Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), degree \(4\), 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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(-1.22788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.8 |
Dual form | 17.4.d.a.15.2 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.161134 | + | 0.161134i | −0.0569694 | + | 0.0569694i | −0.735018 | − | 0.678048i | \(-0.762826\pi\) |
0.678048 | + | 0.735018i | \(0.262826\pi\) | |||||||
\(3\) | 3.15299 | − | 7.61199i | 0.606793 | − | 1.46493i | −0.259675 | − | 0.965696i | \(-0.583615\pi\) |
0.866468 | − | 0.499232i | \(-0.166385\pi\) | |||||||
\(4\) | 7.94807i | 0.993509i | ||||||||
\(5\) | 2.54200 | + | 1.05293i | 0.227364 | + | 0.0941771i | 0.493457 | − | 0.869770i | \(-0.335733\pi\) |
−0.266094 | + | 0.963947i | \(0.585733\pi\) | |||||||
\(6\) | 0.718496 | + | 1.73460i | 0.0488875 | + | 0.118025i | ||||
\(7\) | −19.8837 | + | 8.23610i | −1.07362 | + | 0.444707i | −0.848266 | − | 0.529570i | \(-0.822353\pi\) |
−0.225352 | + | 0.974277i | \(0.572353\pi\) | |||||||
\(8\) | −2.56978 | − | 2.56978i | −0.113569 | − | 0.113569i | ||||
\(9\) | −28.9092 | − | 28.9092i | −1.07071 | − | 1.07071i | ||||
\(10\) | −0.579266 | + | 0.239940i | −0.0183180 | + | 0.00758756i | ||||
\(11\) | 20.8709 | + | 50.3869i | 0.572075 | + | 1.38111i | 0.899785 | + | 0.436333i | \(0.143723\pi\) |
−0.327711 | + | 0.944778i | \(0.606277\pi\) | |||||||
\(12\) | 60.5007 | + | 25.0602i | 1.45542 | + | 0.602855i | ||||
\(13\) | − | 52.4827i | − | 1.11970i | −0.828594 | − | 0.559850i | \(-0.810859\pi\) | ||
0.828594 | − | 0.559850i | \(-0.189141\pi\) | |||||||
\(14\) | 1.87682 | − | 4.53105i | 0.0358287 | − | 0.0864982i | ||||
\(15\) | 16.0298 | − | 16.0298i | 0.275925 | − | 0.275925i | ||||
\(16\) | −62.7564 | −0.980569 | ||||||||
\(17\) | 33.5380 | − | 61.5484i | 0.478479 | − | 0.878099i | ||||
\(18\) | 9.31650 | 0.121996 | ||||||||
\(19\) | 13.8808 | − | 13.8808i | 0.167604 | − | 0.167604i | −0.618321 | − | 0.785925i | \(-0.712187\pi\) |
0.785925 | + | 0.618321i | \(0.212187\pi\) | |||||||
\(20\) | −8.36878 | + | 20.2040i | −0.0935658 | + | 0.225888i | ||||
\(21\) | 177.323i | 1.84262i | ||||||||
\(22\) | −11.4821 | − | 4.75602i | −0.111272 | − | 0.0460903i | ||||
\(23\) | −5.33276 | − | 12.8744i | −0.0483460 | − | 0.116717i | 0.897862 | − | 0.440278i | \(-0.145120\pi\) |
−0.946207 | + | 0.323560i | \(0.895120\pi\) | |||||||
\(24\) | −27.6636 | + | 11.4586i | −0.235284 | + | 0.0974576i | ||||
\(25\) | −83.0352 | − | 83.0352i | −0.664282 | − | 0.664282i | ||||
\(26\) | 8.45675 | + | 8.45675i | 0.0637886 | + | 0.0637886i | ||||
\(27\) | −105.683 | + | 43.7754i | −0.753286 | + | 0.312021i | ||||
\(28\) | −65.4611 | − | 158.037i | −0.441821 | − | 1.06665i | ||||
\(29\) | 64.6920 | + | 26.7963i | 0.414241 | + | 0.171584i | 0.580063 | − | 0.814571i | \(-0.303028\pi\) |
−0.165822 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(30\) | 5.16589i | 0.0314386i | ||||||||
\(31\) | −63.9131 | + | 154.300i | −0.370295 | + | 0.893971i | 0.623405 | + | 0.781899i | \(0.285749\pi\) |
−0.993700 | + | 0.112072i | \(0.964251\pi\) | |||||||
\(32\) | 30.6704 | − | 30.6704i | 0.169432 | − | 0.169432i | ||||
\(33\) | 449.350 | 2.37036 | ||||||||
\(34\) | 4.51343 | + | 15.3216i | 0.0227661 | + | 0.0772835i | ||||
\(35\) | −59.2165 | −0.285983 | ||||||||
\(36\) | 229.772 | − | 229.772i | 1.06376 | − | 1.06376i | ||||
\(37\) | −76.0152 | + | 183.517i | −0.337752 | + | 0.815405i | 0.660179 | + | 0.751108i | \(0.270480\pi\) |
−0.997931 | + | 0.0642968i | \(0.979520\pi\) | |||||||
\(38\) | 4.47334i | 0.0190966i | ||||||||
\(39\) | −399.498 | − | 165.477i | −1.64028 | − | 0.679426i | ||||
\(40\) | −3.82658 | − | 9.23817i | −0.0151259 | − | 0.0365171i | ||||
\(41\) | 401.250 | − | 166.203i | 1.52841 | − | 0.633087i | 0.549153 | − | 0.835722i | \(-0.314950\pi\) |
0.979254 | + | 0.202634i | \(0.0649503\pi\) | |||||||
\(42\) | −28.5727 | − | 28.5727i | −0.104973 | − | 0.104973i | ||||
\(43\) | 89.9025 | + | 89.9025i | 0.318837 | + | 0.318837i | 0.848320 | − | 0.529483i | \(-0.177614\pi\) |
−0.529483 | + | 0.848320i | \(0.677614\pi\) | |||||||
\(44\) | −400.479 | + | 165.884i | −1.37215 | + | 0.568361i | ||||
\(45\) | −43.0478 | − | 103.927i | −0.142604 | − | 0.344277i | ||||
\(46\) | 2.93379 | + | 1.21522i | 0.00940357 | + | 0.00389509i | ||||
\(47\) | 207.303i | 0.643366i | 0.946847 | + | 0.321683i | \(0.104249\pi\) | ||||
−0.946847 | + | 0.321683i | \(0.895751\pi\) | |||||||
\(48\) | −197.870 | + | 477.701i | −0.595003 | + | 1.43646i | ||||
\(49\) | 84.9906 | − | 84.9906i | 0.247786 | − | 0.247786i | ||||
\(50\) | 26.7596 | 0.0756875 | ||||||||
\(51\) | −362.761 | − | 449.352i | −0.996014 | − | 1.23376i | ||||
\(52\) | 417.136 | 1.11243 | ||||||||
\(53\) | −220.673 | + | 220.673i | −0.571920 | + | 0.571920i | −0.932665 | − | 0.360745i | \(-0.882523\pi\) |
0.360745 | + | 0.932665i | \(0.382523\pi\) | |||||||
\(54\) | 9.97543 | − | 24.0828i | 0.0251386 | − | 0.0606900i | ||||
\(55\) | 150.059i | 0.367891i | ||||||||
\(56\) | 72.2616 | + | 29.9317i | 0.172435 | + | 0.0714249i | ||||
\(57\) | −61.8946 | − | 149.427i | −0.143827 | − | 0.347229i | ||||
\(58\) | −14.7419 | + | 6.10628i | −0.0333742 | + | 0.0138240i | ||||
\(59\) | −407.819 | − | 407.819i | −0.899890 | − | 0.899890i | 0.0955362 | − | 0.995426i | \(-0.469543\pi\) |
−0.995426 | + | 0.0955362i | \(0.969543\pi\) | |||||||
\(60\) | 127.406 | + | 127.406i | 0.274134 | + | 0.274134i | ||||
\(61\) | 72.4205 | − | 29.9976i | 0.152008 | − | 0.0629639i | −0.305382 | − | 0.952230i | \(-0.598784\pi\) |
0.457390 | + | 0.889266i | \(0.348784\pi\) | |||||||
\(62\) | −14.5644 | − | 35.1615i | −0.0298335 | − | 0.0720245i | ||||
\(63\) | 812.920 | + | 336.723i | 1.62569 | + | 0.673382i | ||||
\(64\) | − | 492.167i | − | 0.961264i | ||||||
\(65\) | 55.2607 | − | 133.411i | 0.105450 | − | 0.254579i | ||||
\(66\) | −72.4056 | + | 72.4056i | −0.135038 | + | 0.135038i | ||||
\(67\) | 359.997 | 0.656428 | 0.328214 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328214 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(68\) | 489.191 | + | 266.562i | 0.872399 | + | 0.475373i | ||||
\(69\) | −114.814 | −0.200319 | ||||||||
\(70\) | 9.54178 | − | 9.54178i | 0.0162923 | − | 0.0162923i | ||||
\(71\) | 81.5842 | − | 196.962i | 0.136370 | − | 0.329226i | −0.840911 | − | 0.541173i | \(-0.817980\pi\) |
0.977281 | + | 0.211947i | \(0.0679804\pi\) | |||||||
\(72\) | 148.580i | 0.243199i | ||||||||
\(73\) | 26.8357 | + | 11.1157i | 0.0430258 | + | 0.0178219i | 0.404093 | − | 0.914718i | \(-0.367587\pi\) |
−0.361067 | + | 0.932540i | \(0.617587\pi\) | |||||||
\(74\) | −17.3222 | − | 41.8194i | −0.0272116 | − | 0.0656947i | ||||
\(75\) | −893.873 | + | 370.254i | −1.37621 | + | 0.570044i | ||||
\(76\) | 110.326 | + | 110.326i | 0.166516 | + | 0.166516i | ||||
\(77\) | −829.983 | − | 829.983i | −1.22838 | − | 1.22838i | ||||
\(78\) | 91.0367 | − | 37.7086i | 0.132152 | − | 0.0547393i | ||||
\(79\) | 327.389 | + | 790.386i | 0.466254 | + | 1.12564i | 0.965786 | + | 0.259342i | \(0.0835056\pi\) |
−0.499531 | + | 0.866296i | \(0.666494\pi\) | |||||||
\(80\) | −159.527 | − | 66.0782i | −0.222946 | − | 0.0923471i | ||||
\(81\) | − | 161.379i | − | 0.221371i | ||||||
\(82\) | −37.8740 | + | 91.4360i | −0.0510059 | + | 0.123139i | ||||
\(83\) | 9.67821 | − | 9.67821i | 0.0127991 | − | 0.0127991i | −0.700678 | − | 0.713477i | \(-0.747119\pi\) |
0.713477 | + | 0.700678i | \(0.247119\pi\) | |||||||
\(84\) | −1409.38 | −1.83066 | ||||||||
\(85\) | 150.060 | − | 121.143i | 0.191486 | − | 0.154586i | ||||
\(86\) | −28.9727 | −0.0363280 | ||||||||
\(87\) | 407.946 | − | 407.946i | 0.502718 | − | 0.502718i | ||||
\(88\) | 75.8494 | − | 183.117i | 0.0918815 | − | 0.221822i | ||||
\(89\) | 651.126i | 0.775497i | 0.921765 | + | 0.387748i | \(0.126747\pi\) | ||||
−0.921765 | + | 0.387748i | \(0.873253\pi\) | |||||||
\(90\) | 23.6826 | + | 9.80964i | 0.0277374 | + | 0.0114892i | ||||
\(91\) | 432.253 | + | 1043.55i | 0.497939 | + | 1.20213i | ||||
\(92\) | 102.327 | − | 42.3851i | 0.115960 | − | 0.0480321i | ||||
\(93\) | 973.012 | + | 973.012i | 1.08491 | + | 1.08491i | ||||
\(94\) | −33.4035 | − | 33.4035i | −0.0366522 | − | 0.0366522i | ||||
\(95\) | 49.9006 | − | 20.6695i | 0.0538915 | − | 0.0223226i | ||||
\(96\) | −136.759 | − | 330.166i | −0.145395 | − | 0.351015i | ||||
\(97\) | −1107.41 | − | 458.705i | −1.15918 | − | 0.480149i | −0.281579 | − | 0.959538i | \(-0.590858\pi\) |
−0.877602 | + | 0.479389i | \(0.840858\pi\) | |||||||
\(98\) | 27.3897i | 0.0282325i | ||||||||
\(99\) | 853.282 | − | 2060.01i | 0.866243 | − | 2.09130i | ||||
\(100\) | 659.970 | − | 659.970i | 0.659970 | − | 0.659970i | ||||
\(101\) | 89.2435 | 0.0879214 | 0.0439607 | − | 0.999033i | \(-0.486002\pi\) | ||||
0.0439607 | + | 0.999033i | \(0.486002\pi\) | |||||||
\(102\) | 130.859 | + | 13.9527i | 0.127029 | + | 0.0135444i | ||||
\(103\) | −1242.17 | −1.18830 | −0.594150 | − | 0.804354i | \(-0.702511\pi\) | ||||
−0.594150 | + | 0.804354i | \(0.702511\pi\) | |||||||
\(104\) | −134.869 | + | 134.869i | −0.127163 | + | 0.127163i | ||||
\(105\) | −186.709 | + | 450.755i | −0.173533 | + | 0.418945i | ||||
\(106\) | − | 71.1158i | − | 0.0651639i | ||||||
\(107\) | 1420.54 | + | 588.407i | 1.28345 | + | 0.531621i | 0.917025 | − | 0.398829i | \(-0.130583\pi\) |
0.366420 | + | 0.930449i | \(0.380583\pi\) | |||||||
\(108\) | −347.930 | − | 839.977i | −0.309996 | − | 0.748396i | ||||
\(109\) | 95.9730 | − | 39.7533i | 0.0843353 | − | 0.0349328i | −0.340117 | − | 0.940383i | \(-0.610467\pi\) |
0.424452 | + | 0.905450i | \(0.360467\pi\) | |||||||
\(110\) | −24.1796 | − | 24.1796i | −0.0209585 | − | 0.0209585i | ||||
\(111\) | 1157.25 | + | 1157.25i | 0.989565 | + | 0.989565i | ||||
\(112\) | 1247.83 | − | 516.868i | 1.05276 | − | 0.436066i | ||||
\(113\) | −140.908 | − | 340.183i | −0.117306 | − | 0.283201i | 0.854311 | − | 0.519762i | \(-0.173980\pi\) |
