Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (of order \(6\), 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: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + 109290291168 x^{8} + 1091662316544 x^{6} + \cdots + 1118416232704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-6.77277i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.11 |
Dual form | 74.4.e.a.27.1 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −3.38639 | + | 5.86539i | −0.651710 | + | 1.12880i | 0.330997 | + | 0.943632i | \(0.392615\pi\) |
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 14.5934 | + | 8.42549i | 1.30527 | + | 0.753598i | 0.981303 | − | 0.192470i | \(-0.0616497\pi\) |
0.323968 | + | 0.946068i | \(0.394983\pi\) | |||||||
\(6\) | − | 13.5455i | − | 0.921658i | ||||||
\(7\) | −7.56088 | + | 13.0958i | −0.408249 | + | 0.707108i | −0.994694 | − | 0.102881i | \(-0.967194\pi\) |
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −9.43523 | − | 16.3423i | −0.349453 | − | 0.605271i | ||||
\(10\) | −33.7019 | −1.06575 | ||||||||
\(11\) | −16.4204 | −0.450084 | −0.225042 | − | 0.974349i | \(-0.572252\pi\) | ||||
−0.225042 | + | 0.974349i | \(0.572252\pi\) | |||||||
\(12\) | 13.5455 | + | 23.4616i | 0.325855 | + | 0.564398i | ||||
\(13\) | −75.3996 | − | 43.5320i | −1.60862 | − | 0.928739i | −0.989679 | − | 0.143304i | \(-0.954227\pi\) |
−0.618944 | − | 0.785435i | \(-0.712439\pi\) | |||||||
\(14\) | − | 30.2435i | − | 0.577351i | ||||||
\(15\) | −98.8376 | + | 57.0639i | −1.70132 | + | 0.982256i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.45821 | + | 0.841898i | −0.0208040 | + | 0.0120112i | −0.510366 | − | 0.859957i | \(-0.670490\pi\) |
0.489562 | + | 0.871969i | \(0.337157\pi\) | |||||||
\(18\) | 32.6846 | + | 18.8705i | 0.427991 | + | 0.247101i | ||||
\(19\) | 108.417 | + | 62.5948i | 1.30909 | + | 0.755802i | 0.981944 | − | 0.189173i | \(-0.0605806\pi\) |
0.327143 | + | 0.944975i | \(0.393914\pi\) | |||||||
\(20\) | 58.3735 | − | 33.7019i | 0.652635 | − | 0.376799i | ||||
\(21\) | −51.2081 | − | 88.6951i | −0.532120 | − | 0.921660i | ||||
\(22\) | 28.4409 | − | 16.4204i | 0.275619 | − | 0.159129i | ||||
\(23\) | 85.4461i | 0.774641i | 0.921945 | + | 0.387320i | \(0.126599\pi\) | ||||
−0.921945 | + | 0.387320i | \(0.873401\pi\) | |||||||
\(24\) | −46.9232 | − | 27.0911i | −0.399090 | − | 0.230414i | ||||
\(25\) | 79.4776 | + | 137.659i | 0.635821 | + | 1.10127i | ||||
\(26\) | 174.128 | 1.31344 | ||||||||
\(27\) | −55.0595 | −0.392452 | ||||||||
\(28\) | 30.2435 | + | 52.3833i | 0.204125 | + | 0.353554i | ||||
\(29\) | − | 151.487i | − | 0.970018i | −0.874509 | − | 0.485009i | \(-0.838816\pi\) | ||
0.874509 | − | 0.485009i | \(-0.161184\pi\) | |||||||
\(30\) | 114.128 | − | 197.675i | 0.694560 | − | 1.20301i | ||||
\(31\) | 88.7582i | 0.514240i | 0.966379 | + | 0.257120i | \(0.0827736\pi\) | ||||
−0.966379 | + | 0.257120i | \(0.917226\pi\) | |||||||
\(32\) | 27.7128 | + | 16.0000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 55.6057 | − | 96.3119i | 0.293324 | − | 0.508053i | ||||
\(34\) | 1.68380 | − | 2.91642i | 0.00849320 | − | 0.0147106i | ||||
\(35\) | −220.677 | + | 127.408i | −1.06575 | + | 0.615312i | ||||
\(36\) | −75.4819 | −0.349453 | ||||||||
\(37\) | 112.519 | + | 194.917i | 0.499945 | + | 0.866057i | ||||
\(38\) | −250.379 | −1.06887 | ||||||||
\(39\) | 510.665 | − | 294.832i | 2.09671 | − | 1.21054i | ||||
\(40\) | −67.4039 | + | 116.747i | −0.266437 | + | 0.461483i | ||||
\(41\) | 217.078 | − | 375.990i | 0.826875 | − | 1.43219i | −0.0736023 | − | 0.997288i | \(-0.523450\pi\) |
0.900478 | − | 0.434902i | \(-0.143217\pi\) | |||||||
\(42\) | 177.390 | + | 102.416i | 0.651712 | + | 0.376266i | ||||
\(43\) | 215.822i | 0.765408i | 0.923871 | + | 0.382704i | \(0.125007\pi\) | ||||
−0.923871 | + | 0.382704i | \(0.874993\pi\) | |||||||
\(44\) | −32.8407 | + | 56.8818i | −0.112521 | + | 0.194892i | ||||
\(45\) | − | 317.986i | − | 1.05339i | ||||||
\(46\) | −85.4461 | − | 147.997i | −0.273877 | − | 0.474369i | ||||
\(47\) | −101.825 | −0.316016 | −0.158008 | − | 0.987438i | \(-0.550507\pi\) | ||||
−0.158008 | + | 0.987438i | \(0.550507\pi\) | |||||||
\(48\) | 108.364 | 0.325855 | ||||||||
\(49\) | 57.1662 | + | 99.0148i | 0.166665 | + | 0.288673i | ||||
\(50\) | −275.319 | − | 158.955i | −0.778719 | − | 0.449593i | ||||
\(51\) | − | 11.4040i | − | 0.0313113i | ||||||
\(52\) | −301.599 | + | 174.128i | −0.804311 | + | 0.464369i | ||||
\(53\) | 249.053 | + | 431.373i | 0.645473 | + | 1.11799i | 0.984192 | + | 0.177105i | \(0.0566731\pi\) |
−0.338719 | + | 0.940888i | \(0.609994\pi\) | |||||||
\(54\) | 95.3658 | − | 55.0595i | 0.240327 | − | 0.138753i | ||||
\(55\) | −239.628 | − | 138.350i | −0.587482 | − | 0.339183i | ||||
\(56\) | −104.767 | − | 60.4870i | −0.250000 | − | 0.144338i | ||||
\(57\) | −734.287 | + | 423.941i | −1.70629 | + | 0.985128i | ||||
\(58\) | 151.487 | + | 262.384i | 0.342953 | + | 0.594012i | ||||
\(59\) | −577.395 | + | 333.359i | −1.27407 | + | 0.735587i | −0.975752 | − | 0.218878i | \(-0.929760\pi\) |
−0.298322 | + | 0.954465i | \(0.596427\pi\) | |||||||
\(60\) | 456.511i | 0.982256i | ||||||||
\(61\) | 660.867 | + | 381.552i | 1.38714 | + | 0.800864i | 0.992992 | − | 0.118184i | \(-0.0377071\pi\) |
0.394146 | + | 0.919048i | \(0.371040\pi\) | |||||||
\(62\) | −88.7582 | − | 153.734i | −0.181811 | − | 0.314906i | ||||
\(63\) | 285.355 | 0.570656 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −733.557 | − | 1270.56i | −1.39979 | − | 2.42451i | ||||
\(66\) | 222.423i | 0.414823i | ||||||||
\(67\) | 87.8771 | − | 152.208i | 0.160237 | − | 0.277539i | −0.774717 | − | 0.632309i | \(-0.782107\pi\) |
0.934954 | + | 0.354770i | \(0.115441\pi\) | |||||||
\(68\) | 6.73518i | 0.0120112i | ||||||||
\(69\) | −501.175 | − | 289.353i | −0.874411 | − | 0.504842i | ||||
\(70\) | 254.816 | − | 441.355i | 0.435091 | − | 0.753600i | ||||
\(71\) | 214.143 | − | 370.906i | 0.357944 | − | 0.619978i | −0.629673 | − | 0.776860i | \(-0.716811\pi\) |
0.987617 | + | 0.156883i | \(0.0501444\pi\) | |||||||
\(72\) | 130.738 | − | 75.4819i | 0.213995 | − | 0.123550i | ||||
\(73\) | 162.065 | 0.259839 | 0.129920 | − | 0.991525i | \(-0.458528\pi\) | ||||
0.129920 | + | 0.991525i | \(0.458528\pi\) | |||||||
\(74\) | −389.805 | − | 225.087i | −0.612350 | − | 0.353592i | ||||
\(75\) | −1076.57 | −1.65749 | ||||||||
\(76\) | 433.670 | − | 250.379i | 0.654544 | − | 0.377901i | ||||
\(77\) | 124.152 | − | 215.038i | 0.183746 | − | 0.318258i | ||||
\(78\) | −589.665 | + | 1021.33i | −0.855979 | + | 1.48260i | ||||
\(79\) | 476.666 | + | 275.203i | 0.678849 | + | 0.391934i | 0.799421 | − | 0.600771i | \(-0.205140\pi\) |
−0.120572 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(80\) | − | 269.616i | − | 0.376799i | ||||||
\(81\) | 441.204 | − | 764.188i | 0.605218 | − | 1.04827i | ||||
\(82\) | 868.312i | 1.16938i | ||||||||
\(83\) | 407.247 | + | 705.373i | 0.538568 | + | 0.932828i | 0.998981 | + | 0.0451231i | \(0.0143680\pi\) |
−0.460413 | + | 0.887705i | \(0.652299\pi\) | |||||||
\(84\) | −409.665 | −0.532120 | ||||||||
\(85\) | −28.3736 | −0.0362065 | ||||||||
\(86\) | −215.822 | − | 373.815i | −0.270613 | − | 0.468715i | ||||
\(87\) | 888.534 | + | 512.995i | 1.09495 | + | 0.632171i | ||||
\(88\) | − | 131.363i | − | 0.159129i | ||||||
\(89\) | −290.566 | + | 167.758i | −0.346066 | + | 0.199802i | −0.662951 | − | 0.748662i | \(-0.730696\pi\) |
0.316885 | + | 0.948464i | \(0.397363\pi\) | |||||||
\(90\) | 317.986 | + | 550.767i | 0.372429 | + | 0.645067i | ||||
\(91\) | 1140.18 | − | 658.280i | 1.31344 | − | 0.758314i | ||||
\(92\) | 295.994 | + | 170.892i | 0.335429 | + | 0.193660i | ||||
\(93\) | −520.602 | − | 300.570i | −0.580472 | − | 0.335136i | ||||
\(94\) | 176.367 | − | 101.825i | 0.193519 | − | 0.111728i | ||||
\(95\) | 1054.78 | + | 1826.94i | 1.13914 | + | 1.97305i | ||||
\(96\) | −187.693 | + | 108.364i | −0.199545 | + | 0.115207i | ||||
\(97\) | 1088.06i | 1.13893i | 0.822016 | + | 0.569465i | \(0.192849\pi\) | ||||
−0.822016 | + | 0.569465i | \(0.807151\pi\) | |||||||
\(98\) | −198.030 | − | 114.332i | −0.204123 | − | 0.117850i | ||||
\(99\) | 154.930 | + | 268.347i | 0.157283 | + | 0.272423i | ||||
\(100\) | 635.821 | 0.635821 | ||||||||
\(101\) | −689.403 | −0.679189 | −0.339595 | − | 0.940572i | \(-0.610290\pi\) | ||||
−0.339595 | + | 0.940572i | \(0.610290\pi\) | |||||||
\(102\) | 11.4040 | + | 19.7523i | 0.0110702 | + | 0.0191742i | ||||
\(103\) | − | 1060.53i | − | 1.01453i | −0.861790 | − | 0.507265i | \(-0.830656\pi\) | ||
0.861790 | − | 0.507265i | \(-0.169344\pi\) | |||||||
\(104\) | 348.256 | − | 603.197i | 0.328359 | − | 0.568734i | ||||
\(105\) | − | 1725.81i | − | 1.60402i | ||||||
\(106\) | −862.745 | − | 498.106i | −0.790540 | − | 0.456418i | ||||
\(107\) | 949.293 | − | 1644.22i | 0.857679 | − | 1.48554i | −0.0164583 | − | 0.999865i | \(-0.505239\pi\) |
0.874137 | − | 0.485679i | \(-0.161428\pi\) | |||||||
\(108\) | −110.119 | + | 190.732i | −0.0981130 | + | 0.169937i | ||||
\(109\) | −367.930 | + | 212.424i | −0.323314 | + | 0.186666i | −0.652869 | − | 0.757471i | \(-0.726435\pi\) |
0.329555 | + | 0.944137i | \(0.393101\pi\) | |||||||
\(110\) | 553.398 | 0.479677 | ||||||||
\(111\) | −1524.30 | − | 0.0966041i | −1.30342 | − | 8.26059e-5i | ||||
\(112\) | 241.948 | 0.204125 | ||||||||
\(113\) | 1803.46 | − | 1041.23i | 1.50138 | − | 0.866820i | 0.501378 | − | 0.865228i | \(-0.332827\pi\) |
0.999999 | − | 0.00159207i | \(-0.000506773\pi\) | |||||||
\(114\) | 847.881 | − | 1468.57i | 0.696591 | − | 1.20653i | ||||
