Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(0\) |
Dimension: | \(123\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22237 | −1.57146 | −0.785728 | − | 0.618572i | \(-0.787712\pi\) | ||||
−0.785728 | + | 0.618572i | \(0.787712\pi\) | |||||||
\(3\) | 3.41646 | 1.97250 | 0.986248 | − | 0.165274i | \(-0.0528509\pi\) | ||||
0.986248 | + | 0.165274i | \(0.0528509\pi\) | |||||||
\(4\) | 2.93895 | 1.46947 | ||||||||
\(5\) | 1.79804 | 0.804108 | 0.402054 | − | 0.915616i | \(-0.368296\pi\) | ||||
0.402054 | + | 0.915616i | \(0.368296\pi\) | |||||||
\(6\) | −7.59266 | −3.09969 | ||||||||
\(7\) | 3.28634 | 1.24212 | 0.621061 | − | 0.783763i | \(-0.286702\pi\) | ||||
0.621061 | + | 0.783763i | \(0.286702\pi\) | |||||||
\(8\) | −2.08670 | −0.737759 | ||||||||
\(9\) | 8.67221 | 2.89074 | ||||||||
\(10\) | −3.99592 | −1.26362 | ||||||||
\(11\) | −4.05989 | −1.22410 | −0.612052 | − | 0.790818i | \(-0.709656\pi\) | ||||
−0.612052 | + | 0.790818i | \(0.709656\pi\) | |||||||
\(12\) | 10.0408 | 2.89853 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −7.30349 | −1.95194 | ||||||||
\(15\) | 6.14293 | 1.58610 | ||||||||
\(16\) | −1.24047 | −0.310119 | ||||||||
\(17\) | −4.46412 | −1.08271 | −0.541354 | − | 0.840794i | \(-0.682088\pi\) | ||||
−0.541354 | + | 0.840794i | \(0.682088\pi\) | |||||||
\(18\) | −19.2729 | −4.54267 | ||||||||
\(19\) | 0.417933 | 0.0958805 | 0.0479402 | − | 0.998850i | \(-0.484734\pi\) | ||||
0.0479402 | + | 0.998850i | \(0.484734\pi\) | |||||||
\(20\) | 5.28435 | 1.18162 | ||||||||
\(21\) | 11.2277 | 2.45008 | ||||||||
\(22\) | 9.02260 | 1.92362 | ||||||||
\(23\) | 4.47938 | 0.934014 | 0.467007 | − | 0.884254i | \(-0.345332\pi\) | ||||
0.467007 | + | 0.884254i | \(0.345332\pi\) | |||||||
\(24\) | −7.12912 | −1.45523 | ||||||||
\(25\) | −1.76705 | −0.353411 | ||||||||
\(26\) | 2.22237 | 0.435844 | ||||||||
\(27\) | 19.3789 | 3.72947 | ||||||||
\(28\) | 9.65840 | 1.82527 | ||||||||
\(29\) | 5.39566 | 1.00195 | 0.500975 | − | 0.865462i | \(-0.332975\pi\) | ||||
0.500975 | + | 0.865462i | \(0.332975\pi\) | |||||||
\(30\) | −13.6519 | −2.49249 | ||||||||
\(31\) | 3.46752 | 0.622785 | 0.311392 | − | 0.950281i | \(-0.399205\pi\) | ||||
0.311392 | + | 0.950281i | \(0.399205\pi\) | |||||||
\(32\) | 6.93020 | 1.22510 | ||||||||
\(33\) | −13.8705 | −2.41454 | ||||||||
\(34\) | 9.92095 | 1.70143 | ||||||||
\(35\) | 5.90898 | 0.998799 | ||||||||
\(36\) | 25.4872 | 4.24787 | ||||||||
\(37\) | 1.78289 | 0.293106 | 0.146553 | − | 0.989203i | \(-0.453182\pi\) | ||||
0.146553 | + | 0.989203i | \(0.453182\pi\) | |||||||
\(38\) | −0.928805 | −0.150672 | ||||||||
\(39\) | −3.41646 | −0.547072 | ||||||||
\(40\) | −3.75197 | −0.593238 | ||||||||
\(41\) | 1.09922 | 0.171670 | 0.0858351 | − | 0.996309i | \(-0.472644\pi\) | ||||
0.0858351 | + | 0.996309i | \(0.472644\pi\) | |||||||
\(42\) | −24.9521 | −3.85019 | ||||||||
\(43\) | −7.80801 | −1.19071 | −0.595355 | − | 0.803463i | \(-0.702989\pi\) | ||||
−0.595355 | + | 0.803463i | \(0.702989\pi\) | |||||||
\(44\) | −11.9318 | −1.79879 | ||||||||
\(45\) | 15.5930 | 2.32447 | ||||||||
\(46\) | −9.95485 | −1.46776 | ||||||||
\(47\) | 11.2703 | 1.64394 | 0.821969 | − | 0.569532i | \(-0.192876\pi\) | ||||
0.821969 | + | 0.569532i | \(0.192876\pi\) | |||||||
\(48\) | −4.23804 | −0.611708 | ||||||||
\(49\) | 3.80005 | 0.542865 | ||||||||
\(50\) | 3.92705 | 0.555369 | ||||||||
\(51\) | −15.2515 | −2.13564 | ||||||||
\(52\) | −2.93895 | −0.407559 | ||||||||
\(53\) | −13.1278 | −1.80324 | −0.901618 | − | 0.432532i | \(-0.857620\pi\) | ||||
−0.901618 | + | 0.432532i | \(0.857620\pi\) | |||||||
\(54\) | −43.0672 | −5.86070 | ||||||||
\(55\) | −7.29985 | −0.984311 | ||||||||
\(56\) | −6.85761 | −0.916386 | ||||||||
\(57\) | 1.42785 | 0.189124 | ||||||||
\(58\) | −11.9912 | −1.57452 | ||||||||
\(59\) | 11.8757 | 1.54608 | 0.773041 | − | 0.634357i | \(-0.218735\pi\) | ||||
0.773041 | + | 0.634357i | \(0.218735\pi\) | |||||||
\(60\) | 18.0538 | 2.33073 | ||||||||
\(61\) | −4.80558 | −0.615292 | −0.307646 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307646 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(62\) | −7.70613 | −0.978679 | ||||||||
\(63\) | 28.4999 | 3.59065 | ||||||||
\(64\) | −12.9205 | −1.61507 | ||||||||
\(65\) | −1.79804 | −0.223019 | ||||||||
\(66\) | 30.8254 | 3.79434 | ||||||||
\(67\) | −6.97405 | −0.852016 | −0.426008 | − | 0.904719i | \(-0.640080\pi\) | ||||
−0.426008 | + | 0.904719i | \(0.640080\pi\) | |||||||
\(68\) | −13.1198 | −1.59101 | ||||||||
\(69\) | 15.3036 | 1.84234 | ||||||||
\(70\) | −13.1320 | −1.56957 | ||||||||
\(71\) | −5.74506 | −0.681813 | −0.340907 | − | 0.940097i | \(-0.610734\pi\) | ||||
−0.340907 | + | 0.940097i | \(0.610734\pi\) | |||||||
\(72\) | −18.0963 | −2.13267 | ||||||||
\(73\) | −4.06268 | −0.475500 | −0.237750 | − | 0.971326i | \(-0.576410\pi\) | ||||
−0.237750 | + | 0.971326i | \(0.576410\pi\) | |||||||
\(74\) | −3.96226 | −0.460603 | ||||||||
\(75\) | −6.03707 | −0.697101 | ||||||||
\(76\) | 1.22829 | 0.140894 | ||||||||
\(77\) | −13.3422 | −1.52048 | ||||||||
\(78\) | 7.59266 | 0.859699 | ||||||||
\(79\) | 14.0395 | 1.57956 | 0.789782 | − | 0.613388i | \(-0.210194\pi\) | ||||
0.789782 | + | 0.613388i | \(0.210194\pi\) | |||||||
\(80\) | −2.23042 | −0.249369 | ||||||||
\(81\) | 40.1906 | 4.46563 | ||||||||
\(82\) | −2.44289 | −0.269772 | ||||||||
\(83\) | 10.5828 | 1.16161 | 0.580804 | − | 0.814043i | \(-0.302738\pi\) | ||||
0.580804 | + | 0.814043i | \(0.302738\pi\) | |||||||
\(84\) | 32.9976 | 3.60033 | ||||||||
\(85\) | −8.02667 | −0.870615 | ||||||||
\(86\) | 17.3523 | 1.87115 | ||||||||
\(87\) | 18.4341 | 1.97634 | ||||||||
\(88\) | 8.47177 | 0.903093 | ||||||||
\(89\) | 9.73193 | 1.03158 | 0.515791 | − | 0.856714i | \(-0.327498\pi\) | ||||
0.515791 | + | 0.856714i | \(0.327498\pi\) | |||||||
\(90\) | −34.6535 | −3.65280 | ||||||||
\(91\) | −3.28634 | −0.344502 | ||||||||
\(92\) | 13.1647 | 1.37251 | ||||||||
\(93\) | 11.8466 | 1.22844 | ||||||||
\(94\) | −25.0468 | −2.58338 | ||||||||
\(95\) | 0.751461 | 0.0770983 | ||||||||
\(96\) | 23.6768 | 2.41650 | ||||||||
\(97\) | 19.3207 | 1.96172 | 0.980858 | − | 0.194722i | \(-0.0623805\pi\) | ||||
0.980858 | + | 0.194722i | \(0.0623805\pi\) | |||||||
\(98\) | −8.44515 | −0.853089 | ||||||||
\(99\) | −35.2082 | −3.53856 | ||||||||
\(100\) | −5.19328 | −0.519328 | ||||||||
\(101\) | −2.68935 | −0.267601 | −0.133800 | − | 0.991008i | \(-0.542718\pi\) | ||||
−0.133800 | + | 0.991008i | \(0.542718\pi\) | |||||||
\(102\) | 33.8946 | 3.35606 | ||||||||
\(103\) | 7.46169 | 0.735222 | 0.367611 | − | 0.929980i | \(-0.380176\pi\) | ||||
0.367611 | + | 0.929980i | \(0.380176\pi\) | |||||||
\(104\) | 2.08670 | 0.204618 | ||||||||
\(105\) | 20.1878 | 1.97013 | ||||||||
\(106\) | 29.1748 | 2.83371 | ||||||||
\(107\) | 20.0130 | 1.93473 | 0.967363 | − | 0.253393i | \(-0.0815467\pi\) | ||||
0.967363 | + | 0.253393i | \(0.0815467\pi\) | |||||||
\(108\) | 56.9536 | 5.48036 | ||||||||
\(109\) | −11.9153 | −1.14128 | −0.570638 | − | 0.821201i | \(-0.693304\pi\) | ||||
−0.570638 | + | 0.821201i | \(0.693304\pi\) | |||||||
