Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,4,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("114.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (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: | \(6.72621774065\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.6967728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.13654 - 1.96854i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.49 |
Dual form | 114.4.e.e.7.2 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.60679 | − | 4.51510i | 0.233159 | − | 0.403843i | −0.725577 | − | 0.688141i | \(-0.758427\pi\) |
0.958736 | + | 0.284298i | \(0.0917605\pi\) | |||||||
\(6\) | −3.00000 | − | 5.19615i | −0.204124 | − | 0.353553i | ||||
\(7\) | 31.4905 | 1.70033 | 0.850163 | − | 0.526520i | \(-0.176504\pi\) | ||||
0.850163 | + | 0.526520i | \(0.176504\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | −5.21359 | − | 9.03020i | −0.164868 | − | 0.285560i | ||||
\(11\) | −21.2113 | −0.581403 | −0.290702 | − | 0.956814i | \(-0.593889\pi\) | ||||
−0.290702 | + | 0.956814i | \(0.593889\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −28.1384 | − | 48.7372i | −0.600323 | − | 1.03979i | −0.992772 | − | 0.120016i | \(-0.961705\pi\) |
0.392449 | − | 0.919774i | \(-0.371628\pi\) | |||||||
\(14\) | 31.4905 | − | 54.5431i | 0.601156 | − | 1.04123i | ||||
\(15\) | −7.82038 | − | 13.5453i | −0.134614 | − | 0.233159i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −8.63960 | + | 14.9642i | −0.123259 | + | 0.213492i | −0.921051 | − | 0.389441i | \(-0.872668\pi\) |
0.797792 | + | 0.602933i | \(0.206001\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −42.3436 | − | 71.1759i | −0.511279 | − | 0.859415i | ||||
\(20\) | −20.8543 | −0.233159 | ||||||||
\(21\) | 47.2357 | − | 81.8146i | 0.490842 | − | 0.850163i | ||||
\(22\) | −21.2113 | + | 36.7390i | −0.205557 | + | 0.356035i | ||||
\(23\) | 103.158 | + | 178.675i | 0.935216 | + | 1.61984i | 0.774248 | + | 0.632883i | \(0.218128\pi\) |
0.160969 | + | 0.986960i | \(0.448538\pi\) | |||||||
\(24\) | −12.0000 | + | 20.7846i | −0.102062 | + | 0.176777i | ||||
\(25\) | 48.9093 | + | 84.7133i | 0.391274 | + | 0.677707i | ||||
\(26\) | −112.554 | −0.848985 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −62.9809 | − | 109.086i | −0.425081 | − | 0.736262i | ||||
\(29\) | −103.257 | − | 178.846i | −0.661182 | − | 1.14520i | −0.980305 | − | 0.197488i | \(-0.936722\pi\) |
0.319123 | − | 0.947713i | \(-0.396612\pi\) | |||||||
\(30\) | −31.2815 | −0.190373 | ||||||||
\(31\) | 129.624 | 0.751005 | 0.375503 | − | 0.926821i | \(-0.377470\pi\) | ||||
0.375503 | + | 0.926821i | \(0.377470\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −31.8169 | + | 55.1085i | −0.167837 | + | 0.290702i | ||||
\(34\) | 17.2792 | + | 29.9284i | 0.0871576 | + | 0.150961i | ||||
\(35\) | 82.0891 | − | 142.183i | 0.396446 | − | 0.686664i | ||||
\(36\) | −18.0000 | + | 31.1769i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 440.212 | 1.95596 | 0.977979 | − | 0.208704i | \(-0.0669245\pi\) | ||||
0.977979 | + | 0.208704i | \(0.0669245\pi\) | |||||||
\(38\) | −165.624 | + | 2.16540i | −0.707046 | + | 0.00924405i | ||||
\(39\) | −168.831 | −0.693193 | ||||||||
\(40\) | −20.8543 | + | 36.1208i | −0.0824340 | + | 0.142780i | ||||
\(41\) | −217.727 | + | 377.114i | −0.829347 | + | 1.43647i | 0.0692044 | + | 0.997602i | \(0.477954\pi\) |
−0.898551 | + | 0.438868i | \(0.855379\pi\) | |||||||
\(42\) | −94.4714 | − | 163.629i | −0.347077 | − | 0.601156i | ||||
\(43\) | −64.9984 | + | 112.580i | −0.230515 | + | 0.399264i | −0.957960 | − | 0.286902i | \(-0.907375\pi\) |
0.727445 | + | 0.686166i | \(0.240708\pi\) | |||||||
\(44\) | 42.4225 | + | 73.4780i | 0.145351 | + | 0.251755i | ||||
\(45\) | −46.9223 | −0.155439 | ||||||||
\(46\) | 412.633 | 1.32260 | ||||||||
\(47\) | −54.2410 | − | 93.9482i | −0.168338 | − | 0.291569i | 0.769498 | − | 0.638649i | \(-0.220507\pi\) |
−0.937836 | + | 0.347080i | \(0.887173\pi\) | |||||||
\(48\) | 24.0000 | + | 41.5692i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 648.649 | 1.89111 | ||||||||
\(50\) | 195.637 | 0.553345 | ||||||||
\(51\) | 25.9188 | + | 44.8927i | 0.0711639 | + | 0.123259i | ||||
\(52\) | −112.554 | + | 194.949i | −0.300161 | + | 0.519895i | ||||
\(53\) | 203.640 | + | 352.715i | 0.527776 | + | 0.914134i | 0.999476 | + | 0.0323753i | \(0.0103072\pi\) |
−0.471700 | + | 0.881759i | \(0.656359\pi\) | |||||||
\(54\) | −27.0000 | + | 46.7654i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −55.2934 | + | 95.7709i | −0.135559 | + | 0.234795i | ||||
\(56\) | −251.924 | −0.601156 | ||||||||
\(57\) | −248.436 | + | 3.24810i | −0.577301 | + | 0.00754774i | ||||
\(58\) | −413.027 | −0.935052 | ||||||||
\(59\) | 58.1224 | − | 100.671i | 0.128252 | − | 0.222140i | −0.794747 | − | 0.606941i | \(-0.792397\pi\) |
0.923000 | + | 0.384801i | \(0.125730\pi\) | |||||||
\(60\) | −31.2815 | + | 54.1812i | −0.0673071 | + | 0.116579i | ||||
\(61\) | 170.342 | + | 295.041i | 0.357542 | + | 0.619282i | 0.987550 | − | 0.157308i | \(-0.0502814\pi\) |
−0.630007 | + | 0.776589i | \(0.716948\pi\) | |||||||
\(62\) | 129.624 | − | 224.515i | 0.265520 | − | 0.459895i | ||||
\(63\) | −141.707 | − | 245.444i | −0.283388 | − | 0.490842i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −293.404 | −0.559882 | ||||||||
\(66\) | 63.6338 | + | 110.217i | 0.118678 | + | 0.205557i | ||||
\(67\) | 105.373 | + | 182.511i | 0.192139 | + | 0.332795i | 0.945959 | − | 0.324286i | \(-0.105124\pi\) |
−0.753820 | + | 0.657081i | \(0.771791\pi\) | |||||||
\(68\) | 69.1168 | 0.123259 | ||||||||
\(69\) | 618.949 | 1.07989 | ||||||||
\(70\) | −164.178 | − | 284.365i | −0.280329 | − | 0.485545i | ||||
\(71\) | −79.0086 | + | 136.847i | −0.132065 | + | 0.228743i | −0.924472 | − | 0.381249i | \(-0.875494\pi\) |
0.792408 | + | 0.609992i | \(0.208827\pi\) | |||||||
\(72\) | 36.0000 | + | 62.3538i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −286.774 | + | 496.707i | −0.459785 | + | 0.796371i | −0.998949 | − | 0.0458295i | \(-0.985407\pi\) |
0.539164 | + | 0.842201i | \(0.318740\pi\) | |||||||
\(74\) | 440.212 | − | 762.470i | 0.691535 | − | 1.19777i | ||||
\(75\) | 293.456 | 0.451804 | ||||||||
\(76\) | −161.873 | + | 289.035i | −0.244318 | + | 0.436244i | ||||
\(77\) | −667.952 | −0.988575 | ||||||||
\(78\) | −168.831 | + | 292.423i | −0.245081 | + | 0.424492i | ||||
\(79\) | 442.649 | − | 766.690i | 0.630403 | − | 1.09189i | −0.357066 | − | 0.934079i | \(-0.616223\pi\) |
0.987469 | − | 0.157811i | \(-0.0504438\pi\) | |||||||
\(80\) | 41.7087 | + | 72.2416i | 0.0582897 | + | 0.100961i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 435.454 | + | 754.228i | 0.586437 | + | 1.01574i | ||||
\(83\) | −573.632 | −0.758606 | −0.379303 | − | 0.925273i | \(-0.623836\pi\) | ||||
−0.379303 | + | 0.925273i | \(0.623836\pi\) | |||||||
\(84\) | −377.886 | −0.490842 | ||||||||
\(85\) | 45.0433 | + | 78.0173i | 0.0574780 | + | 0.0995548i | ||||
\(86\) | 129.997 | + | 225.161i | 0.162999 | + | 0.282322i | ||||
\(87\) | −619.540 | −0.763467 | ||||||||
\(88\) | 169.690 | 0.205557 | ||||||||
\(89\) | −107.618 | − | 186.399i | −0.128174 | − | 0.222003i | 0.794795 | − | 0.606878i | \(-0.207578\pi\) |
−0.922969 | + | 0.384874i | \(0.874245\pi\) | |||||||
\(90\) | −46.9223 | + | 81.2718i | −0.0549560 | + | 0.0951866i | ||||
\(91\) | −886.092 | − | 1534.76i | −1.02074 | − | 1.76798i | ||||
\(92\) | 412.633 | − | 714.701i | 0.467608 | − | 0.809921i | ||||
\(93\) | 194.436 | − | 336.773i | 0.216797 | − | 0.375503i | ||||
\(94\) | −216.964 | −0.238065 | ||||||||
\(95\) | −431.748 | + | 5.64475i | −0.466278 | + | 0.00609620i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −264.487 | + | 458.105i | −0.276851 | + | 0.479521i | −0.970601 | − | 0.240696i | \(-0.922624\pi\) |
0.693749 | + | 0.720217i | \(0.255958\pi\) | |||||||
\(98\) | 648.649 | − | 1123.49i | 0.668607 | − | 1.15806i | ||||
\(99\) | 95.4507 | + | 165.325i | 0.0969006 | + | 0.167837i | ||||
\(100\) | 195.637 | − | 338.853i | 0.195637 | − | 0.338853i | ||||
\(101\) | −514.368 | − | 890.911i | −0.506748 | − | 0.877713i | −0.999970 | − | 0.00780915i | \(-0.997514\pi\) |
0.493222 | − | 0.869904i | \(-0.335819\pi\) | |||||||
\(102\) | 103.675 | 0.100641 | ||||||||
\(103\) | 108.300 | 0.103603 | 0.0518016 | − | 0.998657i | \(-0.483504\pi\) | ||||
0.0518016 | + | 0.998657i | \(0.483504\pi\) | |||||||
\(104\) | 225.107 | + | 389.898i | 0.212246 | + | 0.367621i | ||||
\(105\) | −246.267 | − | 426.548i | −0.228888 | − | 0.396446i | ||||
\(106\) | 814.560 | 0.746388 | ||||||||
\(107\) | −1820.02 | −1.64438 | −0.822188 | − | 0.569215i | \(-0.807247\pi\) | ||||
−0.822188 | + | 0.569215i | \(0.807247\pi\) | |||||||
\(108\) | 54.0000 | + | 93.5307i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 59.5717 | − | 103.181i | 0.0523480 | − | 0.0906694i | −0.838664 | − | 0.544649i | \(-0.816663\pi\) |
0.891012 | + | 0.453980i | \(0.149996\pi\) | |||||||
\(110\) | 110.587 | + | 191.542i | 0.0958549 | + | 0.166025i | ||||
\(111\) | 660.318 | − | 1143.70i | 0.564636 | − | 0.977979i | ||||
\(112\) | −251.924 | + | 436.345i | −0.212541 | + | 0.368131i | ||||
\(113\) | 1014.96 | 0.844949 | 0.422474 | − | 0.906375i | \(-0.361162\pi\) | ||||
0.422474 | + | 0.906375i | \(0.361162\pi\) | |||||||
\(114\) | −242.810 | + | 433.552i | −0.199485 | + | 0.356192i | ||||
\(115\) | 1075.65 | 0.872215 | ||||||||
\(116\) | −413.027 | + | 715.383i | −0.330591 | + | 0.572600i | ||||
