Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(5,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.f (of order \(4\), 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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1316x^{16} + 520390x^{12} + 64668772x^{8} + 2536036097x^{4} + 8509693504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.10 | ||
Root | \(3.62388 - 3.62388i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.5 |
Dual form | 39.4.f.b.8.10 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62388 | + | 3.62388i | 1.28123 | + | 1.28123i | 0.939966 | + | 0.341268i | \(0.110856\pi\) |
0.341268 | + | 0.939966i | \(0.389144\pi\) | |||||||
\(3\) | 4.19035 | − | 3.07262i | 0.806433 | − | 0.591326i | ||||
\(4\) | 18.2650i | 2.28312i | ||||||||
\(5\) | −10.8970 | − | 10.8970i | −0.974661 | − | 0.974661i | 0.0250260 | − | 0.999687i | \(-0.492033\pi\) |
−0.999687 | + | 0.0250260i | \(0.992033\pi\) | |||||||
\(6\) | 26.3201 | + | 4.05051i | 1.79086 | + | 0.275602i | ||||
\(7\) | −5.52580 | − | 5.52580i | −0.298365 | − | 0.298365i | 0.542008 | − | 0.840373i | \(-0.317664\pi\) |
−0.840373 | + | 0.542008i | \(0.817664\pi\) | |||||||
\(8\) | −37.1990 | + | 37.1990i | −1.64398 | + | 1.64398i | ||||
\(9\) | 8.11802 | − | 25.7507i | 0.300668 | − | 0.953729i | ||||
\(10\) | − | 78.9791i | − | 2.49754i | ||||||
\(11\) | −25.6188 | + | 25.6188i | −0.702215 | + | 0.702215i | −0.964885 | − | 0.262671i | \(-0.915397\pi\) |
0.262671 | + | 0.964885i | \(0.415397\pi\) | |||||||
\(12\) | 56.1213 | + | 76.5366i | 1.35007 | + | 1.84118i | ||||
\(13\) | 6.01627 | + | 46.4845i | 0.128355 | + | 0.991728i | ||||
\(14\) | − | 40.0497i | − | 0.764551i | ||||||
\(15\) | −79.1448 | − | 12.1799i | −1.36234 | − | 0.209656i | ||||
\(16\) | −123.489 | −1.92952 | ||||||||
\(17\) | 56.1424 | 0.800972 | 0.400486 | − | 0.916303i | \(-0.368841\pi\) | ||||
0.400486 | + | 0.916303i | \(0.368841\pi\) | |||||||
\(18\) | 122.736 | − | 63.8986i | 1.60718 | − | 0.836725i | ||||
\(19\) | 72.4479 | − | 72.4479i | 0.874773 | − | 0.874773i | −0.118215 | − | 0.992988i | \(-0.537717\pi\) |
0.992988 | + | 0.118215i | \(0.0377171\pi\) | |||||||
\(20\) | 199.034 | − | 199.034i | 2.22527 | − | 2.22527i | ||||
\(21\) | −40.1337 | − | 6.17634i | −0.417043 | − | 0.0641804i | ||||
\(22\) | −185.679 | −1.79940 | ||||||||
\(23\) | 8.33293 | 0.0755451 | 0.0377725 | − | 0.999286i | \(-0.487974\pi\) | ||||
0.0377725 | + | 0.999286i | \(0.487974\pi\) | |||||||
\(24\) | −41.5784 | + | 270.175i | −0.353631 | + | 2.29788i | ||||
\(25\) | 112.491i | 0.899927i | ||||||||
\(26\) | −146.652 | + | 190.256i | −1.10618 | + | 1.43509i | ||||
\(27\) | −45.1047 | − | 132.848i | −0.321496 | − | 0.946911i | ||||
\(28\) | 100.929 | − | 100.929i | 0.681204 | − | 0.681204i | ||||
\(29\) | 125.931i | 0.806375i | 0.915117 | + | 0.403187i | \(0.132098\pi\) | ||||
−0.915117 | + | 0.403187i | \(0.867902\pi\) | |||||||
\(30\) | −242.673 | − | 330.950i | −1.47686 | − | 2.01410i | ||||
\(31\) | −89.8241 | + | 89.8241i | −0.520415 | + | 0.520415i | −0.917697 | − | 0.397281i | \(-0.869954\pi\) |
0.397281 | + | 0.917697i | \(0.369954\pi\) | |||||||
\(32\) | −149.918 | − | 149.918i | −0.828189 | − | 0.828189i | ||||
\(33\) | −28.6349 | + | 186.069i | −0.151051 | + | 0.981526i | ||||
\(34\) | 203.453 | + | 203.453i | 1.02623 | + | 1.02623i | ||||
\(35\) | 120.430i | 0.581610i | ||||||||
\(36\) | 470.335 | + | 148.275i | 2.17748 | + | 0.686460i | ||||
\(37\) | −274.724 | − | 274.724i | −1.22066 | − | 1.22066i | −0.967398 | − | 0.253261i | \(-0.918497\pi\) |
−0.253261 | − | 0.967398i | \(-0.581503\pi\) | |||||||
\(38\) | 525.085 | 2.24158 | ||||||||
\(39\) | 168.039 | + | 176.300i | 0.689944 | + | 0.723863i | ||||
\(40\) | 810.717 | 3.20464 | ||||||||
\(41\) | 44.2900 | + | 44.2900i | 0.168706 | + | 0.168706i | 0.786410 | − | 0.617704i | \(-0.211937\pi\) |
−0.617704 | + | 0.786410i | \(0.711937\pi\) | |||||||
\(42\) | −123.057 | − | 167.822i | −0.452099 | − | 0.616559i | ||||
\(43\) | 100.272i | 0.355611i | 0.984066 | + | 0.177806i | \(0.0568998\pi\) | ||||
−0.984066 | + | 0.177806i | \(0.943100\pi\) | |||||||
\(44\) | −467.927 | − | 467.927i | −1.60324 | − | 1.60324i | ||||
\(45\) | −369.069 | + | 192.144i | −1.22261 | + | 0.636513i | ||||
\(46\) | 30.1975 | + | 30.1975i | 0.0967909 | + | 0.0967909i | ||||
\(47\) | −82.5643 | + | 82.5643i | −0.256239 | + | 0.256239i | −0.823523 | − | 0.567283i | \(-0.807994\pi\) |
0.567283 | + | 0.823523i | \(0.307994\pi\) | |||||||
\(48\) | −517.463 | + | 379.436i | −1.55603 | + | 1.14098i | ||||
\(49\) | − | 281.931i | − | 0.821956i | ||||||
\(50\) | −407.653 | + | 407.653i | −1.15302 | + | 1.15302i | ||||
\(51\) | 235.256 | − | 172.504i | 0.645930 | − | 0.473636i | ||||
\(52\) | −849.037 | + | 109.887i | −2.26424 | + | 0.293050i | ||||
\(53\) | − | 31.7229i | − | 0.0822166i | −0.999155 | − | 0.0411083i | \(-0.986911\pi\) | ||
0.999155 | − | 0.0411083i | \(-0.0130889\pi\) | |||||||
\(54\) | 317.971 | − | 644.878i | 0.801302 | − | 1.62513i | ||||
\(55\) | 558.338 | 1.36884 | ||||||||
\(56\) | 411.108 | 0.981012 | ||||||||
\(57\) | 80.9771 | − | 526.187i | 0.188170 | − | 1.22272i | ||||
\(58\) | −456.360 | + | 456.360i | −1.03315 | + | 1.03315i | ||||
\(59\) | −150.550 | + | 150.550i | −0.332203 | + | 0.332203i | −0.853423 | − | 0.521219i | \(-0.825477\pi\) |
0.521219 | + | 0.853423i | \(0.325477\pi\) | |||||||
\(60\) | 222.466 | − | 1445.58i | 0.478671 | − | 3.11039i | ||||
\(61\) | 383.329 | 0.804595 | 0.402297 | − | 0.915509i | \(-0.368212\pi\) | ||||
0.402297 | + | 0.915509i | \(0.368212\pi\) | |||||||
\(62\) | −651.023 | −1.33355 | ||||||||
\(63\) | −187.152 | + | 97.4346i | −0.374268 | + | 0.194851i | ||||
\(64\) | − | 98.6558i | − | 0.192687i | ||||||
\(65\) | 440.983 | − | 572.102i | 0.841496 | − | 1.09170i | ||||
\(66\) | −778.059 | + | 570.520i | −1.45110 | + | 1.06403i | ||||
\(67\) | 227.782 | − | 227.782i | 0.415343 | − | 0.415343i | −0.468252 | − | 0.883595i | \(-0.655116\pi\) |
0.883595 | + | 0.468252i | \(0.155116\pi\) | |||||||
\(68\) | 1025.44i | 1.82872i | ||||||||
\(69\) | 34.9179 | − | 25.6039i | 0.0609220 | − | 0.0446718i | ||||
\(70\) | −436.423 | + | 436.423i | −0.745178 | + | 0.745178i | ||||
\(71\) | −298.396 | − | 298.396i | −0.498776 | − | 0.498776i | 0.412281 | − | 0.911057i | \(-0.364732\pi\) |
−0.911057 | + | 0.412281i | \(0.864732\pi\) | |||||||
\(72\) | 655.917 | + | 1259.88i | 1.07362 | + | 2.06220i | ||||
\(73\) | −560.842 | − | 560.842i | −0.899200 | − | 0.899200i | 0.0961656 | − | 0.995365i | \(-0.469342\pi\) |
−0.995365 | + | 0.0961656i | \(0.969342\pi\) | |||||||
\(74\) | − | 1991.13i | − | 3.12790i | ||||||
\(75\) | 345.642 | + | 471.376i | 0.532150 | + | 0.725731i | ||||
\(76\) | 1323.26 | + | 1323.26i | 1.99721 | + | 1.99721i | ||||
\(77\) | 283.129 | 0.419033 | ||||||||
\(78\) | −29.9369 | + | 1247.84i | −0.0434576 | + | 1.81142i | ||||
\(79\) | 805.731 | 1.14749 | 0.573746 | − | 0.819034i | \(-0.305490\pi\) | ||||
0.573746 | + | 0.819034i | \(0.305490\pi\) | |||||||
\(80\) | 1345.67 | + | 1345.67i | 1.88063 | + | 1.88063i | ||||
\(81\) | −597.195 | − | 418.089i | −0.819198 | − | 0.573511i | ||||
\(82\) | 321.003i | 0.432304i | ||||||||
\(83\) | 828.116 | + | 828.116i | 1.09515 | + | 1.09515i | 0.994969 | + | 0.100182i | \(0.0319425\pi\) |
0.100182 | + | 0.994969i | \(0.468058\pi\) | |||||||
\(84\) | 112.811 | − | 733.041i | 0.146532 | − | 0.952159i | ||||
\(85\) | −611.786 | − | 611.786i | −0.780676 | − | 0.780676i | ||||
\(86\) | −363.372 | + | 363.372i | −0.455621 | + | 0.455621i | ||||
\(87\) | 386.939 | + | 527.696i | 0.476830 | + | 0.650287i | ||||
\(88\) | − | 1905.99i | − | 2.30885i | ||||||
\(89\) | 373.439 | − | 373.439i | 0.444769 | − | 0.444769i | −0.448842 | − | 0.893611i | \(-0.648163\pi\) |
0.893611 | + | 0.448842i | \(0.148163\pi\) | |||||||
\(90\) | −2033.76 | − | 641.154i | −2.38197 | − | 0.750928i | ||||
\(91\) | 223.619 | − | 290.109i | 0.257601 | − | 0.334194i | ||||
\(92\) | 152.201i | 0.172479i | ||||||||
\(93\) | −100.399 | + | 652.389i | −0.111945 | + | 0.727415i | ||||
\(94\) | −598.406 | −0.656605 | ||||||||
\(95\) | −1578.94 | −1.70521 | ||||||||
\(96\) | −1088.85 | − | 167.568i | −1.15761 | − | 0.178149i | ||||
\(97\) | 254.589 | − | 254.589i | 0.266491 | − | 0.266491i | −0.561194 | − | 0.827685i | \(-0.689658\pi\) |
0.827685 | + | 0.561194i | \(0.189658\pi\) | |||||||
\(98\) | 1021.68 | − | 1021.68i | 1.05312 | − | 1.05312i | ||||
\(99\) | 451.728 | + | 867.676i | 0.458589 | + | 0.880856i | ||||
\(100\) | −2054.64 | −2.05464 | ||||||||
\(101\) | −95.1765 | −0.0937665 | −0.0468833 | − | 0.998900i | \(-0.514929\pi\) | ||||
−0.0468833 | + | 0.998900i | \(0.514929\pi\) | |||||||
\(102\) | 1477.67 | + | 227.405i | 1.43443 | + | 0.220750i | ||||
\(103\) | 304.152i | 0.290961i | 0.989361 | + | 0.145481i | \(0.0464728\pi\) | ||||
−0.989361 | + | 0.145481i | \(0.953527\pi\) | |||||||
\(104\) | −1952.97 | − | 1505.38i | −1.84139 | − | 1.41937i | ||||
\(105\) | 370.035 | + | 504.643i | 0.343921 | + | 0.469029i | ||||
\(106\) | 114.960 | − | 114.960i | 0.105339 | − | 0.105339i | ||||
\(107\) | 722.721i | 0.652973i | 0.945202 | + | 0.326486i | \(0.105865\pi\) | ||||
−0.945202 | + | 0.326486i | \(0.894135\pi\) | |||||||
\(108\) | 2426.46 | − | 823.836i | 2.16191 | − | 0.734015i | ||||
\(109\) | −1280.96 | + | 1280.96i | −1.12563 | + | 1.12563i | −0.134755 | + | 0.990879i | \(0.543025\pi\) |
−0.990879 | + | 0.134755i | \(0.956975\pi\) | |||||||
\(110\) | 2023.35 | + | 2023.35i | 1.75381 | + | 1.75381i | ||||
\(111\) | −1995.31 | − | 307.067i | −1.70619 | − | 0.262572i | ||||