\(110\) | 16.2230 | 1.54680 | ||||||||
\(111\) | 6.09119 | 0.578150 | ||||||||
\(112\) | −4.07663 | −0.385205 | ||||||||
\(113\) | −8.41299 | −0.791427 | −0.395714 | − | 0.918374i | \(-0.629503\pi\) | ||||
−0.395714 | + | 0.918374i | \(0.629503\pi\) | |||||||
\(114\) | −3.17323 | −0.297200 | ||||||||
\(115\) | 8.05409 | 0.751048 | ||||||||
\(116\) | 15.8576 | 1.47234 | ||||||||
\(117\) | −8.67221 | −0.801746 | ||||||||
\(118\) | −26.3922 | −2.42960 | ||||||||
\(119\) | −14.6706 | −1.34486 | ||||||||
\(120\) | −12.8184 | −1.17016 | ||||||||
\(121\) | 5.48272 | 0.498429 | ||||||||
\(122\) | 10.6798 | 0.966904 | ||||||||
\(123\) | 3.75546 | 0.338618 | ||||||||
\(124\) | 10.1909 | 0.915167 | ||||||||
\(125\) | −12.1674 | −1.08829 | ||||||||
\(126\) | −63.3374 | −5.64254 | ||||||||
\(127\) | 1.14769 | 0.101841 | 0.0509204 | − | 0.998703i | \(-0.483785\pi\) | ||||
0.0509204 | + | 0.998703i | \(0.483785\pi\) | |||||||
\(128\) | 14.8539 | 1.31291 | ||||||||
\(129\) | −26.6758 | −2.34867 | ||||||||
\(130\) | 3.99592 | 0.350465 | ||||||||
\(131\) | 14.9017 | 1.30197 | 0.650986 | − | 0.759090i | \(-0.274356\pi\) | ||||
0.650986 | + | 0.759090i | \(0.274356\pi\) | |||||||
\(132\) | −40.7646 | −3.54810 | ||||||||
\(133\) | 1.37347 | 0.119095 | ||||||||
\(134\) | 15.4989 | 1.33891 | ||||||||
\(135\) | 34.8440 | 2.99890 | ||||||||
\(136\) | 9.31528 | 0.798778 | ||||||||
\(137\) | 13.2206 | 1.12951 | 0.564757 | − | 0.825257i | \(-0.308970\pi\) | ||||
0.564757 | + | 0.825257i | \(0.308970\pi\) | |||||||
\(138\) | −34.0104 | −2.89515 | ||||||||
\(139\) | −16.6683 | −1.41379 | −0.706895 | − | 0.707318i | \(-0.749905\pi\) | ||||
−0.706895 | + | 0.707318i | \(0.749905\pi\) | |||||||
\(140\) | 17.3662 | 1.46771 | ||||||||
\(141\) | 38.5045 | 3.24266 | ||||||||
\(142\) | 12.7677 | 1.07144 | ||||||||
\(143\) | 4.05989 | 0.339505 | ||||||||
\(144\) | −10.7577 | −0.896472 | ||||||||
\(145\) | 9.70162 | 0.805675 | ||||||||
\(146\) | 9.02879 | 0.747228 | ||||||||
\(147\) | 12.9827 | 1.07080 | ||||||||
\(148\) | 5.23983 | 0.430712 | ||||||||
\(149\) | 21.1768 | 1.73487 | 0.867436 | − | 0.497549i | \(-0.165766\pi\) | ||||
0.867436 | + | 0.497549i | \(0.165766\pi\) | |||||||
\(150\) | 13.4166 | 1.09546 | ||||||||
\(151\) | 1.85169 | 0.150689 | 0.0753443 | − | 0.997158i | \(-0.475994\pi\) | ||||
0.0753443 | + | 0.997158i | \(0.475994\pi\) | |||||||
\(152\) | −0.872101 | −0.0707367 | ||||||||
\(153\) | −38.7138 | −3.12983 | ||||||||
\(154\) | 29.6514 | 2.38938 | ||||||||
\(155\) | 6.23474 | 0.500786 | ||||||||
\(156\) | −10.0408 | −0.803908 | ||||||||
\(157\) | −22.8449 | −1.82322 | −0.911610 | − | 0.411056i | \(-0.865160\pi\) | ||||
−0.911610 | + | 0.411056i | \(0.865160\pi\) | |||||||
\(158\) | −31.2010 | −2.48221 | ||||||||
\(159\) | −44.8505 | −3.55688 | ||||||||
\(160\) | 12.4608 | 0.985110 | ||||||||
\(161\) | 14.7208 | 1.16016 | ||||||||
\(162\) | −89.3187 | −7.01754 | ||||||||
\(163\) | 6.70912 | 0.525499 | 0.262749 | − | 0.964864i | \(-0.415371\pi\) | ||||
0.262749 | + | 0.964864i | \(0.415371\pi\) | |||||||
\(164\) | 3.23057 | 0.252265 | ||||||||
\(165\) | −24.9397 | −1.94155 | ||||||||
\(166\) | −23.5189 | −1.82542 | ||||||||
\(167\) | −6.30922 | −0.488222 | −0.244111 | − | 0.969747i | \(-0.578496\pi\) | ||||
−0.244111 | + | 0.969747i | \(0.578496\pi\) | |||||||
\(168\) | −23.4287 | −1.80757 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 17.8383 | 1.36813 | ||||||||
\(171\) | 3.62441 | 0.277165 | ||||||||
\(172\) | −22.9473 | −1.74972 | ||||||||
\(173\) | −16.0129 | −1.21744 | −0.608719 | − | 0.793386i | \(-0.708316\pi\) | ||||
−0.608719 | + | 0.793386i | \(0.708316\pi\) | |||||||
\(174\) | −40.9674 | −3.10573 | ||||||||
\(175\) | −5.80714 | −0.438979 | ||||||||
\(176\) | 5.03619 | 0.379617 | ||||||||
\(177\) | 40.5728 | 3.04964 | ||||||||
\(178\) | −21.6280 | −1.62109 | ||||||||
\(179\) | 20.2620 | 1.51445 | 0.757225 | − | 0.653154i | \(-0.226555\pi\) | ||||
0.757225 | + | 0.653154i | \(0.226555\pi\) | |||||||
\(180\) | 45.8270 | 3.41574 | ||||||||
\(181\) | −9.23200 | −0.686209 | −0.343105 | − | 0.939297i | \(-0.611479\pi\) | ||||
−0.343105 | + | 0.939297i | \(0.611479\pi\) | |||||||
\(182\) | 7.30349 | 0.541370 | ||||||||
\(183\) | −16.4181 | −1.21366 | ||||||||
\(184\) | −9.34710 | −0.689077 | ||||||||
\(185\) | 3.20571 | 0.235689 | ||||||||
\(186\) | −26.3277 | −1.93044 | ||||||||
\(187\) | 18.1239 | 1.32535 | ||||||||
\(188\) | 33.1228 | 2.41573 | ||||||||
\(189\) | 63.6857 | 4.63246 | ||||||||
\(190\) | −1.67003 | −0.121157 | ||||||||
\(191\) | 18.8404 | 1.36324 | 0.681622 | − | 0.731705i | \(-0.261275\pi\) | ||||
0.681622 | + | 0.731705i | \(0.261275\pi\) | |||||||
\(192\) | −44.1425 | −3.18571 | ||||||||
\(193\) | −12.7373 | −0.916849 | −0.458425 | − | 0.888733i | \(-0.651586\pi\) | ||||
−0.458425 | + | 0.888733i | \(0.651586\pi\) | |||||||
\(194\) | −42.9378 | −3.08275 | ||||||||
\(195\) | −6.14293 | −0.439905 | ||||||||
\(196\) | 11.1682 | 0.797726 | ||||||||
\(197\) | −3.36172 | −0.239513 | −0.119756 | − | 0.992803i | \(-0.538211\pi\) | ||||
−0.119756 | + | 0.992803i | \(0.538211\pi\) | |||||||
\(198\) | 78.2459 | 5.56070 | ||||||||
\(199\) | 24.0099 | 1.70202 | 0.851010 | − | 0.525150i | \(-0.175991\pi\) | ||||
0.851010 | + | 0.525150i | \(0.175991\pi\) | |||||||
\(200\) | 3.68730 | 0.260732 | ||||||||
\(201\) | −23.8266 | −1.68060 | ||||||||
\(202\) | 5.97675 | 0.420523 | ||||||||
\(203\) | 17.7320 | 1.24454 | ||||||||
\(204\) | −44.8234 | −3.13827 | ||||||||
\(205\) | 1.97645 | 0.138041 | ||||||||
\(206\) | −16.5827 | −1.15537 | ||||||||
\(207\) | 38.8461 | 2.69999 | ||||||||
\(208\) | 1.24047 | 0.0860115 | ||||||||
\(209\) | −1.69676 | −0.117368 | ||||||||
\(210\) | −44.8648 | −3.09597 | ||||||||
\(211\) | −4.72483 | −0.325271 | −0.162635 | − | 0.986686i | \(-0.551999\pi\) | ||||
−0.162635 | + | 0.986686i | \(0.551999\pi\) | |||||||
\(212\) | −38.5818 | −2.64981 | ||||||||
\(213\) | −19.6278 | −1.34487 | ||||||||
\(214\) | −44.4763 | −3.04034 | ||||||||
\(215\) | −14.0391 | −0.957459 | ||||||||
\(216\) | −40.4379 | −2.75145 | ||||||||
\(217\) | 11.3955 | 0.773574 | ||||||||
\(218\) | 26.4802 | 1.79347 | ||||||||
\(219\) | −13.8800 | −0.937922 | ||||||||
\(220\) | −21.4539 | −1.44642 | ||||||||
\(221\) | 4.46412 | 0.300289 | ||||||||
\(222\) | −13.5369 | −0.908537 | ||||||||
\(223\) | −13.9942 | −0.937124 | −0.468562 | − | 0.883431i | \(-0.655228\pi\) | ||||
−0.468562 | + | 0.883431i | \(0.655228\pi\) | |||||||
\(224\) | 22.7750 | 1.52172 | ||||||||
\(225\) | −15.3243 | −1.02162 | ||||||||
\(226\) | 18.6968 | 1.24369 | ||||||||
\(227\) | 15.6265 | 1.03717 | 0.518584 | − | 0.855027i | \(-0.326459\pi\) | ||||
0.518584 | + | 0.855027i | \(0.326459\pi\) | |||||||
\(228\) | 4.19639 | 0.277913 | ||||||||
\(229\) | 11.1960 | 0.739855 | 0.369927 | − | 0.929061i | \(-0.379383\pi\) | ||||
0.369927 | + | 0.929061i | \(0.379383\pi\) | |||||||
\(230\) | −17.8992 | −1.18024 | ||||||||
\(231\) | −45.5831 | −2.99915 | ||||||||
\(232\) | −11.2591 | −0.739197 | ||||||||
\(233\) | −20.0152 | −1.31124 | −0.655619 | − | 0.755092i | \(-0.727592\pi\) | ||||
