Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), not 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.2 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.146 |
Dual form | 169.4.c.g.22.2 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.780776 | + | 1.35234i | 0.276046 | + | 0.478126i | 0.970399 | − | 0.241509i | \(-0.0776424\pi\) |
−0.694352 | + | 0.719635i | \(0.744309\pi\) | |||||||
\(3\) | −4.34233 | − | 7.52113i | −0.835682 | − | 1.44744i | −0.893474 | − | 0.449114i | \(-0.851740\pi\) |
0.0577926 | − | 0.998329i | \(-0.481594\pi\) | |||||||
\(4\) | 2.78078 | − | 4.81645i | 0.347597 | − | 0.602056i | ||||
\(5\) | −3.56155 | −0.318555 | −0.159277 | − | 0.987234i | \(-0.550916\pi\) | ||||
−0.159277 | + | 0.987234i | \(0.550916\pi\) | |||||||
\(6\) | 6.78078 | − | 11.7446i | 0.461373 | − | 0.799122i | ||||
\(7\) | 13.5885 | − | 23.5360i | 0.733712 | − | 1.27083i | −0.221574 | − | 0.975144i | \(-0.571119\pi\) |
0.955286 | − | 0.295683i | \(-0.0955473\pi\) | |||||||
\(8\) | 21.1771 | 0.935904 | ||||||||
\(9\) | −24.2116 | + | 41.9358i | −0.896728 | + | 1.55318i | ||||
\(10\) | −2.78078 | − | 4.81645i | −0.0879359 | − | 0.152309i | ||||
\(11\) | −7.63068 | − | 13.2167i | −0.209158 | − | 0.362272i | 0.742292 | − | 0.670077i | \(-0.233739\pi\) |
−0.951450 | + | 0.307805i | \(0.900406\pi\) | |||||||
\(12\) | −48.3002 | −1.16192 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 42.4384 | 0.810154 | ||||||||
\(15\) | 15.4654 | + | 26.7869i | 0.266211 | + | 0.461090i | ||||
\(16\) | −5.71165 | − | 9.89286i | −0.0892445 | − | 0.154576i | ||||
\(17\) | −22.2732 | + | 38.5783i | −0.317767 | + | 0.550389i | −0.980022 | − | 0.198890i | \(-0.936266\pi\) |
0.662255 | + | 0.749279i | \(0.269600\pi\) | |||||||
\(18\) | −75.6155 | −0.990153 | ||||||||
\(19\) | −11.9848 | + | 20.7584i | −0.144711 | + | 0.250647i | −0.929265 | − | 0.369413i | \(-0.879559\pi\) |
0.784554 | + | 0.620061i | \(0.212892\pi\) | |||||||
\(20\) | −9.90388 | + | 17.1540i | −0.110729 | + | 0.191788i | ||||
\(21\) | −236.024 | −2.45260 | ||||||||
\(22\) | 11.9157 | − | 20.6386i | 0.115474 | − | 0.200008i | ||||
\(23\) | −61.3693 | − | 106.295i | −0.556365 | − | 0.963652i | −0.997796 | − | 0.0663568i | \(-0.978862\pi\) |
0.441431 | − | 0.897295i | \(-0.354471\pi\) | |||||||
\(24\) | −91.9579 | − | 159.276i | −0.782117 | − | 1.35467i | ||||
\(25\) | −112.315 | −0.898523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 186.054 | 1.32615 | ||||||||
\(28\) | −75.5734 | − | 130.897i | −0.510072 | − | 0.883471i | ||||
\(29\) | 109.955 | + | 190.447i | 0.704071 | + | 1.21949i | 0.967026 | + | 0.254678i | \(0.0819694\pi\) |
−0.262955 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(30\) | −24.1501 | + | 41.8292i | −0.146973 | + | 0.254564i | ||||
\(31\) | 27.0928 | 0.156968 | 0.0784840 | − | 0.996915i | \(-0.474992\pi\) | ||||
0.0784840 | + | 0.996915i | \(0.474992\pi\) | |||||||
\(32\) | 93.6274 | − | 162.167i | 0.517223 | − | 0.895856i | ||||
\(33\) | −66.2699 | + | 114.783i | −0.349579 | + | 0.605488i | ||||
\(34\) | −69.5616 | −0.350874 | ||||||||
\(35\) | −48.3963 | + | 83.8249i | −0.233728 | + | 0.404828i | ||||
\(36\) | 134.654 | + | 233.228i | 0.623400 | + | 1.07976i | ||||
\(37\) | −47.0961 | − | 81.5729i | −0.209258 | − | 0.362446i | 0.742223 | − | 0.670153i | \(-0.233772\pi\) |
−0.951481 | + | 0.307707i | \(0.900438\pi\) | |||||||
\(38\) | −37.4299 | −0.159788 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.4233 | −0.298137 | ||||||||
\(41\) | 80.1771 | + | 138.871i | 0.305404 | + | 0.528975i | 0.977351 | − | 0.211624i | \(-0.0678752\pi\) |
−0.671947 | + | 0.740599i | \(0.734542\pi\) | |||||||
\(42\) | −184.282 | − | 319.185i | −0.677031 | − | 1.17265i | ||||
\(43\) | 75.6510 | − | 131.031i | 0.268295 | − | 0.464700i | −0.700127 | − | 0.714018i | \(-0.746873\pi\) |
0.968422 | + | 0.249318i | \(0.0802066\pi\) | |||||||
\(44\) | −84.8769 | −0.290811 | ||||||||
\(45\) | 86.2311 | − | 149.357i | 0.285657 | − | 0.494773i | ||||
\(46\) | 95.8314 | − | 165.985i | 0.307165 | − | 0.532025i | ||||
\(47\) | 466.948 | 1.44918 | 0.724589 | − | 0.689181i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689181i | \(0.242030\pi\) | |||||||
\(48\) | −49.6037 | + | 85.9161i | −0.149160 | + | 0.258353i | ||||
\(49\) | −197.797 | − | 342.594i | −0.576667 | − | 0.998817i | ||||
\(50\) | −87.6932 | − | 151.889i | −0.248034 | − | 0.429607i | ||||
\(51\) | 386.870 | 1.06221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −120.847 | −0.313199 | −0.156600 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156600 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(54\) | 145.267 | + | 251.609i | 0.366079 | + | 0.634068i | ||||
\(55\) | 27.1771 | + | 47.0721i | 0.0666283 | + | 0.115404i | ||||
\(56\) | 287.766 | − | 498.425i | 0.686684 | − | 1.18937i | ||||
\(57\) | 208.169 | 0.483730 | ||||||||
\(58\) | −171.700 | + | 297.393i | −0.388712 | + | 0.673269i | ||||
\(59\) | 219.816 | − | 380.733i | 0.485045 | − | 0.840122i | −0.514808 | − | 0.857306i | \(-0.672137\pi\) |
0.999852 | + | 0.0171836i | \(0.00546997\pi\) | |||||||
\(60\) | 172.024 | 0.370136 | ||||||||
\(61\) | 68.6525 | − | 118.910i | 0.144099 | − | 0.249587i | −0.784937 | − | 0.619575i | \(-0.787305\pi\) |
0.929037 | + | 0.369988i | \(0.120638\pi\) | |||||||
\(62\) | 21.1534 | + | 36.6388i | 0.0433304 | + | 0.0750505i | ||||
\(63\) | 658.002 | + | 1139.69i | 1.31588 | + | 2.27917i | ||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −206.968 | −0.386000 | ||||||||
\(67\) | −256.140 | − | 443.648i | −0.467052 | − | 0.808958i | 0.532239 | − | 0.846594i | \(-0.321351\pi\) |
−0.999292 | + | 0.0376358i | \(0.988017\pi\) | |||||||
\(68\) | 123.874 | + | 214.555i | 0.220910 | + | 0.382627i | ||||
\(69\) | −532.972 | + | 923.134i | −0.929887 | + | 1.61061i | ||||
\(70\) | −151.147 | −0.258078 | ||||||||
\(71\) | −205.359 | + | 355.693i | −0.343263 | + | 0.594549i | −0.985037 | − | 0.172345i | \(-0.944866\pi\) |
0.641774 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(72\) | −512.732 | + | 888.078i | −0.839251 | + | 1.45362i | ||||
\(73\) | −308.004 | −0.493823 | −0.246912 | − | 0.969038i | \(-0.579416\pi\) | ||||
−0.246912 | + | 0.969038i | \(0.579416\pi\) | |||||||
\(74\) | 73.5431 | − | 127.380i | 0.115530 | − | 0.200104i | ||||
\(75\) | 487.710 | + | 844.739i | 0.750879 | + | 1.30056i | ||||
\(76\) | 66.6543 | + | 115.449i | 0.100602 | + | 0.174248i | ||||
\(77\) | −414.759 | −0.613847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −586.462 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(80\) | 20.3423 | + | 35.2339i | 0.0284293 | + | 0.0492409i | ||||
\(81\) | −154.193 | − | 267.070i | −0.211513 | − | 0.366352i | ||||
\(82\) | −125.201 | + | 216.854i | −0.168611 | + | 0.292043i | ||||
\(83\) | 1354.20 | 1.79088 | 0.895440 | − | 0.445182i | \(-0.146861\pi\) | ||||
0.895440 | + | 0.445182i | \(0.146861\pi\) | |||||||
\(84\) | −656.329 | + | 1136.80i | −0.852516 | + | 1.47660i | ||||
\(85\) | 79.3272 | − | 137.399i | 0.101226 | − | 0.175329i | ||||
\(86\) | 236.266 | 0.296247 | ||||||||
\(87\) | 954.918 | − | 1653.97i | 1.17676 | − | 2.03820i | ||||
\(88\) | −161.596 | − | 279.892i | −0.195752 | − | 0.339052i | ||||
\(89\) | −219.941 | − | 380.949i | −0.261952 | − | 0.453714i | 0.704809 | − | 0.709398i | \(-0.251033\pi\) |
−0.966761 | + | 0.255683i | \(0.917700\pi\) | |||||||
\(90\) | 269.309 | 0.315418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −682.617 | −0.773563 | ||||||||
\(93\) | −117.646 | − | 203.769i | −0.131175 | − | 0.227202i | ||||
\(94\) | 364.582 | + | 631.474i | 0.400040 | + | 0.692889i | ||||
\(95\) | 42.6847 | − | 73.9320i | 0.0460985 | − | 0.0798449i | ||||
\(96\) | −1626.24 | −1.72894 | ||||||||
\(97\) | 755.634 | − | 1308.80i | 0.790959 | − | 1.36998i | −0.134414 | − | 0.990925i | \(-0.542915\pi\) |
0.925374 | − | 0.379056i | \(-0.123751\pi\) | |||||||
\(98\) | 308.870 | − | 534.979i | 0.318374 | − | 0.551439i | ||||
\(99\) | 739.006 | 0.750231 | ||||||||
\(100\) | −312.324 | + | 540.961i | −0.312324 | + | 0.540961i | ||||
\(101\) | −168.130 | − | 291.209i | −0.165639 | − | 0.286895i | 0.771243 | − | 0.636541i | \(-0.219635\pi\) |
−0.936882 | + | 0.349646i | \(0.886302\pi\) | |||||||
\(102\) | 302.059 | + | 523.182i | 0.293219 | + | 0.507870i | ||||
\(103\) | 322.712 | 0.308716 | 0.154358 | − | 0.988015i | \(-0.450669\pi\) | ||||
0.154358 | + | 0.988015i | \(0.450669\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 840.611 | 0.781288 | ||||||||
\(106\) | −94.3542 | − | 163.426i | −0.0864574 | − | 0.149749i | ||||
\(107\) | −717.309 | − | 1242.42i | −0.648083 | − | 1.12251i | −0.983580 | − | 0.180471i | \(-0.942238\pi\) |
0.335498 | − | 0.942041i | \(-0.391096\pi\) | |||||||
\(108\) | 517.375 | − | 896.119i | 0.460967 | − | 0.798417i | ||||
\(109\) | 849.147 | 0.746179 | 0.373089 | − | 0.927795i | \(-0.378298\pi\) | ||||
0.373089 | + | 0.927795i | \(0.378298\pi\) | |||||||
\(110\) | −42.4384 | + | 73.5055i | −0.0367850 | + | 0.0637134i | ||||
\(111\) | −409.014 | + | 708.433i | −0.349747 | + | 0.605779i | ||||
\(112\) | −310.452 | −0.261919 | ||||||||
\(113\) | −807.263 | + | 1398.22i | −0.672044 | + | 1.16401i | 0.305280 | + | 0.952263i | \(0.401250\pi\) |
−0.977324 | + | 0.211751i | \(0.932083\pi\) | |||||||
\(114\) | 162.533 | + | 281.516i | 0.133532 | + | 0.231284i | ||||
