Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(7,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.c (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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(4.16954 - 7.22186i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.7 |
Dual form | 38.4.c.c.11.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 3.16954 | + | 5.48981i | 0.609979 | + | 1.05651i | 0.991243 | + | 0.132048i | \(0.0421553\pi\) |
−0.381265 | + | 0.924466i | \(0.624511\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.96554 | − | 5.13646i | −0.265246 | − | 0.459419i | 0.702382 | − | 0.711800i | \(-0.252120\pi\) |
−0.967628 | + | 0.252381i | \(0.918786\pi\) | |||||||
\(6\) | −6.33908 | + | 10.9796i | −0.431320 | + | 0.747068i | ||||
\(7\) | 0.660916 | 0.0356861 | 0.0178430 | − | 0.999841i | \(-0.494320\pi\) | ||||
0.0178430 | + | 0.999841i | \(0.494320\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −6.59199 | + | 11.4177i | −0.244148 | + | 0.422877i | ||||
\(10\) | 5.93108 | − | 10.2729i | 0.187557 | − | 0.324859i | ||||
\(11\) | 50.1496 | 1.37461 | 0.687303 | − | 0.726371i | \(-0.258794\pi\) | ||||
0.687303 | + | 0.726371i | \(0.258794\pi\) | |||||||
\(12\) | −25.3563 | −0.609979 | ||||||||
\(13\) | −1.31325 | + | 2.27462i | −0.0280177 | + | 0.0485281i | −0.879694 | − | 0.475540i | \(-0.842253\pi\) |
0.851677 | + | 0.524068i | \(0.175586\pi\) | |||||||
\(14\) | 0.660916 | + | 1.14474i | 0.0126169 | + | 0.0218532i | ||||
\(15\) | 18.7988 | − | 32.5605i | 0.323589 | − | 0.560472i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −28.9052 | − | 50.0654i | −0.412385 | − | 0.714272i | 0.582765 | − | 0.812641i | \(-0.301971\pi\) |
−0.995150 | + | 0.0983685i | \(0.968638\pi\) | |||||||
\(18\) | −26.3680 | −0.345277 | ||||||||
\(19\) | −12.1437 | − | 81.9239i | −0.146629 | − | 0.989192i | ||||
\(20\) | 23.7243 | 0.265246 | ||||||||
\(21\) | 2.09480 | + | 3.62830i | 0.0217678 | + | 0.0377029i | ||||
\(22\) | 50.1496 | + | 86.8616i | 0.485997 | + | 0.841771i | ||||
\(23\) | −18.9828 | + | 32.8792i | −0.172095 | + | 0.298077i | −0.939152 | − | 0.343502i | \(-0.888387\pi\) |
0.767057 | + | 0.641579i | \(0.221720\pi\) | |||||||
\(24\) | −25.3563 | − | 43.9185i | −0.215660 | − | 0.373534i | ||||
\(25\) | 44.9112 | − | 77.7884i | 0.359289 | − | 0.622307i | ||||
\(26\) | −5.25300 | −0.0396230 | ||||||||
\(27\) | 87.5809 | 0.624257 | ||||||||
\(28\) | −1.32183 | + | 2.28948i | −0.00892152 | + | 0.0154525i | ||||
\(29\) | −154.914 | + | 268.319i | −0.991959 | + | 1.71812i | −0.386373 | + | 0.922343i | \(0.626272\pi\) |
−0.605586 | + | 0.795780i | \(0.707061\pi\) | |||||||
\(30\) | 75.1952 | 0.457623 | ||||||||
\(31\) | −282.420 | −1.63626 | −0.818131 | − | 0.575032i | \(-0.804990\pi\) | ||||
−0.818131 | + | 0.575032i | \(0.804990\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 158.951 | + | 275.312i | 0.838480 | + | 1.45229i | ||||
\(34\) | 57.8105 | − | 100.131i | 0.291600 | − | 0.505067i | ||||
\(35\) | −1.95997 | − | 3.39477i | −0.00946559 | − | 0.0163949i | ||||
\(36\) | −26.3680 | − | 45.6707i | −0.122074 | − | 0.211438i | ||||
\(37\) | −21.0744 | −0.0936383 | −0.0468192 | − | 0.998903i | \(-0.514908\pi\) | ||||
−0.0468192 | + | 0.998903i | \(0.514908\pi\) | |||||||
\(38\) | 129.753 | − | 102.957i | 0.553912 | − | 0.439524i | ||||
\(39\) | −16.6496 | −0.0683608 | ||||||||
\(40\) | 23.7243 | + | 41.0917i | 0.0937786 | + | 0.162429i | ||||
\(41\) | 172.046 | + | 297.992i | 0.655343 | + | 1.13509i | 0.981808 | + | 0.189878i | \(0.0608092\pi\) |
−0.326465 | + | 0.945209i | \(0.605857\pi\) | |||||||
\(42\) | −4.18960 | + | 7.25660i | −0.0153921 | + | 0.0266600i | ||||
\(43\) | −132.675 | − | 229.800i | −0.470530 | − | 0.814981i | 0.528902 | − | 0.848683i | \(-0.322604\pi\) |
−0.999432 | + | 0.0337014i | \(0.989270\pi\) | |||||||
\(44\) | −100.299 | + | 173.723i | −0.343651 | + | 0.595222i | ||||
\(45\) | 78.1953 | 0.259037 | ||||||||
\(46\) | −75.9312 | −0.243379 | ||||||||
\(47\) | 69.8967 | − | 121.065i | 0.216925 | − | 0.375725i | −0.736941 | − | 0.675957i | \(-0.763731\pi\) |
0.953866 | + | 0.300231i | \(0.0970639\pi\) | |||||||
\(48\) | 50.7127 | − | 87.8369i | 0.152495 | − | 0.264129i | ||||
\(49\) | −342.563 | −0.998727 | ||||||||
\(50\) | 179.645 | 0.508112 | ||||||||
\(51\) | 183.233 | − | 317.368i | 0.503093 | − | 0.871382i | ||||
\(52\) | −5.25300 | − | 9.09846i | −0.0140088 | − | 0.0242640i | ||||
\(53\) | 66.8936 | − | 115.863i | 0.173369 | − | 0.300283i | −0.766227 | − | 0.642570i | \(-0.777868\pi\) |
0.939596 | + | 0.342287i | \(0.111201\pi\) | |||||||
\(54\) | 87.5809 | + | 151.694i | 0.220708 | + | 0.382278i | ||||
\(55\) | −148.721 | − | 257.592i | −0.364609 | − | 0.631521i | ||||
\(56\) | −5.28733 | −0.0126169 | ||||||||
\(57\) | 411.257 | − | 326.328i | 0.955654 | − | 0.758302i | ||||
\(58\) | −619.656 | −1.40284 | ||||||||
\(59\) | −227.911 | − | 394.754i | −0.502907 | − | 0.871060i | −0.999994 | − | 0.00335970i | \(-0.998931\pi\) |
0.497088 | − | 0.867700i | \(-0.334403\pi\) | |||||||
\(60\) | 75.1952 | + | 130.242i | 0.161794 | + | 0.280236i | ||||
\(61\) | −54.2184 | + | 93.9090i | −0.113802 | + | 0.197112i | −0.917300 | − | 0.398196i | \(-0.869636\pi\) |
0.803498 | + | 0.595308i | \(0.202970\pi\) | |||||||
\(62\) | −282.420 | − | 489.166i | −0.578506 | − | 1.00200i | ||||
\(63\) | −4.35675 | + | 7.54612i | −0.00871269 | + | 0.0150908i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 15.5780 | 0.0297263 | ||||||||
\(66\) | −317.902 | + | 550.623i | −0.592895 | + | 1.02692i | ||||
\(67\) | −13.1980 | + | 22.8596i | −0.0240656 | + | 0.0416828i | −0.877807 | − | 0.479014i | \(-0.840994\pi\) |
0.853742 | + | 0.520697i | \(0.174328\pi\) | |||||||
\(68\) | 231.242 | 0.412385 | ||||||||
\(69\) | −240.667 | −0.419897 | ||||||||
\(70\) | 3.91994 | − | 6.78954i | 0.00669318 | − | 0.0115929i | ||||
\(71\) | 559.526 | + | 969.128i | 0.935261 | + | 1.61992i | 0.774167 | + | 0.632981i | \(0.218169\pi\) |
0.161094 | + | 0.986939i | \(0.448498\pi\) | |||||||
\(72\) | 52.7360 | − | 91.3414i | 0.0863193 | − | 0.149509i | ||||
\(73\) | 235.224 | + | 407.421i | 0.377136 | + | 0.653219i | 0.990644 | − | 0.136470i | \(-0.0435756\pi\) |
−0.613508 | + | 0.789688i | \(0.710242\pi\) | |||||||
\(74\) | −21.0744 | − | 36.5020i | −0.0331061 | − | 0.0573415i | ||||
\(75\) | 569.391 | 0.876635 | ||||||||
\(76\) | 308.080 | + | 121.781i | 0.464990 | + | 0.183806i | ||||
\(77\) | 33.1446 | 0.0490543 | ||||||||
\(78\) | −16.6496 | − | 28.8380i | −0.0241692 | − | 0.0418623i | ||||
\(79\) | −190.946 | − | 330.729i | −0.271938 | − | 0.471011i | 0.697420 | − | 0.716663i | \(-0.254331\pi\) |
−0.969358 | + | 0.245652i | \(0.920998\pi\) | |||||||
\(80\) | −47.4486 | + | 82.1834i | −0.0663115 | + | 0.114855i | ||||
\(81\) | 455.575 | + | 789.079i | 0.624932 | + | 1.08241i | ||||
\(82\) | −344.092 | + | 595.985i | −0.463397 | + | 0.802628i | ||||
\(83\) | 1322.28 | 1.74866 | 0.874330 | − | 0.485332i | \(-0.161301\pi\) | ||||
0.874330 | + | 0.485332i | \(0.161301\pi\) | |||||||
\(84\) | −16.7584 | −0.0217678 | ||||||||
\(85\) | −171.439 | + | 296.942i | −0.218767 | + | 0.378916i | ||||
\(86\) | 265.350 | − | 459.600i | 0.332715 | − | 0.576279i | ||||
\(87\) | −1964.03 | −2.42029 | ||||||||
\(88\) | −401.197 | −0.485997 | ||||||||
\(89\) | −202.744 | + | 351.163i | −0.241470 | + | 0.418239i | −0.961133 | − | 0.276085i | \(-0.910963\pi\) |
0.719663 | + | 0.694323i | \(0.244296\pi\) | |||||||
\(90\) | 78.1953 | + | 135.438i | 0.0915834 | + | 0.158627i | ||||
\(91\) | −0.867948 | + | 1.50333i | −0.000999842 | + | 0.00173178i | ||||
\(92\) | −75.9312 | − | 131.517i | −0.0860475 | − | 0.149039i | ||||
\(93\) | −895.142 | − | 1550.43i | −0.998085 | − | 1.72873i | ||||
\(94\) | 279.587 | 0.306779 | ||||||||
\(95\) | −384.787 | + | 305.324i | −0.415561 | + | 0.329743i | ||||
\(96\) | 202.851 | 0.215660 | ||||||||
\(97\) | −687.074 | − | 1190.05i | −0.719194 | − | 1.24568i | −0.961320 | − | 0.275435i | \(-0.911178\pi\) |
0.242126 | − | 0.970245i | \(-0.422155\pi\) | |||||||
\(98\) | −342.563 | − | 593.337i | −0.353103 | − | 0.611593i | ||||
\(99\) | −330.586 | + | 572.591i | −0.335607 | + | 0.581289i | ||||
\(100\) | 179.645 | + | 311.154i | 0.179645 | + | 0.311154i | ||||
\(101\) | −39.9417 | + | 69.1810i | −0.0393499 | + | 0.0681561i | −0.885030 | − | 0.465535i | \(-0.845862\pi\) |
0.845680 | + | 0.533691i | \(0.179195\pi\) | |||||||
\(102\) | 732.931 | 0.711480 | ||||||||
\(103\) | 1799.73 | 1.72168 | 0.860838 | − | 0.508880i | \(-0.169940\pi\) | ||||
0.860838 | + | 0.508880i | \(0.169940\pi\) | |||||||
\(104\) | 10.5060 | − | 18.1969i | 0.00990575 | − | 0.0171573i | ||||
\(105\) | 12.4244 | − | 21.5197i | 0.0115476 | − | 0.0200011i | ||||
\(106\) | 267.574 | 0.245180 | ||||||||
\(107\) | 69.2556 | 0.0625718 | 0.0312859 | − | 0.999510i | \(-0.490040\pi\) | ||||
0.0312859 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(108\) | −175.162 | + | 303.389i | −0.156064 | + | 0.270311i | ||||
\(109\) | −318.550 | − | 551.744i | −0.279922 | − | 0.484839i | 0.691443 | − | 0.722431i | \(-0.256975\pi\) |
−0.971365 | + | 0.237592i | \(0.923642\pi\) | |||||||
\(110\) | 297.441 | − | 515.183i | 0.257817 | − | 0.446552i | ||||
\(111\) | −66.7963 | − | 115.695i | −0.0571174 | − | 0.0989302i | ||||
\(112\) | −5.28733 | − | 9.15792i | −0.00446076 | − | 0.00772627i | ||||
\(113\) | 235.498 | 0.196051 | 0.0980256 | − | 0.995184i | \(-0.468747\pi\) | ||||
0.0980256 | + | 0.995184i | \(0.468747\pi\) | |||||||
\(114\) | 976.473 | + | 385.989i | 0.802238 | + | 0.317116i | ||||