−0.971617 | + | 0.236562i | \(0.923980\pi\) | |||||||
\(114\) | 34.0510 | + | 14.1044i | 0.0279752 | + | 0.0115877i | ||||
\(115\) | − | 38.3418i | − | 0.0310904i | ||||||
\(116\) | −212.979 | + | 514.176i | −0.170471 | + | 0.411552i | ||||
\(117\) | −1517.23 | + | 1517.23i | −1.19887 | + | 1.19887i | ||||
\(118\) | 131.427 | 0.102532 | ||||||||
\(119\) | −159.940 | + | 1500.03i | −0.123207 | + | 1.15553i | ||||
\(120\) | −82.3860 | −0.0626732 | ||||||||
\(121\) | −1162.08 | + | 1162.08i | −0.873091 | + | 0.873091i | ||||
\(122\) | −6.83578 | + | 16.5030i | −0.00507281 | + | 0.0122468i | ||||
\(123\) | − | 3578.35i | − | 2.62316i | ||||||
\(124\) | −1226.39 | − | 507.986i | −0.888168 | − | 0.367891i | ||||
\(125\) | −255.262 | − | 616.256i | −0.182650 | − | 0.440957i | ||||
\(126\) | −185.247 | + | 76.7316i | −0.130977 | + | 0.0542524i | ||||
\(127\) | −886.309 | − | 886.309i | −0.619269 | − | 0.619269i | 0.326075 | − | 0.945344i | \(-0.394274\pi\) |
−0.945344 | + | 0.326075i | \(0.894274\pi\) | |||||||
\(128\) | 324.668 | + | 324.668i | 0.224194 | + | 0.224194i | ||||
\(129\) | 967.799 | − | 400.875i | 0.660542 | − | 0.273605i | ||||
\(130\) | 12.5927 | + | 30.4014i | 0.00849578 | + | 0.0205106i | ||||
\(131\) | −1806.01 | − | 748.072i | −1.20452 | − | 0.498927i | −0.312060 | − | 0.950062i | \(-0.601019\pi\) |
−0.892455 | + | 0.451136i | \(0.851019\pi\) | |||||||
\(132\) | 3571.47i | 2.35497i | ||||||||
\(133\) | −161.678 | + | 390.326i | −0.105408 | + | 0.254478i | ||||
\(134\) | −58.0078 | + | 58.0078i | −0.0373963 | + | 0.0373963i | ||||
\(135\) | −314.739 | −0.200655 | ||||||||
\(136\) | −244.351 | + | 71.9806i | −0.154065 | + | 0.0453844i | ||||
\(137\) | 1749.91 | 1.09127 | 0.545637 | − | 0.838022i | \(-0.316288\pi\) | ||||
0.545637 | + | 0.838022i | \(0.316288\pi\) | |||||||
\(138\) | 18.5004 | − | 18.5004i | 0.0114120 | − | 0.0114120i | ||||
\(139\) | 78.9509 | − | 190.604i | 0.0481765 | − | 0.116308i | −0.897959 | − | 0.440079i | \(-0.854951\pi\) |
0.946136 | + | 0.323770i | \(0.104951\pi\) | |||||||
\(140\) | − | 470.657i | − | 0.284127i | ||||||
\(141\) | 1577.99 | + | 653.624i | 0.942486 | + | 0.390390i | ||||
\(142\) | 18.5912 | + | 44.8832i | 0.0109869 | + | 0.0265248i | ||||
\(143\) | 2644.44 | − | 1095.36i | 1.54643 | − | 0.640552i | ||||
\(144\) | 1814.24 | + | 1814.24i | 1.04991 | + | 1.04991i | ||||
\(145\) | 136.232 | + | 136.232i | 0.0780241 | + | 0.0780241i | ||||
\(146\) | −6.11526 | + | 2.53303i | −0.00346646 | + | 0.00143585i | ||||
\(147\) | −378.973 | − | 914.922i | −0.212634 | − | 0.513343i | ||||
\(148\) | −1458.61 | − | 604.174i | −0.810112 | − | 0.335559i | ||||
\(149\) | − | 2013.39i | − | 1.10700i | −0.832849 | − | 0.553501i | \(-0.813292\pi\) | ||
0.832849 | − | 0.553501i | \(-0.186708\pi\) | |||||||
\(150\) | 84.3727 | − | 203.694i | 0.0459267 | − | 0.110877i | ||||
\(151\) | 53.4946 | − | 53.4946i | 0.0288300 | − | 0.0288300i | −0.692545 | − | 0.721375i | \(-0.743511\pi\) |
0.721375 | + | 0.692545i | \(0.243511\pi\) | |||||||
\(152\) | −71.3412 | −0.0380693 | ||||||||
\(153\) | −2748.87 | + | 809.759i | −1.45250 | + | 0.427877i | ||||
\(154\) | 267.477 | 0.139960 | ||||||||
\(155\) | −324.935 | + | 324.935i | −0.168383 | + | 0.168383i | ||||
\(156\) | 1315.23 | − | 3175.24i | 0.675016 | − | 1.62963i | ||||
\(157\) | − | 2301.81i | − | 1.17009i | −0.811000 | − | 0.585046i | \(-0.801076\pi\) | ||
0.811000 | − | 0.585046i | \(-0.198924\pi\) | |||||||
\(158\) | −180.111 | − | 74.6046i | −0.0906892 | − | 0.0375647i | ||||
\(159\) | 983.980 | + | 2375.54i | 0.490784 | + | 1.18486i | ||||
\(160\) | 110.258 | − | 45.6704i | 0.0544791 | − | 0.0225660i | ||||
\(161\) | 212.070 | + | 212.070i | 0.103810 | + | 0.103810i | ||||
\(162\) | 26.0037 | + | 26.0037i | 0.0126114 | + | 0.0126114i | ||||
\(163\) | −1748.91 | + | 724.420i | −0.840398 | + | 0.348104i | −0.761010 | − | 0.648740i | \(-0.775296\pi\) |
−0.0793874 | + | 0.996844i | \(0.525296\pi\) | |||||||
\(164\) | 1320.99 | + | 3189.16i | 0.628978 | + | 1.51849i | ||||
\(165\) | 1142.25 | + | 473.135i | 0.538933 | + | 0.223234i | ||||
\(166\) | 3.11898i | 0.00145831i | ||||||||
\(167\) | 41.5126 | − | 100.220i | 0.0192356 | − | 0.0464388i | −0.913970 | − | 0.405782i | \(-0.866999\pi\) |
0.933205 | + | 0.359343i | \(0.116999\pi\) | |||||||
\(168\) | 455.680 | − | 455.680i | 0.209265 | − | 0.209265i | ||||
\(169\) | −557.436 | −0.253726 | ||||||||
\(170\) | −4.65948 | + | 43.7000i | −0.00210215 | + | 0.0197155i | ||||
\(171\) | −802.566 | −0.358911 | ||||||||
\(172\) | −714.551 | + | 714.551i | −0.316768 | + | 0.316768i | ||||
\(173\) | −1054.59 | + | 2546.01i | −0.463463 | + | 1.11890i | 0.503504 | + | 0.863993i | \(0.332044\pi\) |
−0.966966 | + | 0.254905i | \(0.917956\pi\) | |||||||
\(174\) | 131.468i | 0.0572791i | ||||||||
\(175\) | 2334.93 | + | 967.161i | 1.00860 | + | 0.417774i | ||||
\(176\) | −1309.78 | − | 3162.10i | −0.560959 | − | 1.35427i | ||||
\(177\) | −4390.16 | + | 1818.47i | −1.86432 | + | 0.772227i | ||||
\(178\) | −104.918 | − | 104.918i | −0.0441796 | − | 0.0441796i | ||||
\(179\) | −1418.56 | − | 1418.56i | −0.592337 | − | 0.592337i | 0.345925 | − | 0.938262i | \(-0.387565\pi\) |
−0.938262 | + | 0.345925i | \(0.887565\pi\) | |||||||
\(180\) | 826.016 | − | 342.147i | 0.342042 | − | 0.141679i | ||||
\(181\) | −927.705 | − | 2239.68i | −0.380971 | − | 0.919745i | −0.991779 | − | 0.127966i | \(-0.959155\pi\) |
0.610808 | − | 0.791779i | \(-0.290845\pi\) | |||||||
\(182\) | −237.802 | − | 98.5008i | −0.0968520 | − | 0.0401174i | ||||
\(183\) | − | 645.847i | − | 0.260887i | ||||||
\(184\) | −19.3804 | + | 46.7883i | −0.00776489 | + | 0.0187461i | ||||
\(185\) | −386.461 | + | 386.461i | −0.153585 | + | 0.153585i | ||||
\(186\) | −313.571 | −0.123614 | ||||||||
\(187\) | 3801.20 | + | 405.300i | 1.48648 | + | 0.158495i | ||||
\(188\) | −1647.66 | −0.639190 | ||||||||
\(189\) | 1740.83 | − | 1740.83i | 0.669984 | − | 0.669984i | ||||
\(190\) | −4.71012 | + | 11.3712i | −0.00179846 | + | 0.00434188i | ||||
\(191\) | 4153.64i | 1.57354i | 0.617243 | + | 0.786772i | \(0.288249\pi\) | ||||
−0.617243 | + | 0.786772i | \(0.711751\pi\) | |||||||
\(192\) | −3746.37 | − | 1551.80i | −1.40818 | − | 0.583289i | ||||
\(193\) | 794.611 | + | 1918.36i | 0.296360 | + | 0.715475i | 0.999988 | + | 0.00490706i | \(0.00156197\pi\) |
−0.703628 | + | 0.710568i | \(0.748438\pi\) | |||||||
\(194\) | 252.355 | − | 104.529i | 0.0933917 | − | 0.0386841i | ||||
\(195\) | −841.288 | − | 841.288i | −0.308953 | − | 0.308953i | ||||
\(196\) | 675.511 | + | 675.511i | 0.246178 | + | 0.246178i | ||||
\(197\) | 3513.98 | − | 1455.54i | 1.27087 | − | 0.526410i | 0.357638 | − | 0.933860i | \(-0.383582\pi\) |
0.913227 | + | 0.407450i | \(0.133582\pi\) | |||||||
\(198\) | 194.444 | + | 469.430i | 0.0697906 | + | 0.168489i | ||||
\(199\) | 3346.19 | + | 1386.04i | 1.19199 | + | 0.493736i | 0.888401 | − | 0.459068i | \(-0.151817\pi\) |
0.303584 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(200\) | 426.764i | 0.150884i | ||||||||
\(201\) | 1135.07 | − | 2740.30i | 0.398316 | − | 0.961620i | ||||
\(202\) | −14.3802 | + | 14.3802i | −0.00500883 | + | 0.00500883i | ||||
\(203\) | −1507.01 | −0.521042 | ||||||||
\(204\) | 3571.48 | − | 2883.25i | 1.22575 | − | 0.989549i | ||||
\(205\) | 1194.98 | 0.407127 | ||||||||
\(206\) | 200.156 | − | 200.156i | 0.0676968 | − | 0.0676968i | ||||
\(207\) | −218.023 | + | 526.355i | −0.0732061 | + | 0.176735i | ||||
\(208\) | 3293.63i | 1.09794i | ||||||||
\(209\) | 989.117 | + | 409.706i | 0.327362 | + | 0.135598i | ||||
\(210\) | −42.5468 | − | 102.717i | −0.0139810 | − | 0.0337531i | ||||
\(211\) | −584.358 | + | 242.049i | −0.190658 | + | 0.0789732i | −0.475970 | − | 0.879462i | \(-0.657903\pi\) |
0.285312 | + | 0.958435i | \(0.407903\pi\) | |||||||
\(212\) | −1753.92 | − | 1753.92i | −0.568207 | − | 0.568207i | ||||
\(213\) | −1242.04 | − | 1242.04i | −0.399545 | − | 0.399545i | ||||
\(214\) | −323.709 | + | 134.085i | −0.103403 | + | 0.0428311i | ||||
\(215\) | 133.871 | + | 323.193i | 0.0424648 | + | 0.102519i | ||||
\(216\) | 384.075 | + | 159.089i | 0.120986 | + | 0.0501140i | ||||
\(217\) | − | 3594.45i | − | 1.12446i | ||||||
\(218\) | −9.05890 | + | 21.8701i | −0.00281443 | + | 0.00679464i | ||||
\(219\) | 169.226 | − | 169.226i | 0.0522155 | − | 0.0522155i | ||||
\(220\) | −1192.68 | −0.365503 | ||||||||
\(221\) | −3230.23 | − | 1760.16i | −0.983206 | − | 0.535753i | ||||
\(222\) | −372.946 | −0.112750 | ||||||||
\(223\) | 377.462 | − | 377.462i | 0.113348 | − | 0.113348i | −0.648158 | − | 0.761506i | \(-0.724460\pi\) |
0.761506 | + | 0.648158i | \(0.224460\pi\) | |||||||
\(224\) | −357.237 | + | 862.445i | −0.106557 | + | 0.257252i | ||||
\(225\) | 4800.96i | 1.42251i | ||||||||
\(226\) | 77.5201 | + | 32.1099i | 0.0228166 | + | 0.00945096i | ||||
\(227\) | 225.340 | + | 544.019i | 0.0658870 | + | 0.159065i | 0.953393 | − | 0.301730i | \(-0.0975642\pi\) |
−0.887506 | + | 0.460795i | \(0.847564\pi\) | |||||||
\(228\) | 1187.65 | − | 491.943i | 0.344975 | − | 0.142893i | ||||
\(229\) | 1867.57 | + | 1867.57i | 0.538920 | + | 0.538920i | 0.923212 | − | 0.384292i | \(-0.125554\pi\) |
−0.384292 | + | 0.923212i | \(0.625554\pi\) | |||||||
\(230\) | 6.17817 | + | 6.17817i | 0.00177120 | + | 0.00177120i | ||||
\(231\) | −8934.75 | + | 3700.89i | −2.54486 | + | 1.05412i | ||||
\(232\) | −97.3834 | − | 235.104i | −0.0275583 | − | 0.0665317i | ||||
\(233\) | 354.195 | + | 146.712i | 0.0995882 | + | 0.0412508i | 0.431921 | − | 0.901911i | \(-0.357836\pi\) |
−0.332333 | + | 0.943162i | \(0.607836\pi\) | |||||||
\(234\) | − | 488.955i | − | 0.136598i | ||||||
\(235\) | −218.276 | + | 526.964i | −0.0605904 | + | 0.146278i | ||||
\(236\) | 3241.37 | − | 3241.37i | 0.894049 | − | 0.894049i | ||||
\(237\) | 7048.67 | 1.93190 | ||||||||
\(238\) | −215.934 | − | 267.478i | −0.0588107 | − | 0.0728488i | ||||
\(239\) | −4344.62 | −1.17586 | −0.587929 | − | 0.808913i | \(-0.700056\pi\) | ||||
