Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.842530\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.842530 | −0.595759 | −0.297879 | − | 0.954604i | \(-0.596279\pi\) | ||||
−0.297879 | + | 0.954604i | \(0.596279\pi\) | |||||||
\(3\) | 0.161973 | 0.0935149 | 0.0467574 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467574 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(4\) | −1.29014 | −0.645071 | ||||||||
\(5\) | 3.72786 | 1.66715 | 0.833575 | − | 0.552406i | \(-0.186290\pi\) | ||||
0.833575 | + | 0.552406i | \(0.186290\pi\) | |||||||
\(6\) | −0.136467 | −0.0557123 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.77204 | 0.980066 | ||||||||
\(9\) | −2.97376 | −0.991255 | ||||||||
\(10\) | −3.14083 | −0.993219 | ||||||||
\(11\) | −3.51379 | −1.05945 | −0.529724 | − | 0.848170i | \(-0.677705\pi\) | ||||
−0.529724 | + | 0.848170i | \(0.677705\pi\) | |||||||
\(12\) | −0.208968 | −0.0603238 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.842530 | 0.225176 | ||||||||
\(15\) | 0.603811 | 0.155903 | ||||||||
\(16\) | 0.244755 | 0.0611887 | ||||||||
\(17\) | 7.43189 | 1.80250 | 0.901249 | − | 0.433301i | \(-0.142651\pi\) | ||||
0.901249 | + | 0.433301i | \(0.142651\pi\) | |||||||
\(18\) | 2.50549 | 0.590549 | ||||||||
\(19\) | 2.67482 | 0.613646 | 0.306823 | − | 0.951767i | \(-0.400734\pi\) | ||||
0.306823 | + | 0.951767i | \(0.400734\pi\) | |||||||
\(20\) | −4.80947 | −1.07543 | ||||||||
\(21\) | −0.161973 | −0.0353453 | ||||||||
\(22\) | 2.96048 | 0.631176 | ||||||||
\(23\) | −2.49854 | −0.520982 | −0.260491 | − | 0.965476i | \(-0.583884\pi\) | ||||
−0.260491 | + | 0.965476i | \(0.583884\pi\) | |||||||
\(24\) | 0.448995 | 0.0916507 | ||||||||
\(25\) | 8.89694 | 1.77939 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.967586 | −0.186212 | ||||||||
\(28\) | 1.29014 | 0.243814 | ||||||||
\(29\) | 7.30473 | 1.35645 | 0.678227 | − | 0.734853i | \(-0.262749\pi\) | ||||
0.678227 | + | 0.734853i | \(0.262749\pi\) | |||||||
\(30\) | −0.508729 | −0.0928808 | ||||||||
\(31\) | −2.54405 | −0.456925 | −0.228463 | − | 0.973553i | \(-0.573370\pi\) | ||||
−0.228463 | + | 0.973553i | \(0.573370\pi\) | |||||||
\(32\) | −5.75030 | −1.01652 | ||||||||
\(33\) | −0.569138 | −0.0990742 | ||||||||
\(34\) | −6.26159 | −1.07385 | ||||||||
\(35\) | −3.72786 | −0.630123 | ||||||||
\(36\) | 3.83658 | 0.639430 | ||||||||
\(37\) | 2.17903 | 0.358230 | 0.179115 | − | 0.983828i | \(-0.442677\pi\) | ||||
0.179115 | + | 0.983828i | \(0.442677\pi\) | |||||||
\(38\) | −2.25362 | −0.365585 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.3338 | 1.63392 | ||||||||
\(41\) | 8.40738 | 1.31301 | 0.656506 | − | 0.754321i | \(-0.272034\pi\) | ||||
0.656506 | + | 0.754321i | \(0.272034\pi\) | |||||||
\(42\) | 0.136467 | 0.0210573 | ||||||||
\(43\) | 11.8923 | 1.81356 | 0.906780 | − | 0.421603i | \(-0.138533\pi\) | ||||
0.906780 | + | 0.421603i | \(0.138533\pi\) | |||||||
\(44\) | 4.53329 | 0.683420 | ||||||||
\(45\) | −11.0858 | −1.65257 | ||||||||
\(46\) | 2.10510 | 0.310379 | ||||||||
\(47\) | −9.40740 | −1.37221 | −0.686105 | − | 0.727502i | \(-0.740681\pi\) | ||||
−0.686105 | + | 0.727502i | \(0.740681\pi\) | |||||||
\(48\) | 0.0396435 | 0.00572205 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.49594 | −1.06009 | ||||||||
\(51\) | 1.20376 | 0.168560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.84583 | −0.802986 | −0.401493 | − | 0.915862i | \(-0.631509\pi\) | ||||
−0.401493 | + | 0.915862i | \(0.631509\pi\) | |||||||
\(54\) | 0.815220 | 0.110937 | ||||||||
\(55\) | −13.0989 | −1.76626 | ||||||||
\(56\) | −2.77204 | −0.370430 | ||||||||
\(57\) | 0.433247 | 0.0573850 | ||||||||
\(58\) | −6.15445 | −0.808119 | ||||||||
\(59\) | −4.25410 | −0.553836 | −0.276918 | − | 0.960893i | \(-0.589313\pi\) | ||||
−0.276918 | + | 0.960893i | \(0.589313\pi\) | |||||||
\(60\) | −0.779003 | −0.100569 | ||||||||
\(61\) | 5.07200 | 0.649403 | 0.324701 | − | 0.945817i | \(-0.394736\pi\) | ||||
0.324701 | + | 0.945817i | \(0.394736\pi\) | |||||||
\(62\) | 2.14344 | 0.272217 | ||||||||
\(63\) | 2.97376 | 0.374659 | ||||||||
\(64\) | 4.35529 | 0.544412 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.479516 | 0.0590243 | ||||||||
\(67\) | 1.29175 | 0.157812 | 0.0789060 | − | 0.996882i | \(-0.474857\pi\) | ||||
0.0789060 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(68\) | −9.58820 | −1.16274 | ||||||||
\(69\) | −0.404695 | −0.0487195 | ||||||||
\(70\) | 3.14083 | 0.375402 | ||||||||
\(71\) | −1.30601 | −0.154995 | −0.0774975 | − | 0.996993i | \(-0.524693\pi\) | ||||
−0.0774975 | + | 0.996993i | \(0.524693\pi\) | |||||||
\(72\) | −8.24341 | −0.971495 | ||||||||
\(73\) | 4.31232 | 0.504719 | 0.252359 | − | 0.967634i | \(-0.418793\pi\) | ||||
0.252359 | + | 0.967634i | \(0.418793\pi\) | |||||||
\(74\) | −1.83590 | −0.213419 | ||||||||
\(75\) | 1.44106 | 0.166399 | ||||||||
\(76\) | −3.45090 | −0.395845 | ||||||||
\(77\) | 3.51379 | 0.400434 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2264 | 1.60060 | 0.800299 | − | 0.599601i | \(-0.204674\pi\) | ||||
0.800299 | + | 0.599601i | \(0.204674\pi\) | |||||||
\(80\) | 0.912411 | 0.102011 | ||||||||
\(81\) | 8.76457 | 0.973841 | ||||||||
\(82\) | −7.08347 | −0.782238 | ||||||||
\(83\) | 9.81167 | 1.07697 | 0.538485 | − | 0.842635i | \(-0.318997\pi\) | ||||
0.538485 | + | 0.842635i | \(0.318997\pi\) | |||||||
\(84\) | 0.208968 | 0.0228002 | ||||||||
\(85\) | 27.7051 | 3.00504 | ||||||||
\(86\) | −10.0196 | −1.08044 | ||||||||
\(87\) | 1.18316 | 0.126849 | ||||||||
\(88\) | −9.74039 | −1.03833 | ||||||||
\(89\) | 4.77241 | 0.505874 | 0.252937 | − | 0.967483i | \(-0.418603\pi\) | ||||
0.252937 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(90\) | 9.34010 | 0.984533 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.22347 | 0.336070 | ||||||||
\(93\) | −0.412067 | −0.0427293 | ||||||||
\(94\) | 7.92602 | 0.817506 | ||||||||
\(95\) | 9.97135 | 1.02304 | ||||||||
\(96\) | −0.931391 | −0.0950597 | ||||||||
\(97\) | 5.92836 | 0.601934 | 0.300967 | − | 0.953635i | \(-0.402691\pi\) | ||||
0.300967 | + | 0.953635i | \(0.402691\pi\) | |||||||
\(98\) | −0.842530 | −0.0851084 | ||||||||
\(99\) | 10.4492 | 1.05018 | ||||||||
\(100\) | −11.4783 | −1.14783 | ||||||||
\(101\) | −3.18992 | −0.317409 | −0.158705 | − | 0.987326i | \(-0.550732\pi\) | ||||
−0.158705 | + | 0.987326i | \(0.550732\pi\) | |||||||
\(102\) | −1.01421 | −0.100421 | ||||||||
\(103\) | −9.80005 | −0.965627 | −0.482814 | − | 0.875723i | \(-0.660385\pi\) | ||||
−0.482814 | + | 0.875723i | \(0.660385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.603811 | −0.0589259 | ||||||||
\(106\) | 4.92529 | 0.478386 | ||||||||
\(107\) | 9.03013 | 0.872975 | 0.436488 | − | 0.899710i | \(-0.356222\pi\) | ||||
0.436488 | + | 0.899710i | \(0.356222\pi\) | |||||||
\(108\) | 1.24832 | 0.120120 | ||||||||
\(109\) | −2.85038 | −0.273017 | −0.136508 | − | 0.990639i | \(-0.543588\pi\) | ||||
−0.136508 | + | 0.990639i | \(0.543588\pi\) | |||||||
\(110\) | 11.0362 | 1.05226 | ||||||||
\(111\) | 0.352943 | 0.0334998 | ||||||||
\(112\) | −0.244755 | −0.0231271 | ||||||||
