Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,4,Mod(41,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.43424066072\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.16 | ||
Character | \(\chi\) | \(=\) | 126.41 |
Dual form | 126.4.m.a.83.16 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −2.86447 | + | 4.33530i | −0.551267 | + | 0.834329i | ||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 4.49442 | − | 7.78456i | 0.401993 | − | 0.696273i | −0.591973 | − | 0.805958i | \(-0.701651\pi\) |
0.993966 | + | 0.109685i | \(0.0349842\pi\) | |||||||
\(6\) | −0.626101 | + | 10.3734i | −0.0426008 | + | 0.705822i | ||||
\(7\) | −13.8476 | − | 12.2981i | −0.747701 | − | 0.664035i | ||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −10.5897 | − | 24.8366i | −0.392210 | − | 0.919876i | ||||
\(10\) | − | 17.9777i | − | 0.568504i | ||||||
\(11\) | 57.4672 | − | 33.1787i | 1.57518 | − | 0.909432i | 0.579665 | − | 0.814855i | \(-0.303183\pi\) |
0.995517 | − | 0.0945776i | \(-0.0301501\pi\) | |||||||
\(12\) | 9.28899 | + | 18.5934i | 0.223458 | + | 0.447288i | ||||
\(13\) | 42.3739 | + | 24.4646i | 0.904031 | + | 0.521942i | 0.878506 | − | 0.477732i | \(-0.158541\pi\) |
0.0255249 | + | 0.999674i | \(0.491874\pi\) | |||||||
\(14\) | −36.2829 | − | 7.45331i | −0.692644 | − | 0.142284i | ||||
\(15\) | 20.8743 | + | 41.7833i | 0.359315 | + | 0.719227i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −18.7313 | −0.267236 | −0.133618 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133618 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(18\) | −43.1785 | − | 32.4287i | −0.565404 | − | 0.424640i | ||||
\(19\) | − | 109.755i | − | 1.32524i | −0.748958 | − | 0.662618i | \(-0.769445\pi\) | ||
0.748958 | − | 0.662618i | \(-0.230555\pi\) | |||||||
\(20\) | −17.9777 | − | 31.1383i | −0.200997 | − | 0.348136i | ||||
\(21\) | 92.9820 | − | 24.8061i | 0.966207 | − | 0.257768i | ||||
\(22\) | 66.3574 | − | 114.934i | 0.643066 | − | 1.11382i | ||||
\(23\) | −30.4552 | − | 17.5833i | −0.276102 | − | 0.159407i | 0.355556 | − | 0.934655i | \(-0.384292\pi\) |
−0.631657 | + | 0.775248i | \(0.717625\pi\) | |||||||
\(24\) | 34.6824 | + | 22.9157i | 0.294980 | + | 0.194902i | ||||
\(25\) | 22.1004 | + | 38.2790i | 0.176803 | + | 0.306232i | ||||
\(26\) | 97.8583 | 0.738138 | ||||||||
\(27\) | 138.008 | + | 25.2344i | 0.983691 | + | 0.179865i | ||||
\(28\) | −70.2971 | + | 23.3734i | −0.474461 | + | 0.157755i | ||||
\(29\) | −53.0095 | + | 30.6051i | −0.339435 | + | 0.195973i | −0.660022 | − | 0.751246i | \(-0.729453\pi\) |
0.320587 | + | 0.947219i | \(0.396120\pi\) | |||||||
\(30\) | 77.9387 | + | 51.4965i | 0.474320 | + | 0.313398i | ||||
\(31\) | −289.624 | − | 167.214i | −1.67800 | − | 0.968794i | −0.962934 | − | 0.269736i | \(-0.913064\pi\) |
−0.715065 | − | 0.699057i | \(-0.753603\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −20.7732 | + | 344.177i | −0.109580 | + | 1.81556i | ||||
\(34\) | −32.4436 | + | 18.7313i | −0.163648 | + | 0.0944822i | ||||
\(35\) | −157.972 | + | 52.5249i | −0.762920 | + | 0.253666i | ||||
\(36\) | −107.216 | − | 12.9896i | −0.496370 | − | 0.0601372i | ||||
\(37\) | 251.926 | 1.11936 | 0.559680 | − | 0.828709i | \(-0.310924\pi\) | ||||
0.559680 | + | 0.828709i | \(0.310924\pi\) | |||||||
\(38\) | −109.755 | − | 190.101i | −0.468542 | − | 0.811538i | ||||
\(39\) | −227.440 | + | 113.626i | −0.933834 | + | 0.466529i | ||||
\(40\) | −62.2765 | − | 35.9554i | −0.246170 | − | 0.142126i | ||||
\(41\) | −134.377 | + | 232.749i | −0.511859 | + | 0.886567i | 0.488046 | + | 0.872818i | \(0.337710\pi\) |
−0.999905 | + | 0.0137487i | \(0.995624\pi\) | |||||||
\(42\) | 136.243 | − | 135.947i | 0.500543 | − | 0.499456i | ||||
\(43\) | 69.7048 | + | 120.732i | 0.247207 | + | 0.428174i | 0.962750 | − | 0.270394i | \(-0.0871540\pi\) |
−0.715543 | + | 0.698569i | \(0.753821\pi\) | |||||||
\(44\) | − | 265.430i | − | 0.909432i | ||||||
\(45\) | −240.937 | − | 29.1904i | −0.798150 | − | 0.0966989i | ||||
\(46\) | −70.3332 | −0.225436 | ||||||||
\(47\) | 57.9089 | + | 100.301i | 0.179721 | + | 0.311286i | 0.941785 | − | 0.336216i | \(-0.109147\pi\) |
−0.762064 | + | 0.647502i | \(0.775814\pi\) | |||||||
\(48\) | 82.9874 | + | 5.00881i | 0.249546 | + | 0.0150616i | ||||
\(49\) | 40.5134 | + | 340.599i | 0.118115 | + | 0.993000i | ||||
\(50\) | 76.5579 | + | 44.2007i | 0.216538 | + | 0.125019i | ||||
\(51\) | 53.6553 | − | 81.2059i | 0.147318 | − | 0.222963i | ||||
\(52\) | 169.495 | − | 97.8583i | 0.452015 | − | 0.260971i | ||||
\(53\) | 438.701i | 1.13698i | 0.822689 | + | 0.568492i | \(0.192473\pi\) | ||||
−0.822689 | + | 0.568492i | \(0.807527\pi\) | |||||||
\(54\) | 264.271 | − | 94.3008i | 0.665977 | − | 0.237643i | ||||
\(55\) | − | 596.476i | − | 1.46234i | ||||||
\(56\) | −98.3848 | + | 110.781i | −0.234772 | + | 0.264352i | ||||
\(57\) | 475.820 | + | 314.389i | 1.10568 | + | 0.730559i | ||||
\(58\) | −61.2101 | + | 106.019i | −0.138574 | + | 0.240017i | ||||
\(59\) | −113.087 | + | 195.872i | −0.249536 | + | 0.432209i | −0.963397 | − | 0.268078i | \(-0.913611\pi\) |
0.713861 | + | 0.700287i | \(0.246945\pi\) | |||||||
\(60\) | 186.490 | + | 11.2558i | 0.401263 | + | 0.0242187i | ||||
\(61\) | 469.469 | − | 271.048i | 0.985399 | − | 0.568920i | 0.0815032 | − | 0.996673i | \(-0.474028\pi\) |
0.903896 | + | 0.427753i | \(0.140695\pi\) | |||||||
\(62\) | −668.858 | −1.37008 | ||||||||
\(63\) | −158.802 | + | 474.161i | −0.317574 | + | 0.948233i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 380.892 | − | 219.908i | 0.726828 | − | 0.419635i | ||||
\(66\) | 308.197 | + | 616.905i | 0.574794 | + | 1.15054i | ||||
\(67\) | 307.015 | − | 531.766i | 0.559819 | − | 0.969635i | −0.437692 | − | 0.899125i | \(-0.644204\pi\) |
0.997511 | − | 0.0705100i | \(-0.0224627\pi\) | |||||||
\(68\) | −37.4626 | + | 64.8872i | −0.0668090 | + | 0.115717i | ||||
\(69\) | 163.467 | − | 81.6655i | 0.285204 | − | 0.142484i | ||||
\(70\) | −221.091 | + | 248.948i | −0.377507 | + | 0.425071i | ||||
\(71\) | 116.615i | 0.194925i | 0.995239 | + | 0.0974625i | \(0.0310726\pi\) | ||||
−0.995239 | + | 0.0974625i | \(0.968927\pi\) | |||||||
\(72\) | −198.693 | + | 84.7173i | −0.325225 | + | 0.138667i | ||||
\(73\) | − | 352.359i | − | 0.564938i | −0.959276 | − | 0.282469i | \(-0.908847\pi\) | ||
0.959276 | − | 0.282469i | \(-0.0911534\pi\) | |||||||
\(74\) | 436.348 | − | 251.926i | 0.685465 | − | 0.395753i | ||||
\(75\) | −229.257 | − | 13.8371i | −0.352964 | − | 0.0213036i | ||||
\(76\) | −380.202 | − | 219.510i | −0.573844 | − | 0.331309i | ||||
\(77\) | −1203.82 | − | 247.291i | −1.78166 | − | 0.365993i | ||||
\(78\) | −280.312 | + | 424.245i | −0.406911 | + | 0.615850i | ||||
\(79\) | 390.954 | + | 677.153i | 0.556782 | + | 0.964375i | 0.997762 | + | 0.0668582i | \(0.0212975\pi\) |
−0.440980 | + | 0.897517i | \(0.645369\pi\) | |||||||
\(80\) | −143.821 | −0.200997 | ||||||||
\(81\) | −504.718 | + | 526.023i | −0.692343 | + | 0.721568i | ||||
\(82\) | 537.510i | 0.723879i | ||||||||
\(83\) | 122.693 | + | 212.511i | 0.162257 | + | 0.281038i | 0.935678 | − | 0.352855i | \(-0.114789\pi\) |
−0.773421 | + | 0.633893i | \(0.781456\pi\) | |||||||
\(84\) | 100.033 | − | 371.711i | 0.129935 | − | 0.482822i | ||||
\(85\) | −84.1864 | + | 145.815i | −0.107427 | + | 0.186069i | ||||
\(86\) | 241.465 | + | 139.410i | 0.302765 | + | 0.174801i | ||||
\(87\) | 19.1619 | − | 317.479i | 0.0236134 | − | 0.391234i | ||||
\(88\) | −265.430 | − | 459.738i | −0.321533 | − | 0.556911i | ||||
\(89\) | −1642.23 | −1.95592 | −0.977958 | − | 0.208803i | \(-0.933043\pi\) | ||||
−0.977958 | + | 0.208803i | \(0.933043\pi\) | |||||||
\(90\) | −446.505 | + | 190.378i | −0.522953 | + | 0.222973i | ||||
\(91\) | −285.910 | − | 859.894i | −0.329357 | − | 0.990565i | ||||
\(92\) | −121.821 | + | 70.3332i | −0.138051 | + | 0.0797037i | ||||
\(93\) | 1554.54 | − | 776.627i | 1.73332 | − | 0.865940i | ||||
\(94\) | 200.602 | + | 115.818i | 0.220112 | + | 0.127082i | ||||
\(95\) | −854.394 | − | 493.284i | −0.922726 | − | 0.532736i | ||||
\(96\) | 148.747 | − | 74.3119i | 0.158140 | − | 0.0790045i | ||||
\(97\) | 969.077 | − | 559.497i | 1.01438 | − | 0.585652i | 0.101909 | − | 0.994794i | \(-0.467505\pi\) |
0.912471 | + | 0.409141i | \(0.134172\pi\) | |||||||
\(98\) | 410.770 | + | 549.421i | 0.423409 | + | 0.566326i | ||||
\(99\) | −1432.61 | − | 1075.94i | −1.45437 | − | 1.09228i | ||||
\(100\) | 176.803 | 0.176803 | ||||||||
\(101\) | 763.867 | + | 1323.06i | 0.752551 | + | 1.30346i | 0.946583 | + | 0.322461i | \(0.104510\pi\) |
−0.194032 | + | 0.980995i | \(0.562157\pi\) | |||||||
\(102\) | 11.7277 | − | 194.308i | 0.0113845 | − | 0.188621i | ||||
\(103\) | 1493.11 | + | 862.049i | 1.42836 | + | 0.824662i | 0.996991 | − | 0.0775146i | \(-0.0246984\pi\) |
0.431366 | + | 0.902177i | \(0.358032\pi\) | |||||||
\(104\) | 195.717 | − | 338.991i | 0.184534 | − | 0.319623i | ||||
\(105\) | 224.796 | − | 835.314i | 0.208931 | − | 0.776364i | ||||
\(106\) | 438.701 | + | 759.852i | 0.401985 | + | 0.696258i | ||||
\(107\) | − | 669.357i | − | 0.604758i | −0.953188 | − | 0.302379i | \(-0.902219\pi\) | ||
0.953188 | − | 0.302379i | \(-0.0977809\pi\) | |||||||
\(108\) | 363.431 | − | 427.605i | 0.323807 | − | 0.380985i | ||||
\(109\) | −316.634 | −0.278239 | −0.139120 | − | 0.990276i | \(-0.544427\pi\) | ||||
−0.139120 | + | 0.990276i | \(0.544427\pi\) | |||||||
\(110\) | −596.476 | − | 1033.13i | −0.517016 | − | 0.895498i | ||||
\(111\) | −721.632 | + | 1092.17i | −0.617066 | + | 0.933914i | ||||
\(112\) | −59.6265 | + | 290.263i | −0.0503051 | + | 0.244886i | ||||
\(113\) | 580.400 | + | 335.094i | 0.483181 | + | 0.278965i | 0.721741 | − | 0.692163i | \(-0.243342\pi\) |
−0.238560 | + | 0.971128i | \(0.576675\pi\) | |||||||
\(114\) | 1138.53 | + | 68.7176i | 0.935381 | + | 0.0564561i | ||||
\(115\) | −273.757 | + | 158.053i | −0.221982 | + | 0.128161i | ||||
\(116\) | 244.840i | 0.195973i | ||||||||
\(117\) | 158.893 | − | 1311.50i | 0.125553 | − | 1.03631i | ||||
\(118\) | 452.346i | 0.352897i | ||||||||
