Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(23,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.j (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.7 | ||
Character | \(\chi\) | \(=\) | 143.23 |
Dual form | 143.4.j.a.56.7 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.43971 | + | 1.98592i | −1.21612 | + | 0.702129i | −0.964086 | − | 0.265589i | \(-0.914433\pi\) |
−0.252036 | + | 0.967718i | \(0.581100\pi\) | |||||||
\(3\) | −0.953208 | − | 1.65100i | −0.183445 | − | 0.317736i | 0.759606 | − | 0.650383i | \(-0.225392\pi\) |
−0.943051 | + | 0.332647i | \(0.892058\pi\) | |||||||
\(4\) | 3.88775 | − | 6.73378i | 0.485969 | − | 0.841723i | ||||
\(5\) | 18.9601i | 1.69585i | 0.530120 | + | 0.847923i | \(0.322147\pi\) | ||||
−0.530120 | + | 0.847923i | \(0.677853\pi\) | |||||||
\(6\) | 6.55752 | + | 3.78599i | 0.446183 | + | 0.257604i | ||||
\(7\) | 20.6923 | + | 11.9467i | 1.11728 | + | 0.645062i | 0.940705 | − | 0.339226i | \(-0.110165\pi\) |
0.176575 | + | 0.984287i | \(0.443498\pi\) | |||||||
\(8\) | − | 0.891668i | − | 0.0394065i | ||||||
\(9\) | 11.6828 | − | 20.2352i | 0.432696 | − | 0.749451i | ||||
\(10\) | −37.6533 | − | 65.2174i | −1.19070 | − | 2.06236i | ||||
\(11\) | 9.52628 | − | 5.50000i | 0.261116 | − | 0.150756i | ||||
\(12\) | −14.8233 | −0.356594 | ||||||||
\(13\) | 45.9871 | − | 9.06585i | 0.981117 | − | 0.193417i | ||||
\(14\) | −94.9008 | −1.81166 | ||||||||
\(15\) | 31.3033 | − | 18.0729i | 0.538831 | − | 0.311094i | ||||
\(16\) | 32.8728 | + | 56.9373i | 0.513637 | + | 0.889646i | ||||
\(17\) | −52.2228 | + | 90.4526i | −0.745053 | + | 1.29047i | 0.205117 | + | 0.978737i | \(0.434243\pi\) |
−0.950170 | + | 0.311732i | \(0.899091\pi\) | |||||||
\(18\) | 92.8043i | 1.21523i | ||||||||
\(19\) | 29.9585 | + | 17.2966i | 0.361735 | + | 0.208848i | 0.669841 | − | 0.742504i | \(-0.266362\pi\) |
−0.308107 | + | 0.951352i | \(0.599695\pi\) | |||||||
\(20\) | 127.673 | + | 73.7123i | 1.42743 | + | 0.824128i | ||||
\(21\) | − | 45.5508i | − | 0.473333i | ||||||
\(22\) | −21.8451 | + | 37.8368i | −0.211700 | + | 0.366675i | ||||
\(23\) | 36.6739 | + | 63.5210i | 0.332480 | + | 0.575872i | 0.982997 | − | 0.183619i | \(-0.0587814\pi\) |
−0.650518 | + | 0.759491i | \(0.725448\pi\) | |||||||
\(24\) | −1.47215 | + | 0.849945i | −0.0125209 | + | 0.00722893i | ||||
\(25\) | −234.487 | −1.87589 | ||||||||
\(26\) | −140.178 | + | 122.511i | −1.05735 | + | 0.924088i | ||||
\(27\) | −96.0177 | −0.684393 | ||||||||
\(28\) | 160.893 | − | 92.8917i | 1.08593 | − | 0.626960i | ||||
\(29\) | −16.5397 | − | 28.6475i | −0.105908 | − | 0.183438i | 0.808201 | − | 0.588907i | \(-0.200442\pi\) |
−0.914109 | + | 0.405469i | \(0.867108\pi\) | |||||||
\(30\) | −71.7828 | + | 124.332i | −0.436856 | + | 0.756658i | ||||
\(31\) | 82.7750i | 0.479575i | 0.970825 | + | 0.239788i | \(0.0770778\pi\) | ||||
−0.970825 | + | 0.239788i | \(0.922922\pi\) | |||||||
\(32\) | −219.968 | − | 126.999i | −1.21516 | − | 0.701576i | ||||
\(33\) | −18.1610 | − | 10.4853i | −0.0958010 | − | 0.0553107i | ||||
\(34\) | − | 414.841i | − | 2.09249i | ||||||
\(35\) | −226.511 | + | 392.329i | −1.09393 | + | 1.89473i | ||||
\(36\) | −90.8396 | − | 157.339i | −0.420554 | − | 0.728420i | ||||
\(37\) | 221.476 | − | 127.869i | 0.984067 | − | 0.568151i | 0.0805716 | − | 0.996749i | \(-0.474325\pi\) |
0.903496 | + | 0.428597i | \(0.140992\pi\) | |||||||
\(38\) | −137.398 | −0.586552 | ||||||||
\(39\) | −58.8030 | − | 67.2832i | −0.241436 | − | 0.276255i | ||||
\(40\) | 16.9061 | 0.0668274 | ||||||||
\(41\) | −336.344 | + | 194.189i | −1.28117 | + | 0.739687i | −0.977063 | − | 0.212950i | \(-0.931693\pi\) |
−0.304112 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(42\) | 90.4602 | + | 156.682i | 0.332341 | + | 0.575631i | ||||
\(43\) | −116.874 | + | 202.432i | −0.414492 | + | 0.717921i | −0.995375 | − | 0.0960659i | \(-0.969374\pi\) |
0.580883 | + | 0.813987i | \(0.302707\pi\) | |||||||
\(44\) | − | 85.5305i | − | 0.293050i | ||||||
\(45\) | 383.662 | + | 221.507i | 1.27095 | + | 0.733786i | ||||
\(46\) | −252.295 | − | 145.663i | −0.808672 | − | 0.466887i | ||||
\(47\) | 2.58080i | 0.00800953i | 0.999992 | + | 0.00400477i | \(0.00127476\pi\) | ||||
−0.999992 | + | 0.00400477i | \(0.998725\pi\) | |||||||
\(48\) | 62.6692 | − | 108.546i | 0.188448 | − | 0.326402i | ||||
\(49\) | 113.948 | + | 197.363i | 0.332209 | + | 0.575403i | ||||
\(50\) | 806.567 | − | 465.672i | 2.28132 | − | 1.31712i | ||||
\(51\) | 199.117 | 0.546705 | ||||||||
\(52\) | 117.739 | − | 344.913i | 0.313989 | − | 0.919823i | ||||
\(53\) | 74.9220 | 0.194176 | 0.0970880 | − | 0.995276i | \(-0.469047\pi\) | ||||
0.0970880 | + | 0.995276i | \(0.469047\pi\) | |||||||
\(54\) | 330.273 | − | 190.683i | 0.832306 | − | 0.480532i | ||||
\(55\) | 104.281 | + | 180.620i | 0.255658 | + | 0.442813i | ||||
\(56\) | 10.6525 | − | 18.4507i | 0.0254196 | − | 0.0440281i | ||||
\(57\) | − | 65.9489i | − | 0.153248i | ||||||
\(58\) | 113.783 | + | 65.6929i | 0.257595 | + | 0.148722i | ||||
\(59\) | −360.003 | − | 207.848i | −0.794380 | − | 0.458635i | 0.0471223 | − | 0.998889i | \(-0.484995\pi\) |
−0.841502 | + | 0.540254i | \(0.818328\pi\) | |||||||
\(60\) | − | 281.053i | − | 0.604729i | ||||||
\(61\) | 190.758 | − | 330.403i | 0.400395 | − | 0.693505i | −0.593378 | − | 0.804924i | \(-0.702206\pi\) |
0.993774 | + | 0.111419i | \(0.0355395\pi\) | |||||||
\(62\) | −164.385 | − | 284.722i | −0.336724 | − | 0.583222i | ||||
\(63\) | 483.488 | − | 279.142i | 0.966885 | − | 0.558231i | ||||
\(64\) | 482.872 | 0.943110 | ||||||||
\(65\) | 171.890 | + | 871.921i | 0.328005 | + | 1.66382i | ||||
\(66\) | 83.2917 | 0.155341 | ||||||||
\(67\) | 150.377 | − | 86.8205i | 0.274202 | − | 0.158311i | −0.356594 | − | 0.934260i | \(-0.616062\pi\) |
0.630796 | + | 0.775949i | \(0.282729\pi\) | |||||||
\(68\) | 406.059 | + | 703.315i | 0.724145 | + | 1.25426i | ||||
\(69\) | 69.9156 | − | 121.097i | 0.121983 | − | 0.211281i | ||||
\(70\) | − | 1799.33i | − | 3.07230i | ||||||
\(71\) | 551.325 | + | 318.308i | 0.921553 | + | 0.532059i | 0.884130 | − | 0.467241i | \(-0.154752\pi\) |
0.0374226 | + | 0.999300i | \(0.488085\pi\) | |||||||
\(72\) | −18.0431 | − | 10.4172i | −0.0295333 | − | 0.0170510i | ||||
\(73\) | 64.9052i | 0.104063i | 0.998645 | + | 0.0520314i | \(0.0165696\pi\) | ||||
−0.998645 | + | 0.0520314i | \(0.983430\pi\) | |||||||
\(74\) | −507.877 | + | 879.668i | −0.797831 | + | 1.38188i | ||||
\(75\) | 223.514 | + | 387.138i | 0.344123 | + | 0.596039i | ||||
\(76\) | 232.943 | − | 134.490i | 0.351584 | − | 0.202987i | ||||
\(77\) | 262.828 | 0.388987 | ||||||||
\(78\) | 335.884 | + | 114.657i | 0.487582 | + | 0.166440i | ||||
\(79\) | −1333.51 | −1.89913 | −0.949566 | − | 0.313567i | \(-0.898476\pi\) | ||||
−0.949566 | + | 0.313567i | \(0.898476\pi\) | |||||||
\(80\) | −1079.54 | + | 623.272i | −1.50870 | + | 0.871050i | ||||
\(81\) | −223.910 | − | 387.824i | −0.307147 | − | 0.531995i | ||||
\(82\) | 771.285 | − | 1335.91i | 1.03871 | − | 1.79910i | ||||
\(83\) | 864.242i | 1.14293i | 0.820628 | + | 0.571463i | \(0.193624\pi\) | ||||
−0.820628 | + | 0.571463i | \(0.806376\pi\) | |||||||
\(84\) | −306.729 | − | 177.090i | −0.398415 | − | 0.230025i | ||||
\(85\) | −1714.99 | − | 990.152i | −2.18844 | − | 1.26349i | ||||
\(86\) | − | 928.411i | − | 1.16411i | ||||||
\(87\) | −31.5315 | + | 54.6141i | −0.0388566 | + | 0.0673017i | ||||
\(88\) | −4.90417 | − | 8.49428i | −0.00594076 | − | 0.0102897i | ||||
\(89\) | 1004.65 | − | 580.033i | 1.19654 | − | 0.690825i | 0.236761 | − | 0.971568i | \(-0.423914\pi\) |
0.959783 | + | 0.280743i | \(0.0905810\pi\) | |||||||
\(90\) | −1759.58 | −2.06085 | ||||||||
\(91\) | 1059.89 | + | 361.801i | 1.22095 | + | 0.416780i | ||||
\(92\) | 570.316 | 0.646299 | ||||||||
\(93\) | 136.662 | − | 78.9018i | 0.152378 | − | 0.0879757i | ||||
\(94\) | −5.12525 | − | 8.87720i | −0.00562372 | − | 0.00974057i | ||||
\(95\) | −327.945 | + | 568.018i | −0.354173 | + | 0.613446i | ||||
\(96\) | 484.225i | 0.514802i | ||||||||
\(97\) | −604.411 | − | 348.957i | −0.632667 | − | 0.365270i | 0.149117 | − | 0.988820i | \(-0.452357\pi\) |
−0.781784 | + | 0.623549i | \(0.785690\pi\) | |||||||
\(98\) | −783.895 | − | 452.582i | −0.808014 | − | 0.466507i | ||||
\(99\) | − | 257.021i | − | 0.260925i | ||||||
\(100\) | −911.626 | + | 1578.98i | −0.911626 | + | 1.57898i | ||||
\(101\) | 712.003 | + | 1233.23i | 0.701455 | + | 1.21496i | 0.967956 | + | 0.251121i | \(0.0807993\pi\) |
−0.266500 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(102\) | −684.905 | + | 395.430i | −0.664860 | + | 0.383857i | ||||
\(103\) | 1669.26 | 1.59686 | 0.798432 | − | 0.602085i | \(-0.205663\pi\) | ||||
0.798432 | + | 0.602085i | \(0.205663\pi\) | |||||||
\(104\) | −8.08373 | − | 41.0052i | −0.00762188 | − | 0.0386624i | ||||
\(105\) | 863.649 | 0.802700 | ||||||||
\(106\) | −257.710 | + | 148.789i | −0.236142 | + | 0.136336i | ||||
\(107\) | 173.937 | + | 301.267i | 0.157150 | + | 0.272192i | 0.933840 | − | 0.357691i | \(-0.116436\pi\) |
−0.776690 | + | 0.629883i | \(0.783103\pi\) | |||||||
\(108\) | −373.293 | + | 646.563i | −0.332594 | + | 0.576070i | ||||
\(109\) | 804.928i | 0.707322i | 0.935374 | + | 0.353661i | \(0.115063\pi\) | ||||
−0.935374 | + | 0.353661i | \(0.884937\pi\) | |||||||
\(110\) | −717.392 | − | 414.186i | −0.621824 | − | 0.359010i | ||||
\(111\) | −422.226 | − | 243.772i | −0.361044 | − | 0.208449i | ||||
\(112\) | 1570.89i | 1.32531i | ||||||||
\(113\) | 725.091 | − | 1255.90i | 0.603636 | − | 1.04553i | −0.388629 | − | 0.921394i | \(-0.627051\pi\) |
