Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} + \cdots + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.3 | ||
Root | \(0.269375 + 0.466571i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.46 |
Dual form | 105.4.i.d.16.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.230625 | − | 0.399454i | −0.0815382 | − | 0.141228i | 0.822373 | − | 0.568949i | \(-0.192650\pi\) |
−0.903911 | + | 0.427721i | \(0.859317\pi\) | |||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 3.89362 | − | 6.74396i | 0.486703 | − | 0.842994i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 1.38375 | 0.0941522 | ||||||||
\(7\) | −18.0800 | + | 4.01437i | −0.976226 | + | 0.216756i | ||||
\(8\) | −7.28187 | −0.321816 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.15312 | + | 1.99727i | −0.0364650 | + | 0.0631592i | ||||
\(11\) | 12.1628 | − | 21.0667i | 0.333385 | − | 0.577440i | −0.649788 | − | 0.760115i | \(-0.725142\pi\) |
0.983173 | + | 0.182676i | \(0.0584758\pi\) | |||||||
\(12\) | 11.6809 | + | 20.2319i | 0.280998 | + | 0.486703i | ||||
\(13\) | −66.1258 | −1.41077 | −0.705384 | − | 0.708825i | \(-0.749226\pi\) | ||||
−0.705384 | + | 0.708825i | \(0.749226\pi\) | |||||||
\(14\) | 5.77325 | + | 6.29630i | 0.110212 | + | 0.120197i | ||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −29.4696 | − | 51.0429i | −0.460463 | − | 0.797545i | ||||
\(17\) | 9.80377 | − | 16.9806i | 0.139868 | − | 0.242259i | −0.787578 | − | 0.616215i | \(-0.788665\pi\) |
0.927447 | + | 0.373955i | \(0.121999\pi\) | |||||||
\(18\) | −2.07562 | + | 3.59509i | −0.0271794 | + | 0.0470761i | ||||
\(19\) | −32.3499 | − | 56.0317i | −0.390609 | − | 0.676555i | 0.601921 | − | 0.798556i | \(-0.294402\pi\) |
−0.992530 | + | 0.122001i | \(0.961069\pi\) | |||||||
\(20\) | −38.9362 | −0.435320 | ||||||||
\(21\) | 16.6903 | − | 52.9947i | 0.173434 | − | 0.550685i | ||||
\(22\) | −11.2202 | −0.108734 | ||||||||
\(23\) | −73.7290 | − | 127.702i | −0.668415 | − | 1.15773i | −0.978347 | − | 0.206970i | \(-0.933640\pi\) |
0.309932 | − | 0.950759i | \(-0.399694\pi\) | |||||||
\(24\) | 10.9228 | − | 18.9188i | 0.0929003 | − | 0.160908i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 15.2503 | + | 26.4142i | 0.115032 | + | 0.199241i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −43.3238 | + | 137.561i | −0.292408 | + | 0.928449i | ||||
\(29\) | 166.165 | 1.06400 | 0.532002 | − | 0.846743i | \(-0.321440\pi\) | ||||
0.532002 | + | 0.846743i | \(0.321440\pi\) | |||||||
\(30\) | −3.45937 | − | 5.99181i | −0.0210531 | − | 0.0364650i | ||||
\(31\) | −94.9410 | + | 164.443i | −0.550062 | + | 0.952735i | 0.448208 | + | 0.893929i | \(0.352062\pi\) |
−0.998269 | + | 0.0588054i | \(0.981271\pi\) | |||||||
\(32\) | −42.7203 | + | 73.9938i | −0.235999 | + | 0.408762i | ||||
\(33\) | 36.4885 | + | 63.2000i | 0.192480 | + | 0.333385i | ||||
\(34\) | −9.04398 | −0.0456185 | ||||||||
\(35\) | 62.5826 | + | 68.2526i | 0.302240 | + | 0.329623i | ||||
\(36\) | −70.0852 | −0.324469 | ||||||||
\(37\) | 37.9478 | + | 65.7275i | 0.168610 | + | 0.292041i | 0.937931 | − | 0.346821i | \(-0.112739\pi\) |
−0.769321 | + | 0.638862i | \(0.779405\pi\) | |||||||
\(38\) | −14.9214 | + | 25.8446i | −0.0636992 | + | 0.110330i | ||||
\(39\) | 99.1887 | − | 171.800i | 0.407254 | − | 0.705384i | ||||
\(40\) | 18.2047 | + | 31.5314i | 0.0719603 | + | 0.124639i | ||||
\(41\) | 186.313 | 0.709688 | 0.354844 | − | 0.934926i | \(-0.384534\pi\) | ||||
0.354844 | + | 0.934926i | \(0.384534\pi\) | |||||||
\(42\) | −25.0181 | + | 5.55488i | −0.0919139 | + | 0.0204080i | ||||
\(43\) | 110.890 | 0.393269 | 0.196634 | − | 0.980477i | \(-0.436999\pi\) | ||||
0.196634 | + | 0.980477i | \(0.436999\pi\) | |||||||
\(44\) | −94.7150 | − | 164.051i | −0.324519 | − | 0.562083i | ||||
\(45\) | −22.5000 | + | 38.9711i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −34.0075 | + | 58.9027i | −0.109003 | + | 0.188798i | ||||
\(47\) | 190.247 | + | 329.517i | 0.590433 | + | 1.02266i | 0.994174 | + | 0.107787i | \(0.0343764\pi\) |
−0.403741 | + | 0.914873i | \(0.632290\pi\) | |||||||
\(48\) | 176.818 | 0.531697 | ||||||||
\(49\) | 310.770 | − | 145.159i | 0.906034 | − | 0.423205i | ||||
\(50\) | 11.5312 | 0.0326153 | ||||||||
\(51\) | 29.4113 | + | 50.9419i | 0.0807531 | + | 0.139868i | ||||
\(52\) | −257.469 | + | 445.949i | −0.686625 | + | 1.18927i | ||||
\(53\) | 356.155 | − | 616.878i | 0.923049 | − | 1.59877i | 0.128381 | − | 0.991725i | \(-0.459022\pi\) |
0.794668 | − | 0.607044i | \(-0.207645\pi\) | |||||||
\(54\) | −6.22687 | − | 10.7853i | −0.0156920 | − | 0.0271794i | ||||
\(55\) | −121.628 | −0.298189 | ||||||||
\(56\) | 131.656 | − | 29.2321i | 0.314165 | − | 0.0697554i | ||||
\(57\) | 194.099 | 0.451037 | ||||||||
\(58\) | −38.3219 | − | 66.3754i | −0.0867570 | − | 0.150268i | ||||
\(59\) | −154.412 | + | 267.450i | −0.340724 | + | 0.590152i | −0.984567 | − | 0.175006i | \(-0.944006\pi\) |
0.643843 | + | 0.765158i | \(0.277339\pi\) | |||||||
\(60\) | 58.4044 | − | 101.159i | 0.125666 | − | 0.217660i | ||||
\(61\) | −244.847 | − | 424.087i | −0.513925 | − | 0.890144i | −0.999870 | − | 0.0161543i | \(-0.994858\pi\) |
0.485945 | − | 0.873990i | \(-0.338476\pi\) | |||||||
\(62\) | 87.5831 | 0.179404 | ||||||||
\(63\) | 112.649 | + | 122.855i | 0.225276 | + | 0.245686i | ||||
\(64\) | −432.104 | −0.843954 | ||||||||
\(65\) | 165.314 | + | 286.333i | 0.315457 | + | 0.546388i | ||||
\(66\) | 16.8303 | − | 29.1510i | 0.0313889 | − | 0.0543672i | ||||
\(67\) | −378.768 | + | 656.045i | −0.690655 | + | 1.19625i | 0.280969 | + | 0.959717i | \(0.409344\pi\) |
−0.971624 | + | 0.236532i | \(0.923989\pi\) | |||||||
\(68\) | −76.3444 | − | 132.232i | −0.136149 | − | 0.235817i | ||||
\(69\) | 442.374 | 0.771819 | ||||||||
\(70\) | 12.8307 | − | 40.7396i | 0.0219080 | − | 0.0695617i | ||||
\(71\) | −58.0222 | −0.0969855 | −0.0484927 | − | 0.998824i | \(-0.515442\pi\) | ||||
−0.0484927 | + | 0.998824i | \(0.515442\pi\) | |||||||
\(72\) | 32.7684 | + | 56.7565i | 0.0536360 | + | 0.0929003i | ||||
\(73\) | −29.0218 | + | 50.2673i | −0.0465308 | + | 0.0805938i | −0.888353 | − | 0.459162i | \(-0.848150\pi\) |
0.841822 | + | 0.539755i | \(0.181483\pi\) | |||||||
\(74\) | 17.5034 | − | 30.3168i | 0.0274964 | − | 0.0476251i | ||||
\(75\) | −37.5000 | − | 64.9519i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −503.834 | −0.760443 | ||||||||
\(77\) | −135.334 | + | 429.710i | −0.200296 | + | 0.635974i | ||||
\(78\) | −91.5015 | −0.132827 | ||||||||
\(79\) | −432.611 | − | 749.303i | −0.616107 | − | 1.06713i | −0.990189 | − | 0.139734i | \(-0.955375\pi\) |
0.374082 | − | 0.927396i | \(-0.377958\pi\) | |||||||
\(80\) | −147.348 | + | 255.214i | −0.205925 | + | 0.356673i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −42.9684 | − | 74.4235i | −0.0578667 | − | 0.100228i | ||||
\(83\) | 829.080 | 1.09643 | 0.548213 | − | 0.836339i | \(-0.315308\pi\) | ||||
0.548213 | + | 0.836339i | \(0.315308\pi\) | |||||||
\(84\) | −292.408 | − | 318.900i | −0.379813 | − | 0.414224i | ||||
\(85\) | −98.0377 | −0.125102 | ||||||||
\(86\) | −25.5740 | − | 44.2954i | −0.0320664 | − | 0.0555407i | ||||
\(87\) | −249.248 | + | 431.710i | −0.307151 | + | 0.532002i | ||||
\(88\) | −88.5682 | + | 153.405i | −0.107289 | + | 0.185829i | ||||
\(89\) | −546.665 | − | 946.852i | −0.651083 | − | 1.12771i | −0.982860 | − | 0.184351i | \(-0.940982\pi\) |
0.331778 | − | 0.943358i | \(-0.392352\pi\) | |||||||
\(90\) | 20.7562 | 0.0243100 | ||||||||
\(91\) | 1195.55 | − | 265.453i | 1.37723 | − | 0.305792i | ||||
\(92\) | −1148.29 | −1.30128 | ||||||||
\(93\) | −284.823 | − | 493.328i | −0.317578 | − | 0.550062i | ||||
\(94\) | 87.7514 | − | 151.990i | 0.0962858 | − | 0.166772i | ||||
\(95\) | −161.750 | + | 280.158i | −0.174686 | + | 0.302565i | ||||
\(96\) | −128.161 | − | 221.981i | −0.136254 | − | 0.235999i | ||||
\(97\) | 1111.21 | 1.16316 | 0.581581 | − | 0.813489i | \(-0.302434\pi\) | ||||
0.581581 | + | 0.813489i | \(0.302434\pi\) | |||||||
\(98\) | −129.656 | − | 90.6609i | −0.133645 | − | 0.0934504i | ||||
\(99\) | −218.931 | −0.222257 | ||||||||
\(100\) | 97.3406 | + | 168.599i | 0.0973406 | + | 0.168599i | ||||
\(101\) | −198.050 | + | 343.032i | −0.195116 | + | 0.337950i | −0.946938 | − | 0.321415i | \(-0.895842\pi\) |
0.751823 | + | 0.659365i | \(0.229175\pi\) | |||||||
\(102\) | 13.5660 | − | 23.4969i | 0.0131689 | − | 0.0228093i | ||||
\(103\) | −845.383 | − | 1464.25i | −0.808719 | − | 1.40074i | −0.913751 | − | 0.406274i | \(-0.866828\pi\) |
0.105032 | − | 0.994469i | \(-0.466506\pi\) | |||||||
\(104\) | 481.519 | 0.454008 | ||||||||
\(105\) | −271.199 | + | 60.2155i | −0.252060 | + | 0.0559660i | ||||
\(106\) | −328.553 | −0.301055 | ||||||||
\(107\) | −859.661 | − | 1488.98i | −0.776697 | − | 1.34528i | −0.933836 | − | 0.357702i | \(-0.883560\pi\) |
0.157139 | − | 0.987577i | \(-0.449773\pi\) | |||||||
\(108\) | 105.128 | − | 182.087i | 0.0936660 | − | 0.162234i | ||||
\(109\) | 611.860 | − | 1059.77i | 0.537666 | − | 0.931265i | −0.461363 | − | 0.887211i | \(-0.652639\pi\) |
0.999029 | − | 0.0440534i | \(-0.0140272\pi\) | |||||||
\(110\) | 28.0505 | + | 48.5850i | 0.0243138 | + | 0.0421127i | ||||
\(111\) | −227.687 | −0.194694 | ||||||||
\(112\) | 737.714 | + | 804.551i | 0.622388 | + | 0.678776i | ||||
\(113\) | −1247.96 | −1.03892 | −0.519460 | − | 0.854495i | \(-0.673867\pi\) | ||||
−0.519460 | + | 0.854495i | \(0.673867\pi\) | |||||||
\(114\) | −44.7642 | − | 77.5338i | −0.0367768 | − | 0.0636992i | ||||
\(115\) | −368.645 | + | 638.511i | −0.298924 | + | 0.517752i | ||||
\(116\) | 646.985 | − | 1120.61i | 0.517854 | − | 0.896949i | ||||