\(119\) | 259.384 | + | 230.360i | 0.199813 | + | 0.177454i | ||||
\(120\) | 334.266 | − | 166.994i | 0.254285 | − | 0.127037i | ||||
\(121\) | 1536.15 | − | 2660.69i | 1.15413 | − | 1.99902i | ||||
\(122\) | 542.096 | − | 938.938i | 0.402287 | − | 0.696782i | ||||
\(123\) | −624.115 | − | 1249.27i | −0.457517 | − | 0.915794i | ||||
\(124\) | −1158.50 | + | 668.858i | −0.839000 | + | 0.484397i | ||||
\(125\) | 1520.92 | 1.08828 | ||||||||
\(126\) | 199.108 | + | 980.073i | 0.140778 | + | 0.692951i | ||||
\(127\) | −2290.65 | −1.60049 | −0.800246 | − | 0.599671i | \(-0.795298\pi\) | ||||
−0.800246 | + | 0.599671i | \(0.795298\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −723.078 | − | 43.6423i | −0.493515 | − | 0.0297867i | ||||
\(130\) | 439.816 | − | 761.784i | 0.296726 | − | 0.513945i | ||||
\(131\) | 697.263 | − | 1207.69i | 0.465039 | − | 0.805471i | −0.534164 | − | 0.845381i | \(-0.679374\pi\) |
0.999203 | + | 0.0399094i | \(0.0127069\pi\) | |||||||
\(132\) | 1150.72 | + | 760.314i | 0.758766 | + | 0.501340i | ||||
\(133\) | −1349.78 | + | 1519.84i | −0.880003 | + | 0.990881i | ||||
\(134\) | − | 1228.06i | − | 0.791704i | ||||||
\(135\) | 816.705 | − | 960.919i | 0.520672 | − | 0.612613i | ||||
\(136\) | 149.851i | 0.0944822i | ||||||||
\(137\) | 1237.96 | − | 714.737i | 0.772016 | − | 0.445724i | −0.0615774 | − | 0.998102i | \(-0.519613\pi\) |
0.833593 | + | 0.552379i | \(0.186280\pi\) | |||||||
\(138\) | 201.467 | − | 304.915i | 0.124275 | − | 0.188088i | ||||
\(139\) | −210.788 | − | 121.698i | −0.128624 | − | 0.0742612i | 0.434307 | − | 0.900765i | \(-0.356993\pi\) |
−0.562932 | + | 0.826504i | \(0.690327\pi\) | |||||||
\(140\) | −133.993 | + | 652.282i | −0.0808893 | + | 0.393771i | ||||
\(141\) | −600.714 | − | 36.2568i | −0.358789 | − | 0.0216551i | ||||
\(142\) | 116.615 | + | 201.983i | 0.0689164 | + | 0.119367i | ||||
\(143\) | 3246.81 | 1.89868 | ||||||||
\(144\) | −259.429 | + | 345.428i | −0.150133 | + | 0.199900i | ||||
\(145\) | 550.208i | 0.315119i | ||||||||
\(146\) | −352.359 | − | 610.303i | −0.199736 | − | 0.345953i | ||||
\(147\) | −1592.65 | − | 799.997i | −0.893601 | − | 0.448861i | ||||
\(148\) | 503.851 | − | 872.696i | 0.279840 | − | 0.484697i | ||||
\(149\) | 1065.50 | + | 615.165i | 0.585831 | + | 0.338230i | 0.763447 | − | 0.645870i | \(-0.223505\pi\) |
−0.177616 | + | 0.984100i | \(0.556839\pi\) | |||||||
\(150\) | −410.921 | + | 205.290i | −0.223677 | + | 0.111746i | ||||
\(151\) | 837.344 | + | 1450.32i | 0.451272 | + | 0.781626i | 0.998465 | − | 0.0553802i | \(-0.0176371\pi\) |
−0.547193 | + | 0.837006i | \(0.684304\pi\) | |||||||
\(152\) | −878.039 | −0.468542 | ||||||||
\(153\) | 198.358 | + | 465.223i | 0.104813 | + | 0.245824i | ||||
\(154\) | −2332.37 | + | 775.498i | −1.22044 | + | 0.405788i | ||||
\(155\) | −2603.38 | + | 1503.06i | −1.34909 | + | 0.778897i | ||||
\(156\) | −61.2692 | + | 1015.13i | −0.0314452 | + | 0.520994i | ||||
\(157\) | −518.343 | − | 299.266i | −0.263492 | − | 0.152127i | 0.362434 | − | 0.932009i | \(-0.381946\pi\) |
−0.625927 | + | 0.779882i | \(0.715279\pi\) | |||||||
\(158\) | 1354.31 | + | 781.908i | 0.681916 | + | 0.393704i | ||||
\(159\) | −1901.90 | − | 1256.64i | −0.948619 | − | 0.626782i | ||||
\(160\) | −249.106 | + | 143.821i | −0.123085 | + | 0.0710630i | ||||
\(161\) | 205.490 | + | 618.028i | 0.100590 | + | 0.302530i | ||||
\(162\) | −348.174 | + | 1415.82i | −0.168859 | + | 0.686649i | ||||
\(163\) | −1800.96 | −0.865414 | −0.432707 | − | 0.901535i | \(-0.642441\pi\) | ||||
−0.432707 | + | 0.901535i | \(0.642441\pi\) | |||||||
\(164\) | 537.510 | + | 930.995i | 0.255930 | + | 0.443283i | ||||
\(165\) | 2585.90 | + | 1708.59i | 1.22007 | + | 0.806141i | ||||
\(166\) | 425.023 | + | 245.387i | 0.198724 | + | 0.114733i | ||||
\(167\) | −195.287 | + | 338.247i | −0.0904895 | + | 0.156732i | −0.907717 | − | 0.419583i | \(-0.862176\pi\) |
0.817228 | + | 0.576315i | \(0.195510\pi\) | |||||||
\(168\) | −198.449 | − | 743.856i | −0.0911349 | − | 0.341606i | ||||
\(169\) | 98.5300 | + | 170.659i | 0.0448475 | + | 0.0776782i | ||||
\(170\) | 336.746i | 0.151925i | ||||||||
\(171\) | −2725.94 | + | 1162.27i | −1.21905 | + | 0.519770i | ||||
\(172\) | 557.639 | 0.247207 | ||||||||
\(173\) | 510.530 | + | 884.264i | 0.224364 | + | 0.388609i | 0.956128 | − | 0.292948i | \(-0.0946364\pi\) |
−0.731765 | + | 0.681557i | \(0.761303\pi\) | |||||||
\(174\) | −284.290 | − | 569.052i | −0.123862 | − | 0.247930i | ||||
\(175\) | 164.721 | − | 801.865i | 0.0711528 | − | 0.346373i | ||||
\(176\) | −919.475 | − | 530.859i | −0.393796 | − | 0.227358i | ||||
\(177\) | −525.230 | − | 1051.33i | −0.223043 | − | 0.446457i | ||||
\(178\) | −2844.43 | + | 1642.23i | −1.19775 | + | 0.691521i | ||||
\(179\) | 2447.76i | 1.02209i | 0.859554 | + | 0.511045i | \(0.170741\pi\) | ||||
−0.859554 | + | 0.511045i | \(0.829259\pi\) | |||||||
\(180\) | −582.992 | + | 776.249i | −0.241409 | + | 0.321434i | ||||
\(181\) | 676.711i | 0.277898i | 0.990300 | + | 0.138949i | \(0.0443724\pi\) | ||||
−0.990300 | + | 0.138949i | \(0.955628\pi\) | |||||||
\(182\) | −1355.10 | − | 1203.47i | −0.551907 | − | 0.490149i | ||||
\(183\) | −169.703 | + | 2811.70i | −0.0685510 | + | 1.13577i | ||||
\(184\) | −140.666 | + | 243.641i | −0.0563590 | + | 0.0976167i | ||||
\(185\) | 1132.26 | − | 1961.13i | 0.449975 | − | 0.779379i | ||||
\(186\) | 1915.92 | − | 2899.70i | 0.755280 | − | 1.14310i | ||||
\(187\) | −1076.44 | + | 621.481i | −0.420946 | + | 0.243033i | ||||
\(188\) | 463.271 | 0.179721 | ||||||||
\(189\) | −1600.75 | − | 2046.67i | −0.616071 | − | 0.787691i | ||||
\(190\) | −1973.14 | −0.753402 | ||||||||
\(191\) | 1970.38 | − | 1137.60i | 0.746450 | − | 0.430963i | −0.0779596 | − | 0.996957i | \(-0.524841\pi\) |
0.824410 | + | 0.565993i | \(0.191507\pi\) | |||||||
\(192\) | 183.326 | − | 277.459i | 0.0689084 | − | 0.104291i | ||||
\(193\) | −1135.76 | + | 1967.19i | −0.423593 | + | 0.733685i | −0.996288 | − | 0.0860835i | \(-0.972565\pi\) |
0.572694 | + | 0.819769i | \(0.305898\pi\) | |||||||
\(194\) | 1118.99 | − | 1938.15i | 0.414119 | − | 0.717275i | ||||
\(195\) | −137.685 | + | 2281.20i | −0.0505631 | + | 0.837745i | ||||
\(196\) | 1260.90 | + | 540.856i | 0.459510 | + | 0.197105i | ||||
\(197\) | 3485.27i | 1.26048i | 0.776400 | + | 0.630241i | \(0.217044\pi\) | ||||
−0.776400 | + | 0.630241i | \(0.782956\pi\) | |||||||
\(198\) | −3557.29 | − | 430.979i | −1.27679 | − | 0.154689i | ||||
\(199\) | − | 1681.87i | − | 0.599119i | −0.954078 | − | 0.299559i | \(-0.903160\pi\) | ||
0.954078 | − | 0.299559i | \(-0.0968397\pi\) | |||||||
\(200\) | 306.232 | − | 176.803i | 0.108269 | − | 0.0625093i | ||||
\(201\) | 1425.93 | + | 2854.23i | 0.500385 | + | 1.00160i | ||||
\(202\) | 2646.11 | + | 1527.73i | 0.921682 | + | 0.532134i | ||||
\(203\) | 1110.44 | + | 228.109i | 0.383929 | + | 0.0788676i | ||||
\(204\) | −173.995 | − | 348.279i | −0.0597161 | − | 0.119531i | ||||
\(205\) | 1207.90 | + | 2092.14i | 0.411528 | + | 0.712787i | ||||
\(206\) | 3448.20 | 1.16625 | ||||||||
\(207\) | −114.200 | + | 942.605i | −0.0383452 | + | 0.316500i | ||||
\(208\) | − | 782.866i | − | 0.260971i | ||||||
\(209\) | −3641.52 | − | 6307.30i | −1.20521 | − | 2.08749i | ||||
\(210\) | −445.956 | − | 1671.60i | −0.146542 | − | 0.549293i | ||||
\(211\) | −524.934 | + | 909.213i | −0.171270 | + | 0.296648i | −0.938864 | − | 0.344288i | \(-0.888120\pi\) |
0.767594 | + | 0.640936i | \(0.221454\pi\) | |||||||
\(212\) | 1519.70 | + | 877.401i | 0.492329 | + | 0.284246i | ||||
\(213\) | −505.562 | − | 334.040i | −0.162632 | − | 0.107456i | ||||
\(214\) | −669.357 | − | 1159.36i | −0.213814 | − | 0.370337i | ||||
\(215\) | 1253.13 | 0.397502 | ||||||||
\(216\) | 201.875 | − | 1104.06i | 0.0635919 | − | 0.347787i | ||||
\(217\) | 1954.18 | + | 5877.35i | 0.611330 | + | 1.83862i | ||||
\(218\) | −548.427 | + | 316.634i | −0.170386 | + | 0.0983724i | ||||
\(219\) | 1527.58 | + | 1009.32i | 0.471344 | + | 0.311432i | ||||
\(220\) | −2066.25 | − | 1192.95i | −0.633213 | − | 0.365586i | ||||
\(221\) | −793.719 | − | 458.254i | −0.241590 | − | 0.139482i | ||||
\(222\) | −157.731 | + | 2613.33i | −0.0476856 | + | 0.790069i | ||||
\(223\) | 2044.58 | − | 1180.44i | 0.613969 | − | 0.354475i | −0.160548 | − | 0.987028i | \(-0.551326\pi\) |
0.774517 | + | 0.632553i | \(0.217993\pi\) | |||||||
\(224\) | 186.987 | + | 562.377i | 0.0557750 | + | 0.167747i | ||||
\(225\) | 716.686 | − | 954.260i | 0.212351 | − | 0.282744i | ||||
\(226\) | 1340.38 | 0.394515 | ||||||||
\(227\) | 2115.70 | + | 3664.51i | 0.618609 | + | 1.07146i | 0.989740 | + | 0.142881i | \(0.0456367\pi\) |
−0.371131 | + | 0.928580i | \(0.621030\pi\) | |||||||
\(228\) | 2040.72 | − | 1019.51i | 0.592762 | − | 0.296135i | ||||
\(229\) | 1566.76 | + | 904.568i | 0.452115 | + | 0.261029i | 0.708723 | − | 0.705487i | \(-0.249272\pi\) |
−0.256608 | + | 0.966516i | \(0.582605\pi\) | |||||||
\(230\) | −316.107 | + | 547.513i | −0.0906238 | + | 0.156965i | ||||
\(231\) | 4520.38 | − | 4510.56i | 1.28753 | − | 1.28473i | ||||
\(232\) | 244.840 | + | 424.076i | 0.0692869 | + | 0.120008i | ||||
\(233\) | − | 3054.99i | − | 0.858965i | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||
0.903075 | − | 0.429483i | \(-0.141304\pi\) | |||||||
\(234\) | −1036.29 | − | 2430.47i | −0.289505 | − | 0.678995i | ||||
\(235\) | 1041.07 | 0.288986 | ||||||||
\(236\) | 452.346 | + | 783.486i | 0.124768 | + | 0.216104i | ||||
\(237\) | −4055.54 | − | 244.777i | −1.11154 | − | 0.0670885i | ||||
\(238\) | 679.627 | + | 139.610i | 0.185099 | + | 0.0380235i | ||||
\(239\) | −4054.15 | − | 2340.67i | −1.09724 | − | 0.633494i | −0.161748 | − | 0.986832i | \(-0.551713\pi\) |
−0.935496 | + | 0.353338i | \(0.885047\pi\) | |||||||
\(240\) | 411.972 | − | 623.509i | 0.110803 | − | 0.167697i | ||||
\(241\) | −1242.85 | + | 717.561i | −0.332196 | + | 0.191793i | −0.656816 | − | 0.754051i | \(-0.728097\pi\) |
0.324620 | + | 0.945845i | \(0.394764\pi\) | |||||||
\(242\) | − | 6144.61i | − | 1.63219i | ||||||
