Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(25,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.h (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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.18 | ||
Character | \(\chi\) | \(=\) | 63.25 |
Dual form | 63.4.h.a.58.18 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.66978 | 1.29746 | 0.648732 | − | 0.761017i | \(-0.275299\pi\) | ||||
0.648732 | + | 0.761017i | \(0.275299\pi\) | |||||||
\(3\) | 5.19361 | + | 0.162683i | 0.999510 | + | 0.0313084i | ||||
\(4\) | 5.46732 | 0.683415 | ||||||||
\(5\) | −7.38708 | + | 12.7948i | −0.660721 | + | 1.14440i | 0.319706 | + | 0.947517i | \(0.396416\pi\) |
−0.980427 | + | 0.196885i | \(0.936917\pi\) | |||||||
\(6\) | 19.0594 | + | 0.597013i | 1.29683 | + | 0.0406216i | ||||
\(7\) | 15.9165 | − | 9.46920i | 0.859409 | − | 0.511289i | ||||
\(8\) | −9.29438 | −0.410758 | ||||||||
\(9\) | 26.9471 | + | 1.68983i | 0.998040 | + | 0.0625862i | ||||
\(10\) | −27.1090 | + | 46.9542i | −0.857262 | + | 1.48482i | ||||
\(11\) | −24.2954 | − | 42.0808i | −0.665939 | − | 1.15344i | −0.979030 | − | 0.203717i | \(-0.934698\pi\) |
0.313091 | − | 0.949723i | \(-0.398636\pi\) | |||||||
\(12\) | 28.3951 | + | 0.889443i | 0.683080 | + | 0.0213967i | ||||
\(13\) | −33.6012 | − | 58.1989i | −0.716868 | − | 1.24165i | −0.962235 | − | 0.272221i | \(-0.912242\pi\) |
0.245367 | − | 0.969430i | \(-0.421092\pi\) | |||||||
\(14\) | 58.4101 | − | 34.7499i | 1.11505 | − | 0.663379i | ||||
\(15\) | −40.4471 | + | 65.2494i | −0.696226 | + | 1.12315i | ||||
\(16\) | −77.8470 | −1.21636 | ||||||||
\(17\) | −5.40836 | + | 9.36755i | −0.0771599 | + | 0.133645i | −0.902024 | − | 0.431687i | \(-0.857919\pi\) |
0.824864 | + | 0.565332i | \(0.191252\pi\) | |||||||
\(18\) | 98.8899 | + | 6.20130i | 1.29492 | + | 0.0812034i | ||||
\(19\) | 67.2344 | + | 116.453i | 0.811822 | + | 1.40612i | 0.911587 | + | 0.411106i | \(0.134858\pi\) |
−0.0997650 | + | 0.995011i | \(0.531809\pi\) | |||||||
\(20\) | −40.3875 | + | 69.9533i | −0.451546 | + | 0.782101i | ||||
\(21\) | 84.2044 | − | 46.5899i | 0.874995 | − | 0.484131i | ||||
\(22\) | −89.1588 | − | 154.428i | −0.864033 | − | 1.49655i | ||||
\(23\) | −42.1647 | + | 73.0313i | −0.382258 | + | 0.662091i | −0.991385 | − | 0.130983i | \(-0.958187\pi\) |
0.609127 | + | 0.793073i | \(0.291520\pi\) | |||||||
\(24\) | −48.2714 | − | 1.51204i | −0.410556 | − | 0.0128602i | ||||
\(25\) | −46.6379 | − | 80.7792i | −0.373103 | − | 0.646234i | ||||
\(26\) | −123.309 | − | 213.577i | −0.930111 | − | 1.61100i | ||||
\(27\) | 139.678 | + | 13.1601i | 0.995591 | + | 0.0938026i | ||||
\(28\) | 87.0205 | − | 51.7712i | 0.587333 | − | 0.349422i | ||||
\(29\) | −55.1123 | + | 95.4573i | −0.352900 | + | 0.611241i | −0.986756 | − | 0.162210i | \(-0.948138\pi\) |
0.633856 | + | 0.773451i | \(0.281471\pi\) | |||||||
\(30\) | −148.432 | + | 239.451i | −0.903329 | + | 1.45725i | ||||
\(31\) | 151.197 | 0.875991 | 0.437995 | − | 0.898977i | \(-0.355689\pi\) | ||||
0.437995 | + | 0.898977i | \(0.355689\pi\) | |||||||
\(32\) | −211.327 | −1.16743 | ||||||||
\(33\) | −119.335 | − | 222.504i | −0.629500 | − | 1.17372i | ||||
\(34\) | −19.8475 | + | 34.3769i | −0.100112 | + | 0.173400i | ||||
\(35\) | 3.58020 | + | 273.598i | 0.0172904 | + | 1.32133i | ||||
\(36\) | 147.328 | + | 9.23883i | 0.682075 | + | 0.0427724i | ||||
\(37\) | −152.177 | − | 263.578i | −0.676154 | − | 1.17113i | −0.976130 | − | 0.217187i | \(-0.930312\pi\) |
0.299976 | − | 0.953947i | \(-0.403021\pi\) | |||||||
\(38\) | 246.736 | + | 427.359i | 1.05331 | + | 1.82439i | ||||
\(39\) | −165.043 | − | 307.728i | −0.677642 | − | 1.26349i | ||||
\(40\) | 68.6584 | − | 118.920i | 0.271396 | − | 0.470072i | ||||
\(41\) | 127.117 | + | 220.173i | 0.484203 | + | 0.838665i | 0.999835 | − | 0.0181454i | \(-0.00577619\pi\) |
−0.515632 | + | 0.856810i | \(0.672443\pi\) | |||||||
\(42\) | 309.012 | − | 170.975i | 1.13528 | − | 0.628143i | ||||
\(43\) | 41.3056 | − | 71.5433i | 0.146489 | − | 0.253727i | −0.783438 | − | 0.621470i | \(-0.786536\pi\) |
0.929928 | + | 0.367743i | \(0.119869\pi\) | |||||||
\(44\) | −132.831 | − | 230.069i | −0.455113 | − | 0.788279i | ||||
\(45\) | −220.681 | + | 332.299i | −0.731049 | + | 1.10081i | ||||
\(46\) | −154.735 | + | 268.009i | −0.495967 | + | 0.859039i | ||||
\(47\) | 46.0375 | 0.142878 | 0.0714390 | − | 0.997445i | \(-0.477241\pi\) | ||||
0.0714390 | + | 0.997445i | \(0.477241\pi\) | |||||||
\(48\) | −404.306 | − | 12.6644i | −1.21576 | − | 0.0380823i | ||||
\(49\) | 163.669 | − | 301.433i | 0.477168 | − | 0.878812i | ||||
\(50\) | −171.151 | − | 296.442i | −0.484088 | − | 0.838466i | ||||
\(51\) | −29.6128 | + | 47.7715i | −0.0813063 | + | 0.131164i | ||||
\(52\) | −183.708 | − | 318.192i | −0.489918 | − | 0.848564i | ||||
\(53\) | −3.20496 | + | 5.55115i | −0.00830631 | + | 0.0143870i | −0.870149 | − | 0.492789i | \(-0.835977\pi\) |
0.861842 | + | 0.507176i | \(0.169311\pi\) | |||||||
\(54\) | 512.586 | + | 48.2949i | 1.29174 | + | 0.121706i | ||||
\(55\) | 717.887 | 1.76000 | ||||||||
\(56\) | −147.934 | + | 88.0104i | −0.353009 | + | 0.210016i | ||||
\(57\) | 330.244 | + | 615.751i | 0.767401 | + | 1.43085i | ||||
\(58\) | −202.250 | + | 350.308i | −0.457875 | + | 0.793063i | ||||
\(59\) | 11.1917 | 0.0246956 | 0.0123478 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123478 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(60\) | −221.137 | + | 356.739i | −0.475812 | + | 0.767581i | ||||
\(61\) | 272.374 | 0.571705 | 0.285852 | − | 0.958274i | \(-0.407723\pi\) | ||||
0.285852 | + | 0.958274i | \(0.407723\pi\) | |||||||
\(62\) | 554.859 | 1.13657 | ||||||||
\(63\) | 444.904 | − | 228.271i | 0.889724 | − | 0.456499i | ||||
\(64\) | −152.747 | −0.298335 | ||||||||
\(65\) | 992.858 | 1.89460 | ||||||||
\(66\) | −437.933 | − | 816.540i | −0.816754 | − | 1.52287i | ||||
\(67\) | −57.4253 | −0.104711 | −0.0523553 | − | 0.998629i | \(-0.516673\pi\) | ||||
−0.0523553 | + | 0.998629i | \(0.516673\pi\) | |||||||
\(68\) | −29.5692 | + | 51.2154i | −0.0527323 | + | 0.0913350i | ||||
\(69\) | −230.868 | + | 372.436i | −0.402800 | + | 0.649798i | ||||
\(70\) | 13.1386 | + | 1004.05i | 0.0224337 | + | 1.71438i | ||||
\(71\) | 521.182 | 0.871168 | 0.435584 | − | 0.900148i | \(-0.356542\pi\) | ||||
0.435584 | + | 0.900148i | \(0.356542\pi\) | |||||||
\(72\) | −250.456 | − | 15.7059i | −0.409952 | − | 0.0257078i | ||||
\(73\) | −189.314 | + | 327.901i | −0.303527 | + | 0.525725i | −0.976932 | − | 0.213549i | \(-0.931498\pi\) |
0.673405 | + | 0.739274i | \(0.264831\pi\) | |||||||
\(74\) | −558.456 | − | 967.274i | −0.877286 | − | 1.51950i | ||||
\(75\) | −229.077 | − | 427.123i | −0.352688 | − | 0.657598i | ||||
\(76\) | 367.592 | + | 636.688i | 0.554812 | + | 0.960962i | ||||
\(77\) | −785.168 | − | 439.721i | −1.16206 | − | 0.650790i | ||||
\(78\) | −605.673 | − | 1129.30i | −0.879217 | − | 1.63933i | ||||
\(79\) | −944.135 | −1.34460 | −0.672300 | − | 0.740278i | \(-0.734694\pi\) | ||||
−0.672300 | + | 0.740278i | \(0.734694\pi\) | |||||||
\(80\) | 575.062 | − | 996.036i | 0.803673 | − | 1.39200i | ||||
\(81\) | 723.289 | + | 91.0718i | 0.992166 | + | 0.124927i | ||||
\(82\) | 466.492 | + | 807.988i | 0.628237 | + | 1.08814i | ||||
\(83\) | −411.031 | + | 711.926i | −0.543572 | + | 0.941495i | 0.455123 | + | 0.890429i | \(0.349595\pi\) |
−0.998695 | + | 0.0510662i | \(0.983738\pi\) | |||||||
\(84\) | 460.372 | − | 254.722i | 0.597985 | − | 0.330863i | ||||
\(85\) | −79.9039 | − | 138.398i | −0.101962 | − | 0.176604i | ||||
\(86\) | 151.583 | − | 262.549i | 0.190065 | − | 0.329202i | ||||
\(87\) | −301.761 | + | 486.802i | −0.371864 | + | 0.599892i | ||||
\(88\) | 225.811 | + | 391.115i | 0.273540 | + | 0.473784i | ||||
\(89\) | −12.4794 | − | 21.6149i | −0.0148631 | − | 0.0257436i | 0.858498 | − | 0.512817i | \(-0.171398\pi\) |
−0.873361 | + | 0.487073i | \(0.838065\pi\) | |||||||
\(90\) | −809.852 | + | 1219.47i | −0.948510 | + | 1.42826i | ||||
\(91\) | −1085.91 | − | 608.145i | −1.25093 | − | 0.700560i | ||||
\(92\) | −230.528 | + | 399.286i | −0.261241 | + | 0.452483i | ||||
\(93\) | 785.256 | + | 24.5972i | 0.875561 | + | 0.0274259i | ||||
\(94\) | 168.948 | 0.185379 | ||||||||
\(95\) | −1986.66 | −2.14555 | ||||||||
\(96\) | −1097.55 | − | 34.3793i | −1.16685 | − | 0.0365503i | ||||
\(97\) | 22.7166 | − | 39.3463i | 0.0237786 | − | 0.0411857i | −0.853891 | − | 0.520451i | \(-0.825764\pi\) |
0.877670 | + | 0.479266i | \(0.159097\pi\) | |||||||
\(98\) | 600.628 | − | 1106.19i | 0.619108 | − | 1.14023i | ||||
\(99\) | −583.580 | − | 1175.01i | −0.592444 | − | 1.19286i | ||||
\(100\) | −254.985 | − | 441.646i | −0.254985 | − | 0.441646i | ||||
\(101\) | −498.188 | − | 862.887i | −0.490807 | − | 0.850103i | 0.509137 | − | 0.860686i | \(-0.329965\pi\) |
−0.999944 | + | 0.0105823i | \(0.996631\pi\) | |||||||
\(102\) | −108.673 | + | 175.311i | −0.105492 | + | 0.170180i | ||||
\(103\) | −53.7222 | + | 93.0496i | −0.0513923 | + | 0.0890141i | −0.890577 | − | 0.454832i | \(-0.849699\pi\) |
0.839185 | + | 0.543846i | \(0.183033\pi\) | |||||||
\(104\) | 312.302 | + | 540.923i | 0.294459 | + | 0.510018i | ||||
\(105\) | −25.9157 | + | 1421.54i | −0.0240868 | + | 1.32122i | ||||
\(106\) | −11.7615 | + | 20.3715i | −0.0107771 | + | 0.0186666i | ||||
\(107\) | −169.103 | − | 292.895i | −0.152783 | − | 0.264628i | 0.779467 | − | 0.626444i | \(-0.215490\pi\) |
−0.932250 | + | 0.361816i | \(0.882157\pi\) | |||||||
\(108\) | 763.662 | + | 71.9507i | 0.680402 | + | 0.0641061i | ||||
\(109\) | 316.833 | − | 548.771i | 0.278414 | − | 0.482227i | −0.692577 | − | 0.721344i | \(-0.743525\pi\) |
0.970991 | + | 0.239117i | \(0.0768579\pi\) | |||||||
\(110\) | 2634.49 | 2.28354 | ||||||||
\(111\) | −747.466 | − | 1393.68i | −0.639156 | − | 1.19173i | ||||
\(112\) | −1239.05 | + | 737.148i | −1.04535 | + | 0.621911i | ||||
\(113\) | 553.218 | + | 958.202i | 0.460552 | + | 0.797699i | 0.998988 | − | 0.0449666i | \(-0.0143182\pi\) |
