Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28791 | −1.61780 | −0.808898 | − | 0.587948i | \(-0.799936\pi\) | ||||
−0.808898 | + | 0.587948i | \(0.799936\pi\) | |||||||
\(3\) | −0.433636 | −0.250360 | −0.125180 | − | 0.992134i | \(-0.539951\pi\) | ||||
−0.125180 | + | 0.992134i | \(0.539951\pi\) | |||||||
\(4\) | 3.23453 | 1.61727 | ||||||||
\(5\) | 1.92947 | 0.862885 | 0.431442 | − | 0.902140i | \(-0.358005\pi\) | ||||
0.431442 | + | 0.902140i | \(0.358005\pi\) | |||||||
\(6\) | 0.992121 | 0.405032 | ||||||||
\(7\) | 3.12765 | 1.18214 | 0.591069 | − | 0.806621i | \(-0.298706\pi\) | ||||
0.591069 | + | 0.806621i | \(0.298706\pi\) | |||||||
\(8\) | −2.82450 | −0.998611 | ||||||||
\(9\) | −2.81196 | −0.937320 | ||||||||
\(10\) | −4.41445 | −1.39597 | ||||||||
\(11\) | 3.32297 | 1.00191 | 0.500956 | − | 0.865473i | \(-0.332982\pi\) | ||||
0.500956 | + | 0.865473i | \(0.332982\pi\) | |||||||
\(12\) | −1.40261 | −0.404899 | ||||||||
\(13\) | −6.14688 | −1.70484 | −0.852419 | − | 0.522859i | \(-0.824865\pi\) | ||||
−0.852419 | + | 0.522859i | \(0.824865\pi\) | |||||||
\(14\) | −7.15577 | −1.91246 | ||||||||
\(15\) | −0.836688 | −0.216032 | ||||||||
\(16\) | −0.00686423 | −0.00171606 | ||||||||
\(17\) | 0.414157 | 0.100448 | 0.0502240 | − | 0.998738i | \(-0.484006\pi\) | ||||
0.0502240 | + | 0.998738i | \(0.484006\pi\) | |||||||
\(18\) | 6.43351 | 1.51639 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 6.24093 | 1.39551 | ||||||||
\(21\) | −1.35626 | −0.295960 | ||||||||
\(22\) | −7.60265 | −1.62089 | ||||||||
\(23\) | −1.43364 | −0.298935 | −0.149468 | − | 0.988767i | \(-0.547756\pi\) | ||||
−0.149468 | + | 0.988767i | \(0.547756\pi\) | |||||||
\(24\) | 1.22481 | 0.250012 | ||||||||
\(25\) | −1.27715 | −0.255430 | ||||||||
\(26\) | 14.0635 | 2.75808 | ||||||||
\(27\) | 2.52028 | 0.485027 | ||||||||
\(28\) | 10.1165 | 1.91183 | ||||||||
\(29\) | 5.96085 | 1.10690 | 0.553451 | − | 0.832882i | \(-0.313311\pi\) | ||||
0.553451 | + | 0.832882i | \(0.313311\pi\) | |||||||
\(30\) | 1.91427 | 0.349496 | ||||||||
\(31\) | −4.07439 | −0.731782 | −0.365891 | − | 0.930658i | \(-0.619236\pi\) | ||||
−0.365891 | + | 0.930658i | \(0.619236\pi\) | |||||||
\(32\) | 5.66470 | 1.00139 | ||||||||
\(33\) | −1.44096 | −0.250839 | ||||||||
\(34\) | −0.947555 | −0.162504 | ||||||||
\(35\) | 6.03469 | 1.02005 | ||||||||
\(36\) | −9.09538 | −1.51590 | ||||||||
\(37\) | −5.79741 | −0.953088 | −0.476544 | − | 0.879151i | \(-0.658111\pi\) | ||||
−0.476544 | + | 0.879151i | \(0.658111\pi\) | |||||||
\(38\) | −2.28791 | −0.371148 | ||||||||
\(39\) | 2.66551 | 0.426823 | ||||||||
\(40\) | −5.44978 | −0.861687 | ||||||||
\(41\) | −2.66125 | −0.415617 | −0.207809 | − | 0.978169i | \(-0.566633\pi\) | ||||
−0.207809 | + | 0.978169i | \(0.566633\pi\) | |||||||
\(42\) | 3.10300 | 0.478804 | ||||||||
\(43\) | 9.79443 | 1.49364 | 0.746818 | − | 0.665028i | \(-0.231581\pi\) | ||||
0.746818 | + | 0.665028i | \(0.231581\pi\) | |||||||
\(44\) | 10.7482 | 1.62036 | ||||||||
\(45\) | −5.42559 | −0.808799 | ||||||||
\(46\) | 3.28005 | 0.483616 | ||||||||
\(47\) | −1.77055 | −0.258261 | −0.129131 | − | 0.991628i | \(-0.541219\pi\) | ||||
−0.129131 | + | 0.991628i | \(0.541219\pi\) | |||||||
\(48\) | 0.00297658 | 0.000429632 0 | ||||||||
\(49\) | 2.78217 | 0.397452 | ||||||||
\(50\) | 2.92200 | 0.413234 | ||||||||
\(51\) | −0.179594 | −0.0251481 | ||||||||
\(52\) | −19.8823 | −2.75718 | ||||||||
\(53\) | −8.51997 | −1.17031 | −0.585154 | − | 0.810922i | \(-0.698966\pi\) | ||||
−0.585154 | + | 0.810922i | \(0.698966\pi\) | |||||||
\(54\) | −5.76616 | −0.784676 | ||||||||
\(55\) | 6.41156 | 0.864534 | ||||||||
\(56\) | −8.83403 | −1.18050 | ||||||||
\(57\) | −0.433636 | −0.0574365 | ||||||||
\(58\) | −13.6379 | −1.79074 | ||||||||
\(59\) | −15.1036 | −1.96632 | −0.983162 | − | 0.182734i | \(-0.941505\pi\) | ||||
−0.983162 | + | 0.182734i | \(0.941505\pi\) | |||||||
\(60\) | −2.70629 | −0.349381 | ||||||||
\(61\) | −9.57471 | −1.22592 | −0.612958 | − | 0.790115i | \(-0.710021\pi\) | ||||
−0.612958 | + | 0.790115i | \(0.710021\pi\) | |||||||
\(62\) | 9.32184 | 1.18387 | ||||||||
\(63\) | −8.79481 | −1.10804 | ||||||||
\(64\) | −12.9466 | −1.61833 | ||||||||
\(65\) | −11.8602 | −1.47108 | ||||||||
\(66\) | 3.29678 | 0.405806 | ||||||||
\(67\) | 0.513387 | 0.0627202 | 0.0313601 | − | 0.999508i | \(-0.490016\pi\) | ||||
0.0313601 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(68\) | 1.33961 | 0.162451 | ||||||||
\(69\) | 0.621679 | 0.0748414 | ||||||||
\(70\) | −13.8068 | −1.65023 | ||||||||
\(71\) | −6.51152 | −0.772776 | −0.386388 | − | 0.922336i | \(-0.626277\pi\) | ||||
−0.386388 | + | 0.922336i | \(0.626277\pi\) | |||||||
\(72\) | 7.94238 | 0.936018 | ||||||||
\(73\) | −1.35387 | −0.158459 | −0.0792293 | − | 0.996856i | \(-0.525246\pi\) | ||||
−0.0792293 | + | 0.996856i | \(0.525246\pi\) | |||||||
\(74\) | 13.2639 | 1.54190 | ||||||||
\(75\) | 0.553818 | 0.0639494 | ||||||||
\(76\) | 3.23453 | 0.371026 | ||||||||
\(77\) | 10.3931 | 1.18440 | ||||||||
\(78\) | −6.09845 | −0.690513 | ||||||||
\(79\) | 10.5946 | 1.19199 | 0.595995 | − | 0.802988i | \(-0.296758\pi\) | ||||
0.595995 | + | 0.802988i | \(0.296758\pi\) | |||||||
\(80\) | −0.0132443 | −0.00148076 | ||||||||
\(81\) | 7.34300 | 0.815888 | ||||||||
\(82\) | 6.08870 | 0.672384 | ||||||||
\(83\) | 5.31145 | 0.583008 | 0.291504 | − | 0.956570i | \(-0.405844\pi\) | ||||
0.291504 | + | 0.956570i | \(0.405844\pi\) | |||||||
\(84\) | −4.38687 | −0.478647 | ||||||||
\(85\) | 0.799104 | 0.0866750 | ||||||||
\(86\) | −22.4088 | −2.41640 | ||||||||
\(87\) | −2.58484 | −0.277124 | ||||||||
\(88\) | −9.38571 | −1.00052 | ||||||||
\(89\) | −10.1959 | −1.08076 | −0.540382 | − | 0.841420i | \(-0.681720\pi\) | ||||
−0.540382 | + | 0.841420i | \(0.681720\pi\) | |||||||
\(90\) | 12.4133 | 1.30847 | ||||||||
\(91\) | −19.2253 | −2.01536 | ||||||||
\(92\) | −4.63716 | −0.483458 | ||||||||
\(93\) | 1.76680 | 0.183209 | ||||||||
\(94\) | 4.05086 | 0.417814 | ||||||||
\(95\) | 1.92947 | 0.197959 | ||||||||
\(96\) | −2.45642 | −0.250707 | ||||||||
\(97\) | −11.1926 | −1.13643 | −0.568217 | − | 0.822879i | \(-0.692366\pi\) | ||||
−0.568217 | + | 0.822879i | \(0.692366\pi\) | |||||||
\(98\) | −6.36535 | −0.642997 | ||||||||
\(99\) | −9.34405 | −0.939112 | ||||||||
\(100\) | −4.13098 | −0.413098 | ||||||||
\(101\) | −11.4371 | −1.13803 | −0.569017 | − | 0.822326i | \(-0.692676\pi\) | ||||
−0.569017 | + | 0.822326i | \(0.692676\pi\) | |||||||
\(102\) | 0.410894 | 0.0406846 | ||||||||
\(103\) | 11.8303 | 1.16567 | 0.582836 | − | 0.812590i | \(-0.301943\pi\) | ||||
0.582836 | + | 0.812590i | \(0.301943\pi\) | |||||||
\(104\) | 17.3619 | 1.70247 | ||||||||
\(105\) | −2.61686 | −0.255380 | ||||||||
\(106\) | 19.4929 | 1.89332 | ||||||||
\(107\) | 2.94013 | 0.284233 | 0.142116 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142116 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(108\) | 8.15191 | 0.784418 | ||||||||
\(109\) | −6.31183 | −0.604564 | −0.302282 | − | 0.953219i | \(-0.597748\pi\) | ||||
−0.302282 | + | 0.953219i | \(0.597748\pi\) | |||||||
\(110\) | −14.6691 | −1.39864 | ||||||||
\(111\) | 2.51397 | 0.238615 | ||||||||