\(115\) | 218.570 | + | 378.574i | 0.177233 | + | 0.306976i | ||||
\(116\) | 1223.04 | 0.978931 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 686.509 | 0.535579 | ||||||||
\(119\) | 605.321 | + | 1048.45i | 0.466300 | + | 0.807654i | ||||
\(120\) | 327.513 | + | 567.269i | 0.249147 | + | 0.431536i | ||||
\(121\) | 549.045 | − | 950.974i | 0.412506 | − | 0.714481i | ||||
\(122\) | 214.409 | 0.159112 | ||||||||
\(123\) | 696.311 | − | 1206.05i | 0.510441 | − | 0.884109i | ||||
\(124\) | 75.3390 | − | 130.491i | 0.0545616 | − | 0.0945035i | ||||
\(125\) | 845.211 | 0.604784 | ||||||||
\(126\) | −1027.50 | + | 1779.69i | −0.726487 | + | 1.25831i | ||||
\(127\) | −432.587 | − | 749.263i | −0.302251 | − | 0.523514i | 0.674394 | − | 0.738371i | \(-0.264405\pi\) |
−0.976646 | + | 0.214857i | \(0.931071\pi\) | |||||||
\(128\) | −592.066 | − | 1025.49i | −0.408842 | − | 0.708134i | ||||
\(129\) | −1314.01 | −0.896836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −281.400 | −0.187680 | −0.0938400 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938400 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(132\) | 368.563 | + | 638.371i | 0.243025 | + | 0.420932i | ||||
\(133\) | 325.713 | + | 564.152i | 0.212353 | + | 0.367806i | ||||
\(134\) | 399.976 | − | 692.779i | 0.257856 | − | 0.446620i | ||||
\(135\) | −662.641 | −0.422452 | ||||||||
\(136\) | −471.681 | + | 816.976i | −0.297400 | + | 0.515111i | ||||
\(137\) | 1320.72 | − | 2287.55i | 0.823624 | − | 1.42656i | −0.0793428 | − | 0.996847i | \(-0.525282\pi\) |
0.902967 | − | 0.429711i | \(-0.141384\pi\) | |||||||
\(138\) | −1664.53 | −1.02677 | ||||||||
\(139\) | 999.318 | − | 1730.87i | 0.609791 | − | 1.05619i | −0.381483 | − | 0.924376i | \(-0.624587\pi\) |
0.991274 | − | 0.131814i | \(-0.0420801\pi\) | |||||||
\(140\) | 269.159 | + | 466.196i | 0.162486 | + | 0.281434i | ||||
\(141\) | −2027.64 | − | 3511.98i | −1.21105 | − | 2.09760i | ||||
\(142\) | −641.359 | −0.379026 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 553.153 | 0.320112 | ||||||||
\(145\) | −391.609 | − | 678.286i | −0.224285 | − | 0.388473i | ||||
\(146\) | −240.482 | − | 416.527i | −0.136318 | − | 0.236110i | ||||
\(147\) | −1717.80 | + | 2975.31i | −0.963820 | + | 1.66939i | ||||
\(148\) | −523.855 | −0.290950 | ||||||||
\(149\) | 876.491 | − | 1518.13i | 0.481912 | − | 0.834696i | −0.517872 | − | 0.855458i | \(-0.673276\pi\) |
0.999784 | + | 0.0207617i | \(0.00660911\pi\) | |||||||
\(150\) | −761.585 | + | 1319.10i | −0.414554 | + | 0.718029i | ||||
\(151\) | −2794.64 | −1.50613 | −0.753063 | − | 0.657949i | \(-0.771424\pi\) | ||||
−0.753063 | + | 0.657949i | \(0.771424\pi\) | |||||||
\(152\) | −253.804 | + | 439.601i | −0.135436 | + | 0.234582i | ||||
\(153\) | −1078.54 | − | 1868.09i | −0.569901 | − | 0.987098i | ||||
\(154\) | −323.834 | − | 560.898i | −0.169450 | − | 0.293496i | ||||
\(155\) | −96.4924 | −0.0500030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3244.87 | 1.64949 | 0.824743 | − | 0.565508i | \(-0.191320\pi\) | ||||
0.824743 | + | 0.565508i | \(0.191320\pi\) | |||||||
\(158\) | −457.896 | − | 793.099i | −0.230558 | − | 0.399339i | ||||
\(159\) | 524.756 | + | 908.903i | 0.261735 | + | 0.453338i | ||||
\(160\) | −333.459 | + | 577.568i | −0.164764 | + | 0.285380i | ||||
\(161\) | −3335.68 | −1.63285 | ||||||||
\(162\) | 240.781 | − | 417.045i | 0.116775 | − | 0.202260i | ||||
\(163\) | −1640.73 | + | 2841.83i | −0.788418 | + | 1.36558i | 0.138517 | + | 0.990360i | \(0.455766\pi\) |
−0.926936 | + | 0.375221i | \(0.877567\pi\) | |||||||
\(164\) | 891.818 | 0.424630 | ||||||||
\(165\) | 236.024 | − | 408.805i | 0.111360 | − | 0.192881i | ||||
\(166\) | 1057.33 | + | 1831.35i | 0.494366 | + | 0.856266i | ||||
\(167\) | 1563.26 | + | 2707.65i | 0.724364 | + | 1.25463i | 0.959235 | + | 0.282608i | \(0.0911996\pi\) |
−0.234872 | + | 0.972026i | \(0.575467\pi\) | |||||||
\(168\) | −4998.29 | −2.29540 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 247.747 | 0.111773 | ||||||||
\(171\) | −580.346 | − | 1005.19i | −0.259533 | − | 0.449524i | ||||
\(172\) | −420.737 | − | 728.738i | −0.186517 | − | 0.323057i | ||||
\(173\) | −48.7849 | + | 84.4980i | −0.0214396 | + | 0.0371345i | −0.876546 | − | 0.481318i | \(-0.840158\pi\) |
0.855107 | + | 0.518452i | \(0.173492\pi\) | |||||||
\(174\) | 2982.31 | 1.29936 | ||||||||
\(175\) | −1526.20 | + | 2643.46i | −0.659257 | + | 1.14187i | ||||
\(176\) | −87.1675 | + | 150.979i | −0.0373324 | + | 0.0646616i | ||||
\(177\) | −3818.06 | −1.62137 | ||||||||
\(178\) | 343.450 | − | 594.873i | 0.144622 | − | 0.250492i | ||||
\(179\) | 17.3575 | + | 30.0640i | 0.00724782 | + | 0.0125536i | 0.869627 | − | 0.493710i | \(-0.164360\pi\) |
−0.862379 | + | 0.506264i | \(0.831026\pi\) | |||||||
\(180\) | −479.579 | − | 830.654i | −0.198587 | − | 0.343963i | ||||
\(181\) | −1229.35 | −0.504843 | −0.252422 | − | 0.967617i | \(-0.581227\pi\) | ||||
−0.252422 | + | 0.967617i | \(0.581227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1192.45 | −0.481684 | ||||||||
\(184\) | −1299.62 | − | 2251.01i | −0.520704 | − | 0.901885i | ||||
\(185\) | 167.735 | + | 290.526i | 0.0666602 | + | 0.115459i | ||||
\(186\) | 183.710 | − | 318.195i | 0.0724209 | − | 0.125437i | ||||
\(187\) | 679.839 | 0.265854 | ||||||||
\(188\) | 1298.48 | − | 2249.03i | 0.503730 | − | 0.872486i | ||||
\(189\) | 2528.20 | − | 4378.97i | 0.973014 | − | 1.68531i | ||||
\(190\) | 133.309 | 0.0509012 | ||||||||
\(191\) | −2140.40 | + | 3707.28i | −0.810858 | + | 1.40445i | 0.101407 | + | 0.994845i | \(0.467666\pi\) |
−0.912265 | + | 0.409602i | \(0.865668\pi\) | |||||||
\(192\) | −872.903 | − | 1511.91i | −0.328106 | − | 0.568296i | ||||
\(193\) | −236.160 | − | 409.041i | −0.0880786 | − | 0.152557i | 0.818620 | − | 0.574335i | \(-0.194739\pi\) |
−0.906699 | + | 0.421778i | \(0.861406\pi\) | |||||||
\(194\) | 2359.93 | 0.873365 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2200.12 | −0.801791 | ||||||||
\(197\) | 2242.18 | + | 3883.58i | 0.810908 | + | 1.40453i | 0.912229 | + | 0.409681i | \(0.134360\pi\) |
−0.101321 | + | 0.994854i | \(0.532307\pi\) | |||||||
\(198\) | 576.998 | + | 999.390i | 0.207098 | + | 0.358705i | ||||
\(199\) | 183.120 | − | 317.173i | 0.0652314 | − | 0.112984i | −0.831565 | − | 0.555427i | \(-0.812555\pi\) |
0.896797 | + | 0.442443i | \(0.145888\pi\) | |||||||
\(200\) | −2378.51 | −0.840931 | ||||||||
\(201\) | −2224.49 | + | 3852.93i | −0.780614 | + | 1.35206i | ||||
\(202\) | 262.543 | − | 454.739i | 0.0914480 | − | 0.158393i | ||||
\(203\) | 5976.49 | 2.06634 | ||||||||
\(204\) | 1075.80 | − | 1863.34i | 0.369221 | − | 0.639509i | ||||
\(205\) | −285.555 | − | 494.596i | −0.0972879 | − | 0.168508i | ||||
\(206\) | 251.966 | + | 436.418i | 0.0852199 | + | 0.147605i | ||||
\(207\) | 5943.41 | 1.99563 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 365.810 | 0.121070 | ||||||||
\(210\) | 656.329 | + | 1136.80i | 0.215671 | + | 0.373554i | ||||
\(211\) | −1061.28 | − | 1838.19i | −0.346262 | − | 0.599744i | 0.639320 | − | 0.768941i | \(-0.279216\pi\) |
−0.985582 | + | 0.169197i | \(0.945883\pi\) | |||||||
\(212\) | −336.047 | + | 582.051i | −0.108867 | + | 0.188563i | ||||
\(213\) | 3566.95 | 1.14743 | ||||||||
\(214\) | 1120.12 | − | 1940.10i | 0.357801 | − | 0.619730i | ||||
\(215\) | −269.435 | + | 466.675i | −0.0854666 | + | 0.148033i | ||||
\(216\) | 3940.08 | 1.24115 | ||||||||
\(217\) | 368.152 | − | 637.657i | 0.115169 | − | 0.199479i | ||||
\(218\) | 662.994 | + | 1148.34i | 0.205980 | + | 0.356768i | ||||
\(219\) | 1337.45 | + | 2316.54i | 0.412679 | + | 0.714781i | ||||
\(220\) | 302.294 | 0.0926392 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1277.39 | −0.386185 | ||||||||
\(223\) | 2963.21 | + | 5132.43i | 0.889826 | + | 1.54122i | 0.840081 | + | 0.542461i | \(0.182507\pi\) |
0.0497449 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(224\) | −2544.52 | − | 4407.24i | −0.758986 | − | 1.31460i | ||||
\(225\) | 2719.34 | − | 4710.03i | 0.805730 | − | 1.39557i | ||||
\(226\) | −2521.17 | −0.742060 | ||||||||
\(227\) | 447.830 | − | 775.665i | 0.130941 | − | 0.226796i | −0.793099 | − | 0.609093i | \(-0.791534\pi\) |
0.924039 | + | 0.382297i | \(0.124867\pi\) | |||||||
\(228\) | 578.870 | − | 1002.63i | 0.168143 | − | 0.291232i | ||||
\(229\) | 627.717 | 0.181138 | 0.0905692 | − | 0.995890i | \(-0.471131\pi\) | ||||
0.0905692 | + | 0.995890i | \(0.471131\pi\) | |||||||
\(230\) | −341.309 | + | 591.164i | −0.0978488 | + | 0.169479i | ||||
\(231\) | 1801.02 | + | 3119.46i | 0.512981 | + | 0.888509i | ||||
\(232\) | 2328.52 | + | 4033.11i | 0.658942 | + | 1.14132i | ||||
\(233\) | 2303.72 | 0.647734 | 0.323867 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323867 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1663.06 | −0.461643 | ||||||||
\(236\) | −1222.52 | − | 2117.47i | −0.337200 | − | 0.584048i | ||||
\(237\) | 2546.61 | + | 4410.86i | 0.697976 | + | 1.20893i | ||||
\(238\) | −945.240 | + | 1637.20i | −0.257440 | + | 0.445900i | ||||
\(239\) | 544.622 | 0.147400 | 0.0737001 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737001 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(240\) | 176.666 | − | 305.995i | 0.0475156 | − | 0.0822995i | ||||
\(241\) | −2713.05 | + | 4699.14i | −0.725157 | + | 1.25601i | 0.233752 | + | 0.972296i | \(0.424900\pi\) |