0.992265 | − | 0.124134i | \(-0.0396153\pi\) | |||||||
\(114\) | 130.969 | + | 226.845i | 0.107600 | + | 0.186369i | ||||
\(115\) | −1204.37 | + | 695.341i | −0.976589 | + | 0.563834i | ||||
\(116\) | −257.208 | −0.205872 | ||||||||
\(117\) | 353.808 | − | 1036.47i | 0.279569 | − | 0.818990i | ||||
\(118\) | 1651.08 | 1.28808 | ||||||||
\(119\) | −2161.22 | + | 1247.78i | −1.66486 | + | 0.961210i | ||||
\(120\) | −16.1151 | − | 27.9121i | −0.0122591 | − | 0.0212335i | ||||
\(121\) | 60.5000 | − | 104.789i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 1515.32i | 1.12452i | ||||||||
\(123\) | 641.212 | + | 370.204i | 0.470050 | + | 0.271384i | ||||
\(124\) | 557.389 | + | 321.809i | 0.403670 | + | 0.233059i | ||||
\(125\) | − | 2075.88i | − | 1.48538i | ||||||
\(126\) | −1108.71 | + | 1920.34i | −0.783900 | + | 1.35775i | ||||
\(127\) | −921.148 | − | 1595.48i | −0.643612 | − | 1.11477i | −0.984620 | − | 0.174708i | \(-0.944102\pi\) |
0.341009 | − | 0.940060i | \(-0.389231\pi\) | |||||||
\(128\) | 98.8036 | − | 57.0443i | 0.0682272 | − | 0.0393910i | ||||
\(129\) | 445.622 | 0.304146 | ||||||||
\(130\) | −2322.82 | − | 2657.80i | −1.56711 | − | 1.79311i | ||||
\(131\) | −384.902 | −0.256710 | −0.128355 | − | 0.991728i | \(-0.540970\pi\) | ||||
−0.128355 | + | 0.991728i | \(0.540970\pi\) | |||||||
\(132\) | −141.211 | + | 81.5284i | −0.0931126 | + | 0.0537586i | ||||
\(133\) | 413.274 | + | 715.812i | 0.269439 | + | 0.466682i | ||||
\(134\) | −344.837 | + | 597.275i | −0.222309 | + | 0.385050i | ||||
\(135\) | − | 1820.51i | − | 1.16063i | ||||||
\(136\) | 80.6537 | + | 46.5654i | 0.0508529 | + | 0.0293599i | ||||
\(137\) | 293.232 | + | 169.298i | 0.182865 | + | 0.105577i | 0.588638 | − | 0.808397i | \(-0.299664\pi\) |
−0.405773 | + | 0.913974i | \(0.632998\pi\) | |||||||
\(138\) | 555.387i | 0.342592i | ||||||||
\(139\) | −1101.08 | + | 1907.12i | −0.671887 | + | 1.16374i | 0.305482 | + | 0.952198i | \(0.401183\pi\) |
−0.977368 | + | 0.211544i | \(0.932151\pi\) | |||||||
\(140\) | 1761.24 | + | 3050.55i | 1.06323 | + | 1.84156i | ||||
\(141\) | 4.26091 | − | 2.46004i | 0.00254492 | − | 0.00146931i | ||||
\(142\) | −2528.53 | −1.49429 | ||||||||
\(143\) | 388.223 | − | 339.293i | 0.227027 | − | 0.198413i | ||||
\(144\) | 1536.18 | 0.888995 | ||||||||
\(145\) | 543.161 | − | 313.594i | 0.311083 | − | 0.179604i | ||||
\(146\) | −128.896 | − | 223.255i | −0.0730654 | − | 0.126553i | ||||
\(147\) | 217.232 | − | 376.256i | 0.121884 | − | 0.211110i | ||||
\(148\) | − | 1988.50i | − | 1.10442i | ||||||
\(149\) | −1361.71 | − | 786.184i | −0.748695 | − | 0.432259i | 0.0765269 | − | 0.997068i | \(-0.475617\pi\) |
−0.825222 | + | 0.564808i | \(0.808950\pi\) | |||||||
\(150\) | −1537.65 | − | 887.764i | −0.836991 | − | 0.483237i | ||||
\(151\) | 1672.51i | 0.901373i | 0.892682 | + | 0.450686i | \(0.148821\pi\) | ||||
−0.892682 | + | 0.450686i | \(0.851179\pi\) | |||||||
\(152\) | 15.4228 | − | 26.7131i | 0.00822996 | − | 0.0142547i | ||||
\(153\) | 1220.22 | + | 2113.48i | 0.644763 | + | 1.11676i | ||||
\(154\) | −904.052 | + | 521.954i | −0.473056 | + | 0.273119i | ||||
\(155\) | −1569.43 | −0.813286 | ||||||||
\(156\) | −681.682 | + | 134.386i | −0.349860 | + | 0.0689712i | ||||
\(157\) | 3414.16 | 1.73554 | 0.867768 | − | 0.496969i | \(-0.165554\pi\) | ||||
0.867768 | + | 0.496969i | \(0.165554\pi\) | |||||||
\(158\) | 4586.89 | − | 2648.24i | 2.30958 | − | 1.33344i | ||||
\(159\) | −71.4162 | − | 123.697i | −0.0356206 | − | 0.0616967i | ||||
\(160\) | 2407.91 | − | 4170.63i | 1.18976 | − | 2.06073i | ||||
\(161\) | 1752.53i | 0.857879i | ||||||||
\(162\) | 1540.38 | + | 889.336i | 0.747058 | + | 0.431314i | ||||
\(163\) | −1740.55 | − | 1004.91i | −0.836383 | − | 0.482886i | 0.0196499 | − | 0.999807i | \(-0.493745\pi\) |
−0.856033 | + | 0.516921i | \(0.827078\pi\) | |||||||
\(164\) | 3019.83i | 1.43786i | ||||||||
\(165\) | 198.802 | − | 344.336i | 0.0937985 | − | 0.162464i | ||||
\(166\) | −1716.31 | − | 2972.74i | −0.802481 | − | 1.38994i | ||||
\(167\) | 2940.04 | − | 1697.43i | 1.36232 | − | 0.786535i | 0.372386 | − | 0.928078i | \(-0.378540\pi\) |
0.989932 | + | 0.141543i | \(0.0452064\pi\) | |||||||
\(168\) | −40.6162 | −0.0186524 | ||||||||
\(169\) | 2032.62 | − | 833.824i | 0.925180 | − | 0.379529i | ||||
\(170\) | 7865.45 | 3.54854 | ||||||||
\(171\) | 699.999 | − | 404.144i | 0.313042 | − | 0.180735i | ||||
\(172\) | 908.756 | + | 1574.01i | 0.402860 | + | 0.697775i | ||||
\(173\) | −1361.94 | + | 2358.96i | −0.598536 | + | 1.03669i | 0.394502 | + | 0.918895i | \(0.370917\pi\) |
−0.993037 | + | 0.117799i | \(0.962416\pi\) | |||||||
\(174\) | − | 250.476i | − | 0.109129i | ||||||
\(175\) | −4852.07 | − | 2801.34i | −2.09590 | − | 1.21007i | ||||
\(176\) | 626.311 | + | 361.601i | 0.268238 | + | 0.154867i | ||||
\(177\) | 792.489i | 0.336537i | ||||||||
\(178\) | −2303.80 | + | 3990.30i | −0.970095 | + | 1.68025i | ||||
\(179\) | −615.762 | − | 1066.53i | −0.257118 | − | 0.445342i | 0.708350 | − | 0.705861i | \(-0.249440\pi\) |
−0.965469 | + | 0.260519i | \(0.916106\pi\) | |||||||
\(180\) | 2983.16 | − | 1722.33i | 1.23529 | − | 0.713194i | ||||
\(181\) | −4469.55 | −1.83546 | −0.917732 | − | 0.397201i | \(-0.869982\pi\) | ||||
−0.917732 | + | 0.397201i | \(0.869982\pi\) | |||||||
\(182\) | −4364.21 | + | 860.357i | −1.77745 | + | 0.350406i | ||||
\(183\) | −727.329 | −0.293802 | ||||||||
\(184\) | 56.6396 | − | 32.7009i | 0.0226931 | − | 0.0131019i | ||||
\(185\) | 2424.42 | + | 4199.22i | 0.963497 | + | 1.66883i | ||||
\(186\) | −313.385 | + | 542.799i | −0.123540 | + | 0.213978i | ||||
\(187\) | 1148.90i | 0.449284i | ||||||||
\(188\) | 17.3785 | + | 10.0335i | 0.00674180 | + | 0.00389238i | ||||
\(189\) | −1986.83 | − | 1147.10i | −0.764659 | − | 0.441476i | ||||
\(190\) | − | 2605.09i | − | 0.994701i | ||||||
\(191\) | −994.461 | + | 1722.46i | −0.376737 | + | 0.652527i | −0.990585 | − | 0.136897i | \(-0.956287\pi\) |
0.613849 | + | 0.789424i | \(0.289621\pi\) | |||||||
\(192\) | −460.278 | − | 797.225i | −0.173009 | − | 0.299660i | ||||
\(193\) | 4474.47 | − | 2583.33i | 1.66880 | − | 0.963484i | 0.700520 | − | 0.713633i | \(-0.252952\pi\) |
0.968284 | − | 0.249852i | \(-0.0803818\pi\) | |||||||
\(194\) | 2772.00 | 1.02587 | ||||||||
\(195\) | 1275.70 | − | 1114.91i | 0.468485 | − | 0.409439i | ||||
\(196\) | 1772.00 | 0.645773 | ||||||||
\(197\) | 1718.44 | − | 992.141i | 0.621491 | − | 0.358818i | −0.155959 | − | 0.987764i | \(-0.549847\pi\) |
0.777449 | + | 0.628946i | \(0.216513\pi\) | |||||||
\(198\) | 510.424 | + | 884.080i | 0.183203 | + | 0.317317i | ||||
\(199\) | 237.456 | − | 411.287i | 0.0845871 | − | 0.146509i | −0.820628 | − | 0.571463i | \(-0.806376\pi\) |
0.905215 | + | 0.424953i | \(0.139710\pi\) | |||||||
\(200\) | 209.084i | 0.0739224i | ||||||||
\(201\) | −286.682 | − | 165.516i | −0.100602 | − | 0.0580826i | ||||
\(202\) | −4898.17 | − | 2827.96i | −1.70611 | − | 0.985024i | ||||
\(203\) | − | 790.378i | − | 0.273269i | ||||||
\(204\) | 774.117 | − | 1340.81i | 0.265682 | − | 0.460174i | ||||
\(205\) | −3681.84 | − | 6377.13i | −1.25439 | − | 2.17267i | ||||
\(206\) | −5741.77 | + | 3315.01i | −1.94198 | + | 1.12120i | ||||
\(207\) | 1713.81 | 0.575450 | ||||||||
\(208\) | 2027.91 | + | 2320.36i | 0.676010 | + | 0.773501i | ||||
\(209\) | 380.525 | 0.125940 | ||||||||
\(210\) | −2970.70 | + | 1715.14i | −0.976181 | + | 0.563599i | ||||
\(211\) | −357.846 | − | 619.808i | −0.116754 | − | 0.202224i | 0.801725 | − | 0.597693i | \(-0.203916\pi\) |
−0.918480 | + | 0.395468i | \(0.870582\pi\) | |||||||
\(212\) | 291.278 | − | 504.508i | 0.0943635 | − | 0.163442i | ||||
\(213\) | − | 1213.65i | − | 0.390414i | ||||||
\(214\) | −1196.58 | − | 690.848i | −0.382228 | − | 0.220679i | ||||
\(215\) | −3838.14 | − | 2215.95i | −1.21748 | − | 0.702915i | ||||
\(216\) | 85.6159i | 0.0269696i | ||||||||
\(217\) | −988.889 | + | 1712.81i | −0.309356 | + | 0.535820i | ||||
\(218\) | −1598.52 | − | 2768.72i | −0.496631 | − | 0.860190i | ||||
\(219\) | 107.159 | − | 61.8681i | 0.0330645 | − | 0.0190898i | ||||
\(220\) | 1621.67 | 0.496968 | ||||||||
\(221\) | −1581.55 | + | 4633.10i | −0.481386 | + | 1.41021i | ||||
\(222\) | 1936.45 | 0.585432 | ||||||||
\(223\) | 5142.04 | − | 2968.76i | 1.54411 | − | 0.891492i | 0.545536 | − | 0.838087i | \(-0.316326\pi\) |
0.998573 | − | 0.0534048i | \(-0.0170074\pi\) | |||||||
\(224\) | −3034.43 | − | 5255.79i | −0.905119 | − | 1.56771i | ||||
\(225\) | −2739.46 | + | 4744.88i | −0.811691 | + | 1.40589i | ||||
\(226\) | 5759.89i | 1.69532i | ||||||||
\(227\) | −5535.12 | − | 3195.70i | −1.61841 | − | 0.934389i | −0.987332 | − | 0.158670i | \(-0.949280\pi\) |
−0.631078 | − | 0.775720i | \(-0.717387\pi\) | |||||||
\(228\) | −444.086 | − | 256.393i | −0.128993 | − | 0.0744739i | ||||
\(229\) | 3118.24i | 0.899822i | 0.893073 | + | 0.449911i | \(0.148544\pi\) | ||||
−0.893073 | + | 0.449911i | \(0.851456\pi\) | |||||||
\(230\) | 2761.78 | − | 4783.55i | 0.791768 | − | 1.37138i | ||||
\(231\) | −250.529 | − | 433.930i | −0.0713577 | − | 0.123595i | ||||
\(232\) | −25.5441 | + | 14.7479i | −0.00722867 | + | 0.00417347i | ||||
\(233\) | 4422.96 | 1.24360 | 0.621798 | − | 0.783178i | \(-0.286402\pi\) | ||||
0.621798 | + | 0.783178i | \(0.286402\pi\) | |||||||
\(234\) | 841.350 | + | 4267.80i | 0.235046 | + | 1.19228i | ||||
\(235\) | −48.9323 | −0.0135829 | ||||||||
\(236\) | −2799.20 | + | 1616.12i | −0.772088 | + | 0.445765i | ||||
\(237\) | 1271.11 | + | 2201.63i | 0.348386 | + | 0.603423i | ||||
\(238\) | 4955.99 | − | 8584.03i | 1.34979 | − | 2.33790i | ||||