\(112\) | −0.0214689 | −0.00202862 | ||||||||
\(113\) | −2.39064 | −0.224893 | −0.112446 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112446 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(114\) | 0.992121 | 0.0929206 | ||||||||
\(115\) | −2.76617 | −0.257947 | ||||||||
\(116\) | 19.2806 | 1.79015 | ||||||||
\(117\) | 17.2848 | 1.59798 | ||||||||
\(118\) | 34.5557 | 3.18111 | ||||||||
\(119\) | 1.29534 | 0.118743 | ||||||||
\(120\) | 2.36322 | 0.215732 | ||||||||
\(121\) | 0.0421006 | 0.00382733 | ||||||||
\(122\) | 21.9061 | 1.98328 | ||||||||
\(123\) | 1.15401 | 0.104054 | ||||||||
\(124\) | −13.1787 | −1.18349 | ||||||||
\(125\) | −12.1116 | −1.08329 | ||||||||
\(126\) | 20.1217 | 1.79259 | ||||||||
\(127\) | −10.8008 | −0.958412 | −0.479206 | − | 0.877702i | \(-0.659075\pi\) | ||||
−0.479206 | + | 0.877702i | \(0.659075\pi\) | |||||||
\(128\) | 18.2913 | 1.61673 | ||||||||
\(129\) | −4.24722 | −0.373947 | ||||||||
\(130\) | 27.1351 | 2.37991 | ||||||||
\(131\) | 6.67408 | 0.583117 | 0.291559 | − | 0.956553i | \(-0.405826\pi\) | ||||
0.291559 | + | 0.956553i | \(0.405826\pi\) | |||||||
\(132\) | −4.66083 | −0.405673 | ||||||||
\(133\) | 3.12765 | 0.271201 | ||||||||
\(134\) | −1.17458 | −0.101468 | ||||||||
\(135\) | 4.86279 | 0.418523 | ||||||||
\(136\) | −1.16979 | −0.100308 | ||||||||
\(137\) | −16.9404 | −1.44732 | −0.723660 | − | 0.690157i | \(-0.757542\pi\) | ||||
−0.723660 | + | 0.690157i | \(0.757542\pi\) | |||||||
\(138\) | −1.42235 | −0.121078 | ||||||||
\(139\) | 22.2056 | 1.88346 | 0.941729 | − | 0.336372i | \(-0.109200\pi\) | ||||
0.941729 | + | 0.336372i | \(0.109200\pi\) | |||||||
\(140\) | 19.5194 | 1.64969 | ||||||||
\(141\) | 0.767774 | 0.0646583 | ||||||||
\(142\) | 14.8978 | 1.25019 | ||||||||
\(143\) | −20.4259 | −1.70810 | ||||||||
\(144\) | 0.0193019 | 0.00160850 | ||||||||
\(145\) | 11.5013 | 0.955129 | ||||||||
\(146\) | 3.09753 | 0.256354 | ||||||||
\(147\) | −1.20645 | −0.0995062 | ||||||||
\(148\) | −18.7519 | −1.54140 | ||||||||
\(149\) | −21.1259 | −1.73070 | −0.865351 | − | 0.501166i | \(-0.832904\pi\) | ||||
−0.865351 | + | 0.501166i | \(0.832904\pi\) | |||||||
\(150\) | −1.26709 | −0.103457 | ||||||||
\(151\) | 16.5480 | 1.34666 | 0.673329 | − | 0.739343i | \(-0.264864\pi\) | ||||
0.673329 | + | 0.739343i | \(0.264864\pi\) | |||||||
\(152\) | −2.82450 | −0.229097 | ||||||||
\(153\) | −1.16459 | −0.0941518 | ||||||||
\(154\) | −23.7784 | −1.91612 | ||||||||
\(155\) | −7.86141 | −0.631444 | ||||||||
\(156\) | 8.62168 | 0.690287 | ||||||||
\(157\) | −7.26961 | −0.580178 | −0.290089 | − | 0.957000i | \(-0.593685\pi\) | ||||
−0.290089 | + | 0.957000i | \(0.593685\pi\) | |||||||
\(158\) | −24.2396 | −1.92840 | ||||||||
\(159\) | 3.69457 | 0.292998 | ||||||||
\(160\) | 10.9299 | 0.864082 | ||||||||
\(161\) | −4.48393 | −0.353383 | ||||||||
\(162\) | −16.8001 | −1.31994 | ||||||||
\(163\) | 10.8741 | 0.851729 | 0.425864 | − | 0.904787i | \(-0.359970\pi\) | ||||
0.425864 | + | 0.904787i | \(0.359970\pi\) | |||||||
\(164\) | −8.60790 | −0.672164 | ||||||||
\(165\) | −2.78028 | −0.216445 | ||||||||
\(166\) | −12.1521 | −0.943188 | ||||||||
\(167\) | −6.37658 | −0.493434 | −0.246717 | − | 0.969088i | \(-0.579352\pi\) | ||||
−0.246717 | + | 0.969088i | \(0.579352\pi\) | |||||||
\(168\) | 3.83076 | 0.295549 | ||||||||
\(169\) | 24.7841 | 1.90647 | ||||||||
\(170\) | −1.82828 | −0.140223 | ||||||||
\(171\) | −2.81196 | −0.215036 | ||||||||
\(172\) | 31.6804 | 2.41561 | ||||||||
\(173\) | 16.4117 | 1.24776 | 0.623880 | − | 0.781520i | \(-0.285555\pi\) | ||||
0.623880 | + | 0.781520i | \(0.285555\pi\) | |||||||
\(174\) | 5.91388 | 0.448330 | ||||||||
\(175\) | −3.99447 | −0.301954 | ||||||||
\(176\) | −0.0228096 | −0.00171934 | ||||||||
\(177\) | 6.54948 | 0.492289 | ||||||||
\(178\) | 23.3273 | 1.74846 | ||||||||
\(179\) | −10.2673 | −0.767410 | −0.383705 | − | 0.923456i | \(-0.625352\pi\) | ||||
−0.383705 | + | 0.923456i | \(0.625352\pi\) | |||||||
\(180\) | −17.5492 | −1.30804 | ||||||||
\(181\) | −0.0275621 | −0.00204868 | −0.00102434 | − | 0.999999i | \(-0.500326\pi\) | ||||
−0.00102434 | + | 0.999999i | \(0.500326\pi\) | |||||||
\(182\) | 43.9857 | 3.26044 | ||||||||
\(183\) | 4.15194 | 0.306920 | ||||||||
\(184\) | 4.04932 | 0.298520 | ||||||||
\(185\) | −11.1859 | −0.822405 | ||||||||
\(186\) | −4.04229 | −0.296395 | ||||||||
\(187\) | 1.37623 | 0.100640 | ||||||||
\(188\) | −5.72690 | −0.417677 | ||||||||
\(189\) | 7.88253 | 0.573370 | ||||||||
\(190\) | −4.41445 | −0.320258 | ||||||||
\(191\) | 3.94185 | 0.285222 | 0.142611 | − | 0.989779i | \(-0.454450\pi\) | ||||
0.142611 | + | 0.989779i | \(0.454450\pi\) | |||||||
\(192\) | 5.61412 | 0.405164 | ||||||||
\(193\) | 12.8805 | 0.927159 | 0.463579 | − | 0.886055i | \(-0.346565\pi\) | ||||
0.463579 | + | 0.886055i | \(0.346565\pi\) | |||||||
\(194\) | 25.6076 | 1.83852 | ||||||||
\(195\) | 5.14302 | 0.368299 | ||||||||
\(196\) | 8.99901 | 0.642786 | ||||||||
\(197\) | 1.62358 | 0.115675 | 0.0578375 | − | 0.998326i | \(-0.481579\pi\) | ||||
0.0578375 | + | 0.998326i | \(0.481579\pi\) | |||||||
\(198\) | 21.3783 | 1.51929 | ||||||||
\(199\) | 15.0475 | 1.06669 | 0.533345 | − | 0.845898i | \(-0.320935\pi\) | ||||
0.533345 | + | 0.845898i | \(0.320935\pi\) | |||||||
\(200\) | 3.60731 | 0.255075 | ||||||||
\(201\) | −0.222623 | −0.0157026 | ||||||||
\(202\) | 26.1671 | 1.84111 | ||||||||
\(203\) | 18.6434 | 1.30851 | ||||||||
\(204\) | −0.580901 | −0.0406712 | ||||||||
\(205\) | −5.13480 | −0.358630 | ||||||||
\(206\) | −27.0666 | −1.88582 | ||||||||
\(207\) | 4.03135 | 0.280198 | ||||||||
\(208\) | 0.0421936 | 0.00292560 | ||||||||
\(209\) | 3.32297 | 0.229854 | ||||||||
\(210\) | 5.98714 | 0.413152 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −27.5581 | −1.89270 | ||||||||
\(213\) | 2.82363 | 0.193472 | ||||||||
\(214\) | −6.72675 | −0.459831 | ||||||||
\(215\) | 18.8980 | 1.28884 | ||||||||
\(216\) | −7.11852 | −0.484354 | ||||||||
\(217\) | −12.7432 | −0.865068 | ||||||||
\(218\) | 14.4409 | 0.978062 | ||||||||
\(219\) | 0.587087 | 0.0396717 | ||||||||
\(220\) | 20.7384 | 1.39818 | ||||||||
\(221\) | −2.54578 | −0.171247 | ||||||||
\(222\) | −5.75173 | −0.386031 | ||||||||
\(223\) | −12.9664 | −0.868298 | −0.434149 | − | 0.900841i | \(-0.642951\pi\) | ||||
−0.434149 | + | 0.900841i | \(0.642951\pi\) | |||||||
\(224\) | 17.7172 | 1.18378 | ||||||||
\(225\) | 3.59129 | 0.239420 | ||||||||
\(226\) | 5.46957 | 0.363831 | ||||||||
\(227\) | 1.56235 | 0.103697 | 0.0518484 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518484 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(228\) | −1.40261 | −0.0928901 | ||||||||
\(229\) | −20.7640 | −1.37213 | −0.686063 | − | 0.727542i | \(-0.740663\pi\) | ||||
−0.686063 | + | 0.727542i | \(0.740663\pi\) | |||||||
\(230\) | 6.32875 | 0.417305 | ||||||||
\(231\) | −4.50681 | −0.296526 | ||||||||
\(232\) | −16.8364 | −1.10536 | ||||||||
\(233\) | 0.126027 | 0.00825634 | 0.00412817 | − | 0.999991i | \(-0.498686\pi\) | ||||
0.00412817 | + | 0.999991i | \(0.498686\pi\) | |||||||
\(234\) | −39.5460 | −2.58520 | ||||||||
\(235\) | −3.41622 | −0.222850 | ||||||||