\(243\) | −834.722 | − | 3694.88i | −0.220360 | − | 0.975419i | ||||
\(244\) | − | 2168.38i | − | 0.568920i | ||||||
\(245\) | 2833.50 | + | 1215.42i | 0.738880 | + | 0.316939i | ||||
\(246\) | −2330.27 | − | 1539.68i | −0.603953 | − | 0.399050i | ||||
\(247\) | 2685.10 | − | 4650.74i | 0.691697 | − | 1.19805i | ||||
\(248\) | −1337.72 | + | 2316.99i | −0.342520 | + | 0.593263i | ||||
\(249\) | −1272.75 | − | 76.8185i | −0.323925 | − | 0.0195509i | ||||
\(250\) | 2634.31 | − | 1520.92i | 0.666433 | − | 0.384765i | ||||
\(251\) | −6180.07 | −1.55411 | −0.777057 | − | 0.629431i | \(-0.783288\pi\) | ||||
−0.777057 | + | 0.629431i | \(0.783288\pi\) | |||||||
\(252\) | 1324.94 | + | 1498.43i | 0.331204 | + | 0.374572i | ||||
\(253\) | −2333.56 | −0.579881 | ||||||||
\(254\) | −3967.53 | + | 2290.65i | −0.980098 | + | 0.565860i | ||||
\(255\) | −391.003 | − | 782.656i | −0.0960219 | − | 0.192203i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2736.86 | + | 4740.38i | −0.664283 | + | 1.15057i | 0.315196 | + | 0.949027i | \(0.397930\pi\) |
−0.979479 | + | 0.201546i | \(0.935404\pi\) | |||||||
\(258\) | −1296.05 | + | 647.487i | −0.312746 | + | 0.156243i | ||||
\(259\) | −3488.57 | − | 3098.21i | −0.836947 | − | 0.743294i | ||||
\(260\) | − | 1759.26i | − | 0.419635i | ||||||
\(261\) | 1321.48 | + | 992.482i | 0.313401 | + | 0.235376i | ||||
\(262\) | − | 2789.05i | − | 0.657665i | ||||||
\(263\) | −3980.72 | + | 2298.27i | −0.933316 | + | 0.538850i | −0.887859 | − | 0.460116i | \(-0.847808\pi\) |
−0.0454569 | + | 0.998966i | \(0.514474\pi\) | |||||||
\(264\) | 2753.41 | + | 166.186i | 0.641898 | + | 0.0387425i | ||||
\(265\) | 3415.09 | + | 1971.70i | 0.791651 | + | 0.457060i | ||||
\(266\) | −818.037 | + | 3982.22i | −0.188560 | + | 0.917916i | ||||
\(267\) | 4704.13 | − | 7119.58i | 1.07823 | − | 1.63188i | ||||
\(268\) | −1228.06 | − | 2127.06i | −0.279910 | − | 0.484817i | ||||
\(269\) | −1598.04 | −0.362210 | −0.181105 | − | 0.983464i | \(-0.557967\pi\) | ||||
−0.181105 | + | 0.983464i | \(0.557967\pi\) | |||||||
\(270\) | 453.656 | − | 2481.07i | 0.102254 | − | 0.559233i | ||||
\(271\) | 233.977i | 0.0524469i | 0.999656 | + | 0.0262235i | \(0.00834814\pi\) | ||||
−0.999656 | + | 0.0262235i | \(0.991652\pi\) | |||||||
\(272\) | 149.851 | + | 259.549i | 0.0334045 | + | 0.0578583i | ||||
\(273\) | 4546.88 | + | 1223.63i | 1.00802 | + | 0.271274i | ||||
\(274\) | 1429.47 | − | 2475.92i | 0.315174 | − | 0.545898i | ||||
\(275\) | 2540.09 | + | 1466.52i | 0.556994 | + | 0.321581i | ||||
\(276\) | 44.0357 | − | 729.596i | 0.00960375 | − | 0.159118i | ||||
\(277\) | 1072.11 | + | 1856.95i | 0.232552 | + | 0.402791i | 0.958558 | − | 0.284896i | \(-0.0919592\pi\) |
−0.726007 | + | 0.687688i | \(0.758626\pi\) | |||||||
\(278\) | −486.793 | −0.105021 | ||||||||
\(279\) | −1086.03 | + | 8964.03i | −0.233042 | + | 1.92352i | ||||
\(280\) | 420.199 | + | 1263.78i | 0.0896846 | + | 0.269733i | ||||
\(281\) | 7133.55 | − | 4118.56i | 1.51442 | − | 0.874351i | 0.514563 | − | 0.857453i | \(-0.327954\pi\) |
0.999857 | − | 0.0168983i | \(-0.00537914\pi\) | |||||||
\(282\) | −1076.72 | + | 537.915i | −0.227369 | + | 0.113590i | ||||
\(283\) | −5110.18 | − | 2950.36i | −1.07339 | − | 0.619721i | −0.144283 | − | 0.989537i | \(-0.546087\pi\) |
−0.929105 | + | 0.369816i | \(0.879421\pi\) | |||||||
\(284\) | 403.967 | + | 233.230i | 0.0844050 | + | 0.0487312i | ||||
\(285\) | 4585.92 | − | 2291.06i | 0.953145 | − | 0.476177i | ||||
\(286\) | 5623.64 | − | 3246.81i | 1.16270 | − | 0.671286i | ||||
\(287\) | 4723.18 | − | 1570.43i | 0.971429 | − | 0.322994i | ||||
\(288\) | −103.917 | + | 857.728i | −0.0212617 | + | 0.175493i | ||||
\(289\) | −4562.14 | −0.928585 | ||||||||
\(290\) | 550.208 | + | 952.988i | 0.111411 | + | 0.192970i | ||||
\(291\) | −350.301 | + | 5803.90i | −0.0705671 | + | 1.16918i | ||||
\(292\) | −1220.61 | − | 704.718i | −0.244625 | − | 0.141235i | ||||
\(293\) | 938.848 | − | 1626.13i | 0.187195 | − | 0.324231i | −0.757119 | − | 0.653277i | \(-0.773394\pi\) |
0.944314 | + | 0.329046i | \(0.106727\pi\) | |||||||
\(294\) | −3558.54 | + | 207.013i | −0.705913 | + | 0.0410655i | ||||
\(295\) | 1016.52 | + | 1760.66i | 0.200623 | + | 0.347490i | ||||
\(296\) | − | 2015.40i | − | 0.395753i | ||||||
\(297\) | 8768.18 | − | 3128.78i | 1.71307 | − | 0.611280i | ||||
\(298\) | 2460.66 | 0.478329 | ||||||||
\(299\) | −860.335 | − | 1490.14i | −0.166403 | − | 0.288218i | ||||
\(300\) | −506.446 | + | 766.494i | −0.0974656 | + | 0.147512i | ||||
\(301\) | 519.532 | − | 2529.09i | 0.0994861 | − | 0.484301i | ||||
\(302\) | 2900.64 | + | 1674.69i | 0.552693 | + | 0.319098i | ||||
\(303\) | −7923.92 | − | 478.258i | −1.50237 | − | 0.0906772i | ||||
\(304\) | −1520.81 | + | 878.039i | −0.286922 | + | 0.165654i | ||||
\(305\) | − | 4872.82i | − | 0.914808i | ||||||
\(306\) | 808.790 | + | 607.432i | 0.151096 | + | 0.113479i | ||||
\(307\) | − | 9599.67i | − | 1.78463i | −0.451412 | − | 0.892316i | \(-0.649079\pi\) | ||
0.451412 | − | 0.892316i | \(-0.350921\pi\) | |||||||
\(308\) | −3264.28 | + | 3675.57i | −0.603895 | + | 0.679984i | ||||
\(309\) | −8014.21 | + | 4003.78i | −1.47545 | + | 0.737111i | ||||
\(310\) | −3006.13 | + | 5206.77i | −0.550763 | + | 0.953950i | ||||
\(311\) | 0.327604 | − | 0.567426i | 5.97322e−5 | − | 0.000103459i | −0.865996 | − | 0.500052i | \(-0.833314\pi\) |
0.866055 | + | 0.499948i | \(0.166648\pi\) | |||||||
\(312\) | 909.004 | + | 1819.52i | 0.164943 | + | 0.330160i | ||||
\(313\) | 3460.31 | − | 1997.81i | 0.624883 | − | 0.360776i | −0.153885 | − | 0.988089i | \(-0.549178\pi\) |
0.778768 | + | 0.627313i | \(0.215845\pi\) | |||||||
\(314\) | −1197.06 | −0.215141 | ||||||||
\(315\) | 2977.42 | + | 3367.28i | 0.532566 | + | 0.602302i | ||||
\(316\) | 3127.63 | 0.556782 | ||||||||
\(317\) | −3027.91 | + | 1748.17i | −0.536481 | + | 0.309738i | −0.743652 | − | 0.668567i | \(-0.766908\pi\) |
0.207171 | + | 0.978305i | \(0.433575\pi\) | |||||||
\(318\) | −4550.83 | − | 274.671i | −0.802509 | − | 0.0484364i | ||||
\(319\) | −2030.87 | + | 3517.57i | −0.356448 | + | 0.617387i | ||||
\(320\) | −287.643 | + | 498.212i | −0.0502491 | + | 0.0870341i | ||||
\(321\) | 2901.86 | + | 1917.35i | 0.504567 | + | 0.333383i | ||||
\(322\) | 973.947 | + | 864.965i | 0.168559 | + | 0.149697i | ||||
\(323\) | 2055.85i | 0.354151i | ||||||||
\(324\) | 812.762 | + | 2800.44i | 0.139363 | + | 0.480185i | ||||
\(325\) | 2162.70i | 0.369124i | ||||||||
\(326\) | −3119.36 | + | 1800.96i | −0.529956 | + | 0.305970i | ||||
\(327\) | 906.988 | − | 1372.70i | 0.153384 | − | 0.232143i | ||||
\(328\) | 1861.99 | + | 1075.02i | 0.313449 | + | 0.180970i | ||||
\(329\) | 431.613 | − | 2101.10i | 0.0723271 | − | 0.352090i | ||||
\(330\) | 6187.50 | + | 373.454i | 1.03215 | + | 0.0622969i | ||||
\(331\) | 1167.71 | + | 2022.54i | 0.193907 | + | 0.335857i | 0.946542 | − | 0.322581i | \(-0.104551\pi\) |
−0.752634 | + | 0.658439i | \(0.771217\pi\) | |||||||
\(332\) | 981.548 | 0.162257 | ||||||||
\(333\) | −2667.81 | − | 6256.99i | −0.439024 | − | 1.02967i | ||||
\(334\) | 781.147i | 0.127971i | ||||||||
\(335\) | −2759.71 | − | 4779.96i | −0.450087 | − | 0.779573i | ||||
\(336\) | −1087.58 | − | 1089.95i | −0.176584 | − | 0.176969i | ||||
\(337\) | 955.521 | − | 1655.01i | 0.154453 | − | 0.267520i | −0.778407 | − | 0.627760i | \(-0.783972\pi\) |
0.932860 | + | 0.360240i | \(0.117305\pi\) | |||||||
\(338\) | 341.318 | + | 197.060i | 0.0549268 | + | 0.0317120i | ||||
\(339\) | −3115.27 | + | 1556.34i | −0.499110 | + | 0.249348i | ||||
\(340\) | 336.746 | + | 583.261i | 0.0537135 | + | 0.0930346i | ||||
\(341\) | −22191.8 | −3.52421 | ||||||||
\(342\) | −3559.20 | + | 4739.05i | −0.562748 | + | 0.749293i | ||||
\(343\) | 3627.71 | − | 5214.72i | 0.571072 | − | 0.820900i | ||||
\(344\) | 965.858 | − | 557.639i | 0.151383 | − | 0.0874007i | ||||
\(345\) | 98.9574 | − | 1639.56i | 0.0154426 | − | 0.255857i | ||||
\(346\) | 1768.53 | + | 1021.06i | 0.274788 | + | 0.158649i | ||||
\(347\) | 297.253 | + | 171.619i | 0.0459866 | + | 0.0265504i | 0.522817 | − | 0.852445i | \(-0.324881\pi\) |
−0.476830 | + | 0.878995i | \(0.658214\pi\) | |||||||
\(348\) | −1061.46 | − | 701.337i | −0.163506 | − | 0.108033i | ||||
\(349\) | 3767.94 | − | 2175.42i | 0.577918 | − | 0.333661i | −0.182388 | − | 0.983227i | \(-0.558383\pi\) |
0.760306 | + | 0.649566i | \(0.225049\pi\) | |||||||
\(350\) | −516.560 | − | 1553.59i | −0.0788894 | − | 0.237266i | ||||
\(351\) | 5230.59 | + | 4445.59i | 0.795408 | + | 0.676034i | ||||
\(352\) | −2123.44 | −0.321533 | ||||||||
\(353\) | 1617.00 | + | 2800.73i | 0.243808 | + | 0.422288i | 0.961796 | − | 0.273768i | \(-0.0882700\pi\) |
−0.717988 | + | 0.696056i | \(0.754937\pi\) | |||||||
\(354\) | −1961.06 | − | 1295.73i | −0.294432 | − | 0.194540i | ||||
\(355\) | 907.798 | + | 524.118i | 0.135721 | + | 0.0783585i | ||||
\(356\) | −3284.47 | + | 5688.87i | −0.488979 | + | 0.846936i | ||||
\(357\) | −1741.68 | + | 464.651i | −0.258205 | + | 0.0688850i | ||||
\(358\) | 2447.76 | + | 4239.64i | 0.361363 | + | 0.625899i | ||||
\(359\) | 6058.56i | 0.890692i | 0.895358 | + | 0.445346i | \(0.146919\pi\) | ||||
−0.895358 | + | 0.445346i | \(0.853081\pi\) | |||||||
\(360\) | −233.523 | + | 1927.50i | −0.0341882 | + | 0.282189i | ||||
\(361\) | −5187.12 | −0.756250 | ||||||||
\(362\) | 676.711 | + | 1172.10i | 0.0982518 | + | 0.170177i | ||||
\(363\) | 7134.65 | + | 14281.2i | 1.03160 | + | 2.06492i | ||||
\(364\) | −3550.58 | − | 729.368i | −0.511266 | − | 0.105026i | ||||
\(365\) | −2742.96 | − | 1583.65i | −0.393351 | − | 0.227101i | ||||
\(366\) | 2517.76 | + | 5039.71i | 0.359578 | + | 0.719753i | ||||
\(367\) | −7201.91 | + | 4158.03i | −1.02435 | + | 0.591409i | −0.915361 | − | 0.402634i | \(-0.868095\pi\) |
−0.108990 | + | 0.994043i | \(0.534762\pi\) | |||||||
\(368\) | 562.665i | 0.0797037i | ||||||||
\(369\) | 7203.71 | + | 872.757i | 1.01629 | + | 0.123127i | ||||
\(370\) | − | 4529.04i | − | 0.636361i | ||||||