−0.655619 | + | 0.755092i | \(0.727592\pi\) | |||||||
\(234\) | 19.2729 | 1.25991 | ||||||||
\(235\) | 20.2644 | 1.32190 | ||||||||
\(236\) | 34.9020 | 2.27193 | ||||||||
\(237\) | 47.9653 | 3.11568 | ||||||||
\(238\) | 32.6037 | 2.11338 | ||||||||
\(239\) | −26.4183 | −1.70886 | −0.854430 | − | 0.519566i | \(-0.826094\pi\) | ||||
−0.854430 | + | 0.519566i | \(0.826094\pi\) | |||||||
\(240\) | −7.62016 | −0.491879 | ||||||||
\(241\) | −25.0808 | −1.61560 | −0.807798 | − | 0.589459i | \(-0.799341\pi\) | ||||
−0.807798 | + | 0.589459i | \(0.799341\pi\) | |||||||
\(242\) | −12.1847 | −0.783260 | ||||||||
\(243\) | 79.1731 | 5.07896 | ||||||||
\(244\) | −14.1234 | −0.904156 | ||||||||
\(245\) | 6.83265 | 0.436522 | ||||||||
\(246\) | −8.34604 | −0.532124 | ||||||||
\(247\) | −0.417933 | −0.0265925 | ||||||||
\(248\) | −7.23566 | −0.459465 | ||||||||
\(249\) | 36.1556 | 2.29127 | ||||||||
\(250\) | 27.0406 | 1.71020 | ||||||||
\(251\) | −2.58320 | −0.163050 | −0.0815252 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815252 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(252\) | 83.7597 | 5.27636 | ||||||||
\(253\) | −18.1858 | −1.14333 | ||||||||
\(254\) | −2.55059 | −0.160038 | ||||||||
\(255\) | −27.4228 | −1.71728 | ||||||||
\(256\) | −7.16984 | −0.448115 | ||||||||
\(257\) | −10.8616 | −0.677525 | −0.338763 | − | 0.940872i | \(-0.610008\pi\) | ||||
−0.338763 | + | 0.940872i | \(0.610008\pi\) | |||||||
\(258\) | 59.2835 | 3.69083 | ||||||||
\(259\) | 5.85920 | 0.364073 | ||||||||
\(260\) | −5.28435 | −0.327721 | ||||||||
\(261\) | 46.7923 | 2.89637 | ||||||||
\(262\) | −33.1173 | −2.04599 | ||||||||
\(263\) | −23.2838 | −1.43574 | −0.717869 | − | 0.696178i | \(-0.754882\pi\) | ||||
−0.717869 | + | 0.696178i | \(0.754882\pi\) | |||||||
\(264\) | 28.9435 | 1.78135 | ||||||||
\(265\) | −23.6042 | −1.45000 | ||||||||
\(266\) | −3.05237 | −0.187153 | ||||||||
\(267\) | 33.2488 | 2.03479 | ||||||||
\(268\) | −20.4964 | −1.25202 | ||||||||
\(269\) | −10.2088 | −0.622439 | −0.311219 | − | 0.950338i | \(-0.600737\pi\) | ||||
−0.311219 | + | 0.950338i | \(0.600737\pi\) | |||||||
\(270\) | −77.4365 | −4.71264 | ||||||||
\(271\) | 5.61223 | 0.340918 | 0.170459 | − | 0.985365i | \(-0.445475\pi\) | ||||
0.170459 | + | 0.985365i | \(0.445475\pi\) | |||||||
\(272\) | 5.53763 | 0.335768 | ||||||||
\(273\) | −11.2277 | −0.679529 | ||||||||
\(274\) | −29.3812 | −1.77498 | ||||||||
\(275\) | 7.17404 | 0.432611 | ||||||||
\(276\) | 44.9766 | 2.70727 | ||||||||
\(277\) | −2.07933 | −0.124935 | −0.0624673 | − | 0.998047i | \(-0.519897\pi\) | ||||
−0.0624673 | + | 0.998047i | \(0.519897\pi\) | |||||||
\(278\) | 37.0433 | 2.22171 | ||||||||
\(279\) | 30.0711 | 1.80031 | ||||||||
\(280\) | −12.3302 | −0.736873 | ||||||||
\(281\) | 9.70074 | 0.578698 | 0.289349 | − | 0.957224i | \(-0.406561\pi\) | ||||
0.289349 | + | 0.957224i | \(0.406561\pi\) | |||||||
\(282\) | −85.5713 | −5.09570 | ||||||||
\(283\) | −16.4112 | −0.975544 | −0.487772 | − | 0.872971i | \(-0.662190\pi\) | ||||
−0.487772 | + | 0.872971i | \(0.662190\pi\) | |||||||
\(284\) | −16.8844 | −1.00191 | ||||||||
\(285\) | 2.56734 | 0.152076 | ||||||||
\(286\) | −9.02260 | −0.533518 | ||||||||
\(287\) | 3.61243 | 0.213235 | ||||||||
\(288\) | 60.1001 | 3.54143 | ||||||||
\(289\) | 2.92840 | 0.172259 | ||||||||
\(290\) | −21.5606 | −1.26608 | ||||||||
\(291\) | 66.0083 | 3.86948 | ||||||||
\(292\) | −11.9400 | −0.698736 | ||||||||
\(293\) | 4.79139 | 0.279916 | 0.139958 | − | 0.990157i | \(-0.455303\pi\) | ||||
0.139958 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(294\) | −28.8525 | −1.68271 | ||||||||
\(295\) | 21.3529 | 1.24322 | ||||||||
\(296\) | −3.72036 | −0.216242 | ||||||||
\(297\) | −78.6762 | −4.56526 | ||||||||
\(298\) | −47.0628 | −2.72628 | ||||||||
\(299\) | −4.47938 | −0.259049 | ||||||||
\(300\) | −17.7426 | −1.02437 | ||||||||
\(301\) | −25.6598 | −1.47901 | ||||||||
\(302\) | −4.11515 | −0.236801 | ||||||||
\(303\) | −9.18807 | −0.527841 | ||||||||
\(304\) | −0.518436 | −0.0297343 | ||||||||
\(305\) | −8.64063 | −0.494761 | ||||||||
\(306\) | 86.0366 | 4.91839 | ||||||||
\(307\) | 23.7475 | 1.35534 | 0.677671 | − | 0.735365i | \(-0.262989\pi\) | ||||
0.677671 | + | 0.735365i | \(0.262989\pi\) | |||||||
\(308\) | −39.2120 | −2.23431 | ||||||||
\(309\) | 25.4926 | 1.45022 | ||||||||
\(310\) | −13.8559 | −0.786964 | ||||||||
\(311\) | −30.2359 | −1.71452 | −0.857261 | − | 0.514882i | \(-0.827836\pi\) | ||||
−0.857261 | + | 0.514882i | \(0.827836\pi\) | |||||||
\(312\) | 7.12912 | 0.403607 | ||||||||
\(313\) | 16.9689 | 0.959137 | 0.479569 | − | 0.877504i | \(-0.340793\pi\) | ||||
0.479569 | + | 0.877504i | \(0.340793\pi\) | |||||||
\(314\) | 50.7699 | 2.86511 | ||||||||
\(315\) | 51.2439 | 2.88727 | ||||||||
\(316\) | 41.2613 | 2.32113 | ||||||||
\(317\) | 14.4572 | 0.811997 | 0.405999 | − | 0.913874i | \(-0.366924\pi\) | ||||
0.405999 | + | 0.913874i | \(0.366924\pi\) | |||||||
\(318\) | 99.6746 | 5.58948 | ||||||||
\(319\) | −21.9058 | −1.22649 | ||||||||
\(320\) | −23.2316 | −1.29869 | ||||||||
\(321\) | 68.3735 | 3.81624 | ||||||||
\(322\) | −32.7151 | −1.82314 | ||||||||
\(323\) | −1.86571 | −0.103811 | ||||||||
\(324\) | 118.118 | 6.56213 | ||||||||
\(325\) | 1.76705 | 0.0980185 | ||||||||
\(326\) | −14.9102 | −0.825798 | ||||||||
\(327\) | −40.7081 | −2.25116 | ||||||||
\(328\) | −2.29375 | −0.126651 | ||||||||
\(329\) | 37.0380 | 2.04197 | ||||||||
\(330\) | 55.4252 | 3.05106 | ||||||||
\(331\) | −14.8197 | −0.814567 | −0.407283 | − | 0.913302i | \(-0.633524\pi\) | ||||
−0.407283 | + | 0.913302i | \(0.633524\pi\) | |||||||
\(332\) | 31.1022 | 1.70695 | ||||||||
\(333\) | 15.4616 | 0.847292 | ||||||||
\(334\) | 14.0215 | 0.767220 | ||||||||
\(335\) | −12.5396 | −0.685112 | ||||||||
\(336\) | −13.9276 | −0.759815 | ||||||||
\(337\) | −22.6703 | −1.23493 | −0.617464 | − | 0.786599i | \(-0.711840\pi\) | ||||
−0.617464 | + | 0.786599i | \(0.711840\pi\) | |||||||
\(338\) | −2.22237 | −0.120881 | ||||||||
\(339\) | −28.7427 | −1.56109 | ||||||||
\(340\) | −23.5900 | −1.27935 | ||||||||
\(341\) | −14.0778 | −0.762353 | ||||||||
\(342\) | −8.05479 | −0.435553 | ||||||||
\(343\) | −10.5161 | −0.567817 | ||||||||
\(344\) | 16.2929 | 0.878457 | ||||||||
\(345\) | 27.5165 | 1.48144 | ||||||||
\(346\) | 35.5867 | 1.91315 | ||||||||
\(347\) | 13.5698 | 0.728463 | 0.364232 | − | 0.931308i | \(-0.381332\pi\) | ||||
0.364232 | + | 0.931308i | \(0.381332\pi\) | |||||||
\(348\) | 54.1768 | 2.90418 | ||||||||
\(349\) | −30.2693 | −1.62028 | −0.810140 | − | 0.586236i | \(-0.800609\pi\) | ||||
−0.810140 | + | 0.586236i | \(0.800609\pi\) | |||||||
\(350\) | 12.9056 | 0.689836 | ||||||||
\(351\) | −19.3789 | −1.03437 | ||||||||
\(352\) | −28.1358 | −1.49965 | ||||||||
\(353\) | −20.6705 | −1.10018 | −0.550090 | − | 0.835105i | \(-0.685407\pi\) | ||||
−0.550090 | + | 0.835105i | \(0.685407\pi\) | |||||||
\(354\) | −90.1679 | −4.79237 | ||||||||
\(355\) | −10.3298 | −0.548251 | ||||||||
\(356\) | 28.6016 | 1.51588 | ||||||||
\(357\) | −50.1217 | −2.65272 | ||||||||
\(358\) | −45.0297 | −2.37989 | ||||||||