\(115\) | −719.925 | + | 1246.95i | −0.583768 | + | 1.01112i | ||||
\(116\) | −524.768 | − | 302.975i | −0.420030 | − | 0.242504i | ||||
\(117\) | 1642.94i | 1.29820i | ||||||||
\(118\) | 666.718 | − | 1154.79i | 0.520139 | − | 0.900906i | ||||
\(119\) | − | 25.4620i | − | 0.0196142i | ||||||
\(120\) | −456.511 | − | 790.701i | −0.347280 | − | 0.601506i | ||||
\(121\) | −1061.37 | −0.797424 | ||||||||
\(122\) | −1526.21 | −1.13259 | ||||||||
\(123\) | 1470.22 | + | 2546.50i | 1.07777 | + | 1.86675i | ||||
\(124\) | 307.467 | + | 177.516i | 0.222672 | + | 0.128560i | ||||
\(125\) | 572.180i | 0.409418i | ||||||||
\(126\) | −494.249 | + | 285.355i | −0.349454 | + | 0.201757i | ||||
\(127\) | −515.369 | − | 892.645i | −0.360091 | − | 0.623696i | 0.627884 | − | 0.778307i | \(-0.283921\pi\) |
−0.987976 | + | 0.154610i | \(0.950588\pi\) | |||||||
\(128\) | 110.851 | − | 64.0000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −1265.88 | − | 730.857i | −0.863989 | − | 0.498824i | ||||
\(130\) | 2541.11 | + | 1467.11i | 1.71439 | + | 0.989803i | ||||
\(131\) | 314.224 | − | 181.417i | 0.209571 | − | 0.120996i | −0.391541 | − | 0.920161i | \(-0.628058\pi\) |
0.601112 | + | 0.799165i | \(0.294724\pi\) | |||||||
\(132\) | −222.423 | − | 385.248i | −0.146662 | − | 0.254026i | ||||
\(133\) | −1639.46 | + | 946.544i | −1.06887 | + | 0.617111i | ||||
\(134\) | 351.508i | 0.226610i | ||||||||
\(135\) | −803.504 | − | 463.903i | −0.512256 | − | 0.295751i | ||||
\(136\) | −6.73518 | − | 11.6657i | −0.00424660 | − | 0.00735532i | ||||
\(137\) | −1378.59 | −0.859715 | −0.429857 | − | 0.902897i | \(-0.641436\pi\) | ||||
−0.429857 | + | 0.902897i | \(0.641436\pi\) | |||||||
\(138\) | 1157.41 | 0.713954 | ||||||||
\(139\) | 236.291 | + | 409.268i | 0.144187 | + | 0.249739i | 0.929069 | − | 0.369906i | \(-0.120610\pi\) |
−0.784883 | + | 0.619645i | \(0.787277\pi\) | |||||||
\(140\) | 1019.27i | 0.615312i | ||||||||
\(141\) | 344.820 | − | 597.245i | 0.205951 | − | 0.356717i | ||||
\(142\) | 856.570i | 0.506210i | ||||||||
\(143\) | 1238.09 | + | 714.811i | 0.724016 | + | 0.418011i | ||||
\(144\) | −150.964 | + | 261.477i | −0.0873633 | + | 0.151318i | ||||
\(145\) | 1276.36 | − | 2210.71i | 0.731004 | − | 1.26614i | ||||
\(146\) | −280.704 | + | 162.065i | −0.159118 | + | 0.0918670i | ||||
\(147\) | −774.348 | −0.434470 | ||||||||
\(148\) | 900.249 | + | 0.0570544i | 0.500000 | + | 3.16881e-5i | ||||
\(149\) | 1856.02 | 1.02048 | 0.510238 | − | 0.860033i | \(-0.329557\pi\) | ||||
0.510238 | + | 0.860033i | \(0.329557\pi\) | |||||||
\(150\) | 1864.67 | − | 1076.57i | 1.01500 | − | 0.586010i | ||||
\(151\) | −1191.56 | + | 2063.84i | −0.642171 | + | 1.11227i | 0.342776 | + | 0.939417i | \(0.388633\pi\) |
−0.984947 | + | 0.172856i | \(0.944701\pi\) | |||||||
\(152\) | −500.759 | + | 867.339i | −0.267216 | + | 0.462832i | ||||
\(153\) | 27.5171 | + | 15.8870i | 0.0145400 | + | 0.00839470i | ||||
\(154\) | 496.609i | 0.259857i | ||||||||
\(155\) | −747.831 | + | 1295.28i | −0.387530 | + | 0.671222i | ||||
\(156\) | − | 2358.66i | − | 1.21054i | ||||||
\(157\) | −597.821 | − | 1035.46i | −0.303894 | − | 0.526360i | 0.673121 | − | 0.739533i | \(-0.264953\pi\) |
−0.977014 | + | 0.213173i | \(0.931620\pi\) | |||||||
\(158\) | −1100.81 | −0.554278 | ||||||||
\(159\) | −3373.56 | −1.68265 | ||||||||
\(160\) | 269.616 | + | 466.988i | 0.133219 | + | 0.230741i | ||||
\(161\) | −1118.99 | − | 646.047i | −0.547755 | − | 0.316246i | ||||
\(162\) | 1764.82i | 0.855908i | ||||||||
\(163\) | −825.839 | + | 476.798i | −0.396839 | + | 0.229115i | −0.685119 | − | 0.728431i | \(-0.740250\pi\) |
0.288280 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(164\) | −868.312 | − | 1503.96i | −0.413438 | − | 0.716095i | ||||
\(165\) | 1622.95 | − | 937.010i | 0.765736 | − | 0.442098i | ||||
\(166\) | −1410.75 | − | 814.494i | −0.659609 | − | 0.380825i | ||||
\(167\) | −2066.79 | − | 1193.26i | −0.957684 | − | 0.552919i | −0.0622245 | − | 0.998062i | \(-0.519819\pi\) |
−0.895459 | + | 0.445143i | \(0.853153\pi\) | |||||||
\(168\) | 709.561 | − | 409.665i | 0.325856 | − | 0.188133i | ||||
\(169\) | 2691.57 | + | 4661.94i | 1.22511 | + | 2.12196i | ||||
\(170\) | 49.1445 | − | 28.3736i | 0.0221718 | − | 0.0128009i | ||||
\(171\) | − | 2362.39i | − | 1.05647i | ||||||
\(172\) | 747.629 | + | 431.644i | 0.331431 | + | 0.191352i | ||||
\(173\) | 2118.24 | + | 3668.90i | 0.930907 | + | 1.61238i | 0.781774 | + | 0.623561i | \(0.214315\pi\) |
0.149133 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(174\) | −2051.98 | −0.894024 | ||||||||
\(175\) | −2403.68 | −1.03829 | ||||||||
\(176\) | 131.363 | + | 227.527i | 0.0562605 | + | 0.0974461i | ||||
\(177\) | − | 4515.53i | − | 1.91756i | ||||||
\(178\) | 335.516 | − | 581.132i | 0.141281 | − | 0.244706i | ||||
\(179\) | − | 3656.41i | − | 1.52678i | −0.645940 | − | 0.763388i | \(-0.723534\pi\) | ||
0.645940 | − | 0.763388i | \(-0.276466\pi\) | |||||||
\(180\) | −1101.53 | − | 635.971i | −0.456131 | − | 0.263347i | ||||
\(181\) | −1233.96 | + | 2137.28i | −0.506738 | + | 0.877696i | 0.493231 | + | 0.869898i | \(0.335816\pi\) |
−0.999970 | + | 0.00779807i | \(0.997518\pi\) | |||||||
\(182\) | −1316.56 | + | 2280.35i | −0.536209 | + | 0.928741i | ||||
\(183\) | −4475.91 | + | 2584.17i | −1.80802 | + | 1.04386i | ||||
\(184\) | −683.569 | −0.273877 | ||||||||
\(185\) | −0.240355 | + | 3792.52i | −9.55205e−5 | + | 1.50720i | ||||
\(186\) | 1202.28 | 0.473953 | ||||||||
\(187\) | 23.9443 | − | 13.8243i | 0.00936355 | − | 0.00540605i | ||||
\(188\) | −203.651 | + | 352.733i | −0.0790039 | + | 0.136839i | ||||
\(189\) | 416.298 | − | 721.050i | 0.160218 | − | 0.277506i | ||||
\(190\) | −3653.88 | − | 2109.57i | −1.39516 | − | 0.805495i | ||||
\(191\) | − | 1201.72i | − | 0.455253i | −0.973749 | − | 0.227627i | \(-0.926903\pi\) | ||
0.973749 | − | 0.227627i | \(-0.0730965\pi\) | |||||||
\(192\) | 216.729 | − | 375.385i | 0.0814638 | − | 0.141099i | ||||
\(193\) | − | 2844.06i | − | 1.06073i | −0.847771 | − | 0.530363i | \(-0.822056\pi\) | ||
0.847771 | − | 0.530363i | \(-0.177944\pi\) | |||||||
\(194\) | −1088.06 | − | 1884.58i | −0.402672 | − | 0.697449i | ||||
\(195\) | 9936.43 | 3.64904 | ||||||||
\(196\) | 457.330 | 0.166665 | ||||||||
\(197\) | −648.159 | − | 1122.64i | −0.234413 | − | 0.406016i | 0.724689 | − | 0.689076i | \(-0.241984\pi\) |
−0.959102 | + | 0.283061i | \(0.908650\pi\) | |||||||
\(198\) | −536.693 | − | 309.860i | −0.192632 | − | 0.111216i | ||||
\(199\) | − | 3721.05i | − | 1.32552i | −0.748833 | − | 0.662759i | \(-0.769385\pi\) | ||
0.748833 | − | 0.662759i | \(-0.230615\pi\) | |||||||
\(200\) | −1101.27 | + | 635.821i | −0.389359 | + | 0.224797i | ||||
\(201\) | 595.171 | + | 1030.87i | 0.208857 | + | 0.361750i | ||||
\(202\) | 1194.08 | − | 689.403i | 0.415917 | − | 0.240130i | ||||
\(203\) | 1983.85 | + | 1145.38i | 0.685907 | + | 0.396009i | ||||
\(204\) | −39.5045 | − | 22.8079i | −0.0135582 | − | 0.00782782i | ||||
\(205\) | 6335.80 | − | 3657.98i | 2.15859 | − | 1.24626i | ||||
\(206\) | 1060.53 | + | 1836.88i | 0.358691 | + | 0.621271i | ||||
\(207\) | 1396.39 | − | 806.204i | 0.468867 | − | 0.270701i | ||||
\(208\) | 1393.02i | 0.464369i | ||||||||
\(209\) | −1780.25 | − | 1027.83i | −0.589199 | − | 0.340174i | ||||
\(210\) | 1725.81 | + | 2989.20i | 0.567107 | + | 0.982258i | ||||
\(211\) | 4602.50 | 1.50165 | 0.750827 | − | 0.660499i | \(-0.229655\pi\) | ||||
0.750827 | + | 0.660499i | \(0.229655\pi\) | |||||||
\(212\) | 1992.42 | 0.645473 | ||||||||
\(213\) | 1450.34 | + | 2512.06i | 0.466552 | + | 0.808092i | ||||
\(214\) | 3797.17i | 1.21294i | ||||||||
\(215\) | −1818.40 | + | 3149.57i | −0.576810 | + | 0.999064i | ||||
\(216\) | − | 440.476i | − | 0.138753i | ||||||
\(217\) | −1162.36 | − | 671.090i | −0.363623 | − | 0.209938i | ||||
\(218\) | 424.849 | − | 735.859i | 0.131993 | − | 0.228618i | ||||
\(219\) | −548.814 | + | 950.574i | −0.169340 | + | 0.293305i | ||||
\(220\) | −958.514 | + | 553.398i | −0.293741 | + | 0.169591i | ||||
\(221\) | 146.598 | 0.0446210 | ||||||||
\(222\) | 2640.25 | − | 1524.13i | 0.798208 | − | 0.460778i | ||||
\(223\) | 2008.08 | 0.603009 | 0.301504 | − | 0.953465i | \(-0.402511\pi\) | ||||
0.301504 | + | 0.953465i | \(0.402511\pi\) | |||||||
\(224\) | −419.066 | + | 241.948i | −0.125000 | + | 0.0721689i | ||||
\(225\) | 1499.78 | − | 2597.70i | 0.444379 | − | 0.769688i | ||||
\(226\) | −2082.46 | + | 3606.93i | −0.612935 | + | 1.06163i | ||||
\(227\) | −2003.64 | − | 1156.80i | −0.585842 | − | 0.338236i | 0.177609 | − | 0.984101i | \(-0.443164\pi\) |
−0.763452 | + | 0.645865i | \(0.776497\pi\) | |||||||
\(228\) | 3391.52i | 0.985128i | ||||||||
\(229\) | −525.797 | + | 910.708i | −0.151728 | + | 0.262800i | −0.931863 | − | 0.362811i | \(-0.881817\pi\) |
0.780135 | + | 0.625611i | \(0.215150\pi\) | |||||||
\(230\) | − | 2879.70i | − | 0.825573i | ||||||
\(231\) | 840.856 | + | 1456.41i | 0.239499 | + | 0.414824i | ||||
\(232\) | 1211.90 | 0.342953 | ||||||||
\(233\) | 2407.86 | 0.677014 | 0.338507 | − | 0.940964i | \(-0.390078\pi\) | ||||
0.338507 | + | 0.940964i | \(0.390078\pi\) | |||||||
\(234\) | −1642.94 | − | 2845.65i | −0.458984 | − | 0.794984i | ||||
\(235\) | −1485.97 | − | 857.927i | −0.412486 | − | 0.238149i | ||||
\(236\) | 2666.87i | 0.735587i | ||||||||
\(237\) | −3228.35 | + | 1863.89i | −0.884827 | + | 0.510855i | ||||
\(238\) | 25.4620 | + | 44.1014i | 0.00693468 | + | 0.0120112i | ||||
\(239\) | 5167.49 | − | 2983.45i | 1.39857 | − | 0.807462i | 0.404324 | − | 0.914616i | \(-0.367507\pi\) |