−0.538436 | + | 0.842666i | \(0.680985\pi\) | |||||||
\(114\) | 1211.92 | + | 2259.67i | 0.995676 | + | 1.85647i | ||||
\(115\) | −622.947 | − | 1078.98i | −0.505132 | − | 0.874914i | ||||
\(116\) | −301.317 | + | 521.896i | −0.241177 | + | 0.417731i | ||||
\(117\) | −807.106 | − | 1625.07i | −0.637752 | − | 1.28408i | ||||
\(118\) | 41.0713 | 0.0320417 | ||||||||
\(119\) | 2.62120 | + | 200.311i | 0.00201920 | + | 0.154307i | ||||
\(120\) | 375.931 | − | 606.453i | 0.285980 | − | 0.461344i | ||||
\(121\) | −515.030 | + | 892.058i | −0.386950 | + | 0.670217i | ||||
\(122\) | 999.556 | 0.741767 | ||||||||
\(123\) | 624.377 | + | 1164.17i | 0.457709 | + | 0.853413i | ||||
\(124\) | 826.641 | 0.598665 | ||||||||
\(125\) | −468.698 | −0.335373 | ||||||||
\(126\) | 1632.70 | − | 837.706i | 1.15439 | − | 0.592292i | ||||
\(127\) | 1593.37 | 1.11330 | 0.556649 | − | 0.830748i | \(-0.312087\pi\) | ||||
0.556649 | + | 0.830748i | \(0.312087\pi\) | |||||||
\(128\) | 1130.06 | 0.780347 | ||||||||
\(129\) | 226.164 | − | 364.848i | 0.154361 | − | 0.249016i | ||||
\(130\) | 3643.57 | 2.45817 | ||||||||
\(131\) | 79.3879 | − | 137.504i | 0.0529478 | − | 0.0917082i | −0.838337 | − | 0.545153i | \(-0.816472\pi\) |
0.891284 | + | 0.453445i | \(0.149805\pi\) | |||||||
\(132\) | −652.441 | − | 1216.50i | −0.430210 | − | 0.802141i | ||||
\(133\) | 2172.85 | + | 1216.87i | 1.41662 | + | 0.793354i | ||||
\(134\) | −210.738 | −0.135858 | ||||||||
\(135\) | −1200.19 | + | 1689.93i | −0.765155 | + | 1.07738i | ||||
\(136\) | 50.2673 | − | 87.0656i | 0.0316940 | − | 0.0548957i | ||||
\(137\) | 547.359 | + | 948.054i | 0.341343 | + | 0.591224i | 0.984682 | − | 0.174357i | \(-0.0557848\pi\) |
−0.643339 | + | 0.765581i | \(0.722451\pi\) | |||||||
\(138\) | −847.234 | + | 1366.76i | −0.522619 | + | 0.843090i | ||||
\(139\) | −351.707 | − | 609.175i | −0.214614 | − | 0.371723i | 0.738539 | − | 0.674211i | \(-0.235516\pi\) |
−0.953153 | + | 0.302488i | \(0.902183\pi\) | |||||||
\(140\) | 19.5741 | + | 1495.85i | 0.0118165 | + | 0.903016i | ||||
\(141\) | 239.101 | + | 7.48955i | 0.142808 | + | 0.00447329i | ||||
\(142\) | 1912.63 | 1.13031 | ||||||||
\(143\) | −1632.70 | + | 2827.93i | −0.954781 | + | 1.65373i | ||||
\(144\) | −2097.75 | − | 131.548i | −1.21397 | − | 0.0761273i | ||||
\(145\) | −814.238 | − | 1410.30i | −0.466337 | − | 0.807719i | ||||
\(146\) | −694.741 | + | 1203.33i | −0.393816 | + | 0.682110i | ||||
\(147\) | 899.068 | − | 1538.90i | 0.504448 | − | 0.863442i | ||||
\(148\) | −831.999 | − | 1441.07i | −0.462094 | − | 0.800371i | ||||
\(149\) | 1260.78 | − | 2183.74i | 0.693203 | − | 1.20066i | −0.277580 | − | 0.960703i | \(-0.589532\pi\) |
0.970783 | − | 0.239960i | \(-0.0771345\pi\) | |||||||
\(150\) | −840.665 | − | 1567.45i | −0.457600 | − | 0.853211i | ||||
\(151\) | −962.151 | − | 1666.49i | −0.518535 | − | 0.898129i | −0.999768 | − | 0.0215361i | \(-0.993144\pi\) |
0.481233 | − | 0.876593i | \(-0.340189\pi\) | |||||||
\(152\) | −624.902 | − | 1082.36i | −0.333462 | − | 0.577573i | ||||
\(153\) | −161.569 | + | 243.289i | −0.0853730 | + | 0.128554i | ||||
\(154\) | −2881.40 | − | 1613.68i | −1.50773 | − | 0.844377i | ||||
\(155\) | −1116.90 | + | 1934.53i | −0.578785 | + | 1.00249i | ||||
\(156\) | −902.344 | − | 1682.45i | −0.463111 | − | 0.863486i | ||||
\(157\) | −2177.11 | −1.10670 | −0.553350 | − | 0.832949i | \(-0.686651\pi\) | ||||
−0.553350 | + | 0.832949i | \(0.686651\pi\) | |||||||
\(158\) | −3464.77 | −1.74457 | ||||||||
\(159\) | −17.5484 | + | 28.3091i | −0.00875267 | + | 0.0141198i | ||||
\(160\) | 1561.09 | − | 2703.88i | 0.771342 | − | 1.33600i | ||||
\(161\) | 20.4354 | + | 1561.67i | 0.0100033 | + | 0.764451i | ||||
\(162\) | 2654.31 | + | 334.214i | 1.28730 | + | 0.162088i | ||||
\(163\) | −61.7047 | − | 106.876i | −0.0296508 | − | 0.0513568i | 0.850819 | − | 0.525459i | \(-0.176106\pi\) |
−0.880470 | + | 0.474102i | \(0.842773\pi\) | |||||||
\(164\) | 694.989 | + | 1203.76i | 0.330912 | + | 0.573156i | ||||
\(165\) | 3728.42 | + | 116.788i | 1.75914 | + | 0.0551028i | ||||
\(166\) | −1508.39 | + | 2612.62i | −0.705266 | + | 1.22156i | ||||
\(167\) | −1726.77 | − | 2990.86i | −0.800129 | − | 1.38586i | −0.919531 | − | 0.393019i | \(-0.871431\pi\) |
0.119401 | − | 0.992846i | \(-0.461903\pi\) | |||||||
\(168\) | −782.628 | + | 433.025i | −0.359411 | + | 0.198861i | ||||
\(169\) | −1159.57 | + | 2008.44i | −0.527799 | + | 0.914175i | ||||
\(170\) | −293.230 | − | 507.890i | −0.132293 | − | 0.229137i | ||||
\(171\) | 1614.98 | + | 3251.69i | 0.722227 | + | 1.45417i | ||||
\(172\) | 225.831 | − | 391.150i | 0.100113 | − | 0.173401i | ||||
\(173\) | −1769.88 | −0.777812 | −0.388906 | − | 0.921277i | \(-0.627147\pi\) | ||||
−0.388906 | + | 0.921277i | \(0.627147\pi\) | |||||||
\(174\) | −1107.40 | + | 1786.46i | −0.482480 | + | 0.778339i | ||||
\(175\) | −1507.23 | − | 844.097i | −0.651060 | − | 0.364616i | ||||
\(176\) | 1891.32 | + | 3275.86i | 0.810021 | + | 1.40300i | ||||
\(177\) | 58.1255 | + | 1.82071i | 0.0246835 | + | 0.000773181i | ||||
\(178\) | −45.7967 | − | 79.3222i | −0.0192843 | − | 0.0334014i | ||||
\(179\) | 1991.11 | − | 3448.71i | 0.831412 | − | 1.44005i | −0.0655062 | − | 0.997852i | \(-0.520866\pi\) |
0.896918 | − | 0.442196i | \(-0.145800\pi\) | |||||||
\(180\) | −1206.53 | + | 1816.79i | −0.499610 | + | 0.752308i | ||||
\(181\) | 4413.63 | 1.81250 | 0.906250 | − | 0.422743i | \(-0.138933\pi\) | ||||
0.906250 | + | 0.422743i | \(0.138933\pi\) | |||||||
\(182\) | −3985.05 | − | 2231.76i | −1.62303 | − | 0.908952i | ||||
\(183\) | 1414.61 | + | 44.3108i | 0.571424 | + | 0.0178992i | ||||
\(184\) | 391.894 | − | 678.781i | 0.157015 | − | 0.271959i | ||||
\(185\) | 4496.57 | 1.78700 | ||||||||
\(186\) | 2881.72 | + | 90.2664i | 1.13601 | + | 0.0355842i | ||||
\(187\) | 525.592 | 0.205535 | ||||||||
\(188\) | 251.702 | 0.0976450 | ||||||||
\(189\) | 2347.79 | − | 1113.17i | 0.903580 | − | 0.428420i | ||||
\(190\) | −7290.63 | −2.78378 | ||||||||
\(191\) | −4065.55 | −1.54017 | −0.770086 | − | 0.637940i | \(-0.779787\pi\) | ||||
−0.770086 | + | 0.637940i | \(0.779787\pi\) | |||||||
\(192\) | −793.309 | − | 24.8495i | −0.298188 | − | 0.00934039i | ||||
\(193\) | 1291.73 | 0.481764 | 0.240882 | − | 0.970554i | \(-0.422563\pi\) | ||||
0.240882 | + | 0.970554i | \(0.422563\pi\) | |||||||
\(194\) | 83.3650 | − | 144.392i | 0.0308519 | − | 0.0534370i | ||||
\(195\) | 5156.51 | + | 161.522i | 1.89367 | + | 0.0593169i | ||||
\(196\) | 894.828 | − | 1648.03i | 0.326104 | − | 0.600594i | ||||
\(197\) | −1051.46 | −0.380272 | −0.190136 | − | 0.981758i | \(-0.560893\pi\) | ||||
−0.190136 | + | 0.981758i | \(0.560893\pi\) | |||||||
\(198\) | −2141.61 | − | 4312.03i | −0.768675 | − | 1.54769i | ||||
\(199\) | −1374.08 | + | 2379.98i | −0.489479 | + | 0.847802i | −0.999927 | − | 0.0121065i | \(-0.996146\pi\) |
0.510448 | + | 0.859909i | \(0.329480\pi\) | |||||||
\(200\) | 433.471 | + | 750.793i | 0.153255 | + | 0.265446i | ||||
\(201\) | −298.244 | − | 9.34215i | −0.104659 | − | 0.00327833i | ||||
\(202\) | −1828.24 | − | 3166.61i | −0.636805 | − | 1.10298i | ||||
\(203\) | 26.7106 | + | 2041.21i | 0.00923505 | + | 0.705740i | ||||
\(204\) | −161.903 | + | 261.182i | −0.0555660 | + | 0.0896393i | ||||
\(205\) | −3756.09 | −1.27969 | ||||||||
\(206\) | −197.149 | + | 341.472i | −0.0666797 | + | 0.115493i | ||||
\(207\) | −1259.62 | + | 1896.73i | −0.422946 | + | 0.636868i | ||||
\(208\) | 2615.75 | + | 4530.61i | 0.871969 | + | 1.51029i | ||||
\(209\) | 3266.97 | − | 5658.56i | 1.08125 | − | 1.87278i | ||||
\(210\) | −95.1050 | + | 5216.75i | −0.0312518 | + | 1.71424i | ||||
\(211\) | −710.194 | − | 1230.09i | −0.231715 | − | 0.401341i | 0.726598 | − | 0.687063i | \(-0.241100\pi\) |
−0.958313 | + | 0.285721i | \(0.907767\pi\) | |||||||
\(212\) | −17.5225 | + | 30.3499i | −0.00567666 | + | 0.00983226i | ||||
\(213\) | 2706.81 | + | 84.7877i | 0.870741 | + | 0.0272749i | ||||
\(214\) | −620.571 | − | 1074.86i | −0.198231 | − | 0.343345i | ||||
\(215\) | 610.255 | + | 1056.99i | 0.193577 | + | 0.335285i | ||||
\(216\) | −1298.22 | − | 122.315i | −0.408947 | − | 0.0385301i | ||||
\(217\) | 2406.52 | − | 1431.71i | 0.752834 | − | 0.447884i | ||||
\(218\) | 1162.71 | − | 2013.87i | 0.361232 | − | 0.625673i | ||||
\(219\) | −1036.56 | + | 1672.19i | −0.319838 | + | 0.515964i | ||||
\(220\) | 3924.92 | 1.20281 | ||||||||
\(221\) | 726.908 | 0.221254 | ||||||||
\(222\) | −2743.04 | − | 5114.49i | −0.829283 | − | 1.54623i | ||||
\(223\) | −2310.15 | + | 4001.30i | −0.693718 | + | 1.20155i | 0.276893 | + | 0.960901i | \(0.410695\pi\) |
−0.970611 | + | 0.240654i | \(0.922638\pi\) | |||||||
\(224\) | −3363.57 | + | 2001.09i | −1.00330 | + | 0.596891i | ||||
\(225\) | −1120.25 | − | 2255.57i | −0.331927 | − | 0.668318i | ||||
\(226\) | 2030.19 | + | 3516.39i | 0.597550 | + | 1.03499i | ||||
\(227\) | −326.060 | − | 564.753i | −0.0953364 | − | 0.165128i | 0.814413 | − | 0.580286i | \(-0.197059\pi\) |
−0.909749 | + | 0.415159i | \(0.863726\pi\) | |||||||
\(228\) | 1805.55 | + | 3366.51i | 0.524454 | + | 0.977861i | ||||
\(229\) | −2271.83 | + | 3934.92i | −0.655574 | + | 1.13549i | 0.326175 | + | 0.945309i | \(0.394240\pi\) |
−0.981749 | + | 0.190179i | \(0.939093\pi\) | |||||||
\(230\) | −2286.08 | − | 3959.61i | −0.655391 | − | 1.13517i | ||||
\(231\) | −4006.32 | − | 2411.47i | −1.14111 | − | 0.686853i | ||||
\(232\) | 512.235 | − | 887.217i | 0.144956 | − | 0.251072i | ||||
\(233\) | 482.032 | + | 834.903i | 0.135532 | + | 0.234748i | 0.925801 | − | 0.378012i | \(-0.123392\pi\) |
−0.790269 | + | 0.612761i | \(0.790059\pi\) | |||||||
\(234\) | −2961.91 | − | 5963.66i | −0.827461 | − | 1.66605i | ||||
\(235\) | −340.083 | + | 589.041i | −0.0944024 | + | 0.163510i | ||||
\(236\) | 61.1889 | 0.0168774 | ||||||||
\(237\) | −4903.46 | − | 153.595i | −1.34394 | − | 0.0420974i | ||||
\(238\) | 9.61924 | + | 735.099i | 0.00261984 | + | 0.200208i | ||||
\(239\) | −219.927 | − | 380.924i | −0.0595225 | − | 0.103096i | 0.834729 | − | 0.550661i | \(-0.185624\pi\) |