\(371\) | 5395.18 | − | 6074.96i | 0.754997 | − | 0.850125i | ||||
\(372\) | 418.773 | − | 6938.35i | 0.0583665 | − | 0.967034i | ||||
\(373\) | −431.018 | + | 746.545i | −0.0598318 | + | 0.103632i | −0.894390 | − | 0.447288i | \(-0.852390\pi\) |
0.834558 | + | 0.550920i | \(0.185723\pi\) | |||||||
\(374\) | −1242.96 | + | 2152.87i | −0.171850 | + | 0.297654i | ||||
\(375\) | −4356.62 | + | 6593.64i | −0.599933 | + | 0.907984i | ||||
\(376\) | 802.409 | − | 463.271i | 0.110056 | − | 0.0635409i | ||||
\(377\) | −2994.96 | −0.409146 | ||||||||
\(378\) | −4819.25 | − | 1944.19i | −0.655755 | − | 0.264546i | ||||
\(379\) | 9815.25 | 1.33028 | 0.665139 | − | 0.746719i | \(-0.268372\pi\) | ||||
0.665139 | + | 0.746719i | \(0.268372\pi\) | |||||||
\(380\) | −3417.57 | + | 1973.14i | −0.461363 | + | 0.266368i | ||||
\(381\) | 6561.50 | − | 9930.67i | 0.882299 | − | 1.33534i | ||||
\(382\) | 2275.20 | − | 3940.77i | 0.304737 | − | 0.527820i | ||||
\(383\) | 1352.71 | − | 2342.96i | 0.180470 | − | 0.312584i | −0.761570 | − | 0.648082i | \(-0.775571\pi\) |
0.942041 | + | 0.335498i | \(0.108905\pi\) | |||||||
\(384\) | 40.0705 | − | 663.899i | 0.00532510 | − | 0.0882278i | ||||
\(385\) | −7335.52 | + | 8259.78i | −0.971047 | + | 1.09340i | ||||
\(386\) | 4543.03i | 0.599052i | ||||||||
\(387\) | 2260.43 | − | 3009.75i | 0.296910 | − | 0.395334i | ||||
\(388\) | − | 4475.97i | − | 0.585652i | ||||||
\(389\) | −6056.01 | + | 3496.44i | −0.789336 | + | 0.455723i | −0.839729 | − | 0.543006i | \(-0.817286\pi\) |
0.0503926 | + | 0.998729i | \(0.483953\pi\) | |||||||
\(390\) | 2042.72 | + | 4088.84i | 0.265224 | + | 0.530888i | ||||
\(391\) | 570.465 | + | 329.358i | 0.0737843 | + | 0.0425994i | ||||
\(392\) | 2724.79 | − | 324.107i | 0.351079 | − | 0.0417599i | ||||
\(393\) | 3238.43 | + | 6482.24i | 0.415667 | + | 0.832025i | ||||
\(394\) | 3485.27 | + | 6036.66i | 0.445648 | + | 0.771884i | ||||
\(395\) | 7028.45 | 0.895291 | ||||||||
\(396\) | −6592.38 | + | 2810.81i | −0.836565 | + | 0.356688i | ||||
\(397\) | 22.8921i | 0.00289400i | 0.999999 | + | 0.00144700i | \(0.000460595\pi\) | ||||
−0.999999 | + | 0.00144700i | \(0.999539\pi\) | |||||||
\(398\) | −1681.87 | − | 2913.09i | −0.211821 | − | 0.366884i | ||||
\(399\) | −2722.59 | − | 10205.2i | −0.341604 | − | 1.28045i | ||||
\(400\) | 353.606 | − | 612.463i | 0.0442007 | − | 0.0765579i | ||||
\(401\) | −10278.3 | − | 5934.17i | −1.27998 | − | 0.738998i | −0.303137 | − | 0.952947i | \(-0.598034\pi\) |
−0.976845 | + | 0.213949i | \(0.931367\pi\) | |||||||
\(402\) | 5324.01 | + | 3517.74i | 0.660541 | + | 0.436440i | ||||
\(403\) | −8181.66 | − | 14171.0i | −1.01131 | − | 1.75164i | ||||
\(404\) | 6110.94 | 0.752551 | ||||||||
\(405\) | 1826.45 | + | 6293.18i | 0.224091 | + | 0.772125i | ||||
\(406\) | 2151.45 | − | 715.343i | 0.262992 | − | 0.0874431i | ||||
\(407\) | 14477.5 | − | 8358.56i | 1.76320 | − | 1.01798i | ||||
\(408\) | −649.647 | − | 429.242i | −0.0788293 | − | 0.0520849i | ||||
\(409\) | −3271.46 | − | 1888.78i | −0.395510 | − | 0.228348i | 0.289035 | − | 0.957319i | \(-0.406666\pi\) |
−0.684545 | + | 0.728971i | \(0.739999\pi\) | |||||||
\(410\) | 4184.28 | + | 2415.80i | 0.504017 | + | 0.290994i | ||||
\(411\) | −447.498 | + | 7414.28i | −0.0537067 | + | 0.889828i | ||||
\(412\) | 5972.45 | − | 3448.20i | 0.714179 | − | 0.412331i | ||||
\(413\) | 3974.83 | − | 1321.61i | 0.473580 | − | 0.157462i | ||||
\(414\) | 744.805 | + | 1746.84i | 0.0884182 | + | 0.207373i | ||||
\(415\) | 2205.74 | 0.260905 | ||||||||
\(416\) | −782.866 | − | 1355.96i | −0.0922672 | − | 0.159812i | ||||
\(417\) | 1131.39 | − | 565.227i | 0.132865 | − | 0.0663772i | ||||
\(418\) | −12614.6 | − | 7283.04i | −1.47608 | − | 0.852214i | ||||
\(419\) | 5522.32 | − | 9564.93i | 0.643873 | − | 1.11522i | −0.340688 | − | 0.940177i | \(-0.610660\pi\) |
0.984561 | − | 0.175044i | \(-0.0560068\pi\) | |||||||
\(420\) | −2444.02 | − | 2449.34i | −0.283943 | − | 0.284561i | ||||
\(421\) | −1394.24 | − | 2414.90i | −0.161404 | − | 0.279561i | 0.773968 | − | 0.633224i | \(-0.218269\pi\) |
−0.935373 | + | 0.353664i | \(0.884936\pi\) | |||||||
\(422\) | 2099.74i | 0.242212i | ||||||||
\(423\) | 1877.91 | − | 2500.42i | 0.215856 | − | 0.287410i | ||||
\(424\) | 3509.60 | 0.401985 | ||||||||
\(425\) | −413.969 | − | 717.016i | −0.0472481 | − | 0.0818362i | ||||
\(426\) | −1209.70 | − | 73.0129i | −0.137582 | − | 0.00830396i | ||||
\(427\) | −9834.41 | − | 2020.21i | −1.11457 | − | 0.228957i | ||||
\(428\) | −2318.72 | − | 1338.71i | −0.261868 | − | 0.151190i | ||||
\(429\) | −9300.38 | + | 14075.9i | −1.04668 | + | 1.58413i | ||||
\(430\) | 2170.49 | − | 1253.13i | 0.243419 | − | 0.140538i | ||||
\(431\) | 10345.4i | 1.15620i | 0.815966 | + | 0.578100i | \(0.196206\pi\) | ||||
−0.815966 | + | 0.578100i | \(0.803794\pi\) | |||||||
\(432\) | −754.407 | − | 2114.17i | −0.0840195 | − | 0.235459i | ||||
\(433\) | 5236.75i | 0.581206i | 0.956844 | + | 0.290603i | \(0.0938559\pi\) | ||||
−0.956844 | + | 0.290603i | \(0.906144\pi\) | |||||||
\(434\) | 9262.09 | + | 8225.68i | 1.02441 | + | 0.909782i | ||||
\(435\) | −2385.32 | − | 1576.05i | −0.262913 | − | 0.173715i | ||||
\(436\) | −633.268 | + | 1096.85i | −0.0695598 | + | 0.120481i | ||||
\(437\) | −1929.85 | + | 3342.60i | −0.211252 | + | 0.365900i | ||||
\(438\) | 3655.17 | + | 220.612i | 0.398746 | + | 0.0240668i | ||||
\(439\) | 5187.63 | − | 2995.08i | 0.563991 | − | 0.325621i | −0.190755 | − | 0.981638i | \(-0.561093\pi\) |
0.754746 | + | 0.656017i | \(0.227760\pi\) | |||||||
\(440\) | −4771.81 | −0.517016 | ||||||||
\(441\) | 8030.31 | − | 4613.04i | 0.867111 | − | 0.498115i | ||||
\(442\) | −1833.01 | −0.197257 | ||||||||
\(443\) | −3479.08 | + | 2008.65i | −0.373129 | + | 0.215426i | −0.674824 | − | 0.737978i | \(-0.735781\pi\) |
0.301696 | + | 0.953404i | \(0.402447\pi\) | |||||||
\(444\) | 2340.13 | + | 4684.15i | 0.250130 | + | 0.500676i | ||||
\(445\) | −7380.89 | + | 12784.1i | −0.786265 | + | 1.36185i | ||||
\(446\) | 2360.88 | − | 4089.16i | 0.250652 | − | 0.434142i | ||||
\(447\) | −5719.00 | + | 2857.13i | −0.605144 | + | 0.302321i | ||||
\(448\) | 886.248 | + | 787.079i | 0.0934627 | + | 0.0830044i | ||||
\(449\) | 1948.54i | 0.204805i | 0.994743 | + | 0.102402i | \(0.0326529\pi\) | ||||
−0.994743 | + | 0.102402i | \(0.967347\pi\) | |||||||
\(450\) | 287.076 | − | 2369.51i | 0.0300730 | − | 0.248222i | ||||
\(451\) | 17833.9i | 1.86201i | ||||||||
\(452\) | 2321.60 | − | 1340.38i | 0.241590 | − | 0.139482i | ||||
\(453\) | −8686.13 | − | 524.262i | −0.900905 | − | 0.0543752i | ||||
\(454\) | 7329.01 | + | 4231.41i | 0.757638 | + | 0.437422i | ||||
\(455\) | −7978.90 | − | 1639.04i | −0.822103 | − | 0.168878i | ||||
\(456\) | 2515.11 | − | 3806.56i | 0.258291 | − | 0.390918i | ||||
\(457\) | −6701.72 | − | 11607.7i | −0.685980 | − | 1.18815i | −0.973128 | − | 0.230266i | \(-0.926040\pi\) |
0.287147 | − | 0.957886i | \(-0.407293\pi\) | |||||||
\(458\) | 3618.27 | 0.369150 | ||||||||
\(459\) | −2585.07 | − | 472.673i | −0.262878 | − | 0.0480664i | ||||
\(460\) | 1264.43i | 0.128161i | ||||||||
\(461\) | −8561.65 | − | 14829.2i | −0.864980 | − | 1.49819i | −0.867067 | − | 0.498191i | \(-0.833998\pi\) |
0.00208770 | − | 0.999998i | \(-0.499335\pi\) | |||||||
\(462\) | 3318.97 | − | 12332.9i | 0.334226 | − | 1.24194i | ||||
\(463\) | 6153.89 | − | 10658.9i | 0.617701 | − | 1.06989i | −0.372203 | − | 0.928151i | \(-0.621397\pi\) |
0.989904 | − | 0.141739i | \(-0.0452693\pi\) | |||||||
\(464\) | 848.152 | + | 489.681i | 0.0848588 | + | 0.0489933i | ||||
\(465\) | 941.070 | − | 15591.9i | 0.0938518 | − | 1.55496i | ||||
\(466\) | −3054.99 | − | 5291.39i | −0.303690 | − | 0.526007i | ||||
\(467\) | 15514.3 | 1.53730 | 0.768648 | − | 0.639672i | \(-0.220930\pi\) | ||||
0.768648 | + | 0.639672i | \(0.220930\pi\) | |||||||
\(468\) | −4225.37 | − | 3173.41i | −0.417346 | − | 0.313443i | ||||
\(469\) | −10791.1 | + | 3587.99i | −1.06245 | + | 0.353258i | ||||
\(470\) | 1803.18 | − | 1041.07i | 0.176967 | − | 0.102172i | ||||
\(471\) | 2782.18 | − | 1389.94i | 0.272179 | − | 0.135977i | ||||
\(472\) | 1566.97 | + | 904.692i | 0.152809 | + | 0.0882242i | ||||
\(473\) | 8011.48 | + | 4625.43i | 0.778791 | + | 0.449635i | ||||
\(474\) | −7269.17 | + | 3631.57i | −0.704397 | + | 0.351906i | ||||
\(475\) | 4201.30 | − | 2425.62i | 0.405829 | − | 0.234306i | ||||
\(476\) | 1316.76 | − | 437.814i | 0.126793 | − | 0.0421579i | ||||
\(477\) | 10895.9 | − | 4645.69i | 1.04588 | − | 0.445936i | ||||
\(478\) | −9362.66 | −0.895896 | ||||||||
\(479\) | 9726.27 | + | 16846.4i | 0.927776 | + | 1.60695i | 0.787035 | + | 0.616908i | \(0.211615\pi\) |
0.140741 | + | 0.990047i | \(0.455052\pi\) | |||||||
\(480\) | 90.0468 | − | 1491.92i | 0.00856261 | − | 0.141868i | ||||
\(481\) | 10675.1 | + | 6163.25i | 1.01194 | + | 0.584241i | ||||
\(482\) | −1435.12 | + | 2485.71i | −0.135618 | + | 0.234898i | ||||
\(483\) | −3267.96 | − | 879.456i | −0.307862 | − | 0.0828502i | ||||
\(484\) | −6144.61 | − | 10642.8i | −0.577067 | − | 0.999509i | ||||
\(485\) | − | 10058.5i | − | 0.941713i | ||||||
\(486\) | −5140.66 | − | 5565.00i | −0.479805 | − | 0.519411i | ||||
\(487\) | 20747.4 | 1.93050 | 0.965250 | − | 0.261329i | \(-0.0841607\pi\) | ||||
0.965250 | + | 0.261329i | \(0.0841607\pi\) | |||||||
\(488\) | −2168.38 | − | 3755.75i | −0.201144 | − | 0.348391i | ||||
\(489\) | 5158.80 | − | 7807.72i | 0.477074 | − | 0.722040i | ||||
\(490\) | 6123.18 | − | 728.336i | 0.564525 | − | 0.0671487i | ||||
\(491\) | 342.738 | + | 197.880i | 0.0315022 | + | 0.0181878i | 0.515668 | − | 0.856788i | \(-0.327544\pi\) |
−0.484166 | + | 0.874976i | \(0.660877\pi\) | |||||||
\(492\) | −5575.82 | − | 336.536i | −0.510930 | − | 0.0308378i | ||||
\(493\) | 992.939 | − | 573.273i | 0.0907093 | − | 0.0523711i | ||||
\(494\) | − | 10740.4i | − | 0.978207i | ||||||
\(495\) | −14814.5 | + | 6316.48i | −1.34517 | + | 0.573545i | ||||
\(496\) | 5350.86i | 0.484397i | ||||||||
\(497\) | 1434.15 | − | 1614.84i | 0.129437 | − | 0.145746i | ||||