0.994242 | + | 0.107154i | \(0.0341737\pi\) | |||||||
\(240\) | 1581.40 | + | 913.023i | 0.425329 | + | 0.245564i | ||||
\(241\) | −2047.85 | − | 1182.33i | −0.547359 | − | 0.316018i | 0.200697 | − | 0.979653i | \(-0.435679\pi\) |
−0.748056 | + | 0.663635i | \(0.769013\pi\) | |||||||
\(242\) | 1838.35 | − | 1061.37i | 0.488321 | − | 0.281932i | ||||
\(243\) | 2244.87 | + | 3888.23i | 0.592628 | + | 1.02646i | ||||
\(244\) | 2643.47 | − | 1526.21i | 0.693569 | − | 0.400432i | ||||
\(245\) | 1926.61i | 0.502395i | ||||||||
\(246\) | −5092.99 | − | 2940.44i | −1.31999 | − | 0.762096i | ||||
\(247\) | −5449.76 | − | 9439.25i | −1.40389 | − | 2.43160i | ||||
\(248\) | −710.065 | −0.181811 | ||||||||
\(249\) | −5516.39 | −1.40396 | ||||||||
\(250\) | −572.180 | − | 991.044i | −0.144751 | − | 0.250717i | ||||
\(251\) | 374.640i | 0.0942115i | 0.998890 | + | 0.0471058i | \(0.0149998\pi\) | ||||
−0.998890 | + | 0.0471058i | \(0.985000\pi\) | |||||||
\(252\) | 570.709 | − | 988.497i | 0.142664 | − | 0.247101i | ||||
\(253\) | − | 1403.06i | − | 0.348653i | ||||||
\(254\) | 1785.29 | + | 1030.74i | 0.441020 | + | 0.254623i | ||||
\(255\) | 96.0840 | − | 166.422i | 0.0235961 | − | 0.0408697i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1375.99 | − | 794.430i | 0.333977 | − | 0.192822i | −0.323628 | − | 0.946184i | \(-0.604903\pi\) |
0.657605 | + | 0.753363i | \(0.271569\pi\) | |||||||
\(258\) | 2923.43 | 0.705444 | ||||||||
\(259\) | −3403.34 | − | 0.215691i | −0.816498 | − | 5.17466e-5i | ||||
\(260\) | −5868.45 | −1.39979 | ||||||||
\(261\) | −2475.65 | + | 1429.32i | −0.587123 | + | 0.338976i | ||||
\(262\) | −362.834 | + | 628.447i | −0.0855571 | + | 0.148189i | ||||
\(263\) | −1260.57 | + | 2183.37i | −0.295552 | + | 0.511911i | −0.975113 | − | 0.221708i | \(-0.928837\pi\) |
0.679561 | + | 0.733619i | \(0.262170\pi\) | |||||||
\(264\) | 770.495 | + | 444.846i | 0.179624 | + | 0.103706i | ||||
\(265\) | 8393.57i | 1.94571i | ||||||||
\(266\) | 1893.09 | − | 3278.92i | 0.436363 | − | 0.755803i | ||||
\(267\) | − | 2272.38i | − | 0.520851i | ||||||
\(268\) | −351.508 | − | 608.830i | −0.0801186 | − | 0.138769i | ||||
\(269\) | 2167.74 | 0.491336 | 0.245668 | − | 0.969354i | \(-0.420993\pi\) | ||||
0.245668 | + | 0.969354i | \(0.420993\pi\) | |||||||
\(270\) | 1855.61 | 0.418255 | ||||||||
\(271\) | −3647.17 | − | 6317.08i | −0.817526 | − | 1.41600i | −0.907500 | − | 0.420053i | \(-0.862012\pi\) |
0.0899734 | − | 0.995944i | \(-0.471322\pi\) | |||||||
\(272\) | 23.3314 | + | 13.4704i | 0.00520100 | + | 0.00300280i | ||||
\(273\) | 8916.77i | 1.97680i | ||||||||
\(274\) | 2387.79 | − | 1378.59i | 0.526466 | − | 0.303955i | ||||
\(275\) | −1305.05 | − | 2260.42i | −0.286173 | − | 0.495666i | ||||
\(276\) | −2004.70 | + | 1157.41i | −0.437206 | + | 0.252421i | ||||
\(277\) | −1518.51 | − | 876.714i | −0.329381 | − | 0.190168i | 0.326185 | − | 0.945306i | \(-0.394237\pi\) |
−0.655566 | + | 0.755137i | \(0.727570\pi\) | |||||||
\(278\) | −818.536 | − | 472.582i | −0.176592 | − | 0.101955i | ||||
\(279\) | 1450.51 | − | 837.454i | 0.311254 | − | 0.179703i | ||||
\(280\) | −1019.27 | − | 1765.42i | −0.217546 | − | 0.376800i | ||||
\(281\) | 3888.07 | − | 2244.78i | 0.825419 | − | 0.476556i | −0.0268626 | − | 0.999639i | \(-0.508552\pi\) |
0.852282 | + | 0.523083i | \(0.175218\pi\) | |||||||
\(282\) | 1379.28i | 0.291258i | ||||||||
\(283\) | 6033.77 | + | 3483.60i | 1.26739 | + | 0.731726i | 0.974493 | − | 0.224419i | \(-0.0720483\pi\) |
0.292894 | + | 0.956145i | \(0.405382\pi\) | |||||||
\(284\) | −856.570 | − | 1483.62i | −0.178972 | − | 0.309989i | ||||
\(285\) | −14287.6 | −2.96956 | ||||||||
\(286\) | −2859.24 | −0.591156 | ||||||||
\(287\) | 3282.60 | + | 5685.63i | 0.675142 | + | 1.16938i | ||||
\(288\) | − | 603.855i | − | 0.123550i | ||||||
\(289\) | −2455.08 | + | 4252.33i | −0.499711 | + | 0.865526i | ||||
\(290\) | 5105.42i | 1.03380i | ||||||||
\(291\) | −6381.92 | − | 3684.60i | −1.28562 | − | 0.742252i | ||||
\(292\) | 324.130 | − | 561.409i | 0.0649598 | − | 0.112514i | ||||
\(293\) | −1063.94 | + | 1842.80i | −0.212136 | + | 0.367431i | −0.952383 | − | 0.304905i | \(-0.901375\pi\) |
0.740247 | + | 0.672336i | \(0.234709\pi\) | |||||||
\(294\) | 1341.21 | − | 774.348i | 0.266058 | − | 0.153608i | ||||
\(295\) | −11234.8 | −2.21735 | ||||||||
\(296\) | −1559.33 | + | 900.150i | −0.306197 | + | 0.176757i | ||||
\(297\) | 904.097 | 0.176636 | ||||||||
\(298\) | −3214.72 | + | 1856.02i | −0.624911 | + | 0.360793i | ||||
\(299\) | 3719.64 | − | 6442.60i | 0.719439 | − | 1.24610i | ||||
\(300\) | −2153.14 | + | 3729.34i | −0.414371 | + | 0.717712i | ||||
\(301\) | −2826.37 | − | 1631.80i | −0.541226 | − | 0.312477i | ||||
\(302\) | − | 4766.24i | − | 0.908167i | ||||||
\(303\) | 2334.58 | − | 4043.62i | 0.442635 | − | 0.766666i | ||||
\(304\) | − | 2003.03i | − | 0.377901i | ||||||
\(305\) | 6429.52 | + | 11136.3i | 1.20706 | + | 2.09069i | ||||
\(306\) | −63.5480 | −0.0118719 | ||||||||
\(307\) | 7143.74 | 1.32806 | 0.664031 | − | 0.747705i | \(-0.268844\pi\) | ||||
0.664031 | + | 0.747705i | \(0.268844\pi\) | |||||||
\(308\) | −496.609 | − | 860.153i | −0.0918732 | − | 0.159129i | ||||
\(309\) | 6220.40 | + | 3591.35i | 1.14520 | + | 0.661180i | ||||
\(310\) | − | 2991.32i | − | 0.548051i | ||||||
\(311\) | −758.571 | + | 437.961i | −0.138311 | + | 0.0798536i | −0.567559 | − | 0.823333i | \(-0.692112\pi\) |
0.429248 | + | 0.903187i | \(0.358779\pi\) | |||||||
\(312\) | 2358.66 | + | 4085.32i | 0.427990 | + | 0.741300i | ||||
\(313\) | −3778.25 | + | 2181.37i | −0.682298 | + | 0.393925i | −0.800720 | − | 0.599038i | \(-0.795550\pi\) |
0.118422 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(314\) | 2070.91 | + | 1195.64i | 0.372192 | + | 0.214885i | ||||
\(315\) | 4164.29 | + | 2404.25i | 0.744860 | + | 0.430045i | ||||
\(316\) | 1906.66 | − | 1100.81i | 0.339425 | − | 0.195967i | ||||
\(317\) | −2890.51 | − | 5006.52i | −0.512137 | − | 0.887047i | −0.999901 | − | 0.0140719i | \(-0.995521\pi\) |
0.487764 | − | 0.872976i | \(-0.337813\pi\) | |||||||
\(318\) | 5843.18 | − | 3373.56i | 1.03041 | − | 0.594905i | ||||
\(319\) | 2487.48i | 0.436589i | ||||||||
\(320\) | −933.976 | − | 539.231i | −0.163159 | − | 0.0941998i | ||||
\(321\) | 6429.35 | + | 11136.0i | 1.11792 | + | 1.93629i | ||||
\(322\) | 2584.19 | 0.447240 | ||||||||
\(323\) | −210.794 | −0.0363123 | ||||||||
\(324\) | −1764.82 | − | 3056.75i | −0.302609 | − | 0.524134i | ||||
\(325\) | − | 13839.3i | − | 2.36205i | ||||||
\(326\) | 953.597 | − | 1651.68i | 0.162009 | − | 0.280607i | ||||
\(327\) | − | 2877.40i | − | 0.486608i | ||||||
\(328\) | 3007.92 | + | 1736.62i | 0.506356 | + | 0.292345i | ||||
\(329\) | 769.888 | − | 1333.49i | 0.129013 | − | 0.223457i | ||||
\(330\) | −1874.02 | + | 3245.90i | −0.312610 | + | 0.541457i | ||||
\(331\) | −6421.10 | + | 3707.22i | −1.06627 | + | 0.615612i | −0.927160 | − | 0.374665i | \(-0.877758\pi\) |
−0.139110 | + | 0.990277i | \(0.544424\pi\) | |||||||
\(332\) | 3257.98 | 0.538568 | ||||||||
\(333\) | 2123.75 | − | 3677.90i | 0.349491 | − | 0.605248i | ||||
\(334\) | 4773.05 | 0.781946 | ||||||||
\(335\) | 2564.84 | − | 1480.81i | 0.418306 | − | 0.241509i | ||||
\(336\) | −819.330 | + | 1419.12i | −0.133030 | + | 0.230415i | ||||
\(337\) | 2407.08 | − | 4169.19i | 0.389086 | − | 0.673917i | −0.603241 | − | 0.797559i | \(-0.706124\pi\) |
0.992327 | + | 0.123642i | \(0.0394575\pi\) | |||||||
\(338\) | −9323.87 | − | 5383.14i | −1.50045 | − | 0.866285i | ||||
\(339\) | 14104.0i | 2.25966i | ||||||||
\(340\) | −56.7472 | + | 98.2890i | −0.00905162 | + | 0.0156779i | ||||
\(341\) | − | 1457.44i | − | 0.231451i | ||||||
\(342\) | 2362.39 | + | 4091.77i | 0.373518 | + | 0.646953i | ||||
\(343\) | −6915.67 | −1.08866 | ||||||||
\(344\) | −1726.58 | −0.270613 | ||||||||
\(345\) | −4875.89 | − | 8445.29i | −0.760896 | − | 1.31791i | ||||
\(346\) | −7337.81 | − | 4236.48i | −1.14012 | − | 0.658251i | ||||
\(347\) | − | 6483.43i | − | 1.00302i | −0.865151 | − | 0.501511i | \(-0.832778\pi\) | ||
0.865151 | − | 0.501511i | \(-0.167222\pi\) | |||||||
\(348\) | 3554.13 | − | 2051.98i | 0.547476 | − | 0.316085i | ||||
\(349\) | 2174.66 | + | 3766.61i | 0.333543 | + | 0.577714i | 0.983204 | − | 0.182510i | \(-0.0584223\pi\) |
−0.649661 | + | 0.760224i | \(0.725089\pi\) | |||||||
\(350\) | 4163.30 | − | 2403.68i | 0.635822 | − | 0.367092i | ||||
\(351\) | 4151.47 | + | 2396.85i | 0.631307 | + | 0.364485i | ||||
\(352\) | −455.054 | − | 262.726i | −0.0689048 | − | 0.0397822i | ||||
\(353\) | 5061.96 | − | 2922.52i | 0.763232 | − | 0.440652i | −0.0672230 | − | 0.997738i | \(-0.521414\pi\) |
0.830455 | + | 0.557086i | \(0.188081\pi\) | |||||||
\(354\) | 4515.53 | + | 7821.13i | 0.677959 | + | 1.17426i | ||||
\(355\) | 6250.12 | − | 3608.51i | 0.934429 | − | 0.539493i | ||||
\(356\) | 1342.07i | 0.199802i | ||||||||
\(357\) | 149.344 | + | 86.2240i | 0.0221405 | + | 0.0127828i | ||||
\(358\) | 3656.41 | + | 6333.09i | 0.539797 | + | 0.934956i | ||||
\(359\) | −11195.2 | −1.64585 | −0.822924 | − | 0.568152i | \(-0.807659\pi\) | ||||
−0.822924 | + | 0.568152i | \(0.807659\pi\) | |||||||
\(360\) | 2543.89 | 0.372429 | ||||||||
\(361\) | 4406.72 | + | 7632.67i | 0.642473 | + | 1.11280i | ||||
\(362\) | − | 4935.84i | − | 0.716636i | ||||||
\(363\) | 3594.22 | − | 6225.36i | 0.519690 | − | 0.900129i | ||||
\(364\) | − | 5266.24i | − | 0.758314i | ||||||
\(365\) | 2365.07 | + | 1365.47i | 0.339160 | + | 0.195814i | ||||