\(236\) | −48.8532 | −3.18007 | ||||||||
\(237\) | −4.59422 | −0.298426 | ||||||||
\(238\) | −2.96362 | −0.192103 | ||||||||
\(239\) | −25.3406 | −1.63915 | −0.819573 | − | 0.572975i | \(-0.805789\pi\) | ||||
−0.819573 | + | 0.572975i | \(0.805789\pi\) | |||||||
\(240\) | 0.00574322 | 0.000370723 0 | ||||||||
\(241\) | 19.3994 | 1.24962 | 0.624812 | − | 0.780775i | \(-0.285176\pi\) | ||||
0.624812 | + | 0.780775i | \(0.285176\pi\) | |||||||
\(242\) | −0.0963225 | −0.00619184 | ||||||||
\(243\) | −10.7450 | −0.689293 | ||||||||
\(244\) | −30.9697 | −1.98263 | ||||||||
\(245\) | 5.36810 | 0.342956 | ||||||||
\(246\) | −2.64028 | −0.168338 | ||||||||
\(247\) | −6.14688 | −0.391117 | ||||||||
\(248\) | 11.5081 | 0.730766 | ||||||||
\(249\) | −2.30324 | −0.145962 | ||||||||
\(250\) | 27.7102 | 1.75255 | ||||||||
\(251\) | 11.4789 | 0.724539 | 0.362270 | − | 0.932073i | \(-0.382002\pi\) | ||||
0.362270 | + | 0.932073i | \(0.382002\pi\) | |||||||
\(252\) | −28.4471 | −1.79200 | ||||||||
\(253\) | −4.76395 | −0.299507 | ||||||||
\(254\) | 24.7112 | 1.55052 | ||||||||
\(255\) | −0.346520 | −0.0216999 | ||||||||
\(256\) | −15.9555 | −0.997222 | ||||||||
\(257\) | 18.4453 | 1.15058 | 0.575292 | − | 0.817948i | \(-0.304888\pi\) | ||||
0.575292 | + | 0.817948i | \(0.304888\pi\) | |||||||
\(258\) | 9.71725 | 0.604970 | ||||||||
\(259\) | −18.1322 | −1.12668 | ||||||||
\(260\) | −38.3623 | −2.37913 | ||||||||
\(261\) | −16.7617 | −1.03752 | ||||||||
\(262\) | −15.2697 | −0.943365 | ||||||||
\(263\) | 9.32046 | 0.574724 | 0.287362 | − | 0.957822i | \(-0.407222\pi\) | ||||
0.287362 | + | 0.957822i | \(0.407222\pi\) | |||||||
\(264\) | 4.06999 | 0.250490 | ||||||||
\(265\) | −16.4390 | −1.00984 | ||||||||
\(266\) | −7.15577 | −0.438749 | ||||||||
\(267\) | 4.42132 | 0.270580 | ||||||||
\(268\) | 1.66057 | 0.101435 | ||||||||
\(269\) | −29.0995 | −1.77423 | −0.887113 | − | 0.461552i | \(-0.847293\pi\) | ||||
−0.887113 | + | 0.461552i | \(0.847293\pi\) | |||||||
\(270\) | −11.1256 | −0.677085 | ||||||||
\(271\) | −5.36920 | −0.326155 | −0.163078 | − | 0.986613i | \(-0.552142\pi\) | ||||
−0.163078 | + | 0.986613i | \(0.552142\pi\) | |||||||
\(272\) | −0.00284287 | −0.000172374 0 | ||||||||
\(273\) | 8.33677 | 0.504564 | ||||||||
\(274\) | 38.7582 | 2.34147 | ||||||||
\(275\) | −4.24392 | −0.255918 | ||||||||
\(276\) | 2.01084 | 0.121038 | ||||||||
\(277\) | −12.2510 | −0.736090 | −0.368045 | − | 0.929808i | \(-0.619973\pi\) | ||||
−0.368045 | + | 0.929808i | \(0.619973\pi\) | |||||||
\(278\) | −50.8045 | −3.04705 | ||||||||
\(279\) | 11.4570 | 0.685914 | ||||||||
\(280\) | −17.0450 | −1.01863 | ||||||||
\(281\) | −24.0484 | −1.43461 | −0.717303 | − | 0.696762i | \(-0.754623\pi\) | ||||
−0.717303 | + | 0.696762i | \(0.754623\pi\) | |||||||
\(282\) | −1.75660 | −0.104604 | ||||||||
\(283\) | 12.9639 | 0.770627 | 0.385313 | − | 0.922786i | \(-0.374093\pi\) | ||||
0.385313 | + | 0.922786i | \(0.374093\pi\) | |||||||
\(284\) | −21.0617 | −1.24978 | ||||||||
\(285\) | −0.836688 | −0.0495611 | ||||||||
\(286\) | 46.7326 | 2.76335 | ||||||||
\(287\) | −8.32345 | −0.491317 | ||||||||
\(288\) | −15.9289 | −0.938621 | ||||||||
\(289\) | −16.8285 | −0.989910 | ||||||||
\(290\) | −26.3139 | −1.54520 | ||||||||
\(291\) | 4.85350 | 0.284517 | ||||||||
\(292\) | −4.37914 | −0.256270 | ||||||||
\(293\) | 1.83619 | 0.107272 | 0.0536358 | − | 0.998561i | \(-0.482919\pi\) | ||||
0.0536358 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(294\) | 2.76024 | 0.160981 | ||||||||
\(295\) | −29.1420 | −1.69671 | ||||||||
\(296\) | 16.3748 | 0.951764 | ||||||||
\(297\) | 8.37479 | 0.485955 | ||||||||
\(298\) | 48.3342 | 2.79992 | ||||||||
\(299\) | 8.81243 | 0.509636 | ||||||||
\(300\) | 1.79134 | 0.103423 | ||||||||
\(301\) | 30.6335 | 1.76569 | ||||||||
\(302\) | −37.8604 | −2.17862 | ||||||||
\(303\) | 4.95954 | 0.284918 | ||||||||
\(304\) | −0.00686423 | −0.000393691 0 | ||||||||
\(305\) | −18.4741 | −1.05782 | ||||||||
\(306\) | 2.66449 | 0.152319 | ||||||||
\(307\) | −28.2677 | −1.61332 | −0.806661 | − | 0.591015i | \(-0.798728\pi\) | ||||
−0.806661 | + | 0.591015i | \(0.798728\pi\) | |||||||
\(308\) | 33.6167 | 1.91549 | ||||||||
\(309\) | −5.13004 | −0.291838 | ||||||||
\(310\) | 17.9862 | 1.02155 | ||||||||
\(311\) | 5.04129 | 0.285865 | 0.142933 | − | 0.989732i | \(-0.454347\pi\) | ||||
0.142933 | + | 0.989732i | \(0.454347\pi\) | |||||||
\(312\) | −7.52873 | −0.426230 | ||||||||
\(313\) | 2.83741 | 0.160380 | 0.0801900 | − | 0.996780i | \(-0.474447\pi\) | ||||
0.0801900 | + | 0.996780i | \(0.474447\pi\) | |||||||
\(314\) | 16.6322 | 0.938611 | ||||||||
\(315\) | −16.9693 | −0.956113 | ||||||||
\(316\) | 34.2687 | 1.92776 | ||||||||
\(317\) | 2.00520 | 0.112623 | 0.0563117 | − | 0.998413i | \(-0.482066\pi\) | ||||
0.0563117 | + | 0.998413i | \(0.482066\pi\) | |||||||
\(318\) | −8.45284 | −0.474012 | ||||||||
\(319\) | 19.8077 | 1.10902 | ||||||||
\(320\) | −24.9801 | −1.39643 | ||||||||
\(321\) | −1.27495 | −0.0711605 | ||||||||
\(322\) | 10.2588 | 0.571702 | ||||||||
\(323\) | 0.414157 | 0.0230443 | ||||||||
\(324\) | 23.7512 | 1.31951 | ||||||||
\(325\) | 7.85049 | 0.435467 | ||||||||
\(326\) | −24.8791 | −1.37792 | ||||||||
\(327\) | 2.73704 | 0.151359 | ||||||||
\(328\) | 7.51670 | 0.415040 | ||||||||
\(329\) | −5.53765 | −0.305301 | ||||||||
\(330\) | 6.36104 | 0.350164 | ||||||||
\(331\) | 7.43302 | 0.408556 | 0.204278 | − | 0.978913i | \(-0.434515\pi\) | ||||
0.204278 | + | 0.978913i | \(0.434515\pi\) | |||||||
\(332\) | 17.1801 | 0.942878 | ||||||||
\(333\) | 16.3021 | 0.893348 | ||||||||
\(334\) | 14.5890 | 0.798276 | ||||||||
\(335\) | 0.990564 | 0.0541203 | ||||||||
\(336\) | 0.00930968 | 0.000507885 0 | ||||||||
\(337\) | −12.5642 | −0.684417 | −0.342209 | − | 0.939624i | \(-0.611175\pi\) | ||||
−0.342209 | + | 0.939624i | \(0.611175\pi\) | |||||||
\(338\) | −56.7039 | −3.08429 | ||||||||
\(339\) | 1.03667 | 0.0563041 | ||||||||
\(340\) | 2.58473 | 0.140177 | ||||||||
\(341\) | −13.5391 | −0.733181 | ||||||||
\(342\) | 6.43351 | 0.347884 | ||||||||
\(343\) | −13.1919 | −0.712295 | ||||||||
\(344\) | −27.6644 | −1.49156 | ||||||||
\(345\) | 1.19951 | 0.0645795 | ||||||||
\(346\) | −37.5485 | −2.01862 | ||||||||
\(347\) | 4.27954 | 0.229738 | 0.114869 | − | 0.993381i | \(-0.463355\pi\) | ||||
0.114869 | + | 0.993381i | \(0.463355\pi\) | |||||||
\(348\) | −8.36075 | −0.448183 | ||||||||
\(349\) | 29.5194 | 1.58014 | 0.790070 | − | 0.613017i | \(-0.210044\pi\) | ||||
0.790070 | + | 0.613017i | \(0.210044\pi\) | |||||||
\(350\) | 9.13899 | 0.488500 | ||||||||
\(351\) | −15.4918 | −0.826893 | ||||||||
\(352\) | 18.8236 | 1.00330 | ||||||||
\(353\) | 33.5425 | 1.78528 | 0.892642 | − | 0.450766i | \(-0.148849\pi\) | ||||
0.892642 | + | 0.450766i | \(0.148849\pi\) | |||||||
\(354\) | −14.9846 | −0.796424 | ||||||||
\(355\) | −12.5638 | −0.666816 | ||||||||
\(356\) | −32.9790 | −1.74788 | ||||||||
\(357\) | −0.561705 | −0.0297286 | ||||||||
\(358\) | 23.4906 | 1.24151 | ||||||||
\(359\) | 29.4401 | 1.55379 | 0.776895 | − | 0.629631i | \(-0.216794\pi\) | ||||
0.776895 | + | 0.629631i | \(0.216794\pi\) | |||||||