\(112\) | 682.377 | + | 682.377i | 0.575702 | + | 0.575702i | ||||
\(113\) | − | 2249.45i | − | 1.87266i | −0.351119 | − | 0.936331i | \(-0.614199\pi\) | ||
0.351119 | − | 0.936331i | \(-0.385801\pi\) | |||||||
\(114\) | 2200.29 | − | 1613.39i | 1.80768 | − | 1.32550i | ||||
\(115\) | −90.8043 | − | 90.8043i | −0.0736308 | − | 0.0736308i | ||||
\(116\) | −2300.13 | −1.84105 | ||||||||
\(117\) | 1245.85 | + | 222.439i | 0.984432 | + | 0.175765i | ||||
\(118\) | −1091.15 | −0.851260 | ||||||||
\(119\) | −310.232 | − | 310.232i | −0.238982 | − | 0.238982i | ||||
\(120\) | 3397.19 | − | 2491.03i | 2.58433 | − | 1.89499i | ||||
\(121\) | 18.3536i | 0.0137893i | ||||||||
\(122\) | 1389.14 | + | 1389.14i | 1.03087 | + | 1.03087i | ||||
\(123\) | 321.677 | + | 49.5042i | 0.235810 | + | 0.0362898i | ||||
\(124\) | −1640.63 | − | 1640.63i | −1.18817 | − | 1.18817i | ||||
\(125\) | −136.312 | + | 136.312i | −0.0975369 | + | 0.0975369i | ||||
\(126\) | −1031.31 | − | 325.124i | −0.729175 | − | 0.229876i | ||||
\(127\) | 1417.42i | 0.990357i | 0.868791 | + | 0.495179i | \(0.164897\pi\) | ||||
−0.868791 | + | 0.495179i | \(0.835103\pi\) | |||||||
\(128\) | −841.829 | + | 841.829i | −0.581312 | + | 0.581312i | ||||
\(129\) | 308.096 | + | 420.173i | 0.210282 | + | 0.286776i | ||||
\(130\) | 3671.30 | − | 475.159i | 2.47688 | − | 0.320571i | ||||
\(131\) | 459.124i | 0.306213i | 0.988210 | + | 0.153106i | \(0.0489277\pi\) | ||||
−0.988210 | + | 0.153106i | \(0.951072\pi\) | |||||||
\(132\) | −3398.54 | − | 523.015i | −2.24094 | − | 0.344868i | ||||
\(133\) | −800.666 | −0.522004 | ||||||||
\(134\) | 1650.91 | 1.06430 | ||||||||
\(135\) | −956.141 | + | 1939.16i | −0.609567 | + | 1.23627i | ||||
\(136\) | −2088.44 | + | 2088.44i | −1.31678 | + | 1.31678i | ||||
\(137\) | −700.270 | + | 700.270i | −0.436702 | + | 0.436702i | −0.890900 | − | 0.454199i | \(-0.849926\pi\) |
0.454199 | + | 0.890900i | \(0.349926\pi\) | |||||||
\(138\) | 219.324 | + | 33.7526i | 0.135290 | + | 0.0208204i | ||||
\(139\) | 1007.03 | 0.614501 | 0.307250 | − | 0.951629i | \(-0.400591\pi\) | ||||
0.307250 | + | 0.951629i | \(0.400591\pi\) | |||||||
\(140\) | −2199.65 | −1.32789 | ||||||||
\(141\) | −92.2845 | + | 599.662i | −0.0551188 | + | 0.358161i | ||||
\(142\) | − | 2162.70i | − | 1.27810i | ||||||
\(143\) | −1345.01 | − | 1036.75i | −0.786539 | − | 0.606273i | ||||
\(144\) | −1002.49 | + | 3179.93i | −0.580144 | + | 1.84024i | ||||
\(145\) | 1372.28 | − | 1372.28i | 0.785942 | − | 0.785942i | ||||
\(146\) | − | 4064.84i | − | 2.30417i | ||||||
\(147\) | −866.267 | − | 1181.39i | −0.486044 | − | 0.662853i | ||||
\(148\) | 5017.83 | − | 5017.83i | 2.78691 | − | 2.78691i | ||||
\(149\) | −762.942 | − | 762.942i | −0.419481 | − | 0.419481i | 0.465544 | − | 0.885025i | \(-0.345859\pi\) |
−0.885025 | + | 0.465544i | \(0.845859\pi\) | |||||||
\(150\) | −455.646 | + | 2960.77i | −0.248022 | + | 1.61164i | ||||
\(151\) | 263.100 | + | 263.100i | 0.141793 | + | 0.141793i | 0.774440 | − | 0.632647i | \(-0.218032\pi\) |
−0.632647 | + | 0.774440i | \(0.718032\pi\) | |||||||
\(152\) | 5389.98i | 2.87622i | ||||||||
\(153\) | 455.765 | − | 1445.70i | 0.240826 | − | 0.763911i | ||||
\(154\) | 1026.02 | + | 1026.02i | 0.536879 | + | 0.536879i | ||||
\(155\) | 1957.63 | 1.01446 | ||||||||
\(156\) | −3220.12 | + | 3069.23i | −1.65267 | + | 1.57523i | ||||
\(157\) | −1734.01 | −0.881459 | −0.440729 | − | 0.897640i | \(-0.645280\pi\) | ||||
−0.440729 | + | 0.897640i | \(0.645280\pi\) | |||||||
\(158\) | 2919.87 | + | 2919.87i | 1.47020 | + | 1.47020i | ||||
\(159\) | −97.4725 | − | 132.930i | −0.0486168 | − | 0.0663021i | ||||
\(160\) | 3267.33i | 1.61441i | ||||||||
\(161\) | −46.0461 | − | 46.0461i | −0.0225400 | − | 0.0225400i | ||||
\(162\) | −649.059 | − | 3679.27i | −0.314783 | − | 1.78439i | ||||
\(163\) | 1767.27 | + | 1767.27i | 0.849221 | + | 0.849221i | 0.990036 | − | 0.140815i | \(-0.0449723\pi\) |
−0.140815 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(164\) | −808.956 | + | 808.956i | −0.385176 | + | 0.385176i | ||||
\(165\) | 2339.63 | − | 1715.56i | 1.10388 | − | 0.809432i | ||||
\(166\) | 6001.98i | 2.80629i | ||||||||
\(167\) | 2188.39 | − | 2188.39i | 1.01403 | − | 1.01403i | 0.0141267 | − | 0.999900i | \(-0.495503\pi\) |
0.999900 | − | 0.0141267i | \(-0.00449683\pi\) | |||||||
\(168\) | 1722.69 | − | 1263.18i | 0.791120 | − | 0.580098i | ||||
\(169\) | −2124.61 | + | 559.326i | −0.967050 | + | 0.254586i | ||||
\(170\) | − | 4434.07i | − | 2.00046i | ||||||
\(171\) | −1277.45 | − | 2453.72i | −0.571281 | − | 1.09731i | ||||
\(172\) | −1831.46 | −0.811903 | ||||||||
\(173\) | −1215.23 | −0.534060 | −0.267030 | − | 0.963688i | \(-0.586042\pi\) | ||||
−0.267030 | + | 0.963688i | \(0.586042\pi\) | |||||||
\(174\) | −510.086 | + | 3314.53i | −0.222239 | + | 1.44410i | ||||
\(175\) | 621.603 | − | 621.603i | 0.268507 | − | 0.268507i | ||||
\(176\) | 3163.65 | − | 3163.65i | 1.35494 | − | 1.35494i | ||||
\(177\) | −168.274 | + | 1093.44i | −0.0714592 | + | 0.464340i | ||||
\(178\) | 2706.59 | 1.13971 | ||||||||
\(179\) | 1092.00 | 0.455978 | 0.227989 | − | 0.973664i | \(-0.426785\pi\) | ||||
0.227989 | + | 0.973664i | \(0.426785\pi\) | |||||||
\(180\) | −3509.50 | − | 6741.03i | −1.45324 | − | 2.79137i | ||||
\(181\) | − | 94.1651i | − | 0.0386698i | −0.999813 | − | 0.0193349i | \(-0.993845\pi\) | ||
0.999813 | − | 0.0193349i | \(-0.00615488\pi\) | |||||||
\(182\) | 1861.69 | − | 240.949i | 0.758227 | − | 0.0981339i | ||||
\(183\) | 1606.28 | − | 1177.82i | 0.648851 | − | 0.475778i | ||||
\(184\) | −309.977 | + | 309.977i | −0.124194 | + | 0.124194i | ||||
\(185\) | 5987.36i | 2.37946i | ||||||||
\(186\) | −2728.01 | + | 2000.34i | −1.07542 | + | 0.788561i | ||||
\(187\) | −1438.30 | + | 1438.30i | −0.562454 | + | 0.562454i | ||||
\(188\) | −1508.03 | − | 1508.03i | −0.585025 | − | 0.585025i | ||||
\(189\) | −484.852 | + | 983.331i | −0.186602 | + | 0.378449i | ||||
\(190\) | −5721.87 | − | 5721.87i | −2.18478 | − | 2.18478i | ||||
\(191\) | 1272.23i | 0.481966i | 0.970529 | + | 0.240983i | \(0.0774699\pi\) | ||||
−0.970529 | + | 0.240983i | \(0.922530\pi\) | |||||||
\(192\) | −303.132 | − | 413.402i | −0.113941 | − | 0.155389i | ||||
\(193\) | 638.280 | + | 638.280i | 0.238054 | + | 0.238054i | 0.816044 | − | 0.577990i | \(-0.196163\pi\) |
−0.577990 | + | 0.816044i | \(0.696163\pi\) | |||||||
\(194\) | 1845.20 | 0.682875 | ||||||||
\(195\) | 90.0207 | − | 3752.28i | 0.0330591 | − | 1.37798i | ||||
\(196\) | 5149.46 | 1.87663 | ||||||||
\(197\) | −2521.54 | − | 2521.54i | −0.911940 | − | 0.911940i | 0.0844843 | − | 0.996425i | \(-0.473076\pi\) |
−0.996425 | + | 0.0844843i | \(0.973076\pi\) | |||||||
\(198\) | −1507.34 | + | 4781.36i | −0.541022 | + | 1.71614i | ||||
\(199\) | − | 2672.92i | − | 0.952154i | −0.879404 | − | 0.476077i | \(-0.842058\pi\) | ||
0.879404 | − | 0.476077i | \(-0.157942\pi\) | |||||||
\(200\) | −4184.55 | − | 4184.55i | −1.47946 | − | 1.47946i | ||||
\(201\) | 254.598 | − | 1654.37i | 0.0893432 | − | 0.580550i | ||||
\(202\) | −344.908 | − | 344.908i | −0.120137 | − | 0.120137i | ||||
\(203\) | 695.872 | − | 695.872i | 0.240594 | − | 0.240594i | ||||
\(204\) | 3150.78 | + | 4296.95i | 1.08137 | + | 1.47474i | ||||
\(205\) | − | 965.261i | − | 0.328862i | ||||||
\(206\) | −1102.21 | + | 1102.21i | −0.372789 | + | 0.372789i | ||||
\(207\) | 67.6469 | − | 214.579i | 0.0227139 | − | 0.0720495i | ||||
\(208\) | −742.945 | − | 5740.33i | −0.247663 | − | 1.91356i | ||||
\(209\) | 3712.06i | 1.22856i | ||||||||
\(210\) | −487.802 | + | 3169.72i | −0.160293 | + | 1.04158i | ||||
\(211\) | −1686.56 | −0.550272 | −0.275136 | − | 0.961405i | \(-0.588723\pi\) | ||||
−0.275136 | + | 0.961405i | \(0.588723\pi\) | |||||||
\(212\) | 579.418 | 0.187710 | ||||||||
\(213\) | −2167.24 | − | 333.526i | −0.697169 | − | 0.107290i | ||||
\(214\) | −2619.05 | + | 2619.05i | −0.836611 | + | 0.836611i | ||||
\(215\) | 1092.66 | − | 1092.66i | 0.346600 | − | 0.346600i | ||||
\(216\) | 6619.66 | + | 3263.96i | 2.08523 | + | 1.02817i | ||||
\(217\) | 992.700 | 0.310548 | ||||||||
\(218\) | −9284.12 | −2.88440 | ||||||||
\(219\) | −4073.38 | − | 626.869i | −1.25686 | − | 0.193424i | ||||
\(220\) | 10198.0i | 3.12523i | ||||||||
\(221\) | 337.768 | + | 2609.75i | 0.102809 | + | 0.794347i | ||||
\(222\) | −6117.99 | − | 8343.54i | −1.84961 | − | 2.52244i | ||||
\(223\) | −1855.31 | + | 1855.31i | −0.557132 | + | 0.557132i | −0.928490 | − | 0.371358i | \(-0.878892\pi\) |
0.371358 | + | 0.928490i | \(0.378892\pi\) | |||||||
\(224\) | 1656.84i | 0.494206i | ||||||||
\(225\) | 2896.72 | + | 913.204i | 0.858287 | + | 0.270579i | ||||
\(226\) | 8151.74 | − | 8151.74i | 2.39932 | − | 2.39932i | ||||
\(227\) | 4585.45 | + | 4585.45i | 1.34074 | + | 1.34074i | 0.895327 | + | 0.445410i | \(0.146942\pi\) |
0.445410 | + | 0.895327i | \(0.353058\pi\) | |||||||
\(228\) | 9610.79 | + | 1479.04i | 2.79162 | + | 0.429614i | ||||
\(229\) | 2313.70 | + | 2313.70i | 0.667657 | + | 0.667657i | 0.957173 | − | 0.289516i | \(-0.0934945\pi\) |
−0.289516 | + | 0.957173i | \(0.593494\pi\) | |||||||
\(230\) | − | 658.127i | − | 0.188677i | ||||||
\(231\) | 1186.41 | − | 869.947i | 0.337922 | − | 0.247785i | ||||
\(232\) | −4684.52 | − | 4684.52i | −1.32566 | − | 1.32566i | ||||
\(233\) | 4431.01 | 1.24586 | 0.622929 | − | 0.782278i | \(-0.285942\pi\) | ||||
0.622929 | + | 0.782278i | \(0.285942\pi\) | |||||||
\(234\) | 3708.70 | + | 5320.89i | 1.03609 | + | 1.48648i | ||||
\(235\) | 1799.41 | 0.499493 | ||||||||
\(236\) | −2749.80 | − | 2749.80i | −0.758460 | − | 0.758460i | ||||