−0.894251 | + | 0.447565i | \(0.852291\pi\) | |||||||
\(240\) | 3148.68 | − | 5079.47i | 0.846861 | − | 1.36616i | ||||
\(241\) | 3139.96 | + | 5438.58i | 0.839265 | + | 1.45365i | 0.890510 | + | 0.454963i | \(0.150348\pi\) |
−0.0512452 | + | 0.998686i | \(0.516319\pi\) | |||||||
\(242\) | −1890.05 | + | 3273.66i | −0.502054 | + | 0.869583i | ||||
\(243\) | 3741.66 | + | 590.658i | 0.987768 | + | 0.155929i | ||||
\(244\) | 1489.16 | 0.390712 | ||||||||
\(245\) | 2647.74 | + | 4320.81i | 0.690440 | + | 1.12672i | ||||
\(246\) | 2291.33 | + | 4272.26i | 0.593861 | + | 1.10727i | ||||
\(247\) | 4518.30 | − | 7825.93i | 1.16394 | − | 2.01600i | ||||
\(248\) | −1405.28 | −0.359820 | ||||||||
\(249\) | −2250.55 | + | 3630.60i | −0.572783 | + | 0.924015i | ||||
\(250\) | −1720.02 | −0.435135 | ||||||||
\(251\) | 2262.70 | 0.569005 | 0.284503 | − | 0.958675i | \(-0.408172\pi\) | ||||
0.284503 | + | 0.958675i | \(0.408172\pi\) | |||||||
\(252\) | 2432.43 | − | 1248.03i | 0.608051 | − | 0.311979i | ||||
\(253\) | 4097.62 | 1.01824 | ||||||||
\(254\) | 5847.33 | 1.44446 | ||||||||
\(255\) | −392.474 | − | 731.782i | −0.0963832 | − | 0.179710i | ||||
\(256\) | 5369.07 | 1.31081 | ||||||||
\(257\) | 2425.65 | − | 4201.35i | 0.588746 | − | 1.01974i | −0.405651 | − | 0.914028i | \(-0.632955\pi\) |
0.994397 | − | 0.105710i | \(-0.0337116\pi\) | |||||||
\(258\) | 829.972 | − | 1338.91i | 0.200278 | − | 0.323090i | ||||
\(259\) | −4917.99 | − | 2754.24i | −1.17988 | − | 0.660773i | ||||
\(260\) | 5428.27 | 1.29480 | ||||||||
\(261\) | −1646.42 | + | 2479.16i | −0.390463 | + | 0.587956i | ||||
\(262\) | 291.337 | − | 504.610i | 0.0686979 | − | 0.118988i | ||||
\(263\) | −3842.20 | − | 6654.89i | −0.900838 | − | 1.56030i | −0.826409 | − | 0.563070i | \(-0.809620\pi\) |
−0.0744287 | − | 0.997226i | \(-0.523713\pi\) | |||||||
\(264\) | 1109.14 | + | 2068.03i | 0.258572 | + | 0.482116i | ||||
\(265\) | −47.3505 | − | 82.0135i | −0.0109763 | − | 0.0190115i | ||||
\(266\) | 7973.91 | + | 4465.66i | 1.83801 | + | 1.02935i | ||||
\(267\) | −61.2966 | − | 114.290i | −0.0140498 | − | 0.0261963i | ||||
\(268\) | −313.963 | −0.0715609 | ||||||||
\(269\) | −565.528 | + | 979.522i | −0.128182 | + | 0.222017i | −0.922972 | − | 0.384867i | \(-0.874247\pi\) |
0.794791 | + | 0.606884i | \(0.207581\pi\) | |||||||
\(270\) | −4404.44 | + | 6201.68i | −0.992762 | + | 1.39786i | ||||
\(271\) | 284.946 | + | 493.541i | 0.0638718 | + | 0.110629i | 0.896193 | − | 0.443664i | \(-0.146322\pi\) |
−0.832321 | + | 0.554294i | \(0.812988\pi\) | |||||||
\(272\) | 421.024 | − | 729.235i | 0.0938542 | − | 0.162560i | ||||
\(273\) | −5540.85 | − | 3335.13i | −1.22838 | − | 0.739381i | ||||
\(274\) | 2008.69 | + | 3479.15i | 0.442881 | + | 0.767093i | ||||
\(275\) | −2266.17 | + | 3925.12i | −0.496928 | + | 0.860705i | ||||
\(276\) | −1262.23 | + | 2036.23i | −0.275280 | + | 0.444082i | ||||
\(277\) | −2559.30 | − | 4432.83i | −0.555138 | − | 0.961527i | −0.997893 | − | 0.0648845i | \(-0.979332\pi\) |
0.442755 | − | 0.896643i | \(-0.354001\pi\) | |||||||
\(278\) | −1290.69 | − | 2235.54i | −0.278455 | − | 0.482298i | ||||
\(279\) | 4074.31 | + | 255.496i | 0.874274 | + | 0.0548249i | ||||
\(280\) | −33.2758 | − | 2542.92i | −0.00710217 | − | 0.542746i | ||||
\(281\) | −1926.21 | + | 3336.30i | −0.408926 | + | 0.708281i | −0.994770 | − | 0.102143i | \(-0.967430\pi\) |
0.585844 | + | 0.810424i | \(0.300763\pi\) | |||||||
\(282\) | 877.448 | + | 27.4850i | 0.185288 | + | 0.00580393i | ||||
\(283\) | 2040.86 | 0.428680 | 0.214340 | − | 0.976759i | \(-0.431240\pi\) | ||||
0.214340 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(284\) | 2849.47 | 0.595370 | ||||||||
\(285\) | −10317.9 | − | 323.197i | −2.14450 | − | 0.0671739i | ||||
\(286\) | −5991.68 | + | 10377.9i | −1.23879 | + | 2.14565i | ||||
\(287\) | 4108.12 | + | 2300.68i | 0.844928 | + | 0.473188i | ||||
\(288\) | −5694.63 | − | 357.105i | −1.16514 | − | 0.0730647i | ||||
\(289\) | 2398.00 | + | 4153.46i | 0.488093 | + | 0.845401i | ||||
\(290\) | −2988.08 | − | 5175.50i | −0.605055 | − | 1.04799i | ||||
\(291\) | 124.382 | − | 200.654i | 0.0250564 | − | 0.0404210i | ||||
\(292\) | −1035.04 | + | 1792.74i | −0.207435 | + | 0.359288i | ||||
\(293\) | 966.517 | + | 1674.06i | 0.192712 | + | 0.333786i | 0.946148 | − | 0.323735i | \(-0.104938\pi\) |
−0.753436 | + | 0.657521i | \(0.771605\pi\) | |||||||
\(294\) | 3299.39 | − | 5647.42i | 0.654504 | − | 1.12029i | ||||
\(295\) | −82.6743 | + | 143.196i | −0.0163169 | + | 0.0282617i | ||||
\(296\) | 1414.39 | + | 2449.79i | 0.277736 | + | 0.481052i | ||||
\(297\) | −2839.73 | − | 6197.47i | −0.554807 | − | 1.21082i | ||||
\(298\) | 4626.80 | − | 8013.85i | 0.899407 | − | 1.55782i | ||||
\(299\) | 5667.12 | 1.09611 | ||||||||
\(300\) | −1252.44 | − | 2335.22i | −0.241032 | − | 0.449413i | ||||
\(301\) | −20.0190 | − | 1529.85i | −0.00383348 | − | 0.292953i | ||||
\(302\) | −3530.89 | − | 6115.68i | −0.672781 | − | 1.16529i | ||||
\(303\) | −2447.01 | − | 4562.54i | −0.463951 | − | 0.865053i | ||||
\(304\) | −5233.99 | − | 9065.54i | −0.987467 | − | 1.71034i | ||||
\(305\) | −2012.05 | + | 3484.98i | −0.377737 | + | 0.654260i | ||||
\(306\) | −592.923 | + | 892.817i | −0.110768 | + | 0.166794i | ||||
\(307\) | −5467.25 | −1.01639 | −0.508197 | − | 0.861241i | \(-0.669688\pi\) | ||||
−0.508197 | + | 0.861241i | \(0.669688\pi\) | |||||||
\(308\) | −4292.77 | − | 2404.09i | −0.794166 | − | 0.444760i | ||||
\(309\) | −294.150 | + | 474.523i | −0.0541540 | + | 0.0873614i | ||||
\(310\) | −4098.79 | + | 7099.31i | −0.750953 | + | 1.30069i | ||||
\(311\) | 2490.31 | 0.454060 | 0.227030 | − | 0.973888i | \(-0.427098\pi\) | ||||
0.227030 | + | 0.973888i | \(0.427098\pi\) | |||||||
\(312\) | 1533.97 | + | 2860.15i | 0.278347 | + | 0.518987i | ||||
\(313\) | 9324.86 | 1.68394 | 0.841968 | − | 0.539527i | \(-0.181397\pi\) | ||||
0.841968 | + | 0.539527i | \(0.181397\pi\) | |||||||
\(314\) | −7989.51 | −1.43590 | ||||||||
\(315\) | −365.857 | + | 7378.71i | −0.0654404 | + | 1.31982i | ||||
\(316\) | −5161.89 | −0.918921 | ||||||||
\(317\) | −5834.66 | −1.03378 | −0.516888 | − | 0.856053i | \(-0.672910\pi\) | ||||
−0.516888 | + | 0.856053i | \(0.672910\pi\) | |||||||
\(318\) | −64.3987 | + | 103.888i | −0.0113563 | + | 0.0183200i | ||||
\(319\) | 5355.90 | 0.940040 | ||||||||
\(320\) | 1128.36 | − | 1954.37i | 0.197116 | − | 0.341415i | ||||
\(321\) | −830.604 | − | 1548.69i | −0.144423 | − | 0.269282i | ||||
\(322\) | 74.9935 | + | 5730.98i | 0.0129790 | + | 0.991848i | ||||
\(323\) | −1454.51 | −0.250561 | ||||||||
\(324\) | 3954.45 | + | 497.919i | 0.678061 | + | 0.0853770i | ||||
\(325\) | −3134.18 | + | 5428.55i | −0.534932 | + | 0.926529i | ||||
\(326\) | −226.443 | − | 392.211i | −0.0384709 | − | 0.0666336i | ||||
\(327\) | 1734.78 | − | 2798.56i | 0.293375 | − | 0.473274i | ||||
\(328\) | −1181.47 | − | 2046.37i | −0.198890 | − | 0.344488i | ||||
\(329\) | 732.755 | − | 435.939i | 0.122791 | − | 0.0730519i | ||||
\(330\) | 13682.5 | + | 428.588i | 2.28242 | + | 0.0714940i | ||||
\(331\) | 10038.0 | 1.66689 | 0.833443 | − | 0.552606i | \(-0.186366\pi\) | ||||
0.833443 | + | 0.552606i | \(0.186366\pi\) | |||||||
\(332\) | −2247.24 | + | 3892.33i | −0.371486 | + | 0.643432i | ||||
\(333\) | −3655.32 | − | 7359.80i | −0.601532 | − | 1.21116i | ||||
\(334\) | −6336.88 | − | 10975.8i | −1.03814 | − | 1.79811i | ||||
\(335\) | 424.205 | − | 734.745i | 0.0691845 | − | 0.119831i | ||||
\(336\) | −6555.06 | + | 3626.89i | −1.06431 | + | 0.588877i | ||||
\(337\) | 73.3892 | + | 127.114i | 0.0118628 | + | 0.0205470i | 0.871896 | − | 0.489691i | \(-0.162891\pi\) |
−0.860033 | + | 0.510238i | \(0.829557\pi\) | |||||||
\(338\) | −4255.39 | + | 7370.55i | −0.684801 | + | 1.18611i | ||||
\(339\) | 2717.31 | + | 5066.52i | 0.435351 | + | 0.811728i | ||||
\(340\) | −436.861 | − | 756.665i | −0.0696826 | − | 0.120694i | ||||
\(341\) | −3673.38 | − | 6362.48i | −0.583357 | − | 1.01040i | ||||
\(342\) | 5926.64 | + | 11933.0i | 0.937064 | + | 1.88673i | ||||
\(343\) | −249.299 | − | 6347.56i | −0.0392446 | − | 0.999230i | ||||
\(344\) | −383.910 | + | 664.951i | −0.0601716 | + | 0.104220i | ||||
\(345\) | −3059.81 | − | 5705.12i | −0.477492 | − | 0.890300i | ||||
\(346\) | −6495.08 | −1.00918 | ||||||||
\(347\) | 7132.81 | 1.10349 | 0.551743 | − | 0.834015i | \(-0.313963\pi\) | ||||
0.551743 | + | 0.834015i | \(0.313963\pi\) | |||||||
\(348\) | −1649.82 | + | 2661.50i | −0.254137 | + | 0.409976i | ||||
\(349\) | −3376.11 | + | 5847.59i | −0.517819 | + | 0.896889i | 0.481966 | + | 0.876190i | \(0.339923\pi\) |
−0.999786 | + | 0.0206997i | \(0.993411\pi\) | |||||||
\(350\) | −5531.20 | − | 3097.66i | −0.844728 | − | 0.473076i | ||||
\(351\) | −3927.42 | − | 8571.27i | −0.597237 | − | 1.30342i | ||||
\(352\) | 5134.26 | + | 8892.79i | 0.777434 | + | 1.34656i | ||||
\(353\) | −5175.49 | − | 8964.22i | −0.780350 | − | 1.35161i | −0.931738 | − | 0.363132i | \(-0.881707\pi\) |
0.151387 | − | 0.988475i | \(-0.451626\pi\) | |||||||
\(354\) | 213.308 | + | 6.68162i | 0.0320260 | + | 0.00100318i | ||||
\(355\) | −3850.02 | + | 6668.42i | −0.575599 | + | 0.996966i | ||||
\(356\) | −68.2288 | − | 118.176i | −0.0101576 | − | 0.0175936i | ||||
\(357\) | −18.9738 | + | 1040.76i | −0.00281289 | + | 0.154294i | ||||
\(358\) | 7306.96 | − | 12656.0i | 1.07873 | − | 1.86841i | ||||
\(359\) | 3507.97 | + | 6075.98i | 0.515720 | + | 0.893253i | 0.999833 | + | 0.0182477i | \(0.00580875\pi\) |
−0.484114 | + | 0.875005i | \(0.660858\pi\) | |||||||
\(360\) | 2051.10 | − | 3088.52i | 0.300284 | − | 0.452164i | ||||
\(361\) | −5611.42 | + | 9719.27i | −0.818111 | + | 1.41701i | ||||
\(362\) | 16197.1 | 2.35165 | ||||||||
\(363\) | −2819.99 | + | 4549.21i | −0.407744 | + | 0.657773i | ||||
\(364\) | −5937.01 | − | 3324.93i | −0.854901 | − | 0.478773i | ||||
\(365\) | −2796.95 | − | 4844.46i | −0.401094 | − | 0.694714i | ||||