−0.958909 | + | 0.283713i | \(0.908434\pi\) | |||||||
\(242\) | 1714.73 | 0.455483 | ||||||||
\(243\) | 1172.61 | − | 2031.03i | 0.309561 | − | 0.536175i | ||||
\(244\) | −381.814 | − | 661.322i | −0.100177 | − | 0.173511i | ||||
\(245\) | 704.464 | + | 1220.17i | 0.183700 | + | 0.318178i | ||||
\(246\) | 2174.65 | 0.563621 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 573.746 | 0.146907 | ||||||||
\(249\) | −5880.39 | − | 10185.1i | −1.49661 | − | 2.59220i | ||||
\(250\) | 659.921 | + | 1143.02i | 0.166948 | + | 0.289163i | ||||
\(251\) | 2610.61 | − | 4521.71i | 0.656494 | − | 1.13708i | −0.325022 | − | 0.945706i | \(-0.605372\pi\) |
0.981517 | − | 0.191375i | \(-0.0612948\pi\) | |||||||
\(252\) | 7319.02 | 1.82958 | ||||||||
\(253\) | −936.580 | + | 1622.20i | −0.232736 | + | 0.403111i | ||||
\(254\) | 675.508 | − | 1170.01i | 0.166871 | − | 0.289028i | ||||
\(255\) | −1377.86 | −0.338372 | ||||||||
\(256\) | 1728.63 | − | 2994.07i | 0.422029 | − | 0.730975i | ||||
\(257\) | −329.103 | − | 570.023i | −0.0798789 | − | 0.138354i | 0.823319 | − | 0.567579i | \(-0.192120\pi\) |
−0.903198 | + | 0.429225i | \(0.858787\pi\) | |||||||
\(258\) | −1025.95 | − | 1776.99i | −0.247568 | − | 0.428801i | ||||
\(259\) | −2559.87 | −0.614141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10648.7 | −2.52544 | ||||||||
\(262\) | −219.711 | − | 380.550i | −0.0518083 | − | 0.0897346i | ||||
\(263\) | −1623.23 | − | 2811.51i | −0.380580 | − | 0.659184i | 0.610565 | − | 0.791966i | \(-0.290942\pi\) |
−0.991145 | + | 0.132782i | \(0.957609\pi\) | |||||||
\(264\) | −1403.40 | + | 2430.76i | −0.327172 | + | 0.566679i | ||||
\(265\) | 430.401 | 0.0997711 | ||||||||
\(266\) | −508.618 | + | 880.953i | −0.117238 | + | 0.203063i | ||||
\(267\) | −1910.11 | + | 3308.42i | −0.437817 | + | 0.758321i | ||||
\(268\) | −2849.07 | −0.649384 | ||||||||
\(269\) | 1292.90 | − | 2239.37i | 0.293047 | − | 0.507572i | −0.681482 | − | 0.731835i | \(-0.738664\pi\) |
0.974529 | + | 0.224263i | \(0.0719976\pi\) | |||||||
\(270\) | −517.375 | − | 896.119i | −0.116616 | − | 0.201985i | ||||
\(271\) | −494.466 | − | 856.441i | −0.110836 | − | 0.191974i | 0.805271 | − | 0.592907i | \(-0.202020\pi\) |
−0.916108 | + | 0.400932i | \(0.868686\pi\) | |||||||
\(272\) | 508.867 | 0.113436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4124.74 | 0.909433 | ||||||||
\(275\) | 857.043 | + | 1484.44i | 0.187933 | + | 0.325510i | ||||
\(276\) | 2964.15 | + | 5134.06i | 0.646452 | + | 1.11969i | ||||
\(277\) | −4071.20 | + | 7051.53i | −0.883086 | + | 1.52955i | −0.0351939 | + | 0.999381i | \(0.511205\pi\) |
−0.847892 | + | 0.530169i | \(0.822128\pi\) | |||||||
\(278\) | 3120.97 | 0.673322 | ||||||||
\(279\) | −655.961 | + | 1136.16i | −0.140758 | + | 0.243799i | ||||
\(280\) | −1024.89 | + | 1775.17i | −0.218747 | + | 0.378880i | ||||
\(281\) | 1534.21 | 0.325705 | 0.162853 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162853 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(282\) | 3166.27 | − | 5484.14i | 0.668612 | − | 1.15807i | ||||
\(283\) | 3482.50 | + | 6031.87i | 0.731495 | + | 1.26699i | 0.956244 | + | 0.292570i | \(0.0945105\pi\) |
−0.224749 | + | 0.974417i | \(0.572156\pi\) | |||||||
\(284\) | 1142.12 | + | 1978.20i | 0.238634 | + | 0.413327i | ||||
\(285\) | −741.403 | −0.154095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4357.96 | 0.896314 | ||||||||
\(288\) | 4533.75 | + | 7852.68i | 0.927616 | + | 1.60668i | ||||
\(289\) | 1464.31 | + | 2536.26i | 0.298048 | + | 0.516234i | ||||
\(290\) | 611.518 | − | 1059.18i | 0.123826 | − | 0.214473i | ||||
\(291\) | −13124.9 | −2.64396 | ||||||||
\(292\) | −856.490 | + | 1483.48i | −0.171652 | + | 0.297309i | ||||
\(293\) | −320.015 | + | 554.281i | −0.0638070 | + | 0.110517i | −0.896164 | − | 0.443723i | \(-0.853658\pi\) |
0.832357 | + | 0.554240i | \(0.186991\pi\) | |||||||
\(294\) | −5364.87 | −1.06424 | ||||||||
\(295\) | −782.887 | + | 1356.00i | −0.154513 | + | 0.267625i | ||||
\(296\) | −997.358 | − | 1727.48i | −0.195846 | − | 0.339214i | ||||
\(297\) | −1419.72 | − | 2459.03i | −0.277375 | − | 0.480428i | ||||
\(298\) | 2737.37 | 0.532120 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5424.85 | 1.04401 | ||||||||
\(301\) | −2055.97 | − | 3561.05i | −0.393702 | − | 0.681912i | ||||
\(302\) | −2181.99 | − | 3779.32i | −0.415760 | − | 0.720118i | ||||
\(303\) | −1460.15 | + | 2529.05i | −0.276843 | + | 0.479506i | ||||
\(304\) | 273.813 | 0.0516587 | ||||||||
\(305\) | −244.509 | + | 423.503i | −0.0459035 | + | 0.0795072i | ||||
\(306\) | 1684.20 | − | 2917.12i | 0.314638 | − | 0.544969i | ||||
\(307\) | −100.406 | −0.0186660 | −0.00933299 | − | 0.999956i | \(-0.502971\pi\) | ||||
−0.00933299 | + | 0.999956i | \(0.502971\pi\) | |||||||
\(308\) | −1153.35 | + | 1997.67i | −0.213371 | + | 0.369570i | ||||
\(309\) | −1401.32 | − | 2427.16i | −0.257988 | − | 0.446849i | ||||
\(310\) | −75.3390 | − | 130.491i | −0.0138031 | − | 0.0239077i | ||||
\(311\) | −3878.92 | −0.707245 | −0.353623 | − | 0.935388i | \(-0.615050\pi\) | ||||
−0.353623 | + | 0.935388i | \(0.615050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3789.39 | −0.684311 | −0.342155 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342155 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(314\) | 2533.52 | + | 4388.19i | 0.455334 | + | 0.788662i | ||||
\(315\) | −2343.51 | − | 4059.08i | −0.419180 | − | 0.726041i | ||||
\(316\) | −1630.82 | + | 2824.66i | −0.290319 | + | 0.502847i | ||||
\(317\) | 4406.81 | 0.780791 | 0.390396 | − | 0.920647i | \(-0.372338\pi\) | ||||
0.390396 | + | 0.920647i | \(0.372338\pi\) | |||||||
\(318\) | −819.434 | + | 1419.30i | −0.144502 | + | 0.250284i | ||||
\(319\) | 1678.06 | − | 2906.48i | 0.294524 | − | 0.510130i | ||||
\(320\) | −715.950 | −0.125071 | ||||||||
\(321\) | −6229.58 | + | 10790.0i | −1.08318 | + | 1.87613i | ||||
\(322\) | −2604.42 | − | 4510.99i | −0.450741 | − | 0.780706i | ||||
\(323\) | −533.882 | − | 924.710i | −0.0919690 | − | 0.159295i | ||||
\(324\) | −1715.11 | −0.294086 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5124.19 | −0.870559 | ||||||||
\(327\) | −3687.27 | − | 6386.55i | −0.623568 | − | 1.08005i | ||||
\(328\) | 1697.92 | + | 2940.88i | 0.285829 | + | 0.495070i | ||||
\(329\) | 6345.14 | − | 10990.1i | 1.06328 | − | 1.84165i | ||||
\(330\) | 737.127 | 0.122962 | ||||||||
\(331\) | 2065.75 | − | 3577.98i | 0.343032 | − | 0.594149i | −0.641962 | − | 0.766736i | \(-0.721879\pi\) |
0.984994 | + | 0.172587i | \(0.0552127\pi\) | |||||||
\(332\) | 3765.73 | − | 6522.44i | 0.622505 | − | 1.07821i | ||||
\(333\) | 4561.10 | 0.750591 | ||||||||
\(334\) | −2441.11 | + | 4228.13i | −0.399916 | + | 0.692674i | ||||
\(335\) | 912.257 | + | 1580.07i | 0.148782 | + | 0.257698i | ||||
\(336\) | 1348.08 | + | 2334.95i | 0.218881 | + | 0.379113i | ||||
\(337\) | −4560.82 | −0.737221 | −0.368611 | − | 0.929584i | \(-0.620166\pi\) | ||||
−0.368611 | + | 0.929584i | \(0.620166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14021.6 | 2.24646 | ||||||||
\(340\) | −441.182 | − | 764.150i | −0.0703720 | − | 0.121888i | ||||
\(341\) | −206.737 | − | 358.078i | −0.0328311 | − | 0.0568652i | ||||
\(342\) | 906.240 | − | 1569.65i | 0.143286 | − | 0.248179i | ||||
\(343\) | −1429.34 | −0.225007 | ||||||||
\(344\) | 1602.07 | − | 2774.86i | 0.251098 | − | 0.434914i | ||||
\(345\) | 1898.21 | − | 3287.79i | 0.296220 | − | 0.513069i | ||||
\(346\) | −152.360 | −0.0236733 | ||||||||
\(347\) | −5034.70 | + | 8720.36i | −0.778896 | + | 1.34909i | 0.153683 | + | 0.988120i | \(0.450887\pi\) |
−0.932579 | + | 0.360967i | \(0.882447\pi\) | |||||||
\(348\) | −5310.82 | − | 9198.62i | −0.818075 | − | 1.41695i | ||||
\(349\) | −2939.66 | − | 5091.64i | −0.450878 | − | 0.780944i | 0.547563 | − | 0.836765i | \(-0.315556\pi\) |
−0.998441 | + | 0.0558207i | \(0.982222\pi\) | |||||||
\(350\) | −4766.49 | −0.727942 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2857.76 | −0.432725 | ||||||||
\(353\) | 4571.28 | + | 7917.69i | 0.689249 | + | 1.19381i | 0.972081 | + | 0.234644i | \(0.0753925\pi\) |
−0.282833 | + | 0.959169i | \(0.591274\pi\) | |||||||
\(354\) | −2981.05 | − | 5163.33i | −0.447574 | − | 0.775220i | ||||
\(355\) | 731.398 | − | 1266.82i | 0.109348 | − | 0.189397i | ||||
\(356\) | −2446.43 | −0.364215 | ||||||||
\(357\) | 5257.00 | − | 9105.39i | 0.779356 | − | 1.34988i | ||||
\(358\) | −27.1046 | + | 46.9466i | −0.00400146 | + | 0.00693074i | ||||
\(359\) | −2754.32 | −0.404924 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(360\) | 1826.12 | − | 3162.94i | 0.267347 | − | 0.463059i | ||||
\(361\) | 3142.23 | + | 5442.50i | 0.458117 | + | 0.793483i | ||||
\(362\) | −959.845 | − | 1662.50i | −0.139360 | − | 0.241379i | ||||
\(363\) | −9536.54 | −1.37889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1096.97 | 0.157310 | ||||||||
\(366\) | −931.034 | − | 1612.60i | −0.132967 | − | 0.230306i | ||||
\(367\) | −1520.09 | − | 2632.88i | −0.216208 | − | 0.374483i | 0.737438 | − | 0.675415i | \(-0.236036\pi\) |
−0.953646 | + | 0.300932i | \(0.902702\pi\) | |||||||
\(368\) | −701.040 | + | 1214.24i | −0.0993049 | + | 0.172001i | ||||
\(369\) | −7764.88 | −1.09546 | ||||||||
\(370\) | −261.928 | + | 453.672i | −0.0368026 | + | 0.0637440i | ||||
