175\) | −5.97757 | −0.451862 | ||||||||
\(176\) | 16.0645 | 1.21090 | ||||||||
\(177\) | −11.8504 | −0.890731 | ||||||||
\(178\) | 8.95137 | 0.670934 | ||||||||
\(179\) | −17.0965 | −1.27785 | −0.638927 | − | 0.769267i | \(-0.720621\pi\) | ||||
−0.638927 | + | 0.769267i | \(0.720621\pi\) | |||||||
\(180\) | −5.22676 | −0.389580 | ||||||||
\(181\) | −11.9926 | −0.891401 | −0.445700 | − | 0.895182i | \(-0.647045\pi\) | ||||
−0.445700 | + | 0.895182i | \(0.647045\pi\) | |||||||
\(182\) | −4.71479 | −0.349483 | ||||||||
\(183\) | 5.39639 | 0.398912 | ||||||||
\(184\) | 27.2082 | 2.00582 | ||||||||
\(185\) | 12.5578 | 0.923266 | ||||||||
\(186\) | 3.63583 | 0.266592 | ||||||||
\(187\) | −11.3186 | −0.827699 | ||||||||
\(188\) | −20.5135 | −1.49610 | ||||||||
\(189\) | 1.96997 | 0.143294 | ||||||||
\(190\) | −6.95498 | −0.504568 | ||||||||
\(191\) | −19.2489 | −1.39280 | −0.696401 | − | 0.717653i | \(-0.745216\pi\) | ||||
−0.696401 | + | 0.717653i | \(0.745216\pi\) | |||||||
\(192\) | −10.6920 | −0.771629 | ||||||||
\(193\) | −22.7401 | −1.63687 | −0.818434 | − | 0.574600i | \(-0.805158\pi\) | ||||
−0.818434 | + | 0.574600i | \(0.805158\pi\) | |||||||
\(194\) | 5.25064 | 0.376974 | ||||||||
\(195\) | 1.40202 | 0.100401 | ||||||||
\(196\) | −11.6285 | −0.830610 | ||||||||
\(197\) | −27.3503 | −1.94863 | −0.974316 | − | 0.225186i | \(-0.927701\pi\) | ||||
−0.974316 | + | 0.225186i | \(0.927701\pi\) | |||||||
\(198\) | 15.7433 | 1.11883 | ||||||||
\(199\) | 10.4397 | 0.740050 | 0.370025 | − | 0.929022i | \(-0.379349\pi\) | ||||
0.370025 | + | 0.929022i | \(0.379349\pi\) | |||||||
\(200\) | −12.5493 | −0.887370 | ||||||||
\(201\) | 4.09403 | 0.288770 | ||||||||
\(202\) | 10.8492 | 0.763349 | ||||||||
\(203\) | 1.37364 | 0.0964109 | ||||||||
\(204\) | −6.41475 | −0.449123 | ||||||||
\(205\) | 14.0454 | 0.980971 | ||||||||
\(206\) | −2.39333 | −0.166751 | ||||||||
\(207\) | 6.57879 | 0.457257 | ||||||||
\(208\) | −2.44215 | −0.169333 | ||||||||
\(209\) | 13.6343 | 0.943104 | ||||||||
\(210\) | −6.61022 | −0.456148 | ||||||||
\(211\) | 19.4053 | 1.33591 | 0.667956 | − | 0.744200i | \(-0.267169\pi\) | ||||
0.667956 | + | 0.744200i | \(0.267169\pi\) | |||||||
\(212\) | 22.4447 | 1.54151 | ||||||||
\(213\) | 15.6357 | 1.07134 | ||||||||
\(214\) | 0.740583 | 0.0506252 | ||||||||
\(215\) | −10.7367 | −0.732234 | ||||||||
\(216\) | 4.13575 | 0.281402 | ||||||||
\(217\) | 2.99268 | 0.203157 | ||||||||
\(218\) | 7.56536 | 0.512391 | ||||||||
\(219\) | 12.5085 | 0.845244 | ||||||||
\(220\) | −34.3816 | −2.31800 | ||||||||
\(221\) | 1.72068 | 0.115746 | ||||||||
\(222\) | −21.4369 | −1.43875 | ||||||||
\(223\) | 6.29590 | 0.421604 | 0.210802 | − | 0.977529i | \(-0.432392\pi\) | ||||
0.210802 | + | 0.977529i | \(0.432392\pi\) | |||||||
\(224\) | −4.78036 | −0.319401 | ||||||||
\(225\) | −3.03435 | −0.202290 | ||||||||
\(226\) | 21.9015 | 1.45687 | ||||||||
\(227\) | 20.3748 | 1.35232 | 0.676161 | − | 0.736754i | \(-0.263643\pi\) | ||||
0.676161 | + | 0.736754i | \(0.263643\pi\) | |||||||
\(228\) | 7.72715 | 0.511743 | ||||||||
\(229\) | 24.5363 | 1.62140 | 0.810702 | − | 0.585460i | \(-0.199086\pi\) | ||||
0.810702 | + | 0.585460i | \(0.199086\pi\) | |||||||
\(230\) | −22.0751 | −1.45559 | ||||||||
\(231\) | 12.9584 | 0.852602 | ||||||||
\(232\) | 2.88383 | 0.189332 | ||||||||
\(233\) | −14.6915 | −0.962475 | −0.481237 | − | 0.876590i | \(-0.659813\pi\) | ||||
−0.481237 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(234\) | −2.39333 | −0.156457 | ||||||||
\(235\) | 7.71460 | 0.503245 | ||||||||
\(236\) | −44.1787 | −2.87579 | ||||||||
\(237\) | −7.11099 | −0.461909 | ||||||||
\(238\) | −8.11265 | −0.525865 | ||||||||
\(239\) | −8.86244 | −0.573263 | −0.286632 | − | 0.958041i | \(-0.592536\pi\) | ||||
−0.286632 | + | 0.958041i | \(0.592536\pi\) | |||||||
\(240\) | −3.42394 | −0.221015 | ||||||||
\(241\) | −7.51534 | −0.484106 | −0.242053 | − | 0.970263i | \(-0.577821\pi\) | ||||
−0.242053 | + | 0.970263i | \(0.577821\pi\) | |||||||
\(242\) | 77.2324 | 4.96469 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 20.1179 | 1.28792 | ||||||||
\(245\) | 4.37320 | 0.279393 | ||||||||
\(246\) | −23.9763 | −1.52867 | ||||||||
\(247\) | −2.07272 | −0.131884 | ||||||||
\(248\) | 6.28284 | 0.398960 | ||||||||
\(249\) | 4.05475 | 0.256959 | ||||||||
\(250\) | 26.9592 | 1.70505 | ||||||||
\(251\) | −14.5437 | −0.917991 | −0.458996 | − | 0.888439i | \(-0.651791\pi\) | ||||
−0.458996 | + | 0.888439i | \(0.651791\pi\) | |||||||
\(252\) | 7.34411 | 0.462635 | ||||||||
\(253\) | 43.2752 | 2.72069 | ||||||||
\(254\) | 24.8712 | 1.56056 | ||||||||
\(255\) | 2.41242 | 0.151072 | ||||||||
\(256\) | −28.2447 | −1.76530 | ||||||||
\(257\) | −22.7923 | −1.42175 | −0.710874 | − | 0.703320i | \(-0.751700\pi\) | ||||
−0.710874 | + | 0.703320i | \(0.751700\pi\) | |||||||
\(258\) | 18.3281 | 1.14106 | ||||||||
\(259\) | −17.6449 | −1.09640 | ||||||||
\(260\) | 5.22676 | 0.324150 | ||||||||
\(261\) | 0.697292 | 0.0431613 | ||||||||
\(262\) | −40.1175 | −2.47847 | ||||||||
\(263\) | −2.72920 | −0.168289 | −0.0841447 | − | 0.996454i | \(-0.526816\pi\) | ||||
−0.0841447 | + | 0.996454i | \(0.526816\pi\) | |||||||
\(264\) | 27.2049 | 1.67435 | ||||||||
\(265\) | −8.44088 | −0.518519 | ||||||||
\(266\) | 9.77242 | 0.599186 | ||||||||
\(267\) | 3.74013 | 0.228892 | ||||||||
\(268\) | 15.2627 | 0.932315 | ||||||||
\(269\) | −13.7805 | −0.840214 | −0.420107 | − | 0.907474i | \(-0.638008\pi\) | ||||
−0.420107 | + | 0.907474i | \(0.638008\pi\) | |||||||
\(270\) | −3.35549 | −0.204209 | ||||||||
\(271\) | −8.95832 | −0.544179 | −0.272090 | − | 0.962272i | \(-0.587715\pi\) | ||||
−0.272090 | + | 0.962272i | \(0.587715\pi\) | |||||||
\(272\) | −4.20217 | −0.254794 | ||||||||
\(273\) | −1.96997 | −0.119228 | ||||||||