−0.587929 | + | 0.808913i | \(0.700056\pi\) | |||||||
\(240\) | −1005.97 | + | 1005.97i | −0.270564 | + | 0.270564i | ||||
\(241\) | −785.906 | + | 1897.34i | −0.210061 | + | 0.507131i | −0.993432 | − | 0.114422i | \(-0.963498\pi\) |
0.783371 | + | 0.621554i | \(0.213498\pi\) | |||||||
\(242\) | − | 374.502i | − | 0.0994790i | ||||||
\(243\) | −4081.86 | − | 1690.76i | −1.07758 | − | 0.446348i | ||||
\(244\) | 238.423 | + | 575.604i | 0.0625552 | + | 0.151022i | ||||
\(245\) | 305.535 | − | 126.557i | 0.0796732 | − | 0.0330017i | ||||
\(246\) | 576.593 | + | 576.593i | 0.149440 | + | 0.149440i | ||||
\(247\) | −728.503 | − | 728.503i | −0.187666 | − | 0.187666i | ||||
\(248\) | 560.759 | − | 232.274i | 0.143581 | − | 0.0594734i | ||||
\(249\) | −43.1552 | − | 104.186i | −0.0109833 | − | 0.0265161i | ||||
\(250\) | 140.431 | + | 58.1685i | 0.0355266 | + | 0.0147156i | ||||
\(251\) | 907.953i | 0.228325i | 0.993462 | + | 0.114162i | \(0.0364184\pi\) | ||||
−0.993462 | + | 0.114162i | \(0.963582\pi\) | |||||||
\(252\) | −2676.30 | + | 6461.15i | −0.669011 | + | 1.61514i | ||||
\(253\) | 537.402 | − | 537.402i | 0.133542 | − | 0.133542i | ||||
\(254\) | 285.629 | 0.0705589 | ||||||||
\(255\) | −449.002 | − | 1524.22i | −0.110265 | − | 0.374314i | ||||
\(256\) | 3832.71 | 0.935720 | ||||||||
\(257\) | 5296.81 | − | 5296.81i | 1.28563 | − | 1.28563i | 0.348209 | − | 0.937417i | \(-0.386790\pi\) |
0.937417 | − | 0.348209i | \(-0.113210\pi\) | |||||||
\(258\) | −91.3506 | + | 220.540i | −0.0220436 | + | 0.0532179i | ||||
\(259\) | − | 4275.06i | − | 1.02564i | ||||||
\(260\) | 1060.36 | + | 439.216i | 0.252926 | + | 0.104765i | ||||
\(261\) | −1095.53 | − | 2644.85i | −0.259815 | − | 0.627250i | ||||
\(262\) | 411.549 | − | 170.469i | 0.0970441 | − | 0.0401970i | ||||
\(263\) | −5558.34 | − | 5558.34i | −1.30320 | − | 1.30320i | −0.926221 | − | 0.376982i | \(-0.876962\pi\) |
−0.376982 | − | 0.926221i | \(-0.623038\pi\) | |||||||
\(264\) | −1154.73 | − | 1154.73i | −0.269200 | − | 0.269200i | ||||
\(265\) | −793.304 | + | 328.597i | −0.183895 | + | 0.0761720i | ||||
\(266\) | −36.8429 | − | 88.9466i | −0.00849241 | − | 0.0205025i | ||||
\(267\) | 4956.36 | + | 2052.99i | 1.13605 | + | 0.470566i | ||||
\(268\) | 2861.29i | 0.652167i | ||||||||
\(269\) | −2890.74 | + | 6978.86i | −0.655210 | + | 1.58182i | 0.149908 | + | 0.988700i | \(0.452102\pi\) |
−0.805117 | + | 0.593116i | \(0.797898\pi\) | |||||||
\(270\) | 50.7151 | − | 50.7151i | 0.0114312 | − | 0.0114312i | ||||
\(271\) | 6394.46 | 1.43334 | 0.716672 | − | 0.697411i | \(-0.245665\pi\) | ||||
0.716672 | + | 0.697411i | \(0.245665\pi\) | |||||||
\(272\) | −2104.72 | + | 3862.56i | −0.469182 | + | 0.861037i | ||||
\(273\) | 9306.39 | 2.06318 | ||||||||
\(274\) | −281.969 | + | 281.969i | −0.0621693 | + | 0.0621693i | ||||
\(275\) | 2450.86 | − | 5916.91i | 0.537428 | − | 1.29747i | ||||
\(276\) | − | 912.551i | − | 0.199018i | ||||||
\(277\) | −6247.84 | − | 2587.94i | −1.35522 | − | 0.561351i | −0.417480 | − | 0.908686i | \(-0.637087\pi\) |
−0.937741 | + | 0.347335i | \(0.887087\pi\) | |||||||
\(278\) | 17.9912 | + | 43.4345i | 0.00388143 | + | 0.00937061i | ||||
\(279\) | 6308.36 | − | 2613.01i | 1.35366 | − | 0.560705i | ||||
\(280\) | 152.173 | + | 152.173i | 0.0324788 | + | 0.0324788i | ||||
\(281\) | 4453.39 | + | 4453.39i | 0.945433 | + | 0.945433i | 0.998586 | − | 0.0531529i | \(-0.0169271\pi\) |
−0.0531529 | + | 0.998586i | \(0.516927\pi\) | |||||||
\(282\) | −359.588 | + | 148.946i | −0.0759332 | + | 0.0314526i | ||||
\(283\) | −1022.77 | − | 2469.18i | −0.214831 | − | 0.518648i | 0.779323 | − | 0.626623i | \(-0.215563\pi\) |
−0.994154 | + | 0.107975i | \(0.965563\pi\) | |||||||
\(284\) | 1565.47 | + | 648.437i | 0.327089 | + | 0.135485i | ||||
\(285\) | − | 445.014i | − | 0.0924924i | ||||||
\(286\) | −249.609 | + | 602.609i | −0.0516073 | + | 0.124591i | ||||
\(287\) | −6609.47 | + | 6609.47i | −1.35939 | + | 1.35939i | ||||
\(288\) | −1773.31 | −0.362824 | ||||||||
\(289\) | −2663.41 | − | 4128.41i | −0.542115 | − | 0.840304i | ||||
\(290\) | −43.9033 | −0.00888998 | ||||||||
\(291\) | −6983.32 | + | 6983.32i | −1.40677 | + | 1.40677i | ||||
\(292\) | −88.3485 | + | 213.292i | −0.0177062 | + | 0.0427465i | ||||
\(293\) | 2183.30i | 0.435323i | 0.976024 | + | 0.217661i | \(0.0698428\pi\) | ||||
−0.976024 | + | 0.217661i | \(0.930157\pi\) | |||||||
\(294\) | 208.490 | + | 86.3595i | 0.0413585 | + | 0.0171313i | ||||
\(295\) | −607.271 | − | 1466.08i | −0.119853 | − | 0.289351i | ||||
\(296\) | 666.939 | − | 276.255i | 0.130963 | − | 0.0542467i | ||||
\(297\) | −4411.41 | − | 4411.41i | −0.861872 | − | 0.861872i | ||||
\(298\) | 324.425 | + | 324.425i | 0.0630653 | + | 0.0630653i | ||||
\(299\) | −675.684 | + | 279.878i | −0.130688 | + | 0.0541329i | ||||
\(300\) | −2942.81 | − | 7104.57i | −0.566344 | − | 1.36727i | ||||
\(301\) | −2528.04 | − | 1047.15i | −0.484099 | − | 0.200520i | ||||
\(302\) | 17.2396i | 0.00328485i | ||||||||
\(303\) | 281.384 | − | 679.321i | 0.0533501 | − | 0.128799i | ||||
\(304\) | −871.110 | + | 871.110i | −0.164347 | + | 0.164347i | ||||
\(305\) | 215.679 | 0.0404909 | ||||||||
\(306\) | 312.456 | − | 573.416i | 0.0583724 | − | 0.107124i | ||||
\(307\) | −3905.30 | −0.726018 | −0.363009 | − | 0.931786i | \(-0.618250\pi\) | ||||
−0.363009 | + | 0.931786i | \(0.618250\pi\) | |||||||
\(308\) | 6596.76 | − | 6596.76i | 1.22041 | − | 1.22041i | ||||
\(309\) | −3916.56 | + | 9455.40i | −0.721052 | + | 1.74077i | ||||
\(310\) | − | 104.716i | − | 0.0191854i | ||||||
\(311\) | 6806.60 | + | 2819.39i | 1.24105 | + | 0.514060i | 0.904043 | − | 0.427441i | \(-0.140585\pi\) |
0.337008 | + | 0.941502i | \(0.390585\pi\) | |||||||
\(312\) | 601.380 | + | 1451.86i | 0.109123 | + | 0.263447i | ||||
\(313\) | −2149.71 | + | 890.438i | −0.388207 | + | 0.160800i | −0.568246 | − | 0.822859i | \(-0.692378\pi\) |
0.180039 | + | 0.983659i | \(0.442378\pi\) | |||||||
\(314\) | 370.900 | + | 370.900i | 0.0666595 | + | 0.0666595i | ||||
\(315\) | 1711.90 | + | 1711.90i | 0.306205 | + | 0.306205i | ||||
\(316\) | −6282.05 | + | 2602.11i | −1.11833 | + | 0.463228i | ||||
\(317\) | 2858.75 | + | 6901.62i | 0.506508 | + | 1.22282i | 0.945881 | + | 0.324514i | \(0.105201\pi\) |
−0.439372 | + | 0.898305i | \(0.644799\pi\) | |||||||
\(318\) | −541.333 | − | 224.227i | −0.0954604 | − | 0.0395410i | ||||
\(319\) | 3818.89i | 0.670272i | ||||||||
\(320\) | 518.218 | − | 1251.09i | 0.0905290 | − | 0.218556i | ||||
\(321\) | 8957.89 | − | 8957.89i | 1.55757 | − | 1.55757i | ||||
\(322\) | −68.3433 | −0.0118280 | ||||||||
\(323\) | −388.808 | − | 1319.88i | −0.0669779 | − | 0.227368i | ||||
\(324\) | 1282.66 | 0.219934 | ||||||||
\(325\) | −4357.92 | + | 4357.92i | −0.743796 | + | 0.743796i | ||||
\(326\) | 165.079 | − | 398.537i | 0.0280457 | − | 0.0677083i | ||||
\(327\) | − | 855.888i | − | 0.144742i | ||||||
\(328\) | −1458.23 | − | 604.017i | −0.245479 | − | 0.101681i | ||||
\(329\) | −1707.37 | − | 4121.95i | −0.286110 | − | 0.690730i | ||||
\(330\) | −260.293 | + | 107.817i | −0.0434202 | + | 0.0179852i | ||||
\(331\) | 6613.70 | + | 6613.70i | 1.09825 | + | 1.09825i | 0.994615 | + | 0.103637i | \(0.0330482\pi\) |
0.103637 | + | 0.994615i | \(0.466952\pi\) | |||||||
\(332\) | 76.9231 | + | 76.9231i | 0.0127160 | + | 0.0127160i | ||||
\(333\) | 7502.86 | − | 3107.79i | 1.23470 | − | 0.511428i | ||||
\(334\) | 9.45981 | + | 22.8380i | 0.00154975 | + | 0.00374143i | ||||
\(335\) | 915.114 | + | 379.053i | 0.149248 | + | 0.0618205i | ||||
\(336\) | − | 11128.1i | − | 1.80682i | ||||||
\(337\) | 2657.39 | − | 6415.50i | 0.429546 | − | 1.03702i | −0.549885 | − | 0.835240i | \(-0.685329\pi\) |
0.979432 | − | 0.201776i | \(-0.0646714\pi\) | |||||||
\(338\) | 89.8218 | − | 89.8218i | 0.0144546 | − | 0.0144546i | ||||
\(339\) | −3033.75 | −0.486049 | ||||||||
\(340\) | 962.853 | + | 1192.69i | 0.153582 | + | 0.190243i | ||||
\(341\) | −9108.62 | −1.44651 | ||||||||
\(342\) | 129.321 | − | 129.321i | 0.0204470 | − | 0.0204470i | ||||
\(343\) | 1835.05 | − | 4430.19i | 0.288872 | − | 0.697399i | ||||
\(344\) | − | 462.058i | − | 0.0724201i | ||||||
\(345\) | −291.858 | − | 120.891i | −0.0455452 | − | 0.0188654i | ||||
\(346\) | −240.318 | − | 580.178i | −0.0373398 | − | 0.0901462i | ||||
\(347\) | 2226.53 | − | 922.261i | 0.344457 | − | 0.142679i | −0.203747 | − | 0.979024i | \(-0.565312\pi\) |
0.548204 | + | 0.836345i | \(0.315312\pi\) | |||||||
\(348\) | 3242.39 | + | 3242.39i | 0.499454 | + | 0.499454i | ||||
\(349\) | −7781.94 | − | 7781.94i | −1.19357 | − | 1.19357i | −0.976056 | − | 0.217518i | \(-0.930204\pi\) |
−0.217518 | − | 0.976056i | \(-0.569796\pi\) | |||||||
\(350\) | −532.080 | + | 220.395i | −0.0812596 | + | 0.0336588i | ||||
\(351\) | 2297.45 | + | 5546.54i | 0.349370 | + | 0.843454i | ||||
\(352\) | 2185.51 | + | 905.266i | 0.330931 | + | 0.137076i | ||||
\(353\) | 7713.23i | 1.16299i | 0.813552 | + | 0.581493i | \(0.197531\pi\) | ||||
−0.813552 | + | 0.581493i | \(0.802469\pi\) | |||||||
\(354\) | 414.388 | − | 1000.42i | 0.0622160 | − | 0.150203i | ||||
\(355\) | 414.775 | − | 414.775i | 0.0620111 | − | 0.0620111i | ||||
\(356\) | −5175.20 | −0.770463 | ||||||||
\(357\) | 10913.9 | + | 5947.05i | 1.61800 | + | 0.881656i | ||||
\(358\) | 457.157 | 0.0674902 | ||||||||
\(359\) | 7226.67 | − | 7226.67i | 1.06242 | − | 1.06242i | 0.0645037 | − | 0.997917i | \(-0.479454\pi\) |
0.997917 | − | 0.0645037i | \(-0.0205464\pi\) | |||||||
\(360\) | −156.445 | + | 377.691i | −0.0229038 | + | 0.0552947i | ||||
\(361\) | 6473.65i | 0.943818i | ||||||||
\(362\) | 510.373 | + | 211.403i | 0.0741011 | + | 0.0306937i | ||||
\(363\) | 5181.73 | + | 12509.8i | 0.749230 | + | 1.80880i | ||||
\(364\) | −8294.22 | + | 3435.58i | −1.19433 | + | 0.494706i | ||||
\(365\) | 56.5124 | + | 56.5124i | 0.00810409 | + | 0.00810409i | ||||
\(366\) | 104.068 | + | 104.068i | 0.0148626 | + | 0.0148626i | ||||