\(366\) | 5168.33 | − | 8951.81i | 0.738123 | − | 1.27847i | ||||
\(367\) | −1259.14 | + | 2180.90i | −0.179092 | + | 0.310196i | −0.941570 | − | 0.336818i | \(-0.890649\pi\) |
0.762478 | + | 0.647014i | \(0.223983\pi\) | |||||||
\(368\) | 1183.98 | − | 683.569i | 0.167715 | − | 0.0968301i | ||||
\(369\) | −8192.73 | −1.15582 | ||||||||
\(370\) | −3792.10 | − | 6569.07i | −0.532816 | − | 0.923000i | ||||
\(371\) | −7532.24 | −1.05406 | ||||||||
\(372\) | −2082.41 | + | 1202.28i | −0.290236 | + | 0.167568i | ||||
\(373\) | −1927.57 | + | 3338.66i | −0.267576 | + | 0.463456i | −0.968235 | − | 0.250040i | \(-0.919556\pi\) |
0.700659 | + | 0.713496i | \(0.252889\pi\) | |||||||
\(374\) | −27.6485 | + | 47.8887i | −0.00382265 | + | 0.00662103i | ||||
\(375\) | −3356.06 | − | 1937.62i | −0.462150 | − | 0.266822i | ||||
\(376\) | − | 814.602i | − | 0.111728i | ||||||
\(377\) | −6594.55 | + | 11422.1i | −0.900893 | + | 1.56039i | ||||
\(378\) | 1665.19i | 0.226583i | ||||||||
\(379\) | 27.2024 | + | 47.1159i | 0.00368679 | + | 0.00638570i | 0.867863 | − | 0.496804i | \(-0.165493\pi\) |
−0.864176 | + | 0.503189i | \(0.832160\pi\) | |||||||
\(380\) | 8438.27 | 1.13914 | ||||||||
\(381\) | 6980.95 | 0.938701 | ||||||||
\(382\) | 1201.72 | + | 2081.44i | 0.160956 | + | 0.278784i | ||||
\(383\) | −799.417 | − | 461.544i | −0.106654 | − | 0.0615765i | 0.445724 | − | 0.895170i | \(-0.352946\pi\) |
−0.552378 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(384\) | 866.915i | 0.115207i | ||||||||
\(385\) | 3623.60 | − | 2092.09i | 0.479678 | − | 0.276942i | ||||
\(386\) | 2844.06 | + | 4926.06i | 0.375023 | + | 0.649559i | ||||
\(387\) | 3527.03 | − | 2036.33i | 0.463279 | − | 0.267474i | ||||
\(388\) | 3769.16 | + | 2176.13i | 0.493171 | + | 0.284732i | ||||
\(389\) | 427.934 | + | 247.068i | 0.0557766 | + | 0.0322027i | 0.527629 | − | 0.849475i | \(-0.323081\pi\) |
−0.471852 | + | 0.881678i | \(0.656414\pi\) | |||||||
\(390\) | −17210.4 | + | 9936.43i | −2.23457 | + | 1.29013i | ||||
\(391\) | −71.9369 | − | 124.598i | −0.00930436 | − | 0.0161156i | ||||
\(392\) | −792.118 | + | 457.330i | −0.102061 | + | 0.0589251i | ||||
\(393\) | 2457.39i | 0.315418i | ||||||||
\(394\) | 2245.29 | + | 1296.32i | 0.287096 | + | 0.165755i | ||||
\(395\) | 4637.44 | + | 8032.28i | 0.590722 | + | 1.02316i | ||||
\(396\) | 1239.44 | 0.157283 | ||||||||
\(397\) | 4248.92 | 0.537147 | 0.268574 | − | 0.963259i | \(-0.413448\pi\) | ||||
0.268574 | + | 0.963259i | \(0.413448\pi\) | |||||||
\(398\) | 3721.05 | + | 6445.04i | 0.468641 | + | 0.811710i | ||||
\(399\) | − | 12821.5i | − | 1.60871i | ||||||
\(400\) | 1271.64 | − | 2202.55i | 0.158955 | − | 0.275319i | ||||
\(401\) | − | 3788.88i | − | 0.471839i | −0.971773 | − | 0.235920i | \(-0.924190\pi\) | ||
0.971773 | − | 0.235920i | \(-0.0758102\pi\) | |||||||
\(402\) | −2061.73 | − | 1190.34i | −0.255796 | − | 0.147684i | ||||
\(403\) | 3863.82 | − | 6692.33i | 0.477595 | − | 0.827218i | ||||
\(404\) | −1378.81 | + | 2388.16i | −0.169797 | + | 0.294098i | ||||
\(405\) | 12877.3 | − | 7434.72i | 1.57995 | − | 0.912183i | ||||
\(406\) | −4581.51 | −0.560041 | ||||||||
\(407\) | −1847.60 | − | 3200.60i | −0.225017 | − | 0.389798i | ||||
\(408\) | 91.2318 | 0.0110702 | ||||||||
\(409\) | 9861.50 | − | 5693.54i | 1.19222 | − | 0.688331i | 0.233414 | − | 0.972377i | \(-0.425010\pi\) |
0.958811 | + | 0.284046i | \(0.0916770\pi\) | |||||||
\(410\) | −7315.95 | + | 12671.6i | −0.881242 | + | 1.52636i | ||||
\(411\) | 4668.44 | − | 8085.97i | 0.560285 | − | 0.970442i | ||||
\(412\) | −3673.77 | − | 2121.05i | −0.439305 | − | 0.253633i | ||||
\(413\) | − | 10081.9i | − | 1.20121i | ||||||
\(414\) | −1612.41 | + | 2792.77i | −0.191414 | + | 0.331539i | ||||
\(415\) | 13725.0i | 1.62346i | ||||||||
\(416\) | −1393.02 | − | 2412.79i | −0.164179 | − | 0.284367i | ||||
\(417\) | −3200.69 | −0.375872 | ||||||||
\(418\) | 4111.32 | 0.481079 | ||||||||
\(419\) | 3468.14 | + | 6006.99i | 0.404367 | + | 0.700384i | 0.994248 | − | 0.107107i | \(-0.0341586\pi\) |
−0.589881 | + | 0.807490i | \(0.700825\pi\) | |||||||
\(420\) | −5978.39 | − | 3451.63i | −0.694561 | − | 0.401005i | ||||
\(421\) | − | 9388.82i | − | 1.08690i | −0.839443 | − | 0.543448i | \(-0.817118\pi\) | ||
0.839443 | − | 0.543448i | \(-0.182882\pi\) | |||||||
\(422\) | −7971.76 | + | 4602.50i | −0.919571 | + | 0.530915i | ||||
\(423\) | 960.745 | + | 1664.06i | 0.110433 | + | 0.191275i | ||||
\(424\) | −3450.98 | + | 1992.42i | −0.395270 | + | 0.228209i | ||||
\(425\) | −231.790 | − | 133.824i | −0.0264552 | − | 0.0152739i | ||||
\(426\) | −5024.12 | − | 2900.68i | −0.571407 | − | 0.329902i | ||||
\(427\) | −9993.48 | + | 5769.74i | −1.13260 | + | 0.653904i | ||||
\(428\) | −3797.17 | − | 6576.90i | −0.428839 | − | 0.742772i | ||||
\(429\) | −8385.30 | + | 4841.25i | −0.943697 | + | 0.544844i | ||||
\(430\) | − | 7273.62i | − | 0.815733i | ||||||
\(431\) | −1038.51 | − | 599.585i | −0.116063 | − | 0.0670093i | 0.440844 | − | 0.897584i | \(-0.354679\pi\) |
−0.556908 | + | 0.830574i | \(0.688012\pi\) | |||||||
\(432\) | 440.476 | + | 762.927i | 0.0490565 | + | 0.0849683i | ||||
\(433\) | 5267.93 | 0.584667 | 0.292333 | − | 0.956316i | \(-0.405568\pi\) | ||||
0.292333 | + | 0.956316i | \(0.405568\pi\) | |||||||
\(434\) | 2684.36 | 0.296897 | ||||||||
\(435\) | 8644.47 | + | 14972.7i | 0.952806 | + | 1.65031i | ||||
\(436\) | 1699.39i | 0.186666i | ||||||||
\(437\) | −5348.48 | + | 9263.84i | −0.585475 | + | 1.01407i | ||||
\(438\) | − | 2195.26i | − | 0.239483i | ||||||
\(439\) | −13463.2 | − | 7772.98i | −1.46370 | − | 0.845066i | −0.464517 | − | 0.885564i | \(-0.653772\pi\) |
−0.999180 | + | 0.0404980i | \(0.987106\pi\) | |||||||
\(440\) | 1106.80 | − | 1917.03i | 0.119919 | − | 0.207706i | ||||
\(441\) | 1078.75 | − | 1868.46i | 0.116483 | − | 0.201755i | ||||
\(442\) | −253.915 | + | 146.598i | −0.0273247 | + | 0.0157759i | ||||
\(443\) | −3079.97 | −0.330324 | −0.165162 | − | 0.986266i | \(-0.552815\pi\) | ||||
−0.165162 | + | 0.986266i | \(0.552815\pi\) | |||||||
\(444\) | −3048.93 | + | 5280.12i | −0.325891 | + | 0.564377i | ||||
\(445\) | −5653.78 | −0.602281 | ||||||||
\(446\) | −3478.10 | + | 2008.08i | −0.369266 | + | 0.213196i | ||||
\(447\) | −6285.19 | + | 10886.3i | −0.665055 | + | 1.15191i | ||||
\(448\) | 483.896 | − | 838.133i | 0.0510311 | − | 0.0883885i | ||||
\(449\) | −2218.53 | − | 1280.87i | −0.233183 | − | 0.134628i | 0.378857 | − | 0.925455i | \(-0.376317\pi\) |
−0.612039 | + | 0.790827i | \(0.709651\pi\) | |||||||
\(450\) | 5999.12i | 0.628447i | ||||||||
\(451\) | −3564.50 | + | 6173.89i | −0.372163 | + | 0.644606i | ||||
\(452\) | − | 8329.84i | − | 0.866820i | ||||||
\(453\) | −8070.17 | − | 13977.9i | −0.837019 | − | 1.44976i | ||||
\(454\) | 4627.21 | 0.478338 | ||||||||
\(455\) | 22185.3 | 2.28586 | ||||||||
\(456\) | −3391.52 | − | 5874.29i | −0.348295 | − | 0.603265i | ||||
\(457\) | −12130.9 | − | 7003.77i | −1.24170 | − | 0.716898i | −0.272263 | − | 0.962223i | \(-0.587772\pi\) |
−0.969441 | + | 0.245325i | \(0.921105\pi\) | |||||||
\(458\) | − | 2103.19i | − | 0.214576i | ||||||
\(459\) | 80.2883 | − | 46.3545i | 0.00816457 | − | 0.00471382i | ||||
\(460\) | 2879.70 | + | 4987.79i | 0.291884 | + | 0.505558i | ||||
\(461\) | −102.193 | + | 59.0013i | −0.0103245 | + | 0.00596088i | −0.505153 | − | 0.863030i | \(-0.668564\pi\) |
0.494829 | + | 0.868990i | \(0.335231\pi\) | |||||||
\(462\) | −2912.81 | − | 1681.71i | −0.293325 | − | 0.169351i | ||||
\(463\) | 10078.7 | + | 5818.94i | 1.01166 | + | 0.584080i | 0.911676 | − | 0.410909i | \(-0.134789\pi\) |
0.0999806 | + | 0.994989i | \(0.468122\pi\) | |||||||
\(464\) | −2099.07 | + | 1211.90i | −0.210015 | + | 0.121252i | ||||
\(465\) | −5064.89 | − | 8772.65i | −0.505115 | − | 0.874885i | ||||
\(466\) | −4170.54 | + | 2407.86i | −0.414585 | + | 0.239360i | ||||
\(467\) | − | 5413.21i | − | 0.536388i | −0.963365 | − | 0.268194i | \(-0.913573\pi\) | ||
0.963365 | − | 0.268194i | \(-0.0864269\pi\) | |||||||
\(468\) | 5691.31 | + | 3285.88i | 0.562138 | + | 0.324551i | ||||
\(469\) | 1328.86 | + | 2301.65i | 0.130833 | + | 0.226610i | ||||
\(470\) | 3431.71 | 0.336793 | ||||||||
\(471\) | 8097.82 | 0.792203 | ||||||||
\(472\) | −2666.87 | − | 4619.16i | −0.260069 | − | 0.450453i | ||||
\(473\) | − | 3543.87i | − | 0.344498i | ||||||
\(474\) | 3727.78 | − | 6456.70i | 0.361229 | − | 0.625667i | ||||
\(475\) | 19899.6i | 1.92222i | ||||||||
\(476\) | −88.2028 | − | 50.9239i | −0.00849321 | − | 0.00490356i | ||||
\(477\) | 4699.75 | − | 8140.20i | 0.451125 | − | 0.781372i | ||||
\(478\) | −5966.91 | + | 10335.0i | −0.570962 | + | 0.988935i | ||||
\(479\) | −4700.30 | + | 2713.72i | −0.448355 | + | 0.258858i | −0.707135 | − | 0.707078i | \(-0.750013\pi\) |
0.258780 | + | 0.965936i | \(0.416680\pi\) | |||||||
\(480\) | −3652.09 | −0.347280 | ||||||||
\(481\) | 1.24185 | − | 19594.8i | 0.000117720 | − | 1.85748i | ||||
\(482\) | 4729.30 | 0.446917 | ||||||||
\(483\) | 7578.65 | − | 4375.53i | 0.713955 | − | 0.412202i | ||||
\(484\) | −2122.74 | + | 3676.70i | −0.199356 | + | 0.345295i | ||||
\(485\) | −9167.46 | + | 15878.5i | −0.858295 | + | 1.48661i | ||||
\(486\) | −7776.47 | − | 4489.74i | −0.725818 | − | 0.419051i | ||||
\(487\) | 13015.8i | 1.21109i | 0.795811 | + | 0.605545i | \(0.207045\pi\) | ||||
−0.795811 | + | 0.605545i | \(0.792955\pi\) | |||||||
\(488\) | −3052.42 | + | 5286.94i | −0.283148 | + | 0.490427i | ||||
\(489\) | − | 6458.49i | − | 0.597266i | ||||||
\(490\) | −1926.61 | − | 3336.99i | −0.177623 | − | 0.307653i | ||||