\(274\) | 2.02803 | 0.122518 | ||||||||
\(275\) | −19.9599 | −1.20363 | ||||||||
\(276\) | 24.5259 | 1.47629 | ||||||||
\(277\) | 16.8977 | 1.01528 | 0.507641 | − | 0.861568i | \(-0.330517\pi\) | ||||
0.507641 | + | 0.861568i | \(0.330517\pi\) | |||||||
\(278\) | −37.5048 | −2.24939 | ||||||||
\(279\) | 1.51915 | 0.0909493 | ||||||||
\(280\) | −11.4227 | −0.682635 | ||||||||
\(281\) | −8.90419 | −0.531180 | −0.265590 | − | 0.964086i | \(-0.585567\pi\) | ||||
−0.265590 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(282\) | −13.1693 | −0.784221 | ||||||||
\(283\) | 15.3626 | 0.913211 | 0.456606 | − | 0.889669i | \(-0.349065\pi\) | ||||
0.456606 | + | 0.889669i | \(0.349065\pi\) | |||||||
\(284\) | 58.2905 | 3.45891 | ||||||||
\(285\) | −2.90599 | −0.172136 | ||||||||
\(286\) | −15.7433 | −0.930920 | ||||||||
\(287\) | −19.7351 | −1.16493 | ||||||||
\(288\) | −2.42662 | −0.142990 | ||||||||
\(289\) | −14.0393 | −0.825839 | ||||||||
\(290\) | −2.33976 | −0.137395 | ||||||||
\(291\) | 2.19386 | 0.128607 | ||||||||
\(292\) | 46.6320 | 2.72893 | ||||||||
\(293\) | −32.2142 | −1.88197 | −0.940987 | − | 0.338442i | \(-0.890100\pi\) | ||||
−0.940987 | + | 0.338442i | \(0.890100\pi\) | |||||||
\(294\) | −7.46532 | −0.435386 | ||||||||
\(295\) | 16.6145 | 0.967332 | ||||||||
\(296\) | −37.0437 | −2.15312 | ||||||||
\(297\) | 6.57798 | 0.381693 | ||||||||
\(298\) | 52.9761 | 3.06882 | ||||||||
\(299\) | −6.57879 | −0.380461 | ||||||||
\(300\) | −11.3121 | −0.653107 | ||||||||
\(301\) | 15.0860 | 0.869544 | ||||||||
\(302\) | −46.1436 | −2.65527 | ||||||||
\(303\) | 4.53311 | 0.260420 | ||||||||
\(304\) | 5.06190 | 0.290320 | ||||||||
\(305\) | −7.56583 | −0.433218 | ||||||||
\(306\) | −4.11816 | −0.235419 | ||||||||
\(307\) | 10.6243 | 0.606359 | 0.303179 | − | 0.952933i | \(-0.401952\pi\) | ||||
0.303179 | + | 0.952933i | \(0.401952\pi\) | |||||||
\(308\) | 48.3094 | 2.75268 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −5.09750 | −0.289519 | ||||||||
\(311\) | 12.9606 | 0.734929 | 0.367464 | − | 0.930038i | \(-0.380226\pi\) | ||||
0.367464 | + | 0.930038i | \(0.380226\pi\) | |||||||
\(312\) | −4.13575 | −0.234141 | ||||||||
\(313\) | 33.1552 | 1.87404 | 0.937022 | − | 0.349272i | \(-0.113571\pi\) | ||||
0.937022 | + | 0.349272i | \(0.113571\pi\) | |||||||
\(314\) | −49.3453 | −2.78472 | ||||||||
\(315\) | −2.76193 | −0.155617 | ||||||||
\(316\) | −26.5100 | −1.49130 | ||||||||
\(317\) | −2.98155 | −0.167460 | −0.0837301 | − | 0.996488i | \(-0.526683\pi\) | ||||
−0.0837301 | + | 0.996488i | \(0.526683\pi\) | |||||||
\(318\) | 14.4091 | 0.808022 | ||||||||
\(319\) | 4.58677 | 0.256810 | ||||||||
\(320\) | 14.9904 | 0.837988 | ||||||||
\(321\) | 0.309436 | 0.0172710 | ||||||||
\(322\) | 31.0176 | 1.72854 | ||||||||
\(323\) | −3.56649 | −0.198445 | ||||||||
\(324\) | 3.72803 | 0.207113 | ||||||||
\(325\) | 3.03435 | 0.168315 | ||||||||
\(326\) | −49.4844 | −2.74069 | ||||||||
\(327\) | 3.16102 | 0.174805 | ||||||||
\(328\) | −41.4318 | −2.28769 | ||||||||
\(329\) | −10.8398 | −0.597616 | ||||||||
\(330\) | −22.0724 | −1.21504 | ||||||||
\(331\) | −9.54196 | −0.524474 | −0.262237 | − | 0.965004i | \(-0.584460\pi\) | ||||
−0.262237 | + | 0.965004i | \(0.584460\pi\) | |||||||
\(332\) | 15.1162 | 0.829611 | ||||||||
\(333\) | −8.95694 | −0.490837 | ||||||||
\(334\) | −23.7215 | −1.29798 | ||||||||
\(335\) | −5.73990 | −0.313604 | ||||||||
\(336\) | 4.81097 | 0.262460 | ||||||||
\(337\) | −16.0039 | −0.871788 | −0.435894 | − | 0.899998i | \(-0.643568\pi\) | ||||
−0.435894 | + | 0.899998i | \(0.643568\pi\) | |||||||
\(338\) | 2.39333 | 0.130180 | ||||||||
\(339\) | 9.15105 | 0.497017 | ||||||||
\(340\) | 8.99359 | 0.487746 | ||||||||
\(341\) | 9.99296 | 0.541149 | ||||||||
\(342\) | 4.96070 | 0.268244 | ||||||||
\(343\) | −19.9346 | −1.07636 | ||||||||
\(344\) | 31.6716 | 1.70762 | ||||||||
\(345\) | −9.22358 | −0.496581 | ||||||||
\(346\) | −42.4160 | −2.28030 | ||||||||
\(347\) | −1.67653 | −0.0900009 | −0.0450004 | − | 0.998987i | \(-0.514329\pi\) | ||||
−0.0450004 | + | 0.998987i | \(0.514329\pi\) | |||||||
\(348\) | 2.59953 | 0.139349 | ||||||||
\(349\) | 29.0703 | 1.55610 | 0.778049 | − | 0.628203i | \(-0.216209\pi\) | ||||
0.778049 | + | 0.628203i | \(0.216209\pi\) | |||||||
\(350\) | −14.3063 | −0.764704 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −15.9622 | −0.850790 | ||||||||
\(353\) | −0.00454881 | −0.000242109 0 | −0.000121054 | − | 1.00000i | \(-0.500039\pi\) | ||||
−0.000121054 | 1.00000i | \(0.500039\pi\) | ||||||||
\(354\) | −28.3619 | −1.50742 | ||||||||
\(355\) | −21.9216 | −1.16348 | ||||||||
\(356\) | 13.9433 | 0.738995 | ||||||||
\(357\) | −3.38969 | −0.179401 | ||||||||
\(358\) | −40.9176 | −2.16256 | ||||||||
\(359\) | 24.8957 | 1.31395 | 0.656973 | − | 0.753914i | \(-0.271837\pi\) | ||||
0.656973 | + | 0.753914i | \(0.271837\pi\) | |||||||
\(360\) | −5.79839 | −0.305602 | ||||||||
\(361\) | −14.7038 | −0.773887 | ||||||||
\(362\) | −28.7022 | −1.50855 | ||||||||
\(363\) | 32.2699 | 1.69373 | ||||||||
\(364\) | −7.34411 | −0.384936 | ||||||||
\(365\) | −17.5371 | −0.917934 | ||||||||
\(366\) | 12.9153 | 0.675095 | ||||||||
\(367\) | −8.61374 | −0.449634 | −0.224817 | − | 0.974401i | \(-0.572178\pi\) | ||||
−0.224817 | + | 0.974401i | \(0.572178\pi\) | |||||||
\(368\) | 16.0664 | 0.837520 | ||||||||
\(369\) | −10.0180 | −0.521515 | ||||||||
\(370\) | 30.0549 | 1.56248 | ||||||||
\(371\) | 11.8603 | 0.615754 | ||||||||
\(372\) | 5.66345 | 0.293636 | ||||||||
\(373\) | 36.6445 | 1.89738 | 0.948690 | − | 0.316208i | \(-0.102410\pi\) | ||||
0.948690 | + | 0.316208i | \(0.102410\pi\) | |||||||
\(374\) | −27.0892 | −1.40075 | ||||||||
\(375\) | 11.2643 | 0.581686 | ||||||||
\(376\) | −22.7570 | −1.17360 | ||||||||
\(377\) | −0.697292 | −0.0359124 | ||||||||