\(239\) | − | 6366.01i | − | 1.72294i | −0.507808 | − | 0.861470i | \(-0.669544\pi\) | ||
0.507808 | − | 0.861470i | \(-0.330456\pi\) | |||||||
\(240\) | 2058.05 | + | 1188.22i | 0.553528 | + | 0.319579i | ||||
\(241\) | 4691.81 | + | 2708.82i | 1.25405 | + | 0.724025i | 0.971911 | − | 0.235348i | \(-0.0756231\pi\) |
0.282138 | + | 0.959374i | \(0.408956\pi\) | |||||||
\(242\) | 480.592i | 0.127660i | ||||||||
\(243\) | −1723.11 | + | 2984.51i | −0.454886 | + | 0.787886i | ||||
\(244\) | −1483.24 | − | 2569.05i | −0.389159 | − | 0.674043i | ||||
\(245\) | −3742.03 | + | 2160.46i | −0.975795 | + | 0.563375i | ||||
\(246\) | −2940.78 | −0.762185 | ||||||||
\(247\) | 1534.51 | + | 523.819i | 0.395299 | + | 0.134938i | ||||
\(248\) | 73.8078 | 0.0188984 | ||||||||
\(249\) | 1426.87 | − | 823.802i | 0.363149 | − | 0.209664i | ||||
\(250\) | 4122.53 | + | 7140.43i | 1.04293 | + | 1.80640i | ||||
\(251\) | 1255.34 | − | 2174.31i | 0.315683 | − | 0.546779i | −0.663899 | − | 0.747822i | \(-0.731100\pi\) |
0.979582 | + | 0.201043i | \(0.0644330\pi\) | |||||||
\(252\) | − | 4340.94i | − | 1.08513i | ||||||
\(253\) | 698.731 | + | 403.413i | 0.173632 | + | 0.100246i | ||||
\(254\) | 6336.97 | + | 3658.65i | 1.56542 | + | 0.903796i | ||||
\(255\) | 3775.28i | 0.927127i | ||||||||
\(256\) | −2158.06 | + | 3737.87i | −0.526870 | + | 0.912566i | ||||
\(257\) | 2024.97 | + | 3507.35i | 0.491495 | + | 0.851294i | 0.999952 | − | 0.00979315i | \(-0.00311731\pi\) |
−0.508457 | + | 0.861087i | \(0.669784\pi\) | |||||||
\(258\) | −1532.81 | + | 884.969i | −0.369879 | + | 0.213549i | ||||
\(259\) | 6110.47 | 1.46597 | ||||||||
\(260\) | 6539.59 | + | 2232.34i | 1.55988 | + | 0.532477i | ||||
\(261\) | −772.917 | −0.183304 | ||||||||
\(262\) | 1323.95 | − | 764.385i | 0.312191 | − | 0.180244i | ||||
\(263\) | 614.298 | + | 1063.99i | 0.144027 | + | 0.249463i | 0.929010 | − | 0.370055i | \(-0.120661\pi\) |
−0.784982 | + | 0.619518i | \(0.787328\pi\) | |||||||
\(264\) | −9.34939 | + | 16.1936i | −0.00217960 | + | 0.00377518i | ||||
\(265\) | 1420.53i | 0.329292i | ||||||||
\(266\) | −2843.09 | − | 1641.46i | −0.655342 | − | 0.378362i | ||||
\(267\) | −1915.27 | − | 1105.78i | −0.439000 | − | 0.253457i | ||||
\(268\) | − | 1350.15i | − | 0.307736i | ||||||
\(269\) | 1730.57 | − | 2997.43i | 0.392248 | − | 0.679393i | −0.600498 | − | 0.799626i | \(-0.705031\pi\) |
0.992746 | + | 0.120233i | \(0.0383643\pi\) | |||||||
\(270\) | 3615.38 | + | 6262.03i | 0.814908 | + | 1.41146i | ||||
\(271\) | 1695.83 | − | 979.086i | 0.380126 | − | 0.219466i | −0.297747 | − | 0.954645i | \(-0.596235\pi\) |
0.677873 | + | 0.735179i | \(0.262902\pi\) | |||||||
\(272\) | −6866.84 | −1.53075 | ||||||||
\(273\) | −412.957 | − | 2094.75i | −0.0915505 | − | 0.464395i | ||||
\(274\) | −1344.85 | −0.296515 | ||||||||
\(275\) | −2233.79 | + | 1289.68i | −0.489827 | + | 0.282801i | ||||
\(276\) | −543.629 | − | 941.593i | −0.118560 | − | 0.205352i | ||||
\(277\) | 158.786 | − | 275.026i | 0.0344424 | − | 0.0596559i | −0.848290 | − | 0.529531i | \(-0.822368\pi\) |
0.882733 | + | 0.469875i | \(0.155701\pi\) | |||||||
\(278\) | − | 8746.61i | − | 1.88700i | ||||||
\(279\) | 1674.97 | + | 967.043i | 0.359418 | + | 0.207510i | ||||
\(280\) | 349.827 | + | 201.973i | 0.0746649 | + | 0.0431078i | ||||
\(281\) | − | 4543.56i | − | 0.964576i | −0.876013 | − | 0.482288i | \(-0.839806\pi\) | ||
0.876013 | − | 0.482288i | \(-0.160194\pi\) | |||||||
\(282\) | −9.77087 | + | 16.9236i | −0.00206329 | + | 0.00357372i | ||||
\(283\) | −1850.13 | − | 3204.52i | −0.388618 | − | 0.673106i | 0.603646 | − | 0.797253i | \(-0.293714\pi\) |
−0.992264 | + | 0.124146i | \(0.960381\pi\) | |||||||
\(284\) | 4286.83 | − | 2475.00i | 0.895692 | − | 0.517128i | ||||
\(285\) | 1250.40 | 0.259885 | ||||||||
\(286\) | −661.569 | + | 1938.05i | −0.136781 | + | 0.400697i | ||||
\(287\) | −9279.66 | −1.90857 | ||||||||
\(288\) | −5139.69 | + | 2967.40i | −1.05159 | + | 0.607138i | ||||
\(289\) | −2997.95 | − | 5192.60i | −0.610208 | − | 1.05691i | ||||
\(290\) | −1245.55 | + | 2157.35i | −0.252210 | + | 0.436841i | ||||
\(291\) | 1330.51i | 0.268028i | ||||||||
\(292\) | 437.057 | + | 252.335i | 0.0875920 | + | 0.0505712i | ||||
\(293\) | −573.036 | − | 330.843i | −0.114256 | − | 0.0659660i | 0.441783 | − | 0.897122i | \(-0.354346\pi\) |
−0.556039 | + | 0.831156i | \(0.687680\pi\) | |||||||
\(294\) | 1725.62i | 0.342313i | ||||||||
\(295\) | 3940.82 | − | 6825.71i | 0.777775 | − | 1.34715i | ||||
\(296\) | −114.017 | − | 197.483i | −0.0223889 | − | 0.0387787i | ||||
\(297\) | −914.692 | + | 528.098i | −0.178706 | + | 0.103176i | ||||
\(298\) | 6245.19 | 1.21401 | ||||||||
\(299\) | 2262.40 | + | 2588.66i | 0.437584 | + | 0.500690i | ||||
\(300\) | 3475.88 | 0.668932 | ||||||||
\(301\) | −4836.80 | + | 2792.53i | −0.926207 | + | 0.534746i | ||||
\(302\) | −3321.48 | − | 5752.97i | −0.632879 | − | 1.09618i | ||||
\(303\) | 1357.37 | − | 2351.04i | 0.257357 | − | 0.445755i | ||||
\(304\) | 2274.35i | 0.429088i | ||||||||
\(305\) | 6264.49 | + | 3616.80i | 1.17608 | + | 0.679008i | ||||
\(306\) | −8394.39 | − | 4846.51i | −1.56822 | − | 0.905413i | ||||
\(307\) | 7875.04i | 1.46401i | 0.681298 | + | 0.732007i | \(0.261416\pi\) | ||||
−0.681298 | + | 0.732007i | \(0.738584\pi\) | |||||||
\(308\) | 1021.81 | − | 1769.82i | 0.189035 | − | 0.327419i | ||||
\(309\) | −1591.15 | − | 2755.95i | −0.292937 | − | 0.507381i | ||||
\(310\) | 5398.37 | − | 3116.75i | 0.989055 | − | 0.571031i | ||||
\(311\) | −10616.2 | −1.93565 | −0.967825 | − | 0.251626i | \(-0.919035\pi\) | ||||
−0.967825 | + | 0.251626i | \(0.919035\pi\) | |||||||
\(312\) | −59.9943 | + | 52.4327i | −0.0108862 | + | 0.00951417i | ||||
\(313\) | 1032.33 | 0.186423 | 0.0932116 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932116 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(314\) | −11743.7 | + | 6780.24i | −2.11063 | + | 1.21857i | ||||
\(315\) | 5292.56 | + | 9166.99i | 0.946674 | + | 1.63969i | ||||
\(316\) | −5184.35 | + | 8979.56i | −0.922919 | + | 1.59854i | ||||
\(317\) | − | 3941.66i | − | 0.698377i | −0.937052 | − | 0.349189i | \(-0.886457\pi\) | ||
0.937052 | − | 0.349189i | \(-0.113543\pi\) | |||||||
\(318\) | 491.303 | + | 283.654i | 0.0866380 | + | 0.0500205i | ||||
\(319\) | −315.123 | − | 181.936i | −0.0553087 | − | 0.0319325i | ||||
\(320\) | 9155.33i | 1.59937i | ||||||||
\(321\) | 331.595 | − | 574.340i | 0.0576568 | − | 0.0998646i | ||||
\(322\) | −3480.38 | − | 6028.19i | −0.602342 | − | 1.04329i | ||||
\(323\) | −3129.04 | + | 1806.55i | −0.539023 | + | 0.311205i | ||||
\(324\) | −3482.03 | −0.597056 | ||||||||
\(325\) | −10783.4 | + | 2125.82i | −1.84047 | + | 0.362829i | ||||
\(326\) | 7982.66 | 1.35619 | ||||||||
\(327\) | 1328.94 | − | 767.263i | 0.224742 | − | 0.129755i | ||||
\(328\) | 173.152 | + | 299.907i | 0.0291485 | + | 0.0504866i | ||||
\(329\) | −30.8320 | + | 53.4026i | −0.00516664 | + | 0.00894888i | ||||
\(330\) | 1579.22i | 0.263434i | ||||||||
\(331\) | −801.196 | − | 462.571i | −0.133045 | − | 0.0768133i | 0.432000 | − | 0.901873i | \(-0.357808\pi\) |
−0.565045 | + | 0.825060i | \(0.691141\pi\) | |||||||
\(332\) | 5819.61 | + | 3359.96i | 0.962027 | + | 0.555426i | ||||
\(333\) | − | 5975.49i | − | 0.983347i | ||||||
\(334\) | −6741.93 | + | 11677.4i | −1.10450 | + | 1.91304i | ||||
\(335\) | 1646.13 | + | 2851.18i | 0.268470 | + | 0.465004i | ||||
\(336\) | 2593.54 | − | 1497.38i | 0.421099 | − | 0.243122i | ||||
\(337\) | 3019.35 | 0.488056 | 0.244028 | − | 0.969768i | \(-0.421531\pi\) | ||||
0.244028 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(338\) | −5335.72 | + | 6904.74i | −0.858654 | + | 1.11115i | ||||
\(339\) | −2764.65 | −0.442936 | ||||||||
\(340\) | −13334.9 | + | 7698.93i | −2.12703 | + | 1.22804i | ||||
\(341\) | 455.263 | + | 788.538i | 0.0722987 | + | 0.125225i | ||||
\(342\) | −1605.20 | + | 2780.28i | −0.253798 | + | 0.439592i | ||||
\(343\) | − | 2750.24i | − | 0.432942i | ||||||
\(344\) | 180.502 | + | 104.213i | 0.0282908 | + | 0.0163337i | ||||
\(345\) | 2296.02 | + | 1325.61i | 0.358301 | + | 0.206865i | ||||
\(346\) | − | 10818.8i | − | 1.68100i | ||||||
\(347\) | 927.824 | − | 1607.04i | 0.143539 | − | 0.248618i | −0.785288 | − | 0.619131i | \(-0.787485\pi\) |
0.928827 | + | 0.370513i | \(0.120818\pi\) | |||||||
\(348\) | 245.173 | + | 424.652i | 0.0377662 | + | 0.0654130i | ||||
\(349\) | 2226.76 | − | 1285.62i | 0.341535 | − | 0.197186i | −0.319415 | − | 0.947615i | \(-0.603487\pi\) |
0.660951 | + | 0.750429i | \(0.270153\pi\) | |||||||
\(350\) | 22253.0 | 3.39849 | ||||||||
\(351\) | −4415.57 | + | 870.483i | −0.671470 | + | 0.132373i | ||||
\(352\) | −2793.97 | −0.423066 | ||||||||
\(353\) | 5355.78 | − | 3092.16i | 0.807534 | − | 0.466230i | −0.0385646 | − | 0.999256i | \(-0.512279\pi\) |
0.846099 | + | 0.533026i | \(0.178945\pi\) | |||||||
\(354\) | −1573.82 | − | 2725.93i | −0.236293 | − | 0.409271i | ||||
\(355\) | −6035.15 | + | 10453.2i | −0.902289 | + | 1.56281i | ||||
\(356\) | − | 9020.10i | − | 1.34288i | ||||||
\(357\) | 4120.19 | + | 2378.79i | 0.610822 | + | 0.352658i | ||||
\(358\) | 4236.09 | + | 2445.71i | 0.625375 | + | 0.361060i | ||||
\(359\) | − | 9743.48i | − | 1.43243i | −0.697881 | − | 0.716214i | \(-0.745874\pi\) | ||
0.697881 | − | 0.716214i | \(-0.254126\pi\) | |||||||
\(360\) | 197.511 | − | 342.099i | 0.0289159 | − | 0.0500839i | ||||
\(361\) | −2831.16 | − | 4903.71i | −0.412765 | − | 0.714930i | ||||
\(362\) | 15374.0 | − | 8876.16i | 2.23215 | − | 1.28873i | ||||
\(363\) | −230.676 | −0.0333536 | ||||||||
\(364\) | 6556.86 | − | 5730.45i | 0.944156 | − | 0.825157i | ||||