\(366\) | 5191.30 | + | 162.611i | 0.741403 | + | 0.0232236i | ||||
\(367\) | 4868.15 | + | 8431.88i | 0.692412 | + | 1.19929i | 0.971045 | + | 0.238895i | \(0.0767852\pi\) |
−0.278633 | + | 0.960398i | \(0.589881\pi\) | |||||||
\(368\) | 3282.39 | − | 5685.27i | 0.464963 | − | 0.805340i | ||||
\(369\) | 3053.38 | + | 6147.82i | 0.430765 | + | 0.867325i | ||||
\(370\) | 16501.4 | 2.31856 | ||||||||
\(371\) | 1.55330 | + | 118.703i | 0.000217368 | + | 0.0166112i | ||||
\(372\) | 4293.25 | + | 134.481i | 0.598372 | + | 0.0187433i | ||||
\(373\) | 1151.72 | − | 1994.83i | 0.159876 | − | 0.276913i | −0.774948 | − | 0.632025i | \(-0.782224\pi\) |
0.934824 | + | 0.355112i | \(0.115557\pi\) | |||||||
\(374\) | 1928.81 | 0.266675 | ||||||||
\(375\) | −2434.23 | − | 76.2494i | −0.335209 | − | 0.0105000i | ||||
\(376\) | −427.891 | −0.0586882 | ||||||||
\(377\) | 7407.35 | 1.01193 | ||||||||
\(378\) | 8615.89 | − | 4085.10i | 1.17236 | − | 0.555859i | ||||
\(379\) | −11334.4 | −1.53617 | −0.768084 | − | 0.640349i | \(-0.778790\pi\) | ||||
−0.768084 | + | 0.640349i | \(0.778790\pi\) | |||||||
\(380\) | −10861.7 | −1.46630 | ||||||||
\(381\) | 8275.34 | + | 259.215i | 1.11275 | + | 0.0348556i | ||||
\(382\) | −14919.7 | −1.99832 | ||||||||
\(383\) | −6146.43 | + | 10645.9i | −0.820020 | + | 1.42032i | 0.0856460 | + | 0.996326i | \(0.472705\pi\) |
−0.905666 | + | 0.423991i | \(0.860629\pi\) | |||||||
\(384\) | 5869.10 | + | 183.843i | 0.779964 | + | 0.0244314i | ||||
\(385\) | 11426.2 | − | 6797.82i | 1.51256 | − | 0.899867i | ||||
\(386\) | 4740.36 | 0.625072 | ||||||||
\(387\) | 1233.96 | − | 1858.08i | 0.162082 | − | 0.244061i | ||||
\(388\) | 124.199 | − | 215.119i | 0.0162506 | − | 0.0281469i | ||||
\(389\) | 5454.39 | + | 9447.27i | 0.710921 | + | 1.23135i | 0.964512 | + | 0.264040i | \(0.0850551\pi\) |
−0.253591 | + | 0.967312i | \(0.581612\pi\) | |||||||
\(390\) | 18923.3 | + | 592.749i | 2.45697 | + | 0.0769616i | ||||
\(391\) | −456.083 | − | 789.959i | −0.0589900 | − | 0.102174i | ||||
\(392\) | −1521.20 | + | 2801.63i | −0.196000 | + | 0.360979i | ||||
\(393\) | 434.679 | − | 701.226i | 0.0557930 | − | 0.0900055i | ||||
\(394\) | −3858.64 | −0.493389 | ||||||||
\(395\) | 6974.40 | − | 12080.0i | 0.888405 | − | 1.53876i | ||||
\(396\) | −3190.62 | − | 6424.16i | −0.404885 | − | 0.815217i | ||||
\(397\) | −3021.46 | − | 5233.33i | −0.381972 | − | 0.661595i | 0.609372 | − | 0.792884i | \(-0.291422\pi\) |
−0.991344 | + | 0.131290i | \(0.958088\pi\) | |||||||
\(398\) | −5042.60 | + | 8734.03i | −0.635082 | + | 1.09999i | ||||
\(399\) | 11087.0 | + | 6673.44i | 1.39109 | + | 0.837318i | ||||
\(400\) | 3630.62 | + | 6288.42i | 0.453828 | + | 0.786052i | ||||
\(401\) | 7151.44 | − | 12386.7i | 0.890588 | − | 1.54254i | 0.0514171 | − | 0.998677i | \(-0.483626\pi\) |
0.839171 | − | 0.543867i | \(-0.183040\pi\) | |||||||
\(402\) | −1094.49 | − | 34.2837i | −0.135792 | − | 0.00425352i | ||||
\(403\) | −5080.38 | − | 8799.48i | −0.627970 | − | 1.08768i | ||||
\(404\) | −2723.75 | − | 4717.68i | −0.335425 | − | 0.580974i | ||||
\(405\) | −6508.24 | + | 8581.58i | −0.798511 | + | 1.05289i | ||||
\(406\) | 98.0221 | + | 7490.82i | 0.0119822 | + | 0.915672i | ||||
\(407\) | −7394.38 | + | 12807.4i | −0.900555 | + | 1.55981i | ||||
\(408\) | 275.233 | − | 444.007i | 0.0333972 | − | 0.0538765i | ||||
\(409\) | −5632.60 | −0.680963 | −0.340482 | − | 0.940251i | \(-0.610590\pi\) | ||||
−0.340482 | + | 0.940251i | \(0.610590\pi\) | |||||||
\(410\) | −13784.1 | −1.66036 | ||||||||
\(411\) | 2688.53 | + | 5012.86i | 0.322666 | + | 0.601621i | ||||
\(412\) | −293.717 | + | 508.732i | −0.0351223 | + | 0.0608336i | ||||
\(413\) | 178.133 | − | 105.977i | 0.0212236 | − | 0.0126266i | ||||
\(414\) | −4622.55 | + | 6960.59i | −0.548758 | + | 0.826315i | ||||
\(415\) | −6072.64 | − | 10518.1i | −0.718299 | − | 1.24413i | ||||
\(416\) | 7100.82 | + | 12299.0i | 0.836890 | + | 1.44954i | ||||
\(417\) | −1727.53 | − | 3221.03i | −0.202871 | − | 0.378260i | ||||
\(418\) | 11989.1 | − | 20765.7i | 1.40288 | − | 2.42986i | ||||
\(419\) | −2152.39 | − | 3728.05i | −0.250958 | − | 0.434671i | 0.712832 | − | 0.701335i | \(-0.247412\pi\) |
−0.963790 | + | 0.266663i | \(0.914079\pi\) | |||||||
\(420\) | −141.689 | + | 7772.03i | −0.0164613 | + | 0.902943i | ||||
\(421\) | 1529.35 | − | 2648.91i | 0.177045 | − | 0.306651i | −0.763822 | − | 0.645427i | \(-0.776680\pi\) |
0.940867 | + | 0.338776i | \(0.110013\pi\) | |||||||
\(422\) | −2606.26 | − | 4514.17i | −0.300641 | − | 0.520726i | ||||
\(423\) | 1240.58 | + | 77.7955i | 0.142598 | + | 0.00894219i | ||||
\(424\) | 29.7881 | − | 51.5945i | 0.00341188 | − | 0.00590955i | ||||
\(425\) | 1008.94 | 0.115155 | ||||||||
\(426\) | 9933.43 | + | 311.153i | 1.12976 | + | 0.0353883i | ||||
\(427\) | 4335.24 | − | 2579.17i | 0.491328 | − | 0.292306i | ||||
\(428\) | −924.539 | − | 1601.35i | −0.104414 | − | 0.180851i | ||||
\(429\) | −8939.68 | + | 14421.5i | −1.00609 | + | 1.62303i | ||||
\(430\) | 2239.50 | + | 3878.94i | 0.251159 | + | 0.435021i | ||||
\(431\) | −7618.49 | + | 13195.6i | −0.851438 | + | 1.47473i | 0.0284726 | + | 0.999595i | \(0.490936\pi\) |
−0.879911 | + | 0.475139i | \(0.842398\pi\) | |||||||
\(432\) | −10873.5 | − | 1024.48i | −1.21100 | − | 0.114098i | ||||
\(433\) | 1574.49 | 0.174747 | 0.0873734 | − | 0.996176i | \(-0.472153\pi\) | ||||
0.0873734 | + | 0.996176i | \(0.472153\pi\) | |||||||
\(434\) | 8831.40 | − | 5254.07i | 0.976776 | − | 0.581114i | ||||
\(435\) | −3999.40 | − | 7457.01i | −0.440820 | − | 0.821923i | ||||
\(436\) | 1732.23 | − | 3000.31i | 0.190272 | − | 0.329561i | ||||
\(437\) | −11339.7 | −1.24130 | ||||||||
\(438\) | −3803.97 | + | 6136.58i | −0.414979 | + | 0.669445i | ||||
\(439\) | 1092.40 | 0.118764 | 0.0593821 | − | 0.998235i | \(-0.481087\pi\) | ||||
0.0593821 | + | 0.998235i | \(0.481087\pi\) | |||||||
\(440\) | −6672.32 | −0.722933 | ||||||||
\(441\) | 4919.76 | − | 7846.15i | 0.531234 | − | 0.847225i | ||||
\(442\) | 2667.60 | 0.287069 | ||||||||
\(443\) | −12503.6 | −1.34100 | −0.670500 | − | 0.741909i | \(-0.733921\pi\) | ||||
−0.670500 | + | 0.741909i | \(0.733921\pi\) | |||||||
\(444\) | −4086.64 | − | 7619.68i | −0.436809 | − | 0.814446i | ||||
\(445\) | 368.745 | 0.0392813 | ||||||||
\(446\) | −8477.75 | + | 14683.9i | −0.900075 | + | 1.55897i | ||||
\(447\) | 6903.26 | − | 11136.4i | 0.730454 | − | 1.17837i | ||||
\(448\) | −2431.20 | + | 1446.39i | −0.256391 | + | 0.152535i | ||||
\(449\) | 1180.23 | 0.124050 | 0.0620249 | − | 0.998075i | \(-0.480244\pi\) | ||||
0.0620249 | + | 0.998075i | \(0.480244\pi\) | |||||||
\(450\) | −4111.08 | − | 8277.47i | −0.430663 | − | 0.867119i | ||||
\(451\) | 6176.71 | − | 10698.4i | 0.644900 | − | 1.11700i | ||||
\(452\) | 3024.62 | + | 5238.80i | 0.314748 | + | 0.545160i | ||||
\(453\) | −4725.92 | − | 8811.64i | −0.490162 | − | 0.913923i | ||||
\(454\) | −1196.57 | − | 2072.52i | −0.123696 | − | 0.214247i | ||||
\(455\) | 15802.8 | − | 9401.57i | 1.62823 | − | 0.968686i | ||||
\(456\) | −3069.41 | − | 5723.02i | −0.315216 | − | 0.587731i | ||||
\(457\) | −12893.6 | −1.31977 | −0.659886 | − | 0.751366i | \(-0.729395\pi\) | ||||
−0.659886 | + | 0.751366i | \(0.729395\pi\) | |||||||
\(458\) | −8337.12 | + | 14440.3i | −0.850585 | + | 1.47326i | ||||
\(459\) | −878.704 | + | 1237.26i | −0.0893560 | + | 0.125818i | ||||
\(460\) | −3405.85 | − | 5899.11i | −0.345215 | − | 0.597929i | ||||
\(461\) | 1100.30 | − | 1905.78i | 0.111163 | − | 0.192540i | −0.805076 | − | 0.593171i | \(-0.797876\pi\) |
0.916240 | + | 0.400631i | \(0.131209\pi\) | |||||||
\(462\) | −14702.3 | − | 8849.57i | −1.48055 | − | 0.891168i | ||||
\(463\) | 8130.93 | + | 14083.2i | 0.816148 | + | 1.41361i | 0.908501 | + | 0.417883i | \(0.137228\pi\) |
−0.0923526 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(464\) | 4290.33 | − | 7431.06i | 0.429253 | − | 0.743488i | ||||
\(465\) | −6115.46 | + | 9865.49i | −0.609888 | + | 0.983873i | ||||
\(466\) | 1768.95 | + | 3063.92i | 0.175848 | + | 0.304578i | ||||
\(467\) | −879.425 | − | 1523.21i | −0.0871412 | − | 0.150933i | 0.819160 | − | 0.573564i | \(-0.194440\pi\) |
−0.906302 | + | 0.422631i | \(0.861106\pi\) | |||||||
\(468\) | −4412.71 | − | 8884.78i | −0.435850 | − | 0.877562i | ||||
\(469\) | −914.008 | + | 543.772i | −0.0899893 | + | 0.0535374i | ||||
\(470\) | −1248.03 | + | 2161.65i | −0.122484 | + | 0.212148i | ||||
\(471\) | −11307.0 | − | 354.179i | −1.10616 | − | 0.0346491i | ||||
\(472\) | −104.020 | −0.0101439 | ||||||||
\(473\) | −4014.14 | −0.390212 | ||||||||
\(474\) | −17994.7 | − | 563.661i | −1.74372 | − | 0.0546199i | ||||
\(475\) | 6271.34 | − | 10862.3i | 0.605787 | − | 1.04925i | ||||
\(476\) | 14.3309 | + | 1095.17i | 0.00137995 | + | 0.105456i | ||||
\(477\) | −95.7446 | + | 144.171i | −0.00919045 | + | 0.0138389i | ||||
\(478\) | −807.084 | − | 1397.91i | −0.0772284 | − | 0.133763i | ||||
\(479\) | 2144.59 | + | 3714.54i | 0.204570 | + | 0.354325i | 0.949996 | − | 0.312264i | \(-0.101087\pi\) |
−0.745426 | + | 0.666588i | \(0.767754\pi\) | |||||||
\(480\) | 8547.54 | − | 13788.9i | 0.812792 | − | 1.31120i | ||||
\(481\) | −10226.6 | + | 17713.0i | −0.969427 | + | 1.67910i | ||||
\(482\) | 11523.0 | + | 19958.4i | 1.08892 | + | 1.88606i | ||||
\(483\) | −147.924 | + | 8114.01i | −0.0139353 | + | 0.764389i | ||||
\(484\) | −2815.84 | + | 4877.17i | −0.264447 | + | 0.458036i | ||||
\(485\) | 335.619 | + | 581.309i | 0.0314220 | + | 0.0544245i | ||||
\(486\) | 13731.1 | + | 2167.59i | 1.28159 | + | 0.202312i | ||||
\(487\) | −4752.75 | + | 8232.00i | −0.442233 | + | 0.765970i | −0.997855 | − | 0.0654649i | \(-0.979147\pi\) |
0.555622 | + | 0.831435i | \(0.312480\pi\) | |||||||
\(488\) | −2531.55 | −0.234832 | ||||||||
\(489\) | −303.083 | − | 565.109i | −0.0280284 | − | 0.0522599i | ||||
\(490\) | 9716.63 | + | 15856.5i | 0.895821 | + | 1.46188i | ||||
\(491\) | −1097.11 | − | 1900.25i | −0.100839 | − | 0.174658i | 0.811192 | − | 0.584780i | \(-0.198819\pi\) |