\(117\) | −253.246 | + | 438.635i | −0.200108 | + | 0.346597i | ||||
\(118\) | −116.245 | − | 201.342i | −0.0906881 | − | 0.157076i | ||||
\(119\) | −272.065 | + | 471.230i | −0.209581 | + | 0.363005i | ||||
\(120\) | 62.5630 | + | 108.362i | 0.0475933 | + | 0.0824340i | ||||
\(121\) | −881.082 | −0.661970 | ||||||||
\(122\) | 681.369 | 0.505641 | ||||||||
\(123\) | 653.181 | + | 1131.34i | 0.478824 | + | 0.829347i | ||||
\(124\) | −259.248 | − | 449.031i | −0.187751 | − | 0.325195i | ||||
\(125\) | 1161.68 | 0.831233 | ||||||||
\(126\) | −566.828 | −0.400770 | ||||||||
\(127\) | −514.100 | − | 890.448i | −0.359205 | − | 0.622161i | 0.628623 | − | 0.777710i | \(-0.283619\pi\) |
−0.987828 | + | 0.155549i | \(0.950285\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 194.995 | + | 337.741i | 0.133088 | + | 0.230515i | ||||
\(130\) | −293.404 | + | 508.191i | −0.197948 | + | 0.342856i | ||||
\(131\) | 794.584 | − | 1376.26i | 0.529948 | − | 0.917896i | −0.469442 | − | 0.882963i | \(-0.655545\pi\) |
0.999390 | − | 0.0349330i | \(-0.0111218\pi\) | |||||||
\(132\) | 254.535 | 0.167837 | ||||||||
\(133\) | −1333.42 | − | 2241.36i | −0.869340 | − | 1.46128i | ||||
\(134\) | 421.491 | 0.271726 | ||||||||
\(135\) | −70.3834 | + | 121.908i | −0.0448714 | + | 0.0777196i | ||||
\(136\) | 69.1168 | − | 119.714i | 0.0435788 | − | 0.0754807i | ||||
\(137\) | 1162.53 | + | 2013.57i | 0.724977 | + | 1.25570i | 0.958983 | + | 0.283462i | \(0.0914831\pi\) |
−0.234006 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(138\) | 618.949 | − | 1072.05i | 0.381800 | − | 0.661298i | ||||
\(139\) | −317.528 | − | 549.974i | −0.193758 | − | 0.335599i | 0.752735 | − | 0.658324i | \(-0.228734\pi\) |
−0.946493 | + | 0.322725i | \(0.895401\pi\) | |||||||
\(140\) | −656.713 | −0.396446 | ||||||||
\(141\) | −325.446 | −0.194380 | ||||||||
\(142\) | 158.017 | + | 273.694i | 0.0933839 | + | 0.161746i | ||||
\(143\) | 596.852 | + | 1033.78i | 0.349030 | + | 0.604537i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1076.67 | −0.616641 | ||||||||
\(146\) | 573.547 | + | 993.413i | 0.325117 | + | 0.563119i | ||||
\(147\) | 972.974 | − | 1685.24i | 0.545915 | − | 0.945553i | ||||
\(148\) | −880.424 | − | 1524.94i | −0.488989 | − | 0.846955i | ||||
\(149\) | −849.157 | + | 1470.78i | −0.466883 | + | 0.808666i | −0.999284 | − | 0.0378265i | \(-0.987957\pi\) |
0.532401 | + | 0.846492i | \(0.321290\pi\) | |||||||
\(150\) | 293.456 | − | 508.280i | 0.159737 | − | 0.276673i | ||||
\(151\) | −1632.38 | −0.879745 | −0.439873 | − | 0.898060i | \(-0.644976\pi\) | ||||
−0.439873 | + | 0.898060i | \(0.644976\pi\) | |||||||
\(152\) | 338.749 | + | 569.408i | 0.180764 | + | 0.303849i | ||||
\(153\) | 155.513 | 0.0821730 | ||||||||
\(154\) | −667.952 | + | 1156.93i | −0.349514 | + | 0.605376i | ||||
\(155\) | 337.903 | − | 585.265i | 0.175103 | − | 0.303288i | ||||
\(156\) | 337.661 | + | 584.846i | 0.173298 | + | 0.300161i | ||||
\(157\) | −1481.29 | + | 2565.66i | −0.752990 | + | 1.30422i | 0.193377 | + | 0.981124i | \(0.438056\pi\) |
−0.946367 | + | 0.323092i | \(0.895278\pi\) | |||||||
\(158\) | −885.297 | − | 1533.38i | −0.445763 | − | 0.772083i | ||||
\(159\) | 1221.84 | 0.609423 | ||||||||
\(160\) | 166.835 | 0.0824340 | ||||||||
\(161\) | 3248.50 | + | 5626.57i | 1.59017 | + | 2.75426i | ||||
\(162\) | 81.0000 | + | 140.296i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 626.972 | 0.301277 | 0.150639 | − | 0.988589i | \(-0.451867\pi\) | ||||
0.150639 | + | 0.988589i | \(0.451867\pi\) | |||||||
\(164\) | 1741.81 | 0.829347 | ||||||||
\(165\) | 165.880 | + | 287.313i | 0.0782652 | + | 0.135559i | ||||
\(166\) | −573.632 | + | 993.560i | −0.268208 | + | 0.464549i | ||||
\(167\) | −801.078 | − | 1387.51i | −0.371193 | − | 0.642926i | 0.618556 | − | 0.785741i | \(-0.287718\pi\) |
−0.989749 | + | 0.142815i | \(0.954385\pi\) | |||||||
\(168\) | −377.886 | + | 654.517i | −0.173539 | + | 0.300578i | ||||
\(169\) | −485.043 | + | 840.120i | −0.220775 | + | 0.382394i | ||||
\(170\) | 180.173 | 0.0812862 | ||||||||
\(171\) | −364.215 | + | 650.328i | −0.162879 | + | 0.290829i | ||||
\(172\) | 519.987 | 0.230515 | ||||||||
\(173\) | −1145.34 | + | 1983.79i | −0.503346 | + | 0.871821i | 0.496646 | + | 0.867953i | \(0.334565\pi\) |
−0.999993 | + | 0.00386803i | \(0.998769\pi\) | |||||||
\(174\) | −619.540 | + | 1073.07i | −0.269926 | + | 0.467526i | ||||
\(175\) | 1540.18 | + | 2667.66i | 0.665293 | + | 1.15232i | ||||
\(176\) | 169.690 | − | 293.912i | 0.0726754 | − | 0.125878i | ||||
\(177\) | −174.367 | − | 302.013i | −0.0740465 | − | 0.128252i | ||||
\(178\) | −430.471 | −0.181265 | ||||||||
\(179\) | −218.545 | −0.0912558 | −0.0456279 | − | 0.998959i | \(-0.514529\pi\) | ||||
−0.0456279 | + | 0.998959i | \(0.514529\pi\) | |||||||
\(180\) | 93.8446 | + | 162.544i | 0.0388598 | + | 0.0673071i | ||||
\(181\) | 1874.22 | + | 3246.24i | 0.769667 | + | 1.33310i | 0.937744 | + | 0.347328i | \(0.112911\pi\) |
−0.168077 | + | 0.985774i | \(0.553756\pi\) | |||||||
\(182\) | −3544.37 | −1.44355 | ||||||||
\(183\) | 1022.05 | 0.412854 | ||||||||
\(184\) | −825.266 | − | 1429.40i | −0.330649 | − | 0.572701i | ||||
\(185\) | 1147.54 | − | 1987.60i | 0.456049 | − | 0.789899i | ||||
\(186\) | −388.872 | − | 673.546i | −0.153298 | − | 0.265520i | ||||
\(187\) | 183.257 | − | 317.410i | 0.0716634 | − | 0.124125i | ||||
\(188\) | −216.964 | + | 375.793i | −0.0841688 | + | 0.145785i | ||||
\(189\) | −850.242 | −0.327228 | ||||||||
\(190\) | −421.971 | + | 753.453i | −0.161121 | + | 0.287691i | ||||
\(191\) | −141.733 | −0.0536935 | −0.0268467 | − | 0.999640i | \(-0.508547\pi\) | ||||
−0.0268467 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(192\) | 96.0000 | − | 166.277i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 1954.95 | − | 3386.07i | 0.729120 | − | 1.26287i | −0.228135 | − | 0.973629i | \(-0.573263\pi\) |
0.957255 | − | 0.289244i | \(-0.0934038\pi\) | |||||||
\(194\) | 528.974 | + | 916.210i | 0.195763 | + | 0.339072i | ||||
\(195\) | −440.107 | + | 762.287i | −0.161624 | + | 0.279941i | ||||
\(196\) | −1297.30 | − | 2246.99i | −0.472776 | − | 0.818873i | ||||
\(197\) | 1203.16 | 0.435134 | 0.217567 | − | 0.976045i | \(-0.430188\pi\) | ||||
0.217567 | + | 0.976045i | \(0.430188\pi\) | |||||||
\(198\) | 381.803 | 0.137038 | ||||||||
\(199\) | −1851.73 | − | 3207.29i | −0.659626 | − | 1.14251i | −0.980712 | − | 0.195456i | \(-0.937381\pi\) |
0.321086 | − | 0.947050i | \(-0.395952\pi\) | |||||||
\(200\) | −391.274 | − | 677.707i | −0.138336 | − | 0.239605i | ||||
\(201\) | 632.236 | 0.221863 | ||||||||
\(202\) | −2057.47 | −0.716649 | ||||||||
\(203\) | −3251.60 | − | 5631.93i | −1.12422 | − | 1.94721i | ||||
\(204\) | 103.675 | − | 179.571i | 0.0355819 | − | 0.0616297i | ||||
\(205\) | 1135.14 | + | 1966.12i | 0.386739 | + | 0.669851i | ||||
\(206\) | 108.300 | − | 187.581i | 0.0366293 | − | 0.0634438i | ||||
\(207\) | 928.424 | − | 1608.08i | 0.311739 | − | 0.539947i | ||||
\(208\) | 900.430 | 0.300161 | ||||||||
\(209\) | 898.162 | + | 1509.73i | 0.297259 | + | 0.499667i | ||||
\(210\) | −985.069 | −0.323696 | ||||||||
\(211\) | 12.8499 | − | 22.2567i | 0.00419253 | − | 0.00726168i | −0.863922 | − | 0.503626i | \(-0.831999\pi\) |
0.868114 | + | 0.496365i | \(0.165332\pi\) | |||||||
\(212\) | 814.560 | − | 1410.86i | 0.263888 | − | 0.457067i | ||||
\(213\) | 237.026 | + | 410.541i | 0.0762476 | + | 0.132065i | ||||
\(214\) | −1820.02 | + | 3152.37i | −0.581375 | + | 1.00697i | ||||
\(215\) | 338.875 | + | 586.948i | 0.107493 | + | 0.186184i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 4081.92 | 1.27695 | ||||||||
\(218\) | −119.143 | − | 206.362i | −0.0370156 | − | 0.0641129i | ||||
\(219\) | 860.321 | + | 1490.12i | 0.265457 | + | 0.459785i | ||||
\(220\) | 442.347 | 0.135559 | ||||||||
\(221\) | 972.419 | 0.295982 | ||||||||
\(222\) | −1320.64 | − | 2287.41i | −0.399258 | − | 0.691535i | ||||
\(223\) | 1552.59 | − | 2689.17i | 0.466230 | − | 0.807535i | −0.533026 | − | 0.846099i | \(-0.678945\pi\) |
0.999256 | + | 0.0385642i | \(0.0122784\pi\) | |||||||
\(224\) | 503.847 | + | 872.689i | 0.150289 | + | 0.260308i | ||||
\(225\) | 440.183 | − | 762.420i | 0.130425 | − | 0.225902i | ||||
\(226\) | 1014.96 | − | 1757.96i | 0.298735 | − | 0.517423i | ||||
\(227\) | 664.566 | 0.194312 | 0.0971560 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971560 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(228\) | 508.124 | + | 854.111i | 0.147593 | + | 0.248092i | ||||
\(229\) | −6031.99 | −1.74063 | −0.870317 | − | 0.492492i | \(-0.836086\pi\) | ||||
−0.870317 | + | 0.492492i | \(0.836086\pi\) | |||||||
\(230\) | 1075.65 | − | 1863.08i | 0.308375 | − | 0.534121i | ||||
\(231\) | −1001.93 | + | 1735.39i | −0.285377 | + | 0.494287i | ||||
\(232\) | 826.053 | + | 1430.77i | 0.233763 | + | 0.404890i | ||||
\(233\) | 2879.08 | − | 4986.71i | 0.809506 | − | 1.40211i | −0.103701 | − | 0.994609i | \(-0.533068\pi\) |
0.913207 | − | 0.407497i | \(-0.133598\pi\) | |||||||
\(234\) | 506.492 | + | 877.270i | 0.141497 | + | 0.245081i | ||||
\(235\) | −565.581 | −0.156998 | ||||||||
\(236\) | −464.979 | −0.128252 | ||||||||
\(237\) | −1327.95 | − | 2300.07i | −0.363964 | − | 0.630403i | ||||
\(238\) | 544.130 | + | 942.461i | 0.148196 | + | 0.256683i | ||||
\(239\) | −741.406 | −0.200659 | −0.100330 | − | 0.994954i | \(-0.531990\pi\) | ||||
−0.100330 | + | 0.994954i | \(0.531990\pi\) | |||||||
\(240\) | 250.252 | 0.0673071 | ||||||||