\(115\) | 225.177 | 0.182590 | ||||||||
\(116\) | −619.656 | − | 1073.28i | −0.495979 | − | 0.859061i | ||||
\(117\) | −17.3139 | − | 29.9885i | −0.0136809 | − | 0.0236961i | ||||
\(118\) | 455.822 | − | 789.507i | 0.355609 | − | 0.615932i | ||||
\(119\) | −19.1039 | − | 33.0890i | −0.0147164 | − | 0.0254896i | ||||
\(120\) | −150.390 | + | 260.484i | −0.114406 | + | 0.198157i | ||||
\(121\) | 1183.98 | 0.889541 | ||||||||
\(122\) | −216.873 | −0.160941 | ||||||||
\(123\) | −1090.61 | + | 1889.00i | −0.799490 | + | 1.38476i | ||||
\(124\) | 564.840 | − | 978.331i | 0.409065 | − | 0.708522i | ||||
\(125\) | −1274.13 | −0.911692 | ||||||||
\(126\) | −17.4270 | −0.0123216 | ||||||||
\(127\) | −449.158 | + | 777.965i | −0.313830 | + | 0.543569i | −0.979188 | − | 0.202955i | \(-0.934945\pi\) |
0.665358 | + | 0.746524i | \(0.268279\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 841.039 | − | 1456.72i | 0.574026 | − | 0.994243i | ||||
\(130\) | 15.5780 | + | 26.9818i | 0.0105098 | + | 0.0182036i | ||||
\(131\) | −327.217 | − | 566.757i | −0.218237 | − | 0.377998i | 0.736032 | − | 0.676947i | \(-0.236697\pi\) |
−0.954269 | + | 0.298949i | \(0.903364\pi\) | |||||||
\(132\) | −1271.61 | −0.838480 | ||||||||
\(133\) | −8.02597 | − | 54.1448i | −0.00523263 | − | 0.0353004i | ||||
\(134\) | −52.7921 | −0.0340339 | ||||||||
\(135\) | −259.724 | − | 449.856i | −0.165582 | − | 0.286796i | ||||
\(136\) | 231.242 | + | 400.523i | 0.145800 | + | 0.252533i | ||||
\(137\) | −1020.79 | + | 1768.07i | −0.636586 | + | 1.10260i | 0.349590 | + | 0.936903i | \(0.386321\pi\) |
−0.986177 | + | 0.165697i | \(0.947013\pi\) | |||||||
\(138\) | −240.667 | − | 416.848i | −0.148456 | − | 0.257133i | ||||
\(139\) | −919.872 | + | 1593.27i | −0.561313 | + | 0.972223i | 0.436069 | + | 0.899913i | \(0.356370\pi\) |
−0.997382 | + | 0.0723100i | \(0.976963\pi\) | |||||||
\(140\) | 15.6798 | 0.00946559 | ||||||||
\(141\) | 886.162 | 0.529279 | ||||||||
\(142\) | −1119.05 | + | 1938.26i | −0.661330 | + | 1.14546i | ||||
\(143\) | −65.8589 | + | 114.071i | −0.0385133 | + | 0.0667070i | ||||
\(144\) | 210.944 | 0.122074 | ||||||||
\(145\) | 1837.61 | 1.05245 | ||||||||
\(146\) | −470.449 | + | 814.841i | −0.266675 | + | 0.461895i | ||||
\(147\) | −1085.77 | − | 1880.61i | −0.609202 | − | 1.05517i | ||||
\(148\) | 42.1489 | − | 73.0040i | 0.0234096 | − | 0.0405466i | ||||
\(149\) | 166.629 | + | 288.610i | 0.0916159 | + | 0.158683i | 0.908191 | − | 0.418556i | \(-0.137463\pi\) |
−0.816575 | + | 0.577239i | \(0.804130\pi\) | |||||||
\(150\) | 569.391 | + | 986.214i | 0.309937 | + | 0.536827i | ||||
\(151\) | 3042.43 | 1.63966 | 0.819832 | − | 0.572604i | \(-0.194067\pi\) | ||||
0.819832 | + | 0.572604i | \(0.194067\pi\) | |||||||
\(152\) | 97.1497 | + | 655.391i | 0.0518413 | + | 0.349732i | ||||
\(153\) | 762.173 | 0.402732 | ||||||||
\(154\) | 33.1446 | + | 57.4082i | 0.0173433 | + | 0.0300395i | ||||
\(155\) | 837.527 | + | 1450.64i | 0.434012 | + | 0.751730i | ||||
\(156\) | 33.2992 | − | 57.6759i | 0.0170902 | − | 0.0296011i | ||||
\(157\) | −984.390 | − | 1705.01i | −0.500400 | − | 0.866719i | −1.00000 | 0.000462343i | \(-0.999853\pi\) | |
0.499600 | − | 0.866256i | \(-0.333481\pi\) | |||||||
\(158\) | 381.892 | − | 661.457i | 0.192289 | − | 0.333055i | ||||
\(159\) | 848.088 | 0.423005 | ||||||||
\(160\) | −189.795 | −0.0937786 | ||||||||
\(161\) | −12.5460 | + | 21.7304i | −0.00614140 | + | 0.0106372i | ||||
\(162\) | −911.150 | + | 1578.16i | −0.441893 | + | 0.765382i | ||||
\(163\) | −1135.59 | −0.545682 | −0.272841 | − | 0.962059i | \(-0.587963\pi\) | ||||
−0.272841 | + | 0.962059i | \(0.587963\pi\) | |||||||
\(164\) | −1376.37 | −0.655343 | ||||||||
\(165\) | 942.752 | − | 1632.89i | 0.444807 | − | 0.770428i | ||||
\(166\) | 1322.28 | + | 2290.25i | 0.618245 | + | 1.07083i | ||||
\(167\) | −395.161 | + | 684.440i | −0.183105 | + | 0.317147i | −0.942936 | − | 0.332973i | \(-0.891948\pi\) |
0.759831 | + | 0.650120i | \(0.225281\pi\) | |||||||
\(168\) | −16.7584 | − | 29.0264i | −0.00769606 | − | 0.0133300i | ||||
\(169\) | 1095.05 | + | 1896.68i | 0.498430 | + | 0.863306i | ||||
\(170\) | −685.757 | −0.309383 | ||||||||
\(171\) | 1015.43 | + | 401.389i | 0.454105 | + | 0.179503i | ||||
\(172\) | 1061.40 | 0.470530 | ||||||||
\(173\) | −1742.00 | − | 3017.24i | −0.765561 | − | 1.32599i | −0.939949 | − | 0.341314i | \(-0.889128\pi\) |
0.174388 | − | 0.984677i | \(-0.444205\pi\) | |||||||
\(174\) | −1964.03 | − | 3401.79i | −0.855703 | − | 1.48212i | ||||
\(175\) | 29.6825 | − | 51.4116i | 0.0128216 | − | 0.0222077i | ||||
\(176\) | −401.197 | − | 694.893i | −0.171826 | − | 0.297611i | ||||
\(177\) | 1444.75 | − | 2502.38i | 0.613525 | − | 1.06266i | ||||
\(178\) | −810.977 | −0.341491 | ||||||||
\(179\) | −2185.23 | −0.912466 | −0.456233 | − | 0.889860i | \(-0.650802\pi\) | ||||
−0.456233 | + | 0.889860i | \(0.650802\pi\) | |||||||
\(180\) | −156.391 | + | 270.876i | −0.0647592 | + | 0.112166i | ||||
\(181\) | −527.946 | + | 914.429i | −0.216806 | + | 0.375519i | −0.953830 | − | 0.300348i | \(-0.902897\pi\) |
0.737024 | + | 0.675867i | \(0.236231\pi\) | |||||||
\(182\) | −3.47179 | −0.00141399 | ||||||||
\(183\) | −687.390 | −0.277668 | ||||||||
\(184\) | 151.862 | − | 263.033i | 0.0608448 | − | 0.105386i | ||||
\(185\) | 62.4971 | + | 108.248i | 0.0248372 | + | 0.0430193i | ||||
\(186\) | 1790.28 | − | 3100.86i | 0.705752 | − | 1.22240i | ||||
\(187\) | −1449.59 | − | 2510.76i | −0.566867 | − | 0.981843i | ||||
\(188\) | 279.587 | + | 484.259i | 0.108463 | + | 0.187863i | ||||
\(189\) | 57.8836 | 0.0222773 | ||||||||
\(190\) | −913.624 | − | 361.146i | −0.348849 | − | 0.137896i | ||||
\(191\) | 2658.51 | 1.00714 | 0.503568 | − | 0.863955i | \(-0.332020\pi\) | ||||
0.503568 | + | 0.863955i | \(0.332020\pi\) | |||||||
\(192\) | 202.851 | + | 351.348i | 0.0762473 | + | 0.132064i | ||||
\(193\) | 2290.25 | + | 3966.82i | 0.854173 | + | 1.47947i | 0.877410 | + | 0.479742i | \(0.159270\pi\) |
−0.0232365 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(194\) | 1374.15 | − | 2380.09i | 0.508547 | − | 0.880829i | ||||
\(195\) | 49.3750 | + | 85.5201i | 0.0181324 | + | 0.0314063i | ||||
\(196\) | 685.126 | − | 1186.67i | 0.249682 | − | 0.432461i | ||||
\(197\) | −4882.92 | −1.76596 | −0.882978 | − | 0.469414i | \(-0.844465\pi\) | ||||
−0.882978 | + | 0.469414i | \(0.844465\pi\) | |||||||
\(198\) | −1322.34 | −0.474620 | ||||||||
\(199\) | 1178.96 | − | 2042.02i | 0.419972 | − | 0.727412i | −0.575965 | − | 0.817475i | \(-0.695373\pi\) |
0.995936 | + | 0.0900626i | \(0.0287067\pi\) | |||||||
\(200\) | −359.289 | + | 622.307i | −0.127028 | + | 0.220019i | ||||
\(201\) | −167.327 | −0.0587180 | ||||||||
\(202\) | −159.767 | −0.0556492 | ||||||||
\(203\) | −102.385 | + | 177.336i | −0.0353991 | + | 0.0613131i | ||||
\(204\) | 732.931 | + | 1269.47i | 0.251546 | + | 0.435691i | ||||
\(205\) | 1020.42 | − | 1767.42i | 0.347654 | − | 0.602154i | ||||
\(206\) | 1799.73 | + | 3117.22i | 0.608704 | + | 1.05431i | ||||
\(207\) | −250.269 | − | 433.478i | −0.0840333 | − | 0.145550i | ||||
\(208\) | 42.0240 | 0.0140088 | ||||||||
\(209\) | −609.002 | − | 4108.45i | −0.201558 | − | 1.35975i | ||||
\(210\) | 49.6977 | 0.0163308 | ||||||||
\(211\) | 1607.63 | + | 2784.49i | 0.524520 | + | 0.908495i | 0.999592 | + | 0.0285486i | \(0.00908855\pi\) |
−0.475072 | + | 0.879947i | \(0.657578\pi\) | |||||||
\(212\) | 267.574 | + | 463.452i | 0.0866844 | + | 0.150142i | ||||
\(213\) | −3546.88 | + | 6143.38i | −1.14098 | + | 1.97623i | ||||
\(214\) | 69.2556 | + | 119.954i | 0.0221225 | + | 0.0383173i | ||||
\(215\) | −786.907 | + | 1362.96i | −0.249612 | + | 0.432341i | ||||
\(216\) | −700.647 | −0.220708 | ||||||||
\(217\) | −186.656 | −0.0583918 | ||||||||
\(218\) | 637.099 | − | 1103.49i | 0.197935 | − | 0.342833i | ||||
\(219\) | −1491.11 | + | 2582.67i | −0.460090 | + | 0.796899i | ||||
\(220\) | 1189.76 | 0.364609 | ||||||||
\(221\) | 151.839 | 0.0462163 | ||||||||
\(222\) | 133.593 | − | 231.389i | 0.0403881 | − | 0.0699542i | ||||
\(223\) | −1732.32 | − | 3000.47i | −0.520202 | − | 0.901016i | −0.999724 | − | 0.0234864i | \(-0.992523\pi\) |
0.479522 | − | 0.877530i | \(-0.340810\pi\) | |||||||
\(224\) | 10.5747 | − | 18.3158i | 0.00315424 | − | 0.00546330i | ||||
\(225\) | 592.108 | + | 1025.56i | 0.175439 | + | 0.303870i | ||||
\(226\) | 235.498 | + | 407.894i | 0.0693146 | + | 0.120056i | ||||
\(227\) | 4831.61 | 1.41271 | 0.706354 | − | 0.707858i | \(-0.250338\pi\) | ||||
0.706354 | + | 0.707858i | \(0.250338\pi\) | |||||||
\(228\) | 307.920 | + | 2077.29i | 0.0894408 | + | 0.603386i | ||||
\(229\) | −4645.49 | −1.34054 | −0.670268 | − | 0.742119i | \(-0.733821\pi\) | ||||
−0.670268 | + | 0.742119i | \(0.733821\pi\) | |||||||
\(230\) | 225.177 | + | 390.018i | 0.0645553 | + | 0.111813i | ||||
\(231\) | 105.053 | + | 181.958i | 0.0299221 | + | 0.0518266i | ||||
\(232\) | 1239.31 | − | 2146.55i | 0.350710 | − | 0.607448i | ||||
\(233\) | 414.255 | + | 717.511i | 0.116475 | + | 0.201741i | 0.918369 | − | 0.395726i | \(-0.129507\pi\) |
−0.801893 | + | 0.597467i | \(0.796174\pi\) | |||||||
\(234\) | 34.6277 | − | 59.9770i | 0.00967387 | − | 0.0167556i | ||||
\(235\) | −829.126 | −0.230154 | ||||||||
\(236\) | 1823.29 | 0.502907 | ||||||||
\(237\) | 1210.42 | − | 2096.52i | 0.331753 | − | 0.574613i | ||||
\(238\) | 38.2079 | − | 66.1780i | 0.0104061 | − | 0.0180239i | ||||
\(239\) | 2735.22 | 0.740279 | 0.370139 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370139 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(240\) | −601.562 | −0.161794 | ||||||||
