Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.6 | ||
Root | \(2.85284 + 0.928053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.a.146.8 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.90883i | − | 0.674874i | −0.941348 | − | 0.337437i | \(-0.890440\pi\) | ||
0.941348 | − | 0.337437i | \(-0.109560\pi\) | |||||||
\(3\) | 5.08298 | + | 1.07856i | 0.978221 | + | 0.207568i | ||||
\(4\) | 4.35636 | 0.544546 | ||||||||
\(5\) | −1.24741 | −0.111572 | −0.0557859 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557859 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(6\) | 2.05878 | − | 9.70256i | 0.140082 | − | 0.660175i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 23.5862i | − | 1.04237i | ||||||
\(9\) | 24.6734 | + | 10.9646i | 0.913831 | + | 0.406095i | ||||
\(10\) | 2.38110i | 0.0752969i | ||||||||
\(11\) | − | 40.6907i | − | 1.11534i | −0.830064 | − | 0.557668i | \(-0.811696\pi\) | ||
0.830064 | − | 0.557668i | \(-0.188304\pi\) | |||||||
\(12\) | 22.1433 | + | 4.69858i | 0.532686 | + | 0.113030i | ||||
\(13\) | 19.5973i | 0.418101i | 0.977905 | + | 0.209050i | \(0.0670373\pi\) | ||||
−0.977905 | + | 0.209050i | \(0.932963\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.34057 | − | 1.34540i | −0.109142 | − | 0.0231588i | ||||
\(16\) | −10.1712 | −0.158925 | ||||||||
\(17\) | 104.718 | 1.49400 | 0.746999 | − | 0.664825i | \(-0.231494\pi\) | ||||
0.746999 | + | 0.664825i | \(0.231494\pi\) | |||||||
\(18\) | 20.9295 | − | 47.0974i | 0.274063 | − | 0.616720i | ||||
\(19\) | 40.4544i | 0.488467i | 0.969716 | + | 0.244234i | \(0.0785364\pi\) | ||||
−0.969716 | + | 0.244234i | \(0.921464\pi\) | |||||||
\(20\) | −5.43418 | −0.0607559 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −77.6716 | −0.752711 | ||||||||
\(23\) | 80.4045i | 0.728935i | 0.931216 | + | 0.364467i | \(0.118749\pi\) | ||||
−0.931216 | + | 0.364467i | \(0.881251\pi\) | |||||||
\(24\) | 25.4391 | − | 119.888i | 0.216364 | − | 1.01967i | ||||
\(25\) | −123.444 | −0.987552 | ||||||||
\(26\) | 37.4079 | 0.282165 | ||||||||
\(27\) | 113.589 | + | 82.3444i | 0.809636 | + | 0.586933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 211.712i | − | 1.35565i | −0.735222 | − | 0.677827i | \(-0.762922\pi\) | ||
0.735222 | − | 0.677827i | \(-0.237078\pi\) | |||||||
\(30\) | −2.56815 | + | 12.1031i | −0.0156292 | + | 0.0736570i | ||||
\(31\) | 100.025i | 0.579517i | 0.957100 | + | 0.289758i | \(0.0935749\pi\) | ||||
−0.957100 | + | 0.289758i | \(0.906425\pi\) | |||||||
\(32\) | − | 169.275i | − | 0.935119i | ||||||
\(33\) | 43.8872 | − | 206.830i | 0.231508 | − | 1.09105i | ||||
\(34\) | − | 199.890i | − | 1.00826i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 107.486 | + | 47.7656i | 0.497622 | + | 0.221137i | ||||
\(37\) | −189.975 | −0.844100 | −0.422050 | − | 0.906572i | \(-0.638689\pi\) | ||||
−0.422050 | + | 0.906572i | \(0.638689\pi\) | |||||||
\(38\) | 77.2206 | 0.329654 | ||||||||
\(39\) | −21.1368 | + | 99.6127i | −0.0867844 | + | 0.408995i | ||||
\(40\) | 29.4217i | 0.116299i | ||||||||
\(41\) | −186.753 | −0.711362 | −0.355681 | − | 0.934607i | \(-0.615751\pi\) | ||||
−0.355681 | + | 0.934607i | \(0.615751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 158.618 | 0.562536 | 0.281268 | − | 0.959629i | \(-0.409245\pi\) | ||||
0.281268 | + | 0.959629i | \(0.409245\pi\) | |||||||
\(44\) | − | 177.263i | − | 0.607352i | ||||||
\(45\) | −30.7779 | − | 13.6773i | −0.101958 | − | 0.0453088i | ||||
\(46\) | 153.479 | 0.491939 | ||||||||
\(47\) | −358.069 | −1.11127 | −0.555635 | − | 0.831426i | \(-0.687525\pi\) | ||||
−0.555635 | + | 0.831426i | \(0.687525\pi\) | |||||||
\(48\) | −51.6999 | − | 10.9702i | −0.155463 | − | 0.0329877i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 235.634i | 0.666473i | ||||||||
\(51\) | 532.282 | + | 112.945i | 1.46146 | + | 0.310106i | ||||
\(52\) | 85.3729i | 0.227675i | ||||||||
\(53\) | 423.152i | 1.09669i | 0.836254 | + | 0.548343i | \(0.184741\pi\) | ||||
−0.836254 | + | 0.548343i | \(0.815259\pi\) | |||||||
\(54\) | 157.182 | − | 216.822i | 0.396105 | − | 0.546402i | ||||
\(55\) | 50.7580i | 0.124440i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.6323 | + | 205.629i | −0.101390 | + | 0.477829i | ||||
\(58\) | −404.123 | −0.914895 | ||||||||
\(59\) | −625.562 | −1.38036 | −0.690180 | − | 0.723638i | \(-0.742469\pi\) | ||||
−0.690180 | + | 0.723638i | \(0.742469\pi\) | |||||||
\(60\) | −27.6218 | − | 5.86106i | −0.0594327 | − | 0.0126110i | ||||
\(61\) | 807.799i | 1.69554i | 0.530362 | + | 0.847772i | \(0.322056\pi\) | ||||
−0.530362 | + | 0.847772i | \(0.677944\pi\) | |||||||
\(62\) | 190.931 | 0.391101 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −404.486 | −0.790012 | ||||||||
\(65\) | − | 24.4459i | − | 0.0466483i | ||||||
\(66\) | −394.804 | − | 83.7732i | −0.736318 | − | 0.156239i | ||||
\(67\) | 298.544 | 0.544373 | 0.272187 | − | 0.962245i | \(-0.412253\pi\) | ||||