\(491\) | −8167.85 | −0.750733 | −0.375367 | − | 0.926876i | \(-0.622483\pi\) | ||||
−0.375367 | + | 0.926876i | \(0.622483\pi\) | |||||||
\(492\) | 11761.8 | 1.07777 | ||||||||
\(493\) | 127.537 | + | 220.901i | 0.0116511 | + | 0.0201802i | ||||
\(494\) | 18878.5 | + | 10899.5i | 1.71940 | + | 0.992697i | ||||
\(495\) | 5221.44i | 0.474114i | ||||||||
\(496\) | 1229.87 | − | 710.065i | 0.111336 | − | 0.0642800i | ||||
\(497\) | 3238.21 | + | 5608.75i | 0.292261 | + | 0.506211i | ||||
\(498\) | 9554.66 | − | 5516.39i | 0.859748 | − | 0.496376i | ||||
\(499\) | 16660.1 | + | 9618.70i | 1.49460 | + | 0.862910i | 0.999981 | − | 0.00619792i | \(-0.00197287\pi\) |
0.494623 | + | 0.869108i | \(0.335306\pi\) | |||||||
\(500\) | 1982.09 | + | 1144.36i | 0.177283 | + | 0.102355i | ||||
\(501\) | 13997.9 | − | 8081.70i | 1.24827 | − | 0.720686i | ||||
\(502\) | −374.640 | − | 648.896i | −0.0333088 | − | 0.0576925i | ||||
\(503\) | 6038.11 | − | 3486.10i | 0.535240 | − | 0.309021i | −0.207907 | − | 0.978149i | \(-0.566665\pi\) |
0.743148 | + | 0.669127i | \(0.233332\pi\) | |||||||
\(504\) | 2282.84i | 0.201757i | ||||||||
\(505\) | −10060.7 | − | 5808.55i | −0.886526 | − | 0.511836i | ||||
\(506\) | 1403.06 | + | 2430.16i | 0.123268 | + | 0.213506i | ||||
\(507\) | −36458.8 | −3.19367 | ||||||||
\(508\) | −4122.95 | −0.360091 | ||||||||
\(509\) | 6493.86 | + | 11247.7i | 0.565491 | + | 0.979460i | 0.997004 | + | 0.0773529i | \(0.0246468\pi\) |
−0.431512 | + | 0.902107i | \(0.642020\pi\) | |||||||
\(510\) | 384.336i | 0.0333700i | ||||||||
\(511\) | −1225.35 | + | 2122.37i | −0.106079 | + | 0.183734i | ||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | −5969.41 | − | 3446.44i | −0.513754 | − | 0.296616i | ||||
\(514\) | −1588.86 | + | 2751.99i | −0.136346 | + | 0.236157i | ||||
\(515\) | 8935.44 | − | 15476.6i | 0.764549 | − | 1.32424i | ||||
\(516\) | −5063.52 | + | 2923.43i | −0.431994 | + | 0.249412i | ||||
\(517\) | 1672.01 | 0.142234 | ||||||||
\(518\) | 5894.97 | − | 3402.96i | 0.500019 | − | 0.288644i | ||||
\(519\) | −28692.7 | −2.42673 | ||||||||
\(520\) | 10164.5 | − | 5868.45i | 0.857194 | − | 0.494901i | ||||
\(521\) | 1407.68 | − | 2438.18i | 0.118372 | − | 0.205026i | −0.800751 | − | 0.598998i | \(-0.795566\pi\) |
0.919123 | + | 0.393972i | \(0.128899\pi\) | |||||||
\(522\) | 2858.64 | − | 4951.31i | 0.239692 | − | 0.415159i | ||||
\(523\) | 2612.40 | + | 1508.27i | 0.218417 | + | 0.126103i | 0.605217 | − | 0.796060i | \(-0.293086\pi\) |
−0.386800 | + | 0.922164i | \(0.626420\pi\) | |||||||
\(524\) | − | 1451.34i | − | 0.120996i | ||||||
\(525\) | 8139.80 | − | 14098.6i | 0.676667 | − | 1.17202i | ||||
\(526\) | − | 5042.29i | − | 0.417974i | ||||||
\(527\) | −74.7253 | − | 129.428i | −0.00617663 | − | 0.0106982i | ||||
\(528\) | −1779.38 | −0.146662 | ||||||||
\(529\) | 4865.97 | 0.399932 | ||||||||
\(530\) | −8393.57 | − | 14538.1i | −0.687912 | − | 1.19150i | ||||
\(531\) | 10895.7 | + | 6290.64i | 0.890458 | + | 0.514106i | ||||
\(532\) | 7572.35i | 0.617111i | ||||||||
\(533\) | −32735.2 | + | 18899.7i | −2.66026 | + | 1.53590i | ||||
\(534\) | 2272.38 | + | 3935.87i | 0.184149 | + | 0.318955i | ||||
\(535\) | 27706.8 | − | 15996.5i | 2.23901 | − | 1.29269i | ||||
\(536\) | 1217.66 | + | 703.016i | 0.0981248 | + | 0.0566524i | ||||
\(537\) | 21446.3 | + | 12382.0i | 1.72342 | + | 0.995016i | ||||
\(538\) | −3754.63 | + | 2167.74i | −0.300880 | + | 0.173713i | ||||
\(539\) | −938.690 | − | 1625.86i | −0.0750134 | − | 0.129927i | ||||
\(540\) | −3214.01 | + | 1855.61i | −0.256128 | + | 0.147876i | ||||
\(541\) | 13211.4i | 1.04991i | 0.851130 | + | 0.524954i | \(0.175918\pi\) | ||||
−0.851130 | + | 0.524954i | \(0.824082\pi\) | |||||||
\(542\) | 12634.2 | + | 7294.33i | 1.00126 | + | 0.578078i | ||||
\(543\) | −8357.34 | − | 14475.3i | −0.660493 | − | 1.14401i | ||||
\(544\) | −53.8815 | −0.00424660 | ||||||||
\(545\) | −7159.11 | −0.562684 | ||||||||
\(546\) | −8916.77 | − | 15444.3i | −0.698906 | − | 1.21054i | ||||
\(547\) | 14450.3i | 1.12952i | 0.825255 | + | 0.564761i | \(0.191031\pi\) | ||||
−0.825255 | + | 0.564761i | \(0.808969\pi\) | |||||||
\(548\) | −2757.18 | + | 4775.58i | −0.214929 | + | 0.372267i | ||||
\(549\) | − | 14400.1i | − | 1.11946i | ||||||
\(550\) | 4520.83 | + | 2610.10i | 0.350489 | + | 0.202355i | ||||
\(551\) | 9482.33 | − | 16423.9i | 0.733141 | − | 1.26984i | ||||
\(552\) | 2314.83 | − | 4009.40i | 0.178488 | − | 0.309151i | ||||
\(553\) | −7208.03 | + | 4161.56i | −0.554279 | + | 0.320013i | ||||
\(554\) | 3506.86 | 0.268939 | ||||||||
\(555\) | −22243.8 | − | 12844.3i | −1.70125 | − | 0.982364i | ||||
\(556\) | 1890.33 | 0.144187 | ||||||||
\(557\) | −12889.1 | + | 7441.53i | −0.980484 | + | 0.566083i | −0.902416 | − | 0.430866i | \(-0.858208\pi\) |
−0.0780675 | + | 0.996948i | \(0.524875\pi\) | |||||||
\(558\) | −1674.91 | + | 2901.03i | −0.127069 | + | 0.220090i | ||||
\(559\) | 9395.16 | − | 16272.9i | 0.710864 | − | 1.23125i | ||||
\(560\) | 3530.84 | + | 2038.53i | 0.266438 | + | 0.153828i | ||||
\(561\) | 187.257i | 0.0140927i | ||||||||
\(562\) | −4489.55 | + | 7776.14i | −0.336976 | + | 0.583659i | ||||
\(563\) | 1078.27i | 0.0807167i | 0.999185 | + | 0.0403584i | \(0.0128500\pi\) | ||||
−0.999185 | + | 0.0403584i | \(0.987150\pi\) | |||||||
\(564\) | −1379.28 | − | 2388.98i | −0.102975 | − | 0.178359i | ||||
\(565\) | 35091.5 | 2.61294 | ||||||||
\(566\) | −13934.4 | −1.03482 | ||||||||
\(567\) | 6671.78 | + | 11555.9i | 0.494160 | + | 0.855909i | ||||
\(568\) | 2967.25 | + | 1713.14i | 0.219195 | + | 0.126552i | ||||
\(569\) | − | 9857.95i | − | 0.726304i | −0.931730 | − | 0.363152i | \(-0.881701\pi\) | ||
0.931730 | − | 0.363152i | \(-0.118299\pi\) | |||||||
\(570\) | 24746.9 | − | 14287.6i | 1.81848 | − | 1.04990i | ||||
\(571\) | −1583.74 | − | 2743.13i | −0.116073 | − | 0.201044i | 0.802135 | − | 0.597142i | \(-0.203697\pi\) |
−0.918208 | + | 0.396098i | \(0.870364\pi\) | |||||||
\(572\) | 4952.36 | − | 2859.24i | 0.362008 | − | 0.209005i | ||||
\(573\) | 7048.56 | + | 4069.49i | 0.513888 | + | 0.296693i | ||||
\(574\) | −11371.3 | − | 6565.20i | −0.826877 | − | 0.477398i | ||||
\(575\) | −11762.4 | + | 6791.05i | −0.853092 | + | 0.492533i | ||||
\(576\) | 603.855 | + | 1045.91i | 0.0436816 | + | 0.0756588i | ||||
\(577\) | 6218.31 | − | 3590.14i | 0.448651 | − | 0.259029i | −0.258609 | − | 0.965982i | \(-0.583264\pi\) |
0.707260 | + | 0.706953i | \(0.249931\pi\) | |||||||
\(578\) | − | 9820.33i | − | 0.706699i | ||||||
\(579\) | 16681.6 | + | 9631.10i | 1.19734 | + | 0.691286i | ||||
\(580\) | −5105.42 | − | 8842.85i | −0.365502 | − | 0.633068i | ||||
\(581\) | −12316.6 | −0.879480 | ||||||||
\(582\) | 14738.4 | 1.04970 | ||||||||
\(583\) | −4089.54 | − | 7083.29i | −0.290517 | − | 0.503190i | ||||
\(584\) | 1296.52i | 0.0918670i | ||||||||
\(585\) | −13842.6 | + | 23976.0i | −0.978323 | + | 1.69451i | ||||
\(586\) | − | 4255.76i | − | 0.300006i | ||||||
\(587\) | 12557.9 | + | 7250.28i | 0.882995 | + | 0.509798i | 0.871645 | − | 0.490138i | \(-0.163054\pi\) |
0.0113504 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(588\) | −1548.70 | + | 2682.42i | −0.108618 | + | 0.188131i | ||||
\(589\) | −5555.80 | + | 9622.93i | −0.388664 | + | 0.673185i | ||||
\(590\) | 19459.3 | − | 11234.8i | 1.35784 | − | 0.783951i | ||||
\(591\) | 8779.67 | 0.611078 | ||||||||
\(592\) | 1800.70 | − | 3118.44i | 0.125014 | − | 0.216498i | ||||
\(593\) | 17193.2 | 1.19062 | 0.595311 | − | 0.803495i | \(-0.297029\pi\) | ||||
0.595311 | + | 0.803495i | \(0.297029\pi\) | |||||||
\(594\) | −1565.94 | + | 904.097i | −0.108167 | + | 0.0624504i | ||||
\(595\) | 214.529 | − | 371.576i | 0.0147813 | − | 0.0256019i | ||||
\(596\) | 3712.04 | − | 6429.43i | 0.255119 | − | 0.441879i | ||||
\(597\) | 21825.4 | + | 12600.9i | 1.49624 | + | 0.863854i | ||||
\(598\) | 14878.6i | 1.01744i | ||||||||
\(599\) | −345.402 | + | 598.254i | −0.0235605 | + | 0.0408080i | −0.877565 | − | 0.479457i | \(-0.840834\pi\) |
0.854005 | + | 0.520265i | \(0.174167\pi\) | |||||||
\(600\) | − | 8612.55i | − | 0.586010i | ||||||
\(601\) | 4310.22 | + | 7465.51i | 0.292541 | + | 0.506697i | 0.974410 | − | 0.224778i | \(-0.0721657\pi\) |
−0.681869 | + | 0.731475i | \(0.738832\pi\) | |||||||
\(602\) | 6527.21 | 0.441909 | ||||||||
\(603\) | −3316.56 | −0.223982 | ||||||||
\(604\) | 4766.24 | + | 8255.38i | 0.321086 | + | 0.556137i | ||||
\(605\) | −15489.0 | − | 8942.57i | −1.04085 | − | 0.600938i | ||||
\(606\) | 9338.34i | 0.625980i | ||||||||
\(607\) | −6586.57 | + | 3802.76i | −0.440430 | + | 0.254282i | −0.703780 | − | 0.710418i | \(-0.748506\pi\) |
0.263350 | + | 0.964700i | \(0.415173\pi\) | |||||||
\(608\) | 2003.03 | + | 3469.36i | 0.133608 | + | 0.231416i | ||||
\(609\) | −13436.2 | + | 7757.39i | −0.894026 | + | 0.516166i | ||||
\(610\) | −22272.5 | − | 12859.0i | −1.47834 | − | 0.853520i | ||||
\(611\) | 7677.59 | + | 4432.66i | 0.508350 | + | 0.293496i | ||||
\(612\) | 110.068 | − | 63.5480i | 0.00727002 | − | 0.00419735i | ||||
\(613\) | −261.702 | − | 453.281i | −0.0172432 | − | 0.0298660i | 0.857275 | − | 0.514859i | \(-0.172156\pi\) |
−0.874518 | + | 0.484993i | \(0.838822\pi\) | |||||||
\(614\) | −12373.3 | + | 7143.74i | −0.813268 | + | 0.469541i | ||||
\(615\) | 49549.3i | 3.24881i | ||||||||
\(616\) | 1720.31 | + | 993.219i | 0.112521 | + | 0.0649642i | ||||
\(617\) | −11965.5 | − | 20724.8i | −0.780734 | − | 1.35227i | −0.931515 | − | 0.363703i | \(-0.881512\pi\) |
0.150781 | − | 0.988567i | \(-0.451821\pi\) | |||||||
\(618\) | −14365.4 | −0.935050 | ||||||||