\(241\) | −2042.41 | + | 3537.56i | −0.545906 | + | 0.945537i | 0.452644 | + | 0.891692i | \(0.350481\pi\) |
−0.998549 | + | 0.0538450i | \(0.982852\pi\) | |||||||
\(242\) | 1183.98 | + | 2050.71i | 0.314500 | + | 0.544731i | ||||
\(243\) | −1705.59 | + | 2954.16i | −0.450261 | + | 0.779875i | ||||
\(244\) | −216.873 | − | 375.636i | −0.0569012 | − | 0.0985558i | ||||
\(245\) | 1015.88 | + | 1759.56i | 0.264908 | + | 0.458834i | ||||
\(246\) | −4362.45 | −1.13065 | ||||||||
\(247\) | 202.293 | + | 79.9643i | 0.0521118 | + | 0.0205992i | ||||
\(248\) | 2259.36 | 0.578506 | ||||||||
\(249\) | 4191.01 | + | 7259.05i | 1.06665 | + | 1.84748i | ||||
\(250\) | −1274.13 | − | 2206.85i | −0.322332 | − | 0.558295i | ||||
\(251\) | 1268.37 | − | 2196.89i | 0.318960 | − | 0.552455i | −0.661311 | − | 0.750112i | \(-0.730000\pi\) |
0.980271 | + | 0.197657i | \(0.0633331\pi\) | |||||||
\(252\) | −17.4270 | − | 30.1845i | −0.00435634 | − | 0.00754541i | ||||
\(253\) | −951.979 | + | 1648.88i | −0.236563 | + | 0.409739i | ||||
\(254\) | −1796.63 | −0.443822 | ||||||||
\(255\) | −2173.54 | −0.533773 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3301.28 | − | 5717.98i | 0.801276 | − | 1.38785i | −0.117501 | − | 0.993073i | \(-0.537488\pi\) |
0.918777 | − | 0.394778i | \(-0.129178\pi\) | |||||||
\(258\) | 3364.16 | 0.811796 | ||||||||
\(259\) | −13.9284 | −0.00334159 | ||||||||
\(260\) | −31.1560 | + | 53.9637i | −0.00743158 | + | 0.0128719i | ||||
\(261\) | −2042.38 | − | 3537.51i | −0.484369 | − | 0.838952i | ||||
\(262\) | 654.434 | − | 1133.51i | 0.154317 | − | 0.267285i | ||||
\(263\) | −1952.28 | − | 3381.44i | −0.457728 | − | 0.792808i | 0.541112 | − | 0.840950i | \(-0.318003\pi\) |
−0.998841 | + | 0.0481419i | \(0.984670\pi\) | |||||||
\(264\) | −1271.61 | − | 2202.49i | −0.296448 | − | 0.513462i | ||||
\(265\) | −793.502 | −0.183941 | ||||||||
\(266\) | 85.7556 | − | 68.0462i | 0.0197670 | − | 0.0156849i | ||||
\(267\) | −2570.43 | −0.589167 | ||||||||
\(268\) | −52.7921 | − | 91.4386i | −0.0120328 | − | 0.0208414i | ||||
\(269\) | 798.358 | + | 1382.80i | 0.180955 | + | 0.313422i | 0.942206 | − | 0.335035i | \(-0.108748\pi\) |
−0.761251 | + | 0.648457i | \(0.775415\pi\) | |||||||
\(270\) | 519.449 | − | 899.712i | 0.117084 | − | 0.202795i | ||||
\(271\) | −2005.70 | − | 3473.97i | −0.449584 | − | 0.778703i | 0.548775 | − | 0.835970i | \(-0.315094\pi\) |
−0.998359 | + | 0.0572677i | \(0.981761\pi\) | |||||||
\(272\) | −462.484 | + | 801.046i | −0.103096 | + | 0.178568i | ||||
\(273\) | −11.0040 | −0.00243953 | ||||||||
\(274\) | −4083.18 | −0.900269 | ||||||||
\(275\) | 2252.28 | − | 3901.05i | 0.493881 | − | 0.855427i | ||||
\(276\) | 481.334 | − | 833.695i | 0.104974 | − | 0.181821i | ||||
\(277\) | 4850.78 | 1.05218 | 0.526092 | − | 0.850427i | \(-0.323657\pi\) | ||||
0.526092 | + | 0.850427i | \(0.323657\pi\) | |||||||
\(278\) | −3679.49 | −0.793817 | ||||||||
\(279\) | 1861.71 | − | 3224.58i | 0.399490 | − | 0.691937i | ||||
\(280\) | 15.6798 | + | 27.1582i | 0.00334659 | + | 0.00579647i | ||||
\(281\) | −3149.49 | + | 5455.08i | −0.668623 | + | 1.15809i | 0.309666 | + | 0.950845i | \(0.399783\pi\) |
−0.978289 | + | 0.207244i | \(0.933551\pi\) | |||||||
\(282\) | 886.162 | + | 1534.88i | 0.187128 | + | 0.324116i | ||||
\(283\) | −2878.50 | − | 4985.72i | −0.604627 | − | 1.04724i | −0.992110 | − | 0.125368i | \(-0.959989\pi\) |
0.387484 | − | 0.921877i | \(-0.373344\pi\) | |||||||
\(284\) | −4476.21 | −0.935261 | ||||||||
\(285\) | −2895.77 | − | 1144.67i | −0.601862 | − | 0.237910i | ||||
\(286\) | −263.436 | −0.0544660 | ||||||||
\(287\) | 113.708 | + | 196.948i | 0.0233866 | + | 0.0405068i | ||||
\(288\) | 210.944 | + | 365.365i | 0.0431597 | + | 0.0747547i | ||||
\(289\) | 785.474 | − | 1360.48i | 0.159877 | − | 0.276914i | ||||
\(290\) | 1837.61 | + | 3182.84i | 0.372098 | + | 0.644492i | ||||
\(291\) | 4355.42 | − | 7543.81i | 0.877386 | − | 1.51968i | ||||
\(292\) | −1881.80 | −0.377136 | ||||||||
\(293\) | 5424.24 | 1.08153 | 0.540763 | − | 0.841175i | \(-0.318135\pi\) | ||||
0.540763 | + | 0.841175i | \(0.318135\pi\) | |||||||
\(294\) | 2171.54 | − | 3761.21i | 0.430771 | − | 0.746117i | ||||
\(295\) | −1351.76 | + | 2341.31i | −0.266788 | + | 0.462090i | ||||
\(296\) | 168.596 | 0.0331061 | ||||||||
\(297\) | 4392.14 | 0.858108 | ||||||||
\(298\) | −333.258 | + | 577.219i | −0.0647822 | + | 0.112206i | ||||
\(299\) | −49.8583 | − | 86.3571i | −0.00964341 | − | 0.0167029i | ||||
\(300\) | −1138.78 | + | 1972.43i | −0.219159 | + | 0.379594i | ||||
\(301\) | −87.6871 | − | 151.879i | −0.0167914 | − | 0.0290835i | ||||
\(302\) | 3042.43 | + | 5269.64i | 0.579709 | + | 1.00409i | ||||
\(303\) | −506.387 | −0.0960105 | ||||||||
\(304\) | −1038.02 | + | 823.660i | −0.195838 | + | 0.155395i | ||||
\(305\) | 643.147 | 0.120743 | ||||||||
\(306\) | 762.173 | + | 1320.12i | 0.142387 | + | 0.246622i | ||||
\(307\) | −2814.93 | − | 4875.60i | −0.523311 | − | 0.906402i | −0.999632 | − | 0.0271299i | \(-0.991363\pi\) |
0.476321 | − | 0.879272i | \(-0.341970\pi\) | |||||||
\(308\) | −66.2893 | + | 114.816i | −0.0122636 | + | 0.0212411i | ||||
\(309\) | 5704.32 | + | 9880.17i | 1.05019 | + | 1.81897i | ||||
\(310\) | −1675.05 | + | 2901.28i | −0.306893 | + | 0.531554i | ||||
\(311\) | 3054.01 | 0.556839 | 0.278420 | − | 0.960460i | \(-0.410189\pi\) | ||||
0.278420 | + | 0.960460i | \(0.410189\pi\) | |||||||
\(312\) | 133.197 | 0.0241692 | ||||||||
\(313\) | 1650.47 | − | 2858.70i | 0.298051 | − | 0.516240i | −0.677639 | − | 0.735395i | \(-0.736997\pi\) |
0.975690 | + | 0.219155i | \(0.0703300\pi\) | |||||||
\(314\) | 1968.78 | − | 3410.03i | 0.353836 | − | 0.612863i | ||||
\(315\) | 51.6805 | 0.00924402 | ||||||||
\(316\) | 1527.57 | 0.271938 | ||||||||
\(317\) | 1585.12 | − | 2745.51i | 0.280850 | − | 0.486446i | −0.690745 | − | 0.723099i | \(-0.742717\pi\) |
0.971594 | + | 0.236653i | \(0.0760504\pi\) | |||||||
\(318\) | 848.088 | + | 1468.93i | 0.149555 | + | 0.259037i | ||||
\(319\) | −7768.87 | + | 13456.1i | −1.36355 | + | 2.36174i | ||||
\(320\) | −189.795 | − | 328.734i | −0.0331557 | − | 0.0574274i | ||||
\(321\) | 219.508 | + | 380.200i | 0.0381675 | + | 0.0661080i | ||||
\(322\) | −50.1841 | −0.00868525 | ||||||||
\(323\) | −3750.53 | + | 2976.01i | −0.646084 | + | 0.512661i | ||||
\(324\) | −3644.60 | −0.624932 | ||||||||
\(325\) | 117.959 | + | 204.311i | 0.0201329 | + | 0.0348712i | ||||
\(326\) | −1135.59 | − | 1966.90i | −0.192928 | − | 0.334160i | ||||
\(327\) | 2019.31 | − | 3497.55i | 0.341493 | − | 0.591483i | ||||
\(328\) | −1376.37 | − | 2383.94i | −0.231699 | − | 0.401314i | ||||
\(329\) | 46.1958 | − | 80.0135i | 0.00774121 | − | 0.0134082i | ||||
\(330\) | 3771.01 | 0.629052 | ||||||||
\(331\) | 1414.75 | 0.234929 | 0.117465 | − | 0.993077i | \(-0.462523\pi\) | ||||
0.117465 | + | 0.993077i | \(0.462523\pi\) | |||||||
\(332\) | −2644.55 | + | 4580.50i | −0.437165 | + | 0.757192i | ||||
\(333\) | 138.923 | − | 240.621i | 0.0228616 | − | 0.0395975i | ||||
\(334\) | −1580.65 | −0.258949 | ||||||||
\(335\) | 156.557 | 0.0255332 | ||||||||
\(336\) | 33.5168 | − | 58.0528i | 0.00544194 | − | 0.00942572i | ||||
\(337\) | 1079.89 | + | 1870.42i | 0.174555 | + | 0.302339i | 0.940007 | − | 0.341154i | \(-0.110818\pi\) |
−0.765452 | + | 0.643493i | \(0.777485\pi\) | |||||||
\(338\) | −2190.10 | + | 3793.37i | −0.352443 | + | 0.610450i | ||||
\(339\) | 746.421 | + | 1292.84i | 0.119587 | + | 0.207131i | ||||
\(340\) | −685.757 | − | 1187.77i | −0.109384 | − | 0.189458i | ||||
\(341\) | −14163.2 | −2.24922 | ||||||||
\(342\) | 320.205 | + | 2160.17i | 0.0506278 | + | 0.341545i | ||||
\(343\) | −453.100 | −0.0713267 | ||||||||
\(344\) | 1061.40 | + | 1838.40i | 0.166357 | + | 0.288139i | ||||
\(345\) | 713.708 | + | 1236.18i | 0.111376 | + | 0.192909i | ||||
\(346\) | 3484.01 | − | 6034.48i | 0.541333 | − | 0.937617i | ||||
\(347\) | 2734.38 | + | 4736.09i | 0.423024 | + | 0.732699i | 0.996234 | − | 0.0867100i | \(-0.0276353\pi\) |
−0.573210 | + | 0.819409i | \(0.694302\pi\) | |||||||
\(348\) | 3928.05 | − | 6803.58i | 0.605074 | − | 1.04802i | ||||
\(349\) | −3235.26 | −0.496216 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(350\) | 118.730 | 0.0181325 | ||||||||
\(351\) | −115.016 | + | 199.213i | −0.0174902 | + | 0.0302940i | ||||
\(352\) | 802.393 | − | 1389.79i | 0.121499 | − | 0.210443i | ||||
\(353\) | −6191.72 | −0.933576 | −0.466788 | − | 0.884369i | \(-0.654589\pi\) | ||||
−0.466788 | + | 0.884369i | \(0.654589\pi\) | |||||||
\(354\) | 5778.99 | 0.867655 | ||||||||
\(355\) | 3318.59 | − | 5747.97i | 0.496148 | − | 0.859354i | ||||
\(356\) | −810.977 | − | 1404.65i | −0.120735 | − | 0.209119i | ||||
\(357\) | 121.101 | − | 209.754i | 0.0179534 | − | 0.0310962i | ||||
\(358\) | −2185.23 | − | 3784.92i | −0.322606 | − | 0.558769i | ||||
\(359\) | 3203.54 | + | 5548.69i | 0.470964 | + | 0.815734i | 0.999448 | − | 0.0332089i | \(-0.0105727\pi\) |
−0.528484 | + | 0.848943i | \(0.677239\pi\) | |||||||
\(360\) | −625.562 | −0.0915834 | ||||||||
\(361\) | −6564.06 | + | 1989.72i | −0.957000 | + | 0.290089i | ||||
\(362\) | −2111.78 | −0.306610 | ||||||||
\(363\) | 3752.67 | + | 6499.82i | 0.542601 | + | 0.939813i | ||||
\(364\) | −3.47179 | − | 6.01332i | −0.000499921 | − | 0.000865889i | ||||
\(365\) | 1395.13 | − | 2416.44i | 0.200068 | − | 0.346527i | ||||
\(366\) | −687.390 | − | 1190.59i | −0.0981706 | − | 0.170036i | ||||
\(367\) | −4184.47 | + | 7247.72i | −0.595171 | + | 1.03087i | 0.398352 | + | 0.917233i | \(0.369582\pi\) |