\(371\) | −1642.13 | + | 2844.25i | −0.229798 | + | 0.398022i | ||||
\(372\) | −1308.59 | −0.182385 | ||||||||
\(373\) | 2692.36 | − | 4663.31i | 0.373740 | − | 0.647337i | −0.616397 | − | 0.787435i | \(-0.711408\pi\) |
0.990138 | + | 0.140098i | \(0.0447418\pi\) | |||||||
\(374\) | 530.802 | + | 919.376i | 0.0733880 | + | 0.127112i | ||||
\(375\) | −3670.18 | − | 6356.95i | −0.505407 | − | 0.875390i | ||||
\(376\) | 9888.59 | 1.35629 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7895.84 | 1.07439 | ||||||||
\(379\) | 1712.13 | + | 2965.50i | 0.232049 | + | 0.401920i | 0.958411 | − | 0.285392i | \(-0.0921239\pi\) |
−0.726362 | + | 0.687312i | \(0.758791\pi\) | |||||||
\(380\) | −237.393 | − | 411.177i | −0.0320474 | − | 0.0555077i | ||||
\(381\) | −3756.87 | + | 6507.09i | −0.505171 | + | 0.874983i | ||||
\(382\) | −6684.69 | −0.895336 | ||||||||
\(383\) | 191.493 | − | 331.675i | 0.0255478 | − | 0.0442501i | −0.852969 | − | 0.521962i | \(-0.825200\pi\) |
0.878517 | + | 0.477712i | \(0.158534\pi\) | |||||||
\(384\) | −5141.89 | + | 8906.01i | −0.683323 | + | 1.18355i | ||||
\(385\) | 1477.19 | 0.195544 | ||||||||
\(386\) | 368.776 | − | 638.739i | 0.0486275 | − | 0.0842253i | ||||
\(387\) | 3663.27 | + | 6344.97i | 0.481175 | + | 0.833419i | ||||
\(388\) | −4202.50 | − | 7278.94i | −0.549870 | − | 0.952403i | ||||
\(389\) | 8588.34 | 1.11940 | 0.559699 | − | 0.828696i | \(-0.310917\pi\) | ||||
0.559699 | + | 0.828696i | \(0.310917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5467.56 | 0.707178 | ||||||||
\(392\) | −4188.76 | − | 7255.15i | −0.539705 | − | 0.934796i | ||||
\(393\) | 1221.93 | + | 2116.45i | 0.156841 | + | 0.271656i | ||||
\(394\) | −3501.29 | + | 6064.41i | −0.447696 | + | 0.775433i | ||||
\(395\) | 2088.72 | 0.266063 | ||||||||
\(396\) | 2055.01 | − | 3559.38i | 0.260778 | − | 0.451681i | ||||
\(397\) | 3619.58 | − | 6269.30i | 0.457586 | − | 0.792562i | −0.541247 | − | 0.840864i | \(-0.682048\pi\) |
0.998833 | + | 0.0483020i | \(0.0153810\pi\) | |||||||
\(398\) | 571.904 | 0.0720275 | ||||||||
\(399\) | 2828.71 | − | 4899.46i | 0.354918 | − | 0.614737i | ||||
\(400\) | 641.505 | + | 1111.12i | 0.0801882 | + | 0.138890i | ||||
\(401\) | −2134.81 | − | 3697.60i | −0.265854 | − | 0.460472i | 0.701933 | − | 0.712243i | \(-0.252321\pi\) |
−0.967787 | + | 0.251770i | \(0.918987\pi\) | |||||||
\(402\) | −6947.32 | −0.861942 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1870.12 | −0.230302 | ||||||||
\(405\) | 549.167 | + | 951.185i | 0.0673786 | + | 0.116703i | ||||
\(406\) | 4666.30 | + | 8082.27i | 0.570405 | + | 0.987971i | ||||
\(407\) | −718.751 | + | 1244.91i | −0.0875360 | + | 0.151617i | ||||
\(408\) | 8192.78 | 0.994125 | ||||||||
\(409\) | −6781.26 | + | 11745.5i | −0.819834 | + | 1.41999i | 0.0859711 | + | 0.996298i | \(0.472601\pi\) |
−0.905805 | + | 0.423696i | \(0.860733\pi\) | |||||||
\(410\) | 445.909 | − | 772.337i | 0.0537119 | − | 0.0930317i | ||||
\(411\) | −22939.9 | −2.75315 | ||||||||
\(412\) | 897.390 | − | 1554.33i | 0.107309 | − | 0.185864i | ||||
\(413\) | −5973.96 | − | 10347.2i | −0.711767 | − | 1.23282i | ||||
\(414\) | 4640.47 | + | 8037.54i | 0.550886 | + | 0.954163i | ||||
\(415\) | −4823.06 | −0.570494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17357.5 | −2.03837 | ||||||||
\(418\) | 285.616 | + | 494.701i | 0.0334209 | + | 0.0578867i | ||||
\(419\) | 7288.44 | + | 12624.0i | 0.849794 | + | 1.47189i | 0.881392 | + | 0.472386i | \(0.156607\pi\) |
−0.0315973 | + | 0.999501i | \(0.510059\pi\) | |||||||
\(420\) | 2337.55 | − | 4048.76i | 0.271573 | − | 0.470379i | ||||
\(421\) | 15848.4 | 1.83469 | 0.917343 | − | 0.398099i | \(-0.130330\pi\) | ||||
0.917343 | + | 0.398099i | \(0.130330\pi\) | |||||||
\(422\) | 1657.24 | − | 2870.42i | 0.191169 | − | 0.331114i | ||||
\(423\) | −11305.6 | + | 19581.8i | −1.29952 | + | 2.25083i | ||||
\(424\) | −2559.18 | −0.293124 | ||||||||
\(425\) | 2501.62 | − | 4332.94i | 0.285521 | − | 0.494537i | ||||
\(426\) | 2784.99 | + | 4823.75i | 0.316745 | + | 0.548618i | ||||
\(427\) | −1865.77 | − | 3231.62i | −0.211455 | − | 0.366250i | ||||
\(428\) | −7978.70 | −0.901087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −841.474 | −0.0943709 | ||||||||
\(431\) | −5347.36 | − | 9261.90i | −0.597618 | − | 1.03510i | −0.993172 | − | 0.116662i | \(-0.962781\pi\) |
0.395554 | − | 0.918443i | \(-0.370553\pi\) | |||||||
\(432\) | −1062.67 | − | 1840.61i | −0.118352 | − | 0.204991i | ||||
\(433\) | 8039.50 | − | 13924.8i | 0.892272 | − | 1.54546i | 0.0551273 | − | 0.998479i | \(-0.482444\pi\) |
0.837145 | − | 0.546981i | \(-0.184223\pi\) | |||||||
\(434\) | 1149.78 | 0.127168 | ||||||||
\(435\) | −3400.99 | + | 5890.69i | −0.374862 | + | 0.649280i | ||||
\(436\) | 2361.29 | − | 4089.87i | 0.259370 | − | 0.449241i | ||||
\(437\) | 2942.01 | 0.322049 | ||||||||
\(438\) | −2088.50 | + | 3617.40i | −0.227837 | + | 0.394625i | ||||
\(439\) | −3017.90 | − | 5227.16i | −0.328101 | − | 0.568288i | 0.654034 | − | 0.756465i | \(-0.273075\pi\) |
−0.982135 | + | 0.188177i | \(0.939742\pi\) | |||||||
\(440\) | 575.531 | + | 996.849i | 0.0623577 | + | 0.108007i | ||||
\(441\) | 19156.0 | 2.06845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10201.3 | 1.09409 | 0.547043 | − | 0.837105i | \(-0.315753\pi\) | ||||
0.547043 | + | 0.837105i | \(0.315753\pi\) | |||||||
\(444\) | 2274.75 | + | 3939.98i | 0.243142 | + | 0.421134i | ||||
\(445\) | 783.332 | + | 1356.77i | 0.0834461 | + | 0.144533i | ||||
\(446\) | −4627.21 | + | 8014.56i | −0.491266 | + | 0.850897i | ||||
\(447\) | −15224.0 | −1.61090 | ||||||||
\(448\) | 2731.59 | − | 4731.26i | 0.288071 | − | 0.498953i | ||||
\(449\) | 2911.27 | − | 5042.47i | 0.305994 | − | 0.529997i | −0.671488 | − | 0.741015i | \(-0.734345\pi\) |
0.977482 | + | 0.211018i | \(0.0676779\pi\) | |||||||
\(450\) | 8492.78 | 0.889675 | ||||||||
\(451\) | 1223.61 | − | 2119.36i | 0.127755 | − | 0.221279i | ||||
\(452\) | 4489.64 | + | 7776.28i | 0.467201 | + | 0.809216i | ||||
\(453\) | 12135.3 | + | 21018.9i | 1.25864 | + | 2.18003i | ||||
\(454\) | 1398.62 | 0.144583 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4408.40 | 0.452724 | ||||||||
\(457\) | −2310.80 | − | 4002.42i | −0.236531 | − | 0.409684i | 0.723186 | − | 0.690654i | \(-0.242677\pi\) |
−0.959717 | + | 0.280970i | \(0.909344\pi\) | |||||||
\(458\) | 490.106 | + | 848.889i | 0.0500026 | + | 0.0866070i | ||||
\(459\) | −4144.02 | + | 7177.65i | −0.421408 | + | 0.729900i | ||||
\(460\) | 2431.18 | 0.246422 | ||||||||
\(461\) | −2563.88 | + | 4440.78i | −0.259028 | + | 0.448650i | −0.965982 | − | 0.258610i | \(-0.916736\pi\) |
0.706954 | + | 0.707260i | \(0.250069\pi\) | |||||||
\(462\) | −2812.39 | + | 4871.20i | −0.283213 | + | 0.490539i | ||||
\(463\) | 6486.27 | 0.651064 | 0.325532 | − | 0.945531i | \(-0.394457\pi\) | ||||
0.325532 | + | 0.945531i | \(0.394457\pi\) | |||||||
\(464\) | 1256.04 | − | 2175.53i | 0.125669 | − | 0.217665i | ||||
\(465\) | 419.002 | + | 725.733i | 0.0417866 | + | 0.0723764i | ||||
\(466\) | 1798.69 | + | 3115.43i | 0.178804 | + | 0.309698i | ||||
\(467\) | 12978.0 | 1.28598 | 0.642990 | − | 0.765875i | \(-0.277694\pi\) | ||||
0.642990 | + | 0.765875i | \(0.277694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13922.3 | −1.37073 | ||||||||
\(470\) | −1298.48 | − | 2249.03i | −0.127435 | − | 0.220723i | ||||
\(471\) | −14090.3 | − | 24405.1i | −1.37844 | − | 2.38754i | ||||
\(472\) | 4655.07 | − | 8062.81i | 0.453955 | − | 0.786273i | ||||
\(473\) | −2309.08 | −0.224464 | ||||||||
\(474\) | −3976.67 | + | 6887.79i | −0.385347 | + | 0.667440i | ||||
\(475\) | 1346.08 | − | 2331.48i | 0.130026 | − | 0.225212i | ||||
\(476\) | 6733.04 | 0.648337 | ||||||||
\(477\) | 2925.89 | − | 5067.80i | 0.280854 | − | 0.486454i | ||||
\(478\) | 425.228 | + | 736.516i | 0.0406893 | + | 0.0704759i | ||||
\(479\) | 2904.48 | + | 5030.71i | 0.277055 | + | 0.479873i | 0.970651 | − | 0.240491i | \(-0.0773084\pi\) |
−0.693597 | + | 0.720363i | \(0.743975\pi\) | |||||||
\(480\) | 5791.95 | 0.550761 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8473.14 | −0.800707 | ||||||||
\(483\) | 14484.6 | + | 25088.1i | 1.36454 | + | 2.36345i | ||||
\(484\) | −3053.54 | − | 5288.89i | −0.286772 | − | 0.496703i | ||||
\(485\) | −2691.23 | + | 4661.35i | −0.251964 | + | 0.436414i | ||||
\(486\) | 3662.20 | 0.341812 | ||||||||
\(487\) | 2693.57 | − | 4665.40i | 0.250631 | − | 0.434106i | −0.713069 | − | 0.701094i | \(-0.752695\pi\) |
0.963700 | + | 0.266989i | \(0.0860286\pi\) | |||||||
\(488\) | 1453.86 | − | 2518.16i | 0.134863 | − | 0.233589i | ||||
\(489\) | 28498.4 | 2.63547 | ||||||||
\(490\) | −1100.06 | + | 1905.36i | −0.101419 | + | 0.175664i | ||||
\(491\) | −7629.53 | − | 13214.7i | −0.701255 | − | 1.21461i | −0.968026 | − | 0.250849i | \(-0.919290\pi\) |
0.266772 | − | 0.963760i | \(-0.414043\pi\) | |||||||
\(492\) | −3872.57 | − | 6707.48i | −0.354855 | − | 0.614628i | ||||
\(493\) | −9796.16 | −0.894922 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2632.01 | −0.238990 | ||||||||
\(496\) | −154.744 | − | 268.025i | −0.0140085 | − | 0.0242635i | ||||
\(497\) | 5581.07 | + | 9666.69i | 0.503712 | + | 0.872456i | ||||
\(498\) | 9182.55 | − | 15904.6i | 0.826264 | − | 1.43113i | ||||
\(499\) | 1856.04 | 0.166509 | 0.0832544 | − | 0.996528i | \(-0.473469\pi\) | ||||