\(367\) | 9536.68 | − | 3950.22i | 1.35643 | − | 0.561853i | 0.418356 | − | 0.908283i | \(-0.362606\pi\) |
0.938076 | + | 0.346430i | \(0.112606\pi\) | |||||||
\(368\) | 334.665 | + | 807.952i | 0.0474065 | + | 0.114450i | ||||
\(369\) | −16404.6 | − | 6795.01i | −2.31434 | − | 0.958629i | ||||
\(370\) | − | 124.544i | − | 0.0174993i | ||||||
\(371\) | 2570.31 | − | 6205.27i | 0.359687 | − | 0.868361i | ||||
\(372\) | −7733.57 | + | 7733.57i | −1.07787 | + | 1.07787i | ||||
\(373\) | −2744.09 | −0.380921 | −0.190461 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190461 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(374\) | −677.810 | + | 547.195i | −0.0937132 | + | 0.0756545i | ||||
\(375\) | −5495.78 | −0.756802 | ||||||||
\(376\) | 532.722 | − | 532.722i | 0.0730666 | − | 0.0730666i | ||||
\(377\) | 1406.34 | − | 3395.21i | 0.192123 | − | 0.463826i | ||||
\(378\) | 561.014i | 0.0763372i | ||||||||
\(379\) | −5917.45 | − | 2451.09i | −0.802003 | − | 0.332200i | −0.0562446 | − | 0.998417i | \(-0.517913\pi\) |
−0.745758 | + | 0.666217i | \(0.767913\pi\) | |||||||
\(380\) | 164.283 | + | 396.614i | 0.0221777 | + | 0.0535417i | ||||
\(381\) | −9541.10 | + | 3952.05i | −1.28295 | + | 0.531417i | ||||
\(382\) | −669.293 | − | 669.293i | −0.0896440 | − | 0.0896440i | ||||
\(383\) | −2611.23 | − | 2611.23i | −0.348375 | − | 0.348375i | 0.511129 | − | 0.859504i | \(-0.329227\pi\) |
−0.859504 | + | 0.511129i | \(0.829227\pi\) | |||||||
\(384\) | 3495.04 | − | 1447.69i | 0.464468 | − | 0.192389i | ||||
\(385\) | −1235.90 | − | 2983.73i | −0.163604 | − | 0.394974i | ||||
\(386\) | −437.152 | − | 181.074i | −0.0576437 | − | 0.0238768i | ||||
\(387\) | − | 5198.01i | − | 0.682765i | ||||||
\(388\) | 3645.82 | − | 8801.79i | 0.477032 | − | 1.15166i | ||||
\(389\) | −1508.22 | + | 1508.22i | −0.196581 | + | 0.196581i | −0.798532 | − | 0.601952i | \(-0.794390\pi\) |
0.601952 | + | 0.798532i | \(0.294390\pi\) | |||||||
\(390\) | 271.120 | 0.0352018 | ||||||||
\(391\) | −971.250 | − | 103.559i | −0.125622 | − | 0.0133944i | ||||
\(392\) | −436.813 | −0.0562816 | ||||||||
\(393\) | −11388.6 | + | 11388.6i | −1.46178 | + | 1.46178i | ||||
\(394\) | −331.685 | + | 800.758i | −0.0424112 | + | 0.102390i | ||||
\(395\) | 2353.88i | 0.299840i | ||||||||
\(396\) | 16373.1 | + | 6781.95i | 2.07772 | + | 0.860621i | ||||
\(397\) | −904.995 | − | 2184.85i | −0.114409 | − | 0.276208i | 0.856295 | − | 0.516488i | \(-0.172761\pi\) |
−0.970704 | + | 0.240280i | \(0.922761\pi\) | |||||||
\(398\) | −762.522 | + | 315.847i | −0.0960346 | + | 0.0397788i | ||||
\(399\) | 2461.39 | + | 2461.39i | 0.308831 | + | 0.308831i | ||||
\(400\) | 5210.99 | + | 5210.99i | 0.651374 | + | 0.651374i | ||||
\(401\) | 1906.65 | − | 789.759i | 0.237440 | − | 0.0983509i | −0.260791 | − | 0.965395i | \(-0.583983\pi\) |
0.498231 | + | 0.867044i | \(0.333983\pi\) | |||||||
\(402\) | 258.657 | + | 624.453i | 0.0320911 | + | 0.0774748i | ||||
\(403\) | 8098.08 | + | 3354.33i | 1.00098 | + | 0.414619i | ||||
\(404\) | 709.314i | 0.0873507i | ||||||||
\(405\) | 169.922 | − | 410.227i | 0.0208481 | − | 0.0503317i | ||||
\(406\) | 242.831 | − | 242.831i | 0.0296835 | − | 0.0296835i | ||||
\(407\) | −10833.4 | −1.31938 | ||||||||
\(408\) | −222.519 | + | 2086.95i | −0.0270009 | + | 0.253234i | ||||
\(409\) | 9245.03 | 1.11769 | 0.558847 | − | 0.829271i | \(-0.311244\pi\) | ||||
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(410\) | −192.552 | + | 192.552i | −0.0231938 | + | 0.0231938i | ||||
\(411\) | 5517.43 | − | 13320.3i | 0.662178 | − | 1.59864i | ||||
\(412\) | − | 9872.87i | − | 1.18059i | ||||||
\(413\) | 11467.8 | + | 4750.11i | 1.36633 | + | 0.565951i | ||||
\(414\) | −49.6826 | − | 119.945i | −0.00589799 | − | 0.0142390i | ||||
\(415\) | 34.7925 | − | 14.4115i | 0.00411542 | − | 0.00170466i | ||||
\(416\) | −1609.67 | − | 1609.67i | −0.189712 | − | 0.189712i | ||||
\(417\) | −1201.95 | − | 1201.95i | −0.141150 | − | 0.141150i | ||||
\(418\) | −225.398 | + | 93.3628i | −0.0263746 | + | 0.0109247i | ||||
\(419\) | 1590.19 | + | 3839.06i | 0.185408 | + | 0.447614i | 0.989065 | − | 0.147478i | \(-0.0471155\pi\) |
−0.803657 | + | 0.595092i | \(0.797116\pi\) | |||||||
\(420\) | −3582.63 | − | 1483.98i | −0.416225 | − | 0.172406i | ||||
\(421\) | 4609.26i | 0.533591i | 0.963753 | + | 0.266795i | \(0.0859648\pi\) | ||||
−0.963753 | + | 0.266795i | \(0.914035\pi\) | |||||||
\(422\) | 55.1576 | − | 133.162i | 0.00636263 | − | 0.0153608i | ||||
\(423\) | 5992.96 | − | 5992.96i | 0.688859 | − | 0.688859i | ||||
\(424\) | 1134.16 | 0.129905 | ||||||||
\(425\) | −7895.52 | + | 2325.85i | −0.901150 | + | 0.265460i | ||||
\(426\) | 400.269 | 0.0455237 | ||||||||
\(427\) | −1192.93 | + | 1192.93i | −0.135198 | + | 0.135198i | ||||
\(428\) | −4676.70 | + | 11290.5i | −0.528170 | + | 1.27511i | ||||
\(429\) | − | 23583.1i | − | 2.65409i | ||||||
\(430\) | −73.6486 | − | 30.5063i | −0.00825965 | − | 0.00342126i | ||||
\(431\) | −6632.04 | − | 16011.2i | −0.741193 | − | 1.78940i | −0.600958 | − | 0.799281i | \(-0.705214\pi\) |
−0.140235 | − | 0.990118i | \(-0.544786\pi\) | |||||||
\(432\) | 6632.29 | − | 2747.19i | 0.738649 | − | 0.305958i | ||||
\(433\) | 8028.41 | + | 8028.41i | 0.891041 | + | 0.891041i | 0.994621 | − | 0.103580i | \(-0.0330297\pi\) |
−0.103580 | + | 0.994621i | \(0.533030\pi\) | |||||||
\(434\) | 579.188 | + | 579.188i | 0.0640597 | + | 0.0640597i | ||||
\(435\) | 1466.54 | − | 607.461i | 0.161644 | − | 0.0669552i | ||||
\(436\) | 315.962 | + | 762.801i | 0.0347061 | + | 0.0837879i | ||||
\(437\) | −252.730 | − | 104.684i | −0.0276653 | − | 0.0114593i | ||||
\(438\) | 54.5359i | 0.00594938i | ||||||||
\(439\) | −1962.43 | + | 4737.72i | −0.213352 | + | 0.515078i | −0.993934 | − | 0.109975i | \(-0.964923\pi\) |
0.780582 | + | 0.625053i | \(0.214923\pi\) | |||||||
\(440\) | 385.619 | − | 385.619i | 0.0417810 | − | 0.0417810i | ||||
\(441\) | −4914.02 | −0.530614 | ||||||||
\(442\) | 804.121 | − | 236.877i | 0.0865343 | − | 0.0254912i | ||||
\(443\) | −3133.00 | −0.336012 | −0.168006 | − | 0.985786i | \(-0.553733\pi\) | ||||
−0.168006 | + | 0.985786i | \(0.553733\pi\) | |||||||
\(444\) | −9197.94 | + | 9197.94i | −0.983141 | + | 0.983141i | ||||
\(445\) | −685.591 | + | 1655.16i | −0.0730340 | + | 0.176320i | ||||
\(446\) | 121.644i | 0.0129148i | ||||||||
\(447\) | −15325.9 | − | 6348.19i | −1.62168 | − | 0.671721i | ||||
\(448\) | 4053.54 | + | 9786.11i | 0.427481 | + | 1.03203i | ||||
\(449\) | 10855.2 | − | 4496.37i | 1.14095 | − | 0.472599i | 0.269464 | − | 0.963010i | \(-0.413154\pi\) |
0.871491 | + | 0.490411i | \(0.163154\pi\) | |||||||
\(450\) | −773.598 | − | 773.598i | −0.0810395 | − | 0.0810395i | ||||
\(451\) | 16748.9 | + | 16748.9i | 1.74873 | + | 1.74873i | ||||
\(452\) | 2703.80 | − | 1119.95i | 0.281363 | − | 0.116544i | ||||
\(453\) | −238.532 | − | 575.868i | −0.0247400 | − | 0.0597277i | ||||
\(454\) | −123.970 | − | 51.3500i | −0.0128154 | − | 0.00530831i | ||||
\(455\) | 3107.84i | 0.320215i | ||||||||
\(456\) | −224.938 | + | 543.048i | −0.0231002 | + | 0.0557688i | ||||
\(457\) | −8774.30 | + | 8774.30i | −0.898128 | + | 0.898128i | −0.995270 | − | 0.0971425i | \(-0.969030\pi\) |
0.0971425 | + | 0.995270i | \(0.469030\pi\) | |||||||
\(458\) | −601.859 | −0.0614039 | ||||||||
\(459\) | −850.090 | + | 7972.76i | −0.0864462 | + | 0.810755i | ||||
\(460\) | 304.744 | 0.0308886 | ||||||||
\(461\) | 5211.73 | − | 5211.73i | 0.526539 | − | 0.526539i | −0.393000 | − | 0.919539i | \(-0.628563\pi\) |
0.919539 | + | 0.393000i | \(0.128563\pi\) | |||||||
\(462\) | 843.352 | − | 2036.03i | 0.0849270 | − | 0.205032i | ||||
\(463\) | − | 11446.9i | − | 1.14899i | −0.818508 | − | 0.574495i | \(-0.805198\pi\) | ||
0.818508 | − | 0.574495i | \(-0.194802\pi\) | |||||||
\(464\) | −4059.84 | − | 1681.64i | −0.406192 | − | 0.168250i | ||||
\(465\) | 1448.88 | + | 3497.91i | 0.144495 | + | 0.348843i | ||||
\(466\) | −80.7131 | + | 33.4325i | −0.00802352 | + | 0.00332345i | ||||
\(467\) | 3124.20 | + | 3124.20i | 0.309573 | + | 0.309573i | 0.844744 | − | 0.535171i | \(-0.179753\pi\) |
−0.535171 | + | 0.844744i | \(0.679753\pi\) | |||||||
\(468\) | −12059.1 | − | 12059.1i | −1.19109 | − | 1.19109i | ||||
\(469\) | −7158.08 | + | 2964.97i | −0.704754 | + | 0.291919i | ||||
\(470\) | −49.7402 | − | 120.083i | −0.00488158 | − | 0.0117852i | ||||
\(471\) | −17521.4 | − | 7257.59i | −1.71410 | − | 0.710004i | ||||
\(472\) | 2096.01i | 0.204399i | ||||||||
\(473\) | −2653.56 | + | 6406.25i | −0.257951 | + | 0.622748i | ||||
\(474\) | −1135.78 | + | 1135.78i | −0.110059 | + | 0.110059i | ||||
\(475\) | −2305.19 | −0.222673 | ||||||||
\(476\) | −11922.4 | − | 1271.21i | −1.14803 | − | 0.122407i | ||||
\(477\) | 12758.9 | 1.22472 | ||||||||
\(478\) | 700.065 | − | 700.065i | 0.0669879 | − | 0.0669879i | ||||
\(479\) | −108.152 | + | 261.102i | −0.0103165 | + | 0.0249062i | −0.928954 | − | 0.370196i | \(-0.879291\pi\) |
0.918637 | + | 0.395102i | \(0.129291\pi\) | |||||||
\(480\) | − | 983.281i | − | 0.0935009i | ||||||
\(481\) | 9631.46 | + | 3989.48i | 0.913008 | + | 0.378180i | ||||
\(482\) | −179.090 | − | 432.363i | −0.0169240 | − | 0.0408580i | ||||
\(483\) | 2282.93 | − | 945.620i | 0.215066 | − | 0.0890832i | ||||
\(484\) | −9236.32 | − | 9236.32i | −0.867423 | − | 0.867423i | ||||
\(485\) | −2332.06 | − | 2332.06i | −0.218337 | − | 0.218337i | ||||
\(486\) | 930.166 | − | 385.287i | 0.0868172 | − | 0.0359609i | ||||
\(487\) | −2909.21 | − | 7023.45i | −0.270696 | − | 0.653518i | 0.728818 | − | 0.684708i | \(-0.240070\pi\) |
−0.999513 | + | 0.0311903i | \(0.990070\pi\) | |||||||
\(488\) | −263.192 | − | 109.018i | −0.0244142 | − | 0.0101127i | ||||
\(489\) | 15596.7i | 1.44235i | ||||||||
\(490\) | −28.8395 | + | 69.6247i | −0.00265885 | + | 0.00641903i | ||||
\(491\) | −9075.67 | + | 9075.67i | −0.834174 | + | 0.834174i | −0.988085 | − | 0.153911i | \(-0.950813\pi\) |
0.153911 | + | 0.988085i | \(0.450813\pi\) | |||||||