\(117\) | 297.566 | + | 515.399i | 0.235128 | + | 0.407254i | ||||
\(118\) | 142.445 | 0.111128 | ||||||||
\(119\) | −109.085 | + | 346.365i | −0.0840322 | + | 0.266817i | ||||
\(120\) | −109.228 | −0.0830926 | ||||||||
\(121\) | 369.631 | + | 640.219i | 0.277709 | + | 0.481006i | ||||
\(122\) | −112.936 | + | 195.610i | −0.0838090 | + | 0.145162i | ||||
\(123\) | −279.470 | + | 484.055i | −0.204869 | + | 0.354844i | ||||
\(124\) | 739.329 | + | 1280.56i | 0.535433 | + | 0.927398i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 23.0952 | − | 73.3313i | 0.0163292 | − | 0.0518482i | ||||
\(127\) | 389.193 | 0.271931 | 0.135966 | − | 0.990714i | \(-0.456586\pi\) | ||||
0.135966 | + | 0.990714i | \(0.456586\pi\) | |||||||
\(128\) | 441.417 | + | 764.556i | 0.304813 | + | 0.527952i | ||||
\(129\) | −166.335 | + | 288.100i | −0.113527 | + | 0.196634i | ||||
\(130\) | 76.2513 | − | 132.071i | 0.0514437 | − | 0.0891031i | ||||
\(131\) | 1116.00 | + | 1932.97i | 0.744316 | + | 1.28919i | 0.950514 | + | 0.310683i | \(0.100558\pi\) |
−0.206197 | + | 0.978510i | \(0.566109\pi\) | |||||||
\(132\) | 568.290 | 0.374722 | ||||||||
\(133\) | 809.817 | + | 883.186i | 0.527970 | + | 0.575804i | ||||
\(134\) | 349.413 | 0.225259 | ||||||||
\(135\) | −67.5000 | − | 116.913i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | −71.3898 | + | 123.651i | −0.0450119 | + | 0.0779629i | ||||
\(137\) | −259.449 | + | 449.379i | −0.161797 | + | 0.280241i | −0.935513 | − | 0.353291i | \(-0.885062\pi\) |
0.773716 | + | 0.633533i | \(0.218396\pi\) | |||||||
\(138\) | −102.022 | − | 176.708i | −0.0629328 | − | 0.109003i | ||||
\(139\) | 643.835 | 0.392873 | 0.196437 | − | 0.980517i | \(-0.437063\pi\) | ||||
0.196437 | + | 0.980517i | \(0.437063\pi\) | |||||||
\(140\) | 703.966 | − | 156.304i | 0.424971 | − | 0.0943581i | ||||
\(141\) | −1141.48 | −0.681774 | ||||||||
\(142\) | 13.3814 | + | 23.1772i | 0.00790802 | + | 0.0136971i | ||||
\(143\) | −804.277 | + | 1393.05i | −0.470329 | + | 0.814634i | ||||
\(144\) | −265.227 | + | 459.386i | −0.153488 | + | 0.265848i | ||||
\(145\) | −415.413 | − | 719.517i | −0.237918 | − | 0.412087i | ||||
\(146\) | 26.7726 | 0.0151762 | ||||||||
\(147\) | −89.0198 | + | 1025.14i | −0.0499472 | + | 0.575186i | ||||
\(148\) | 591.018 | 0.328252 | ||||||||
\(149\) | −1468.37 | − | 2543.30i | −0.807341 | − | 1.39836i | −0.914699 | − | 0.404135i | \(-0.867572\pi\) |
0.107358 | − | 0.994220i | \(-0.465761\pi\) | |||||||
\(150\) | −17.2969 | + | 29.9591i | −0.00941522 | + | 0.0163076i | ||||
\(151\) | 1024.22 | − | 1774.00i | 0.551984 | − | 0.956064i | −0.446148 | − | 0.894959i | \(-0.647204\pi\) |
0.998131 | − | 0.0611046i | \(-0.0194623\pi\) | |||||||
\(152\) | 235.568 | + | 408.015i | 0.125704 | + | 0.217726i | ||||
\(153\) | −176.468 | −0.0932456 | ||||||||
\(154\) | 202.861 | − | 45.0421i | 0.106149 | − | 0.0235688i | ||||
\(155\) | 949.410 | 0.491990 | ||||||||
\(156\) | −772.407 | − | 1337.85i | −0.396423 | − | 0.686625i | ||||
\(157\) | 267.714 | − | 463.694i | 0.136088 | − | 0.235712i | −0.789924 | − | 0.613204i | \(-0.789880\pi\) |
0.926013 | + | 0.377492i | \(0.123214\pi\) | |||||||
\(158\) | −199.542 | + | 345.616i | −0.100473 | + | 0.174024i | ||||
\(159\) | 1068.46 | + | 1850.63i | 0.532923 | + | 0.923049i | ||||
\(160\) | 427.203 | 0.211084 | ||||||||
\(161\) | 1845.66 | + | 2012.88i | 0.903468 | + | 0.985322i | ||||
\(162\) | 37.3612 | 0.0181196 | ||||||||
\(163\) | 301.890 | + | 522.888i | 0.145066 | + | 0.251262i | 0.929398 | − | 0.369080i | \(-0.120327\pi\) |
−0.784331 | + | 0.620342i | \(0.786994\pi\) | |||||||
\(164\) | 725.433 | − | 1256.49i | 0.345407 | − | 0.598263i | ||||
\(165\) | 182.443 | − | 316.000i | 0.0860796 | − | 0.149094i | ||||
\(166\) | −191.207 | − | 331.180i | −0.0894007 | − | 0.154847i | ||||
\(167\) | −1246.61 | −0.577638 | −0.288819 | − | 0.957384i | \(-0.593263\pi\) | ||||
−0.288819 | + | 0.957384i | \(0.593263\pi\) | |||||||
\(168\) | −121.537 | + | 385.900i | −0.0558140 | + | 0.177219i | ||||
\(169\) | 2175.62 | 0.990268 | ||||||||
\(170\) | 22.6099 | + | 39.1616i | 0.0102006 | + | 0.0176680i | ||||
\(171\) | −291.149 | + | 504.285i | −0.130203 | + | 0.225518i | ||||
\(172\) | 431.764 | − | 747.837i | 0.191405 | − | 0.331523i | ||||
\(173\) | −1035.97 | − | 1794.35i | −0.455278 | − | 0.788564i | 0.543426 | − | 0.839457i | \(-0.317127\pi\) |
−0.998704 | + | 0.0508924i | \(0.983793\pi\) | |||||||
\(174\) | 229.931 | 0.100178 | ||||||||
\(175\) | 139.086 | − | 441.622i | 0.0600794 | − | 0.190763i | ||||
\(176\) | −1433.74 | −0.614045 | ||||||||
\(177\) | −463.236 | − | 802.349i | −0.196717 | − | 0.340724i | ||||
\(178\) | −252.149 | + | 436.735i | −0.106176 | + | 0.183903i | ||||
\(179\) | −1378.07 | + | 2386.88i | −0.575428 | + | 0.996670i | 0.420568 | + | 0.907261i | \(0.361831\pi\) |
−0.995995 | + | 0.0894085i | \(0.971502\pi\) | |||||||
\(180\) | 175.213 | + | 303.478i | 0.0725534 | + | 0.125666i | ||||
\(181\) | −2331.83 | −0.957589 | −0.478795 | − | 0.877927i | \(-0.658926\pi\) | ||||
−0.478795 | + | 0.877927i | \(0.658926\pi\) | |||||||
\(182\) | −381.760 | − | 416.348i | −0.155483 | − | 0.169570i | ||||
\(183\) | 1469.08 | 0.593429 | ||||||||
\(184\) | 536.884 | + | 929.911i | 0.215107 | + | 0.372576i | ||||
\(185\) | 189.739 | − | 328.637i | 0.0754048 | − | 0.130605i | ||||
\(186\) | −131.375 | + | 227.548i | −0.0517895 | + | 0.0897021i | ||||
\(187\) | −238.483 | − | 413.065i | −0.0932601 | − | 0.161531i | ||||
\(188\) | 2963.00 | 1.14946 | ||||||||
\(189\) | −488.159 | + | 108.388i | −0.187875 | + | 0.0417146i | ||||
\(190\) | 149.214 | 0.0569743 | ||||||||
\(191\) | 2037.79 | + | 3529.56i | 0.771987 | + | 1.33712i | 0.936472 | + | 0.350742i | \(0.114070\pi\) |
−0.164485 | + | 0.986380i | \(0.552596\pi\) | |||||||
\(192\) | 648.156 | − | 1122.64i | 0.243628 | − | 0.421977i | ||||
\(193\) | 1982.63 | − | 3434.02i | 0.739446 | − | 1.28076i | −0.213300 | − | 0.976987i | \(-0.568421\pi\) |
0.952745 | − | 0.303771i | \(-0.0982456\pi\) | |||||||
\(194\) | −256.274 | − | 443.879i | −0.0948421 | − | 0.164271i | ||||
\(195\) | −991.887 | −0.364259 | ||||||||
\(196\) | 231.073 | − | 2661.01i | 0.0842103 | − | 0.969757i | ||||
\(197\) | 421.063 | 0.152282 | 0.0761409 | − | 0.997097i | \(-0.475740\pi\) | ||||
0.0761409 | + | 0.997097i | \(0.475740\pi\) | |||||||
\(198\) | 50.4910 | + | 87.4529i | 0.0181224 | + | 0.0313889i | ||||
\(199\) | −2681.86 | + | 4645.11i | −0.955336 | + | 1.65469i | −0.221739 | + | 0.975106i | \(0.571173\pi\) |
−0.733597 | + | 0.679585i | \(0.762160\pi\) | |||||||
\(200\) | 91.0233 | − | 157.657i | 0.0321816 | − | 0.0557402i | ||||
\(201\) | −1136.30 | − | 1968.14i | −0.398750 | − | 0.690655i | ||||
\(202\) | 182.701 | 0.0636376 | ||||||||
\(203\) | −3004.26 | + | 667.048i | −1.03871 | + | 0.230629i | ||||
\(204\) | 458.066 | 0.157211 | ||||||||
\(205\) | −465.783 | − | 806.759i | −0.158691 | − | 0.274861i | ||||
\(206\) | −389.933 | + | 675.384i | −0.131883 | + | 0.228428i | ||||
\(207\) | −663.561 | + | 1149.32i | −0.222805 | + | 0.385910i | ||||
\(208\) | 1948.70 | + | 3375.25i | 0.649606 | + | 1.12515i | ||||
\(209\) | −1573.87 | −0.520893 | ||||||||
\(210\) | 86.5987 | + | 94.4445i | 0.0284566 | + | 0.0310347i | ||||
\(211\) | −4090.88 | −1.33473 | −0.667365 | − | 0.744731i | \(-0.732578\pi\) | ||||
−0.667365 | + | 0.744731i | \(0.732578\pi\) | |||||||
\(212\) | −2773.47 | − | 4803.78i | −0.898502 | − | 1.55625i | ||||
\(213\) | 87.0333 | − | 150.746i | 0.0279973 | − | 0.0484927i | ||||
\(214\) | −396.519 | + | 686.790i | −0.126661 | + | 0.219383i | ||||
\(215\) | −277.225 | − | 480.167i | −0.0879376 | − | 0.152312i | ||||
\(216\) | −196.610 | −0.0619335 | ||||||||
\(217\) | 1056.40 | − | 3354.25i | 0.330474 | − | 1.04931i | ||||
\(218\) | −564.441 | −0.175361 | ||||||||
\(219\) | −87.0655 | − | 150.802i | −0.0268646 | − | 0.0465308i | ||||
\(220\) | −473.575 | + | 820.256i | −0.145129 | + | 0.251371i | ||||
\(221\) | −648.282 | + | 1122.86i | −0.197322 | + | 0.341772i | ||||
\(222\) | 52.5102 | + | 90.9504i | 0.0158750 | + | 0.0274964i | ||||
\(223\) | −4356.21 | −1.30813 | −0.654066 | − | 0.756437i | \(-0.726938\pi\) | ||||
−0.654066 | + | 0.756437i | \(0.726938\pi\) | |||||||
\(224\) | 475.343 | − | 1509.30i | 0.141787 | − | 0.450198i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 287.810 | + | 498.502i | 0.0847117 | + | 0.146725i | ||||
\(227\) | 2493.37 | − | 4318.64i | 0.729034 | − | 1.26272i | −0.228258 | − | 0.973601i | \(-0.573303\pi\) |
0.957292 | − | 0.289123i | \(-0.0933638\pi\) | |||||||
\(228\) | 755.750 | − | 1309.00i | 0.219521 | − | 0.380222i | ||||
\(229\) | 293.923 | + | 509.090i | 0.0848166 | + | 0.146907i | 0.905313 | − | 0.424745i | \(-0.139636\pi\) |
−0.820496 | + | 0.571652i | \(0.806303\pi\) | |||||||
\(230\) | 340.075 | 0.0974951 | ||||||||
\(231\) | −913.419 | − | 996.174i | −0.260167 | − | 0.283738i | ||||
\(232\) | −1209.99 | −0.342414 | ||||||||
\(233\) | 137.363 | + | 237.919i | 0.0386220 | + | 0.0668953i | 0.884690 | − | 0.466179i | \(-0.154370\pi\) |
−0.846068 | + | 0.533075i | \(0.821036\pi\) | |||||||
\(234\) | 137.252 | − | 237.728i | 0.0383439 | − | 0.0664135i | ||||
\(235\) | 951.235 | − | 1647.59i | 0.264050 | − | 0.457348i | ||||
\(236\) | 1202.45 | + | 2082.70i | 0.331663 | + | 0.574458i | ||||
\(237\) | 2595.66 | 0.711420 | ||||||||
\(238\) | 163.515 | − | 36.3059i | 0.0445340 | − | 0.00988806i | ||||
\(239\) | 813.576 | 0.220192 | 0.110096 | − | 0.993921i | \(-0.464884\pi\) | ||||
0.110096 | + | 0.993921i | \(0.464884\pi\) | |||||||
\(240\) | −442.044 | − | 765.643i | −0.118891 | − | 0.205925i | ||||
\(241\) | 1099.32 | − | 1904.08i | 0.293832 | − | 0.508933i | −0.680880 | − | 0.732395i | \(-0.738403\pi\) |