−0.993523 | + | 0.113633i | \(0.963751\pi\) | |||||||
\(368\) | 607.449 | 0.0860475 | ||||||||
\(369\) | −4536.50 | −0.640003 | ||||||||
\(370\) | −124.994 | + | 216.496i | −0.0175625 | + | 0.0304192i | ||||
\(371\) | 44.2110 | − | 76.5758i | 0.00618685 | − | 0.0107159i | ||||
\(372\) | 7161.13 | 0.998085 | ||||||||
\(373\) | 10254.9 | 1.42354 | 0.711769 | − | 0.702414i | \(-0.247894\pi\) | ||||
0.711769 | + | 0.702414i | \(0.247894\pi\) | |||||||
\(374\) | 2899.17 | − | 5021.51i | 0.400836 | − | 0.694268i | ||||
\(375\) | −4038.40 | − | 6994.72i | −0.556113 | − | 0.963215i | ||||
\(376\) | −559.174 | + | 968.517i | −0.0766946 | + | 0.132839i | ||||
\(377\) | −406.881 | − | 704.739i | −0.0555848 | − | 0.0962757i | ||||
\(378\) | 57.8836 | + | 100.257i | 0.00787622 | + | 0.0136420i | ||||
\(379\) | 6607.19 | 0.895484 | 0.447742 | − | 0.894163i | \(-0.352228\pi\) | ||||
0.447742 | + | 0.894163i | \(0.352228\pi\) | |||||||
\(380\) | −288.101 | − | 1943.59i | −0.0388928 | − | 0.262379i | ||||
\(381\) | −5694.50 | −0.765717 | ||||||||
\(382\) | 2658.51 | + | 4604.68i | 0.356077 | + | 0.616743i | ||||
\(383\) | 4.97873 | + | 8.62342i | 0.000664233 | + | 0.00115049i | 0.866357 | − | 0.499425i | \(-0.166455\pi\) |
−0.865693 | + | 0.500575i | \(0.833122\pi\) | |||||||
\(384\) | −405.701 | + | 702.695i | −0.0539150 | + | 0.0933835i | ||||
\(385\) | −98.2917 | − | 170.246i | −0.0130115 | − | 0.0225365i | ||||
\(386\) | −4580.49 | + | 7933.64i | −0.603992 | + | 1.04614i | ||||
\(387\) | 3498.38 | 0.459515 | ||||||||
\(388\) | 5496.59 | 0.719194 | ||||||||
\(389\) | 6190.75 | − | 10722.7i | 0.806898 | − | 1.39759i | −0.108104 | − | 0.994140i | \(-0.534478\pi\) |
0.915002 | − | 0.403449i | \(-0.132189\pi\) | |||||||
\(390\) | −98.7501 | + | 171.040i | −0.0128216 | + | 0.0222076i | ||||
\(391\) | 2194.81 | 0.283878 | ||||||||
\(392\) | 2740.51 | 0.353103 | ||||||||
\(393\) | 2074.26 | − | 3592.72i | 0.266240 | − | 0.461142i | ||||
\(394\) | −4882.92 | − | 8457.46i | −0.624360 | − | 1.08142i | ||||
\(395\) | −1132.52 | + | 1961.58i | −0.144261 | + | 0.249867i | ||||
\(396\) | −1322.34 | − | 2290.36i | −0.167804 | − | 0.290644i | ||||
\(397\) | −301.966 | − | 523.020i | −0.0381744 | − | 0.0661199i | 0.846307 | − | 0.532696i | \(-0.178821\pi\) |
−0.884481 | + | 0.466576i | \(0.845488\pi\) | |||||||
\(398\) | 4715.84 | 0.593930 | ||||||||
\(399\) | 271.806 | − | 215.675i | 0.0341036 | − | 0.0270608i | ||||
\(400\) | −1437.16 | −0.179645 | ||||||||
\(401\) | −5170.14 | − | 8954.94i | −0.643851 | − | 1.11518i | −0.984566 | − | 0.175016i | \(-0.944002\pi\) |
0.340715 | − | 0.940167i | \(-0.389331\pi\) | |||||||
\(402\) | −167.327 | − | 289.818i | −0.0207599 | − | 0.0359573i | ||||
\(403\) | 370.888 | − | 642.397i | 0.0458443 | − | 0.0794046i | ||||
\(404\) | −159.767 | − | 276.724i | −0.0196750 | − | 0.0340780i | ||||
\(405\) | 2702.05 | − | 4680.09i | 0.331521 | − | 0.574211i | ||||
\(406\) | −409.540 | −0.0500619 | ||||||||
\(407\) | −1056.87 | −0.128716 | ||||||||
\(408\) | −1465.86 | + | 2538.95i | −0.177870 | + | 0.308080i | ||||
\(409\) | 80.7101 | − | 139.794i | 0.00975760 | − | 0.0169007i | −0.861105 | − | 0.508427i | \(-0.830227\pi\) |
0.870863 | + | 0.491526i | \(0.163561\pi\) | |||||||
\(410\) | 4081.67 | 0.491657 | ||||||||
\(411\) | −12941.8 | −1.55322 | ||||||||
\(412\) | −3599.46 | + | 6234.44i | −0.430419 | + | 0.745507i | ||||
\(413\) | −150.630 | − | 260.899i | −0.0179468 | − | 0.0310847i | ||||
\(414\) | 500.538 | − | 866.957i | 0.0594205 | − | 0.102919i | ||||
\(415\) | −3921.27 | − | 6791.83i | −0.463825 | − | 0.803368i | ||||
\(416\) | 42.0240 | + | 72.7877i | 0.00495287 | + | 0.00857863i | ||||
\(417\) | −11662.3 | −1.36956 | ||||||||
\(418\) | 6507.04 | − | 5163.27i | 0.761411 | − | 0.604172i | ||||
\(419\) | 7483.41 | 0.872526 | 0.436263 | − | 0.899819i | \(-0.356302\pi\) | ||||
0.436263 | + | 0.899819i | \(0.356302\pi\) | |||||||
\(420\) | 49.6977 | + | 86.0789i | 0.00577381 | + | 0.0100005i | ||||
\(421\) | −3024.77 | − | 5239.05i | −0.350162 | − | 0.606498i | 0.636116 | − | 0.771594i | \(-0.280540\pi\) |
−0.986278 | + | 0.165096i | \(0.947207\pi\) | |||||||
\(422\) | −3215.26 | + | 5568.99i | −0.370892 | + | 0.642403i | ||||
\(423\) | 921.517 | + | 1596.11i | 0.105924 | + | 0.183465i | ||||
\(424\) | −535.149 | + | 926.905i | −0.0612951 | + | 0.106166i | ||||
\(425\) | −5192.67 | −0.592663 | ||||||||
\(426\) | −14187.5 | −1.61359 | ||||||||
\(427\) | −35.8338 | + | 62.0659i | −0.00406117 | + | 0.00703415i | ||||
\(428\) | −138.511 | + | 239.908i | −0.0156430 | + | 0.0270944i | ||||
\(429\) | −834.970 | −0.0939691 | ||||||||
\(430\) | −3147.63 | −0.353005 | ||||||||
\(431\) | −5454.85 | + | 9448.08i | −0.609631 | + | 1.05591i | 0.381670 | + | 0.924299i | \(0.375349\pi\) |
−0.991301 | + | 0.131613i | \(0.957984\pi\) | |||||||
\(432\) | −700.647 | − | 1213.56i | −0.0780321 | − | 0.135156i | ||||
\(433\) | 3824.48 | − | 6624.19i | 0.424464 | − | 0.735193i | −0.571906 | − | 0.820319i | \(-0.693796\pi\) |
0.996370 | + | 0.0851261i | \(0.0271293\pi\) | |||||||
\(434\) | −186.656 | − | 323.297i | −0.0206446 | − | 0.0357575i | ||||
\(435\) | 5824.39 | + | 10088.1i | 0.641973 | + | 1.11193i | ||||
\(436\) | 2548.40 | 0.279922 | ||||||||
\(437\) | 2924.11 | + | 1155.87i | 0.320090 | + | 0.126528i | ||||
\(438\) | −5964.43 | −0.650665 | ||||||||
\(439\) | 5707.94 | + | 9886.44i | 0.620558 | + | 1.07484i | 0.989382 | + | 0.145339i | \(0.0464272\pi\) |
−0.368824 | + | 0.929499i | \(0.620239\pi\) | |||||||
\(440\) | 1189.76 | + | 2060.73i | 0.128909 | + | 0.223276i | ||||
\(441\) | 2258.17 | − | 3911.27i | 0.243837 | − | 0.422338i | ||||
\(442\) | 151.839 | + | 262.993i | 0.0163399 | + | 0.0283016i | ||||
\(443\) | 1576.33 | − | 2730.28i | 0.169060 | − | 0.292820i | −0.769030 | − | 0.639213i | \(-0.779260\pi\) |
0.938090 | + | 0.346393i | \(0.112594\pi\) | |||||||
\(444\) | 534.371 | 0.0571174 | ||||||||
\(445\) | 2404.98 | 0.256196 | ||||||||
\(446\) | 3464.65 | − | 6000.95i | 0.367838 | − | 0.637115i | ||||
\(447\) | −1056.27 | + | 1829.52i | −0.111767 | + | 0.193587i | ||||
\(448\) | 42.2986 | 0.00446076 | ||||||||
\(449\) | 5217.04 | 0.548346 | 0.274173 | − | 0.961680i | \(-0.411596\pi\) | ||||
0.274173 | + | 0.961680i | \(0.411596\pi\) | |||||||
\(450\) | −1184.22 | + | 2051.12i | −0.124054 | + | 0.214869i | ||||
\(451\) | 8628.03 | + | 14944.2i | 0.900838 | + | 1.56030i | ||||
\(452\) | −470.996 | + | 815.789i | −0.0490128 | + | 0.0848927i | ||||
\(453\) | 9643.10 | + | 16702.3i | 1.00016 | + | 1.73233i | ||||
\(454\) | 4831.61 | + | 8368.59i | 0.499468 | + | 0.865104i | ||||
\(455\) | 10.2957 | 0.00106082 | ||||||||
\(456\) | −3290.05 | + | 2610.62i | −0.337875 | + | 0.268100i | ||||
\(457\) | 15868.7 | 1.62430 | 0.812151 | − | 0.583447i | \(-0.198297\pi\) | ||||
0.812151 | + | 0.583447i | \(0.198297\pi\) | |||||||
\(458\) | −4645.49 | − | 8046.23i | −0.473951 | − | 0.820907i | ||||
\(459\) | −2531.55 | − | 4384.77i | −0.257435 | − | 0.445890i | ||||
\(460\) | −450.354 | + | 780.036i | −0.0456475 | + | 0.0790638i | ||||
\(461\) | 2170.58 | + | 3759.56i | 0.219293 | + | 0.379827i | 0.954592 | − | 0.297916i | \(-0.0962915\pi\) |
−0.735299 | + | 0.677743i | \(0.762958\pi\) | |||||||
\(462\) | −210.107 | + | 363.915i | −0.0211581 | + | 0.0366469i | ||||
\(463\) | −1394.23 | −0.139946 | −0.0699732 | − | 0.997549i | \(-0.522291\pi\) | ||||
−0.0699732 | + | 0.997549i | \(0.522291\pi\) | |||||||
\(464\) | 4957.25 | 0.495979 | ||||||||
\(465\) | −5309.16 | + | 9195.73i | −0.529476 | + | 0.917079i | ||||
\(466\) | −828.510 | + | 1435.02i | −0.0823605 | + | 0.142653i | ||||
\(467\) | 6138.35 | 0.608242 | 0.304121 | − | 0.952633i | \(-0.401637\pi\) | ||||
0.304121 | + | 0.952633i | \(0.401637\pi\) | |||||||
\(468\) | 138.511 | 0.0136809 | ||||||||
\(469\) | −8.72278 | + | 15.1083i | −0.000858807 | + | 0.00148750i | ||||
\(470\) | −829.126 | − | 1436.09i | −0.0813717 | − | 0.140940i | ||||
\(471\) | 6240.13 | − | 10808.2i | 0.610467 | − | 1.05736i | ||||
\(472\) | 1823.29 | + | 3158.03i | 0.177804 | + | 0.307966i | ||||
\(473\) | −6653.60 | − | 11524.4i | −0.646793 | − | 1.12028i | ||||
\(474\) | 4841.70 | 0.469170 | ||||||||
\(475\) | −6918.12 | − | 2734.66i | −0.668263 | − | 0.264157i | ||||
\(476\) | 152.831 | 0.0147164 | ||||||||
\(477\) | 881.925 | + | 1527.54i | 0.0846552 | + | 0.146627i | ||||
\(478\) | 2735.22 | + | 4737.54i | 0.261728 | + | 0.453326i | ||||
\(479\) | −3566.47 | + | 6177.31i | −0.340201 | + | 0.589245i | −0.984470 | − | 0.175554i | \(-0.943828\pi\) |
0.644269 | + | 0.764799i | \(0.277162\pi\) | |||||||
\(480\) | −601.562 | − | 1041.94i | −0.0572029 | − | 0.0990784i | ||||
\(481\) | 27.6760 | − | 47.9363i | 0.00262353 | − | 0.00454409i | ||||
\(482\) | −8169.65 | −0.772027 | ||||||||
\(483\) | −159.061 | −0.0149845 | ||||||||
\(484\) | −2367.96 | + | 4101.43i | −0.222385 | + | 0.385183i | ||||
\(485\) | −4075.09 | + | 7058.26i | −0.381526 | + | 0.660823i | ||||
\(486\) | −6822.35 | −0.636765 | ||||||||
\(487\) | −14396.6 | −1.33957 | −0.669787 | − | 0.742553i | \(-0.733615\pi\) | ||||
−0.669787 | + | 0.742553i | \(0.733615\pi\) | |||||||
\(488\) | 433.747 | − | 751.272i | 0.0402352 | − | 0.0696895i | ||||
\(489\) | −3599.29 | − | 6234.16i | −0.332854 | − | 0.576520i | ||||
\(490\) | −2031.77 | + | 3519.13i | −0.187318 | + | 0.324445i | ||||
\(491\) | −3827.91 | − | 6630.13i | −0.351835 | − | 0.609396i | 0.634736 | − | 0.772729i | \(-0.281109\pi\) |
−0.986571 | + | 0.163333i | \(0.947775\pi\) | |||||||
\(492\) | −4362.45 | − | 7555.99i | −0.399745 | − | 0.692379i | ||||