\(359\) | −17.2013 | −0.907850 | −0.453925 | − | 0.891040i | \(-0.649977\pi\) | ||||
−0.453925 | + | 0.891040i | \(0.649977\pi\) | |||||||
\(360\) | −32.5378 | −1.71490 | ||||||||
\(361\) | −18.8253 | −0.990807 | ||||||||
\(362\) | 20.5170 | 1.07835 | ||||||||
\(363\) | 18.7315 | 0.983149 | ||||||||
\(364\) | −9.65840 | −0.506238 | ||||||||
\(365\) | −7.30485 | −0.382353 | ||||||||
\(366\) | 36.4871 | 1.90721 | ||||||||
\(367\) | −7.83476 | −0.408971 | −0.204485 | − | 0.978870i | \(-0.565552\pi\) | ||||
−0.204485 | + | 0.978870i | \(0.565552\pi\) | |||||||
\(368\) | −5.55655 | −0.289655 | ||||||||
\(369\) | 9.53271 | 0.496253 | ||||||||
\(370\) | −7.12430 | −0.370375 | ||||||||
\(371\) | −43.1423 | −2.23984 | ||||||||
\(372\) | 34.8167 | 1.80516 | ||||||||
\(373\) | 21.2783 | 1.10175 | 0.550876 | − | 0.834587i | \(-0.314294\pi\) | ||||
0.550876 | + | 0.834587i | \(0.314294\pi\) | |||||||
\(374\) | −40.2780 | −2.08273 | ||||||||
\(375\) | −41.5696 | −2.14664 | ||||||||
\(376\) | −23.5177 | −1.21283 | ||||||||
\(377\) | −5.39566 | −0.277891 | ||||||||
\(378\) | −141.534 | −7.27970 | ||||||||
\(379\) | 15.5519 | 0.798847 | 0.399423 | − | 0.916767i | \(-0.369210\pi\) | ||||
0.399423 | + | 0.916767i | \(0.369210\pi\) | |||||||
\(380\) | 2.20851 | 0.113294 | ||||||||
\(381\) | 3.92103 | 0.200881 | ||||||||
\(382\) | −41.8704 | −2.14228 | ||||||||
\(383\) | 9.84593 | 0.503103 | 0.251552 | − | 0.967844i | \(-0.419059\pi\) | ||||
0.251552 | + | 0.967844i | \(0.419059\pi\) | |||||||
\(384\) | 50.7478 | 2.58971 | ||||||||
\(385\) | −23.9898 | −1.22263 | ||||||||
\(386\) | 28.3070 | 1.44079 | ||||||||
\(387\) | −67.7127 | −3.44203 | ||||||||
\(388\) | 56.7825 | 2.88269 | ||||||||
\(389\) | −15.4843 | −0.785085 | −0.392542 | − | 0.919734i | \(-0.628404\pi\) | ||||
−0.392542 | + | 0.919734i | \(0.628404\pi\) | |||||||
\(390\) | 13.6519 | 0.691291 | ||||||||
\(391\) | −19.9965 | −1.01127 | ||||||||
\(392\) | −7.92956 | −0.400504 | ||||||||
\(393\) | 50.9113 | 2.56813 | ||||||||
\(394\) | 7.47101 | 0.376384 | ||||||||
\(395\) | 25.2435 | 1.27014 | ||||||||
\(396\) | −103.475 | −5.19983 | ||||||||
\(397\) | 10.2481 | 0.514336 | 0.257168 | − | 0.966367i | \(-0.417211\pi\) | ||||
0.257168 | + | 0.966367i | \(0.417211\pi\) | |||||||
\(398\) | −53.3591 | −2.67465 | ||||||||
\(399\) | 4.69242 | 0.234915 | ||||||||
\(400\) | 2.19198 | 0.109599 | ||||||||
\(401\) | −17.6518 | −0.881488 | −0.440744 | − | 0.897633i | \(-0.645285\pi\) | ||||
−0.440744 | + | 0.897633i | \(0.645285\pi\) | |||||||
\(402\) | 52.9516 | 2.64098 | ||||||||
\(403\) | −3.46752 | −0.172729 | ||||||||
\(404\) | −7.90387 | −0.393232 | ||||||||
\(405\) | 72.2644 | 3.59085 | ||||||||
\(406\) | −39.4072 | −1.95574 | ||||||||
\(407\) | −7.23835 | −0.358792 | ||||||||
\(408\) | 31.8253 | 1.57559 | ||||||||
\(409\) | −11.8531 | −0.586099 | −0.293050 | − | 0.956097i | \(-0.594670\pi\) | ||||
−0.293050 | + | 0.956097i | \(0.594670\pi\) | |||||||
\(410\) | −4.39241 | −0.216926 | ||||||||
\(411\) | 45.1678 | 2.22796 | ||||||||
\(412\) | 21.9295 | 1.08039 | ||||||||
\(413\) | 39.0275 | 1.92042 | ||||||||
\(414\) | −86.3306 | −4.24292 | ||||||||
\(415\) | 19.0282 | 0.934059 | ||||||||
\(416\) | −6.93020 | −0.339781 | ||||||||
\(417\) | −56.9468 | −2.78870 | ||||||||
\(418\) | 3.77085 | 0.184438 | ||||||||
\(419\) | 1.88470 | 0.0920738 | 0.0460369 | − | 0.998940i | \(-0.485341\pi\) | ||||
0.0460369 | + | 0.998940i | \(0.485341\pi\) | |||||||
\(420\) | 59.3309 | 2.89505 | ||||||||
\(421\) | −12.8246 | −0.625035 | −0.312518 | − | 0.949912i | \(-0.601172\pi\) | ||||
−0.312518 | + | 0.949912i | \(0.601172\pi\) | |||||||
\(422\) | 10.5003 | 0.511148 | ||||||||
\(423\) | 97.7382 | 4.75219 | ||||||||
\(424\) | 27.3937 | 1.33035 | ||||||||
\(425\) | 7.88834 | 0.382641 | ||||||||
\(426\) | 43.6203 | 2.11341 | ||||||||
\(427\) | −15.7928 | −0.764267 | ||||||||
\(428\) | 58.8171 | 2.84303 | ||||||||
\(429\) | 13.8705 | 0.669672 | ||||||||
\(430\) | 31.2002 | 1.50461 | ||||||||
\(431\) | −7.16635 | −0.345191 | −0.172596 | − | 0.984993i | \(-0.555215\pi\) | ||||
−0.172596 | + | 0.984993i | \(0.555215\pi\) | |||||||
\(432\) | −24.0390 | −1.15658 | ||||||||
\(433\) | −2.01706 | −0.0969337 | −0.0484668 | − | 0.998825i | \(-0.515434\pi\) | ||||
−0.0484668 | + | 0.998825i | \(0.515434\pi\) | |||||||
\(434\) | −25.3250 | −1.21564 | ||||||||
\(435\) | 33.1452 | 1.58919 | ||||||||
\(436\) | −35.0184 | −1.67708 | ||||||||
\(437\) | 1.87208 | 0.0895538 | ||||||||
\(438\) | 30.8465 | 1.47390 | ||||||||
\(439\) | −3.68912 | −0.176072 | −0.0880360 | − | 0.996117i | \(-0.528059\pi\) | ||||
−0.0880360 | + | 0.996117i | \(0.528059\pi\) | |||||||
\(440\) | 15.2326 | 0.726184 | ||||||||
\(441\) | 32.9549 | 1.56928 | ||||||||
\(442\) | −9.92095 | −0.471892 | ||||||||
\(443\) | −8.36432 | −0.397401 | −0.198700 | − | 0.980060i | \(-0.563672\pi\) | ||||
−0.198700 | + | 0.980060i | \(0.563672\pi\) | |||||||
\(444\) | 17.9017 | 0.849577 | ||||||||
\(445\) | 17.4984 | 0.829504 | ||||||||
\(446\) | 31.1004 | 1.47265 | ||||||||
\(447\) | 72.3498 | 3.42203 | ||||||||
\(448\) | −42.4613 | −2.00611 | ||||||||
\(449\) | 2.94379 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(450\) | 34.0562 | 1.60543 | ||||||||
\(451\) | −4.46273 | −0.210142 | ||||||||
\(452\) | −24.7253 | −1.16298 | ||||||||
\(453\) | 6.32624 | 0.297233 | ||||||||
\(454\) | −34.7280 | −1.62986 | ||||||||
\(455\) | −5.90898 | −0.277017 | ||||||||
\(456\) | −2.97950 | −0.139528 | ||||||||
\(457\) | 12.7984 | 0.598686 | 0.299343 | − | 0.954146i | \(-0.403233\pi\) | ||||
0.299343 | + | 0.954146i | \(0.403233\pi\) | |||||||
\(458\) | −24.8818 | −1.16265 | ||||||||
\(459\) | −86.5098 | −4.03793 | ||||||||
\(460\) | 23.6706 | 1.10365 | ||||||||
\(461\) | 8.19307 | 0.381589 | 0.190795 | − | 0.981630i | \(-0.438894\pi\) | ||||
0.190795 | + | 0.981630i | \(0.438894\pi\) | |||||||
\(462\) | 101.303 | 4.71303 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | −6.69319 | −0.310723 | ||||||||
\(465\) | 21.3007 | 0.987798 | ||||||||
\(466\) | 44.4812 | 2.06055 | ||||||||
\(467\) | −18.2894 | −0.846332 | −0.423166 | − | 0.906052i | \(-0.639081\pi\) | ||||
−0.423166 | + | 0.906052i | \(0.639081\pi\) | |||||||
\(468\) | −25.4872 | −1.17815 | ||||||||
\(469\) | −22.9191 | −1.05831 | ||||||||
\(470\) | −45.0351 | −2.07731 | ||||||||
\(471\) | −78.0487 | −3.59629 | ||||||||
\(472\) | −24.7809 | −1.14064 | ||||||||
\(473\) | 31.6997 | 1.45755 | ||||||||
\(474\) | −106.597 | −4.89616 | ||||||||
\(475\) | −0.738510 | −0.0338852 | ||||||||
\(476\) | −43.1163 | −1.97623 | ||||||||
\(477\) | −113.847 | −5.21268 | ||||||||
\(478\) | 58.7115 | 2.68540 | ||||||||
\(479\) | −30.1722 | −1.37860 | −0.689301 | − | 0.724475i | \(-0.742082\pi\) | ||||
−0.689301 | + | 0.724475i | \(0.742082\pi\) | |||||||
\(480\) | 42.5717 | 1.94313 | ||||||||
\(481\) | −1.78289 | −0.0812929 | ||||||||
\(482\) | 55.7389 | 2.53884 | ||||||||
\(483\) | 50.2929 | 2.28841 | ||||||||
\(484\) | 16.1134 | 0.732429 | ||||||||
\(485\) | 34.7393 | 1.57743 | ||||||||
\(486\) | −175.952 | −7.98136 | ||||||||