\(498\) | −2281.29 | + | 1139.70i | −0.205275 | + | 0.102552i | ||||
\(499\) | −10146.7 | + | 17574.6i | −0.910278 | + | 1.57665i | −0.0966055 | + | 0.995323i | \(0.530799\pi\) |
−0.813672 | + | 0.581324i | \(0.802535\pi\) | |||||||
\(500\) | 3041.84 | − | 5268.62i | 0.272070 | − | 0.471239i | ||||
\(501\) | −907.008 | − | 1815.52i | −0.0808825 | − | 0.161899i | ||||
\(502\) | −10704.2 | + | 6180.07i | −0.951696 | + | 0.549462i | ||||
\(503\) | −9434.59 | −0.836318 | −0.418159 | − | 0.908374i | \(-0.637324\pi\) | ||||
−0.418159 | + | 0.908374i | \(0.637324\pi\) | |||||||
\(504\) | 3793.29 | + | 1270.42i | 0.335251 | + | 0.112279i | ||||
\(505\) | 13732.6 | 1.21008 | ||||||||
\(506\) | −4041.85 | + | 2333.56i | −0.355103 | + | 0.205019i | ||||
\(507\) | −1022.09 | − | 61.6897i | −0.0895321 | − | 0.00540382i | ||||
\(508\) | −4581.31 | + | 7935.05i | −0.400123 | + | 0.693034i | ||||
\(509\) | 1055.39 | − | 1828.00i | 0.0919048 | − | 0.159184i | −0.816408 | − | 0.577476i | \(-0.804038\pi\) |
0.908313 | + | 0.418292i | \(0.137371\pi\) | |||||||
\(510\) | −1459.89 | − | 964.597i | −0.126755 | − | 0.0837511i | ||||
\(511\) | −4333.34 | + | 4879.33i | −0.375139 | + | 0.422405i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 2769.59 | − | 15147.1i | 0.238364 | − | 1.30362i | ||||
\(514\) | 10947.4i | 0.939438i | ||||||||
\(515\) | 13421.4 | − | 7748.82i | 1.14838 | − | 0.663017i | ||||
\(516\) | −1597.34 | + | 2417.53i | −0.136277 | + | 0.206252i | ||||
\(517\) | 6655.72 | + | 3842.68i | 0.566186 | + | 0.326888i | ||||
\(518\) | −9140.59 | − | 1877.68i | −0.775317 | − | 0.159267i | ||||
\(519\) | −5295.95 | − | 319.643i | −0.447912 | − | 0.0270343i | ||||
\(520\) | −1759.26 | − | 3047.14i | −0.148363 | − | 0.256973i | ||||
\(521\) | 2781.94 | 0.233933 | 0.116967 | − | 0.993136i | \(-0.462683\pi\) | ||||
0.116967 | + | 0.993136i | \(0.462683\pi\) | |||||||
\(522\) | 3281.35 | + | 397.548i | 0.275136 | + | 0.0333338i | ||||
\(523\) | − | 16345.8i | − | 1.36664i | −0.730119 | − | 0.683320i | \(-0.760536\pi\) | ||
0.730119 | − | 0.683320i | \(-0.239464\pi\) | |||||||
\(524\) | −2789.05 | − | 4830.78i | −0.232520 | − | 0.402736i | ||||
\(525\) | 3004.49 | + | 3011.03i | 0.249765 | + | 0.250309i | ||||
\(526\) | −4596.54 | + | 7961.45i | −0.381024 | + | 0.659954i | ||||
\(527\) | 5425.04 | + | 3132.15i | 0.448422 | + | 0.258897i | ||||
\(528\) | 4935.24 | − | 2465.57i | 0.406778 | − | 0.203220i | ||||
\(529\) | −5465.16 | − | 9465.93i | −0.449179 | − | 0.778000i | ||||
\(530\) | 7886.82 | 0.646380 | ||||||||
\(531\) | 6062.34 | + | 734.476i | 0.495449 | + | 0.0600255i | ||||
\(532\) | 2565.34 | + | 7715.45i | 0.209063 | + | 0.628773i | ||||
\(533\) | −11388.2 | + | 6574.97i | −0.925473 | + | 0.534322i | ||||
\(534\) | 1028.20 | − | 17035.6i | 0.0833235 | − | 1.38053i | ||||
\(535\) | −5210.65 | − | 3008.37i | −0.421077 | − | 0.243109i | ||||
\(536\) | −4254.13 | − | 2456.12i | −0.342818 | − | 0.197926i | ||||
\(537\) | −10611.8 | − | 7011.52i | −0.852759 | − | 0.563444i | ||||
\(538\) | −2767.89 | + | 1598.04i | −0.221807 | + | 0.128060i | ||||
\(539\) | 13628.8 | + | 18229.1i | 1.08912 | + | 1.45674i | ||||
\(540\) | −1695.31 | − | 4750.99i | −0.135101 | − | 0.378611i | ||||
\(541\) | −4367.39 | −0.347077 | −0.173539 | − | 0.984827i | \(-0.555520\pi\) | ||||
−0.173539 | + | 0.984827i | \(0.555520\pi\) | |||||||
\(542\) | 233.977 | + | 405.261i | 0.0185428 | + | 0.0321170i | ||||
\(543\) | −2933.75 | − | 1938.42i | −0.231858 | − | 0.153196i | ||||
\(544\) | 519.098 | + | 299.701i | 0.0409120 | + | 0.0236206i | ||||
\(545\) | −1423.09 | + | 2464.86i | −0.111850 | + | 0.193730i | ||||
\(546\) | 9099.06 | − | 2427.48i | 0.713194 | − | 0.190269i | ||||
\(547\) | −1279.61 | − | 2216.36i | −0.100023 | − | 0.173244i | 0.811671 | − | 0.584115i | \(-0.198558\pi\) |
−0.911694 | + | 0.410870i | \(0.865225\pi\) | |||||||
\(548\) | − | 5717.90i | − | 0.445724i | ||||||
\(549\) | −11703.4 | − | 8789.73i | −0.909819 | − | 0.683309i | ||||
\(550\) | 5866.09 | 0.454784 | ||||||||
\(551\) | 3359.05 | + | 5818.05i | 0.259710 | + | 0.449832i | ||||
\(552\) | −653.324 | − | 1307.73i | −0.0503756 | − | 0.100835i | ||||
\(553\) | 2913.90 | − | 14184.9i | 0.224072 | − | 1.09079i | ||||
\(554\) | 3713.90 | + | 2144.22i | 0.284816 | + | 0.164439i | ||||
\(555\) | 5258.77 | + | 10526.3i | 0.402203 | + | 0.805073i | ||||
\(556\) | −843.150 | + | 486.793i | −0.0643121 | + | 0.0371306i | ||||
\(557\) | 11605.3i | 0.882823i | 0.897305 | + | 0.441411i | \(0.145522\pi\) | ||||
−0.897305 | + | 0.441411i | \(0.854478\pi\) | |||||||
\(558\) | 7082.98 | + | 16612.2i | 0.537359 | + | 1.26030i | ||||
\(559\) | 6821.19i | 0.516110i | ||||||||
\(560\) | 1991.59 | + | 1768.73i | 0.150285 | + | 0.133469i | ||||
\(561\) | 389.110 | − | 6446.89i | 0.0292838 | − | 0.485183i | ||||
\(562\) | 8237.12 | − | 14267.1i | 0.618259 | − | 1.07086i | ||||
\(563\) | −147.052 | + | 254.701i | −0.0110080 | + | 0.0190664i | −0.871477 | − | 0.490437i | \(-0.836837\pi\) |
0.860469 | + | 0.509503i | \(0.170171\pi\) | |||||||
\(564\) | −1327.02 | + | 2008.42i | −0.0990741 | + | 0.149946i | ||||
\(565\) | 5217.12 | − | 3012.11i | 0.388471 | − | 0.224284i | ||||
\(566\) | −11801.5 | −0.876418 | ||||||||
\(567\) | 13458.2 | − | 1077.10i | 0.996813 | − | 0.0797777i | ||||
\(568\) | 932.921 | 0.0689164 | ||||||||
\(569\) | −6601.43 | + | 3811.34i | −0.486373 | + | 0.280808i | −0.723069 | − | 0.690776i | \(-0.757269\pi\) |
0.236695 | + | 0.971584i | \(0.423936\pi\) | |||||||
\(570\) | 5651.99 | − | 8554.14i | 0.415326 | − | 0.628585i | ||||
\(571\) | −2212.29 | + | 3831.80i | −0.162139 | + | 0.280834i | −0.935636 | − | 0.352967i | \(-0.885173\pi\) |
0.773496 | + | 0.633801i | \(0.218506\pi\) | |||||||
\(572\) | 6493.62 | − | 11247.3i | 0.474671 | − | 0.822155i | ||||
\(573\) | −712.254 | + | 11800.8i | −0.0519281 | + | 0.860361i | ||||
\(574\) | 6610.35 | − | 7443.24i | 0.480681 | − | 0.541245i | ||||
\(575\) | − | 1554.39i | − | 0.112735i | ||||||
\(576\) | 677.738 | + | 1589.55i | 0.0490262 | + | 0.114984i | ||||
\(577\) | 21320.1i | 1.53825i | 0.639099 | + | 0.769124i | \(0.279307\pi\) | ||||
−0.639099 | + | 0.769124i | \(0.720693\pi\) | |||||||
\(578\) | −7901.85 | + | 4562.14i | −0.568640 | + | 0.328304i | ||||
\(579\) | −5275.01 | − | 10558.8i | −0.378622 | − | 0.757873i | ||||
\(580\) | 1905.98 | + | 1100.42i | 0.136451 | + | 0.0787798i | ||||
\(581\) | 914.473 | − | 4451.67i | 0.0652990 | − | 0.317877i | ||||
\(582\) | 5197.16 | + | 10402.9i | 0.370153 | + | 0.740921i | ||||
\(583\) | 14555.5 | + | 25210.9i | 1.03401 | + | 1.79096i | ||||
\(584\) | −2818.87 | −0.199736 | ||||||||
\(585\) | −9495.30 | − | 7131.33i | −0.671081 | − | 0.504007i | ||||
\(586\) | − | 3755.39i | − | 0.264734i | ||||||
\(587\) | 7958.62 | + | 13784.7i | 0.559604 | + | 0.969262i | 0.997529 | + | 0.0702508i | \(0.0223800\pi\) |
−0.437926 | + | 0.899011i | \(0.644287\pi\) | |||||||
\(588\) | −5956.57 | + | 3917.10i | −0.417763 | + | 0.274725i | ||||
\(589\) | −18352.6 | + | 31787.6i | −1.28388 | + | 2.22375i | ||||
\(590\) | 3521.32 | + | 2033.03i | 0.245712 | + | 0.141862i | ||||
\(591\) | −15109.7 | − | 9983.43i | −1.05166 | − | 0.694862i | ||||
\(592\) | −2015.40 | − | 3490.78i | −0.139920 | − | 0.242348i | ||||
\(593\) | 10320.7 | 0.714702 | 0.357351 | − | 0.933970i | \(-0.383680\pi\) | ||||
0.357351 | + | 0.933970i | \(0.383680\pi\) | |||||||
\(594\) | 12058.2 | − | 14187.4i | 0.832916 | − | 0.979992i | ||||
\(595\) | 2959.03 | − | 983.861i | 0.203880 | − | 0.0677888i | ||||
\(596\) | 4261.99 | − | 2460.66i | 0.292916 | − | 0.169115i | ||||
\(597\) | 7291.42 | + | 4817.66i | 0.499862 | + | 0.330274i | ||||
\(598\) | −2980.29 | − | 1720.67i | −0.203801 | − | 0.117665i | ||||
\(599\) | −14115.3 | − | 8149.48i | −0.962832 | − | 0.555891i | −0.0657884 | − | 0.997834i | \(-0.520956\pi\) |
−0.897043 | + | 0.441942i | \(0.854290\pi\) | |||||||
\(600\) | −110.696 | + | 1834.05i | −0.00753194 | + | 0.124791i | ||||
\(601\) | 10634.4 | − | 6139.76i | 0.721772 | − | 0.416715i | −0.0936324 | − | 0.995607i | \(-0.529848\pi\) |
0.815405 | + | 0.578891i | \(0.196515\pi\) | |||||||
\(602\) | −1629.24 | − | 4900.05i | −0.110304 | − | 0.331746i | ||||
\(603\) | −16458.5 | − | 1994.01i | −1.11151 | − | 0.134664i | ||||
\(604\) | 6698.75 | 0.451272 | ||||||||
\(605\) | −13808.2 | − | 23916.6i | −0.927908 | − | 1.60718i | ||||
\(606\) | −14202.9 | + | 7095.55i | −0.952067 | + | 0.475639i | ||||
\(607\) | 16715.3 | + | 9650.56i | 1.11771 | + | 0.645312i | 0.940816 | − | 0.338918i | \(-0.110061\pi\) |
0.176896 | + | 0.984229i | \(0.443394\pi\) | |||||||
\(608\) | −1756.08 | + | 3041.61i | −0.117135 | + | 0.202884i | ||||
\(609\) | −4169.74 | + | 4160.68i | −0.277449 | + | 0.276846i | ||||
\(610\) | −4872.82 | − | 8439.96i | −0.323434 | − | 0.560203i | ||||
\(611\) | 5666.86i | 0.375216i | ||||||||
\(612\) | 2008.30 | + | 243.313i | 0.132648 | + | 0.0160708i | ||||
\(613\) | 6168.41 | 0.406427 | 0.203214 | − | 0.979134i | \(-0.434861\pi\) | ||||
0.203214 | + | 0.979134i | \(0.434861\pi\) | |||||||
\(614\) | −9599.67 | − | 16627.1i | −0.630963 | − | 1.09286i | ||||
\(615\) | −12530.0 | − | 756.266i | −0.821561 | − | 0.0495863i | ||||
\(616\) | −1978.33 | + | 9630.55i | −0.129398 | + | 0.629912i | ||||
\(617\) | 1923.21 | + | 1110.37i | 0.125487 | + | 0.0724500i | 0.561430 | − | 0.827525i | \(-0.310252\pi\) |
−0.435942 | + | 0.899975i | \(0.643585\pi\) | |||||||
\(618\) | −9877.24 | + | 14949.0i | −0.642914 | + | 0.973035i | ||||
\(619\) | 4974.55 | − | 2872.06i | 0.323011 | − | 0.186491i | −0.329723 | − | 0.944078i | \(-0.606955\pi\) |
0.652734 | + | 0.757587i | \(0.273622\pi\) | |||||||
\(620\) | 12024.5i | 0.778897i | ||||||||
\(621\) | −3759.35 | − | 3195.15i | −0.242927 | − | 0.206469i | ||||
\(622\) | − | 1.31041i | − | 8.44740e-5i | ||||||
\(623\) | 22741.0 | + | 20196.4i | 1.46244 | + | 1.29880i | ||||
\(624\) | 3393.96 | + | 2242.49i | 0.217736 | + | 0.143865i | ||||
\(625\) | 4073.10 | − | 7054.82i | 0.260679 | − | 0.451508i | ||||
\(626\) | 3995.62 | − | 6920.62i | 0.255107 | − | 0.441859i | ||||