\(378\) | 4.71479 | 0.242503 | ||||||||
\(379\) | −15.9850 | −0.821097 | −0.410548 | − | 0.911839i | \(-0.634663\pi\) | ||||
−0.410548 | + | 0.911839i | \(0.634663\pi\) | |||||||
\(380\) | −10.8336 | −0.555752 | ||||||||
\(381\) | 10.3919 | 0.532393 | ||||||||
\(382\) | −46.0690 | −2.35709 | ||||||||
\(383\) | −14.9441 | −0.763607 | −0.381804 | − | 0.924244i | \(-0.624697\pi\) | ||||
−0.381804 | + | 0.924244i | \(0.624697\pi\) | |||||||
\(384\) | −20.7363 | −1.05819 | ||||||||
\(385\) | −18.1679 | −0.925924 | ||||||||
\(386\) | −54.4246 | −2.77014 | ||||||||
\(387\) | 7.65800 | 0.389278 | ||||||||
\(388\) | 8.17880 | 0.415216 | ||||||||
\(389\) | 15.2501 | 0.773211 | 0.386606 | − | 0.922245i | \(-0.373648\pi\) | ||||
0.386606 | + | 0.922245i | \(0.373648\pi\) | |||||||
\(390\) | 3.35549 | 0.169912 | ||||||||
\(391\) | −11.3200 | −0.572477 | ||||||||
\(392\) | −12.9003 | −0.651564 | ||||||||
\(393\) | −16.7622 | −0.845541 | ||||||||
\(394\) | −65.4584 | −3.29775 | ||||||||
\(395\) | 9.96973 | 0.501632 | ||||||||
\(396\) | 24.5229 | 1.23232 | ||||||||
\(397\) | −34.8612 | −1.74963 | −0.874816 | − | 0.484455i | \(-0.839018\pi\) | ||||
−0.874816 | + | 0.484455i | \(0.839018\pi\) | |||||||
\(398\) | 24.9856 | 1.25242 | ||||||||
\(399\) | 4.08319 | 0.204415 | ||||||||
\(400\) | −7.41035 | −0.370517 | ||||||||
\(401\) | 16.8962 | 0.843755 | 0.421878 | − | 0.906653i | \(-0.361371\pi\) | ||||
0.421878 | + | 0.906653i | \(0.361371\pi\) | |||||||
\(402\) | 9.79836 | 0.488698 | ||||||||
\(403\) | −1.51915 | −0.0756744 | ||||||||
\(404\) | 16.8996 | 0.840785 | ||||||||
\(405\) | −1.40202 | −0.0696668 | ||||||||
\(406\) | 3.28758 | 0.163160 | ||||||||
\(407\) | −58.9186 | −2.92049 | ||||||||
\(408\) | −7.11631 | −0.352310 | ||||||||
\(409\) | 25.0110 | 1.23671 | 0.618356 | − | 0.785898i | \(-0.287799\pi\) | ||||
0.618356 | + | 0.785898i | \(0.287799\pi\) | |||||||
\(410\) | 33.6152 | 1.66014 | ||||||||
\(411\) | 0.847367 | 0.0417975 | ||||||||
\(412\) | −3.72803 | −0.183667 | ||||||||
\(413\) | −23.3450 | −1.14873 | ||||||||
\(414\) | 15.7452 | 0.773835 | ||||||||
\(415\) | −5.68483 | −0.279057 | ||||||||
\(416\) | 2.42662 | 0.118975 | ||||||||
\(417\) | −15.6706 | −0.767390 | ||||||||
\(418\) | 32.6314 | 1.59605 | ||||||||
\(419\) | 23.1170 | 1.12934 | 0.564669 | − | 0.825317i | \(-0.309004\pi\) | ||||
0.564669 | + | 0.825317i | \(0.309004\pi\) | |||||||
\(420\) | −10.2966 | −0.502421 | ||||||||
\(421\) | 21.5315 | 1.04938 | 0.524691 | − | 0.851293i | \(-0.324181\pi\) | ||||
0.524691 | + | 0.851293i | \(0.324181\pi\) | |||||||
\(422\) | 46.4432 | 2.26082 | ||||||||
\(423\) | −5.50250 | −0.267541 | ||||||||
\(424\) | 24.8994 | 1.20922 | ||||||||
\(425\) | 5.22114 | 0.253263 | ||||||||
\(426\) | 37.4215 | 1.81308 | ||||||||
\(427\) | 10.6307 | 0.514457 | ||||||||
\(428\) | 1.15359 | 0.0557607 | ||||||||
\(429\) | −6.57798 | −0.317588 | ||||||||
\(430\) | −25.6964 | −1.23919 | ||||||||
\(431\) | 3.19695 | 0.153992 | 0.0769959 | − | 0.997031i | \(-0.475467\pi\) | ||||
0.0769959 | + | 0.997031i | \(0.475467\pi\) | |||||||
\(432\) | 2.44215 | 0.117498 | ||||||||
\(433\) | −3.18997 | −0.153300 | −0.0766501 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766501 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(434\) | 7.16248 | 0.343810 | ||||||||
\(435\) | −0.977615 | −0.0468731 | ||||||||
\(436\) | 11.7844 | 0.564369 | ||||||||
\(437\) | 13.6360 | 0.652297 | ||||||||
\(438\) | 29.9369 | 1.43044 | ||||||||
\(439\) | 35.8403 | 1.71057 | 0.855283 | − | 0.518161i | \(-0.173383\pi\) | ||||
0.855283 | + | 0.518161i | \(0.173383\pi\) | |||||||
\(440\) | −38.1417 | −1.81834 | ||||||||
\(441\) | −3.11922 | −0.148534 | ||||||||
\(442\) | 4.11816 | 0.195881 | ||||||||
\(443\) | 21.8064 | 1.03605 | 0.518026 | − | 0.855365i | \(-0.326667\pi\) | ||||
0.518026 | + | 0.855365i | \(0.326667\pi\) | |||||||
\(444\) | −33.3917 | −1.58470 | ||||||||
\(445\) | −5.24373 | −0.248577 | ||||||||
\(446\) | 15.0682 | 0.713498 | ||||||||
\(447\) | 22.1349 | 1.04694 | ||||||||
\(448\) | −21.0629 | −0.995130 | ||||||||
\(449\) | 4.63333 | 0.218660 | 0.109330 | − | 0.994005i | \(-0.465129\pi\) | ||||
0.109330 | + | 0.994005i | \(0.465129\pi\) | |||||||
\(450\) | −7.26220 | −0.342343 | ||||||||
\(451\) | −65.8980 | −3.10302 | ||||||||
\(452\) | 34.1154 | 1.60465 | ||||||||
\(453\) | −19.2801 | −0.905858 | ||||||||
\(454\) | 48.7636 | 2.28859 | ||||||||
\(455\) | 2.76193 | 0.129481 | ||||||||
\(456\) | 8.57224 | 0.401432 | ||||||||
\(457\) | −26.2234 | −1.22668 | −0.613341 | − | 0.789819i | \(-0.710175\pi\) | ||||
−0.613341 | + | 0.789819i | \(0.710175\pi\) | |||||||
\(458\) | 58.7234 | 2.74397 | ||||||||
\(459\) | −1.72068 | −0.0803145 | ||||||||
\(460\) | −34.3858 | −1.60325 | ||||||||
\(461\) | −21.4423 | −0.998666 | −0.499333 | − | 0.866410i | \(-0.666422\pi\) | ||||
−0.499333 | + | 0.866410i | \(0.666422\pi\) | |||||||
\(462\) | 31.0138 | 1.44289 | ||||||||
\(463\) | 3.85624 | 0.179215 | 0.0896074 | − | 0.995977i | \(-0.471439\pi\) | ||||
0.0896074 | + | 0.995977i | \(0.471439\pi\) | |||||||
\(464\) | 1.70290 | 0.0790549 | ||||||||
\(465\) | −2.12988 | −0.0987707 | ||||||||
\(466\) | −35.1617 | −1.62884 | ||||||||
\(467\) | −10.5382 | −0.487648 | −0.243824 | − | 0.969820i | \(-0.578402\pi\) | ||||
−0.243824 | + | 0.969820i | \(0.578402\pi\) | |||||||
\(468\) | −3.72803 | −0.172328 | ||||||||
\(469\) | 8.06511 | 0.372412 | ||||||||
\(470\) | 18.4636 | 0.851662 | ||||||||
\(471\) | −20.6178 | −0.950020 | ||||||||
\(472\) | −49.0103 | −2.25588 | ||||||||
\(473\) | 50.3742 | 2.31621 | ||||||||
\(474\) | −17.0190 | −0.781706 | ||||||||
\(475\) | −6.28934 | −0.288575 | ||||||||
\(476\) | −12.6369 | −0.579210 | ||||||||
\(477\) | 6.02052 | 0.275661 | ||||||||
\(478\) | −21.2107 | −0.970157 | ||||||||