\(365\) | −1230.61 | −0.176474 | ||||||||
\(366\) | 2501.80 | − | 1444.42i | 0.357299 | − | 0.206287i | ||||
\(367\) | 1458.40 | + | 2526.02i | 0.207432 | + | 0.359284i | 0.950905 | − | 0.309483i | \(-0.100156\pi\) |
−0.743473 | + | 0.668766i | \(0.766823\pi\) | |||||||
\(368\) | −2411.14 | + | 4176.23i | −0.341548 | + | 0.591578i | ||||
\(369\) | 9074.65i | 1.28024i | ||||||||
\(370\) | −16678.6 | − | 9629.41i | −2.34346 | − | 1.35300i | ||||
\(371\) | 1550.31 | + | 895.071i | 0.216949 | + | 0.125255i | ||||
\(372\) | − | 1227.00i | − | 0.171014i | ||||||
\(373\) | 1415.45 | − | 2451.64i | 0.196486 | − | 0.340324i | −0.750900 | − | 0.660415i | \(-0.770380\pi\) |
0.947387 | + | 0.320091i | \(0.103714\pi\) | |||||||
\(374\) | −2281.63 | − | 3951.90i | −0.315455 | − | 0.546384i | ||||
\(375\) | −3427.29 | + | 1978.75i | −0.471958 | + | 0.272485i | ||||
\(376\) | 2.30121 | 0.000315628 | ||||||||
\(377\) | −1020.32 | − | 1167.47i | −0.139388 | − | 0.159490i | ||||
\(378\) | 9112.16 | 1.23989 | ||||||||
\(379\) | 1177.67 | − | 679.927i | 0.159611 | − | 0.0921517i | −0.418067 | − | 0.908416i | \(-0.637292\pi\) |
0.577678 | + | 0.816265i | \(0.303959\pi\) | |||||||
\(380\) | 2549.94 | + | 4416.62i | 0.344235 | + | 0.596232i | ||||
\(381\) | −1756.09 | + | 3041.64i | −0.236135 | + | 0.408997i | ||||
\(382\) | − | 7899.68i | − | 1.05807i | ||||||
\(383\) | −169.154 | − | 97.6609i | −0.0225675 | − | 0.0130293i | 0.488674 | − | 0.872467i | \(-0.337481\pi\) |
−0.511241 | + | 0.859437i | \(0.670814\pi\) | |||||||
\(384\) | −188.361 | − | 108.750i | −0.0250319 | − | 0.0144522i | ||||
\(385\) | 4983.25i | 0.659662i | ||||||||
\(386\) | −10260.6 | + | 17771.9i | −1.35298 | + | 2.34343i | ||||
\(387\) | 2730.83 | + | 4729.94i | 0.358698 | + | 0.621283i | ||||
\(388\) | −4699.60 | + | 2713.32i | −0.614913 | + | 0.355020i | ||||
\(389\) | 62.8690 | 0.00819431 | 0.00409715 | − | 0.999992i | \(-0.498696\pi\) | ||||
0.00409715 | + | 0.999992i | \(0.498696\pi\) | |||||||
\(390\) | −2173.91 | + | 6368.41i | −0.282257 | + | 0.826865i | ||||
\(391\) | −7660.86 | −0.990860 | ||||||||
\(392\) | 175.982 | − | 101.604i | 0.0226746 | − | 0.0130912i | ||||
\(393\) | 366.892 | + | 635.475i | 0.0470922 | + | 0.0815661i | ||||
\(394\) | −3940.62 | + | 6825.36i | −0.503872 | + | 0.872732i | ||||
\(395\) | − | 25283.5i | − | 3.22064i | ||||||
\(396\) | −1730.73 | − | 999.235i | −0.219627 | − | 0.126802i | ||||
\(397\) | 7030.41 | + | 4059.01i | 0.888781 | + | 0.513138i | 0.873543 | − | 0.486746i | \(-0.161816\pi\) |
0.0152372 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(398\) | 1886.28i | 0.237564i | ||||||||
\(399\) | 787.873 | − | 1364.64i | 0.0988545 | − | 0.171221i | ||||
\(400\) | −7708.23 | − | 13351.0i | −0.963529 | − | 1.66888i | ||||
\(401\) | 444.981 | − | 256.910i | 0.0554147 | − | 0.0319937i | −0.472037 | − | 0.881579i | \(-0.656481\pi\) |
0.527451 | + | 0.849585i | \(0.323148\pi\) | |||||||
\(402\) | 1314.81 | 0.163126 | ||||||||
\(403\) | 750.426 | + | 3806.58i | 0.0927578 | + | 0.470519i | ||||
\(404\) | 11072.4 | 1.36354 | ||||||||
\(405\) | 7353.20 | − | 4245.37i | 0.902181 | − | 0.520875i | ||||
\(406\) | 1569.63 | + | 2718.67i | 0.191870 | + | 0.332329i | ||||
\(407\) | 1406.56 | − | 2436.24i | 0.171304 | − | 0.296707i | ||||
\(408\) | − | 177.546i | − | 0.0215437i | ||||||
\(409\) | −3287.79 | − | 1898.21i | −0.397483 | − | 0.229487i | 0.287914 | − | 0.957656i | \(-0.407038\pi\) |
−0.685397 | + | 0.728169i | \(0.740372\pi\) | |||||||
\(410\) | 25328.9 | + | 14623.7i | 3.05099 | + | 1.76149i | ||||
\(411\) | − | 645.503i | − | 0.0774704i | ||||||
\(412\) | 6489.66 | − | 11240.4i | 0.776026 | − | 1.34412i | ||||
\(413\) | −4966.20 | − | 8601.70i | −0.591696 | − | 1.02485i | ||||
\(414\) | −5895.02 | + | 3403.49i | −0.699818 | + | 0.404040i | ||||
\(415\) | −16386.1 | −1.93823 | ||||||||
\(416\) | −11267.0 | − | 3846.10i | −1.32791 | − | 0.453295i | ||||
\(417\) | 4198.23 | 0.493017 | ||||||||
\(418\) | −1308.90 | + | 755.691i | −0.153158 | + | 0.0884260i | ||||
\(419\) | −6781.01 | − | 11745.1i | −0.790630 | − | 1.36941i | −0.925577 | − | 0.378559i | \(-0.876420\pi\) |
0.134947 | − | 0.990853i | \(-0.456914\pi\) | |||||||
\(420\) | 3357.65 | − | 5815.62i | 0.390087 | − | 0.675651i | ||||
\(421\) | − | 9302.08i | − | 1.07685i | −0.842672 | − | 0.538427i | \(-0.819019\pi\) | ||
0.842672 | − | 0.538427i | \(-0.180981\pi\) | |||||||
\(422\) | 2461.78 | + | 1421.31i | 0.283975 | + | 0.163953i | ||||
\(423\) | 52.2229 | + | 30.1509i | 0.00600275 | + | 0.00346569i | ||||
\(424\) | − | 66.8055i | − | 0.00765180i | ||||||
\(425\) | 12245.6 | − | 21209.9i | 1.39764 | − | 2.42078i | ||||
\(426\) | 2410.22 | + | 4174.62i | 0.274121 | + | 0.474791i | ||||
\(427\) | 7894.46 | − | 4557.87i | 0.894707 | − | 0.516559i | ||||
\(428\) | 2704.89 | 0.305481 | ||||||||
\(429\) | −930.231 | − | 317.542i | −0.104690 | − | 0.0357368i | ||||
\(430\) | 17602.8 | 1.97415 | ||||||||
\(431\) | 1066.95 | − | 616.002i | 0.119241 | − | 0.0688440i | −0.439193 | − | 0.898393i | \(-0.644736\pi\) |
0.558434 | + | 0.829549i | \(0.311402\pi\) | |||||||
\(432\) | −3156.37 | − | 5466.99i | −0.351530 | − | 0.608868i | ||||
\(433\) | 7445.66 | − | 12896.3i | 0.826364 | − | 1.43130i | −0.0745088 | − | 0.997220i | \(-0.523739\pi\) |
0.900873 | − | 0.434084i | \(-0.142928\pi\) | |||||||
\(434\) | − | 7855.42i | − | 0.868830i | ||||||
\(435\) | −1035.49 | − | 597.841i | −0.114133 | − | 0.0658949i | ||||
\(436\) | 5420.21 | + | 3129.36i | 0.595369 | + | 0.343736i | ||||
\(437\) | 2537.33i | 0.277750i | ||||||||
\(438\) | −245.730 | + | 425.617i | −0.0268070 | + | 0.0464310i | ||||
\(439\) | 7293.50 | + | 12632.7i | 0.792938 | + | 1.37341i | 0.924140 | + | 0.382053i | \(0.124783\pi\) |
−0.131202 | + | 0.991356i | \(0.541884\pi\) | |||||||
\(440\) | 161.053 | − | 92.9838i | 0.0174497 | − | 0.0100746i | ||||
\(441\) | 5324.91 | 0.574982 | ||||||||
\(442\) | −3760.89 | − | 19077.3i | −0.404723 | − | 2.05298i | ||||
\(443\) | −2871.31 | −0.307946 | −0.153973 | − | 0.988075i | \(-0.549207\pi\) | ||||
−0.153973 | + | 0.988075i | \(0.549207\pi\) | |||||||
\(444\) | −3283.02 | + | 1895.45i | −0.350913 | + | 0.202599i | ||||
\(445\) | 10997.5 | + | 19048.2i | 1.17153 | + | 2.02915i | ||||
\(446\) | −11791.4 | + | 20423.3i | −1.25188 | + | 2.16833i | ||||
\(447\) | 2997.59i | 0.317183i | ||||||||
\(448\) | 9991.74 | + | 5768.74i | 1.05372 | + | 0.608364i | ||||
\(449\) | −1432.36 | − | 826.973i | −0.150551 | − | 0.0869205i | 0.422832 | − | 0.906208i | \(-0.361036\pi\) |
−0.573383 | + | 0.819287i | \(0.694369\pi\) | |||||||
\(450\) | − | 21761.4i | − | 2.27965i | ||||||
\(451\) | −2136.07 | + | 3699.79i | −0.223024 | + | 0.386289i | ||||
\(452\) | −5637.95 | − | 9765.22i | −0.586697 | − | 1.01619i | ||||
\(453\) | 2761.33 | − | 1594.25i | 0.286398 | − | 0.165352i | ||||
\(454\) | 25385.6 | 2.62425 | ||||||||
\(455\) | −6859.79 | + | 20095.6i | −0.706795 | + | 2.07054i | ||||
\(456\) | −58.8045 | −0.00603898 | ||||||||
\(457\) | −10579.0 | + | 6107.80i | −1.08286 | + | 0.625188i | −0.931666 | − | 0.363317i | \(-0.881644\pi\) |
−0.151191 | + | 0.988505i | \(0.548311\pi\) | |||||||
\(458\) | −6192.58 | − | 10725.9i | −0.631791 | − | 1.09429i | ||||
\(459\) | 5014.32 | − | 8685.06i | 0.509909 | − | 0.883189i | ||||
\(460\) | 10813.3i | 1.09602i | ||||||||
\(461\) | 13616.0 | + | 7861.22i | 1.37562 | + | 0.794215i | 0.991629 | − | 0.129121i | \(-0.0412155\pi\) |
0.383993 | + | 0.923336i | \(0.374549\pi\) | |||||||
\(462\) | 1723.50 | + | 995.062i | 0.173559 | + | 0.100205i | ||||
\(463\) | 11087.5i | 1.11291i | 0.830876 | + | 0.556457i | \(0.187840\pi\) | ||||
−0.830876 | + | 0.556457i | \(0.812160\pi\) | |||||||
\(464\) | 1087.41 | − | 1883.45i | 0.108797 | − | 0.188442i | ||||
\(465\) | 1495.99 | + | 2591.13i | 0.149193 | + | 0.258410i | ||||
\(466\) | −15213.7 | + | 8783.65i | −1.51237 | + | 0.873164i | ||||
\(467\) | −5899.70 | −0.584594 | −0.292297 | − | 0.956328i | \(-0.594420\pi\) | ||||
−0.292297 | + | 0.956328i | \(0.594420\pi\) | |||||||
\(468\) | −5603.85 | − | 6412.01i | −0.553501 | − | 0.633323i | ||||
\(469\) | 4148.88 | 0.408480 | ||||||||
\(470\) | 168.313 | − | 97.1755i | 0.0165185 | − | 0.00953696i | ||||
\(471\) | −3254.40 | − | 5636.79i | −0.318375 | − | 0.551442i | ||||
\(472\) | −185.331 | + | 321.003i | −0.0180732 | + | 0.0313037i | ||||
\(473\) | 2571.23i | 0.249948i | ||||||||
\(474\) | −8744.52 | − | 5048.65i | −0.847361 | − | 0.489224i | ||||
\(475\) | −7024.88 | − | 4055.81i | −0.678576 | − | 0.391776i | ||||
\(476\) | 19404.3i | 1.86847i | ||||||||
\(477\) | 875.298 | − | 1516.06i | 0.0840191 | − | 0.145525i | ||||
\(478\) | 12642.4 | + | 21897.2i | 1.20973 | + | 2.09531i | ||||
\(479\) | 6737.82 | − | 3890.08i | 0.642712 | − | 0.371070i | −0.142947 | − | 0.989730i | \(-0.545658\pi\) |
0.785658 | + | 0.618661i | \(0.212324\pi\) | |||||||
\(480\) | −9180.97 | −0.873025 | ||||||||
\(481\) | 9025.80 | − | 7888.21i | 0.855595 | − | 0.747758i | ||||
\(482\) | −21518.0 | −2.03344 | ||||||||
\(483\) | 2893.43 | − | 1670.52i | 0.272579 | − | 0.157374i | ||||
\(484\) | −470.418 | − | 814.788i | −0.0441790 | − | 0.0765203i | ||||
\(485\) | 6616.27 | − | 11459.7i | 0.619442 | − | 1.07291i | ||||
\(486\) | − | 13687.8i | − | 1.27755i | ||||||
\(487\) | 14864.3 | + | 8581.88i | 1.38309 | + | 0.798526i | 0.992524 | − | 0.122050i | \(-0.0389469\pi\) |
0.390563 | + | 0.920576i | \(0.372280\pi\) | |||||||
\(488\) | −294.610 | − | 170.093i | −0.0273286 | − | 0.0157782i | ||||
\(489\) | 3831.54i | 0.354332i | ||||||||
\(490\) | 8581.01 | − | 14862.8i | 0.791124 | − | 1.37027i | ||||