\(487\) | 10.0469 | 0.455269 | 0.227635 | − | 0.973747i | \(-0.426901\pi\) | ||||
0.227635 | + | 0.973747i | \(0.426901\pi\) | |||||||
\(488\) | 10.0278 | 0.453937 | ||||||||
\(489\) | 22.9214 | 1.03654 | ||||||||
\(490\) | −15.1847 | −0.685975 | ||||||||
\(491\) | −24.0537 | −1.08553 | −0.542765 | − | 0.839885i | \(-0.682622\pi\) | ||||
−0.542765 | + | 0.839885i | \(0.682622\pi\) | |||||||
\(492\) | 11.0371 | 0.497591 | ||||||||
\(493\) | −24.0869 | −1.08482 | ||||||||
\(494\) | 0.928805 | 0.0417889 | ||||||||
\(495\) | −63.3058 | −2.84539 | ||||||||
\(496\) | −4.30137 | −0.193137 | ||||||||
\(497\) | −18.8802 | −0.846894 | ||||||||
\(498\) | −80.3513 | −3.60063 | ||||||||
\(499\) | 29.4803 | 1.31972 | 0.659860 | − | 0.751389i | \(-0.270616\pi\) | ||||
0.659860 | + | 0.751389i | \(0.270616\pi\) | |||||||
\(500\) | −35.7595 | −1.59921 | ||||||||
\(501\) | −21.5552 | −0.963017 | ||||||||
\(502\) | 5.74085 | 0.256226 | ||||||||
\(503\) | 22.7117 | 1.01266 | 0.506332 | − | 0.862339i | \(-0.331001\pi\) | ||||
0.506332 | + | 0.862339i | \(0.331001\pi\) | |||||||
\(504\) | −59.4706 | −2.64903 | ||||||||
\(505\) | −4.83556 | −0.215180 | ||||||||
\(506\) | 40.4156 | 1.79669 | ||||||||
\(507\) | 3.41646 | 0.151730 | ||||||||
\(508\) | 3.37300 | 0.149653 | ||||||||
\(509\) | −17.5167 | −0.776412 | −0.388206 | − | 0.921573i | \(-0.626905\pi\) | ||||
−0.388206 | + | 0.921573i | \(0.626905\pi\) | |||||||
\(510\) | 60.9438 | 2.69864 | ||||||||
\(511\) | −13.3513 | −0.590629 | ||||||||
\(512\) | −13.7737 | −0.608718 | ||||||||
\(513\) | 8.09909 | 0.357584 | ||||||||
\(514\) | 24.1384 | 1.06470 | ||||||||
\(515\) | 13.4164 | 0.591198 | ||||||||
\(516\) | −78.3987 | −3.45131 | ||||||||
\(517\) | −45.7561 | −2.01235 | ||||||||
\(518\) | −13.0213 | −0.572125 | ||||||||
\(519\) | −54.7075 | −2.40139 | ||||||||
\(520\) | 3.75197 | 0.164535 | ||||||||
\(521\) | −4.02031 | −0.176133 | −0.0880665 | − | 0.996115i | \(-0.528069\pi\) | ||||
−0.0880665 | + | 0.996115i | \(0.528069\pi\) | |||||||
\(522\) | −103.990 | −4.55152 | ||||||||
\(523\) | −17.8356 | −0.779898 | −0.389949 | − | 0.920837i | \(-0.627507\pi\) | ||||
−0.389949 | + | 0.920837i | \(0.627507\pi\) | |||||||
\(524\) | 43.7955 | 1.91321 | ||||||||
\(525\) | −19.8399 | −0.865884 | ||||||||
\(526\) | 51.7453 | 2.25620 | ||||||||
\(527\) | −15.4794 | −0.674295 | ||||||||
\(528\) | 17.2060 | 0.748794 | ||||||||
\(529\) | −2.93520 | −0.127617 | ||||||||
\(530\) | 52.4575 | 2.27861 | ||||||||
\(531\) | 102.988 | 4.46932 | ||||||||
\(532\) | 4.03657 | 0.175007 | ||||||||
\(533\) | −1.09922 | −0.0476127 | ||||||||
\(534\) | −73.8912 | −3.19759 | ||||||||
\(535\) | 35.9841 | 1.55573 | ||||||||
\(536\) | 14.5527 | 0.628582 | ||||||||
\(537\) | 69.2242 | 2.98724 | ||||||||
\(538\) | 22.6877 | 0.978135 | ||||||||
\(539\) | −15.4278 | −0.664523 | ||||||||
\(540\) | 102.405 | 4.40680 | ||||||||
\(541\) | −22.9843 | −0.988171 | −0.494086 | − | 0.869413i | \(-0.664497\pi\) | ||||
−0.494086 | + | 0.869413i | \(0.664497\pi\) | |||||||
\(542\) | −12.4725 | −0.535738 | ||||||||
\(543\) | −31.5408 | −1.35354 | ||||||||
\(544\) | −30.9372 | −1.32642 | ||||||||
\(545\) | −21.4241 | −0.917710 | ||||||||
\(546\) | 24.9521 | 1.06785 | ||||||||
\(547\) | 2.29716 | 0.0982195 | 0.0491097 | − | 0.998793i | \(-0.484362\pi\) | ||||
0.0491097 | + | 0.998793i | \(0.484362\pi\) | |||||||
\(548\) | 38.8548 | 1.65979 | ||||||||
\(549\) | −41.6750 | −1.77865 | ||||||||
\(550\) | −15.9434 | −0.679829 | ||||||||
\(551\) | 2.25503 | 0.0960674 | ||||||||
\(552\) | −31.9340 | −1.35920 | ||||||||
\(553\) | 46.1385 | 1.96201 | ||||||||
\(554\) | 4.62104 | 0.196329 | ||||||||
\(555\) | 10.9522 | 0.464895 | ||||||||
\(556\) | −48.9874 | −2.07753 | ||||||||
\(557\) | −13.9334 | −0.590376 | −0.295188 | − | 0.955439i | \(-0.595382\pi\) | ||||
−0.295188 | + | 0.955439i | \(0.595382\pi\) | |||||||
\(558\) | −66.8292 | −2.82910 | ||||||||
\(559\) | 7.80801 | 0.330244 | ||||||||
\(560\) | −7.32994 | −0.309746 | ||||||||
\(561\) | 61.9195 | 2.61424 | ||||||||
\(562\) | −21.5587 | −0.909398 | ||||||||
\(563\) | −18.4209 | −0.776346 | −0.388173 | − | 0.921586i | \(-0.626894\pi\) | ||||
−0.388173 | + | 0.921586i | \(0.626894\pi\) | |||||||
\(564\) | 113.163 | 4.76501 | ||||||||
\(565\) | −15.1269 | −0.636393 | ||||||||
\(566\) | 36.4718 | 1.53302 | ||||||||
\(567\) | 132.080 | 5.54685 | ||||||||
\(568\) | 11.9882 | 0.503014 | ||||||||
\(569\) | −36.3145 | −1.52238 | −0.761191 | − | 0.648527i | \(-0.775385\pi\) | ||||
−0.761191 | + | 0.648527i | \(0.775385\pi\) | |||||||
\(570\) | −5.70559 | −0.238981 | ||||||||
\(571\) | −26.2098 | −1.09684 | −0.548422 | − | 0.836202i | \(-0.684771\pi\) | ||||
−0.548422 | + | 0.836202i | \(0.684771\pi\) | |||||||
\(572\) | 11.9318 | 0.498894 | ||||||||
\(573\) | 64.3675 | 2.68899 | ||||||||
\(574\) | −8.02818 | −0.335090 | ||||||||
\(575\) | −7.91529 | −0.330091 | ||||||||
\(576\) | −112.050 | −4.66874 | ||||||||
\(577\) | −29.9862 | −1.24834 | −0.624170 | − | 0.781288i | \(-0.714563\pi\) | ||||
−0.624170 | + | 0.781288i | \(0.714563\pi\) | |||||||
\(578\) | −6.50799 | −0.270697 | ||||||||
\(579\) | −43.5164 | −1.80848 | ||||||||
\(580\) | 28.5126 | 1.18392 | ||||||||
\(581\) | 34.7786 | 1.44286 | ||||||||
\(582\) | −146.695 | −6.08071 | ||||||||
\(583\) | 53.2973 | 2.20735 | ||||||||
\(584\) | 8.47757 | 0.350805 | ||||||||
\(585\) | −15.5930 | −0.644691 | ||||||||
\(586\) | −10.6483 | −0.439876 | ||||||||
\(587\) | 7.57230 | 0.312542 | 0.156271 | − | 0.987714i | \(-0.450053\pi\) | ||||
0.156271 | + | 0.987714i | \(0.450053\pi\) | |||||||
\(588\) | 38.1556 | 1.57351 | ||||||||
\(589\) | 1.44919 | 0.0597129 | ||||||||
\(590\) | −47.4542 | −1.95366 | ||||||||
\(591\) | −11.4852 | −0.472438 | ||||||||
\(592\) | −2.21163 | −0.0908976 | ||||||||
\(593\) | 9.54738 | 0.392064 | 0.196032 | − | 0.980598i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980598i | \(0.437194\pi\) | |||||||
\(594\) | 174.848 | 7.17410 | ||||||||
\(595\) | −26.3784 | −1.08141 | ||||||||
\(596\) | 62.2376 | 2.54935 | ||||||||
\(597\) | 82.0290 | 3.35723 | ||||||||
\(598\) | 9.95485 | 0.407084 | ||||||||
\(599\) | −33.5561 | −1.37107 | −0.685534 | − | 0.728041i | \(-0.740431\pi\) | ||||
−0.685534 | + | 0.728041i | \(0.740431\pi\) | |||||||
\(600\) | 12.5975 | 0.514292 | ||||||||
\(601\) | 33.5669 | 1.36922 | 0.684611 | − | 0.728908i | \(-0.259972\pi\) | ||||
0.684611 | + | 0.728908i | \(0.259972\pi\) | |||||||
\(602\) | 57.0257 | 2.32419 | ||||||||
\(603\) | −60.4804 | −2.46295 | ||||||||
\(604\) | 5.44203 | 0.221433 | ||||||||
\(605\) | 9.85815 | 0.400791 | ||||||||
\(606\) | 20.4193 | 0.829479 | ||||||||
\(607\) | −24.7411 | −1.00421 | −0.502105 | − | 0.864807i | \(-0.667441\pi\) | ||||
−0.502105 | + | 0.864807i | \(0.667441\pi\) | |||||||
\(608\) | 2.89636 | 0.117463 | ||||||||
\(609\) | 60.5807 | 2.45485 | ||||||||
\(610\) | 19.2027 | 0.777495 | ||||||||
\(611\) | −11.2703 | −0.455946 | ||||||||
\(612\) | −113.778 | −4.59920 | ||||||||
\(613\) | 5.90221 | 0.238388 | 0.119194 | − | 0.992871i | \(-0.461969\pi\) | ||||
0.119194 | + | 0.992871i | \(0.461969\pi\) | |||||||