\(627\) | 37775.1 | + | 2279.96i | 2.40605 | + | 0.145220i | ||||
\(628\) | −2073.37 | + | 1197.06i | −0.131746 | + | 0.0760637i | ||||
\(629\) | −4718.90 | −0.299133 | ||||||||
\(630\) | 8524.32 | + | 2854.89i | 0.539075 | + | 0.180542i | ||||
\(631\) | −24057.5 | −1.51777 | −0.758885 | − | 0.651225i | \(-0.774256\pi\) | ||||
−0.758885 | + | 0.651225i | \(0.774256\pi\) | |||||||
\(632\) | 5417.22 | − | 3127.63i | 0.340958 | − | 0.196852i | ||||
\(633\) | −2438.05 | − | 4880.16i | −0.153087 | − | 0.306428i | ||||
\(634\) | −3496.33 | + | 6055.82i | −0.219017 | + | 0.379349i | ||||
\(635\) | −10295.2 | + | 17831.7i | −0.643387 | + | 1.11438i | ||||
\(636\) | −8156.94 | + | 4075.08i | −0.508559 | + | 0.254069i | ||||
\(637\) | −6615.90 | + | 15423.6i | −0.411509 | + | 0.959351i | ||||
\(638\) | 8123.49i | 0.504094i | ||||||||
\(639\) | 2896.33 | − | 1234.92i | 0.179307 | − | 0.0764515i | ||||
\(640\) | 1150.57i | 0.0710630i | ||||||||
\(641\) | 11837.8 | − | 6834.54i | 0.729429 | − | 0.421136i | −0.0887844 | − | 0.996051i | \(-0.528298\pi\) |
0.818213 | + | 0.574915i | \(0.194965\pi\) | |||||||
\(642\) | 6943.52 | + | 419.085i | 0.426852 | + | 0.0257632i | ||||
\(643\) | −20421.6 | − | 11790.4i | −1.25249 | − | 0.723124i | −0.280885 | − | 0.959741i | \(-0.590628\pi\) |
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 2551.89 | + | 524.215i | 0.156147 | + | 0.0320761i | ||||
\(645\) | −3589.55 | + | 5432.70i | −0.219129 | + | 0.331647i | ||||
\(646\) | 2055.85 | + | 3560.84i | 0.125211 | + | 0.216872i | ||||
\(647\) | −25891.5 | −1.57326 | −0.786629 | − | 0.617425i | \(-0.788176\pi\) | ||||
−0.786629 | + | 0.617425i | \(0.788176\pi\) | |||||||
\(648\) | 4208.19 | + | 4037.74i | 0.255113 | + | 0.244780i | ||||
\(649\) | 15008.3i | 0.907744i | ||||||||
\(650\) | 2162.70 | + | 3745.91i | 0.130505 | + | 0.226041i | ||||
\(651\) | −31077.8 | − | 8363.50i | −1.87102 | − | 0.503520i | ||||
\(652\) | −3601.93 | + | 6238.72i | −0.216353 | + | 0.374735i | ||||
\(653\) | 15330.2 | + | 8850.89i | 0.918708 | + | 0.530416i | 0.883223 | − | 0.468954i | \(-0.155369\pi\) |
0.0354854 | + | 0.999370i | \(0.488702\pi\) | |||||||
\(654\) | 198.245 | − | 3284.58i | 0.0118532 | − | 0.196387i | ||||
\(655\) | −6267.58 | − | 10855.8i | −0.373885 | − | 0.647588i | ||||
\(656\) | 4300.08 | 0.255930 | ||||||||
\(657\) | −8751.41 | + | 3731.36i | −0.519673 | + | 0.221574i | ||||
\(658\) | −1353.53 | − | 4070.83i | −0.0801914 | − | 0.241181i | ||||
\(659\) | −16234.0 | + | 9372.72i | −0.959618 | + | 0.554036i | −0.896055 | − | 0.443942i | \(-0.853580\pi\) |
−0.0635624 | + | 0.997978i | \(0.520246\pi\) | |||||||
\(660\) | 11090.5 | − | 5540.66i | 0.654088 | − | 0.326773i | ||||
\(661\) | 10069.2 | + | 5813.43i | 0.592504 | + | 0.342082i | 0.766087 | − | 0.642737i | \(-0.222201\pi\) |
−0.173583 | + | 0.984819i | \(0.555535\pi\) | |||||||
\(662\) | 4045.08 | + | 2335.43i | 0.237487 | + | 0.137113i | ||||
\(663\) | 4260.25 | − | 2128.36i | 0.249554 | − | 0.124673i | ||||
\(664\) | 1700.09 | − | 981.548i | 0.0993619 | − | 0.0573666i | ||||
\(665\) | 5764.86 | + | 17338.2i | 0.336168 | + | 1.01105i | ||||
\(666\) | −10877.8 | − | 8169.61i | −0.632890 | − | 0.475324i | ||||
\(667\) | 2152.55 | 0.124958 | ||||||||
\(668\) | 781.147 | + | 1352.99i | 0.0452447 | + | 0.0783662i | ||||
\(669\) | −739.074 | + | 12245.2i | −0.0427119 | + | 0.707663i | ||||
\(670\) | −9559.92 | − | 5519.42i | −0.551242 | − | 0.318259i | ||||
\(671\) | 17986.0 | − | 31152.7i | 1.03479 | − | 1.79231i | ||||
\(672\) | −2973.69 | − | 800.265i | −0.170703 | − | 0.0459388i | ||||
\(673\) | −2240.43 | − | 3880.53i | −0.128324 | − | 0.222264i | 0.794703 | − | 0.606998i | \(-0.207626\pi\) |
−0.923027 | + | 0.384734i | \(0.874293\pi\) | |||||||
\(674\) | − | 3822.08i | − | 0.218429i | ||||||
\(675\) | 2084.08 | + | 5840.49i | 0.118839 | + | 0.333038i | ||||
\(676\) | 788.240 | 0.0448475 | ||||||||
\(677\) | 6548.02 | + | 11341.5i | 0.371730 | + | 0.643855i | 0.989832 | − | 0.142243i | \(-0.0454315\pi\) |
−0.618102 | + | 0.786098i | \(0.712098\pi\) | |||||||
\(678\) | −3839.46 | + | 5810.93i | −0.217483 | + | 0.329156i | ||||
\(679\) | −20300.2 | − | 4170.10i | −1.14735 | − | 0.235691i | ||||
\(680\) | 1166.52 | + | 673.492i | 0.0657854 | + | 0.0379812i | ||||
\(681\) | −21947.1 | − | 1324.64i | −1.23497 | − | 0.0745381i | ||||
\(682\) | −38437.4 | + | 22191.8i | −2.15813 | + | 1.24600i | ||||
\(683\) | − | 12353.9i | − | 0.692109i | −0.938214 | − | 0.346054i | \(-0.887521\pi\) | ||
0.938214 | − | 0.346054i | \(-0.112479\pi\) | |||||||
\(684\) | −1425.67 | + | 11767.5i | −0.0796959 | + | 0.657808i | ||||
\(685\) | − | 12849.3i | − | 0.716711i | ||||||
\(686\) | 1068.65 | − | 12659.9i | 0.0594770 | − | 0.704601i | ||||
\(687\) | −8409.50 | + | 4201.26i | −0.467019 | + | 0.233316i | ||||
\(688\) | 1115.28 | − | 1931.72i | 0.0618017 | − | 0.107044i | ||||
\(689\) | −10732.6 | + | 18589.4i | −0.593440 | + | 1.02787i | ||||
\(690\) | −1468.16 | − | 2938.75i | −0.0810026 | − | 0.162140i | ||||
\(691\) | 10460.0 | − | 6039.10i | 0.575858 | − | 0.332472i | −0.183627 | − | 0.982996i | \(-0.558784\pi\) |
0.759486 | + | 0.650524i | \(0.225451\pi\) | |||||||
\(692\) | 4084.24 | 0.224364 | ||||||||
\(693\) | 6606.15 | + | 32517.6i | 0.362117 | + | 1.78245i | ||||
\(694\) | 686.476 | 0.0375479 | ||||||||
\(695\) | −1894.74 | + | 1093.93i | −0.103412 | + | 0.0597050i | ||||
\(696\) | −2539.84 | − | 153.295i | −0.138322 | − | 0.00834860i | ||||
\(697\) | 2517.07 | − | 4359.69i | 0.136787 | − | 0.236923i | ||||
\(698\) | 4350.85 | − | 7535.89i | 0.235934 | − | 0.408650i | ||||
\(699\) | 13244.3 | + | 8750.91i | 0.716659 | + | 0.473519i | ||||
\(700\) | −2448.30 | − | 2174.34i | −0.132196 | − | 0.117403i | ||||
\(701\) | − | 14395.9i | − | 0.775645i | −0.921734 | − | 0.387822i | \(-0.873227\pi\) | ||
0.921734 | − | 0.387822i | \(-0.126773\pi\) | |||||||
\(702\) | 13505.2 | + | 2469.39i | 0.726100 | + | 0.132765i | ||||
\(703\) | − | 27650.0i | − | 1.48342i | ||||||
\(704\) | −3677.90 | + | 2123.44i | −0.196898 | + | 0.113679i | ||||
\(705\) | −2982.10 | + | 4513.34i | −0.159309 | + | 0.241110i | ||||
\(706\) | 5601.45 | + | 3234.00i | 0.298603 | + | 0.172398i | ||||
\(707\) | 5693.34 | − | 27715.3i | 0.302857 | − | 1.47432i | ||||
\(708\) | −4692.38 | − | 283.214i | −0.249083 | − | 0.0150337i | ||||
\(709\) | −14380.2 | − | 24907.2i | −0.761719 | − | 1.31934i | −0.941964 | − | 0.335715i | \(-0.891022\pi\) |
0.180244 | − | 0.983622i | \(-0.442311\pi\) | |||||||
\(710\) | 2096.47 | 0.110816 | ||||||||
\(711\) | 12678.1 | − | 16880.8i | 0.668730 | − | 0.890408i | ||||
\(712\) | 13137.9i | 0.691521i | ||||||||
\(713\) | 5880.36 | + | 10185.1i | 0.308866 | + | 0.534971i | ||||
\(714\) | −2552.02 | + | 2546.48i | −0.133763 | + | 0.133473i | ||||
\(715\) | 14592.5 | − | 25275.0i | 0.763258 | − | 1.32200i | ||||
\(716\) | 8479.28 | + | 4895.51i | 0.442578 | + | 0.255522i | ||||
\(717\) | 21760.5 | − | 10871.2i | 1.13342 | − | 0.566238i | ||||
\(718\) | 6058.56 | + | 10493.7i | 0.314907 | + | 0.545435i | ||||
\(719\) | −12676.1 | −0.657493 | −0.328746 | − | 0.944418i | \(-0.606626\pi\) | ||||
−0.328746 | + | 0.944418i | \(0.606626\pi\) | |||||||
\(720\) | 1523.02 | + | 3572.04i | 0.0788328 | + | 0.184892i | ||||
\(721\) | −10074.5 | − | 30299.8i | −0.520380 | − | 1.56508i | ||||
\(722\) | −8984.36 | + | 5187.12i | −0.463107 | + | 0.267375i | ||||
\(723\) | 449.266 | − | 7443.57i | 0.0231098 | − | 0.382890i | ||||
\(724\) | 2344.20 | + | 1353.42i | 0.120333 | + | 0.0694745i | ||||
\(725\) | −2343.06 | − | 1352.77i | −0.120026 | − | 0.0692972i | ||||
\(726\) | 26638.7 | + | 17601.0i | 1.36179 | + | 0.899773i | ||||
\(727\) | 12063.6 | − | 6964.93i | 0.615426 | − | 0.355316i | −0.159660 | − | 0.987172i | \(-0.551040\pi\) |
0.775086 | + | 0.631856i | \(0.217706\pi\) | |||||||
\(728\) | −6879.15 | + | 2287.28i | −0.350218 | + | 0.116445i | ||||
\(729\) | 18409.5 | + | 6965.09i | 0.935297 | + | 0.353863i | ||||
\(730\) | −6334.59 | −0.321170 | ||||||||
\(731\) | −1305.66 | − | 2261.48i | −0.0660625 | − | 0.114424i | ||||
\(732\) | 9400.60 | + | 6211.26i | 0.474667 | + | 0.313627i | ||||
\(733\) | 868.392 | + | 501.367i | 0.0437583 | + | 0.0252638i | 0.521720 | − | 0.853117i | \(-0.325291\pi\) |
−0.477961 | + | 0.878381i | \(0.658624\pi\) | |||||||
\(734\) | −8316.05 | + | 14403.8i | −0.418190 | + | 0.724325i | ||||
\(735\) | −13385.7 | + | 8802.55i | −0.671752 | + | 0.441751i | ||||
\(736\) | 562.665 | + | 974.565i | 0.0281795 | + | 0.0488084i | ||||
\(737\) | − | 40745.5i | − | 2.03647i | ||||||
\(738\) | 13349.9 | − | 5692.05i | 0.665878 | − | 0.283912i | ||||
\(739\) | 25136.6 | 1.25124 | 0.625619 | − | 0.780129i | \(-0.284847\pi\) | ||||
0.625619 | + | 0.780129i | \(0.284847\pi\) | |||||||
\(740\) | −4529.04 | − | 7844.52i | −0.224987 | − | 0.389690i | ||||
\(741\) | 12471.0 | + | 24962.6i | 0.618262 | + | 1.23755i | ||||
\(742\) | 3269.77 | − | 15917.3i | 0.161775 | − | 0.787525i | ||||
\(743\) | −20262.2 | − | 11698.4i | −1.00047 | − | 0.577620i | −0.0920810 | − | 0.995752i | \(-0.529352\pi\) |
−0.908387 | + | 0.418131i | \(0.862685\pi\) | |||||||
\(744\) | −6213.01 | − | 12436.3i | −0.306156 | − | 0.612821i | ||||
\(745\) | 9577.58 | − | 5529.62i | 0.471000 | − | 0.271932i | ||||
\(746\) | 1724.07i | 0.0846150i | ||||||||
\(747\) | 3978.79 | − | 5297.72i | 0.194881 | − | 0.259482i | ||||
\(748\) | 4971.85i | 0.243033i | ||||||||
\(749\) | −8231.82 | + | 9269.00i | −0.401581 | + | 0.452179i | ||||
\(750\) | −952.249 | + | 15777.1i | −0.0463616 | + | 0.768133i | ||||
\(751\) | 13579.4 | − | 23520.2i | 0.659811 | − | 1.14283i | −0.320853 | − | 0.947129i | \(-0.603970\pi\) |
0.980664 | − | 0.195697i | \(-0.0626971\pi\) | |||||||
\(752\) | 926.542 | − | 1604.82i | 0.0449302 | − | 0.0778214i | ||||
\(753\) | 17702.6 | − | 26792.5i | 0.856731 | − | 1.29664i | ||||
\(754\) | −5187.42 | + | 2994.96i | −0.250550 | + | 0.144655i | ||||
\(755\) | 15053.5 | 0.725633 | ||||||||
\(756\) | −10291.4 | + | 1451.81i | −0.495098 | + | 0.0698437i | ||||