\(491\) | 19.4948 | + | 33.7659i | 0.00179182 | + | 0.00310353i | 0.866920 | − | 0.498447i | \(-0.166096\pi\) |
−0.865128 | + | 0.501551i | \(0.832763\pi\) | |||||||
\(492\) | 4985.75 | − | 2878.52i | 0.456859 | − | 0.263768i | ||||
\(493\) | 3454.99 | 0.315629 | ||||||||
\(494\) | −6318.55 | + | 1245.63i | −0.575476 | + | 0.113449i | ||||
\(495\) | 4873.16 | 0.442489 | ||||||||
\(496\) | −4712.99 | + | 2721.05i | −0.426652 | + | 0.246328i | ||||
\(497\) | 7605.46 | + | 13173.0i | 0.686421 | + | 1.18892i | ||||
\(498\) | −3272.01 | + | 5667.28i | −0.294422 | + | 0.509954i | ||||
\(499\) | 16093.8i | 1.44380i | 0.691997 | + | 0.721900i | \(0.256731\pi\) | ||||
−0.691997 | + | 0.721900i | \(0.743269\pi\) | |||||||
\(500\) | −13978.5 | − | 8070.51i | −1.25028 | − | 0.721848i | ||||
\(501\) | −5604.94 | − | 3236.01i | −0.499821 | − | 0.288572i | ||||
\(502\) | 9972.03i | 0.886600i | ||||||||
\(503\) | 4155.38 | − | 7197.33i | 0.368348 | − | 0.637998i | −0.620959 | − | 0.783843i | \(-0.713257\pi\) |
0.989307 | + | 0.145845i | \(0.0465900\pi\) | |||||||
\(504\) | −248.902 | − | 431.110i | −0.0219979 | − | 0.0381016i | ||||
\(505\) | −23382.1 | + | 13499.7i | −2.06038 | + | 1.18956i | ||||
\(506\) | −3204.58 | −0.281543 | ||||||||
\(507\) | −3314.16 | − | 2561.06i | −0.290309 | − | 0.224340i | ||||
\(508\) | −14324.8 | −1.25110 | ||||||||
\(509\) | 17255.0 | − | 9962.19i | 1.50258 | − | 0.867517i | 0.502589 | − | 0.864526i | \(-0.332381\pi\) |
0.999996 | − | 0.00299168i | \(-0.000952284\pi\) | |||||||
\(510\) | −7497.41 | − | 12985.9i | −0.650962 | − | 1.12750i | ||||
\(511\) | −775.403 | + | 1343.04i | −0.0671269 | + | 0.116267i | ||||
\(512\) | − | 16230.2i | − | 1.40094i | ||||||
\(513\) | −2876.55 | − | 1660.78i | −0.247569 | − | 0.142934i | ||||
\(514\) | −13930.6 | − | 8042.86i | −1.19544 | − | 0.690185i | ||||
\(515\) | 31649.4i | 2.70803i | ||||||||
\(516\) | 1732.47 | − | 3000.72i | 0.147805 | − | 0.256007i | ||||
\(517\) | 14.1944 | + | 24.5854i | 0.00120748 | + | 0.00209142i | ||||
\(518\) | −21018.3 | + | 12134.9i | −1.78280 | + | 1.02930i | ||||
\(519\) | 5192.86 | 0.439193 | ||||||||
\(520\) | 777.464 | − | 153.269i | 0.0655655 | − | 0.0129255i | ||||
\(521\) | −2392.35 | −0.201172 | −0.100586 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(522\) | 2658.61 | − | 1534.95i | 0.222920 | − | 0.128703i | ||||
\(523\) | −808.843 | − | 1400.96i | −0.0676257 | − | 0.117131i | 0.830230 | − | 0.557421i | \(-0.188209\pi\) |
−0.897856 | + | 0.440290i | \(0.854876\pi\) | |||||||
\(524\) | −1496.40 | + | 2591.85i | −0.124753 | + | 0.216079i | ||||
\(525\) | 10681.1i | 0.887922i | ||||||||
\(526\) | −4226.02 | − | 2439.89i | −0.350310 | − | 0.202252i | ||||
\(527\) | −7487.22 | − | 4322.75i | −0.618877 | − | 0.357309i | ||||
\(528\) | − | 1378.72i | − | 0.113639i | ||||||
\(529\) | 3393.55 | − | 5877.81i | 0.278915 | − | 0.483094i | ||||
\(530\) | −2821.06 | − | 4886.22i | −0.231206 | − | 0.400460i | ||||
\(531\) | −8411.68 | + | 4856.49i | −0.687450 | + | 0.396899i | ||||
\(532\) | 6426.83 | 0.523756 | ||||||||
\(533\) | −13707.0 | + | 11979.4i | −1.11391 | + | 0.973519i | ||||
\(534\) | 8783.99 | 0.711836 | ||||||||
\(535\) | −5712.06 | + | 3297.86i | −0.461596 | + | 0.266503i | ||||
\(536\) | −77.4150 | − | 134.087i | −0.00623847 | − | 0.0108053i | ||||
\(537\) | −1173.90 | + | 2033.25i | −0.0943341 | + | 0.163392i | ||||
\(538\) | 13747.1i | 1.10163i | ||||||||
\(539\) | 2171.00 | + | 1253.42i | 0.173491 | + | 0.100165i | ||||
\(540\) | −12258.9 | − | 7077.69i | −0.976925 | − | 0.564028i | ||||
\(541\) | 9634.48i | 0.765654i | 0.923820 | + | 0.382827i | \(0.125049\pi\) | ||||
−0.923820 | + | 0.382827i | \(0.874951\pi\) | |||||||
\(542\) | −3888.77 | + | 6735.55i | −0.308187 | + | 0.533795i | ||||
\(543\) | 4260.41 | + | 7379.24i | 0.336706 | + | 0.583193i | ||||
\(544\) | 22974.7 | − | 13264.5i | 1.81072 | − | 1.04542i | ||||
\(545\) | −15261.5 | −1.19951 | ||||||||
\(546\) | 5580.45 | + | 6385.23i | 0.437402 | + | 0.500481i | ||||
\(547\) | −11969.0 | −0.935571 | −0.467786 | − | 0.883842i | \(-0.654948\pi\) | ||||
−0.467786 | + | 0.883842i | \(0.654948\pi\) | |||||||
\(548\) | 2280.03 | − | 1316.37i | 0.177733 | − | 0.102614i | ||||
\(549\) | −4457.18 | − | 7720.06i | −0.346499 | − | 0.600153i | ||||
\(550\) | 5122.39 | − | 8872.23i | 0.397126 | − | 0.687842i | ||||
\(551\) | − | 1144.32i | − | 0.0884747i | ||||||
\(552\) | −107.979 | − | 62.3415i | −0.00832587 | − | 0.00480694i | ||||
\(553\) | −27593.4 | − | 15931.0i | −2.12186 | − | 1.22506i | ||||
\(554\) | 1261.35i | 0.0967319i | ||||||||
\(555\) | 4621.95 | − | 8005.46i | 0.353497 | − | 0.612275i | ||||
\(556\) | 8561.44 | + | 14828.8i | 0.653032 | + | 1.13109i | ||||
\(557\) | −16998.4 | + | 9814.02i | −1.29308 | + | 0.746559i | −0.979199 | − | 0.202904i | \(-0.934962\pi\) |
−0.313880 | + | 0.949463i | \(0.601629\pi\) | |||||||
\(558\) | −7681.88 | −0.582796 | ||||||||
\(559\) | −3539.48 | + | 10368.8i | −0.267807 | + | 0.784534i | ||||
\(560\) | −29784.2 | −2.24752 | ||||||||
\(561\) | 1896.84 | − | 1095.14i | 0.142754 | − | 0.0824189i | ||||
\(562\) | 9023.14 | + | 15628.5i | 0.677257 | + | 1.17304i | ||||
\(563\) | −9842.82 | + | 17048.3i | −0.736812 | + | 1.27620i | 0.217112 | + | 0.976147i | \(0.430336\pi\) |
−0.953924 | + | 0.300049i | \(0.902997\pi\) | |||||||
\(564\) | − | 38.2560i | − | 0.00285615i | ||||||
\(565\) | 23811.9 | + | 13747.8i | 1.77305 | + | 1.02367i | ||||
\(566\) | 12727.8 | + | 7348.42i | 0.945214 | + | 0.545720i | ||||
\(567\) | − | 10700.0i | − | 0.792516i | ||||||
\(568\) | 283.825 | − | 491.599i | 0.0209666 | − | 0.0363152i | ||||
\(569\) | 3758.01 | + | 6509.06i | 0.276878 | + | 0.479568i | 0.970607 | − | 0.240669i | \(-0.0773667\pi\) |
−0.693729 | + | 0.720236i | \(0.744033\pi\) | |||||||
\(570\) | −4301.02 | + | 2483.19i | −0.316052 | + | 0.182473i | ||||
\(571\) | 5919.57 | 0.433846 | 0.216923 | − | 0.976189i | \(-0.430398\pi\) | ||||
0.216923 | + | 0.976189i | \(0.430398\pi\) | |||||||
\(572\) | −775.407 | − | 3933.30i | −0.0566808 | − | 0.287517i | ||||
\(573\) | 3791.71 | 0.276442 | ||||||||
\(574\) | 31919.4 | − | 18428.6i | 2.32106 | − | 1.34006i | ||||
\(575\) | −8599.53 | − | 14894.8i | −0.623696 | − | 1.08027i | ||||
\(576\) | 5641.30 | − | 9771.01i | 0.408080 | − | 0.706815i | ||||
\(577\) | − | 14557.1i | − | 1.05029i | −0.851011 | − | 0.525147i | \(-0.824010\pi\) | ||
0.851011 | − | 0.525147i | \(-0.175990\pi\) | |||||||
\(578\) | 20624.2 | + | 11907.4i | 1.48417 | + | 0.856889i | ||||
\(579\) | −8530.19 | − | 4924.91i | −0.612267 | − | 0.353493i | ||||
\(580\) | − | 4876.70i | − | 0.349128i | ||||||
\(581\) | −10324.8 | + | 17883.2i | −0.737258 | + | 1.27697i | ||||
\(582\) | −2642.30 | − | 4576.59i | −0.188190 | − | 0.325955i | ||||
\(583\) | 713.728 | − | 412.071i | 0.0507025 | − | 0.0292731i | ||||
\(584\) | 57.8739 | 0.00410075 | ||||||||
\(585\) | 19651.6 | + | 6708.25i | 1.38888 | + | 0.474106i | ||||
\(586\) | 2628.11 | 0.185266 | ||||||||
\(587\) | 9353.47 | − | 5400.23i | 0.657681 | − | 0.379713i | −0.133712 | − | 0.991020i | \(-0.542690\pi\) |
0.791393 | + | 0.611308i | \(0.209356\pi\) | |||||||
\(588\) | −1689.09 | − | 2925.58i | −0.118464 | − | 0.205185i | ||||
\(589\) | −1431.72 | + | 2479.82i | −0.100158 | + | 0.173479i | ||||
\(590\) | 31304.6i | 2.18439i | ||||||||
\(591\) | −3276.06 | − | 1891.43i | −0.228019 | − | 0.131647i | ||||
\(592\) | 14561.1 | + | 8406.85i | 1.01091 | + | 0.583648i | ||||
\(593\) | − | 2821.58i | − | 0.195394i | −0.995216 | − | 0.0976968i | \(-0.968852\pi\) | ||
0.995216 | − | 0.0976968i | \(-0.0311475\pi\) | |||||||
\(594\) | 2097.52 | − | 3633.01i | 0.144886 | − | 0.250950i | ||||
\(595\) | −23658.1 | − | 40977.1i | −1.63006 | − | 2.82335i | ||||
\(596\) | −10588.0 | + | 6112.97i | −0.727685 | + | 0.420129i | ||||
\(597\) | −905.381 | −0.0620683 | ||||||||
\(598\) | −12922.9 | − | 4411.33i | −0.883705 | − | 0.301660i | ||||
\(599\) | −10033.3 | −0.684388 | −0.342194 | − | 0.939629i | \(-0.611170\pi\) | ||||
−0.342194 | + | 0.939629i | \(0.611170\pi\) | |||||||
\(600\) | 345.199 | − | 199.301i | 0.0234878 | − | 0.0135607i | ||||
\(601\) | 2788.01 | + | 4828.97i | 0.189226 | + | 0.327750i | 0.944993 | − | 0.327092i | \(-0.106069\pi\) |
−0.755766 | + | 0.654842i | \(0.772735\pi\) | |||||||
\(602\) | 11091.5 | − | 19211.0i | 0.750921 | − | 1.30063i | ||||
\(603\) | − | 4057.22i | − | 0.274001i | ||||||
\(604\) | 11262.3 | + | 6502.32i | 0.758706 | + | 0.438039i | ||||
\(605\) | 1986.81 | + | 1147.09i | 0.133513 | + | 0.0770839i | ||||
\(606\) | 10782.5i | 0.722790i | ||||||||
\(607\) | −6487.42 | + | 11236.5i | −0.433799 | + | 0.751362i | −0.997197 | − | 0.0748237i | \(-0.976161\pi\) |
0.563398 | + | 0.826186i | \(0.309494\pi\) | |||||||
\(608\) | −4393.29 | − | 7609.39i | −0.293045 | − | 0.507569i | ||||
\(609\) | −1304.92 | + | 753.394i | −0.0868275 | + | 0.0501299i | ||||
\(610\) | −28730.7 | −1.90700 | ||||||||
\(611\) | 23.3971 | + | 118.683i | 0.00154918 | + | 0.00785828i | ||||
\(612\) | 18975.6 | 1.25334 | ||||||||
\(613\) | −20826.3 | + | 12024.0i | −1.37221 | + | 0.792246i | −0.991206 | − | 0.132327i | \(-0.957755\pi\) |
−0.381004 | + | 0.924573i | \(0.624422\pi\) | |||||||
\(614\) | −15639.2 | − | 27087.9i | −1.02793 | − | 1.78042i | ||||
\(615\) | −7019.12 | + | 12157.5i | −0.460225 | + | 0.797132i | ||||
\(616\) | − | 234.355i | − | 0.0153286i | ||||||
\(617\) | 19739.2 | + | 11396.4i | 1.28796 | + | 0.743602i | 0.978290 | − | 0.207243i | \(-0.0664491\pi\) |
0.309667 | + | 0.950845i | \(0.399782\pi\) | |||||||
\(618\) | 10946.2 | + | 6319.79i | 0.712493 | + | 0.411358i | ||||