\(241\) | −2637.03 | − | 4567.48i | −0.704840 | − | 1.22082i | −0.966749 | − | 0.255726i | \(-0.917686\pi\) |
0.261910 | − | 0.965092i | \(-0.415648\pi\) | |||||||
\(242\) | −881.082 | + | 1526.08i | −0.234042 | + | 0.405372i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 681.369 | − | 1180.17i | 0.178771 | − | 0.309641i | ||||
\(245\) | 1690.89 | − | 2928.71i | 0.440928 | − | 0.763709i | ||||
\(246\) | 2612.72 | 0.677159 | ||||||||
\(247\) | −2277.43 | + | 4066.49i | −0.586678 | + | 1.04755i | ||||
\(248\) | −1036.99 | −0.265520 | ||||||||
\(249\) | −860.448 | + | 1490.34i | −0.218991 | + | 0.379303i | ||||
\(250\) | 1161.68 | − | 2012.10i | 0.293885 | − | 0.509024i | ||||
\(251\) | −1423.18 | − | 2465.02i | −0.357889 | − | 0.619882i | 0.629719 | − | 0.776823i | \(-0.283170\pi\) |
−0.987608 | + | 0.156941i | \(0.949837\pi\) | |||||||
\(252\) | −566.828 | + | 981.775i | −0.141694 | + | 0.245421i | ||||
\(253\) | −2188.12 | − | 3789.93i | −0.543738 | − | 0.941782i | ||||
\(254\) | −2056.40 | −0.507993 | ||||||||
\(255\) | 270.260 | 0.0663699 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3220.36 | − | 5577.82i | −0.781635 | − | 1.35383i | −0.930989 | − | 0.365048i | \(-0.881053\pi\) |
0.149353 | − | 0.988784i | \(-0.452281\pi\) | |||||||
\(258\) | 779.981 | 0.188215 | ||||||||
\(259\) | 13862.5 | 3.32576 | ||||||||
\(260\) | 586.809 | + | 1016.38i | 0.139971 | + | 0.242436i | ||||
\(261\) | −929.310 | + | 1609.61i | −0.220394 | + | 0.381734i | ||||
\(262\) | −1589.17 | − | 2752.52i | −0.374730 | − | 0.649051i | ||||
\(263\) | −2070.20 | + | 3585.70i | −0.485377 | + | 0.840698i | −0.999859 | − | 0.0168037i | \(-0.994651\pi\) |
0.514482 | + | 0.857501i | \(0.327984\pi\) | |||||||
\(264\) | 254.535 | − | 440.868i | 0.0593392 | − | 0.102779i | ||||
\(265\) | 2123.39 | 0.492222 | ||||||||
\(266\) | −5215.58 | + | 68.1894i | −1.20221 | + | 0.0157179i | ||||
\(267\) | −645.706 | −0.148002 | ||||||||
\(268\) | 421.491 | − | 730.044i | 0.0960696 | − | 0.166397i | ||||
\(269\) | −1583.00 | + | 2741.83i | −0.358799 | + | 0.621459i | −0.987761 | − | 0.155978i | \(-0.950147\pi\) |
0.628961 | + | 0.777437i | \(0.283480\pi\) | |||||||
\(270\) | 140.767 | + | 243.815i | 0.0317289 | + | 0.0549560i | ||||
\(271\) | −3222.11 | + | 5580.86i | −0.722249 | + | 1.25097i | 0.237847 | + | 0.971303i | \(0.423558\pi\) |
−0.960096 | + | 0.279669i | \(0.909775\pi\) | |||||||
\(272\) | −138.234 | − | 239.428i | −0.0308149 | − | 0.0533729i | ||||
\(273\) | −5316.55 | −1.17865 | ||||||||
\(274\) | 4650.13 | 1.02527 | ||||||||
\(275\) | −1037.43 | − | 1796.88i | −0.227488 | − | 0.394021i | ||||
\(276\) | −1237.90 | − | 2144.10i | −0.269974 | − | 0.467608i | ||||
\(277\) | 399.738 | 0.0867073 | 0.0433537 | − | 0.999060i | \(-0.486196\pi\) | ||||
0.0433537 | + | 0.999060i | \(0.486196\pi\) | |||||||
\(278\) | −1270.11 | −0.274015 | ||||||||
\(279\) | −583.308 | − | 1010.32i | −0.125168 | − | 0.216797i | ||||
\(280\) | −656.713 | + | 1137.46i | −0.140165 | + | 0.242772i | ||||
\(281\) | −315.183 | − | 545.914i | −0.0669120 | − | 0.115895i | 0.830629 | − | 0.556827i | \(-0.187981\pi\) |
−0.897541 | + | 0.440932i | \(0.854648\pi\) | |||||||
\(282\) | −325.446 | + | 563.689i | −0.0687236 | + | 0.119033i | ||||
\(283\) | −998.317 | + | 1729.13i | −0.209695 | + | 0.363203i | −0.951619 | − | 0.307282i | \(-0.900581\pi\) |
0.741923 | + | 0.670485i | \(0.233914\pi\) | |||||||
\(284\) | 632.069 | 0.132065 | ||||||||
\(285\) | −632.956 | + | 1130.18i | −0.131555 | + | 0.234899i | ||||
\(286\) | 2387.41 | 0.493603 | ||||||||
\(287\) | −6856.32 | + | 11875.5i | −1.41016 | + | 2.44247i | ||||
\(288\) | 144.000 | − | 249.415i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 2307.21 | + | 3996.21i | 0.469614 | + | 0.813396i | ||||
\(290\) | −1076.67 | + | 1864.86i | −0.218016 | + | 0.377614i | ||||
\(291\) | 793.461 | + | 1374.31i | 0.159840 | + | 0.276851i | ||||
\(292\) | 2294.19 | 0.459785 | ||||||||
\(293\) | 9676.85 | 1.92945 | 0.964723 | − | 0.263268i | \(-0.0848004\pi\) | ||||
0.964723 | + | 0.263268i | \(0.0848004\pi\) | |||||||
\(294\) | −1945.95 | − | 3370.48i | −0.386020 | − | 0.668607i | ||||
\(295\) | −303.026 | − | 524.857i | −0.0598063 | − | 0.103588i | ||||
\(296\) | −3521.70 | −0.691535 | ||||||||
\(297\) | 572.704 | 0.111891 | ||||||||
\(298\) | 1698.31 | + | 2941.57i | 0.330136 | + | 0.571813i | ||||
\(299\) | 5805.42 | − | 10055.3i | 1.12286 | − | 1.94486i | ||||
\(300\) | −586.911 | − | 1016.56i | −0.112951 | − | 0.195637i | ||||
\(301\) | −2046.83 | + | 3545.21i | −0.391951 | + | 0.678879i | ||||
\(302\) | −1632.38 | + | 2827.37i | −0.311037 | + | 0.538732i | ||||
\(303\) | −3086.21 | −0.585142 | ||||||||
\(304\) | 1324.99 | − | 17.3232i | 0.249979 | − | 0.00326827i | ||||
\(305\) | 1776.19 | 0.333456 | ||||||||
\(306\) | 155.513 | − | 269.356i | 0.0290525 | − | 0.0503205i | ||||
\(307\) | −3397.76 | + | 5885.09i | −0.631662 | + | 1.09407i | 0.355550 | + | 0.934657i | \(0.384294\pi\) |
−0.987212 | + | 0.159414i | \(0.949040\pi\) | |||||||
\(308\) | 1335.90 | + | 2313.86i | 0.247144 | + | 0.428065i | ||||
\(309\) | 162.450 | − | 281.372i | 0.0299077 | − | 0.0518016i | ||||
\(310\) | −675.806 | − | 1170.53i | −0.123817 | − | 0.214457i | ||||
\(311\) | −4418.47 | −0.805622 | −0.402811 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402811 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(312\) | 1350.64 | 0.245081 | ||||||||
\(313\) | 695.780 | + | 1205.13i | 0.125648 | + | 0.217629i | 0.921986 | − | 0.387223i | \(-0.126566\pi\) |
−0.796338 | + | 0.604852i | \(0.793232\pi\) | |||||||
\(314\) | 2962.57 | + | 5131.32i | 0.532444 | + | 0.922221i | ||||
\(315\) | −1477.60 | −0.264297 | ||||||||
\(316\) | −3541.19 | −0.630403 | ||||||||
\(317\) | −2999.34 | − | 5195.01i | −0.531419 | − | 0.920444i | −0.999328 | − | 0.0366675i | \(-0.988326\pi\) |
0.467909 | − | 0.883777i | \(-0.345008\pi\) | |||||||
\(318\) | 1221.84 | − | 2116.29i | 0.215464 | − | 0.373194i | ||||
\(319\) | 2190.20 | + | 3793.54i | 0.384413 | + | 0.665823i | ||||
\(320\) | 166.835 | − | 288.966i | 0.0291448 | − | 0.0504803i | ||||
\(321\) | −2730.04 | + | 4728.56i | −0.474691 | + | 0.822188i | ||||
\(322\) | 12994.0 | 2.24884 | ||||||||
\(323\) | 1430.92 | − | 18.7082i | 0.246498 | − | 0.00322276i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 2752.46 | − | 4767.40i | 0.469782 | − | 0.813686i | ||||
\(326\) | 626.972 | − | 1085.95i | 0.106518 | − | 0.184494i | ||||
\(327\) | −178.715 | − | 309.543i | −0.0302231 | − | 0.0523480i | ||||
\(328\) | 1741.81 | − | 3016.91i | 0.293218 | − | 0.507869i | ||||
\(329\) | −1708.08 | − | 2958.47i | −0.286229 | − | 0.495763i | ||||
\(330\) | 663.521 | 0.110684 | ||||||||
\(331\) | −6604.73 | −1.09676 | −0.548382 | − | 0.836228i | \(-0.684756\pi\) | ||||
−0.548382 | + | 0.836228i | \(0.684756\pi\) | |||||||
\(332\) | 1147.26 | + | 1987.12i | 0.189651 | + | 0.328486i | ||||
\(333\) | −1980.95 | − | 3431.11i | −0.325993 | − | 0.564636i | ||||
\(334\) | −3204.31 | −0.524947 | ||||||||
\(335\) | 1098.74 | 0.179196 | ||||||||
\(336\) | 755.771 | + | 1309.03i | 0.122710 | + | 0.212541i | ||||
\(337\) | 2396.45 | − | 4150.77i | 0.387367 | − | 0.670940i | −0.604727 | − | 0.796433i | \(-0.706718\pi\) |
0.992095 | + | 0.125493i | \(0.0400511\pi\) | |||||||
\(338\) | 970.087 | + | 1680.24i | 0.156112 | + | 0.270393i | ||||
\(339\) | 1522.44 | − | 2636.94i | 0.243916 | − | 0.422474i | ||||
\(340\) | 180.173 | − | 312.069i | 0.0287390 | − | 0.0497774i | ||||
\(341\) | −2749.49 | −0.436637 | ||||||||
\(342\) | 762.186 | + | 1281.17i | 0.120510 | + | 0.202566i | ||||
\(343\) | 9625.03 | 1.51517 | ||||||||
\(344\) | 519.987 | − | 900.644i | 0.0814995 | − | 0.141161i | ||||
\(345\) | 1613.47 | − | 2794.62i | 0.251787 | − | 0.436108i | ||||
\(346\) | 2290.69 | + | 3967.59i | 0.355919 | + | 0.616471i | ||||
\(347\) | −2435.68 | + | 4218.72i | −0.376813 | + | 0.652660i | −0.990597 | − | 0.136815i | \(-0.956314\pi\) |
0.613783 | + | 0.789475i | \(0.289647\pi\) | |||||||
\(348\) | 1239.08 | + | 2146.15i | 0.190867 | + | 0.330591i | ||||
\(349\) | −2676.44 | −0.410506 | −0.205253 | − | 0.978709i | \(-0.565802\pi\) | ||||
−0.205253 | + | 0.978709i | \(0.565802\pi\) | |||||||
\(350\) | 6160.70 | 0.940867 | ||||||||
\(351\) | 759.738 | + | 1315.90i | 0.115532 | + | 0.200108i | ||||
\(352\) | −339.380 | − | 587.824i | −0.0513893 | − | 0.0890088i | ||||
\(353\) | 3111.41 | 0.469132 | 0.234566 | − | 0.972100i | \(-0.424633\pi\) | ||||
0.234566 | + | 0.972100i | \(0.424633\pi\) | |||||||
\(354\) | −697.469 | −0.104718 | ||||||||
\(355\) | 411.918 | + | 713.463i | 0.0615841 | + | 0.106667i | ||||
\(356\) | −430.471 | + | 745.598i | −0.0640868 | + | 0.111002i | ||||
\(357\) | 816.195 | + | 1413.69i | 0.121002 | + | 0.209581i | ||||
\(358\) | −218.545 | + | 378.530i | −0.0322638 | + | 0.0558826i | ||||
\(359\) | 467.879 | − | 810.391i | 0.0687847 | − | 0.119139i | −0.829582 | − | 0.558385i | \(-0.811421\pi\) |
0.898367 | + | 0.439246i | \(0.144755\pi\) | |||||||
\(360\) | 375.378 | 0.0549560 | ||||||||
\(361\) | −3273.03 | + | 6027.70i | −0.477188 | + | 0.878801i | ||||
\(362\) | 7496.88 | 1.08847 | ||||||||
\(363\) | −1321.62 | + | 2289.12i | −0.191094 | + | 0.330985i | ||||
\(364\) | −3544.37 | + | 6139.03i | −0.510372 | + | 0.883990i | ||||
\(365\) | 1495.12 | + | 2589.62i | 0.214406 | + | 0.371362i | ||||
\(366\) | 1022.05 | − | 1770.25i | 0.145966 | − | 0.252821i | ||||
\(367\) | −5504.62 | − | 9534.29i | −0.782940 | − | 1.35609i | −0.930222 | − | 0.366997i | \(-0.880386\pi\) |