\(492\) | 28441.0 | 2.60613 | ||||||||
\(493\) | 3818.91 | − | 3082.99i | 0.348874 | − | 0.281645i | ||||
\(494\) | 234.773 | 0.0213825 | ||||||||
\(495\) | 4338.09 | − | 4338.09i | 0.393904 | − | 0.393904i | ||||
\(496\) | 4010.96 | − | 9683.31i | 0.363100 | − | 0.876600i | ||||
\(497\) | 4588.27i | 0.414108i | ||||||||
\(498\) | 23.7416 | + | 9.83410i | 0.00213632 | + | 0.000884893i | ||||
\(499\) | 1039.84 | + | 2510.39i | 0.0932855 | + | 0.225211i | 0.963634 | − | 0.267225i | \(-0.0861066\pi\) |
−0.870349 | + | 0.492436i | \(0.836107\pi\) | |||||||
\(500\) | 4898.05 | − | 2028.84i | 0.438095 | − | 0.181465i | ||||
\(501\) | −631.988 | − | 631.988i | −0.0563575 | − | 0.0563575i | ||||
\(502\) | −146.302 | − | 146.302i | −0.0130075 | − | 0.0130075i | ||||
\(503\) | 7589.15 | − | 3143.53i | 0.672731 | − | 0.278654i | −0.0200537 | − | 0.999799i | \(-0.506384\pi\) |
0.692784 | + | 0.721145i | \(0.256384\pi\) | |||||||
\(504\) | −1223.72 | − | 2954.32i | −0.108153 | − | 0.261103i | ||||
\(505\) | 226.857 | + | 93.9673i | 0.0199901 | + | 0.00828018i | ||||
\(506\) | 173.187i | 0.0152157i | ||||||||
\(507\) | −1757.59 | + | 4243.20i | −0.153959 | + | 0.371690i | ||||
\(508\) | 7044.45 | − | 7044.45i | 0.615250 | − | 0.615250i | ||||
\(509\) | 8243.18 | 0.717824 | 0.358912 | − | 0.933371i | \(-0.383148\pi\) | ||||
0.358912 | + | 0.933371i | \(0.383148\pi\) | |||||||
\(510\) | 317.953 | + | 173.253i | 0.0276062 | + | 0.0150427i | ||||
\(511\) | −625.144 | −0.0541188 | ||||||||
\(512\) | −3214.92 | + | 3214.92i | −0.277502 | + | 0.277502i | ||||
\(513\) | −859.330 | + | 2074.61i | −0.0739578 | + | 0.178550i | ||||
\(514\) | 1706.99i | 0.146483i | ||||||||
\(515\) | −3157.60 | − | 1307.92i | −0.270176 | − | 0.111911i | ||||
\(516\) | 3186.19 | + | 7692.13i | 0.271829 | + | 0.656254i | ||||
\(517\) | −10445.3 | + | 4326.60i | −0.888560 | + | 0.368054i | ||||
\(518\) | 688.858 | + | 688.858i | 0.0584299 | + | 0.0584299i | ||||
\(519\) | 16055.1 | + | 16055.1i | 1.35788 | + | 1.35788i | ||||
\(520\) | −484.844 | + | 200.829i | −0.0408881 | + | 0.0169364i | ||||
\(521\) | −3426.22 | − | 8271.63i | −0.288110 | − | 0.695559i | 0.711867 | − | 0.702314i | \(-0.247850\pi\) |
−0.999977 | + | 0.00675482i | \(0.997850\pi\) | |||||||
\(522\) | 602.703 | + | 249.648i | 0.0505356 | + | 0.0209325i | ||||
\(523\) | − | 15665.1i | − | 1.30973i | −0.755747 | − | 0.654864i | \(-0.772726\pi\) | ||
0.755747 | − | 0.654864i | \(-0.227274\pi\) | |||||||
\(524\) | 5945.73 | − | 14354.3i | 0.495688 | − | 1.19670i | ||||
\(525\) | 14724.0 | − | 14724.0i | 1.22402 | − | 1.22402i | ||||
\(526\) | 1791.28 | 0.148485 | ||||||||
\(527\) | 7353.40 | + | 9108.65i | 0.607816 | + | 0.752902i | ||||
\(528\) | −28199.6 | −2.32430 | ||||||||
\(529\) | 8466.06 | − | 8466.06i | 0.695821 | − | 0.695821i | ||||
\(530\) | 74.8800 | − | 180.776i | 0.00613694 | − | 0.0148159i | ||||
\(531\) | 23579.4i | 1.92704i | ||||||||
\(532\) | −3102.34 | − | 1285.03i | −0.252826 | − | 0.104724i | ||||
\(533\) | −8722.79 | − | 21058.7i | −0.708867 | − | 1.71136i | ||||
\(534\) | −1129.45 | + | 467.832i | −0.0915279 | + | 0.0379121i | ||||
\(535\) | 2991.46 | + | 2991.46i | 0.241742 | + | 0.241742i | ||||
\(536\) | −925.113 | − | 925.113i | −0.0745500 | − | 0.0745500i | ||||
\(537\) | −15270.8 | + | 6325.37i | −1.22716 | + | 0.508305i | ||||
\(538\) | −658.735 | − | 1590.33i | −0.0527882 | − | 0.127442i | ||||
\(539\) | 6056.24 | + | 2508.58i | 0.483972 | + | 0.200468i | ||||
\(540\) | − | 2501.57i | − | 0.199353i | ||||||
\(541\) | −3547.46 | + | 8564.31i | −0.281917 | + | 0.680607i | −0.999880 | − | 0.0154734i | \(-0.995074\pi\) |
0.717963 | + | 0.696081i | \(0.245074\pi\) | |||||||
\(542\) | −1030.37 | + | 1030.37i | −0.0816568 | + | 0.0816568i | ||||
\(543\) | −19973.4 | −1.57853 | ||||||||
\(544\) | −859.092 | − | 2916.34i | −0.0677082 | − | 0.229847i | ||||
\(545\) | 285.821 | 0.0224647 | ||||||||
\(546\) | −1499.57 | + | 1499.57i | −0.117538 | + | 0.117538i | ||||
\(547\) | −6005.27 | + | 14498.0i | −0.469409 | + | 1.13325i | 0.495013 | + | 0.868886i | \(0.335163\pi\) |
−0.964422 | + | 0.264368i | \(0.914837\pi\) | |||||||
\(548\) | 13908.4i | 1.08419i | ||||||||
\(549\) | −2960.82 | − | 1226.41i | −0.230173 | − | 0.0953407i | ||||
\(550\) | 558.498 | + | 1348.33i | 0.0432989 | + | 0.104533i | ||||
\(551\) | 1269.93 | − | 526.023i | 0.0981868 | − | 0.0406703i | ||||
\(552\) | 295.046 | + | 295.046i | 0.0227500 | + | 0.0227500i | ||||
\(553\) | −13019.4 | − | 13019.4i | −1.00116 | − | 1.00116i | ||||
\(554\) | 1423.74 | − | 589.734i | 0.109186 | − | 0.0452263i | ||||
\(555\) | 1723.23 | + | 4160.25i | 0.131797 | + | 0.318185i | ||||
\(556\) | 1514.94 | + | 627.508i | 0.115553 | + | 0.0478638i | ||||
\(557\) | 3540.22i | 0.269307i | 0.990893 | + | 0.134654i | \(0.0429922\pi\) | ||||
−0.990893 | + | 0.134654i | \(0.957008\pi\) | |||||||
\(558\) | −595.447 | + | 1437.54i | −0.0451743 | + | 0.109060i | ||||
\(559\) | 4718.33 | − | 4718.33i | 0.357002 | − | 0.357002i | ||||
\(560\) | 3716.21 | 0.280426 | ||||||||
\(561\) | 15070.3 | − | 27656.8i | 1.13417 | − | 2.08141i | ||||
\(562\) | −1435.18 | −0.107722 | ||||||||
\(563\) | −222.747 | + | 222.747i | −0.0166744 | + | 0.0166744i | −0.715395 | − | 0.698720i | \(-0.753753\pi\) |
0.698720 | + | 0.715395i | \(0.253753\pi\) | |||||||
\(564\) | −5195.05 | + | 12542.0i | −0.387856 | + | 0.936368i | ||||
\(565\) | − | 1013.11i | − | 0.0754371i | ||||||
\(566\) | 562.671 | + | 233.066i | 0.0417859 | + | 0.0173083i | ||||
\(567\) | 1329.14 | + | 3208.82i | 0.0984453 | + | 0.237668i | ||||
\(568\) | −715.801 | + | 296.494i | −0.0528773 | + | 0.0219025i | ||||
\(569\) | −6032.76 | − | 6032.76i | −0.444475 | − | 0.444475i | 0.449038 | − | 0.893513i | \(-0.351767\pi\) |
−0.893513 | + | 0.449038i | \(0.851767\pi\) | |||||||
\(570\) | 71.7068 | + | 71.7068i | 0.00526924 | + | 0.00526924i | ||||
\(571\) | −8156.50 | + | 3378.53i | −0.597791 | + | 0.247613i | −0.660999 | − | 0.750387i | \(-0.729867\pi\) |
0.0632073 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(572\) | 8706.03 | + | 21018.2i | 0.636394 | + | 1.53639i | ||||
\(573\) | 31617.5 | + | 13096.4i | 2.30513 | + | 0.954816i | ||||
\(574\) | − | 2130.02i | − | 0.154887i | ||||||
\(575\) | −626.223 | + | 1511.84i | −0.0454180 | + | 0.109649i | ||||
\(576\) | −14228.2 | + | 14228.2i | −1.02924 | + | 1.02924i | ||||
\(577\) | −21726.1 | −1.56754 | −0.783769 | − | 0.621052i | \(-0.786705\pi\) | ||||
−0.783769 | + | 0.621052i | \(0.786705\pi\) | |||||||
\(578\) | 1094.39 | + | 236.062i | 0.0787557 | + | 0.0169877i | ||||
\(579\) | 17108.0 | 1.22795 | ||||||||
\(580\) | −1082.79 | + | 1082.79i | −0.0775176 | + | 0.0775176i | ||||
\(581\) | −112.728 | + | 272.149i | −0.00804947 | + | 0.0194331i | ||||
\(582\) | − | 2250.50i | − | 0.160286i | ||||||
\(583\) | −15724.7 | − | 6513.37i | −1.11707 | − | 0.462704i | ||||
\(584\) | −40.3969 | − | 97.5267i | −0.00286239 | − | 0.00691042i | ||||
\(585\) | −5454.35 | + | 2259.27i | −0.385487 | + | 0.159674i | ||||
\(586\) | −351.803 | − | 351.803i | −0.0248001 | − | 0.0248001i | ||||
\(587\) | −17447.6 | − | 17447.6i | −1.22682 | − | 1.22682i | −0.965162 | − | 0.261653i | \(-0.915732\pi\) |
−0.261653 | − | 0.965162i | \(-0.584268\pi\) | |||||||
\(588\) | 7271.87 | − | 3012.11i | 0.510011 | − | 0.211254i | ||||
\(589\) | 1254.64 | + | 3028.98i | 0.0877702 | + | 0.211896i | ||||
\(590\) | 334.087 | + | 138.384i | 0.0233121 | + | 0.00965621i | ||||
\(591\) | − | 31337.7i | − | 2.18115i | ||||||
\(592\) | 4770.44 | − | 11516.9i | 0.331189 | − | 0.799561i | ||||
\(593\) | 6673.49 | − | 6673.49i | 0.462137 | − | 0.462137i | −0.437218 | − | 0.899356i | \(-0.644036\pi\) |
0.899356 | + | 0.437218i | \(0.144036\pi\) | |||||||
\(594\) | 1421.66 | 0.0982007 | ||||||||
\(595\) | −1986.00 | + | 3644.68i | −0.136837 | + | 0.251121i | ||||
\(596\) | 16002.6 | 1.09982 | ||||||||
\(597\) | 21101.0 | − | 21101.0i | 1.44658 | − | 1.44658i | ||||
\(598\) | 63.7779 | − | 153.973i | 0.00436132 | − | 0.0105292i | ||||
\(599\) | 28257.9i | 1.92753i | 0.266759 | + | 0.963763i | \(0.414047\pi\) | ||||
−0.266759 | + | 0.963763i | \(0.585953\pi\) | |||||||
\(600\) | 3248.52 | + | 1345.58i | 0.221034 | + | 0.0915553i | ||||
\(601\) | 6674.25 | + | 16113.1i | 0.452993 | + | 1.09362i | 0.971179 | + | 0.238353i | \(0.0766075\pi\) |
−0.518186 | + | 0.855268i | \(0.673393\pi\) | |||||||
\(602\) | 576.084 | − | 238.622i | 0.0390024 | − | 0.0161553i | ||||
\(603\) | −10407.2 | − | 10407.2i | −0.702845 | − | 0.702845i | ||||
\(604\) | 425.179 | + | 425.179i | 0.0286428 | + | 0.0286428i | ||||
\(605\) | −4177.61 | + | 1730.42i | −0.280734 | + | 0.116284i | ||||
\(606\) | 64.1211 | + | 154.802i | 0.00429826 | + | 0.0103769i | ||||
\(607\) | 418.146 | + | 173.202i | 0.0279605 | + | 0.0115816i | 0.396620 | − | 0.917983i | \(-0.370183\pi\) |
−0.368659 | + | 0.929565i | \(0.620183\pi\) | |||||||
\(608\) | − | 851.460i | − | 0.0567948i | ||||||
\(609\) | −4751.60 | + | 11471.4i | −0.316165 | + | 0.763289i | ||||
\(610\) | −34.7531 | + | 34.7531i | −0.00230674 | + | 0.00230674i | ||||
\(611\) | 10879.8 | 0.720377 | ||||||||
\(612\) | −6436.03 | − | 21848.2i | −0.425100 | − | 1.44307i | ||||
\(613\) | −10731.9 | −0.707106 | −0.353553 | − | 0.935415i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935415i | \(0.615027\pi\) | |||||||
\(614\) | 629.277 | − | 629.277i | 0.0413608 | − | 0.0413608i | ||||
\(615\) | 3767.76 | − | 9096.17i | 0.247042 | − | 0.596411i | ||||
\(616\) | 4265.74i | 0.279012i | ||||||||
\(617\) | 18626.4 | + | 7715.29i | 1.21535 | + | 0.503413i | 0.895928 | − | 0.444200i | \(-0.146512\pi\) |
0.319420 | + | 0.947613i | \(0.396512\pi\) | |||||||
\(618\) | −892.496 | − | 2154.68i | −0.0580930 | − | 0.140249i | ||||
\(619\) | 2395.44 | − | 992.223i | 0.155543 | − | 0.0644278i | −0.303554 | − | 0.952814i | \(-0.598173\pi\) |
0.459096 | + | 0.888386i | \(0.348173\pi\) | |||||||