0.974713 | + | 0.223462i | \(0.0717359\pi\) | |||||||
\(242\) | 170.492 | − | 295.301i | 0.0452878 | − | 0.0784408i | ||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3813.36 | −1.00051 | ||||||||
\(245\) | −1405.48 | − | 982.774i | −0.366502 | − | 0.256274i | ||||
\(246\) | 257.811 | 0.0668187 | ||||||||
\(247\) | 2139.16 | + | 3705.14i | 0.551059 | + | 0.954463i | ||||
\(248\) | 691.348 | − | 1197.45i | 0.177019 | − | 0.306605i | ||||
\(249\) | −1243.62 | + | 2154.01i | −0.316511 | + | 0.548213i | ||||
\(250\) | −28.8281 | − | 49.9318i | −0.00729300 | − | 0.0126318i | ||||
\(251\) | 4122.98 | 1.03681 | 0.518407 | − | 0.855134i | \(-0.326525\pi\) | ||||
0.518407 | + | 0.855134i | \(0.326525\pi\) | |||||||
\(252\) | 1267.14 | − | 281.348i | 0.316755 | − | 0.0703304i | ||||
\(253\) | −3587.01 | −0.891358 | ||||||||
\(254\) | −89.7576 | − | 155.465i | −0.0221728 | − | 0.0384044i | ||||
\(255\) | 147.057 | − | 254.709i | 0.0361139 | − | 0.0625511i | ||||
\(256\) | −1524.81 | + | 2641.06i | −0.372269 | + | 0.644789i | ||||
\(257\) | −3561.19 | − | 6168.16i | −0.864362 | − | 1.49712i | −0.867679 | − | 0.497124i | \(-0.834389\pi\) |
0.00331747 | − | 0.999994i | \(-0.498944\pi\) | |||||||
\(258\) | 153.444 | 0.0370271 | ||||||||
\(259\) | −949.949 | − | 1036.01i | −0.227903 | − | 0.248551i | ||||
\(260\) | 2574.69 | 0.614136 | ||||||||
\(261\) | −747.744 | − | 1295.13i | −0.177334 | − | 0.307151i | ||||
\(262\) | 514.755 | − | 891.582i | 0.121380 | − | 0.210237i | ||||
\(263\) | −1786.87 | + | 3094.95i | −0.418947 | + | 0.725638i | −0.995834 | − | 0.0911862i | \(-0.970934\pi\) |
0.576886 | + | 0.816824i | \(0.304267\pi\) | |||||||
\(264\) | −265.705 | − | 460.214i | −0.0619431 | − | 0.107289i | ||||
\(265\) | −3561.55 | −0.825601 | ||||||||
\(266\) | 166.028 | − | 527.170i | 0.0382701 | − | 0.121514i | ||||
\(267\) | 3279.99 | 0.751806 | ||||||||
\(268\) | 2949.56 | + | 5108.79i | 0.672287 | + | 1.16444i | ||||
\(269\) | −2668.25 | + | 4621.55i | −0.604781 | + | 1.04751i | 0.387305 | + | 0.921952i | \(0.373406\pi\) |
−0.992086 | + | 0.125560i | \(0.959927\pi\) | |||||||
\(270\) | −31.1344 | + | 53.9263i | −0.00701769 | + | 0.0121550i | ||||
\(271\) | −851.237 | − | 1474.39i | −0.190808 | − | 0.330489i | 0.754710 | − | 0.656058i | \(-0.227777\pi\) |
−0.945518 | + | 0.325569i | \(0.894444\pi\) | |||||||
\(272\) | −1155.65 | −0.257617 | ||||||||
\(273\) | −1103.66 | + | 3504.31i | −0.244676 | + | 0.776889i | ||||
\(274\) | 239.342 | 0.0527707 | ||||||||
\(275\) | 304.071 | + | 526.666i | 0.0666770 | + | 0.115488i | ||||
\(276\) | 1722.44 | − | 2983.35i | 0.375647 | − | 0.650639i | ||||
\(277\) | 336.684 | − | 583.154i | 0.0730302 | − | 0.126492i | −0.827198 | − | 0.561911i | \(-0.810066\pi\) |
0.900228 | + | 0.435419i | \(0.143400\pi\) | |||||||
\(278\) | −148.484 | − | 257.182i | −0.0320342 | − | 0.0554848i | ||||
\(279\) | 1708.94 | 0.366708 | ||||||||
\(280\) | −455.718 | − | 497.006i | −0.0972656 | − | 0.106078i | ||||
\(281\) | 8340.39 | 1.77063 | 0.885313 | − | 0.464995i | \(-0.153944\pi\) | ||||
0.885313 | + | 0.464995i | \(0.153944\pi\) | |||||||
\(282\) | 263.254 | + | 455.970i | 0.0555906 | + | 0.0962858i | ||||
\(283\) | 680.220 | − | 1178.18i | 0.142880 | − | 0.247475i | −0.785700 | − | 0.618607i | \(-0.787697\pi\) |
0.928580 | + | 0.371133i | \(0.121031\pi\) | |||||||
\(284\) | −225.917 | + | 391.299i | −0.0472031 | + | 0.0817582i | ||||
\(285\) | −485.249 | − | 840.475i | −0.100855 | − | 0.174686i | ||||
\(286\) | 741.946 | 0.153399 | ||||||||
\(287\) | −3368.53 | + | 747.929i | −0.692816 | + | 0.153829i | ||||
\(288\) | 768.966 | 0.157332 | ||||||||
\(289\) | 2264.27 | + | 3921.83i | 0.460874 | + | 0.798257i | ||||
\(290\) | −191.609 | + | 331.877i | −0.0387989 | + | 0.0672017i | ||||
\(291\) | −1666.82 | + | 2887.02i | −0.335776 | + | 0.581581i | ||||
\(292\) | 226.000 | + | 391.444i | 0.0452934 | + | 0.0784504i | ||||
\(293\) | 4688.92 | 0.934914 | 0.467457 | − | 0.884016i | \(-0.345170\pi\) | ||||
0.467457 | + | 0.884016i | \(0.345170\pi\) | |||||||
\(294\) | 430.027 | − | 200.864i | 0.0853051 | − | 0.0398457i | ||||
\(295\) | 1544.12 | 0.304753 | ||||||||
\(296\) | −276.331 | − | 478.619i | −0.0542615 | − | 0.0939836i | ||||
\(297\) | 328.397 | − | 568.800i | 0.0641600 | − | 0.111128i | ||||
\(298\) | −677.287 | + | 1173.10i | −0.131658 | + | 0.228039i | ||||
\(299\) | 4875.38 | + | 8444.41i | 0.942979 | + | 1.63329i | ||||
\(300\) | −584.044 | −0.112399 | ||||||||
\(301\) | −2004.89 | + | 445.153i | −0.383919 | + | 0.0852432i | ||||
\(302\) | −944.840 | −0.180031 | ||||||||
\(303\) | −594.149 | − | 1029.10i | −0.112650 | − | 0.195116i | ||||
\(304\) | −1906.68 | + | 3302.46i | −0.359722 | + | 0.623057i | ||||
\(305\) | −1224.23 | + | 2120.43i | −0.229834 | + | 0.398084i | ||||
\(306\) | 40.6979 | + | 70.4908i | 0.00760309 | + | 0.0131689i | ||||
\(307\) | −469.928 | −0.0873622 | −0.0436811 | − | 0.999046i | \(-0.513909\pi\) | ||||
−0.0436811 | + | 0.999046i | \(0.513909\pi\) | |||||||
\(308\) | 2371.01 | + | 2585.82i | 0.438638 | + | 0.478379i | ||||
\(309\) | 5072.30 | 0.933829 | ||||||||
\(310\) | −218.958 | − | 379.246i | −0.0401160 | − | 0.0694830i | ||||
\(311\) | 4128.43 | − | 7150.65i | 0.752739 | − | 1.30378i | −0.193752 | − | 0.981051i | \(-0.562066\pi\) |
0.946491 | − | 0.322731i | \(-0.104601\pi\) | |||||||
\(312\) | −722.279 | + | 1251.02i | −0.131061 | + | 0.227004i | ||||
\(313\) | −3106.28 | − | 5380.23i | −0.560949 | − | 0.971593i | −0.997414 | − | 0.0718713i | \(-0.977103\pi\) |
0.436465 | − | 0.899721i | \(-0.356230\pi\) | |||||||
\(314\) | −246.966 | −0.0443857 | ||||||||
\(315\) | 250.355 | − | 794.920i | 0.0447806 | − | 0.142186i | ||||
\(316\) | −6737.69 | −1.19945 | ||||||||
\(317\) | 3533.63 | + | 6120.43i | 0.626084 | + | 1.08441i | 0.988330 | + | 0.152327i | \(0.0486767\pi\) |
−0.362246 | + | 0.932083i | \(0.617990\pi\) | |||||||
\(318\) | 492.829 | − | 853.605i | 0.0869072 | − | 0.150528i | ||||
\(319\) | 2021.04 | − | 3500.55i | 0.354723 | − | 0.614398i | ||||
\(320\) | 1080.26 | + | 1871.07i | 0.188714 | + | 0.326862i | ||||
\(321\) | 5157.97 | 0.896852 | ||||||||
\(322\) | 378.397 | − | 1201.48i | 0.0654883 | − | 0.207937i | ||||
\(323\) | −1268.60 | −0.218536 | ||||||||
\(324\) | 315.384 | + | 546.260i | 0.0540781 | + | 0.0936660i | ||||
\(325\) | 826.572 | − | 1431.67i | 0.141077 | − | 0.244352i | ||||
\(326\) | 139.247 | − | 241.182i | 0.0236569 | − | 0.0409750i | ||||
\(327\) | 1835.58 | + | 3179.32i | 0.310422 | + | 0.537666i | ||||
\(328\) | −1356.71 | −0.228389 | ||||||||
\(329\) | −4762.46 | − | 5193.94i | −0.798064 | − | 0.870368i | ||||
\(330\) | −168.303 | −0.0280751 | ||||||||
\(331\) | 3929.08 | + | 6805.36i | 0.652452 | + | 1.13008i | 0.982526 | + | 0.186125i | \(0.0595930\pi\) |
−0.330074 | + | 0.943955i | \(0.607074\pi\) | |||||||
\(332\) | 3228.13 | − | 5591.28i | 0.533634 | − | 0.924281i | ||||
\(333\) | 341.530 | − | 591.547i | 0.0562034 | − | 0.0973471i | ||||
\(334\) | 287.499 | + | 497.963i | 0.0470996 | + | 0.0815789i | ||||
\(335\) | 3787.68 | 0.617740 | ||||||||
\(336\) | −3196.86 | + | 709.811i | −0.519056 | + | 0.115248i | ||||
\(337\) | 1340.37 | 0.216661 | 0.108331 | − | 0.994115i | \(-0.465449\pi\) | ||||
0.108331 | + | 0.994115i | \(0.465449\pi\) | |||||||
\(338\) | −501.752 | − | 869.060i | −0.0807447 | − | 0.139854i | ||||
\(339\) | 1871.94 | − | 3242.29i | 0.299910 | − | 0.519460i | ||||
\(340\) | −381.722 | + | 661.162i | −0.0608876 | + | 0.105460i | ||||
\(341\) | 2309.50 | + | 4000.18i | 0.366765 | + | 0.635255i | ||||
\(342\) | 268.585 | 0.0424661 | ||||||||
\(343\) | −5035.98 | + | 3872.02i | −0.792762 | + | 0.609531i | ||||
\(344\) | −807.486 | −0.126560 | ||||||||
\(345\) | −1105.93 | − | 1915.53i | −0.172584 | − | 0.298924i | ||||
\(346\) | −477.840 | + | 827.642i | −0.0742451 | + | 0.128596i | ||||
\(347\) | 2328.74 | − | 4033.50i | 0.360270 | − | 0.624005i | −0.627736 | − | 0.778427i | \(-0.716018\pi\) |
0.988005 | + | 0.154422i | \(0.0493514\pi\) | |||||||
\(348\) | 1940.95 | + | 3361.83i | 0.298983 | + | 0.517854i | ||||
\(349\) | −4780.79 | −0.733265 | −0.366633 | − | 0.930366i | \(-0.619489\pi\) | ||||
−0.366633 | + | 0.930366i | \(0.619489\pi\) | |||||||
\(350\) | −208.484 | + | 46.2907i | −0.0318399 | + | 0.00706955i | ||||
\(351\) | −1785.40 | −0.271503 | ||||||||
\(352\) | 1039.20 | + | 1799.95i | 0.157357 | + | 0.272550i | ||||
\(353\) | 5497.32 | − | 9521.63i | 0.828874 | − | 1.43565i | −0.0700477 | − | 0.997544i | \(-0.522315\pi\) |
0.898922 | − | 0.438109i | \(-0.144352\pi\) | |||||||
\(354\) | −213.668 | + | 370.083i | −0.0320800 | + | 0.0555641i | ||||
\(355\) | 145.056 | + | 251.244i | 0.0216866 | + | 0.0375623i | ||||
\(356\) | −8514.03 | −1.26754 | ||||||||
\(357\) | −736.255 | − | 802.959i | −0.109151 | − | 0.119040i | ||||
\(358\) | 1271.27 | 0.187677 | ||||||||
\(359\) | −2396.24 | − | 4150.41i | −0.352280 | − | 0.610168i | 0.634368 | − | 0.773031i | \(-0.281260\pi\) |
−0.986649 | + | 0.162863i | \(0.947927\pi\) | |||||||
\(360\) | 163.842 | − | 283.783i | 0.0239868 | − | 0.0415463i | ||||
\(361\) | 1336.47 | − | 2314.83i | 0.194849 | − | 0.337488i | ||||
\(362\) | 537.779 | + | 931.460i | 0.0780802 | + | 0.135239i | ||||
\(363\) | −2217.78 | −0.320671 | ||||||||
\(364\) | 2864.82 | − | 9096.32i | 0.412521 | − | 1.30983i | ||||
\(365\) | 290.218 | 0.0416184 | ||||||||
\(366\) | −338.807 | − | 586.830i | −0.0483872 | − | 0.0838090i | ||||
\(367\) | −3274.38 | + | 5671.39i | −0.465725 | + | 0.806660i | −0.999234 | − | 0.0391349i | \(-0.987540\pi\) |
0.533509 | + | 0.845795i | \(0.320873\pi\) | |||||||