\(360\) | 15.3246 | 0.807676 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.0630596 | 0.00331434 | ||||||||
\(363\) | −0.0182564 | −0.000958210 0 | ||||||||
\(364\) | −62.1847 | −3.25937 | ||||||||
\(365\) | −2.61225 | −0.136731 | ||||||||
\(366\) | −9.49927 | −0.496535 | ||||||||
\(367\) | −15.2551 | −0.796312 | −0.398156 | − | 0.917318i | \(-0.630350\pi\) | ||||
−0.398156 | + | 0.917318i | \(0.630350\pi\) | |||||||
\(368\) | 0.00984086 | 0.000512990 0 | ||||||||
\(369\) | 7.48333 | 0.389566 | ||||||||
\(370\) | 25.5924 | 1.33048 | ||||||||
\(371\) | −26.6474 | −1.38347 | ||||||||
\(372\) | 5.71478 | 0.296298 | ||||||||
\(373\) | −14.4505 | −0.748220 | −0.374110 | − | 0.927384i | \(-0.622052\pi\) | ||||
−0.374110 | + | 0.927384i | \(0.622052\pi\) | |||||||
\(374\) | −3.14869 | −0.162815 | ||||||||
\(375\) | 5.25201 | 0.271213 | ||||||||
\(376\) | 5.00092 | 0.257903 | ||||||||
\(377\) | −36.6406 | −1.88709 | ||||||||
\(378\) | −18.0345 | −0.927596 | ||||||||
\(379\) | −1.98740 | −0.102086 | −0.0510429 | − | 0.998696i | \(-0.516255\pi\) | ||||
−0.0510429 | + | 0.998696i | \(0.516255\pi\) | |||||||
\(380\) | 6.24093 | 0.320153 | ||||||||
\(381\) | 4.68360 | 0.239948 | ||||||||
\(382\) | −9.01860 | −0.461432 | ||||||||
\(383\) | 11.2057 | 0.572585 | 0.286292 | − | 0.958142i | \(-0.407577\pi\) | ||||
0.286292 | + | 0.958142i | \(0.407577\pi\) | |||||||
\(384\) | −7.93175 | −0.404766 | ||||||||
\(385\) | 20.0531 | 1.02200 | ||||||||
\(386\) | −29.4694 | −1.49995 | ||||||||
\(387\) | −27.5415 | −1.40001 | ||||||||
\(388\) | −36.2027 | −1.83792 | ||||||||
\(389\) | −18.1661 | −0.921057 | −0.460528 | − | 0.887645i | \(-0.652340\pi\) | ||||
−0.460528 | + | 0.887645i | \(0.652340\pi\) | |||||||
\(390\) | −11.7668 | −0.595833 | ||||||||
\(391\) | −0.593754 | −0.0300274 | ||||||||
\(392\) | −7.85823 | −0.396900 | ||||||||
\(393\) | −2.89412 | −0.145989 | ||||||||
\(394\) | −3.71460 | −0.187139 | ||||||||
\(395\) | 20.4420 | 1.02855 | ||||||||
\(396\) | −30.2236 | −1.51879 | ||||||||
\(397\) | 3.10587 | 0.155879 | 0.0779396 | − | 0.996958i | \(-0.475166\pi\) | ||||
0.0779396 | + | 0.996958i | \(0.475166\pi\) | |||||||
\(398\) | −34.4274 | −1.72569 | ||||||||
\(399\) | −1.35626 | −0.0678979 | ||||||||
\(400\) | 0.00876665 | 0.000438333 0 | ||||||||
\(401\) | 4.21538 | 0.210506 | 0.105253 | − | 0.994445i | \(-0.466435\pi\) | ||||
0.105253 | + | 0.994445i | \(0.466435\pi\) | |||||||
\(402\) | 0.509341 | 0.0254036 | ||||||||
\(403\) | 25.0448 | 1.24757 | ||||||||
\(404\) | −36.9937 | −1.84050 | ||||||||
\(405\) | 14.1681 | 0.704018 | ||||||||
\(406\) | −42.6545 | −2.11691 | ||||||||
\(407\) | −19.2646 | −0.954910 | ||||||||
\(408\) | 0.507262 | 0.0251132 | ||||||||
\(409\) | 4.00260 | 0.197916 | 0.0989580 | − | 0.995092i | \(-0.468449\pi\) | ||||
0.0989580 | + | 0.995092i | \(0.468449\pi\) | |||||||
\(410\) | 11.7480 | 0.580190 | ||||||||
\(411\) | 7.34599 | 0.362351 | ||||||||
\(412\) | 38.2654 | 1.88520 | ||||||||
\(413\) | −47.2388 | −2.32447 | ||||||||
\(414\) | −9.22336 | −0.453303 | ||||||||
\(415\) | 10.2483 | 0.503068 | ||||||||
\(416\) | −34.8203 | −1.70720 | ||||||||
\(417\) | −9.62917 | −0.471542 | ||||||||
\(418\) | −7.60265 | −0.371858 | ||||||||
\(419\) | −33.7660 | −1.64958 | −0.824789 | − | 0.565440i | \(-0.808706\pi\) | ||||
−0.824789 | + | 0.565440i | \(0.808706\pi\) | |||||||
\(420\) | −8.46433 | −0.413017 | ||||||||
\(421\) | 0.542851 | 0.0264569 | 0.0132285 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132285 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(422\) | −2.28791 | −0.111374 | ||||||||
\(423\) | 4.97871 | 0.242073 | ||||||||
\(424\) | 24.0647 | 1.16868 | ||||||||
\(425\) | −0.528941 | −0.0256574 | ||||||||
\(426\) | −6.46022 | −0.312998 | ||||||||
\(427\) | −29.9463 | −1.44920 | ||||||||
\(428\) | 9.50994 | 0.459680 | ||||||||
\(429\) | 8.85740 | 0.427639 | ||||||||
\(430\) | −43.2370 | −2.08507 | ||||||||
\(431\) | −29.5803 | −1.42483 | −0.712417 | − | 0.701757i | \(-0.752399\pi\) | ||||
−0.712417 | + | 0.701757i | \(0.752399\pi\) | |||||||
\(432\) | −0.0172998 | −0.000832335 0 | ||||||||
\(433\) | 16.5113 | 0.793482 | 0.396741 | − | 0.917931i | \(-0.370141\pi\) | ||||
0.396741 | + | 0.917931i | \(0.370141\pi\) | |||||||
\(434\) | 29.1554 | 1.39950 | ||||||||
\(435\) | −4.98737 | −0.239126 | ||||||||
\(436\) | −20.4158 | −0.977741 | ||||||||
\(437\) | −1.43364 | −0.0685804 | ||||||||
\(438\) | −1.34320 | −0.0641807 | ||||||||
\(439\) | 22.6708 | 1.08202 | 0.541010 | − | 0.841016i | \(-0.318042\pi\) | ||||
0.541010 | + | 0.841016i | \(0.318042\pi\) | |||||||
\(440\) | −18.1094 | −0.863334 | ||||||||
\(441\) | −7.82334 | −0.372540 | ||||||||
\(442\) | 5.82451 | 0.277044 | ||||||||
\(443\) | 29.6849 | 1.41037 | 0.705186 | − | 0.709022i | \(-0.250863\pi\) | ||||
0.705186 | + | 0.709022i | \(0.250863\pi\) | |||||||
\(444\) | 8.13150 | 0.385904 | ||||||||
\(445\) | −19.6727 | −0.932575 | ||||||||
\(446\) | 29.6661 | 1.40473 | ||||||||
\(447\) | 9.16096 | 0.433298 | ||||||||
\(448\) | −40.4924 | −1.91309 | ||||||||
\(449\) | −28.1898 | −1.33036 | −0.665179 | − | 0.746684i | \(-0.731645\pi\) | ||||
−0.665179 | + | 0.746684i | \(0.731645\pi\) | |||||||
\(450\) | −8.21656 | −0.387332 | ||||||||
\(451\) | −8.84324 | −0.416412 | ||||||||
\(452\) | −7.73261 | −0.363711 | ||||||||
\(453\) | −7.17582 | −0.337149 | ||||||||
\(454\) | −3.57451 | −0.167760 | ||||||||
\(455\) | −37.0946 | −1.73902 | ||||||||
\(456\) | 1.22481 | 0.0573568 | ||||||||
\(457\) | −0.358204 | −0.0167561 | −0.00837803 | − | 0.999965i | \(-0.502667\pi\) | ||||
−0.00837803 | + | 0.999965i | \(0.502667\pi\) | |||||||
\(458\) | 47.5062 | 2.21982 | ||||||||
\(459\) | 1.04379 | 0.0487200 | ||||||||
\(460\) | −8.94726 | −0.417168 | ||||||||
\(461\) | −25.3002 | −1.17835 | −0.589174 | − | 0.808006i | \(-0.700547\pi\) | ||||
−0.589174 | + | 0.808006i | \(0.700547\pi\) | |||||||
\(462\) | 10.3112 | 0.479719 | ||||||||
\(463\) | −5.62977 | −0.261638 | −0.130819 | − | 0.991406i | \(-0.541761\pi\) | ||||
−0.130819 | + | 0.991406i | \(0.541761\pi\) | |||||||
\(464\) | −0.0409166 | −0.00189951 | ||||||||
\(465\) | 3.40899 | 0.158088 | ||||||||
\(466\) | −0.288340 | −0.0133571 | ||||||||
\(467\) | 36.6216 | 1.69465 | 0.847323 | − | 0.531078i | \(-0.178213\pi\) | ||||
0.847323 | + | 0.531078i | \(0.178213\pi\) | |||||||
\(468\) | 55.9082 | 2.58436 | ||||||||
\(469\) | 1.60569 | 0.0741439 | ||||||||
\(470\) | 7.81601 | 0.360526 | ||||||||
\(471\) | 3.15237 | 0.145253 | ||||||||
\(472\) | 42.6602 | 1.96359 | ||||||||
\(473\) | 32.5465 | 1.49649 | ||||||||
\(474\) | 10.5112 | 0.482793 | ||||||||
\(475\) | −1.27715 | −0.0585996 | ||||||||
\(476\) | 4.18981 | 0.192040 | ||||||||
\(477\) | 23.9578 | 1.09695 | ||||||||
\(478\) | 57.9770 | 2.65181 | ||||||||
\(479\) | 0.363547 | 0.0166109 | 0.00830544 | − | 0.999966i | \(-0.497356\pi\) | ||||
0.00830544 | + | 0.999966i | \(0.497356\pi\) | |||||||
\(480\) | −4.73959 | −0.216332 | ||||||||
\(481\) | 35.6360 | 1.62486 | ||||||||
\(482\) | −44.3840 | −2.02164 | ||||||||
\(483\) | 1.94439 | 0.0884729 | ||||||||
\(484\) | 0.136176 | 0.00618981 | ||||||||
\(485\) | −21.5957 | −0.980611 | ||||||||
\(486\) | 24.5836 | 1.11514 | ||||||||