\(620\) | −2582.60 | − | 2582.60i | −0.167290 | − | 0.167290i | ||||
\(621\) | 1127.16 | + | 1127.16i | 0.0728367 | + | 0.0728367i | ||||
\(622\) | −1551.07 | + | 642.476i | −0.0999877 | + | 0.0414163i | ||||
\(623\) | −5362.74 | − | 12946.8i | −0.344869 | − | 0.832588i | ||||
\(624\) | 25071.1 | + | 10384.8i | 1.60841 | + | 0.666224i | ||||
\(625\) | 12843.4i | 0.821977i | ||||||||
\(626\) | 202.911 | − | 489.871i | 0.0129552 | − | 0.0312766i | ||||
\(627\) | 6237.35 | − | 6237.35i | 0.397282 | − | 0.397282i | ||||
\(628\) | 18295.0 | 1.16250 | ||||||||
\(629\) | 8745.78 | + | 10833.4i | 0.554399 | + | 0.686734i | ||||
\(630\) | −551.690 | −0.0348887 | ||||||||
\(631\) | −14799.4 | + | 14799.4i | −0.933685 | + | 0.933685i | −0.997934 | − | 0.0642487i | \(-0.979535\pi\) |
0.0642487 | + | 0.997934i | \(0.479535\pi\) | |||||||
\(632\) | 1189.80 | − | 2872.43i | 0.0748856 | − | 0.180790i | ||||
\(633\) | 5211.31i | 0.327221i | ||||||||
\(634\) | −1572.73 | − | 651.445i | −0.0985188 | − | 0.0408078i | ||||
\(635\) | −1319.78 | − | 3186.22i | −0.0824783 | − | 0.199120i | ||||
\(636\) | −18881.0 | + | 7820.75i | −1.17717 | + | 0.487599i | ||||
\(637\) | −4460.54 | − | 4460.54i | −0.277446 | − | 0.277446i | ||||
\(638\) | −615.353 | − | 615.353i | −0.0381850 | − | 0.0381850i | ||||
\(639\) | −8052.54 | + | 3335.47i | −0.498519 | + | 0.206493i | ||||
\(640\) | 483.453 | + | 1167.16i | 0.0298596 | + | 0.0720876i | ||||
\(641\) | −8975.50 | − | 3717.77i | −0.553059 | − | 0.229085i | 0.0886097 | − | 0.996066i | \(-0.471758\pi\) |
−0.641669 | + | 0.766982i | \(0.721758\pi\) | |||||||
\(642\) | 2886.84i | 0.177468i | ||||||||
\(643\) | −9268.20 | + | 22375.4i | −0.568433 | + | 1.37232i | 0.334443 | + | 0.942416i | \(0.391452\pi\) |
−0.902876 | + | 0.429902i | \(0.858548\pi\) | |||||||
\(644\) | −1685.55 | + | 1685.55i | −0.103136 | + | 0.103136i | ||||
\(645\) | 2882.24 | 0.175951 | ||||||||
\(646\) | 275.327 | + | 150.027i | 0.0167687 | + | 0.00913734i | ||||
\(647\) | 5143.07 | 0.312511 | 0.156256 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156256 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(648\) | −414.709 | + | 414.709i | −0.0251409 | + | 0.0251409i | ||||
\(649\) | 12037.2 | − | 29060.3i | 0.728043 | − | 1.75765i | ||||
\(650\) | − | 1404.42i | − | 0.0847473i | ||||||
\(651\) | −27360.9 | − | 11333.3i | −1.64725 | − | 0.682313i | ||||
\(652\) | −5757.74 | − | 13900.4i | −0.345845 | − | 0.834943i | ||||
\(653\) | −2700.35 | + | 1118.52i | −0.161827 | + | 0.0670308i | −0.462126 | − | 0.886814i | \(-0.652913\pi\) |
0.300300 | + | 0.953845i | \(0.402913\pi\) | |||||||
\(654\) | 137.913 | + | 137.913i | 0.00824588 | + | 0.00824588i | ||||
\(655\) | −3803.20 | − | 3803.20i | −0.226875 | − | 0.226875i | ||||
\(656\) | −25181.0 | + | 10430.3i | −1.49871 | + | 0.620786i | ||||
\(657\) | −454.452 | − | 1097.15i | −0.0269861 | − | 0.0651502i | ||||
\(658\) | 939.300 | + | 389.071i | 0.0556500 | + | 0.0230510i | ||||
\(659\) | − | 17368.4i | − | 1.02667i | −0.858188 | − | 0.513336i | \(-0.828409\pi\) | ||
0.858188 | − | 0.513336i | \(-0.171591\pi\) | |||||||
\(660\) | −3760.51 | + | 9078.68i | −0.221785 | + | 0.535435i | ||||
\(661\) | 5685.94 | − | 5685.94i | 0.334580 | − | 0.334580i | −0.519743 | − | 0.854323i | \(-0.673972\pi\) |
0.854323 | + | 0.519743i | \(0.173972\pi\) | |||||||
\(662\) | −2131.38 | −0.125134 | ||||||||
\(663\) | −23583.2 | + | 19038.7i | −1.38144 | + | 1.11524i | ||||
\(664\) | −49.7417 | −0.00290715 | ||||||||
\(665\) | −821.973 | + | 821.973i | −0.0479319 | + | 0.0479319i | ||||
\(666\) | −708.196 | + | 1709.74i | −0.0412042 | + | 0.0994758i | ||||
\(667\) | − | 975.769i | − | 0.0566446i | ||||||
\(668\) | 796.558 | + | 329.945i | 0.0461374 | + | 0.0191107i | ||||
\(669\) | −1683.10 | − | 4063.37i | −0.0972683 | − | 0.234826i | ||||
\(670\) | −208.534 | + | 86.3777i | −0.0120244 | + | 0.00498069i | ||||
\(671\) | 3022.97 | + | 3022.97i | 0.173920 | + | 0.173920i | ||||
\(672\) | 5438.56 | + | 5438.56i | 0.312198 | + | 0.312198i | ||||
\(673\) | 8385.45 | − | 3473.37i | 0.480290 | − | 0.198943i | −0.129384 | − | 0.991595i | \(-0.541300\pi\) |
0.609675 | + | 0.792652i | \(0.291300\pi\) | |||||||
\(674\) | 605.559 | + | 1461.95i | 0.0346072 | + | 0.0835493i | ||||
\(675\) | 12410.3 | + | 5140.52i | 0.707664 | + | 0.293124i | ||||
\(676\) | − | 4430.54i | − | 0.252079i | ||||||
\(677\) | −9550.85 | + | 23057.8i | −0.542199 | + | 1.30899i | 0.380969 | + | 0.924588i | \(0.375591\pi\) |
−0.923168 | + | 0.384397i | \(0.874409\pi\) | |||||||
\(678\) | 488.840 | − | 488.840i | 0.0276900 | − | 0.0276900i | ||||
\(679\) | 25797.4 | 1.45805 | ||||||||
\(680\) | −696.930 | − | 74.3097i | −0.0393030 | − | 0.00419066i | ||||
\(681\) | 4851.56 | 0.272999 | ||||||||
\(682\) | 1467.71 | − | 1467.71i | 0.0824068 | − | 0.0824068i | ||||
\(683\) | −2322.36 | + | 5606.67i | −0.130106 | + | 0.314105i | −0.975486 | − | 0.220061i | \(-0.929374\pi\) |
0.845380 | + | 0.534166i | \(0.179374\pi\) | |||||||
\(684\) | − | 6378.85i | − | 0.356581i | ||||||
\(685\) | 4448.26 | + | 1842.53i | 0.248116 | + | 0.102773i | ||||
\(686\) | 418.166 | + | 1009.54i | 0.0232735 | + | 0.0561873i | ||||
\(687\) | 20104.4 | − | 8327.51i | 1.11649 | − | 0.462466i | ||||
\(688\) | −5641.96 | − | 5641.96i | −0.312642 | − | 0.312642i | ||||
\(689\) | 11581.5 | + | 11581.5i | 0.640378 | + | 0.640378i | ||||
\(690\) | 66.5079 | − | 27.5485i | 0.00366944 | − | 0.00151993i | ||||
\(691\) | 6641.71 | + | 16034.5i | 0.365648 | + | 0.882752i | 0.994452 | + | 0.105189i | \(0.0335446\pi\) |
−0.628804 | + | 0.777564i | \(0.716455\pi\) | |||||||
\(692\) | −20235.8 | − | 8381.96i | −1.11163 | − | 0.460454i | ||||
\(693\) | 47988.2i | 2.63048i | ||||||||
\(694\) | −210.163 | + | 507.378i | −0.0114952 | + | 0.0277519i | ||||
\(695\) | 401.387 | − | 401.387i | 0.0219072 | − | 0.0219072i | ||||
\(696\) | −2096.66 | −0.114186 | ||||||||
\(697\) | 3227.56 | − | 30270.4i | 0.175398 | − | 1.64501i | ||||
\(698\) | 2507.87 | 0.135995 | ||||||||
\(699\) | 2233.54 | − | 2233.54i | 0.120859 | − | 0.120859i | ||||
\(700\) | −7687.07 | + | 18558.2i | −0.415063 | + | 1.00205i | ||||
\(701\) | − | 34827.5i | − | 1.87649i | −0.345976 | − | 0.938243i | \(-0.612452\pi\) | ||
0.345976 | − | 0.938243i | \(-0.387548\pi\) | |||||||
\(702\) | −1263.93 | − | 523.538i | −0.0679545 | − | 0.0281477i | ||||
\(703\) | 1492.21 | + | 3602.52i | 0.0800566 | + | 0.193274i | ||||
\(704\) | 24798.8 | − | 10272.0i | 1.32761 | − | 0.549915i | ||||
\(705\) | 3323.03 | + | 3323.03i | 0.177521 | + | 0.177521i | ||||
\(706\) | −1242.86 | − | 1242.86i | −0.0662546 | − | 0.0662546i | ||||
\(707\) | −1774.49 | + | 735.018i | −0.0943941 | + | 0.0390993i | ||||
\(708\) | −14453.3 | − | 34893.3i | −0.767215 | − | 1.85222i | ||||
\(709\) | −23731.7 | − | 9830.00i | −1.25707 | − | 0.520696i | −0.348062 | − | 0.937472i | \(-0.613160\pi\) |
−0.909009 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(710\) | 133.669i | 0.00706548i | ||||||||
\(711\) | 13384.9 | − | 32314.0i | 0.706009 | − | 1.70446i | ||||
\(712\) | 1673.25 | − | 1673.25i | 0.0880725 | − | 0.0880725i | ||||
\(713\) | 2327.35 | 0.122244 | ||||||||
\(714\) | −2716.88 | + | 800.335i | −0.142404 | + | 0.0419493i | ||||
\(715\) | 7875.52 | 0.411927 | ||||||||
\(716\) | 11274.8 | − | 11274.8i | 0.588492 | − | 0.588492i | ||||
\(717\) | −13698.5 | + | 33071.2i | −0.713502 | + | 1.72255i | ||||
\(718\) | 2328.92i | 0.121051i | ||||||||
\(719\) | −16792.7 | − | 6955.77i | −0.871018 | − | 0.360788i | −0.0980115 | − | 0.995185i | \(-0.531248\pi\) |
−0.773007 | + | 0.634398i | \(0.781248\pi\) | |||||||
\(720\) | 2701.53 | + | 6522.06i | 0.139833 | + | 0.337587i | ||||
\(721\) | 24699.0 | − | 10230.7i | 1.27578 | − | 0.528446i | ||||
\(722\) | −1043.12 | − | 1043.12i | −0.0537688 | − | 0.0537688i | ||||
\(723\) | 11964.6 | + | 11964.6i | 0.615448 | + | 0.615448i | ||||
\(724\) | 17801.1 | − | 7373.46i | 0.913775 | − | 0.378498i | ||||
\(725\) | −3146.68 | − | 7596.75i | −0.161193 | − | 0.389153i | ||||
\(726\) | −2850.71 | − | 1180.80i | −0.145730 | − | 0.0603632i | ||||
\(727\) | − | 8657.73i | − | 0.441674i | −0.975311 | − | 0.220837i | \(-0.929121\pi\) | ||
0.975311 | − | 0.220837i | \(-0.0708789\pi\) | |||||||
\(728\) | 1570.90 | − | 3792.48i | 0.0799744 | − | 0.193075i | ||||
\(729\) | −22659.1 | + | 22659.1i | −1.15120 | + | 1.15120i | ||||
\(730\) | −18.2121 | −0.000923371 | ||||||||
\(731\) | 8548.50 | − | 2518.21i | 0.432528 | − | 0.127414i | ||||
\(732\) | 5133.24 | 0.259194 | ||||||||
\(733\) | −7989.74 | + | 7989.74i | −0.402603 | + | 0.402603i | −0.879149 | − | 0.476546i | \(-0.841888\pi\) |
0.476546 | + | 0.879149i | \(0.341888\pi\) | |||||||
\(734\) | −900.168 | + | 2173.20i | −0.0452668 | + | 0.109284i | ||||
\(735\) | − | 2724.77i | − | 0.136741i | ||||||
\(736\) | −558.421 | − | 231.306i | −0.0279670 | − | 0.0115843i | ||||
\(737\) | 7513.48 | + | 18139.1i | 0.375526 | + | 0.906600i | ||||
\(738\) | 3738.25 | − | 1548.43i | 0.186459 | − | 0.0772338i | ||||
\(739\) | 8885.48 | + | 8885.48i | 0.442297 | + | 0.442297i | 0.892783 | − | 0.450486i | \(-0.148749\pi\) |
−0.450486 | + | 0.892783i | \(0.648749\pi\) | |||||||
\(740\) | −3071.62 | − | 3071.62i | −0.152588 | − | 0.152588i | ||||
\(741\) | −7842.32 | + | 3248.40i | −0.388792 | + | 0.161043i | ||||
\(742\) | 585.716 | + | 1414.04i | 0.0289789 | + | 0.0699612i | ||||
\(743\) | 12980.0 | + | 5376.49i | 0.640902 | + | 0.265470i | 0.679377 | − | 0.733789i | \(-0.262250\pi\) |
−0.0384753 | + | 0.999260i | \(0.512250\pi\) | |||||||
\(744\) | − | 5000.85i | − | 0.246425i | ||||||
\(745\) | 2119.96 | − | 5118.04i | 0.104254 | − | 0.251692i | ||||
\(746\) | 442.166 | − | 442.166i | 0.0217009 | − | 0.0217009i | ||||
\(747\) | −559.578 | −0.0274082 | ||||||||
\(748\) | −3221.36 | + | 30212.2i | −0.157466 | + | 1.47683i | ||||
\(749\) | −33091.7 | −1.61435 | ||||||||
\(750\) | 885.556 | − | 885.556i | 0.0431146 | − | 0.0431146i | ||||