\(237\) | 3376.29 | − | 2475.70i | 0.925374 | − | 0.678541i | ||||
\(238\) | − | 2248.48i | − | 0.612384i | ||||||
\(239\) | 599.904 | + | 599.904i | 0.162362 | + | 0.162362i | 0.783612 | − | 0.621250i | \(-0.213375\pi\) |
−0.621250 | + | 0.783612i | \(0.713375\pi\) | |||||||
\(240\) | 9773.54 | + | 1504.09i | 2.62866 | + | 0.404536i | ||||
\(241\) | −3944.84 | − | 3944.84i | −1.05440 | − | 1.05440i | −0.998433 | − | 0.0559637i | \(-0.982177\pi\) |
−0.0559637 | − | 0.998433i | \(-0.517823\pi\) | |||||||
\(242\) | −66.5110 | + | 66.5110i | −0.0176673 | + | 0.0176673i | ||||
\(243\) | −3787.09 | + | 83.0147i | −0.999760 | + | 0.0219152i | ||||
\(244\) | 7001.49i | 1.83699i | ||||||||
\(245\) | −3072.21 | + | 3072.21i | −0.801129 | + | 0.801129i | ||||
\(246\) | 986.321 | + | 1345.12i | 0.255632 | + | 0.348624i | ||||
\(247\) | 3803.57 | + | 2931.84i | 0.979819 | + | 0.755256i | ||||
\(248\) | − | 6682.73i | − | 1.71110i | ||||||
\(249\) | 6014.58 | + | 925.609i | 1.53076 | + | 0.235575i | ||||
\(250\) | −987.956 | −0.249935 | ||||||||
\(251\) | −7257.21 | −1.82498 | −0.912492 | − | 0.409095i | \(-0.865845\pi\) | ||||
−0.912492 | + | 0.409095i | \(0.865845\pi\) | |||||||
\(252\) | −1779.64 | − | 3418.32i | −0.444868 | − | 0.854500i | ||||
\(253\) | −213.480 | + | 213.480i | −0.0530489 | + | 0.0530489i | ||||
\(254\) | −5136.54 | + | 5136.54i | −1.26888 | + | 1.26888i | ||||
\(255\) | −4443.38 | − | 683.810i | −1.09120 | − | 0.167929i | ||||
\(256\) | −6890.62 | −1.68228 | ||||||||
\(257\) | 5812.08 | 1.41069 | 0.705346 | − | 0.708863i | \(-0.250792\pi\) | ||||
0.705346 | + | 0.708863i | \(0.250792\pi\) | |||||||
\(258\) | −406.151 | + | 2639.16i | −0.0980072 | + | 0.636848i | ||||
\(259\) | 3036.14i | 0.728404i | ||||||||
\(260\) | 10449.4 | + | 8054.55i | 2.49249 | + | 1.92124i | ||||
\(261\) | 3242.82 | + | 1022.31i | 0.769063 | + | 0.242451i | ||||
\(262\) | −1663.81 | + | 1663.81i | −0.392330 | + | 0.392330i | ||||
\(263\) | − | 4064.06i | − | 0.952854i | −0.879214 | − | 0.476427i | \(-0.841932\pi\) | ||
0.879214 | − | 0.476427i | \(-0.158068\pi\) | |||||||
\(264\) | −5856.37 | − | 7986.75i | −1.36528 | − | 1.86193i | ||||
\(265\) | −345.686 | + | 345.686i | −0.0801333 | + | 0.0801333i | ||||
\(266\) | −2901.51 | − | 2901.51i | −0.668809 | − | 0.668809i | ||||
\(267\) | 417.403 | − | 2712.27i | 0.0956728 | − | 0.621679i | ||||
\(268\) | 4160.43 | + | 4160.43i | 0.948279 | + | 0.948279i | ||||
\(269\) | − | 6370.89i | − | 1.44401i | −0.691885 | − | 0.722007i | \(-0.743220\pi\) | ||
0.691885 | − | 0.722007i | \(-0.256780\pi\) | |||||||
\(270\) | −10492.2 | + | 3562.33i | −2.36494 | + | 0.802949i | ||||
\(271\) | −4460.06 | − | 4460.06i | −0.999739 | − | 0.999739i | 0.000260702 | − | 1.00000i | \(-0.499917\pi\) |
−1.00000 | 0.000260702i | \(0.999917\pi\) | ||||||||
\(272\) | −6932.98 | −1.54549 | ||||||||
\(273\) | 45.6488 | − | 1902.75i | 0.0101201 | − | 0.421831i | ||||
\(274\) | −5075.39 | −1.11903 | ||||||||
\(275\) | −2881.88 | − | 2881.88i | −0.631942 | − | 0.631942i | ||||
\(276\) | 467.655 | + | 637.774i | 0.101991 | + | 0.139092i | ||||
\(277\) | 7121.99i | 1.54483i | 0.635116 | + | 0.772417i | \(0.280952\pi\) | ||||
−0.635116 | + | 0.772417i | \(0.719048\pi\) | |||||||
\(278\) | 3649.37 | + | 3649.37i | 0.787319 | + | 0.787319i | ||||
\(279\) | 1583.84 | + | 3042.22i | 0.339863 | + | 0.652807i | ||||
\(280\) | −4479.86 | − | 4479.86i | −0.956154 | − | 0.956154i | ||||
\(281\) | −691.650 | + | 691.650i | −0.146834 | + | 0.146834i | −0.776702 | − | 0.629868i | \(-0.783109\pi\) |
0.629868 | + | 0.776702i | \(0.283109\pi\) | |||||||
\(282\) | −2507.53 | + | 1838.67i | −0.529508 | + | 0.388267i | ||||
\(283\) | − | 8723.01i | − | 1.83226i | −0.400884 | − | 0.916129i | \(-0.631297\pi\) | ||
0.400884 | − | 0.916129i | \(-0.368703\pi\) | |||||||
\(284\) | 5450.20 | − | 5450.20i | 1.13877 | − | 1.13877i | ||||
\(285\) | −6616.29 | + | 4851.47i | −1.37514 | + | 1.00834i | ||||
\(286\) | −1117.09 | − | 8631.18i | −0.230962 | − | 1.78452i | ||||
\(287\) | − | 489.476i | − | 0.100672i | ||||||
\(288\) | −5077.54 | + | 2643.46i | −1.03888 | + | 0.540858i | ||||
\(289\) | −1761.03 | −0.358443 | ||||||||
\(290\) | 9945.94 | 2.01395 | ||||||||
\(291\) | 284.562 | − | 1849.07i | 0.0573241 | − | 0.372490i | ||||
\(292\) | 10243.8 | − | 10243.8i | 2.05298 | − | 2.05298i | ||||
\(293\) | 2908.77 | − | 2908.77i | 0.579974 | − | 0.579974i | −0.354922 | − | 0.934896i | \(-0.615493\pi\) |
0.934896 | + | 0.354922i | \(0.115493\pi\) | |||||||
\(294\) | 1141.96 | − | 7420.45i | 0.226533 | − | 1.47201i | ||||
\(295\) | 3281.11 | 0.647571 | ||||||||
\(296\) | 20438.9 | 4.01347 | ||||||||
\(297\) | 4558.93 | + | 2247.88i | 0.890694 | + | 0.439175i | ||||
\(298\) | − | 5529.61i | − | 1.07491i | ||||||
\(299\) | 50.1332 | + | 387.352i | 0.00969658 | + | 0.0749202i | ||||
\(300\) | −8609.67 | + | 6313.14i | −1.65693 | + | 1.21496i | ||||
\(301\) | 554.081 | − | 554.081i | 0.106102 | − | 0.106102i | ||||
\(302\) | 1906.89i | 0.363341i | ||||||||
\(303\) | −398.823 | + | 292.441i | −0.0756164 | + | 0.0554466i | ||||
\(304\) | −8946.54 | + | 8946.54i | −1.68789 | + | 1.68789i | ||||
\(305\) | −4177.15 | − | 4177.15i | −0.784207 | − | 0.784207i | ||||
\(306\) | 6890.69 | − | 3587.42i | 1.28730 | − | 0.670193i | ||||
\(307\) | 5956.29 | + | 5956.29i | 1.10731 | + | 1.10731i | 0.993503 | + | 0.113805i | \(0.0363039\pi\) |
0.113805 | + | 0.993503i | \(0.463696\pi\) | |||||||
\(308\) | 5171.34i | 0.956703i | ||||||||
\(309\) | 934.544 | + | 1274.50i | 0.172053 | + | 0.234641i | ||||
\(310\) | 7094.22 | + | 7094.22i | 1.29976 | + | 1.29976i | ||||
\(311\) | −7339.31 | −1.33818 | −0.669090 | − | 0.743181i | \(-0.733316\pi\) | ||||
−0.669090 | + | 0.743181i | \(0.733316\pi\) | |||||||
\(312\) | −12809.1 | − | 307.302i | −2.32427 | − | 0.0557613i | ||||
\(313\) | 6450.33 | 1.16484 | 0.582419 | − | 0.812889i | \(-0.302106\pi\) | ||||
0.582419 | + | 0.812889i | \(0.302106\pi\) | |||||||
\(314\) | −6283.84 | − | 6283.84i | −1.12936 | − | 1.12936i | ||||
\(315\) | 3101.15 | + | 977.652i | 0.554698 | + | 0.174871i | ||||
\(316\) | 14716.6i | 2.61986i | ||||||||
\(317\) | −2715.05 | − | 2715.05i | −0.481049 | − | 0.481049i | 0.424418 | − | 0.905467i | \(-0.360479\pi\) |
−0.905467 | + | 0.424418i | \(0.860479\pi\) | |||||||
\(318\) | 128.494 | − | 834.950i | 0.0226591 | − | 0.147238i | ||||
\(319\) | −3226.21 | − | 3226.21i | −0.566248 | − | 0.566248i | ||||
\(320\) | −1075.06 | + | 1075.06i | −0.187805 | + | 0.187805i | ||||
\(321\) | 2220.65 | + | 3028.45i | 0.386120 | + | 0.526579i | ||||
\(322\) | − | 333.731i | − | 0.0577581i | ||||||
\(323\) | 4067.40 | − | 4067.40i | 0.700669 | − | 0.700669i | ||||
\(324\) | 7636.39 | − | 10907.8i | 1.30939 | − | 1.87033i | ||||
\(325\) | −5229.08 | + | 676.776i | −0.892483 | + | 0.115510i | ||||
\(326\) | 12808.7i | 2.17610i | ||||||||
\(327\) | −1431.77 | + | 9303.60i | −0.242132 | + | 1.57337i | ||||
\(328\) | −3295.09 | −0.554698 | ||||||||
\(329\) | 912.468 | 0.152906 | ||||||||
\(330\) | 14695.5 | + | 2261.55i | 2.45140 | + | 0.377256i | ||||
\(331\) | −3143.32 | + | 3143.32i | −0.521972 | + | 0.521972i | −0.918167 | − | 0.396195i | \(-0.870331\pi\) |
0.396195 | + | 0.918167i | \(0.370331\pi\) | |||||||
\(332\) | −15125.5 | + | 15125.5i | −2.50036 | + | 2.50036i | ||||
\(333\) | −9304.55 | + | 4844.12i | −1.53119 | + | 0.797165i | ||||
\(334\) | 15860.9 | 2.59841 | ||||||||
\(335\) | −4964.30 | −0.809638 | ||||||||
\(336\) | 4956.08 | + | 762.713i | 0.804692 | + | 0.123837i | ||||
\(337\) | − | 4789.10i | − | 0.774121i | −0.922054 | − | 0.387060i | \(-0.873490\pi\) | ||
0.922054 | − | 0.387060i | \(-0.126510\pi\) | |||||||
\(338\) | −9726.25 | − | 5672.39i | −1.56520 | − | 0.912833i | ||||
\(339\) | −6911.71 | − | 9425.99i | −1.10735 | − | 1.51018i | ||||
\(340\) | 11174.2 | − | 11174.2i | 1.78238 | − | 1.78238i | ||||
\(341\) | − | 4602.37i | − | 0.730887i | ||||||
\(342\) | 4262.65 | − | 13521.3i | 0.673970 | − | 2.13786i | ||||
\(343\) | −3453.24 | + | 3453.24i | −0.543608 | + | 0.543608i | ||||
\(344\) | −3730.00 | − | 3730.00i | −0.584617 | − | 0.584617i | ||||
\(345\) | −659.509 | − | 101.495i | −0.102918 | − | 0.0158385i | ||||
\(346\) | −4403.85 | − | 4403.85i | −0.684256 | − | 0.684256i | ||||
\(347\) | 5964.36i | 0.922719i | 0.887213 | + | 0.461359i | \(0.152638\pi\) | ||||
−0.887213 | + | 0.461359i | \(0.847362\pi\) | |||||||
\(348\) | −9638.35 | + | 7067.43i | −1.48468 | + | 1.08866i | ||||
\(349\) | −1366.88 | − | 1366.88i | −0.209649 | − | 0.209649i | 0.594469 | − | 0.804118i | \(-0.297362\pi\) |
−0.804118 | + | 0.594469i | \(0.797362\pi\) | |||||||
\(350\) | 4505.22 | 0.688041 | ||||||||
\(351\) | 5904.00 | − | 2895.92i | 0.897813 | − | 0.440378i | ||||
\(352\) | 7681.45 | 1.16313 | ||||||||
\(353\) | 881.210 | + | 881.210i | 0.132867 | + | 0.132867i | 0.770413 | − | 0.637546i | \(-0.220050\pi\) |
−0.637546 | + | 0.770413i | \(0.720050\pi\) | |||||||
\(354\) | −4572.31 | + | 3352.70i | −0.686484 | + | 0.503372i | ||||
\(355\) | 6503.27i | 0.972275i | ||||||||
\(356\) | 6820.85 | + | 6820.85i | 1.01546 | + | 1.01546i | ||||
\(357\) | −2253.20 | − | 346.755i | −0.334040 | − | 0.0514067i | ||||
\(358\) | 3957.28 | + | 3957.28i | 0.584215 | + | 0.584215i | ||||
\(359\) | 3468.03 | − | 3468.03i | 0.509849 | − | 0.509849i | −0.404631 | − | 0.914480i | \(-0.632600\pi\) |
0.914480 | + | 0.404631i | \(0.132600\pi\) | |||||||
\(360\) | 6581.42 | − | 20876.5i | 0.963532 | − | 3.05636i | ||||
\(361\) | − | 3638.40i | − | 0.530457i | ||||||
\(362\) | 341.243 | − | 341.243i | 0.0495451 | − | 0.0495451i | ||||