\(757\) | 20937.2 | 1.00525 | 0.502626 | − | 0.864504i | \(-0.332367\pi\) | ||||
0.502626 | + | 0.864504i | \(0.332367\pi\) | |||||||
\(758\) | 17000.5 | − | 9815.25i | 0.814626 | − | 0.470325i | ||||
\(759\) | 6684.41 | − | 10116.7i | 0.319669 | − | 0.483811i | ||||
\(760\) | −3946.27 | + | 6835.15i | −0.188351 | + | 0.326233i | ||||
\(761\) | −11543.8 | + | 19994.5i | −0.549885 | + | 0.952429i | 0.448397 | + | 0.893835i | \(0.351995\pi\) |
−0.998282 | + | 0.0585944i | \(0.981338\pi\) | |||||||
\(762\) | 1434.18 | − | 23761.9i | 0.0681822 | − | 1.12966i | ||||
\(763\) | 4384.63 | + | 3894.00i | 0.208040 | + | 0.184761i | ||||
\(764\) | − | 9100.81i | − | 0.430963i | ||||||
\(765\) | 4513.07 | + | 546.775i | 0.213294 | + | 0.0258414i | ||||
\(766\) | − | 5410.83i | − | 0.255224i | ||||||
\(767\) | −9583.83 | + | 5533.23i | −0.451176 | + | 0.260487i | ||||
\(768\) | −594.495 | − | 1189.98i | −0.0279323 | − | 0.0559110i | ||||
\(769\) | −18738.6 | − | 10818.8i | −0.878716 | − | 0.507327i | −0.00848126 | − | 0.999964i | \(-0.502700\pi\) |
−0.870235 | + | 0.492637i | \(0.836033\pi\) | |||||||
\(770\) | −4445.72 | + | 21641.9i | −0.208069 | + | 1.01288i | ||||
\(771\) | −12711.3 | − | 25443.8i | −0.593759 | − | 1.18850i | ||||
\(772\) | 4543.03 | + | 7868.75i | 0.211797 | + | 0.366843i | ||||
\(773\) | 13555.7 | 0.630742 | 0.315371 | − | 0.948968i | \(-0.397871\pi\) | ||||
0.315371 | + | 0.948968i | \(0.397871\pi\) | |||||||
\(774\) | 905.440 | − | 7473.47i | 0.0420483 | − | 0.347065i | ||||
\(775\) | − | 14782.0i | − | 0.685142i | ||||||
\(776\) | −4475.97 | − | 7752.61i | −0.207059 | − | 0.358637i | ||||
\(777\) | 23424.5 | − | 6249.29i | 1.08153 | − | 0.288536i | ||||
\(778\) | −6992.88 | + | 12112.0i | −0.322245 | + | 0.558145i | ||||
\(779\) | 25545.3 | + | 14748.6i | 1.17491 | + | 0.678335i | ||||
\(780\) | 7626.94 | + | 5039.36i | 0.350113 | + | 0.231331i | ||||
\(781\) | 3869.14 | + | 6701.55i | 0.177271 | + | 0.307042i | ||||
\(782\) | 1317.43 | 0.0602447 | ||||||||
\(783\) | −8088.04 | + | 2886.08i | −0.369148 | + | 0.131724i | ||||
\(784\) | 4395.37 | − | 3286.16i | 0.200226 | − | 0.149698i | ||||
\(785\) | −4659.31 | + | 2690.05i | −0.211844 | + | 0.122308i | ||||
\(786\) | 12091.4 | + | 7989.14i | 0.548709 | + | 0.362549i | ||||
\(787\) | 19060.3 | + | 11004.5i | 0.863311 | + | 0.498433i | 0.865120 | − | 0.501566i | \(-0.167242\pi\) |
−0.00180871 | + | 0.999998i | \(0.500576\pi\) | |||||||
\(788\) | 12073.3 | + | 6970.53i | 0.545805 | + | 0.315120i | ||||
\(789\) | 1438.95 | − | 23841.0i | 0.0649278 | − | 1.07574i | ||||
\(790\) | 12173.6 | − | 7028.45i | 0.548251 | − | 0.316533i | ||||
\(791\) | −3916.14 | − | 11778.1i | −0.176033 | − | 0.529431i | ||||
\(792\) | −8607.53 | + | 11460.8i | −0.386181 | + | 0.514196i | ||||
\(793\) | 26524.3 | 1.18777 | ||||||||
\(794\) | 22.8921 | + | 39.6502i | 0.00102318 | + | 0.00177221i | ||||
\(795\) | −18330.4 | + | 9157.57i | −0.817749 | + | 0.408535i | ||||
\(796\) | −5826.17 | − | 3363.74i | −0.259426 | − | 0.149780i | ||||
\(797\) | −14681.9 | + | 25429.8i | −0.652520 | + | 1.13020i | 0.329989 | + | 0.943985i | \(0.392955\pi\) |
−0.982509 | + | 0.186214i | \(0.940378\pi\) | |||||||
\(798\) | −14920.9 | − | 14953.4i | −0.661897 | − | 0.663338i | ||||
\(799\) | −1084.71 | − | 1878.77i | −0.0480279 | − | 0.0831867i | ||||
\(800\) | − | 1414.42i | − | 0.0625093i | ||||||
\(801\) | 17390.7 | + | 40787.6i | 0.767129 | + | 1.79920i | ||||
\(802\) | −23736.7 | −1.04510 | ||||||||
\(803\) | −11690.8 | − | 20249.1i | −0.513773 | − | 0.889881i | ||||
\(804\) | 12739.2 | + | 768.890i | 0.558802 | + | 0.0337272i | ||||
\(805\) | 5734.64 | + | 1178.02i | 0.251080 | + | 0.0515774i | ||||
\(806\) | −28342.1 | − | 16363.3i | −1.23860 | − | 0.715103i | ||||
\(807\) | 4577.54 | − | 6928.00i | 0.199674 | − | 0.302202i | ||||
\(808\) | 10584.5 | − | 6110.94i | 0.460841 | − | 0.266067i | ||||
\(809\) | − | 41755.6i | − | 1.81465i | −0.420432 | − | 0.907324i | \(-0.638122\pi\) | ||
0.420432 | − | 0.907324i | \(-0.361878\pi\) | |||||||
\(810\) | 9456.68 | + | 9073.66i | 0.410215 | + | 0.393600i | ||||
\(811\) | − | 505.959i | − | 0.0219070i | −0.999940 | − | 0.0109535i | \(-0.996513\pi\) | ||
0.999940 | − | 0.0109535i | \(-0.00348668\pi\) | |||||||
\(812\) | 3011.07 | − | 3390.46i | 0.130133 | − | 0.146529i | ||||
\(813\) | −1014.36 | − | 670.220i | −0.0437580 | − | 0.0289122i | ||||
\(814\) | 16717.1 | − | 28954.9i | 0.719822 | − | 1.24677i | ||||
\(815\) | −8094.29 | + | 14019.7i | −0.347890 | + | 0.602564i | ||||
\(816\) | −1554.46 | − | 93.8216i | −0.0666877 | − | 0.00402502i | ||||
\(817\) | 13251.0 | − | 7650.44i | 0.567432 | − | 0.327607i | ||||
\(818\) | −7555.12 | −0.322932 | ||||||||
\(819\) | −18329.2 | + | 16207.0i | −0.782020 | + | 0.691477i | ||||
\(820\) | 9663.18 | 0.411528 | ||||||||
\(821\) | −22334.9 | + | 12895.0i | −0.949442 | + | 0.548161i | −0.892908 | − | 0.450240i | \(-0.851338\pi\) |
−0.0565347 | + | 0.998401i | \(0.518005\pi\) | |||||||
\(822\) | 6639.19 | + | 13289.4i | 0.281713 | + | 0.563894i | ||||
\(823\) | −7652.99 | + | 13255.4i | −0.324139 | + | 0.561425i | −0.981338 | − | 0.192292i | \(-0.938408\pi\) |
0.657199 | + | 0.753717i | \(0.271741\pi\) | |||||||
\(824\) | 6896.39 | − | 11944.9i | 0.291562 | − | 0.505001i | ||||
\(825\) | −13633.8 | + | 6811.26i | −0.575356 | + | 0.287439i | ||||
\(826\) | 5563.00 | − | 6263.92i | 0.234336 | − | 0.263861i | ||||
\(827\) | 8921.04i | 0.375109i | 0.982254 | + | 0.187554i | \(0.0600561\pi\) | ||||
−0.982254 | + | 0.187554i | \(0.939944\pi\) | |||||||
\(828\) | 3036.88 | + | 2280.81i | 0.127462 | + | 0.0957291i | ||||
\(829\) | − | 1174.38i | − | 0.0492011i | −0.999697 | − | 0.0246006i | \(-0.992169\pi\) | ||
0.999697 | − | 0.0246006i | \(-0.00783139\pi\) | |||||||
\(830\) | 3820.46 | − | 2205.74i | 0.159771 | − | 0.0922440i | ||||
\(831\) | −11121.4 | − | 671.249i | −0.464258 | − | 0.0280209i | ||||
\(832\) | −2711.93 | − | 1565.73i | −0.113004 | − | 0.0652428i | ||||
\(833\) | −758.869 | − | 6379.87i | −0.0315645 | − | 0.265365i | ||||
\(834\) | 1394.40 | − | 2110.39i | 0.0578947 | − | 0.0876223i | ||||
\(835\) | 1755.40 | + | 3040.45i | 0.0727523 | + | 0.126011i | ||||
\(836\) | −29132.2 | −1.20521 | ||||||||
\(837\) | −35750.9 | − | 30385.4i | −1.47638 | − | 1.25481i | ||||
\(838\) | − | 22089.3i | − | 0.910574i | ||||||
\(839\) | −13404.5 | − | 23217.3i | −0.551579 | − | 0.955363i | −0.998161 | − | 0.0606203i | \(-0.980692\pi\) |
0.446582 | − | 0.894743i | \(-0.352641\pi\) | |||||||
\(840\) | −6682.51 | − | 1798.36i | −0.274486 | − | 0.0738684i | ||||
\(841\) | −10321.2 | + | 17876.8i | −0.423189 | + | 0.732985i | ||||
\(842\) | −4829.80 | − | 2788.49i | −0.197679 | − | 0.114130i | ||||
\(843\) | −2578.63 | + | 42723.6i | −0.105353 | + | 1.74553i | ||||
\(844\) | 2099.74 | + | 3636.85i | 0.0856350 | + | 0.148324i | ||||
\(845\) | 1771.34 | 0.0721136 | ||||||||
\(846\) | 752.215 | − | 6208.76i | 0.0305694 | − | 0.252319i | ||||
\(847\) | −53993.5 | + | 17952.5i | −2.19037 | + | 0.728284i | ||||
\(848\) | 6078.81 | − | 3509.60i | 0.246164 | − | 0.142123i | ||||
\(849\) | 27428.7 | − | 13703.0i | 1.10877 | − | 0.553927i | ||||
\(850\) | −1434.03 | − | 827.938i | −0.0578669 | − | 0.0334095i | ||||
\(851\) | −7672.43 | − | 4429.68i | −0.309057 | − | 0.178434i | ||||
\(852\) | −2168.27 | + | 1083.24i | −0.0871876 | + | 0.0435576i | ||||
\(853\) | −34918.2 | + | 20160.0i | −1.40161 | + | 0.809222i | −0.994558 | − | 0.104181i | \(-0.966778\pi\) |
−0.407056 | + | 0.913403i | \(0.633445\pi\) | |||||||
\(854\) | −19053.9 | + | 6335.31i | −0.763479 | + | 0.253852i | ||||
\(855\) | −3203.79 | + | 26444.0i | −0.128149 | + | 1.05774i | ||||
\(856\) | −5354.85 | −0.213814 | ||||||||
\(857\) | −3860.50 | − | 6686.58i | −0.153876 | − | 0.266522i | 0.778773 | − | 0.627306i | \(-0.215842\pi\) |
−0.932649 | + | 0.360784i | \(0.882509\pi\) | |||||||
\(858\) | −2032.83 | + | 33680.5i | −0.0808854 | + | 1.34013i | ||||
\(859\) | −37480.7 | − | 21639.5i | −1.48874 | − | 0.859523i | −0.488820 | − | 0.872385i | \(-0.662573\pi\) |
−0.999917 | + | 0.0128616i | \(0.995906\pi\) | |||||||
\(860\) | 2506.26 | − | 4340.97i | 0.0993754 | − | 0.172123i | ||||
\(861\) | −6721.10 | + | 24974.8i | −0.266033 | + | 0.988548i | ||||
\(862\) | 10345.4 | + | 17918.8i | 0.408779 | + | 0.708025i | ||||
\(863\) | 21165.5i | 0.834856i | 0.908710 | + | 0.417428i | \(0.137068\pi\) | ||||
−0.908710 | + | 0.417428i | \(0.862932\pi\) | |||||||
\(864\) | −3420.84 | − | 2907.44i | −0.134698 | − | 0.114483i | ||||
\(865\) | 9178.15 | 0.360770 | ||||||||
\(866\) | 5236.75 | + | 9070.32i | 0.205487 | + | 0.355915i | ||||
\(867\) | 13068.1 | − | 19778.2i | 0.511898 | − | 0.774745i | ||||
\(868\) | 24268.1 | + | 4985.21i | 0.948978 | + | 0.194941i | ||||
\(869\) | 44934.1 | + | 25942.7i | 1.75407 | + | 1.01271i | ||||
\(870\) | −5707.54 | − | 344.486i | −0.222418 | − | 0.0134243i | ||||
\(871\) | 26018.8 | − | 15022.0i | 1.01219 | − | 0.584386i | ||||
\(872\) | 2533.07i | 0.0983724i | ||||||||
\(873\) | −24158.2 | − | 18143.7i | −0.936577 | − | 0.703405i | ||||
\(874\) | 7719.41i | 0.298756i | ||||||||
\(875\) | −21061.1 | − | 18704.4i | −0.813709 | − | 0.722657i | ||||
\(876\) | 6551.55 | − | 3273.06i | 0.252690 | − | 0.126240i | ||||
\(877\) | 7087.12 | − | 12275.2i | 0.272879 | − | 0.472640i | −0.696719 | − | 0.717344i | \(-0.745357\pi\) |
0.969598 | + | 0.244704i | \(0.0786908\pi\) | |||||||
\(878\) | 5990.16 | − | 10375.3i | 0.230249 | − | 0.398802i | ||||
\(879\) | 4360.48 | + | 8728.19i | 0.167321 | + | 0.334920i | ||||
\(880\) | −8265.02 | + | 4771.81i | −0.316606 | + | 0.182793i | ||||
\(881\) | −16308.0 | −0.623645 | −0.311823 | − | 0.950140i | \(-0.600939\pi\) | ||||
−0.311823 | + | 0.950140i | \(0.600939\pi\) | |||||||
\(882\) | 9295.87 | − | 16020.3i | 0.354885 | − | 0.611602i | ||||
\(883\) | −28226.0 | −1.07574 | −0.537871 | − | 0.843027i | \(-0.680771\pi\) | ||||
−0.537871 | + | 0.843027i | \(0.680771\pi\) | |||||||