0.272187 | + | 0.962245i | \(0.412253\pi\) | |||||||
\(68\) | 456.192 | 0.813550 | ||||||||
\(69\) | −86.7208 | + | 408.695i | −0.151304 | + | 0.713059i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 455.386i | 0.761189i | 0.924742 | + | 0.380594i | \(0.124281\pi\) | ||||
−0.924742 | + | 0.380594i | \(0.875719\pi\) | |||||||
\(72\) | 258.613 | − | 581.953i | 0.423302 | − | 0.952553i | ||||
\(73\) | 501.679i | 0.804344i | 0.915564 | + | 0.402172i | \(0.131745\pi\) | ||||
−0.915564 | + | 0.402172i | \(0.868255\pi\) | |||||||
\(74\) | 362.630i | 0.569661i | ||||||||
\(75\) | −627.464 | − | 133.141i | −0.966043 | − | 0.204984i | ||||
\(76\) | 176.234i | 0.265993i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 190.144 | + | 40.3465i | 0.276020 | + | 0.0585685i | ||||
\(79\) | −61.9122 | −0.0881731 | −0.0440865 | − | 0.999028i | \(-0.514038\pi\) | ||||
−0.0440865 | + | 0.999028i | \(0.514038\pi\) | |||||||
\(80\) | 12.6876 | 0.0177315 | ||||||||
\(81\) | 488.557 | + | 541.067i | 0.670174 | + | 0.742204i | ||||
\(82\) | 356.479i | 0.480080i | ||||||||
\(83\) | −73.1180 | −0.0966957 | −0.0483478 | − | 0.998831i | \(-0.515396\pi\) | ||||
−0.0483478 | + | 0.998831i | \(0.515396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.627 | −0.166688 | ||||||||
\(86\) | − | 302.775i | − | 0.379641i | ||||||
\(87\) | 228.343 | − | 1076.13i | 0.281391 | − | 1.32613i | ||||
\(88\) | −959.739 | −1.16260 | ||||||||
\(89\) | −114.745 | −0.136662 | −0.0683309 | − | 0.997663i | \(-0.521767\pi\) | ||||
−0.0683309 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(90\) | −26.1077 | + | 58.7498i | −0.0305777 | + | 0.0688086i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 350.271i | 0.396938i | ||||||||
\(93\) | −107.883 | + | 508.425i | −0.120289 | + | 0.566895i | ||||
\(94\) | 683.493i | 0.749967i | ||||||||
\(95\) | − | 50.4633i | − | 0.0544992i | ||||||
\(96\) | 182.572 | − | 860.420i | 0.194101 | − | 0.914753i | ||||
\(97\) | − | 1416.51i | − | 1.48273i | −0.671101 | − | 0.741366i | \(-0.734178\pi\) | ||
0.671101 | − | 0.741366i | \(-0.265822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 446.156 | − | 1003.98i | 0.452933 | − | 1.01923i | ||||
\(100\) | −537.767 | −0.537767 | ||||||||
\(101\) | −240.811 | −0.237244 | −0.118622 | − | 0.992940i | \(-0.537848\pi\) | ||||
−0.118622 | + | 0.992940i | \(0.537848\pi\) | |||||||
\(102\) | 215.592 | − | 1016.04i | 0.209283 | − | 0.986300i | ||||
\(103\) | − | 1109.04i | − | 1.06094i | −0.847705 | − | 0.530469i | \(-0.822016\pi\) | ||
0.847705 | − | 0.530469i | \(-0.177984\pi\) | |||||||
\(104\) | 462.226 | 0.435817 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 807.725 | 0.740124 | ||||||||
\(107\) | 1067.69i | 0.964646i | 0.875993 | + | 0.482323i | \(0.160207\pi\) | ||||
−0.875993 | + | 0.482323i | \(0.839793\pi\) | |||||||
\(108\) | 494.834 | + | 358.722i | 0.440883 | + | 0.319612i | ||||
\(109\) | 10.0875 | 0.00886430 | 0.00443215 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443215 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(110\) | 96.8885 | 0.0839814 | ||||||||
\(111\) | −965.640 | − | 204.899i | −0.825716 | − | 0.175208i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 884.294i | − | 0.736171i | −0.929792 | − | 0.368086i | \(-0.880013\pi\) | ||
0.929792 | − | 0.368086i | \(-0.119987\pi\) | |||||||
\(114\) | 392.511 | + | 83.2868i | 0.322474 | + | 0.0684256i | ||||
\(115\) | − | 100.297i | − | 0.0813286i | ||||||
\(116\) | − | 922.295i | − | 0.738215i | ||||||
\(117\) | −214.876 | + | 483.532i | −0.169789 | + | 0.382073i | ||||
\(118\) | 1194.09i | 0.931569i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −31.7330 | + | 149.550i | −0.0241401 | + | 0.113767i | ||||
\(121\) | −324.732 | −0.243976 | ||||||||
\(122\) | 1541.95 | 1.14428 | ||||||||
\(123\) | −949.260 | − | 201.423i | −0.695869 | − | 0.147656i | ||||
\(124\) | 435.745i | 0.315573i | ||||||||
\(125\) | 309.912 | 0.221755 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −840.132 | −0.587005 | −0.293503 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293503 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(128\) | − | 582.101i | − | 0.401961i | ||||||
\(129\) | 806.254 | + | 171.079i | 0.550284 | + | 0.116765i | ||||
\(130\) | −46.6631 | −0.0314817 | ||||||||
\(131\) | 517.902 | 0.345415 | 0.172707 | − | 0.984973i | \(-0.444748\pi\) | ||||
0.172707 | + | 0.984973i | \(0.444748\pi\) | |||||||
\(132\) | 191.189 | − | 901.027i | 0.126067 | − | 0.594124i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 569.871i | − | 0.367383i | ||||||
\(135\) | −141.692 | − | 102.717i | −0.0903325 | − | 0.0654852i | ||||
\(136\) | − | 2469.91i | − | 1.55730i | ||||||
\(137\) | − | 1098.07i | − | 0.684777i | −0.939558 | − | 0.342389i | \(-0.888764\pi\) | ||
0.939558 | − | 0.342389i | \(-0.111236\pi\) | |||||||
\(138\) | 780.129 | + | 165.535i | 0.481225 | + | 0.102111i | ||||
\(139\) | 828.268i | 0.505416i | 0.967543 | + | 0.252708i | \(0.0813212\pi\) | ||||