\(368\) | −4345.53 | + | 7526.67i | −0.615561 | + | 1.06618i | ||||
\(369\) | −838.409 | − | 1452.17i | −0.118281 | − | 0.204869i | ||||
\(370\) | −175.034 | −0.0245935 | ||||||||
\(371\) | −3962.89 | + | 12582.9i | −0.554563 | + | 1.76084i | ||||
\(372\) | −4435.98 | −0.618265 | ||||||||
\(373\) | 6425.33 | + | 11129.0i | 0.891933 | + | 1.54487i | 0.837555 | + | 0.546353i | \(0.183984\pi\) |
0.0543786 | + | 0.998520i | \(0.482682\pi\) | |||||||
\(374\) | −110.000 | + | 190.526i | −0.0152085 | + | 0.0263419i | ||||
\(375\) | −187.500 | + | 324.760i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −1385.35 | − | 2399.50i | −0.190011 | − | 0.329109i | ||||
\(377\) | −10987.8 | −1.50106 | ||||||||
\(378\) | 155.878 | + | 170.000i | 0.0212103 | + | 0.0231319i | ||||
\(379\) | 9958.10 | 1.34964 | 0.674820 | − | 0.737983i | \(-0.264221\pi\) | ||||
0.674820 | + | 0.737983i | \(0.264221\pi\) | |||||||
\(380\) | 1259.58 | + | 2181.66i | 0.170040 | + | 0.294518i | ||||
\(381\) | −583.789 | + | 1011.15i | −0.0784998 | + | 0.135966i | ||||
\(382\) | 939.932 | − | 1628.01i | 0.125893 | − | 0.218053i | ||||
\(383\) | −6437.58 | − | 11150.2i | −0.858864 | − | 1.48760i | −0.873014 | − | 0.487696i | \(-0.837837\pi\) |
0.0141497 | − | 0.999900i | \(-0.495496\pi\) | |||||||
\(384\) | −2648.50 | −0.351968 | ||||||||
\(385\) | 2199.04 | − | 488.261i | 0.291099 | − | 0.0646340i | ||||
\(386\) | −1828.98 | −0.241172 | ||||||||
\(387\) | −499.005 | − | 864.301i | −0.0655448 | − | 0.113527i | ||||
\(388\) | 4326.65 | − | 7493.98i | 0.566114 | − | 0.980539i | ||||
\(389\) | 4459.26 | − | 7723.67i | 0.581218 | − | 1.00670i | −0.414118 | − | 0.910223i | \(-0.635910\pi\) |
0.995335 | − | 0.0964750i | \(-0.0307568\pi\) | |||||||
\(390\) | 228.754 | + | 396.213i | 0.0297010 | + | 0.0514437i | ||||
\(391\) | −2891.29 | −0.373961 | ||||||||
\(392\) | −2262.98 | + | 1057.03i | −0.291576 | + | 0.136194i | ||||
\(393\) | −6696.00 | −0.859462 | ||||||||
\(394\) | −97.1077 | − | 168.196i | −0.0124168 | − | 0.0215065i | ||||
\(395\) | −2163.05 | + | 3746.52i | −0.275532 | + | 0.477235i | ||||
\(396\) | −852.435 | + | 1476.46i | −0.108173 | + | 0.187361i | ||||
\(397\) | −729.059 | − | 1262.77i | −0.0921673 | − | 0.159638i | 0.816256 | − | 0.577691i | \(-0.196046\pi\) |
−0.908423 | + | 0.418053i | \(0.862713\pi\) | |||||||
\(398\) | 2474.01 | 0.311586 | ||||||||
\(399\) | −3509.31 | + | 779.187i | −0.440314 | + | 0.0977647i | ||||
\(400\) | 1473.48 | 0.184185 | ||||||||
\(401\) | −4313.13 | − | 7470.56i | −0.537126 | − | 0.930329i | −0.999057 | − | 0.0434135i | \(-0.986177\pi\) |
0.461931 | − | 0.886916i | \(-0.347157\pi\) | |||||||
\(402\) | −524.120 | + | 907.802i | −0.0650267 | + | 0.112630i | ||||
\(403\) | 6278.05 | − | 10873.9i | 0.776010 | − | 1.34409i | ||||
\(404\) | 1542.26 | + | 2671.28i | 0.189927 | + | 0.328963i | ||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 959.313 | + | 1046.23i | 0.117266 | + | 0.127890i | ||||
\(407\) | 1846.21 | 0.224848 | ||||||||
\(408\) | −214.169 | − | 370.952i | −0.0259876 | − | 0.0450119i | ||||
\(409\) | 2949.72 | − | 5109.06i | 0.356612 | − | 0.617670i | −0.630781 | − | 0.775961i | \(-0.717265\pi\) |
0.987392 | + | 0.158291i | \(0.0505985\pi\) | |||||||
\(410\) | −214.842 | + | 372.118i | −0.0258788 | + | 0.0448234i | ||||
\(411\) | −778.348 | − | 1348.14i | −0.0934138 | − | 0.161797i | ||||
\(412\) | −13166.4 | −1.57442 | ||||||||
\(413\) | 1718.12 | − | 5455.34i | 0.204705 | − | 0.649976i | ||||
\(414\) | 612.135 | 0.0726685 | ||||||||
\(415\) | −2072.70 | − | 3590.02i | −0.245168 | − | 0.424644i | ||||
\(416\) | 2824.91 | − | 4892.90i | 0.332940 | − | 0.576668i | ||||
\(417\) | −965.752 | + | 1672.73i | −0.113413 | + | 0.196437i | ||||
\(418\) | 362.973 | + | 628.688i | 0.0424727 | + | 0.0735649i | ||||
\(419\) | −8973.53 | −1.04627 | −0.523133 | − | 0.852251i | \(-0.675237\pi\) | ||||
−0.523133 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(420\) | −649.858 | + | 2063.41i | −0.0754995 | + | 0.239724i | ||||
\(421\) | 7513.39 | 0.869787 | 0.434894 | − | 0.900482i | \(-0.356786\pi\) | ||||
0.434894 | + | 0.900482i | \(0.356786\pi\) | |||||||
\(422\) | 943.459 | + | 1634.12i | 0.108831 | + | 0.188502i | ||||
\(423\) | 1712.22 | − | 2965.66i | 0.196811 | − | 0.340887i | ||||
\(424\) | −2593.47 | + | 4492.02i | −0.297052 | + | 0.514509i | ||||
\(425\) | 245.094 | + | 424.516i | 0.0279737 | + | 0.0484519i | ||||
\(426\) | −80.2882 | −0.00913140 | ||||||||
\(427\) | 6129.26 | + | 6684.57i | 0.694650 | + | 0.757585i | ||||
\(428\) | −13388.8 | −1.51208 | ||||||||
\(429\) | −2412.83 | − | 4179.15i | −0.271545 | − | 0.470329i | ||||
\(430\) | −127.870 | + | 221.477i | −0.0143405 | + | 0.0248386i | ||||
\(431\) | −22.1507 | + | 38.3662i | −0.00247555 | + | 0.00428778i | −0.867261 | − | 0.497855i | \(-0.834121\pi\) |
0.864785 | + | 0.502142i | \(0.167455\pi\) | |||||||
\(432\) | −795.680 | − | 1378.16i | −0.0886161 | − | 0.153488i | ||||
\(433\) | 357.810 | 0.0397119 | 0.0198560 | − | 0.999803i | \(-0.493679\pi\) | ||||
0.0198560 | + | 0.999803i | \(0.493679\pi\) | |||||||
\(434\) | −1583.50 | + | 351.591i | −0.175139 | + | 0.0388869i | ||||
\(435\) | 2492.48 | 0.274725 | ||||||||
\(436\) | −4764.71 | − | 8252.72i | −0.523367 | − | 0.906499i | ||||
\(437\) | −4770.25 | + | 8262.32i | −0.522179 | + | 0.904440i | ||||
\(438\) | −40.1590 | + | 69.5574i | −0.00438098 | + | 0.00758808i | ||||
\(439\) | −2381.77 | − | 4125.35i | −0.258943 | − | 0.448502i | 0.707016 | − | 0.707197i | \(-0.250041\pi\) |
−0.965959 | + | 0.258696i | \(0.916707\pi\) | |||||||
\(440\) | 885.682 | 0.0959619 | ||||||||
\(441\) | −2529.87 | − | 1768.99i | −0.273174 | − | 0.191015i | ||||
\(442\) | 598.040 | 0.0643572 | ||||||||
\(443\) | 4481.17 | + | 7761.61i | 0.480602 | + | 0.832427i | 0.999752 | − | 0.0222561i | \(-0.00708491\pi\) |
−0.519150 | + | 0.854683i | \(0.673752\pi\) | |||||||
\(444\) | −886.526 | + | 1535.51i | −0.0947583 | + | 0.164126i | ||||
\(445\) | −2733.33 | + | 4734.26i | −0.291173 | + | 0.504327i | ||||
\(446\) | 1004.65 | + | 1740.11i | 0.106663 | + | 0.184745i | ||||
\(447\) | 8810.24 | 0.932237 | ||||||||
\(448\) | 7812.43 | − | 1734.63i | 0.823890 | − | 0.182932i | ||||
\(449\) | 14967.7 | 1.57321 | 0.786604 | − | 0.617457i | \(-0.211837\pi\) | ||||
0.786604 | + | 0.617457i | \(0.211837\pi\) | |||||||
\(450\) | −51.8906 | − | 89.8772i | −0.00543588 | − | 0.00941522i | ||||
\(451\) | 2266.10 | − | 3924.99i | 0.236599 | − | 0.409802i | ||||
\(452\) | −4859.08 | + | 8416.16i | −0.505645 | + | 0.875803i | ||||
\(453\) | 3072.65 | + | 5321.99i | 0.318688 | + | 0.551984i | ||||
\(454\) | −2300.13 | −0.237777 | ||||||||
\(455\) | −4138.32 | − | 4513.26i | −0.426390 | − | 0.465021i | ||||
\(456\) | −1413.41 | −0.145151 | ||||||||
\(457\) | 7024.34 | + | 12166.5i | 0.719004 | + | 1.24535i | 0.961395 | + | 0.275172i | \(0.0887349\pi\) |
−0.242391 | + | 0.970179i | \(0.577932\pi\) | |||||||
\(458\) | 135.572 | − | 234.818i | 0.0138316 | − | 0.0239570i | ||||
\(459\) | 264.702 | − | 458.477i | 0.0269177 | − | 0.0466228i | ||||
\(460\) | 2870.73 | + | 4972.25i | 0.290975 | + | 0.503983i | ||||
\(461\) | 7891.75 | 0.797300 | 0.398650 | − | 0.917103i | \(-0.369479\pi\) | ||||
0.398650 | + | 0.917103i | \(0.369479\pi\) | |||||||
\(462\) | −187.269 | + | 594.612i | −0.0188583 | + | 0.0598784i | ||||
\(463\) | −12775.4 | −1.28234 | −0.641172 | − | 0.767397i | \(-0.721551\pi\) | ||||
−0.641172 | + | 0.767397i | \(0.721551\pi\) | |||||||
\(464\) | −4896.83 | − | 8481.55i | −0.489934 | − | 0.848591i | ||||
\(465\) | −1424.12 | + | 2466.64i | −0.142025 | + | 0.245995i | ||||
\(466\) | 63.3586 | − | 109.740i | 0.00629835 | − | 0.0109091i | ||||
\(467\) | 5122.58 | + | 8872.58i | 0.507591 | + | 0.879173i | 0.999961 | + | 0.00878746i | \(0.00279717\pi\) |
−0.492371 | + | 0.870386i | \(0.663869\pi\) | |||||||
\(468\) | 4634.44 | 0.457750 | ||||||||
\(469\) | 4214.50 | − | 13381.8i | 0.414941 | − | 1.31751i | ||||
\(470\) | −877.514 | −0.0861206 | ||||||||
\(471\) | 803.142 | + | 1391.08i | 0.0785707 | + | 0.136088i | ||||
\(472\) | 1124.41 | − | 1947.53i | 0.109651 | − | 0.189920i | ||||
\(473\) | 1348.74 | − | 2336.08i | 0.131110 | − | 0.227089i | ||||
\(474\) | −598.625 | − | 1036.85i | −0.0580079 | − | 0.100473i | ||||
\(475\) | 1617.50 | 0.156244 | ||||||||
\(476\) | 1911.13 | + | 2084.28i | 0.184027 | + | 0.200699i | ||||
\(477\) | −6410.79 | −0.615366 | ||||||||
\(478\) | −187.631 | − | 324.986i | −0.0179540 | − | 0.0310973i | ||||
\(479\) | −7692.56 | + | 13323.9i | −0.733783 | + | 1.27095i | 0.221473 | + | 0.975167i | \(0.428914\pi\) |
−0.955255 | + | 0.295782i | \(0.904420\pi\) | |||||||
\(480\) | −640.805 | + | 1109.91i | −0.0609346 | + | 0.105542i | ||||
\(481\) | −2509.33 | − | 4346.28i | −0.237870 | − | 0.412003i | ||||
\(482\) | −1014.12 | −0.0958343 | ||||||||
\(483\) | −7998.10 | + | 1775.85i | −0.753470 | + | 0.167296i | ||||
\(484\) | 5756.81 | 0.540647 | ||||||||
\(485\) | −2778.03 | − | 4811.70i | −0.260091 | − | 0.450490i | ||||
\(486\) | −56.0419 | + | 97.0674i | −0.00523068 | + | 0.00905980i | ||||
\(487\) | 2000.90 | − | 3465.67i | 0.186180 | − | 0.322473i | −0.757794 | − | 0.652494i | \(-0.773723\pi\) |
0.943973 | + | 0.330021i | \(0.107056\pi\) | |||||||
\(488\) | 1782.94 | + | 3088.14i | 0.165389 | + | 0.286463i | ||||
\(489\) | −1811.34 | −0.167508 | ||||||||
\(490\) | −68.4340 | + | 788.078i | −0.00630925 | + | 0.0726566i | ||||
\(491\) | 4696.86 | 0.431703 | 0.215852 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215852 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(492\) | 2176.30 | + | 3769.46i | 0.199421 | + | 0.345407i | ||||