0.0832544 | + | 0.996528i | \(0.473469\pi\) | |||||||
\(500\) | 2350.34 | − | 4070.91i | 0.210221 | − | 0.364114i | ||||
\(501\) | 13576.4 | − | 23515.0i | 1.21067 | − | 2.09695i | ||||
\(502\) | 8153.20 | 0.724891 | ||||||||
\(503\) | −524.732 | + | 908.862i | −0.0465142 | + | 0.0805649i | −0.888345 | − | 0.459176i | \(-0.848145\pi\) |
0.841831 | + | 0.539741i | \(0.181478\pi\) | |||||||
\(504\) | 13934.6 | + | 24135.4i | 1.23154 | + | 2.13308i | ||||
\(505\) | 598.803 | + | 1037.16i | 0.0527651 | + | 0.0913919i | ||||
\(506\) | −2925.04 | −0.256984 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4811.71 | −0.420246 | ||||||||
\(509\) | 275.553 | + | 477.272i | 0.0239954 | + | 0.0415613i | 0.877774 | − | 0.479075i | \(-0.159028\pi\) |
−0.853778 | + | 0.520637i | \(0.825695\pi\) | |||||||
\(510\) | −1075.80 | − | 1863.34i | −0.0934063 | − | 0.161784i | ||||
\(511\) | −4185.32 | + | 7249.19i | −0.362324 | + | 0.627564i | ||||
\(512\) | −4074.36 | −0.351686 | ||||||||
\(513\) | −2229.83 | + | 3862.18i | −0.191909 | + | 0.332396i | ||||
\(514\) | 513.911 | − | 890.121i | 0.0441005 | − | 0.0763843i | ||||
\(515\) | −1149.36 | −0.0983431 | ||||||||
\(516\) | −3653.96 | + | 6328.84i | −0.311738 | + | 0.539945i | ||||
\(517\) | −3563.13 | − | 6171.52i | −0.303107 | − | 0.524997i | ||||
\(518\) | −1998.69 | − | 3461.83i | −0.169531 | − | 0.293637i | ||||
\(519\) | 847.361 | 0.0716667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8995.30 | −0.756413 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(522\) | −8314.27 | − | 14400.7i | −0.697137 | − | 1.20748i | ||||
\(523\) | −1331.96 | − | 2307.02i | −0.111362 | − | 0.192885i | 0.804958 | − | 0.593332i | \(-0.202188\pi\) |
−0.916320 | + | 0.400448i | \(0.868855\pi\) | |||||||
\(524\) | −782.512 | + | 1355.35i | −0.0652370 | + | 0.112994i | ||||
\(525\) | 26509.1 | 2.20372 | ||||||||
\(526\) | 2534.76 | − | 4390.32i | 0.210115 | − | 0.363930i | ||||
\(527\) | −603.443 | + | 1045.19i | −0.0498793 | + | 0.0863935i | ||||
\(528\) | 1514.04 | 0.124792 | ||||||||
\(529\) | −1448.89 | + | 2509.54i | −0.119083 | + | 0.206258i | ||||
\(530\) | 336.047 | + | 582.051i | 0.0275414 | + | 0.0477032i | ||||
\(531\) | 10644.2 | + | 18436.3i | 0.869906 | + | 1.50672i | ||||
\(532\) | 3622.94 | 0.295253 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5965.49 | −0.483431 | ||||||||
\(535\) | 2554.73 | + | 4424.93i | 0.206450 | + | 0.357582i | ||||
\(536\) | −5424.30 | − | 9395.16i | −0.437116 | − | 0.757107i | ||||
\(537\) | 150.744 | − | 261.096i | 0.0121137 | − | 0.0209816i | ||||
\(538\) | 4037.86 | 0.323577 | ||||||||
\(539\) | −3018.65 | + | 5228.46i | −0.241229 | + | 0.417821i | ||||
\(540\) | −1842.66 | + | 3191.57i | −0.146843 | + | 0.254340i | ||||
\(541\) | −6169.23 | −0.490270 | −0.245135 | − | 0.969489i | \(-0.578832\pi\) | ||||
−0.245135 | + | 0.969489i | \(0.578832\pi\) | |||||||
\(542\) | 772.135 | − | 1337.38i | 0.0611920 | − | 0.105988i | ||||
\(543\) | 5338.23 | + | 9246.08i | 0.421888 | + | 0.730732i | ||||
\(544\) | 4170.76 | + | 7223.97i | 0.328713 | + | 0.569348i | ||||
\(545\) | −3024.28 | −0.237699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5140.42 | 0.401807 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(548\) | −7345.24 | − | 12722.3i | −0.572578 | − | 0.991735i | ||||
\(549\) | 3324.38 | + | 5757.99i | 0.258435 | + | 0.447623i | ||||
\(550\) | −1338.32 | + | 2318.03i | −0.103756 | + | 0.179711i | ||||
\(551\) | −5271.15 | −0.407547 | ||||||||
\(552\) | −11286.8 | + | 19549.3i | −0.870285 | + | 1.50738i | ||||
\(553\) | −7969.16 | + | 13803.0i | −0.612809 | + | 1.06142i | ||||
\(554\) | −12714.8 | −0.975090 | ||||||||
\(555\) | 1456.72 | − | 2523.12i | 0.111413 | − | 0.192974i | ||||
\(556\) | −5557.76 | − | 9626.32i | −0.423923 | − | 0.734257i | ||||
\(557\) | −1389.28 | − | 2406.30i | −0.105683 | − | 0.183049i | 0.808334 | − | 0.588724i | \(-0.200370\pi\) |
−0.914017 | + | 0.405675i | \(0.867036\pi\) | |||||||
\(558\) | −2048.64 | −0.155422 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1105.69 | 0.0834356 | ||||||||
\(561\) | −2952.08 | − | 5113.16i | −0.222170 | − | 0.384809i | ||||
\(562\) | 1197.87 | + | 2074.78i | 0.0899097 | + | 0.155728i | ||||
\(563\) | −2453.07 | + | 4248.85i | −0.183632 | + | 0.318059i | −0.943115 | − | 0.332468i | \(-0.892119\pi\) |
0.759483 | + | 0.650527i | \(0.225452\pi\) | |||||||
\(564\) | −22553.7 | −1.68383 | ||||||||
\(565\) | 2875.11 | − | 4979.84i | 0.214083 | − | 0.370802i | ||||
\(566\) | −5438.11 | + | 9419.08i | −0.403853 | + | 0.699494i | ||||
\(567\) | −8381.04 | −0.620759 | ||||||||
\(568\) | −4348.91 | + | 7532.54i | −0.321261 | + | 0.556440i | ||||
\(569\) | 4681.58 | + | 8108.73i | 0.344924 | + | 0.597426i | 0.985340 | − | 0.170602i | \(-0.0545713\pi\) |
−0.640416 | + | 0.768028i | \(0.721238\pi\) | |||||||
\(570\) | −578.870 | − | 1002.63i | −0.0425372 | − | 0.0736766i | ||||
\(571\) | 7199.32 | 0.527640 | 0.263820 | − | 0.964572i | \(-0.415018\pi\) | ||||
0.263820 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37177.3 | 2.71048 | ||||||||
\(574\) | 3402.59 | + | 5893.46i | 0.247424 | + | 0.428551i | ||||
\(575\) | 6892.72 | + | 11938.5i | 0.499906 | + | 0.865863i | ||||
\(576\) | −4867.07 | + | 8430.01i | −0.352074 | + | 0.609810i | ||||
\(577\) | −11449.6 | −0.826086 | −0.413043 | − | 0.910711i | \(-0.635534\pi\) | ||||
−0.413043 | + | 0.910711i | \(0.635534\pi\) | |||||||
\(578\) | −2286.60 | + | 3960.50i | −0.164550 | + | 0.285009i | ||||
\(579\) | −2050.97 | + | 3552.38i | −0.147211 | + | 0.254978i | ||||
\(580\) | −4355.91 | −0.311843 | ||||||||
\(581\) | 18401.6 | − | 31872.6i | 1.31399 | − | 2.27590i | ||||
\(582\) | −10247.6 | − | 17749.3i | −0.729855 | − | 1.26415i | ||||
\(583\) | 922.142 | + | 1597.20i | 0.0655081 | + | 0.113463i | ||||
\(584\) | −6522.62 | −0.462171 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −999.439 | −0.0704547 | ||||||||
\(587\) | 2719.70 | + | 4710.65i | 0.191233 | + | 0.331226i | 0.945659 | − | 0.325160i | \(-0.105418\pi\) |
−0.754426 | + | 0.656385i | \(0.772085\pi\) | |||||||
\(588\) | 9553.63 | + | 16547.4i | 0.670042 | + | 1.16055i | ||||
\(589\) | −324.703 | + | 562.402i | −0.0227150 | + | 0.0393436i | ||||
\(590\) | −2445.04 | −0.170611 | ||||||||
\(591\) | 19472.6 | − | 33727.5i | 1.35532 | − | 2.34749i | ||||
\(592\) | −537.993 | + | 931.831i | −0.0373503 | + | 0.0646926i | ||||
\(593\) | −28405.8 | −1.96709 | −0.983547 | − | 0.180651i | \(-0.942180\pi\) | ||||
−0.983547 | + | 0.180651i | \(0.942180\pi\) | |||||||
\(594\) | 2216.97 | − | 3839.90i | 0.153137 | − | 0.265241i | ||||
\(595\) | −2155.88 | − | 3734.10i | −0.148542 | − | 0.257282i | ||||
\(596\) | −4874.65 | − | 8443.14i | −0.335022 | − | 0.580276i | ||||
\(597\) | −3180.67 | −0.218051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10482.3 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(600\) | 10328.3 | + | 17889.1i | 0.702750 | + | 1.21720i | ||||
\(601\) | −1599.77 | − | 2770.88i | −0.108579 | − | 0.188064i | 0.806616 | − | 0.591076i | \(-0.201297\pi\) |
−0.915195 | + | 0.403012i | \(0.867963\pi\) | |||||||
\(602\) | 3210.51 | − | 5560.77i | 0.217360 | − | 0.376479i | ||||
\(603\) | 24806.3 | 1.67527 | ||||||||
\(604\) | −7771.28 | + | 13460.3i | −0.523525 | + | 0.906772i | ||||
\(605\) | −1955.45 | + | 3386.95i | −0.131406 | + | 0.227602i | ||||
\(606\) | −4560.20 | −0.305686 | ||||||||
\(607\) | −5671.40 | + | 9823.15i | −0.379234 | + | 0.656853i | −0.990951 | − | 0.134224i | \(-0.957146\pi\) |
0.611717 | + | 0.791077i | \(0.290479\pi\) | |||||||
\(608\) | 2244.22 | + | 3887.10i | 0.149696 | + | 0.259281i | ||||
\(609\) | −25951.9 | − | 44950.0i | −1.72680 | − | 2.99091i | ||||
\(610\) | −763.629 | −0.0506859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −11996.7 | −0.792384 | ||||||||
\(613\) | −7192.70 | − | 12458.1i | −0.473916 | − | 0.820846i | 0.525638 | − | 0.850708i | \(-0.323826\pi\) |
−0.999554 | + | 0.0298622i | \(0.990493\pi\) | |||||||
\(614\) | −78.3944 | − | 135.783i | −0.00515267 | − | 0.00892469i | ||||
\(615\) | −2479.95 | + | 4295.39i | −0.162603 | + | 0.281637i | ||||
\(616\) | −8783.39 | −0.574502 | ||||||||
\(617\) | −11028.4 | + | 19101.7i | −0.719588 | + | 1.24636i | 0.241575 | + | 0.970382i | \(0.422336\pi\) |
−0.961163 | + | 0.275981i | \(0.910997\pi\) | |||||||
\(618\) | 2188.24 | − | 3790.14i | 0.142433 | − | 0.246702i | ||||
\(619\) | 13621.4 | 0.884477 | 0.442238 | − | 0.896898i | \(-0.354185\pi\) | ||||
0.442238 | + | 0.896898i | \(0.354185\pi\) | |||||||
\(620\) | −268.324 | + | 464.751i | −0.0173809 | + | 0.0301046i | ||||
\(621\) | −11418.0 | − | 19776.6i | −0.737824 | − | 1.27795i | ||||
\(622\) | −3028.57 | − | 5245.63i | −0.195232 | − | 0.338152i | ||||
\(623\) | −11954.7 | −0.768789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11029.2 | 0.705866 | ||||||||
\(626\) | −2958.67 | − | 5124.57i | −0.188901 | − | 0.327187i | ||||
\(627\) | −1588.47 | − | 2751.31i | −0.101176 | − | 0.175242i | ||||
\(628\) | 9023.27 | − | 15628.8i | 0.573356 | − | 0.993082i | ||||
\(629\) | 4195.92 | 0.265982 | ||||||||
\(630\) | 3659.51 | − | 6338.46i | 0.231426 | − | 0.400842i | ||||
\(631\) | 9368.74 | − | 16227.1i | 0.591068 | − | 1.02376i | −0.403021 | − | 0.915191i | \(-0.632040\pi\) |
0.994089 | − | 0.108569i | \(-0.0346267\pi\) | |||||||
\(632\) | −12419.6 | −0.781683 | ||||||||