0.147282 | − | 0.989095i | \(-0.452947\pi\) | |||||||
\(368\) | −3301.06 | −0.467608 | ||||||||
\(369\) | 3919.08 | 0.552898 | ||||||||
\(370\) | −2295.08 | − | 3975.20i | −0.322475 | − | 0.558543i | ||||
\(371\) | 6412.72 | + | 11107.2i | 0.897390 | + | 1.55433i | ||||
\(372\) | −1555.49 | −0.216797 | ||||||||
\(373\) | −6151.39 | −0.853906 | −0.426953 | − | 0.904274i | \(-0.640413\pi\) | ||||
−0.426953 | + | 0.904274i | \(0.640413\pi\) | |||||||
\(374\) | −366.514 | − | 634.820i | −0.0506737 | − | 0.0877694i | ||||
\(375\) | 1742.53 | − | 3018.14i | 0.239956 | − | 0.415617i | ||||
\(376\) | 433.928 | + | 751.586i | 0.0595163 | + | 0.103085i | ||||
\(377\) | −5810.96 | + | 10064.9i | −0.793845 | + | 1.37498i | ||||
\(378\) | −850.242 | + | 1472.66i | −0.115692 | + | 0.200385i | ||||
\(379\) | 13458.6 | 1.82407 | 0.912037 | − | 0.410109i | \(-0.134509\pi\) | ||||
0.912037 | + | 0.410109i | \(0.134509\pi\) | |||||||
\(380\) | 883.049 | + | 1484.33i | 0.119209 | + | 0.200380i | ||||
\(381\) | −3084.60 | −0.414774 | ||||||||
\(382\) | −141.733 | + | 245.489i | −0.0189835 | + | 0.0328804i | ||||
\(383\) | 5545.19 | − | 9604.56i | 0.739807 | − | 1.28138i | −0.212775 | − | 0.977101i | \(-0.568250\pi\) |
0.952582 | − | 0.304282i | \(-0.0984166\pi\) | |||||||
\(384\) | −192.000 | − | 332.554i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −1741.21 | + | 3015.87i | −0.230495 | + | 0.399229i | ||||
\(386\) | −3909.89 | − | 6772.14i | −0.515566 | − | 0.892986i | ||||
\(387\) | 1169.97 | 0.153677 | ||||||||
\(388\) | 2115.90 | 0.276851 | ||||||||
\(389\) | −636.543 | − | 1102.53i | −0.0829667 | − | 0.143702i | 0.821556 | − | 0.570127i | \(-0.193106\pi\) |
−0.904523 | + | 0.426425i | \(0.859773\pi\) | |||||||
\(390\) | 880.213 | + | 1524.57i | 0.114285 | + | 0.197948i | ||||
\(391\) | −3564.98 | −0.461097 | ||||||||
\(392\) | −5189.19 | −0.668607 | ||||||||
\(393\) | −2383.75 | − | 4128.78i | −0.305965 | − | 0.529948i | ||||
\(394\) | 1203.16 | − | 2083.93i | 0.153843 | − | 0.266464i | ||||
\(395\) | −2307.79 | − | 3997.20i | −0.293968 | − | 0.509168i | ||||
\(396\) | 381.803 | − | 661.302i | 0.0484503 | − | 0.0839183i | ||||
\(397\) | 6164.46 | − | 10677.2i | 0.779309 | − | 1.34980i | −0.153032 | − | 0.988221i | \(-0.548904\pi\) |
0.932341 | − | 0.361581i | \(-0.117763\pi\) | |||||||
\(398\) | −7406.92 | −0.932853 | ||||||||
\(399\) | −7823.36 | + | 102.284i | −0.981599 | + | 0.0128336i | ||||
\(400\) | −1565.10 | −0.195637 | ||||||||
\(401\) | −4899.77 | + | 8486.65i | −0.610181 | + | 1.05687i | 0.381028 | + | 0.924563i | \(0.375570\pi\) |
−0.991209 | + | 0.132302i | \(0.957763\pi\) | |||||||
\(402\) | 632.236 | − | 1095.07i | 0.0784405 | − | 0.135863i | ||||
\(403\) | −3647.42 | − | 6317.51i | −0.450846 | − | 0.780887i | ||||
\(404\) | −2057.47 | + | 3563.65i | −0.253374 | + | 0.438856i | ||||
\(405\) | 211.150 | + | 365.723i | 0.0259065 | + | 0.0448714i | ||||
\(406\) | −13006.4 | −1.58989 | ||||||||
\(407\) | −9337.46 | −1.13720 | ||||||||
\(408\) | −207.350 | − | 359.141i | −0.0251602 | − | 0.0435788i | ||||
\(409\) | −4042.33 | − | 7001.52i | −0.488705 | − | 0.846461i | 0.511211 | − | 0.859455i | \(-0.329197\pi\) |
−0.999916 | + | 0.0129939i | \(0.995864\pi\) | |||||||
\(410\) | 4540.55 | 0.546931 | ||||||||
\(411\) | 6975.20 | 0.837132 | ||||||||
\(412\) | −216.600 | − | 375.163i | −0.0259008 | − | 0.0448615i | ||||
\(413\) | 1830.30 | − | 3170.17i | 0.218071 | − | 0.377710i | ||||
\(414\) | −1856.85 | − | 3216.15i | −0.220433 | − | 0.381800i | ||||
\(415\) | −1495.34 | + | 2590.00i | −0.176876 | + | 0.306357i | ||||
\(416\) | 900.430 | − | 1559.59i | 0.106123 | − | 0.183811i | ||||
\(417\) | −1905.17 | −0.223733 | ||||||||
\(418\) | 3513.09 | − | 45.9308i | 0.411079 | − | 0.00537452i | ||||
\(419\) | −78.3882 | −0.00913965 | −0.00456983 | − | 0.999990i | \(-0.501455\pi\) | ||||
−0.00456983 | + | 0.999990i | \(0.501455\pi\) | |||||||
\(420\) | −985.069 | + | 1706.19i | −0.114444 | + | 0.198223i | ||||
\(421\) | −3542.60 | + | 6135.95i | −0.410108 | + | 0.710328i | −0.994901 | − | 0.100854i | \(-0.967842\pi\) |
0.584793 | + | 0.811183i | \(0.301176\pi\) | |||||||
\(422\) | −25.6998 | − | 44.5134i | −0.00296457 | − | 0.00513478i | ||||
\(423\) | −488.169 | + | 845.534i | −0.0561125 | + | 0.0971898i | ||||
\(424\) | −1629.12 | − | 2821.72i | −0.186597 | − | 0.323195i | ||||
\(425\) | −1690.23 | −0.192913 | ||||||||
\(426\) | 948.103 | 0.107830 | ||||||||
\(427\) | 5364.16 | + | 9290.99i | 0.607938 | + | 1.05298i | ||||
\(428\) | 3640.05 | + | 6304.75i | 0.411094 | + | 0.712036i | ||||
\(429\) | 3581.11 | 0.403025 | ||||||||
\(430\) | 1355.50 | 0.152019 | ||||||||
\(431\) | 7450.70 | + | 12905.0i | 0.832686 | + | 1.44225i | 0.895900 | + | 0.444255i | \(0.146532\pi\) |
−0.0632142 | + | 0.998000i | \(0.520135\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −2114.74 | − | 3662.84i | −0.234707 | − | 0.406524i | 0.724481 | − | 0.689295i | \(-0.242080\pi\) |
−0.959187 | + | 0.282771i | \(0.908746\pi\) | |||||||
\(434\) | 4081.92 | − | 7070.09i | 0.451471 | − | 0.781971i | ||||
\(435\) | −1615.01 | + | 2797.28i | −0.178009 | + | 0.308321i | ||||
\(436\) | −476.573 | −0.0523480 | ||||||||
\(437\) | 8349.29 | − | 14908.1i | 0.913960 | − | 1.63193i | ||||
\(438\) | 3441.28 | 0.375413 | ||||||||
\(439\) | −5260.77 | + | 9111.93i | −0.571943 | + | 0.990634i | 0.424423 | + | 0.905464i | \(0.360477\pi\) |
−0.996366 | + | 0.0851705i | \(0.972857\pi\) | |||||||
\(440\) | 442.347 | − | 766.168i | 0.0479274 | − | 0.0830127i | ||||
\(441\) | −2918.92 | − | 5055.72i | −0.315184 | − | 0.545915i | ||||
\(442\) | 972.419 | − | 1684.28i | 0.104645 | − | 0.181251i | ||||
\(443\) | −6933.71 | − | 12009.5i | −0.743636 | − | 1.28801i | −0.950829 | − | 0.309715i | \(-0.899766\pi\) |
0.207194 | − | 0.978300i | \(-0.433567\pi\) | |||||||
\(444\) | −5282.55 | −0.564636 | ||||||||
\(445\) | −1122.15 | −0.119539 | ||||||||
\(446\) | −3105.19 | − | 5378.34i | −0.329675 | − | 0.571013i | ||||
\(447\) | 2547.47 | + | 4412.35i | 0.269555 | + | 0.466883i | ||||
\(448\) | 2015.39 | 0.212541 | ||||||||
\(449\) | 9599.89 | 1.00901 | 0.504507 | − | 0.863408i | \(-0.331674\pi\) | ||||
0.504507 | + | 0.863408i | \(0.331674\pi\) | |||||||
\(450\) | −880.367 | − | 1524.84i | −0.0922242 | − | 0.159737i | ||||
\(451\) | 4618.26 | − | 7999.06i | 0.482185 | − | 0.835169i | ||||
\(452\) | −2029.92 | − | 3515.92i | −0.211237 | − | 0.365874i | ||||
\(453\) | −2448.58 | + | 4241.06i | −0.253961 | + | 0.439873i | ||||
\(454\) | 664.566 | − | 1151.06i | 0.0686996 | − | 0.118991i | ||||
\(455\) | −9239.44 | −0.951981 | ||||||||
\(456\) | 1987.49 | − | 25.9848i | 0.204107 | − | 0.00266853i | ||||
\(457\) | −6261.10 | −0.640880 | −0.320440 | − | 0.947269i | \(-0.603831\pi\) | ||||
−0.320440 | + | 0.947269i | \(0.603831\pi\) | |||||||
\(458\) | −6031.99 | + | 10447.7i | −0.615407 | + | 1.06592i | ||||
\(459\) | 233.269 | − | 404.034i | 0.0237213 | − | 0.0410865i | ||||
\(460\) | −2151.30 | − | 3726.16i | −0.218054 | − | 0.377680i | ||||
\(461\) | 4912.78 | − | 8509.18i | 0.496336 | − | 0.859679i | −0.503655 | − | 0.863905i | \(-0.668012\pi\) |
0.999991 | + | 0.00422602i | \(0.00134519\pi\) | |||||||
\(462\) | 2003.86 | + | 3470.78i | 0.201792 | + | 0.349514i | ||||
\(463\) | 9276.57 | 0.931142 | 0.465571 | − | 0.885011i | \(-0.345849\pi\) | ||||
0.465571 | + | 0.885011i | \(0.345849\pi\) | |||||||
\(464\) | 3304.21 | 0.330591 | ||||||||
\(465\) | −1013.71 | − | 1755.80i | −0.101096 | − | 0.175103i | ||||
\(466\) | −5758.16 | − | 9973.43i | −0.572407 | − | 0.991438i | ||||
\(467\) | 18209.4 | 1.80435 | 0.902174 | − | 0.431372i | \(-0.141970\pi\) | ||||
0.902174 | + | 0.431372i | \(0.141970\pi\) | |||||||
\(468\) | 2025.97 | 0.200108 | ||||||||
\(469\) | 3318.24 | + | 5747.35i | 0.326699 | + | 0.565859i | ||||
\(470\) | −565.581 | + | 979.615i | −0.0555070 | + | 0.0961410i | ||||
\(471\) | 4443.86 | + | 7696.98i | 0.434739 | + | 0.752990i | ||||
\(472\) | −464.979 | + | 805.367i | −0.0453441 | + | 0.0785382i | ||||
\(473\) | 1378.70 | − | 2387.97i | 0.134022 | − | 0.232134i | ||||
\(474\) | −5311.78 | −0.514722 | ||||||||
\(475\) | 3958.55 | − | 7068.23i | 0.382381 | − | 0.682764i | ||||
\(476\) | 2176.52 | 0.209581 | ||||||||
\(477\) | 1832.76 | − | 3174.43i | 0.175925 | − | 0.304711i | ||||
\(478\) | −741.406 | + | 1284.15i | −0.0709437 | + | 0.122878i | ||||
\(479\) | −6370.84 | − | 11034.6i | −0.607706 | − | 1.05258i | −0.991618 | − | 0.129208i | \(-0.958757\pi\) |
0.383912 | − | 0.923370i | \(-0.374577\pi\) | |||||||
\(480\) | 250.252 | − | 433.449i | 0.0237967 | − | 0.0412170i | ||||
\(481\) | −12386.9 | − | 21454.7i | −1.17421 | − | 2.03378i | ||||
\(482\) | −10548.1 | −0.996794 | ||||||||
\(483\) | 19491.0 | 1.83617 | ||||||||
\(484\) | 1762.16 | + | 3052.16i | 0.165493 | + | 0.286641i | ||||
\(485\) | 1378.93 | + | 2388.37i | 0.129101 | + | 0.223609i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −5006.72 | −0.465864 | −0.232932 | − | 0.972493i | \(-0.574832\pi\) | ||||
−0.232932 | + | 0.972493i | \(0.574832\pi\) | |||||||
\(488\) | −1362.74 | − | 2360.33i | −0.126410 | − | 0.218949i | ||||
\(489\) | 940.458 | − | 1628.92i | 0.0869713 | − | 0.150639i | ||||
\(490\) | −3381.79 | − | 5857.43i | −0.311783 | − | 0.540024i | ||||
\(491\) | −481.656 | + | 834.253i | −0.0442705 | + | 0.0766788i | −0.887312 | − | 0.461170i | \(-0.847430\pi\) |
0.843041 | + | 0.537849i | \(0.180763\pi\) | |||||||
\(492\) | 2612.72 | − | 4525.37i | 0.239412 | − | 0.414673i | ||||