−0.912030 | + | 0.410122i | \(0.865486\pi\) | |||||||
\(492\) | 3413.67 | + | 6364.90i | 0.312805 | + | 0.583236i | ||||
\(493\) | −596.134 | − | 1032.53i | −0.0544595 | − | 0.0943266i | ||||
\(494\) | 16581.2 | − | 28719.5i | 1.51017 | − | 2.61569i | ||||
\(495\) | 19345.0 | + | 1213.11i | 1.75655 | + | 0.110152i | ||||
\(496\) | −11770.2 | −1.06552 | ||||||||
\(497\) | 8295.39 | − | 4935.18i | 0.748690 | − | 0.445419i | ||||
\(498\) | −8259.04 | + | 13323.5i | −0.743165 | + | 1.19888i | ||||
\(499\) | 3835.89 | − | 6643.96i | 0.344124 | − | 0.596041i | −0.641070 | − | 0.767482i | \(-0.721509\pi\) |
0.985194 | + | 0.171442i | \(0.0548425\pi\) | |||||||
\(500\) | −2562.52 | −0.229199 | ||||||||
\(501\) | −8481.61 | − | 15814.2i | −0.756348 | − | 1.41024i | ||||
\(502\) | 8303.62 | 0.738265 | ||||||||
\(503\) | 8273.15 | 0.733363 | 0.366681 | − | 0.930347i | \(-0.380494\pi\) | ||||
0.366681 | + | 0.930347i | \(0.380494\pi\) | |||||||
\(504\) | −4135.11 | + | 2121.64i | −0.365461 | + | 0.187511i | ||||
\(505\) | 14720.6 | 1.29715 | ||||||||
\(506\) | 15037.4 | 1.32113 | ||||||||
\(507\) | −6349.11 | + | 10242.4i | −0.556162 | + | 0.897202i | ||||
\(508\) | 8711.47 | 0.760844 | ||||||||
\(509\) | 2597.50 | − | 4499.00i | 0.226193 | − | 0.391777i | −0.730484 | − | 0.682930i | \(-0.760705\pi\) |
0.956677 | + | 0.291153i | \(0.0940388\pi\) | |||||||
\(510\) | −1440.30 | − | 2685.48i | −0.125054 | − | 0.233167i | ||||
\(511\) | 91.7523 | + | 7011.68i | 0.00794302 | + | 0.607003i | ||||
\(512\) | 10662.8 | 0.920379 | ||||||||
\(513\) | 7858.59 | + | 17150.7i | 0.676345 | + | 1.47607i | ||||
\(514\) | 8901.61 | − | 15418.0i | 0.763877 | − | 1.32307i | ||||
\(515\) | −793.701 | − | 1374.73i | −0.0679119 | − | 0.117627i | ||||
\(516\) | 1236.51 | − | 1994.74i | 0.105493 | − | 0.170181i | ||||
\(517\) | −1118.50 | − | 1937.30i | −0.0951480 | − | 0.164801i | ||||
\(518\) | −18048.0 | − | 10107.5i | −1.53085 | − | 0.857329i | ||||
\(519\) | −9192.06 | − | 287.930i | −0.777431 | − | 0.0243521i | ||||
\(520\) | −9228.00 | −0.778220 | ||||||||
\(521\) | −1022.06 | + | 1770.25i | −0.0859445 | + | 0.148860i | −0.905793 | − | 0.423720i | \(-0.860724\pi\) |
0.819849 | + | 0.572580i | \(0.194057\pi\) | |||||||
\(522\) | −6042.01 | + | 9098.00i | −0.506613 | + | 0.762852i | ||||
\(523\) | 5284.21 | + | 9152.52i | 0.441802 | + | 0.765224i | 0.997823 | − | 0.0659445i | \(-0.0210060\pi\) |
−0.556021 | + | 0.831168i | \(0.687673\pi\) | |||||||
\(524\) | 434.039 | − | 751.778i | 0.0361853 | − | 0.0626748i | ||||
\(525\) | −7690.62 | − | 4629.11i | −0.639326 | − | 0.384821i | ||||
\(526\) | −14100.1 | − | 24422.0i | −1.16881 | − | 2.02443i | ||||
\(527\) | −817.725 | + | 1416.34i | −0.0675914 | + | 0.117072i | ||||
\(528\) | 9289.85 | + | 17321.2i | 0.765698 | + | 1.42767i | ||||
\(529\) | 2527.78 | + | 4378.25i | 0.207757 | + | 0.359846i | ||||
\(530\) | −173.766 | − | 300.972i | −0.0142414 | − | 0.0246668i | ||||
\(531\) | 301.585 | + | 18.9121i | 0.0246472 | + | 0.00154560i | ||||
\(532\) | 11879.7 | + | 6653.03i | 0.968139 | + | 0.542191i | ||||
\(533\) | 8542.55 | − | 14796.1i | 0.694220 | − | 1.20242i | ||||
\(534\) | −224.945 | − | 419.418i | −0.0182291 | − | 0.0339888i | ||||
\(535\) | 4996.70 | 0.403787 | ||||||||
\(536\) | 533.733 | 0.0430107 | ||||||||
\(537\) | 10902.1 | − | 17587.3i | 0.876090 | − | 1.41331i | ||||
\(538\) | −2075.36 | + | 3594.64i | −0.166311 | + | 0.288059i | ||||
\(539\) | −16660.9 | + | 436.112i | −1.33142 | + | 0.0348510i | ||||
\(540\) | −6561.83 | + | 9239.40i | −0.522919 | + | 0.736297i | ||||
\(541\) | 1228.08 | + | 2127.10i | 0.0975957 | + | 0.169041i | 0.910689 | − | 0.413093i | \(-0.135551\pi\) |
−0.813093 | + | 0.582133i | \(0.802218\pi\) | |||||||
\(542\) | 1045.69 | + | 1811.19i | 0.0828714 | + | 0.143537i | ||||
\(543\) | 22922.6 | + | 718.024i | 1.81161 | + | 0.0567465i | ||||
\(544\) | 1142.93 | − | 1979.61i | 0.0900785 | − | 0.156021i | ||||
\(545\) | 4680.95 | + | 8107.64i | 0.367908 | + | 0.637235i | ||||
\(546\) | −20333.7 | − | 12239.2i | −1.59378 | − | 0.959321i | ||||
\(547\) | −5932.12 | + | 10274.7i | −0.463691 | + | 0.803136i | −0.999141 | − | 0.0414303i | \(-0.986809\pi\) |
0.535450 | + | 0.844567i | \(0.320142\pi\) | |||||||
\(548\) | 2992.59 | + | 5183.32i | 0.233279 | + | 0.404052i | ||||
\(549\) | 7339.69 | + | 460.266i | 0.570584 | + | 0.0357808i | ||||
\(550\) | −8316.36 | + | 14404.4i | −0.644747 | + | 1.11673i | ||||
\(551\) | −14821.8 | −1.14597 | ||||||||
\(552\) | 2145.77 | − | 3461.57i | 0.165453 | − | 0.266910i | ||||
\(553\) | −15027.3 | + | 8940.20i | −1.15556 | + | 0.687479i | ||||
\(554\) | −9392.07 | − | 16267.5i | −0.720272 | − | 1.24755i | ||||
\(555\) | 23353.4 | + | 731.517i | 1.78612 | + | 0.0559481i | ||||
\(556\) | −1922.90 | − | 3330.55i | −0.146671 | − | 0.254041i | ||||
\(557\) | 10764.5 | − | 18644.6i | 0.818861 | − | 1.41831i | −0.0876619 | − | 0.996150i | \(-0.527940\pi\) |
0.906522 | − | 0.422158i | \(-0.138727\pi\) | |||||||
\(558\) | 14951.8 | + | 937.616i | 1.13434 | + | 0.0711334i | ||||
\(559\) | −5551.66 | −0.420054 | ||||||||
\(560\) | −278.708 | − | 21298.8i | −0.0210314 | − | 1.60721i | ||||
\(561\) | 2729.72 | + | 85.5052i | 0.205435 | + | 0.00643499i | ||||
\(562\) | −7068.79 | + | 12243.5i | −0.530567 | + | 0.918969i | ||||
\(563\) | 606.036 | 0.0453666 | 0.0226833 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226833 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(564\) | 1307.24 | + | 40.9478i | 0.0975971 | + | 0.00305711i | ||||
\(565\) | −16346.7 | −1.21718 | ||||||||
\(566\) | 7489.51 | 0.556197 | ||||||||
\(567\) | 12374.6 | − | 5399.43i | 0.916550 | − | 0.399920i | ||||
\(568\) | −4844.07 | −0.357839 | ||||||||
\(569\) | 14991.6 | 1.10453 | 0.552267 | − | 0.833667i | \(-0.313763\pi\) | ||||
0.552267 | + | 0.833667i | \(0.313763\pi\) | |||||||
\(570\) | −37864.6 | − | 1186.06i | −2.78241 | − | 0.0871557i | ||||
\(571\) | −851.541 | −0.0624096 | −0.0312048 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312048 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(572\) | −8926.52 | + | 15461.2i | −0.652512 | + | 1.13018i | ||||
\(573\) | −21114.9 | − | 661.398i | −1.53942 | − | 0.0482204i | ||||
\(574\) | 15075.9 | + | 8443.01i | 1.09627 | + | 0.613945i | ||||
\(575\) | 7865.89 | 0.570487 | ||||||||
\(576\) | −4116.09 | − | 258.117i | −0.297750 | − | 0.0186716i | ||||
\(577\) | −5390.01 | + | 9335.77i | −0.388889 | + | 0.673576i | −0.992300 | − | 0.123855i | \(-0.960474\pi\) |
0.603411 | + | 0.797430i | \(0.293808\pi\) | |||||||
\(578\) | 8800.14 | + | 15242.3i | 0.633283 | + | 1.09688i | ||||
\(579\) | 6708.72 | + | 210.143i | 0.481528 | + | 0.0150833i | ||||
\(580\) | −4451.70 | − | 7710.57i | −0.318701 | − | 0.552007i | ||||
\(581\) | 199.209 | + | 15223.5i | 0.0142248 | + | 1.08705i | ||||
\(582\) | 456.455 | − | 736.355i | 0.0325098 | − | 0.0524449i | ||||
\(583\) | 311.462 | 0.0221260 | ||||||||
\(584\) | 1759.55 | − | 3047.64i | 0.124676 | − | 0.215945i | ||||
\(585\) | 26754.6 | + | 1677.76i | 1.89088 | + | 0.118576i | ||||
\(586\) | 3546.91 | + | 6143.43i | 0.250037 | + | 0.433076i | ||||
\(587\) | −3253.78 | + | 5635.71i | −0.228787 | + | 0.396270i | −0.957449 | − | 0.288603i | \(-0.906809\pi\) |
0.728662 | + | 0.684873i | \(0.240143\pi\) | |||||||
\(588\) | 4915.49 | − | 8413.64i | 0.344747 | − | 0.590089i | ||||
\(589\) | 10165.6 | + | 17607.4i | 0.711149 | + | 1.23175i | ||||
\(590\) | −303.397 | + | 525.499i | −0.0211706 | + | 0.0366686i | ||||
\(591\) | −5460.87 | − | 171.055i | −0.380085 | − | 0.0119057i | ||||
\(592\) | 11846.5 | + | 20518.7i | 0.822446 | + | 1.42452i | ||||
\(593\) | 1577.16 | + | 2731.71i | 0.109218 | + | 0.189170i | 0.915454 | − | 0.402424i | \(-0.131832\pi\) |
−0.806236 | + | 0.591594i | \(0.798499\pi\) | |||||||
\(594\) | −10421.2 | − | 22743.4i | −0.719843 | − | 1.57100i | ||||
\(595\) | −2582.30 | − | 1446.18i | −0.177923 | − | 0.0996428i | ||||
\(596\) | 6893.10 | − | 11939.2i | 0.473746 | − | 0.820551i | ||||
\(597\) | −7523.64 | + | 12137.2i | −0.515782 | + | 0.832062i | ||||
\(598\) | 20797.1 | 1.42217 | ||||||||
\(599\) | −13901.4 | −0.948241 | −0.474121 | − | 0.880460i | \(-0.657234\pi\) | ||||
−0.474121 | + | 0.880460i | \(0.657234\pi\) | |||||||
\(600\) | 2129.13 | + | 3969.84i | 0.144869 | + | 0.270114i | ||||
\(601\) | 11759.0 | − | 20367.2i | 0.798103 | − | 1.38236i | −0.122747 | − | 0.992438i | \(-0.539170\pi\) |
0.920850 | − | 0.389917i | \(-0.127496\pi\) | |||||||
\(602\) | −73.4656 | − | 5614.21i | −0.00497381 | − | 0.380097i | ||||
\(603\) | −1547.44 | − | 97.0388i | −0.104505 | − | 0.00655344i | ||||
\(604\) | −5260.39 | − | 9111.26i | −0.354375 | − | 0.613795i | ||||
\(605\) | −7609.14 | − | 13179.4i | −0.511331 | − | 0.885652i | ||||
\(606\) | −8980.02 | − | 16743.5i | −0.601961 | − | 1.12238i | ||||
\(607\) | 11419.4 | − | 19779.0i | 0.763591 | − | 1.32258i | −0.177397 | − | 0.984139i | \(-0.556768\pi\) |
0.940988 | − | 0.338440i | \(-0.109899\pi\) | |||||||
\(608\) | −14208.4 | − | 24609.7i | −0.947742 | − | 1.64154i | ||||
\(609\) | −193.348 | + | 10605.6i | −0.0128651 | + | 0.705683i | ||||
\(610\) | −7383.80 | + | 12789.1i | −0.490100 | + | 0.848879i | ||||
\(611\) | −1546.91 | − | 2679.33i | −0.102425 | − | 0.177405i | ||||
\(612\) | −883.349 | + | 1330.14i | −0.0583452 | + | 0.0878556i | ||||
\(613\) | −4081.47 | + | 7069.32i | −0.268922 | + | 0.465786i | −0.968584 | − | 0.248688i | \(-0.920001\pi\) |
0.699662 | + | 0.714474i | \(0.253334\pi\) | |||||||
\(614\) | −20063.6 | −1.31873 | ||||||||
\(615\) | −19507.7 | − | 611.054i | −1.27906 | − | 0.0400652i | ||||
\(616\) | 7297.66 | + | 4086.93i | 0.477323 | + | 0.267317i | ||||
\(617\) | −4664.01 | − | 8078.29i | −0.304321 | − | 0.527099i | 0.672789 | − | 0.739834i | \(-0.265096\pi\) |
−0.977110 | + | 0.212735i | \(0.931763\pi\) | |||||||
\(618\) | −1079.47 | + | 1741.40i | −0.0702629 | + | 0.113348i | ||||
\(619\) | −11268.3 | − | 19517.3i | −0.731683 | − | 1.26731i | −0.956163 | − | 0.292834i | \(-0.905402\pi\) |
