Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 20x^{9} - 7x^{8} + 134x^{7} + 70x^{6} - 354x^{5} - 193x^{4} + 341x^{3} + 163x^{2} - 72x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.434885\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.565115 | −0.326270 | −0.163135 | − | 0.986604i | \(-0.552161\pi\) | ||||
−0.163135 | + | 0.986604i | \(0.552161\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.615969 | −0.275470 | −0.137735 | − | 0.990469i | \(-0.543982\pi\) | ||||
−0.137735 | + | 0.990469i | \(0.543982\pi\) | |||||||
\(6\) | −0.565115 | −0.230707 | ||||||||
\(7\) | 3.05802 | 1.15582 | 0.577911 | − | 0.816100i | \(-0.303868\pi\) | ||||
0.577911 | + | 0.816100i | \(0.303868\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.68064 | −0.893548 | ||||||||
\(10\) | −0.615969 | −0.194786 | ||||||||
\(11\) | −3.11632 | −0.939606 | −0.469803 | − | 0.882771i | \(-0.655675\pi\) | ||||
−0.469803 | + | 0.882771i | \(0.655675\pi\) | |||||||
\(12\) | −0.565115 | −0.163135 | ||||||||
\(13\) | −6.07042 | −1.68363 | −0.841816 | − | 0.539765i | \(-0.818513\pi\) | ||||
−0.841816 | + | 0.539765i | \(0.818513\pi\) | |||||||
\(14\) | 3.05802 | 0.817290 | ||||||||
\(15\) | 0.348093 | 0.0898773 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.35747 | −1.78445 | −0.892224 | − | 0.451594i | \(-0.850856\pi\) | ||||
−0.892224 | + | 0.451594i | \(0.850856\pi\) | |||||||
\(18\) | −2.68064 | −0.631834 | ||||||||
\(19\) | 1.30846 | 0.300181 | 0.150091 | − | 0.988672i | \(-0.452043\pi\) | ||||
0.150091 | + | 0.988672i | \(0.452043\pi\) | |||||||
\(20\) | −0.615969 | −0.137735 | ||||||||
\(21\) | −1.72813 | −0.377110 | ||||||||
\(22\) | −3.11632 | −0.664402 | ||||||||
\(23\) | −1.38346 | −0.288472 | −0.144236 | − | 0.989543i | \(-0.546072\pi\) | ||||
−0.144236 | + | 0.989543i | \(0.546072\pi\) | |||||||
\(24\) | −0.565115 | −0.115354 | ||||||||
\(25\) | −4.62058 | −0.924117 | ||||||||
\(26\) | −6.07042 | −1.19051 | ||||||||
\(27\) | 3.21022 | 0.617807 | ||||||||
\(28\) | 3.05802 | 0.577911 | ||||||||
\(29\) | 3.58342 | 0.665424 | 0.332712 | − | 0.943029i | \(-0.392036\pi\) | ||||
0.332712 | + | 0.943029i | \(0.392036\pi\) | |||||||
\(30\) | 0.348093 | 0.0635529 | ||||||||
\(31\) | 2.91808 | 0.524103 | 0.262051 | − | 0.965054i | \(-0.415601\pi\) | ||||
0.262051 | + | 0.965054i | \(0.415601\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.76108 | 0.306565 | ||||||||
\(34\) | −7.35747 | −1.26179 | ||||||||
\(35\) | −1.88364 | −0.318394 | ||||||||
\(36\) | −2.68064 | −0.446774 | ||||||||
\(37\) | −9.97748 | −1.64029 | −0.820144 | − | 0.572157i | \(-0.806107\pi\) | ||||
−0.820144 | + | 0.572157i | \(0.806107\pi\) | |||||||
\(38\) | 1.30846 | 0.212260 | ||||||||
\(39\) | 3.43049 | 0.549318 | ||||||||
\(40\) | −0.615969 | −0.0973932 | ||||||||
\(41\) | 6.14047 | 0.958980 | 0.479490 | − | 0.877547i | \(-0.340822\pi\) | ||||
0.479490 | + | 0.877547i | \(0.340822\pi\) | |||||||
\(42\) | −1.72813 | −0.266657 | ||||||||
\(43\) | −3.20281 | −0.488424 | −0.244212 | − | 0.969722i | \(-0.578529\pi\) | ||||
−0.244212 | + | 0.969722i | \(0.578529\pi\) | |||||||
\(44\) | −3.11632 | −0.469803 | ||||||||
\(45\) | 1.65119 | 0.246145 | ||||||||
\(46\) | −1.38346 | −0.203981 | ||||||||
\(47\) | 7.36719 | 1.07461 | 0.537307 | − | 0.843387i | \(-0.319442\pi\) | ||||
0.537307 | + | 0.843387i | \(0.319442\pi\) | |||||||
\(48\) | −0.565115 | −0.0815674 | ||||||||
\(49\) | 2.35148 | 0.335925 | ||||||||
\(50\) | −4.62058 | −0.653449 | ||||||||
\(51\) | 4.15782 | 0.582211 | ||||||||
\(52\) | −6.07042 | −0.841816 | ||||||||
\(53\) | −3.83489 | −0.526762 | −0.263381 | − | 0.964692i | \(-0.584838\pi\) | ||||
−0.263381 | + | 0.964692i | \(0.584838\pi\) | |||||||
\(54\) | 3.21022 | 0.436856 | ||||||||
\(55\) | 1.91956 | 0.258833 | ||||||||
\(56\) | 3.05802 | 0.408645 | ||||||||
\(57\) | −0.739431 | −0.0979401 | ||||||||
\(58\) | 3.58342 | 0.470526 | ||||||||
\(59\) | −1.10698 | −0.144116 | −0.0720582 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720582 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(60\) | 0.348093 | 0.0449387 | ||||||||
\(61\) | 7.64720 | 0.979124 | 0.489562 | − | 0.871969i | \(-0.337157\pi\) | ||||
0.489562 | + | 0.871969i | \(0.337157\pi\) | |||||||
\(62\) | 2.91808 | 0.370597 | ||||||||
\(63\) | −8.19746 | −1.03278 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.73919 | 0.463789 | ||||||||
\(66\) | 1.76108 | 0.216774 | ||||||||
\(67\) | −16.1681 | −1.97524 | −0.987621 | − | 0.156858i | \(-0.949863\pi\) | ||||
−0.987621 | + | 0.156858i | \(0.949863\pi\) | |||||||
\(68\) | −7.35747 | −0.892224 | ||||||||
\(69\) | 0.781816 | 0.0941196 | ||||||||
\(70\) | −1.88364 | −0.225138 | ||||||||
\(71\) | 15.1235 | 1.79483 | 0.897417 | − | 0.441182i | \(-0.145441\pi\) | ||||
0.897417 | + | 0.441182i | \(0.145441\pi\) | |||||||
\(72\) | −2.68064 | −0.315917 | ||||||||
\(73\) | −11.5095 | −1.34708 | −0.673541 | − | 0.739150i | \(-0.735228\pi\) | ||||
−0.673541 | + | 0.739150i | \(0.735228\pi\) | |||||||
\(74\) | −9.97748 | −1.15986 | ||||||||
\(75\) | 2.61116 | 0.301511 | ||||||||
\(76\) | 1.30846 | 0.150091 | ||||||||
\(77\) | −9.52976 | −1.08602 | ||||||||
\(78\) | 3.43049 | 0.388426 | ||||||||
\(79\) | 6.87816 | 0.773853 | 0.386927 | − | 0.922111i | \(-0.373537\pi\) | ||||
0.386927 | + | 0.922111i | \(0.373537\pi\) | |||||||
\(80\) | −0.615969 | −0.0688674 | ||||||||
\(81\) | 6.22779 | 0.691976 | ||||||||
\(82\) | 6.14047 | 0.678102 | ||||||||
\(83\) | 3.52486 | 0.386904 | 0.193452 | − | 0.981110i | \(-0.438032\pi\) | ||||
0.193452 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(84\) | −1.72813 | −0.188555 | ||||||||
\(85\) | 4.53197 | 0.491561 | ||||||||
\(86\) | −3.20281 | −0.345368 | ||||||||
\(87\) | −2.02504 | −0.217108 | ||||||||
\(88\) | −3.11632 | −0.332201 | ||||||||
\(89\) | −10.5489 | −1.11818 | −0.559089 | − | 0.829108i | \(-0.688849\pi\) | ||||
−0.559089 | + | 0.829108i | \(0.688849\pi\) | |||||||
\(90\) | 1.65119 | 0.174051 | ||||||||
\(91\) | −18.5635 | −1.94598 | ||||||||
\(92\) | −1.38346 | −0.144236 | ||||||||
\(93\) | −1.64905 | −0.170999 | ||||||||
\(94\) | 7.36719 | 0.759867 | ||||||||
\(95\) | −0.805970 | −0.0826908 | ||||||||
\(96\) | −0.565115 | −0.0576769 | ||||||||
\(97\) | −7.96436 | −0.808658 | −0.404329 | − | 0.914614i | \(-0.632495\pi\) | ||||
−0.404329 | + | 0.914614i | \(0.632495\pi\) | |||||||
\(98\) | 2.35148 | 0.237535 | ||||||||
\(99\) | 8.35375 | 0.839583 | ||||||||
\(100\) | −4.62058 | −0.462058 | ||||||||
\(101\) | 1.66068 | 0.165244 | 0.0826220 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826220 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(102\) | 4.15782 | 0.411685 | ||||||||
\(103\) | −14.0622 | −1.38559 | −0.692796 | − | 0.721134i | \(-0.743621\pi\) | ||||
−0.692796 | + | 0.721134i | \(0.743621\pi\) | |||||||
\(104\) | −6.07042 | −0.595254 | ||||||||
\(105\) | 1.06448 | 0.103882 | ||||||||
\(106\) | −3.83489 | −0.372477 | ||||||||
\(107\) | 12.5752 | 1.21570 | 0.607848 | − | 0.794054i | \(-0.292033\pi\) | ||||
0.607848 | + | 0.794054i | \(0.292033\pi\) | |||||||
\(108\) | 3.21022 | 0.308904 | ||||||||