\(619\) | −6344.72 | −0.411980 | −0.205990 | − | 0.978554i | \(-0.566041\pi\) | ||||
−0.205990 | + | 0.978554i | \(0.566041\pi\) | |||||||
\(620\) | 2991.32 | + | 5181.12i | 0.193765 | + | 0.335611i | ||||
\(621\) | − | 4704.62i | − | 0.304009i | ||||||
\(622\) | 875.922 | − | 1517.14i | 0.0564651 | − | 0.0978003i | ||||
\(623\) | − | 5073.60i | − | 0.326275i | ||||||
\(624\) | −8170.64 | − | 4717.32i | −0.524178 | − | 0.302634i | ||||
\(625\) | 5113.81 | − | 8857.39i | 0.327284 | − | 0.566873i | ||||
\(626\) | 4362.75 | − | 7556.50i | 0.278547 | − | 0.482458i | ||||
\(627\) | 12057.2 | − | 6961.26i | 0.767975 | − | 0.443390i | ||||
\(628\) | −4782.57 | −0.303894 | ||||||||
\(629\) | −328.176 | − | 189.500i | −0.0208032 | − | 0.0120125i | ||||
\(630\) | −9617.01 | −0.608176 | ||||||||
\(631\) | −17527.7 | + | 10119.6i | −1.10581 | + | 0.638439i | −0.937741 | − | 0.347336i | \(-0.887086\pi\) |
−0.168069 | + | 0.985775i | \(0.553753\pi\) | |||||||
\(632\) | −2201.63 | + | 3813.33i | −0.138570 | + | 0.240010i | ||||
\(633\) | −15585.8 | + | 26995.5i | −0.978643 | + | 1.69506i | ||||
\(634\) | 10013.0 | + | 5781.03i | 0.627237 | + | 0.362136i | ||||
\(635\) | − | 17368.9i | − | 1.08546i | ||||||
\(636\) | −6747.12 | + | 11686.4i | −0.420662 | + | 0.728607i | ||||
\(637\) | − | 9954.24i | − | 0.619154i | ||||||
\(638\) | −2487.48 | − | 4308.44i | −0.154358 | − | 0.267355i | ||||
\(639\) | −8081.94 | −0.500339 | ||||||||
\(640\) | 2156.92 | 0.133219 | ||||||||
\(641\) | 6975.19 | + | 12081.4i | 0.429803 | + | 0.744440i | 0.996855 | − | 0.0792414i | \(-0.0252498\pi\) |
−0.567053 | + | 0.823681i | \(0.691916\pi\) | |||||||
\(642\) | −22271.9 | − | 12858.7i | −1.36916 | − | 0.790486i | ||||
\(643\) | 9082.55i | 0.557046i | 0.960430 | + | 0.278523i | \(0.0898449\pi\) | ||||
−0.960430 | + | 0.278523i | \(0.910155\pi\) | |||||||
\(644\) | −4475.95 | + | 2584.19i | −0.273877 | + | 0.158123i | ||||
\(645\) | −12315.6 | − | 21331.3i | −0.751826 | − | 1.30220i | ||||
\(646\) | 365.106 | − | 210.794i | 0.0222367 | − | 0.0128383i | ||||
\(647\) | −26714.4 | − | 15423.6i | −1.62327 | − | 0.937193i | −0.986039 | − | 0.166516i | \(-0.946748\pi\) |
−0.637227 | − | 0.770676i | \(-0.719919\pi\) | |||||||
\(648\) | 6113.50 | + | 3529.63i | 0.370619 | + | 0.213977i | ||||
\(649\) | 9481.03 | − | 5473.87i | 0.573440 | − | 0.331076i | ||||
\(650\) | 13839.3 | + | 23970.3i | 0.835110 | + | 1.44645i | ||||
\(651\) | 7872.41 | − | 4545.14i | 0.473954 | − | 0.273638i | ||||
\(652\) | 3814.39i | 0.229115i | ||||||||
\(653\) | −25950.6 | − | 14982.6i | −1.55517 | − | 0.897879i | −0.997707 | − | 0.0676776i | \(-0.978441\pi\) |
−0.557464 | − | 0.830201i | \(-0.688226\pi\) | |||||||
\(654\) | 2877.40 | + | 4983.81i | 0.172042 | + | 0.297985i | ||||
\(655\) | 6114.11 | 0.364730 | ||||||||
\(656\) | −6946.50 | −0.413438 | ||||||||
\(657\) | −1529.12 | − | 2648.51i | −0.0908016 | − | 0.157273i | ||||
\(658\) | 3079.55i | 0.182452i | ||||||||
\(659\) | 12415.0 | − | 21503.4i | 0.733870 | − | 1.27110i | −0.221347 | − | 0.975195i | \(-0.571045\pi\) |
0.955217 | − | 0.295905i | \(-0.0956212\pi\) | |||||||
\(660\) | − | 7496.08i | − | 0.442098i | ||||||
\(661\) | 23643.6 | + | 13650.6i | 1.39127 | + | 0.803249i | 0.993456 | − | 0.114219i | \(-0.0364364\pi\) |
0.397812 | + | 0.917467i | \(0.369770\pi\) | |||||||
\(662\) | 7414.45 | − | 12842.2i | 0.435303 | − | 0.753967i | ||||
\(663\) | −496.438 | + | 859.855i | −0.0290800 | + | 0.0503680i | ||||
\(664\) | −5642.98 | + | 3257.98i | −0.329804 | + | 0.190413i | ||||
\(665\) | −31900.4 | −1.86022 | ||||||||
\(666\) | −0.538321 | + | 8494.06i | −3.13206e−5 | + | 0.494201i | ||||
\(667\) | 12944.0 | 0.751415 | ||||||||
\(668\) | −8267.17 | + | 4773.05i | −0.478842 | + | 0.276460i | ||||
\(669\) | −6800.14 | + | 11778.2i | −0.392987 | + | 0.680674i | ||||
\(670\) | −2961.63 | + | 5129.69i | −0.170773 | + | 0.295787i | ||||
\(671\) | −10851.7 | − | 6265.22i | −0.624329 | − | 0.360456i | ||||
\(672\) | − | 3277.32i | − | 0.188133i | ||||||
\(673\) | 6832.69 | − | 11834.6i | 0.391354 | − | 0.677844i | −0.601275 | − | 0.799042i | \(-0.705340\pi\) |
0.992628 | + | 0.121198i | \(0.0386736\pi\) | |||||||
\(674\) | 9628.32i | 0.550251i | ||||||||
\(675\) | −4376.00 | − | 7579.45i | −0.249529 | − | 0.432197i | ||||
\(676\) | 21532.6 | 1.22511 | ||||||||
\(677\) | −25968.9 | −1.47425 | −0.737124 | − | 0.675758i | \(-0.763816\pi\) | ||||
−0.737124 | + | 0.675758i | \(0.763816\pi\) | |||||||
\(678\) | −14104.0 | − | 24428.9i | −0.798912 | − | 1.38376i | ||||
\(679\) | −14249.1 | − | 8226.72i | −0.805346 | − | 0.464967i | ||||
\(680\) | − | 226.989i | − | 0.0128009i | ||||||
\(681\) | 13570.2 | − | 7834.76i | 0.763599 | − | 0.440864i | ||||
\(682\) | 1457.44 | + | 2524.36i | 0.0818304 | + | 0.141734i | ||||
\(683\) | 1939.61 | − | 1119.84i | 0.108663 | − | 0.0627369i | −0.444683 | − | 0.895688i | \(-0.646684\pi\) |
0.553347 | + | 0.832951i | \(0.313350\pi\) | |||||||
\(684\) | −8183.55 | − | 4724.77i | −0.457465 | − | 0.264117i | ||||
\(685\) | −20118.3 | − | 11615.3i | −1.12216 | − | 0.647880i | ||||
\(686\) | 11978.3 | − | 6915.67i | 0.666667 | − | 0.384900i | ||||
\(687\) | −3561.11 | − | 6168.02i | −0.197765 | − | 0.342539i | ||||
\(688\) | 2990.52 | − | 1726.58i | 0.165716 | − | 0.0956760i | ||||
\(689\) | − | 43367.1i | − | 2.39790i | ||||||
\(690\) | 16890.6 | + | 9751.78i | 0.931903 | + | 0.538034i | ||||
\(691\) | 2426.93 | + | 4203.57i | 0.133611 | + | 0.231420i | 0.925066 | − | 0.379807i | \(-0.124010\pi\) |
−0.791455 | + | 0.611227i | \(0.790676\pi\) | |||||||
\(692\) | 16945.9 | 0.930907 | ||||||||
\(693\) | −4685.63 | −0.256843 | ||||||||
\(694\) | 6483.43 | + | 11229.6i | 0.354622 | + | 0.614224i | ||||
\(695\) | 7963.47i | 0.434635i | ||||||||
\(696\) | −4103.96 | + | 7108.27i | −0.223506 | + | 0.387124i | ||||
\(697\) | 731.030i | 0.0397270i | ||||||||
\(698\) | −7533.23 | − | 4349.31i | −0.408505 | − | 0.235851i | ||||
\(699\) | −8153.95 | + | 14123.1i | −0.441217 | + | 0.764210i | ||||
\(700\) | −4807.37 | + | 8326.60i | −0.259573 | + | 0.449594i | ||||
\(701\) | 13809.4 | − | 7972.84i | 0.744041 | − | 0.429572i | −0.0794959 | − | 0.996835i | \(-0.525331\pi\) |
0.823537 | + | 0.567263i | \(0.191998\pi\) | |||||||
\(702\) | −9587.40 | −0.515460 | ||||||||
\(703\) | −1.78565 | + | 28175.5i | −9.57998e−5 | + | 1.51160i | ||||
\(704\) | 1050.90 | 0.0562605 | ||||||||
\(705\) | 10064.2 | − | 5810.55i | 0.537643 | − | 0.310408i | ||||
\(706\) | −5845.05 | + | 10123.9i | −0.311588 | + | 0.539687i | ||||
\(707\) | 5212.49 | − | 9028.30i | 0.277278 | − | 0.480260i | ||||
\(708\) | −15642.3 | − | 9031.06i | −0.830327 | − | 0.479390i | ||||
\(709\) | 22666.0i | 1.20062i | 0.799767 | + | 0.600311i | \(0.204956\pi\) | ||||
−0.799767 | + | 0.600311i | \(0.795044\pi\) | |||||||
\(710\) | −7217.02 | + | 12500.2i | −0.381479 | + | 0.660741i | ||||
\(711\) | − | 10386.4i | − | 0.547850i | ||||||
\(712\) | −1342.07 | − | 2324.53i | −0.0706405 | − | 0.122353i | ||||
\(713\) | −7584.04 | −0.398351 | ||||||||
\(714\) | −344.896 | −0.0180776 | ||||||||
\(715\) | 12045.3 | + | 20863.0i | 0.630024 | + | 1.09123i | ||||
\(716\) | −12666.2 | − | 7312.82i | −0.661114 | − | 0.381694i | ||||
\(717\) | 40412.5i | 2.10493i | ||||||||
\(718\) | 19390.6 | − | 11195.2i | 1.00787 | − | 0.581895i | ||||
\(719\) | 4558.49 | + | 7895.54i | 0.236444 | + | 0.409533i | 0.959691 | − | 0.281056i | \(-0.0906848\pi\) |
−0.723248 | + | 0.690589i | \(0.757351\pi\) | |||||||
\(720\) | −4406.14 | + | 2543.89i | −0.228065 | + | 0.131674i | ||||
\(721\) | 13888.5 | + | 8018.50i | 0.717383 | + | 0.414181i | ||||
\(722\) | −15265.3 | − | 8813.44i | −0.786866 | − | 0.454297i | ||||
\(723\) | 13869.6 | − | 8007.63i | 0.713439 | − | 0.411904i | ||||
\(724\) | 4935.84 | + | 8549.13i | 0.253369 | + | 0.438848i | ||||
\(725\) | 20853.7 | − | 12039.9i | 1.06826 | − | 0.616758i | ||||
\(726\) | 14376.9i | 0.734952i | ||||||||
\(727\) | −1259.67 | − | 727.271i | −0.0642622 | − | 0.0371018i | 0.467525 | − | 0.883980i | \(-0.345146\pi\) |
−0.531787 | + | 0.846878i | \(0.678479\pi\) | |||||||
\(728\) | 5266.24 | + | 9121.40i | 0.268104 | + | 0.464370i | ||||
\(729\) | −6583.01 | −0.334451 | ||||||||
\(730\) | −5461.90 | −0.276923 | ||||||||
\(731\) | −181.700 | − | 314.714i | −0.00919346 | − | 0.0159235i | ||||
\(732\) | 20673.3i | 1.04386i | ||||||||
\(733\) | 3073.97 | − | 5324.27i | 0.154897 | − | 0.268290i | −0.778124 | − | 0.628110i | \(-0.783829\pi\) |
0.933022 | + | 0.359820i | \(0.117162\pi\) | |||||||
\(734\) | − | 5036.57i | − | 0.253274i | ||||||
\(735\) | −11300.3 | − | 6524.26i | −0.567101 | − | 0.327416i | ||||
\(736\) | −1367.14 | + | 2367.95i | −0.0684692 | + | 0.118592i | ||||
\(737\) | −1442.97 | + | 2499.30i | −0.0721202 | + | 0.124916i | ||||
\(738\) | 14190.2 | − | 8192.73i | 0.707790 | − | 0.408643i | ||||
\(739\) | 20606.1 | 1.02572 | 0.512860 | − | 0.858472i | \(-0.328586\pi\) | ||||
0.512860 | + | 0.858472i | \(0.328586\pi\) | |||||||
\(740\) | 13137.2 | + | 7585.87i | 0.652611 | + | 0.376841i | ||||
\(741\) | 73819.9 | 3.65971 | ||||||||
\(742\) | 13046.2 | − | 7532.24i | 0.645474 | − | 0.372665i | ||||
\(743\) | 13443.9 | − | 23285.5i | 0.663806 | − | 1.14975i | −0.315801 | − | 0.948825i | \(-0.602273\pi\) |
0.979608 | − | 0.200921i | \(-0.0643933\pi\) | |||||||
\(744\) | 2404.56 | − | 4164.81i | 0.118488 | − | 0.205228i | ||||
\(745\) | 27085.6 | + | 15637.9i | 1.33200 | + | 0.769029i | ||||
\(746\) | − | 7710.30i | − | 0.378410i | ||||||
\(747\) | 7684.94 | − | 13310.7i | 0.376409 | − | 0.651959i | ||||