\(487\) | −10.4494 | −0.473508 | −0.236754 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236754 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(488\) | 27.0438 | 1.22421 | ||||||||
\(489\) | −4.71542 | −0.213239 | ||||||||
\(490\) | −12.2817 | −0.554832 | ||||||||
\(491\) | −36.9990 | −1.66974 | −0.834872 | − | 0.550445i | \(-0.814458\pi\) | ||||
−0.834872 | + | 0.550445i | \(0.814458\pi\) | |||||||
\(492\) | 3.73270 | 0.168283 | ||||||||
\(493\) | 2.46873 | 0.111186 | ||||||||
\(494\) | 14.0635 | 0.632747 | ||||||||
\(495\) | −18.0290 | −0.810345 | ||||||||
\(496\) | 0.0279676 | 0.00125578 | ||||||||
\(497\) | −20.3657 | −0.913528 | ||||||||
\(498\) | 5.26960 | 0.236136 | ||||||||
\(499\) | −20.2733 | −0.907558 | −0.453779 | − | 0.891114i | \(-0.649924\pi\) | ||||
−0.453779 | + | 0.891114i | \(0.649924\pi\) | |||||||
\(500\) | −39.1753 | −1.75197 | ||||||||
\(501\) | 2.76511 | 0.123536 | ||||||||
\(502\) | −26.2626 | −1.17216 | ||||||||
\(503\) | −24.7611 | −1.10404 | −0.552022 | − | 0.833829i | \(-0.686144\pi\) | ||||
−0.552022 | + | 0.833829i | \(0.686144\pi\) | |||||||
\(504\) | 24.8409 | 1.10650 | ||||||||
\(505\) | −22.0675 | −0.981992 | ||||||||
\(506\) | 10.8995 | 0.484541 | ||||||||
\(507\) | −10.7473 | −0.477304 | ||||||||
\(508\) | −34.9354 | −1.55001 | ||||||||
\(509\) | −3.39562 | −0.150508 | −0.0752541 | − | 0.997164i | \(-0.523977\pi\) | ||||
−0.0752541 | + | 0.997164i | \(0.523977\pi\) | |||||||
\(510\) | 0.792807 | 0.0351061 | ||||||||
\(511\) | −4.23443 | −0.187320 | ||||||||
\(512\) | −0.0776599 | −0.00343211 | ||||||||
\(513\) | 2.52028 | 0.111273 | ||||||||
\(514\) | −42.2011 | −1.86141 | ||||||||
\(515\) | 22.8262 | 1.00584 | ||||||||
\(516\) | −13.7378 | −0.604771 | ||||||||
\(517\) | −5.88348 | −0.258755 | ||||||||
\(518\) | 41.4849 | 1.82274 | ||||||||
\(519\) | −7.11671 | −0.312389 | ||||||||
\(520\) | 33.4992 | 1.46904 | ||||||||
\(521\) | −0.754794 | −0.0330681 | −0.0165341 | − | 0.999863i | \(-0.505263\pi\) | ||||
−0.0165341 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(522\) | 38.3492 | 1.67850 | ||||||||
\(523\) | 9.11617 | 0.398622 | 0.199311 | − | 0.979936i | \(-0.436130\pi\) | ||||
0.199311 | + | 0.979936i | \(0.436130\pi\) | |||||||
\(524\) | 21.5875 | 0.943056 | ||||||||
\(525\) | 1.73215 | 0.0755971 | ||||||||
\(526\) | −21.3244 | −0.929787 | ||||||||
\(527\) | −1.68744 | −0.0735060 | ||||||||
\(528\) | 0.00989107 | 0.000430454 0 | ||||||||
\(529\) | −20.9447 | −0.910638 | ||||||||
\(530\) | 37.6110 | 1.63372 | ||||||||
\(531\) | 42.4708 | 1.84308 | ||||||||
\(532\) | 10.1165 | 0.438605 | ||||||||
\(533\) | 16.3584 | 0.708560 | ||||||||
\(534\) | −10.1156 | −0.437744 | ||||||||
\(535\) | 5.67288 | 0.245260 | ||||||||
\(536\) | −1.45006 | −0.0626331 | ||||||||
\(537\) | 4.45225 | 0.192129 | ||||||||
\(538\) | 66.5770 | 2.87034 | ||||||||
\(539\) | 9.24504 | 0.398212 | ||||||||
\(540\) | 15.7289 | 0.676863 | ||||||||
\(541\) | −20.9768 | −0.901861 | −0.450930 | − | 0.892559i | \(-0.648908\pi\) | ||||
−0.450930 | + | 0.892559i | \(0.648908\pi\) | |||||||
\(542\) | 12.2842 | 0.527653 | ||||||||
\(543\) | 0.0119519 | 0.000512906 0 | ||||||||
\(544\) | 2.34608 | 0.100587 | ||||||||
\(545\) | −12.1785 | −0.521669 | ||||||||
\(546\) | −19.0738 | −0.816282 | ||||||||
\(547\) | −45.1326 | −1.92973 | −0.964865 | − | 0.262745i | \(-0.915372\pi\) | ||||
−0.964865 | + | 0.262745i | \(0.915372\pi\) | |||||||
\(548\) | −54.7944 | −2.34070 | ||||||||
\(549\) | 26.9237 | 1.14908 | ||||||||
\(550\) | 9.70972 | 0.414024 | ||||||||
\(551\) | 5.96085 | 0.253941 | ||||||||
\(552\) | −1.75593 | −0.0747375 | ||||||||
\(553\) | 33.1363 | 1.40910 | ||||||||
\(554\) | 28.0291 | 1.19084 | ||||||||
\(555\) | 4.85062 | 0.205897 | ||||||||
\(556\) | 71.8249 | 3.04605 | ||||||||
\(557\) | −11.2775 | −0.477843 | −0.238922 | − | 0.971039i | \(-0.576794\pi\) | ||||
−0.238922 | + | 0.971039i | \(0.576794\pi\) | |||||||
\(558\) | −26.2126 | −1.10967 | ||||||||
\(559\) | −60.2052 | −2.54641 | ||||||||
\(560\) | −0.0414235 | −0.00175046 | ||||||||
\(561\) | −0.596784 | −0.0251962 | ||||||||
\(562\) | 55.0205 | 2.32090 | ||||||||
\(563\) | −23.6175 | −0.995358 | −0.497679 | − | 0.867361i | \(-0.665814\pi\) | ||||
−0.497679 | + | 0.867361i | \(0.665814\pi\) | |||||||
\(564\) | 2.48339 | 0.104570 | ||||||||
\(565\) | −4.61267 | −0.194056 | ||||||||
\(566\) | −29.6603 | −1.24672 | ||||||||
\(567\) | 22.9663 | 0.964493 | ||||||||
\(568\) | 18.3918 | 0.771703 | ||||||||
\(569\) | 22.2960 | 0.934697 | 0.467348 | − | 0.884073i | \(-0.345209\pi\) | ||||
0.467348 | + | 0.884073i | \(0.345209\pi\) | |||||||
\(570\) | 1.91427 | 0.0801798 | ||||||||
\(571\) | −17.1415 | −0.717348 | −0.358674 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358674 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(572\) | −66.0682 | −2.76245 | ||||||||
\(573\) | −1.70933 | −0.0714083 | ||||||||
\(574\) | 19.0433 | 0.794852 | ||||||||
\(575\) | 1.83098 | 0.0763570 | ||||||||
\(576\) | 36.4053 | 1.51689 | ||||||||
\(577\) | −5.43556 | −0.226285 | −0.113143 | − | 0.993579i | \(-0.536092\pi\) | ||||
−0.113143 | + | 0.993579i | \(0.536092\pi\) | |||||||
\(578\) | 38.5020 | 1.60147 | ||||||||
\(579\) | −5.58545 | −0.232123 | ||||||||
\(580\) | 37.2012 | 1.54470 | ||||||||
\(581\) | 16.6123 | 0.689196 | ||||||||
\(582\) | −11.1044 | −0.460291 | ||||||||
\(583\) | −28.3116 | −1.17255 | ||||||||
\(584\) | 3.82401 | 0.158239 | ||||||||
\(585\) | 33.3505 | 1.37887 | ||||||||
\(586\) | −4.20105 | −0.173544 | ||||||||
\(587\) | 36.6084 | 1.51099 | 0.755495 | − | 0.655154i | \(-0.227396\pi\) | ||||
0.755495 | + | 0.655154i | \(0.227396\pi\) | |||||||
\(588\) | −3.90230 | −0.160928 | ||||||||
\(589\) | −4.07439 | −0.167882 | ||||||||
\(590\) | 66.6742 | 2.74493 | ||||||||
\(591\) | −0.704041 | −0.0289604 | ||||||||
\(592\) | 0.0397947 | 0.00163555 | ||||||||
\(593\) | −34.3256 | −1.40958 | −0.704791 | − | 0.709415i | \(-0.748959\pi\) | ||||
−0.704791 | + | 0.709415i | \(0.748959\pi\) | |||||||
\(594\) | −19.1608 | −0.786176 | ||||||||
\(595\) | 2.49931 | 0.102462 | ||||||||
\(596\) | −68.3324 | −2.79901 | ||||||||
\(597\) | −6.52515 | −0.267057 | ||||||||
\(598\) | −20.1621 | −0.824488 | ||||||||
\(599\) | −38.1948 | −1.56060 | −0.780298 | − | 0.625408i | \(-0.784932\pi\) | ||||
−0.780298 | + | 0.625408i | \(0.784932\pi\) | |||||||
\(600\) | −1.56426 | −0.0638606 | ||||||||
\(601\) | 28.6278 | 1.16775 | 0.583877 | − | 0.811842i | \(-0.301535\pi\) | ||||
0.583877 | + | 0.811842i | \(0.301535\pi\) | |||||||
\(602\) | −70.0867 | −2.85652 | ||||||||
\(603\) | −1.44362 | −0.0587889 | ||||||||
\(604\) | 53.5251 | 2.17790 | ||||||||
\(605\) | 0.0812319 | 0.00330255 | ||||||||
\(606\) | −11.3470 | −0.460940 | ||||||||
\(607\) | 24.1016 | 0.978255 | 0.489128 | − | 0.872212i | \(-0.337315\pi\) | ||||
0.489128 | + | 0.872212i | \(0.337315\pi\) | |||||||
\(608\) | 5.66470 | 0.229734 | ||||||||
\(609\) | −8.08446 | −0.327599 | ||||||||
\(610\) | 42.2671 | 1.71135 | ||||||||
\(611\) | 10.8834 | 0.440294 | ||||||||
\(612\) | −3.76692 | −0.152269 | ||||||||
\(613\) | 32.1756 | 1.29956 | 0.649779 | − | 0.760123i | \(-0.274861\pi\) | ||||
0.649779 | + | 0.760123i | \(0.274861\pi\) | |||||||