\(109\) | −5.61259 | −0.537589 | −0.268794 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268794 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(110\) | 1.91956 | 0.183022 | ||||||||
\(111\) | 5.63843 | 0.535176 | ||||||||
\(112\) | 3.05802 | 0.288956 | ||||||||
\(113\) | 15.3358 | 1.44267 | 0.721334 | − | 0.692587i | \(-0.243529\pi\) | ||||
0.721334 | + | 0.692587i | \(0.243529\pi\) | |||||||
\(114\) | −0.739431 | −0.0692541 | ||||||||
\(115\) | 0.852170 | 0.0794652 | ||||||||
\(116\) | 3.58342 | 0.332712 | ||||||||
\(117\) | 16.2726 | 1.50441 | ||||||||
\(118\) | −1.10698 | −0.101906 | ||||||||
\(119\) | −22.4993 | −2.06250 | ||||||||
\(120\) | 0.348093 | 0.0317764 | ||||||||
\(121\) | −1.28855 | −0.117141 | ||||||||
\(122\) | 7.64720 | 0.692345 | ||||||||
\(123\) | −3.47008 | −0.312886 | ||||||||
\(124\) | 2.91808 | 0.262051 | ||||||||
\(125\) | 5.92598 | 0.530035 | ||||||||
\(126\) | −8.19746 | −0.730288 | ||||||||
\(127\) | −10.9479 | −0.971471 | −0.485736 | − | 0.874106i | \(-0.661448\pi\) | ||||
−0.485736 | + | 0.874106i | \(0.661448\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.80996 | 0.159358 | ||||||||
\(130\) | 3.73919 | 0.327948 | ||||||||
\(131\) | −14.6494 | −1.27992 | −0.639960 | − | 0.768408i | \(-0.721049\pi\) | ||||
−0.639960 | + | 0.768408i | \(0.721049\pi\) | |||||||
\(132\) | 1.76108 | 0.153282 | ||||||||
\(133\) | 4.00130 | 0.346956 | ||||||||
\(134\) | −16.1681 | −1.39671 | ||||||||
\(135\) | −1.97739 | −0.170187 | ||||||||
\(136\) | −7.35747 | −0.630897 | ||||||||
\(137\) | 4.82347 | 0.412097 | 0.206048 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206048 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(138\) | 0.781816 | 0.0665526 | ||||||||
\(139\) | −21.4686 | −1.82094 | −0.910470 | − | 0.413576i | \(-0.864280\pi\) | ||||
−0.910470 | + | 0.413576i | \(0.864280\pi\) | |||||||
\(140\) | −1.88364 | −0.159197 | ||||||||
\(141\) | −4.16331 | −0.350614 | ||||||||
\(142\) | 15.1235 | 1.26914 | ||||||||
\(143\) | 18.9174 | 1.58195 | ||||||||
\(144\) | −2.68064 | −0.223387 | ||||||||
\(145\) | −2.20727 | −0.183304 | ||||||||
\(146\) | −11.5095 | −0.952531 | ||||||||
\(147\) | −1.32886 | −0.109602 | ||||||||
\(148\) | −9.97748 | −0.820144 | ||||||||
\(149\) | −13.8144 | −1.13172 | −0.565861 | − | 0.824501i | \(-0.691456\pi\) | ||||
−0.565861 | + | 0.824501i | \(0.691456\pi\) | |||||||
\(150\) | 2.61116 | 0.213201 | ||||||||
\(151\) | 8.21835 | 0.668800 | 0.334400 | − | 0.942431i | \(-0.391466\pi\) | ||||
0.334400 | + | 0.942431i | \(0.391466\pi\) | |||||||
\(152\) | 1.30846 | 0.106130 | ||||||||
\(153\) | 19.7227 | 1.59449 | ||||||||
\(154\) | −9.52976 | −0.767930 | ||||||||
\(155\) | −1.79745 | −0.144374 | ||||||||
\(156\) | 3.43049 | 0.274659 | ||||||||
\(157\) | −1.12390 | −0.0896969 | −0.0448485 | − | 0.998994i | \(-0.514281\pi\) | ||||
−0.0448485 | + | 0.998994i | \(0.514281\pi\) | |||||||
\(158\) | 6.87816 | 0.547197 | ||||||||
\(159\) | 2.16715 | 0.171867 | ||||||||
\(160\) | −0.615969 | −0.0486966 | ||||||||
\(161\) | −4.23066 | −0.333422 | ||||||||
\(162\) | 6.22779 | 0.489301 | ||||||||
\(163\) | 21.6481 | 1.69561 | 0.847803 | − | 0.530311i | \(-0.177925\pi\) | ||||
0.847803 | + | 0.530311i | \(0.177925\pi\) | |||||||
\(164\) | 6.14047 | 0.479490 | ||||||||
\(165\) | −1.08477 | −0.0844493 | ||||||||
\(166\) | 3.52486 | 0.273582 | ||||||||
\(167\) | −5.38914 | −0.417024 | −0.208512 | − | 0.978020i | \(-0.566862\pi\) | ||||
−0.208512 | + | 0.978020i | \(0.566862\pi\) | |||||||
\(168\) | −1.72813 | −0.133328 | ||||||||
\(169\) | 23.8500 | 1.83461 | ||||||||
\(170\) | 4.53197 | 0.347586 | ||||||||
\(171\) | −3.50752 | −0.268227 | ||||||||
\(172\) | −3.20281 | −0.244212 | ||||||||
\(173\) | −5.65710 | −0.430101 | −0.215051 | − | 0.976603i | \(-0.568992\pi\) | ||||
−0.215051 | + | 0.976603i | \(0.568992\pi\) | |||||||
\(174\) | −2.02504 | −0.153518 | ||||||||
\(175\) | −14.1298 | −1.06811 | ||||||||
\(176\) | −3.11632 | −0.234901 | ||||||||
\(177\) | 0.625571 | 0.0470208 | ||||||||
\(178\) | −10.5489 | −0.790672 | ||||||||
\(179\) | −15.0737 | −1.12666 | −0.563331 | − | 0.826231i | \(-0.690480\pi\) | ||||
−0.563331 | + | 0.826231i | \(0.690480\pi\) | |||||||
\(180\) | 1.65119 | 0.123073 | ||||||||
\(181\) | 26.6368 | 1.97990 | 0.989948 | − | 0.141430i | \(-0.0451700\pi\) | ||||
0.989948 | + | 0.141430i | \(0.0451700\pi\) | |||||||
\(182\) | −18.5635 | −1.37601 | ||||||||
\(183\) | −4.32155 | −0.319458 | ||||||||
\(184\) | −1.38346 | −0.101990 | ||||||||
\(185\) | 6.14582 | 0.451849 | ||||||||
\(186\) | −1.64905 | −0.120914 | ||||||||
\(187\) | 22.9282 | 1.67668 | ||||||||
\(188\) | 7.36719 | 0.537307 | ||||||||
\(189\) | 9.81691 | 0.714075 | ||||||||
\(190\) | −0.805970 | −0.0584712 | ||||||||
\(191\) | 22.1179 | 1.60039 | 0.800196 | − | 0.599739i | \(-0.204729\pi\) | ||||
0.800196 | + | 0.599739i | \(0.204729\pi\) | |||||||
\(192\) | −0.565115 | −0.0407837 | ||||||||
\(193\) | −4.12444 | −0.296883 | −0.148442 | − | 0.988921i | \(-0.547426\pi\) | ||||
−0.148442 | + | 0.988921i | \(0.547426\pi\) | |||||||
\(194\) | −7.96436 | −0.571808 | ||||||||
\(195\) | −2.11307 | −0.151320 | ||||||||
\(196\) | 2.35148 | 0.167963 | ||||||||
\(197\) | 26.2138 | 1.86765 | 0.933827 | − | 0.357724i | \(-0.116447\pi\) | ||||
0.933827 | + | 0.357724i | \(0.116447\pi\) | |||||||
\(198\) | 8.35375 | 0.593675 | ||||||||
\(199\) | 10.2490 | 0.726531 | 0.363265 | − | 0.931686i | \(-0.381662\pi\) | ||||
0.363265 | + | 0.931686i | \(0.381662\pi\) | |||||||
\(200\) | −4.62058 | −0.326725 | ||||||||
\(201\) | 9.13682 | 0.644461 | ||||||||
\(202\) | 1.66068 | 0.116845 | ||||||||
\(203\) | 10.9582 | 0.769112 | ||||||||
\(204\) | 4.15782 | 0.291105 | ||||||||
\(205\) | −3.78234 | −0.264170 | ||||||||
\(206\) | −14.0622 | −0.979761 | ||||||||
\(207\) | 3.70857 | 0.257764 | ||||||||
\(208\) | −6.07042 | −0.420908 | ||||||||
\(209\) | −4.07758 | −0.282052 | ||||||||
\(210\) | 1.06448 | 0.0734558 | ||||||||
\(211\) | 0.885119 | 0.0609341 | 0.0304671 | − | 0.999536i | \(-0.490301\pi\) | ||||
0.0304671 | + | 0.999536i | \(0.490301\pi\) | |||||||
\(212\) | −3.83489 | −0.263381 | ||||||||
\(213\) | −8.54655 | −0.585600 | ||||||||
\(214\) | 12.5752 | 0.859626 | ||||||||
\(215\) | 1.97283 | 0.134546 | ||||||||
\(216\) | 3.21022 | 0.218428 | ||||||||
\(217\) | 8.92355 | 0.605770 | ||||||||
\(218\) | −5.61259 | −0.380133 | ||||||||
\(219\) | 6.50419 | 0.439512 | ||||||||
\(220\) | 1.91956 | 0.129416 | ||||||||
\(221\) | 44.6629 | 3.00435 | ||||||||
\(222\) | 5.63843 | 0.378427 | ||||||||
\(223\) | −14.0423 | −0.940340 | −0.470170 | − | 0.882576i | \(-0.655807\pi\) | ||||
−0.470170 | + | 0.882576i | \(0.655807\pi\) | |||||||
\(224\) | 3.05802 | 0.204322 | ||||||||
\(225\) | 12.3861 | 0.825743 | ||||||||
\(226\) | 15.3358 | 1.02012 | ||||||||
\(227\) | 22.5229 | 1.49490 | 0.747449 | − | 0.664320i | \(-0.231279\pi\) | ||||
0.747449 | + | 0.664320i | \(0.231279\pi\) | |||||||
\(228\) | −0.739431 | −0.0489700 | ||||||||
\(229\) | −17.3340 | −1.14546 | −0.572731 | − | 0.819743i | \(-0.694116\pi\) | ||||
−0.572731 | + | 0.819743i | \(0.694116\pi\) | |||||||
\(230\) | 0.852170 | 0.0561904 | ||||||||
\(231\) | 5.38542 | 0.354334 | ||||||||
\(232\) | 3.58342 | 0.235263 | ||||||||