\(751\) | −3111.79 | + | 7512.52i | −0.151199 | + | 0.365027i | −0.981272 | − | 0.192628i | \(-0.938299\pi\) |
0.830073 | + | 0.557655i | \(0.188299\pi\) | |||||||
\(752\) | − | 13009.6i | − | 0.630865i | ||||||
\(753\) | 6911.33 | + | 2862.77i | 0.334479 | + | 0.138546i | ||||
\(754\) | 320.474 | + | 773.693i | 0.0154788 | + | 0.0373690i | ||||
\(755\) | 192.309 | − | 79.6572i | 0.00927001 | − | 0.00383976i | ||||
\(756\) | 13836.3 | + | 13836.3i | 0.665635 | + | 0.665635i | ||||
\(757\) | 16245.0 | + | 16245.0i | 0.779964 | + | 0.779964i | 0.979824 | − | 0.199860i | \(-0.0640488\pi\) |
−0.199860 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(758\) | 1348.46 | − | 558.549i | 0.0646149 | − | 0.0267644i | ||||
\(759\) | −2396.28 | − | 5785.12i | −0.114597 | − | 0.276662i | ||||
\(760\) | −181.349 | − | 75.1174i | −0.00865557 | − | 0.00358525i | ||||
\(761\) | 15071.9i | 0.717946i | 0.933348 | + | 0.358973i | \(0.116873\pi\) | ||||
−0.933348 | + | 0.358973i | \(0.883127\pi\) | |||||||
\(762\) | 900.585 | − | 2174.20i | 0.0428146 | − | 0.103364i | ||||
\(763\) | −1580.89 | + | 1580.89i | −0.0750091 | + | 0.0750091i | ||||
\(764\) | −33013.4 | −1.56333 | ||||||||
\(765\) | −7840.25 | − | 835.961i | −0.370542 | − | 0.0395088i | ||||
\(766\) | 841.515 | 0.0396934 | ||||||||
\(767\) | −21403.4 | + | 21403.4i | −1.00761 | + | 1.00761i | ||||
\(768\) | 12084.5 | − | 29174.5i | 0.567788 | − | 1.37076i | ||||
\(769\) | 10392.1i | 0.487321i | 0.969861 | + | 0.243660i | \(0.0783482\pi\) | ||||
−0.969861 | + | 0.243660i | \(0.921652\pi\) | |||||||
\(770\) | 679.926 | + | 281.635i | 0.0318219 | + | 0.0131811i | ||||
\(771\) | −23618.5 | − | 57020.0i | −1.10324 | − | 2.66346i | ||||
\(772\) | −15247.3 | + | 6315.63i | −0.710831 | + | 0.294436i | ||||
\(773\) | −24316.4 | − | 24316.4i | −1.13144 | − | 1.13144i | −0.989938 | − | 0.141499i | \(-0.954808\pi\) |
−0.141499 | − | 0.989938i | \(-0.545192\pi\) | |||||||
\(774\) | 837.577 | + | 837.577i | 0.0388967 | + | 0.0388967i | ||||
\(775\) | 18119.4 | − | 7505.29i | 0.839829 | − | 0.347868i | ||||
\(776\) | 1667.03 | + | 4024.57i | 0.0771172 | + | 0.186177i | ||||
\(777\) | −32541.7 | − | 13479.2i | −1.50248 | − | 0.622348i | ||||
\(778\) | − | 486.052i | − | 0.0223982i | ||||||
\(779\) | 3262.64 | − | 7876.71i | 0.150059 | − | 0.362275i | ||||
\(780\) | 6686.62 | − | 6686.62i | 0.306948 | − | 0.306948i | ||||
\(781\) | 11627.0 | 0.532712 | ||||||||
\(782\) | 173.188 | − | 139.814i | 0.00791968 | − | 0.00639355i | ||||
\(783\) | −8009.87 | −0.365580 | ||||||||
\(784\) | −5333.70 | + | 5333.70i | −0.242971 | + | 0.242971i | ||||
\(785\) | 2423.65 | − | 5851.21i | 0.110196 | − | 0.266036i | ||||
\(786\) | − | 3670.19i | − | 0.166554i | ||||||
\(787\) | 23671.4 | + | 9805.02i | 1.07217 | + | 0.444106i | 0.847754 | − | 0.530389i | \(-0.177954\pi\) |
0.224411 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(788\) | 11568.7 | + | 27929.3i | 0.522993 | + | 1.26262i | ||||
\(789\) | −59835.5 | + | 24784.7i | −2.69987 | + | 1.11832i | ||||
\(790\) | −379.290 | − | 379.290i | −0.0170817 | − | 0.0170817i | ||||
\(791\) | 5603.56 | + | 5603.56i | 0.251883 | + | 0.251883i | ||||
\(792\) | −7486.50 | + | 3101.01i | −0.335885 | + | 0.139128i | ||||
\(793\) | −1574.35 | − | 3800.83i | −0.0705006 | − | 0.170203i | ||||
\(794\) | 497.879 | + | 206.228i | 0.0222532 | + | 0.00921759i | ||||
\(795\) | 7074.69i | 0.315614i | ||||||||
\(796\) | −11016.3 | + | 26595.7i | −0.490532 | + | 1.18425i | ||||
\(797\) | 20108.4 | − | 20108.4i | 0.893698 | − | 0.893698i | −0.101171 | − | 0.994869i | \(-0.532259\pi\) |
0.994869 | + | 0.101171i | \(0.0322589\pi\) | |||||||
\(798\) | −793.226 | −0.0351878 | ||||||||
\(799\) | 12759.2 | + | 6952.51i | 0.564939 | + | 0.307838i | ||||
\(800\) | −5093.45 | −0.225101 | ||||||||
\(801\) | 18823.5 | − | 18823.5i | 0.830333 | − | 0.830333i | ||||
\(802\) | −179.969 | + | 434.483i | −0.00792383 | + | 0.0191298i | ||||
\(803\) | 1584.16i | 0.0696188i | ||||||||
\(804\) | 21780.1 | + | 9021.60i | 0.955378 | + | 0.395731i | ||||
\(805\) | 315.787 | + | 762.377i | 0.0138261 | + | 0.0333792i | ||||
\(806\) | −1845.37 | + | 764.378i | −0.0806458 | + | 0.0334046i | ||||
\(807\) | 44008.5 | + | 44008.5i | 1.91967 | + | 1.91967i | ||||
\(808\) | −229.336 | − | 229.336i | −0.00998515 | − | 0.00998515i | ||||
\(809\) | 20652.5 | − | 8554.55i | 0.897532 | − | 0.371770i | 0.114261 | − | 0.993451i | \(-0.463550\pi\) |
0.783271 | + | 0.621681i | \(0.213550\pi\) | |||||||
\(810\) | 38.7213 | + | 93.4816i | 0.00167967 | + | 0.00405507i | ||||
\(811\) | −5572.70 | − | 2308.29i | −0.241287 | − | 0.0999444i | 0.258763 | − | 0.965941i | \(-0.416685\pi\) |
−0.500050 | + | 0.865996i | \(0.666685\pi\) | |||||||
\(812\) | − | 11977.8i | − | 0.517660i | ||||||
\(813\) | 20161.7 | − | 48674.6i | 0.869743 | − | 2.09975i | ||||
\(814\) | 1745.62 | − | 1745.62i | 0.0751646 | − | 0.0751646i | ||||
\(815\) | −5208.49 | −0.223859 | ||||||||
\(816\) | 22765.6 | + | 28199.7i | 0.976660 | + | 1.20979i | ||||
\(817\) | 2495.84 | 0.106877 | ||||||||
\(818\) | −1489.69 | + | 1489.69i | −0.0636744 | + | 0.0636744i | ||||
\(819\) | 17672.1 | − | 42664.3i | 0.753985 | − | 1.82028i | ||||
\(820\) | 9497.78i | 0.404484i | ||||||||
\(821\) | 11698.6 | + | 4845.73i | 0.497302 | + | 0.205989i | 0.617214 | − | 0.786795i | \(-0.288261\pi\) |
−0.119912 | + | 0.992785i | \(0.538261\pi\) | |||||||
\(822\) | 1257.30 | + | 3035.39i | 0.0533496 | + | 0.128797i | ||||
\(823\) | 10190.3 | − | 4220.95i | 0.431605 | − | 0.178777i | −0.156295 | − | 0.987710i | \(-0.549955\pi\) |
0.587900 | + | 0.808934i | \(0.299955\pi\) | |||||||
\(824\) | 3192.10 | + | 3192.10i | 0.134954 | + | 0.134954i | ||||
\(825\) | −37311.9 | − | 37311.9i | −1.57459 | − | 1.57459i | ||||
\(826\) | −2613.25 | + | 1082.44i | −0.110081 | + | 0.0455969i | ||||
\(827\) | 10962.5 | + | 26465.9i | 0.460948 | + | 1.11283i | 0.968009 | + | 0.250917i | \(0.0807322\pi\) |
−0.507060 | + | 0.861911i | \(0.669268\pi\) | |||||||
\(828\) | −4183.50 | − | 1732.86i | −0.175588 | − | 0.0727309i | ||||
\(829\) | − | 15663.7i | − | 0.656239i | −0.944636 | − | 0.328120i | \(-0.893585\pi\) | ||
0.944636 | − | 0.328120i | \(-0.106415\pi\) | |||||||
\(830\) | −3.28407 | + | 7.92844i | −0.000137339 | + | 0.000331567i | ||||
\(831\) | −39398.8 | + | 39398.8i | −1.64468 | + | 1.64468i | ||||
\(832\) | −25830.3 | −1.07633 | ||||||||
\(833\) | −2380.62 | − | 8081.44i | −0.0990201 | − | 0.336141i | ||||
\(834\) | 387.349 | 0.0160825 | ||||||||
\(835\) | 211.050 | − | 211.050i | 0.00874694 | − | 0.00874694i | ||||
\(836\) | −3256.37 | + | 7861.57i | −0.134718 | + | 0.325237i | ||||
\(837\) | − | 19104.7i | − | 0.788955i | ||||||
\(838\) | −874.837 | − | 362.369i | −0.0360629 | − | 0.0149378i | ||||
\(839\) | 8669.06 | + | 20929.0i | 0.356721 | + | 0.861201i | 0.995757 | + | 0.0920240i | \(0.0293337\pi\) |
−0.639036 | + | 0.769177i | \(0.720666\pi\) | |||||||
\(840\) | 1638.14 | − | 678.540i | 0.0672871 | − | 0.0278712i | ||||
\(841\) | −13778.6 | − | 13778.6i | −0.564952 | − | 0.564952i | ||||
\(842\) | −742.709 | − | 742.709i | −0.0303984 | − | 0.0303984i | ||||
\(843\) | 47940.6 | − | 19857.7i | 1.95868 | − | 0.811310i | ||||
\(844\) | −1923.82 | − | 4644.52i | −0.0784606 | − | 0.189421i | ||||
\(845\) | −1417.00 | − | 586.942i | −0.0576880 | − | 0.0238952i | ||||
\(846\) | 1931.34i | 0.0784879i | ||||||||
\(847\) | 13535.5 | − | 32677.6i | 0.549097 | − | 1.32564i | ||||
\(848\) | 13848.6 | − | 13848.6i | 0.560807 | − | 0.560807i | ||||
\(849\) | −22020.1 | −0.890141 | ||||||||
\(850\) | 897.462 | − | 1647.01i | 0.0362149 | − | 0.0664611i | ||||
\(851\) | 2768.04 | 0.111501 | ||||||||
\(852\) | 9871.80 | − | 9871.80i | 0.396951 | − | 0.396951i | ||||
\(853\) | −1702.92 | + | 4111.21i | −0.0683551 | + | 0.165024i | −0.954365 | − | 0.298642i | \(-0.903466\pi\) |
0.886010 | + | 0.463666i | \(0.153466\pi\) | |||||||
\(854\) | − | 384.442i | − | 0.0154044i | ||||||
\(855\) | −2040.12 | − | 845.047i | −0.0816033 | − | 0.0338012i | ||||
\(856\) | −2138.39 | − | 5162.54i | −0.0853841 | − | 0.206135i | ||||
\(857\) | −20994.3 | + | 8696.11i | −0.836815 | + | 0.346620i | −0.759597 | − | 0.650394i | \(-0.774604\pi\) |
−0.0772178 | + | 0.997014i | \(0.524604\pi\) | |||||||
\(858\) | 3800.04 | + | 3800.04i | 0.151202 | + | 0.151202i | ||||
\(859\) | −29733.4 | − | 29733.4i | −1.18102 | − | 1.18102i | −0.979482 | − | 0.201533i | \(-0.935408\pi\) |
−0.201533 | − | 0.979482i | \(-0.564592\pi\) | |||||||
\(860\) | −2568.76 | + | 1064.02i | −0.101854 | + | 0.0421892i | ||||
\(861\) | 29471.6 | + | 71150.8i | 1.16654 | + | 2.81628i | ||||
\(862\) | 3648.59 | + | 1511.30i | 0.144166 | + | 0.0597157i | ||||
\(863\) | − | 7875.51i | − | 0.310644i | −0.987864 | − | 0.155322i | \(-0.950359\pi\) | ||
0.987864 | − | 0.155322i | \(-0.0496414\pi\) | |||||||
\(864\) | −1898.73 | + | 4583.95i | −0.0747642 | + | 0.180497i | ||||
\(865\) | −5361.54 | + | 5361.54i | −0.210749 | + | 0.210749i | ||||
\(866\) | −2587.30 | −0.101524 | ||||||||
\(867\) | −39823.2 | + | 7257.02i | −1.55994 | + | 0.284269i | ||||
\(868\) | 28568.9 | 1.11716 | ||||||||
\(869\) | −32992.2 | + | 32992.2i | −1.28790 | + | 1.28790i | ||||
\(870\) | −138.427 | + | 334.192i | −0.00539438 | + | 0.0130232i | ||||
\(871\) | − | 18893.6i | − | 0.735002i | ||||||
\(872\) | −348.786 | − | 144.472i | −0.0135452 | − | 0.00561060i | ||||
\(873\) | 18753.6 | + | 45275.2i | 0.727048 | + | 1.75525i | ||||
\(874\) | 57.5917 | − | 23.8552i | 0.00222891 | − | 0.000923244i | ||||
\(875\) | 10151.1 | + | 10151.1i | 0.392194 | + | 0.392194i | ||||
\(876\) | 1345.02 | + | 1345.02i | 0.0518766 | + | 0.0518766i | ||||
\(877\) | −24138.0 | + | 9998.27i | −0.929397 | + | 0.384969i | −0.795450 | − | 0.606020i | \(-0.792765\pi\) |
−0.133947 | + | 0.990988i | \(0.542765\pi\) | |||||||
\(878\) | −447.194 | − | 1079.62i | −0.0171891 | − | 0.0414983i | ||||
\(879\) | 16619.2 | + | 6883.91i | 0.637716 | + | 0.264151i | ||||