\(614\) | 64.6739 | 2.61003 | ||||||||
\(615\) | 2.22663 | 0.0897866 | ||||||||
\(616\) | −29.3552 | −1.18275 | ||||||||
\(617\) | 9.13019 | 0.367568 | 0.183784 | − | 0.982967i | \(-0.441165\pi\) | ||||
0.183784 | + | 0.982967i | \(0.441165\pi\) | |||||||
\(618\) | 11.7371 | 0.472134 | ||||||||
\(619\) | 18.4061 | 0.739804 | 0.369902 | − | 0.929071i | \(-0.379391\pi\) | ||||
0.369902 | + | 0.929071i | \(0.379391\pi\) | |||||||
\(620\) | −25.4280 | −1.02121 | ||||||||
\(621\) | −3.61318 | −0.144992 | ||||||||
\(622\) | −11.5340 | −0.462472 | ||||||||
\(623\) | −31.8892 | −1.27761 | ||||||||
\(624\) | −0.0182967 | −0.000732453 0 | ||||||||
\(625\) | −16.9831 | −0.679326 | ||||||||
\(626\) | −6.49174 | −0.259462 | ||||||||
\(627\) | −1.44096 | −0.0575463 | ||||||||
\(628\) | −23.5138 | −0.938303 | ||||||||
\(629\) | −2.40104 | −0.0957357 | ||||||||
\(630\) | 38.8243 | 1.54680 | ||||||||
\(631\) | −11.1359 | −0.443314 | −0.221657 | − | 0.975125i | \(-0.571147\pi\) | ||||
−0.221657 | + | 0.975125i | \(0.571147\pi\) | |||||||
\(632\) | −29.9245 | −1.19033 | ||||||||
\(633\) | −0.433636 | −0.0172355 | ||||||||
\(634\) | −4.58772 | −0.182202 | ||||||||
\(635\) | −20.8397 | −0.826999 | ||||||||
\(636\) | 11.9502 | 0.473856 | ||||||||
\(637\) | −17.1016 | −0.677592 | ||||||||
\(638\) | −45.3182 | −1.79417 | ||||||||
\(639\) | 18.3101 | 0.724338 | ||||||||
\(640\) | 35.2924 | 1.39506 | ||||||||
\(641\) | −7.03126 | −0.277718 | −0.138859 | − | 0.990312i | \(-0.544343\pi\) | ||||
−0.138859 | + | 0.990312i | \(0.544343\pi\) | |||||||
\(642\) | 2.91696 | 0.115123 | ||||||||
\(643\) | 38.9204 | 1.53487 | 0.767434 | − | 0.641127i | \(-0.221533\pi\) | ||||
0.767434 | + | 0.641127i | \(0.221533\pi\) | |||||||
\(644\) | −14.5034 | −0.571514 | ||||||||
\(645\) | −8.19487 | −0.322673 | ||||||||
\(646\) | −0.947555 | −0.0372811 | ||||||||
\(647\) | 0.954552 | 0.0375273 | 0.0187637 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187637 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(648\) | −20.7403 | −0.814756 | ||||||||
\(649\) | −50.1888 | −1.97008 | ||||||||
\(650\) | −17.9612 | −0.704496 | ||||||||
\(651\) | 5.52593 | 0.216578 | ||||||||
\(652\) | 35.1728 | 1.37747 | ||||||||
\(653\) | −31.9323 | −1.24961 | −0.624804 | − | 0.780781i | \(-0.714821\pi\) | ||||
−0.624804 | + | 0.780781i | \(0.714821\pi\) | |||||||
\(654\) | −6.26210 | −0.244867 | ||||||||
\(655\) | 12.8774 | 0.503163 | ||||||||
\(656\) | 0.0182674 | 0.000713223 0 | ||||||||
\(657\) | 3.80703 | 0.148526 | ||||||||
\(658\) | 12.6697 | 0.493914 | ||||||||
\(659\) | −1.96616 | −0.0765908 | −0.0382954 | − | 0.999266i | \(-0.512193\pi\) | ||||
−0.0382954 | + | 0.999266i | \(0.512193\pi\) | |||||||
\(660\) | −8.99292 | −0.350049 | ||||||||
\(661\) | −48.5702 | −1.88916 | −0.944582 | − | 0.328276i | \(-0.893532\pi\) | ||||
−0.944582 | + | 0.328276i | \(0.893532\pi\) | |||||||
\(662\) | −17.0061 | −0.660961 | ||||||||
\(663\) | 1.10394 | 0.0428735 | ||||||||
\(664\) | −15.0022 | −0.582198 | ||||||||
\(665\) | 6.03469 | 0.234015 | ||||||||
\(666\) | −37.2977 | −1.44526 | ||||||||
\(667\) | −8.54573 | −0.330892 | ||||||||
\(668\) | −20.6252 | −0.798015 | ||||||||
\(669\) | 5.62272 | 0.217387 | ||||||||
\(670\) | −2.26632 | −0.0875556 | ||||||||
\(671\) | −31.8164 | −1.22826 | ||||||||
\(672\) | −7.68281 | −0.296371 | ||||||||
\(673\) | −2.66734 | −0.102818 | −0.0514092 | − | 0.998678i | \(-0.516371\pi\) | ||||
−0.0514092 | + | 0.998678i | \(0.516371\pi\) | |||||||
\(674\) | 28.7458 | 1.10725 | ||||||||
\(675\) | −3.21877 | −0.123890 | ||||||||
\(676\) | 80.1651 | 3.08327 | ||||||||
\(677\) | 5.39660 | 0.207408 | 0.103704 | − | 0.994608i | \(-0.466931\pi\) | ||||
0.103704 | + | 0.994608i | \(0.466931\pi\) | |||||||
\(678\) | −2.37180 | −0.0910886 | ||||||||
\(679\) | −35.0064 | −1.34342 | ||||||||
\(680\) | −2.25707 | −0.0865546 | ||||||||
\(681\) | −0.677491 | −0.0259615 | ||||||||
\(682\) | 30.9761 | 1.18614 | ||||||||
\(683\) | 40.2981 | 1.54196 | 0.770981 | − | 0.636858i | \(-0.219766\pi\) | ||||
0.770981 | + | 0.636858i | \(0.219766\pi\) | |||||||
\(684\) | −9.09538 | −0.347770 | ||||||||
\(685\) | −32.6861 | −1.24887 | ||||||||
\(686\) | 30.1819 | 1.15235 | ||||||||
\(687\) | 9.00403 | 0.343525 | ||||||||
\(688\) | −0.0672312 | −0.00256317 | ||||||||
\(689\) | 52.3712 | 1.99519 | ||||||||
\(690\) | −2.74437 | −0.104477 | ||||||||
\(691\) | 14.2210 | 0.540993 | 0.270497 | − | 0.962721i | \(-0.412812\pi\) | ||||
0.270497 | + | 0.962721i | \(0.412812\pi\) | |||||||
\(692\) | 53.0842 | 2.01796 | ||||||||
\(693\) | −29.2249 | −1.11016 | ||||||||
\(694\) | −9.79120 | −0.371669 | ||||||||
\(695\) | 42.8451 | 1.62521 | ||||||||
\(696\) | 7.30088 | 0.276739 | ||||||||
\(697\) | −1.10218 | −0.0417479 | ||||||||
\(698\) | −67.5378 | −2.55634 | ||||||||
\(699\) | −0.0546501 | −0.00206706 | ||||||||
\(700\) | −12.9202 | −0.488339 | ||||||||
\(701\) | −9.93859 | −0.375375 | −0.187688 | − | 0.982229i | \(-0.560099\pi\) | ||||
−0.187688 | + | 0.982229i | \(0.560099\pi\) | |||||||
\(702\) | 35.4439 | 1.33774 | ||||||||
\(703\) | −5.79741 | −0.218653 | ||||||||
\(704\) | −43.0211 | −1.62142 | ||||||||
\(705\) | 1.48140 | 0.0557926 | ||||||||
\(706\) | −76.7421 | −2.88823 | ||||||||
\(707\) | −35.7712 | −1.34531 | ||||||||
\(708\) | 21.1845 | 0.796162 | ||||||||
\(709\) | 21.3935 | 0.803451 | 0.401725 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401725 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(710\) | 28.7448 | 1.07877 | ||||||||
\(711\) | −29.7917 | −1.11728 | ||||||||
\(712\) | 28.7983 | 1.07926 | ||||||||
\(713\) | 5.84122 | 0.218755 | ||||||||
\(714\) | 1.28513 | 0.0480948 | ||||||||
\(715\) | −39.4111 | −1.47389 | ||||||||
\(716\) | −33.2098 | −1.24111 | ||||||||
\(717\) | 10.9886 | 0.410377 | ||||||||
\(718\) | −67.3563 | −2.51372 | ||||||||
\(719\) | 29.1510 | 1.08715 | 0.543574 | − | 0.839361i | \(-0.317071\pi\) | ||||
0.543574 | + | 0.839361i | \(0.317071\pi\) | |||||||
\(720\) | 0.0372425 | 0.00138795 | ||||||||
\(721\) | 37.0009 | 1.37799 | ||||||||
\(722\) | −2.28791 | −0.0851472 | ||||||||
\(723\) | −8.41227 | −0.312856 | ||||||||
\(724\) | −0.0891506 | −0.00331325 | ||||||||
\(725\) | −7.61289 | −0.282736 | ||||||||
\(726\) | 0.0417689 | 0.00155019 | ||||||||
\(727\) | −7.77117 | −0.288217 | −0.144108 | − | 0.989562i | \(-0.546031\pi\) | ||||
−0.144108 | + | 0.989562i | \(0.546031\pi\) | |||||||
\(728\) | 54.3018 | 2.01256 | ||||||||
\(729\) | −17.3696 | −0.643317 | ||||||||
\(730\) | 5.97660 | 0.221204 | ||||||||
\(731\) | 4.05643 | 0.150033 | ||||||||
\(732\) | 13.4296 | 0.496372 | ||||||||
\(733\) | −36.8697 | −1.36181 | −0.680906 | − | 0.732370i | \(-0.738414\pi\) | ||||
−0.680906 | + | 0.732370i | \(0.738414\pi\) | |||||||
\(734\) | 34.9024 | 1.28827 | ||||||||
\(735\) | −2.32780 | −0.0858623 | ||||||||
\(736\) | −8.12116 | −0.299350 | ||||||||
\(737\) | 1.70597 | 0.0628401 | ||||||||
\(738\) | −17.1212 | −0.630239 | ||||||||
\(739\) | 9.28480 | 0.341547 | 0.170773 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170773 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(740\) | −36.1812 | −1.33005 | ||||||||