\(493\) | 1629.05 | − | 2821.59i | 0.148821 | − | 0.257765i | ||||
\(494\) | 986.689 | − | 1709.00i | 0.0898648 | − | 0.155650i | ||||
\(495\) | 547.328 | + | 947.999i | 0.0496981 | + | 0.0860796i | ||||
\(496\) | 11191.5 | 1.01313 | ||||||||
\(497\) | 1049.04 | − | 232.922i | 0.0946797 | − | 0.0210221i | ||||
\(498\) | 1147.24 | 0.103231 | ||||||||
\(499\) | −1267.89 | − | 2196.04i | −0.113744 | − | 0.197011i | 0.803533 | − | 0.595260i | \(-0.202951\pi\) |
−0.917277 | + | 0.398250i | \(0.869618\pi\) | |||||||
\(500\) | 486.703 | − | 842.994i | 0.0435320 | − | 0.0753997i | ||||
\(501\) | 1869.91 | − | 3238.79i | 0.166750 | − | 0.288819i | ||||
\(502\) | −950.863 | − | 1646.94i | −0.0845400 | − | 0.146428i | ||||
\(503\) | 6098.69 | 0.540610 | 0.270305 | − | 0.962775i | \(-0.412875\pi\) | ||||
0.270305 | + | 0.962775i | \(0.412875\pi\) | |||||||
\(504\) | −820.293 | − | 894.611i | −0.0724975 | − | 0.0790658i | ||||
\(505\) | 1980.50 | 0.174517 | ||||||||
\(506\) | 827.255 | + | 1432.85i | 0.0726798 | + | 0.125885i | ||||
\(507\) | −3263.43 | + | 5652.42i | −0.285866 | + | 0.495134i | ||||
\(508\) | 1515.37 | − | 2624.70i | 0.132350 | − | 0.229237i | ||||
\(509\) | −1986.06 | − | 3439.95i | −0.172948 | − | 0.299554i | 0.766501 | − | 0.642243i | \(-0.221996\pi\) |
−0.939449 | + | 0.342688i | \(0.888663\pi\) | |||||||
\(510\) | −135.660 | −0.0117786 | ||||||||
\(511\) | 322.922 | − | 1025.34i | 0.0279555 | − | 0.0887635i | ||||
\(512\) | 8469.31 | 0.731043 | ||||||||
\(513\) | −873.448 | − | 1512.86i | −0.0751728 | − | 0.130203i | ||||
\(514\) | −1642.60 | + | 2845.07i | −0.140957 | + | 0.244145i | ||||
\(515\) | −4226.92 | + | 7321.23i | −0.361670 | + | 0.626431i | ||||
\(516\) | 1295.29 | + | 2243.51i | 0.110508 | + | 0.191405i | ||||
\(517\) | 9255.77 | 0.787366 | ||||||||
\(518\) | −194.758 | + | 618.392i | −0.0165197 | + | 0.0524528i | ||||
\(519\) | 6215.80 | 0.525710 | ||||||||
\(520\) | −1203.80 | − | 2085.04i | −0.101519 | − | 0.175837i | ||||
\(521\) | −4056.88 | + | 7026.72i | −0.341142 | + | 0.590876i | −0.984645 | − | 0.174568i | \(-0.944147\pi\) |
0.643503 | + | 0.765444i | \(0.277480\pi\) | |||||||
\(522\) | −344.897 | + | 597.379i | −0.0289190 | + | 0.0500892i | ||||
\(523\) | −503.888 | − | 872.760i | −0.0421290 | − | 0.0729696i | 0.844192 | − | 0.536041i | \(-0.180081\pi\) |
−0.886321 | + | 0.463071i | \(0.846747\pi\) | |||||||
\(524\) | 17381.1 | 1.44904 | ||||||||
\(525\) | 938.739 | + | 1023.79i | 0.0780380 | + | 0.0851082i | ||||
\(526\) | 1648.39 | 0.136641 | ||||||||
\(527\) | 1861.56 | + | 3224.32i | 0.153873 | + | 0.266515i | ||||
\(528\) | 2150.60 | − | 3724.96i | 0.177260 | − | 0.307023i | ||||
\(529\) | −4788.42 | + | 8293.78i | −0.393558 | + | 0.681662i | ||||
\(530\) | 821.382 | + | 1422.68i | 0.0673180 | + | 0.116598i | ||||
\(531\) | 2779.42 | 0.227150 | ||||||||
\(532\) | 9109.29 | − | 2022.57i | 0.742364 | − | 0.164830i | ||||
\(533\) | −12320.1 | −1.00121 | ||||||||
\(534\) | −756.448 | − | 1310.21i | −0.0613009 | − | 0.106176i | ||||
\(535\) | −4298.31 | + | 7444.88i | −0.347349 | + | 0.601627i | ||||
\(536\) | 2758.14 | − | 4777.23i | 0.222264 | − | 0.384972i | ||||
\(537\) | −4134.20 | − | 7160.64i | −0.332223 | − | 0.575428i | ||||
\(538\) | 2461.46 | 0.197251 | ||||||||
\(539\) | 721.823 | − | 8312.43i | 0.0576829 | − | 0.664270i | ||||
\(540\) | −1051.28 | −0.0837775 | ||||||||
\(541\) | 10424.4 | + | 18055.7i | 0.828432 | + | 1.43489i | 0.899268 | + | 0.437398i | \(0.144100\pi\) |
−0.0708364 | + | 0.997488i | \(0.522567\pi\) | |||||||
\(542\) | −392.633 | + | 680.060i | −0.0311163 | + | 0.0538950i | ||||
\(543\) | 3497.75 | − | 6058.28i | 0.276432 | − | 0.478795i | ||||
\(544\) | 837.641 | + | 1450.84i | 0.0660176 | + | 0.114346i | ||||
\(545\) | −6118.60 | −0.480903 | ||||||||
\(546\) | 1654.34 | − | 367.321i | 0.129669 | − | 0.0287910i | ||||
\(547\) | −9029.66 | −0.705814 | −0.352907 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352907 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(548\) | 2020.40 | + | 3499.43i | 0.157495 | + | 0.272789i | ||||
\(549\) | −2203.62 | + | 3816.78i | −0.171308 | + | 0.296715i | ||||
\(550\) | 140.253 | − | 242.925i | 0.0108734 | − | 0.0188334i | ||||
\(551\) | −5375.43 | − | 9310.52i | −0.415610 | − | 0.719857i | ||||
\(552\) | −3221.31 | −0.248384 | ||||||||
\(553\) | 10829.6 | + | 11810.7i | 0.832766 | + | 0.908215i | ||||
\(554\) | −310.591 | −0.0238190 | ||||||||
\(555\) | 569.217 | + | 985.912i | 0.0435350 | + | 0.0754048i | ||||
\(556\) | 2506.85 | − | 4341.99i | 0.191212 | − | 0.331190i | ||||
\(557\) | −2990.54 | + | 5179.77i | −0.227492 | + | 0.394028i | −0.957064 | − | 0.289876i | \(-0.906386\pi\) |
0.729572 | + | 0.683904i | \(0.239719\pi\) | |||||||
\(558\) | −394.124 | − | 682.643i | −0.0299007 | − | 0.0517895i | ||||
\(559\) | −7332.68 | −0.554811 | ||||||||
\(560\) | 1639.52 | − | 5205.77i | 0.123719 | − | 0.392829i | ||||
\(561\) | 1430.90 | 0.107687 | ||||||||
\(562\) | −1923.50 | − | 3331.60i | −0.144374 | − | 0.250063i | ||||
\(563\) | −98.2176 | + | 170.118i | −0.00735236 | + | 0.0127347i | −0.869678 | − | 0.493619i | \(-0.835674\pi\) |
0.862326 | + | 0.506354i | \(0.169007\pi\) | |||||||
\(564\) | −4444.50 | + | 7698.10i | −0.331821 | + | 0.574731i | ||||
\(565\) | 3119.89 | + | 5403.81i | 0.232309 | + | 0.402372i | ||||
\(566\) | −627.503 | −0.0466006 | ||||||||
\(567\) | 450.638 | − | 1430.86i | 0.0333775 | − | 0.105979i | ||||
\(568\) | 422.510 | 0.0312115 | ||||||||
\(569\) | −8629.01 | − | 14945.9i | −0.635759 | − | 1.10117i | −0.986354 | − | 0.164639i | \(-0.947354\pi\) |
0.350595 | − | 0.936527i | \(-0.385979\pi\) | |||||||
\(570\) | −223.821 | + | 387.669i | −0.0164471 | + | 0.0284872i | ||||
\(571\) | −6360.59 | + | 11016.9i | −0.466169 | + | 0.807428i | −0.999253 | − | 0.0386336i | \(-0.987699\pi\) |
0.533084 | + | 0.846062i | \(0.321033\pi\) | |||||||
\(572\) | 6263.11 | + | 10848.0i | 0.457821 | + | 0.792969i | ||||
\(573\) | −12226.8 | −0.891414 | ||||||||
\(574\) | 1075.63 | + | 1173.08i | 0.0782160 | + | 0.0853023i | ||||
\(575\) | 3686.45 | 0.267366 | ||||||||
\(576\) | 1944.47 | + | 3367.92i | 0.140659 | + | 0.243628i | ||||
\(577\) | −9891.17 | + | 17132.0i | −0.713648 | + | 1.23607i | 0.249831 | + | 0.968289i | \(0.419625\pi\) |
−0.963479 | + | 0.267785i | \(0.913708\pi\) | |||||||
\(578\) | 1044.40 | − | 1808.95i | 0.0751576 | − | 0.130177i | ||||
\(579\) | 5947.90 | + | 10302.1i | 0.426919 | + | 0.739446i | ||||
\(580\) | −6469.85 | −0.463183 | ||||||||
\(581\) | −14989.7 | + | 3328.23i | −1.07036 | + | 0.237656i | ||||
\(582\) | 1537.64 | 0.109514 | ||||||||
\(583\) | −8663.71 | − | 15006.0i | −0.615461 | − | 1.06601i | ||||
\(584\) | 211.333 | − | 366.040i | 0.0149744 | − | 0.0259364i | ||||
\(585\) | 1487.83 | − | 2577.00i | 0.105152 | − | 0.182129i | ||||
\(586\) | −1081.38 | − | 1873.01i | −0.0762312 | − | 0.132036i | ||||
\(587\) | 20560.9 | 1.44572 | 0.722860 | − | 0.690994i | \(-0.242827\pi\) | ||||
0.722860 | + | 0.690994i | \(0.242827\pi\) | |||||||
\(588\) | 6566.90 | + | 4591.86i | 0.460569 | + | 0.322050i | ||||
\(589\) | 12285.3 | 0.859437 | ||||||||
\(590\) | −356.113 | − | 616.805i | −0.0248490 | − | 0.0430398i | ||||
\(591\) | −631.595 | + | 1093.95i | −0.0439600 | + | 0.0761409i | ||||
\(592\) | 2236.61 | − | 3873.93i | 0.155277 | − | 0.268948i | ||||
\(593\) | −127.642 | − | 221.082i | −0.00883917 | − | 0.0153099i | 0.861572 | − | 0.507635i | \(-0.169480\pi\) |
−0.870411 | + | 0.492326i | \(0.836147\pi\) | |||||||
\(594\) | −302.946 | −0.0209260 | ||||||||
\(595\) | 1772.52 | − | 393.560i | 0.122128 | − | 0.0271166i | ||||
\(596\) | −22869.2 | −1.57174 | ||||||||
\(597\) | −8045.57 | − | 13935.3i | −0.551564 | − | 0.955336i | ||||
\(598\) | 2248.77 | − | 3894.98i | 0.153778 | − | 0.266351i | ||||
\(599\) | 1466.63 | − | 2540.29i | 0.100042 | − | 0.173278i | −0.811660 | − | 0.584130i | \(-0.801436\pi\) |
0.911702 | + | 0.410853i | \(0.134769\pi\) | |||||||
\(600\) | 273.070 | + | 472.971i | 0.0185801 | + | 0.0321816i | ||||
\(601\) | 8366.35 | 0.567838 | 0.283919 | − | 0.958848i | \(-0.408365\pi\) | ||||
0.283919 | + | 0.958848i | \(0.408365\pi\) | |||||||
\(602\) | 640.195 | + | 698.196i | 0.0433428 | + | 0.0472697i | ||||
\(603\) | 6817.82 | 0.460436 | ||||||||
\(604\) | −7975.83 | − | 13814.5i | −0.537304 | − | 0.930639i | ||||
\(605\) | 1848.15 | − | 3201.10i | 0.124195 | − | 0.215112i | ||||
\(606\) | −274.051 | + | 474.671i | −0.0183706 | + | 0.0318188i | ||||
\(607\) | −12169.2 | − | 21077.6i | −0.813725 | − | 1.40941i | −0.910240 | − | 0.414081i | \(-0.864103\pi\) |
0.0965150 | − | 0.995332i | \(-0.469230\pi\) | |||||||
\(608\) | 5528.00 | 0.368733 | ||||||||
\(609\) | 2773.35 | − | 8805.87i | 0.184535 | − | 0.585931i | ||||
\(610\) | 1129.36 | 0.0749611 | ||||||||
\(611\) | −12580.2 | − | 21789.6i | −0.832965 | − | 1.44274i | ||||
\(612\) | −687.100 | + | 1190.09i | −0.0453829 | + | 0.0786056i | ||||
\(613\) | −5686.39 | + | 9849.11i | −0.374667 | + | 0.648943i | −0.990277 | − | 0.139108i | \(-0.955576\pi\) |
0.615610 | + | 0.788051i | \(0.288910\pi\) | |||||||
\(614\) | 108.377 | + | 187.715i | 0.00712336 | + | 0.0123380i | ||||
\(615\) | 2794.70 | 0.183241 | ||||||||
\(616\) | 985.486 | − | 3129.09i | 0.0644584 | − | 0.204667i | ||||
\(617\) | −4455.61 | −0.290723 | −0.145362 | − | 0.989379i | \(-0.546435\pi\) | ||||
−0.145362 | + | 0.989379i | \(0.546435\pi\) | |||||||
\(618\) | −1169.80 | − | 2026.15i | −0.0761427 | − | 0.131883i | ||||
\(619\) | −10318.7 | + | 17872.5i | −0.670021 | + | 1.16051i | 0.307876 | + | 0.951426i | \(0.400382\pi\) |
−0.977898 | + | 0.209084i | \(0.932952\pi\) | |||||||
\(620\) | 3696.65 | − | 6402.78i | 0.239453 | − | 0.414745i | ||||