\(479\) | −37.5474 | −1.71559 | −0.857793 | − | 0.513996i | \(-0.828165\pi\) | ||||
−0.857793 | + | 0.513996i | \(0.828165\pi\) | |||||||
\(480\) | 3.40216 | 0.155287 | ||||||||
\(481\) | 8.95694 | 0.408401 | ||||||||
\(482\) | −17.9867 | −0.819271 | ||||||||
\(483\) | 12.9600 | 0.589701 | ||||||||
\(484\) | 120.303 | 5.46832 | ||||||||
\(485\) | −3.07584 | −0.139667 | ||||||||
\(486\) | 2.39333 | 0.108564 | ||||||||
\(487\) | −34.2698 | −1.55291 | −0.776457 | − | 0.630170i | \(-0.782985\pi\) | ||||
−0.776457 | + | 0.630170i | \(0.782985\pi\) | |||||||
\(488\) | 22.3181 | 1.01029 | ||||||||
\(489\) | −20.6759 | −0.934999 | ||||||||
\(490\) | 10.4665 | 0.472829 | ||||||||
\(491\) | 4.81346 | 0.217228 | 0.108614 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108614 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(492\) | −37.3473 | −1.68375 | ||||||||
\(493\) | −1.19982 | −0.0540370 | ||||||||
\(494\) | −4.96070 | −0.223192 | ||||||||
\(495\) | −9.22245 | −0.414518 | ||||||||
\(496\) | 3.71001 | 0.166584 | ||||||||
\(497\) | 30.8019 | 1.38166 | ||||||||
\(498\) | 9.70435 | 0.434862 | ||||||||
\(499\) | 9.73682 | 0.435880 | 0.217940 | − | 0.975962i | \(-0.430066\pi\) | ||||
0.217940 | + | 0.975962i | \(0.430066\pi\) | |||||||
\(500\) | 41.9936 | 1.87801 | ||||||||
\(501\) | −9.91149 | −0.442813 | ||||||||
\(502\) | −34.8079 | −1.55355 | ||||||||
\(503\) | −25.4110 | −1.13302 | −0.566511 | − | 0.824054i | \(-0.691707\pi\) | ||||
−0.566511 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(504\) | 8.14730 | 0.362910 | ||||||||
\(505\) | −6.35549 | −0.282816 | ||||||||
\(506\) | 103.572 | 4.60433 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 38.7413 | 1.71887 | ||||||||
\(509\) | 14.8081 | 0.656357 | 0.328179 | − | 0.944616i | \(-0.393565\pi\) | ||||
0.328179 | + | 0.944616i | \(0.393565\pi\) | |||||||
\(510\) | 5.77373 | 0.255665 | ||||||||
\(511\) | 24.6413 | 1.09007 | ||||||||
\(512\) | −26.1265 | −1.15464 | ||||||||
\(513\) | 2.07272 | 0.0915127 | ||||||||
\(514\) | −54.5496 | −2.40608 | ||||||||
\(515\) | 1.40202 | 0.0617803 | ||||||||
\(516\) | 28.5493 | 1.25681 | ||||||||
\(517\) | −36.1954 | −1.59187 | ||||||||
\(518\) | −42.2301 | −1.85548 | ||||||||
\(519\) | −17.7226 | −0.777935 | ||||||||
\(520\) | 5.79839 | 0.254276 | ||||||||
\(521\) | −12.6812 | −0.555576 | −0.277788 | − | 0.960642i | \(-0.589601\pi\) | ||||
−0.277788 | + | 0.960642i | \(0.589601\pi\) | |||||||
\(522\) | 1.66885 | 0.0730436 | ||||||||
\(523\) | −11.3759 | −0.497432 | −0.248716 | − | 0.968576i | \(-0.580009\pi\) | ||||
−0.248716 | + | 0.968576i | \(0.580009\pi\) | |||||||
\(524\) | −62.4900 | −2.72989 | ||||||||
\(525\) | −5.97757 | −0.260883 | ||||||||
\(526\) | −6.53187 | −0.284803 | ||||||||
\(527\) | −2.61398 | −0.113867 | ||||||||
\(528\) | 16.0645 | 0.699116 | ||||||||
\(529\) | 20.2805 | 0.881759 | ||||||||
\(530\) | −20.2018 | −0.877511 | ||||||||
\(531\) | −11.8504 | −0.514264 | ||||||||
\(532\) | 15.2223 | 0.659969 | ||||||||
\(533\) | 10.0180 | 0.433926 | ||||||||
\(534\) | 8.95137 | 0.387364 | ||||||||
\(535\) | −0.433835 | −0.0187563 | ||||||||
\(536\) | 16.9319 | 0.731345 | ||||||||
\(537\) | −17.0965 | −0.737769 | ||||||||
\(538\) | −32.9814 | −1.42193 | ||||||||
\(539\) | −20.5182 | −0.883780 | ||||||||
\(540\) | −5.22676 | −0.224924 | ||||||||
\(541\) | 16.3771 | 0.704107 | 0.352054 | − | 0.935980i | \(-0.385483\pi\) | ||||
0.352054 | + | 0.935980i | \(0.385483\pi\) | |||||||
\(542\) | −21.4402 | −0.920937 | ||||||||
\(543\) | −11.9926 | −0.514651 | ||||||||
\(544\) | 4.17543 | 0.179020 | ||||||||
\(545\) | −4.43180 | −0.189837 | ||||||||
\(546\) | −4.71479 | −0.201774 | ||||||||
\(547\) | 24.3646 | 1.04176 | 0.520878 | − | 0.853631i | \(-0.325604\pi\) | ||||
0.520878 | + | 0.853631i | \(0.325604\pi\) | |||||||
\(548\) | 3.15901 | 0.134946 | ||||||||
\(549\) | 5.39639 | 0.230312 | ||||||||
\(550\) | −47.7706 | −2.03695 | ||||||||
\(551\) | 1.44529 | 0.0615714 | ||||||||
\(552\) | 27.2082 | 1.15806 | ||||||||
\(553\) | −14.0084 | −0.595699 | ||||||||
\(554\) | 40.4417 | 1.71820 | ||||||||
\(555\) | 12.5578 | 0.533048 | ||||||||
\(556\) | −58.4203 | −2.47757 | ||||||||
\(557\) | 27.0486 | 1.14609 | 0.573044 | − | 0.819525i | \(-0.305762\pi\) | ||||
0.573044 | + | 0.819525i | \(0.305762\pi\) | |||||||
\(558\) | 3.63583 | 0.153917 | ||||||||
\(559\) | −7.65800 | −0.323899 | ||||||||
\(560\) | −6.74507 | −0.285031 | ||||||||
\(561\) | −11.3186 | −0.477872 | ||||||||
\(562\) | −21.3107 | −0.898937 | ||||||||
\(563\) | −26.4163 | −1.11331 | −0.556657 | − | 0.830742i | \(-0.687916\pi\) | ||||
−0.556657 | + | 0.830742i | \(0.687916\pi\) | |||||||
\(564\) | −20.5135 | −0.863774 | ||||||||
\(565\) | −12.8299 | −0.539759 | ||||||||
\(566\) | 36.7678 | 1.54546 | ||||||||
\(567\) | 1.96997 | 0.0827310 | ||||||||
\(568\) | 64.6655 | 2.71330 | ||||||||
\(569\) | −35.8171 | −1.50153 | −0.750766 | − | 0.660569i | \(-0.770315\pi\) | ||||
−0.750766 | + | 0.660569i | \(0.770315\pi\) | |||||||
\(570\) | −6.95498 | −0.291312 | ||||||||
\(571\) | 18.6546 | 0.780669 | 0.390334 | − | 0.920673i | \(-0.372359\pi\) | ||||
0.390334 | + | 0.920673i | \(0.372359\pi\) | |||||||
\(572\) | −24.5229 | −1.02536 | ||||||||
\(573\) | −19.2489 | −0.804134 | ||||||||
\(574\) | −47.2326 | −1.97145 | ||||||||
\(575\) | −19.9623 | −0.832487 | ||||||||
\(576\) | −10.6920 | −0.445500 | ||||||||
\(577\) | 20.1123 | 0.837288 | 0.418644 | − | 0.908151i | \(-0.362506\pi\) | ||||
0.418644 | + | 0.908151i | \(0.362506\pi\) | |||||||
\(578\) | −33.6006 | −1.39760 | ||||||||
\(579\) | −22.7401 | −0.945047 | ||||||||
\(580\) | −3.64458 | −0.151333 | ||||||||
\(581\) | 7.98773 | 0.331387 | ||||||||
\(582\) | 5.25064 | 0.217646 | ||||||||
\(583\) | 39.6029 | 1.64018 | ||||||||
\(584\) | 51.7319 | 2.14068 | ||||||||