\(363\) | 56.3935 | + | 76.9078i | 0.00815397 | + | 0.0111201i | ||||
\(364\) | 5298.82 | + | 4084.40i | 0.763005 | + | 0.588133i | ||||
\(365\) | 12223.0i | 1.75283i | ||||||||
\(366\) | 10089.3 | + | 1552.68i | 1.44091 | + | 0.221748i | ||||
\(367\) | 11162.8 | 1.58772 | 0.793858 | − | 0.608103i | \(-0.208069\pi\) | ||||
0.793858 | + | 0.608103i | \(0.208069\pi\) | |||||||
\(368\) | −1029.03 | −0.145766 | ||||||||
\(369\) | 1500.05 | − | 780.951i | 0.211624 | − | 0.110175i | ||||
\(370\) | −21697.5 | + | 21697.5i | −3.04864 | + | 3.04864i | ||||
\(371\) | −175.295 | + | 175.295i | −0.0245306 | + | 0.0245306i | ||||
\(372\) | −11915.9 | − | 1833.78i | −1.66078 | − | 0.255584i | ||||
\(373\) | −8300.58 | −1.15225 | −0.576123 | − | 0.817363i | \(-0.695435\pi\) | ||||
−0.576123 | + | 0.817363i | \(0.695435\pi\) | |||||||
\(374\) | −10424.5 | −1.44127 | ||||||||
\(375\) | −152.360 | + | 990.029i | −0.0209809 | + | 0.136333i | ||||
\(376\) | − | 6142.62i | − | 0.842504i | ||||||
\(377\) | −5853.85 | + | 757.637i | −0.799705 | + | 0.103502i | ||||
\(378\) | −5320.51 | + | 1806.43i | −0.723962 | + | 0.245801i | ||||
\(379\) | −1071.43 | + | 1071.43i | −0.145213 | + | 0.145213i | −0.775976 | − | 0.630763i | \(-0.782742\pi\) |
0.630763 | + | 0.775976i | \(0.282742\pi\) | |||||||
\(380\) | − | 28839.2i | − | 3.89321i | ||||||
\(381\) | 4355.18 | + | 5939.47i | 0.585624 | + | 0.798657i | ||||
\(382\) | −4610.42 | + | 4610.42i | −0.617512 | + | 0.617512i | ||||
\(383\) | 8245.75 | + | 8245.75i | 1.10010 | + | 1.10010i | 0.994398 | + | 0.105702i | \(0.0337090\pi\) |
0.105702 | + | 0.994398i | \(0.466291\pi\) | |||||||
\(384\) | −940.936 | + | 6114.18i | −0.125044 | + | 0.812533i | ||||
\(385\) | −3085.27 | − | 3085.27i | −0.408415 | − | 0.408415i | ||||
\(386\) | 4626.10i | 0.610006i | ||||||||
\(387\) | 2582.06 | + | 814.007i | 0.339157 | + | 0.106921i | ||||
\(388\) | 4650.07 | + | 4650.07i | 0.608431 | + | 0.608431i | ||||
\(389\) | −625.277 | −0.0814983 | −0.0407491 | − | 0.999169i | \(-0.512974\pi\) | ||||
−0.0407491 | + | 0.999169i | \(0.512974\pi\) | |||||||
\(390\) | 13924.0 | − | 13271.6i | 1.80787 | − | 1.72316i | ||||
\(391\) | 467.831 | 0.0605095 | ||||||||
\(392\) | 10487.5 | + | 10487.5i | 1.35128 | + | 1.35128i | ||||
\(393\) | 1410.71 | + | 1923.89i | 0.181072 | + | 0.246940i | ||||
\(394\) | − | 18275.5i | − | 2.33682i | ||||||
\(395\) | −8780.08 | − | 8780.08i | −1.11841 | − | 1.11841i | ||||
\(396\) | −15848.1 | + | 8250.79i | −2.01110 | + | 1.04701i | ||||
\(397\) | 7922.36 | + | 7922.36i | 1.00154 | + | 1.00154i | 0.999999 | + | 0.00154180i | \(0.000490772\pi\) |
0.00154180 | + | 0.999999i | \(0.499509\pi\) | |||||||
\(398\) | 9686.35 | − | 9686.35i | 1.21993 | − | 1.21993i | ||||
\(399\) | −3355.07 | + | 2460.14i | −0.420961 | + | 0.308674i | ||||
\(400\) | − | 13891.4i | − | 1.73643i | ||||||
\(401\) | 1157.56 | − | 1157.56i | 0.144154 | − | 0.144154i | −0.631347 | − | 0.775501i | \(-0.717498\pi\) |
0.775501 | + | 0.631347i | \(0.217498\pi\) | |||||||
\(402\) | 6917.88 | − | 5072.61i | 0.858289 | − | 0.629350i | ||||
\(403\) | −4715.83 | − | 3635.02i | −0.582909 | − | 0.449313i | ||||
\(404\) | − | 1738.40i | − | 0.214080i | ||||||
\(405\) | 1951.73 | + | 11063.6i | 0.239462 | + | 1.35742i | ||||
\(406\) | 5043.51 | 0.616515 | ||||||||
\(407\) | 14076.2 | 1.71433 | ||||||||
\(408\) | −2334.31 | + | 15168.3i | −0.283249 | + | 1.84054i | ||||
\(409\) | 8539.04 | − | 8539.04i | 1.03234 | − | 1.03234i | 0.0328837 | − | 0.999459i | \(-0.489531\pi\) |
0.999459 | − | 0.0328837i | \(-0.0104691\pi\) | |||||||
\(410\) | 3497.99 | − | 3497.99i | 0.421349 | − | 0.421349i | ||||
\(411\) | −782.712 | + | 5086.04i | −0.0939375 | + | 0.610403i | ||||
\(412\) | −5555.33 | −0.664300 | ||||||||
\(413\) | 1663.82 | 0.198236 | ||||||||
\(414\) | 1022.75 | − | 532.463i | 0.121414 | − | 0.0632104i | ||||
\(415\) | − | 18048.0i | − | 2.13480i | ||||||
\(416\) | 6066.92 | − | 7870.81i | 0.715036 | − | 0.927640i | ||||
\(417\) | 4219.83 | − | 3094.23i | 0.495553 | − | 0.363370i | ||||
\(418\) | −13452.0 | + | 13452.0i | −1.57407 | + | 1.57407i | ||||
\(419\) | 1105.77i | 0.128927i | 0.997920 | + | 0.0644633i | \(0.0205335\pi\) | ||||
−0.997920 | + | 0.0644633i | \(0.979466\pi\) | |||||||
\(420\) | −9217.28 | + | 6758.67i | −1.07085 | + | 0.785213i | ||||
\(421\) | 343.406 | − | 343.406i | 0.0397544 | − | 0.0397544i | −0.686950 | − | 0.726705i | \(-0.741051\pi\) |
0.726705 | + | 0.686950i | \(0.241051\pi\) | |||||||
\(422\) | −6111.88 | − | 6111.88i | −0.705028 | − | 0.705028i | ||||
\(423\) | 1455.83 | + | 2796.35i | 0.167340 | + | 0.321426i | ||||
\(424\) | 1180.06 | + | 1180.06i | 0.135162 | + | 0.135162i | ||||
\(425\) | 6315.51i | 0.720817i | ||||||||
\(426\) | −6645.16 | − | 9062.47i | −0.755772 | − | 1.03070i | ||||
\(427\) | −2118.20 | − | 2118.20i | −0.240063 | − | 0.240063i | ||||
\(428\) | −13200.5 | −1.49082 | ||||||||
\(429\) | −8821.57 | − | 211.638i | −0.992796 | − | 0.0238181i | ||||
\(430\) | 7919.36 | 0.888152 | ||||||||
\(431\) | −3243.73 | − | 3243.73i | −0.362518 | − | 0.362518i | 0.502221 | − | 0.864739i | \(-0.332516\pi\) |
−0.864739 | + | 0.502221i | \(0.832516\pi\) | |||||||
\(432\) | 5569.95 | + | 16405.3i | 0.620334 | + | 1.82708i | ||||
\(433\) | − | 3401.90i | − | 0.377563i | −0.982019 | − | 0.188782i | \(-0.939546\pi\) | ||
0.982019 | − | 0.188782i | \(-0.0604538\pi\) | |||||||
\(434\) | 3597.42 | + | 3597.42i | 0.397884 | + | 0.397884i | ||||
\(435\) | 1533.84 | − | 9966.82i | 0.169062 | − | 1.09856i | ||||
\(436\) | −23396.8 | − | 23396.8i | −2.56996 | − | 2.56996i | ||||
\(437\) | 603.704 | − | 603.704i | 0.0660848 | − | 0.0660848i | ||||
\(438\) | −12489.7 | − | 17033.1i | −1.36252 | − | 1.85816i | ||||
\(439\) | 5909.73i | 0.642496i | 0.946995 | + | 0.321248i | \(0.104102\pi\) | ||||
−0.946995 | + | 0.321248i | \(0.895898\pi\) | |||||||
\(440\) | −20769.6 | + | 20769.6i | −2.25035 | + | 2.25035i | ||||
\(441\) | −7259.92 | − | 2288.72i | −0.783924 | − | 0.247136i | ||||
\(442\) | −8233.38 | + | 10681.4i | −0.886022 | + | 1.14947i | ||||
\(443\) | 5220.08i | 0.559850i | 0.960022 | + | 0.279925i | \(0.0903096\pi\) | ||||
−0.960022 | + | 0.279925i | \(0.909690\pi\) | |||||||
\(444\) | 5608.57 | − | 36444.3i | 0.599484 | − | 3.89543i | ||||
\(445\) | −8138.75 | −0.866997 | ||||||||
\(446\) | −13446.8 | −1.42763 | ||||||||
\(447\) | −5541.22 | − | 852.761i | −0.586333 | − | 0.0902332i | ||||
\(448\) | −545.153 | + | 545.153i | −0.0574912 | + | 0.0574912i | ||||
\(449\) | 9235.45 | − | 9235.45i | 0.970708 | − | 0.970708i | −0.0288752 | − | 0.999583i | \(-0.509193\pi\) |
0.999583 | + | 0.0288752i | \(0.00919253\pi\) | |||||||
\(450\) | 7188.01 | + | 13806.7i | 0.752991 | + | 1.44634i | ||||
\(451\) | −2269.32 | −0.236936 | ||||||||
\(452\) | 41086.2 | 4.27551 | ||||||||
\(453\) | 1910.89 | + | 294.075i | 0.198193 | + | 0.0305007i | ||||
\(454\) | 33234.2i | 3.43560i | ||||||||
\(455\) | −5598.11 | + | 724.538i | −0.576799 | + | 0.0746524i | ||||
\(456\) | 16561.3 | + | 22585.9i | 1.70078 | + | 2.31948i | ||||
\(457\) | −149.867 | + | 149.867i | −0.0153402 | + | 0.0153402i | −0.714735 | − | 0.699395i | \(-0.753453\pi\) |
0.699395 | + | 0.714735i | \(0.253453\pi\) | |||||||
\(458\) | 16769.1i | 1.71085i | ||||||||
\(459\) | −2532.29 | − | 7458.40i | −0.257510 | − | 0.758449i | ||||
\(460\) | 1658.54 | − | 1658.54i | 0.168108 | − | 0.168108i | ||||
\(461\) | 3767.65 | + | 3767.65i | 0.380644 | + | 0.380644i | 0.871334 | − | 0.490690i | \(-0.163255\pi\) |
−0.490690 | + | 0.871334i | \(0.663255\pi\) | |||||||
\(462\) | 7451.98 | + | 1146.82i | 0.750427 | + | 0.115486i | ||||
\(463\) | 7320.97 | + | 7320.97i | 0.734848 | + | 0.734848i | 0.971576 | − | 0.236728i | \(-0.0760751\pi\) |
−0.236728 | + | 0.971576i | \(0.576075\pi\) | |||||||
\(464\) | − | 15551.2i | − | 1.55592i | ||||||
\(465\) | 8203.16 | − | 6015.06i | 0.818091 | − | 0.599875i | ||||
\(466\) | 16057.4 | + | 16057.4i | 1.59624 | + | 1.59624i | ||||
\(467\) | −1280.61 | −0.126894 | −0.0634468 | − | 0.997985i | \(-0.520209\pi\) | ||||
−0.0634468 | + | 0.997985i | \(0.520209\pi\) | |||||||
\(468\) | −4062.84 | + | 22755.3i | −0.401292 | + | 2.24758i | ||||
\(469\) | −2517.36 | −0.247848 | ||||||||
\(470\) | 6520.85 | + | 6520.85i | 0.639967 | + | 0.639967i | ||||
\(471\) | −7266.10 | + | 5327.95i | −0.710837 | + | 0.521229i | ||||
\(472\) | − | 11200.6i | − | 1.09227i | ||||||
\(473\) | −2568.84 | − | 2568.84i | −0.249715 | − | 0.249715i | ||||
\(474\) | 21206.9 | + | 3263.62i | 2.05499 | + | 0.316251i | ||||
\(475\) | 8149.73 | + | 8149.73i | 0.787232 | + | 0.787232i | ||||
\(476\) | 5666.37 | − | 5666.37i | 0.545626 | − | 0.545626i | ||||
\(477\) | −816.887 | − | 257.527i | −0.0784123 | − | 0.0247199i | ||||
\(478\) | 4347.96i | 0.416048i | ||||||||
\(479\) | 10265.8 | − | 10265.8i | 0.979243 | − | 0.979243i | −0.0205458 | − | 0.999789i | \(-0.506540\pi\) |
0.999789 | + | 0.0205458i | \(0.00654040\pi\) | |||||||
\(480\) | 10039.3 | + | 13691.2i | 0.954640 | + | 1.30191i | ||||
\(481\) | 11117.6 | − | 14423.2i | 1.05388 | − | 1.36724i | ||||
\(482\) | − | 28591.2i | − | 2.70186i | ||||||
\(483\) | −334.432 | − | 51.4671i | −0.0315055 | − | 0.00484851i | ||||
\(484\) | −335.227 | −0.0314826 | ||||||||
\(485\) | −5548.54 | −0.519477 | ||||||||
\(486\) | −14024.8 | − | 13423.1i | −1.30900 | − | 1.25285i | ||||
\(487\) | 11709.3 | − | 11709.3i | 1.08952 | − | 1.08952i | 0.0939453 | − | 0.995577i | \(-0.470052\pi\) |
0.995577 | − | 0.0939453i | \(-0.0299479\pi\) | |||||||