−0.967543 | + | 0.252708i | \(0.918679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1820.06 | − | 386.197i | −1.08707 | − | 0.230664i | ||||
\(142\) | 869.255 | 0.513706 | ||||||||
\(143\) | 797.427 | 0.466323 | ||||||||
\(144\) | −250.958 | − | 111.523i | −0.145230 | − | 0.0645385i | ||||
\(145\) | 264.092i | 0.151253i | ||||||||
\(146\) | 957.621 | 0.542830 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −827.601 | −0.459651 | ||||||||
\(149\) | 892.592i | 0.490765i | 0.969426 | + | 0.245382i | \(0.0789135\pi\) | ||||
−0.969426 | + | 0.245382i | \(0.921086\pi\) | |||||||
\(150\) | −254.144 | + | 1197.72i | −0.138339 | + | 0.651957i | ||||
\(151\) | 1425.04 | 0.767999 | 0.383999 | − | 0.923333i | \(-0.374546\pi\) | ||||
0.383999 | + | 0.923333i | \(0.374546\pi\) | |||||||
\(152\) | 954.166 | 0.509165 | ||||||||
\(153\) | 2583.76 | + | 1148.19i | 1.36526 | + | 0.606705i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 124.772i | − | 0.0646577i | ||||||
\(156\) | −92.0795 | + | 433.949i | −0.0472581 | + | 0.222716i | ||||
\(157\) | 282.754i | 0.143734i | 0.997414 | + | 0.0718670i | \(0.0228957\pi\) | ||||
−0.997414 | + | 0.0718670i | \(0.977104\pi\) | |||||||
\(158\) | 118.180i | 0.0595057i | ||||||||
\(159\) | −456.393 | + | 2150.87i | −0.227637 | + | 1.07280i | ||||
\(160\) | 211.155i | 0.104333i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1032.81 | − | 932.572i | 0.500894 | − | 0.452283i | ||||
\(163\) | 2316.13 | 1.11297 | 0.556484 | − | 0.830859i | \(-0.312150\pi\) | ||||
0.556484 | + | 0.830859i | \(0.312150\pi\) | |||||||
\(164\) | −813.562 | −0.387369 | ||||||||
\(165\) | −54.7454 | + | 258.002i | −0.0258298 | + | 0.121730i | ||||
\(166\) | 139.570i | 0.0652574i | ||||||||
\(167\) | −2344.70 | −1.08646 | −0.543229 | − | 0.839585i | \(-0.682798\pi\) | ||||
−0.543229 | + | 0.839585i | \(0.682798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1812.95 | 0.825192 | ||||||||
\(170\) | 249.345i | 0.112493i | ||||||||
\(171\) | −443.565 | + | 998.149i | −0.198364 | + | 0.446376i | ||||
\(172\) | 690.999 | 0.306327 | ||||||||
\(173\) | −1033.80 | −0.454326 | −0.227163 | − | 0.973857i | \(-0.572945\pi\) | ||||
−0.227163 | + | 0.973857i | \(0.572945\pi\) | |||||||
\(174\) | −2054.15 | − | 435.869i | −0.894969 | − | 0.189903i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 413.872i | 0.177255i | ||||||||
\(177\) | −3179.72 | − | 674.704i | −1.35030 | − | 0.286519i | ||||
\(178\) | 219.028i | 0.0922294i | ||||||||
\(179\) | 144.882i | 0.0604973i | 0.999542 | + | 0.0302486i | \(0.00962991\pi\) | ||||
−0.999542 | + | 0.0302486i | \(0.990370\pi\) | |||||||
\(180\) | −134.080 | − | 59.5834i | −0.0555207 | − | 0.0246727i | ||||
\(181\) | − | 2057.17i | − | 0.844797i | −0.906410 | − | 0.422398i | \(-0.861188\pi\) | ||
0.906410 | − | 0.422398i | \(-0.138812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −871.257 | + | 4106.03i | −0.351941 | + | 1.65862i | ||||
\(184\) | 1896.44 | 0.759822 | ||||||||
\(185\) | 236.977 | 0.0941778 | ||||||||
\(186\) | 970.498 | + | 205.930i | 0.382583 | + | 0.0811800i | ||||
\(187\) | − | 4261.07i | − | 1.66631i | ||||||
\(188\) | −1559.88 | −0.605137 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −96.3259 | −0.0367801 | ||||||||
\(191\) | − | 2948.72i | − | 1.11708i | −0.829479 | − | 0.558538i | \(-0.811362\pi\) | ||
0.829479 | − | 0.558538i | \(-0.188638\pi\) | |||||||
\(192\) | −2056.00 | − | 436.261i | −0.772806 | − | 0.163981i | ||||
\(193\) | −2270.80 | −0.846920 | −0.423460 | − | 0.905915i | \(-0.639185\pi\) | ||||
−0.423460 | + | 0.905915i | \(0.639185\pi\) | |||||||
\(194\) | −2703.88 | −1.00066 | ||||||||
\(195\) | 26.3662 | − | 124.258i | 0.00968270 | − | 0.0456323i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 495.849i | − | 0.179329i | −0.995972 | − | 0.0896645i | \(-0.971421\pi\) | ||
0.995972 | − | 0.0896645i | \(-0.0285795\pi\) | |||||||
\(198\) | −1916.43 | − | 851.636i | −0.687851 | − | 0.305672i | ||||
\(199\) | − | 839.706i | − | 0.299121i | −0.988753 | − | 0.149561i | \(-0.952214\pi\) | ||
0.988753 | − | 0.149561i | \(-0.0477859\pi\) | |||||||
\(200\) | 2911.58i | 1.02940i | ||||||||
\(201\) | 1517.50 | + | 321.997i | 0.532517 | + | 0.112995i | ||||
\(202\) | 459.668i | 0.160109i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2318.81 | + | 492.028i | 0.795831 | + | 0.168867i | ||||
\(205\) | 232.957 | 0.0793680 | ||||||||
\(206\) | −2116.96 | −0.715999 | ||||||||
\(207\) | −881.601 | + | 1983.86i | −0.296017 | + | 0.666123i | ||||
\(208\) | − | 199.328i | − | 0.0664465i | ||||||
\(209\) | 1646.12 | 0.544805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4001.71 | 1.30564 | 0.652818 | − | 0.757514i | \(-0.273586\pi\) | ||||
0.652818 | + | 0.757514i | \(0.273586\pi\) | |||||||
\(212\) | 1843.40i | 0.597195i | ||||||||
\(213\) | −491.160 | + | 2314.72i | −0.157999 | + | 0.744611i | ||||
\(214\) | 2038.03 | 0.651014 | ||||||||