\(493\) | 3568.38 | 0.325988 | ||||||||
\(494\) | 4765.94 | + | 8011.12i | 0.434068 | + | 0.729630i | ||||
\(495\) | 995.281 | 0.0903728 | ||||||||
\(496\) | −1036.99 | + | 1796.12i | −0.0938756 | + | 0.162597i | ||||
\(497\) | −2488.02 | + | 4309.37i | −0.224553 | + | 0.388937i | ||||
\(498\) | 1720.90 | + | 2980.68i | 0.154850 | + | 0.268208i | ||||
\(499\) | −2482.42 | + | 4299.68i | −0.222702 | + | 0.385732i | −0.955628 | − | 0.294577i | \(-0.904821\pi\) |
0.732925 | + | 0.680309i | \(0.238154\pi\) | |||||||
\(500\) | −2323.37 | − | 4024.19i | −0.207808 | − | 0.359935i | ||||
\(501\) | −4806.47 | −0.428617 | ||||||||
\(502\) | −5692.71 | −0.506132 | ||||||||
\(503\) | 7384.24 | + | 12789.9i | 0.654567 | + | 1.13374i | 0.982002 | + | 0.188869i | \(0.0604823\pi\) |
−0.327435 | + | 0.944874i | \(0.606184\pi\) | |||||||
\(504\) | 1133.66 | + | 1963.55i | 0.100193 | + | 0.173539i | ||||
\(505\) | −5363.40 | −0.472610 | ||||||||
\(506\) | −8752.46 | −0.768962 | ||||||||
\(507\) | 1455.13 | + | 2520.36i | 0.127465 | + | 0.220775i | ||||
\(508\) | −2056.40 | + | 3561.79i | −0.179603 | + | 0.311081i | ||||
\(509\) | −3007.96 | − | 5209.94i | −0.261936 | − | 0.453686i | 0.704820 | − | 0.709386i | \(-0.251028\pi\) |
−0.966756 | + | 0.255699i | \(0.917694\pi\) | |||||||
\(510\) | 270.260 | − | 468.104i | 0.0234653 | − | 0.0406431i | ||||
\(511\) | −9030.63 | + | 15641.5i | −0.781784 | + | 1.35409i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1143.28 | + | 1921.75i | 0.0983957 | + | 0.165394i | ||||
\(514\) | −12881.4 | −1.10540 | ||||||||
\(515\) | 282.316 | − | 488.986i | 0.0241560 | − | 0.0418394i | ||||
\(516\) | 779.981 | − | 1350.97i | 0.0665441 | − | 0.115258i | ||||
\(517\) | 1150.52 | + | 1992.76i | 0.0978721 | + | 0.169519i | ||||
\(518\) | 13862.5 | − | 24010.5i | 1.17584 | − | 2.03661i | ||||
\(519\) | 3436.03 | + | 5951.38i | 0.290607 | + | 0.503346i | ||||
\(520\) | 2347.23 | 0.197948 | ||||||||
\(521\) | 10009.4 | 0.841685 | 0.420842 | − | 0.907134i | \(-0.361735\pi\) | ||||
0.420842 | + | 0.907134i | \(0.361735\pi\) | |||||||
\(522\) | 1858.62 | + | 3219.22i | 0.155842 | + | 0.269926i | ||||
\(523\) | −1244.04 | − | 2154.75i | −0.104012 | − | 0.180154i | 0.809322 | − | 0.587365i | \(-0.199835\pi\) |
−0.913334 | + | 0.407211i | \(0.866501\pi\) | |||||||
\(524\) | −6356.67 | −0.529948 | ||||||||
\(525\) | 9241.05 | 0.768214 | ||||||||
\(526\) | 4140.40 | + | 7171.39i | 0.343213 | + | 0.594463i | ||||
\(527\) | −1119.90 | + | 1939.72i | −0.0925685 | + | 0.160333i | ||||
\(528\) | −509.070 | − | 881.736i | −0.0419592 | − | 0.0726754i | ||||
\(529\) | −15199.7 | + | 26326.7i | −1.24926 | + | 2.16378i | ||||
\(530\) | 2123.39 | − | 3677.82i | 0.174027 | − | 0.301423i | ||||
\(531\) | −1046.20 | −0.0855016 | ||||||||
\(532\) | −5097.47 | + | 9101.83i | −0.415420 | + | 0.741757i | ||||
\(533\) | 24506.0 | 1.99150 | ||||||||
\(534\) | −645.706 | + | 1118.40i | −0.0523267 | + | 0.0906325i | ||||
\(535\) | −4744.43 | + | 8217.59i | −0.383401 | + | 0.664070i | ||||
\(536\) | −842.982 | − | 1460.09i | −0.0679315 | − | 0.117661i | ||||
\(537\) | −327.817 | + | 567.796i | −0.0263433 | + | 0.0456279i | ||||
\(538\) | 3165.99 | + | 5483.66i | 0.253709 | + | 0.439438i | ||||
\(539\) | −13758.7 | −1.09949 | ||||||||
\(540\) | 563.067 | 0.0448714 | ||||||||
\(541\) | 4866.02 | + | 8428.19i | 0.386703 | + | 0.669790i | 0.992004 | − | 0.126207i | \(-0.0402804\pi\) |
−0.605301 | + | 0.795997i | \(0.706947\pi\) | |||||||
\(542\) | 6444.23 | + | 11161.7i | 0.510707 | + | 0.884571i | ||||
\(543\) | 11245.3 | 0.888735 | ||||||||
\(544\) | −552.934 | −0.0435788 | ||||||||
\(545\) | −310.582 | − | 537.944i | −0.0244108 | − | 0.0422807i | ||||
\(546\) | −5316.55 | + | 9208.54i | −0.416717 | + | 0.721775i | ||||
\(547\) | −6216.18 | − | 10766.7i | −0.485895 | − | 0.841596i | 0.513973 | − | 0.857806i | \(-0.328173\pi\) |
−0.999869 | + | 0.0162107i | \(0.994840\pi\) | |||||||
\(548\) | 4650.13 | − | 8054.26i | 0.362489 | − | 0.627849i | ||||
\(549\) | 1533.08 | − | 2655.37i | 0.119181 | − | 0.206427i | ||||
\(550\) | −4149.71 | −0.321717 | ||||||||
\(551\) | −8357.25 | + | 14922.4i | −0.646154 | + | 1.15375i | ||||
\(552\) | −4951.59 | −0.381800 | ||||||||
\(553\) | 13939.2 | − | 24143.4i | 1.07189 | − | 1.85657i | ||||
\(554\) | 399.738 | − | 692.367i | 0.0306557 | − | 0.0530972i | ||||
\(555\) | −3442.63 | − | 5962.80i | −0.263300 | − | 0.456049i | ||||
\(556\) | −1270.11 | + | 2199.90i | −0.0968790 | + | 0.167799i | ||||
\(557\) | 8952.74 | + | 15506.6i | 0.681041 | + | 1.17960i | 0.974664 | + | 0.223676i | \(0.0718058\pi\) |
−0.293623 | + | 0.955921i | \(0.594861\pi\) | |||||||
\(558\) | −2333.23 | −0.177014 | ||||||||
\(559\) | 7315.81 | 0.553535 | ||||||||
\(560\) | 1313.43 | + | 2274.92i | 0.0991114 | + | 0.171666i | ||||
\(561\) | −549.770 | − | 952.230i | −0.0413749 | − | 0.0716634i | ||||
\(562\) | −1260.73 | −0.0946278 | ||||||||
\(563\) | −1825.07 | −0.136621 | −0.0683106 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683106 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(564\) | 650.892 | + | 1127.38i | 0.0485949 | + | 0.0841688i | ||||
\(565\) | 2645.79 | − | 4582.64i | 0.197007 | − | 0.341226i | ||||
\(566\) | 1996.63 | + | 3458.27i | 0.148277 | + | 0.256823i | ||||
\(567\) | −1275.36 | + | 2208.99i | −0.0944625 | + | 0.163614i | ||||
\(568\) | 632.069 | − | 1094.78i | 0.0466919 | − | 0.0808728i | ||||
\(569\) | −4974.94 | −0.366538 | −0.183269 | − | 0.983063i | \(-0.558668\pi\) | ||||
−0.183269 | + | 0.983063i | \(0.558668\pi\) | |||||||
\(570\) | 1324.57 | + | 2226.49i | 0.0973338 | + | 0.163610i | ||||
\(571\) | 14203.4 | 1.04097 | 0.520485 | − | 0.853871i | \(-0.325751\pi\) | ||||
0.520485 | + | 0.853871i | \(0.325751\pi\) | |||||||
\(572\) | 2387.41 | − | 4135.11i | 0.174515 | − | 0.302269i | ||||
\(573\) | −212.600 | + | 368.234i | −0.0155000 | + | 0.0268467i | ||||
\(574\) | 13712.6 | + | 23751.0i | 0.997133 | + | 1.72709i | ||||
\(575\) | −10090.8 | + | 17477.8i | −0.731852 | + | 1.26760i | ||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 5279.89 | 0.380944 | 0.190472 | − | 0.981693i | \(-0.438998\pi\) | ||||
0.190472 | + | 0.981693i | \(0.438998\pi\) | |||||||
\(578\) | 9228.86 | 0.664135 | ||||||||
\(579\) | −5864.84 | − | 10158.2i | −0.420958 | − | 0.729120i | ||||
\(580\) | 2153.35 | + | 3729.71i | 0.154160 | + | 0.267013i | ||||
\(581\) | −18063.9 | −1.28988 | ||||||||
\(582\) | 3173.84 | 0.226048 | ||||||||
\(583\) | −4319.46 | − | 7481.53i | −0.306851 | − | 0.531481i | ||||
\(584\) | 2294.19 | − | 3973.65i | 0.162559 | − | 0.281560i | ||||
\(585\) | 1320.32 | + | 2286.86i | 0.0933137 | + | 0.161624i | ||||
\(586\) | 9676.85 | − | 16760.8i | 0.682162 | − | 1.18154i | ||||
\(587\) | −6614.29 | + | 11456.3i | −0.465078 | + | 0.805539i | −0.999205 | − | 0.0398654i | \(-0.987307\pi\) |
0.534127 | + | 0.845404i | \(0.320640\pi\) | |||||||
\(588\) | −7783.79 | −0.545915 | ||||||||
\(589\) | −5488.75 | − | 9226.11i | −0.383973 | − | 0.645425i | ||||
\(590\) | −1212.10 | −0.0845789 | ||||||||
\(591\) | 1804.74 | − | 3125.90i | 0.125612 | − | 0.217567i | ||||
\(592\) | −3521.70 | + | 6099.76i | −0.244495 | + | 0.423477i | ||||
\(593\) | 348.240 | + | 603.169i | 0.0241155 | + | 0.0417693i | 0.877831 | − | 0.478970i | \(-0.158990\pi\) |
−0.853716 | + | 0.520739i | \(0.825656\pi\) | |||||||
\(594\) | 572.704 | − | 991.953i | 0.0395595 | − | 0.0685190i | ||||
\(595\) | 1418.43 | + | 2456.80i | 0.0977313 | + | 0.169276i | ||||
\(596\) | 6793.25 | 0.466883 | ||||||||
\(597\) | −11110.4 | −0.761671 | ||||||||
\(598\) | −11610.8 | − | 20110.6i | −0.793985 | − | 1.37522i | ||||
\(599\) | −11348.5 | − | 19656.2i | −0.774105 | − | 1.34079i | −0.935296 | − | 0.353865i | \(-0.884867\pi\) |
0.161192 | − | 0.986923i | \(-0.448466\pi\) | |||||||
\(600\) | −2347.64 | −0.159737 | ||||||||
\(601\) | 15591.5 | 1.05822 | 0.529110 | − | 0.848553i | \(-0.322526\pi\) | ||||
0.529110 | + | 0.848553i | \(0.322526\pi\) | |||||||
\(602\) | 4093.66 | + | 7090.42i | 0.277151 | + | 0.480040i | ||||
\(603\) | 948.354 | − | 1642.60i | 0.0640464 | − | 0.110932i | ||||
\(604\) | 3264.77 | + | 5654.75i | 0.219936 | + | 0.380941i | ||||
\(605\) | −2296.80 | + | 3978.17i | −0.154344 | + | 0.267332i | ||||
\(606\) | −3086.21 | + | 5345.47i | −0.206879 | + | 0.358325i | ||||
\(607\) | 13728.2 | 0.917975 | 0.458988 | − | 0.888443i | \(-0.348212\pi\) | ||||
0.458988 | + | 0.888443i | \(0.348212\pi\) | |||||||
\(608\) | 1294.99 | − | 2312.28i | 0.0863794 | − | 0.154236i | ||||
\(609\) | −19509.6 | −1.29814 | ||||||||
\(610\) | 1776.19 | − | 3076.45i | 0.117895 | − | 0.204200i | ||||
\(611\) | −3052.52 | + | 5287.11i | −0.202114 | + | 0.350072i | ||||
\(612\) | −311.026 | − | 538.712i | −0.0205432 | − | 0.0355819i | ||||
\(613\) | −10985.7 | + | 19027.7i | −0.723829 | + | 1.25371i | 0.235625 | + | 0.971844i | \(0.424286\pi\) |
−0.959454 | + | 0.281864i | \(0.909047\pi\) | |||||||
\(614\) | 6795.52 | + | 11770.2i | 0.446653 | + | 0.773625i | ||||
\(615\) | 6810.83 | 0.446568 | ||||||||
\(616\) | 5343.62 | 0.349514 | ||||||||
\(617\) | 9259.34 | + | 16037.6i | 0.604160 | + | 1.04644i | 0.992184 | + | 0.124787i | \(0.0398247\pi\) |
−0.388023 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(618\) | −324.901 | − | 562.744i | −0.0211479 | − | 0.0366293i | ||||
\(619\) | −7363.53 | −0.478134 | −0.239067 | − | 0.971003i | \(-0.576842\pi\) | ||||
−0.239067 | + | 0.971003i | \(0.576842\pi\) | |||||||
\(620\) | −2703.22 | −0.175103 | ||||||||