\(621\) | −1990.68 | − | 3447.96i | −0.128637 | − | 0.222805i | ||||
\(622\) | −3808.47 | −0.245508 | ||||||||
\(623\) | 13684.7 | + | 14924.5i | 0.880041 | + | 0.959773i | ||||
\(624\) | −11692.2 | −0.750101 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −1432.77 | + | 2481.63i | −0.0914776 | + | 0.158444i | ||||
\(627\) | 2360.80 | − | 4089.03i | 0.150369 | − | 0.260447i | ||||
\(628\) | −2084.75 | − | 3610.90i | −0.132469 | − | 0.229444i | ||||
\(629\) | 1488.13 | 0.0943330 | ||||||||
\(630\) | −375.272 | + | 83.3232i | −0.0237321 | + | 0.00526933i | ||||
\(631\) | −24223.2 | −1.52823 | −0.764114 | − | 0.645081i | \(-0.776823\pi\) | ||||
−0.764114 | + | 0.645081i | \(0.776823\pi\) | |||||||
\(632\) | 3150.21 | + | 5456.33i | 0.198273 | + | 0.343419i | ||||
\(633\) | 6136.32 | − | 10628.4i | 0.385303 | − | 0.667365i | ||||
\(634\) | 1629.89 | − | 2823.05i | 0.102100 | − | 0.176842i | ||||
\(635\) | −972.982 | − | 1685.25i | −0.0608057 | − | 0.105319i | ||||
\(636\) | 16640.8 | 1.03750 | ||||||||
\(637\) | −20549.9 | + | 9598.77i | −1.27820 | + | 0.597044i | ||||
\(638\) | −1864.41 | −0.115694 | ||||||||
\(639\) | 261.100 | + | 452.238i | 0.0161642 | + | 0.0279973i | ||||
\(640\) | 2207.08 | − | 3822.78i | 0.136317 | − | 0.236107i | ||||
\(641\) | 7186.97 | − | 12448.2i | 0.442852 | − | 0.767043i | −0.555048 | − | 0.831819i | \(-0.687300\pi\) |
0.997900 | + | 0.0647760i | \(0.0206333\pi\) | |||||||
\(642\) | −1189.56 | − | 2060.37i | −0.0731278 | − | 0.126661i | ||||
\(643\) | −6980.39 | −0.428118 | −0.214059 | − | 0.976821i | \(-0.568668\pi\) | ||||
−0.214059 | + | 0.976821i | \(0.568668\pi\) | |||||||
\(644\) | 20761.1 | − | 4609.66i | 1.27034 | − | 0.282059i | ||||
\(645\) | 1663.35 | 0.101542 | ||||||||
\(646\) | 292.572 | + | 506.749i | 0.0178190 | + | 0.0308635i | ||||
\(647\) | 11900.9 | − | 20612.9i | 0.723140 | − | 1.25252i | −0.236595 | − | 0.971608i | \(-0.576031\pi\) |
0.959735 | − | 0.280907i | \(-0.0906353\pi\) | |||||||
\(648\) | 294.916 | − | 510.809i | 0.0178787 | − | 0.0309668i | ||||
\(649\) | 3756.18 | + | 6505.89i | 0.227185 | + | 0.393496i | ||||
\(650\) | −762.513 | −0.0460126 | ||||||||
\(651\) | 7129.99 | + | 7775.97i | 0.429257 | + | 0.468148i | ||||
\(652\) | 4701.78 | 0.282417 | ||||||||
\(653\) | 1144.87 | + | 1982.97i | 0.0686096 | + | 0.118835i | 0.898289 | − | 0.439404i | \(-0.144810\pi\) |
−0.829680 | + | 0.558239i | \(0.811477\pi\) | |||||||
\(654\) | 846.662 | − | 1466.46i | 0.0506225 | − | 0.0876807i | ||||
\(655\) | 5580.00 | − | 9664.85i | 0.332868 | − | 0.576545i | ||||
\(656\) | −5490.57 | − | 9509.95i | −0.326785 | − | 0.566008i | ||||
\(657\) | 522.393 | 0.0310205 | ||||||||
\(658\) | −976.398 | + | 3100.24i | −0.0578480 | + | 0.183677i | ||||
\(659\) | 9991.32 | 0.590602 | 0.295301 | − | 0.955404i | \(-0.404580\pi\) | ||||
0.295301 | + | 0.955404i | \(0.404580\pi\) | |||||||
\(660\) | −1420.73 | − | 2460.77i | −0.0837904 | − | 0.145129i | ||||
\(661\) | −8567.85 | + | 14839.9i | −0.504161 | + | 0.873233i | 0.495827 | + | 0.868421i | \(0.334865\pi\) |
−0.999988 | + | 0.00481187i | \(0.998468\pi\) | |||||||
\(662\) | 1812.29 | − | 3138.97i | 0.106400 | − | 0.184290i | ||||
\(663\) | −1944.85 | − | 3368.57i | −0.113924 | − | 0.197322i | ||||
\(664\) | −6037.25 | −0.352848 | ||||||||
\(665\) | 1799.77 | − | 5714.58i | 0.104950 | − | 0.333236i | ||||
\(666\) | −315.061 | −0.0183309 | ||||||||
\(667\) | −12251.2 | − | 21219.7i | −0.711196 | − | 1.23183i | ||||
\(668\) | −4853.83 | + | 8407.08i | −0.281138 | + | 0.486946i | ||||
\(669\) | 6534.32 | − | 11317.8i | 0.377625 | − | 0.654066i | ||||
\(670\) | −873.533 | − | 1513.00i | −0.0503695 | − | 0.0872425i | ||||
\(671\) | −11912.1 | −0.685339 | ||||||||
\(672\) | 3208.26 | + | 3498.93i | 0.184169 | + | 0.200854i | ||||
\(673\) | −29969.3 | −1.71654 | −0.858271 | − | 0.513196i | \(-0.828461\pi\) | ||||
−0.858271 | + | 0.513196i | \(0.828461\pi\) | |||||||
\(674\) | −309.124 | − | 535.418i | −0.0176662 | − | 0.0305987i | ||||
\(675\) | −337.500 | + | 584.567i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | 8471.04 | − | 14672.3i | 0.481966 | − | 0.834790i | ||||
\(677\) | −1592.07 | − | 2757.54i | −0.0903814 | − | 0.156545i | 0.817290 | − | 0.576226i | \(-0.195475\pi\) |
−0.907672 | + | 0.419681i | \(0.862142\pi\) | |||||||
\(678\) | −1726.86 | −0.0978166 | ||||||||
\(679\) | −20090.7 | + | 4460.82i | −1.13551 | + | 0.252122i | ||||
\(680\) | 713.898 | 0.0402599 | ||||||||
\(681\) | 7480.11 | + | 12955.9i | 0.420908 | + | 0.729034i | ||||
\(682\) | 1065.26 | − | 1845.08i | 0.0598107 | − | 0.103595i | ||||
\(683\) | 608.929 | − | 1054.70i | 0.0341142 | − | 0.0590876i | −0.848464 | − | 0.529253i | \(-0.822472\pi\) |
0.882578 | + | 0.470165i | \(0.155806\pi\) | |||||||
\(684\) | 2267.25 | + | 3926.99i | 0.126741 | + | 0.219521i | ||||
\(685\) | 2594.49 | 0.144716 | ||||||||
\(686\) | 2708.12 | + | 1118.66i | 0.150724 | + | 0.0622604i | ||||
\(687\) | −1763.54 | −0.0979378 | ||||||||
\(688\) | −3267.88 | − | 5660.14i | −0.181086 | − | 0.313649i | ||||
\(689\) | −23551.0 | + | 40791.5i | −1.30221 | + | 2.25549i | ||||
\(690\) | −510.112 | + | 883.540i | −0.0281444 | + | 0.0487475i | ||||
\(691\) | −546.615 | − | 946.766i | −0.0300929 | − | 0.0521225i | 0.850587 | − | 0.525835i | \(-0.176247\pi\) |
−0.880680 | + | 0.473712i | \(0.842914\pi\) | |||||||
\(692\) | −16134.7 | −0.886341 | ||||||||
\(693\) | 3958.26 | − | 878.870i | 0.216973 | − | 0.0481753i | ||||
\(694\) | −2148.27 | −0.117503 | ||||||||
\(695\) | −1609.59 | − | 2787.89i | −0.0878491 | − | 0.152159i | ||||
\(696\) | 1814.99 | − | 3143.65i | 0.0988463 | − | 0.171207i | ||||
\(697\) | 1826.57 | − | 3163.71i | 0.0992630 | − | 0.171928i | ||||
\(698\) | 1102.57 | + | 1909.71i | 0.0597892 | + | 0.103558i | ||||
\(699\) | −824.177 | −0.0445969 | ||||||||
\(700\) | −2436.73 | − | 2657.50i | −0.131571 | − | 0.143491i | ||||
\(701\) | −5736.18 | −0.309062 | −0.154531 | − | 0.987988i | \(-0.549387\pi\) | ||||
−0.154531 | + | 0.987988i | \(0.549387\pi\) | |||||||
\(702\) | 411.757 | + | 713.184i | 0.0221378 | + | 0.0383439i | ||||
\(703\) | 2455.21 | − | 4252.56i | 0.131721 | − | 0.228148i | ||||
\(704\) | −5255.62 | + | 9102.99i | −0.281361 | + | 0.487332i | ||||
\(705\) | 2853.70 | + | 4942.76i | 0.152449 | + | 0.264050i | ||||
\(706\) | −5071.27 | −0.270340 | ||||||||
\(707\) | 2203.67 | − | 6997.05i | 0.117224 | − | 0.372208i | ||||
\(708\) | −7214.67 | −0.382972 | ||||||||
\(709\) | 5958.32 | + | 10320.1i | 0.315613 | + | 0.546658i | 0.979568 | − | 0.201115i | \(-0.0644566\pi\) |
−0.663955 | + | 0.747773i | \(0.731123\pi\) | |||||||
\(710\) | 66.9068 | − | 115.886i | 0.00353658 | − | 0.00612553i | ||||
\(711\) | −3893.49 | + | 6743.73i | −0.205369 | + | 0.355710i | ||||
\(712\) | 3980.74 | + | 6894.85i | 0.209529 | + | 0.362915i | ||||
\(713\) | 27999.6 | 1.47068 | ||||||||
\(714\) | −150.947 | + | 479.283i | −0.00791182 | + | 0.0251214i | ||||
\(715\) | 8042.77 | 0.420675 | ||||||||
\(716\) | 10731.3 | + | 18587.2i | 0.560125 | + | 0.970164i | ||||
\(717\) | −1220.36 | + | 2113.73i | −0.0635639 | + | 0.110096i | ||||
\(718\) | −1105.27 | + | 1914.38i | −0.0574486 | + | 0.0995040i | ||||
\(719\) | 1828.06 | + | 3166.30i | 0.0948195 | + | 0.164232i | 0.909533 | − | 0.415631i | \(-0.136439\pi\) |
−0.814714 | + | 0.579863i | \(0.803106\pi\) | |||||||
\(720\) | 2652.27 | 0.137283 | ||||||||
\(721\) | 21162.5 | + | 23079.8i | 1.09311 | + | 1.19215i | ||||
\(722\) | −1232.89 | −0.0635504 | ||||||||
\(723\) | 3297.97 | + | 5712.25i | 0.169644 | + | 0.293832i | ||||
\(724\) | −9079.28 | + | 15725.8i | −0.466062 | + | 0.807243i | ||||
\(725\) | −2077.07 | + | 3597.58i | −0.106400 | + | 0.184291i | ||||
\(726\) | 511.476 | + | 885.903i | 0.0261469 | + | 0.0452878i | ||||
\(727\) | 22145.5 | 1.12975 | 0.564876 | − | 0.825176i | \(-0.308924\pi\) | ||||
0.564876 | + | 0.825176i | \(0.308924\pi\) | |||||||
\(728\) | −8705.84 | + | 1933.00i | −0.443214 | + | 0.0984087i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −66.9316 | − | 115.929i | −0.00339349 | − | 0.00587770i | ||||
\(731\) | 1087.14 | − | 1882.98i | 0.0550059 | − | 0.0952730i | ||||
\(732\) | 5720.05 | − | 9907.41i | 0.288824 | − | 0.500257i | ||||
\(733\) | 6567.55 | + | 11375.3i | 0.330938 | + | 0.573202i | 0.982696 | − | 0.185225i | \(-0.0593014\pi\) |
−0.651758 | + | 0.758427i | \(0.725968\pi\) | |||||||
\(734\) | 3020.61 | 0.151898 | ||||||||
\(735\) | 4661.55 | − | 2177.39i | 0.233937 | − | 0.109271i | ||||
\(736\) | 12598.9 | 0.630980 | ||||||||
\(737\) | 9213.79 | + | 15958.7i | 0.460508 | + | 0.797623i | ||||
\(738\) | −386.716 | + | 669.812i | −0.0192889 | + | 0.0334094i | ||||
\(739\) | 8126.92 | − | 14076.2i | 0.404538 | − | 0.700681i | −0.589729 | − | 0.807601i | \(-0.700766\pi\) |
0.994268 | + | 0.106920i | \(0.0340989\pi\) | |||||||
\(740\) | −1477.54 | − | 2559.18i | −0.0733995 | − | 0.127132i | ||||
\(741\) | −12835.0 | −0.636309 | ||||||||
\(742\) | 5940.22 | − | 1318.93i | 0.293898 | − | 0.0652554i | ||||
\(743\) | −708.312 | −0.0349737 | −0.0174869 | − | 0.999847i | \(-0.505567\pi\) | ||||
−0.0174869 | + | 0.999847i | \(0.505567\pi\) | |||||||
\(744\) | 2074.04 | + | 3592.35i | 0.102202 | + | 0.177019i | ||||
\(745\) | −7341.87 | + | 12716.5i | −0.361054 | + | 0.625364i | ||||
\(746\) | 2963.68 | − | 5133.25i | 0.145453 | − | 0.251933i | ||||
\(747\) | −3730.86 | − | 6462.04i | −0.182738 | − | 0.316511i | ||||
\(748\) | −3714.26 | −0.181560 | ||||||||
\(749\) | 21519.9 | + | 23469.6i | 1.04983 | + | 1.14494i | ||||
\(750\) | 172.969 | 0.00842123 | ||||||||
\(751\) | −5923.12 | − | 10259.1i | −0.287800 | − | 0.498484i | 0.685484 | − | 0.728087i | \(-0.259590\pi\) |