\(585\) | 1.40202 | 0.0579663 | ||||||||
\(586\) | −77.0993 | −3.18494 | ||||||||
\(587\) | 16.7804 | 0.692602 | 0.346301 | − | 0.938124i | \(-0.387438\pi\) | ||||
0.346301 | + | 0.938124i | \(0.387438\pi\) | |||||||
\(588\) | −11.6285 | −0.479553 | ||||||||
\(589\) | 3.14877 | 0.129743 | ||||||||
\(590\) | 39.7639 | 1.63706 | ||||||||
\(591\) | −27.3503 | −1.12504 | ||||||||
\(592\) | −21.8742 | −0.899025 | ||||||||
\(593\) | 7.76849 | 0.319014 | 0.159507 | − | 0.987197i | \(-0.449010\pi\) | ||||
0.159507 | + | 0.987197i | \(0.449010\pi\) | |||||||
\(594\) | 15.7433 | 0.645955 | ||||||||
\(595\) | 4.75240 | 0.194830 | ||||||||
\(596\) | 82.5195 | 3.38013 | ||||||||
\(597\) | 10.4397 | 0.427268 | ||||||||
\(598\) | −15.7452 | −0.643870 | ||||||||
\(599\) | −1.73615 | −0.0709371 | −0.0354685 | − | 0.999371i | \(-0.511292\pi\) | ||||
−0.0354685 | + | 0.999371i | \(0.511292\pi\) | |||||||
\(600\) | −12.5493 | −0.512323 | ||||||||
\(601\) | −9.81766 | −0.400471 | −0.200235 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200235 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(602\) | 36.1059 | 1.47157 | ||||||||
\(603\) | 4.09403 | 0.166722 | ||||||||
\(604\) | −71.8768 | −2.92462 | ||||||||
\(605\) | −45.2429 | −1.83939 | ||||||||
\(606\) | 10.8492 | 0.440720 | ||||||||
\(607\) | 34.0658 | 1.38269 | 0.691344 | − | 0.722526i | \(-0.257019\pi\) | ||||
0.691344 | + | 0.722526i | \(0.257019\pi\) | |||||||
\(608\) | −5.02969 | −0.203981 | ||||||||
\(609\) | 1.37364 | 0.0556629 | ||||||||
\(610\) | −18.1075 | −0.733152 | ||||||||
\(611\) | 5.50250 | 0.222607 | ||||||||
\(612\) | −6.41475 | −0.259301 | ||||||||
\(613\) | 24.0149 | 0.969951 | 0.484976 | − | 0.874528i | \(-0.338828\pi\) | ||||
0.484976 | + | 0.874528i | \(0.338828\pi\) | |||||||
\(614\) | 25.4274 | 1.02617 | ||||||||
\(615\) | 14.0454 | 0.566364 | ||||||||
\(616\) | 53.5928 | 2.15932 | ||||||||
\(617\) | 6.66177 | 0.268193 | 0.134096 | − | 0.990968i | \(-0.457187\pi\) | ||||
0.134096 | + | 0.990968i | \(0.457187\pi\) | |||||||
\(618\) | −2.39333 | −0.0962739 | ||||||||
\(619\) | 37.9680 | 1.52606 | 0.763032 | − | 0.646360i | \(-0.223710\pi\) | ||||
0.763032 | + | 0.646360i | \(0.223710\pi\) | |||||||
\(620\) | −7.94025 | −0.318888 | ||||||||
\(621\) | 6.57879 | 0.263998 | ||||||||
\(622\) | 31.0190 | 1.24375 | ||||||||
\(623\) | 7.36795 | 0.295191 | ||||||||
\(624\) | −2.44215 | −0.0977644 | ||||||||
\(625\) | −0.620999 | −0.0248399 | ||||||||
\(626\) | 79.3514 | 3.17152 | ||||||||
\(627\) | 13.6343 | 0.544501 | ||||||||
\(628\) | −76.8640 | −3.06721 | ||||||||
\(629\) | 15.4120 | 0.614518 | ||||||||
\(630\) | −6.61022 | −0.263357 | ||||||||
\(631\) | −14.7677 | −0.587894 | −0.293947 | − | 0.955822i | \(-0.594969\pi\) | ||||
−0.293947 | + | 0.955822i | \(0.594969\pi\) | |||||||
\(632\) | −29.4093 | −1.16984 | ||||||||
\(633\) | 19.4053 | 0.771290 | ||||||||
\(634\) | −7.13582 | −0.283400 | ||||||||
\(635\) | −14.5696 | −0.578177 | ||||||||
\(636\) | 22.4447 | 0.889990 | ||||||||
\(637\) | 3.11922 | 0.123588 | ||||||||
\(638\) | 10.9777 | 0.434610 | ||||||||
\(639\) | 15.6357 | 0.618540 | ||||||||
\(640\) | 29.0726 | 1.14920 | ||||||||
\(641\) | −10.5131 | −0.415244 | −0.207622 | − | 0.978209i | \(-0.566572\pi\) | ||||
−0.207622 | + | 0.978209i | \(0.566572\pi\) | |||||||
\(642\) | 0.740583 | 0.0292285 | ||||||||
\(643\) | 15.2864 | 0.602836 | 0.301418 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(644\) | 48.3153 | 1.90389 | ||||||||
\(645\) | −10.7367 | −0.422755 | ||||||||
\(646\) | −8.53578 | −0.335836 | ||||||||
\(647\) | 27.1963 | 1.06920 | 0.534598 | − | 0.845107i | \(-0.320463\pi\) | ||||
0.534598 | + | 0.845107i | \(0.320463\pi\) | |||||||
\(648\) | 4.13575 | 0.162468 | ||||||||
\(649\) | −77.9518 | −3.05988 | ||||||||
\(650\) | 7.26220 | 0.284847 | ||||||||
\(651\) | 2.99268 | 0.117293 | ||||||||
\(652\) | −77.0806 | −3.01871 | ||||||||
\(653\) | 9.22026 | 0.360817 | 0.180408 | − | 0.983592i | \(-0.442258\pi\) | ||||
0.180408 | + | 0.983592i | \(0.442258\pi\) | |||||||
\(654\) | 7.56536 | 0.295829 | ||||||||
\(655\) | 23.5009 | 0.918256 | ||||||||
\(656\) | −24.4654 | −0.955215 | ||||||||
\(657\) | 12.5085 | 0.488002 | ||||||||
\(658\) | −25.9431 | −1.01137 | ||||||||
\(659\) | 40.4699 | 1.57648 | 0.788242 | − | 0.615366i | \(-0.210992\pi\) | ||||
0.788242 | + | 0.615366i | \(0.210992\pi\) | |||||||
\(660\) | −34.3816 | −1.33830 | ||||||||
\(661\) | 0.625564 | 0.0243316 | 0.0121658 | − | 0.999926i | \(-0.496127\pi\) | ||||
0.0121658 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(662\) | −22.8371 | −0.887588 | ||||||||
\(663\) | 1.72068 | 0.0668257 | ||||||||
\(664\) | 16.7694 | 0.650780 | ||||||||
\(665\) | −5.72470 | −0.221994 | ||||||||
\(666\) | −21.4369 | −0.830663 | ||||||||
\(667\) | 4.58734 | 0.177622 | ||||||||
\(668\) | −36.9504 | −1.42965 | ||||||||
\(669\) | 6.29590 | 0.243413 | ||||||||
\(670\) | −13.7375 | −0.530725 | ||||||||
\(671\) | 35.4973 | 1.37036 | ||||||||
\(672\) | −4.78036 | −0.184406 | ||||||||
\(673\) | 0.191479 | 0.00738099 | 0.00369050 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369050 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(674\) | −38.3026 | −1.47536 | ||||||||
\(675\) | −3.03435 | −0.116792 | ||||||||
\(676\) | 3.72803 | 0.143386 | ||||||||
\(677\) | −43.2058 | −1.66053 | −0.830266 | − | 0.557367i | \(-0.811812\pi\) | ||||
−0.830266 | + | 0.557367i | \(0.811812\pi\) | |||||||
\(678\) | 21.9015 | 0.841122 | ||||||||
\(679\) | 4.32185 | 0.165857 | ||||||||
\(680\) | 9.97719 | 0.382608 | ||||||||
\(681\) | 20.3748 | 0.780763 | ||||||||
\(682\) | 23.9165 | 0.915808 | ||||||||
\(683\) | 1.98340 | 0.0758926 | 0.0379463 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379463 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(684\) | 7.72715 | 0.295455 | ||||||||