\(614\) | −52.7759 | −2.12986 | ||||||||
\(615\) | 6.75247 | 0.272286 | ||||||||
\(616\) | 27.8411 | 1.12175 | ||||||||
\(617\) | −31.0882 | −1.25156 | −0.625781 | − | 0.779998i | \(-0.715220\pi\) | ||||
−0.625781 | + | 0.779998i | \(0.715220\pi\) | |||||||
\(618\) | −56.6541 | −2.27896 | ||||||||
\(619\) | 2.23055 | 0.0896534 | 0.0448267 | − | 0.998995i | \(-0.485726\pi\) | ||||
0.0448267 | + | 0.998995i | \(0.485726\pi\) | |||||||
\(620\) | 18.3236 | 0.735893 | ||||||||
\(621\) | 86.8054 | 3.48338 | ||||||||
\(622\) | 67.1956 | 2.69430 | ||||||||
\(623\) | 31.9825 | 1.28135 | ||||||||
\(624\) | 4.23804 | 0.169657 | ||||||||
\(625\) | −13.0423 | −0.521690 | ||||||||
\(626\) | −37.7112 | −1.50724 | ||||||||
\(627\) | −5.79693 | −0.231507 | ||||||||
\(628\) | −67.1399 | −2.67918 | ||||||||
\(629\) | −7.95906 | −0.317348 | ||||||||
\(630\) | −113.883 | −4.53721 | ||||||||
\(631\) | −24.0250 | −0.956420 | −0.478210 | − | 0.878245i | \(-0.658714\pi\) | ||||
−0.478210 | + | 0.878245i | \(0.658714\pi\) | |||||||
\(632\) | −29.2961 | −1.16534 | ||||||||
\(633\) | −16.1422 | −0.641595 | ||||||||
\(634\) | −32.1293 | −1.27602 | ||||||||
\(635\) | 2.06359 | 0.0818910 | ||||||||
\(636\) | −131.813 | −5.22674 | ||||||||
\(637\) | −3.80005 | −0.150564 | ||||||||
\(638\) | 48.6829 | 1.92738 | ||||||||
\(639\) | −49.8224 | −1.97094 | ||||||||
\(640\) | 26.7079 | 1.05572 | ||||||||
\(641\) | 14.2998 | 0.564810 | 0.282405 | − | 0.959295i | \(-0.408868\pi\) | ||||
0.282405 | + | 0.959295i | \(0.408868\pi\) | |||||||
\(642\) | −151.952 | −5.99705 | ||||||||
\(643\) | 14.7046 | 0.579892 | 0.289946 | − | 0.957043i | \(-0.406363\pi\) | ||||
0.289946 | + | 0.957043i | \(0.406363\pi\) | |||||||
\(644\) | 43.2636 | 1.70482 | ||||||||
\(645\) | −47.9641 | −1.88858 | ||||||||
\(646\) | 4.14630 | 0.163134 | ||||||||
\(647\) | −37.0064 | −1.45487 | −0.727436 | − | 0.686175i | \(-0.759288\pi\) | ||||
−0.727436 | + | 0.686175i | \(0.759288\pi\) | |||||||
\(648\) | −83.8657 | −3.29456 | ||||||||
\(649\) | −48.2140 | −1.89256 | ||||||||
\(650\) | −3.92705 | −0.154032 | ||||||||
\(651\) | 38.9322 | 1.52587 | ||||||||
\(652\) | 19.7178 | 0.772207 | ||||||||
\(653\) | 39.9763 | 1.56439 | 0.782196 | − | 0.623032i | \(-0.214099\pi\) | ||||
0.782196 | + | 0.623032i | \(0.214099\pi\) | |||||||
\(654\) | 90.4686 | 3.53760 | ||||||||
\(655\) | 26.7939 | 1.04693 | ||||||||
\(656\) | −1.36356 | −0.0532381 | ||||||||
\(657\) | −35.2324 | −1.37455 | ||||||||
\(658\) | −82.3123 | −3.20887 | ||||||||
\(659\) | −0.892490 | −0.0347665 | −0.0173832 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173832 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(660\) | −73.2964 | −2.85306 | ||||||||
\(661\) | 12.9330 | 0.503036 | 0.251518 | − | 0.967853i | \(-0.419070\pi\) | ||||
0.251518 | + | 0.967853i | \(0.419070\pi\) | |||||||
\(662\) | 32.9350 | 1.28006 | ||||||||
\(663\) | 15.2515 | 0.592319 | ||||||||
\(664\) | −22.0830 | −0.856987 | ||||||||
\(665\) | 2.46956 | 0.0957654 | ||||||||
\(666\) | −34.3615 | −1.33148 | ||||||||
\(667\) | 24.1692 | 0.935835 | ||||||||
\(668\) | −18.5425 | −0.717431 | ||||||||
\(669\) | −47.8108 | −1.84847 | ||||||||
\(670\) | 27.8677 | 1.07662 | ||||||||
\(671\) | 19.5101 | 0.753181 | ||||||||
\(672\) | 77.8099 | 3.00158 | ||||||||
\(673\) | −7.92814 | −0.305607 | −0.152804 | − | 0.988257i | \(-0.548830\pi\) | ||||
−0.152804 | + | 0.988257i | \(0.548830\pi\) | |||||||
\(674\) | 50.3819 | 1.94064 | ||||||||
\(675\) | −34.2435 | −1.31803 | ||||||||
\(676\) | 2.93895 | 0.113037 | ||||||||
\(677\) | −10.6291 | −0.408511 | −0.204256 | − | 0.978918i | \(-0.565477\pi\) | ||||
−0.204256 | + | 0.978918i | \(0.565477\pi\) | |||||||
\(678\) | 63.8770 | 2.45318 | ||||||||
\(679\) | 63.4944 | 2.43669 | ||||||||
\(680\) | 16.7492 | 0.642304 | ||||||||
\(681\) | 53.3874 | 2.04581 | ||||||||
\(682\) | 31.2860 | 1.19800 | ||||||||
\(683\) | −33.7028 | −1.28960 | −0.644802 | − | 0.764350i | \(-0.723060\pi\) | ||||
−0.644802 | + | 0.764350i | \(0.723060\pi\) | |||||||
\(684\) | 10.6520 | 0.407288 | ||||||||
\(685\) | 23.7712 | 0.908252 | ||||||||
\(686\) | 23.3708 | 0.892300 | ||||||||
\(687\) | 38.2508 | 1.45936 | ||||||||
\(688\) | 9.68564 | 0.369261 | ||||||||
\(689\) | 13.1278 | 0.500128 | ||||||||
\(690\) | −61.1520 | −2.32802 | ||||||||
\(691\) | −10.4729 | −0.398408 | −0.199204 | − | 0.979958i | \(-0.563836\pi\) | ||||
−0.199204 | + | 0.979958i | \(0.563836\pi\) | |||||||
\(692\) | −47.0611 | −1.78900 | ||||||||
\(693\) | −115.706 | −4.39532 | ||||||||
\(694\) | −30.1571 | −1.14475 | ||||||||
\(695\) | −29.9703 | −1.13684 | ||||||||
\(696\) | −38.4663 | −1.45806 | ||||||||
\(697\) | −4.90708 | −0.185869 | ||||||||
\(698\) | 67.2698 | 2.54620 | ||||||||
\(699\) | −68.3811 | −2.58641 | ||||||||
\(700\) | −17.0669 | −0.645068 | ||||||||
\(701\) | 12.3305 | 0.465717 | 0.232859 | − | 0.972511i | \(-0.425192\pi\) | ||||
0.232859 | + | 0.972511i | \(0.425192\pi\) | |||||||
\(702\) | 43.0672 | 1.62547 | ||||||||
\(703\) | 0.745131 | 0.0281031 | ||||||||
\(704\) | 52.4560 | 1.97701 | ||||||||
\(705\) | 69.2326 | 2.60745 | ||||||||
\(706\) | 45.9376 | 1.72889 | ||||||||
\(707\) | −8.83814 | −0.332392 | ||||||||
\(708\) | 119.241 | 4.48137 | ||||||||
\(709\) | −2.70298 | −0.101512 | −0.0507562 | − | 0.998711i | \(-0.516163\pi\) | ||||
−0.0507562 | + | 0.998711i | \(0.516163\pi\) | |||||||
\(710\) | 22.9568 | 0.861553 | ||||||||
\(711\) | 121.753 | 4.56610 | ||||||||
\(712\) | −20.3076 | −0.761059 | ||||||||
\(713\) | 15.5323 | 0.581690 | ||||||||
\(714\) | 111.389 | 4.16864 | ||||||||
\(715\) | 7.29985 | 0.272999 | ||||||||
\(716\) | 59.5489 | 2.22545 | ||||||||
\(717\) | −90.2573 | −3.37072 | ||||||||
\(718\) | 38.2277 | 1.42665 | ||||||||
\(719\) | 14.3855 | 0.536487 | 0.268244 | − | 0.963351i | \(-0.413557\pi\) | ||||
0.268244 | + | 0.963351i | \(0.413557\pi\) | |||||||
\(720\) | −19.3427 | −0.720860 | ||||||||
\(721\) | 24.5217 | 0.913235 | ||||||||
\(722\) | 41.8369 | 1.55701 | ||||||||
\(723\) | −85.6876 | −3.18676 | ||||||||
\(724\) | −27.1324 | −1.00837 | ||||||||
\(725\) | −9.53442 | −0.354100 | ||||||||
\(726\) | −41.6284 | −1.54498 | ||||||||
\(727\) | −29.3651 | −1.08909 | −0.544545 | − | 0.838732i | \(-0.683298\pi\) | ||||
−0.544545 | + | 0.838732i | \(0.683298\pi\) | |||||||
\(728\) | 6.85761 | 0.254160 | ||||||||
\(729\) | 149.920 | 5.55259 | ||||||||
\(730\) | 16.2341 | 0.600852 | ||||||||
\(731\) | 34.8559 | 1.28919 | ||||||||
\(732\) | −48.2519 | −1.78344 | ||||||||
\(733\) | −25.8494 | −0.954769 | −0.477385 | − | 0.878694i | \(-0.658415\pi\) | ||||
−0.477385 | + | 0.878694i | \(0.658415\pi\) | |||||||
\(734\) | 17.4118 | 0.642680 | ||||||||
\(735\) | 23.3435 | 0.861038 | ||||||||
\(736\) | 31.0429 | 1.14426 | ||||||||
\(737\) | 28.3139 | 1.04296 | ||||||||
\(738\) | −21.1853 | −0.779840 | ||||||||
\(739\) | 46.7138 | 1.71839 | 0.859197 | − | 0.511645i | \(-0.170964\pi\) | ||||
0.859197 | + | 0.511645i | \(0.170964\pi\) | |||||||
\(740\) | 9.42143 | 0.346339 | ||||||||
\(741\) | −1.42785 | −0.0524535 | ||||||||
\(742\) | 95.8784 | 3.51981 | ||||||||