\(748\) | − | 110.594i | − | 0.00540605i | ||||||
\(749\) | 14355.0 | + | 24863.6i | 0.700293 | + | 1.21294i | ||||
\(750\) | 7750.49 | 0.377344 | ||||||||
\(751\) | −28416.5 | −1.38074 | −0.690369 | − | 0.723457i | \(-0.742552\pi\) | ||||
−0.690369 | + | 0.723457i | \(0.742552\pi\) | |||||||
\(752\) | 814.602 | + | 1410.93i | 0.0395020 | + | 0.0684194i | ||||
\(753\) | −2197.41 | − | 1268.68i | −0.106346 | − | 0.0613986i | ||||
\(754\) | − | 26378.2i | − | 1.27406i | ||||||
\(755\) | −34777.8 | + | 20079.0i | −1.67641 | + | 0.967878i | ||||
\(756\) | −1665.19 | − | 2884.20i | −0.0801091 | − | 0.138753i | ||||
\(757\) | 2452.37 | − | 1415.87i | 0.117745 | − | 0.0679799i | −0.439971 | − | 0.898012i | \(-0.645011\pi\) |
0.557716 | + | 0.830032i | \(0.311678\pi\) | |||||||
\(758\) | −94.2318 | − | 54.4047i | −0.00451537 | − | 0.00260695i | ||||
\(759\) | 8229.47 | + | 4751.29i | 0.393559 | + | 0.227221i | ||||
\(760\) | −14615.5 | + | 8438.27i | −0.697579 | + | 0.402748i | ||||
\(761\) | 16346.9 | + | 28313.7i | 0.778680 | + | 1.34871i | 0.932703 | + | 0.360646i | \(0.117444\pi\) |
−0.154023 | + | 0.988067i | \(0.549223\pi\) | |||||||
\(762\) | −12091.4 | + | 6980.95i | −0.574834 | + | 0.331881i | ||||
\(763\) | − | 6424.46i | − | 0.304824i | ||||||
\(764\) | −4162.88 | − | 2403.44i | −0.197130 | − | 0.113813i | ||||
\(765\) | 267.712 | + | 463.690i | 0.0126525 | + | 0.0219147i | ||||
\(766\) | 1846.18 | 0.0870823 | ||||||||
\(767\) | 58047.1 | 2.73267 | ||||||||
\(768\) | −866.915 | − | 1501.54i | −0.0407319 | − | 0.0705497i | ||||
\(769\) | − | 38366.0i | − | 1.79911i | −0.436809 | − | 0.899555i | \(-0.643891\pi\) | ||
0.436809 | − | 0.899555i | \(-0.356109\pi\) | |||||||
\(770\) | −4184.18 | + | 7247.21i | −0.195828 | + | 0.339183i | ||||
\(771\) | 10761.0i | 0.502656i | ||||||||
\(772\) | −9852.12 | − | 5688.13i | −0.459308 | − | 0.265182i | ||||
\(773\) | −3972.86 | + | 6881.20i | −0.184856 | + | 0.320181i | −0.943528 | − | 0.331292i | \(-0.892515\pi\) |
0.758672 | + | 0.651473i | \(0.225849\pi\) | |||||||
\(774\) | −4072.66 | + | 7054.05i | −0.189133 | + | 0.327588i | ||||
\(775\) | −12218.4 | + | 7054.29i | −0.566319 | + | 0.326965i | ||||
\(776\) | −8704.51 | −0.402672 | ||||||||
\(777\) | 11526.3 | − | 19961.2i | 0.532179 | − | 0.921626i | ||||
\(778\) | −988.271 | −0.0455414 | ||||||||
\(779\) | 47070.1 | − | 27175.9i | 2.16490 | − | 1.24991i | ||||
\(780\) | 19872.9 | − | 34420.8i | 0.912259 | − | 1.58008i | ||||
\(781\) | −3516.30 | + | 6090.41i | −0.161105 | + | 0.279042i | ||||
\(782\) | 249.197 | + | 143.874i | 0.0113955 | + | 0.00657918i | ||||
\(783\) | 8340.82i | 0.380685i | ||||||||
\(784\) | 914.659 | − | 1584.24i | 0.0416663 | − | 0.0721682i | ||||
\(785\) | − | 20147.7i | − | 0.916056i | ||||||
\(786\) | −2457.39 | − | 4256.33i | −0.111517 | − | 0.193153i | ||||
\(787\) | −18768.7 | −0.850106 | −0.425053 | − | 0.905168i | \(-0.639745\pi\) | ||||
−0.425053 | + | 0.905168i | \(0.639745\pi\) | |||||||
\(788\) | −5185.27 | −0.234413 | ||||||||
\(789\) | −8537.57 | − | 14787.5i | −0.385229 | − | 0.667236i | ||||
\(790\) | −16064.6 | − | 9274.88i | −0.723483 | − | 0.417703i | ||||
\(791\) | 31490.5i | 1.41551i | ||||||||
\(792\) | −2146.77 | + | 1239.44i | −0.0963159 | + | 0.0556080i | ||||
\(793\) | −33219.4 | − | 57537.8i | −1.48759 | − | 2.57658i | ||||
\(794\) | −7359.35 | + | 4248.92i | −0.328934 | + | 0.189910i | ||||
\(795\) | −49231.6 | − | 28423.9i | −2.19631 | − | 1.26804i | ||||
\(796\) | −12890.1 | − | 7442.09i | −0.573966 | − | 0.331379i | ||||
\(797\) | 19946.1 | − | 11515.9i | 0.886484 | − | 0.511812i | 0.0136929 | − | 0.999906i | \(-0.495641\pi\) |
0.872791 | + | 0.488095i | \(0.162308\pi\) | |||||||
\(798\) | 12821.5 | + | 22207.4i | 0.568765 | + | 0.985130i | ||||
\(799\) | 148.483 | − | 85.7265i | 0.00657439 | − | 0.00379573i | ||||
\(800\) | 5086.57i | 0.224797i | ||||||||
\(801\) | 5483.11 | + | 3165.68i | 0.241868 | + | 0.139643i | ||||
\(802\) | 3788.88 | + | 6562.53i | 0.166820 | + | 0.288941i | ||||
\(803\) | −2661.16 | −0.116949 | ||||||||
\(804\) | 4761.37 | 0.208857 | ||||||||
\(805\) | −10886.5 | − | 18856.0i | −0.476646 | − | 0.825574i | ||||
\(806\) | 15455.3i | 0.675421i | ||||||||
\(807\) | −7340.80 | + | 12714.6i | −0.320209 | + | 0.554618i | ||||
\(808\) | − | 5515.22i | − | 0.240130i | ||||||
\(809\) | 2273.28 | + | 1312.48i | 0.0987937 | + | 0.0570386i | 0.548583 | − | 0.836096i | \(-0.315168\pi\) |
−0.449789 | + | 0.893135i | \(0.648501\pi\) | |||||||
\(810\) | −14869.4 | + | 25754.6i | −0.645011 | + | 1.11719i | ||||
\(811\) | 5944.94 | − | 10296.9i | 0.257405 | − | 0.445838i | −0.708141 | − | 0.706071i | \(-0.750466\pi\) |
0.965546 | + | 0.260233i | \(0.0837994\pi\) | |||||||
\(812\) | 7935.41 | − | 4581.51i | 0.342954 | − | 0.198004i | ||||
\(813\) | 49402.9 | 2.13116 | ||||||||
\(814\) | 6400.74 | + | 3696.01i | 0.275609 | + | 0.159146i | ||||
\(815\) | −16069.0 | −0.690642 | ||||||||
\(816\) | −158.018 | + | 91.2318i | −0.00677909 | + | 0.00391391i | ||||
\(817\) | −13509.3 | + | 23398.9i | −0.578497 | + | 1.00199i | ||||
\(818\) | −11387.1 | + | 19723.0i | −0.486724 | + | 0.843030i | ||||
\(819\) | −21515.6 | − | 12422.1i | −0.917970 | − | 0.529990i | ||||
\(820\) | − | 29263.8i | − | 1.24626i | ||||||
\(821\) | −7166.10 | + | 12412.0i | −0.304627 | + | 0.527629i | −0.977178 | − | 0.212421i | \(-0.931865\pi\) |
0.672551 | + | 0.740050i | \(0.265198\pi\) | |||||||
\(822\) | 18673.8i | 0.792363i | ||||||||
\(823\) | −8584.24 | − | 14868.3i | −0.363582 | − | 0.629742i | 0.624966 | − | 0.780652i | \(-0.285113\pi\) |
−0.988548 | + | 0.150910i | \(0.951780\pi\) | |||||||
\(824\) | 8484.20 | 0.358691 | ||||||||
\(825\) | 17677.6 | 0.746008 | ||||||||
\(826\) | 10081.9 | + | 17462.4i | 0.424692 | + | 0.735588i | ||||
\(827\) | −7620.91 | − | 4399.93i | −0.320441 | − | 0.185007i | 0.331148 | − | 0.943579i | \(-0.392564\pi\) |
−0.651589 | + | 0.758572i | \(0.725897\pi\) | |||||||
\(828\) | − | 6449.63i | − | 0.270701i | ||||||
\(829\) | −35843.6 | + | 20694.3i | −1.50169 | + | 0.867001i | −0.501692 | + | 0.865046i | \(0.667289\pi\) |
−0.999998 | + | 0.00195493i | \(0.999378\pi\) | |||||||
\(830\) | −13725.0 | − | 23772.4i | −0.573979 | − | 0.994161i | ||||
\(831\) | 10284.6 | − | 5937.79i | 0.429323 | − | 0.247870i | ||||
\(832\) | 4825.58 | + | 2786.05i | 0.201078 | + | 0.116092i | ||||
\(833\) | −166.721 | − | 96.2562i | −0.00693461 | − | 0.00400370i | ||||
\(834\) | 5543.76 | − | 3200.69i | 0.230173 | − | 0.132891i | ||||
\(835\) | −20107.6 | − | 34827.5i | −0.833358 | − | 1.44342i | ||||
\(836\) | −7121.01 | + | 4111.32i | −0.294600 | + | 0.170087i | ||||
\(837\) | − | 4886.98i | − | 0.201814i | ||||||
\(838\) | −12014.0 | − | 6936.28i | −0.495246 | − | 0.285930i | ||||
\(839\) | 6796.12 | + | 11771.2i | 0.279652 | + | 0.484372i | 0.971298 | − | 0.237865i | \(-0.0764475\pi\) |
−0.691646 | + | 0.722237i | \(0.743114\pi\) | |||||||
\(840\) | 13806.5 | 0.567107 | ||||||||
\(841\) | 1440.55 | 0.0590657 | ||||||||
\(842\) | 9388.82 | + | 16261.9i | 0.384276 | + | 0.665585i | ||||
\(843\) | 30406.7i | 1.24231i | ||||||||
\(844\) | 9204.99 | − | 15943.5i | 0.375413 | − | 0.650235i | ||||
\(845\) | 90711.2i | 3.69297i | ||||||||
\(846\) | −3328.12 | − | 1921.49i | −0.135252 | − | 0.0780877i | ||||
\(847\) | 8024.90 | − | 13899.5i | 0.325548 | − | 0.563865i | ||||
\(848\) | 3984.85 | − | 6901.96i | 0.161368 | − | 0.279498i | ||||
\(849\) | −40865.4 | + | 23593.6i | −1.65194 | + | 0.953747i | ||||
\(850\) | 535.297 | 0.0216006 | ||||||||
\(851\) | −16654.9 | + | 9614.29i | −0.670883 | + | 0.387278i | ||||
\(852\) | 11602.7 | 0.466552 | ||||||||
\(853\) | −34986.4 | + | 20199.4i | −1.40435 | + | 0.810802i | −0.994835 | − | 0.101502i | \(-0.967635\pi\) |
−0.409514 | + | 0.912304i | \(0.634302\pi\) | |||||||
\(854\) | 11539.5 | − | 19987.0i | 0.462380 | − | 0.800866i | ||||
\(855\) | 19904.3 | − | 34475.2i | 0.796154 | − | 1.37898i | ||||
\(856\) | 13153.8 | + | 7594.35i | 0.525219 | + | 0.303235i | ||||
\(857\) | − | 10500.4i | − | 0.418539i | −0.977858 | − | 0.209270i | \(-0.932891\pi\) | ||
0.977858 | − | 0.209270i | \(-0.0671087\pi\) | |||||||
\(858\) | 9682.51 | − | 16770.6i | 0.385263 | − | 0.667295i | ||||
\(859\) | 30169.6i | 1.19834i | 0.800622 | + | 0.599169i | \(0.204502\pi\) | ||||
−0.800622 | + | 0.599169i | \(0.795498\pi\) | |||||||
\(860\) | 7273.62 | + | 12598.3i | 0.288405 | + | 0.499532i | ||||
\(861\) | −44464.6 | −1.75999 | ||||||||
\(862\) | 2398.34 | 0.0947654 | ||||||||
\(863\) | 3487.86 | + | 6041.14i | 0.137576 | + | 0.238288i | 0.926579 | − | 0.376101i | \(-0.122736\pi\) |
−0.789003 | + | 0.614390i | \(0.789402\pi\) | |||||||
\(864\) | −1525.85 | − | 880.952i | −0.0600817 | − | 0.0346882i | ||||
\(865\) | 71388.9i | 2.80612i | ||||||||
\(866\) | −9124.33 | + | 5267.93i | −0.358034 | + | 0.206711i | ||||
\(867\) | −16627.7 | − | 28800.1i | −0.651334 | − | 1.12814i | ||||
\(868\) | −4649.45 | + | 2684.36i | −0.181812 | + | 0.104969i | ||||
\(869\) | −7827.03 | − | 4518.94i | −0.305539 | − | 0.176403i | ||||
\(870\) | −29945.3 | − | 17288.9i | −1.16694 | − | 0.673735i | ||||
\(871\) | −13251.8 | + | 7650.93i | −0.515522 | + | 0.297637i | ||||
\(872\) | −1699.39 | − | 2943.44i | −0.0659963 | − | 0.114309i | ||||
\(873\) | 17781.5 | − | 10266.1i | 0.689360 | − | 0.398002i | ||||
\(874\) | − | 21393.9i | − | 0.827987i | ||||||
\(875\) | −7493.16 | − | 4326.18i | −0.289503 | − | 0.167145i | ||||
\(876\) | 2195.26 | + | 3802.30i | 0.0846699 | + | 0.146653i | ||||