\(685\) | −1.18802 | −0.0453920 | ||||||||
\(686\) | −47.7100 | −1.82158 | ||||||||
\(687\) | 24.5363 | 0.936118 | ||||||||
\(688\) | 18.7020 | 0.713008 | ||||||||
\(689\) | −6.02052 | −0.229364 | ||||||||
\(690\) | −22.0751 | −0.840383 | ||||||||
\(691\) | −29.4304 | −1.11958 | −0.559792 | − | 0.828633i | \(-0.689119\pi\) | ||||
−0.559792 | + | 0.828633i | \(0.689119\pi\) | |||||||
\(692\) | −66.0703 | −2.51162 | ||||||||
\(693\) | 12.9584 | 0.492250 | ||||||||
\(694\) | −4.01249 | −0.152312 | ||||||||
\(695\) | 21.9704 | 0.833384 | ||||||||
\(696\) | 2.88383 | 0.109311 | ||||||||
\(697\) | 17.2377 | 0.652926 | ||||||||
\(698\) | 69.5749 | 2.63345 | ||||||||
\(699\) | −14.6915 | −0.555685 | ||||||||
\(700\) | −22.2846 | −0.842278 | ||||||||
\(701\) | −13.8461 | −0.522958 | −0.261479 | − | 0.965209i | \(-0.584210\pi\) | ||||
−0.261479 | + | 0.965209i | \(0.584210\pi\) | |||||||
\(702\) | −2.39333 | −0.0903304 | ||||||||
\(703\) | −18.5652 | −0.700200 | ||||||||
\(704\) | −70.3318 | −2.65073 | ||||||||
\(705\) | 7.71460 | 0.290549 | ||||||||
\(706\) | −0.0108868 | −0.000409730 0 | ||||||||
\(707\) | 8.93008 | 0.335850 | ||||||||
\(708\) | −44.1787 | −1.66034 | ||||||||
\(709\) | 39.0064 | 1.46492 | 0.732458 | − | 0.680812i | \(-0.238373\pi\) | ||||
0.732458 | + | 0.680812i | \(0.238373\pi\) | |||||||
\(710\) | −52.4656 | −1.96900 | ||||||||
\(711\) | −7.11099 | −0.266683 | ||||||||
\(712\) | 15.4682 | 0.579697 | ||||||||
\(713\) | 9.99418 | 0.374285 | ||||||||
\(714\) | −8.11265 | −0.303608 | ||||||||
\(715\) | 9.22245 | 0.344900 | ||||||||
\(716\) | −63.7364 | −2.38194 | ||||||||
\(717\) | −8.86244 | −0.330974 | ||||||||
\(718\) | 59.5837 | 2.22364 | ||||||||
\(719\) | −28.5523 | −1.06482 | −0.532410 | − | 0.846487i | \(-0.678714\pi\) | ||||
−0.532410 | + | 0.846487i | \(0.678714\pi\) | |||||||
\(720\) | −3.42394 | −0.127603 | ||||||||
\(721\) | −1.96997 | −0.0733655 | ||||||||
\(722\) | −35.1912 | −1.30968 | ||||||||
\(723\) | −7.51534 | −0.279499 | ||||||||
\(724\) | −44.7087 | −1.66159 | ||||||||
\(725\) | −2.11583 | −0.0785798 | ||||||||
\(726\) | 77.2324 | 2.86636 | ||||||||
\(727\) | 33.2187 | 1.23201 | 0.616006 | − | 0.787741i | \(-0.288750\pi\) | ||||
0.616006 | + | 0.787741i | \(0.288750\pi\) | |||||||
\(728\) | −8.14730 | −0.301959 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −41.9721 | −1.55346 | ||||||||
\(731\) | −13.1770 | −0.487368 | ||||||||
\(732\) | 20.1179 | 0.743579 | ||||||||
\(733\) | 48.4551 | 1.78973 | 0.894864 | − | 0.446338i | \(-0.147272\pi\) | ||||
0.894864 | + | 0.446338i | \(0.147272\pi\) | |||||||
\(734\) | −20.6155 | −0.760933 | ||||||||
\(735\) | 4.37320 | 0.161308 | ||||||||
\(736\) | −15.9642 | −0.588448 | ||||||||
\(737\) | 26.9304 | 0.991995 | ||||||||
\(738\) | −23.9763 | −0.882580 | ||||||||
\(739\) | −30.5567 | −1.12405 | −0.562024 | − | 0.827121i | \(-0.689977\pi\) | ||||
−0.562024 | + | 0.827121i | \(0.689977\pi\) | |||||||
\(740\) | 46.8158 | 1.72098 | ||||||||
\(741\) | −2.07272 | −0.0761432 | ||||||||
\(742\) | 28.3855 | 1.04206 | ||||||||
\(743\) | 48.9834 | 1.79703 | 0.898513 | − | 0.438947i | \(-0.144648\pi\) | ||||
0.898513 | + | 0.438947i | \(0.144648\pi\) | |||||||
\(744\) | 6.28284 | 0.230340 | ||||||||
\(745\) | −31.0335 | −1.13698 | ||||||||
\(746\) | 87.7024 | 3.21101 | ||||||||
\(747\) | 4.05475 | 0.148355 | ||||||||
\(748\) | −42.1961 | −1.54284 | ||||||||
\(749\) | 0.609580 | 0.0222736 | ||||||||
\(750\) | 26.9592 | 0.984410 | ||||||||
\(751\) | 18.8810 | 0.688979 | 0.344489 | − | 0.938790i | \(-0.388052\pi\) | ||||
0.344489 | + | 0.938790i | \(0.388052\pi\) | |||||||
\(752\) | −13.4380 | −0.490032 | ||||||||
\(753\) | −14.5437 | −0.530002 | ||||||||
\(754\) | −1.66885 | −0.0607759 | ||||||||
\(755\) | 27.0310 | 0.983759 | ||||||||
\(756\) | 7.34411 | 0.267103 | ||||||||
\(757\) | 37.6388 | 1.36801 | 0.684003 | − | 0.729479i | \(-0.260238\pi\) | ||||
0.684003 | + | 0.729479i | \(0.260238\pi\) | |||||||
\(758\) | −38.2575 | −1.38957 | ||||||||
\(759\) | 43.2752 | 1.57079 | ||||||||
\(760\) | −12.0184 | −0.435954 | ||||||||
\(761\) | −19.3933 | −0.703008 | −0.351504 | − | 0.936186i | \(-0.614330\pi\) | ||||
−0.351504 | + | 0.936186i | \(0.614330\pi\) | |||||||
\(762\) | 24.8712 | 0.900990 | ||||||||
\(763\) | 6.22711 | 0.225436 | ||||||||
\(764\) | −71.7605 | −2.59620 | ||||||||
\(765\) | 2.41242 | 0.0872214 | ||||||||
\(766\) | −35.7661 | −1.29228 | ||||||||
\(767\) | 11.8504 | 0.427894 | ||||||||
\(768\) | −28.2447 | −1.01919 | ||||||||
\(769\) | 25.2397 | 0.910166 | 0.455083 | − | 0.890449i | \(-0.349610\pi\) | ||||
0.455083 | + | 0.890449i | \(0.349610\pi\) | |||||||
\(770\) | −43.4819 | −1.56698 | ||||||||
\(771\) | −22.7923 | −0.820846 | ||||||||
\(772\) | −84.7758 | −3.05115 | ||||||||
\(773\) | −10.0563 | −0.361700 | −0.180850 | − | 0.983511i | \(-0.557885\pi\) | ||||
−0.180850 | + | 0.983511i | \(0.557885\pi\) | |||||||
\(774\) | 18.3281 | 0.658791 | ||||||||
\(775\) | −4.60964 | −0.165583 | ||||||||
\(776\) | 9.07328 | 0.325712 | ||||||||
\(777\) | −17.6449 | −0.633007 | ||||||||
\(778\) | 36.4985 | 1.30854 | ||||||||
\(779\) | −20.7644 | −0.743962 | ||||||||
\(780\) | 5.22676 | 0.187148 | ||||||||
\(781\) | 102.852 | 3.68032 | ||||||||
\(782\) | −27.0925 | −0.968826 | ||||||||
\(783\) | 0.697292 | 0.0249192 | ||||||||
\(784\) | −7.61762 | −0.272058 | ||||||||
\(785\) | 28.9066 | 1.03172 | ||||||||
\(786\) | −40.1175 | −1.43094 | ||||||||
\(787\) | −39.6445 | −1.41317 | −0.706586 | − | 0.707627i | \(-0.749766\pi\) | ||||
−0.706586 | + | 0.707627i | \(0.749766\pi\) | |||||||
\(788\) | −101.963 | −3.63228 | ||||||||
\(789\) | −2.72920 | −0.0971620 | ||||||||
\(790\) | 23.8609 | 0.848932 | ||||||||
\(791\) | 18.0273 | 0.640977 | ||||||||
\(792\) | 27.2049 | 0.966684 | ||||||||