\(621\) | −2785.27 | − | 4824.23i | −0.179982 | − | 0.311739i | ||||
\(622\) | −4418.47 | + | 7653.02i | −0.284831 | + | 0.493341i | ||||
\(623\) | −3388.93 | − | 5869.80i | −0.217937 | − | 0.377478i | ||||
\(624\) | 1350.64 | − | 2339.39i | 0.0866492 | − | 0.150081i | ||||
\(625\) | −3085.39 | + | 5344.05i | −0.197465 | + | 0.342019i | ||||
\(626\) | 2783.12 | 0.177693 | ||||||||
\(627\) | 5269.64 | − | 68.8963i | 0.335645 | − | 0.00438828i | ||||
\(628\) | 11850.3 | 0.752990 | ||||||||
\(629\) | −3803.26 | + | 6587.43i | −0.241090 | + | 0.417581i | ||||
\(630\) | −1477.60 | + | 2559.29i | −0.0934431 | + | 0.161848i | ||||
\(631\) | 10189.5 | + | 17648.7i | 0.642848 | + | 1.11345i | 0.984794 | + | 0.173726i | \(0.0555808\pi\) |
−0.341946 | + | 0.939720i | \(0.611086\pi\) | |||||||
\(632\) | −3541.19 | + | 6133.52i | −0.222881 | + | 0.386042i | ||||
\(633\) | −38.5497 | − | 66.7701i | −0.00242056 | − | 0.00419253i | ||||
\(634\) | −11997.4 | −0.751540 | ||||||||
\(635\) | −5360.61 | −0.335007 | ||||||||
\(636\) | −2443.68 | − | 4232.58i | −0.152356 | − | 0.263888i | ||||
\(637\) | −18252.0 | − | 31613.3i | −1.13527 | − | 1.96635i | ||||
\(638\) | 8760.81 | 0.543643 | ||||||||
\(639\) | 1422.16 | 0.0880432 | ||||||||
\(640\) | −333.670 | − | 577.933i | −0.0206085 | − | 0.0356950i | ||||
\(641\) | −993.124 | + | 1720.14i | −0.0611951 | + | 0.105993i | −0.895000 | − | 0.446066i | \(-0.852825\pi\) |
0.833805 | + | 0.552059i | \(0.186158\pi\) | |||||||
\(642\) | 5460.07 | + | 9457.12i | 0.335657 | + | 0.581375i | ||||
\(643\) | 5578.32 | − | 9661.94i | 0.342127 | − | 0.592581i | −0.642701 | − | 0.766117i | \(-0.722186\pi\) |
0.984827 | + | 0.173536i | \(0.0555194\pi\) | |||||||
\(644\) | 12994.0 | − | 22506.3i | 0.795086 | − | 1.37713i | ||||
\(645\) | 2033.25 | 0.124123 | ||||||||
\(646\) | 1398.52 | − | 2497.14i | 0.0851766 | − | 0.152088i | ||||
\(647\) | −18657.7 | −1.13371 | −0.566854 | − | 0.823818i | \(-0.691840\pi\) | ||||
−0.566854 | + | 0.823818i | \(0.691840\pi\) | |||||||
\(648\) | 324.000 | − | 561.184i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −1232.85 | + | 2135.36i | −0.0745664 | + | 0.129153i | ||||
\(650\) | −5504.92 | − | 9534.80i | −0.332186 | − | 0.575363i | ||||
\(651\) | 6122.88 | − | 10605.1i | 0.368625 | − | 0.638476i | ||||
\(652\) | −1253.94 | − | 2171.89i | −0.0753193 | − | 0.130457i | ||||
\(653\) | 7972.68 | 0.477787 | 0.238894 | − | 0.971046i | \(-0.423215\pi\) | ||||
0.238894 | + | 0.971046i | \(0.423215\pi\) | |||||||
\(654\) | −714.860 | −0.0427420 | ||||||||
\(655\) | −4142.63 | − | 7175.25i | −0.247124 | − | 0.428031i | ||||
\(656\) | −3483.63 | − | 6033.82i | −0.207337 | − | 0.359118i | ||||
\(657\) | 5161.93 | 0.306523 | ||||||||
\(658\) | −6832.30 | −0.404789 | ||||||||
\(659\) | −2663.80 | − | 4613.84i | −0.157461 | − | 0.272731i | 0.776491 | − | 0.630128i | \(-0.216998\pi\) |
−0.933953 | + | 0.357397i | \(0.883664\pi\) | |||||||
\(660\) | 663.521 | − | 1149.25i | 0.0391326 | − | 0.0677796i | ||||
\(661\) | 3472.53 | + | 6014.60i | 0.204336 | + | 0.353920i | 0.949921 | − | 0.312491i | \(-0.101163\pi\) |
−0.745585 | + | 0.666410i | \(0.767830\pi\) | |||||||
\(662\) | −6604.73 | + | 11439.7i | −0.387765 | + | 0.671628i | ||||
\(663\) | 1458.63 | − | 2526.42i | 0.0854426 | − | 0.147991i | ||||
\(664\) | 4589.06 | 0.268208 | ||||||||
\(665\) | −13595.9 | + | 177.756i | −0.792823 | + | 0.0103655i | ||||
\(666\) | −7923.82 | −0.461024 | ||||||||
\(667\) | 21303.5 | − | 36898.8i | 1.23670 | − | 2.14202i | ||||
\(668\) | −3204.31 | + | 5550.03i | −0.185597 | + | 0.321463i | ||||
\(669\) | −4657.78 | − | 8067.52i | −0.269178 | − | 0.466230i | ||||
\(670\) | 1098.74 | − | 1903.07i | 0.0633552 | − | 0.109735i | ||||
\(671\) | −3613.17 | − | 6258.20i | −0.207876 | − | 0.360052i | ||||
\(672\) | 3023.08 | 0.173539 | ||||||||
\(673\) | −8261.87 | −0.473212 | −0.236606 | − | 0.971606i | \(-0.576035\pi\) | ||||
−0.236606 | + | 0.971606i | \(0.576035\pi\) | |||||||
\(674\) | −4792.90 | − | 8301.54i | −0.273910 | − | 0.474426i | ||||
\(675\) | −1320.55 | − | 2287.26i | −0.0753007 | − | 0.130425i | ||||
\(676\) | 3880.35 | 0.220775 | ||||||||
\(677\) | 12128.3 | 0.688523 | 0.344261 | − | 0.938874i | \(-0.388129\pi\) | ||||
0.344261 | + | 0.938874i | \(0.388129\pi\) | |||||||
\(678\) | −3044.87 | − | 5273.88i | −0.172474 | − | 0.298735i | ||||
\(679\) | −8328.82 | + | 14425.9i | −0.470737 | + | 0.815341i | ||||
\(680\) | −360.346 | − | 624.138i | −0.0203215 | − | 0.0351980i | ||||
\(681\) | 996.849 | − | 1726.59i | 0.0560930 | − | 0.0971560i | ||||
\(682\) | −2749.49 | + | 4762.25i | −0.154374 | + | 0.267384i | ||||
\(683\) | 3609.67 | 0.202226 | 0.101113 | − | 0.994875i | \(-0.467760\pi\) | ||||
0.101113 | + | 0.994875i | \(0.467760\pi\) | |||||||
\(684\) | 2981.23 | − | 38.9772i | 0.166652 | − | 0.00217884i | ||||
\(685\) | 12121.9 | 0.676139 | ||||||||
\(686\) | 9625.03 | − | 16671.0i | 0.535693 | − | 0.927848i | ||||
\(687\) | −9047.99 | + | 15671.6i | −0.502478 | + | 0.870317i | ||||
\(688\) | −1039.97 | − | 1801.29i | −0.0576288 | − | 0.0998161i | ||||
\(689\) | 11460.2 | − | 19849.7i | 0.633672 | − | 1.09755i | ||||
\(690\) | −3226.95 | − | 5589.23i | −0.178040 | − | 0.308375i | ||||
\(691\) | −375.152 | −0.0206534 | −0.0103267 | − | 0.999947i | \(-0.503287\pi\) | ||||
−0.0103267 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(692\) | 9162.75 | 0.503346 | ||||||||
\(693\) | 3005.79 | + | 5206.17i | 0.164762 | + | 0.285377i | ||||
\(694\) | 4871.36 | + | 8437.45i | 0.266447 | + | 0.461500i | ||||
\(695\) | −3310.92 | −0.180705 | ||||||||
\(696\) | 4956.32 | 0.269926 | ||||||||
\(697\) | −3762.15 | − | 6516.23i | −0.204450 | − | 0.354117i | ||||
\(698\) | −2676.44 | + | 4635.73i | −0.145136 | + | 0.251382i | ||||
\(699\) | −8637.24 | − | 14960.1i | −0.467368 | − | 0.809506i | ||||
\(700\) | 6160.70 | − | 10670.6i | 0.332647 | − | 0.576161i | ||||
\(701\) | −6900.20 | + | 11951.5i | −0.371779 | + | 0.643940i | −0.989839 | − | 0.142191i | \(-0.954585\pi\) |
0.618060 | + | 0.786131i | \(0.287919\pi\) | |||||||
\(702\) | 3038.95 | 0.163387 | ||||||||
\(703\) | −18640.2 | − | 31332.5i | −1.00004 | − | 1.68098i | ||||
\(704\) | −1357.52 | −0.0726754 | ||||||||
\(705\) | −848.371 | + | 1469.42i | −0.0453213 | + | 0.0784988i | ||||
\(706\) | 3111.41 | − | 5389.12i | 0.165863 | − | 0.287284i | ||||
\(707\) | −16197.7 | − | 28055.2i | −0.861636 | − | 1.49240i | ||||
\(708\) | −697.469 | + | 1208.05i | −0.0370233 | + | 0.0641262i | ||||
\(709\) | 12672.6 | + | 21949.6i | 0.671270 | + | 1.16267i | 0.977544 | + | 0.210730i | \(0.0675841\pi\) |
−0.306275 | + | 0.951943i | \(0.599083\pi\) | |||||||
\(710\) | 1647.67 | 0.0870931 | ||||||||
\(711\) | −7967.68 | −0.420269 | ||||||||
\(712\) | 860.942 | + | 1491.20i | 0.0453162 | + | 0.0784900i | ||||
\(713\) | 13371.8 | + | 23160.6i | 0.702352 | + | 1.21651i | ||||
\(714\) | 3264.78 | 0.171122 | ||||||||
\(715\) | 6223.48 | 0.325517 | ||||||||
\(716\) | 437.089 | + | 757.061i | 0.0228140 | + | 0.0395149i | ||||
\(717\) | −1112.11 | + | 1926.23i | −0.0579253 | + | 0.100330i | ||||
\(718\) | −935.758 | − | 1620.78i | −0.0486382 | − | 0.0842438i | ||||
\(719\) | 9963.90 | − | 17258.0i | 0.516816 | − | 0.895151i | −0.482993 | − | 0.875624i | \(-0.660450\pi\) |
0.999809 | − | 0.0195275i | \(-0.00621618\pi\) | |||||||
\(720\) | 375.378 | − | 650.174i | 0.0194299 | − | 0.0336536i | ||||
\(721\) | 3410.42 | 0.176159 | ||||||||
\(722\) | 7167.25 | + | 11696.8i | 0.369442 | + | 0.602920i | ||||
\(723\) | −15822.2 | −0.813879 | ||||||||
\(724\) | 7496.88 | − | 12985.0i | 0.384833 | − | 0.666551i | ||||
\(725\) | 10100.4 | − | 17494.4i | 0.517407 | − | 0.896175i | ||||
\(726\) | 2643.25 | + | 4578.24i | 0.135124 | + | 0.234042i | ||||
\(727\) | −3329.24 | + | 5766.41i | −0.169841 | + | 0.294174i | −0.938364 | − | 0.345649i | \(-0.887659\pi\) |
0.768523 | + | 0.639823i | \(0.220992\pi\) | |||||||
\(728\) | 7088.74 | + | 12278.1i | 0.360888 | + | 0.625076i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5980.48 | 0.303216 | ||||||||
\(731\) | −1123.12 | − | 1945.30i | −0.0568264 | − | 0.0984262i | ||||
\(732\) | −2044.11 | − | 3540.50i | −0.103214 | − | 0.178771i | ||||
\(733\) | 27502.1 | 1.38583 | 0.692914 | − | 0.721021i | \(-0.256327\pi\) | ||||
0.692914 | + | 0.721021i | \(0.256327\pi\) | |||||||
\(734\) | −22018.5 | −1.10724 | ||||||||
\(735\) | −5072.68 | − | 8786.14i | −0.254570 | − | 0.440928i | ||||
\(736\) | −3301.06 | + | 5717.61i | −0.165324 | + | 0.286350i | ||||
\(737\) | −2235.09 | − | 3871.29i | −0.111710 | − | 0.193488i | ||||
\(738\) | 3919.08 | − | 6788.05i | 0.195479 | − | 0.338579i | ||||
\(739\) | −6421.84 | + | 11123.0i | −0.319663 | + | 0.553673i | −0.980418 | − | 0.196929i | \(-0.936903\pi\) |
0.660754 | + | 0.750602i | \(0.270237\pi\) | |||||||
\(740\) | −9180.34 | −0.456049 | ||||||||
\(741\) | 7148.90 | + | 12016.7i | 0.354415 | + | 0.595741i | ||||
\(742\) | 25650.9 | 1.26910 | ||||||||
\(743\) | −2403.24 | + | 4162.54i | −0.118663 | + | 0.205530i | −0.919238 | − | 0.393702i | \(-0.871194\pi\) |
0.800575 | + | 0.599232i | \(0.204527\pi\) | |||||||
\(744\) | −1555.49 | + | 2694.18i | −0.0766491 | + | 0.132760i | ||||
\(745\) | 4427.15 | + | 7668.05i | 0.217716 | + | 0.377095i | ||||
\(746\) | −6151.39 | + | 10654.5i | −0.301901 | + | 0.522909i | ||||
\(747\) | 2581.34 | + | 4471.02i | 0.126434 | + | 0.218991i | ||||
\(748\) | −1466.05 | −0.0716634 | ||||||||
\(749\) | −57313.4 | −2.79598 | ||||||||