\(488\) | −14259.5 | + | 14259.5i | −1.32274 | + | 1.32274i | ||||
\(489\) | 12835.6 | + | 1975.32i | 1.18701 | + | 0.182673i | ||||
\(490\) | −22266.6 | −2.05287 | ||||||||
\(491\) | −12228.2 | −1.12393 | −0.561966 | − | 0.827161i | \(-0.689955\pi\) | ||||
−0.561966 | + | 0.827161i | \(0.689955\pi\) | |||||||
\(492\) | −904.193 | + | 5875.42i | −0.0828540 | + | 0.538383i | ||||
\(493\) | 7070.09i | 0.645884i | ||||||||
\(494\) | 3159.05 | + | 24408.3i | 0.287717 | + | 2.22304i | ||||
\(495\) | 4532.60 | − | 14377.6i | 0.411566 | − | 1.30550i | ||||
\(496\) | 11092.3 | − | 11092.3i | 1.00415 | − | 1.00415i | ||||
\(497\) | 3297.76i | 0.297635i | ||||||||
\(498\) | 18441.8 | + | 25150.4i | 1.65943 | + | 2.26308i | ||||
\(499\) | 4752.27 | − | 4752.27i | 0.426334 | − | 0.426334i | −0.461043 | − | 0.887378i | \(-0.652525\pi\) |
0.887378 | + | 0.461043i | \(0.152525\pi\) | |||||||
\(500\) | −2489.73 | − | 2489.73i | −0.222689 | − | 0.222689i | ||||
\(501\) | 2446.02 | − | 15894.2i | 0.218124 | − | 1.41736i | ||||
\(502\) | −26299.2 | − | 26299.2i | −2.33823 | − | 2.33823i | ||||
\(503\) | 10187.2i | 0.903032i | 0.892263 | + | 0.451516i | \(0.149117\pi\) | ||||
−0.892263 | + | 0.451516i | \(0.850883\pi\) | |||||||
\(504\) | 3337.39 | − | 10586.3i | 0.294958 | − | 0.935620i | ||||
\(505\) | 1037.14 | + | 1037.14i | 0.0913905 | + | 0.0913905i | ||||
\(506\) | −1547.25 | −0.135936 | ||||||||
\(507\) | −7184.25 | + | 8871.88i | −0.629317 | + | 0.777148i | ||||
\(508\) | −25889.1 | −2.26111 | ||||||||
\(509\) | −4048.48 | − | 4048.48i | −0.352545 | − | 0.352545i | 0.508510 | − | 0.861056i | \(-0.330196\pi\) |
−0.861056 | + | 0.508510i | \(0.830196\pi\) | |||||||
\(510\) | −13624.2 | − | 18580.3i | −1.18292 | − | 1.61323i | ||||
\(511\) | 6198.20i | 0.536580i | ||||||||
\(512\) | −18236.1 | − | 18236.1i | −1.57408 | − | 1.57408i | ||||
\(513\) | −12892.3 | − | 6356.81i | −1.10957 | − | 0.547096i | ||||
\(514\) | 21062.3 | + | 21062.3i | 1.80743 | + | 1.80743i | ||||
\(515\) | 3314.36 | − | 3314.36i | 0.283588 | − | 0.283588i | ||||
\(516\) | −7674.44 | + | 5627.37i | −0.654745 | + | 0.480099i | ||||
\(517\) | − | 4230.40i | − | 0.359870i | ||||||
\(518\) | −11002.6 | + | 11002.6i | −0.933256 | + | 0.933256i | ||||
\(519\) | −5092.25 | + | 3733.95i | −0.430684 | + | 0.315804i | ||||
\(520\) | 4877.49 | + | 37685.8i | 0.411331 | + | 3.17813i | ||||
\(521\) | 8616.63i | 0.724571i | 0.932067 | + | 0.362285i | \(0.118003\pi\) | ||||
−0.932067 | + | 0.362285i | \(0.881997\pi\) | |||||||
\(522\) | 8046.84 | + | 15456.3i | 0.674714 | + | 1.29599i | ||||
\(523\) | 1509.59 | 0.126214 | 0.0631068 | − | 0.998007i | \(-0.479899\pi\) | ||||
0.0631068 | + | 0.998007i | \(0.479899\pi\) | |||||||
\(524\) | −8385.89 | −0.699121 | ||||||||
\(525\) | 694.783 | − | 4514.68i | 0.0577577 | − | 0.375308i | ||||
\(526\) | 14727.6 | − | 14727.6i | 1.22083 | − | 1.22083i | ||||
\(527\) | −5042.94 | + | 5042.94i | −0.416838 | + | 0.416838i | ||||
\(528\) | 3536.10 | − | 22977.5i | 0.291456 | − | 1.89388i | ||||
\(529\) | −12097.6 | −0.994293 | ||||||||
\(530\) | −2505.45 | −0.205339 | ||||||||
\(531\) | 2654.60 | + | 5098.95i | 0.216949 | + | 0.416715i | ||||
\(532\) | − | 14624.1i | − | 1.19180i | ||||||
\(533\) | −1792.34 | + | 2325.26i | −0.145656 | + | 0.188965i | ||||
\(534\) | 11341.6 | − | 8316.32i | 0.919096 | − | 0.673937i | ||||
\(535\) | 7875.52 | − | 7875.52i | 0.636427 | − | 0.636427i | ||||
\(536\) | 16946.5i | 1.36563i | ||||||||
\(537\) | 4575.87 | − | 3355.31i | 0.367716 | − | 0.269632i | ||||
\(538\) | 23087.3 | − | 23087.3i | 1.85012 | − | 1.85012i | ||||
\(539\) | 7222.74 | + | 7222.74i | 0.577190 | + | 0.577190i | ||||
\(540\) | −35418.6 | − | 17463.9i | −2.82255 | − | 1.39171i | ||||
\(541\) | −6622.18 | − | 6622.18i | −0.526266 | − | 0.526266i | 0.393191 | − | 0.919457i | \(-0.371371\pi\) |
−0.919457 | + | 0.393191i | \(0.871371\pi\) | |||||||
\(542\) | − | 32325.4i | − | 2.56180i | ||||||
\(543\) | −289.334 | − | 394.585i | −0.0228665 | − | 0.0311846i | ||||
\(544\) | −8416.77 | − | 8416.77i | −0.663356 | − | 0.663356i | ||||
\(545\) | 27917.4 | 2.19422 | ||||||||
\(546\) | 7060.77 | − | 6729.91i | 0.553430 | − | 0.527498i | ||||
\(547\) | −10463.4 | −0.817884 | −0.408942 | − | 0.912560i | \(-0.634102\pi\) | ||||
−0.408942 | + | 0.912560i | \(0.634102\pi\) | |||||||
\(548\) | −12790.4 | − | 12790.4i | −0.997043 | − | 0.997043i | ||||
\(549\) | 3111.87 | − | 9870.99i | 0.241915 | − | 0.767365i | ||||
\(550\) | − | 20887.2i | − | 1.61933i | ||||||
\(551\) | 9123.47 | + | 9123.47i | 0.705395 | + | 0.705395i | ||||
\(552\) | −346.470 | + | 2251.35i | −0.0267151 | + | 0.173594i | ||||
\(553\) | −4452.31 | − | 4452.31i | −0.342371 | − | 0.342371i | ||||
\(554\) | −25809.2 | + | 25809.2i | −1.97929 | + | 1.97929i | ||||
\(555\) | 18396.9 | + | 25089.1i | 1.40703 | + | 1.91887i | ||||
\(556\) | 18393.5i | 1.40298i | ||||||||
\(557\) | −17108.9 | + | 17108.9i | −1.30149 | + | 1.30149i | −0.374097 | + | 0.927390i | \(0.622047\pi\) |
−0.927390 | + | 0.374097i | \(0.877953\pi\) | |||||||
\(558\) | −5285.02 | + | 16764.3i | −0.400955 | + | 1.27184i | ||||
\(559\) | −4661.07 | + | 603.261i | −0.352669 | + | 0.0456444i | ||||
\(560\) | − | 14871.8i | − | 1.12223i | ||||||
\(561\) | −1607.63 | + | 10446.3i | −0.120988 | + | 0.786176i | ||||
\(562\) | −5012.91 | −0.376257 | ||||||||
\(563\) | 376.567 | 0.0281890 | 0.0140945 | − | 0.999901i | \(-0.495513\pi\) | ||||
0.0140945 | + | 0.999901i | \(0.495513\pi\) | |||||||
\(564\) | −10952.8 | − | 1685.57i | −0.817724 | − | 0.125843i | ||||
\(565\) | −24512.4 | + | 24512.4i | −1.82521 | + | 1.82521i | ||||
\(566\) | 31611.1 | − | 31611.1i | 2.34755 | − | 2.34755i | ||||
\(567\) | 989.705 | + | 5610.26i | 0.0733046 | + | 0.415536i | ||||
\(568\) | 22200.1 | 1.63995 | ||||||||
\(569\) | −12913.5 | −0.951425 | −0.475712 | − | 0.879601i | \(-0.657810\pi\) | ||||
−0.475712 | + | 0.879601i | \(0.657810\pi\) | |||||||
\(570\) | −41557.7 | − | 6395.49i | −3.05379 | − | 0.469961i | ||||
\(571\) | 18982.9i | 1.39126i | 0.718401 | + | 0.695630i | \(0.244875\pi\) | ||||
−0.718401 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(572\) | 18936.1 | − | 24566.5i | 1.38420 | − | 1.79576i | ||||
\(573\) | 3909.09 | + | 5331.10i | 0.284999 | + | 0.388673i | ||||
\(574\) | 1773.80 | − | 1773.80i | 0.128984 | − | 0.128984i | ||||
\(575\) | 937.379i | 0.0679851i | ||||||||
\(576\) | −2540.46 | − | 800.890i | −0.183771 | − | 0.0579348i | ||||
\(577\) | −6271.53 | + | 6271.53i | −0.452491 | + | 0.452491i | −0.896181 | − | 0.443690i | \(-0.853669\pi\) |
0.443690 | + | 0.896181i | \(0.353669\pi\) | |||||||
\(578\) | −6381.76 | − | 6381.76i | −0.459250 | − | 0.459250i | ||||
\(579\) | 4635.81 | + | 713.424i | 0.332742 | + | 0.0512071i | ||||
\(580\) | 25064.6 | + | 25064.6i | 1.79440 | + | 1.79440i | ||||
\(581\) | − | 9152.01i | − | 0.653510i | ||||||
\(582\) | 7732.03 | − | 5669.60i | 0.550693 | − | 0.403802i | ||||
\(583\) | 812.703 | + | 812.703i | 0.0577337 | + | 0.0577337i | ||||
\(584\) | 41725.5 | 2.95653 | ||||||||
\(585\) | −11152.1 | − | 16000.0i | −0.788176 | − | 1.13080i | ||||
\(586\) | 21082.1 | 1.48617 | ||||||||
\(587\) | 1122.24 | + | 1122.24i | 0.0789096 | + | 0.0789096i | 0.745460 | − | 0.666550i | \(-0.232230\pi\) |
−0.666550 | + | 0.745460i | \(0.732230\pi\) | |||||||
\(588\) | 21578.0 | − | 15822.3i | 1.51337 | − | 1.10970i | ||||
\(589\) | 13015.1i | 0.910491i | ||||||||
\(590\) | 11890.3 | + | 11890.3i | 0.829690 | + | 0.829690i | ||||
\(591\) | −18313.9 | − | 2818.40i | −1.27467 | − | 0.196165i | ||||
\(592\) | 33925.5 | + | 33925.5i | 2.35529 | + | 2.35529i | ||||
\(593\) | 19312.7 | − | 19312.7i | 1.33740 | − | 1.33740i | 0.438829 | − | 0.898571i | \(-0.355393\pi\) |
0.898571 | − | 0.438829i | \(-0.144607\pi\) | |||||||
\(594\) | 8374.99 | + | 24667.0i | 0.578502 | + | 1.70387i | ||||
\(595\) | 6761.21i | 0.465853i | ||||||||
\(596\) | 13935.1 | − | 13935.1i | 0.957725 | − | 0.957725i | ||||
\(597\) | −8212.88 | − | 11200.5i | −0.563033 | − | 0.767848i | ||||
\(598\) | −1222.04 | + | 1585.39i | −0.0835667 | + | 0.108414i | ||||
\(599\) | 21860.2i | 1.49112i | 0.666437 | + | 0.745561i | \(0.267818\pi\) | ||||
−0.666437 | + | 0.745561i | \(0.732182\pi\) | |||||||
\(600\) | −30392.2 | − | 4677.19i | −2.06793 | − | 0.318242i | ||||
\(601\) | −14808.8 | −1.00510 | −0.502549 | − | 0.864549i | \(-0.667604\pi\) | ||||
−0.502549 | + | 0.864549i | \(0.667604\pi\) | |||||||
\(602\) | 4015.84 | 0.271883 | ||||||||
\(603\) | −4016.40 | − | 7714.68i | −0.271245 | − | 0.521005i | ||||
\(604\) | −4805.52 | + | 4805.52i | −0.323731 | + | 0.323731i | ||||
\(605\) | 199.999 | − | 199.999i | 0.0134399 | − | 0.0134399i | ||||
\(606\) | −2505.06 | − | 385.513i | −0.167922 | − | 0.0258423i | ||||
\(607\) | −10415.3 | −0.696450 | −0.348225 | − | 0.937411i | \(-0.613215\pi\) | ||||
−0.348225 | + | 0.937411i | \(0.613215\pi\) | |||||||
\(608\) | −21722.5 | −1.44896 | ||||||||
\(609\) | 777.796 | − | 5054.09i | 0.0517535 | − | 0.336293i | ||||
\(610\) | − | 30275.0i | − | 2.00950i | ||||||
\(611\) | −4334.69 | − | 3341.23i | −0.287009 | − | 0.221230i | ||||
\(612\) | 26405.8 | + | 8324.54i | 1.74410 | + | 0.549836i | ||||
\(613\) | 10986.0 | − | 10986.0i | 0.723848 | − | 0.723848i | −0.245539 | − | 0.969387i | \(-0.578965\pi\) |
0.969387 | + | 0.245539i | \(0.0789649\pi\) | |||||||
\(614\) | 43169.7i | 2.83744i | ||||||||
\(615\) | −2965.88 | − | 4044.78i | −0.194465 | − | 0.265205i | ||||
\(616\) | −10532.1 | + | 10532.1i | −0.688881 | + | 0.688881i | ||||
\(617\) | −5191.30 | − | 5191.30i | −0.338726 | − | 0.338726i | 0.517162 | − | 0.855888i | \(-0.326989\pi\) |