\(233\) | −26.5014 | −1.73617 | −0.868083 | − | 0.496419i | \(-0.834648\pi\) | ||||
−0.868083 | + | 0.496419i | \(0.834648\pi\) | |||||||
\(234\) | 16.2726 | 1.06378 | ||||||||
\(235\) | −4.53796 | −0.296024 | ||||||||
\(236\) | −1.10698 | −0.0720582 | ||||||||
\(237\) | −3.88695 | −0.252485 | ||||||||
\(238\) | −22.4993 | −1.45841 | ||||||||
\(239\) | 20.0415 | 1.29638 | 0.648188 | − | 0.761480i | \(-0.275527\pi\) | ||||
0.648188 | + | 0.761480i | \(0.275527\pi\) | |||||||
\(240\) | 0.348093 | 0.0224693 | ||||||||
\(241\) | −5.59198 | −0.360211 | −0.180106 | − | 0.983647i | \(-0.557644\pi\) | ||||
−0.180106 | + | 0.983647i | \(0.557644\pi\) | |||||||
\(242\) | −1.28855 | −0.0828311 | ||||||||
\(243\) | −13.1501 | −0.843578 | ||||||||
\(244\) | 7.64720 | 0.489562 | ||||||||
\(245\) | −1.44844 | −0.0925372 | ||||||||
\(246\) | −3.47008 | −0.221244 | ||||||||
\(247\) | −7.94290 | −0.505395 | ||||||||
\(248\) | 2.91808 | 0.185298 | ||||||||
\(249\) | −1.99195 | −0.126235 | ||||||||
\(250\) | 5.92598 | 0.374792 | ||||||||
\(251\) | −15.5175 | −0.979458 | −0.489729 | − | 0.871875i | \(-0.662904\pi\) | ||||
−0.489729 | + | 0.871875i | \(0.662904\pi\) | |||||||
\(252\) | −8.19746 | −0.516391 | ||||||||
\(253\) | 4.31131 | 0.271050 | ||||||||
\(254\) | −10.9479 | −0.686934 | ||||||||
\(255\) | −2.56108 | −0.160381 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.79991 | 0.237032 | 0.118516 | − | 0.992952i | \(-0.462186\pi\) | ||||
0.118516 | + | 0.992952i | \(0.462186\pi\) | |||||||
\(258\) | 1.80996 | 0.112683 | ||||||||
\(259\) | −30.5113 | −1.89588 | ||||||||
\(260\) | 3.73919 | 0.231895 | ||||||||
\(261\) | −9.60587 | −0.594588 | ||||||||
\(262\) | −14.6494 | −0.905040 | ||||||||
\(263\) | −3.58984 | −0.221359 | −0.110679 | − | 0.993856i | \(-0.535303\pi\) | ||||
−0.110679 | + | 0.993856i | \(0.535303\pi\) | |||||||
\(264\) | 1.76108 | 0.108387 | ||||||||
\(265\) | 2.36217 | 0.145107 | ||||||||
\(266\) | 4.00130 | 0.245335 | ||||||||
\(267\) | 5.96133 | 0.364828 | ||||||||
\(268\) | −16.1681 | −0.987621 | ||||||||
\(269\) | 10.4559 | 0.637507 | 0.318753 | − | 0.947838i | \(-0.396736\pi\) | ||||
0.318753 | + | 0.947838i | \(0.396736\pi\) | |||||||
\(270\) | −1.97739 | −0.120340 | ||||||||
\(271\) | −3.88450 | −0.235966 | −0.117983 | − | 0.993016i | \(-0.537643\pi\) | ||||
−0.117983 | + | 0.993016i | \(0.537643\pi\) | |||||||
\(272\) | −7.35747 | −0.446112 | ||||||||
\(273\) | 10.4905 | 0.634914 | ||||||||
\(274\) | 4.82347 | 0.291396 | ||||||||
\(275\) | 14.3992 | 0.868305 | ||||||||
\(276\) | 0.781816 | 0.0470598 | ||||||||
\(277\) | 25.3987 | 1.52606 | 0.763029 | − | 0.646364i | \(-0.223711\pi\) | ||||
0.763029 | + | 0.646364i | \(0.223711\pi\) | |||||||
\(278\) | −21.4686 | −1.28760 | ||||||||
\(279\) | −7.82234 | −0.468311 | ||||||||
\(280\) | −1.88364 | −0.112569 | ||||||||
\(281\) | 8.72731 | 0.520628 | 0.260314 | − | 0.965524i | \(-0.416174\pi\) | ||||
0.260314 | + | 0.965524i | \(0.416174\pi\) | |||||||
\(282\) | −4.16331 | −0.247922 | ||||||||
\(283\) | −22.9032 | −1.36145 | −0.680725 | − | 0.732539i | \(-0.738335\pi\) | ||||
−0.680725 | + | 0.732539i | \(0.738335\pi\) | |||||||
\(284\) | 15.1235 | 0.897417 | ||||||||
\(285\) | 0.455466 | 0.0269795 | ||||||||
\(286\) | 18.9174 | 1.11861 | ||||||||
\(287\) | 18.7777 | 1.10841 | ||||||||
\(288\) | −2.68064 | −0.157958 | ||||||||
\(289\) | 37.1323 | 2.18425 | ||||||||
\(290\) | −2.20727 | −0.129615 | ||||||||
\(291\) | 4.50078 | 0.263841 | ||||||||
\(292\) | −11.5095 | −0.673541 | ||||||||
\(293\) | −2.82047 | −0.164774 | −0.0823868 | − | 0.996600i | \(-0.526254\pi\) | ||||
−0.0823868 | + | 0.996600i | \(0.526254\pi\) | |||||||
\(294\) | −1.32886 | −0.0775005 | ||||||||
\(295\) | 0.681864 | 0.0396997 | ||||||||
\(296\) | −9.97748 | −0.579929 | ||||||||
\(297\) | −10.0041 | −0.580495 | ||||||||
\(298\) | −13.8144 | −0.800248 | ||||||||
\(299\) | 8.39820 | 0.485681 | ||||||||
\(300\) | 2.61116 | 0.150756 | ||||||||
\(301\) | −9.79425 | −0.564531 | ||||||||
\(302\) | 8.21835 | 0.472913 | ||||||||
\(303\) | −0.938477 | −0.0539141 | ||||||||
\(304\) | 1.30846 | 0.0750453 | ||||||||
\(305\) | −4.71044 | −0.269719 | ||||||||
\(306\) | 19.7227 | 1.12747 | ||||||||
\(307\) | 0.877326 | 0.0500716 | 0.0250358 | − | 0.999687i | \(-0.492030\pi\) | ||||
0.0250358 | + | 0.999687i | \(0.492030\pi\) | |||||||
\(308\) | −9.52976 | −0.543009 | ||||||||
\(309\) | 7.94678 | 0.452076 | ||||||||
\(310\) | −1.79745 | −0.102088 | ||||||||
\(311\) | −10.6787 | −0.605535 | −0.302767 | − | 0.953065i | \(-0.597910\pi\) | ||||
−0.302767 | + | 0.953065i | \(0.597910\pi\) | |||||||
\(312\) | 3.43049 | 0.194213 | ||||||||
\(313\) | 27.2477 | 1.54013 | 0.770066 | − | 0.637964i | \(-0.220223\pi\) | ||||
0.770066 | + | 0.637964i | \(0.220223\pi\) | |||||||
\(314\) | −1.12390 | −0.0634253 | ||||||||
\(315\) | 5.04938 | 0.284500 | ||||||||
\(316\) | 6.87816 | 0.386927 | ||||||||
\(317\) | −26.4081 | −1.48323 | −0.741615 | − | 0.670826i | \(-0.765940\pi\) | ||||
−0.741615 | + | 0.670826i | \(0.765940\pi\) | |||||||
\(318\) | 2.16715 | 0.121528 | ||||||||
\(319\) | −11.1671 | −0.625236 | ||||||||
\(320\) | −0.615969 | −0.0344337 | ||||||||
\(321\) | −7.10647 | −0.396644 | ||||||||
\(322\) | −4.23066 | −0.235765 | ||||||||
\(323\) | −9.62695 | −0.535658 | ||||||||
\(324\) | 6.22779 | 0.345988 | ||||||||
\(325\) | 28.0489 | 1.55587 | ||||||||
\(326\) | 21.6481 | 1.19898 | ||||||||
\(327\) | 3.17176 | 0.175399 | ||||||||
\(328\) | 6.14047 | 0.339051 | ||||||||
\(329\) | 22.5290 | 1.24206 | ||||||||
\(330\) | −1.08477 | −0.0597146 | ||||||||
\(331\) | −33.2619 | −1.82824 | −0.914119 | − | 0.405446i | \(-0.867116\pi\) | ||||
−0.914119 | + | 0.405446i | \(0.867116\pi\) | |||||||
\(332\) | 3.52486 | 0.193452 | ||||||||
\(333\) | 26.7461 | 1.46568 | ||||||||
\(334\) | −5.38914 | −0.294881 | ||||||||
\(335\) | 9.95901 | 0.544119 | ||||||||
\(336\) | −1.72813 | −0.0942774 | ||||||||
\(337\) | −22.5248 | −1.22701 | −0.613503 | − | 0.789692i | \(-0.710240\pi\) | ||||
−0.613503 | + | 0.789692i | \(0.710240\pi\) | |||||||
\(338\) | 23.8500 | 1.29727 | ||||||||
\(339\) | −8.66649 | −0.470699 | ||||||||
\(340\) | 4.53197 | 0.245780 | ||||||||
\(341\) | −9.09367 | −0.492450 | ||||||||
\(342\) | −3.50752 | −0.189665 | ||||||||
\(343\) | −14.2153 | −0.767552 | ||||||||
\(344\) | −3.20281 | −0.172684 | ||||||||
\(345\) | −0.481574 | −0.0259271 | ||||||||
\(346\) | −5.65710 | −0.304128 | ||||||||
\(347\) | −12.8300 | −0.688748 | −0.344374 | − | 0.938832i | \(-0.611909\pi\) | ||||
−0.344374 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(348\) | −2.02504 | −0.108554 | ||||||||
\(349\) | −28.4649 | −1.52369 | −0.761847 | − | 0.647757i | \(-0.775707\pi\) | ||||
−0.761847 | + | 0.647757i | \(0.775707\pi\) | |||||||
\(350\) | −14.1298 | −0.755271 | ||||||||
\(351\) | −19.4874 | −1.04016 | ||||||||
\(352\) | −3.11632 | −0.166100 | ||||||||
\(353\) | −15.6535 | −0.833149 | −0.416575 | − | 0.909102i | \(-0.636770\pi\) | ||||
−0.416575 | + | 0.909102i | \(0.636770\pi\) | |||||||
\(354\) | 0.625571 | 0.0332487 | ||||||||
\(355\) | −9.31563 | −0.494422 | ||||||||
\(356\) | −10.5489 | −0.559089 | ||||||||
\(357\) | 12.7147 | 0.672932 | ||||||||
\(358\) | −15.0737 | −0.796671 | ||||||||