\(619\) | 17190.9i | 1.11625i | 0.829756 | + | 0.558126i | \(0.188480\pi\) | ||||
−0.829756 | + | 0.558126i | \(0.811520\pi\) | |||||||
\(620\) | −6101.54 | + | 10568.2i | −0.395232 | + | 0.684561i | ||||
\(621\) | −3521.34 | − | 6099.14i | −0.227547 | − | 0.394123i | ||||
\(622\) | 36516.5 | − | 21082.8i | 2.35399 | − | 1.35907i | ||||
\(623\) | 27718.0 | 1.78250 | ||||||||
\(624\) | 1897.91 | − | 5559.87i | 0.121758 | − | 0.356688i | ||||
\(625\) | 10048.1 | 0.643081 | ||||||||
\(626\) | −3550.90 | + | 2050.11i | −0.226713 | + | 0.130893i | ||||
\(627\) | −362.719 | − | 628.248i | −0.0231030 | − | 0.0400156i | ||||
\(628\) | 13273.4 | − | 22990.2i | 0.843417 | − | 1.46084i | ||||
\(629\) | 26710.8i | 1.69321i | ||||||||
\(630\) | −36409.8 | − | 21021.2i | −2.30254 | − | 1.32937i | ||||
\(631\) | 5122.80 | + | 2957.65i | 0.323194 | + | 0.186596i | 0.652815 | − | 0.757517i | \(-0.273588\pi\) |
−0.329621 | + | 0.944113i | \(0.606921\pi\) | |||||||
\(632\) | 1189.05i | 0.0748382i | ||||||||
\(633\) | −682.204 | + | 1181.61i | −0.0428360 | + | 0.0741941i | ||||
\(634\) | 7827.82 | + | 13558.2i | 0.490351 | + | 0.849312i | ||||
\(635\) | 30250.4 | − | 17465.1i | 1.89048 | − | 1.09147i | ||||
\(636\) | −1110.59 | −0.0692420 | ||||||||
\(637\) | 7029.39 | + | 8043.12i | 0.437228 | + | 0.500283i | ||||
\(638\) | 1445.24 | 0.0896829 | ||||||||
\(639\) | 12882.0 | − | 7437.44i | 0.797504 | − | 0.460439i | ||||
\(640\) | 1081.57 | + | 1873.33i | 0.0668011 | + | 0.115703i | ||||
\(641\) | 3967.18 | − | 6871.36i | 0.244453 | − | 0.423405i | −0.717525 | − | 0.696533i | \(-0.754725\pi\) |
0.961978 | + | 0.273128i | \(0.0880584\pi\) | |||||||
\(642\) | 2634.09i | 0.161930i | ||||||||
\(643\) | −4052.13 | − | 2339.50i | −0.248523 | − | 0.143485i | 0.370565 | − | 0.928807i | \(-0.379164\pi\) |
−0.619088 | + | 0.785322i | \(0.712497\pi\) | |||||||
\(644\) | 11801.1 | + | 6813.39i | 0.722097 | + | 0.416903i | ||||
\(645\) | 8449.05i | 0.515784i | ||||||||
\(646\) | 7175.34 | − | 12428.0i | 0.437012 | − | 0.756927i | ||||
\(647\) | 4876.24 | + | 8445.90i | 0.296298 | + | 0.513204i | 0.975286 | − | 0.220946i | \(-0.0709144\pi\) |
−0.678988 | + | 0.734150i | \(0.737581\pi\) | |||||||
\(648\) | −345.810 | + | 199.654i | −0.0209641 | + | 0.0121036i | ||||
\(649\) | −4572.65 | −0.276568 | ||||||||
\(650\) | 32869.9 | − | 28727.1i | 1.98348 | − | 1.73349i | ||||
\(651\) | 3770.47 | 0.226999 | ||||||||
\(652\) | −13533.7 | + | 7813.66i | −0.812913 | + | 0.469335i | ||||
\(653\) | −5794.63 | − | 10036.6i | −0.347261 | − | 0.601474i | 0.638501 | − | 0.769621i | \(-0.279555\pi\) |
−0.985762 | + | 0.168147i | \(0.946222\pi\) | |||||||
\(654\) | −3047.45 | + | 5278.33i | −0.182209 | + | 0.315595i | ||||
\(655\) | − | 7297.80i | − | 0.435341i | ||||||
\(656\) | −22113.2 | − | 12767.0i | −1.31612 | − | 0.759861i | ||||
\(657\) | 1313.37 | + | 758.274i | 0.0779899 | + | 0.0450275i | ||||
\(658\) | − | 244.920i | − | 0.0145106i | ||||||
\(659\) | 8801.73 | − | 15245.0i | 0.520284 | − | 0.901158i | −0.479438 | − | 0.877576i | \(-0.659160\pi\) |
0.999722 | − | 0.0235820i | \(-0.00750707\pi\) | |||||||
\(660\) | −1545.79 | − | 2677.38i | −0.0911663 | − | 0.157905i | ||||
\(661\) | 1808.75 | − | 1044.28i | 0.106433 | − | 0.0614491i | −0.445839 | − | 0.895113i | \(-0.647094\pi\) |
0.552272 | + | 0.833664i | \(0.313761\pi\) | |||||||
\(662\) | 3674.51 | 0.215731 | ||||||||
\(663\) | 9156.80 | − | 1805.17i | 0.536381 | − | 0.105742i | ||||
\(664\) | 770.616 | 0.0450387 | ||||||||
\(665\) | −13571.9 | + | 7835.73i | −0.791422 | + | 0.456927i | ||||
\(666\) | 11866.8 | + | 20554.0i | 0.690436 | + | 1.19587i | ||||
\(667\) | 1213.15 | − | 2101.23i | 0.0704246 | − | 0.121979i | ||||
\(668\) | − | 26396.8i | − | 1.52893i | ||||||
\(669\) | −9802.86 | − | 5659.69i | −0.566518 | − | 0.327079i | ||||
\(670\) | −11324.4 | − | 6538.15i | −0.652986 | − | 0.377001i | ||||
\(671\) | − | 4196.68i | − | 0.241447i | ||||||
\(672\) | −5784.89 | + | 10019.7i | −0.332079 | + | 0.575178i | ||||
\(673\) | −6537.71 | − | 11323.6i | −0.374458 | − | 0.648580i | 0.615788 | − | 0.787912i | \(-0.288838\pi\) |
−0.990246 | + | 0.139332i | \(0.955505\pi\) | |||||||
\(674\) | −10385.7 | + | 5996.20i | −0.593535 | + | 0.342678i | ||||
\(675\) | 22514.9 | 1.28385 | ||||||||
\(676\) | 2287.53 | − | 16928.9i | 0.130151 | − | 0.963184i | ||||
\(677\) | 27932.0 | 1.58570 | 0.792848 | − | 0.609420i | \(-0.208598\pi\) | ||||
0.792848 | + | 0.609420i | \(0.208598\pi\) | |||||||
\(678\) | 9509.61 | − | 5490.38i | 0.538664 | − | 0.310998i | ||||
\(679\) | −8337.78 | − | 14441.5i | −0.471244 | − | 0.816218i | ||||
\(680\) | −882.887 | + | 1529.20i | −0.0497899 | + | 0.0862387i | ||||
\(681\) | 12184.7i | 0.685636i | ||||||||
\(682\) | −3131.95 | − | 1808.23i | −0.175848 | − | 0.101526i | ||||
\(683\) | 10882.5 | + | 6283.02i | 0.609674 | + | 0.351996i | 0.772838 | − | 0.634603i | \(-0.218836\pi\) |
−0.163164 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(684\) | − | 6284.85i | − | 0.351326i | ||||||
\(685\) | −3209.90 | + | 5559.72i | −0.179043 | + | 0.310111i | ||||
\(686\) | 5461.76 | + | 9460.04i | 0.303981 | + | 0.526510i | ||||
\(687\) | 5148.23 | − | 2972.33i | 0.285906 | − | 0.165068i | ||||
\(688\) | −15367.9 | −0.851594 | ||||||||
\(689\) | 3445.44 | − | 679.232i | 0.190509 | − | 0.0375568i | ||||
\(690\) | −10530.2 | −0.580983 | ||||||||
\(691\) | 20021.6 | − | 11559.5i | 1.10225 | − | 0.636386i | 0.165441 | − | 0.986220i | \(-0.447095\pi\) |
0.936812 | + | 0.349834i | \(0.113762\pi\) | |||||||
\(692\) | 10589.8 | + | 18342.1i | 0.581739 | + | 1.00760i | ||||
\(693\) | 3070.56 | − | 5318.37i | 0.168313 | − | 0.291527i | ||||
\(694\) | 7370.33i | 0.403133i | ||||||||
\(695\) | −36159.3 | − | 20876.6i | −1.97353 | − | 1.13942i | ||||
\(696\) | 48.6976 | + | 28.1156i | 0.00265213 | + | 0.00153121i | ||||
\(697\) | − | 40564.3i | − | 2.20442i | ||||||
\(698\) | −5106.28 | + | 8844.34i | −0.276899 | + | 0.479603i | ||||
\(699\) | −4216.00 | − | 7302.33i | −0.228131 | − | 0.395135i | ||||
\(700\) | −37727.3 | + | 21781.9i | −2.03708 | + | 1.17611i | ||||
\(701\) | 933.303 | 0.0502858 | 0.0251429 | − | 0.999684i | \(-0.491996\pi\) | ||||
0.0251429 | + | 0.999684i | \(0.491996\pi\) | |||||||
\(702\) | 13459.6 | − | 11763.2i | 0.723647 | − | 0.632440i | ||||
\(703\) | 8846.81 | 0.474628 | ||||||||
\(704\) | 4599.98 | − | 2655.80i | 0.246262 | − | 0.142179i | ||||
\(705\) | 46.6426 | + | 80.7874i | 0.00249172 | + | 0.00431578i | ||||
\(706\) | −12281.6 | + | 21272.3i | −0.654707 | + | 1.13399i | ||||
\(707\) | 34024.4i | 1.80993i | ||||||||
\(708\) | 5336.45 | + | 3081.00i | 0.283271 | + | 0.163547i | ||||
\(709\) | 746.116 | + | 430.770i | 0.0395218 | + | 0.0228179i | 0.519631 | − | 0.854391i | \(-0.326070\pi\) |
−0.480109 | + | 0.877209i | \(0.659403\pi\) | |||||||
\(710\) | − | 47941.3i | − | 2.53409i | ||||||
\(711\) | −15579.1 | + | 26983.8i | −0.821747 | + | 1.42331i | ||||
\(712\) | −517.197 | − | 895.811i | −0.0272230 | − | 0.0471516i | ||||
\(713\) | −5257.95 | + | 3035.68i | −0.276174 | + | 0.159449i | ||||
\(714\) | −18896.4 | −0.990446 | ||||||||
\(715\) | 6433.04 | + | 7360.77i | 0.336478 | + | 0.385003i | ||||
\(716\) | −9575.71 | −0.499806 | ||||||||
\(717\) | −10510.3 | + | 6068.13i | −0.547440 | + | 0.316065i | ||||
\(718\) | 19349.8 | + | 33514.8i | 1.00575 | + | 1.74201i | ||||
\(719\) | 3375.71 | − | 5846.90i | 0.175094 | − | 0.303272i | −0.765100 | − | 0.643912i | \(-0.777310\pi\) |
0.940194 | + | 0.340640i | \(0.110644\pi\) | |||||||
\(720\) | 29126.2i | 1.50760i | ||||||||
\(721\) | 34540.8 | + | 19942.1i | 1.78414 | + | 1.03008i | ||||
\(722\) | 19476.7 | + | 11244.9i | 1.00395 | + | 0.579629i | ||||
\(723\) | − | 10328.3i | − | 0.531275i | ||||||
\(724\) | −17376.5 | + | 30097.0i | −0.891978 | + | 1.54495i | ||||
\(725\) | 3878.33 | + | 6717.46i | 0.198672 | + | 0.344111i | ||||
\(726\) | 793.460 | − | 458.105i | 0.0405621 | − | 0.0234185i | ||||
\(727\) | −28103.8 | −1.43372 | −0.716858 | − | 0.697219i | \(-0.754421\pi\) | ||||
−0.716858 | + | 0.697219i | \(0.754421\pi\) | |||||||
\(728\) | 322.606 | − | 945.066i | 0.0164239 | − | 0.0481133i | ||||
\(729\) | −5521.25 | −0.280509 | ||||||||
\(730\) | 4232.95 | − | 2443.89i | 0.214614 | − | 0.123908i | ||||
\(731\) | −12207.0 | − | 21143.2i | −0.617637 | − | 1.06978i | ||||
\(732\) | −2827.68 | + | 4897.68i | −0.142779 | + | 0.247300i | ||||
\(733\) | − | 12646.8i | − | 0.637269i | −0.947878 | − | 0.318635i | \(-0.896776\pi\) | ||
0.947878 | − | 0.318635i | \(-0.103224\pi\) | |||||||
\(734\) | −10032.9 | − | 5792.52i | −0.504527 | − | 0.291289i | ||||
\(735\) | 7133.87 | + | 4118.74i | 0.358009 | + | 0.206697i | ||||
\(736\) | − | 18630.1i | − | 0.933038i | ||||||
\(737\) | 955.025 | − | 1654.15i | 0.0477324 | − | 0.0826750i | ||||
\(738\) | −18021.5 | − | 31214.2i | −0.898891 | − | 1.55693i | ||||
\(739\) | 14422.2 | − | 8326.64i | 0.717899 | − | 0.414479i | −0.0960796 | − | 0.995374i | \(-0.530630\pi\) |
0.813979 | + | 0.580894i | \(0.197297\pi\) | |||||||
\(740\) | 37702.2 | 1.87292 | ||||||||
\(741\) | −597.883 | − | 3032.80i | −0.0296407 | − | 0.150354i | ||||
\(742\) | −7110.16 | −0.351782 | ||||||||
\(743\) | 4457.06 | − | 2573.29i | 0.220072 | − | 0.127059i | −0.385911 | − | 0.922536i | \(-0.626113\pi\) |
0.605984 | + | 0.795477i | \(0.292780\pi\) | |||||||
\(744\) | −70.3542 | − | 121.857i | −0.00346682 | − | 0.00600470i | ||||
\(745\) | 14906.1 | − | 25818.2i | 0.733045 | − | 1.26967i | ||||
\(746\) | 11243.9i | 0.551834i | ||||||||
\(747\) | 17488.1 | + | 10096.8i | 0.856567 | + | 0.494539i | ||||