\(113\) | 11.5351 | 1.08513 | 0.542566 | − | 0.840013i | \(-0.317453\pi\) | ||||
0.542566 | + | 0.840013i | \(0.317453\pi\) | |||||||
\(114\) | −0.365024 | −0.0341876 | ||||||||
\(115\) | −9.31421 | −0.868554 | ||||||||
\(116\) | −9.42414 | −0.875009 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.58421 | 0.329953 | ||||||||
\(119\) | −7.43189 | −0.681281 | ||||||||
\(120\) | 1.67379 | 0.152796 | ||||||||
\(121\) | 1.34673 | 0.122430 | ||||||||
\(122\) | −4.27331 | −0.386887 | ||||||||
\(123\) | 1.36176 | 0.122786 | ||||||||
\(124\) | 3.28219 | 0.294749 | ||||||||
\(125\) | 14.5273 | 1.29936 | ||||||||
\(126\) | −2.50549 | −0.223206 | ||||||||
\(127\) | 0.885393 | 0.0785659 | 0.0392830 | − | 0.999228i | \(-0.487493\pi\) | ||||
0.0392830 | + | 0.999228i | \(0.487493\pi\) | |||||||
\(128\) | 7.83114 | 0.692181 | ||||||||
\(129\) | 1.92623 | 0.169595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3660 | 1.16779 | 0.583896 | − | 0.811829i | \(-0.301528\pi\) | ||||
0.583896 | + | 0.811829i | \(0.301528\pi\) | |||||||
\(132\) | 0.734269 | 0.0639099 | ||||||||
\(133\) | −2.67482 | −0.231936 | ||||||||
\(134\) | −1.08834 | −0.0940179 | ||||||||
\(135\) | −3.60703 | −0.310443 | ||||||||
\(136\) | 20.6015 | 1.76657 | ||||||||
\(137\) | −18.2881 | −1.56246 | −0.781230 | − | 0.624243i | \(-0.785408\pi\) | ||||
−0.781230 | + | 0.624243i | \(0.785408\pi\) | |||||||
\(138\) | 0.340968 | 0.0290251 | ||||||||
\(139\) | 3.21091 | 0.272346 | 0.136173 | − | 0.990685i | \(-0.456520\pi\) | ||||
0.136173 | + | 0.990685i | \(0.456520\pi\) | |||||||
\(140\) | 4.80947 | 0.406475 | ||||||||
\(141\) | −1.52374 | −0.128322 | ||||||||
\(142\) | 1.10035 | 0.0923397 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.727843 | −0.0606536 | ||||||||
\(145\) | 27.2310 | 2.26141 | ||||||||
\(146\) | −3.63326 | −0.300691 | ||||||||
\(147\) | 0.161973 | 0.0133593 | ||||||||
\(148\) | −2.81126 | −0.231084 | ||||||||
\(149\) | 0.508593 | 0.0416656 | 0.0208328 | − | 0.999783i | \(-0.493368\pi\) | ||||
0.0208328 | + | 0.999783i | \(0.493368\pi\) | |||||||
\(150\) | −1.21414 | −0.0991339 | ||||||||
\(151\) | 15.4491 | 1.25723 | 0.628614 | − | 0.777718i | \(-0.283623\pi\) | ||||
0.628614 | + | 0.777718i | \(0.283623\pi\) | |||||||
\(152\) | 7.41472 | 0.601413 | ||||||||
\(153\) | −22.1007 | −1.78674 | ||||||||
\(154\) | −2.96048 | −0.238562 | ||||||||
\(155\) | −9.48387 | −0.761763 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.63873 | −0.689446 | −0.344723 | − | 0.938705i | \(-0.612027\pi\) | ||||
−0.344723 | + | 0.938705i | \(0.612027\pi\) | |||||||
\(158\) | −11.9862 | −0.953570 | ||||||||
\(159\) | −0.946864 | −0.0750912 | ||||||||
\(160\) | −21.4363 | −1.69469 | ||||||||
\(161\) | 2.49854 | 0.196913 | ||||||||
\(162\) | −7.38442 | −0.580175 | ||||||||
\(163\) | −4.33684 | −0.339688 | −0.169844 | − | 0.985471i | \(-0.554326\pi\) | ||||
−0.169844 | + | 0.985471i | \(0.554326\pi\) | |||||||
\(164\) | −10.8467 | −0.846986 | ||||||||
\(165\) | −2.12167 | −0.165172 | ||||||||
\(166\) | −8.26663 | −0.641615 | ||||||||
\(167\) | −11.0384 | −0.854173 | −0.427087 | − | 0.904211i | \(-0.640460\pi\) | ||||
−0.427087 | + | 0.904211i | \(0.640460\pi\) | |||||||
\(168\) | −0.448995 | −0.0346407 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −23.3423 | −1.79028 | ||||||||
\(171\) | −7.95428 | −0.608279 | ||||||||
\(172\) | −15.3428 | −1.16988 | ||||||||
\(173\) | −10.3380 | −0.785987 | −0.392994 | − | 0.919541i | \(-0.628561\pi\) | ||||
−0.392994 | + | 0.919541i | \(0.628561\pi\) | |||||||
\(174\) | −0.996852 | −0.0755712 | ||||||||
\(175\) | −8.89694 | −0.672546 | ||||||||
\(176\) | −0.860017 | −0.0648262 | ||||||||
\(177\) | −0.689047 | −0.0517920 | ||||||||
\(178\) | −4.02090 | −0.301379 | ||||||||
\(179\) | 18.0134 | 1.34639 | 0.673194 | − | 0.739466i | \(-0.264922\pi\) | ||||
0.673194 | + | 0.739466i | \(0.264922\pi\) | |||||||
\(180\) | 14.3022 | 1.06603 | ||||||||
\(181\) | −21.3187 | −1.58460 | −0.792302 | − | 0.610129i | \(-0.791118\pi\) | ||||
−0.792302 | + | 0.610129i | \(0.791118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.821524 | 0.0607288 | ||||||||
\(184\) | −6.92606 | −0.510596 | ||||||||
\(185\) | 8.12311 | 0.597223 | ||||||||
\(186\) | 0.347178 | 0.0254564 | ||||||||
\(187\) | −26.1141 | −1.90965 | ||||||||
\(188\) | 12.1369 | 0.885174 | ||||||||
\(189\) | 0.967586 | 0.0703815 | ||||||||
\(190\) | −8.40117 | −0.609485 | ||||||||
\(191\) | 5.90224 | 0.427071 | 0.213535 | − | 0.976935i | \(-0.431502\pi\) | ||||
0.213535 | + | 0.976935i | \(0.431502\pi\) | |||||||
\(192\) | 0.705438 | 0.0509106 | ||||||||
\(193\) | 3.24842 | 0.233827 | 0.116913 | − | 0.993142i | \(-0.462700\pi\) | ||||
0.116913 | + | 0.993142i | \(0.462700\pi\) | |||||||
\(194\) | −4.99483 | −0.358608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.29014 | −0.0921531 | ||||||||
\(197\) | −8.99244 | −0.640685 | −0.320342 | − | 0.947302i | \(-0.603798\pi\) | ||||
−0.320342 | + | 0.947302i | \(0.603798\pi\) | |||||||
\(198\) | −8.80376 | −0.625656 | ||||||||
\(199\) | 5.58657 | 0.396021 | 0.198011 | − | 0.980200i | \(-0.436552\pi\) | ||||
0.198011 | + | 0.980200i | \(0.436552\pi\) | |||||||
\(200\) | 24.6627 | 1.74392 | ||||||||
\(201\) | 0.209228 | 0.0147578 | ||||||||
\(202\) | 2.68761 | 0.189099 | ||||||||
\(203\) | −7.30473 | −0.512691 | ||||||||
\(204\) | −1.55303 | −0.108734 | ||||||||
\(205\) | 31.3415 | 2.18899 | ||||||||
\(206\) | 8.25684 | 0.575281 | ||||||||
\(207\) | 7.43007 | 0.516426 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.39876 | −0.650126 | ||||||||
\(210\) | 0.508729 | 0.0351056 | ||||||||
\(211\) | −19.2145 | −1.32278 | −0.661391 | − | 0.750041i | \(-0.730034\pi\) | ||||
−0.661391 | + | 0.750041i | \(0.730034\pi\) | |||||||
\(212\) | 7.54195 | 0.517984 | ||||||||
\(213\) | −0.211538 | −0.0144943 | ||||||||
\(214\) | −7.60815 | −0.520083 | ||||||||
\(215\) | 44.3329 | 3.02348 | ||||||||
\(216\) | −2.68219 | −0.182500 | ||||||||
\(217\) | 2.54405 | 0.172701 | ||||||||
\(218\) | 2.40153 | 0.162652 | ||||||||
\(219\) | 0.698478 | 0.0471987 | ||||||||
\(220\) | 16.8995 | 1.13936 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.297365 | −0.0199578 | ||||||||
\(223\) | −13.3068 | −0.891089 | −0.445545 | − | 0.895260i | \(-0.646990\pi\) | ||||
−0.445545 | + | 0.895260i | \(0.646990\pi\) | |||||||
\(224\) | 5.75030 | 0.384208 | ||||||||
\(225\) | −26.4574 | −1.76383 | ||||||||
\(226\) | −9.71868 | −0.646477 | ||||||||
\(227\) | −13.3532 | −0.886286 | −0.443143 | − | 0.896451i | \(-0.646137\pi\) | ||||
−0.443143 | + | 0.896451i | \(0.646137\pi\) | |||||||
\(228\) | −0.558951 | −0.0370174 | ||||||||
\(229\) | 10.5744 | 0.698773 | 0.349387 | − | 0.936979i | \(-0.386390\pi\) | ||||
0.349387 | + | 0.936979i | \(0.386390\pi\) | |||||||
\(230\) | 7.84750 | 0.517449 | ||||||||
\(231\) | 0.569138 | 0.0374465 | ||||||||
\(232\) | 20.2490 | 1.32941 | ||||||||
\(233\) | 5.25696 | 0.344395 | 0.172197 | − | 0.985062i | \(-0.444913\pi\) | ||||
0.172197 | + | 0.985062i | \(0.444913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.0695 | −2.28768 | ||||||||
\(236\) | 5.48840 | 0.357264 | ||||||||