\(215\) | −197.862 | −0.0627632 | ||||||||
\(216\) | 1942.19 | − | 2679.13i | 0.611803 | − | 0.843943i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 19.2554i | − | 0.00598228i | ||||||
\(219\) | −541.089 | + | 2550.03i | −0.166956 | + | 0.786826i | ||||
\(220\) | 221.120i | 0.0677633i | ||||||||
\(221\) | 2052.20i | 0.624642i | ||||||||
\(222\) | −391.117 | + | 1843.24i | −0.118244 | + | 0.557254i | ||||
\(223\) | 3040.54i | 0.913047i | 0.889711 | + | 0.456523i | \(0.150905\pi\) | ||||
−0.889711 | + | 0.456523i | \(0.849095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3045.79 | − | 1353.51i | −0.902455 | − | 0.401040i | ||||
\(226\) | −1687.97 | −0.496823 | ||||||||
\(227\) | −4396.47 | −1.28548 | −0.642741 | − | 0.766084i | \(-0.722203\pi\) | ||||
−0.642741 | + | 0.766084i | \(0.722203\pi\) | |||||||
\(228\) | −190.078 | + | 895.795i | −0.0552116 | + | 0.260199i | ||||
\(229\) | − | 1983.56i | − | 0.572389i | −0.958172 | − | 0.286194i | \(-0.907610\pi\) | ||
0.958172 | − | 0.286194i | \(-0.0923903\pi\) | |||||||
\(230\) | −191.451 | −0.0548865 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4993.49 | −1.41310 | ||||||||
\(233\) | − | 4373.75i | − | 1.22976i | −0.788621 | − | 0.614879i | \(-0.789205\pi\) | ||
0.788621 | − | 0.614879i | \(-0.210795\pi\) | |||||||
\(234\) | 922.982 | + | 410.162i | 0.257851 | + | 0.114586i | ||||
\(235\) | 446.659 | 0.123986 | ||||||||
\(236\) | −2725.18 | −0.751669 | ||||||||
\(237\) | −314.699 | − | 66.7758i | −0.0862527 | − | 0.0183019i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3826.41i | 1.03561i | 0.855500 | + | 0.517803i | \(0.173250\pi\) | ||||
−0.855500 | + | 0.517803i | \(0.826750\pi\) | |||||||
\(240\) | 64.4911 | + | 13.6843i | 0.0173453 | + | 0.00368050i | ||||
\(241\) | − | 3439.89i | − | 0.919430i | −0.888066 | − | 0.459715i | \(-0.847952\pi\) | ||
0.888066 | − | 0.459715i | \(-0.152048\pi\) | |||||||
\(242\) | 619.858i | 0.164653i | ||||||||
\(243\) | 1899.75 | + | 3277.17i | 0.501520 | + | 0.865146i | ||||
\(244\) | 3519.07i | 0.923300i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −384.483 | + | 1811.98i | −0.0996493 | + | 0.469624i | ||||
\(247\) | −792.797 | −0.204229 | ||||||||
\(248\) | 2359.21 | 0.604073 | ||||||||
\(249\) | −371.657 | − | 78.8618i | −0.0945897 | − | 0.0200709i | ||||
\(250\) | − | 591.569i | − | 0.149656i | ||||||
\(251\) | −2046.61 | −0.514664 | −0.257332 | − | 0.966323i | \(-0.582843\pi\) | ||||
−0.257332 | + | 0.966323i | \(0.582843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3271.72 | 0.813008 | ||||||||
\(254\) | 1603.67i | 0.396154i | ||||||||
\(255\) | −663.975 | − | 140.889i | −0.163058 | − | 0.0345991i | ||||
\(256\) | −4347.02 | −1.06128 | ||||||||
\(257\) | 6051.14 | 1.46871 | 0.734357 | − | 0.678763i | \(-0.237484\pi\) | ||||
0.734357 | + | 0.678763i | \(0.237484\pi\) | |||||||
\(258\) | 326.560 | − | 1539.00i | 0.0788014 | − | 0.371372i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 106.495i | − | 0.0254021i | ||||||
\(261\) | 2321.33 | − | 5223.66i | 0.550524 | − | 1.23884i | ||||
\(262\) | − | 988.588i | − | 0.233111i | ||||||
\(263\) | − | 6274.28i | − | 1.47106i | −0.677492 | − | 0.735530i | \(-0.736933\pi\) | ||
0.677492 | − | 0.735530i | \(-0.263067\pi\) | |||||||
\(264\) | −4878.34 | − | 1035.13i | −1.13728 | − | 0.241318i | ||||
\(265\) | − | 527.844i | − | 0.122359i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −583.245 | − | 123.758i | −0.133685 | − | 0.0283666i | ||||
\(268\) | 1300.57 | 0.296436 | ||||||||
\(269\) | 3336.35 | 0.756212 | 0.378106 | − | 0.925762i | \(-0.376575\pi\) | ||||
0.378106 | + | 0.925762i | \(0.376575\pi\) | |||||||
\(270\) | −196.070 | + | 270.466i | −0.0441942 | + | 0.0609631i | ||||
\(271\) | 2843.17i | 0.637308i | 0.947871 | + | 0.318654i | \(0.103231\pi\) | ||||
−0.947871 | + | 0.318654i | \(0.896769\pi\) | |||||||
\(272\) | −1065.11 | −0.237433 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2096.03 | −0.462138 | ||||||||
\(275\) | 5023.02i | 1.10145i | ||||||||
\(276\) | −377.787 | + | 1780.42i | −0.0823918 | + | 0.388293i | ||||
\(277\) | 6348.34 | 1.37702 | 0.688510 | − | 0.725226i | \(-0.258265\pi\) | ||||
0.688510 | + | 0.725226i | \(0.258265\pi\) | |||||||
\(278\) | 1581.02 | 0.341092 | ||||||||
\(279\) | −1096.73 | + | 2467.96i | −0.235339 | + | 0.529580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3735.88i | − | 0.793110i | −0.918011 | − | 0.396555i | \(-0.870206\pi\) | ||
0.918011 | − | 0.396555i | \(-0.129794\pi\) | |||||||
\(282\) | −737.185 | + | 3474.18i | −0.155669 | + | 0.733633i | ||||
\(283\) | 5517.12i | 1.15886i | 0.815021 | + | 0.579432i | \(0.196726\pi\) | ||||
−0.815021 | + | 0.579432i | \(0.803274\pi\) | |||||||
\(284\) | 1983.83i | 0.414502i | ||||||||
\(285\) | 54.4275 | − | 256.504i | 0.0113123 | − | 0.0533122i | ||||
\(286\) | − | 1522.15i | − | 0.314709i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1856.02 | − | 4176.59i | 0.379747 | − | 0.854541i | ||||