\(633\) | −9216.83 | + | 15964.0i | −0.578730 | + | 1.00239i | ||||
\(634\) | 3440.73 | + | 5959.52i | 0.215534 | + | 0.373317i | ||||
\(635\) | 1540.68 | + | 2668.54i | 0.0962836 | + | 0.166768i | ||||
\(636\) | 5836.91 | 0.363913 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5240.75 | 0.325209 | ||||||||
\(639\) | −9944.18 | − | 17223.8i | −0.615627 | − | 1.06630i | ||||
\(640\) | 2108.67 | + | 3652.33i | 0.130239 | + | 0.225580i | ||||
\(641\) | −14899.4 | + | 25806.5i | −0.918081 | + | 1.59016i | −0.115753 | + | 0.993278i | \(0.536928\pi\) |
−0.802327 | + | 0.596884i | \(0.796405\pi\) | |||||||
\(642\) | −19455.6 | −1.19603 | ||||||||
\(643\) | 11491.8 | − | 19904.3i | 0.704807 | − | 1.22076i | −0.261955 | − | 0.965080i | \(-0.584367\pi\) |
0.966761 | − | 0.255681i | \(-0.0822996\pi\) | |||||||
\(644\) | −9275.77 | + | 16066.1i | −0.567573 | + | 0.983064i | ||||
\(645\) | 4679.90 | 0.285692 | ||||||||
\(646\) | 833.684 | − | 1443.98i | 0.0507753 | − | 0.0879455i | ||||
\(647\) | 12452.7 | + | 21568.7i | 0.756672 | + | 1.31059i | 0.944539 | + | 0.328400i | \(0.106509\pi\) |
−0.187866 | + | 0.982195i | \(0.560157\pi\) | |||||||
\(648\) | −3265.36 | − | 5655.77i | −0.197956 | − | 0.342870i | ||||
\(649\) | −6709.39 | −0.405804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6394.54 | −0.384980 | ||||||||
\(652\) | 9125.03 | + | 15805.0i | 0.548104 | + | 0.949344i | ||||
\(653\) | −5038.92 | − | 8727.67i | −0.301973 | − | 0.523033i | 0.674610 | − | 0.738175i | \(-0.264312\pi\) |
−0.976583 | + | 0.215142i | \(0.930979\pi\) | |||||||
\(654\) | 5757.87 | − | 9972.93i | 0.344267 | − | 0.596288i | ||||
\(655\) | 1002.22 | 0.0597864 | ||||||||
\(656\) | 915.886 | − | 1586.36i | 0.0545112 | − | 0.0944162i | ||||
\(657\) | 7457.28 | − | 12916.4i | 0.442825 | − | 0.766996i | ||||
\(658\) | 19816.5 | 1.17406 | ||||||||
\(659\) | −6167.30 | + | 10682.1i | −0.364558 | + | 0.631433i | −0.988705 | − | 0.149874i | \(-0.952113\pi\) |
0.624147 | + | 0.781307i | \(0.285447\pi\) | |||||||
\(660\) | −1312.66 | − | 2273.59i | −0.0774169 | − | 0.134090i | ||||
\(661\) | 6374.56 | + | 11041.1i | 0.375101 | + | 0.649694i | 0.990342 | − | 0.138645i | \(-0.0442747\pi\) |
−0.615241 | + | 0.788339i | \(0.710941\pi\) | |||||||
\(662\) | 6451.54 | 0.378771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28678.1 | 1.67609 | ||||||||
\(665\) | −1160.04 | − | 2009.26i | −0.0676460 | − | 0.117166i | ||||
\(666\) | 3561.20 | + | 6168.18i | 0.207198 | + | 0.358877i | ||||
\(667\) | 13495.7 | − | 23375.2i | 0.783440 | − | 1.35696i | ||||
\(668\) | 17388.3 | 1.00715 | ||||||||
\(669\) | 25734.5 | − | 44573.4i | 1.48722 | − | 2.57594i | ||||
\(670\) | −1424.54 | + | 2467.37i | −0.0821413 | + | 0.142273i | ||||
\(671\) | −2095.46 | −0.120558 | ||||||||
\(672\) | −22098.3 | + | 38275.3i | −1.26854 | + | 2.19718i | ||||
\(673\) | 6809.12 | + | 11793.7i | 0.390004 | + | 0.675506i | 0.992450 | − | 0.122654i | \(-0.0391404\pi\) |
−0.602446 | + | 0.798160i | \(0.705807\pi\) | |||||||
\(674\) | −3560.98 | − | 6167.80i | −0.203507 | − | 0.352485i | ||||
\(675\) | −20896.7 | −1.19158 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9655.67 | 0.548150 | 0.274075 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274075 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(678\) | 10947.7 | + | 18962.0i | 0.620126 | + | 1.07409i | ||||
\(679\) | −20535.9 | − | 35569.3i | −1.16067 | − | 2.01034i | ||||
\(680\) | 1679.92 | − | 2909.70i | 0.0947381 | − | 0.164091i | ||||
\(681\) | −7778.51 | −0.437699 | ||||||||
\(682\) | 322.830 | − | 559.158i | 0.0181258 | − | 0.0313948i | ||||
\(683\) | −8158.38 | + | 14130.7i | −0.457060 | + | 0.791650i | −0.998804 | − | 0.0488929i | \(-0.984431\pi\) |
0.541744 | + | 0.840543i | \(0.317764\pi\) | |||||||
\(684\) | −6455.25 | −0.360852 | ||||||||
\(685\) | −4703.80 | + | 8147.23i | −0.262369 | + | 0.454437i | ||||
\(686\) | −1116.00 | − | 1932.97i | −0.0621123 | − | 0.107582i | ||||
\(687\) | −2725.75 | − | 4721.14i | −0.151374 | − | 0.262188i | ||||
\(688\) | −1728.37 | −0.0957753 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5928.30 | 0.327082 | ||||||||
\(691\) | −1175.42 | − | 2035.89i | −0.0647106 | − | 0.112082i | 0.831855 | − | 0.554993i | \(-0.187279\pi\) |
−0.896566 | + | 0.442911i | \(0.853946\pi\) | |||||||
\(692\) | 271.320 | + | 469.940i | 0.0149047 | + | 0.0258157i | ||||
\(693\) | 10042.0 | − | 17393.3i | 0.550454 | − | 0.953414i | ||||
\(694\) | −15723.9 | −0.860045 | ||||||||
\(695\) | −3559.12 | + | 6164.58i | −0.194252 | + | 0.336455i | ||||
\(696\) | 20222.4 | − | 35026.2i | 1.10133 | − | 1.90756i | ||||
\(697\) | −7143.20 | −0.388189 | ||||||||
\(698\) | 4590.44 | − | 7950.87i | 0.248926 | − | 0.431153i | ||||
\(699\) | −10003.5 | − | 17326.6i | −0.541299 | − | 0.937558i | ||||
\(700\) | 8488.05 | + | 14701.7i | 0.458312 | + | 0.793819i | ||||
\(701\) | −8076.90 | −0.435179 | −0.217589 | − | 0.976040i | \(-0.569819\pi\) | ||||
−0.217589 | + | 0.976040i | \(0.569819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2257.76 | 0.121128 | ||||||||
\(704\) | −1533.93 | − | 2656.85i | −0.0821197 | − | 0.142236i | ||||
\(705\) | 7221.55 | + | 12508.1i | 0.385786 | + | 0.668202i | ||||
\(706\) | −7138.30 | + | 12363.9i | −0.380529 | + | 0.659095i | ||||
\(707\) | −9138.55 | −0.486125 | ||||||||
\(708\) | −10617.2 | + | 18389.5i | −0.563584 | + | 0.976156i | ||||
\(709\) | 6812.44 | − | 11799.5i | 0.360856 | − | 0.625021i | −0.627246 | − | 0.778821i | \(-0.715818\pi\) |
0.988102 | + | 0.153801i | \(0.0491513\pi\) | |||||||
\(710\) | 2284.23 | 0.120741 | ||||||||
\(711\) | 14199.2 | − | 24593.8i | 0.748962 | − | 1.29724i | ||||
\(712\) | −4657.71 | − | 8067.40i | −0.245162 | − | 0.424633i | ||||
\(713\) | −1662.67 | − | 2879.82i | −0.0873315 | − | 0.151263i | ||||
\(714\) | 16418.2 | 0.860553 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 193.069 | 0.0100773 | ||||||||
\(717\) | −2364.93 | − | 4096.18i | −0.123180 | − | 0.213354i | ||||
\(718\) | −2150.51 | − | 3724.79i | −0.111778 | − | 0.193605i | ||||
\(719\) | −8117.89 | + | 14060.6i | −0.421066 | + | 0.729307i | −0.996044 | − | 0.0888616i | \(-0.971677\pi\) |
0.574978 | + | 0.818169i | \(0.305010\pi\) | |||||||
\(720\) | −1970.09 | −0.101973 | ||||||||
\(721\) | 4385.19 | − | 7595.36i | 0.226509 | − | 0.392325i | ||||
\(722\) | −4906.75 | + | 8498.75i | −0.252923 | + | 0.438076i | ||||
\(723\) | 47123.8 | 2.42400 | ||||||||
\(724\) | −3418.54 | + | 5921.08i | −0.175482 | + | 0.303944i | ||||
\(725\) | −12349.6 | − | 21390.1i | −0.632623 | − | 1.09574i | ||||
\(726\) | −7445.91 | − | 12896.7i | −0.380638 | − | 0.659285i | ||||
\(727\) | 24181.2 | 1.23361 | 0.616803 | − | 0.787118i | \(-0.288428\pi\) | ||||
0.616803 | + | 0.787118i | \(0.288428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | 856.490 | + | 1483.48i | 0.0434248 | + | 0.0752139i | ||||
\(731\) | 3369.98 | + | 5836.98i | 0.170511 | + | 0.295333i | ||||
\(732\) | −3315.93 | + | 5743.36i | −0.167432 | + | 0.290001i | ||||
\(733\) | 3053.70 | 0.153876 | 0.0769379 | − | 0.997036i | \(-0.475486\pi\) | ||||
0.0769379 | + | 0.997036i | \(0.475486\pi\) | |||||||
\(734\) | 2373.71 | − | 4111.38i | 0.119367 | − | 0.206749i | ||||
\(735\) | 6118.03 | − | 10596.7i | 0.307030 | − | 0.531791i | ||||
\(736\) | −22983.4 | −1.15106 | ||||||||
\(737\) | −3909.05 | + | 6770.67i | −0.195375 | + | 0.338400i | ||||
\(738\) | −6062.63 | − | 10500.8i | −0.302396 | − | 0.523766i | ||||
\(739\) | 4016.81 | + | 6957.32i | 0.199947 | + | 0.346318i | 0.948511 | − | 0.316744i | \(-0.102590\pi\) |
−0.748564 | + | 0.663062i | \(0.769256\pi\) | |||||||
\(740\) | 1865.74 | 0.0926836 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5128.54 | −0.253739 | ||||||||
\(743\) | 8069.81 | + | 13977.3i | 0.398456 | + | 0.690146i | 0.993536 | − | 0.113521i | \(-0.0362128\pi\) |
−0.595080 | + | 0.803667i | \(0.702880\pi\) | |||||||
\(744\) | −2491.40 | − | 4315.22i | −0.122767 | − | 0.212639i | ||||
\(745\) | −3121.67 | + | 5406.89i | −0.153515 | + | 0.265897i | ||||
\(746\) | 8408.53 | 0.412678 | ||||||||
\(747\) | −32787.5 | + | 56789.6i | −1.60593 | + | 2.78156i | ||||
\(748\) | 1890.48 | − | 3274.41i | 0.0924102 | − | 0.160059i | ||||
\(749\) | −38988.7 | −1.90202 | ||||||||
\(750\) | 5731.19 | − | 9926.71i | 0.279031 | − | 0.483296i | ||||
\(751\) | 9245.56 | + | 16013.8i | 0.449235 | + | 0.778097i | 0.998336 | − | 0.0576584i | \(-0.0183634\pi\) |
−0.549102 | + | 0.835755i | \(0.685030\pi\) | |||||||
\(752\) | −2667.04 | − | 4619.45i | −0.129331 | − | 0.224008i | ||||
\(753\) | −45344.5 | −2.19448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9953.28 | 0.479784 | ||||||||
\(756\) | −14060.7 | − | 24353.9i | −0.676434 | − | 1.17162i | ||||
\(757\) | −80.3149 | − | 139.109i | −0.00385613 | − | 0.00667902i | 0.864091 | − | 0.503336i | \(-0.167894\pi\) |
−0.867947 | + | 0.496657i | \(0.834561\pi\) | |||||||
\(758\) | −2673.59 | + | 4630.79i | −0.128112 | + | 0.221897i | ||||
\(759\) | 16267.7 | 0.777973 | ||||||||
\(760\) | 903.936 | − | 1565.66i | 0.0431437 | − | 0.0747271i | ||||
\(761\) | −13399.5 | + | 23208.7i | −0.638282 | + | 1.10554i | 0.347528 | + | 0.937670i | \(0.387021\pi\) |
−0.985810 | + | 0.167867i | \(0.946312\pi\) | |||||||
\(762\) | −11733.1 | −0.557803 | ||||||||
\(763\) | 11538.7 | − | 19985.6i | 0.547481 | − | 0.948264i | ||||