\(884\) | −3174.87 | + | 1833.01i | −0.120795 | + | 0.0697409i | ||||
\(885\) | −10544.8 | − | 636.442i | −0.400518 | − | 0.0241738i | ||||
\(886\) | −4017.29 | + | 6958.16i | −0.152329 | + | 0.263842i | ||||
\(887\) | −25871.3 | + | 44810.5i | −0.979340 | + | 1.69627i | −0.314540 | + | 0.949244i | \(0.601850\pi\) |
−0.664800 | + | 0.747022i | \(0.731483\pi\) | |||||||
\(888\) | 8737.38 | + | 5773.06i | 0.330189 | + | 0.218166i | ||||
\(889\) | 31720.1 | + | 28170.7i | 1.19669 | + | 1.06278i | ||||
\(890\) | 29523.6i | 1.11195i | ||||||||
\(891\) | −11552.0 | + | 46975.0i | −0.434349 | + | 1.76624i | ||||
\(892\) | − | 9443.51i | − | 0.354475i | ||||||
\(893\) | 11008.5 | − | 6355.78i | 0.412527 | − | 0.238172i | ||||
\(894\) | −7048.47 | + | 10667.7i | −0.263687 | + | 0.399084i | ||||
\(895\) | 19054.7 | + | 11001.3i | 0.711653 | + | 0.410873i | ||||
\(896\) | 2322.10 | + | 477.012i | 0.0865804 | + | 0.0177856i | ||||
\(897\) | 8924.63 | + | 538.657i | 0.332201 | + | 0.0200504i | ||||
\(898\) | 1948.54 | + | 3374.97i | 0.0724094 | + | 0.125417i | ||||
\(899\) | 20470.4 | 0.759430 | ||||||||
\(900\) | −1872.28 | − | 4391.19i | −0.0693438 | − | 0.162637i | ||||
\(901\) | − | 8217.44i | − | 0.303843i | ||||||
\(902\) | 17833.9 | + | 30889.2i | 0.658319 | + | 1.14024i | ||||
\(903\) | 9476.19 | + | 9496.83i | 0.349223 | + | 0.349983i | ||||
\(904\) | 2680.75 | − | 4643.20i | 0.0986289 | − | 0.170830i | ||||
\(905\) | 5267.90 | + | 3041.42i | 0.193493 | + | 0.111713i | ||||
\(906\) | −15569.1 | + | 7778.08i | −0.570914 | + | 0.285220i | ||||
\(907\) | 3027.85 | + | 5244.40i | 0.110847 | + | 0.191993i | 0.916112 | − | 0.400922i | \(-0.131310\pi\) |
−0.805265 | + | 0.592915i | \(0.797977\pi\) | |||||||
\(908\) | 16925.6 | 0.618609 | ||||||||
\(909\) | 24771.2 | − | 32982.6i | 0.903860 | − | 1.20348i | ||||
\(910\) | −15458.9 | + | 5139.99i | −0.563140 | + | 0.187241i | ||||
\(911\) | 10003.4 | − | 5775.46i | 0.363806 | − | 0.210043i | −0.306943 | − | 0.951728i | \(-0.599306\pi\) |
0.670749 | + | 0.741685i | \(0.265973\pi\) | |||||||
\(912\) | 549.741 | − | 9108.27i | 0.0199602 | − | 0.330707i | ||||
\(913\) | 14101.7 | + | 8141.62i | 0.511170 | + | 0.295124i | ||||
\(914\) | −23215.4 | − | 13403.4i | −0.840151 | − | 0.485061i | ||||
\(915\) | 21125.1 | + | 13958.0i | 0.763251 | + | 0.504304i | ||||
\(916\) | 6267.03 | − | 3618.27i | 0.226057 | − | 0.130514i | ||||
\(917\) | −24507.8 | + | 8148.69i | −0.882572 | + | 0.293450i | ||||
\(918\) | −4950.15 | + | 1766.38i | −0.177973 | + | 0.0635068i | ||||
\(919\) | −36885.9 | −1.32400 | −0.661999 | − | 0.749505i | \(-0.730292\pi\) | ||||
−0.661999 | + | 0.749505i | \(0.730292\pi\) | |||||||
\(920\) | 1264.43 | + | 2190.05i | 0.0453119 | + | 0.0784825i | ||||
\(921\) | 41617.4 | + | 27497.9i | 1.48897 | + | 0.983808i | ||||
\(922\) | −29658.4 | − | 17123.3i | −1.05938 | − | 0.611633i | ||||
\(923\) | −2852.94 | + | 4941.44i | −0.101740 | + | 0.176218i | ||||
\(924\) | −6584.28 | − | 24680.2i | −0.234423 | − | 0.878700i | ||||
\(925\) | 5567.65 | + | 9643.45i | 0.197906 | + | 0.342783i | ||||
\(926\) | − | 24615.6i | − | 0.873562i | ||||||
\(927\) | 5598.85 | − | 46212.7i | 0.198371 | − | 1.63735i | ||||
\(928\) | 1958.72 | 0.0692869 | ||||||||
\(929\) | 11193.6 | + | 19388.0i | 0.395319 | + | 0.684713i | 0.993142 | − | 0.116915i | \(-0.0373007\pi\) |
−0.597823 | + | 0.801628i | \(0.703967\pi\) | |||||||
\(930\) | −13961.9 | − | 27947.1i | −0.492291 | − | 0.985399i | ||||
\(931\) | 37382.4 | − | 4446.54i | 1.31596 | − | 0.156530i | ||||
\(932\) | −10582.8 | − | 6109.97i | −0.371943 | − | 0.214741i | ||||
\(933\) | 1.52155 | + | 3.04563i | 5.33906e−5 | + | 0.000106870i | ||||
\(934\) | 26871.6 | − | 15514.3i | 0.941398 | − | 0.543516i | ||||
\(935\) | 11172.8i | 0.390791i | ||||||||
\(936\) | −10492.0 | − | 1271.14i | −0.366390 | − | 0.0443895i | ||||
\(937\) | − | 18336.5i | − | 0.639304i | −0.947535 | − | 0.319652i | \(-0.896434\pi\) | ||
0.947535 | − | 0.319652i | \(-0.103566\pi\) | |||||||
\(938\) | −15102.8 | + | 17005.7i | −0.525719 | + | 0.591958i | ||||
\(939\) | −1250.83 | + | 20724.2i | −0.0434711 | + | 0.720242i | ||||
\(940\) | 2082.13 | − | 3606.36i | 0.0722465 | − | 0.125135i | ||||
\(941\) | −5273.49 | + | 9133.95i | −0.182689 | + | 0.316427i | −0.942796 | − | 0.333372i | \(-0.891814\pi\) |
0.760106 | + | 0.649799i | \(0.225147\pi\) | |||||||
\(942\) | 3428.95 | − | 5189.63i | 0.118600 | − | 0.179498i | ||||
\(943\) | 8184.98 | − | 4725.60i | 0.282651 | − | 0.163188i | ||||
\(944\) | 3618.77 | 0.124768 | ||||||||
\(945\) | −23126.9 | + | 3262.52i | −0.796104 | + | 0.112307i | ||||
\(946\) | 18501.7 | 0.635880 | ||||||||
\(947\) | 9941.78 | − | 5739.89i | 0.341145 | − | 0.196960i | −0.319633 | − | 0.947541i | \(-0.603560\pi\) |
0.660778 | + | 0.750581i | \(0.270226\pi\) | |||||||
\(948\) | −8959.00 | + | 13559.2i | −0.306936 | + | 0.464539i | ||||
\(949\) | 8620.31 | − | 14930.8i | 0.294865 | − | 0.510721i | ||||
\(950\) | 4851.24 | − | 8402.60i | 0.165679 | − | 0.286965i | ||||
\(951\) | 1094.53 | − | 18134.5i | 0.0373213 | − | 0.618350i | ||||
\(952\) | 1842.88 | − | 2075.07i | 0.0627395 | − | 0.0706445i | ||||
\(953\) | − | 3274.36i | − | 0.111298i | −0.998450 | − | 0.0556489i | \(-0.982277\pi\) | ||
0.998450 | − | 0.0556489i | \(-0.0177228\pi\) | |||||||
\(954\) | 14226.5 | − | 18942.4i | 0.482808 | − | 0.642855i | ||||
\(955\) | − | 20451.4i | − | 0.692977i | ||||||
\(956\) | −16216.6 | + | 9362.66i | −0.548622 | + | 0.316747i | ||||
\(957\) | −9432.38 | − | 18880.4i | −0.318605 | − | 0.637740i | ||||
\(958\) | 33692.8 | + | 19452.5i | 1.13629 | + | 0.656037i | ||||
\(959\) | −25932.7 | − | 5327.16i | −0.873213 | − | 0.179378i | ||||
\(960\) | −1335.96 | − | 2674.13i | −0.0449144 | − | 0.0899033i | ||||
\(961\) | 41025.8 | + | 71058.8i | 1.37712 | + | 2.38525i | ||||
\(962\) | 24653.0 | 0.826242 | ||||||||
\(963\) | −16624.6 | + | 7088.26i | −0.556303 | + | 0.237192i | ||||
\(964\) | 5740.49i | 0.191793i | ||||||||
\(965\) | 10209.1 | + | 17682.7i | 0.340563 | + | 0.589873i | ||||
\(966\) | −6539.72 | + | 1744.69i | −0.217818 | + | 0.0581103i | ||||
\(967\) | −8316.55 | + | 14404.7i | −0.276569 | + | 0.479031i | −0.970530 | − | 0.240981i | \(-0.922531\pi\) |
0.693961 | + | 0.720013i | \(0.255864\pi\) | |||||||
\(968\) | −21285.6 | − | 12289.2i | −0.706760 | − | 0.408048i | ||||
\(969\) | −8912.74 | − | 5888.92i | −0.295478 | − | 0.195232i | ||||
\(970\) | −10058.5 | − | 17421.8i | −0.332946 | − | 0.576679i | ||||
\(971\) | −23196.9 | −0.766658 | −0.383329 | − | 0.923612i | \(-0.625223\pi\) | ||||
−0.383329 | + | 0.923612i | \(0.625223\pi\) | |||||||
\(972\) | −14468.9 | − | 4498.20i | −0.477459 | − | 0.148436i | ||||
\(973\) | 1422.25 | + | 4277.52i | 0.0468605 | + | 0.140936i | ||||
\(974\) | 35935.5 | − | 20747.4i | 1.18218 | − | 0.682535i | ||||
\(975\) | −9375.97 | − | 6194.99i | −0.307971 | − | 0.203486i | ||||
\(976\) | −7511.50 | − | 4336.77i | −0.246350 | − | 0.142230i | ||||
\(977\) | 40553.6 | + | 23413.6i | 1.32797 | + | 0.766703i | 0.984985 | − | 0.172639i | \(-0.0552294\pi\) |
0.342983 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(978\) | 1127.59 | − | 18682.2i | 0.0368673 | − | 0.610828i | ||||
\(979\) | −94374.6 | + | 54487.2i | −3.08092 | + | 1.77877i | ||||
\(980\) | 9877.32 | − | 7384.70i | 0.321959 | − | 0.240710i | ||||
\(981\) | 3353.05 | + | 7864.13i | 0.109128 | + | 0.255945i | ||||
\(982\) | 791.521 | 0.0257214 | ||||||||
\(983\) | 7117.50 | + | 12327.9i | 0.230939 | + | 0.399998i | 0.958085 | − | 0.286485i | \(-0.0924869\pi\) |
−0.727146 | + | 0.686483i | \(0.759154\pi\) | |||||||
\(984\) | −9994.14 | + | 4992.92i | −0.323782 | + | 0.161757i | ||||
\(985\) | 27131.3 | + | 15664.3i | 0.877639 | + | 0.506705i | ||||
\(986\) | 1146.55 | − | 1985.88i | 0.0370319 | − | 0.0641412i | ||||
\(987\) | 7872.57 | + | 7889.71i | 0.253887 | + | 0.254440i | ||||
\(988\) | −10740.4 | − | 18602.9i | −0.345848 | − | 0.599027i | ||||
\(989\) | − | 4902.56i | − | 0.157626i | ||||||
\(990\) | −19342.9 | + | 25754.9i | −0.620968 | + | 0.826814i | ||||
\(991\) | 16183.4 | 0.518752 | 0.259376 | − | 0.965776i | \(-0.416483\pi\) | ||||
0.259376 | + | 0.965776i | \(0.416483\pi\) | |||||||
\(992\) | 5350.86 | + | 9267.97i | 0.171260 | + | 0.296631i | ||||
\(993\) | −12113.2 | − | 731.106i | −0.387110 | − | 0.0233645i | ||||
\(994\) | 869.169 | − | 4231.13i | 0.0277348 | − | 0.135014i | ||||
\(995\) | −13092.6 | − | 7559.04i | −0.417150 | − | 0.240842i | ||||
\(996\) | −2811.61 | + | 4255.30i | −0.0894471 | + | 0.135376i | ||||
\(997\) | −40829.3 | + | 23572.8i | −1.29697 | + | 0.748805i | −0.979879 | − | 0.199591i | \(-0.936039\pi\) |
−0.317089 | + | 0.948396i | \(0.602705\pi\) | |||||||
\(998\) | 40586.8i | 1.28733i | ||||||||
\(999\) | 34767.8 | + | 6357.18i | 1.10110 | + | 0.201334i |
(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 | 126.4.m.a.41.16 | ✓ | 48 | |
3.2 | odd | 2 | 378.4.m.a.125.5 | 48 | |||
7.6 | odd | 2 | inner | 126.4.m.a.41.21 | yes | 48 | |
9.2 | odd | 6 | inner | 126.4.m.a.83.21 | yes | 48 | |
9.4 | even | 3 | 1134.4.d.b.1133.4 | 48 | |||
9.5 | odd | 6 | 1134.4.d.b.1133.45 | 48 | |||
9.7 | even | 3 | 378.4.m.a.251.6 | 48 | |||
21.20 | even | 2 | 378.4.m.a.125.6 | 48 | |||
63.13 | odd | 6 | 1134.4.d.b.1133.46 | 48 | |||
63.20 | even | 6 | inner | 126.4.m.a.83.16 | yes | 48 | |
63.34 | odd | 6 | 378.4.m.a.251.5 | 48 | |||
63.41 | even | 6 | 1134.4.d.b.1133.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.m.a.41.16 | ✓ | 48 | 1.1 | even | 1 | trivial | |
126.4.m.a.41.21 | yes | 48 | 7.6 | odd | 2 | inner | |
126.4.m.a.83.16 | yes | 48 | 63.20 | even | 6 | inner | |
126.4.m.a.83.21 | yes | 48 | 9.2 | odd | 6 | inner | |
378.4.m.a.125.5 | 48 | 3.2 | odd | 2 | |||
378.4.m.a.125.6 | 48 | 21.20 | even | 2 | |||
378.4.m.a.251.5 | 48 | 63.34 | odd | 6 | |||
378.4.m.a.251.6 | 48 | 9.7 | even | 3 | |||
1134.4.d.b.1133.3 | 48 | 63.41 | even | 6 | |||
1134.4.d.b.1133.4 | 48 | 9.4 | even | 3 | |||
1134.4.d.b.1133.45 | 48 | 9.5 | odd | 6 | |||
1134.4.d.b.1133.46 | 48 | 63.13 | odd | 6 |