\(237\) | 2.30429 | 0.149680 | ||||||||
\(238\) | 6.26159 | 0.405879 | ||||||||
\(239\) | −20.0403 | −1.29630 | −0.648149 | − | 0.761513i | \(-0.724457\pi\) | ||||
−0.648149 | + | 0.761513i | \(0.724457\pi\) | |||||||
\(240\) | 0.147786 | 0.00953952 | ||||||||
\(241\) | −23.3489 | −1.50403 | −0.752017 | − | 0.659144i | \(-0.770919\pi\) | ||||
−0.752017 | + | 0.659144i | \(0.770919\pi\) | |||||||
\(242\) | −1.13466 | −0.0729390 | ||||||||
\(243\) | 4.32238 | 0.277281 | ||||||||
\(244\) | −6.54360 | −0.418911 | ||||||||
\(245\) | 3.72786 | 0.238164 | ||||||||
\(246\) | −1.14733 | −0.0731509 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.05223 | −0.447817 | ||||||||
\(249\) | 1.58922 | 0.100713 | ||||||||
\(250\) | −12.2397 | −0.774104 | ||||||||
\(251\) | 14.4261 | 0.910570 | 0.455285 | − | 0.890346i | \(-0.349537\pi\) | ||||
0.455285 | + | 0.890346i | \(0.349537\pi\) | |||||||
\(252\) | −3.83658 | −0.241682 | ||||||||
\(253\) | 8.77935 | 0.551953 | ||||||||
\(254\) | −0.745970 | −0.0468063 | ||||||||
\(255\) | 4.48746 | 0.281016 | ||||||||
\(256\) | −15.3086 | −0.956785 | ||||||||
\(257\) | 13.0464 | 0.813810 | 0.406905 | − | 0.913471i | \(-0.366608\pi\) | ||||
0.406905 | + | 0.913471i | \(0.366608\pi\) | |||||||
\(258\) | −1.62291 | −0.101038 | ||||||||
\(259\) | −2.17903 | −0.135398 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.7225 | −1.34459 | ||||||||
\(262\) | −11.2612 | −0.695722 | ||||||||
\(263\) | 16.7189 | 1.03093 | 0.515464 | − | 0.856911i | \(-0.327619\pi\) | ||||
0.515464 | + | 0.856911i | \(0.327619\pi\) | |||||||
\(264\) | −1.57768 | −0.0970992 | ||||||||
\(265\) | −21.7924 | −1.33870 | ||||||||
\(266\) | 2.25362 | 0.138178 | ||||||||
\(267\) | 0.772999 | 0.0473068 | ||||||||
\(268\) | −1.66654 | −0.101800 | ||||||||
\(269\) | 6.17733 | 0.376639 | 0.188319 | − | 0.982108i | \(-0.439696\pi\) | ||||
0.188319 | + | 0.982108i | \(0.439696\pi\) | |||||||
\(270\) | 3.03903 | 0.184949 | ||||||||
\(271\) | −30.1026 | −1.82860 | −0.914301 | − | 0.405036i | \(-0.867259\pi\) | ||||
−0.914301 | + | 0.405036i | \(0.867259\pi\) | |||||||
\(272\) | 1.81899 | 0.110292 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.4083 | 0.930850 | ||||||||
\(275\) | −31.2620 | −1.88517 | ||||||||
\(276\) | 0.522114 | 0.0314276 | ||||||||
\(277\) | −6.01177 | −0.361212 | −0.180606 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180606 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(278\) | −2.70529 | −0.162252 | ||||||||
\(279\) | 7.56541 | 0.452929 | ||||||||
\(280\) | −10.3338 | −0.617562 | ||||||||
\(281\) | −26.4812 | −1.57974 | −0.789868 | − | 0.613277i | \(-0.789851\pi\) | ||||
−0.789868 | + | 0.613277i | \(0.789851\pi\) | |||||||
\(282\) | 1.28380 | 0.0764490 | ||||||||
\(283\) | −0.200682 | −0.0119293 | −0.00596465 | − | 0.999982i | \(-0.501899\pi\) | ||||
−0.00596465 | + | 0.999982i | \(0.501899\pi\) | |||||||
\(284\) | 1.68494 | 0.0999829 | ||||||||
\(285\) | 1.61509 | 0.0956694 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.40738 | −0.496272 | ||||||||
\(288\) | 17.1000 | 1.00763 | ||||||||
\(289\) | 38.2330 | 2.24900 | ||||||||
\(290\) | −22.9429 | −1.34726 | ||||||||
\(291\) | 0.960232 | 0.0562898 | ||||||||
\(292\) | −5.56351 | −0.325580 | ||||||||
\(293\) | 1.96008 | 0.114509 | 0.0572544 | − | 0.998360i | \(-0.481765\pi\) | ||||
0.0572544 | + | 0.998360i | \(0.481765\pi\) | |||||||
\(294\) | −0.136467 | −0.00795890 | ||||||||
\(295\) | −15.8587 | −0.923328 | ||||||||
\(296\) | 6.04036 | 0.351089 | ||||||||
\(297\) | 3.39990 | 0.197282 | ||||||||
\(298\) | −0.428505 | −0.0248226 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.85917 | −0.107339 | ||||||||
\(301\) | −11.8923 | −0.685462 | ||||||||
\(302\) | −13.0163 | −0.749004 | ||||||||
\(303\) | −0.516680 | −0.0296825 | ||||||||
\(304\) | 0.654674 | 0.0375482 | ||||||||
\(305\) | 18.9077 | 1.08265 | ||||||||
\(306\) | 18.6205 | 1.06446 | ||||||||
\(307\) | 25.1368 | 1.43463 | 0.717317 | − | 0.696747i | \(-0.245370\pi\) | ||||
0.717317 | + | 0.696747i | \(0.245370\pi\) | |||||||
\(308\) | −4.53329 | −0.258308 | ||||||||
\(309\) | −1.58734 | −0.0903005 | ||||||||
\(310\) | 7.99045 | 0.453827 | ||||||||
\(311\) | −29.5322 | −1.67462 | −0.837308 | − | 0.546731i | \(-0.815872\pi\) | ||||
−0.837308 | + | 0.546731i | \(0.815872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.68905 | 0.378087 | 0.189044 | − | 0.981969i | \(-0.439461\pi\) | ||||
0.189044 | + | 0.981969i | \(0.439461\pi\) | |||||||
\(314\) | 7.27839 | 0.410743 | ||||||||
\(315\) | 11.0858 | 0.624613 | ||||||||
\(316\) | −18.3541 | −1.03250 | ||||||||
\(317\) | 20.6867 | 1.16188 | 0.580941 | − | 0.813946i | \(-0.302685\pi\) | ||||
0.580941 | + | 0.813946i | \(0.302685\pi\) | |||||||
\(318\) | 0.797761 | 0.0447362 | ||||||||
\(319\) | −25.6673 | −1.43709 | ||||||||
\(320\) | 16.2359 | 0.907616 | ||||||||
\(321\) | 1.46263 | 0.0816362 | ||||||||
\(322\) | −2.10510 | −0.117312 | ||||||||
\(323\) | 19.8790 | 1.10610 | ||||||||
\(324\) | −11.3076 | −0.628197 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.65392 | 0.202372 | ||||||||
\(327\) | −0.461683 | −0.0255311 | ||||||||
\(328\) | 23.3056 | 1.28684 | ||||||||
\(329\) | 9.40740 | 0.518647 | ||||||||
\(330\) | 1.78757 | 0.0984024 | ||||||||
\(331\) | −35.4014 | −1.94584 | −0.972918 | − | 0.231149i | \(-0.925752\pi\) | ||||
−0.972918 | + | 0.231149i | \(0.925752\pi\) | |||||||
\(332\) | −12.6585 | −0.694723 | ||||||||
\(333\) | −6.47992 | −0.355097 | ||||||||
\(334\) | 9.30014 | 0.508881 | ||||||||
\(335\) | 4.81545 | 0.263096 | ||||||||
\(336\) | −0.0396435 | −0.00216273 | ||||||||
\(337\) | −6.69897 | −0.364916 | −0.182458 | − | 0.983214i | \(-0.558405\pi\) | ||||
−0.182458 | + | 0.983214i | \(0.558405\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.86837 | 0.101476 | ||||||||
\(340\) | −35.7435 | −1.93846 | ||||||||
\(341\) | 8.93927 | 0.484089 | ||||||||
\(342\) | 6.70172 | 0.362388 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 32.9660 | 1.77741 | ||||||||
\(345\) | −1.50865 | −0.0812228 | ||||||||
\(346\) | 8.71012 | 0.468259 | ||||||||
\(347\) | −7.38059 | −0.396211 | −0.198105 | − | 0.980181i | \(-0.563479\pi\) | ||||
−0.198105 | + | 0.980181i | \(0.563479\pi\) | |||||||
\(348\) | −1.52645 | −0.0818264 | ||||||||
\(349\) | 15.2129 | 0.814326 | 0.407163 | − | 0.913355i | \(-0.366518\pi\) | ||||
0.407163 | + | 0.913355i | \(0.366518\pi\) | |||||||
\(350\) | 7.49594 | 0.400675 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.2054 | 1.07695 | ||||||||
\(353\) | −12.5476 | −0.667843 | −0.333921 | − | 0.942601i | \(-0.608372\pi\) | ||||
−0.333921 | + | 0.942601i | \(0.608372\pi\) | |||||||
\(354\) | 0.580543 | 0.0308555 | ||||||||
\(355\) | −4.86863 | −0.258400 | ||||||||
\(356\) | −6.15709 | −0.326325 | ||||||||
\(357\) | −1.20376 | −0.0637099 | ||||||||
\(358\) | −15.1769 | −0.802123 | ||||||||
\(359\) | 17.8460 | 0.941877 | 0.470939 | − | 0.882166i | \(-0.343915\pi\) | ||||
0.470939 | + | 0.882166i | \(0.343915\pi\) | |||||||
\(360\) | −30.7303 | −1.61963 | ||||||||
\(361\) | −11.8453 | −0.623439 | ||||||||
\(362\) | 17.9616 | 0.944042 | ||||||||