\(493\) | 17911.3 | 1.63628 | ||||||||
\(494\) | 63.7909 | + | 430.346i | 0.00580989 | + | 0.0391947i | ||||
\(495\) | 3921.46 | 0.356074 | ||||||||
\(496\) | 2259.36 | + | 3913.33i | 0.204533 | + | 0.354261i | ||||
\(497\) | 369.800 | + | 640.512i | 0.0333758 | + | 0.0578086i | ||||
\(498\) | −8382.03 | + | 14518.1i | −0.754232 | + | 1.30637i | ||||
\(499\) | −9319.05 | − | 16141.1i | −0.836028 | − | 1.44804i | −0.893191 | − | 0.449678i | \(-0.851539\pi\) |
0.0571628 | − | 0.998365i | \(-0.481795\pi\) | |||||||
\(500\) | 2548.26 | − | 4413.71i | 0.227923 | − | 0.394774i | ||||
\(501\) | −5009.92 | −0.446760 | ||||||||
\(502\) | 5073.49 | 0.451077 | ||||||||
\(503\) | 3739.79 | − | 6477.50i | 0.331509 | − | 0.574190i | −0.651299 | − | 0.758821i | \(-0.725776\pi\) |
0.982808 | + | 0.184631i | \(0.0591091\pi\) | |||||||
\(504\) | 34.8540 | − | 60.3689i | 0.00308040 | − | 0.00533541i | ||||
\(505\) | 473.794 | 0.0417496 | ||||||||
\(506\) | −3807.92 | −0.334550 | ||||||||
\(507\) | −6941.62 | + | 12023.2i | −0.608063 | + | 1.05320i | ||||
\(508\) | −1796.63 | − | 3111.86i | −0.156915 | − | 0.271784i | ||||
\(509\) | 9355.19 | − | 16203.7i | 0.814659 | − | 1.41103i | −0.0949131 | − | 0.995486i | \(-0.530257\pi\) |
0.909572 | − | 0.415546i | \(-0.136409\pi\) | |||||||
\(510\) | −2173.54 | − | 3764.67i | −0.188717 | − | 0.326868i | ||||
\(511\) | 155.464 | + | 269.271i | 0.0134585 | + | 0.0233108i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −1063.56 | − | 7174.97i | −0.0915344 | − | 0.617510i | ||||
\(514\) | 13205.1 | 1.13318 | ||||||||
\(515\) | −5337.17 | − | 9244.24i | −0.456667 | − | 0.790971i | ||||
\(516\) | 3364.16 | + | 5826.89i | 0.287013 | + | 0.497121i | ||||
\(517\) | 3505.29 | − | 6071.34i | 0.298187 | − | 0.516474i | ||||
\(518\) | −13.9284 | − | 24.1248i | −0.00118143 | − | 0.00204630i | ||||
\(519\) | 11042.7 | − | 19126.5i | 0.933952 | − | 1.61765i | ||||
\(520\) | −124.624 | −0.0105098 | ||||||||
\(521\) | −13796.0 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(522\) | 4084.77 | − | 7075.03i | 0.342501 | − | 0.593229i | ||||
\(523\) | −6222.14 | + | 10777.1i | −0.520221 | + | 0.901048i | 0.479503 | + | 0.877540i | \(0.340817\pi\) |
−0.999724 | + | 0.0235083i | \(0.992516\pi\) | |||||||
\(524\) | 2617.74 | 0.218237 | ||||||||
\(525\) | 376.320 | 0.0312837 | ||||||||
\(526\) | 3904.55 | − | 6762.88i | 0.323663 | − | 0.560600i | ||||
\(527\) | 8163.42 | + | 14139.5i | 0.674770 | + | 1.16874i | ||||
\(528\) | 2543.22 | − | 4404.98i | 0.209620 | − | 0.363073i | ||||
\(529\) | 5362.81 | + | 9288.65i | 0.440767 | + | 0.763430i | ||||
\(530\) | −793.502 | − | 1374.39i | −0.0650331 | − | 0.112641i | ||||
\(531\) | 6009.55 | 0.491135 | ||||||||
\(532\) | 203.615 | + | 80.4869i | 0.0165937 | + | 0.00655930i | ||||
\(533\) | −903.757 | −0.0734448 | ||||||||
\(534\) | −2570.43 | − | 4452.11i | −0.208302 | − | 0.360790i | ||||
\(535\) | −205.380 | − | 355.729i | −0.0165969 | − | 0.0287467i | ||||
\(536\) | 105.584 | − | 182.877i | 0.00850847 | − | 0.0147371i | ||||
\(537\) | −6926.17 | − | 11996.5i | −0.556585 | − | 0.964034i | ||||
\(538\) | −1596.72 | + | 2765.59i | −0.127954 | + | 0.221623i | ||||
\(539\) | −17179.4 | −1.37286 | ||||||||
\(540\) | 2077.80 | 0.165582 | ||||||||
\(541\) | −8883.44 | + | 15386.6i | −0.705968 | + | 1.22277i | 0.260373 | + | 0.965508i | \(0.416155\pi\) |
−0.966341 | + | 0.257265i | \(0.917179\pi\) | |||||||
\(542\) | 4011.39 | − | 6947.93i | 0.317904 | − | 0.550626i | ||||
\(543\) | −6693.39 | −0.528988 | ||||||||
\(544\) | −1849.94 | −0.145800 | ||||||||
\(545\) | −1889.34 | + | 3272.44i | −0.148496 | + | 0.257203i | ||||
\(546\) | −11.0040 | − | 19.0595i | −0.000862504 | − | 0.00149390i | ||||
\(547\) | 3595.49 | − | 6227.58i | 0.281046 | − | 0.486786i | −0.690597 | − | 0.723240i | \(-0.742652\pi\) |
0.971643 | + | 0.236454i | \(0.0759853\pi\) | |||||||
\(548\) | −4083.18 | − | 7072.27i | −0.318293 | − | 0.551300i | ||||
\(549\) | −714.814 | − | 1238.09i | −0.0555693 | − | 0.0962488i | ||||
\(550\) | 9009.10 | 0.698453 | ||||||||
\(551\) | 23863.0 | + | 9432.77i | 1.84500 | + | 0.729310i | ||||
\(552\) | 1925.34 | 0.148456 | ||||||||
\(553\) | −126.199 | − | 218.584i | −0.00970442 | − | 0.0168085i | ||||
\(554\) | 4850.78 | + | 8401.80i | 0.372003 | + | 0.644329i | ||||
\(555\) | −396.174 | + | 686.194i | −0.0303003 | + | 0.0524817i | ||||
\(556\) | −3679.49 | − | 6373.06i | −0.280657 | − | 0.486112i | ||||
\(557\) | −9244.53 | + | 16012.0i | −0.703238 | + | 1.21804i | 0.264086 | + | 0.964499i | \(0.414930\pi\) |
−0.967324 | + | 0.253544i | \(0.918404\pi\) | |||||||
\(558\) | 7446.84 | 0.564964 | ||||||||
\(559\) | 696.943 | 0.0527326 | ||||||||
\(560\) | −31.3595 | + | 54.3163i | −0.00236640 | + | 0.00409872i | ||||
\(561\) | 9189.05 | − | 15915.9i | 0.691554 | − | 1.19781i | ||||
\(562\) | −12598.0 | −0.945576 | ||||||||
\(563\) | 4932.37 | 0.369227 | 0.184613 | − | 0.982811i | \(-0.440897\pi\) | ||||
0.184613 | + | 0.982811i | \(0.440897\pi\) | |||||||
\(564\) | −1772.32 | + | 3069.76i | −0.132320 | + | 0.229184i | ||||
\(565\) | −698.379 | − | 1209.63i | −0.0520018 | − | 0.0900697i | ||||
\(566\) | 5757.01 | − | 9971.43i | 0.427536 | − | 0.740513i | ||||
\(567\) | 301.097 | + | 521.515i | 0.0223014 | + | 0.0386271i | ||||
\(568\) | −4476.21 | − | 7753.02i | −0.330665 | − | 0.572728i | ||||
\(569\) | −15002.9 | −1.10537 | −0.552683 | − | 0.833392i | \(-0.686396\pi\) | ||||
−0.552683 | + | 0.833392i | \(0.686396\pi\) | |||||||
\(570\) | −913.149 | − | 6160.29i | −0.0671010 | − | 0.452677i | ||||
\(571\) | −13385.3 | −0.981013 | −0.490507 | − | 0.871438i | \(-0.663188\pi\) | ||||
−0.490507 | + | 0.871438i | \(0.663188\pi\) | |||||||
\(572\) | −263.436 | − | 456.284i | −0.0192566 | − | 0.0333535i | ||||
\(573\) | 8426.26 | + | 14594.7i | 0.614332 | + | 1.06405i | ||||
\(574\) | −227.416 | + | 393.896i | −0.0165368 | + | 0.0286427i | ||||
\(575\) | 1705.08 | + | 2953.28i | 0.123664 | + | 0.214192i | ||||
\(576\) | −421.888 | + | 730.731i | −0.0305185 | + | 0.0528596i | ||||
\(577\) | 4891.89 | 0.352950 | 0.176475 | − | 0.984305i | \(-0.443531\pi\) | ||||
0.176475 | + | 0.984305i | \(0.443531\pi\) | |||||||
\(578\) | 3141.89 | 0.226100 | ||||||||
\(579\) | −14518.1 | + | 25146.0i | −1.04206 | + | 1.80489i | ||||
\(580\) | −3675.23 | + | 6365.68i | −0.263113 | + | 0.455725i | ||||
\(581\) | 873.914 | 0.0624029 | ||||||||
\(582\) | 17421.7 | 1.24081 | ||||||||
\(583\) | 3354.69 | − | 5810.49i | 0.238314 | − | 0.412771i | ||||
\(584\) | −1881.80 | − | 3259.36i | −0.133338 | − | 0.230948i | ||||
\(585\) | −102.690 | + | 177.864i | −0.00725762 | + | 0.0125706i | ||||
\(586\) | 5424.24 | + | 9395.05i | 0.382377 | + | 0.662297i | ||||
\(587\) | 6191.21 | + | 10723.5i | 0.435330 | + | 0.754013i | 0.997322 | − | 0.0731291i | \(-0.0232985\pi\) |
−0.561993 | + | 0.827142i | \(0.689965\pi\) | |||||||
\(588\) | 8686.15 | 0.609202 | ||||||||
\(589\) | 3429.62 | + | 23136.9i | 0.239924 | + | 1.61858i | ||||
\(590\) | −5407.03 | −0.377295 | ||||||||
\(591\) | −15476.6 | − | 26806.3i | −1.07720 | − | 1.86576i | ||||
\(592\) | 168.596 | + | 292.016i | 0.0117048 | + | 0.0202733i | ||||
\(593\) | −11263.1 | + | 19508.2i | −0.779964 | + | 1.35094i | 0.151998 | + | 0.988381i | \(0.451429\pi\) |
−0.931962 | + | 0.362557i | \(0.881904\pi\) | |||||||
\(594\) | 4392.14 | + | 7607.41i | 0.303387 | + | 0.525481i | ||||
\(595\) | −113.307 | + | 196.253i | −0.00780694 | + | 0.0135220i | ||||
\(596\) | −1333.03 | −0.0916159 | ||||||||
\(597\) | 14947.1 | 1.02469 | ||||||||
\(598\) | 99.7166 | − | 172.714i | 0.00681892 | − | 0.0118107i | ||||
\(599\) | 4370.13 | − | 7569.30i | 0.298095 | − | 0.516316i | −0.677605 | − | 0.735426i | \(-0.736982\pi\) |
0.975700 | + | 0.219110i | \(0.0703155\pi\) | |||||||
\(600\) | −4555.13 | −0.309937 | ||||||||
\(601\) | −6198.75 | −0.420719 | −0.210360 | − | 0.977624i | \(-0.567463\pi\) | ||||
−0.210360 | + | 0.977624i | \(0.567463\pi\) | |||||||
\(602\) | 175.374 | − | 303.757i | 0.0118733 | − | 0.0205651i | ||||
\(603\) | −174.003 | − | 301.381i | −0.0117511 | − | 0.0203536i | ||||
\(604\) | −6084.86 | + | 10539.3i | −0.409916 | + | 0.709995i | ||||
\(605\) | −3511.14 | − | 6081.47i | −0.235947 | − | 0.408673i | ||||
\(606\) | −506.387 | − | 877.088i | −0.0339448 | − | 0.0587942i | ||||
\(607\) | 9848.40 | 0.658541 | 0.329271 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329271 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(608\) | −2464.64 | − | 974.247i | −0.164399 | − | 0.0649851i | ||||
\(609\) | −1298.06 | −0.0863709 | ||||||||
\(610\) | 643.147 | + | 1113.96i | 0.0426889 | + | 0.0739394i | ||||
\(611\) | 183.584 | + | 317.976i | 0.0121555 | + | 0.0210539i | ||||
\(612\) | −1524.35 | + | 2640.24i | −0.100683 | + | 0.174388i | ||||
\(613\) | −4831.89 | − | 8369.08i | −0.318366 | − | 0.551426i | 0.661782 | − | 0.749697i | \(-0.269801\pi\) |
−0.980147 | + | 0.198271i | \(0.936467\pi\) | |||||||
\(614\) | 5629.86 | − | 9751.20i | 0.370037 | − | 0.640923i | ||||
\(615\) | 12937.0 | 0.848246 | ||||||||
\(616\) | −265.157 | −0.0173433 | ||||||||
\(617\) | −2596.83 | + | 4497.84i | −0.169440 | + | 0.293479i | −0.938223 | − | 0.346031i | \(-0.887529\pi\) |
0.768783 | + | 0.639510i | \(0.220863\pi\) | |||||||
\(618\) | −11408.6 | + | 19760.3i | −0.742593 | + | 1.28621i | ||||
\(619\) | 5299.50 | 0.344112 | 0.172056 | − | 0.985087i | \(-0.444959\pi\) | ||||
0.172056 | + | 0.985087i | \(0.444959\pi\) | |||||||
\(620\) | −6700.22 | −0.434012 | ||||||||
\(621\) | −1662.53 | + | 2879.59i | −0.107432 | + | 0.186077i | ||||