\(359\) | 30.0022 | 1.58345 | 0.791727 | − | 0.610875i | \(-0.209182\pi\) | ||||
0.791727 | + | 0.610875i | \(0.209182\pi\) | |||||||
\(360\) | 1.65119 | 0.0870255 | ||||||||
\(361\) | −17.2879 | −0.909891 | ||||||||
\(362\) | 26.6368 | 1.40000 | ||||||||
\(363\) | 0.728180 | 0.0382195 | ||||||||
\(364\) | −18.5635 | −0.972989 | ||||||||
\(365\) | 7.08948 | 0.371080 | ||||||||
\(366\) | −4.32155 | −0.225891 | ||||||||
\(367\) | 26.6928 | 1.39335 | 0.696676 | − | 0.717386i | \(-0.254662\pi\) | ||||
0.696676 | + | 0.717386i | \(0.254662\pi\) | |||||||
\(368\) | −1.38346 | −0.0721180 | ||||||||
\(369\) | −16.4604 | −0.856895 | ||||||||
\(370\) | 6.14582 | 0.319506 | ||||||||
\(371\) | −11.7272 | −0.608844 | ||||||||
\(372\) | −1.64905 | −0.0854994 | ||||||||
\(373\) | 27.8906 | 1.44412 | 0.722061 | − | 0.691829i | \(-0.243195\pi\) | ||||
0.722061 | + | 0.691829i | \(0.243195\pi\) | |||||||
\(374\) | 22.9282 | 1.18559 | ||||||||
\(375\) | −3.34886 | −0.172934 | ||||||||
\(376\) | 7.36719 | 0.379934 | ||||||||
\(377\) | −21.7528 | −1.12033 | ||||||||
\(378\) | 9.81691 | 0.504928 | ||||||||
\(379\) | 20.0434 | 1.02956 | 0.514780 | − | 0.857322i | \(-0.327874\pi\) | ||||
0.514780 | + | 0.857322i | \(0.327874\pi\) | |||||||
\(380\) | −0.805970 | −0.0413454 | ||||||||
\(381\) | 6.18684 | 0.316962 | ||||||||
\(382\) | 22.1179 | 1.13165 | ||||||||
\(383\) | −5.82733 | −0.297763 | −0.148881 | − | 0.988855i | \(-0.547567\pi\) | ||||
−0.148881 | + | 0.988855i | \(0.547567\pi\) | |||||||
\(384\) | −0.565115 | −0.0288384 | ||||||||
\(385\) | 5.87004 | 0.299165 | ||||||||
\(386\) | −4.12444 | −0.209928 | ||||||||
\(387\) | 8.58559 | 0.436430 | ||||||||
\(388\) | −7.96436 | −0.404329 | ||||||||
\(389\) | −31.8482 | −1.61477 | −0.807384 | − | 0.590027i | \(-0.799117\pi\) | ||||
−0.807384 | + | 0.590027i | \(0.799117\pi\) | |||||||
\(390\) | −2.11307 | −0.107000 | ||||||||
\(391\) | 10.1788 | 0.514763 | ||||||||
\(392\) | 2.35148 | 0.118768 | ||||||||
\(393\) | 8.27858 | 0.417599 | ||||||||
\(394\) | 26.2138 | 1.32063 | ||||||||
\(395\) | −4.23673 | −0.213173 | ||||||||
\(396\) | 8.35375 | 0.419792 | ||||||||
\(397\) | −24.9264 | −1.25102 | −0.625509 | − | 0.780217i | \(-0.715109\pi\) | ||||
−0.625509 | + | 0.780217i | \(0.715109\pi\) | |||||||
\(398\) | 10.2490 | 0.513735 | ||||||||
\(399\) | −2.26119 | −0.113201 | ||||||||
\(400\) | −4.62058 | −0.231029 | ||||||||
\(401\) | −6.99992 | −0.349559 | −0.174780 | − | 0.984608i | \(-0.555921\pi\) | ||||
−0.174780 | + | 0.984608i | \(0.555921\pi\) | |||||||
\(402\) | 9.13682 | 0.455703 | ||||||||
\(403\) | −17.7140 | −0.882396 | ||||||||
\(404\) | 1.66068 | 0.0826220 | ||||||||
\(405\) | −3.83612 | −0.190618 | ||||||||
\(406\) | 10.9582 | 0.543844 | ||||||||
\(407\) | 31.0930 | 1.54122 | ||||||||
\(408\) | 4.15782 | 0.205843 | ||||||||
\(409\) | −4.72367 | −0.233571 | −0.116785 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116785 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(410\) | −3.78234 | −0.186796 | ||||||||
\(411\) | −2.72582 | −0.134455 | ||||||||
\(412\) | −14.0622 | −0.692796 | ||||||||
\(413\) | −3.38516 | −0.166573 | ||||||||
\(414\) | 3.70857 | 0.182266 | ||||||||
\(415\) | −2.17120 | −0.106580 | ||||||||
\(416\) | −6.07042 | −0.297627 | ||||||||
\(417\) | 12.1322 | 0.594117 | ||||||||
\(418\) | −4.07758 | −0.199441 | ||||||||
\(419\) | −22.0804 | −1.07870 | −0.539349 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539349 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(420\) | 1.06448 | 0.0519411 | ||||||||
\(421\) | 23.1422 | 1.12788 | 0.563941 | − | 0.825815i | \(-0.309285\pi\) | ||||
0.563941 | + | 0.825815i | \(0.309285\pi\) | |||||||
\(422\) | 0.885119 | 0.0430869 | ||||||||
\(423\) | −19.7488 | −0.960220 | ||||||||
\(424\) | −3.83489 | −0.186239 | ||||||||
\(425\) | 33.9958 | 1.64904 | ||||||||
\(426\) | −8.54655 | −0.414082 | ||||||||
\(427\) | 23.3853 | 1.13169 | ||||||||
\(428\) | 12.5752 | 0.607848 | ||||||||
\(429\) | −10.6905 | −0.516142 | ||||||||
\(430\) | 1.97283 | 0.0951383 | ||||||||
\(431\) | 14.6390 | 0.705136 | 0.352568 | − | 0.935786i | \(-0.385309\pi\) | ||||
0.352568 | + | 0.935786i | \(0.385309\pi\) | |||||||
\(432\) | 3.21022 | 0.154452 | ||||||||
\(433\) | −7.87846 | −0.378614 | −0.189307 | − | 0.981918i | \(-0.560624\pi\) | ||||
−0.189307 | + | 0.981918i | \(0.560624\pi\) | |||||||
\(434\) | 8.92355 | 0.428344 | ||||||||
\(435\) | 1.24736 | 0.0598065 | ||||||||
\(436\) | −5.61259 | −0.268794 | ||||||||
\(437\) | −1.81021 | −0.0865939 | ||||||||
\(438\) | 6.50419 | 0.310782 | ||||||||
\(439\) | −0.803456 | −0.0383469 | −0.0191734 | − | 0.999816i | \(-0.506103\pi\) | ||||
−0.0191734 | + | 0.999816i | \(0.506103\pi\) | |||||||
\(440\) | 1.91956 | 0.0915112 | ||||||||
\(441\) | −6.30348 | −0.300165 | ||||||||
\(442\) | 44.6629 | 2.12440 | ||||||||
\(443\) | 18.7417 | 0.890443 | 0.445222 | − | 0.895420i | \(-0.353125\pi\) | ||||
0.445222 | + | 0.895420i | \(0.353125\pi\) | |||||||
\(444\) | 5.63843 | 0.267588 | ||||||||
\(445\) | 6.49777 | 0.308024 | ||||||||
\(446\) | −14.0423 | −0.664921 | ||||||||
\(447\) | 7.80674 | 0.369246 | ||||||||
\(448\) | 3.05802 | 0.144478 | ||||||||
\(449\) | 19.2173 | 0.906919 | 0.453460 | − | 0.891277i | \(-0.350190\pi\) | ||||
0.453460 | + | 0.891277i | \(0.350190\pi\) | |||||||
\(450\) | 12.3861 | 0.583888 | ||||||||
\(451\) | −19.1357 | −0.901064 | ||||||||
\(452\) | 15.3358 | 0.721334 | ||||||||
\(453\) | −4.64432 | −0.218209 | ||||||||
\(454\) | 22.5229 | 1.05705 | ||||||||
\(455\) | 11.4345 | 0.536058 | ||||||||
\(456\) | −0.739431 | −0.0346270 | ||||||||
\(457\) | 31.7684 | 1.48606 | 0.743031 | − | 0.669257i | \(-0.233388\pi\) | ||||
0.743031 | + | 0.669257i | \(0.233388\pi\) | |||||||
\(458\) | −17.3340 | −0.809965 | ||||||||
\(459\) | −23.6191 | −1.10244 | ||||||||
\(460\) | 0.852170 | 0.0397326 | ||||||||
\(461\) | −20.9500 | −0.975737 | −0.487868 | − | 0.872917i | \(-0.662225\pi\) | ||||
−0.487868 | + | 0.872917i | \(0.662225\pi\) | |||||||
\(462\) | 5.38542 | 0.250552 | ||||||||
\(463\) | 13.6195 | 0.632950 | 0.316475 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316475 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(464\) | 3.58342 | 0.166356 | ||||||||
\(465\) | 1.01576 | 0.0471050 | ||||||||
\(466\) | −26.5014 | −1.22765 | ||||||||
\(467\) | −21.5848 | −0.998827 | −0.499413 | − | 0.866364i | \(-0.666451\pi\) | ||||
−0.499413 | + | 0.866364i | \(0.666451\pi\) | |||||||
\(468\) | 16.2726 | 0.752203 | ||||||||
\(469\) | −49.4422 | −2.28303 | ||||||||
\(470\) | −4.53796 | −0.209320 | ||||||||
\(471\) | 0.635133 | 0.0292654 | ||||||||
\(472\) | −1.10698 | −0.0509528 | ||||||||
\(473\) | 9.98098 | 0.458926 | ||||||||
\(474\) | −3.88695 | −0.178534 | ||||||||
\(475\) | −6.04585 | −0.277403 | ||||||||
\(476\) | −22.4993 | −1.03125 | ||||||||
\(477\) | 10.2800 | 0.470688 | ||||||||
\(478\) | 20.0415 | 0.916676 | ||||||||
\(479\) | 15.4702 | 0.706850 | 0.353425 | − | 0.935463i | \(-0.385017\pi\) | ||||
0.353425 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(480\) | 0.348093 | 0.0158882 | ||||||||
\(481\) | 60.5675 | 2.76164 | ||||||||
\(482\) | −5.59198 | −0.254708 | ||||||||