\(880\) | − | 9417.18i | − | 0.360742i | ||||||
\(881\) | 2449.18 | − | 5912.84i | 0.0936604 | − | 0.226116i | −0.870106 | − | 0.492865i | \(-0.835949\pi\) |
0.963766 | + | 0.266749i | \(0.0859495\pi\) | |||||||
\(882\) | 791.815 | − | 791.815i | 0.0302288 | − | 0.0302288i | ||||
\(883\) | −43393.3 | −1.65379 | −0.826897 | − | 0.562354i | \(-0.809896\pi\) | ||||
−0.826897 | + | 0.562354i | \(0.809896\pi\) | |||||||
\(884\) | 13989.9 | − | 25674.1i | 0.532275 | − | 0.976824i | ||||
\(885\) | −13074.5 | −0.496605 | ||||||||
\(886\) | 504.832 | − | 504.832i | 0.0191424 | − | 0.0191424i | ||||
\(887\) | 7831.78 | − | 18907.6i | 0.296466 | − | 0.715733i | −0.703521 | − | 0.710675i | \(-0.748390\pi\) |
0.999987 | − | 0.00505836i | \(-0.00161013\pi\) | |||||||
\(888\) | − | 5947.77i | − | 0.224768i | ||||||
\(889\) | 24922.8 | + | 10323.4i | 0.940253 | + | 0.389466i | ||||
\(890\) | −156.231 | − | 377.175i | −0.00588413 | − | 0.0142055i | ||||
\(891\) | 8131.41 | − | 3368.14i | 0.305738 | − | 0.126641i | ||||
\(892\) | 3000.09 | + | 3000.09i | 0.112613 | + | 0.112613i | ||||
\(893\) | 2877.53 | + | 2877.53i | 0.107831 | + | 0.107831i | ||||
\(894\) | 3492.43 | − | 1446.61i | 0.130654 | − | 0.0541185i | ||||
\(895\) | −2112.34 | − | 5099.64i | −0.0788913 | − | 0.190460i | ||||
\(896\) | −9129.60 | − | 3781.60i | −0.340400 | − | 0.140998i | ||||
\(897\) | 6025.76i | 0.224297i | ||||||||
\(898\) | −1024.62 | + | 2473.66i | −0.0380759 | + | 0.0919233i | ||||
\(899\) | −8269.33 | + | 8269.33i | −0.306783 | + | 0.306783i | ||||
\(900\) | −38158.4 | −1.41327 | ||||||||
\(901\) | 6181.15 | + | 20983.0i | 0.228550 | + | 0.775854i | ||||
\(902\) | −5397.64 | −0.199248 | ||||||||
\(903\) | −15941.8 | + | 15941.8i | −0.587496 | + | 0.587496i | ||||
\(904\) | −512.091 | + | 1236.30i | −0.0188406 | + | 0.0454852i | ||||
\(905\) | − | 6670.07i | − | 0.244995i | ||||||
\(906\) | 131.228 | + | 54.3562i | 0.00481208 | + | 0.00199323i | ||||
\(907\) | −11555.0 | − | 27896.3i | −0.423019 | − | 1.02126i | −0.981452 | − | 0.191709i | \(-0.938597\pi\) |
0.558433 | − | 0.829550i | \(-0.311403\pi\) | |||||||
\(908\) | −4323.90 | + | 1791.02i | −0.158033 | + | 0.0654593i | ||||
\(909\) | −2579.96 | − | 2579.96i | −0.0941384 | − | 0.0941384i | ||||
\(910\) | −500.779 | − | 500.779i | −0.0182425 | − | 0.0182425i | ||||
\(911\) | 21246.6 | − | 8800.64i | 0.772703 | − | 0.320064i | 0.0387363 | − | 0.999249i | \(-0.487667\pi\) |
0.733967 | + | 0.679185i | \(0.237667\pi\) | |||||||
\(912\) | 3884.28 | + | 9377.49i | 0.141032 | + | 0.340482i | ||||
\(913\) | 689.648 | + | 285.662i | 0.0249989 | + | 0.0103549i | ||||
\(914\) | − | 2827.68i | − | 0.102332i | ||||||
\(915\) | 680.032 | − | 1641.74i | 0.0245696 | − | 0.0593162i | ||||
\(916\) | −14843.6 | + | 14843.6i | −0.535422 | + | 0.535422i | ||||
\(917\) | 42071.3 | 1.51507 | ||||||||
\(918\) | −1147.70 | − | 1421.66i | −0.0412635 | − | 0.0511131i | ||||
\(919\) | −40432.8 | −1.45131 | −0.725656 | − | 0.688057i | \(-0.758464\pi\) | ||||
−0.725656 | + | 0.688057i | \(0.758464\pi\) | |||||||
\(920\) | −98.5299 | + | 98.5299i | −0.00353091 | + | 0.00353091i | ||||
\(921\) | −12313.4 | + | 29727.1i | −0.440543 | + | 1.06356i | ||||
\(922\) | 1679.57i | 0.0599932i | ||||||||
\(923\) | −10337.1 | − | 4281.76i | −0.368634 | − | 0.152693i | ||||
\(924\) | −29415.0 | − | 71014.0i | −1.04727 | − | 2.52834i | ||||
\(925\) | 21550.3 | − | 8926.43i | 0.766021 | − | 0.317296i | ||||
\(926\) | 1844.48 | + | 1844.48i | 0.0654574 | + | 0.0654574i | ||||
\(927\) | 35910.2 | + | 35910.2i | 1.27232 | + | 1.27232i | ||||
\(928\) | 2805.98 | − | 1162.28i | 0.0992574 | − | 0.0411137i | ||||
\(929\) | −13044.2 | − | 31491.4i | −0.460673 | − | 1.11216i | −0.968121 | − | 0.250482i | \(-0.919411\pi\) |
0.507448 | − | 0.861682i | \(-0.330589\pi\) | |||||||
\(930\) | −797.097 | − | 330.168i | −0.0281052 | − | 0.0116416i | ||||
\(931\) | − | 2359.48i | − | 0.0830599i | ||||||
\(932\) | −1166.08 | + | 2815.16i | −0.0409830 | + | 0.0989418i | ||||
\(933\) | 42922.3 | − | 42922.3i | 1.50612 | − | 1.50612i | ||||
\(934\) | −1006.83 | −0.0352724 | ||||||||
\(935\) | 9235.91 | + | 5032.68i | 0.323044 | + | 0.176028i | ||||
\(936\) | 7797.89 | 0.272310 | ||||||||
\(937\) | −539.977 | + | 539.977i | −0.0188263 | + | 0.0188263i | −0.716457 | − | 0.697631i | \(-0.754238\pi\) |
0.697631 | + | 0.716457i | \(0.254238\pi\) | |||||||
\(938\) | 675.652 | − | 1631.17i | 0.0235190 | − | 0.0567799i | ||||
\(939\) | 19171.1i | 0.666268i | ||||||||
\(940\) | −4188.35 | − | 1734.87i | −0.145329 | − | 0.0601971i | ||||
\(941\) | −170.281 | − | 411.094i | −0.00589904 | − | 0.0142415i | 0.920903 | − | 0.389793i | \(-0.127453\pi\) |
−0.926802 | + | 0.375551i | \(0.877453\pi\) | |||||||
\(942\) | 3992.73 | − | 1653.84i | 0.138100 | − | 0.0572029i | ||||
\(943\) | −4279.54 | − | 4279.54i | −0.147785 | − | 0.147785i | ||||
\(944\) | 25593.3 | + | 25593.3i | 0.882404 | + | 0.882404i | ||||
\(945\) | 6258.18 | − | 2592.22i | 0.215427 | − | 0.0892328i | ||||
\(946\) | −604.687 | − | 1459.84i | −0.0207823 | − | 0.0501729i | ||||
\(947\) | −10304.9 | − | 4268.42i | −0.353604 | − | 0.146468i | 0.198808 | − | 0.980038i | \(-0.436293\pi\) |
−0.552413 | + | 0.833571i | \(0.686293\pi\) | |||||||
\(948\) | 56023.3i | 1.91936i | ||||||||
\(949\) | 583.383 | − | 1408.41i | 0.0199551 | − | 0.0481759i | ||||
\(950\) | 371.445 | − | 371.445i | 0.0126855 | − | 0.0126855i | ||||
\(951\) | 61548.7 | 2.09869 | ||||||||
\(952\) | 4265.75 | − | 3443.74i | 0.145225 | − | 0.117240i | ||||
\(953\) | 48344.2 | 1.64325 | 0.821627 | − | 0.570026i | \(-0.193067\pi\) | ||||
0.821627 | + | 0.570026i | \(0.193067\pi\) | |||||||
\(954\) | −2055.90 | + | 2055.90i | −0.0697717 | + | 0.0697717i | ||||
\(955\) | −4373.50 | + | 10558.6i | −0.148192 | + | 0.357767i | ||||
\(956\) | − | 34531.3i | − | 1.16822i | ||||||
\(957\) | 29069.4 | + | 12040.9i | 0.981901 | + | 0.406717i | ||||
\(958\) | −24.6455 | − | 59.4994i | −0.000831168 | − | 0.00200662i | ||||
\(959\) | −34794.6 | + | 14412.4i | −1.17161 | + | 0.485298i | ||||
\(960\) | −7889.35 | − | 7889.35i | −0.265237 | − | 0.265237i | ||||
\(961\) | 1341.84 | + | 1341.84i | 0.0450417 | + | 0.0450417i | ||||
\(962\) | −2194.80 | + | 909.115i | −0.0735583 | + | 0.0304688i | ||||
\(963\) | −24056.3 | − | 58077.0i | −0.804987 | − | 1.94341i | ||||
\(964\) | −15080.2 | − | 6246.43i | −0.503840 | − | 0.208697i | ||||
\(965\) | 5713.15i | 0.190583i | ||||||||
\(966\) | −215.486 | + | 520.229i | −0.00717717 | + | 0.0173272i | ||||
\(967\) | −618.214 | + | 618.214i | −0.0205589 | + | 0.0205589i | −0.717311 | − | 0.696753i | \(-0.754628\pi\) |
0.696753 | + | 0.717311i | \(0.254628\pi\) | |||||||
\(968\) | 5972.59 | 0.198312 | ||||||||
\(969\) | −11272.8 | − | 1201.95i | −0.373720 | − | 0.0398476i | ||||
\(970\) | 751.547 | 0.0248770 | ||||||||
\(971\) | 20420.3 | − | 20420.3i | 0.674892 | − | 0.674892i | −0.283948 | − | 0.958840i | \(-0.591644\pi\) |
0.958840 | + | 0.283948i | \(0.0916443\pi\) | |||||||
\(972\) | 13438.3 | − | 32442.9i | 0.443450 | − | 1.07058i | ||||
\(973\) | 4440.17i | 0.146295i | ||||||||
\(974\) | 1600.49 | + | 662.944i | 0.0526519 | + | 0.0218091i | ||||
\(975\) | 19432.0 | + | 46912.9i | 0.638277 | + | 1.54094i | ||||
\(976\) | −4544.85 | + | 1882.54i | −0.149055 | + | 0.0617404i | ||||
\(977\) | −3143.83 | − | 3143.83i | −0.102948 | − | 0.102948i | 0.653757 | − | 0.756705i | \(-0.273192\pi\) |
−0.756705 | + | 0.653757i | \(0.773192\pi\) | |||||||
\(978\) | −2513.16 | − | 2513.16i | −0.0821699 | − | 0.0821699i | ||||
\(979\) | −32808.2 | + | 13589.6i | −1.07105 | + | 0.443642i | ||||
\(980\) | 1005.88 | + | 2428.42i | 0.0327875 | + | 0.0791561i | ||||
\(981\) | −3923.74 | − | 1625.27i | −0.127702 | − | 0.0528958i | ||||
\(982\) | − | 2924.80i | − | 0.0950448i | ||||||
\(983\) | −15780.7 | + | 38098.1i | −0.512032 | + | 1.23615i | 0.430667 | + | 0.902511i | \(0.358278\pi\) |
−0.942699 | + | 0.333644i | \(0.891722\pi\) | |||||||
\(984\) | −9195.55 | + | 9195.55i | −0.297910 | + | 0.297910i | ||||
\(985\) | 10465.1 | 0.338524 | ||||||||
\(986\) | −118.580 | + | 1112.13i | −0.00382998 | + | 0.0359203i | ||||
\(987\) | −36759.5 | −1.18548 | ||||||||
\(988\) | 5790.19 | − | 5790.19i | 0.186448 | − | 0.186448i | ||||
\(989\) | 678.014 | − | 1636.87i | 0.0217994 | − | 0.0526284i | ||||
\(990\) | 1398.03i | 0.0448810i | ||||||||
\(991\) | −30566.7 | − | 12661.1i | −0.979801 | − | 0.405847i | −0.165449 | − | 0.986218i | \(-0.552907\pi\) |
−0.814352 | + | 0.580372i | \(0.802907\pi\) | |||||||
\(992\) | 2772.20 | + | 6692.68i | 0.0887272 | + | 0.214206i | ||||
\(993\) | 71196.3 | − | 29490.5i | 2.27527 | − | 0.942449i | ||||
\(994\) | −739.325 | − | 739.325i | −0.0235915 | − | 0.0235915i | ||||
\(995\) | 7046.62 | + | 7046.62i | 0.224515 | + | 0.224515i | ||||
\(996\) | 828.076 | − | 343.000i | 0.0263440 | − | 0.0109120i | ||||
\(997\) | −4318.18 | − | 10425.0i | −0.137170 | − | 0.331157i | 0.840336 | − | 0.542066i | \(-0.182358\pi\) |
−0.977506 | + | 0.210909i | \(0.932358\pi\) | |||||||
\(998\) | −572.061 | − | 236.956i | −0.0181446 | − | 0.00751573i | ||||
\(999\) | − | 22722.2i | − | 0.719619i |
(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 | 17.4.d.a.8.2 | ✓ | 12 | |
3.2 | odd | 2 | 153.4.l.a.127.2 | 12 | |||
17.6 | odd | 16 | 289.4.b.e.288.5 | 12 | |||
17.7 | odd | 16 | 289.4.a.g.1.7 | 12 | |||
17.10 | odd | 16 | 289.4.a.g.1.8 | 12 | |||
17.11 | odd | 16 | 289.4.b.e.288.6 | 12 | |||
17.15 | even | 8 | inner | 17.4.d.a.15.2 | yes | 12 | |
51.32 | odd | 8 | 153.4.l.a.100.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.8.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
17.4.d.a.15.2 | yes | 12 | 17.15 | even | 8 | inner | |
153.4.l.a.100.2 | 12 | 51.32 | odd | 8 | |||
153.4.l.a.127.2 | 12 | 3.2 | odd | 2 | |||
289.4.a.g.1.7 | 12 | 17.7 | odd | 16 | |||
289.4.a.g.1.8 | 12 | 17.10 | odd | 16 | |||
289.4.b.e.288.5 | 12 | 17.6 | odd | 16 | |||
289.4.b.e.288.6 | 12 | 17.11 | odd | 16 |