\(877\) | 21969.1 | 0.845887 | 0.422944 | − | 0.906156i | \(-0.360997\pi\) | ||||
0.422944 | + | 0.906156i | \(0.360997\pi\) | |||||||
\(878\) | 31091.9 | 1.19510 | ||||||||
\(879\) | −7205.82 | − | 12480.8i | −0.276503 | − | 0.478917i | ||||
\(880\) | 4427.18i | 0.169591i | ||||||||
\(881\) | −12876.9 | + | 22303.4i | −0.492433 | + | 0.852919i | −0.999962 | − | 0.00871576i | \(-0.997226\pi\) |
0.507529 | + | 0.861635i | \(0.330559\pi\) | |||||||
\(882\) | 4315.01i | 0.164732i | ||||||||
\(883\) | 11974.9 | + | 6913.71i | 0.456385 | + | 0.263494i | 0.710523 | − | 0.703674i | \(-0.248458\pi\) |
−0.254138 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(884\) | 293.196 | − | 507.830i | 0.0111553 | − | 0.0193215i | ||||
\(885\) | 38045.5 | − | 65896.8i | 1.44507 | − | 2.50293i | ||||
\(886\) | 5334.66 | − | 3079.97i | 0.202281 | − | 0.116787i | ||||
\(887\) | 18967.7 | 0.718007 | 0.359004 | − | 0.933336i | \(-0.383117\pi\) | ||||
0.359004 | + | 0.933336i | \(0.383117\pi\) | |||||||
\(888\) | 0.772833 | − | 12194.4i | 2.92056e−5 | − | 0.460829i | ||||
\(889\) | 15586.6 | 0.588028 | ||||||||
\(890\) | 9792.63 | − | 5653.78i | 0.368820 | − | 0.212938i | ||||
\(891\) | −7244.73 | + | 12548.2i | −0.272399 | + | 0.471809i | ||||
\(892\) | 4016.16 | − | 6956.19i | 0.150752 | − | 0.261111i | ||||
\(893\) | −11039.6 | − | 6373.73i | −0.413692 | − | 0.238845i | ||||
\(894\) | − | 25140.8i | − | 0.940529i | ||||||
\(895\) | 30807.0 | − | 53359.4i | 1.15058 | − | 1.99286i | ||||
\(896\) | 1935.59i | 0.0721689i | ||||||||
\(897\) | 25192.3 | + | 43634.3i | 0.937732 | + | 1.62420i | ||||
\(898\) | 5123.48 | 0.190393 | ||||||||
\(899\) | 13445.7 | 0.498822 | ||||||||
\(900\) | −5999.12 | − | 10390.8i | −0.222190 | − | 0.384844i | ||||
\(901\) | −726.343 | − | 419.355i | −0.0268568 | − | 0.0155058i | ||||
\(902\) | − | 14258.0i | − | 0.526319i | ||||||
\(903\) | 19142.3 | − | 11051.8i | 0.705445 | − | 0.407289i | ||||
\(904\) | 8329.84 | + | 14427.7i | 0.306467 | + | 0.530817i | ||||
\(905\) | −36015.3 | + | 20793.4i | −1.32286 | + | 0.763754i | ||||
\(906\) | 27955.9 | + | 16140.3i | 1.02514 | + | 0.591862i | ||||
\(907\) | −28140.9 | − | 16247.1i | −1.03021 | − | 0.594793i | −0.113167 | − | 0.993576i | \(-0.536099\pi\) |
−0.917045 | + | 0.398783i | \(0.869433\pi\) | |||||||
\(908\) | −8014.56 | + | 4627.21i | −0.292921 | + | 0.169118i | ||||
\(909\) | 6504.67 | + | 11266.4i | 0.237345 | + | 0.411093i | ||||
\(910\) | −38426.1 | + | 22185.3i | −1.39980 | + | 0.808172i | ||||
\(911\) | 3300.84i | 0.120046i | 0.998197 | + | 0.0600228i | \(0.0191173\pi\) | ||||
−0.998197 | + | 0.0600228i | \(0.980883\pi\) | |||||||
\(912\) | 11748.6 | + | 6783.05i | 0.426573 | + | 0.246282i | ||||
\(913\) | −6687.14 | − | 11582.5i | −0.242401 | − | 0.419851i | ||||
\(914\) | 28015.1 | 1.01385 | ||||||||
\(915\) | −87091.4 | −3.14661 | ||||||||
\(916\) | 2103.19 | + | 3642.83i | 0.0758639 | + | 0.131400i | ||||
\(917\) | 5486.69i | 0.197586i | ||||||||
\(918\) | −92.7089 | + | 160.577i | −0.00333317 | + | 0.00577322i | ||||
\(919\) | − | 40530.5i | − | 1.45482i | −0.686203 | − | 0.727410i | \(-0.740724\pi\) | ||
0.686203 | − | 0.727410i | \(-0.259276\pi\) | |||||||
\(920\) | −9975.57 | − | 5759.40i | −0.357483 | − | 0.206393i | ||||
\(921\) | −24191.5 | + | 41900.9i | −0.865511 | + | 1.49911i | ||||
\(922\) | 118.003 | − | 204.386i | 0.00421498 | − | 0.00730055i | ||||
\(923\) | −32292.6 | + | 18644.1i | −1.15160 | + | 0.664874i | ||||
\(924\) | 6726.85 | 0.239499 | ||||||||
\(925\) | −17889.4 | + | 30980.8i | −0.635891 | + | 1.10123i | ||||
\(926\) | −23275.8 | −0.826014 | ||||||||
\(927\) | −17331.4 | + | 10006.3i | −0.614066 | + | 0.354531i | ||||
\(928\) | 2423.80 | − | 4198.14i | 0.0857383 | − | 0.148503i | ||||
\(929\) | −15798.2 | + | 27363.2i | −0.557935 | + | 0.966371i | 0.439734 | + | 0.898128i | \(0.355073\pi\) |
−0.997669 | + | 0.0682431i | \(0.978261\pi\) | |||||||
\(930\) | 17545.3 | + | 10129.8i | 0.618637 | + | 0.357170i | ||||
\(931\) | 14313.2i | 0.503864i | ||||||||
\(932\) | 4815.72 | − | 8341.07i | 0.169253 | − | 0.293156i | ||||
\(933\) | − | 5932.42i | − | 0.208166i | ||||||
\(934\) | 5413.21 | + | 9375.95i | 0.189642 | + | 0.328469i | ||||
\(935\) | 465.905 | 0.0162960 | ||||||||
\(936\) | −13143.5 | −0.458984 | ||||||||
\(937\) | 151.865 | + | 263.039i | 0.00529480 | + | 0.00917086i | 0.868661 | − | 0.495408i | \(-0.164981\pi\) |
−0.863366 | + | 0.504578i | \(0.831648\pi\) | |||||||
\(938\) | −4603.29 | − | 2657.71i | −0.160237 | − | 0.0925132i | ||||
\(939\) | − | 29547.9i | − | 1.02690i | ||||||
\(940\) | −5943.89 | + | 3431.71i | −0.206243 | + | 0.119074i | ||||
\(941\) | 16266.0 | + | 28173.5i | 0.563502 | + | 0.976015i | 0.997187 | + | 0.0749502i | \(0.0238798\pi\) |
−0.433685 | + | 0.901065i | \(0.642787\pi\) | |||||||
\(942\) | −14025.8 | + | 8097.82i | −0.485123 | + | 0.280086i | ||||
\(943\) | 32126.9 | + | 18548.5i | 1.10943 | + | 0.640531i | ||||
\(944\) | 9238.31 | + | 5333.74i | 0.318518 | + | 0.183897i | ||||
\(945\) | 12150.4 | − | 7015.03i | 0.418256 | − | 0.241480i | ||||
\(946\) | 3543.87 | + | 6138.17i | 0.121798 | + | 0.210961i | ||||
\(947\) | −14211.7 | + | 8205.12i | −0.487664 | + | 0.281553i | −0.723605 | − | 0.690214i | \(-0.757516\pi\) |
0.235941 | + | 0.971767i | \(0.424183\pi\) | |||||||
\(948\) | 14911.1i | 0.510855i | ||||||||
\(949\) | −12219.6 | − | 7055.00i | −0.417983 | − | 0.241323i | ||||
\(950\) | −19899.6 | − | 34467.0i | −0.679607 | − | 1.17711i | ||||
\(951\) | 39153.6 | 1.33506 | ||||||||
\(952\) | 203.696 | 0.00693468 | ||||||||
\(953\) | −8490.84 | − | 14706.6i | −0.288610 | − | 0.499887i | 0.684868 | − | 0.728667i | \(-0.259860\pi\) |
−0.973478 | + | 0.228780i | \(0.926526\pi\) | |||||||
\(954\) | 18799.0i | 0.637987i | ||||||||
\(955\) | 10125.1 | − | 17537.1i | 0.343078 | − | 0.594229i | ||||
\(956\) | − | 23867.6i | − | 0.807462i | ||||||
\(957\) | −14590.0 | − | 8423.56i | −0.492820 | − | 0.284530i | ||||
\(958\) | 5427.44 | − | 9400.60i | 0.183040 | − | 0.317035i | ||||
\(959\) | 10423.4 | − | 18053.8i | 0.350978 | − | 0.607911i | ||||
\(960\) | 6325.61 | − | 3652.09i | 0.212665 | − | 0.122782i | ||||
\(961\) | 21913.0 | 0.735557 | ||||||||
\(962\) | 19592.7 | + | 33940.5i | 0.656645 | + | 1.13751i | ||||
\(963\) | −35827.2 | −1.19887 | ||||||||
\(964\) | −8191.39 | + | 4729.30i | −0.273680 | + | 0.158009i | ||||
\(965\) | 23962.6 | − | 41504.5i | 0.799362 | − | 1.38453i | ||||
\(966\) | −8751.07 | + | 15157.3i | −0.291471 | + | 0.504843i | ||||
\(967\) | −481.795 | − | 278.165i | −0.0160222 | − | 0.00925044i | 0.491967 | − | 0.870614i | \(-0.336278\pi\) |
−0.507990 | + | 0.861363i | \(0.669611\pi\) | |||||||
\(968\) | − | 8490.97i | − | 0.281932i | ||||||
\(969\) | 713.829 | − | 1236.39i | 0.0236651 | − | 0.0409892i | ||||
\(970\) | − | 36669.9i | − | 1.21381i | ||||||
\(971\) | 6766.45 | + | 11719.8i | 0.223631 | + | 0.387340i | 0.955908 | − | 0.293667i | \(-0.0948756\pi\) |
−0.732277 | + | 0.681007i | \(0.761542\pi\) | |||||||
\(972\) | 17959.0 | 0.592628 | ||||||||
\(973\) | −7146.27 | −0.235456 | ||||||||
\(974\) | −13015.8 | − | 22544.0i | −0.428185 | − | 0.741638i | ||||
\(975\) | 81172.9 | + | 46865.2i | 2.66627 | + | 1.53937i | ||||
\(976\) | − | 12209.7i | − | 0.400432i | ||||||
\(977\) | 6481.97 | − | 3742.36i | 0.212258 | − | 0.122547i | −0.390102 | − | 0.920772i | \(-0.627560\pi\) |
0.602361 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(978\) | 6458.49 | + | 11186.4i | 0.211166 | + | 0.365749i | ||||
\(979\) | 4771.19 | − | 2754.65i | 0.155759 | − | 0.0899275i | ||||
\(980\) | 6673.98 | + | 3853.23i | 0.217543 | + | 0.125599i | ||||
\(981\) | 6943.01 | + | 4008.55i | 0.225966 | + | 0.130462i | ||||
\(982\) | 14147.1 | − | 8167.85i | 0.459728 | − | 0.265424i | ||||
\(983\) | −2587.38 | − | 4481.47i | −0.0839517 | − | 0.145409i | 0.820992 | − | 0.570939i | \(-0.193421\pi\) |
−0.904944 | + | 0.425531i | \(0.860087\pi\) | |||||||
\(984\) | −20372.0 | + | 11761.8i | −0.659995 | + | 0.381048i | ||||
\(985\) | − | 21844.2i | − | 0.706614i | ||||||
\(986\) | −441.801 | − | 255.074i | −0.0142696 | − | 0.00823855i | ||||
\(987\) | 5214.28 | + | 9031.40i | 0.168158 | + | 0.291259i | ||||
\(988\) | −43598.0 | −1.40389 | ||||||||
\(989\) | −18441.1 | −0.592916 | ||||||||
\(990\) | −5221.44 | − | 9043.80i | −0.167624 | − | 0.290334i | ||||
\(991\) | − | 52973.7i | − | 1.69805i | −0.528354 | − | 0.849024i | \(-0.677191\pi\) | ||
0.528354 | − | 0.849024i | \(-0.322809\pi\) | |||||||
\(992\) | −1420.13 | + | 2459.74i | −0.0454528 | + | 0.0787266i | ||||
\(993\) | − | 50216.4i | − | 1.60480i | ||||||
\(994\) | −11217.5 | − | 6476.43i | −0.357945 | − | 0.206660i | ||||
\(995\) | 31351.6 | − | 54302.6i | 0.998908 | − | 1.73016i | ||||
\(996\) | −11032.8 | + | 19109.3i | −0.350991 | + | 0.607934i | ||||
\(997\) | 16252.7 | − | 9383.50i | 0.516277 | − | 0.298073i | −0.219133 | − | 0.975695i | \(-0.570323\pi\) |
0.735410 | + | 0.677622i | \(0.236990\pi\) | |||||||
\(998\) | −38474.8 | −1.22034 | ||||||||
\(999\) | −6195.23 | − | 10732.0i | −0.196204 | − | 0.339886i |
(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 | 74.4.e.a.11.1 | ✓ | 20 | |
3.2 | odd | 2 | 666.4.s.d.307.6 | 20 | |||
37.27 | even | 6 | inner | 74.4.e.a.27.1 | yes | 20 | |
111.101 | odd | 6 | 666.4.s.d.397.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.e.a.11.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
74.4.e.a.27.1 | yes | 20 | 37.27 | even | 6 | inner | |
666.4.s.d.307.6 | 20 | 3.2 | odd | 2 | |||
666.4.s.d.397.6 | 20 | 111.101 | odd | 6 |