−0.973284 | + | 0.229603i | \(0.926257\pi\) | |||||||
\(752\) | 11213.0 | − | 19421.5i | 0.543745 | − | 0.941794i | ||||
\(753\) | −6184.48 | + | 10711.8i | −0.299303 | + | 0.518407i | ||||
\(754\) | 2534.06 | + | 4389.12i | 0.122394 | + | 0.211993i | ||||
\(755\) | −10242.2 | −0.493709 | ||||||||
\(756\) | −1169.74 | + | 3714.14i | −0.0562740 | + | 0.178680i | ||||
\(757\) | −17808.6 | −0.855040 | −0.427520 | − | 0.904006i | \(-0.640613\pi\) | ||||
−0.427520 | + | 0.904006i | \(0.640613\pi\) | |||||||
\(758\) | −2296.59 | − | 3977.81i | −0.110047 | − | 0.190607i | ||||
\(759\) | 5380.52 | − | 9319.33i | 0.257313 | − | 0.445679i | ||||
\(760\) | 1177.84 | − | 2040.08i | 0.0562167 | − | 0.0973702i | ||||
\(761\) | −16821.3 | − | 29135.3i | −0.801275 | − | 1.38785i | −0.918777 | − | 0.394776i | \(-0.870822\pi\) |
0.117502 | − | 0.993073i | \(-0.462511\pi\) | |||||||
\(762\) | 538.545 | 0.0256029 | ||||||||
\(763\) | −6808.09 | + | 21616.9i | −0.323027 | + | 1.02567i | ||||
\(764\) | 31737.6 | 1.50291 | ||||||||
\(765\) | 441.170 | + | 764.128i | 0.0208504 | + | 0.0361139i | ||||
\(766\) | −2969.33 | + | 5143.03i | −0.140060 | + | 0.242592i | ||||
\(767\) | 10210.6 | − | 17685.3i | 0.480683 | − | 0.832568i | ||||
\(768\) | −4574.44 | − | 7923.17i | −0.214930 | − | 0.372269i | ||||
\(769\) | 12365.6 | 0.579864 | 0.289932 | − | 0.957047i | \(-0.406367\pi\) | ||||
0.289932 | + | 0.957047i | \(0.406367\pi\) | |||||||
\(770\) | −702.191 | − | 765.809i | −0.0328639 | − | 0.0358413i | ||||
\(771\) | 21367.1 | 0.998079 | ||||||||
\(772\) | −15439.3 | − | 26741.6i | −0.719781 | − | 1.24670i | ||||
\(773\) | 510.178 | − | 883.655i | 0.0237385 | − | 0.0411162i | −0.853912 | − | 0.520417i | \(-0.825776\pi\) |
0.877651 | + | 0.479301i | \(0.159110\pi\) | |||||||
\(774\) | −230.166 | + | 398.659i | −0.0106888 | + | 0.0185136i | ||||
\(775\) | −2373.53 | − | 4111.07i | −0.110012 | − | 0.190547i | ||||
\(776\) | −8091.71 | −0.374324 | ||||||||
\(777\) | 4116.57 | − | 914.018i | 0.190066 | − | 0.0422011i | ||||
\(778\) | −4113.67 | −0.189566 | ||||||||
\(779\) | −6027.21 | − | 10439.4i | −0.277211 | − | 0.480143i | ||||
\(780\) | −3862.03 | + | 6689.24i | −0.177286 | + | 0.307068i | ||||
\(781\) | −705.715 | + | 1222.33i | −0.0323335 | + | 0.0560032i | ||||
\(782\) | 666.803 | + | 1154.94i | 0.0304921 | + | 0.0528139i | ||||
\(783\) | 4486.46 | 0.204768 | ||||||||
\(784\) | −16567.6 | − | 11584.8i | −0.754720 | − | 0.527733i | ||||
\(785\) | −2677.14 | −0.121721 | ||||||||
\(786\) | 1544.27 | + | 2674.75i | 0.0700790 | + | 0.121380i | ||||
\(787\) | 13356.9 | − | 23134.9i | 0.604985 | − | 1.04786i | −0.387069 | − | 0.922051i | \(-0.626513\pi\) |
0.992054 | − | 0.125814i | \(-0.0401541\pi\) | |||||||
\(788\) | 1639.46 | − | 2839.63i | 0.0741160 | − | 0.128373i | ||||
\(789\) | −5360.61 | − | 9284.85i | −0.241879 | − | 0.418947i | ||||
\(790\) | 1995.42 | 0.0898654 | ||||||||
\(791\) | 22563.0 | − | 5009.76i | 1.01422 | − | 0.225192i | ||||
\(792\) | 1594.23 | 0.0715258 | ||||||||
\(793\) | 16190.7 | + | 28043.1i | 0.725029 | + | 1.25579i | ||||
\(794\) | −336.278 | + | 582.451i | −0.0150303 | + | 0.0260333i | ||||
\(795\) | 5342.32 | − | 9253.17i | 0.238330 | − | 0.412800i | ||||
\(796\) | 20884.3 | + | 36172.7i | 0.929930 | + | 1.61069i | ||||
\(797\) | 8315.90 | 0.369591 | 0.184796 | − | 0.982777i | \(-0.440838\pi\) | ||||
0.184796 | + | 0.982777i | \(0.440838\pi\) | |||||||
\(798\) | 1120.58 | + | 1222.11i | 0.0497096 | + | 0.0542133i | ||||
\(799\) | 7460.55 | 0.330332 | ||||||||
\(800\) | −1068.01 | − | 1849.84i | −0.0471997 | − | 0.0817523i | ||||
\(801\) | −4919.99 | + | 8521.66i | −0.217028 | + | 0.375903i | ||||
\(802\) | −1989.43 | + | 3445.80i | −0.0875926 | + | 0.151715i | ||||
\(803\) | 705.976 | + | 1222.79i | 0.0310253 | + | 0.0537375i | ||||
\(804\) | −17697.4 | −0.776291 | ||||||||
\(805\) | 4101.86 | − | 13024.1i | 0.179592 | − | 0.570237i | ||||
\(806\) | −5791.50 | −0.253098 | ||||||||
\(807\) | −8004.75 | − | 13864.6i | −0.349171 | − | 0.604781i | ||||
\(808\) | 1442.17 | − | 2497.91i | 0.0627914 | − | 0.108758i | ||||
\(809\) | −20743.0 | + | 35927.9i | −0.901465 | + | 1.56138i | −0.0758710 | + | 0.997118i | \(0.524174\pi\) |
−0.825594 | + | 0.564265i | \(0.809160\pi\) | |||||||
\(810\) | −93.4031 | − | 161.779i | −0.00405167 | − | 0.00701769i | ||||
\(811\) | 9818.41 | 0.425119 | 0.212559 | − | 0.977148i | \(-0.431820\pi\) | ||||
0.212559 | + | 0.977148i | \(0.431820\pi\) | |||||||
\(812\) | −7198.92 | + | 22857.8i | −0.311124 | + | 0.987873i | ||||
\(813\) | 5107.42 | 0.220326 | ||||||||
\(814\) | −425.782 | − | 737.477i | −0.0183337 | − | 0.0317550i | ||||
\(815\) | 1509.45 | − | 2614.44i | 0.0648757 | − | 0.112368i | ||||
\(816\) | 1733.48 | − | 3002.48i | 0.0743676 | − | 0.128808i | ||||
\(817\) | −3587.28 | − | 6213.35i | −0.153614 | − | 0.266068i | ||||
\(818\) | −2721.12 | −0.116310 | ||||||||
\(819\) | −7448.98 | − | 8123.86i | −0.317813 | − | 0.346606i | ||||
\(820\) | −7254.33 | −0.308942 | ||||||||
\(821\) | 5492.63 | + | 9513.51i | 0.233488 | + | 0.404414i | 0.958832 | − | 0.283973i | \(-0.0916526\pi\) |
−0.725344 | + | 0.688387i | \(0.758319\pi\) | |||||||
\(822\) | −359.013 | + | 621.829i | −0.0152336 | + | 0.0263854i | ||||
\(823\) | −2955.04 | + | 5118.28i | −0.125159 | + | 0.216782i | −0.921795 | − | 0.387677i | \(-0.873278\pi\) |
0.796636 | + | 0.604460i | \(0.206611\pi\) | |||||||
\(824\) | 6155.97 | + | 10662.5i | 0.260259 | + | 0.450782i | ||||
\(825\) | −1824.43 | −0.0769919 | ||||||||
\(826\) | −2575.40 | + | 571.827i | −0.108486 | + | 0.0240877i | ||||
\(827\) | 34384.5 | 1.44579 | 0.722894 | − | 0.690958i | \(-0.242811\pi\) | ||||
0.722894 | + | 0.690958i | \(0.242811\pi\) | |||||||
\(828\) | 5167.31 | + | 8950.05i | 0.216880 | + | 0.375647i | ||||
\(829\) | 16529.5 | − | 28629.9i | 0.692513 | − | 1.19947i | −0.278498 | − | 0.960437i | \(-0.589837\pi\) |
0.971012 | − | 0.239032i | \(-0.0768299\pi\) | |||||||
\(830\) | −956.033 | + | 1655.90i | −0.0399812 | + | 0.0692495i | ||||
\(831\) | 1010.05 | + | 1749.46i | 0.0421640 | + | 0.0730302i | ||||
\(832\) | 28573.2 | 1.19062 | ||||||||
\(833\) | 581.820 | − | 6700.17i | 0.0242003 | − | 0.278688i | ||||
\(834\) | 890.906 | 0.0369899 | ||||||||
\(835\) | 3116.52 | + | 5397.98i | 0.129164 | + | 0.223718i | ||||
\(836\) | −6128.05 | + | 10614.1i | −0.253520 | + | 0.439110i | ||||
\(837\) | −2563.41 | + | 4439.95i | −0.105859 | + | 0.183354i | ||||
\(838\) | 2069.52 | + | 3584.52i | 0.0853108 | + | 0.147763i | ||||
\(839\) | −26115.7 | −1.07463 | −0.537315 | − | 0.843382i | \(-0.680561\pi\) | ||||
−0.537315 | + | 0.843382i | \(0.680561\pi\) | |||||||
\(840\) | 1974.84 | − | 438.481i | 0.0811171 | − | 0.0180108i | ||||
\(841\) | 3221.89 | 0.132104 | ||||||||
\(842\) | −1732.78 | − | 3001.26i | −0.0709209 | − | 0.122839i | ||||
\(843\) | −12510.6 | + | 21669.0i | −0.511136 | + | 0.885313i | ||||
\(844\) | −15928.4 | + | 27588.7i | −0.649617 | + | 1.12517i | ||||
\(845\) | −5439.05 | − | 9420.70i | −0.221431 | − | 0.383529i | ||||
\(846\) | −1579.52 | −0.0641905 | ||||||||
\(847\) | −9252.98 | − | 10091.3i | −0.375367 | − | 0.409376i | ||||
\(848\) | −41983.0 | −1.70012 | ||||||||
\(849\) | 2040.66 | + | 3534.53i | 0.0824915 | + | 0.142880i | ||||
\(850\) | 113.050 | − | 195.808i | 0.00456185 | − | 0.00790136i | ||||
\(851\) | 5595.70 | − | 9692.04i | 0.225403 | − | 0.390410i | ||||
\(852\) | −677.750 | − | 1173.90i | −0.0272527 | − | 0.0472031i | ||||
\(853\) | 35915.8 | 1.44166 | 0.720829 | − | 0.693113i | \(-0.243761\pi\) | ||||
0.720829 | + | 0.693113i | \(0.243761\pi\) | |||||||
\(854\) | 1256.62 | − | 3989.99i | 0.0503520 | − | 0.159877i | ||||
\(855\) | 2911.49 | 0.116457 | ||||||||
\(856\) | 6259.94 | + | 10842.5i | 0.249954 | + | 0.432932i | ||||
\(857\) | 2576.53 | − | 4462.69i | 0.102699 | − | 0.177879i | −0.810097 | − | 0.586296i | \(-0.800586\pi\) |
0.912796 | + | 0.408417i | \(0.133919\pi\) | |||||||
\(858\) | −1112.92 | + | 1927.63i | −0.0442825 | + | 0.0766996i | ||||
\(859\) | 14866.2 | + | 25748.9i | 0.590485 | + | 1.02275i | 0.994167 | + | 0.107851i | \(0.0343969\pi\) |
−0.403682 | + | 0.914899i | \(0.632270\pi\) | |||||||
\(860\) | −4317.64 | −0.171198 | ||||||||
\(861\) | 3109.62 | − | 9873.59i | 0.123084 | − | 0.390814i | ||||
\(862\) | 20.4340 | 0.000807409 | ||||||||
\(863\) | 367.393 | + | 636.344i | 0.0144916 | + | 0.0251001i | 0.873180 | − | 0.487397i | \(-0.162054\pi\) |
−0.858689 | + | 0.512498i | \(0.828720\pi\) | |||||||
\(864\) | −1153.45 | + | 1997.83i | −0.0454180 | + | 0.0786662i | ||||
\(865\) | −5179.83 | + | 8971.73i | −0.203606 | + | 0.352657i | ||||
\(866\) | −82.5200 | − | 142.929i | −0.00323804 | − | 0.00560845i | ||||
\(867\) | −13585.6 | −0.532171 | ||||||||
\(868\) | −18507.7 | − | 20184.5i | −0.723723 | − | 0.789292i | ||||
\(869\) | −21047.1 | −0.821604 | ||||||||
\(870\) | −574.828 | − | 995.631i | −0.0224006 | − | 0.0387989i | ||||
\(871\) | 25046.3 | − | 43381.5i | 0.974354 | − | 1.68763i | ||||
\(872\) | −4455.49 | + | 7717.13i | −0.173030 | + | 0.299696i | ||||
\(873\) | −5000.46 | − | 8661.05i | −0.193860 | − | 0.335776i | ||||
\(874\) | 4400.56 | 0.170310 | ||||||||
\(875\) | −2259.99 | + | 501.796i | −0.0873163 | + | 0.0193872i | ||||
\(876\) | −1356.00 | −0.0523003 | ||||||||
\(877\) | −9395.53 | − | 16273.5i | −0.361761 | − | 0.626589i | 0.626490 | − | 0.779430i | \(-0.284491\pi\) |
−0.988251 | + | 0.152841i | \(0.951158\pi\) | |||||||
\(878\) | −1098.59 | + | 1902.82i | −0.0422274 | + | 0.0731401i | ||||
\(879\) | −7033.38 | + | 12182.2i | −0.269886 | + | 0.467457i | ||||