\(622\) | 3054.01 | + | 5289.70i | 0.196872 | + | 0.340993i | ||||
\(623\) | −133.997 | + | 232.089i | −0.00861713 | + | 0.0149253i | ||||
\(624\) | 133.197 | + | 230.704i | 0.00854510 | + | 0.0148005i | ||||
\(625\) | −1835.42 | − | 3179.04i | −0.117467 | − | 0.203458i | ||||
\(626\) | 6601.88 | 0.421508 | ||||||||
\(627\) | 20624.3 | − | 16365.2i | 1.31365 | − | 1.04237i | ||||
\(628\) | 7875.12 | 0.500400 | ||||||||
\(629\) | 609.162 | + | 1055.10i | 0.0386151 | + | 0.0668833i | ||||
\(630\) | 51.6805 | + | 89.5132i | 0.00326825 | + | 0.00566078i | ||||
\(631\) | 7139.19 | − | 12365.4i | 0.450407 | − | 0.780128i | −0.548004 | − | 0.836476i | \(-0.684612\pi\) |
0.998411 | + | 0.0563477i | \(0.0179455\pi\) | |||||||
\(632\) | 1527.57 | + | 2645.83i | 0.0961447 | + | 0.166528i | ||||
\(633\) | −10190.9 | + | 17651.1i | −0.639892 | + | 1.10833i | ||||
\(634\) | 6340.49 | 0.397181 | ||||||||
\(635\) | 5327.99 | 0.332968 | ||||||||
\(636\) | −1696.18 | + | 2937.86i | −0.105751 | + | 0.183167i | ||||
\(637\) | 449.871 | − | 779.200i | 0.0279820 | − | 0.0484663i | ||||
\(638\) | −31075.5 | −1.92835 | ||||||||
\(639\) | −14753.6 | −0.913369 | ||||||||
\(640\) | 379.589 | − | 657.467i | 0.0234446 | − | 0.0406073i | ||||
\(641\) | 6435.92 | + | 11147.3i | 0.396574 | + | 0.686886i | 0.993301 | − | 0.115559i | \(-0.0368658\pi\) |
−0.596727 | + | 0.802444i | \(0.703532\pi\) | |||||||
\(642\) | −439.017 | + | 760.399i | −0.0269885 | + | 0.0467454i | ||||
\(643\) | −8535.69 | − | 14784.2i | −0.523506 | − | 0.906740i | −0.999626 | − | 0.0273590i | \(-0.991290\pi\) |
0.476119 | − | 0.879381i | \(-0.342043\pi\) | |||||||
\(644\) | −50.1841 | − | 86.9214i | −0.00307070 | − | 0.00531861i | ||||
\(645\) | −9976.54 | −0.609032 | ||||||||
\(646\) | −8905.13 | − | 3520.10i | −0.542365 | − | 0.214391i | ||||
\(647\) | −6628.94 | −0.402798 | −0.201399 | − | 0.979509i | \(-0.564549\pi\) | ||||
−0.201399 | + | 0.979509i | \(0.564549\pi\) | |||||||
\(648\) | −3644.60 | − | 6312.63i | −0.220947 | − | 0.382691i | ||||
\(649\) | −11429.6 | − | 19796.7i | −0.691299 | − | 1.19736i | ||||
\(650\) | −235.918 | + | 408.622i | −0.0142361 | + | 0.0246577i | ||||
\(651\) | −591.613 | − | 1024.70i | −0.0356178 | − | 0.0616918i | ||||
\(652\) | 2271.18 | − | 3933.79i | 0.136420 | − | 0.236287i | ||||
\(653\) | 30340.7 | 1.81826 | 0.909129 | − | 0.416515i | \(-0.136749\pi\) | ||||
0.909129 | + | 0.416515i | \(0.136749\pi\) | |||||||
\(654\) | 8077.25 | 0.482944 | ||||||||
\(655\) | −1940.75 | + | 3361.48i | −0.115773 | + | 0.200525i | ||||
\(656\) | 2752.74 | − | 4767.88i | 0.163836 | − | 0.283772i | ||||
\(657\) | −6202.39 | −0.368308 | ||||||||
\(658\) | 184.783 | 0.0109477 | ||||||||
\(659\) | −1428.03 | + | 2473.43i | −0.0844132 | + | 0.146208i | −0.905141 | − | 0.425111i | \(-0.860235\pi\) |
0.820728 | + | 0.571319i | \(0.193568\pi\) | |||||||
\(660\) | 3771.01 | + | 6531.58i | 0.222403 | + | 0.385214i | ||||
\(661\) | 10640.5 | − | 18429.8i | 0.626122 | − | 1.08447i | −0.362201 | − | 0.932100i | \(-0.617975\pi\) |
0.988323 | − | 0.152375i | \(-0.0486921\pi\) | |||||||
\(662\) | 1414.75 | + | 2450.41i | 0.0830600 | + | 0.143864i | ||||
\(663\) | 481.261 | + | 833.568i | 0.0281910 | + | 0.0488282i | ||||
\(664\) | −10578.2 | −0.618245 | ||||||||
\(665\) | −254.312 | + | 201.794i | −0.0148297 | + | 0.0117673i | ||||
\(666\) | 555.690 | 0.0323312 | ||||||||
\(667\) | −5881.40 | − | 10186.9i | −0.341422 | − | 0.591361i | ||||
\(668\) | −1580.65 | − | 2737.76i | −0.0915524 | − | 0.158573i | ||||
\(669\) | 10981.3 | − | 19020.3i | 0.634624 | − | 1.09920i | ||||
\(670\) | 156.557 | + | 271.165i | 0.00902735 | + | 0.0156358i | ||||
\(671\) | −2719.03 | + | 4709.49i | −0.156434 | + | 0.270951i | ||||
\(672\) | 134.067 | 0.00769606 | ||||||||
\(673\) | −14334.7 | −0.821046 | −0.410523 | − | 0.911850i | \(-0.634654\pi\) | ||||
−0.410523 | + | 0.911850i | \(0.634654\pi\) | |||||||
\(674\) | −2159.77 | + | 3740.83i | −0.123429 | + | 0.213786i | ||||
\(675\) | 3933.36 | − | 6812.77i | 0.224289 | − | 0.388480i | ||||
\(676\) | −8760.41 | −0.498430 | ||||||||
\(677\) | 3300.00 | 0.187340 | 0.0936700 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936700 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(678\) | −1492.84 | + | 2585.68i | −0.0845608 | + | 0.146464i | ||||
\(679\) | −454.098 | − | 786.521i | −0.0256652 | − | 0.0444535i | ||||
\(680\) | 1371.51 | − | 2375.53i | 0.0773458 | − | 0.133967i | ||||
\(681\) | 15314.0 | + | 26524.6i | 0.861722 | + | 1.49255i | ||||
\(682\) | −14163.2 | − | 24531.4i | −0.795218 | − | 1.37736i | ||||
\(683\) | −1847.09 | −0.103480 | −0.0517400 | − | 0.998661i | \(-0.516477\pi\) | ||||
−0.0517400 | + | 0.998661i | \(0.516477\pi\) | |||||||
\(684\) | −3421.32 | + | 2714.78i | −0.191253 | + | 0.151758i | ||||
\(685\) | 12108.8 | 0.675408 | ||||||||
\(686\) | −453.100 | − | 784.791i | −0.0252178 | − | 0.0436785i | ||||
\(687\) | −14724.1 | − | 25502.9i | −0.817698 | − | 1.41630i | ||||
\(688\) | −2122.80 | + | 3676.80i | −0.117632 | + | 0.203745i | ||||
\(689\) | 175.696 | + | 304.314i | 0.00971478 | + | 0.0168265i | ||||
\(690\) | −1427.42 | + | 2472.36i | −0.0787547 | + | 0.136407i | ||||
\(691\) | 34144.6 | 1.87977 | 0.939886 | − | 0.341489i | \(-0.110931\pi\) | ||||
0.939886 | + | 0.341489i | \(0.110931\pi\) | |||||||
\(692\) | 13936.0 | 0.765561 | ||||||||
\(693\) | −218.489 | + | 378.435i | −0.0119765 | + | 0.0207439i | ||||
\(694\) | −5468.76 | + | 9472.17i | −0.299123 | + | 0.518096i | ||||
\(695\) | 10911.7 | 0.595544 | ||||||||
\(696\) | 15712.2 | 0.855703 | ||||||||
\(697\) | 9946.06 | − | 17227.1i | 0.540508 | − | 0.936187i | ||||
\(698\) | −3235.26 | − | 5603.63i | −0.175439 | − | 0.303869i | ||||
\(699\) | −2626.00 | + | 4548.36i | −0.142095 | + | 0.246116i | ||||
\(700\) | 118.730 | + | 205.646i | 0.00641082 | + | 0.0111039i | ||||
\(701\) | −3366.06 | − | 5830.18i | −0.181361 | − | 0.314127i | 0.760983 | − | 0.648772i | \(-0.224717\pi\) |
−0.942344 | + | 0.334645i | \(0.891384\pi\) | |||||||
\(702\) | −460.062 | −0.0247349 | ||||||||
\(703\) | 255.922 | + | 1726.50i | 0.0137301 | + | 0.0926262i | ||||
\(704\) | 3209.57 | 0.171826 | ||||||||
\(705\) | −2627.95 | − | 4551.74i | −0.140389 | − | 0.243161i | ||||
\(706\) | −6191.72 | − | 10724.4i | −0.330069 | − | 0.571696i | ||||
\(707\) | −26.3981 | + | 45.7228i | −0.00140425 | + | 0.00243223i | ||||
\(708\) | 5778.99 | + | 10009.5i | 0.306762 | + | 0.531328i | ||||
\(709\) | −15459.5 | + | 26776.7i | −0.818892 | + | 1.41836i | 0.0876068 | + | 0.996155i | \(0.472078\pi\) |
−0.906499 | + | 0.422208i | \(0.861255\pi\) | |||||||
\(710\) | 13274.4 | 0.701660 | ||||||||
\(711\) | 5034.87 | 0.265573 | ||||||||
\(712\) | 1621.95 | − | 2809.31i | 0.0853726 | − | 0.147870i | ||||
\(713\) | 5361.12 | − | 9285.73i | 0.281593 | − | 0.487733i | ||||
\(714\) | 484.406 | 0.0253900 | ||||||||
\(715\) | 781.229 | 0.0408620 | ||||||||
\(716\) | 4370.45 | − | 7569.85i | 0.228117 | − | 0.395110i | ||||
\(717\) | 8669.39 | + | 15015.8i | 0.451554 | + | 0.782115i | ||||
\(718\) | −6407.07 | + | 11097.4i | −0.333022 | + | 0.576811i | ||||
\(719\) | 3730.56 | + | 6461.52i | 0.193500 | + | 0.335152i | 0.946408 | − | 0.322974i | \(-0.104683\pi\) |
−0.752908 | + | 0.658126i | \(0.771349\pi\) | |||||||
\(720\) | −625.562 | − | 1083.51i | −0.0323796 | − | 0.0560831i | ||||
\(721\) | 1189.47 | 0.0614399 | ||||||||
\(722\) | −10010.4 | − | 9379.57i | −0.515993 | − | 0.483478i | ||||
\(723\) | −25894.0 | −1.33196 | ||||||||
\(724\) | −2111.78 | − | 3657.72i | −0.108403 | − | 0.187760i | ||||
\(725\) | 13914.7 | + | 24101.0i | 0.712800 | + | 1.23461i | ||||
\(726\) | −7505.35 | + | 12999.6i | −0.383677 | + | 0.664548i | ||||
\(727\) | 5473.85 | + | 9480.99i | 0.279249 | + | 0.483673i | 0.971198 | − | 0.238273i | \(-0.0765813\pi\) |
−0.691949 | + | 0.721946i | \(0.743248\pi\) | |||||||
\(728\) | 6.94358 | − | 12.0266i | 0.000353498 | − | 0.000612276i | ||||
\(729\) | 2977.33 | 0.151264 | ||||||||
\(730\) | 5580.54 | 0.282938 | ||||||||
\(731\) | −7670.02 | + | 13284.9i | −0.388079 | + | 0.672173i | ||||
\(732\) | 1374.78 | − | 2381.19i | 0.0694171 | − | 0.120234i | ||||
\(733\) | −36104.8 | −1.81932 | −0.909661 | − | 0.415352i | \(-0.863659\pi\) | ||||
−0.909661 | + | 0.415352i | \(0.863659\pi\) | |||||||
\(734\) | −16737.9 | −0.841698 | ||||||||
\(735\) | −6439.78 | + | 11154.0i | −0.323177 | + | 0.559758i | ||||
\(736\) | 607.449 | + | 1052.13i | 0.0304224 | + | 0.0526931i | ||||
\(737\) | −661.875 | + | 1146.40i | −0.0330807 | + | 0.0572975i | ||||
\(738\) | −4536.50 | − | 7857.45i | −0.226275 | − | 0.391920i | ||||
\(739\) | −11391.7 | − | 19731.0i | −0.567052 | − | 0.982162i | −0.996856 | − | 0.0792399i | \(-0.974751\pi\) |
0.429804 | − | 0.902922i | \(-0.358583\pi\) | |||||||
\(740\) | −499.977 | −0.0248372 | ||||||||
\(741\) | 202.188 | + | 1364.00i | 0.0100237 | + | 0.0676219i | ||||
\(742\) | 176.844 | 0.00874953 | ||||||||
\(743\) | −11318.0 | − | 19603.4i | −0.558839 | − | 0.967937i | −0.997594 | − | 0.0693306i | \(-0.977914\pi\) |
0.438755 | − | 0.898607i | \(-0.355420\pi\) | |||||||
\(744\) | 7161.13 | + | 12403.4i | 0.352876 | + | 0.611200i | ||||
\(745\) | 988.289 | − | 1711.77i | 0.0486015 | − | 0.0841802i | ||||
\(746\) | 10254.9 | + | 17762.0i | 0.503297 | + | 0.871735i | ||||
\(747\) | −8716.44 | + | 15097.3i | −0.426932 | + | 0.739467i | ||||
\(748\) | 11596.7 | 0.566867 | ||||||||
\(749\) | 45.7721 | 0.00223294 | ||||||||
\(750\) | 8076.80 | − | 13989.4i | 0.393231 | − | 0.681096i | ||||
\(751\) | 1429.62 | − | 2476.17i | 0.0694642 | − | 0.120315i | −0.829201 | − | 0.558950i | \(-0.811204\pi\) |