−0.855888 | + | 0.517162i | \(0.826989\pi\) | |||||||
\(618\) | −1231.97 | + | 8005.32i | −0.0801896 | + | 0.521070i | ||||
\(619\) | −4160.25 | − | 4160.25i | −0.270137 | − | 0.270137i | 0.559019 | − | 0.829155i | \(-0.311178\pi\) |
−0.829155 | + | 0.559019i | \(0.811178\pi\) | |||||||
\(620\) | 35756.1i | 2.31613i | ||||||||
\(621\) | −375.854 | − | 1107.01i | −0.0242875 | − | 0.0715344i | ||||
\(622\) | −26596.8 | − | 26596.8i | −1.71452 | − | 1.71452i | ||||
\(623\) | −4127.10 | −0.265407 | ||||||||
\(624\) | −20751.1 | − | 21771.2i | −1.33126 | − | 1.39671i | ||||
\(625\) | 17032.2 | 1.09006 | ||||||||
\(626\) | 23375.2 | + | 23375.2i | 1.49243 | + | 1.49243i | ||||
\(627\) | 11405.7 | + | 15554.8i | 0.726478 | + | 0.990749i | ||||
\(628\) | − | 31671.6i | − | 2.01248i | ||||||
\(629\) | −15423.7 | − | 15423.7i | −0.977714 | − | 0.977714i | ||||
\(630\) | 7695.29 | + | 14781.1i | 0.486647 | + | 0.934749i | ||||
\(631\) | 17293.3 | + | 17293.3i | 1.09102 | + | 1.09102i | 0.995420 | + | 0.0956027i | \(0.0304778\pi\) |
0.0956027 | + | 0.995420i | \(0.469522\pi\) | |||||||
\(632\) | −29972.4 | + | 29972.4i | −1.88645 | + | 1.88645i | ||||
\(633\) | −7067.27 | + | 5182.15i | −0.443758 | + | 0.325390i | ||||
\(634\) | − | 19678.0i | − | 1.23267i | ||||||
\(635\) | 15445.6 | − | 15445.6i | 0.965263 | − | 0.965263i | ||||
\(636\) | 2427.96 | − | 1780.33i | 0.151376 | − | 0.110998i | ||||
\(637\) | 13105.4 | − | 1696.17i | 0.815157 | − | 0.105502i | ||||
\(638\) | − | 23382.8i | − | 1.45099i | ||||||
\(639\) | −10106.3 | + | 5261.52i | −0.625663 | + | 0.325732i | ||||
\(640\) | 18346.9 | 1.13316 | ||||||||
\(641\) | −22729.0 | −1.40053 | −0.700266 | − | 0.713882i | \(-0.746935\pi\) | ||||
−0.700266 | + | 0.713882i | \(0.746935\pi\) | |||||||
\(642\) | −2927.39 | + | 19022.1i | −0.179961 | + | 1.16938i | ||||
\(643\) | 2952.83 | − | 2952.83i | 0.181101 | − | 0.181101i | −0.610734 | − | 0.791836i | \(-0.709126\pi\) |
0.791836 | + | 0.610734i | \(0.209126\pi\) | |||||||
\(644\) | 841.031 | − | 841.031i | 0.0514616 | − | 0.0514616i | ||||
\(645\) | 1221.30 | − | 7935.98i | 0.0745561 | − | 0.484463i | ||||
\(646\) | 29479.5 | 1.79544 | ||||||||
\(647\) | −20088.7 | −1.22066 | −0.610332 | − | 0.792146i | \(-0.708964\pi\) | ||||
−0.610332 | + | 0.792146i | \(0.708964\pi\) | |||||||
\(648\) | 37767.6 | − | 6662.56i | 2.28958 | − | 0.403905i | ||||
\(649\) | − | 7713.85i | − | 0.466556i | ||||||
\(650\) | −21402.1 | − | 16497.0i | −1.29148 | − | 0.995485i | ||||
\(651\) | 4159.76 | − | 3050.19i | 0.250436 | − | 0.183635i | ||||
\(652\) | −32279.1 | + | 32279.1i | −1.93887 | + | 1.93887i | ||||
\(653\) | − | 27423.1i | − | 1.64341i | −0.569911 | − | 0.821707i | \(-0.693022\pi\) | ||
0.569911 | − | 0.821707i | \(-0.306978\pi\) | |||||||
\(654\) | −38903.7 | + | 28526.5i | −2.32608 | + | 1.70562i | ||||
\(655\) | 5003.10 | − | 5003.10i | 0.298454 | − | 0.298454i | ||||
\(656\) | −5469.35 | − | 5469.35i | −0.325522 | − | 0.325522i | ||||
\(657\) | −18995.0 | + | 9889.14i | −1.12795 | + | 0.587233i | ||||
\(658\) | 3306.67 | + | 3306.67i | 0.195908 | + | 0.195908i | ||||
\(659\) | − | 16634.1i | − | 0.983269i | −0.870802 | − | 0.491634i | \(-0.836400\pi\) | ||
0.870802 | − | 0.491634i | \(-0.163600\pi\) | |||||||
\(660\) | 31334.7 | + | 42733.3i | 1.84803 | + | 2.52029i | ||||
\(661\) | −1386.40 | − | 1386.40i | −0.0815806 | − | 0.0815806i | 0.665139 | − | 0.746720i | \(-0.268372\pi\) |
−0.746720 | + | 0.665139i | \(0.768372\pi\) | |||||||
\(662\) | −22782.0 | −1.33754 | ||||||||
\(663\) | 9434.13 | + | 9897.92i | 0.552626 | + | 0.579794i | ||||
\(664\) | −61610.1 | −3.60081 | ||||||||
\(665\) | 8724.88 | + | 8724.88i | 0.508777 | + | 0.508777i | ||||
\(666\) | −51273.0 | − | 16164.1i | −2.98317 | − | 0.940458i | ||||
\(667\) | 1049.38i | 0.0609176i | ||||||||
\(668\) | 39970.8 | + | 39970.8i | 2.31515 | + | 2.31515i | ||||
\(669\) | −2073.73 | + | 13475.0i | −0.119843 | + | 0.778736i | ||||
\(670\) | −17990.0 | − | 17990.0i | −1.03734 | − | 1.03734i | ||||
\(671\) | −9820.44 | + | 9820.44i | −0.564998 | + | 0.564998i | ||||
\(672\) | 5090.83 | + | 6942.72i | 0.292237 | + | 0.398544i | ||||
\(673\) | 19549.9i | 1.11975i | 0.828576 | + | 0.559877i | \(0.189152\pi\) | ||||
−0.828576 | + | 0.559877i | \(0.810848\pi\) | |||||||
\(674\) | 17355.1 | − | 17355.1i | 0.991830 | − | 0.991830i | ||||
\(675\) | 14944.2 | − | 5073.87i | 0.852151 | − | 0.289323i | ||||
\(676\) | −10216.1 | − | 38805.9i | −0.581251 | − | 2.20789i | ||||
\(677\) | − | 12671.1i | − | 0.719334i | −0.933081 | − | 0.359667i | \(-0.882890\pi\) | ||
0.933081 | − | 0.359667i | \(-0.117110\pi\) | |||||||
\(678\) | 9111.43 | − | 59205.8i | 0.516110 | − | 3.35367i | ||||
\(679\) | −2813.62 | −0.159023 | ||||||||
\(680\) | 45515.6 | 2.56683 | ||||||||
\(681\) | 33304.0 | + | 5125.29i | 1.87403 | + | 0.288402i | ||||
\(682\) | 16678.4 | − | 16678.4i | 0.936437 | − | 0.936437i | ||||
\(683\) | −2374.89 | + | 2374.89i | −0.133049 | + | 0.133049i | −0.770495 | − | 0.637446i | \(-0.779991\pi\) |
0.637446 | + | 0.770495i | \(0.279991\pi\) | |||||||
\(684\) | 44817.1 | − | 23332.6i | 2.50530 | − | 1.30430i | ||||
\(685\) | 15261.7 | 0.851272 | ||||||||
\(686\) | −25028.3 | −1.39298 | ||||||||
\(687\) | 16804.3 | + | 2586.08i | 0.933223 | + | 0.143618i | ||||
\(688\) | − | 12382.5i | − | 0.686159i | ||||||
\(689\) | 1474.62 | − | 190.854i | 0.0815365 | − | 0.0105529i | ||||
\(690\) | −2022.17 | − | 2757.78i | −0.111569 | − | 0.152155i | ||||
\(691\) | −746.709 | + | 746.709i | −0.0411087 | + | 0.0411087i | −0.727362 | − | 0.686254i | \(-0.759254\pi\) |
0.686254 | + | 0.727362i | \(0.259254\pi\) | |||||||
\(692\) | − | 22196.2i | − | 1.21932i | ||||||
\(693\) | 2298.45 | − | 7290.76i | 0.125990 | − | 0.399644i | ||||
\(694\) | −21614.1 | + | 21614.1i | −1.18222 | + | 1.18222i | ||||
\(695\) | −10973.7 | − | 10973.7i | −0.598930 | − | 0.598930i | ||||
\(696\) | −34023.5 | − | 5236.02i | −1.85296 | − | 0.285159i | ||||
\(697\) | 2486.55 | + | 2486.55i | 0.135129 | + | 0.135129i | ||||
\(698\) | − | 9906.83i | − | 0.537219i | ||||||
\(699\) | 18567.5 | − | 13614.8i | 1.00470 | − | 0.736708i | ||||
\(700\) | 11353.5 | + | 11353.5i | 0.613034 | + | 0.613034i | ||||
\(701\) | 20307.4 | 1.09415 | 0.547076 | − | 0.837083i | \(-0.315741\pi\) | ||||
0.547076 | + | 0.837083i | \(0.315741\pi\) | |||||||
\(702\) | 31889.8 | + | 10900.9i | 1.71453 | + | 0.586081i | ||||
\(703\) | −39806.4 | −2.13560 | ||||||||
\(704\) | 2527.45 | + | 2527.45i | 0.135308 | + | 0.135308i | ||||
\(705\) | 7540.17 | − | 5528.91i | 0.402807 | − | 0.295363i | ||||
\(706\) | 6386.79i | 0.340468i | ||||||||
\(707\) | 525.927 | + | 525.927i | 0.0279767 | + | 0.0279767i | ||||
\(708\) | −19971.7 | − | 3073.53i | −1.06014 | − | 0.163150i | ||||
\(709\) | −15238.6 | − | 15238.6i | −0.807191 | − | 0.807191i | 0.177017 | − | 0.984208i | \(-0.443355\pi\) |
−0.984208 | + | 0.177017i | \(0.943355\pi\) | |||||||
\(710\) | −23567.0 | + | 23567.0i | −1.24571 | + | 1.24571i | ||||
\(711\) | 6540.94 | − | 20748.1i | 0.345013 | − | 1.09440i | ||||
\(712\) | 27783.1i | 1.46238i | ||||||||
\(713\) | −748.498 | + | 748.498i | −0.0393148 | + | 0.0393148i | ||||
\(714\) | −6908.73 | − | 9421.93i | −0.362119 | − | 0.493847i | ||||
\(715\) | 3359.11 | + | 25954.0i | 0.175698 | + | 1.35752i | ||||
\(716\) | 19945.4i | 1.04105i | ||||||||
\(717\) | 4357.08 | + | 670.530i | 0.226943 | + | 0.0349252i | ||||
\(718\) | 25135.4 | 1.30647 | ||||||||
\(719\) | 25119.9 | 1.30294 | 0.651469 | − | 0.758675i | \(-0.274153\pi\) | ||||
0.651469 | + | 0.758675i | \(0.274153\pi\) | |||||||
\(720\) | 45576.0 | − | 23727.7i | 2.35905 | − | 1.22817i | ||||
\(721\) | 1680.68 | − | 1680.68i | 0.0868127 | − | 0.0868127i | ||||
\(722\) | 13185.1 | − | 13185.1i | 0.679639 | − | 0.679639i | ||||
\(723\) | −28651.3 | − | 4409.26i | −1.47379 | − | 0.226808i | ||||
\(724\) | 1719.92 | 0.0882879 | ||||||||
\(725\) | −14166.1 | −0.725679 | ||||||||
\(726\) | −74.3413 | + | 483.068i | −0.00380036 | + | 0.0246947i | ||||
\(727\) | − | 12204.0i | − | 0.622590i | −0.950313 | − | 0.311295i | \(-0.899237\pi\) | ||
0.950313 | − | 0.311295i | \(-0.100763\pi\) | |||||||
\(728\) | 2473.34 | + | 19110.1i | 0.125918 | + | 0.972897i | ||||
\(729\) | −15614.1 | + | 11984.1i | −0.793280 | + | 0.608857i | ||||
\(730\) | −44294.8 | + | 44294.8i | −2.24578 | + | 2.24578i | ||||
\(731\) | 5629.49i | 0.284835i | ||||||||
\(732\) | 21512.9 | + | 29338.7i | 1.08626 | + | 1.48141i | ||||
\(733\) | 5320.85 | − | 5320.85i | 0.268117 | − | 0.268117i | −0.560224 | − | 0.828341i | \(-0.689285\pi\) |
0.828341 | + | 0.560224i | \(0.189285\pi\) | |||||||
\(734\) | 40452.5 | + | 40452.5i | 2.03424 | + | 2.03424i | ||||
\(735\) | −3433.90 | + | 22313.4i | −0.172328 | + | 1.11978i | ||||
\(736\) | −1249.26 | − | 1249.26i | −0.0625656 | − | 0.0625656i | ||||
\(737\) | 11671.0i | 0.583320i | ||||||||
\(738\) | 8266.06 | + | 2605.91i | 0.412300 | + | 0.129980i | ||||
\(739\) | −10461.0 | − | 10461.0i | −0.520724 | − | 0.520724i | 0.397066 | − | 0.917790i | \(-0.370028\pi\) |
−0.917790 | + | 0.397066i | \(0.870028\pi\) | |||||||
\(740\) | −109359. | −5.43259 | ||||||||
\(741\) | 24946.7 | + | 598.494i | 1.23676 | + | 0.0296710i | ||||
\(742\) | −1270.49 | −0.0628588 | ||||||||
\(743\) | −14399.3 | − | 14399.3i | −0.710981 | − | 0.710981i | 0.255760 | − | 0.966740i | \(-0.417674\pi\) |
−0.966740 | + | 0.255760i | \(0.917674\pi\) | |||||||
\(744\) | −20533.5 | − | 28002.9i | −1.01182 | − | 1.37989i | ||||
\(745\) | 16627.6i | 0.817703i | ||||||||