\(793\) | −5.39639 | −0.191631 | ||||||||
\(794\) | −83.4343 | −2.96097 | ||||||||
\(795\) | −8.44088 | −0.299367 | ||||||||
\(796\) | 38.9195 | 1.37946 | ||||||||
\(797\) | 2.50007 | 0.0885569 | 0.0442784 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442784 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(798\) | 9.77242 | 0.345940 | ||||||||
\(799\) | 9.46805 | 0.334956 | ||||||||
\(800\) | 7.36320 | 0.260328 | ||||||||
\(801\) | 3.74013 | 0.132151 | ||||||||
\(802\) | 40.4382 | 1.42792 | ||||||||
\(803\) | 82.2805 | 2.90362 | ||||||||
\(804\) | 15.2627 | 0.538272 | ||||||||
\(805\) | −18.1702 | −0.640414 | ||||||||
\(806\) | −3.63583 | −0.128067 | ||||||||
\(807\) | −13.7805 | −0.485098 | ||||||||
\(808\) | 18.7478 | 0.659545 | ||||||||
\(809\) | −10.7324 | −0.377332 | −0.188666 | − | 0.982041i | \(-0.560416\pi\) | ||||
−0.188666 | + | 0.982041i | \(0.560416\pi\) | |||||||
\(810\) | −3.35549 | −0.117900 | ||||||||
\(811\) | −18.9480 | −0.665354 | −0.332677 | − | 0.943041i | \(-0.607952\pi\) | ||||
−0.332677 | + | 0.943041i | \(0.607952\pi\) | |||||||
\(812\) | 5.12099 | 0.179711 | ||||||||
\(813\) | −8.95832 | −0.314182 | ||||||||
\(814\) | −141.012 | −4.94245 | ||||||||
\(815\) | 28.9880 | 1.01541 | ||||||||
\(816\) | −4.20217 | −0.147105 | ||||||||
\(817\) | 15.8729 | 0.555321 | ||||||||
\(818\) | 59.8595 | 2.09294 | ||||||||
\(819\) | −1.96997 | −0.0688363 | ||||||||
\(820\) | 52.3616 | 1.82855 | ||||||||
\(821\) | 12.8088 | 0.447030 | 0.223515 | − | 0.974700i | \(-0.428247\pi\) | ||||
0.223515 | + | 0.974700i | \(0.428247\pi\) | |||||||
\(822\) | 2.02803 | 0.0707356 | ||||||||
\(823\) | −29.5627 | −1.03049 | −0.515246 | − | 0.857043i | \(-0.672299\pi\) | ||||
−0.515246 | + | 0.857043i | \(0.672299\pi\) | |||||||
\(824\) | −4.13575 | −0.144076 | ||||||||
\(825\) | −19.9599 | −0.694914 | ||||||||
\(826\) | −55.8722 | −1.94404 | ||||||||
\(827\) | −29.9252 | −1.04060 | −0.520300 | − | 0.853983i | \(-0.674180\pi\) | ||||
−0.520300 | + | 0.853983i | \(0.674180\pi\) | |||||||
\(828\) | 24.5259 | 0.852335 | ||||||||
\(829\) | −0.595191 | −0.0206718 | −0.0103359 | − | 0.999947i | \(-0.503290\pi\) | ||||
−0.0103359 | + | 0.999947i | \(0.503290\pi\) | |||||||
\(830\) | −13.6057 | −0.472260 | ||||||||
\(831\) | 16.8977 | 0.586174 | ||||||||
\(832\) | 10.6920 | 0.370679 | ||||||||
\(833\) | 5.36718 | 0.185962 | ||||||||
\(834\) | −37.5048 | −1.29869 | ||||||||
\(835\) | 13.8961 | 0.480894 | ||||||||
\(836\) | 50.8291 | 1.75796 | ||||||||
\(837\) | 1.51915 | 0.0525096 | ||||||||
\(838\) | 55.3266 | 1.91123 | ||||||||
\(839\) | 26.2642 | 0.906739 | 0.453370 | − | 0.891323i | \(-0.350222\pi\) | ||||
0.453370 | + | 0.891323i | \(0.350222\pi\) | |||||||
\(840\) | −11.4227 | −0.394119 | ||||||||
\(841\) | −28.5138 | −0.983234 | ||||||||
\(842\) | 51.5321 | 1.77591 | ||||||||
\(843\) | −8.90419 | −0.306677 | ||||||||
\(844\) | 72.3434 | 2.49016 | ||||||||
\(845\) | −1.40202 | −0.0482309 | ||||||||
\(846\) | −13.1693 | −0.452770 | ||||||||
\(847\) | 63.5706 | 2.18431 | ||||||||
\(848\) | 14.7031 | 0.504905 | ||||||||
\(849\) | 15.3626 | 0.527243 | ||||||||
\(850\) | 12.4959 | 0.428607 | ||||||||
\(851\) | −58.9258 | −2.01995 | ||||||||
\(852\) | 58.2905 | 1.99700 | ||||||||
\(853\) | −15.0010 | −0.513624 | −0.256812 | − | 0.966461i | \(-0.582672\pi\) | ||||
−0.256812 | + | 0.966461i | \(0.582672\pi\) | |||||||
\(854\) | 25.4428 | 0.870635 | ||||||||
\(855\) | −2.90599 | −0.0993826 | ||||||||
\(856\) | 1.27975 | 0.0437410 | ||||||||
\(857\) | −14.1049 | −0.481813 | −0.240907 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240907 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(858\) | −15.7433 | −0.537467 | ||||||||
\(859\) | −27.3185 | −0.932095 | −0.466047 | − | 0.884760i | \(-0.654322\pi\) | ||||
−0.466047 | + | 0.884760i | \(0.654322\pi\) | |||||||
\(860\) | −40.0266 | −1.36489 | ||||||||
\(861\) | −19.7351 | −0.672570 | ||||||||
\(862\) | 7.65136 | 0.260606 | ||||||||
\(863\) | 23.7194 | 0.807418 | 0.403709 | − | 0.914887i | \(-0.367721\pi\) | ||||
0.403709 | + | 0.914887i | \(0.367721\pi\) | |||||||
\(864\) | −2.42662 | −0.0825552 | ||||||||
\(865\) | 24.8474 | 0.844835 | ||||||||
\(866\) | −7.63465 | −0.259436 | ||||||||
\(867\) | −14.0393 | −0.476798 | ||||||||
\(868\) | 11.1568 | 0.378687 | ||||||||
\(869\) | −46.7760 | −1.58677 | ||||||||
\(870\) | −2.33976 | −0.0793252 | ||||||||
\(871\) | −4.09403 | −0.138721 | ||||||||
\(872\) | 13.0732 | 0.442714 | ||||||||
\(873\) | 2.19386 | 0.0742511 | ||||||||
\(874\) | 32.6354 | 1.10391 | ||||||||
\(875\) | 22.1903 | 0.750170 | ||||||||
\(876\) | 46.6320 | 1.57555 | ||||||||
\(877\) | 20.3693 | 0.687823 | 0.343912 | − | 0.939002i | \(-0.388248\pi\) | ||||
0.343912 | + | 0.939002i | \(0.388248\pi\) | |||||||
\(878\) | 85.7778 | 2.89486 | ||||||||
\(879\) | −32.2142 | −1.08656 | ||||||||
\(880\) | −22.5226 | −0.759238 | ||||||||
\(881\) | −39.2551 | −1.32254 | −0.661269 | − | 0.750149i | \(-0.729982\pi\) | ||||
−0.661269 | + | 0.750149i | \(0.729982\pi\) | |||||||
\(882\) | −7.46532 | −0.251370 | ||||||||
\(883\) | −26.3435 | −0.886531 | −0.443265 | − | 0.896390i | \(-0.646180\pi\) | ||||
−0.443265 | + | 0.896390i | \(0.646180\pi\) | |||||||
\(884\) | 6.41475 | 0.215751 | ||||||||
\(885\) | 16.6145 | 0.558490 | ||||||||
\(886\) | 52.1898 | 1.75335 | ||||||||
\(887\) | 39.8770 | 1.33894 | 0.669470 | − | 0.742839i | \(-0.266521\pi\) | ||||
0.669470 | + | 0.742839i | \(0.266521\pi\) | |||||||
\(888\) | −37.0437 | −1.24310 | ||||||||
\(889\) | 20.4717 | 0.686599 | ||||||||
\(890\) | −12.5500 | −0.420676 | ||||||||
\(891\) | 6.57798 | 0.220371 | ||||||||
\(892\) | 23.4713 | 0.785877 | ||||||||
\(893\) | −11.4051 | −0.381658 | ||||||||
\(894\) | 52.9761 | 1.77178 | ||||||||
\(895\) | 23.9696 | 0.801216 | ||||||||