\(289\) | 6052.96 | 1.23203 | ||||||||
\(290\) | 504.107 | 0.102077 | ||||||||
\(291\) | 1527.79 | − | 7200.11i | 0.307768 | − | 1.45044i | ||||
\(292\) | 2185.50i | 0.438002i | ||||||||
\(293\) | 7574.50 | 1.51026 | 0.755131 | − | 0.655574i | \(-0.227573\pi\) | ||||
0.755131 | + | 0.655574i | \(0.227573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 780.333 | 0.154009 | ||||||||
\(296\) | 4480.79i | 0.879868i | ||||||||
\(297\) | 3350.65 | − | 4622.00i | 0.654628 | − | 0.903016i | ||||
\(298\) | 1703.81 | 0.331204 | ||||||||
\(299\) | −1575.71 | −0.304768 | ||||||||
\(300\) | −2733.46 | − | 580.012i | −0.526055 | − | 0.111623i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 2720.15i | − | 0.518302i | ||||||
\(303\) | −1224.04 | − | 259.728i | −0.232077 | − | 0.0492442i | ||||
\(304\) | − | 411.469i | − | 0.0776295i | ||||||
\(305\) | − | 1007.66i | − | 0.189175i | ||||||
\(306\) | 2191.71 | − | 4931.97i | 0.409449 | − | 0.921379i | ||||
\(307\) | − | 10635.6i | − | 1.97723i | −0.150480 | − | 0.988613i | \(-0.548082\pi\) | ||
0.150480 | − | 0.988613i | \(-0.451918\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1196.16 | − | 5637.21i | 0.220217 | − | 1.03783i | ||||
\(310\) | −238.169 | −0.0436358 | ||||||||
\(311\) | 5771.19 | 1.05226 | 0.526132 | − | 0.850403i | \(-0.323642\pi\) | ||||
0.526132 | + | 0.850403i | \(0.323642\pi\) | |||||||
\(312\) | 2349.49 | + | 498.536i | 0.426325 | + | 0.0904618i | ||||
\(313\) | − | 2344.52i | − | 0.423387i | −0.977336 | − | 0.211694i | \(-0.932102\pi\) | ||
0.977336 | − | 0.211694i | \(-0.0678979\pi\) | |||||||
\(314\) | 539.730 | 0.0970023 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −269.712 | −0.0480142 | ||||||||
\(317\) | − | 7912.13i | − | 1.40186i | −0.713231 | − | 0.700929i | \(-0.752769\pi\) | ||
0.713231 | − | 0.700929i | \(-0.247231\pi\) | |||||||
\(318\) | 4105.65 | + | 871.177i | 0.724005 | + | 0.153626i | ||||
\(319\) | −8614.71 | −1.51201 | ||||||||
\(320\) | 504.560 | 0.0881431 | ||||||||
\(321\) | −1151.56 | + | 5427.03i | −0.200230 | + | 0.943637i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4236.32i | 0.729769i | ||||||||
\(324\) | 2128.33 | + | 2357.08i | 0.364940 | + | 0.404164i | ||||
\(325\) | − | 2419.17i | − | 0.412896i | ||||||
\(326\) | − | 4421.11i | − | 0.751112i | ||||||
\(327\) | 51.2747 | + | 10.8800i | 0.00867124 | + | 0.00183995i | ||||
\(328\) | 4404.78i | 0.741505i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 492.482 | + | 104.500i | 0.0821523 | + | 0.0174319i | ||||
\(331\) | −4880.03 | −0.810365 | −0.405182 | − | 0.914236i | \(-0.632792\pi\) | ||||
−0.405182 | + | 0.914236i | \(0.632792\pi\) | |||||||
\(332\) | −318.528 | −0.0526552 | ||||||||
\(333\) | −4687.34 | − | 2082.99i | −0.771365 | − | 0.342785i | ||||
\(334\) | 4475.64i | 0.733222i | ||||||||
\(335\) | −372.407 | −0.0607367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4136.39 | −0.668616 | −0.334308 | − | 0.942464i | \(-0.608503\pi\) | ||||
−0.334308 | + | 0.942464i | \(0.608503\pi\) | |||||||
\(338\) | − | 3460.61i | − | 0.556900i | ||||||
\(339\) | 953.760 | − | 4494.85i | 0.152806 | − | 0.720138i | ||||
\(340\) | −569.059 | −0.0907692 | ||||||||
\(341\) | 4070.09 | 0.646356 | ||||||||
\(342\) | 1905.30 | + | 846.691i | 0.301248 | + | 0.133871i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3741.20i | − | 0.586373i | ||||||
\(345\) | 108.176 | − | 509.810i | 0.0168812 | − | 0.0795573i | ||||
\(346\) | 1973.35i | 0.306613i | ||||||||
\(347\) | − | 2320.76i | − | 0.359034i | −0.983755 | − | 0.179517i | \(-0.942547\pi\) | ||
0.983755 | − | 0.179517i | \(-0.0574535\pi\) | |||||||
\(348\) | 994.747 | − | 4688.01i | 0.153230 | − | 0.722137i | ||||
\(349\) | − | 226.795i | − | 0.0347853i | −0.999849 | − | 0.0173926i | \(-0.994463\pi\) | ||
0.999849 | − | 0.0173926i | \(-0.00553653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1613.73 | + | 2226.03i | −0.245397 | + | 0.338509i | ||||
\(352\) | −6887.90 | −1.04297 | ||||||||
\(353\) | −1485.71 | −0.224012 | −0.112006 | − | 0.993708i | \(-0.535728\pi\) | ||||
−0.112006 | + | 0.993708i | \(0.535728\pi\) | |||||||
\(354\) | −1287.90 | + | 6069.55i | −0.193364 | + | 0.911280i | ||||
\(355\) | − | 568.054i | − | 0.0849272i | ||||||
\(356\) | −499.869 | −0.0744185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 276.556 | 0.0408280 | ||||||||
\(359\) | 10877.2i | 1.59910i | 0.600599 | + | 0.799550i | \(0.294929\pi\) | ||||
−0.600599 | + | 0.799550i | \(0.705071\pi\) | |||||||
\(360\) | −322.596 | + | 725.934i | −0.0472286 | + | 0.106278i | ||||
\(361\) | 5222.44 | 0.761400 | ||||||||
\(362\) | −3926.79 | −0.570131 | ||||||||
\(363\) | −1650.61 | − | 350.241i | −0.238662 | − | 0.0506416i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 625.800i | − | 0.0897421i | ||||||
\(366\) | 7837.72 | + | 1663.08i | 1.11936 | + | 0.237516i | ||||