\(746\) | −30080.3 | − | 30080.3i | −1.47630 | − | 1.47630i | ||||
\(747\) | 28047.2 | − | 14601.9i | 1.37375 | − | 0.715201i | ||||
\(748\) | −26270.5 | − | 26270.5i | −1.28415 | − | 1.28415i | ||||
\(749\) | 3993.61 | − | 3993.61i | 0.194824 | − | 0.194824i | ||||
\(750\) | −4139.88 | + | 3035.61i | −0.201556 | + | 0.147793i | ||||
\(751\) | − | 31201.6i | − | 1.51606i | −0.652217 | − | 0.758032i | \(-0.726161\pi\) | ||
0.652217 | − | 0.758032i | \(-0.273839\pi\) | |||||||
\(752\) | 10195.8 | − | 10195.8i | 0.494419 | − | 0.494419i | ||||
\(753\) | −30410.2 | + | 22298.6i | −1.47173 | + | 1.07916i | ||||
\(754\) | −23959.2 | − | 18468.1i | −1.15722 | − | 0.891998i | ||||
\(755\) | − | 5734.03i | − | 0.276401i | ||||||
\(756\) | −17960.5 | − | 8855.80i | −0.864044 | − | 0.426035i | ||||
\(757\) | 27779.7 | 1.33378 | 0.666890 | − | 0.745156i | \(-0.267625\pi\) | ||||
0.666890 | + | 0.745156i | \(0.267625\pi\) | |||||||
\(758\) | −7765.47 | −0.372104 | ||||||||
\(759\) | −238.612 | + | 1550.50i | −0.0114112 | + | 0.0741495i | ||||
\(760\) | 58734.8 | − | 58734.8i | 2.80334 | − | 2.80334i | ||||
\(761\) | 5304.71 | − | 5304.71i | 0.252688 | − | 0.252688i | −0.569384 | − | 0.822072i | \(-0.692818\pi\) |
0.822072 | + | 0.569384i | \(0.192818\pi\) | |||||||
\(762\) | −5741.26 | + | 37306.5i | −0.272945 | + | 1.77359i | ||||
\(763\) | 14156.7 | 0.671700 | ||||||||
\(764\) | −23237.3 | −1.10039 | ||||||||
\(765\) | −20720.4 | + | 10787.4i | −0.979278 | + | 0.509830i | ||||
\(766\) | 59763.2i | 2.81897i | ||||||||
\(767\) | −7904.01 | − | 6092.50i | −0.372095 | − | 0.286816i | ||||
\(768\) | −28874.1 | + | 21172.2i | −1.35665 | + | 0.994775i | ||||
\(769\) | 5037.38 | − | 5037.38i | 0.236219 | − | 0.236219i | −0.579063 | − | 0.815283i | \(-0.696582\pi\) |
0.815283 | + | 0.579063i | \(0.196582\pi\) | |||||||
\(770\) | − | 22361.3i | − | 1.04655i | ||||||
\(771\) | 24354.6 | − | 17858.3i | 1.13763 | − | 0.834178i | ||||
\(772\) | −11658.2 | + | 11658.2i | −0.543506 | + | 0.543506i | ||||
\(773\) | 24302.4 | + | 24302.4i | 1.13078 | + | 1.13078i | 0.990047 | + | 0.140737i | \(0.0449470\pi\) |
0.140737 | + | 0.990047i | \(0.455053\pi\) | |||||||
\(774\) | 6407.21 | + | 12306.9i | 0.297548 | + | 0.571529i | ||||
\(775\) | −10104.4 | − | 10104.4i | −0.468336 | − | 0.468336i | ||||
\(776\) | 18940.9i | 0.876211i | ||||||||
\(777\) | 9328.91 | + | 12722.5i | 0.430724 | + | 0.587409i | ||||
\(778\) | −2265.93 | − | 2265.93i | −0.104418 | − | 0.104418i | ||||
\(779\) | 6417.44 | 0.295159 | ||||||||
\(780\) | 68535.3 | + | 1644.23i | 3.14610 | + | 0.0754778i | ||||
\(781\) | 15289.1 | 0.700496 | ||||||||
\(782\) | 1695.36 | + | 1695.36i | 0.0775268 | + | 0.0775268i | ||||
\(783\) | 16729.7 | − | 5680.10i | 0.763565 | − | 0.259247i | ||||
\(784\) | 34815.5i | 1.58598i | ||||||||
\(785\) | 18895.6 | + | 18895.6i | 0.859124 | + | 0.859124i | ||||
\(786\) | −1859.69 | + | 12084.2i | −0.0843929 | + | 0.548383i | ||||
\(787\) | −8837.40 | − | 8837.40i | −0.400279 | − | 0.400279i | 0.478053 | − | 0.878331i | \(-0.341343\pi\) |
−0.878331 | + | 0.478053i | \(0.841343\pi\) | |||||||
\(788\) | 46055.8 | − | 46055.8i | 2.08207 | − | 2.08207i | ||||
\(789\) | −12487.3 | − | 17029.8i | −0.563447 | − | 0.768413i | ||||
\(790\) | − | 63635.9i | − | 2.86590i | ||||||
\(791\) | −12430.0 | + | 12430.0i | −0.558737 | + | 0.558737i | ||||
\(792\) | −49080.5 | − | 15472.8i | −2.20202 | − | 0.694197i | ||||
\(793\) | 2306.21 | + | 17818.8i | 0.103274 | + | 0.797939i | ||||
\(794\) | 57419.3i | 2.56642i | ||||||||
\(795\) | −386.383 | + | 2510.71i | −0.0172372 | + | 0.112007i | ||||
\(796\) | 48820.9 | 2.17388 | ||||||||
\(797\) | −1869.09 | −0.0830697 | −0.0415348 | − | 0.999137i | \(-0.513225\pi\) | ||||
−0.0415348 | + | 0.999137i | \(0.513225\pi\) | |||||||
\(798\) | −21073.6 | − | 3243.10i | −0.934834 | − | 0.143865i | ||||
\(799\) | −4635.36 | + | 4635.36i | −0.205241 | + | 0.205241i | ||||
\(800\) | 16864.4 | − | 16864.4i | 0.745310 | − | 0.745310i | ||||
\(801\) | −6584.72 | − | 12647.9i | −0.290461 | − | 0.557916i | ||||
\(802\) | 8389.70 | 0.369390 | ||||||||
\(803\) | 28736.2 | 1.26286 | ||||||||
\(804\) | 30217.1 | + | 4650.23i | 1.32546 | + | 0.203981i | ||||
\(805\) | 1003.53i | 0.0439378i | ||||||||
\(806\) | −3916.73 | − | 30262.4i | −0.171167 | − | 1.32252i | ||||
\(807\) | −19575.3 | − | 26696.2i | −0.853883 | − | 1.16450i | ||||
\(808\) | 3540.47 | − | 3540.47i | 0.154150 | − | 0.154150i | ||||
\(809\) | 34524.9i | 1.50041i | 0.661206 | + | 0.750204i | \(0.270045\pi\) | ||||
−0.661206 | + | 0.750204i | \(0.729955\pi\) | |||||||
\(810\) | −33020.3 | + | 47165.9i | −1.43236 | + | 2.04598i | ||||
\(811\) | −24704.1 | + | 24704.1i | −1.06964 | + | 1.06964i | −0.0722533 | + | 0.997386i | \(0.523019\pi\) |
−0.997386 | + | 0.0722533i | \(0.976981\pi\) | |||||||
\(812\) | 12710.1 | + | 12710.1i | 0.549306 | + | 0.549306i | ||||
\(813\) | −32393.3 | − | 4985.13i | −1.39739 | − | 0.215051i | ||||
\(814\) | 51010.5 | + | 51010.5i | 2.19646 | + | 2.19646i | ||||
\(815\) | − | 38515.9i | − | 1.65540i | ||||||
\(816\) | −29051.6 | + | 21302.4i | −1.24634 | + | 0.913890i | ||||
\(817\) | 7264.47 | + | 7264.47i | 0.311079 | + | 0.311079i | ||||
\(818\) | 61888.8 | 2.64535 | ||||||||
\(819\) | −5655.15 | − | 8113.45i | −0.241278 | − | 0.346162i | ||||
\(820\) | 17630.5 | 0.750832 | ||||||||
\(821\) | 6855.71 | + | 6855.71i | 0.291432 | + | 0.291432i | 0.837646 | − | 0.546214i | \(-0.183931\pi\) |
−0.546214 | + | 0.837646i | \(0.683931\pi\) | |||||||
\(822\) | −21267.6 | + | 15594.7i | −0.902426 | + | 0.661714i | ||||
\(823\) | − | 29097.2i | − | 1.23240i | −0.787590 | − | 0.616199i | \(-0.788672\pi\) | ||
0.787590 | − | 0.616199i | \(-0.211328\pi\) | |||||||
\(824\) | −11314.2 | − | 11314.2i | −0.478334 | − | 0.478334i | ||||
\(825\) | −20931.0 | − | 3221.16i | −0.883303 | − | 0.135935i | ||||
\(826\) | 6029.49 | + | 6029.49i | 0.253987 | + | 0.253987i | ||||
\(827\) | −17156.1 | + | 17156.1i | −0.721374 | + | 0.721374i | −0.968885 | − | 0.247511i | \(-0.920387\pi\) |
0.247511 | + | 0.968885i | \(0.420387\pi\) | |||||||
\(828\) | 3919.27 | + | 1235.57i | 0.164498 | + | 0.0518587i | ||||
\(829\) | 1732.47i | 0.0725828i | 0.999341 | + | 0.0362914i | \(0.0115545\pi\) | ||||
−0.999341 | + | 0.0362914i | \(0.988446\pi\) | |||||||
\(830\) | 65403.8 | − | 65403.8i | 2.73518 | − | 2.73518i | ||||
\(831\) | 21883.2 | + | 29843.6i | 0.913500 | + | 1.24580i | ||||
\(832\) | 4585.96 | − | 593.540i | 0.191093 | − | 0.0247323i | ||||
\(833\) | − | 15828.3i | − | 0.658364i | ||||||
\(834\) | 26505.3 | + | 4079.00i | 1.10048 | + | 0.169358i | ||||
\(835\) | −47693.9 | −1.97666 | ||||||||
\(836\) | −67800.6 | −2.80494 | ||||||||
\(837\) | 15984.4 | + | 7881.45i | 0.660099 | + | 0.325475i | ||||
\(838\) | −4007.16 | + | 4007.16i | −0.165185 | + | 0.165185i | ||||
\(839\) | −18160.5 | + | 18160.5i | −0.747282 | + | 0.747282i | −0.973968 | − | 0.226686i | \(-0.927211\pi\) |
0.226686 | + | 0.973968i | \(0.427211\pi\) | |||||||
\(840\) | −32537.1 | − | 5007.27i | −1.33647 | − | 0.205675i | ||||
\(841\) | 8530.29 | 0.349760 | ||||||||
\(842\) | 2488.93 | 0.101869 | ||||||||
\(843\) | −773.076 | + | 5023.43i | −0.0315850 | + | 0.205238i | ||||
\(844\) | − | 30804.9i | − | 1.25634i | ||||||
\(845\) | 29246.9 | + | 17056.9i | 1.19068 | + | 0.694411i | ||||
\(846\) | −4857.87 | + | 15409.4i | −0.197420 | + | 0.626223i | ||||
\(847\) | 101.418 | − | 101.418i | 0.00411425 | − | 0.00411425i | ||||
\(848\) | 3917.44i | 0.158639i | ||||||||
\(849\) | −26802.5 | − | 36552.4i | −1.08346 | − | 1.47759i | ||||
\(850\) | −22886.6 | + | 22886.6i | −0.923535 | + | 0.923535i | ||||
\(851\) | −2289.26 | − | 2289.26i | −0.0922148 | − | 0.0922148i | ||||
\(852\) | 6091.84 | − | 39584.6i | 0.244957 | − | 1.59172i | ||||
\(853\) | 27718.1 | + | 27718.1i | 1.11260 | + | 1.11260i | 0.992798 | + | 0.119803i | \(0.0382265\pi\) |
0.119803 | + | 0.992798i | \(0.461774\pi\) | |||||||
\(854\) | − | 15352.2i | − | 0.615154i | ||||||
\(855\) | −12817.8 | + | 40658.7i | −0.512703 | + | 1.62631i | ||||
\(856\) | −26884.5 | − | 26884.5i | −1.07347 | − | 1.07347i | ||||
\(857\) | −44171.2 | −1.76063 | −0.880316 | − | 0.474389i | \(-0.842669\pi\) | ||||
−0.880316 | + | 0.474389i | \(0.842669\pi\) | |||||||
\(858\) | −31201.3 | − | 32735.2i | −1.24149 | − | 1.30252i | ||||
\(859\) | −2523.54 | −0.100235 | −0.0501176 | − | 0.998743i | \(-0.515960\pi\) | ||||
−0.0501176 | + | 0.998743i | \(0.515960\pi\) | |||||||
\(860\) | 19957.5 | + | 19957.5i | 0.791330 | + | 0.791330i | ||||
\(861\) | −1503.97 | − | 2051.07i | −0.0595299 | − | 0.0811852i | ||||
\(862\) | − | 23509.8i | − | 0.928940i | ||||||
\(863\) | 29567.9 | + | 29567.9i | 1.16628 | + | 1.16628i | 0.983074 | + | 0.183211i | \(0.0586491\pi\) |
0.183211 | + | 0.983074i | \(0.441351\pi\) | |||||||
\(864\) | −13154.3 | + | 26678.3i | −0.517961 | + | 1.05048i | ||||
\(865\) | 13242.4 | + | 13242.4i | 0.520528 | + | 0.520528i | ||||
\(866\) | 12328.1 | − | 12328.1i | 0.483747 | − | 0.483747i | ||||
\(867\) | −7379.34 | + | 5410.98i | −0.289060 | + | 0.211957i | ||||
\(868\) | 18131.6i | 0.709018i | ||||||||
\(869\) | −20641.9 | + | 20641.9i | −0.805785 | + | 0.805785i | ||||
\(870\) | 41676.9 | − | 30560.1i | 1.62412 | − | 1.19090i | ||||
\(871\) | 11958.7 | + | 9217.92i | 0.465219 | + | 0.358596i | ||||
\(872\) | − | 95301.1i | − | 3.70104i | ||||||
\(873\) | −4489.09 | − | 8622.61i | −0.174035 | − | 0.334286i | ||||
\(874\) | 4375.50 | 0.169340 | ||||||||
\(875\) | 1506.47 | 0.0582032 | ||||||||
\(876\) | 11449.7 | − | 74400.1i | 0.441611 | − | 2.86957i | ||||