\(748\) | 7736.46 | + | 4466.65i | 0.378172 | + | 0.218338i | ||||
\(749\) | 8311.88i | 0.405486i | ||||||||
\(750\) | 7859.26 | − | 13612.6i | 0.382639 | − | 0.662751i | ||||
\(751\) | 11255.2 | + | 19494.5i | 0.546880 | + | 0.947225i | 0.998486 | + | 0.0550070i | \(0.0175181\pi\) |
−0.451606 | + | 0.892218i | \(0.649149\pi\) | |||||||
\(752\) | −146.944 | + | 84.8380i | −0.00712565 | + | 0.00411399i | ||||
\(753\) | −4786.40 | −0.231642 | ||||||||
\(754\) | 5828.12 | + | 1989.48i | 0.281496 | + | 0.0960909i | ||||
\(755\) | −31711.1 | −1.52859 | ||||||||
\(756\) | −15448.6 | + | 8919.25i | −0.743201 | + | 0.429087i | ||||
\(757\) | −9717.88 | − | 16831.9i | −0.466582 | − | 0.808143i | 0.532690 | − | 0.846311i | \(-0.321181\pi\) |
−0.999271 | + | 0.0381676i | \(0.987848\pi\) | |||||||
\(758\) | −2700.56 | + | 4677.51i | −0.129405 | + | 0.224135i | ||||
\(759\) | − | 1538.14i | − | 0.0735588i | ||||||
\(760\) | 506.483 | + | 292.418i | 0.0241738 | + | 0.0139567i | ||||
\(761\) | −19246.8 | − | 11112.1i | −0.916815 | − | 0.529323i | −0.0341971 | − | 0.999415i | \(-0.510887\pi\) |
−0.882617 | + | 0.470092i | \(0.844221\pi\) | |||||||
\(762\) | − | 13949.8i | − | 0.663187i | ||||||
\(763\) | −9616.24 | + | 16655.8i | −0.456266 | + | 0.790276i | ||||
\(764\) | 7732.44 | + | 13393.0i | 0.366165 | + | 0.634216i | ||||
\(765\) | −40071.8 | + | 23135.5i | −1.89386 | + | 1.09342i | ||||
\(766\) | 775.786 | 0.0365931 | ||||||||
\(767\) | −18439.8 | − | 6294.58i | −0.868087 | − | 0.296329i | ||||
\(768\) | 8228.32 | 0.386607 | ||||||||
\(769\) | −13389.5 | + | 7730.45i | −0.627879 | + | 0.362506i | −0.779930 | − | 0.625866i | \(-0.784746\pi\) |
0.152051 | + | 0.988373i | \(0.451412\pi\) | |||||||
\(770\) | −9896.32 | − | 17140.9i | −0.463167 | − | 0.802229i | ||||
\(771\) | 3860.44 | − | 6686.47i | 0.180325 | − | 0.312331i | ||||
\(772\) | − | 40173.5i | − | 1.87289i | ||||||
\(773\) | −30037.6 | − | 17342.2i | −1.39764 | − | 0.806929i | −0.403497 | − | 0.914981i | \(-0.632205\pi\) |
−0.994145 | + | 0.108052i | \(0.965539\pi\) | |||||||
\(774\) | −18786.6 | − | 10846.4i | −0.872441 | − | 0.503704i | ||||
\(775\) | − | 19409.6i | − | 0.899632i | ||||||
\(776\) | −311.154 | + | 538.934i | −0.0143940 | + | 0.0249312i | ||||
\(777\) | −5824.55 | − | 10088.4i | −0.268925 | − | 0.465792i | ||||
\(778\) | −216.251 | + | 124.853i | −0.00996528 | + | 0.00575346i | ||||
\(779\) | −13435.2 | −0.617927 | ||||||||
\(780\) | −2547.98 | − | 12924.8i | −0.116965 | − | 0.593309i | ||||
\(781\) | 7002.77 | 0.320843 | ||||||||
\(782\) | 26351.1 | − | 15213.8i | 1.20501 | − | 0.695711i | ||||
\(783\) | 1588.10 | + | 2750.67i | 0.0724829 | + | 0.125544i | ||||
\(784\) | −7491.56 | + | 12975.8i | −0.341270 | + | 0.591097i | ||||
\(785\) | 64732.8i | 2.94320i | ||||||||
\(786\) | −2524.00 | − | 1457.23i | −0.114540 | − | 0.0661296i | ||||
\(787\) | −9250.75 | − | 5340.92i | −0.419001 | − | 0.241910i | 0.275649 | − | 0.961258i | \(-0.411107\pi\) |
−0.694650 | + | 0.719348i | \(0.744441\pi\) | |||||||
\(788\) | − | 15428.8i | − | 0.697497i | ||||||
\(789\) | 1171.11 | − | 2028.42i | 0.0528422 | − | 0.0915254i | ||||
\(790\) | 50211.0 | + | 86968.0i | 2.26130 | + | 3.91669i | ||||
\(791\) | 30007.6 | − | 17324.9i | 1.34886 | − | 0.778765i | ||||
\(792\) | −229.178 | −0.0102822 | ||||||||
\(793\) | 5777.03 | − | 16923.7i | 0.258699 | − | 0.757852i | ||||
\(794\) | −32243.4 | −1.44115 | ||||||||
\(795\) | 2345.30 | − | 1354.06i | 0.104628 | − | 0.0604070i | ||||
\(796\) | −1846.34 | − | 3197.96i | −0.0822134 | − | 0.142398i | ||||
\(797\) | 14382.0 | − | 24910.3i | 0.639191 | − | 1.10711i | −0.346420 | − | 0.938080i | \(-0.612603\pi\) |
0.985611 | − | 0.169032i | \(-0.0540640\pi\) | |||||||
\(798\) | 6258.61i | 0.277634i | ||||||||
\(799\) | −233.440 | − | 134.777i | −0.0103361 | − | 0.00596752i | ||||
\(800\) | 51579.6 | + | 29779.5i | 2.27952 | + | 1.31608i | ||||
\(801\) | − | 27105.6i | − | 1.19567i | ||||||
\(802\) | −1020.40 | + | 1767.39i | −0.0449274 | + | 0.0778165i | ||||
\(803\) | 356.979 | + | 618.305i | 0.0156880 | + | 0.0271725i | ||||
\(804\) | −2229.10 | + | 1286.97i | −0.0977788 | + | 0.0564526i | ||||
\(805\) | −33228.2 | −1.45483 | ||||||||
\(806\) | −10140.8 | − | 11603.3i | −0.443170 | − | 0.507081i | ||||
\(807\) | −6598.37 | −0.287823 | ||||||||
\(808\) | 1099.63 | − | 634.871i | 0.0478772 | − | 0.0276419i | ||||
\(809\) | −18646.4 | − | 32296.6i | −0.810350 | − | 1.40357i | −0.912619 | − | 0.408811i | \(-0.865943\pi\) |
0.102269 | − | 0.994757i | \(-0.467390\pi\) | |||||||
\(810\) | −16861.9 | + | 29205.7i | −0.731442 | + | 1.26689i | ||||
\(811\) | − | 12322.2i | − | 0.533526i | −0.963762 | − | 0.266763i | \(-0.914046\pi\) | ||
0.963762 | − | 0.266763i | \(-0.0859542\pi\) | |||||||
\(812\) | −5322.23 | − | 3072.79i | −0.230017 | − | 0.132800i | ||||
\(813\) | −3232.95 | − | 1866.55i | −0.139464 | − | 0.0805198i | ||||
\(814\) | 11173.3i | 0.481110i | ||||||||
\(815\) | 19053.2 | − | 33001.1i | 0.818900 | − | 1.41838i | ||||
\(816\) | 6545.53 | + | 11337.2i | 0.280808 | + | 0.486374i | ||||
\(817\) | −7002.76 | + | 4043.05i | −0.299872 | + | 0.173131i | ||||
\(818\) | 15078.7 | 0.644518 | ||||||||
\(819\) | 19703.5 | − | 17220.1i | 0.840655 | − | 0.734701i | ||||
\(820\) | −57256.3 | −2.43839 | ||||||||
\(821\) | 27271.2 | − | 15745.0i | 1.15928 | − | 0.669313i | 0.208152 | − | 0.978097i | \(-0.433255\pi\) |
0.951132 | + | 0.308784i | \(0.0999219\pi\) | |||||||
\(822\) | 1281.92 | + | 2220.35i | 0.0543941 | + | 0.0942134i | ||||
\(823\) | −9045.82 | + | 15667.8i | −0.383132 | + | 0.663604i | −0.991508 | − | 0.130045i | \(-0.958488\pi\) |
0.608376 | + | 0.793649i | \(0.291821\pi\) | |||||||
\(824\) | − | 1488.42i | − | 0.0629268i | ||||||
\(825\) | 4258.52 | + | 2458.66i | 0.179712 | + | 0.103757i | ||||
\(826\) | 34164.6 | + | 19724.9i | 1.43915 | + | 0.830894i | ||||
\(827\) | 5898.04i | 0.247999i | 0.992282 | + | 0.123999i | \(0.0395721\pi\) | ||||
−0.992282 | + | 0.123999i | \(0.960428\pi\) | |||||||
\(828\) | 6662.88 | − | 11540.4i | 0.279651 | − | 0.484370i | ||||
\(829\) | −15131.0 | − | 26207.6i | −0.633921 | − | 1.09798i | −0.986743 | − | 0.162293i | \(-0.948111\pi\) |
0.352822 | − | 0.935691i | \(-0.385222\pi\) | |||||||
\(830\) | 56363.6 | − | 32541.5i | 2.35712 | − | 1.36088i | ||||
\(831\) | −605.425 | −0.0252731 | ||||||||
\(832\) | 22205.9 | − | 4377.65i | 0.925301 | − | 0.182413i | ||||
\(833\) | −23802.7 | −0.990054 | ||||||||
\(834\) | −14440.7 | + | 8337.34i | −0.599569 | + | 0.346161i | ||||
\(835\) | 32183.6 | + | 55743.5i | 1.33384 | + | 2.31028i | ||||
\(836\) | 1479.38 | − | 2562.37i | 0.0612029 | − | 0.106006i | ||||
\(837\) | − | 7947.87i | − | 0.328218i | ||||||
\(838\) | 46649.5 | + | 26933.1i | 1.92301 | + | 1.11025i | ||||
\(839\) | −5885.51 | − | 3398.00i | −0.242182 | − | 0.139824i | 0.373997 | − | 0.927430i | \(-0.377987\pi\) |
−0.616179 | + | 0.787606i | \(0.711320\pi\) | |||||||
\(840\) | − | 770.088i | − | 0.0316316i | ||||||
\(841\) | 11647.4 | − | 20173.9i | 0.477567 | − | 0.827170i | ||||
\(842\) | 18473.2 | + | 31996.5i | 0.756090 | + | 1.30959i | ||||
\(843\) | −7501.43 | + | 4330.96i | −0.306481 | + | 0.176947i | ||||
\(844\) | −5564.87 | −0.226956 | ||||||||
\(845\) | 15809.4 | + | 38538.8i | 0.643622 | + | 1.56896i | ||||
\(846\) | −239.509 | −0.00973344 | ||||||||
\(847\) | 2503.77 | − | 1445.55i | 0.101571 | − | 0.0586420i | ||||
\(848\) | 2462.89 | + | 4265.86i | 0.0997360 | + | 0.172748i | ||||
\(849\) | −3527.12 | + | 6109.15i | −0.142580 | + | 0.246956i | ||||
\(850\) | 97274.8i | 3.92529i | ||||||||
\(851\) | 16244.8 | + | 9378.93i | 0.654364 | + | 0.377797i | ||||
\(852\) | −8172.48 | − | 4718.38i | −0.328620 | − | 0.189729i | ||||
\(853\) | − | 35573.6i | − | 1.42792i | −0.700187 | − | 0.713960i | \(-0.746900\pi\) | ||
0.700187 | − | 0.713960i | \(-0.253100\pi\) | |||||||
\(854\) | −18103.1 | + | 31355.5i | −0.725382 | + | 1.25640i | ||||
\(855\) | 7662.63 | + | 13272.1i | 0.306499 | + | 0.530872i | ||||
\(856\) | 268.630 | − | 155.094i | 0.0107261 | − | 0.00619274i | ||||
\(857\) | 8396.49 | 0.334677 | 0.167339 | − | 0.985899i | \(-0.446483\pi\) | ||||
0.167339 | + | 0.985899i | \(0.446483\pi\) | |||||||
\(858\) | 3830.34 | − | 755.111i | 0.152408 | − | 0.0300455i | ||||
\(859\) | −11034.7 | −0.438297 | −0.219149 | − | 0.975691i | \(-0.570328\pi\) | ||||
−0.219149 | + | 0.975691i | \(0.570328\pi\) | |||||||
\(860\) | −29843.5 | + | 17230.1i | −1.18332 | + | 0.683189i | ||||
\(861\) | 8845.44 | + | 15320.8i | 0.350118 | + | 0.606423i | ||||
\(862\) | −2446.66 | + | 4237.74i | −0.0966746 | + | 0.167445i | ||||
\(863\) | 33691.1i | 1.32892i | 0.747324 | + | 0.664460i | \(0.231338\pi\) | ||||
−0.747324 | + | 0.664460i | \(0.768662\pi\) | |||||||
\(864\) | 21120.9 | + | 12194.1i | 0.831651 | + | 0.480154i | ||||
\(865\) | −44726.1 | − | 25822.6i | −1.75807 | − | 1.01502i | ||||
\(866\) | 59145.9i | 2.32085i | ||||||||
\(867\) | −5715.34 | + | 9899.26i | −0.223879 | + | 0.387770i | ||||
\(868\) | 7689.11 | + | 13317.9i | 0.300674 | + | 0.520783i | ||||
\(869\) | −12703.4 | + | 7334.30i | −0.495895 | + | 0.286305i | ||||
\(870\) | 4749.05 | 0.185067 | ||||||||
\(871\) | 6128.32 | − | 5355.92i | 0.238404 | − | 0.208356i | ||||
\(872\) | 717.728 | 0.0278731 | ||||||||
\(873\) | −14122.4 | + | 8153.59i | −0.547505 | + | 0.316102i | ||||
\(874\) | −5038.93 | − | 8727.68i | −0.195016 | − | 0.337778i | ||||
\(875\) | 24799.9 | − | 42954.8i | 0.958161 | − | 1.65958i | ||||
\(876\) | − | 962.112i | − | 0.0371082i | ||||||