\(483\) | 2.39081 | 0.108786 | ||||||||
\(484\) | −1.28855 | −0.0585705 | ||||||||
\(485\) | 4.90579 | 0.222761 | ||||||||
\(486\) | −13.1501 | −0.596500 | ||||||||
\(487\) | 9.28893 | 0.420922 | 0.210461 | − | 0.977602i | \(-0.432504\pi\) | ||||
0.210461 | + | 0.977602i | \(0.432504\pi\) | |||||||
\(488\) | 7.64720 | 0.346173 | ||||||||
\(489\) | −12.2337 | −0.553225 | ||||||||
\(490\) | −1.44844 | −0.0654337 | ||||||||
\(491\) | −21.0597 | −0.950411 | −0.475205 | − | 0.879875i | \(-0.657626\pi\) | ||||
−0.475205 | + | 0.879875i | \(0.657626\pi\) | |||||||
\(492\) | −3.47008 | −0.156443 | ||||||||
\(493\) | −26.3649 | −1.18741 | ||||||||
\(494\) | −7.94290 | −0.357368 | ||||||||
\(495\) | −5.14564 | −0.231280 | ||||||||
\(496\) | 2.91808 | 0.131026 | ||||||||
\(497\) | 46.2481 | 2.07451 | ||||||||
\(498\) | −1.99195 | −0.0892615 | ||||||||
\(499\) | −27.9653 | −1.25190 | −0.625950 | − | 0.779863i | \(-0.715289\pi\) | ||||
−0.625950 | + | 0.779863i | \(0.715289\pi\) | |||||||
\(500\) | 5.92598 | 0.265018 | ||||||||
\(501\) | 3.04549 | 0.136062 | ||||||||
\(502\) | −15.5175 | −0.692582 | ||||||||
\(503\) | −42.8231 | −1.90939 | −0.954693 | − | 0.297592i | \(-0.903816\pi\) | ||||
−0.954693 | + | 0.297592i | \(0.903816\pi\) | |||||||
\(504\) | −8.19746 | −0.365144 | ||||||||
\(505\) | −1.02293 | −0.0455197 | ||||||||
\(506\) | 4.31131 | 0.191661 | ||||||||
\(507\) | −13.4780 | −0.598579 | ||||||||
\(508\) | −10.9479 | −0.485736 | ||||||||
\(509\) | 2.04492 | 0.0906396 | 0.0453198 | − | 0.998973i | \(-0.485569\pi\) | ||||
0.0453198 | + | 0.998973i | \(0.485569\pi\) | |||||||
\(510\) | −2.56108 | −0.113407 | ||||||||
\(511\) | −35.1962 | −1.55699 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.20045 | 0.185454 | ||||||||
\(514\) | 3.79991 | 0.167607 | ||||||||
\(515\) | 8.66188 | 0.381688 | ||||||||
\(516\) | 1.80996 | 0.0796789 | ||||||||
\(517\) | −22.9585 | −1.00971 | ||||||||
\(518\) | −30.5113 | −1.34059 | ||||||||
\(519\) | 3.19692 | 0.140329 | ||||||||
\(520\) | 3.73919 | 0.163974 | ||||||||
\(521\) | 5.68194 | 0.248930 | 0.124465 | − | 0.992224i | \(-0.460278\pi\) | ||||
0.124465 | + | 0.992224i | \(0.460278\pi\) | |||||||
\(522\) | −9.60587 | −0.420437 | ||||||||
\(523\) | 13.7368 | 0.600669 | 0.300335 | − | 0.953834i | \(-0.402902\pi\) | ||||
0.300335 | + | 0.953834i | \(0.402902\pi\) | |||||||
\(524\) | −14.6494 | −0.639960 | ||||||||
\(525\) | 7.98498 | 0.348493 | ||||||||
\(526\) | −3.58984 | −0.156524 | ||||||||
\(527\) | −21.4697 | −0.935234 | ||||||||
\(528\) | 1.76108 | 0.0766412 | ||||||||
\(529\) | −21.0860 | −0.916784 | ||||||||
\(530\) | 2.36217 | 0.102606 | ||||||||
\(531\) | 2.96742 | 0.128775 | ||||||||
\(532\) | 4.00130 | 0.173478 | ||||||||
\(533\) | −37.2752 | −1.61457 | ||||||||
\(534\) | 5.96133 | 0.257972 | ||||||||
\(535\) | −7.74596 | −0.334887 | ||||||||
\(536\) | −16.1681 | −0.698354 | ||||||||
\(537\) | 8.51839 | 0.367596 | ||||||||
\(538\) | 10.4559 | 0.450785 | ||||||||
\(539\) | −7.32796 | −0.315637 | ||||||||
\(540\) | −1.97739 | −0.0850935 | ||||||||
\(541\) | 34.1616 | 1.46872 | 0.734361 | − | 0.678759i | \(-0.237482\pi\) | ||||
0.734361 | + | 0.678759i | \(0.237482\pi\) | |||||||
\(542\) | −3.88450 | −0.166853 | ||||||||
\(543\) | −15.0529 | −0.645980 | ||||||||
\(544\) | −7.35747 | −0.315449 | ||||||||
\(545\) | 3.45718 | 0.148089 | ||||||||
\(546\) | 10.4905 | 0.448952 | ||||||||
\(547\) | −5.97905 | −0.255646 | −0.127823 | − | 0.991797i | \(-0.540799\pi\) | ||||
−0.127823 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(548\) | 4.82347 | 0.206048 | ||||||||
\(549\) | −20.4994 | −0.874894 | ||||||||
\(550\) | 14.3992 | 0.613985 | ||||||||
\(551\) | 4.68876 | 0.199748 | ||||||||
\(552\) | 0.781816 | 0.0332763 | ||||||||
\(553\) | 21.0335 | 0.894437 | ||||||||
\(554\) | 25.3987 | 1.07909 | ||||||||
\(555\) | −3.47310 | −0.147425 | ||||||||
\(556\) | −21.4686 | −0.910470 | ||||||||
\(557\) | −19.6992 | −0.834681 | −0.417340 | − | 0.908750i | \(-0.637038\pi\) | ||||
−0.417340 | + | 0.908750i | \(0.637038\pi\) | |||||||
\(558\) | −7.82234 | −0.331146 | ||||||||
\(559\) | 19.4424 | 0.822326 | ||||||||
\(560\) | −1.88364 | −0.0795985 | ||||||||
\(561\) | −12.9571 | −0.547049 | ||||||||
\(562\) | 8.72731 | 0.368139 | ||||||||
\(563\) | −27.5569 | −1.16139 | −0.580693 | − | 0.814123i | \(-0.697218\pi\) | ||||
−0.580693 | + | 0.814123i | \(0.697218\pi\) | |||||||
\(564\) | −4.16331 | −0.175307 | ||||||||
\(565\) | −9.44636 | −0.397411 | ||||||||
\(566\) | −22.9032 | −0.962691 | ||||||||
\(567\) | 19.0447 | 0.799802 | ||||||||
\(568\) | 15.1235 | 0.634570 | ||||||||
\(569\) | −15.7614 | −0.660751 | −0.330375 | − | 0.943850i | \(-0.607175\pi\) | ||||
−0.330375 | + | 0.943850i | \(0.607175\pi\) | |||||||
\(570\) | 0.455466 | 0.0190774 | ||||||||
\(571\) | −9.25289 | −0.387221 | −0.193611 | − | 0.981078i | \(-0.562020\pi\) | ||||
−0.193611 | + | 0.981078i | \(0.562020\pi\) | |||||||
\(572\) | 18.9174 | 0.790975 | ||||||||
\(573\) | −12.4991 | −0.522159 | ||||||||
\(574\) | 18.7777 | 0.783765 | ||||||||
\(575\) | 6.39241 | 0.266582 | ||||||||
\(576\) | −2.68064 | −0.111694 | ||||||||
\(577\) | −33.7348 | −1.40440 | −0.702198 | − | 0.711982i | \(-0.747798\pi\) | ||||
−0.702198 | + | 0.711982i | \(0.747798\pi\) | |||||||
\(578\) | 37.1323 | 1.54450 | ||||||||
\(579\) | 2.33078 | 0.0968641 | ||||||||
\(580\) | −2.20727 | −0.0916520 | ||||||||
\(581\) | 10.7791 | 0.447192 | ||||||||
\(582\) | 4.50078 | 0.186563 | ||||||||
\(583\) | 11.9507 | 0.494949 | ||||||||
\(584\) | −11.5095 | −0.476266 | ||||||||
\(585\) | −10.0234 | −0.414418 | ||||||||
\(586\) | −2.82047 | −0.116513 | ||||||||
\(587\) | −20.9968 | −0.866630 | −0.433315 | − | 0.901243i | \(-0.642656\pi\) | ||||
−0.433315 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(588\) | −1.32886 | −0.0548011 | ||||||||
\(589\) | 3.81819 | 0.157326 | ||||||||
\(590\) | 0.681864 | 0.0280719 | ||||||||
\(591\) | −14.8138 | −0.609359 | ||||||||
\(592\) | −9.97748 | −0.410072 | ||||||||
\(593\) | −8.39567 | −0.344769 | −0.172384 | − | 0.985030i | \(-0.555147\pi\) | ||||
−0.172384 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(594\) | −10.0041 | −0.410472 | ||||||||
\(595\) | 13.8588 | 0.568157 | ||||||||
\(596\) | −13.8144 | −0.565861 | ||||||||
\(597\) | −5.79186 | −0.237045 | ||||||||
\(598\) | 8.39820 | 0.343428 | ||||||||
\(599\) | −0.0503407 | −0.00205686 | −0.00102843 | − | 0.999999i | \(-0.500327\pi\) | ||||
−0.00102843 | + | 0.999999i | \(0.500327\pi\) | |||||||
\(600\) | 2.61116 | 0.106600 | ||||||||
\(601\) | 38.1249 | 1.55515 | 0.777573 | − | 0.628792i | \(-0.216450\pi\) | ||||
0.777573 | + | 0.628792i | \(0.216450\pi\) | |||||||
\(602\) | −9.79425 | −0.399184 | ||||||||
\(603\) | 43.3408 | 1.76497 | ||||||||
\(604\) | 8.21835 | 0.334400 | ||||||||
\(605\) | 0.793706 | 0.0322688 | ||||||||
\(606\) | −0.938477 | −0.0381230 | ||||||||
\(607\) | 7.64435 | 0.310274 | 0.155137 | − | 0.987893i | \(-0.450418\pi\) | ||||
0.155137 | + | 0.987893i | \(0.450418\pi\) | |||||||
\(608\) | 1.30846 | 0.0530651 | ||||||||
\(609\) | −6.19262 | −0.250938 | ||||||||
\(610\) | −4.71044 | −0.190720 | ||||||||
\(611\) | −44.7219 | −1.80926 | ||||||||