\(741\) | 2.66551 | 0.0979200 | ||||||||
\(742\) | 60.9670 | 2.23817 | ||||||||
\(743\) | −18.2761 | −0.670484 | −0.335242 | − | 0.942132i | \(-0.608818\pi\) | ||||
−0.335242 | + | 0.942132i | \(0.608818\pi\) | |||||||
\(744\) | −4.99033 | −0.182954 | ||||||||
\(745\) | −40.7618 | −1.49340 | ||||||||
\(746\) | 33.0615 | 1.21047 | ||||||||
\(747\) | −14.9356 | −0.546465 | ||||||||
\(748\) | 4.45146 | 0.162762 | ||||||||
\(749\) | 9.19567 | 0.336003 | ||||||||
\(750\) | −12.0161 | −0.438767 | ||||||||
\(751\) | 21.2805 | 0.776535 | 0.388267 | − | 0.921547i | \(-0.373074\pi\) | ||||
0.388267 | + | 0.921547i | \(0.373074\pi\) | |||||||
\(752\) | 0.0121535 | 0.000443191 0 | ||||||||
\(753\) | −4.97765 | −0.181396 | ||||||||
\(754\) | 83.8305 | 3.05293 | ||||||||
\(755\) | 31.9289 | 1.16201 | ||||||||
\(756\) | 25.4963 | 0.927291 | ||||||||
\(757\) | 0.280839 | 0.0102073 | 0.00510364 | − | 0.999987i | \(-0.498375\pi\) | ||||
0.00510364 | + | 0.999987i | \(0.498375\pi\) | |||||||
\(758\) | 4.54699 | 0.165154 | ||||||||
\(759\) | 2.06582 | 0.0749845 | ||||||||
\(760\) | −5.44978 | −0.197684 | ||||||||
\(761\) | 51.7868 | 1.87727 | 0.938635 | − | 0.344912i | \(-0.112091\pi\) | ||||
0.938635 | + | 0.344912i | \(0.112091\pi\) | |||||||
\(762\) | −10.7156 | −0.388187 | ||||||||
\(763\) | −19.7412 | −0.714679 | ||||||||
\(764\) | 12.7500 | 0.461281 | ||||||||
\(765\) | −2.24705 | −0.0812422 | ||||||||
\(766\) | −25.6376 | −0.926326 | ||||||||
\(767\) | 92.8402 | 3.35227 | ||||||||
\(768\) | 6.91890 | 0.249664 | ||||||||
\(769\) | −15.6573 | −0.564618 | −0.282309 | − | 0.959324i | \(-0.591100\pi\) | ||||
−0.282309 | + | 0.959324i | \(0.591100\pi\) | |||||||
\(770\) | −45.8797 | −1.65339 | ||||||||
\(771\) | −7.99854 | −0.288060 | ||||||||
\(772\) | 41.6624 | 1.49946 | ||||||||
\(773\) | −18.7346 | −0.673838 | −0.336919 | − | 0.941534i | \(-0.609385\pi\) | ||||
−0.336919 | + | 0.941534i | \(0.609385\pi\) | |||||||
\(774\) | 63.0125 | 2.26494 | ||||||||
\(775\) | 5.20360 | 0.186919 | ||||||||
\(776\) | 31.6134 | 1.13486 | ||||||||
\(777\) | 7.86279 | 0.282076 | ||||||||
\(778\) | 41.5623 | 1.49008 | ||||||||
\(779\) | −2.66125 | −0.0953492 | ||||||||
\(780\) | 16.6353 | 0.595638 | ||||||||
\(781\) | −21.6376 | −0.774253 | ||||||||
\(782\) | 1.35846 | 0.0485783 | ||||||||
\(783\) | 15.0230 | 0.536878 | ||||||||
\(784\) | −0.0190974 | −0.000682051 0 | ||||||||
\(785\) | −14.0265 | −0.500627 | ||||||||
\(786\) | 6.62149 | 0.236181 | ||||||||
\(787\) | −46.5132 | −1.65802 | −0.829009 | − | 0.559235i | \(-0.811095\pi\) | ||||
−0.829009 | + | 0.559235i | \(0.811095\pi\) | |||||||
\(788\) | 5.25151 | 0.187077 | ||||||||
\(789\) | −4.04169 | −0.143888 | ||||||||
\(790\) | −46.7695 | −1.66398 | ||||||||
\(791\) | −7.47708 | −0.265854 | ||||||||
\(792\) | 26.3923 | 0.937808 | ||||||||
\(793\) | 58.8546 | 2.08999 | ||||||||
\(794\) | −7.10595 | −0.252181 | ||||||||
\(795\) | 7.12855 | 0.252824 | ||||||||
\(796\) | 48.6717 | 1.72512 | ||||||||
\(797\) | 32.8054 | 1.16203 | 0.581013 | − | 0.813894i | \(-0.302656\pi\) | ||||
0.581013 | + | 0.813894i | \(0.302656\pi\) | |||||||
\(798\) | 3.10300 | 0.109845 | ||||||||
\(799\) | −0.733286 | −0.0259418 | ||||||||
\(800\) | −7.23467 | −0.255784 | ||||||||
\(801\) | 28.6705 | 1.01302 | ||||||||
\(802\) | −9.64441 | −0.340556 | ||||||||
\(803\) | −4.49887 | −0.158762 | ||||||||
\(804\) | −0.720081 | −0.0253953 | ||||||||
\(805\) | −8.65160 | −0.304929 | ||||||||
\(806\) | −57.3002 | −2.01831 | ||||||||
\(807\) | 12.6186 | 0.444195 | ||||||||
\(808\) | 32.3041 | 1.13645 | ||||||||
\(809\) | 8.27972 | 0.291099 | 0.145550 | − | 0.989351i | \(-0.453505\pi\) | ||||
0.145550 | + | 0.989351i | \(0.453505\pi\) | |||||||
\(810\) | −32.4153 | −1.13896 | ||||||||
\(811\) | 6.45437 | 0.226644 | 0.113322 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113322 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(812\) | 60.3027 | 2.11621 | ||||||||
\(813\) | 2.32828 | 0.0816562 | ||||||||
\(814\) | 44.0756 | 1.54485 | ||||||||
\(815\) | 20.9813 | 0.734944 | ||||||||
\(816\) | 0.00123277 | 4.31557e−5 0 | ||||||||
\(817\) | 9.79443 | 0.342664 | ||||||||
\(818\) | −9.15760 | −0.320188 | ||||||||
\(819\) | 54.0607 | 1.88903 | ||||||||
\(820\) | −16.6087 | −0.580000 | ||||||||
\(821\) | −3.90894 | −0.136423 | −0.0682115 | − | 0.997671i | \(-0.521729\pi\) | ||||
−0.0682115 | + | 0.997671i | \(0.521729\pi\) | |||||||
\(822\) | −16.8070 | −0.586210 | ||||||||
\(823\) | −3.61262 | −0.125928 | −0.0629639 | − | 0.998016i | \(-0.520055\pi\) | ||||
−0.0629639 | + | 0.998016i | \(0.520055\pi\) | |||||||
\(824\) | −33.4146 | −1.16405 | ||||||||
\(825\) | 1.84032 | 0.0640717 | ||||||||
\(826\) | 108.078 | 3.76052 | ||||||||
\(827\) | 25.1855 | 0.875785 | 0.437892 | − | 0.899027i | \(-0.355725\pi\) | ||||
0.437892 | + | 0.899027i | \(0.355725\pi\) | |||||||
\(828\) | 13.0395 | 0.453155 | ||||||||
\(829\) | 33.9331 | 1.17855 | 0.589273 | − | 0.807934i | \(-0.299414\pi\) | ||||
0.589273 | + | 0.807934i | \(0.299414\pi\) | |||||||
\(830\) | −23.4471 | −0.813862 | ||||||||
\(831\) | 5.31247 | 0.184287 | ||||||||
\(832\) | 79.5812 | 2.75898 | ||||||||
\(833\) | 1.15225 | 0.0399233 | ||||||||
\(834\) | 22.0307 | 0.762860 | ||||||||
\(835\) | −12.3034 | −0.425777 | ||||||||
\(836\) | 10.7482 | 0.371736 | ||||||||
\(837\) | −10.2686 | −0.354934 | ||||||||
\(838\) | 77.2536 | 2.66868 | ||||||||
\(839\) | 1.77048 | 0.0611238 | 0.0305619 | − | 0.999533i | \(-0.490270\pi\) | ||||
0.0305619 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(840\) | 7.39133 | 0.255025 | ||||||||
\(841\) | 6.53171 | 0.225231 | ||||||||
\(842\) | −1.24199 | −0.0428019 | ||||||||
\(843\) | 10.4282 | 0.359168 | ||||||||
\(844\) | 3.23453 | 0.111337 | ||||||||
\(845\) | 47.8202 | 1.64507 | ||||||||
\(846\) | −11.3909 | −0.391626 | ||||||||
\(847\) | 0.131676 | 0.00452444 | ||||||||
\(848\) | 0.0584830 | 0.00200832 | ||||||||
\(849\) | −5.62164 | −0.192934 | ||||||||
\(850\) | 1.21017 | 0.0415085 | ||||||||
\(851\) | 8.31141 | 0.284911 | ||||||||
\(852\) | 9.13313 | 0.312896 | ||||||||
\(853\) | −43.9146 | −1.50361 | −0.751804 | − | 0.659386i | \(-0.770816\pi\) | ||||
−0.751804 | + | 0.659386i | \(0.770816\pi\) | |||||||
\(854\) | 68.5145 | 2.34452 | ||||||||
\(855\) | −5.42559 | −0.185551 | ||||||||
\(856\) | −8.30439 | −0.283838 | ||||||||
\(857\) | 18.9573 | 0.647568 | 0.323784 | − | 0.946131i | \(-0.395045\pi\) | ||||
0.323784 | + | 0.946131i | \(0.395045\pi\) | |||||||
\(858\) | −20.2649 | −0.691833 | ||||||||
\(859\) | 6.81862 | 0.232648 | 0.116324 | − | 0.993211i | \(-0.462889\pi\) | ||||
0.116324 | + | 0.993211i | \(0.462889\pi\) | |||||||
\(860\) | 61.1263 | 2.08439 | ||||||||
\(861\) | 3.60935 | 0.123006 | ||||||||
\(862\) | 67.6771 | 2.30509 | ||||||||
\(863\) | 24.4917 | 0.833707 | 0.416853 | − | 0.908974i | \(-0.363133\pi\) | ||||
0.416853 | + | 0.908974i | \(0.363133\pi\) | |||||||
\(864\) | 14.2766 | 0.485700 | ||||||||
\(865\) | 31.6659 | 1.07667 | ||||||||
\(866\) | −37.7763 | −1.28369 | ||||||||
\(867\) | 7.29743 | 0.247834 | ||||||||
\(868\) | −41.2184 | −1.39905 | ||||||||
\(869\) | 35.2056 | 1.19427 | ||||||||
\(870\) | 11.4106 | 0.386857 | ||||||||