\(363\) | 0.218134 | 0.0114491 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0757 | 0.841442 | ||||||||
\(366\) | −0.692159 | −0.0361797 | ||||||||
\(367\) | −30.9271 | −1.61438 | −0.807190 | − | 0.590291i | \(-0.799013\pi\) | ||||
−0.807190 | + | 0.590291i | \(0.799013\pi\) | |||||||
\(368\) | −0.611529 | −0.0318782 | ||||||||
\(369\) | −25.0016 | −1.30153 | ||||||||
\(370\) | −6.84397 | −0.355801 | ||||||||
\(371\) | 5.84583 | 0.303500 | ||||||||
\(372\) | 0.531625 | 0.0275635 | ||||||||
\(373\) | −28.6520 | −1.48354 | −0.741772 | − | 0.670652i | \(-0.766014\pi\) | ||||
−0.741772 | + | 0.670652i | \(0.766014\pi\) | |||||||
\(374\) | 22.0019 | 1.13769 | ||||||||
\(375\) | 2.35302 | 0.121509 | ||||||||
\(376\) | −26.0777 | −1.34486 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.815220 | −0.0419304 | ||||||||
\(379\) | 4.61700 | 0.237159 | 0.118580 | − | 0.992945i | \(-0.462166\pi\) | ||||
0.118580 | + | 0.992945i | \(0.462166\pi\) | |||||||
\(380\) | −12.8645 | −0.659933 | ||||||||
\(381\) | 0.143409 | 0.00734708 | ||||||||
\(382\) | −4.97281 | −0.254431 | ||||||||
\(383\) | 27.7969 | 1.42036 | 0.710178 | − | 0.704022i | \(-0.248614\pi\) | ||||
0.710178 | + | 0.704022i | \(0.248614\pi\) | |||||||
\(384\) | 1.26843 | 0.0647293 | ||||||||
\(385\) | 13.0989 | 0.667583 | ||||||||
\(386\) | −2.73689 | −0.139304 | ||||||||
\(387\) | −35.3649 | −1.79770 | ||||||||
\(388\) | −7.64844 | −0.388291 | ||||||||
\(389\) | 16.8702 | 0.855352 | 0.427676 | − | 0.903932i | \(-0.359332\pi\) | ||||
0.427676 | + | 0.903932i | \(0.359332\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.5689 | −0.939069 | ||||||||
\(392\) | 2.77204 | 0.140009 | ||||||||
\(393\) | 2.16492 | 0.109206 | ||||||||
\(394\) | 7.57640 | 0.381694 | ||||||||
\(395\) | 53.0341 | 2.66844 | ||||||||
\(396\) | −13.4810 | −0.677443 | ||||||||
\(397\) | 24.2776 | 1.21846 | 0.609228 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609228 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(398\) | −4.70685 | −0.235933 | ||||||||
\(399\) | −0.433247 | −0.0216895 | ||||||||
\(400\) | 2.17757 | 0.108878 | ||||||||
\(401\) | −24.0304 | −1.20002 | −0.600010 | − | 0.799992i | \(-0.704837\pi\) | ||||
−0.600010 | + | 0.799992i | \(0.704837\pi\) | |||||||
\(402\) | −0.176281 | −0.00879207 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.11546 | 0.204752 | ||||||||
\(405\) | 32.6731 | 1.62354 | ||||||||
\(406\) | 6.15445 | 0.305440 | ||||||||
\(407\) | −7.65665 | −0.379526 | ||||||||
\(408\) | 3.33688 | 0.165200 | ||||||||
\(409\) | −2.04813 | −0.101274 | −0.0506368 | − | 0.998717i | \(-0.516125\pi\) | ||||
−0.0506368 | + | 0.998717i | \(0.516125\pi\) | |||||||
\(410\) | −26.4062 | −1.30411 | ||||||||
\(411\) | −2.96218 | −0.146113 | ||||||||
\(412\) | 12.6435 | 0.622899 | ||||||||
\(413\) | 4.25410 | 0.209331 | ||||||||
\(414\) | −6.26006 | −0.307665 | ||||||||
\(415\) | 36.5765 | 1.79547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.520079 | 0.0254684 | ||||||||
\(418\) | 7.91874 | 0.387318 | ||||||||
\(419\) | −25.9332 | −1.26692 | −0.633461 | − | 0.773775i | \(-0.718366\pi\) | ||||
−0.633461 | + | 0.773775i | \(0.718366\pi\) | |||||||
\(420\) | 0.779003 | 0.0380114 | ||||||||
\(421\) | 22.5137 | 1.09725 | 0.548626 | − | 0.836068i | \(-0.315151\pi\) | ||||
0.548626 | + | 0.836068i | \(0.315151\pi\) | |||||||
\(422\) | 16.1888 | 0.788059 | ||||||||
\(423\) | 27.9754 | 1.36021 | ||||||||
\(424\) | −16.2049 | −0.786979 | ||||||||
\(425\) | 66.1211 | 3.20735 | ||||||||
\(426\) | 0.178227 | 0.00863514 | ||||||||
\(427\) | −5.07200 | −0.245451 | ||||||||
\(428\) | −11.6502 | −0.563131 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −37.3518 | −1.80126 | ||||||||
\(431\) | −2.78073 | −0.133943 | −0.0669716 | − | 0.997755i | \(-0.521334\pi\) | ||||
−0.0669716 | + | 0.997755i | \(0.521334\pi\) | |||||||
\(432\) | −0.236821 | −0.0113941 | ||||||||
\(433\) | 25.5607 | 1.22837 | 0.614186 | − | 0.789162i | \(-0.289485\pi\) | ||||
0.614186 | + | 0.789162i | \(0.289485\pi\) | |||||||
\(434\) | −2.14344 | −0.102888 | ||||||||
\(435\) | 4.41067 | 0.211476 | ||||||||
\(436\) | 3.67740 | 0.176115 | ||||||||
\(437\) | −6.68314 | −0.319698 | ||||||||
\(438\) | −0.588488 | −0.0281191 | ||||||||
\(439\) | −31.6821 | −1.51210 | −0.756052 | − | 0.654512i | \(-0.772874\pi\) | ||||
−0.756052 | + | 0.654512i | \(0.772874\pi\) | |||||||
\(440\) | −36.3108 | −1.73105 | ||||||||
\(441\) | −2.97376 | −0.141608 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1943 | −0.816928 | −0.408464 | − | 0.912774i | \(-0.633935\pi\) | ||||
−0.408464 | + | 0.912774i | \(0.633935\pi\) | |||||||
\(444\) | −0.455346 | −0.0216098 | ||||||||
\(445\) | 17.7909 | 0.843368 | ||||||||
\(446\) | 11.2114 | 0.530874 | ||||||||
\(447\) | 0.0823781 | 0.00389635 | ||||||||
\(448\) | −4.35529 | −0.205768 | ||||||||
\(449\) | −14.3503 | −0.677230 | −0.338615 | − | 0.940925i | \(-0.609958\pi\) | ||||
−0.338615 | + | 0.940925i | \(0.609958\pi\) | |||||||
\(450\) | 22.2912 | 1.05082 | ||||||||
\(451\) | −29.5418 | −1.39107 | ||||||||
\(452\) | −14.8819 | −0.699988 | ||||||||
\(453\) | 2.50232 | 0.117569 | ||||||||
\(454\) | 11.2505 | 0.528013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20098 | 0.0562411 | ||||||||
\(457\) | −15.0888 | −0.705822 | −0.352911 | − | 0.935657i | \(-0.614808\pi\) | ||||
−0.352911 | + | 0.935657i | \(0.614808\pi\) | |||||||
\(458\) | −8.90921 | −0.416300 | ||||||||
\(459\) | −7.19100 | −0.335647 | ||||||||
\(460\) | 12.0167 | 0.560280 | ||||||||
\(461\) | −15.8856 | −0.739868 | −0.369934 | − | 0.929058i | \(-0.620620\pi\) | ||||
−0.369934 | + | 0.929058i | \(0.620620\pi\) | |||||||
\(462\) | −0.479516 | −0.0223091 | ||||||||
\(463\) | −7.03356 | −0.326877 | −0.163439 | − | 0.986553i | \(-0.552259\pi\) | ||||
−0.163439 | + | 0.986553i | \(0.552259\pi\) | |||||||
\(464\) | 1.78787 | 0.0829996 | ||||||||
\(465\) | −1.53613 | −0.0712362 | ||||||||
\(466\) | −4.42915 | −0.205176 | ||||||||
\(467\) | −0.621410 | −0.0287554 | −0.0143777 | − | 0.999897i | \(-0.504577\pi\) | ||||
−0.0143777 | + | 0.999897i | \(0.504577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.29175 | −0.0596473 | ||||||||
\(470\) | 29.5471 | 1.36291 | ||||||||
\(471\) | −1.39924 | −0.0644734 | ||||||||
\(472\) | −11.7926 | −0.542796 | ||||||||
\(473\) | −41.7871 | −1.92137 | ||||||||
\(474\) | −1.94143 | −0.0891730 | ||||||||
\(475\) | 23.7977 | 1.09191 | ||||||||
\(476\) | 9.58820 | 0.439475 | ||||||||
\(477\) | 17.3841 | 0.795964 | ||||||||
\(478\) | 16.8846 | 0.772281 | ||||||||
\(479\) | 24.6401 | 1.12584 | 0.562919 | − | 0.826512i | \(-0.309678\pi\) | ||||
0.562919 | + | 0.826512i | \(0.309678\pi\) | |||||||
\(480\) | −3.47210 | −0.158479 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19.6721 | 0.896041 | ||||||||
\(483\) | 0.404695 | 0.0184143 | ||||||||
\(484\) | −1.73748 | −0.0789764 | ||||||||
\(485\) | 22.1001 | 1.00351 | ||||||||
\(486\) | −3.64173 | −0.165192 | ||||||||
\(487\) | −20.8751 | −0.945941 | −0.472971 | − | 0.881078i | \(-0.656818\pi\) | ||||
−0.472971 | + | 0.881078i | \(0.656818\pi\) | |||||||