\(612\) | 19.7227 | 0.797245 | ||||||||
\(613\) | −11.4483 | −0.462393 | −0.231196 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231196 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(614\) | 0.877326 | 0.0354060 | ||||||||
\(615\) | 2.13746 | 0.0861906 | ||||||||
\(616\) | −9.52976 | −0.383965 | ||||||||
\(617\) | 0.885025 | 0.0356298 | 0.0178149 | − | 0.999841i | \(-0.494329\pi\) | ||||
0.0178149 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(618\) | 7.94678 | 0.319666 | ||||||||
\(619\) | −17.1369 | −0.688789 | −0.344395 | − | 0.938825i | \(-0.611916\pi\) | ||||
−0.344395 | + | 0.938825i | \(0.611916\pi\) | |||||||
\(620\) | −1.79745 | −0.0721872 | ||||||||
\(621\) | −4.44122 | −0.178220 | ||||||||
\(622\) | −10.6787 | −0.428178 | ||||||||
\(623\) | −32.2587 | −1.29242 | ||||||||
\(624\) | 3.43049 | 0.137329 | ||||||||
\(625\) | 19.4527 | 0.778108 | ||||||||
\(626\) | 27.2477 | 1.08904 | ||||||||
\(627\) | 2.30430 | 0.0920250 | ||||||||
\(628\) | −1.12390 | −0.0448485 | ||||||||
\(629\) | 73.4090 | 2.92701 | ||||||||
\(630\) | 5.04938 | 0.201172 | ||||||||
\(631\) | 1.37336 | 0.0546727 | 0.0273363 | − | 0.999626i | \(-0.491297\pi\) | ||||
0.0273363 | + | 0.999626i | \(0.491297\pi\) | |||||||
\(632\) | 6.87816 | 0.273598 | ||||||||
\(633\) | −0.500195 | −0.0198810 | ||||||||
\(634\) | −26.4081 | −1.04880 | ||||||||
\(635\) | 6.74358 | 0.267611 | ||||||||
\(636\) | 2.16715 | 0.0859333 | ||||||||
\(637\) | −14.2745 | −0.565574 | ||||||||
\(638\) | −11.1671 | −0.442109 | ||||||||
\(639\) | −40.5409 | −1.60377 | ||||||||
\(640\) | −0.615969 | −0.0243483 | ||||||||
\(641\) | 18.4117 | 0.727220 | 0.363610 | − | 0.931551i | \(-0.381544\pi\) | ||||
0.363610 | + | 0.931551i | \(0.381544\pi\) | |||||||
\(642\) | −7.10647 | −0.280470 | ||||||||
\(643\) | 31.7565 | 1.25236 | 0.626178 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626178 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(644\) | −4.23066 | −0.166711 | ||||||||
\(645\) | −1.11488 | −0.0438982 | ||||||||
\(646\) | −9.62695 | −0.378767 | ||||||||
\(647\) | 6.89081 | 0.270906 | 0.135453 | − | 0.990784i | \(-0.456751\pi\) | ||||
0.135453 | + | 0.990784i | \(0.456751\pi\) | |||||||
\(648\) | 6.22779 | 0.244651 | ||||||||
\(649\) | 3.44970 | 0.135413 | ||||||||
\(650\) | 28.0489 | 1.10017 | ||||||||
\(651\) | −5.04283 | −0.197644 | ||||||||
\(652\) | 21.6481 | 0.847803 | ||||||||
\(653\) | −1.55548 | −0.0608706 | −0.0304353 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304353 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(654\) | 3.17176 | 0.124026 | ||||||||
\(655\) | 9.02354 | 0.352579 | ||||||||
\(656\) | 6.14047 | 0.239745 | ||||||||
\(657\) | 30.8528 | 1.20368 | ||||||||
\(658\) | 22.5290 | 0.878272 | ||||||||
\(659\) | 15.2618 | 0.594516 | 0.297258 | − | 0.954797i | \(-0.403928\pi\) | ||||
0.297258 | + | 0.954797i | \(0.403928\pi\) | |||||||
\(660\) | −1.08477 | −0.0422246 | ||||||||
\(661\) | 25.6214 | 0.996556 | 0.498278 | − | 0.867017i | \(-0.333966\pi\) | ||||
0.498278 | + | 0.867017i | \(0.333966\pi\) | |||||||
\(662\) | −33.2619 | −1.29276 | ||||||||
\(663\) | −25.2397 | −0.980229 | ||||||||
\(664\) | 3.52486 | 0.136791 | ||||||||
\(665\) | −2.46467 | −0.0955759 | ||||||||
\(666\) | 26.7461 | 1.03639 | ||||||||
\(667\) | −4.95753 | −0.191956 | ||||||||
\(668\) | −5.38914 | −0.208512 | ||||||||
\(669\) | 7.93550 | 0.306804 | ||||||||
\(670\) | 9.95901 | 0.384750 | ||||||||
\(671\) | −23.8311 | −0.919990 | ||||||||
\(672\) | −1.72813 | −0.0666642 | ||||||||
\(673\) | −39.7843 | −1.53357 | −0.766787 | − | 0.641902i | \(-0.778146\pi\) | ||||
−0.766787 | + | 0.641902i | \(0.778146\pi\) | |||||||
\(674\) | −22.5248 | −0.867624 | ||||||||
\(675\) | −14.8331 | −0.570926 | ||||||||
\(676\) | 23.8500 | 0.917307 | ||||||||
\(677\) | −40.3238 | −1.54977 | −0.774885 | − | 0.632102i | \(-0.782192\pi\) | ||||
−0.774885 | + | 0.632102i | \(0.782192\pi\) | |||||||
\(678\) | −8.66649 | −0.332834 | ||||||||
\(679\) | −24.3552 | −0.934665 | ||||||||
\(680\) | 4.53197 | 0.173793 | ||||||||
\(681\) | −12.7280 | −0.487739 | ||||||||
\(682\) | −9.09367 | −0.348215 | ||||||||
\(683\) | 1.31813 | 0.0504370 | 0.0252185 | − | 0.999682i | \(-0.491972\pi\) | ||||
0.0252185 | + | 0.999682i | \(0.491972\pi\) | |||||||
\(684\) | −3.50752 | −0.134113 | ||||||||
\(685\) | −2.97111 | −0.113520 | ||||||||
\(686\) | −14.2153 | −0.542741 | ||||||||
\(687\) | 9.79571 | 0.373730 | ||||||||
\(688\) | −3.20281 | −0.122106 | ||||||||
\(689\) | 23.2794 | 0.886874 | ||||||||
\(690\) | −0.481574 | −0.0183332 | ||||||||
\(691\) | 10.3532 | 0.393855 | 0.196928 | − | 0.980418i | \(-0.436904\pi\) | ||||
0.196928 | + | 0.980418i | \(0.436904\pi\) | |||||||
\(692\) | −5.65710 | −0.215051 | ||||||||
\(693\) | 25.5459 | 0.970409 | ||||||||
\(694\) | −12.8300 | −0.487019 | ||||||||
\(695\) | 13.2240 | 0.501613 | ||||||||
\(696\) | −2.02504 | −0.0767591 | ||||||||
\(697\) | −45.1783 | −1.71125 | ||||||||
\(698\) | −28.4649 | −1.07741 | ||||||||
\(699\) | 14.9764 | 0.566458 | ||||||||
\(700\) | −14.1298 | −0.534057 | ||||||||
\(701\) | −25.2927 | −0.955291 | −0.477646 | − | 0.878553i | \(-0.658510\pi\) | ||||
−0.477646 | + | 0.878553i | \(0.658510\pi\) | |||||||
\(702\) | −19.4874 | −0.735504 | ||||||||
\(703\) | −13.0551 | −0.492384 | ||||||||
\(704\) | −3.11632 | −0.117451 | ||||||||
\(705\) | 2.56447 | 0.0965835 | ||||||||
\(706\) | −15.6535 | −0.589125 | ||||||||
\(707\) | 5.07840 | 0.190993 | ||||||||
\(708\) | 0.625571 | 0.0235104 | ||||||||
\(709\) | 23.3678 | 0.877596 | 0.438798 | − | 0.898586i | \(-0.355404\pi\) | ||||
0.438798 | + | 0.898586i | \(0.355404\pi\) | |||||||
\(710\) | −9.31563 | −0.349609 | ||||||||
\(711\) | −18.4379 | −0.691475 | ||||||||
\(712\) | −10.5489 | −0.395336 | ||||||||
\(713\) | −4.03706 | −0.151189 | ||||||||
\(714\) | 12.7147 | 0.475835 | ||||||||
\(715\) | −11.6525 | −0.435779 | ||||||||
\(716\) | −15.0737 | −0.563331 | ||||||||
\(717\) | −11.3258 | −0.422968 | ||||||||
\(718\) | 30.0022 | 1.11967 | ||||||||
\(719\) | −40.4323 | −1.50787 | −0.753935 | − | 0.656949i | \(-0.771847\pi\) | ||||
−0.753935 | + | 0.656949i | \(0.771847\pi\) | |||||||
\(720\) | 1.65119 | 0.0615363 | ||||||||
\(721\) | −43.0025 | −1.60150 | ||||||||
\(722\) | −17.2879 | −0.643390 | ||||||||
\(723\) | 3.16012 | 0.117526 | ||||||||
\(724\) | 26.6368 | 0.989948 | ||||||||
\(725\) | −16.5575 | −0.614929 | ||||||||
\(726\) | 0.728180 | 0.0270253 | ||||||||
\(727\) | 9.46152 | 0.350908 | 0.175454 | − | 0.984488i | \(-0.443861\pi\) | ||||
0.175454 | + | 0.984488i | \(0.443861\pi\) | |||||||
\(728\) | −18.5635 | −0.688007 | ||||||||
\(729\) | −11.2521 | −0.416743 | ||||||||
\(730\) | 7.08948 | 0.262393 | ||||||||
\(731\) | 23.5646 | 0.871567 | ||||||||
\(732\) | −4.32155 | −0.159729 | ||||||||
\(733\) | 7.17204 | 0.264905 | 0.132453 | − | 0.991189i | \(-0.457715\pi\) | ||||
0.132453 | + | 0.991189i | \(0.457715\pi\) | |||||||
\(734\) | 26.6928 | 0.985249 | ||||||||
\(735\) | 0.818534 | 0.0301921 | ||||||||
\(736\) | −1.38346 | −0.0509951 | ||||||||
\(737\) | 50.3848 | 1.85595 | ||||||||
\(738\) | −16.4604 | −0.605916 | ||||||||