\(743\) | 31.3998 | 1.15195 | 0.575974 | − | 0.817468i | \(-0.304623\pi\) | ||||
0.575974 | + | 0.817468i | \(0.304623\pi\) | |||||||
\(744\) | −24.7204 | −0.906293 | ||||||||
\(745\) | 38.0768 | 1.39502 | ||||||||
\(746\) | −47.2885 | −1.73135 | ||||||||
\(747\) | 91.7759 | 3.35791 | ||||||||
\(748\) | 53.2651 | 1.94756 | ||||||||
\(749\) | 65.7695 | 2.40316 | ||||||||
\(750\) | 92.3832 | 3.37336 | ||||||||
\(751\) | 29.1819 | 1.06486 | 0.532431 | − | 0.846473i | \(-0.321278\pi\) | ||||
0.532431 | + | 0.846473i | \(0.321278\pi\) | |||||||
\(752\) | −13.9805 | −0.509816 | ||||||||
\(753\) | −8.82542 | −0.321616 | ||||||||
\(754\) | 11.9912 | 0.436693 | ||||||||
\(755\) | 3.32942 | 0.121170 | ||||||||
\(756\) | 187.169 | 6.80728 | ||||||||
\(757\) | 38.0007 | 1.38116 | 0.690579 | − | 0.723257i | \(-0.257356\pi\) | ||||
0.690579 | + | 0.723257i | \(0.257356\pi\) | |||||||
\(758\) | −34.5621 | −1.25535 | ||||||||
\(759\) | −62.1310 | −2.25521 | ||||||||
\(760\) | −1.56807 | −0.0568799 | ||||||||
\(761\) | 8.59225 | 0.311469 | 0.155734 | − | 0.987799i | \(-0.450226\pi\) | ||||
0.155734 | + | 0.987799i | \(0.450226\pi\) | |||||||
\(762\) | −8.71401 | −0.315675 | ||||||||
\(763\) | −39.1577 | −1.41760 | ||||||||
\(764\) | 55.3710 | 2.00325 | ||||||||
\(765\) | −69.6090 | −2.51672 | ||||||||
\(766\) | −21.8813 | −0.790605 | ||||||||
\(767\) | −11.8757 | −0.428806 | ||||||||
\(768\) | −24.4955 | −0.883904 | ||||||||
\(769\) | 3.38494 | 0.122064 | 0.0610321 | − | 0.998136i | \(-0.480561\pi\) | ||||
0.0610321 | + | 0.998136i | \(0.480561\pi\) | |||||||
\(770\) | 53.3143 | 1.92132 | ||||||||
\(771\) | −37.1081 | −1.33642 | ||||||||
\(772\) | −37.4342 | −1.34729 | ||||||||
\(773\) | 10.8238 | 0.389303 | 0.194652 | − | 0.980872i | \(-0.437642\pi\) | ||||
0.194652 | + | 0.980872i | \(0.437642\pi\) | |||||||
\(774\) | 150.483 | 5.40900 | ||||||||
\(775\) | −6.12729 | −0.220099 | ||||||||
\(776\) | −40.3164 | −1.44727 | ||||||||
\(777\) | 20.0177 | 0.718132 | ||||||||
\(778\) | 34.4119 | 1.23373 | ||||||||
\(779\) | 0.459403 | 0.0164598 | ||||||||
\(780\) | −18.0538 | −0.646429 | ||||||||
\(781\) | 23.3243 | 0.834610 | ||||||||
\(782\) | 44.4397 | 1.58916 | ||||||||
\(783\) | 104.562 | 3.73674 | ||||||||
\(784\) | −4.71387 | −0.168353 | ||||||||
\(785\) | −41.0760 | −1.46607 | ||||||||
\(786\) | −113.144 | −4.03571 | ||||||||
\(787\) | 30.0825 | 1.07232 | 0.536162 | − | 0.844115i | \(-0.319874\pi\) | ||||
0.536162 | + | 0.844115i | \(0.319874\pi\) | |||||||
\(788\) | −9.87993 | −0.351958 | ||||||||
\(789\) | −79.5481 | −2.83199 | ||||||||
\(790\) | −56.1006 | −1.99597 | ||||||||
\(791\) | −27.6480 | −0.983049 | ||||||||
\(792\) | 73.4690 | 2.61061 | ||||||||
\(793\) | 4.80558 | 0.170651 | ||||||||
\(794\) | −22.7751 | −0.808257 | ||||||||
\(795\) | −80.6430 | −2.86011 | ||||||||
\(796\) | 70.5640 | 2.50107 | ||||||||
\(797\) | 30.1788 | 1.06899 | 0.534494 | − | 0.845172i | \(-0.320502\pi\) | ||||
0.534494 | + | 0.845172i | \(0.320502\pi\) | |||||||
\(798\) | −10.4283 | −0.369158 | ||||||||
\(799\) | −50.3119 | −1.77991 | ||||||||
\(800\) | −12.2460 | −0.432962 | ||||||||
\(801\) | 84.3974 | 2.98203 | ||||||||
\(802\) | 39.2289 | 1.38522 | ||||||||
\(803\) | 16.4940 | 0.582061 | ||||||||
\(804\) | −70.0251 | −2.46959 | ||||||||
\(805\) | 26.4685 | 0.932893 | ||||||||
\(806\) | 7.70613 | 0.271437 | ||||||||
\(807\) | −34.8778 | −1.22776 | ||||||||
\(808\) | 5.61187 | 0.197425 | ||||||||
\(809\) | 14.0526 | 0.494063 | 0.247031 | − | 0.969008i | \(-0.420545\pi\) | ||||
0.247031 | + | 0.969008i | \(0.420545\pi\) | |||||||
\(810\) | −160.599 | −5.64286 | ||||||||
\(811\) | −25.4786 | −0.894676 | −0.447338 | − | 0.894365i | \(-0.647628\pi\) | ||||
−0.447338 | + | 0.894365i | \(0.647628\pi\) | |||||||
\(812\) | 52.1135 | 1.82882 | ||||||||
\(813\) | 19.1740 | 0.672460 | ||||||||
\(814\) | 16.0863 | 0.563826 | ||||||||
\(815\) | 12.0633 | 0.422558 | ||||||||
\(816\) | 18.9191 | 0.662301 | ||||||||
\(817\) | −3.26323 | −0.114166 | ||||||||
\(818\) | 26.3421 | 0.921029 | ||||||||
\(819\) | −28.4999 | −0.995866 | ||||||||
\(820\) | 5.80869 | 0.202848 | ||||||||
\(821\) | 22.2392 | 0.776154 | 0.388077 | − | 0.921627i | \(-0.373139\pi\) | ||||
0.388077 | + | 0.921627i | \(0.373139\pi\) | |||||||
\(822\) | −100.380 | −3.50115 | ||||||||
\(823\) | 16.7355 | 0.583363 | 0.291681 | − | 0.956516i | \(-0.405785\pi\) | ||||
0.291681 | + | 0.956516i | \(0.405785\pi\) | |||||||
\(824\) | −15.5703 | −0.542417 | ||||||||
\(825\) | 24.5098 | 0.853323 | ||||||||
\(826\) | −86.7338 | −3.01786 | ||||||||
\(827\) | 21.2077 | 0.737465 | 0.368732 | − | 0.929536i | \(-0.379792\pi\) | ||||
0.368732 | + | 0.929536i | \(0.379792\pi\) | |||||||
\(828\) | 114.167 | 3.96757 | ||||||||
\(829\) | 43.3397 | 1.50525 | 0.752624 | − | 0.658450i | \(-0.228788\pi\) | ||||
0.752624 | + | 0.658450i | \(0.228788\pi\) | |||||||
\(830\) | −42.2878 | −1.46783 | ||||||||
\(831\) | −7.10394 | −0.246433 | ||||||||
\(832\) | 12.9205 | 0.447939 | ||||||||
\(833\) | −16.9639 | −0.587765 | ||||||||
\(834\) | 126.557 | 4.38231 | ||||||||
\(835\) | −11.3442 | −0.392584 | ||||||||
\(836\) | −4.98670 | −0.172469 | ||||||||
\(837\) | 67.1967 | 2.32266 | ||||||||
\(838\) | −4.18852 | −0.144690 | ||||||||
\(839\) | 41.7931 | 1.44286 | 0.721429 | − | 0.692488i | \(-0.243486\pi\) | ||||
0.721429 | + | 0.692488i | \(0.243486\pi\) | |||||||
\(840\) | −42.1258 | −1.45348 | ||||||||
\(841\) | 0.113183 | 0.00390287 | ||||||||
\(842\) | 28.5012 | 0.982215 | ||||||||
\(843\) | 33.1422 | 1.14148 | ||||||||
\(844\) | −13.8860 | −0.477977 | ||||||||
\(845\) | 1.79804 | 0.0618544 | ||||||||
\(846\) | −217.211 | −7.46787 | ||||||||
\(847\) | 18.0181 | 0.619109 | ||||||||
\(848\) | 16.2847 | 0.559217 | ||||||||
\(849\) | −56.0682 | −1.92426 | ||||||||
\(850\) | −17.5309 | −0.601303 | ||||||||
\(851\) | 7.98625 | 0.273765 | ||||||||
\(852\) | −57.6850 | −1.97626 | ||||||||
\(853\) | −18.3044 | −0.626732 | −0.313366 | − | 0.949632i | \(-0.601457\pi\) | ||||
−0.313366 | + | 0.949632i | \(0.601457\pi\) | |||||||
\(854\) | 35.0975 | 1.20101 | ||||||||
\(855\) | 6.51683 | 0.222871 | ||||||||
\(856\) | −41.7610 | −1.42736 | ||||||||
\(857\) | 43.0938 | 1.47206 | 0.736028 | − | 0.676951i | \(-0.236699\pi\) | ||||
0.736028 | + | 0.676951i | \(0.236699\pi\) | |||||||
\(858\) | −30.8254 | −1.05236 | ||||||||
\(859\) | −37.6722 | −1.28536 | −0.642679 | − | 0.766136i | \(-0.722177\pi\) | ||||
−0.642679 | + | 0.766136i | \(0.722177\pi\) | |||||||
\(860\) | −41.2602 | −1.40696 | ||||||||
\(861\) | 12.3417 | 0.420605 | ||||||||
\(862\) | 15.9263 | 0.542453 | ||||||||
\(863\) | 4.48735 | 0.152751 | 0.0763757 | − | 0.997079i | \(-0.475665\pi\) | ||||
0.0763757 | + | 0.997079i | \(0.475665\pi\) | |||||||
\(864\) | 134.300 | 4.56896 | ||||||||
\(865\) | −28.7918 | −0.978952 | ||||||||
\(866\) | 4.48266 | 0.152327 | ||||||||
\(867\) | 10.0048 | 0.339779 | ||||||||
\(868\) | 33.4907 | 1.13675 | ||||||||
\(869\) | −56.9987 | −1.93355 | ||||||||
\(870\) | −73.6611 | −2.49734 | ||||||||
\(871\) | 6.97405 | 0.236307 | ||||||||
\(872\) | 24.8636 | 0.841987 | ||||||||