\(764\) | 11903.9 | + | 20618.2i | 0.563703 | + | 0.976363i | ||||
\(765\) | 3841.28 | + | 6653.30i | 0.181545 | + | 0.314445i | ||||
\(766\) | 598.052 | 0.0282095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30025.1 | −1.41073 | ||||||||
\(769\) | 2572.91 | + | 4456.41i | 0.120652 | + | 0.208976i | 0.920025 | − | 0.391860i | \(-0.128168\pi\) |
−0.799373 | + | 0.600835i | \(0.794835\pi\) | |||||||
\(770\) | 1153.35 | + | 1997.67i | 0.0539792 | + | 0.0934947i | ||||
\(771\) | −2858.15 | + | 4950.45i | −0.133507 | + | 0.231240i | ||||
\(772\) | −2626.83 | −0.122463 | ||||||||
\(773\) | −6405.28 | + | 11094.3i | −0.298036 | + | 0.516214i | −0.975687 | − | 0.219170i | \(-0.929665\pi\) |
0.677650 | + | 0.735384i | \(0.262998\pi\) | |||||||
\(774\) | −5720.39 | + | 9908.01i | −0.265653 | + | 0.460124i | ||||
\(775\) | −3042.94 | −0.141039 | ||||||||
\(776\) | 16002.1 | − | 27716.5i | 0.740262 | − | 1.28217i | ||||
\(777\) | 11115.8 | + | 19253.1i | 0.513227 | + | 0.888934i | ||||
\(778\) | 6705.57 | + | 11614.4i | 0.309006 | + | 0.535214i | ||||
\(779\) | −3843.64 | −0.176781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6268.13 | 0.287185 | ||||||||
\(782\) | 4268.94 | + | 7394.03i | 0.195214 | + | 0.338120i | ||||
\(783\) | 20457.5 | + | 35433.4i | 0.933705 | + | 1.61722i | ||||
\(784\) | −2259.49 | + | 3913.55i | −0.102929 | + | 0.178278i | ||||
\(785\) | −11556.8 | −0.525452 | ||||||||
\(786\) | −1908.11 | + | 3304.95i | −0.0865905 | + | 0.149979i | ||||
\(787\) | −14036.5 | + | 24311.9i | −0.635764 | + | 1.10118i | 0.350588 | + | 0.936530i | \(0.385982\pi\) |
−0.986353 | + | 0.164646i | \(0.947352\pi\) | |||||||
\(788\) | 24940.0 | 1.12748 | ||||||||
\(789\) | −14097.2 | + | 24417.0i | −0.636087 | + | 1.10174i | ||||
\(790\) | 1630.82 | + | 2824.66i | 0.0734455 | + | 0.127211i | ||||
\(791\) | 21939.1 | + | 37999.6i | 0.986173 | + | 1.70810i | ||||
\(792\) | 15650.0 | 0.702144 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11304.3 | 0.505259 | ||||||||
\(795\) | −1868.94 | − | 3237.11i | −0.0833769 | − | 0.144413i | ||||
\(796\) | −1018.43 | − | 1763.98i | −0.0453485 | − | 0.0785459i | ||||
\(797\) | −15046.6 | + | 26061.4i | −0.668729 | + | 1.15827i | 0.309531 | + | 0.950889i | \(0.399828\pi\) |
−0.978260 | + | 0.207383i | \(0.933505\pi\) | |||||||
\(798\) | 8834.35 | 0.391896 | ||||||||
\(799\) | −10400.4 | + | 18014.1i | −0.460501 | + | 0.797612i | ||||
\(800\) | −10515.8 | + | 18213.9i | −0.464737 | + | 0.804947i | ||||
\(801\) | 21300.6 | 0.939598 | ||||||||
\(802\) | 3333.62 | − | 5774.00i | 0.146776 | − | 0.254223i | ||||
\(803\) | 2350.28 | + | 4070.80i | 0.103287 | + | 0.178899i | ||||
\(804\) | 12371.6 | + | 21428.3i | 0.542678 | + | 0.939946i | ||||
\(805\) | 11880.2 | 0.520151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22456.8 | −0.979575 | ||||||||
\(808\) | −3560.50 | − | 6166.96i | −0.155022 | − | 0.268506i | ||||
\(809\) | 12168.6 | + | 21076.6i | 0.528831 | + | 0.915961i | 0.999435 | + | 0.0336170i | \(0.0107026\pi\) |
−0.470604 | + | 0.882344i | \(0.655964\pi\) | |||||||
\(810\) | −857.553 | + | 1485.33i | −0.0371992 | + | 0.0644309i | ||||
\(811\) | 19078.7 | 0.826071 | 0.413035 | − | 0.910715i | \(-0.364469\pi\) | ||||
0.413035 | + | 0.910715i | \(0.364469\pi\) | |||||||
\(812\) | 16619.3 | − | 28785.4i | 0.718254 | − | 1.24405i | ||||
\(813\) | −4294.27 | + | 7437.89i | −0.185248 | + | 0.320859i | ||||
\(814\) | −2244.74 | −0.0966559 | ||||||||
\(815\) | 5843.56 | − | 10121.3i | 0.251155 | − | 0.435013i | ||||
\(816\) | −2209.67 | − | 3827.25i | −0.0947963 | − | 0.164192i | ||||
\(817\) | 1813.33 | + | 3140.78i | 0.0776505 | + | 0.134495i | ||||
\(818\) | −21178.6 | −0.905248 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3176.26 | −0.135268 | ||||||||
\(821\) | −1006.96 | − | 1744.10i | −0.0428052 | − | 0.0741408i | 0.843829 | − | 0.536612i | \(-0.180296\pi\) |
−0.886634 | + | 0.462471i | \(0.846963\pi\) | |||||||
\(822\) | −17911.0 | − | 31022.7i | −0.759996 | − | 1.31635i | ||||
\(823\) | 3846.05 | − | 6661.55i | 0.162898 | − | 0.282147i | −0.773009 | − | 0.634395i | \(-0.781249\pi\) |
0.935907 | + | 0.352248i | \(0.114583\pi\) | |||||||
\(824\) | 6834.10 | 0.288929 | ||||||||
\(825\) | 7443.12 | − | 12891.9i | 0.314105 | − | 0.544045i | ||||
\(826\) | 9328.66 | − | 16157.7i | 0.392961 | − | 0.680628i | ||||
\(827\) | −4762.76 | −0.200263 | −0.100131 | − | 0.994974i | \(-0.531926\pi\) | ||||
−0.100131 | + | 0.994974i | \(0.531926\pi\) | |||||||
\(828\) | 16527.3 | − | 28626.1i | 0.693675 | − | 1.20148i | ||||
\(829\) | −9988.83 | − | 17301.2i | −0.418488 | − | 0.724842i | 0.577300 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916901i | \(0.970773\pi\) | |||||||
\(830\) | −3765.73 | − | 6522.44i | −0.157483 | − | 0.272768i | ||||
\(831\) | 70714.0 | 2.95191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17622.3 | 0.732984 | ||||||||
\(834\) | −13552.3 | − | 23473.3i | −0.562683 | − | 0.974596i | ||||
\(835\) | −5567.63 | − | 9643.43i | −0.230750 | − | 0.399670i | ||||
\(836\) | 1017.24 | − | 1761.91i | 0.0420836 | − | 0.0728909i | ||||
\(837\) | 5040.72 | 0.208164 | ||||||||
\(838\) | −11381.3 | + | 19713.0i | −0.469165 | + | 0.812617i | ||||
\(839\) | 15307.9 | − | 26514.0i | 0.629901 | − | 1.09102i | −0.357670 | − | 0.933848i | \(-0.616429\pi\) |
0.987571 | − | 0.157172i | \(-0.0502378\pi\) | |||||||
\(840\) | 17801.7 | 0.731210 | ||||||||
\(841\) | −11985.5 | + | 20759.5i | −0.491431 | + | 0.851183i | ||||
\(842\) | 12374.0 | + | 21432.5i | 0.506458 | + | 0.877211i | ||||
\(843\) | −6662.04 | − | 11539.0i | −0.272186 | − | 0.471440i | ||||
\(844\) | −11804.7 | −0.481439 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −35308.5 | −1.43491 | ||||||||
\(847\) | −14921.4 | − | 25844.7i | −0.605321 | − | 1.04845i | ||||
\(848\) | 690.233 | + | 1195.52i | 0.0279513 | + | 0.0484131i | ||||
\(849\) | 30244.3 | − | 52384.7i | 1.22259 | − | 2.11760i | ||||
\(850\) | 7812.83 | 0.315268 | ||||||||
\(851\) | −5780.51 | + | 10012.1i | −0.232848 | + | 0.403304i | ||||
\(852\) | 9918.89 | − | 17180.0i | 0.398845 | − | 0.690819i | ||||
\(853\) | 5660.88 | 0.227227 | 0.113614 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113614 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(854\) | 2913.50 | − | 5046.34i | 0.116742 | − | 0.202204i | ||||
\(855\) | 2066.93 | + | 3580.03i | 0.0826755 | + | 0.143198i | ||||
\(856\) | −15190.5 | − | 26310.7i | −0.606543 | − | 1.05056i | ||||
\(857\) | 41346.1 | 1.64802 | 0.824012 | − | 0.566572i | \(-0.191731\pi\) | ||||
0.824012 | + | 0.566572i | \(0.191731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34810.5 | −1.38268 | −0.691339 | − | 0.722530i | \(-0.742979\pi\) | ||||
−0.691339 | + | 0.722530i | \(0.742979\pi\) | |||||||
\(860\) | 1498.48 | + | 2595.44i | 0.0594159 | + | 0.102911i | ||||
\(861\) | −18923.7 | − | 32776.8i | −0.749033 | − | 1.29736i | ||||
\(862\) | 8350.19 | − | 14462.9i | 0.329940 | − | 0.571473i | ||||
\(863\) | −8360.51 | −0.329774 | −0.164887 | − | 0.986312i | \(-0.552726\pi\) | ||||
−0.164887 | + | 0.986312i | \(0.552726\pi\) | |||||||
\(864\) | 17419.7 | − | 30171.9i | 0.685916 | − | 1.18804i | ||||
\(865\) | 173.750 | − | 300.944i | 0.00682969 | − | 0.0118294i | ||||
\(866\) | 25108.2 | 0.985233 | ||||||||
\(867\) | 12717.0 | − | 22026.5i | 0.498146 | − | 0.862815i | ||||
\(868\) | −2047.49 | − | 3546.36i | −0.0800651 | − | 0.138677i | ||||
\(869\) | 4475.11 | + | 7751.11i | 0.174692 | + | 0.302576i | ||||
\(870\) | −10621.6 | −0.413917 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17982.4 | 0.698352 | ||||||||
\(873\) | 36590.3 | + | 63376.3i | 1.41855 | + | 2.45700i | ||||
\(874\) | 2297.05 | + | 3978.61i | 0.0889003 | + | 0.153980i | ||||
\(875\) | 11485.2 | − | 19892.9i | 0.443737 | − | 0.768576i | ||||
\(876\) | 14876.6 | 0.573784 | ||||||||
\(877\) | 20289.7 | − | 35142.7i | 0.781223 | − | 1.35312i | −0.150006 | − | 0.988685i | \(-0.547929\pi\) |
0.931229 | − | 0.364434i | \(-0.118737\pi\) | |||||||
\(878\) | 4712.61 | − | 8162.48i | 0.181142 | − | 0.313748i | ||||
\(879\) | 5558.43 | 0.213289 | ||||||||
\(880\) | 310.452 | − | 537.718i | 0.0118924 | − | 0.0205983i | ||||
\(881\) | −5222.62 | − | 9045.84i | −0.199721 | − | 0.345927i | 0.748717 | − | 0.662890i | \(-0.230670\pi\) |
−0.948438 | + | 0.316963i | \(0.897337\pi\) | |||||||
\(882\) | 14956.5 | + | 25905.4i | 0.570989 | + | 0.988981i | ||||
\(883\) | 18227.6 | 0.694685 | 0.347343 | − | 0.937738i | \(-0.387084\pi\) | ||||
0.347343 | + | 0.937738i | \(0.387084\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13598.2 | 0.516496 | ||||||||
\(886\) | 7964.96 | + | 13795.7i | 0.302018 | + | 0.523111i | ||||
\(887\) | 11758.8 | + | 20366.9i | 0.445122 | + | 0.770974i | 0.998061 | − | 0.0622477i | \(-0.0198269\pi\) |
−0.552938 | + | 0.833222i | \(0.686494\pi\) | |||||||
\(888\) | −8661.72 | + | 15002.5i | −0.327329 | + | 0.566950i | ||||
\(889\) | −23512.9 | −0.887061 | ||||||||
\(890\) | −1223.21 | + | 2118.67i | −0.0460699 | + | 0.0797955i | ||||
\(891\) | −2353.20 | + | 4075.86i | −0.0884794 | + | 0.153251i | ||||
\(892\) | 32960.1 | 1.23720 | ||||||||
\(893\) | −5596.30 | + | 9693.07i | −0.209712 | + | 0.363232i | ||||
\(894\) | −11886.6 | − | 20588.1i | −0.444683 | − | 0.770213i | ||||
\(895\) | −61.8196 | − | 107.075i | −0.00230883 | − | 0.00399901i | ||||