0.224480 | − | 0.974479i | \(-0.427932\pi\) | |||||||
\(620\) | −6106.46 | + | 10576.7i | −0.395551 | + | 0.685114i | ||||
\(621\) | −6850.56 | + | 9645.94i | −0.442679 | + | 0.623314i | ||||
\(622\) | 9138.91 | 0.589127 | ||||||||
\(623\) | −403.304 | − | 225.864i | −0.0259359 | − | 0.0145249i | ||||
\(624\) | 12848.1 | + | 23955.7i | 0.824256 | + | 1.53685i | ||||
\(625\) | 9292.05 | − | 16094.3i | 0.594691 | − | 1.03004i | ||||
\(626\) | 34220.2 | 2.18485 | ||||||||
\(627\) | 17887.9 | − | 28856.8i | 1.13935 | − | 1.83801i | ||||
\(628\) | −11902.9 | −0.756336 | ||||||||
\(629\) | 3292.11 | 0.208688 | ||||||||
\(630\) | −1342.62 | + | 27078.3i | −0.0849066 | + | 1.71242i | ||||
\(631\) | 23538.2 | 1.48501 | 0.742505 | − | 0.669841i | \(-0.233638\pi\) | ||||
0.742505 | + | 0.669841i | \(0.233638\pi\) | |||||||
\(632\) | 8775.15 | 0.552305 | ||||||||
\(633\) | −3488.35 | − | 6504.15i | −0.219036 | − | 0.408399i | ||||
\(634\) | −21411.9 | −1.34129 | ||||||||
\(635\) | −11770.4 | + | 20386.9i | −0.735579 | + | 1.27406i | ||||
\(636\) | −95.9425 | + | 154.775i | −0.00598171 | + | 0.00964971i | ||||
\(637\) | −23042.5 | + | 603.155i | −1.43324 | + | 0.0375163i | ||||
\(638\) | 19655.0 | 1.21967 | ||||||||
\(639\) | 14044.3 | + | 880.708i | 0.869460 | + | 0.0545231i | ||||
\(640\) | −8347.86 | + | 14458.9i | −0.515591 | + | 0.893030i | ||||
\(641\) | 8286.30 | + | 14352.3i | 0.510591 | + | 0.884370i | 0.999925 | + | 0.0122733i | \(0.00390682\pi\) |
−0.489333 | + | 0.872097i | \(0.662760\pi\) | |||||||
\(642\) | −3048.14 | − | 5683.36i | −0.187384 | − | 0.349383i | ||||
\(643\) | 6927.97 | + | 11999.6i | 0.424903 | + | 0.735953i | 0.996411 | − | 0.0846429i | \(-0.0269749\pi\) |
−0.571509 | + | 0.820596i | \(0.693642\pi\) | |||||||
\(644\) | 111.727 | + | 8538.14i | 0.00683643 | + | 0.522437i | ||||
\(645\) | 2997.47 | + | 5588.88i | 0.182985 | + | 0.341181i | ||||
\(646\) | −5337.74 | −0.325094 | ||||||||
\(647\) | 6854.14 | − | 11871.7i | 0.416482 | − | 0.721368i | −0.579101 | − | 0.815256i | \(-0.696596\pi\) |
0.995583 | + | 0.0938878i | \(0.0299295\pi\) | |||||||
\(648\) | −6722.53 | − | 846.456i | −0.407540 | − | 0.0513147i | ||||
\(649\) | −271.908 | − | 470.958i | −0.0164458 | − | 0.0284849i | ||||
\(650\) | −11501.7 | + | 19921.6i | −0.694055 | + | 1.20214i | ||||
\(651\) | 12731.4 | − | 7044.24i | 0.766488 | − | 0.424095i | ||||
\(652\) | −337.360 | − | 584.324i | −0.0202638 | − | 0.0350980i | ||||
\(653\) | 8590.26 | − | 14878.8i | 0.514798 | − | 0.891656i | −0.485055 | − | 0.874484i | \(-0.661200\pi\) |
0.999853 | − | 0.0171720i | \(-0.00546630\pi\) | |||||||
\(654\) | 6366.28 | − | 10270.1i | 0.380644 | − | 0.614057i | ||||
\(655\) | 1172.89 | + | 2031.51i | 0.0699673 | + | 0.121187i | ||||
\(656\) | −9895.67 | − | 17139.8i | −0.588965 | − | 1.02012i | ||||
\(657\) | −5655.55 | + | 8516.06i | −0.335835 | + | 0.505698i | ||||
\(658\) | 2689.05 | − | 1599.80i | 0.159317 | − | 0.0947823i | ||||
\(659\) | −14769.0 | + | 25580.7i | −0.873018 | + | 1.51211i | −0.0141586 | + | 0.999900i | \(0.504507\pi\) |
−0.858859 | + | 0.512212i | \(0.828826\pi\) | |||||||
\(660\) | 20384.5 | + | 638.520i | 1.20222 | + | 0.0376581i | ||||
\(661\) | −4081.40 | −0.240164 | −0.120082 | − | 0.992764i | \(-0.538316\pi\) | ||||
−0.120082 | + | 0.992764i | \(0.538316\pi\) | |||||||
\(662\) | 36837.4 | 2.16273 | ||||||||
\(663\) | 3775.27 | + | 118.256i | 0.221145 | + | 0.00692712i | ||||
\(664\) | 3820.28 | − | 6616.92i | 0.223276 | − | 0.386726i | ||||
\(665\) | −31620.7 | + | 18812.1i | −1.84391 | + | 1.09700i | ||||
\(666\) | −13414.2 | − | 27008.9i | −0.780467 | − | 1.57143i | ||||
\(667\) | −4647.58 | − | 8049.85i | −0.269798 | − | 0.467303i | ||||
\(668\) | −9440.82 | − | 16352.0i | −0.546821 | − | 0.947121i | ||||
\(669\) | −12649.0 | + | 20405.3i | −0.730997 | + | 1.17925i | ||||
\(670\) | 1556.74 | − | 2696.36i | 0.0897645 | − | 0.155477i | ||||
\(671\) | −6617.44 | − | 11461.7i | −0.380720 | − | 0.659427i | ||||
\(672\) | −17794.6 | + | 9845.69i | −1.02149 | + | 0.565187i | ||||
\(673\) | 8519.48 | − | 14756.2i | 0.487967 | − | 0.845183i | −0.511937 | − | 0.859023i | \(-0.671072\pi\) |
0.999904 | + | 0.0138393i | \(0.00440534\pi\) | |||||||
\(674\) | 269.322 | + | 466.480i | 0.0153916 | + | 0.0266590i | ||||
\(675\) | −5451.20 | − | 11896.8i | −0.310840 | − | 0.678383i | ||||
\(676\) | −6339.77 | + | 10980.8i | −0.360706 | + | 0.624761i | ||||
\(677\) | 13593.0 | 0.771672 | 0.385836 | − | 0.922567i | \(-0.373913\pi\) | ||||
0.385836 | + | 0.922567i | \(0.373913\pi\) | |||||||
\(678\) | 9971.95 | + | 18593.0i | 0.564853 | + | 1.05319i | ||||
\(679\) | −11.0098 | − | 841.363i | −0.000622262 | − | 0.0475531i | ||||
\(680\) | 742.658 | + | 1286.32i | 0.0418818 | + | 0.0725414i | ||||
\(681\) | −1601.55 | − | 2986.15i | −0.0901198 | − | 0.168031i | ||||
\(682\) | −13480.5 | − | 23348.9i | −0.756885 | − | 1.31096i | ||||
\(683\) | −11066.4 | + | 19167.6i | −0.619976 | + | 1.07383i | 0.369513 | + | 0.929225i | \(0.379524\pi\) |
−0.989489 | + | 0.144605i | \(0.953809\pi\) | |||||||
\(684\) | 8829.63 | + | 17778.0i | 0.493581 | + | 0.993802i | ||||
\(685\) | −16173.5 | −0.902130 | ||||||||
\(686\) | −914.875 | − | 23294.2i | −0.0509185 | − | 1.29647i | ||||
\(687\) | −12439.1 | + | 20066.8i | −0.690803 | + | 1.11441i | ||||
\(688\) | −3215.51 | + | 5569.43i | −0.178184 | + | 0.308623i | ||||
\(689\) | 430.761 | 0.0238181 | ||||||||
\(690\) | −11228.8 | − | 20936.6i | −0.619529 | − | 1.15513i | ||||
\(691\) | −11095.7 | −0.610853 | −0.305427 | − | 0.952216i | \(-0.598799\pi\) | ||||
−0.305427 | + | 0.952216i | \(0.598799\pi\) | |||||||
\(692\) | −9676.51 | −0.531569 | ||||||||
\(693\) | −20414.9 | − | 13176.0i | −1.11905 | − | 0.722243i | ||||
\(694\) | 26175.9 | 1.43173 | ||||||||
\(695\) | 10392.4 | 0.567201 | ||||||||
\(696\) | 2804.68 | − | 4524.52i | 0.152746 | − | 0.246410i | ||||
\(697\) | −2749.98 | −0.149444 | ||||||||
\(698\) | −12389.6 | + | 21459.4i | −0.671852 | + | 1.16368i | ||||
\(699\) | 2367.66 | + | 4414.58i | 0.128116 | + | 0.238876i | ||||
\(700\) | −8240.49 | − | 4614.95i | −0.444945 | − | 0.249184i | ||||
\(701\) | −21416.9 | −1.15393 | −0.576965 | − | 0.816769i | \(-0.695763\pi\) | ||||
−0.576965 | + | 0.816769i | \(0.695763\pi\) | |||||||
\(702\) | −14412.8 | − | 31454.7i | −0.774894 | − | 1.69114i | ||||
\(703\) | 20463.0 | − | 35443.0i | 1.09783 | − | 1.90150i | ||||
\(704\) | 3711.05 | + | 6427.73i | 0.198673 | + | 0.344111i | ||||
\(705\) | −1862.08 | + | 3003.92i | −0.0994754 | + | 0.160474i | ||||
\(706\) | −18992.9 | − | 32896.7i | −1.01248 | − | 1.75366i | ||||
\(707\) | −16100.2 | − | 9016.68i | −0.856453 | − | 0.479642i | ||||
\(708\) | 317.791 | + | 9.95442i | 0.0168691 | + | 0.000528404i | ||||
\(709\) | 13755.1 | 0.728610 | 0.364305 | − | 0.931280i | \(-0.381307\pi\) | ||||
0.364305 | + | 0.931280i | \(0.381307\pi\) | |||||||
\(710\) | −14128.7 | + | 24471.7i | −0.746819 | + | 1.29353i | ||||
\(711\) | −25441.7 | − | 1595.42i | −1.34196 | − | 0.0841535i | ||||
\(712\) | 115.988 | + | 200.898i | 0.00610512 | + | 0.0105744i | ||||
\(713\) | −6375.15 | + | 11042.1i | −0.334855 | + | 0.579985i | ||||
\(714\) | −69.6299 | + | 3819.38i | −0.00364963 | + | 0.200191i | ||||
\(715\) | −24121.8 | − | 41780.3i | −1.26169 | − | 2.18531i | ||||
\(716\) | 10886.1 | − | 18855.2i | 0.568200 | − | 0.984151i | ||||
\(717\) | −1080.24 | − | 2014.15i | −0.0562656 | − | 0.104909i | ||||
\(718\) | 12873.5 | + | 22297.5i | 0.669128 | + | 1.15896i | ||||
\(719\) | 4117.57 | + | 7131.84i | 0.213574 | + | 0.369920i | 0.952830 | − | 0.303503i | \(-0.0981564\pi\) |
−0.739257 | + | 0.673424i | \(0.764823\pi\) | |||||||
\(720\) | 17179.4 | − | 25868.5i | 0.889218 | − | 1.33898i | ||||
\(721\) | 26.0369 | + | 1989.73i | 0.00134489 | + | 0.102776i | ||||
\(722\) | −20592.7 | + | 35667.6i | −1.06147 | + | 1.83852i | ||||
\(723\) | 15423.0 | + | 28756.6i | 0.793342 | + | 1.47921i | ||||
\(724\) | 24130.7 | 1.23869 | ||||||||
\(725\) | 10281.3 | 0.526673 | ||||||||
\(726\) | −10348.7 | + | 16694.6i | −0.529033 | + | 0.853438i | ||||
\(727\) | −11627.4 | + | 20139.3i | −0.593174 | + | 1.02741i | 0.400627 | + | 0.916241i | \(0.368792\pi\) |
−0.993802 | + | 0.111167i | \(0.964541\pi\) | |||||||
\(728\) | 10092.9 | + | 5652.34i | 0.513827 | + | 0.287760i | ||||
\(729\) | 19336.6 | + | 3676.35i | 0.982402 | + | 0.186778i | ||||
\(730\) | −10264.2 | − | 17778.1i | −0.520405 | − | 0.901368i | ||||
\(731\) | 446.790 | + | 773.864i | 0.0226062 | + | 0.0391551i | ||||
\(732\) | 7734.10 | + | 242.262i | 0.390520 | + | 0.0122326i | ||||
\(733\) | 13121.6 | − | 22727.4i | 0.661199 | − | 1.14523i | −0.319102 | − | 0.947720i | \(-0.603381\pi\) |
0.980301 | − | 0.197510i | \(-0.0632855\pi\) | |||||||
\(734\) | 17865.1 | + | 30943.2i | 0.898380 | + | 1.55604i | ||||
\(735\) | 13048.4 | + | 22871.3i | 0.654825 | + | 1.14779i | ||||
\(736\) | 8910.51 | − | 15433.5i | 0.446258 | − | 0.772941i | ||||
\(737\) | 1395.17 | + | 2416.50i | 0.0697309 | + | 0.120778i | ||||
\(738\) | 11205.2 | + | 22561.2i | 0.558903 | + | 1.12532i | ||||
\(739\) | −2483.59 | + | 4301.70i | −0.123627 | + | 0.214128i | −0.921195 | − | 0.389100i | \(-0.872786\pi\) |
0.797568 | + | 0.603228i | \(0.206119\pi\) | |||||||
\(740\) | 24584.2 | 1.22126 | ||||||||
\(741\) | 24739.4 | − | 39909.8i | 1.22649 | − | 1.97857i | ||||
\(742\) | 5.70030 | + | 435.615i | 0.000282028 | + | 0.0215524i | ||||
\(743\) | −1432.63 | − | 2481.40i | −0.0707379 | − | 0.122522i | 0.828487 | − | 0.560008i | \(-0.189202\pi\) |
−0.899225 | + | 0.437487i | \(0.855869\pi\) | |||||||
\(744\) | −7298.47 | − | 228.616i | −0.359644 | − | 0.0112654i | ||||
\(745\) | 18627.0 | + | 32262.9i | 0.916027 | + | 1.58661i | ||||
\(746\) | 4226.56 | − | 7320.61i | 0.207433 | − | 0.359285i | ||||
\(747\) | −12279.1 | + | 18489.8i | −0.601431 | + | 0.905629i | ||||
\(748\) | 2873.58 | 0.140466 | ||||||||
\(749\) | −5465.00 | − | 3060.58i | −0.266604 | − | 0.149307i | ||||