\(877\) | −2355.90 | + | 2355.90i | −0.0907103 | + | 0.0907103i | −0.751006 | − | 0.660296i | \(-0.770431\pi\) |
0.660296 | + | 0.751006i | \(0.270431\pi\) | |||||||
\(878\) | −21416.1 | + | 21416.1i | −0.823188 | + | 0.823188i | ||||
\(879\) | 3251.22 | − | 21126.3i | 0.124756 | − | 0.810664i | ||||
\(880\) | −68948.8 | −2.64121 | ||||||||
\(881\) | 18429.8 | 0.704786 | 0.352393 | − | 0.935852i | \(-0.385368\pi\) | ||||
0.352393 | + | 0.935852i | \(0.385368\pi\) | |||||||
\(882\) | −18015.0 | − | 34603.1i | −0.687751 | − | 1.32103i | ||||
\(883\) | − | 41907.5i | − | 1.59717i | −0.601883 | − | 0.798584i | \(-0.705583\pi\) | ||
0.601883 | − | 0.798584i | \(-0.294417\pi\) | |||||||
\(884\) | −47667.0 | + | 6169.32i | −1.81359 | + | 0.234725i | ||||
\(885\) | 13749.0 | − | 10081.6i | 0.522223 | − | 0.382926i | ||||
\(886\) | −18916.9 | + | 18916.9i | −0.717299 | + | 0.717299i | ||||
\(887\) | 10415.9i | 0.394287i | 0.980375 | + | 0.197143i | \(0.0631665\pi\) | ||||
−0.980375 | + | 0.197143i | \(0.936834\pi\) | |||||||
\(888\) | 85646.2 | − | 62801.0i | 3.23660 | − | 2.37327i | ||||
\(889\) | 7832.36 | − | 7832.36i | 0.295488 | − | 0.295488i | ||||
\(890\) | −29493.8 | − | 29493.8i | −1.11083 | − | 1.11083i | ||||
\(891\) | 26010.4 | − | 4588.48i | 0.977980 | − | 0.172525i | ||||
\(892\) | −33887.1 | − | 33887.1i | −1.27200 | − | 1.27200i | ||||
\(893\) | 11963.2i | 0.448303i | ||||||||
\(894\) | −16990.4 | − | 23171.0i | −0.635619 | − | 0.866839i | ||||
\(895\) | −11899.6 | − | 11899.6i | −0.444424 | − | 0.444424i | ||||
\(896\) | 9303.56 | 0.346886 | ||||||||
\(897\) | 1400.26 | + | 1469.10i | 0.0521219 | + | 0.0546843i | ||||
\(898\) | 66936.3 | 2.48741 | ||||||||
\(899\) | −11311.7 | − | 11311.7i | −0.419650 | − | 0.419650i | ||||
\(900\) | −16679.6 | + | 52908.5i | −0.617764 | + | 1.95957i | ||||
\(901\) | − | 1781.00i | − | 0.0658532i | ||||||
\(902\) | −8223.72 | − | 8223.72i | −0.303570 | − | 0.303570i | ||||
\(903\) | 619.312 | − | 4024.27i | 0.0228233 | − | 0.148305i | ||||
\(904\) | 83677.4 | + | 83677.4i | 3.07862 | + | 3.07862i | ||||
\(905\) | −1026.12 | + | 1026.12i | −0.0376900 | + | 0.0376900i | ||||
\(906\) | 5859.13 | + | 7990.51i | 0.214853 | + | 0.293010i | ||||
\(907\) | 31708.3i | 1.16081i | 0.814327 | + | 0.580407i | \(0.197107\pi\) | ||||
−0.814327 | + | 0.580407i | \(0.802893\pi\) | |||||||
\(908\) | −83753.2 | + | 83753.2i | −3.06106 | + | 3.06106i | ||||
\(909\) | −772.645 | + | 2450.86i | −0.0281925 | + | 0.0894278i | ||||
\(910\) | −22912.5 | − | 17661.2i | −0.834662 | − | 0.643367i | ||||
\(911\) | − | 44647.0i | − | 1.62373i | −0.583842 | − | 0.811867i | \(-0.698451\pi\) | ||
0.583842 | − | 0.811867i | \(-0.301549\pi\) | |||||||
\(912\) | −9999.80 | + | 64978.4i | −0.363077 | + | 2.35927i | ||||
\(913\) | −42430.7 | −1.53806 | ||||||||
\(914\) | −1086.20 | −0.0393089 | ||||||||
\(915\) | −30338.5 | − | 4668.92i | −1.09613 | − | 0.168688i | ||||
\(916\) | −42259.6 | + | 42259.6i | −1.52434 | + | 1.52434i | ||||
\(917\) | 2537.03 | − | 2537.03i | 0.0913633 | − | 0.0913633i | ||||
\(918\) | 17851.6 | − | 36205.0i | 0.641821 | − | 1.30168i | ||||
\(919\) | 5532.82 | 0.198597 | 0.0992986 | − | 0.995058i | \(-0.468340\pi\) | ||||
0.0992986 | + | 0.995058i | \(0.468340\pi\) | |||||||
\(920\) | 6755.65 | 0.242095 | ||||||||
\(921\) | 43260.4 | + | 6657.52i | 1.54775 | + | 0.238190i | ||||
\(922\) | 27307.0i | 0.975388i | ||||||||
\(923\) | 12075.6 | − | 15666.0i | 0.430630 | − | 0.558671i | ||||
\(924\) | 15889.6 | + | 21669.7i | 0.565723 | + | 0.771516i | ||||
\(925\) | 30904.0 | − | 30904.0i | 1.09850 | − | 1.09850i | ||||
\(926\) | 53060.6i | 1.88302i | ||||||||
\(927\) | 7832.13 | + | 2469.11i | 0.277498 | + | 0.0874826i | ||||
\(928\) | 18879.4 | − | 18879.4i | 0.667831 | − | 0.667831i | ||||
\(929\) | −35330.9 | − | 35330.9i | −1.24776 | − | 1.24776i | −0.956707 | − | 0.291054i | \(-0.905994\pi\) |
−0.291054 | − | 0.956707i | \(-0.594006\pi\) | |||||||
\(930\) | 51525.1 | + | 7929.41i | 1.81675 | + | 0.279587i | ||||
\(931\) | −20425.3 | − | 20425.3i | −0.719025 | − | 0.719025i | ||||
\(932\) | 80932.3i | 2.84445i | ||||||||
\(933\) | −30754.3 | + | 22550.9i | −1.07915 | + | 0.791301i | ||||
\(934\) | −4640.76 | − | 4640.76i | −0.162580 | − | 0.162580i | ||||
\(935\) | 31346.4 | 1.09640 | ||||||||
\(936\) | −54618.7 | + | 38069.7i | −1.90734 | + | 1.32943i | ||||
\(937\) | 19008.7 | 0.662738 | 0.331369 | − | 0.943501i | \(-0.392489\pi\) | ||||
0.331369 | + | 0.943501i | \(0.392489\pi\) | |||||||
\(938\) | −9122.59 | − | 9122.59i | −0.317551 | − | 0.317551i | ||||
\(939\) | 27029.1 | − | 19819.4i | 0.939363 | − | 0.688799i | ||||
\(940\) | 32866.2i | 1.14040i | ||||||||
\(941\) | 18292.4 | + | 18292.4i | 0.633703 | + | 0.633703i | 0.948995 | − | 0.315292i | \(-0.102102\pi\) |
−0.315292 | + | 0.948995i | \(0.602102\pi\) | |||||||
\(942\) | −45639.3 | − | 7023.62i | −1.57857 | − | 0.242932i | ||||
\(943\) | 369.066 | + | 369.066i | 0.0127449 | + | 0.0127449i | ||||
\(944\) | 18591.4 | − | 18591.4i | 0.640993 | − | 0.640993i | ||||
\(945\) | 15998.8 | − | 5431.95i | 0.550733 | − | 0.186986i | ||||
\(946\) | − | 18618.3i | − | 0.639887i | ||||||
\(947\) | −5237.93 | + | 5237.93i | −0.179736 | + | 0.179736i | −0.791241 | − | 0.611505i | \(-0.790564\pi\) |
0.611505 | + | 0.791241i | \(0.290564\pi\) | |||||||
\(948\) | 45218.7 | + | 61667.9i | 1.54919 | + | 2.11274i | ||||
\(949\) | 22696.3 | − | 29444.6i | 0.776345 | − | 1.00718i | ||||
\(950\) | 59067.3i | 2.01726i | ||||||||
\(951\) | −19719.3 | − | 3034.69i | −0.672390 | − | 0.103477i | ||||
\(952\) | 23080.6 | 0.785763 | ||||||||
\(953\) | −47998.2 | −1.63149 | −0.815747 | − | 0.578409i | \(-0.803674\pi\) | ||||
−0.815747 | + | 0.578409i | \(0.803674\pi\) | |||||||
\(954\) | −2027.05 | − | 3893.55i | −0.0687926 | − | 0.132136i | ||||
\(955\) | 13863.6 | − | 13863.6i | 0.469754 | − | 0.469754i | ||||
\(956\) | −10957.2 | + | 10957.2i | −0.370693 | + | 0.370693i | ||||
\(957\) | −23431.9 | − | 3606.03i | −0.791478 | − | 0.121804i | ||||
\(958\) | 74404.2 | 2.50928 | ||||||||
\(959\) | 7739.11 | 0.260593 | ||||||||
\(960\) | −1201.62 | + | 7808.10i | −0.0403981 | + | 0.262506i | ||||
\(961\) | 13654.3i | 0.458336i | ||||||||
\(962\) | 92556.7 | − | 11979.2i | 3.10203 | − | 0.401481i | ||||
\(963\) | 18610.6 | + | 5867.07i | 0.622759 | + | 0.196328i | ||||
\(964\) | 72052.4 | − | 72052.4i | 2.40731 | − | 2.40731i | ||||
\(965\) | − | 13910.7i | − | 0.464044i | ||||||
\(966\) | −1025.43 | − | 1398.45i | −0.0341539 | − | 0.0465780i | ||||
\(967\) | 21748.1 | − | 21748.1i | 0.723237 | − | 0.723237i | −0.246026 | − | 0.969263i | \(-0.579125\pi\) |
0.969263 | + | 0.246026i | \(0.0791248\pi\) | |||||||
\(968\) | −682.734 | − | 682.734i | −0.0226693 | − | 0.0226693i | ||||
\(969\) | 4546.25 | − | 29541.4i | 0.150719 | − | 0.979366i | ||||
\(970\) | −20107.2 | − | 20107.2i | −0.665571 | − | 0.665571i | ||||
\(971\) | − | 23145.5i | − | 0.764959i | −0.923964 | − | 0.382479i | \(-0.875070\pi\) | ||
0.923964 | − | 0.382479i | \(-0.124930\pi\) | |||||||
\(972\) | −1516.26 | − | 69171.0i | −0.0500350 | − | 2.28257i | ||||
\(973\) | −5564.67 | − | 5564.67i | −0.183346 | − | 0.183346i | ||||
\(974\) | 84865.9 | 2.79187 | ||||||||
\(975\) | −19832.2 | + | 18902.9i | −0.651424 | + | 0.620900i | ||||
\(976\) | −47337.1 | −1.55248 | ||||||||
\(977\) | −11819.9 | − | 11819.9i | −0.387054 | − | 0.387054i | 0.486581 | − | 0.873635i | \(-0.338244\pi\) |
−0.873635 | + | 0.486581i | \(0.838244\pi\) | |||||||
\(978\) | 39356.3 | + | 53673.0i | 1.28678 | + | 1.75488i | ||||
\(979\) | 19134.1i | 0.624646i | ||||||||
\(980\) | −56113.9 | − | 56113.9i | −1.82907 | − | 1.82907i | ||||
\(981\) | 22586.8 | + | 43384.6i | 0.735108 | + | 1.41199i | ||||
\(982\) | −44313.4 | − | 44313.4i | −1.44002 | − | 1.44002i | ||||
\(983\) | 10116.8 | − | 10116.8i | 0.328257 | − | 0.328257i | −0.523666 | − | 0.851923i | \(-0.675436\pi\) |
0.851923 | + | 0.523666i | \(0.175436\pi\) | |||||||
\(984\) | −13807.6 | + | 10124.6i | −0.447326 | + | 0.328007i | ||||
\(985\) | 54954.6i | 1.77767i | ||||||||
\(986\) | −25621.1 | + | 25621.1i | −0.827528 | + | 0.827528i | ||||
\(987\) | 3823.56 | − | 2803.67i | 0.123308 | − | 0.0904171i | ||||
\(988\) | −53549.9 | + | 69472.1i | −1.72434 | + | 2.23704i | ||||
\(989\) | 835.556i | 0.0268647i | ||||||||
\(990\) | 68528.2 | − | 35677.0i | 2.19997 | − | 1.14534i | ||||
\(991\) | −20658.3 | −0.662191 | −0.331095 | − | 0.943597i | \(-0.607418\pi\) | ||||
−0.331095 | + | 0.943597i | \(0.607418\pi\) | |||||||
\(992\) | 26932.5 | 0.862005 | ||||||||
\(993\) | −3513.38 | + | 22829.8i | −0.112280 | + | 0.729590i | ||||
\(994\) | −11950.7 | + | 11950.7i | −0.381340 | + | 0.381340i | ||||
\(995\) | −29127.0 | + | 29127.0i | −0.928027 | + | 0.928027i | ||||
\(996\) | −16906.2 | + | 109856.i | −0.537845 | + | 3.49490i | ||||
\(997\) | −19139.1 | −0.607964 | −0.303982 | − | 0.952678i | \(-0.598316\pi\) | ||||
−0.303982 | + | 0.952678i | \(0.598316\pi\) | |||||||
\(998\) | 34443.3 | 1.09247 | ||||||||
\(999\) | −24105.2 | + | 48887.9i | −0.763418 | + | 1.54829i |
(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 | 39.4.f.b.5.10 | yes | 20 | |
3.2 | odd | 2 | inner | 39.4.f.b.5.1 | ✓ | 20 | |
13.8 | odd | 4 | inner | 39.4.f.b.8.1 | yes | 20 | |
39.8 | even | 4 | inner | 39.4.f.b.8.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.f.b.5.1 | ✓ | 20 | 3.2 | odd | 2 | inner | |
39.4.f.b.5.10 | yes | 20 | 1.1 | even | 1 | trivial | |
39.4.f.b.8.1 | yes | 20 | 13.8 | odd | 4 | inner | |
39.4.f.b.8.10 | yes | 20 | 39.8 | even | 4 | inner |