\(877\) | 23591.6 | + | 13620.6i | 0.908358 | + | 0.524441i | 0.879903 | − | 0.475154i | \(-0.157608\pi\) |
0.0284558 | + | 0.999595i | \(0.490941\pi\) | |||||||
\(878\) | −50175.1 | − | 28968.6i | −1.92862 | − | 1.11349i | ||||
\(879\) | 1261.45i | 0.0484045i | ||||||||
\(880\) | −6856.00 | + | 11874.9i | −0.262631 | + | 0.454891i | ||||
\(881\) | −9116.15 | − | 15789.6i | −0.348616 | − | 0.603821i | 0.637388 | − | 0.770543i | \(-0.280015\pi\) |
−0.986004 | + | 0.166722i | \(0.946682\pi\) | |||||||
\(882\) | −18316.2 | + | 10574.8i | −0.699248 | + | 0.403711i | ||||
\(883\) | −17899.6 | −0.682184 | −0.341092 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341092 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(884\) | 25049.6 | + | 28662.1i | 0.953065 | + | 1.09051i | ||||
\(885\) | −15025.7 | −0.570716 | ||||||||
\(886\) | 9876.49 | − | 5702.20i | 0.374500 | − | 0.216218i | ||||
\(887\) | 14300.5 | + | 24769.2i | 0.541334 | + | 0.937618i | 0.998828 | + | 0.0484051i | \(0.0154138\pi\) |
−0.457494 | + | 0.889213i | \(0.651253\pi\) | |||||||
\(888\) | −217.364 | + | 376.485i | −0.00821425 | + | 0.0142275i | ||||
\(889\) | − | 44018.8i | − | 1.66068i | ||||||
\(890\) | −75656.5 | − | 43680.3i | −2.84945 | − | 1.64513i | ||||
\(891\) | −4266.07 | − | 2463.01i | −0.160402 | − | 0.0926084i | ||||
\(892\) | − | 46167.2i | − | 1.73295i | ||||||
\(893\) | −44.6389 | + | 77.3169i | −0.00167277 | + | 0.00289733i | ||||
\(894\) | −5952.96 | − | 10310.8i | −0.222703 | − | 0.385734i | ||||
\(895\) | 20221.6 | − | 11674.9i | 0.755232 | − | 0.436033i | ||||
\(896\) | 2725.97 | 0.101639 | ||||||||
\(897\) | 2117.36 | − | 6202.76i | 0.0788146 | − | 0.230885i | ||||
\(898\) | 6569.21 | 0.244117 | ||||||||
\(899\) | 2371.30 | − | 1369.07i | 0.0879725 | − | 0.0507910i | ||||
\(900\) | 21300.7 | + | 36893.8i | 0.788913 | + | 1.36644i | ||||
\(901\) | −3912.64 | + | 6776.89i | −0.144671 | + | 0.250578i | ||||
\(902\) | − | 16968.3i | − | 0.626366i | ||||||
\(903\) | 9220.94 | + | 5323.71i | 0.339816 | + | 0.196193i | ||||
\(904\) | −1119.84 | − | 646.541i | −0.0412006 | − | 0.0237872i | ||||
\(905\) | − | 84743.2i | − | 3.11266i | ||||||
\(906\) | −6332.12 | + | 10967.5i | −0.232197 | + | 0.402177i | ||||
\(907\) | 8705.33 | + | 15078.1i | 0.318694 | + | 0.551995i | 0.980216 | − | 0.197931i | \(-0.0634223\pi\) |
−0.661522 | + | 0.749926i | \(0.730089\pi\) | |||||||
\(908\) | −43038.4 | + | 24848.2i | −1.57299 | + | 0.908168i | ||||
\(909\) | 33272.7 | 1.21407 | ||||||||
\(910\) | −16312.5 | − | 82746.0i | −0.594235 | − | 3.01429i | ||||
\(911\) | −3462.76 | −0.125934 | −0.0629672 | − | 0.998016i | \(-0.520056\pi\) | ||||
−0.0629672 | + | 0.998016i | \(0.520056\pi\) | |||||||
\(912\) | 3754.96 | − | 2167.92i | 0.136337 | − | 0.0787140i | ||||
\(913\) | 4753.33 | + | 8233.01i | 0.172303 | + | 0.298437i | ||||
\(914\) | 24259.2 | − | 42018.2i | 0.877924 | − | 1.52061i | ||||
\(915\) | − | 13790.3i | − | 0.498243i | ||||||
\(916\) | 20997.6 | + | 12122.9i | 0.757401 | + | 0.437285i | ||||
\(917\) | −7964.51 | − | 4598.31i | −0.286817 | − | 0.165594i | ||||
\(918\) | 39832.1i | 1.43209i | ||||||||
\(919\) | −18188.4 | + | 31503.1i | −0.652860 | + | 1.13079i | 0.329566 | + | 0.944133i | \(0.393098\pi\) |
−0.982426 | + | 0.186654i | \(0.940236\pi\) | |||||||
\(920\) | 620.014 | + | 1073.89i | 0.0222187 | + | 0.0384840i | ||||
\(921\) | 13001.7 | − | 7506.55i | 0.465170 | − | 0.268566i | ||||
\(922\) | −62447.0 | −2.23057 | ||||||||
\(923\) | 28239.5 | + | 9639.80i | 1.00706 | + | 0.343768i | ||||
\(924\) | −3895.98 | −0.138710 | ||||||||
\(925\) | −51933.2 | + | 29983.7i | −1.84600 | + | 1.06579i | ||||
\(926\) | −22018.9 | − | 38137.8i | −0.781409 | − | 1.35344i | ||||
\(927\) | 19501.6 | − | 33777.8i | 0.690956 | − | 1.19677i | ||||
\(928\) | 8402.06i | 0.297210i | ||||||||
\(929\) | 30410.5 | + | 17557.5i | 1.07399 | + | 0.620069i | 0.929269 | − | 0.369403i | \(-0.120438\pi\) |
0.144722 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(930\) | −10291.5 | − | 5941.83i | −0.362874 | − | 0.209506i | ||||
\(931\) | 7883.62i | 0.277524i | ||||||||
\(932\) | 17195.4 | − | 29783.3i | 0.604349 | − | 1.04676i | ||||
\(933\) | 10119.4 | + | 17527.3i | 0.355085 | + | 0.615025i | ||||
\(934\) | 20293.3 | − | 11716.3i | 0.710938 | − | 0.410460i | ||||
\(935\) | −21783.3 | −0.761916 | ||||||||
\(936\) | −924.188 | − | 315.479i | −0.0322735 | − | 0.0110168i | ||||
\(937\) | −32377.3 | −1.12884 | −0.564418 | − | 0.825489i | \(-0.690900\pi\) | ||||
−0.564418 | + | 0.825489i | \(0.690900\pi\) | |||||||
\(938\) | −14270.9 | + | 8239.33i | −0.496762 | + | 0.286806i | ||||
\(939\) | −984.021 | − | 1704.37i | −0.0341984 | − | 0.0592334i | ||||
\(940\) | −190.236 | + | 329.499i | −0.00660088 | + | 0.0114331i | ||||
\(941\) | − | 32628.7i | − | 1.13036i | −0.824969 | − | 0.565178i | \(-0.808807\pi\) | ||
0.824969 | − | 0.565178i | \(-0.191193\pi\) | |||||||
\(942\) | 22388.4 | + | 12926.0i | 0.774367 | + | 0.447081i | ||||
\(943\) | −24670.1 | − | 14243.3i | −0.851929 | − | 0.491861i | ||||
\(944\) | − | 27330.2i | − | 0.942289i | ||||||
\(945\) | 21749.1 | − | 37670.5i | 0.748675 | − | 1.29674i | ||||
\(946\) | −5106.26 | − | 8844.31i | −0.175496 | − | 0.303967i | ||||
\(947\) | −26531.1 | + | 15317.7i | −0.910394 | + | 0.525616i | −0.880558 | − | 0.473938i | \(-0.842832\pi\) |
−0.0298362 | + | 0.999555i | \(0.509499\pi\) | |||||||
\(948\) | 19767.1 | 0.677220 | ||||||||
\(949\) | 588.421 | + | 2984.80i | 0.0201275 | + | 0.102098i | ||||
\(950\) | 32218.1 | 1.10031 | ||||||||
\(951\) | −6507.70 | + | 3757.22i | −0.221900 | + | 0.128114i | ||||
\(952\) | 1112.61 | + | 1927.09i | 0.0378780 | + | 0.0656065i | ||||
\(953\) | −4201.38 | + | 7277.00i | −0.142808 | + | 0.247351i | −0.928553 | − | 0.371200i | \(-0.878946\pi\) |
0.785745 | + | 0.618551i | \(0.212280\pi\) | |||||||
\(954\) | 6953.08i | 0.235969i | ||||||||
\(955\) | −32658.0 | − | 18855.1i | −1.10659 | − | 0.638887i | ||||
\(956\) | −42867.3 | − | 24749.4i | −1.45024 | − | 0.837295i | ||||
\(957\) | 693.692i | 0.0234314i | ||||||||
\(958\) | −15450.8 | + | 26761.5i | −0.521077 | + | 0.902532i | ||||
\(959\) | 4045.10 | + | 7006.31i | 0.136208 | + | 0.235918i | ||||
\(960\) | 15115.5 | − | 8726.93i | 0.508177 | − | 0.293396i | ||||
\(961\) | 22939.3 | 0.770008 | ||||||||
\(962\) | −15380.8 | + | 45057.7i | −0.515486 | + | 1.51010i | ||||
\(963\) | 8128.25 | 0.271993 | ||||||||
\(964\) | 36481.1 | − | 21062.4i | 1.21886 | − | 0.703708i | ||||
\(965\) | 48980.4 | + | 84836.5i | 1.63392 | + | 2.83003i | ||||
\(966\) | −6635.05 | + | 11492.2i | −0.220993 | + | 0.382771i | ||||
\(967\) | − | 33517.8i | − | 1.11464i | −0.830296 | − | 0.557322i | \(-0.811829\pi\) | ||
0.830296 | − | 0.557322i | \(-0.188171\pi\) | |||||||
\(968\) | −93.4370 | − | 53.9459i | −0.00310246 | − | 0.00179121i | ||||
\(969\) | 5965.25 | + | 3444.04i | 0.197762 | + | 0.114178i | ||||
\(970\) | 52557.5i | 1.73971i | ||||||||
\(971\) | −17855.2 | + | 30926.1i | −0.590114 | + | 1.02211i | 0.404102 | + | 0.914714i | \(0.367584\pi\) |
−0.994217 | + | 0.107394i | \(0.965749\pi\) | |||||||
\(972\) | 13398.0 | + | 23206.0i | 0.442121 | + | 0.765776i | ||||
\(973\) | −45567.7 | + | 26308.5i | −1.50137 | + | 0.866817i | ||||
\(974\) | −68171.7 | −2.24267 | ||||||||
\(975\) | 13788.5 | + | 15777.0i | 0.452909 | + | 0.518224i | ||||
\(976\) | 25083.0 | 0.822632 | ||||||||
\(977\) | 20410.8 | − | 11784.2i | 0.668373 | − | 0.385885i | −0.127087 | − | 0.991892i | \(-0.540563\pi\) |
0.795460 | + | 0.606006i | \(0.207229\pi\) | |||||||
\(978\) | −7609.14 | − | 13179.4i | −0.248787 | − | 0.430911i | ||||
\(979\) | 6380.37 | − | 11051.1i | 0.208291 | − | 0.360771i | ||||
\(980\) | 33597.4i | 1.09513i | ||||||||
\(981\) | 16287.9 | + | 9403.80i | 0.530103 | + | 0.306055i | ||||
\(982\) | −134.113 | − | 77.4300i | −0.00435816 | − | 0.00251618i | ||||
\(983\) | 17698.8i | 0.574268i | 0.957890 | + | 0.287134i | \(0.0927025\pi\) | ||||
−0.957890 | + | 0.287134i | \(0.907298\pi\) | |||||||
\(984\) | 330.099 | − | 571.748i | 0.0106943 | − | 0.0185230i | ||||
\(985\) | 18811.1 | + | 32581.8i | 0.608500 | + | 1.05395i | ||||
\(986\) | −11884.2 | + | 6861.34i | −0.383843 | + | 0.221612i | ||||
\(987\) | 117.557 | 0.00379118 | ||||||||
\(988\) | 9493.09 | − | 8296.60i | 0.305684 | − | 0.267156i | ||||
\(989\) | −17144.9 | −0.551240 | ||||||||
\(990\) | −16762.3 | + | 9677.70i | −0.538121 | + | 0.310684i | ||||
\(991\) | −6761.26 | − | 11710.8i | −0.216729 | − | 0.375386i | 0.737077 | − | 0.675809i | \(-0.236205\pi\) |
−0.953806 | + | 0.300423i | \(0.902872\pi\) | |||||||
\(992\) | 10512.3 | − | 18207.9i | 0.336458 | − | 0.582763i | ||||
\(993\) | 1763.70i | 0.0563640i | ||||||||
\(994\) | −52321.2 | − | 30207.6i | −1.66954 | − | 0.963912i | ||||
\(995\) | 7798.05 | + | 4502.21i | 0.248457 | + | 0.143447i | ||||
\(996\) | − | 12810.9i | − | 0.407561i | ||||||
\(997\) | −9376.26 | + | 16240.2i | −0.297843 | + | 0.515879i | −0.975642 | − | 0.219368i | \(-0.929600\pi\) |
0.677800 | + | 0.735247i | \(0.262934\pi\) | |||||||
\(998\) | −31961.0 | − | 55358.0i | −1.01373 | − | 1.75584i | ||||
\(999\) | −21265.7 | + | 12277.7i | −0.673489 | + | 0.388839i |
(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 | 143.4.j.a.23.7 | ✓ | 72 | |
13.2 | odd | 12 | 1859.4.a.l.1.7 | 36 | |||
13.4 | even | 6 | inner | 143.4.j.a.56.7 | yes | 72 | |
13.11 | odd | 12 | 1859.4.a.m.1.30 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.j.a.23.7 | ✓ | 72 | 1.1 | even | 1 | trivial | |
143.4.j.a.56.7 | yes | 72 | 13.4 | even | 6 | inner | |
1859.4.a.l.1.7 | 36 | 13.2 | odd | 12 | |||
1859.4.a.m.1.30 | 36 | 13.11 | odd | 12 |