\(739\) | 17.7817 | 0.654111 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(740\) | 6.14582 | 0.225925 | ||||||||
\(741\) | 4.48866 | 0.164895 | ||||||||
\(742\) | −11.7272 | −0.430518 | ||||||||
\(743\) | 33.3538 | 1.22363 | 0.611816 | − | 0.791000i | \(-0.290439\pi\) | ||||
0.611816 | + | 0.791000i | \(0.290439\pi\) | |||||||
\(744\) | −1.64905 | −0.0604572 | ||||||||
\(745\) | 8.50925 | 0.311755 | ||||||||
\(746\) | 27.8906 | 1.02115 | ||||||||
\(747\) | −9.44889 | −0.345717 | ||||||||
\(748\) | 22.9282 | 0.838339 | ||||||||
\(749\) | 38.4553 | 1.40513 | ||||||||
\(750\) | −3.34886 | −0.122283 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 7.36719 | 0.268654 | ||||||||
\(753\) | 8.76920 | 0.319567 | ||||||||
\(754\) | −21.7528 | −0.792192 | ||||||||
\(755\) | −5.06225 | −0.184234 | ||||||||
\(756\) | 9.81691 | 0.357038 | ||||||||
\(757\) | −21.3897 | −0.777421 | −0.388711 | − | 0.921360i | \(-0.627079\pi\) | ||||
−0.388711 | + | 0.921360i | \(0.627079\pi\) | |||||||
\(758\) | 20.0434 | 0.728009 | ||||||||
\(759\) | −2.43639 | −0.0884354 | ||||||||
\(760\) | −0.805970 | −0.0292356 | ||||||||
\(761\) | 38.3593 | 1.39052 | 0.695262 | − | 0.718756i | \(-0.255288\pi\) | ||||
0.695262 | + | 0.718756i | \(0.255288\pi\) | |||||||
\(762\) | 6.18684 | 0.224126 | ||||||||
\(763\) | −17.1634 | −0.621357 | ||||||||
\(764\) | 22.1179 | 0.800196 | ||||||||
\(765\) | −12.1486 | −0.439233 | ||||||||
\(766\) | −5.82733 | −0.210550 | ||||||||
\(767\) | 6.71983 | 0.242639 | ||||||||
\(768\) | −0.565115 | −0.0203918 | ||||||||
\(769\) | 1.31168 | 0.0473002 | 0.0236501 | − | 0.999720i | \(-0.492471\pi\) | ||||
0.0236501 | + | 0.999720i | \(0.492471\pi\) | |||||||
\(770\) | 5.87004 | 0.211541 | ||||||||
\(771\) | −2.14739 | −0.0773363 | ||||||||
\(772\) | −4.12444 | −0.148442 | ||||||||
\(773\) | −11.7641 | −0.423125 | −0.211563 | − | 0.977364i | \(-0.567855\pi\) | ||||
−0.211563 | + | 0.977364i | \(0.567855\pi\) | |||||||
\(774\) | 8.58559 | 0.308603 | ||||||||
\(775\) | −13.4832 | −0.484332 | ||||||||
\(776\) | −7.96436 | −0.285904 | ||||||||
\(777\) | 17.2424 | 0.618568 | ||||||||
\(778\) | −31.8482 | −1.14181 | ||||||||
\(779\) | 8.03456 | 0.287868 | ||||||||
\(780\) | −2.11307 | −0.0756601 | ||||||||
\(781\) | −47.1298 | −1.68644 | ||||||||
\(782\) | 10.1788 | 0.363993 | ||||||||
\(783\) | 11.5036 | 0.411104 | ||||||||
\(784\) | 2.35148 | 0.0839813 | ||||||||
\(785\) | 0.692287 | 0.0247088 | ||||||||
\(786\) | 8.27858 | 0.295287 | ||||||||
\(787\) | 18.7554 | 0.668558 | 0.334279 | − | 0.942474i | \(-0.391507\pi\) | ||||
0.334279 | + | 0.942474i | \(0.391507\pi\) | |||||||
\(788\) | 26.2138 | 0.933827 | ||||||||
\(789\) | 2.02867 | 0.0722227 | ||||||||
\(790\) | −4.23673 | −0.150736 | ||||||||
\(791\) | 46.8971 | 1.66747 | ||||||||
\(792\) | 8.35375 | 0.296837 | ||||||||
\(793\) | −46.4217 | −1.64848 | ||||||||
\(794\) | −24.9264 | −0.884603 | ||||||||
\(795\) | −1.33490 | −0.0473440 | ||||||||
\(796\) | 10.2490 | 0.363265 | ||||||||
\(797\) | −4.61506 | −0.163474 | −0.0817369 | − | 0.996654i | \(-0.526047\pi\) | ||||
−0.0817369 | + | 0.996654i | \(0.526047\pi\) | |||||||
\(798\) | −2.26119 | −0.0800454 | ||||||||
\(799\) | −54.2038 | −1.91759 | ||||||||
\(800\) | −4.62058 | −0.163362 | ||||||||
\(801\) | 28.2778 | 0.999146 | ||||||||
\(802\) | −6.99992 | −0.247176 | ||||||||
\(803\) | 35.8672 | 1.26573 | ||||||||
\(804\) | 9.13682 | 0.322231 | ||||||||
\(805\) | 2.60595 | 0.0918477 | ||||||||
\(806\) | −17.7140 | −0.623948 | ||||||||
\(807\) | −5.90878 | −0.207999 | ||||||||
\(808\) | 1.66068 | 0.0584226 | ||||||||
\(809\) | 22.5980 | 0.794505 | 0.397252 | − | 0.917709i | \(-0.369964\pi\) | ||||
0.397252 | + | 0.917709i | \(0.369964\pi\) | |||||||
\(810\) | −3.83612 | −0.134788 | ||||||||
\(811\) | −33.4298 | −1.17388 | −0.586940 | − | 0.809631i | \(-0.699667\pi\) | ||||
−0.586940 | + | 0.809631i | \(0.699667\pi\) | |||||||
\(812\) | 10.9582 | 0.384556 | ||||||||
\(813\) | 2.19519 | 0.0769887 | ||||||||
\(814\) | 31.0930 | 1.08981 | ||||||||
\(815\) | −13.3345 | −0.467088 | ||||||||
\(816\) | 4.15782 | 0.145553 | ||||||||
\(817\) | −4.19075 | −0.146616 | ||||||||
\(818\) | −4.72367 | −0.165159 | ||||||||
\(819\) | 49.7620 | 1.73883 | ||||||||
\(820\) | −3.78234 | −0.132085 | ||||||||
\(821\) | −38.3449 | −1.33825 | −0.669123 | − | 0.743151i | \(-0.733330\pi\) | ||||
−0.669123 | + | 0.743151i | \(0.733330\pi\) | |||||||
\(822\) | −2.72582 | −0.0950738 | ||||||||
\(823\) | 1.17504 | 0.0409592 | 0.0204796 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204796 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(824\) | −14.0622 | −0.489880 | ||||||||
\(825\) | −8.13722 | −0.283302 | ||||||||
\(826\) | −3.38516 | −0.117785 | ||||||||
\(827\) | 13.6131 | 0.473373 | 0.236686 | − | 0.971586i | \(-0.423939\pi\) | ||||
0.236686 | + | 0.971586i | \(0.423939\pi\) | |||||||
\(828\) | 3.70857 | 0.128882 | ||||||||
\(829\) | −11.0355 | −0.383279 | −0.191639 | − | 0.981465i | \(-0.561380\pi\) | ||||
−0.191639 | + | 0.981465i | \(0.561380\pi\) | |||||||
\(830\) | −2.17120 | −0.0753635 | ||||||||
\(831\) | −14.3532 | −0.497906 | ||||||||
\(832\) | −6.07042 | −0.210454 | ||||||||
\(833\) | −17.3009 | −0.599441 | ||||||||
\(834\) | 12.1322 | 0.420104 | ||||||||
\(835\) | 3.31954 | 0.114877 | ||||||||
\(836\) | −4.07758 | −0.141026 | ||||||||
\(837\) | 9.36768 | 0.323794 | ||||||||
\(838\) | −22.0804 | −0.762755 | ||||||||
\(839\) | 9.52844 | 0.328958 | 0.164479 | − | 0.986381i | \(-0.447406\pi\) | ||||
0.164479 | + | 0.986381i | \(0.447406\pi\) | |||||||
\(840\) | 1.06448 | 0.0367279 | ||||||||
\(841\) | −16.1591 | −0.557211 | ||||||||
\(842\) | 23.1422 | 0.797533 | ||||||||
\(843\) | −4.93194 | −0.169865 | ||||||||
\(844\) | 0.885119 | 0.0304671 | ||||||||
\(845\) | −14.6908 | −0.505380 | ||||||||
\(846\) | −19.7488 | −0.678978 | ||||||||
\(847\) | −3.94041 | −0.135394 | ||||||||
\(848\) | −3.83489 | −0.131691 | ||||||||
\(849\) | 12.9429 | 0.444200 | ||||||||
\(850\) | 33.9958 | 1.16605 | ||||||||
\(851\) | 13.8035 | 0.473177 | ||||||||
\(852\) | −8.54655 | −0.292800 | ||||||||
\(853\) | −16.1384 | −0.552568 | −0.276284 | − | 0.961076i | \(-0.589103\pi\) | ||||
−0.276284 | + | 0.961076i | \(0.589103\pi\) | |||||||
\(854\) | 23.3853 | 0.800228 | ||||||||
\(855\) | 2.16052 | 0.0738882 | ||||||||
\(856\) | 12.5752 | 0.429813 | ||||||||
\(857\) | 29.8866 | 1.02091 | 0.510454 | − | 0.859905i | \(-0.329477\pi\) | ||||
0.510454 | + | 0.859905i | \(0.329477\pi\) | |||||||
\(858\) | −10.6905 | −0.364968 | ||||||||
\(859\) | −47.5137 | −1.62115 | −0.810574 | − | 0.585636i | \(-0.800845\pi\) | ||||
−0.810574 | + | 0.585636i | \(0.800845\pi\) | |||||||
\(860\) | 1.97283 | 0.0672730 | ||||||||
\(861\) | −10.6116 | −0.361641 | ||||||||
\(862\) | 14.6390 | 0.498606 | ||||||||
\(863\) | −21.0562 | −0.716762 | −0.358381 | − | 0.933575i | \(-0.616671\pi\) | ||||
−0.358381 | + | 0.933575i | \(0.616671\pi\) | |||||||
\(864\) | 3.21022 | 0.109214 | ||||||||
\(865\) | 3.48460 | 0.118480 | ||||||||
\(866\) | −7.87846 | −0.267721 | ||||||||
\(867\) | −20.9840 | −0.712655 | ||||||||
\(868\) | 8.92355 | 0.302885 | ||||||||
\(869\) | −21.4345 | −0.727117 | ||||||||
\(870\) | 1.24736 | 0.0422896 | ||||||||
\(871\) | 98.1469 | 3.32558 | ||||||||