\(488\) | 14.0598 | 0.636457 | ||||||||
\(489\) | −0.702449 | −0.0317659 | ||||||||
\(490\) | −3.14083 | −0.141888 | ||||||||
\(491\) | −2.48344 | −0.112076 | −0.0560380 | − | 0.998429i | \(-0.517847\pi\) | ||||
−0.0560380 | + | 0.998429i | \(0.517847\pi\) | |||||||
\(492\) | −1.75687 | −0.0792058 | ||||||||
\(493\) | 54.2879 | 2.44501 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 38.9531 | 1.75081 | ||||||||
\(496\) | −0.622668 | −0.0279586 | ||||||||
\(497\) | 1.30601 | 0.0585826 | ||||||||
\(498\) | −1.33897 | −0.0600005 | ||||||||
\(499\) | −0.427604 | −0.0191422 | −0.00957109 | − | 0.999954i | \(-0.503047\pi\) | ||||
−0.00957109 | + | 0.999954i | \(0.503047\pi\) | |||||||
\(500\) | −18.7422 | −0.838178 | ||||||||
\(501\) | −1.78791 | −0.0798779 | ||||||||
\(502\) | −12.1545 | −0.542480 | ||||||||
\(503\) | 36.2684 | 1.61713 | 0.808565 | − | 0.588407i | \(-0.200245\pi\) | ||||
0.808565 | + | 0.588407i | \(0.200245\pi\) | |||||||
\(504\) | 8.24341 | 0.367191 | ||||||||
\(505\) | −11.8916 | −0.529169 | ||||||||
\(506\) | −7.39687 | −0.328831 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.14228 | −0.0506806 | ||||||||
\(509\) | 16.9910 | 0.753113 | 0.376557 | − | 0.926394i | \(-0.377108\pi\) | ||||
0.376557 | + | 0.926394i | \(0.377108\pi\) | |||||||
\(510\) | −3.78082 | −0.167418 | ||||||||
\(511\) | −4.31232 | −0.190766 | ||||||||
\(512\) | −2.76435 | −0.122168 | ||||||||
\(513\) | −2.58812 | −0.114268 | ||||||||
\(514\) | −10.9920 | −0.484834 | ||||||||
\(515\) | −36.5332 | −1.60985 | ||||||||
\(516\) | −2.48511 | −0.109401 | ||||||||
\(517\) | 33.0556 | 1.45379 | ||||||||
\(518\) | 1.83590 | 0.0806647 | ||||||||
\(519\) | −1.67448 | −0.0735015 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3640 | 0.716920 | 0.358460 | − | 0.933545i | \(-0.383302\pi\) | ||||
0.358460 | + | 0.933545i | \(0.383302\pi\) | |||||||
\(522\) | 18.3019 | 0.801052 | ||||||||
\(523\) | −12.5863 | −0.550359 | −0.275180 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275180 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(524\) | −17.2440 | −0.753309 | ||||||||
\(525\) | −1.44106 | −0.0628930 | ||||||||
\(526\) | −14.0861 | −0.614185 | ||||||||
\(527\) | −18.9071 | −0.823607 | ||||||||
\(528\) | −0.139299 | −0.00606222 | ||||||||
\(529\) | −16.7573 | −0.728578 | ||||||||
\(530\) | 18.3608 | 0.797541 | ||||||||
\(531\) | 12.6507 | 0.548993 | ||||||||
\(532\) | 3.45090 | 0.149615 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.651275 | −0.0281834 | ||||||||
\(535\) | 33.6631 | 1.45538 | ||||||||
\(536\) | 3.58078 | 0.154666 | ||||||||
\(537\) | 2.91768 | 0.125907 | ||||||||
\(538\) | −5.20459 | −0.224386 | ||||||||
\(539\) | −3.51379 | −0.151350 | ||||||||
\(540\) | 4.65358 | 0.200258 | ||||||||
\(541\) | −44.7256 | −1.92290 | −0.961452 | − | 0.274974i | \(-0.911331\pi\) | ||||
−0.961452 | + | 0.274974i | \(0.911331\pi\) | |||||||
\(542\) | 25.3623 | 1.08941 | ||||||||
\(543\) | −3.45304 | −0.148184 | ||||||||
\(544\) | −42.7356 | −1.83228 | ||||||||
\(545\) | −10.6258 | −0.455160 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.5754 | 1.00801 | 0.504006 | − | 0.863700i | \(-0.331859\pi\) | ||||
0.504006 | + | 0.863700i | \(0.331859\pi\) | |||||||
\(548\) | 23.5943 | 1.00790 | ||||||||
\(549\) | −15.0829 | −0.643724 | ||||||||
\(550\) | 26.3392 | 1.12311 | ||||||||
\(551\) | 19.5388 | 0.832382 | ||||||||
\(552\) | −1.12183 | −0.0477484 | ||||||||
\(553\) | −14.2264 | −0.604969 | ||||||||
\(554\) | 5.06510 | 0.215195 | ||||||||
\(555\) | 1.31572 | 0.0558492 | ||||||||
\(556\) | −4.14253 | −0.175682 | ||||||||
\(557\) | −19.5362 | −0.827774 | −0.413887 | − | 0.910328i | \(-0.635829\pi\) | ||||
−0.413887 | + | 0.910328i | \(0.635829\pi\) | |||||||
\(558\) | −6.37409 | −0.269837 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.912411 | −0.0385564 | ||||||||
\(561\) | −4.22977 | −0.178581 | ||||||||
\(562\) | 22.3112 | 0.941142 | ||||||||
\(563\) | 26.1631 | 1.10264 | 0.551322 | − | 0.834293i | \(-0.314124\pi\) | ||||
0.551322 | + | 0.834293i | \(0.314124\pi\) | |||||||
\(564\) | 1.96584 | 0.0827769 | ||||||||
\(565\) | 43.0013 | 1.80908 | ||||||||
\(566\) | 0.169081 | 0.00710698 | ||||||||
\(567\) | −8.76457 | −0.368077 | ||||||||
\(568\) | −3.62032 | −0.151905 | ||||||||
\(569\) | −13.5349 | −0.567412 | −0.283706 | − | 0.958911i | \(-0.591564\pi\) | ||||
−0.283706 | + | 0.958911i | \(0.591564\pi\) | |||||||
\(570\) | −1.36076 | −0.0569959 | ||||||||
\(571\) | −8.45496 | −0.353829 | −0.176914 | − | 0.984226i | \(-0.556612\pi\) | ||||
−0.176914 | + | 0.984226i | \(0.556612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.956001 | 0.0399375 | ||||||||
\(574\) | 7.08347 | 0.295658 | ||||||||
\(575\) | −22.2294 | −0.927029 | ||||||||
\(576\) | −12.9516 | −0.539651 | ||||||||
\(577\) | −16.9054 | −0.703780 | −0.351890 | − | 0.936041i | \(-0.614461\pi\) | ||||
−0.351890 | + | 0.936041i | \(0.614461\pi\) | |||||||
\(578\) | −32.2125 | −1.33986 | ||||||||
\(579\) | 0.526155 | 0.0218663 | ||||||||
\(580\) | −35.1319 | −1.45877 | ||||||||
\(581\) | −9.81167 | −0.407057 | ||||||||
\(582\) | −0.809025 | −0.0335351 | ||||||||
\(583\) | 20.5410 | 0.850722 | ||||||||
\(584\) | 11.9539 | 0.494658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.65142 | −0.0682197 | ||||||||
\(587\) | −10.2055 | −0.421227 | −0.210613 | − | 0.977569i | \(-0.567546\pi\) | ||||
−0.210613 | + | 0.977569i | \(0.567546\pi\) | |||||||
\(588\) | −0.208968 | −0.00861768 | ||||||||
\(589\) | −6.80488 | −0.280390 | ||||||||
\(590\) | 13.3614 | 0.550081 | ||||||||
\(591\) | −1.45653 | −0.0599136 | ||||||||
\(592\) | 0.533327 | 0.0219196 | ||||||||
\(593\) | 3.79490 | 0.155838 | 0.0779190 | − | 0.996960i | \(-0.475172\pi\) | ||||
0.0779190 | + | 0.996960i | \(0.475172\pi\) | |||||||
\(594\) | −2.86451 | −0.117532 | ||||||||
\(595\) | −27.7051 | −1.13580 | ||||||||
\(596\) | −0.656158 | −0.0268773 | ||||||||
\(597\) | 0.904871 | 0.0370339 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.8629 | 0.607281 | 0.303640 | − | 0.952787i | \(-0.401798\pi\) | ||||
0.303640 | + | 0.952787i | \(0.401798\pi\) | |||||||
\(600\) | 3.99468 | 0.163082 | ||||||||
\(601\) | 6.70162 | 0.273365 | 0.136682 | − | 0.990615i | \(-0.456356\pi\) | ||||
0.136682 | + | 0.990615i | \(0.456356\pi\) | |||||||
\(602\) | 10.0196 | 0.408370 | ||||||||
\(603\) | −3.84135 | −0.156432 | ||||||||
\(604\) | −19.9315 | −0.811001 | ||||||||
\(605\) | 5.02044 | 0.204110 | ||||||||
\(606\) | 0.435319 | 0.0176836 | ||||||||
\(607\) | 0.0721187 | 0.00292721 | 0.00146360 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146360 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(608\) | −15.3810 | −0.623783 | ||||||||
\(609\) | −1.18316 | −0.0479443 | ||||||||
\(610\) | −15.9303 | −0.644999 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 28.5131 | 1.15257 | ||||||||
\(613\) | 3.55353 | 0.143526 | 0.0717628 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717628 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(614\) | −21.1785 | −0.854695 | ||||||||
\(615\) | 5.07647 | 0.204703 | ||||||||
\(616\) | 9.74039 | 0.392451 | ||||||||