\(871\) | −3.15573 | −0.106928 | ||||||||
\(872\) | 17.8278 | 0.603724 | ||||||||
\(873\) | 31.4731 | 1.06520 | ||||||||
\(874\) | 3.28005 | 0.110949 | ||||||||
\(875\) | −37.8807 | −1.28060 | ||||||||
\(876\) | 1.89895 | 0.0641597 | ||||||||
\(877\) | −5.60868 | −0.189392 | −0.0946958 | − | 0.995506i | \(-0.530188\pi\) | ||||
−0.0946958 | + | 0.995506i | \(0.530188\pi\) | |||||||
\(878\) | −51.8688 | −1.75049 | ||||||||
\(879\) | −0.796240 | −0.0268565 | ||||||||
\(880\) | −0.0440104 | −0.00148359 | ||||||||
\(881\) | −39.3862 | −1.32696 | −0.663478 | − | 0.748196i | \(-0.730920\pi\) | ||||
−0.663478 | + | 0.748196i | \(0.730920\pi\) | |||||||
\(882\) | 17.8991 | 0.602694 | ||||||||
\(883\) | −12.9715 | −0.436526 | −0.218263 | − | 0.975890i | \(-0.570039\pi\) | ||||
−0.218263 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(884\) | −8.23440 | −0.276953 | ||||||||
\(885\) | 12.6370 | 0.424789 | ||||||||
\(886\) | −67.9164 | −2.28170 | ||||||||
\(887\) | 19.6718 | 0.660516 | 0.330258 | − | 0.943891i | \(-0.392864\pi\) | ||||
0.330258 | + | 0.943891i | \(0.392864\pi\) | |||||||
\(888\) | −7.10069 | −0.238284 | ||||||||
\(889\) | −33.7809 | −1.13298 | ||||||||
\(890\) | 45.0094 | 1.50872 | ||||||||
\(891\) | 24.4005 | 0.817448 | ||||||||
\(892\) | −41.9404 | −1.40427 | ||||||||
\(893\) | −1.77055 | −0.0592492 | ||||||||
\(894\) | −20.9594 | −0.700989 | ||||||||
\(895\) | −19.8103 | −0.662187 | ||||||||
\(896\) | 57.2086 | 1.91120 | ||||||||
\(897\) | −3.82139 | −0.127592 | ||||||||
\(898\) | 64.4957 | 2.15225 | ||||||||
\(899\) | −24.2868 | −0.810011 | ||||||||
\(900\) | 11.6162 | 0.387205 | ||||||||
\(901\) | −3.52861 | −0.117555 | ||||||||
\(902\) | 20.2325 | 0.673670 | ||||||||
\(903\) | −13.2838 | −0.442057 | ||||||||
\(904\) | 6.75237 | 0.224580 | ||||||||
\(905\) | −0.0531802 | −0.00176777 | ||||||||
\(906\) | 16.4176 | 0.545439 | ||||||||
\(907\) | 23.6875 | 0.786529 | 0.393265 | − | 0.919425i | \(-0.371346\pi\) | ||||
0.393265 | + | 0.919425i | \(0.371346\pi\) | |||||||
\(908\) | 5.05347 | 0.167705 | ||||||||
\(909\) | 32.1607 | 1.06670 | ||||||||
\(910\) | 84.8690 | 2.81338 | ||||||||
\(911\) | −59.3177 | −1.96528 | −0.982641 | − | 0.185518i | \(-0.940604\pi\) | ||||
−0.982641 | + | 0.185518i | \(0.940604\pi\) | |||||||
\(912\) | 0.00297658 | 9.85644e−5 0 | ||||||||
\(913\) | 17.6498 | 0.584122 | ||||||||
\(914\) | 0.819538 | 0.0271079 | ||||||||
\(915\) | 8.01104 | 0.264837 | ||||||||
\(916\) | −67.1619 | −2.21909 | ||||||||
\(917\) | 20.8742 | 0.689325 | ||||||||
\(918\) | −2.38810 | −0.0788190 | ||||||||
\(919\) | −38.4131 | −1.26713 | −0.633566 | − | 0.773689i | \(-0.718410\pi\) | ||||
−0.633566 | + | 0.773689i | \(0.718410\pi\) | |||||||
\(920\) | 7.81304 | 0.257588 | ||||||||
\(921\) | 12.2579 | 0.403911 | ||||||||
\(922\) | 57.8846 | 1.90633 | ||||||||
\(923\) | 40.0256 | 1.31746 | ||||||||
\(924\) | −14.5774 | −0.479562 | ||||||||
\(925\) | 7.40415 | 0.243447 | ||||||||
\(926\) | 12.8804 | 0.423277 | ||||||||
\(927\) | −33.2663 | −1.09261 | ||||||||
\(928\) | 33.7664 | 1.10844 | ||||||||
\(929\) | −43.1954 | −1.41719 | −0.708597 | − | 0.705613i | \(-0.750672\pi\) | ||||
−0.708597 | + | 0.705613i | \(0.750672\pi\) | |||||||
\(930\) | −7.79946 | −0.255755 | ||||||||
\(931\) | 2.78217 | 0.0911818 | ||||||||
\(932\) | 0.407640 | 0.0133527 | ||||||||
\(933\) | −2.18609 | −0.0715693 | ||||||||
\(934\) | −83.7870 | −2.74159 | ||||||||
\(935\) | 2.65539 | 0.0868407 | ||||||||
\(936\) | −48.8209 | −1.59576 | ||||||||
\(937\) | 40.1404 | 1.31133 | 0.655666 | − | 0.755051i | \(-0.272388\pi\) | ||||
0.655666 | + | 0.755051i | \(0.272388\pi\) | |||||||
\(938\) | −3.67368 | −0.119950 | ||||||||
\(939\) | −1.23040 | −0.0401527 | ||||||||
\(940\) | −11.0499 | −0.360407 | ||||||||
\(941\) | 20.0028 | 0.652072 | 0.326036 | − | 0.945357i | \(-0.394287\pi\) | ||||
0.326036 | + | 0.945357i | \(0.394287\pi\) | |||||||
\(942\) | −7.21233 | −0.234990 | ||||||||
\(943\) | 3.81528 | 0.124243 | ||||||||
\(944\) | 0.103675 | 0.00337433 | ||||||||
\(945\) | 15.2091 | 0.494752 | ||||||||
\(946\) | −74.4636 | −2.42102 | ||||||||
\(947\) | −13.6086 | −0.442220 | −0.221110 | − | 0.975249i | \(-0.570968\pi\) | ||||
−0.221110 | + | 0.975249i | \(0.570968\pi\) | |||||||
\(948\) | −14.8601 | −0.482635 | ||||||||
\(949\) | 8.32208 | 0.270146 | ||||||||
\(950\) | 2.92200 | 0.0948023 | ||||||||
\(951\) | −0.869528 | −0.0281964 | ||||||||
\(952\) | −3.65868 | −0.118579 | ||||||||
\(953\) | 55.8908 | 1.81048 | 0.905241 | − | 0.424899i | \(-0.139691\pi\) | ||||
0.905241 | + | 0.424899i | \(0.139691\pi\) | |||||||
\(954\) | −54.8133 | −1.77465 | ||||||||
\(955\) | 7.60568 | 0.246114 | ||||||||
\(956\) | −81.9649 | −2.65094 | ||||||||
\(957\) | −8.58933 | −0.277654 | ||||||||
\(958\) | −0.831762 | −0.0268730 | ||||||||
\(959\) | −52.9837 | −1.71093 | ||||||||
\(960\) | 10.8323 | 0.349610 | ||||||||
\(961\) | −14.3993 | −0.464495 | ||||||||
\(962\) | −81.5319 | −2.62869 | ||||||||
\(963\) | −8.26752 | −0.266417 | ||||||||
\(964\) | 62.7479 | 2.02097 | ||||||||
\(965\) | 24.8525 | 0.800031 | ||||||||
\(966\) | −4.44860 | −0.143131 | ||||||||
\(967\) | 19.3635 | 0.622689 | 0.311344 | − | 0.950297i | \(-0.399221\pi\) | ||||
0.311344 | + | 0.950297i | \(0.399221\pi\) | |||||||
\(968\) | −0.118913 | −0.00382202 | ||||||||
\(969\) | −0.179594 | −0.00576938 | ||||||||
\(970\) | 49.4091 | 1.58643 | ||||||||
\(971\) | 27.8321 | 0.893175 | 0.446588 | − | 0.894740i | \(-0.352639\pi\) | ||||
0.446588 | + | 0.894740i | \(0.352639\pi\) | |||||||
\(972\) | −34.7551 | −1.11477 | ||||||||
\(973\) | 69.4514 | 2.22651 | ||||||||
\(974\) | 23.9073 | 0.766039 | ||||||||
\(975\) | −3.40425 | −0.109023 | ||||||||
\(976\) | 0.0657231 | 0.00210374 | ||||||||
\(977\) | −32.5766 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(978\) | 10.7885 | 0.344977 | ||||||||
\(979\) | −33.8807 | −1.08283 | ||||||||
\(980\) | 17.3633 | 0.554650 | ||||||||
\(981\) | 17.7486 | 0.566670 | ||||||||
\(982\) | 84.6505 | 2.70131 | ||||||||
\(983\) | −17.3041 | −0.551915 | −0.275958 | − | 0.961170i | \(-0.588995\pi\) | ||||
−0.275958 | + | 0.961170i | \(0.588995\pi\) | |||||||
\(984\) | −3.25951 | −0.103909 | ||||||||
\(985\) | 3.13264 | 0.0998142 | ||||||||
\(986\) | −5.64823 | −0.179876 | ||||||||
\(987\) | 2.40133 | 0.0764351 | ||||||||
\(988\) | −19.8823 | −0.632540 | ||||||||
\(989\) | −14.0417 | −0.446500 | ||||||||
\(990\) | 41.2488 | 1.31097 | ||||||||
\(991\) | 56.7783 | 1.80362 | 0.901811 | − | 0.432130i | \(-0.142238\pi\) | ||||
0.901811 | + | 0.432130i | \(0.142238\pi\) | |||||||
\(992\) | −23.0802 | −0.732797 | ||||||||
\(993\) | −3.22323 | −0.102286 | ||||||||
\(994\) | 46.5950 | 1.47790 | ||||||||
\(995\) | 29.0337 | 0.920431 | ||||||||
\(996\) | −7.44990 | −0.236059 | ||||||||
\(997\) | −28.4672 | −0.901565 | −0.450783 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450783 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(998\) | 46.3835 | 1.46824 | ||||||||
\(999\) | −14.6111 | −0.462274 |
(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 | 4009.2.a.c.1.11 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.11 | ✓ | 71 | 1.1 | even | 1 | trivial |