\(367\) | 3810.15i | 0.541930i | 0.962589 | + | 0.270965i | \(0.0873428\pi\) | ||||
−0.962589 | + | 0.270965i | \(0.912657\pi\) | |||||||
\(368\) | − | 817.809i | − | 0.115846i | ||||||
\(369\) | −4607.83 | − | 2047.66i | −0.650065 | − | 0.288881i | ||||
\(370\) | − | 452.349i | − | 0.0635581i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −469.976 | + | 2214.89i | −0.0655030 | + | 0.308700i | ||||
\(373\) | −9739.09 | −1.35193 | −0.675967 | − | 0.736932i | \(-0.736274\pi\) | ||||
−0.675967 | + | 0.736932i | \(0.736274\pi\) | |||||||
\(374\) | −8133.66 | −1.12455 | ||||||||
\(375\) | 1575.28 | + | 334.257i | 0.216925 | + | 0.0460292i | ||||
\(376\) | 8445.48i | 1.15836i | ||||||||
\(377\) | 4148.98 | 0.566800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 320.171 | 0.0433933 | 0.0216967 | − | 0.999765i | \(-0.493093\pi\) | ||||
0.0216967 | + | 0.999765i | \(0.493093\pi\) | |||||||
\(380\) | − | 219.836i | − | 0.0296773i | ||||||
\(381\) | −4270.38 | − | 906.129i | −0.574220 | − | 0.121844i | ||||
\(382\) | −5628.60 | −0.753886 | ||||||||
\(383\) | 4370.26 | 0.583054 | 0.291527 | − | 0.956563i | \(-0.405837\pi\) | ||||
0.291527 | + | 0.956563i | \(0.405837\pi\) | |||||||
\(384\) | 627.829 | − | 2958.81i | 0.0834343 | − | 0.393206i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4334.57i | 0.571564i | ||||||||
\(387\) | 3913.66 | + | 1739.18i | 0.514063 | + | 0.228443i | ||||
\(388\) | − | 6170.84i | − | 0.807415i | ||||||
\(389\) | 13714.8i | 1.78758i | 0.448483 | + | 0.893791i | \(0.351964\pi\) | ||||
−0.448483 | + | 0.893791i | \(0.648036\pi\) | |||||||
\(390\) | −237.187 | − | 50.3287i | −0.0307960 | − | 0.00653460i | ||||
\(391\) | 8419.84i | 1.08903i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2632.49 | + | 558.587i | 0.337892 | + | 0.0716971i | ||||
\(394\) | −946.493 | −0.121024 | ||||||||
\(395\) | 77.2300 | 0.00983763 | ||||||||
\(396\) | 1943.62 | − | 4373.70i | 0.246642 | − | 0.555017i | ||||
\(397\) | − | 2519.10i | − | 0.318464i | −0.987241 | − | 0.159232i | \(-0.949098\pi\) | ||
0.987241 | − | 0.159232i | \(-0.0509018\pi\) | |||||||
\(398\) | −1602.86 | −0.201869 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1255.57 | 0.156946 | ||||||||
\(401\) | − | 2619.97i | − | 0.326272i | −0.986604 | − | 0.163136i | \(-0.947839\pi\) | ||
0.986604 | − | 0.163136i | \(-0.0521609\pi\) | |||||||
\(402\) | 614.637 | − | 2896.64i | 0.0762570 | − | 0.359382i | ||||
\(403\) | −1960.22 | −0.242296 | ||||||||
\(404\) | −1049.06 | −0.129190 | ||||||||
\(405\) | −609.431 | − | 674.933i | −0.0747725 | − | 0.0828091i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7730.22i | 0.941456i | ||||||||
\(408\) | 2663.94 | − | 12554.5i | 0.323247 | − | 1.52339i | ||||
\(409\) | 13924.2i | 1.68339i | 0.539954 | + | 0.841694i | \(0.318442\pi\) | ||||
−0.539954 | + | 0.841694i | \(0.681558\pi\) | |||||||
\(410\) | − | 444.676i | − | 0.0535634i | ||||||
\(411\) | 1184.33 | − | 5581.47i | 0.142138 | − | 0.669863i | ||||
\(412\) | − | 4831.36i | − | 0.577729i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3786.85 | + | 1682.83i | 0.449549 | + | 0.199774i | ||||
\(415\) | 91.2082 | 0.0107885 | ||||||||
\(416\) | 3317.32 | 0.390974 | ||||||||
\(417\) | −893.334 | + | 4210.07i | −0.104908 | + | 0.494408i | ||||
\(418\) | − | 3142.16i | − | 0.367675i | ||||||
\(419\) | −15171.1 | −1.76887 | −0.884433 | − | 0.466666i | \(-0.845455\pi\) | ||||
−0.884433 | + | 0.466666i | \(0.845455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1052.53 | −0.121846 | −0.0609228 | − | 0.998142i | \(-0.519404\pi\) | ||||
−0.0609228 | + | 0.998142i | \(0.519404\pi\) | |||||||
\(422\) | − | 7638.60i | − | 0.881140i | ||||||
\(423\) | −8834.78 | − | 3926.07i | −1.01551 | − | 0.451281i | ||||
\(424\) | 9980.54 | 1.14316 | ||||||||
\(425\) | −12926.9 | −1.47540 | ||||||||
\(426\) | 4418.41 | + | 937.541i | 0.502518 | + | 0.106629i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4651.23i | 0.525294i | ||||||||
\(429\) | 4053.31 | + | 860.070i | 0.456167 | + | 0.0967939i | ||||
\(430\) | 377.685i | 0.0423572i | ||||||||
\(431\) | 7994.67i | 0.893479i | 0.894664 | + | 0.446740i | \(0.147415\pi\) | ||||
−0.894664 | + | 0.446740i | \(0.852585\pi\) | |||||||
\(432\) | −1155.33 | − | 837.540i | −0.128671 | − | 0.0932781i | ||||
\(433\) | − | 12889.4i | − | 1.43055i | −0.698845 | − | 0.715273i | \(-0.746303\pi\) | ||
0.698845 | − | 0.715273i | \(-0.253697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −284.838 | + | 1342.38i | −0.0313953 | + | 0.147959i | ||||
\(436\) | 43.9449 | 0.00482701 | ||||||||
\(437\) | −3252.72 | −0.356061 | ||||||||
\(438\) | 4867.57 | + | 1032.85i | 0.531008 | + | 0.112674i | ||||
\(439\) | 14383.8i | 1.56378i | 0.623415 | + | 0.781891i | \(0.285745\pi\) | ||||
−0.623415 | + | 0.781891i | \(0.714255\pi\) | |||||||
\(440\) | 1197.19 | 0.129713 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3917.30 | 0.421554 | ||||||||