\(617\) | 33.1215 | 1.33342 | 0.666711 | − | 0.745316i | \(-0.267701\pi\) | ||||
0.666711 | + | 0.745316i | \(0.267701\pi\) | |||||||
\(618\) | 1.33738 | 0.0537973 | ||||||||
\(619\) | 3.55028 | 0.142698 | 0.0713489 | − | 0.997451i | \(-0.477270\pi\) | ||||
0.0713489 | + | 0.997451i | \(0.477270\pi\) | |||||||
\(620\) | 12.2355 | 0.491391 | ||||||||
\(621\) | 2.41755 | 0.0970130 | ||||||||
\(622\) | 24.8817 | 0.997667 | ||||||||
\(623\) | −4.77241 | −0.191202 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.67087 | 0.386835 | ||||||||
\(626\) | −5.63572 | −0.225249 | ||||||||
\(627\) | −1.52234 | −0.0607964 | ||||||||
\(628\) | 11.1452 | 0.444742 | ||||||||
\(629\) | 16.1943 | 0.645709 | ||||||||
\(630\) | −9.34010 | −0.372119 | ||||||||
\(631\) | 27.9899 | 1.11426 | 0.557131 | − | 0.830425i | \(-0.311902\pi\) | ||||
0.557131 | + | 0.830425i | \(0.311902\pi\) | |||||||
\(632\) | 39.4363 | 1.56869 | ||||||||
\(633\) | −3.11222 | −0.123700 | ||||||||
\(634\) | −17.4292 | −0.692201 | ||||||||
\(635\) | 3.30062 | 0.130981 | ||||||||
\(636\) | 1.22159 | 0.0484392 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.6255 | 0.856160 | ||||||||
\(639\) | 3.88377 | 0.153640 | ||||||||
\(640\) | 29.1934 | 1.15397 | ||||||||
\(641\) | 9.33085 | 0.368547 | 0.184273 | − | 0.982875i | \(-0.441007\pi\) | ||||
0.184273 | + | 0.982875i | \(0.441007\pi\) | |||||||
\(642\) | −1.23231 | −0.0486355 | ||||||||
\(643\) | −7.22132 | −0.284781 | −0.142390 | − | 0.989811i | \(-0.545479\pi\) | ||||
−0.142390 | + | 0.989811i | \(0.545479\pi\) | |||||||
\(644\) | −3.22347 | −0.127023 | ||||||||
\(645\) | 7.18071 | 0.282740 | ||||||||
\(646\) | −16.7486 | −0.658966 | ||||||||
\(647\) | −7.65676 | −0.301018 | −0.150509 | − | 0.988609i | \(-0.548091\pi\) | ||||
−0.150509 | + | 0.988609i | \(0.548091\pi\) | |||||||
\(648\) | 24.2958 | 0.954429 | ||||||||
\(649\) | 14.9480 | 0.586761 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.412067 | 0.0161502 | ||||||||
\(652\) | 5.59515 | 0.219123 | ||||||||
\(653\) | −11.6265 | −0.454979 | −0.227490 | − | 0.973780i | \(-0.573052\pi\) | ||||
−0.227490 | + | 0.973780i | \(0.573052\pi\) | |||||||
\(654\) | 0.388982 | 0.0152104 | ||||||||
\(655\) | 49.8265 | 1.94688 | ||||||||
\(656\) | 2.05774 | 0.0803414 | ||||||||
\(657\) | −12.8238 | −0.500305 | ||||||||
\(658\) | −7.92602 | −0.308988 | ||||||||
\(659\) | 42.8815 | 1.67043 | 0.835213 | − | 0.549927i | \(-0.185344\pi\) | ||||
0.835213 | + | 0.549927i | \(0.185344\pi\) | |||||||
\(660\) | 2.73725 | 0.106547 | ||||||||
\(661\) | −41.0681 | −1.59736 | −0.798682 | − | 0.601753i | \(-0.794469\pi\) | ||||
−0.798682 | + | 0.601753i | \(0.794469\pi\) | |||||||
\(662\) | 29.8267 | 1.15925 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.1984 | 1.05550 | ||||||||
\(665\) | −9.97135 | −0.386672 | ||||||||
\(666\) | 5.45952 | 0.211552 | ||||||||
\(667\) | −18.2512 | −0.706687 | ||||||||
\(668\) | 14.2410 | 0.551003 | ||||||||
\(669\) | −2.15534 | −0.0833301 | ||||||||
\(670\) | −4.05716 | −0.156742 | ||||||||
\(671\) | −17.8219 | −0.688009 | ||||||||
\(672\) | 0.931391 | 0.0359292 | ||||||||
\(673\) | −33.2669 | −1.28234 | −0.641172 | − | 0.767397i | \(-0.721551\pi\) | ||||
−0.641172 | + | 0.767397i | \(0.721551\pi\) | |||||||
\(674\) | 5.64408 | 0.217402 | ||||||||
\(675\) | −8.60856 | −0.331343 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.6928 | 1.41022 | 0.705110 | − | 0.709098i | \(-0.250898\pi\) | ||||
0.705110 | + | 0.709098i | \(0.250898\pi\) | |||||||
\(678\) | −1.57416 | −0.0604552 | ||||||||
\(679\) | −5.92836 | −0.227510 | ||||||||
\(680\) | 76.7997 | 2.94513 | ||||||||
\(681\) | −2.16286 | −0.0828810 | ||||||||
\(682\) | −7.53160 | −0.288400 | ||||||||
\(683\) | 19.0493 | 0.728903 | 0.364451 | − | 0.931222i | \(-0.381257\pi\) | ||||
0.364451 | + | 0.931222i | \(0.381257\pi\) | |||||||
\(684\) | 10.2622 | 0.392384 | ||||||||
\(685\) | −68.1756 | −2.60486 | ||||||||
\(686\) | 0.842530 | 0.0321680 | ||||||||
\(687\) | 1.71276 | 0.0653457 | ||||||||
\(688\) | 2.91070 | 0.110969 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.27108 | 0.0483892 | ||||||||
\(691\) | 30.5436 | 1.16193 | 0.580967 | − | 0.813927i | \(-0.302674\pi\) | ||||
0.580967 | + | 0.813927i | \(0.302674\pi\) | |||||||
\(692\) | 13.3376 | 0.507018 | ||||||||
\(693\) | −10.4492 | −0.396932 | ||||||||
\(694\) | 6.21837 | 0.236046 | ||||||||
\(695\) | 11.9698 | 0.454041 | ||||||||
\(696\) | 3.27979 | 0.124320 | ||||||||
\(697\) | 62.4827 | 2.36670 | ||||||||
\(698\) | −12.8173 | −0.485142 | ||||||||
\(699\) | 0.851483 | 0.0322060 | ||||||||
\(700\) | 11.4783 | 0.433840 | ||||||||
\(701\) | 8.37561 | 0.316343 | 0.158171 | − | 0.987412i | \(-0.449440\pi\) | ||||
0.158171 | + | 0.987412i | \(0.449440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.82850 | 0.219826 | ||||||||
\(704\) | −15.3036 | −0.576776 | ||||||||
\(705\) | −5.68029 | −0.213932 | ||||||||
\(706\) | 10.5718 | 0.397873 | ||||||||
\(707\) | 3.18992 | 0.119969 | ||||||||
\(708\) | 0.888969 | 0.0334095 | ||||||||
\(709\) | 8.96509 | 0.336691 | 0.168345 | − | 0.985728i | \(-0.446158\pi\) | ||||
0.168345 | + | 0.985728i | \(0.446158\pi\) | |||||||
\(710\) | 4.10197 | 0.153944 | ||||||||
\(711\) | −42.3061 | −1.58660 | ||||||||
\(712\) | 13.2293 | 0.495790 | ||||||||
\(713\) | 6.35642 | 0.238050 | ||||||||
\(714\) | 1.01421 | 0.0379557 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.2399 | −0.868517 | ||||||||
\(717\) | −3.24598 | −0.121223 | ||||||||
\(718\) | −15.0358 | −0.561132 | ||||||||
\(719\) | −14.3101 | −0.533678 | −0.266839 | − | 0.963741i | \(-0.585979\pi\) | ||||
−0.266839 | + | 0.963741i | \(0.585979\pi\) | |||||||
\(720\) | −2.71330 | −0.101119 | ||||||||
\(721\) | 9.80005 | 0.364973 | ||||||||
\(722\) | 9.98006 | 0.371419 | ||||||||
\(723\) | −3.78188 | −0.140650 | ||||||||
\(724\) | 27.5041 | 1.02218 | ||||||||
\(725\) | 64.9897 | 2.41366 | ||||||||
\(726\) | −0.183784 | −0.00682088 | ||||||||
\(727\) | −19.0723 | −0.707354 | −0.353677 | − | 0.935368i | \(-0.615069\pi\) | ||||
−0.353677 | + | 0.935368i | \(0.615069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.5936 | −0.947911 | ||||||||
\(730\) | −13.5443 | −0.501297 | ||||||||
\(731\) | 88.3824 | 3.26894 | ||||||||
\(732\) | −1.05988 | −0.0391744 | ||||||||
\(733\) | 26.7063 | 0.986418 | 0.493209 | − | 0.869911i | \(-0.335824\pi\) | ||||
0.493209 | + | 0.869911i | \(0.335824\pi\) | |||||||
\(734\) | 26.0570 | 0.961782 | ||||||||
\(735\) | 0.603811 | 0.0222719 | ||||||||
\(736\) | 14.3674 | 0.529588 | ||||||||
\(737\) | −4.53893 | −0.167194 | ||||||||
\(738\) | 21.0646 | 0.775397 | ||||||||
\(739\) | 27.5346 | 1.01288 | 0.506438 | − | 0.862276i | \(-0.330962\pi\) | ||||
0.506438 | + | 0.862276i | \(0.330962\pi\) | |||||||
\(740\) | −10.4800 | −0.385251 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.92529 | −0.180813 | ||||||||
\(743\) | −28.8668 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(744\) | −1.14227 | −0.0418775 | ||||||||
\(745\) | 1.89596 | 0.0694628 | ||||||||
\(746\) | 24.1402 | 0.883835 | ||||||||
\(747\) | −29.1776 | −1.06755 | ||||||||