\(880\) | 3584.34 | + | 6208.26i | 0.137305 | + | 0.237819i | ||||
\(881\) | −29665.5 | −1.13446 | −0.567229 | − | 0.823560i | \(-0.691984\pi\) | ||||
−0.567229 | + | 0.823560i | \(0.691984\pi\) | |||||||
\(882\) | −123.181 | + | 1418.54i | −0.00470264 | + | 0.0541550i | ||||
\(883\) | 22894.4 | 0.872545 | 0.436273 | − | 0.899814i | \(-0.356298\pi\) | ||||
0.436273 | + | 0.899814i | \(0.356298\pi\) | |||||||
\(884\) | 5048.33 | + | 8743.97i | 0.192074 | + | 0.332683i | ||||
\(885\) | −2316.18 | + | 4011.74i | −0.0879747 | + | 0.152377i | ||||
\(886\) | 2066.94 | − | 3580.04i | 0.0783749 | − | 0.135749i | ||||
\(887\) | 15071.7 | + | 26105.0i | 0.570528 | + | 0.988183i | 0.996512 | + | 0.0834524i | \(0.0265947\pi\) |
−0.425984 | + | 0.904731i | \(0.640072\pi\) | |||||||
\(888\) | 1657.98 | 0.0626558 | ||||||||
\(889\) | −7036.59 | + | 1562.36i | −0.265466 | + | 0.0589426i | ||||
\(890\) | 2521.49 | 0.0949670 | ||||||||
\(891\) | 985.190 | + | 1706.40i | 0.0370428 | + | 0.0641600i | ||||
\(892\) | −16961.5 | + | 29378.1i | −0.636672 | + | 1.10275i | ||||
\(893\) | 12308.9 | − | 21319.7i | 0.461258 | − | 0.798922i | ||||
\(894\) | −2031.86 | − | 3519.29i | −0.0760130 | − | 0.131658i | ||||
\(895\) | 13780.7 | 0.514678 | ||||||||
\(896\) | −11050.0 | − | 12051.1i | −0.412003 | − | 0.449330i | ||||
\(897\) | −29252.3 | −1.08886 | ||||||||
\(898\) | −3451.93 | − | 5978.92i | −0.128277 | − | 0.222182i | ||||
\(899\) | −15775.9 | + | 27324.7i | −0.585268 | + | 1.01371i | ||||
\(900\) | 876.065 | − | 1517.39i | 0.0324469 | − | 0.0561996i | ||||
\(901\) | −6983.32 | − | 12095.5i | −0.258211 | − | 0.447235i | ||||
\(902\) | −2090.47 | −0.0771675 | ||||||||
\(903\) | 1850.79 | − | 5876.57i | 0.0682063 | − | 0.216567i | ||||
\(904\) | 9087.46 | 0.334341 | ||||||||
\(905\) | 5829.58 | + | 10097.1i | 0.214124 | + | 0.370873i | ||||
\(906\) | 1417.26 | − | 2454.77i | 0.0519705 | − | 0.0900156i | ||||
\(907\) | 7377.73 | − | 12778.6i | 0.270092 | − | 0.467813i | −0.698793 | − | 0.715324i | \(-0.746279\pi\) |
0.968885 | + | 0.247511i | \(0.0796125\pi\) | |||||||
\(908\) | −19416.5 | − | 33630.3i | −0.709646 | − | 1.22914i | ||||
\(909\) | 3564.90 | 0.130077 | ||||||||
\(910\) | −848.438 | + | 2693.94i | −0.0309071 | + | 0.0981354i | ||||
\(911\) | −21035.2 | −0.765012 | −0.382506 | − | 0.923953i | \(-0.624939\pi\) | ||||
−0.382506 | + | 0.923953i | \(0.624939\pi\) | |||||||
\(912\) | −5720.04 | − | 9907.39i | −0.207686 | − | 0.359722i | ||||
\(913\) | 10084.0 | − | 17465.9i | 0.365532 | − | 0.633120i | ||||
\(914\) | 3239.98 | − | 5611.80i | 0.117253 | − | 0.203087i | ||||
\(915\) | −3672.70 | − | 6361.30i | −0.132695 | − | 0.229834i | ||||
\(916\) | 4577.71 | 0.165122 | ||||||||
\(917\) | −27936.9 | − | 30468.0i | −1.00606 | − | 1.09721i | ||||
\(918\) | −244.187 | −0.00877929 | ||||||||
\(919\) | −26221.2 | − | 45416.5i | −0.941194 | − | 1.63020i | −0.763197 | − | 0.646166i | \(-0.776371\pi\) |
−0.177997 | − | 0.984031i | \(-0.556962\pi\) | |||||||
\(920\) | 2684.42 | − | 4649.56i | 0.0961987 | − | 0.166621i | ||||
\(921\) | 704.892 | − | 1220.91i | 0.0252193 | − | 0.0436811i | ||||
\(922\) | −1820.03 | − | 3152.39i | −0.0650105 | − | 0.112601i | ||||
\(923\) | 3836.76 | 0.136824 | ||||||||
\(924\) | −10274.7 | + | 2281.33i | −0.365813 | + | 0.0812231i | ||||
\(925\) | −1897.39 | −0.0674441 | ||||||||
\(926\) | 2946.34 | + | 5103.20i | 0.104560 | + | 0.181103i | ||||
\(927\) | −7608.45 | + | 13178.2i | −0.269573 | + | 0.466914i | ||||
\(928\) | −7098.63 | + | 12295.2i | −0.251103 | + | 0.434924i | ||||
\(929\) | −8363.15 | − | 14485.4i | −0.295356 | − | 0.511572i | 0.679711 | − | 0.733480i | \(-0.262105\pi\) |
−0.975068 | + | 0.221907i | \(0.928772\pi\) | |||||||
\(930\) | 1313.75 | 0.0463220 | ||||||||
\(931\) | −18186.9 | − | 12717.1i | −0.640227 | − | 0.447674i | ||||
\(932\) | 2139.36 | 0.0751899 | ||||||||
\(933\) | 12385.3 | + | 21451.9i | 0.434594 | + | 0.752739i | ||||
\(934\) | 2362.79 | − | 4092.48i | 0.0827761 | − | 0.143372i | ||||
\(935\) | −1192.42 | + | 2065.33i | −0.0417072 | + | 0.0722389i | ||||
\(936\) | −2166.84 | − | 3753.07i | −0.0756680 | − | 0.131061i | ||||
\(937\) | 15038.3 | 0.524312 | 0.262156 | − | 0.965025i | \(-0.415566\pi\) | ||||
0.262156 | + | 0.965025i | \(0.415566\pi\) | |||||||
\(938\) | −6317.38 | + | 1402.67i | −0.219904 | + | 0.0488261i | ||||
\(939\) | 18637.7 | 0.647729 | ||||||||
\(940\) | −7407.50 | − | 12830.2i | −0.257028 | − | 0.445185i | ||||
\(941\) | 4984.58 | − | 8633.54i | 0.172681 | − | 0.299092i | −0.766675 | − | 0.642035i | \(-0.778090\pi\) |
0.939356 | + | 0.342943i | \(0.111424\pi\) | |||||||
\(942\) | 370.449 | − | 641.636i | 0.0128130 | − | 0.0221928i | ||||
\(943\) | −13736.7 | − | 23792.6i | −0.474366 | − | 0.821626i | ||||
\(944\) | 18201.9 | 0.627564 | ||||||||
\(945\) | 1689.73 | + | 1842.82i | 0.0581661 | + | 0.0634359i | ||||
\(946\) | −1244.21 | −0.0427619 | ||||||||
\(947\) | 18383.5 | + | 31841.2i | 0.630817 | + | 1.09261i | 0.987385 | + | 0.158338i | \(0.0506135\pi\) |
−0.356568 | + | 0.934269i | \(0.616053\pi\) | |||||||
\(948\) | 10106.5 | − | 17505.0i | 0.346250 | − | 0.599723i | ||||
\(949\) | 1919.09 | − | 3323.96i | 0.0656442 | − | 0.113699i | ||||
\(950\) | −373.035 | − | 646.115i | −0.0127398 | − | 0.0220661i | ||||
\(951\) | −21201.8 | −0.722940 | ||||||||
\(952\) | 794.344 | − | 2522.18i | 0.0270429 | − | 0.0858660i | ||||
\(953\) | 33586.1 | 1.14162 | 0.570808 | − | 0.821083i | \(-0.306630\pi\) | ||||
0.570808 | + | 0.821083i | \(0.306630\pi\) | |||||||
\(954\) | 1478.49 | + | 2560.82i | 0.0501759 | + | 0.0869072i | ||||
\(955\) | 10189.0 | − | 17647.8i | 0.345243 | − | 0.597979i | ||||
\(956\) | 3167.76 | − | 5486.72i | 0.107168 | − | 0.185620i | ||||
\(957\) | 6063.12 | + | 10501.6i | 0.204799 | + | 0.354723i | ||||
\(958\) | 7096.38 | 0.239325 | ||||||||
\(959\) | 2886.86 | − | 9166.29i | 0.0972070 | − | 0.308649i | ||||
\(960\) | −6481.56 | −0.217908 | ||||||||
\(961\) | −3132.10 | − | 5424.95i | −0.105136 | − | 0.182100i | ||||
\(962\) | −1157.43 | + | 2004.72i | −0.0387910 | + | 0.0671880i | ||||
\(963\) | −7736.95 | + | 13400.8i | −0.258899 | + | 0.448426i | ||||
\(964\) | −8560.70 | − | 14827.6i | −0.286018 | − | 0.495398i | ||||
\(965\) | −19826.3 | −0.661380 | ||||||||
\(966\) | 2553.93 | + | 2785.32i | 0.0850636 | + | 0.0927703i | ||||
\(967\) | −7604.27 | −0.252882 | −0.126441 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(968\) | −2691.60 | − | 4661.99i | −0.0893712 | − | 0.154796i | ||||
\(969\) | 1902.91 | − | 3295.93i | 0.0630858 | − | 0.109268i | ||||
\(970\) | −1281.37 | + | 2219.39i | −0.0424147 | + | 0.0734644i | ||||
\(971\) | 3386.23 | + | 5865.12i | 0.111915 | + | 0.193842i | 0.916542 | − | 0.399938i | \(-0.130968\pi\) |
−0.804627 | + | 0.593780i | \(0.797635\pi\) | |||||||
\(972\) | −1892.30 | −0.0624440 | ||||||||
\(973\) | −11640.5 | + | 2584.59i | −0.383533 | + | 0.0851574i | ||||
\(974\) | −1845.83 | −0.0607231 | ||||||||
\(975\) | 2479.72 | + | 4295.00i | 0.0814508 | + | 0.141077i | ||||
\(976\) | −14431.1 | + | 24995.4i | −0.473286 | + | 0.819756i | ||||
\(977\) | −17248.5 | + | 29875.3i | −0.564819 | + | 0.978295i | 0.432248 | + | 0.901755i | \(0.357721\pi\) |
−0.997067 | + | 0.0765399i | \(0.975613\pi\) | |||||||
\(978\) | 417.740 | + | 723.546i | 0.0136583 | + | 0.0236569i | ||||
\(979\) | −26596.0 | −0.868245 | ||||||||
\(980\) | −12100.2 | + | 5651.95i | −0.394415 | + | 0.184230i | ||||
\(981\) | −11013.5 | −0.358444 | ||||||||
\(982\) | −1083.21 | − | 1876.18i | −0.0352003 | − | 0.0609688i | ||||
\(983\) | 8836.09 | − | 15304.6i | 0.286701 | − | 0.496581i | −0.686319 | − | 0.727301i | \(-0.740775\pi\) |
0.973020 | + | 0.230719i | \(0.0741079\pi\) | |||||||
\(984\) | 2035.06 | − | 3524.83i | 0.0659302 | − | 0.114194i | ||||
\(985\) | −1052.66 | − | 1823.26i | −0.0340513 | − | 0.0589785i | ||||
\(986\) | −1502.79 | −0.0485383 | ||||||||
\(987\) | 20637.9 | − | 4582.33i | 0.665565 | − | 0.147778i | ||||
\(988\) | 33316.4 | 1.07281 | ||||||||
\(989\) | −8175.80 | − | 14160.9i | −0.262867 | − | 0.455299i | ||||
\(990\) | 252.455 | − | 437.265i | 0.00810459 | − | 0.0140376i | ||||
\(991\) | −17433.6 | + | 30195.8i | −0.558825 | + | 0.967913i | 0.438770 | + | 0.898599i | \(0.355414\pi\) |
−0.997595 | + | 0.0693136i | \(0.977919\pi\) | |||||||
\(992\) | −8111.82 | − | 14050.1i | −0.259628 | − | 0.449688i | ||||
\(993\) | −23574.5 | −0.753387 | ||||||||
\(994\) | −334.976 | − | 365.325i | −0.0106889 | − | 0.0116574i | ||||
\(995\) | 26818.6 | 0.854479 | ||||||||
\(996\) | 9684.38 | + | 16773.8i | 0.308094 | + | 0.533634i | ||||
\(997\) | 2499.05 | − | 4328.49i | 0.0793840 | − | 0.137497i | −0.823600 | − | 0.567171i | \(-0.808038\pi\) |
0.902984 | + | 0.429674i | \(0.141371\pi\) | |||||||
\(998\) | −584.812 | + | 1012.92i | −0.0185490 | + | 0.0321278i | ||||
\(999\) | 1024.59 | + | 1774.64i | 0.0324490 | + | 0.0562034i |
(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 | 105.4.i.d.46.3 | yes | 10 | |
3.2 | odd | 2 | 315.4.j.h.46.3 | 10 | |||
7.2 | even | 3 | inner | 105.4.i.d.16.3 | ✓ | 10 | |
7.3 | odd | 6 | 735.4.a.z.1.3 | 5 | |||
7.4 | even | 3 | 735.4.a.ba.1.3 | 5 | |||
21.2 | odd | 6 | 315.4.j.h.226.3 | 10 | |||
21.11 | odd | 6 | 2205.4.a.br.1.3 | 5 | |||
21.17 | even | 6 | 2205.4.a.bs.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.i.d.16.3 | ✓ | 10 | 7.2 | even | 3 | inner | |
105.4.i.d.46.3 | yes | 10 | 1.1 | even | 1 | trivial | |
315.4.j.h.46.3 | 10 | 3.2 | odd | 2 | |||
315.4.j.h.226.3 | 10 | 21.2 | odd | 6 | |||
735.4.a.z.1.3 | 5 | 7.3 | odd | 6 | |||
735.4.a.ba.1.3 | 5 | 7.4 | even | 3 | |||
2205.4.a.br.1.3 | 5 | 21.11 | odd | 6 | |||
2205.4.a.bs.1.3 | 5 | 21.17 | even | 6 |