\(896\) | −32181.2 | −1.19989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9092.21 | 0.337874 | ||||||||
\(899\) | 2978.98 | + | 5159.74i | 0.110517 | + | 0.191420i | ||||
\(900\) | −15123.7 | − | 26195.1i | −0.560139 | − | 0.970189i | ||||
\(901\) | 2691.64 | − | 4662.06i | 0.0995245 | − | 0.172381i | ||||
\(902\) | 3821.47 | 0.141065 | ||||||||
\(903\) | −17855.4 | + | 30926.5i | −0.658019 | + | 1.13972i | ||||
\(904\) | −17095.5 | + | 29610.2i | −0.628968 | + | 1.08940i | ||||
\(905\) | 4378.38 | 0.160820 | ||||||||
\(906\) | −18949.9 | + | 32822.1i | −0.694886 | + | 1.20358i | ||||
\(907\) | 15282.3 | + | 26469.7i | 0.559471 | + | 0.969032i | 0.997541 | + | 0.0700908i | \(0.0223289\pi\) |
−0.438070 | + | 0.898941i | \(0.644338\pi\) | |||||||
\(908\) | −2490.63 | − | 4313.90i | −0.0910292 | − | 0.157667i | ||||
\(909\) | 16282.8 | 0.594132 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32766.5 | −1.19166 | −0.595831 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595831 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(912\) | −1188.99 | − | 2059.38i | −0.0431702 | − | 0.0747730i | ||||
\(913\) | −10333.5 | − | 17898.1i | −0.374577 | − | 0.648786i | ||||
\(914\) | 3608.44 | − | 6249.99i | 0.130587 | − | 0.226183i | ||||
\(915\) | 4246.96 | 0.153443 | ||||||||
\(916\) | 1745.54 | − | 3023.36i | 0.0629632 | − | 0.109055i | ||||
\(917\) | −3823.82 | + | 6623.05i | −0.137703 | + | 0.238509i | ||||
\(918\) | −12942.2 | −0.465312 | ||||||||
\(919\) | −10343.4 | + | 17915.2i | −0.371269 | + | 0.643057i | −0.989761 | − | 0.142734i | \(-0.954411\pi\) |
0.618492 | + | 0.785791i | \(0.287744\pi\) | |||||||
\(920\) | 4628.68 | + | 8017.10i | 0.165873 | + | 0.287300i | ||||
\(921\) | 435.995 | + | 755.165i | 0.0155988 | + | 0.0270179i | ||||
\(922\) | −8007.28 | −0.286015 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20033.0 | 0.713242 | ||||||||
\(925\) | 5289.62 | + | 9161.88i | 0.188023 | + | 0.325666i | ||||
\(926\) | 5064.32 | + | 8771.67i | 0.179724 | + | 0.311290i | ||||
\(927\) | −7813.39 | + | 13533.2i | −0.276834 | + | 0.479491i | ||||
\(928\) | 41179.0 | 1.45665 | ||||||||
\(929\) | −22816.1 | + | 39518.6i | −0.805782 | + | 1.39566i | 0.109979 | + | 0.993934i | \(0.464922\pi\) |
−0.915762 | + | 0.401722i | \(0.868412\pi\) | |||||||
\(930\) | −654.294 | + | 1133.27i | −0.0230700 | + | 0.0399585i | ||||
\(931\) | 9482.26 | 0.333801 | ||||||||
\(932\) | 6406.14 | − | 11095.8i | 0.225150 | − | 0.389972i | ||||
\(933\) | 16843.5 | + | 29173.9i | 0.591032 | + | 1.02370i | ||||
\(934\) | 10133.0 | + | 17550.8i | 0.354990 | + | 0.614860i | ||||
\(935\) | −2421.28 | −0.0846892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17761.4 | −0.619253 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(938\) | −10870.2 | − | 18827.7i | −0.378384 | − | 0.655380i | ||||
\(939\) | 16454.8 | + | 28500.5i | 0.571866 | + | 0.990501i | ||||
\(940\) | −4624.60 | + | 8010.04i | −0.160466 | + | 0.277935i | ||||
\(941\) | −44888.3 | −1.55507 | −0.777534 | − | 0.628841i | \(-0.783530\pi\) | ||||
−0.777534 | + | 0.628841i | \(0.783530\pi\) | |||||||
\(942\) | 22002.8 | − | 38109.9i | 0.761029 | − | 1.31814i | ||||
\(943\) | 9840.83 | − | 17044.8i | 0.339832 | − | 0.588606i | ||||
\(944\) | −5022.05 | −0.173150 | ||||||||
\(945\) | −9004.32 | + | 15595.9i | −0.309958 | + | 0.536864i | ||||
\(946\) | −1802.87 | − | 3122.67i | −0.0619624 | − | 0.107322i | ||||
\(947\) | −8034.78 | − | 13916.6i | −0.275708 | − | 0.477540i | 0.694606 | − | 0.719391i | \(-0.255579\pi\) |
−0.970313 | + | 0.241851i | \(0.922246\pi\) | |||||||
\(948\) | 28326.2 | 0.970457 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4203.96 | 0.143573 | ||||||||
\(951\) | −19135.8 | − | 33144.2i | −0.652493 | − | 1.13015i | ||||
\(952\) | 12818.9 | + | 22203.0i | 0.436411 | + | 0.755887i | ||||
\(953\) | −1756.02 | + | 3041.51i | −0.0596883 | + | 0.103383i | −0.894325 | − | 0.447417i | \(-0.852344\pi\) |
0.834637 | + | 0.550800i | \(0.185677\pi\) | |||||||
\(954\) | 9137.88 | 0.310115 | ||||||||
\(955\) | 7623.14 | − | 13203.7i | 0.258303 | − | 0.447393i | ||||
\(956\) | 1514.47 | − | 2623.14i | 0.0512359 | − | 0.0887432i | ||||
\(957\) | −29146.7 | −0.984513 | ||||||||
\(958\) | −4535.50 | + | 7855.72i | −0.152960 | + | 0.264934i | ||||
\(959\) | −35893.2 | − | 62168.9i | −1.20861 | − | 2.09337i | ||||
\(960\) | 3108.89 | + | 5384.75i | 0.104520 | + | 0.181034i | ||||
\(961\) | −29057.0 | −0.975361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69468.9 | 2.32461 | ||||||||
\(964\) | 15088.8 | + | 26134.5i | 0.504125 | + | 0.873170i | ||||
\(965\) | 841.097 | + | 1456.82i | 0.0280579 | + | 0.0485977i | ||||
\(966\) | −22618.5 | + | 39176.4i | −0.753352 | + | 1.30484i | ||||
\(967\) | −37011.9 | −1.23084 | −0.615421 | − | 0.788199i | \(-0.711014\pi\) | ||||
−0.615421 | + | 0.788199i | \(0.711014\pi\) | |||||||
\(968\) | 11627.2 | − | 20138.9i | 0.386066 | − | 0.668685i | ||||
\(969\) | −4636.58 | + | 8030.79i | −0.153714 | + | 0.266240i | ||||
\(970\) | −8405.00 | −0.278215 | ||||||||
\(971\) | −9766.15 | + | 16915.5i | −0.322771 | + | 0.559056i | −0.981059 | − | 0.193711i | \(-0.937948\pi\) |
0.658288 | + | 0.752766i | \(0.271281\pi\) | |||||||
\(972\) | −6521.55 | − | 11295.7i | −0.215205 | − | 0.372745i | ||||
\(973\) | −27158.5 | − | 47040.0i | −0.894823 | − | 1.54988i | ||||
\(974\) | 8412.30 | 0.276743 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1568.47 | −0.0514402 | ||||||||
\(977\) | −15100.6 | − | 26155.0i | −0.494485 | − | 0.856473i | 0.505495 | − | 0.862830i | \(-0.331310\pi\) |
−0.999980 | + | 0.00635674i | \(0.997977\pi\) | |||||||
\(978\) | 22250.9 | + | 38539.7i | 0.727511 | + | 1.26009i | ||||
\(979\) | −3356.60 | + | 5813.81i | −0.109579 | + | 0.189796i | ||||
\(980\) | 7835.83 | 0.255415 | ||||||||
\(981\) | −20559.2 | + | 35609.7i | −0.669119 | + | 1.15895i | ||||
\(982\) | 11913.9 | − | 20635.5i | 0.387157 | − | 0.670576i | ||||
\(983\) | −38774.9 | −1.25812 | −0.629058 | − | 0.777359i | \(-0.716559\pi\) | ||||
−0.629058 | + | 0.777359i | \(0.716559\pi\) | |||||||
\(984\) | 14745.8 | − | 25540.5i | 0.477723 | − | 0.827441i | ||||
\(985\) | −7985.65 | − | 13831.6i | −0.258319 | − | 0.447421i | ||||
\(986\) | −7648.61 | − | 13247.8i | −0.247040 | − | 0.427886i | ||||
\(987\) | −110211. | −3.55425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18570.6 | −0.597079 | ||||||||
\(990\) | −2055.01 | − | 3559.38i | −0.0659722 | − | 0.114267i | ||||
\(991\) | 13864.5 | + | 24014.0i | 0.444419 | + | 0.769757i | 0.998012 | − | 0.0630311i | \(-0.0200767\pi\) |
−0.553592 | + | 0.832788i | \(0.686743\pi\) | |||||||
\(992\) | 2536.63 | − | 4393.57i | 0.0811875 | − | 0.140621i | ||||
\(993\) | −35880.6 | −1.14666 | ||||||||
\(994\) | −8715.13 | + | 15095.1i | −0.278096 | + | 0.481676i | ||||
\(995\) | −652.192 | + | 1129.63i | −0.0207798 | + | 0.0359916i | ||||
\(996\) | −65408.2 | −2.08086 | ||||||||
\(997\) | 24459.1 | − | 42364.4i | 0.776958 | − | 1.34573i | −0.156729 | − | 0.987642i | \(-0.550095\pi\) |
0.933687 | − | 0.358090i | \(-0.116572\pi\) | |||||||
\(998\) | 1449.16 | + | 2510.01i | 0.0459641 | + | 0.0796122i | ||||
\(999\) | −8762.42 | − | 15177.0i | −0.277508 | − | 0.480658i |
(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 | 169.4.c.g.146.2 | 4 | ||
13.2 | odd | 12 | 169.4.b.f.168.3 | 4 | |||
13.3 | even | 3 | 13.4.a.b.1.1 | ✓ | 2 | ||
13.4 | even | 6 | 169.4.c.j.22.1 | 4 | |||
13.5 | odd | 4 | 169.4.e.f.23.3 | 8 | |||
13.6 | odd | 12 | 169.4.e.f.147.2 | 8 | |||
13.7 | odd | 12 | 169.4.e.f.147.3 | 8 | |||
13.8 | odd | 4 | 169.4.e.f.23.2 | 8 | |||
13.9 | even | 3 | inner | 169.4.c.g.22.2 | 4 | ||
13.10 | even | 6 | 169.4.a.g.1.2 | 2 | |||
13.11 | odd | 12 | 169.4.b.f.168.2 | 4 | |||
13.12 | even | 2 | 169.4.c.j.146.1 | 4 | |||
39.23 | odd | 6 | 1521.4.a.r.1.1 | 2 | |||
39.29 | odd | 6 | 117.4.a.d.1.2 | 2 | |||
52.3 | odd | 6 | 208.4.a.h.1.1 | 2 | |||
65.3 | odd | 12 | 325.4.b.e.274.3 | 4 | |||
65.29 | even | 6 | 325.4.a.f.1.2 | 2 | |||
65.42 | odd | 12 | 325.4.b.e.274.2 | 4 | |||
91.55 | odd | 6 | 637.4.a.b.1.1 | 2 | |||
104.3 | odd | 6 | 832.4.a.z.1.2 | 2 | |||
104.29 | even | 6 | 832.4.a.s.1.1 | 2 | |||
143.120 | odd | 6 | 1573.4.a.b.1.2 | 2 | |||
156.107 | even | 6 | 1872.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.1 | ✓ | 2 | 13.3 | even | 3 | ||
117.4.a.d.1.2 | 2 | 39.29 | odd | 6 | |||
169.4.a.g.1.2 | 2 | 13.10 | even | 6 | |||
169.4.b.f.168.2 | 4 | 13.11 | odd | 12 | |||
169.4.b.f.168.3 | 4 | 13.2 | odd | 12 | |||
169.4.c.g.22.2 | 4 | 13.9 | even | 3 | inner | ||
169.4.c.g.146.2 | 4 | 1.1 | even | 1 | trivial | ||
169.4.c.j.22.1 | 4 | 13.4 | even | 6 | |||
169.4.c.j.146.1 | 4 | 13.12 | even | 2 | |||
169.4.e.f.23.2 | 8 | 13.8 | odd | 4 | |||
169.4.e.f.23.3 | 8 | 13.5 | odd | 4 | |||
169.4.e.f.147.2 | 8 | 13.6 | odd | 12 | |||
169.4.e.f.147.3 | 8 | 13.7 | odd | 12 | |||
208.4.a.h.1.1 | 2 | 52.3 | odd | 6 | |||
325.4.a.f.1.2 | 2 | 65.29 | even | 6 | |||
325.4.b.e.274.2 | 4 | 65.42 | odd | 12 | |||
325.4.b.e.274.3 | 4 | 65.3 | odd | 12 | |||
637.4.a.b.1.1 | 2 | 91.55 | odd | 6 | |||
832.4.a.s.1.1 | 2 | 104.29 | even | 6 | |||
832.4.a.z.1.2 | 2 | 104.3 | odd | 6 | |||
1521.4.a.r.1.1 | 2 | 39.23 | odd | 6 | |||
1573.4.a.b.1.2 | 2 | 143.120 | odd | 6 | |||
1872.4.a.bb.1.2 | 2 | 156.107 | even | 6 |