0.898666 | + | 0.438634i | \(0.144538\pi\) | |||||||
\(752\) | −2236.69 | −0.108463 | ||||||||
\(753\) | 16080.6 | 0.778235 | ||||||||
\(754\) | 813.763 | − | 1409.48i | 0.0393044 | − | 0.0680772i | ||||
\(755\) | −9022.44 | − | 15627.3i | −0.434914 | − | 0.753294i | ||||
\(756\) | −115.767 | + | 200.515i | −0.00556933 | + | 0.00964636i | ||||
\(757\) | −10045.6 | − | 17399.4i | −0.482315 | − | 0.835394i | 0.517479 | − | 0.855696i | \(-0.326871\pi\) |
−0.999794 | + | 0.0203020i | \(0.993537\pi\) | |||||||
\(758\) | 6607.19 | + | 11444.0i | 0.316601 | + | 0.548370i | ||||
\(759\) | −12069.3 | −0.577193 | ||||||||
\(760\) | 3078.29 | − | 2442.59i | 0.146923 | − | 0.116582i | ||||
\(761\) | −9968.77 | −0.474859 | −0.237430 | − | 0.971405i | \(-0.576305\pi\) | ||||
−0.237430 | + | 0.971405i | \(0.576305\pi\) | |||||||
\(762\) | −5694.50 | − | 9863.17i | −0.270722 | − | 0.468904i | ||||
\(763\) | −210.534 | − | 364.656i | −0.00998933 | − | 0.0173020i | ||||
\(764\) | −5317.02 | + | 9209.35i | −0.251784 | + | 0.436103i | ||||
\(765\) | −2260.25 | − | 3914.87i | −0.106823 | − | 0.185023i | ||||
\(766\) | −9.95746 | + | 17.2468i | −0.000469684 | + | 0.000813516i | ||||
\(767\) | 1197.22 | 0.0563611 | ||||||||
\(768\) | −1622.81 | −0.0762473 | ||||||||
\(769\) | −10031.2 | + | 17374.5i | −0.470396 | + | 0.814749i | −0.999427 | − | 0.0338532i | \(-0.989222\pi\) |
0.529031 | + | 0.848602i | \(0.322555\pi\) | |||||||
\(770\) | 196.583 | − | 340.493i | 0.00920049 | − | 0.0159357i | ||||
\(771\) | 41854.1 | 1.95504 | ||||||||
\(772\) | −18322.0 | −0.854173 | ||||||||
\(773\) | −294.482 | + | 510.058i | −0.0137022 | + | 0.0237329i | −0.872795 | − | 0.488087i | \(-0.837695\pi\) |
0.859093 | + | 0.511820i | \(0.171028\pi\) | |||||||
\(774\) | 3498.38 | + | 6059.37i | 0.162463 | + | 0.281395i | ||||
\(775\) | −12683.8 | + | 21969.0i | −0.587891 | + | 1.01826i | ||||
\(776\) | 5496.59 | + | 9520.38i | 0.254273 | + | 0.440414i | ||||
\(777\) | −44.1468 | − | 76.4644i | −0.00203830 | − | 0.00353043i | ||||
\(778\) | 24763.0 | 1.14113 | ||||||||
\(779\) | 22323.4 | − | 17713.4i | 1.02673 | − | 0.814697i | ||||
\(780\) | −395.000 | −0.0181324 | ||||||||
\(781\) | 28060.0 | + | 48601.4i | 1.28562 | + | 2.22675i | ||||
\(782\) | 2194.81 | + | 3801.52i | 0.100366 | + | 0.173839i | ||||
\(783\) | −13567.5 | + | 23499.6i | −0.619237 | + | 1.07255i | ||||
\(784\) | 2740.51 | + | 4746.69i | 0.124841 | + | 0.216231i | ||||
\(785\) | −5838.49 | + | 10112.6i | −0.265458 | + | 0.459787i | ||||
\(786\) | 8297.03 | 0.376521 | ||||||||
\(787\) | −14959.0 | −0.677550 | −0.338775 | − | 0.940867i | \(-0.610013\pi\) | ||||
−0.338775 | + | 0.940867i | \(0.610013\pi\) | |||||||
\(788\) | 9765.83 | − | 16914.9i | 0.441489 | − | 0.764682i | ||||
\(789\) | 12375.6 | − | 21435.2i | 0.558409 | − | 0.967192i | ||||
\(790\) | −4530.07 | −0.204016 | ||||||||
\(791\) | 155.644 | 0.00699630 | ||||||||
\(792\) | 2644.69 | − | 4580.73i | 0.118655 | − | 0.205517i | ||||
\(793\) | −142.405 | − | 246.652i | −0.00637696 | − | 0.0110452i | ||||
\(794\) | 603.931 | − | 1046.04i | 0.0269933 | − | 0.0467539i | ||||
\(795\) | −2515.04 | − | 4356.18i | −0.112200 | − | 0.194337i | ||||
\(796\) | 4715.84 | + | 8168.08i | 0.209986 | + | 0.363706i | ||||
\(797\) | −18464.2 | −0.820622 | −0.410311 | − | 0.911946i | \(-0.634580\pi\) | ||||
−0.410311 | + | 0.911946i | \(0.634580\pi\) | |||||||
\(798\) | 645.367 | + | 255.107i | 0.0286287 | + | 0.0113166i | ||||
\(799\) | −8081.53 | −0.357827 | ||||||||
\(800\) | −1437.16 | − | 2489.23i | −0.0635140 | − | 0.110009i | ||||
\(801\) | −2672.98 | − | 4629.73i | −0.117909 | − | 0.204224i | ||||
\(802\) | 10340.3 | − | 17909.9i | 0.455271 | − | 0.788553i | ||||
\(803\) | 11796.4 | + | 20432.0i | 0.518413 | + | 0.897919i | ||||
\(804\) | 334.653 | − | 579.637i | 0.0146795 | − | 0.0254256i | ||||
\(805\) | 148.823 | 0.00651592 | ||||||||
\(806\) | 1483.55 | 0.0648336 | ||||||||
\(807\) | −5060.86 | + | 8765.67i | −0.220757 | + | 0.382362i | ||||
\(808\) | 319.533 | − | 553.448i | 0.0139123 | − | 0.0240968i | ||||
\(809\) | 13632.5 | 0.592449 | 0.296225 | − | 0.955118i | \(-0.404272\pi\) | ||||
0.296225 | + | 0.955118i | \(0.404272\pi\) | |||||||
\(810\) | 10808.2 | 0.468842 | ||||||||
\(811\) | −11453.1 | + | 19837.3i | −0.495896 | + | 0.858916i | −0.999989 | − | 0.00473284i | \(-0.998493\pi\) |
0.504093 | + | 0.863649i | \(0.331827\pi\) | |||||||
\(812\) | −409.540 | − | 709.345i | −0.0176996 | − | 0.0306565i | ||||
\(813\) | 12714.3 | − | 22021.8i | 0.548473 | − | 0.949984i | ||||
\(814\) | −1056.87 | − | 1830.56i | −0.0455079 | − | 0.0788220i | ||||
\(815\) | 3367.63 | + | 5832.91i | 0.144740 | + | 0.250697i | ||||
\(816\) | −5863.45 | −0.251546 | ||||||||
\(817\) | −17215.0 | + | 13659.9i | −0.737179 | + | 0.584944i | ||||
\(818\) | 322.840 | 0.0137993 | ||||||||
\(819\) | −11.4430 | − | 19.8199i | −0.000488219 | − | 0.000845620i | ||||
\(820\) | 4081.67 | + | 7069.66i | 0.173827 | + | 0.301077i | ||||
\(821\) | 21072.8 | − | 36499.1i | 0.895792 | − | 1.55156i | 0.0629700 | − | 0.998015i | \(-0.479943\pi\) |
0.832822 | − | 0.553541i | \(-0.186724\pi\) | |||||||
\(822\) | −12941.8 | − | 22415.9i | −0.549145 | − | 0.951147i | ||||
\(823\) | 14169.1 | − | 24541.6i | 0.600126 | − | 1.03945i | −0.392676 | − | 0.919677i | \(-0.628450\pi\) |
0.992801 | − | 0.119772i | \(-0.0382162\pi\) | |||||||
\(824\) | −14397.8 | −0.608704 | ||||||||
\(825\) | 28554.7 | 1.20503 | ||||||||
\(826\) | 301.260 | − | 521.798i | 0.0126903 | − | 0.0219802i | ||||
\(827\) | −6794.88 | + | 11769.1i | −0.285709 | + | 0.494862i | −0.972781 | − | 0.231727i | \(-0.925562\pi\) |
0.687072 | + | 0.726589i | \(0.258896\pi\) | |||||||
\(828\) | 2002.15 | 0.0840333 | ||||||||
\(829\) | −25202.9 | −1.05589 | −0.527946 | − | 0.849278i | \(-0.677038\pi\) | ||||
−0.527946 | + | 0.849278i | \(0.677038\pi\) | |||||||
\(830\) | 7842.53 | − | 13583.7i | 0.327974 | − | 0.568067i | ||||
\(831\) | 15374.8 | + | 26629.9i | 0.641810 | + | 1.11165i | ||||
\(832\) | −84.0480 | + | 145.575i | −0.00350221 | + | 0.00606601i | ||||
\(833\) | 9901.87 | + | 17150.5i | 0.411860 | + | 0.713363i | ||||
\(834\) | −11662.3 | − | 20199.7i | −0.484211 | − | 0.838679i | ||||
\(835\) | 4687.47 | 0.194271 | ||||||||
\(836\) | 15450.1 | + | 6107.26i | 0.639178 | + | 0.252660i | ||||
\(837\) | −24734.6 | −1.02145 | ||||||||
\(838\) | 7483.41 | + | 12961.6i | 0.308485 | + | 0.534311i | ||||
\(839\) | 1877.33 | + | 3251.63i | 0.0772497 | + | 0.133800i | 0.902062 | − | 0.431606i | \(-0.142053\pi\) |
−0.824813 | + | 0.565406i | \(0.808719\pi\) | |||||||
\(840\) | −99.3954 | + | 172.158i | −0.00408270 | + | 0.00707144i | ||||
\(841\) | −35802.2 | − | 62011.2i | −1.46796 | − | 2.54259i | ||||
\(842\) | 6049.53 | − | 10478.1i | 0.247602 | − | 0.428859i | ||||
\(843\) | −39929.8 | −1.63138 | ||||||||
\(844\) | −12861.0 | −0.524520 | ||||||||
\(845\) | 6494.83 | − | 11249.4i | 0.264413 | − | 0.457977i | ||||
\(846\) | −1843.03 | + | 3192.23i | −0.0748993 | + | 0.129729i | ||||
\(847\) | 782.511 | 0.0317443 | ||||||||
\(848\) | −2140.60 | −0.0866844 | ||||||||
\(849\) | 18247.1 | − | 31604.9i | 0.737619 | − | 1.27759i | ||||
\(850\) | −5192.67 | − | 8993.97i | −0.209538 | − | 0.362930i | ||||
\(851\) | 400.052 | − | 692.910i | 0.0161147 | − | 0.0279115i | ||||
\(852\) | −14187.5 | − | 24573.5i | −0.570489 | − | 0.988117i | ||||
\(853\) | −11744.1 | − | 20341.5i | −0.471409 | − | 0.816505i | 0.528056 | − | 0.849210i | \(-0.322921\pi\) |
−0.999465 | + | 0.0327050i | \(0.989588\pi\) | |||||||
\(854\) | −143.335 | −0.00574336 | ||||||||
\(855\) | −949.581 | − | 6406.06i | −0.0379824 | − | 0.256237i | ||||
\(856\) | −554.044 | −0.0221225 | ||||||||
\(857\) | −1651.39 | − | 2860.29i | −0.0658231 | − | 0.114009i | 0.831236 | − | 0.555920i | \(-0.187634\pi\) |
−0.897059 | + | 0.441911i | \(0.854301\pi\) | |||||||
\(858\) | −834.970 | − | 1446.21i | −0.0332231 | − | 0.0575441i | ||||
\(859\) | 4411.39 | − | 7640.75i | 0.175221 | − | 0.303491i | −0.765017 | − | 0.644010i | \(-0.777269\pi\) |
0.940238 | + | 0.340519i | \(0.110603\pi\) | |||||||
\(860\) | −3147.63 | − | 5451.85i | −0.124806 | − | 0.216170i | ||||
\(861\) | −720.804 | + | 1248.47i | −0.0285307 | + | 0.0494166i | ||||
\(862\) | −21819.4 | −0.862148 | ||||||||
\(863\) | −20731.7 | −0.817745 | −0.408873 | − | 0.912591i | \(-0.634078\pi\) | ||||
−0.408873 | + | 0.912591i | \(0.634078\pi\) | |||||||
\(864\) | 1401.29 | − | 2427.11i | 0.0551771 | − | 0.0955695i | ||||
\(865\) | −10332.0 | + | 17895.5i | −0.406124 | + | 0.703427i | ||||
\(866\) | 15297.9 | 0.600282 | ||||||||
\(867\) | 9958.37 | 0.390085 | ||||||||
\(868\) | 373.312 | − | 646.595i | 0.0145979 | − | 0.0252844i | ||||
\(869\) | −9575.87 | − | 16585.9i | −0.373808 | − | 0.647455i | ||||
\(870\) | −11648.8 | + | 20176.3i | −0.453944 | + | 0.786253i | ||||
\(871\) | −34.6646 | − | 60.0408i | −0.00134852 | − | 0.00233571i | ||||
\(872\) | 2548.40 | + | 4413.95i | 0.0989674 | + | 0.171417i | ||||
\(873\) | 18116.8 | 0.702359 | ||||||||
\(874\) | 922.086 | + | 6220.58i | 0.0356865 | + | 0.240749i | ||||
\(875\) | −842.091 | −0.0325347 | ||||||||
\(876\) | −5964.43 | − | 10330.7i | −0.230045 | − | 0.398450i | ||||
\(877\) | 5516.25 | + | 9554.43i | 0.212395 | + | 0.367879i | 0.952464 | − | 0.304652i | \(-0.0985402\pi\) |
−0.740068 | + | 0.672532i | \(0.765207\pi\) | |||||||
\(878\) | −11415.9 | + | 19772.9i | −0.438801 | + | 0.760025i | ||||
\(879\) | 17192.3 | + | 29778.0i | 0.659708 | + | 1.14265i | ||||
\(880\) | −2379.53 | + | 4121.46i | −0.0911521 | + | 0.157880i | ||||