\(750\) | −3485.05 | − | 6036.29i | −0.169675 | − | 0.293885i | ||||
\(751\) | 2147.88 | + | 3720.24i | 0.104364 | + | 0.180764i | 0.913478 | − | 0.406888i | \(-0.133386\pi\) |
−0.809114 | + | 0.587652i | \(0.800053\pi\) | |||||||
\(752\) | 1735.71 | 0.0841688 | ||||||||
\(753\) | −8539.07 | −0.413255 | ||||||||
\(754\) | 11621.9 | + | 20129.8i | 0.561333 | + | 0.972258i | ||||
\(755\) | −4255.29 | + | 7370.38i | −0.205120 | + | 0.355279i | ||||
\(756\) | 1700.48 | + | 2945.33i | 0.0818069 | + | 0.141694i | ||||
\(757\) | −10412.5 | + | 18035.0i | −0.499933 | + | 0.865910i | −1.00000 | 7.71784e-5i | \(-0.999975\pi\) | |
0.500067 | + | 0.865987i | \(0.333309\pi\) | |||||||
\(758\) | 13458.6 | − | 23311.0i | 0.644907 | − | 1.11701i | ||||
\(759\) | −13128.7 | −0.627854 | ||||||||
\(760\) | 3453.98 | − | 45.1580i | 0.164854 | − | 0.00215533i | ||||
\(761\) | −19534.2 | −0.930507 | −0.465253 | − | 0.885178i | \(-0.654037\pi\) | ||||
−0.465253 | + | 0.885178i | \(0.654037\pi\) | |||||||
\(762\) | −3084.60 | + | 5342.69i | −0.146645 | + | 0.253996i | ||||
\(763\) | 1875.94 | − | 3249.22i | 0.0890086 | − | 0.154167i | ||||
\(764\) | 283.466 | + | 490.978i | 0.0134234 | + | 0.0232500i | ||||
\(765\) | 405.390 | − | 702.156i | 0.0191593 | − | 0.0331849i | ||||
\(766\) | −11090.4 | − | 19209.1i | −0.523123 | − | 0.906075i | ||||
\(767\) | −6541.89 | −0.307971 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −284.228 | − | 492.298i | −0.0133284 | − | 0.0230855i | 0.859284 | − | 0.511498i | \(-0.170909\pi\) |
−0.872613 | + | 0.488413i | \(0.837576\pi\) | |||||||
\(770\) | 3482.43 | + | 6031.74i | 0.162984 | + | 0.282297i | ||||
\(771\) | −19322.1 | −0.902555 | ||||||||
\(772\) | −15639.6 | −0.729120 | ||||||||
\(773\) | −48.4982 | − | 84.0014i | −0.00225661 | − | 0.00390857i | 0.864895 | − | 0.501953i | \(-0.167385\pi\) |
−0.867152 | + | 0.498044i | \(0.834052\pi\) | |||||||
\(774\) | 1169.97 | − | 2026.45i | 0.0543330 | − | 0.0941075i | ||||
\(775\) | 6339.81 | + | 10980.9i | 0.293849 | + | 0.508961i | ||||
\(776\) | 2115.90 | − | 3664.84i | 0.0978817 | − | 0.169536i | ||||
\(777\) | 20793.7 | − | 36015.8i | 0.960065 | − | 1.66288i | ||||
\(778\) | −2546.17 | −0.117333 | ||||||||
\(779\) | 36060.8 | − | 471.465i | 1.65855 | − | 0.0216842i | ||||
\(780\) | 3520.85 | 0.161624 | ||||||||
\(781\) | 1675.87 | − | 2902.70i | 0.0767829 | − | 0.132992i | ||||
\(782\) | −3564.98 | + | 6174.73i | −0.163022 | + | 0.282363i | ||||
\(783\) | 2787.93 | + | 4828.83i | 0.127245 | + | 0.220394i | ||||
\(784\) | −5189.19 | + | 8987.95i | −0.236388 | + | 0.409436i | ||||
\(785\) | 7722.81 | + | 13376.3i | 0.351132 | + | 0.608179i | ||||
\(786\) | −9535.01 | −0.432700 | ||||||||
\(787\) | 4906.36 | 0.222227 | 0.111114 | − | 0.993808i | \(-0.464558\pi\) | ||||
0.111114 | + | 0.993808i | \(0.464558\pi\) | |||||||
\(788\) | −2406.32 | − | 4167.86i | −0.108784 | − | 0.188419i | ||||
\(789\) | 6210.61 | + | 10757.1i | 0.280233 | + | 0.485377i | ||||
\(790\) | −9231.15 | −0.415734 | ||||||||
\(791\) | 31961.5 | 1.43669 | ||||||||
\(792\) | −763.605 | − | 1322.60i | −0.0342595 | − | 0.0593392i | ||||
\(793\) | 9586.33 | − | 16604.0i | 0.429282 | − | 0.743538i | ||||
\(794\) | −12328.9 | − | 21354.3i | −0.551054 | − | 0.954454i | ||||
\(795\) | 3185.09 | − | 5516.73i | 0.142092 | − | 0.246111i | ||||
\(796\) | −7406.92 | + | 12829.2i | −0.329813 | + | 0.571253i | ||||
\(797\) | −32043.3 | −1.42413 | −0.712066 | − | 0.702113i | \(-0.752240\pi\) | ||||
−0.712066 | + | 0.702113i | \(0.752240\pi\) | |||||||
\(798\) | −7646.20 | + | 13652.7i | −0.339189 | + | 0.605642i | ||||
\(799\) | 1874.48 | 0.0829968 | ||||||||
\(800\) | −1565.10 | + | 2710.83i | −0.0691681 | + | 0.119803i | ||||
\(801\) | −968.560 | + | 1677.59i | −0.0427246 | + | 0.0740011i | ||||
\(802\) | 9799.54 | + | 16973.3i | 0.431463 | + | 0.747316i | ||||
\(803\) | 6082.83 | − | 10535.8i | 0.267321 | − | 0.463013i | ||||
\(804\) | −1264.47 | − | 2190.13i | −0.0554658 | − | 0.0960696i | ||||
\(805\) | 33872.7 | 1.48305 | ||||||||
\(806\) | −14589.7 | −0.637592 | ||||||||
\(807\) | 4748.99 | + | 8225.49i | 0.207153 | + | 0.358799i | ||||
\(808\) | 4114.94 | + | 7127.29i | 0.179162 | + | 0.310318i | ||||
\(809\) | 18714.9 | 0.813326 | 0.406663 | − | 0.913578i | \(-0.366692\pi\) | ||||
0.406663 | + | 0.913578i | \(0.366692\pi\) | |||||||
\(810\) | 844.601 | 0.0366374 | ||||||||
\(811\) | 4564.67 | + | 7906.24i | 0.197641 | + | 0.342325i | 0.947763 | − | 0.318975i | \(-0.103338\pi\) |
−0.750122 | + | 0.661300i | \(0.770005\pi\) | |||||||
\(812\) | −13006.4 | + | 22527.7i | −0.562112 | + | 0.973607i | ||||
\(813\) | 9666.34 | + | 16742.6i | 0.416991 | + | 0.722249i | ||||
\(814\) | −9337.46 | + | 16172.9i | −0.402061 | + | 0.696390i | ||||
\(815\) | 1634.39 | − | 2830.84i | 0.0702454 | − | 0.121669i | ||||
\(816\) | −829.401 | −0.0355819 | ||||||||
\(817\) | 10765.3 | − | 140.747i | 0.460991 | − | 0.00602708i | ||||
\(818\) | −16169.3 | −0.691133 | ||||||||
\(819\) | −7974.83 | + | 13812.8i | −0.340248 | + | 0.589327i | ||||
\(820\) | 4540.55 | − | 7864.47i | 0.193369 | − | 0.334926i | ||||
\(821\) | −11414.4 | − | 19770.2i | −0.485218 | − | 0.840422i | 0.514638 | − | 0.857408i | \(-0.327926\pi\) |
−0.999856 | + | 0.0169856i | \(0.994593\pi\) | |||||||
\(822\) | 6975.20 | − | 12081.4i | 0.295971 | − | 0.512636i | ||||
\(823\) | 18938.9 | + | 32803.1i | 0.802149 | + | 1.38936i | 0.918199 | + | 0.396120i | \(0.129643\pi\) |
−0.116050 | + | 0.993243i | \(0.537023\pi\) | |||||||
\(824\) | −866.401 | −0.0366293 | ||||||||
\(825\) | −6224.56 | −0.262681 | ||||||||
\(826\) | −3660.60 | − | 6340.35i | −0.154199 | − | 0.267081i | ||||
\(827\) | 2060.45 | + | 3568.80i | 0.0866370 | + | 0.150060i | 0.906088 | − | 0.423090i | \(-0.139055\pi\) |
−0.819451 | + | 0.573150i | \(0.805721\pi\) | |||||||
\(828\) | −7427.39 | −0.311739 | ||||||||
\(829\) | −17959.7 | −0.752431 | −0.376216 | − | 0.926532i | \(-0.622775\pi\) | ||||
−0.376216 | + | 0.926532i | \(0.622775\pi\) | |||||||
\(830\) | 2990.68 | + | 5180.01i | 0.125070 | + | 0.216627i | ||||
\(831\) | 599.607 | − | 1038.55i | 0.0250303 | − | 0.0433537i | ||||
\(832\) | −1800.86 | − | 3119.18i | −0.0750404 | − | 0.129974i | ||||
\(833\) | −5604.07 | + | 9706.53i | −0.233097 | + | 0.403735i | ||||
\(834\) | −1905.17 | + | 3299.85i | −0.0791014 | + | 0.137008i | ||||
\(835\) | −8352.98 | −0.346188 | ||||||||
\(836\) | 3433.54 | − | 6130.79i | 0.142047 | − | 0.253634i | ||||
\(837\) | −3499.85 | −0.144531 | ||||||||
\(838\) | −78.3882 | + | 135.772i | −0.00323136 | + | 0.00559687i | ||||
\(839\) | 24100.4 | − | 41743.1i | 0.991702 | − | 1.71768i | 0.384515 | − | 0.923119i | \(-0.374369\pi\) |
0.607187 | − | 0.794559i | \(-0.292298\pi\) | |||||||
\(840\) | 1970.14 | + | 3412.38i | 0.0809241 | + | 0.140165i | ||||
\(841\) | −9129.37 | + | 15812.5i | −0.374323 | + | 0.648347i | ||||
\(842\) | 7085.19 | + | 12271.9i | 0.289990 | + | 0.502278i | ||||
\(843\) | −1891.10 | −0.0772633 | ||||||||
\(844\) | −102.799 | −0.00419253 | ||||||||
\(845\) | 2528.82 | + | 4380.04i | 0.102951 | + | 0.178317i | ||||
\(846\) | 976.339 | + | 1691.07i | 0.0396776 | + | 0.0687236i | ||||
\(847\) | −27745.7 | −1.12556 | ||||||||
\(848\) | −6516.48 | −0.263888 | ||||||||
\(849\) | 2994.95 | + | 5187.40i | 0.121068 | + | 0.209695i | ||||
\(850\) | −1690.23 | + | 2927.56i | −0.0682050 | + | 0.118135i | ||||
\(851\) | 45411.5 | + | 78655.0i | 1.82924 | + | 3.16834i | ||||
\(852\) | 948.103 | − | 1642.16i | 0.0381238 | − | 0.0660324i | ||||
\(853\) | −18435.6 | + | 31931.4i | −0.740004 | + | 1.28172i | 0.212490 | + | 0.977163i | \(0.431843\pi\) |
−0.952493 | + | 0.304560i | \(0.901490\pi\) | |||||||
\(854\) | 21456.6 | 0.859755 | ||||||||
\(855\) | 1986.86 | + | 3339.74i | 0.0794727 | + | 0.133587i | ||||
\(856\) | 14560.2 | 0.581375 | ||||||||
\(857\) | −16835.4 | + | 29159.8i | −0.671047 | + | 1.16229i | 0.306560 | + | 0.951851i | \(0.400822\pi\) |
−0.977607 | + | 0.210437i | \(0.932511\pi\) | |||||||
\(858\) | 3581.11 | − | 6202.67i | 0.142491 | − | 0.246801i | ||||
\(859\) | −10423.3 | − | 18053.6i | −0.414013 | − | 0.717091i | 0.581312 | − | 0.813681i | \(-0.302540\pi\) |
−0.995324 | + | 0.0965901i | \(0.969206\pi\) | |||||||
\(860\) | 1355.50 | − | 2347.79i | 0.0537467 | − | 0.0930919i | ||||
\(861\) | 20569.0 | + | 35626.5i | 0.814156 | + | 1.41016i | ||||
\(862\) | 29802.8 | 1.17760 | ||||||||
\(863\) | −47623.4 | −1.87847 | −0.939235 | − | 0.343275i | \(-0.888464\pi\) | ||||
−0.939235 | + | 0.343275i | \(0.888464\pi\) | |||||||
\(864\) | −432.000 | − | 748.246i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 5971.35 | + | 10342.7i | 0.234719 | + | 0.406545i | ||||
\(866\) | −8458.97 | −0.331925 | ||||||||
\(867\) | 13843.3 | 0.542264 | ||||||||
\(868\) | −8163.84 | − | 14140.2i | −0.319238 | − | 0.552937i | ||||
\(869\) | −9389.14 | + | 16262.5i | −0.366519 | + | 0.634829i | ||||
\(870\) | 3230.02 | + | 5594.57i | 0.125871 | + | 0.218016i | ||||
\(871\) | 5930.05 | − | 10271.1i | 0.230691 | − | 0.399569i | ||||
\(872\) | −476.573 | + | 825.449i | −0.0185078 | + | 0.0320565i | ||||
\(873\) | 4760.77 | 0.184568 | ||||||||
\(874\) | −17472.4 | − | 29369.5i | −0.676215 | − | 1.13666i | ||||
\(875\) | 36582.0 | 1.41337 | ||||||||
\(876\) | 3441.28 | − | 5960.48i | 0.132729 | − | 0.229893i | ||||
\(877\) | 4698.68 | − | 8138.35i | 0.180916 | − | 0.313355i | −0.761277 | − | 0.648427i | \(-0.775427\pi\) |
0.942193 | + | 0.335072i | \(0.108761\pi\) | |||||||
\(878\) | 10521.5 | + | 18223.9i | 0.404425 | + | 0.700484i | ||||