\(750\) | −8933.11 | − | 279.819i | −0.434921 | − | 0.0136234i | ||||
\(751\) | −3196.62 | + | 5536.71i | −0.155321 | + | 0.269025i | −0.933176 | − | 0.359420i | \(-0.882975\pi\) |
0.777855 | + | 0.628444i | \(0.216308\pi\) | |||||||
\(752\) | −3583.88 | −0.173791 | ||||||||
\(753\) | 11751.6 | + | 368.104i | 0.568727 | + | 0.0178147i | ||||
\(754\) | 27183.4 | 1.31294 | ||||||||
\(755\) | 28430.0 | 1.37043 | ||||||||
\(756\) | 12836.1 | − | 6086.07i | 0.617520 | − | 0.292788i | ||||
\(757\) | 20110.5 | 0.965558 | 0.482779 | − | 0.875742i | \(-0.339628\pi\) | ||||
0.482779 | + | 0.875742i | \(0.339628\pi\) | |||||||
\(758\) | −41594.7 | −1.99313 | ||||||||
\(759\) | 21281.4 | + | 666.616i | 1.01774 | + | 0.0318796i | ||||
\(760\) | 18464.8 | 0.881301 | ||||||||
\(761\) | 3367.40 | − | 5832.51i | 0.160405 | − | 0.277830i | −0.774609 | − | 0.632440i | \(-0.782053\pi\) |
0.935014 | + | 0.354611i | \(0.115387\pi\) | |||||||
\(762\) | 30368.7 | + | 951.264i | 1.44376 | + | 0.0452239i | ||||
\(763\) | −153.556 | − | 11734.7i | −0.00728583 | − | 0.556780i | ||||
\(764\) | −22227.7 | −1.05258 | ||||||||
\(765\) | −1919.31 | − | 3864.44i | −0.0907095 | − | 0.182639i | ||||
\(766\) | −22556.1 | + | 39068.3i | −1.06395 | + | 1.84281i | ||||
\(767\) | −376.056 | − | 651.347i | −0.0177035 | − | 0.0306634i | ||||
\(768\) | 27884.8 | + | 873.458i | 1.31016 | + | 0.0410393i | ||||
\(769\) | 16586.6 | + | 28728.8i | 0.777799 | + | 1.34719i | 0.933208 | + | 0.359338i | \(0.116997\pi\) |
−0.155408 | + | 0.987850i | \(0.549669\pi\) | |||||||
\(770\) | 41931.8 | − | 24946.5i | 1.96249 | − | 1.16755i | ||||
\(771\) | 13281.3 | − | 21425.5i | 0.620384 | − | 1.00081i | ||||
\(772\) | 7062.29 | 0.329245 | ||||||||
\(773\) | −15610.5 | + | 27038.2i | −0.726353 | + | 1.25808i | 0.232061 | + | 0.972701i | \(0.425453\pi\) |
−0.958415 | + | 0.285380i | \(0.907880\pi\) | |||||||
\(774\) | 4528.37 | − | 6818.77i | 0.210296 | − | 0.316661i | ||||
\(775\) | −7051.50 | − | 12213.5i | −0.326835 | − | 0.566095i | ||||
\(776\) | −211.137 | + | 365.700i | −0.00976723 | + | 0.0169173i | ||||
\(777\) | −25094.0 | − | 15104.5i | −1.15861 | − | 0.697389i | ||||
\(778\) | 20016.4 | + | 34669.5i | 0.922395 | + | 1.59764i | ||||
\(779\) | −17093.3 | + | 29606.4i | −0.786174 | + | 1.36169i | ||||
\(780\) | 28192.3 | + | 883.090i | 1.29416 | + | 0.0405381i | ||||
\(781\) | −12662.3 | − | 21931.8i | −0.580145 | − | 1.00484i | ||||
\(782\) | −1673.73 | − | 2898.98i | −0.0765375 | − | 0.132567i | ||||
\(783\) | −8954.18 | + | 12608.0i | −0.408680 | + | 0.575443i | ||||
\(784\) | −12741.1 | + | 23465.6i | −0.580407 | + | 1.06895i | ||||
\(785\) | 16082.5 | − | 27855.6i | 0.731219 | − | 1.26651i | ||||
\(786\) | 1595.18 | − | 2573.35i | 0.0723895 | − | 0.116779i | ||||
\(787\) | −41836.8 | −1.89494 | −0.947471 | − | 0.319841i | \(-0.896370\pi\) | ||||
−0.947471 | + | 0.319841i | \(0.896370\pi\) | |||||||
\(788\) | −5748.68 | −0.259883 | ||||||||
\(789\) | −18872.2 | − | 35187.9i | −0.851546 | − | 1.58774i | ||||
\(790\) | 25594.5 | − | 44331.1i | 1.15267 | − | 1.99649i | ||||
\(791\) | 17878.7 | + | 10012.7i | 0.803657 | + | 0.450075i | ||||
\(792\) | 5424.01 | + | 10921.0i | 0.243351 | + | 0.489975i | ||||
\(793\) | −9152.10 | − | 15851.9i | −0.409837 | − | 0.709858i | ||||
\(794\) | −11088.1 | − | 19205.2i | −0.495595 | − | 0.858396i | ||||
\(795\) | −232.578 | − | 433.649i | −0.0103757 | − | 0.0193458i | ||||
\(796\) | −7512.56 | + | 13012.1i | −0.334517 | + | 0.579401i | ||||
\(797\) | 518.230 | + | 897.601i | 0.0230322 | + | 0.0398929i | 0.877312 | − | 0.479921i | \(-0.159335\pi\) |
−0.854280 | + | 0.519814i | \(0.826001\pi\) | |||||||
\(798\) | 40686.8 | + | 24490.1i | 1.80489 | + | 1.08639i | ||||
\(799\) | −248.987 | + | 431.259i | −0.0110245 | + | 0.0190949i | ||||
\(800\) | 9855.83 | + | 17070.8i | 0.435570 | + | 0.754430i | ||||
\(801\) | −299.757 | − | 603.547i | −0.0132227 | − | 0.0266233i | ||||
\(802\) | 26244.3 | − | 45456.4i | 1.15551 | − | 2.00140i | ||||
\(803\) | 18397.8 | 0.808523 | ||||||||
\(804\) | −1630.60 | − | 51.0765i | −0.0715258 | − | 0.00224046i | ||||
\(805\) | −20132.2 | − | 11274.7i | −0.881448 | − | 0.493641i | ||||
\(806\) | −18643.9 | − | 32292.2i | −0.814769 | − | 1.41122i | ||||
\(807\) | −3096.48 | + | 4995.25i | −0.135070 | + | 0.217895i | ||||
\(808\) | 4630.35 | + | 8020.00i | 0.201603 | + | 0.349186i | ||||
\(809\) | −588.485 | + | 1019.29i | −0.0255748 | + | 0.0442969i | −0.878530 | − | 0.477688i | \(-0.841475\pi\) |
0.852955 | + | 0.521985i | \(0.174808\pi\) | |||||||
\(810\) | −23883.8 | + | 31492.6i | −1.03604 | + | 1.36609i | ||||
\(811\) | −32977.3 | −1.42785 | −0.713927 | − | 0.700220i | \(-0.753085\pi\) | ||||
−0.713927 | + | 0.700220i | \(0.753085\pi\) | |||||||
\(812\) | 146.035 | + | 11160.0i | 0.00631137 | + | 0.482313i | ||||
\(813\) | 1399.61 | + | 2609.62i | 0.0603768 | + | 0.112575i | ||||
\(814\) | −27135.8 | + | 47000.6i | −1.16844 | + | 2.02380i | ||||
\(815\) | 1823.27 | 0.0783637 | ||||||||
\(816\) | 2305.27 | − | 3718.87i | 0.0988977 | − | 0.159542i | ||||
\(817\) | 11108.6 | 0.475693 | ||||||||
\(818\) | −20670.4 | −0.883526 | ||||||||
\(819\) | −28234.4 | − | 18222.7i | −1.20463 | − | 0.777477i | ||||
\(820\) | −20535.8 | −0.874561 | ||||||||
\(821\) | −33010.1 | −1.40324 | −0.701620 | − | 0.712551i | \(-0.747540\pi\) | ||||
−0.701620 | + | 0.712551i | \(0.747540\pi\) | |||||||
\(822\) | 9866.34 | + | 18396.1i | 0.418647 | + | 0.780582i | ||||
\(823\) | −41858.3 | −1.77289 | −0.886445 | − | 0.462834i | \(-0.846833\pi\) | ||||
−0.886445 | + | 0.462834i | \(0.846833\pi\) | |||||||
\(824\) | 499.315 | − | 864.839i | 0.0211098 | − | 0.0365632i | ||||
\(825\) | −12408.2 | + | 20016.9i | −0.523632 | + | 0.844725i | ||||
\(826\) | 653.711 | − | 388.912i | 0.0275369 | − | 0.0163826i | ||||
\(827\) | 5874.82 | 0.247022 | 0.123511 | − | 0.992343i | \(-0.460585\pi\) | ||||
0.123511 | + | 0.992343i | \(0.460585\pi\) | |||||||
\(828\) | −6886.77 | + | 10370.0i | −0.289048 | + | 0.435246i | ||||
\(829\) | −6821.01 | + | 11814.3i | −0.285770 | + | 0.494969i | −0.972796 | − | 0.231665i | \(-0.925583\pi\) |
0.687025 | + | 0.726633i | \(0.258916\pi\) | |||||||
\(830\) | −22285.3 | − | 38599.2i | −0.931967 | − | 1.61421i | ||||
\(831\) | −12570.8 | − | 23438.7i | −0.524762 | − | 0.978436i | ||||
\(832\) | 5132.48 | + | 8889.72i | 0.213866 | + | 0.370428i | ||||
\(833\) | 1938.51 | + | 3163.43i | 0.0806306 | + | 0.131580i | ||||
\(834\) | −6339.65 | − | 11820.5i | −0.263218 | − | 0.490779i | ||||
\(835\) | 51023.2 | 2.11465 | ||||||||
\(836\) | 17861.6 | − | 30937.1i | 0.738942 | − | 1.27988i | ||||
\(837\) | 21118.8 | + | 1989.77i | 0.872128 | + | 0.0821702i | ||||
\(838\) | −7898.81 | − | 13681.1i | −0.325609 | − | 0.563971i | ||||
\(839\) | 15177.6 | − | 26288.4i | 0.624541 | − | 1.08174i | −0.364089 | − | 0.931364i | \(-0.618619\pi\) |
0.988629 | − | 0.150372i | \(-0.0480472\pi\) | |||||||
\(840\) | 240.870 | − | 13212.4i | 0.00989383 | − | 0.542702i | ||||
\(841\) | 6119.77 | + | 10599.7i | 0.250923 | + | 0.434612i | ||||
\(842\) | 5612.38 | − | 9720.93i | 0.229710 | − | 0.397869i | ||||
\(843\) | −10546.7 | + | 17014.1i | −0.430901 | + | 0.695131i | ||||
\(844\) | −3882.86 | − | 6725.31i | −0.158357 | − | 0.274283i | ||||
\(845\) | −17131.7 | − | 29673.0i | −0.697455 | − | 1.20803i | ||||
\(846\) | 4552.65 | + | 285.493i | 0.185016 | + | 0.0116022i | ||||
\(847\) | 249.613 | + | 19075.3i | 0.0101261 | + | 0.773833i | ||||
\(848\) | 249.496 | − | 432.140i | 0.0101035 | − | 0.0174997i | ||||
\(849\) | 10599.4 | + | 332.014i | 0.428470 | + | 0.0134213i | ||||
\(850\) | 3702.59 | 0.149409 | ||||||||
\(851\) | 25665.9 | 1.03386 | ||||||||
\(852\) | 14799.0 | + | 463.562i | 0.595078 | + | 0.0186401i | ||||
\(853\) | −5545.12 | + | 9604.43i | −0.222581 | + | 0.385521i | −0.955591 | − | 0.294697i | \(-0.904781\pi\) |
0.733010 | + | 0.680218i | \(0.238115\pi\) | |||||||
\(854\) | 15909.4 | − | 9464.99i | 0.637481 | − | 0.379257i | ||||
\(855\) | −53534.7 | − | 3357.12i | −2.14134 | − | 0.134282i | ||||
\(856\) | 1571.71 | + | 2722.27i | 0.0627568 | + | 0.108698i | ||||
\(857\) | −3771.48 | − | 6532.39i | −0.150328 | − | 0.260376i | 0.781020 | − | 0.624506i | \(-0.214700\pi\) |
−0.931348 | + | 0.364130i | \(0.881366\pi\) | |||||||
\(858\) | −32806.7 | + | 52923.9i | −1.30536 | + | 2.10582i | ||||
\(859\) | −426.088 | + | 738.006i | −0.0169242 | + | 0.0293136i | −0.874363 | − | 0.485272i | \(-0.838721\pi\) |
0.857439 | + | 0.514585i | \(0.172054\pi\) | |||||||
\(860\) | 3336.46 | + | 5778.92i | 0.132293 | + | 0.229139i | ||||
\(861\) | 20961.7 | + | 12617.2i | 0.829699 | + | 0.499410i | ||||
\(862\) | −27958.2 | + | 48425.1i | −1.10471 | + | 1.91342i | ||||
\(863\) | −21041.4 | − | 36444.7i | −0.829962 | − | 1.43754i | −0.898067 | − | 0.439858i | \(-0.855029\pi\) |
0.0681055 | − | 0.997678i | \(-0.478305\pi\) | |||||||
\(864\) | −29517.6 | − | 2781.09i | −1.16228 | − | 0.109508i | ||||
\(865\) | 13074.3 | − | 22645.3i | 0.513917 | − | 0.890130i | ||||
\(866\) | 5778.06 | 0.226728 | ||||||||
\(867\) | 11778.6 | + | 21961.5i | 0.461385 | + | 0.860268i | ||||
\(868\) | 13157.2 | − | 7827.63i | 0.514499 | − | 0.306091i | ||||
\(869\) | 22938.1 | + | 39730.0i | 0.895422 | + | 1.55092i | ||||
\(870\) | −14676.9 | − | 27365.6i | −0.571948 | − | 1.06642i | ||||
\(871\) | 1929.56 | + | 3342.09i | 0.0750637 | + | 0.130014i | ||||
\(872\) | −2944.77 | + | 5100.49i | −0.114361 | + | 0.198079i | ||||
\(873\) | 678.634 | − | 1021.88i | 0.0263096 | − | 0.0396167i | ||||
\(874\) | −41614.1 | −1.61055 | ||||||||
\(875\) | −7460.02 | + | 4438.19i | −0.288223 | + | 0.171472i | ||||
\(876\) | −5667.23 | + | 9142.40i | −0.218582 | + | 0.352618i | ||||
\(877\) | 4272.23 | − | 7399.73i | 0.164496 | − | 0.284916i | −0.771980 | − | 0.635647i | \(-0.780734\pi\) |
0.936476 | + | 0.350731i | \(0.114067\pi\) | |||||||
\(878\) | 4008.88 | 0.154092 | ||||||||
\(879\) | 4747.37 | + | 8851.62i | 0.182167 | + | 0.339656i | ||||
\(880\) | −55885.4 | −2.14079 | ||||||||