\(443\) | − | 3963.12i | − | 0.425042i | −0.977157 | − | 0.212521i | \(-0.931833\pi\) | ||
0.977157 | − | 0.212521i | \(-0.0681674\pi\) | |||||||
\(444\) | −4206.68 | − | 892.614i | −0.449640 | − | 0.0954089i | ||||
\(445\) | 143.134 | 0.0152476 | ||||||||
\(446\) | 5803.87 | 0.616191 | ||||||||
\(447\) | −962.710 | + | 4537.03i | −0.101867 | + | 0.480076i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13479.1i | − | 1.41675i | −0.705838 | − | 0.708373i | \(-0.749430\pi\) | ||
0.705838 | − | 0.708373i | \(-0.250570\pi\) | |||||||
\(450\) | −2583.62 | + | 5813.89i | −0.270651 | + | 0.609043i | ||||
\(451\) | 7599.09i | 0.793408i | ||||||||
\(452\) | − | 3852.31i | − | 0.400879i | ||||||
\(453\) | 7243.44 | + | 1536.98i | 0.751272 | + | 0.159412i | ||||
\(454\) | 8392.13i | 0.867538i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4850.01 | + | 1029.12i | 0.498076 | + | 0.105686i | ||||
\(457\) | 3979.58 | 0.407346 | 0.203673 | − | 0.979039i | \(-0.434712\pi\) | ||||
0.203673 | + | 0.979039i | \(0.434712\pi\) | |||||||
\(458\) | −3786.27 | −0.386290 | ||||||||
\(459\) | 11894.8 | + | 8622.98i | 1.20959 | + | 0.876876i | ||||
\(460\) | − | 436.932i | − | 0.0442871i | ||||||
\(461\) | 9053.72 | 0.914694 | 0.457347 | − | 0.889288i | \(-0.348800\pi\) | ||||
0.457347 | + | 0.889288i | \(0.348800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5736.10 | −0.575764 | −0.287882 | − | 0.957666i | \(-0.592951\pi\) | ||||
−0.287882 | + | 0.957666i | \(0.592951\pi\) | |||||||
\(464\) | 2153.36i | 0.215447i | ||||||||
\(465\) | 134.574 | − | 634.215i | 0.0134209 | − | 0.0632495i | ||||
\(466\) | −8348.75 | −0.829932 | ||||||||
\(467\) | −12392.6 | −1.22797 | −0.613984 | − | 0.789318i | \(-0.710434\pi\) | ||||
−0.613984 | + | 0.789318i | \(0.710434\pi\) | |||||||
\(468\) | −936.077 | + | 2106.44i | −0.0924576 | + | 0.208056i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 852.596i | − | 0.0836752i | ||||||
\(471\) | −304.966 | + | 1437.23i | −0.0298346 | + | 0.140604i | ||||
\(472\) | 14754.6i | 1.43885i | ||||||||
\(473\) | − | 6454.28i | − | 0.627417i | ||||||
\(474\) | −127.464 | + | 600.707i | −0.0123515 | + | 0.0582097i | ||||
\(475\) | − | 4993.85i | − | 0.482387i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4639.67 | + | 10440.6i | −0.445359 | + | 1.00219i | ||||
\(478\) | 7303.97 | 0.698903 | ||||||||
\(479\) | −8267.73 | −0.788648 | −0.394324 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394324 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(480\) | −227.743 | + | 1073.30i | −0.0216562 | + | 0.102061i | ||||
\(481\) | − | 3723.00i | − | 0.352919i | ||||||
\(482\) | −6566.17 | −0.620499 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1414.65 | −0.132856 | ||||||||
\(485\) | 1766.97i | 0.165431i | ||||||||
\(486\) | 6255.56 | − | 3626.31i | 0.583864 | − | 0.338462i | ||||
\(487\) | 940.150 | 0.0874790 | 0.0437395 | − | 0.999043i | \(-0.486073\pi\) | ||||
0.0437395 | + | 0.999043i | \(0.486073\pi\) | |||||||
\(488\) | 19052.9 | 1.76739 | ||||||||
\(489\) | 11772.9 | + | 2498.08i | 1.08873 | + | 0.231017i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1057.30i | 0.0971801i | 0.998819 | + | 0.0485900i | \(0.0154728\pi\) | ||||
−0.998819 | + | 0.0485900i | \(0.984527\pi\) | |||||||
\(492\) | −4135.32 | − | 877.472i | −0.378932 | − | 0.0804055i | ||||
\(493\) | − | 22170.2i | − | 2.02534i | ||||||
\(494\) | 1513.32i | 0.137828i | ||||||||
\(495\) | −556.539 | + | 1252.37i | −0.0505345 | + | 0.113717i | ||||
\(496\) | − | 1017.37i | − | 0.0920995i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −150.534 | + | 709.431i | −0.0135454 | + | 0.0638361i | ||||
\(499\) | −6173.30 | −0.553817 | −0.276909 | − | 0.960896i | \(-0.589310\pi\) | ||||
−0.276909 | + | 0.960896i | \(0.589310\pi\) | |||||||
\(500\) | 1350.09 | 0.120756 | ||||||||
\(501\) | −11918.1 | − | 2528.89i | −1.06280 | − | 0.225514i | ||||
\(502\) | 3906.63i | 0.347333i | ||||||||
\(503\) | −4284.28 | −0.379775 | −0.189887 | − | 0.981806i | \(-0.560812\pi\) | ||||
−0.189887 | + | 0.981806i | \(0.560812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 300.390 | 0.0264697 | ||||||||
\(506\) | − | 6245.15i | − | 0.548678i | ||||||
\(507\) | 9215.17 | + | 1955.36i | 0.807219 | + | 0.171284i | ||||
\(508\) | −3659.92 | −0.319651 | ||||||||
\(509\) | −15101.0 | −1.31501 | −0.657507 | − | 0.753449i | \(-0.728389\pi\) | ||||
−0.657507 | + | 0.753449i | \(0.728389\pi\) | |||||||
\(510\) | −268.932 | + | 1267.42i | −0.0233500 | + | 0.110043i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3640.92i | 0.314272i | ||||||||
\(513\) | −3331.19 | + | 4595.17i | −0.286697 | + | 0.395481i | ||||
\(514\) | − | 11550.6i | − | 0.991197i | ||||||
\(515\) | 1383.42i | 0.118371i | ||||||||
\(516\) | 3512.34 | + | 745.281i | 0.299655 | + | 0.0635837i | ||||
\(517\) | 14570.1i | 1.23944i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5254.79 | − | 1115.01i | −0.444431 | − | 0.0943037i | ||||
\(520\) | −576.586 | −0.0486249 | ||||||||