\(748\) | 33.6910 | 1.23186 | ||||||||
\(749\) | −9.03013 | −0.329954 | ||||||||
\(750\) | −1.98249 | −0.0723902 | ||||||||
\(751\) | 6.62174 | 0.241631 | 0.120815 | − | 0.992675i | \(-0.461449\pi\) | ||||
0.120815 | + | 0.992675i | \(0.461449\pi\) | |||||||
\(752\) | −2.30250 | −0.0839637 | ||||||||
\(753\) | 2.33664 | 0.0851519 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.5920 | 2.09599 | ||||||||
\(756\) | −1.24832 | −0.0454011 | ||||||||
\(757\) | 35.9013 | 1.30485 | 0.652427 | − | 0.757852i | \(-0.273751\pi\) | ||||
0.652427 | + | 0.757852i | \(0.273751\pi\) | |||||||
\(758\) | −3.88996 | −0.141290 | ||||||||
\(759\) | 1.42201 | 0.0516158 | ||||||||
\(760\) | 27.6410 | 1.00265 | ||||||||
\(761\) | −27.2881 | −0.989191 | −0.494596 | − | 0.869123i | \(-0.664684\pi\) | ||||
−0.494596 | + | 0.869123i | \(0.664684\pi\) | |||||||
\(762\) | −0.120827 | −0.00437709 | ||||||||
\(763\) | 2.85038 | 0.103191 | ||||||||
\(764\) | −7.61473 | −0.275491 | ||||||||
\(765\) | −82.3883 | −2.97876 | ||||||||
\(766\) | −23.4197 | −0.846190 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.47957 | −0.0894736 | ||||||||
\(769\) | 20.3268 | 0.733003 | 0.366501 | − | 0.930418i | \(-0.380556\pi\) | ||||
0.366501 | + | 0.930418i | \(0.380556\pi\) | |||||||
\(770\) | −11.0362 | −0.397718 | ||||||||
\(771\) | 2.11315 | 0.0761033 | ||||||||
\(772\) | −4.19093 | −0.150835 | ||||||||
\(773\) | −4.74178 | −0.170550 | −0.0852750 | − | 0.996357i | \(-0.527177\pi\) | ||||
−0.0852750 | + | 0.996357i | \(0.527177\pi\) | |||||||
\(774\) | 29.7960 | 1.07100 | ||||||||
\(775\) | −22.6343 | −0.813047 | ||||||||
\(776\) | 16.4337 | 0.589935 | ||||||||
\(777\) | −0.352943 | −0.0126617 | ||||||||
\(778\) | −14.2136 | −0.509584 | ||||||||
\(779\) | 22.4882 | 0.805724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.58905 | 0.164209 | ||||||||
\(782\) | 15.6448 | 0.559459 | ||||||||
\(783\) | −7.06795 | −0.252588 | ||||||||
\(784\) | 0.244755 | 0.00874124 | ||||||||
\(785\) | −32.2040 | −1.14941 | ||||||||
\(786\) | −1.82401 | −0.0650604 | ||||||||
\(787\) | −31.6106 | −1.12679 | −0.563397 | − | 0.826186i | \(-0.690506\pi\) | ||||
−0.563397 | + | 0.826186i | \(0.690506\pi\) | |||||||
\(788\) | 11.6015 | 0.413287 | ||||||||
\(789\) | 2.70799 | 0.0964072 | ||||||||
\(790\) | −44.6829 | −1.58974 | ||||||||
\(791\) | −11.5351 | −0.410141 | ||||||||
\(792\) | 28.9656 | 1.02925 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.4546 | −0.725906 | ||||||||
\(795\) | −3.52978 | −0.125188 | ||||||||
\(796\) | −7.20747 | −0.255462 | ||||||||
\(797\) | −47.1670 | −1.67074 | −0.835370 | − | 0.549688i | \(-0.814747\pi\) | ||||
−0.835370 | + | 0.549688i | \(0.814747\pi\) | |||||||
\(798\) | 0.365024 | 0.0129217 | ||||||||
\(799\) | −69.9148 | −2.47341 | ||||||||
\(800\) | −51.1601 | −1.80878 | ||||||||
\(801\) | −14.1920 | −0.501450 | ||||||||
\(802\) | 20.2463 | 0.714923 | ||||||||
\(803\) | −15.1526 | −0.534724 | ||||||||
\(804\) | −0.269933 | −0.00951982 | ||||||||
\(805\) | 9.31421 | 0.328283 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00056 | 0.0352213 | ||||||||
\(808\) | −8.84261 | −0.311082 | ||||||||
\(809\) | −11.6238 | −0.408672 | −0.204336 | − | 0.978901i | \(-0.565504\pi\) | ||||
−0.204336 | + | 0.978901i | \(0.565504\pi\) | |||||||
\(810\) | −27.5281 | −0.967238 | ||||||||
\(811\) | 9.29601 | 0.326427 | 0.163214 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163214 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(812\) | 9.42414 | 0.330722 | ||||||||
\(813\) | −4.87579 | −0.171001 | ||||||||
\(814\) | 6.45096 | 0.226106 | ||||||||
\(815\) | −16.1671 | −0.566310 | ||||||||
\(816\) | 0.294626 | 0.0103140 | ||||||||
\(817\) | 31.8098 | 1.11288 | ||||||||
\(818\) | 1.72561 | 0.0603347 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −40.4350 | −1.41205 | ||||||||
\(821\) | 44.2153 | 1.54312 | 0.771562 | − | 0.636154i | \(-0.219476\pi\) | ||||
0.771562 | + | 0.636154i | \(0.219476\pi\) | |||||||
\(822\) | 2.49572 | 0.0870483 | ||||||||
\(823\) | 20.1303 | 0.701700 | 0.350850 | − | 0.936432i | \(-0.385893\pi\) | ||||
0.350850 | + | 0.936432i | \(0.385893\pi\) | |||||||
\(824\) | −27.1662 | −0.946378 | ||||||||
\(825\) | −5.06359 | −0.176291 | ||||||||
\(826\) | −3.58421 | −0.124710 | ||||||||
\(827\) | 13.4329 | 0.467109 | 0.233554 | − | 0.972344i | \(-0.424964\pi\) | ||||
0.233554 | + | 0.972344i | \(0.424964\pi\) | |||||||
\(828\) | −9.58585 | −0.333131 | ||||||||
\(829\) | −4.62491 | −0.160630 | −0.0803148 | − | 0.996770i | \(-0.525593\pi\) | ||||
−0.0803148 | + | 0.996770i | \(0.525593\pi\) | |||||||
\(830\) | −30.8168 | −1.06967 | ||||||||
\(831\) | −0.973741 | −0.0337787 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.43189 | 0.257500 | ||||||||
\(834\) | −0.438182 | −0.0151730 | ||||||||
\(835\) | −41.1494 | −1.42403 | ||||||||
\(836\) | 12.1257 | 0.419378 | ||||||||
\(837\) | 2.46159 | 0.0850849 | ||||||||
\(838\) | 21.8495 | 0.754780 | ||||||||
\(839\) | −44.5747 | −1.53889 | −0.769446 | − | 0.638712i | \(-0.779467\pi\) | ||||
−0.769446 | + | 0.638712i | \(0.779467\pi\) | |||||||
\(840\) | −1.67379 | −0.0577513 | ||||||||
\(841\) | 24.3590 | 0.839966 | ||||||||
\(842\) | −18.9685 | −0.653698 | ||||||||
\(843\) | −4.28923 | −0.147729 | ||||||||
\(844\) | 24.7895 | 0.853289 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.5701 | −0.810357 | ||||||||
\(847\) | −1.34673 | −0.0462743 | ||||||||
\(848\) | −1.43079 | −0.0491337 | ||||||||
\(849\) | −0.0325050 | −0.00111557 | ||||||||
\(850\) | −55.7090 | −1.91080 | ||||||||
\(851\) | −5.44439 | −0.186631 | ||||||||
\(852\) | 0.272914 | 0.00934989 | ||||||||
\(853\) | −4.58159 | −0.156870 | −0.0784352 | − | 0.996919i | \(-0.524992\pi\) | ||||
−0.0784352 | + | 0.996919i | \(0.524992\pi\) | |||||||
\(854\) | 4.27331 | 0.146230 | ||||||||
\(855\) | −29.6525 | −1.01409 | ||||||||
\(856\) | 25.0319 | 0.855573 | ||||||||
\(857\) | 15.4008 | 0.526080 | 0.263040 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263040 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.8596 | −1.80355 | −0.901774 | − | 0.432208i | \(-0.857735\pi\) | ||||
−0.901774 | + | 0.432208i | \(0.857735\pi\) | |||||||
\(860\) | −57.1958 | −1.95036 | ||||||||
\(861\) | −1.36176 | −0.0464088 | ||||||||
\(862\) | 2.34285 | 0.0797979 | ||||||||
\(863\) | 33.2346 | 1.13132 | 0.565659 | − | 0.824639i | \(-0.308622\pi\) | ||||
0.565659 | + | 0.824639i | \(0.308622\pi\) | |||||||
\(864\) | 5.56391 | 0.189288 | ||||||||
\(865\) | −38.5388 | −1.31036 | ||||||||
\(866\) | −21.5357 | −0.731813 | ||||||||
\(867\) | 6.19270 | 0.210315 | ||||||||
\(868\) | −3.28219 | −0.111405 | ||||||||
\(869\) | −49.9887 | −1.69575 | ||||||||
\(870\) | −3.71613 | −0.125988 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.90138 | −0.267574 | ||||||||
\(873\) | −17.6296 | −0.596670 | ||||||||
\(874\) | 5.63075 | 0.190463 | ||||||||
\(875\) | −14.5273 | −0.491111 | ||||||||
\(876\) | −0.901136 | −0.0304466 | ||||||||
\(877\) | 24.1314 | 0.814858 | 0.407429 | − | 0.913237i | \(-0.366425\pi\) | ||||
0.407429 | + | 0.913237i | \(0.366425\pi\) | |||||||
\(878\) | 26.6931 | 0.900849 | ||||||||