\(881\) | −17116.7 | −0.654571 | −0.327286 | − | 0.944925i | \(-0.606134\pi\) | ||||
−0.327286 | + | 0.944925i | \(0.606134\pi\) | |||||||
\(882\) | 18054.4 | − | 28793.7i | 0.689257 | − | 1.09925i | ||||
\(883\) | −11673.8 | −0.444909 | −0.222454 | − | 0.974943i | \(-0.571407\pi\) | ||||
−0.222454 | + | 0.974943i | \(0.571407\pi\) | |||||||
\(884\) | 3974.24 | 0.151208 | ||||||||
\(885\) | −452.674 | + | 730.255i | −0.0171937 | + | 0.0277370i | ||||
\(886\) | −45885.5 | −1.73990 | ||||||||
\(887\) | −243.833 | + | 422.331i | −0.00923011 | + | 0.0159870i | −0.870604 | − | 0.491985i | \(-0.836271\pi\) |
0.861373 | + | 0.507972i | \(0.169605\pi\) | |||||||
\(888\) | 6947.24 | + | 12953.4i | 0.262538 | + | 0.489512i | ||||
\(889\) | 25360.8 | − | 15087.9i | 0.956778 | − | 0.569216i | ||||
\(890\) | 1353.21 | 0.0509661 | ||||||||
\(891\) | −13740.2 | − | 32649.2i | −0.516626 | − | 1.22760i | ||||
\(892\) | −12630.3 | + | 21876.4i | −0.474097 | + | 0.821161i | ||||
\(893\) | 3095.31 | + | 5361.23i | 0.115992 | + | 0.200903i | ||||
\(894\) | 25333.5 | − | 40868.1i | 0.947739 | − | 1.52890i | ||||
\(895\) | 29417.0 | + | 50951.8i | 1.09866 | + | 1.90294i | ||||
\(896\) | 17986.6 | − | 10700.8i | 0.670637 | − | 0.398982i | ||||
\(897\) | 29432.8 | + | 921.947i | 1.09558 | + | 0.0343176i | ||||
\(898\) | 4331.18 | 0.160950 | ||||||||
\(899\) | −8332.80 | + | 14432.8i | −0.309137 | + | 0.535441i | ||||
\(900\) | −6124.78 | − | 12331.9i | −0.226844 | − | 0.456739i | ||||
\(901\) | −34.6671 | − | 60.0451i | −0.00128183 | − | 0.00222019i | ||||
\(902\) | 22667.2 | − | 39260.7i | 0.836735 | − | 1.44927i | ||||
\(903\) | 144.910 | − | 7948.68i | 0.00534031 | − | 0.292930i | ||||
\(904\) | −5141.82 | − | 8905.90i | −0.189175 | − | 0.327661i | ||||
\(905\) | −32603.8 | + | 56471.5i | −1.19756 | + | 2.07423i | ||||
\(906\) | −17343.1 | − | 32336.8i | −0.635968 | − | 1.18578i | ||||
\(907\) | 8816.70 | + | 15271.0i | 0.322772 | + | 0.559057i | 0.981059 | − | 0.193710i | \(-0.0620521\pi\) |
−0.658287 | + | 0.752767i | \(0.728719\pi\) | |||||||
\(908\) | −1782.68 | − | 3087.68i | −0.0651544 | − | 0.112851i | ||||
\(909\) | −11966.6 | − | 24094.1i | −0.436641 | − | 0.879155i | ||||
\(910\) | 57992.9 | − | 34501.7i | 2.11258 | − | 1.25684i | ||||
\(911\) | 22056.5 | − | 38203.0i | 0.802157 | − | 1.38938i | −0.116036 | − | 0.993245i | \(-0.537019\pi\) |
0.918194 | − | 0.396132i | \(-0.129648\pi\) | |||||||
\(912\) | −25708.5 | − | 47934.3i | −0.933435 | − | 1.74042i | ||||
\(913\) | 39944.6 | 1.44794 | ||||||||
\(914\) | −47316.6 | −1.71236 | ||||||||
\(915\) | −11016.8 | + | 17772.3i | −0.398036 | + | 0.642112i | ||||
\(916\) | −12420.8 | + | 21513.5i | −0.448030 | + | 0.776010i | ||||
\(917\) | −38.4759 | − | 2940.32i | −0.00138559 | − | 0.105886i | ||||
\(918\) | −3224.66 | + | 4540.48i | −0.115936 | + | 0.163244i | ||||
\(919\) | 18791.0 | + | 32546.9i | 0.674490 | + | 1.16825i | 0.976618 | + | 0.214984i | \(0.0689699\pi\) |
−0.302127 | + | 0.953268i | \(0.597697\pi\) | |||||||
\(920\) | 5789.91 | + | 10028.4i | 0.207487 | + | 0.359377i | ||||
\(921\) | −28394.8 | − | 889.432i | −1.01589 | − | 0.0318217i | ||||
\(922\) | 4037.88 | − | 6993.81i | 0.144230 | − | 0.249814i | ||||
\(923\) | −17512.3 | − | 30332.2i | −0.624513 | − | 1.08169i | ||||
\(924\) | −21903.8 | − | 13184.3i | −0.779852 | − | 0.469406i | ||||
\(925\) | −14194.4 | + | 24585.5i | −0.504551 | + | 0.873908i | ||||
\(926\) | 29838.8 | + | 51682.3i | 1.05892 | + | 1.83411i | ||||
\(927\) | −1604.89 | + | 2416.63i | −0.0568626 | + | 0.0856231i | ||||
\(928\) | 11646.7 | − | 20172.7i | 0.411984 | − | 0.713578i | ||||
\(929\) | 36130.7 | 1.27600 | 0.638002 | − | 0.770034i | \(-0.279761\pi\) | ||||
0.638002 | + | 0.770034i | \(0.279761\pi\) | |||||||
\(930\) | −22442.4 | + | 36204.2i | −0.791308 | + | 1.27654i | ||||
\(931\) | 46107.0 | − | 1206.89i | 1.62309 | − | 0.0424856i | ||||
\(932\) | 2635.42 | + | 4564.69i | 0.0926246 | + | 0.160431i | ||||
\(933\) | 12933.7 | + | 405.132i | 0.453837 | + | 0.0142159i | ||||
\(934\) | −3227.30 | − | 5589.85i | −0.113063 | − | 0.195830i | ||||
\(935\) | −3882.59 | + | 6724.85i | −0.135801 | + | 0.235215i | ||||
\(936\) | 7501.56 | + | 15104.0i | 0.261962 | + | 0.527447i | ||||
\(937\) | 31882.6 | 1.11159 | 0.555794 | − | 0.831320i | \(-0.312414\pi\) | ||||
0.555794 | + | 0.831320i | \(0.312414\pi\) | |||||||
\(938\) | −3354.21 | + | 1995.52i | −0.116758 | + | 0.0694629i | ||||
\(939\) | 48429.6 | + | 1517.00i | 1.68311 | + | 0.0527214i | ||||
\(940\) | −1859.34 | + | 3220.48i | −0.0645160 | + | 0.111745i | ||||
\(941\) | 12858.3 | 0.445449 | 0.222725 | − | 0.974881i | \(-0.428505\pi\) | ||||
0.222725 | + | 0.974881i | \(0.428505\pi\) | |||||||
\(942\) | −41494.3 | − | 1299.76i | −1.43520 | − | 0.0449559i | ||||
\(943\) | −21439.4 | −0.740363 | ||||||||
\(944\) | −871.244 | −0.0300387 | ||||||||
\(945\) | −3100.51 | + | 38262.6i | −0.106730 | + | 1.31712i | ||||
\(946\) | −14731.0 | −0.506286 | ||||||||
\(947\) | −27049.3 | −0.928176 | −0.464088 | − | 0.885789i | \(-0.653618\pi\) | ||||
−0.464088 | + | 0.885789i | \(0.653618\pi\) | |||||||
\(948\) | −26808.8 | − | 839.754i | −0.918470 | − | 0.0287700i | ||||
\(949\) | 25444.6 | 0.870356 | ||||||||
\(950\) | 23014.5 | − | 39862.2i | 0.785988 | − | 1.36137i | ||||
\(951\) | −30302.9 | − | 949.202i | −1.03327 | − | 0.0323659i | ||||
\(952\) | −24.3624 | − | 1861.77i | −0.000829402 | − | 0.0633827i | ||||
\(953\) | 50782.8 | 1.72615 | 0.863073 | − | 0.505079i | \(-0.168537\pi\) | ||||
0.863073 | + | 0.505079i | \(0.168537\pi\) | |||||||
\(954\) | −351.362 | + | 529.078i | −0.0119243 | + | 0.0179555i | ||||
\(955\) | 30032.6 | − | 52017.9i | 1.01762 | − | 1.76258i | ||||
\(956\) | −1202.41 | − | 2082.64i | −0.0406786 | − | 0.0704574i | ||||
\(957\) | 27816.4 | + | 871.316i | 0.939579 | + | 0.0294312i | ||||
\(958\) | 7870.19 | + | 13631.6i | 0.265422 | + | 0.459724i | ||||
\(959\) | 17689.3 | + | 9906.62i | 0.595640 | + | 0.333578i | ||||
\(960\) | 6178.18 | − | 9966.67i | 0.207708 | − | 0.335076i | ||||
\(961\) | −6930.58 | −0.232640 | ||||||||
\(962\) | −37529.5 | + | 65003.1i | −1.25780 | + | 2.17857i | ||||
\(963\) | −4061.88 | − | 8178.40i | −0.135921 | − | 0.273671i | ||||
\(964\) | 17167.2 | + | 29734.5i | 0.573566 | + | 0.993446i | ||||
\(965\) | −9542.09 | + | 16527.4i | −0.318312 | + | 0.551332i | ||||
\(966\) | −542.849 | + | 29776.7i | −0.0180806 | + | 0.991768i | ||||
\(967\) | −20334.5 | − | 35220.3i | −0.676228 | − | 1.17126i | −0.976108 | − | 0.217284i | \(-0.930280\pi\) |
0.299881 | − | 0.953977i | \(-0.403053\pi\) | |||||||
\(968\) | 4786.89 | − | 8291.13i | 0.158943 | − | 0.275297i | ||||
\(969\) | −7554.15 | − | 236.625i | −0.250438 | − | 0.00784467i | ||||
\(970\) | 1231.65 | + | 2133.28i | 0.0407689 | + | 0.0706138i | ||||
\(971\) | 15500.8 | + | 26848.2i | 0.512302 | + | 0.887333i | 0.999898 | + | 0.0142635i | \(0.00454036\pi\) |
−0.487597 | + | 0.873069i | \(0.662126\pi\) | |||||||
\(972\) | 20456.9 | + | 3229.32i | 0.675056 | + | 0.106564i | ||||
\(973\) | −11366.3 | − | 6365.53i | −0.374499 | − | 0.209732i | ||||
\(974\) | −17441.6 | + | 30209.7i | −0.573782 | + | 0.993820i | ||||
\(975\) | −17160.8 | + | 27683.9i | −0.563678 | + | 0.909327i | ||||
\(976\) | −21203.5 | −0.695398 | ||||||||
\(977\) | 38305.3 | 1.25434 | 0.627172 | − | 0.778881i | \(-0.284212\pi\) | ||||
0.627172 | + | 0.778881i | \(0.284212\pi\) | |||||||
\(978\) | −1112.25 | − | 2073.83i | −0.0363659 | − | 0.0678054i | ||||
\(979\) | −606.383 | + | 1050.29i | −0.0197958 | + | 0.0342873i | ||||
\(980\) | 14476.0 | + | 23623.3i | 0.471857 | + | 0.770018i | ||||
\(981\) | 9465.06 | − | 14252.4i | 0.308049 | − | 0.463857i | ||||
\(982\) | −4026.16 | − | 6973.51i | −0.130835 | − | 0.226613i | ||||
\(983\) | −23580.5 | − | 40842.5i | −0.765106 | − | 1.32520i | −0.940190 | − | 0.340650i | \(-0.889353\pi\) |
0.175084 | − | 0.984554i | \(-0.443980\pi\) | |||||||
\(984\) | −5803.20 | − | 10820.3i | −0.188007 | − | 0.350546i | ||||
\(985\) | 7767.23 | − | 13453.2i | 0.251253 | − | 0.435183i | ||||
\(986\) | −2187.68 | − | 3789.18i | −0.0706593 | − | 0.122385i | ||||
\(987\) | 3876.56 | − | 2144.89i | 0.125018 | − | 0.0691717i | ||||
\(988\) | 24703.0 | − | 42786.9i | 0.795453 | − | 1.37777i | ||||
\(989\) | 3483.27 | + | 6033.20i | 0.111993 | + | 0.193978i | ||||
\(990\) | 70991.9 | + | 4451.84i | 2.27906 | + | 0.142918i | ||||
\(991\) | −4334.97 | + | 7508.39i | −0.138955 | + | 0.240678i | −0.927101 | − | 0.374810i | \(-0.877708\pi\) |
0.788146 | + | 0.615488i | \(0.211041\pi\) | |||||||
\(992\) | −31951.9 | −1.02265 | ||||||||
\(993\) | 52133.5 | + | 1633.02i | 1.66607 | + | 0.0521876i | ||||
\(994\) | 30442.3 | − | 18111.0i | 0.971399 | − | 0.577915i | ||||
\(995\) | −20300.9 | − | 35162.3i | −0.646817 | − | 1.12032i | ||||
\(996\) | −12304.5 | + | 19849.6i | −0.391448 | + | 0.631486i | ||||
\(997\) | 11280.4 | + | 19538.2i | 0.358328 | + | 0.620643i | 0.987682 | − | 0.156477i | \(-0.0500136\pi\) |
−0.629354 | + | 0.777119i | \(0.716680\pi\) | |||||||
\(998\) | 14076.9 | − | 24381.9i | 0.446489 | − | 0.773342i | ||||
\(999\) | −17787.0 | − | 38818.6i | −0.563318 | − | 1.22939i |
(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 | 63.4.h.a.25.18 | yes | 44 | |
3.2 | odd | 2 | 189.4.h.a.46.5 | 44 | |||
7.2 | even | 3 | 63.4.g.a.16.5 | yes | 44 | ||
9.4 | even | 3 | 63.4.g.a.4.5 | ✓ | 44 | ||
9.5 | odd | 6 | 189.4.g.a.172.18 | 44 | |||
21.2 | odd | 6 | 189.4.g.a.100.18 | 44 | |||
63.23 | odd | 6 | 189.4.h.a.37.5 | 44 | |||
63.58 | even | 3 | inner | 63.4.h.a.58.18 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.5 | ✓ | 44 | 9.4 | even | 3 | ||
63.4.g.a.16.5 | yes | 44 | 7.2 | even | 3 | ||
63.4.h.a.25.18 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.h.a.58.18 | yes | 44 | 63.58 | even | 3 | inner | |
189.4.g.a.100.18 | 44 | 21.2 | odd | 6 | |||
189.4.g.a.172.18 | 44 | 9.5 | odd | 6 | |||
189.4.h.a.37.5 | 44 | 63.23 | odd | 6 | |||
189.4.h.a.46.5 | 44 | 3.2 | odd | 2 |