\(872\) | −5.61259 | −0.190066 | ||||||||
\(873\) | 21.3496 | 0.722575 | ||||||||
\(874\) | −1.81021 | −0.0612312 | ||||||||
\(875\) | 18.1217 | 0.612627 | ||||||||
\(876\) | 6.50419 | 0.219756 | ||||||||
\(877\) | −15.2397 | −0.514610 | −0.257305 | − | 0.966330i | \(-0.582834\pi\) | ||||
−0.257305 | + | 0.966330i | \(0.582834\pi\) | |||||||
\(878\) | −0.803456 | −0.0271153 | ||||||||
\(879\) | 1.59389 | 0.0537606 | ||||||||
\(880\) | 1.91956 | 0.0647082 | ||||||||
\(881\) | −14.3190 | −0.482419 | −0.241209 | − | 0.970473i | \(-0.577544\pi\) | ||||
−0.241209 | + | 0.970473i | \(0.577544\pi\) | |||||||
\(882\) | −6.30348 | −0.212249 | ||||||||
\(883\) | 27.2461 | 0.916903 | 0.458452 | − | 0.888719i | \(-0.348404\pi\) | ||||
0.458452 | + | 0.888719i | \(0.348404\pi\) | |||||||
\(884\) | 44.6629 | 1.50218 | ||||||||
\(885\) | −0.385332 | −0.0129528 | ||||||||
\(886\) | 18.7417 | 0.629639 | ||||||||
\(887\) | 27.7062 | 0.930282 | 0.465141 | − | 0.885237i | \(-0.346004\pi\) | ||||
0.465141 | + | 0.885237i | \(0.346004\pi\) | |||||||
\(888\) | 5.63843 | 0.189213 | ||||||||
\(889\) | −33.4790 | −1.12285 | ||||||||
\(890\) | 6.49777 | 0.217806 | ||||||||
\(891\) | −19.4078 | −0.650185 | ||||||||
\(892\) | −14.0423 | −0.470170 | ||||||||
\(893\) | 9.63967 | 0.322579 | ||||||||
\(894\) | 7.80674 | 0.261097 | ||||||||
\(895\) | 9.28493 | 0.310361 | ||||||||
\(896\) | 3.05802 | 0.102161 | ||||||||
\(897\) | −4.74595 | −0.158463 | ||||||||
\(898\) | 19.2173 | 0.641289 | ||||||||
\(899\) | 10.4567 | 0.348751 | ||||||||
\(900\) | 12.3861 | 0.412871 | ||||||||
\(901\) | 28.2151 | 0.939980 | ||||||||
\(902\) | −19.1357 | −0.637148 | ||||||||
\(903\) | 5.53488 | 0.184189 | ||||||||
\(904\) | 15.3358 | 0.510060 | ||||||||
\(905\) | −16.4074 | −0.545401 | ||||||||
\(906\) | −4.64432 | −0.154297 | ||||||||
\(907\) | −1.32457 | −0.0439817 | −0.0219908 | − | 0.999758i | \(-0.507000\pi\) | ||||
−0.0219908 | + | 0.999758i | \(0.507000\pi\) | |||||||
\(908\) | 22.5229 | 0.747449 | ||||||||
\(909\) | −4.45170 | −0.147653 | ||||||||
\(910\) | 11.4345 | 0.379050 | ||||||||
\(911\) | −35.3152 | −1.17004 | −0.585022 | − | 0.811017i | \(-0.698914\pi\) | ||||
−0.585022 | + | 0.811017i | \(0.698914\pi\) | |||||||
\(912\) | −0.739431 | −0.0244850 | ||||||||
\(913\) | −10.9846 | −0.363537 | ||||||||
\(914\) | 31.7684 | 1.05080 | ||||||||
\(915\) | 2.66194 | 0.0880010 | ||||||||
\(916\) | −17.3340 | −0.572731 | ||||||||
\(917\) | −44.7980 | −1.47936 | ||||||||
\(918\) | −23.6191 | −0.779546 | ||||||||
\(919\) | −32.9683 | −1.08752 | −0.543762 | − | 0.839239i | \(-0.683001\pi\) | ||||
−0.543762 | + | 0.839239i | \(0.683001\pi\) | |||||||
\(920\) | 0.852170 | 0.0280952 | ||||||||
\(921\) | −0.495790 | −0.0163368 | ||||||||
\(922\) | −20.9500 | −0.689950 | ||||||||
\(923\) | −91.8063 | −3.02184 | ||||||||
\(924\) | 5.38542 | 0.177167 | ||||||||
\(925\) | 46.1018 | 1.51582 | ||||||||
\(926\) | 13.6195 | 0.447563 | ||||||||
\(927\) | 37.6958 | 1.23809 | ||||||||
\(928\) | 3.58342 | 0.117631 | ||||||||
\(929\) | 29.6196 | 0.971787 | 0.485893 | − | 0.874018i | \(-0.338494\pi\) | ||||
0.485893 | + | 0.874018i | \(0.338494\pi\) | |||||||
\(930\) | 1.01576 | 0.0333082 | ||||||||
\(931\) | 3.07681 | 0.100839 | ||||||||
\(932\) | −26.5014 | −0.868083 | ||||||||
\(933\) | 6.03471 | 0.197567 | ||||||||
\(934\) | −21.5848 | −0.706277 | ||||||||
\(935\) | −14.1231 | −0.461873 | ||||||||
\(936\) | 16.2726 | 0.531888 | ||||||||
\(937\) | −9.17199 | −0.299636 | −0.149818 | − | 0.988714i | \(-0.547869\pi\) | ||||
−0.149818 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(938\) | −49.4422 | −1.61435 | ||||||||
\(939\) | −15.3981 | −0.502498 | ||||||||
\(940\) | −4.53796 | −0.148012 | ||||||||
\(941\) | 39.6871 | 1.29376 | 0.646882 | − | 0.762590i | \(-0.276073\pi\) | ||||
0.646882 | + | 0.762590i | \(0.276073\pi\) | |||||||
\(942\) | 0.635133 | 0.0206938 | ||||||||
\(943\) | −8.49512 | −0.276639 | ||||||||
\(944\) | −1.10698 | −0.0360291 | ||||||||
\(945\) | −6.04691 | −0.196706 | ||||||||
\(946\) | 9.98098 | 0.324510 | ||||||||
\(947\) | 46.2987 | 1.50450 | 0.752252 | − | 0.658875i | \(-0.228968\pi\) | ||||
0.752252 | + | 0.658875i | \(0.228968\pi\) | |||||||
\(948\) | −3.88695 | −0.126242 | ||||||||
\(949\) | 69.8674 | 2.26799 | ||||||||
\(950\) | −6.04585 | −0.196153 | ||||||||
\(951\) | 14.9237 | 0.483933 | ||||||||
\(952\) | −22.4993 | −0.729205 | ||||||||
\(953\) | −24.9769 | −0.809081 | −0.404541 | − | 0.914520i | \(-0.632569\pi\) | ||||
−0.404541 | + | 0.914520i | \(0.632569\pi\) | |||||||
\(954\) | 10.2800 | 0.332826 | ||||||||
\(955\) | −13.6239 | −0.440859 | ||||||||
\(956\) | 20.0415 | 0.648188 | ||||||||
\(957\) | 6.31069 | 0.203996 | ||||||||
\(958\) | 15.4702 | 0.499819 | ||||||||
\(959\) | 14.7503 | 0.476311 | ||||||||
\(960\) | 0.348093 | 0.0112347 | ||||||||
\(961\) | −22.4848 | −0.725316 | ||||||||
\(962\) | 60.5675 | 1.95277 | ||||||||
\(963\) | −33.7098 | −1.08628 | ||||||||
\(964\) | −5.59198 | −0.180106 | ||||||||
\(965\) | 2.54052 | 0.0817824 | ||||||||
\(966\) | 2.39081 | 0.0769230 | ||||||||
\(967\) | −39.6029 | −1.27354 | −0.636771 | − | 0.771053i | \(-0.719730\pi\) | ||||
−0.636771 | + | 0.771053i | \(0.719730\pi\) | |||||||
\(968\) | −1.28855 | −0.0414156 | ||||||||
\(969\) | 5.44034 | 0.174769 | ||||||||
\(970\) | 4.90579 | 0.157516 | ||||||||
\(971\) | −42.4582 | −1.36255 | −0.681274 | − | 0.732029i | \(-0.738574\pi\) | ||||
−0.681274 | + | 0.732029i | \(0.738574\pi\) | |||||||
\(972\) | −13.1501 | −0.421789 | ||||||||
\(973\) | −65.6512 | −2.10468 | ||||||||
\(974\) | 9.28893 | 0.297636 | ||||||||
\(975\) | −15.8509 | −0.507634 | ||||||||
\(976\) | 7.64720 | 0.244781 | ||||||||
\(977\) | 48.1765 | 1.54130 | 0.770652 | − | 0.637257i | \(-0.219931\pi\) | ||||
0.770652 | + | 0.637257i | \(0.219931\pi\) | |||||||
\(978\) | −12.2337 | −0.391189 | ||||||||
\(979\) | 32.8737 | 1.05065 | ||||||||
\(980\) | −1.44844 | −0.0462686 | ||||||||
\(981\) | 15.0454 | 0.480362 | ||||||||
\(982\) | −21.0597 | −0.672042 | ||||||||
\(983\) | −57.1523 | −1.82288 | −0.911438 | − | 0.411437i | \(-0.865027\pi\) | ||||
−0.911438 | + | 0.411437i | \(0.865027\pi\) | |||||||
\(984\) | −3.47008 | −0.110622 | ||||||||
\(985\) | −16.1469 | −0.514482 | ||||||||
\(986\) | −26.3649 | −0.839628 | ||||||||
\(987\) | −12.7315 | −0.405248 | ||||||||
\(988\) | −7.94290 | −0.252697 | ||||||||
\(989\) | 4.43097 | 0.140897 | ||||||||
\(990\) | −5.14564 | −0.163539 | ||||||||
\(991\) | 7.28628 | 0.231456 | 0.115728 | − | 0.993281i | \(-0.463080\pi\) | ||||
0.115728 | + | 0.993281i | \(0.463080\pi\) | |||||||
\(992\) | 2.91808 | 0.0926492 | ||||||||
\(993\) | 18.7968 | 0.596499 | ||||||||
\(994\) | 46.2481 | 1.46690 | ||||||||
\(995\) | −6.31305 | −0.200137 | ||||||||
\(996\) | −1.99195 | −0.0631174 | ||||||||
\(997\) | −35.6704 | −1.12969 | −0.564847 | − | 0.825196i | \(-0.691065\pi\) | ||||
−0.564847 | + | 0.825196i | \(0.691065\pi\) | |||||||
\(998\) | −27.9653 | −0.885227 | ||||||||
\(999\) | −32.0299 | −1.01338 |
(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 | 1502.2.a.f.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.f.1.7 | ✓ | 11 | 1.1 | even | 1 | trivial |