\(881\) | −23834.2 | −0.911457 | −0.455728 | − | 0.890119i | \(-0.650621\pi\) | ||||
−0.455728 | + | 0.890119i | \(0.650621\pi\) | |||||||
\(882\) | 9032.70 | 0.344838 | ||||||||
\(883\) | 22621.3 | − | 39181.3i | 0.862138 | − | 1.49327i | −0.00772377 | − | 0.999970i | \(-0.502459\pi\) |
0.869861 | − | 0.493296i | \(-0.164208\pi\) | |||||||
\(884\) | −303.678 | + | 525.987i | −0.0115541 | + | 0.0200123i | ||||
\(885\) | −17137.8 | −0.650940 | ||||||||
\(886\) | 6305.31 | 0.239087 | ||||||||
\(887\) | 1818.47 | − | 3149.68i | 0.0688369 | − | 0.119229i | −0.829553 | − | 0.558428i | \(-0.811405\pi\) |
0.898390 | + | 0.439199i | \(0.144738\pi\) | |||||||
\(888\) | 534.371 | + | 925.557i | 0.0201940 | + | 0.0349771i | ||||
\(889\) | −296.856 | + | 514.169i | −0.0111994 | + | 0.0193978i | ||||
\(890\) | 2404.98 | + | 4165.56i | 0.0905790 | + | 0.156887i | ||||
\(891\) | 22846.9 | + | 39572.0i | 0.859035 | + | 1.48789i | ||||
\(892\) | 13858.6 | 0.520202 | ||||||||
\(893\) | −10766.9 | − | 4256.04i | −0.403472 | − | 0.159488i | ||||
\(894\) | −4225.10 | −0.158063 | ||||||||
\(895\) | 6480.38 | + | 11224.3i | 0.242028 | + | 0.419205i | ||||
\(896\) | 42.2986 | + | 73.2633i | 0.00157712 | + | 0.00273165i | ||||
\(897\) | 316.056 | − | 547.425i | 0.0117645 | − | 0.0203768i | ||||
\(898\) | 5217.04 | + | 9036.17i | 0.193869 | + | 0.335792i | ||||
\(899\) | 43750.8 | − | 75778.6i | 1.62310 | − | 2.81130i | ||||
\(900\) | −4736.87 | −0.175439 | ||||||||
\(901\) | −7734.30 | −0.285979 | ||||||||
\(902\) | −17256.1 | + | 29888.4i | −0.636989 | + | 1.10330i | ||||
\(903\) | 555.856 | − | 962.771i | 0.0204848 | − | 0.0354806i | ||||
\(904\) | −1883.98 | −0.0693146 | ||||||||
\(905\) | 6262.58 | 0.230028 | ||||||||
\(906\) | −19286.2 | + | 33404.7i | −0.707220 | + | 1.22494i | ||||
\(907\) | 22853.4 | + | 39583.2i | 0.836641 | + | 1.44911i | 0.892687 | + | 0.450677i | \(0.148817\pi\) |
−0.0560457 | + | 0.998428i | \(0.517849\pi\) | |||||||
\(908\) | −9663.21 | + | 16737.2i | −0.353177 | + | 0.611721i | ||||
\(909\) | −526.590 | − | 912.081i | −0.0192144 | − | 0.0332803i | ||||
\(910\) | 10.2957 | + | 17.8327i | 0.000375055 | + | 0.000649614i | ||||
\(911\) | −38271.0 | −1.39185 | −0.695924 | − | 0.718115i | \(-0.745005\pi\) | ||||
−0.695924 | + | 0.718115i | \(0.745005\pi\) | |||||||
\(912\) | −7811.79 | − | 3087.92i | −0.283634 | − | 0.112117i | ||||
\(913\) | 66311.6 | 2.40372 | ||||||||
\(914\) | 15868.7 | + | 27485.4i | 0.574277 | + | 0.994678i | ||||
\(915\) | 2038.48 | + | 3530.75i | 0.0736504 | + | 0.127566i | ||||
\(916\) | 9290.98 | − | 16092.5i | 0.335134 | − | 0.580469i | ||||
\(917\) | −216.263 | − | 374.579i | −0.00778804 | − | 0.0134893i | ||||
\(918\) | 5063.09 | − | 8769.53i | 0.182034 | − | 0.315292i | ||||
\(919\) | 15748.1 | 0.565267 | 0.282634 | − | 0.959228i | \(-0.408792\pi\) | ||||
0.282634 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(920\) | −1801.41 | −0.0645553 | ||||||||
\(921\) | 17844.1 | − | 30906.8i | 0.638417 | − | 1.10577i | ||||
\(922\) | −4341.17 | + | 7519.12i | −0.155064 | + | 0.268578i | ||||
\(923\) | −2939.19 | −0.104815 | ||||||||
\(924\) | −840.427 | −0.0299221 | ||||||||
\(925\) | −946.478 | + | 1639.35i | −0.0336432 | + | 0.0582718i | ||||
\(926\) | −1394.23 | − | 2414.87i | −0.0494785 | − | 0.0856993i | ||||
\(927\) | −11863.8 | + | 20548.7i | −0.420343 | + | 0.728056i | ||||
\(928\) | 4957.25 | + | 8586.20i | 0.175355 | + | 0.303724i | ||||
\(929\) | −7167.36 | − | 12414.2i | −0.253125 | − | 0.438426i | 0.711259 | − | 0.702930i | \(-0.248125\pi\) |
−0.964385 | + | 0.264504i | \(0.914792\pi\) | |||||||
\(930\) | −21236.6 | −0.748792 | ||||||||
\(931\) | 4159.99 | + | 28064.1i | 0.146443 | + | 0.987932i | ||||
\(932\) | −3314.04 | −0.116475 | ||||||||
\(933\) | 9679.81 | + | 16765.9i | 0.339660 | + | 0.588308i | ||||
\(934\) | 6138.35 | + | 10631.9i | 0.215046 | + | 0.372471i | ||||
\(935\) | −8597.61 | + | 14891.5i | −0.300718 | + | 0.520860i | ||||
\(936\) | 138.511 | + | 239.908i | 0.00483694 | + | 0.00837782i | ||||
\(937\) | −9420.92 | + | 16317.5i | −0.328461 | + | 0.568911i | −0.982207 | − | 0.187803i | \(-0.939863\pi\) |
0.653746 | + | 0.756714i | \(0.273197\pi\) | |||||||
\(938\) | −34.8911 | −0.00121454 | ||||||||
\(939\) | 20924.9 | 0.727220 | ||||||||
\(940\) | 1658.25 | − | 2872.18i | 0.0575385 | − | 0.0996596i | ||||
\(941\) | −7510.34 | + | 13008.3i | −0.260181 | + | 0.450647i | −0.966290 | − | 0.257457i | \(-0.917116\pi\) |
0.706109 | + | 0.708103i | \(0.250449\pi\) | |||||||
\(942\) | 24960.5 | 0.863331 | ||||||||
\(943\) | −13063.6 | −0.451125 | ||||||||
\(944\) | −3646.58 | + | 6316.06i | −0.125727 | + | 0.217765i | ||||
\(945\) | −171.656 | − | 297.317i | −0.00590896 | − | 0.0102346i | ||||
\(946\) | 13307.2 | − | 23048.8i | 0.457352 | − | 0.792156i | ||||
\(947\) | 11229.2 | + | 19449.5i | 0.385321 | + | 0.667396i | 0.991814 | − | 0.127693i | \(-0.0407573\pi\) |
−0.606492 | + | 0.795089i | \(0.707424\pi\) | |||||||
\(948\) | 4841.70 | + | 8386.06i | 0.165877 | + | 0.287307i | ||||
\(949\) | −1235.63 | −0.0422659 | ||||||||
\(950\) | −2181.55 | − | 14717.2i | −0.0745041 | − | 0.502620i | ||||
\(951\) | 20096.5 | 0.685249 | ||||||||
\(952\) | 152.831 | + | 264.712i | 0.00520304 | + | 0.00901193i | ||||
\(953\) | 7481.14 | + | 12957.7i | 0.254289 | + | 0.440442i | 0.964702 | − | 0.263343i | \(-0.0848251\pi\) |
−0.710413 | + | 0.703785i | \(0.751492\pi\) | |||||||
\(954\) | −1763.85 | + | 3055.08i | −0.0598603 | + | 0.103681i | ||||
\(955\) | −7883.92 | − | 13655.3i | −0.267139 | − | 0.462698i | ||||
\(956\) | −5470.44 | + | 9475.08i | −0.185070 | + | 0.320550i | ||||
\(957\) | −98495.0 | −3.32695 | ||||||||
\(958\) | −14265.9 | −0.481117 | ||||||||
\(959\) | −674.659 | + | 1168.54i | −0.0227173 | + | 0.0393475i | ||||
\(960\) | 1203.12 | − | 2083.87i | 0.0404486 | − | 0.0700590i | ||||
\(961\) | 49970.0 | 1.67735 | ||||||||
\(962\) | 110.704 | 0.00371023 | ||||||||
\(963\) | −456.532 | + | 790.737i | −0.0152768 | + | 0.0264602i | ||||
\(964\) | −8169.65 | − | 14150.2i | −0.272953 | − | 0.472768i | ||||
\(965\) | 13583.6 | − | 23527.5i | 0.453132 | − | 0.784848i | ||||
\(966\) | −159.061 | − | 275.501i | −0.00529782 | − | 0.00917609i | ||||
\(967\) | 20515.6 | + | 35534.1i | 0.682253 | + | 1.18170i | 0.974292 | + | 0.225290i | \(0.0723331\pi\) |
−0.292039 | + | 0.956407i | \(0.594334\pi\) | |||||||
\(968\) | −9471.84 | −0.314500 | ||||||||
\(969\) | −28225.2 | − | 11157.1i | −0.935732 | − | 0.369885i | ||||
\(970\) | −16300.4 | −0.539560 | ||||||||
\(971\) | −2012.11 | − | 3485.08i | −0.0665002 | − | 0.115182i | 0.830858 | − | 0.556484i | \(-0.187850\pi\) |
−0.897358 | + | 0.441302i | \(0.854517\pi\) | |||||||
\(972\) | −6822.35 | − | 11816.7i | −0.225131 | − | 0.389938i | ||||
\(973\) | −607.958 | + | 1053.01i | −0.0200311 | + | 0.0346949i | ||||
\(974\) | −14396.6 | − | 24935.6i | −0.473611 | − | 0.820318i | ||||
\(975\) | −747.753 | + | 1295.15i | −0.0245613 | + | 0.0425414i | ||||
\(976\) | 1734.99 | 0.0569012 | ||||||||
\(977\) | −42051.2 | −1.37701 | −0.688505 | − | 0.725232i | \(-0.741733\pi\) | ||||
−0.688505 | + | 0.725232i | \(0.741733\pi\) | |||||||
\(978\) | 7198.59 | − | 12468.3i | 0.235363 | − | 0.407661i | ||||
\(979\) | −10167.5 | + | 17610.7i | −0.331926 | + | 0.574913i | ||||
\(980\) | −8127.08 | −0.264908 | ||||||||
\(981\) | 8399.51 | 0.273370 | ||||||||
\(982\) | 7655.81 | − | 13260.3i | 0.248785 | − | 0.430908i | ||||
\(983\) | −21502.2 | − | 37242.9i | −0.697674 | − | 1.20841i | −0.969271 | − | 0.245996i | \(-0.920885\pi\) |
0.271597 | − | 0.962411i | \(-0.412448\pi\) | |||||||
\(984\) | 8724.91 | − | 15112.0i | 0.282663 | − | 0.489586i | ||||
\(985\) | 14480.5 | + | 25080.9i | 0.468413 | + | 0.811315i | ||||
\(986\) | 17911.3 | + | 31023.3i | 0.578511 | + | 1.00201i | ||||
\(987\) | 585.679 | 0.0188879 | ||||||||
\(988\) | −681.591 | + | 540.835i | −0.0219477 | + | 0.0174152i | ||||
\(989\) | 10074.2 | 0.323903 | ||||||||
\(990\) | 3921.46 | + | 6792.17i | 0.125891 | + | 0.218050i | ||||
\(991\) | −3307.45 | − | 5728.68i | −0.106019 | − | 0.183630i | 0.808135 | − | 0.588997i | \(-0.200477\pi\) |
−0.914154 | + | 0.405367i | \(0.867144\pi\) | |||||||
\(992\) | −4518.72 | + | 7826.65i | −0.144626 | + | 0.250500i | ||||
\(993\) | 4484.10 | + | 7766.69i | 0.143302 | + | 0.248206i | ||||
\(994\) | −739.600 | + | 1281.02i | −0.0236003 | + | 0.0408769i | ||||
\(995\) | −13985.0 | −0.445583 | ||||||||
\(996\) | −33528.1 | −1.06665 | ||||||||
\(997\) | 23301.4 | − | 40359.2i | 0.740184 | − | 1.28204i | −0.212228 | − | 0.977220i | \(-0.568072\pi\) |
0.952411 | − | 0.304815i | \(-0.0985948\pi\) | |||||||
\(998\) | 18638.1 | − | 32282.1i | 0.591161 | − | 1.02392i | ||||
\(999\) | −1845.72 | −0.0584544 |
(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 | 38.4.c.c.7.3 | ✓ | 6 | |
3.2 | odd | 2 | 342.4.g.f.235.2 | 6 | |||
4.3 | odd | 2 | 304.4.i.e.273.1 | 6 | |||
19.7 | even | 3 | 722.4.a.j.1.1 | 3 | |||
19.11 | even | 3 | inner | 38.4.c.c.11.3 | yes | 6 | |
19.12 | odd | 6 | 722.4.a.k.1.3 | 3 | |||
57.11 | odd | 6 | 342.4.g.f.163.2 | 6 | |||
76.11 | odd | 6 | 304.4.i.e.49.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.c.c.7.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
38.4.c.c.11.3 | yes | 6 | 19.11 | even | 3 | inner | |
304.4.i.e.49.1 | 6 | 76.11 | odd | 6 | |||
304.4.i.e.273.1 | 6 | 4.3 | odd | 2 | |||
342.4.g.f.163.2 | 6 | 57.11 | odd | 6 | |||
342.4.g.f.235.2 | 6 | 3.2 | odd | 2 | |||
722.4.a.j.1.1 | 3 | 19.7 | even | 3 | |||
722.4.a.k.1.3 | 3 | 19.12 | odd | 6 |