\(896\) | −40.8498 | −1.36470 | ||||||||
\(897\) | −6.57879 | −0.219659 | ||||||||
\(898\) | 11.0891 | 0.370048 | ||||||||
\(899\) | 1.05929 | 0.0353294 | ||||||||
\(900\) | −11.3121 | −0.377071 | ||||||||
\(901\) | −10.3594 | −0.345122 | ||||||||
\(902\) | −157.716 | −5.25136 | ||||||||
\(903\) | 15.0860 | 0.502032 | ||||||||
\(904\) | 37.8465 | 1.25875 | ||||||||
\(905\) | 16.8138 | 0.558909 | ||||||||
\(906\) | −46.1436 | −1.53302 | ||||||||
\(907\) | 3.86966 | 0.128490 | 0.0642450 | − | 0.997934i | \(-0.479536\pi\) | ||||
0.0642450 | + | 0.997934i | \(0.479536\pi\) | |||||||
\(908\) | 75.9578 | 2.52075 | ||||||||
\(909\) | 4.53311 | 0.150354 | ||||||||
\(910\) | 6.61022 | 0.219127 | ||||||||
\(911\) | −39.7419 | −1.31671 | −0.658354 | − | 0.752709i | \(-0.728747\pi\) | ||||
−0.658354 | + | 0.752709i | \(0.728747\pi\) | |||||||
\(912\) | 5.06190 | 0.167616 | ||||||||
\(913\) | 26.6721 | 0.882716 | ||||||||
\(914\) | −62.7614 | −2.07596 | ||||||||
\(915\) | −7.56583 | −0.250119 | ||||||||
\(916\) | 91.4720 | 3.02232 | ||||||||
\(917\) | −33.0210 | −1.09045 | ||||||||
\(918\) | −4.11816 | −0.135919 | ||||||||
\(919\) | 56.2813 | 1.85655 | 0.928275 | − | 0.371895i | \(-0.121292\pi\) | ||||
0.928275 | + | 0.371895i | \(0.121292\pi\) | |||||||
\(920\) | −38.1464 | −1.25765 | ||||||||
\(921\) | 10.6243 | 0.350082 | ||||||||
\(922\) | −51.3184 | −1.69008 | ||||||||
\(923\) | −15.6357 | −0.514656 | ||||||||
\(924\) | 48.3094 | 1.58926 | ||||||||
\(925\) | 27.1785 | 0.893622 | ||||||||
\(926\) | 9.22927 | 0.303293 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −1.69206 | −0.0555446 | ||||||||
\(929\) | 23.1522 | 0.759598 | 0.379799 | − | 0.925069i | \(-0.375993\pi\) | ||||
0.379799 | + | 0.925069i | \(0.375993\pi\) | |||||||
\(930\) | −5.09750 | −0.167154 | ||||||||
\(931\) | −6.46526 | −0.211890 | ||||||||
\(932\) | −54.7705 | −1.79407 | ||||||||
\(933\) | 12.9606 | 0.424311 | ||||||||
\(934\) | −25.2213 | −0.825266 | ||||||||
\(935\) | 15.8689 | 0.518968 | ||||||||
\(936\) | −4.13575 | −0.135181 | ||||||||
\(937\) | 24.5599 | 0.802336 | 0.401168 | − | 0.916005i | \(-0.368604\pi\) | ||||
0.401168 | + | 0.916005i | \(0.368604\pi\) | |||||||
\(938\) | 19.3025 | 0.630248 | ||||||||
\(939\) | 33.1552 | 1.08198 | ||||||||
\(940\) | 28.7603 | 0.938057 | ||||||||
\(941\) | 9.14925 | 0.298257 | 0.149129 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149129 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(942\) | −49.3453 | −1.60776 | ||||||||
\(943\) | −65.9061 | −2.14620 | ||||||||
\(944\) | −28.9405 | −0.941934 | ||||||||
\(945\) | −2.76193 | −0.0898456 | ||||||||
\(946\) | 120.562 | 3.91981 | ||||||||
\(947\) | −4.05012 | −0.131611 | −0.0658056 | − | 0.997832i | \(-0.520962\pi\) | ||||
−0.0658056 | + | 0.997832i | \(0.520962\pi\) | |||||||
\(948\) | −26.5100 | −0.861005 | ||||||||
\(949\) | −12.5085 | −0.406042 | ||||||||
\(950\) | −15.0525 | −0.488367 | ||||||||
\(951\) | −2.98155 | −0.0966832 | ||||||||
\(952\) | −14.0189 | −0.454355 | ||||||||
\(953\) | 44.9117 | 1.45483 | 0.727417 | − | 0.686196i | \(-0.240721\pi\) | ||||
0.727417 | + | 0.686196i | \(0.240721\pi\) | |||||||
\(954\) | 14.4091 | 0.466512 | ||||||||
\(955\) | 26.9873 | 0.873288 | ||||||||
\(956\) | −33.0394 | −1.06857 | ||||||||
\(957\) | 4.58677 | 0.148269 | ||||||||
\(958\) | −89.8634 | −2.90335 | ||||||||
\(959\) | 1.66929 | 0.0539041 | ||||||||
\(960\) | 14.9904 | 0.483812 | ||||||||
\(961\) | −28.6922 | −0.925554 | ||||||||
\(962\) | 21.4369 | 0.691154 | ||||||||
\(963\) | 0.309436 | 0.00997144 | ||||||||
\(964\) | −28.0174 | −0.902380 | ||||||||
\(965\) | 31.8820 | 1.02632 | ||||||||
\(966\) | 31.0176 | 0.997975 | ||||||||
\(967\) | −28.2801 | −0.909428 | −0.454714 | − | 0.890638i | \(-0.650259\pi\) | ||||
−0.454714 | + | 0.890638i | \(0.650259\pi\) | |||||||
\(968\) | 133.460 | 4.28957 | ||||||||
\(969\) | −3.56649 | −0.114572 | ||||||||
\(970\) | −7.36149 | −0.236363 | ||||||||
\(971\) | 35.6652 | 1.14455 | 0.572275 | − | 0.820062i | \(-0.306061\pi\) | ||||
0.572275 | + | 0.820062i | \(0.306061\pi\) | |||||||
\(972\) | 3.72803 | 0.119577 | ||||||||
\(973\) | −30.8705 | −0.989663 | ||||||||
\(974\) | −82.0190 | −2.62806 | ||||||||
\(975\) | 3.03435 | 0.0971769 | ||||||||
\(976\) | 13.1788 | 0.421843 | ||||||||
\(977\) | −1.02333 | −0.0327391 | −0.0163696 | − | 0.999866i | \(-0.505211\pi\) | ||||
−0.0163696 | + | 0.999866i | \(0.505211\pi\) | |||||||
\(978\) | −49.4844 | −1.58234 | ||||||||
\(979\) | 24.6025 | 0.786300 | ||||||||
\(980\) | 16.3034 | 0.520794 | ||||||||
\(981\) | 3.16102 | 0.100923 | ||||||||
\(982\) | 11.5202 | 0.367624 | ||||||||
\(983\) | 11.9059 | 0.379740 | 0.189870 | − | 0.981809i | \(-0.439193\pi\) | ||||
0.189870 | + | 0.981809i | \(0.439193\pi\) | |||||||
\(984\) | −41.4318 | −1.32080 | ||||||||
\(985\) | 38.3457 | 1.22179 | ||||||||
\(986\) | −2.87156 | −0.0914491 | ||||||||
\(987\) | −10.8398 | −0.345034 | ||||||||
\(988\) | −7.72715 | −0.245834 | ||||||||
\(989\) | 50.3804 | 1.60200 | ||||||||
\(990\) | −22.0724 | −0.701506 | ||||||||
\(991\) | −40.6099 | −1.29002 | −0.645009 | − | 0.764175i | \(-0.723146\pi\) | ||||
−0.645009 | + | 0.764175i | \(0.723146\pi\) | |||||||
\(992\) | −3.68640 | −0.117043 | ||||||||
\(993\) | −9.54196 | −0.302805 | ||||||||
\(994\) | 73.7192 | 2.33823 | ||||||||
\(995\) | −14.6366 | −0.464012 | ||||||||
\(996\) | 15.1162 | 0.478976 | ||||||||
\(997\) | −23.8641 | −0.755784 | −0.377892 | − | 0.925850i | \(-0.623351\pi\) | ||||
−0.377892 | + | 0.925850i | \(0.623351\pi\) | |||||||
\(998\) | 23.3034 | 0.737657 | ||||||||
\(999\) | −8.95694 | −0.283385 |
(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 | 4017.2.a.l.1.28 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.l.1.28 | ✓ | 32 | 1.1 | even | 1 | trivial |