\(879\) | 0.317478 | 0.0107083 | ||||||||
\(880\) | −3.20602 | −0.108075 | ||||||||
\(881\) | 59.0833 | 1.99057 | 0.995284 | − | 0.0970036i | \(-0.0309258\pi\) | ||||
0.995284 | + | 0.0970036i | \(0.0309258\pi\) | |||||||
\(882\) | 2.50549 | 0.0843641 | ||||||||
\(883\) | −8.09950 | −0.272570 | −0.136285 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136285 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.56867 | −0.0863449 | ||||||||
\(886\) | 14.4868 | 0.486692 | ||||||||
\(887\) | −34.8540 | −1.17028 | −0.585142 | − | 0.810931i | \(-0.698961\pi\) | ||||
−0.585142 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(888\) | 0.978373 | 0.0328320 | ||||||||
\(889\) | −0.885393 | −0.0296951 | ||||||||
\(890\) | −14.9893 | −0.502444 | ||||||||
\(891\) | −30.7969 | −1.03173 | ||||||||
\(892\) | 17.1677 | 0.574816 | ||||||||
\(893\) | −25.1631 | −0.842051 | ||||||||
\(894\) | −0.0694061 | −0.00232129 | ||||||||
\(895\) | 67.1516 | 2.24463 | ||||||||
\(896\) | −7.83114 | −0.261620 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0905 | 0.403466 | ||||||||
\(899\) | −18.5836 | −0.619798 | ||||||||
\(900\) | 34.1338 | 1.13779 | ||||||||
\(901\) | −43.4456 | −1.44738 | ||||||||
\(902\) | 24.8898 | 0.828741 | ||||||||
\(903\) | −1.92623 | −0.0641009 | ||||||||
\(904\) | 31.9758 | 1.06350 | ||||||||
\(905\) | −79.4730 | −2.64177 | ||||||||
\(906\) | −2.10828 | −0.0700430 | ||||||||
\(907\) | 10.2919 | 0.341738 | 0.170869 | − | 0.985294i | \(-0.445343\pi\) | ||||
0.170869 | + | 0.985294i | \(0.445343\pi\) | |||||||
\(908\) | 17.2276 | 0.571718 | ||||||||
\(909\) | 9.48609 | 0.314634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.2867 | −1.79860 | −0.899299 | − | 0.437334i | \(-0.855923\pi\) | ||||
−0.899299 | + | 0.437334i | \(0.855923\pi\) | |||||||
\(912\) | 0.106039 | 0.00351131 | ||||||||
\(913\) | −34.4762 | −1.14099 | ||||||||
\(914\) | 12.7127 | 0.420500 | ||||||||
\(915\) | 3.06253 | 0.101244 | ||||||||
\(916\) | −13.6424 | −0.450759 | ||||||||
\(917\) | −13.3660 | −0.441384 | ||||||||
\(918\) | 6.05863 | 0.199965 | ||||||||
\(919\) | 43.4286 | 1.43258 | 0.716289 | − | 0.697803i | \(-0.245839\pi\) | ||||
0.716289 | + | 0.697803i | \(0.245839\pi\) | |||||||
\(920\) | −25.8194 | −0.851240 | ||||||||
\(921\) | 4.07147 | 0.134160 | ||||||||
\(922\) | 13.3841 | 0.440783 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.734269 | −0.0241557 | ||||||||
\(925\) | 19.3867 | 0.637430 | ||||||||
\(926\) | 5.92599 | 0.194740 | ||||||||
\(927\) | 29.1430 | 0.957183 | ||||||||
\(928\) | −42.0044 | −1.37886 | ||||||||
\(929\) | −30.8380 | −1.01176 | −0.505881 | − | 0.862603i | \(-0.668832\pi\) | ||||
−0.505881 | + | 0.862603i | \(0.668832\pi\) | |||||||
\(930\) | 1.29423 | 0.0424396 | ||||||||
\(931\) | 2.67482 | 0.0876637 | ||||||||
\(932\) | −6.78223 | −0.222159 | ||||||||
\(933\) | −4.78340 | −0.156602 | ||||||||
\(934\) | 0.523556 | 0.0171313 | ||||||||
\(935\) | −97.3498 | −3.18368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4073 | 0.732013 | 0.366007 | − | 0.930612i | \(-0.380725\pi\) | ||||
0.366007 | + | 0.930612i | \(0.380725\pi\) | |||||||
\(938\) | 1.08834 | 0.0355354 | ||||||||
\(939\) | 1.08344 | 0.0353568 | ||||||||
\(940\) | 45.2446 | 1.47572 | ||||||||
\(941\) | −12.2484 | −0.399287 | −0.199644 | − | 0.979869i | \(-0.563978\pi\) | ||||
−0.199644 | + | 0.979869i | \(0.563978\pi\) | |||||||
\(942\) | 1.17890 | 0.0384106 | ||||||||
\(943\) | −21.0062 | −0.684055 | ||||||||
\(944\) | −1.04121 | −0.0338885 | ||||||||
\(945\) | 3.60703 | 0.117337 | ||||||||
\(946\) | 35.2069 | 1.14468 | ||||||||
\(947\) | 53.1071 | 1.72575 | 0.862875 | − | 0.505418i | \(-0.168662\pi\) | ||||
0.862875 | + | 0.505418i | \(0.168662\pi\) | |||||||
\(948\) | −2.97286 | −0.0965541 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20.0503 | −0.650517 | ||||||||
\(951\) | 3.35068 | 0.108653 | ||||||||
\(952\) | −20.6015 | −0.667700 | ||||||||
\(953\) | −9.63675 | −0.312165 | −0.156082 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156082 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(954\) | −14.6466 | −0.474203 | ||||||||
\(955\) | 22.0027 | 0.711991 | ||||||||
\(956\) | 25.8548 | 0.836205 | ||||||||
\(957\) | −4.15740 | −0.134390 | ||||||||
\(958\) | −20.7601 | −0.670727 | ||||||||
\(959\) | 18.2881 | 0.590555 | ||||||||
\(960\) | 2.62977 | 0.0848756 | ||||||||
\(961\) | −24.5278 | −0.791219 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.8535 | −0.865341 | ||||||||
\(964\) | 30.1234 | 0.970209 | ||||||||
\(965\) | 12.1097 | 0.389824 | ||||||||
\(966\) | −0.340968 | −0.0109705 | ||||||||
\(967\) | −12.8720 | −0.413937 | −0.206968 | − | 0.978348i | \(-0.566360\pi\) | ||||
−0.206968 | + | 0.978348i | \(0.566360\pi\) | |||||||
\(968\) | 3.73321 | 0.119990 | ||||||||
\(969\) | 3.21985 | 0.103436 | ||||||||
\(970\) | −18.6200 | −0.597853 | ||||||||
\(971\) | −58.2615 | −1.86970 | −0.934850 | − | 0.355042i | \(-0.884467\pi\) | ||||
−0.934850 | + | 0.355042i | \(0.884467\pi\) | |||||||
\(972\) | −5.57649 | −0.178866 | ||||||||
\(973\) | −3.21091 | −0.102937 | ||||||||
\(974\) | 17.5879 | 0.563553 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.24139 | 0.0397361 | ||||||||
\(977\) | −29.7552 | −0.951954 | −0.475977 | − | 0.879458i | \(-0.657906\pi\) | ||||
−0.475977 | + | 0.879458i | \(0.657906\pi\) | |||||||
\(978\) | 0.591835 | 0.0189248 | ||||||||
\(979\) | −16.7692 | −0.535948 | ||||||||
\(980\) | −4.80947 | −0.153633 | ||||||||
\(981\) | 8.47636 | 0.270629 | ||||||||
\(982\) | 2.09237 | 0.0667703 | ||||||||
\(983\) | −11.6376 | −0.371181 | −0.185591 | − | 0.982627i | \(-0.559420\pi\) | ||||
−0.185591 | + | 0.982627i | \(0.559420\pi\) | |||||||
\(984\) | 3.77487 | 0.120338 | ||||||||
\(985\) | −33.5226 | −1.06812 | ||||||||
\(986\) | −45.7392 | −1.45663 | ||||||||
\(987\) | 1.52374 | 0.0485012 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.7134 | −0.944832 | ||||||||
\(990\) | −32.8192 | −1.04306 | ||||||||
\(991\) | 3.02153 | 0.0959820 | 0.0479910 | − | 0.998848i | \(-0.484718\pi\) | ||||
0.0479910 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(992\) | 14.6291 | 0.464473 | ||||||||
\(993\) | −5.73405 | −0.181965 | ||||||||
\(994\) | −1.10035 | −0.0349011 | ||||||||
\(995\) | 20.8259 | 0.660227 | ||||||||
\(996\) | −2.05032 | −0.0649670 | ||||||||
\(997\) | 20.0738 | 0.635742 | 0.317871 | − | 0.948134i | \(-0.397032\pi\) | ||||
0.317871 | + | 0.948134i | \(0.397032\pi\) | |||||||
\(998\) | 0.360269 | 0.0114041 | ||||||||
\(999\) | −2.10840 | −0.0667067 |
(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 | 1183.2.a.q.1.6 | ✓ | 12 | |
7.6 | odd | 2 | 8281.2.a.cn.1.6 | 12 | |||
13.5 | odd | 4 | 1183.2.c.j.337.14 | 24 | |||
13.8 | odd | 4 | 1183.2.c.j.337.11 | 24 | |||
13.12 | even | 2 | 1183.2.a.r.1.7 | yes | 12 | ||
91.90 | odd | 2 | 8281.2.a.cq.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1183.2.a.r.1.7 | yes | 12 | 13.12 | even | 2 | ||
1183.2.c.j.337.11 | 24 | 13.8 | odd | 4 | |||
1183.2.c.j.337.14 | 24 | 13.5 | odd | 4 | |||
8281.2.a.cn.1.6 | 12 | 7.6 | odd | 2 | |||
8281.2.a.cq.1.7 | 12 | 91.90 | odd | 2 |