\(873\) | 167.553 | 5.67081 | ||||||||
\(874\) | −4.16046 | −0.140730 | ||||||||
\(875\) | −39.9864 | −1.35179 | ||||||||
\(876\) | −40.7925 | −1.37825 | ||||||||
\(877\) | −18.8002 | −0.634836 | −0.317418 | − | 0.948286i | \(-0.602816\pi\) | ||||
−0.317418 | + | 0.948286i | \(0.602816\pi\) | |||||||
\(878\) | 8.19861 | 0.276690 | ||||||||
\(879\) | 16.3696 | 0.552133 | ||||||||
\(880\) | 9.05528 | 0.305253 | ||||||||
\(881\) | −53.2861 | −1.79525 | −0.897627 | − | 0.440755i | \(-0.854711\pi\) | ||||
−0.897627 | + | 0.440755i | \(0.854711\pi\) | |||||||
\(882\) | −73.2381 | −2.46606 | ||||||||
\(883\) | −2.76365 | −0.0930044 | −0.0465022 | − | 0.998918i | \(-0.514807\pi\) | ||||
−0.0465022 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(884\) | 13.1198 | 0.441268 | ||||||||
\(885\) | 72.9515 | 2.45224 | ||||||||
\(886\) | 18.5886 | 0.624498 | ||||||||
\(887\) | 20.7524 | 0.696796 | 0.348398 | − | 0.937347i | \(-0.386726\pi\) | ||||
0.348398 | + | 0.937347i | \(0.386726\pi\) | |||||||
\(888\) | −12.7105 | −0.426535 | ||||||||
\(889\) | 3.77170 | 0.126499 | ||||||||
\(890\) | −38.8880 | −1.30353 | ||||||||
\(891\) | −163.170 | −5.46639 | ||||||||
\(892\) | −41.1284 | −1.37708 | ||||||||
\(893\) | 4.71022 | 0.157622 | ||||||||
\(894\) | −160.788 | −5.37757 | ||||||||
\(895\) | 36.4318 | 1.21778 | ||||||||
\(896\) | 48.8150 | 1.63079 | ||||||||
\(897\) | −15.3036 | −0.510973 | ||||||||
\(898\) | −6.54219 | −0.218316 | ||||||||
\(899\) | 18.7096 | 0.623999 | ||||||||
\(900\) | −45.0372 | −1.50124 | ||||||||
\(901\) | 58.6039 | 1.95238 | ||||||||
\(902\) | 9.91787 | 0.330229 | ||||||||
\(903\) | −87.6657 | −2.91733 | ||||||||
\(904\) | 17.5554 | 0.583883 | ||||||||
\(905\) | −16.5995 | −0.551786 | ||||||||
\(906\) | −14.0593 | −0.467088 | ||||||||
\(907\) | 7.76420 | 0.257806 | 0.128903 | − | 0.991657i | \(-0.458854\pi\) | ||||
0.128903 | + | 0.991657i | \(0.458854\pi\) | |||||||
\(908\) | 45.9255 | 1.52409 | ||||||||
\(909\) | −23.3226 | −0.773563 | ||||||||
\(910\) | 13.1320 | 0.435320 | ||||||||
\(911\) | −57.5721 | −1.90745 | −0.953725 | − | 0.300680i | \(-0.902786\pi\) | ||||
−0.953725 | + | 0.300680i | \(0.902786\pi\) | |||||||
\(912\) | −1.77122 | −0.0586508 | ||||||||
\(913\) | −42.9649 | −1.42193 | ||||||||
\(914\) | −28.4429 | −0.940808 | ||||||||
\(915\) | −29.5204 | −0.975914 | ||||||||
\(916\) | 32.9046 | 1.08720 | ||||||||
\(917\) | 48.9723 | 1.61721 | ||||||||
\(918\) | 192.257 | 6.34543 | ||||||||
\(919\) | −19.9024 | −0.656521 | −0.328261 | − | 0.944587i | \(-0.606462\pi\) | ||||
−0.328261 | + | 0.944587i | \(0.606462\pi\) | |||||||
\(920\) | −16.8065 | −0.554093 | ||||||||
\(921\) | 81.1325 | 2.67341 | ||||||||
\(922\) | −18.2081 | −0.599651 | ||||||||
\(923\) | 5.74506 | 0.189101 | ||||||||
\(924\) | −133.966 | −4.40717 | ||||||||
\(925\) | −3.15047 | −0.103587 | ||||||||
\(926\) | −2.22237 | −0.0730318 | ||||||||
\(927\) | 64.7094 | 2.12534 | ||||||||
\(928\) | 37.3930 | 1.22749 | ||||||||
\(929\) | 2.30016 | 0.0754659 | 0.0377329 | − | 0.999288i | \(-0.487986\pi\) | ||||
0.0377329 | + | 0.999288i | \(0.487986\pi\) | |||||||
\(930\) | −47.3382 | −1.55228 | ||||||||
\(931\) | 1.58817 | 0.0520502 | ||||||||
\(932\) | −58.8236 | −1.92683 | ||||||||
\(933\) | −103.300 | −3.38189 | ||||||||
\(934\) | 40.6459 | 1.32997 | ||||||||
\(935\) | 32.5874 | 1.06572 | ||||||||
\(936\) | 18.0963 | 0.591496 | ||||||||
\(937\) | −17.7147 | −0.578714 | −0.289357 | − | 0.957221i | \(-0.593441\pi\) | ||||
−0.289357 | + | 0.957221i | \(0.593441\pi\) | |||||||
\(938\) | 50.9349 | 1.66308 | ||||||||
\(939\) | 57.9735 | 1.89189 | ||||||||
\(940\) | 59.5560 | 1.94250 | ||||||||
\(941\) | 0.846668 | 0.0276006 | 0.0138003 | − | 0.999905i | \(-0.495607\pi\) | ||||
0.0138003 | + | 0.999905i | \(0.495607\pi\) | |||||||
\(942\) | 173.453 | 5.65142 | ||||||||
\(943\) | 4.92384 | 0.160342 | ||||||||
\(944\) | −14.7315 | −0.479469 | ||||||||
\(945\) | 114.509 | 3.72499 | ||||||||
\(946\) | −70.4485 | −2.29048 | ||||||||
\(947\) | 27.2245 | 0.884679 | 0.442339 | − | 0.896848i | \(-0.354149\pi\) | ||||
0.442339 | + | 0.896848i | \(0.354149\pi\) | |||||||
\(948\) | 140.968 | 4.57842 | ||||||||
\(949\) | 4.06268 | 0.131880 | ||||||||
\(950\) | 1.64125 | 0.0532491 | ||||||||
\(951\) | 49.3925 | 1.60166 | ||||||||
\(952\) | 30.6132 | 0.992179 | ||||||||
\(953\) | 11.9329 | 0.386545 | 0.193273 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193273 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(954\) | 253.010 | 8.19151 | ||||||||
\(955\) | 33.8758 | 1.09619 | ||||||||
\(956\) | −77.6422 | −2.51113 | ||||||||
\(957\) | −74.8404 | −2.41925 | ||||||||
\(958\) | 67.0539 | 2.16641 | ||||||||
\(959\) | 43.4475 | 1.40299 | ||||||||
\(960\) | −79.3700 | −2.56166 | ||||||||
\(961\) | −18.9763 | −0.612139 | ||||||||
\(962\) | 3.96226 | 0.127748 | ||||||||
\(963\) | 173.557 | 5.59279 | ||||||||
\(964\) | −73.7112 | −2.37408 | ||||||||
\(965\) | −22.9021 | −0.737246 | ||||||||
\(966\) | −111.770 | −3.59613 | ||||||||
\(967\) | −50.6049 | −1.62734 | −0.813671 | − | 0.581325i | \(-0.802534\pi\) | ||||
−0.813671 | + | 0.581325i | \(0.802534\pi\) | |||||||
\(968\) | −11.4408 | −0.367721 | ||||||||
\(969\) | −6.37411 | −0.204766 | ||||||||
\(970\) | −77.2038 | −2.47887 | ||||||||
\(971\) | 1.98036 | 0.0635528 | 0.0317764 | − | 0.999495i | \(-0.489884\pi\) | ||||
0.0317764 | + | 0.999495i | \(0.489884\pi\) | |||||||
\(972\) | 232.686 | 7.46340 | ||||||||
\(973\) | −54.7779 | −1.75610 | ||||||||
\(974\) | −22.3280 | −0.715435 | ||||||||
\(975\) | 6.03707 | 0.193341 | ||||||||
\(976\) | 5.96120 | 0.190813 | ||||||||
\(977\) | −37.7398 | −1.20740 | −0.603702 | − | 0.797210i | \(-0.706308\pi\) | ||||
−0.603702 | + | 0.797210i | \(0.706308\pi\) | |||||||
\(978\) | −50.9400 | −1.62888 | ||||||||
\(979\) | −39.5106 | −1.26276 | ||||||||
\(980\) | 20.0808 | 0.641458 | ||||||||
\(981\) | −103.332 | −3.29913 | ||||||||
\(982\) | 53.4564 | 1.70586 | ||||||||
\(983\) | 11.7034 | 0.373280 | 0.186640 | − | 0.982428i | \(-0.440240\pi\) | ||||
0.186640 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(984\) | −7.83651 | −0.249819 | ||||||||
\(985\) | −6.04451 | −0.192594 | ||||||||
\(986\) | 53.5301 | 1.70475 | ||||||||
\(987\) | 126.539 | 4.02778 | ||||||||
\(988\) | −1.22829 | −0.0390770 | ||||||||
\(989\) | −34.9750 | −1.11214 | ||||||||
\(990\) | 140.689 | 4.47140 | ||||||||
\(991\) | 20.3129 | 0.645262 | 0.322631 | − | 0.946525i | \(-0.395433\pi\) | ||||
0.322631 | + | 0.946525i | \(0.395433\pi\) | |||||||
\(992\) | 24.0306 | 0.762972 | ||||||||
\(993\) | −50.6311 | −1.60673 | ||||||||
\(994\) | 41.9590 | 1.33086 | ||||||||
\(995\) | 43.1708 | 1.36861 | ||||||||
\(996\) | 106.259 | 3.36696 | ||||||||
\(997\) | −30.5373 | −0.967125 | −0.483563 | − | 0.875310i | \(-0.660658\pi\) | ||||
−0.483563 | + | 0.875310i | \(0.660658\pi\) | |||||||
\(998\) | −65.5163 | −2.07388 | ||||||||
\(999\) | 34.5505 | 1.09313 |
(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 | 6019.2.a.d.1.15 | ✓ | 123 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.d.1.15 | ✓ | 123 | 1.1 | even | 1 | trivial |