\(879\) | 14515.3 | − | 25141.2i | 0.556983 | − | 0.964723i | ||||
\(880\) | −884.694 | − | 1532.34i | −0.0338898 | − | 0.0586989i | ||||
\(881\) | 49897.4 | 1.90816 | 0.954079 | − | 0.299555i | \(-0.0968384\pi\) | ||||
0.954079 | + | 0.299555i | \(0.0968384\pi\) | |||||||
\(882\) | −11675.7 | −0.445738 | ||||||||
\(883\) | 1631.56 | + | 2825.95i | 0.0621818 | + | 0.107702i | 0.895440 | − | 0.445181i | \(-0.146861\pi\) |
−0.833259 | + | 0.552883i | \(0.813527\pi\) | |||||||
\(884\) | −1944.84 | − | 3368.56i | −0.0739955 | − | 0.128164i | ||||
\(885\) | −1818.16 | −0.0690584 | ||||||||
\(886\) | −27734.8 | −1.05166 | ||||||||
\(887\) | −19308.8 | − | 33443.9i | −0.730921 | − | 1.26599i | −0.956490 | − | 0.291765i | \(-0.905758\pi\) |
0.225569 | − | 0.974227i | \(-0.427576\pi\) | |||||||
\(888\) | −5282.55 | + | 9149.64i | −0.199629 | + | 0.345768i | ||||
\(889\) | −16189.3 | − | 28040.6i | −0.610765 | − | 1.05788i | ||||
\(890\) | −1122.15 | + | 1943.62i | −0.0422635 | + | 0.0732025i | ||||
\(891\) | 859.056 | − | 1487.93i | 0.0323002 | − | 0.0559456i | ||||
\(892\) | −12420.8 | −0.466230 | ||||||||
\(893\) | −4390.09 | + | 7838.77i | −0.164512 | + | 0.293745i | ||||
\(894\) | 10189.9 | 0.381209 | ||||||||
\(895\) | −569.701 | + | 986.751i | −0.0212771 | + | 0.0368530i | ||||
\(896\) | 2015.39 | − | 3490.76i | 0.0751445 | − | 0.130154i | ||||
\(897\) | −17416.3 | − | 30165.9i | −0.648286 | − | 1.12286i | ||||
\(898\) | 9599.89 | − | 16627.5i | 0.356740 | − | 0.617892i | ||||
\(899\) | −13384.5 | − | 23182.7i | −0.496551 | − | 0.860052i | ||||
\(900\) | −3521.47 | −0.130425 | ||||||||
\(901\) | −7037.47 | −0.260213 | ||||||||
\(902\) | −9236.52 | − | 15998.1i | −0.340956 | − | 0.590554i | ||||
\(903\) | 6140.49 | + | 10635.6i | 0.226293 | + | 0.391951i | ||||
\(904\) | −8119.66 | −0.298735 | ||||||||
\(905\) | 19542.8 | 0.717818 | ||||||||
\(906\) | 4897.15 | + | 8482.12i | 0.179577 | + | 0.311037i | ||||
\(907\) | −290.222 | + | 502.680i | −0.0106248 | + | 0.0184027i | −0.871289 | − | 0.490770i | \(-0.836715\pi\) |
0.860664 | + | 0.509173i | \(0.170049\pi\) | |||||||
\(908\) | −1329.13 | − | 2302.13i | −0.0485780 | − | 0.0841395i | ||||
\(909\) | −4629.31 | + | 8018.20i | −0.168916 | + | 0.292571i | ||||
\(910\) | −9239.44 | + | 16003.2i | −0.336576 | + | 0.582967i | ||||
\(911\) | −16704.1 | −0.607498 | −0.303749 | − | 0.952752i | \(-0.598238\pi\) | ||||
−0.303749 | + | 0.952752i | \(0.598238\pi\) | |||||||
\(912\) | 1942.48 | − | 3468.42i | 0.0705285 | − | 0.125933i | ||||
\(913\) | 12167.5 | 0.441056 | ||||||||
\(914\) | −6261.10 | + | 10844.5i | −0.226585 | + | 0.392457i | ||||
\(915\) | 2664.28 | − | 4614.67i | 0.0962606 | − | 0.166728i | ||||
\(916\) | 12064.0 | + | 20895.4i | 0.435158 | + | 0.753717i | ||||
\(917\) | 25021.8 | − | 43339.1i | 0.901083 | − | 1.56072i | ||||
\(918\) | −466.538 | − | 808.068i | −0.0167735 | − | 0.0290525i | ||||
\(919\) | 46725.6 | 1.67719 | 0.838594 | − | 0.544756i | \(-0.183378\pi\) | ||||
0.838594 | + | 0.544756i | \(0.183378\pi\) | |||||||
\(920\) | −8605.19 | −0.308375 | ||||||||
\(921\) | 10193.3 | + | 17655.3i | 0.364690 | + | 0.631662i | ||||
\(922\) | −9825.55 | − | 17018.4i | −0.350962 | − | 0.607885i | ||||
\(923\) | 8892.72 | 0.317126 | ||||||||
\(924\) | 8015.43 | 0.285377 | ||||||||
\(925\) | 21530.5 | + | 37291.8i | 0.765316 | + | 1.32557i | ||||
\(926\) | 9276.57 | − | 16067.5i | 0.329208 | − | 0.570206i | ||||
\(927\) | −487.351 | − | 844.116i | −0.0172672 | − | 0.0299077i | ||||
\(928\) | 3304.21 | − | 5723.06i | 0.116882 | − | 0.202445i | ||||
\(929\) | 9098.05 | − | 15758.3i | 0.321310 | − | 0.556526i | −0.659448 | − | 0.751750i | \(-0.729210\pi\) |
0.980759 | + | 0.195224i | \(0.0625434\pi\) | |||||||
\(930\) | −4054.84 | −0.142971 | ||||||||
\(931\) | −27466.2 | − | 46168.2i | −0.966882 | − | 1.62524i | ||||
\(932\) | −23032.6 | −0.809506 | ||||||||
\(933\) | −6627.71 | + | 11479.5i | −0.232563 | + | 0.402811i | ||||
\(934\) | 18209.4 | − | 31539.6i | 0.637933 | − | 1.10493i | ||||
\(935\) | −955.425 | − | 1654.85i | −0.0334179 | − | 0.0578815i | ||||
\(936\) | 2025.97 | − | 3509.08i | 0.0707487 | − | 0.122540i | ||||
\(937\) | 14372.3 | + | 24893.5i | 0.501091 | + | 0.867915i | 0.999999 | + | 0.00126003i | \(0.000401079\pi\) |
−0.498908 | + | 0.866655i | \(0.666266\pi\) | |||||||
\(938\) | 13272.9 | 0.462022 | ||||||||
\(939\) | 4174.68 | 0.145086 | ||||||||
\(940\) | 1131.16 | + | 1959.23i | 0.0392494 | + | 0.0679819i | ||||
\(941\) | −5551.31 | − | 9615.15i | −0.192314 | − | 0.333098i | 0.753703 | − | 0.657216i | \(-0.228266\pi\) |
−0.946017 | + | 0.324118i | \(0.894933\pi\) | |||||||
\(942\) | 17775.4 | 0.614814 | ||||||||
\(943\) | −89841.3 | −3.10248 | ||||||||
\(944\) | 929.958 | + | 1610.73i | 0.0320631 | + | 0.0555349i | ||||
\(945\) | −2216.41 | + | 3838.93i | −0.0762960 | + | 0.132149i | ||||
\(946\) | −2757.40 | − | 4775.95i | −0.0947681 | − | 0.164143i | ||||
\(947\) | 17405.4 | − | 30147.0i | 0.597254 | − | 1.03447i | −0.395971 | − | 0.918263i | \(-0.629592\pi\) |
0.993225 | − | 0.116211i | \(-0.0370747\pi\) | |||||||
\(948\) | −5311.78 | + | 9200.28i | −0.181982 | + | 0.315202i | ||||
\(949\) | 32277.4 | 1.10408 | ||||||||
\(950\) | −8283.99 | − | 13924.7i | −0.282914 | − | 0.475553i | ||||
\(951\) | −17996.0 | −0.613629 | ||||||||
\(952\) | 2176.52 | − | 3769.84i | 0.0740981 | − | 0.128342i | ||||
\(953\) | −16618.4 | + | 28783.9i | −0.564872 | + | 0.978387i | 0.432189 | + | 0.901783i | \(0.357741\pi\) |
−0.997062 | + | 0.0766045i | \(0.975592\pi\) | |||||||
\(954\) | −3665.52 | − | 6348.87i | −0.124398 | − | 0.215464i | ||||
\(955\) | −369.469 | + | 639.939i | −0.0125191 | + | 0.0216837i | ||||
\(956\) | 1482.81 | + | 2568.30i | 0.0501648 | + | 0.0868880i | ||||
\(957\) | 13141.2 | 0.443882 | ||||||||
\(958\) | −25483.4 | −0.859426 | ||||||||
\(959\) | 36608.7 | + | 63408.1i | 1.23270 | + | 2.13509i | ||||
\(960\) | −500.504 | − | 866.899i | −0.0168268 | − | 0.0291448i | ||||
\(961\) | −12988.6 | −0.435991 | ||||||||
\(962\) | −49547.5 | −1.66058 | ||||||||
\(963\) | 8190.11 | + | 14185.7i | 0.274063 | + | 0.474691i | ||||
\(964\) | −10548.1 | + | 18269.9i | −0.352420 | + | 0.610409i | ||||
\(965\) | −10192.3 | − | 17653.6i | −0.340001 | − | 0.588900i | ||||
\(966\) | 19491.0 | − | 33759.4i | 0.649185 | − | 1.12442i | ||||
\(967\) | 2601.77 | − | 4506.40i | 0.0865225 | − | 0.149861i | −0.819516 | − | 0.573056i | \(-0.805758\pi\) |
0.906039 | + | 0.423194i | \(0.139091\pi\) | |||||||
\(968\) | 7048.66 | 0.234042 | ||||||||
\(969\) | 2097.78 | − | 3745.71i | 0.0695464 | − | 0.124179i | ||||
\(970\) | 5515.70 | 0.182576 | ||||||||
\(971\) | 18518.2 | − | 32074.4i | 0.612026 | − | 1.06006i | −0.378873 | − | 0.925449i | \(-0.623688\pi\) |
0.990899 | − | 0.134611i | \(-0.0429784\pi\) | |||||||
\(972\) | 486.000 | − | 841.777i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −9999.10 | − | 17318.9i | −0.329452 | − | 0.570627i | ||||
\(974\) | −5006.72 | + | 8671.89i | −0.164708 | + | 0.285282i | ||||
\(975\) | −8257.38 | − | 14302.2i | −0.271229 | − | 0.469782i | ||||
\(976\) | −5450.95 | −0.178771 | ||||||||
\(977\) | 28630.1 | 0.937520 | 0.468760 | − | 0.883326i | \(-0.344701\pi\) | ||||
0.468760 | + | 0.883326i | \(0.344701\pi\) | |||||||
\(978\) | −1880.92 | − | 3257.84i | −0.0614980 | − | 0.106518i | ||||
\(979\) | 2282.71 | + | 3953.77i | 0.0745206 | + | 0.129073i | ||||
\(980\) | −13527.2 | −0.440928 | ||||||||
\(981\) | −1072.29 | −0.0348987 | ||||||||
\(982\) | 963.312 | + | 1668.51i | 0.0313040 | + | 0.0542201i | ||||
\(983\) | 12831.3 | − | 22224.4i | 0.416332 | − | 0.721108i | −0.579235 | − | 0.815160i | \(-0.696649\pi\) |
0.995567 | + | 0.0940523i | \(0.0299821\pi\) | |||||||
\(984\) | −5225.44 | − | 9050.74i | −0.169290 | − | 0.293218i | ||||
\(985\) | 3136.39 | − | 5432.38i | 0.101455 | − | 0.175726i | ||||
\(986\) | 3568.38 | − | 6180.62i | 0.115254 | − | 0.199626i | ||||
\(987\) | −10248.5 | −0.330508 | ||||||||
\(988\) | 18641.6 | − | 243.724i | 0.600272 | − | 0.00784806i | ||||
\(989\) | −26820.5 | −0.862327 | ||||||||
\(990\) | 995.281 | − | 1723.88i | 0.0319516 | − | 0.0553418i | ||||
\(991\) | 11814.9 | − | 20464.0i | 0.378720 | − | 0.655963i | −0.612156 | − | 0.790737i | \(-0.709698\pi\) |
0.990876 | + | 0.134774i | \(0.0430310\pi\) | |||||||
\(992\) | 2073.98 | + | 3592.25i | 0.0663801 | + | 0.114974i | ||||
\(993\) | −9907.10 | + | 17159.6i | −0.316609 | + | 0.548382i | ||||
\(994\) | 4976.04 | + | 8618.75i | 0.158783 | + | 0.275020i | ||||
\(995\) | −19308.3 | −0.615190 | ||||||||
\(996\) | 6883.58 | 0.218991 | ||||||||
\(997\) | −25651.8 | − | 44430.2i | −0.814845 | − | 1.41135i | −0.909439 | − | 0.415836i | \(-0.863489\pi\) |
0.0945948 | − | 0.995516i | \(-0.469844\pi\) | |||||||
\(998\) | 4964.84 | + | 8599.36i | 0.157474 | + | 0.272754i | ||||
\(999\) | −11885.7 | −0.376424 |
(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 | 114.4.e.e.49.2 | yes | 6 | |
3.2 | odd | 2 | 342.4.g.g.163.2 | 6 | |||
19.7 | even | 3 | inner | 114.4.e.e.7.2 | ✓ | 6 | |
19.8 | odd | 6 | 2166.4.a.w.1.2 | 3 | |||
19.11 | even | 3 | 2166.4.a.s.1.2 | 3 | |||
57.26 | odd | 6 | 342.4.g.g.235.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.e.7.2 | ✓ | 6 | 19.7 | even | 3 | inner | |
114.4.e.e.49.2 | yes | 6 | 1.1 | even | 1 | trivial | |
342.4.g.g.163.2 | 6 | 3.2 | odd | 2 | |||
342.4.g.g.235.2 | 6 | 57.26 | odd | 6 | |||
2166.4.a.s.1.2 | 3 | 19.11 | even | 3 | |||
2166.4.a.w.1.2 | 3 | 19.8 | odd | 6 |