\(521\) | 13788.0 | 1.15943 | 0.579715 | − | 0.814819i | \(-0.303164\pi\) | ||||
0.579715 | + | 0.814819i | \(0.303164\pi\) | |||||||
\(522\) | −9971.09 | − | 4431.03i | −0.836059 | − | 0.371534i | ||||
\(523\) | − | 961.304i | − | 0.0803726i | −0.999192 | − | 0.0401863i | \(-0.987205\pi\) | ||
0.999192 | − | 0.0401863i | \(-0.0127951\pi\) | |||||||
\(524\) | 2256.17 | 0.188094 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11976.5 | −0.992780 | ||||||||
\(527\) | 10474.5i | 0.865797i | ||||||||
\(528\) | −446.384 | + | 2103.71i | −0.0367924 | + | 0.173394i | ||||
\(529\) | 5702.11 | 0.468654 | ||||||||
\(530\) | −1007.57 | −0.0825770 | ||||||||
\(531\) | −15434.8 | − | 6859.02i | −1.26142 | − | 0.560557i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3659.84i | − | 0.297421i | ||||||
\(534\) | −236.234 | + | 1113.32i | −0.0191439 | + | 0.0902207i | ||||
\(535\) | − | 1331.84i | − | 0.107627i | ||||||
\(536\) | − | 7041.53i | − | 0.567440i | ||||||
\(537\) | −156.264 | + | 736.434i | −0.0125573 | + | 0.0591797i | ||||
\(538\) | − | 6368.54i | − | 0.510348i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −617.261 | − | 447.474i | −0.0491902 | − | 0.0356596i | ||||
\(541\) | −1195.69 | −0.0950218 | −0.0475109 | − | 0.998871i | \(-0.515129\pi\) | ||||
−0.0475109 | + | 0.998871i | \(0.515129\pi\) | |||||||
\(542\) | 5427.14 | 0.430102 | ||||||||
\(543\) | 2218.77 | − | 10456.6i | 0.175353 | − | 0.826397i | ||||
\(544\) | − | 17726.2i | − | 1.39707i | ||||||
\(545\) | −12.5833 | −0.000989006 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18601.8 | 1.45403 | 0.727014 | − | 0.686622i | \(-0.240907\pi\) | ||||
0.727014 | + | 0.686622i | \(0.240907\pi\) | |||||||
\(548\) | − | 4783.59i | − | 0.372892i | ||||||
\(549\) | −8857.17 | + | 19931.2i | −0.688552 | + | 1.54944i | ||||
\(550\) | 9588.10 | 0.743341 | ||||||||
\(551\) | 8564.69 | 0.662192 | ||||||||
\(552\) | 9639.56 | + | 2045.41i | 0.743274 | + | 0.157715i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 12117.9i | − | 0.929315i | ||||||
\(555\) | 1204.55 | + | 255.593i | 0.0921267 | + | 0.0195483i | ||||
\(556\) | 3608.24i | 0.275222i | ||||||||
\(557\) | − | 6822.07i | − | 0.518959i | −0.965749 | − | 0.259480i | \(-0.916449\pi\) | ||
0.965749 | − | 0.259480i | \(-0.0835511\pi\) | |||||||
\(558\) | 4710.92 | + | 2093.47i | 0.357400 | + | 0.158824i | ||||
\(559\) | 3108.49i | 0.235197i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4595.80 | − | 21658.9i | 0.345873 | − | 1.63002i | ||||
\(562\) | −7131.16 | −0.535249 | ||||||||
\(563\) | 11359.6 | 0.850356 | 0.425178 | − | 0.905110i | \(-0.360211\pi\) | ||||
0.425178 | + | 0.905110i | \(0.360211\pi\) | |||||||
\(564\) | −7928.83 | − | 1682.42i | −0.591957 | − | 0.125607i | ||||
\(565\) | 1103.08i | 0.0821360i | ||||||||
\(566\) | 10531.2 | 0.782087 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10740.8 | 0.793443 | ||||||||
\(569\) | 21324.1i | 1.57110i | 0.618800 | + | 0.785549i | \(0.287619\pi\) | ||||
−0.618800 | + | 0.785549i | \(0.712381\pi\) | |||||||
\(570\) | −489.623 | − | 103.893i | −0.0359790 | − | 0.00763437i | ||||
\(571\) | −14768.0 | −1.08235 | −0.541175 | − | 0.840910i | \(-0.682020\pi\) | ||||
−0.541175 | + | 0.840910i | \(0.682020\pi\) | |||||||
\(572\) | 3473.88 | 0.253934 | ||||||||
\(573\) | 3180.36 | − | 14988.3i | 0.231870 | − | 1.09275i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9925.45i | − | 0.719861i | ||||||
\(576\) | −9980.06 | − | 4435.01i | −0.721937 | − | 0.320820i | ||||
\(577\) | − | 19304.9i | − | 1.39285i | −0.717631 | − | 0.696424i | \(-0.754773\pi\) | ||
0.717631 | − | 0.696424i | \(-0.245227\pi\) | |||||||
\(578\) | − | 11554.1i | − | 0.831464i | ||||||
\(579\) | −11542.4 | − | 2449.18i | −0.828475 | − | 0.175794i | ||||
\(580\) | 1150.48i | 0.0823640i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13743.8 | − | 2916.29i | −0.978863 | − | 0.207705i | ||||
\(583\) | 17218.3 | 1.22317 | ||||||||
\(584\) | 11832.7 | 0.838426 | ||||||||
\(585\) | 268.038 | − | 603.164i | 0.0189436 | − | 0.0426286i | ||||
\(586\) | − | 14458.4i | − | 1.01924i | ||||||
\(587\) | 4397.46 | 0.309204 | 0.154602 | − | 0.987977i | \(-0.450590\pi\) | ||||
0.154602 | + | 0.987977i | \(0.450590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4046.45 | −0.283075 | ||||||||
\(590\) | − | 1489.52i | − | 0.103937i | ||||||
\(591\) | 534.801 | − | 2520.39i | 0.0372230 | − | 0.175423i | ||||
\(592\) | 1932.27 | 0.134148 | ||||||||
\(593\) | 21940.2 | 1.51935 | 0.759677 | − | 0.650301i | \(-0.225357\pi\) | ||||
0.759677 | + | 0.650301i | \(0.225357\pi\) | |||||||
\(594\) | −8822.62 | − | 6395.82i | −0.609422 | − | 0.441791i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3888.46i | 0.267244i | ||||||||
\(597\) | 905.670 | − | 4268.21i | 0.0620881 | − | 0.292607i | ||||
\(598\) | 3007.77i | 0.205680i | ||||||||
\(599\) | 5502.23i | 0.375317i | 0.982234 | + | 0.187659i | \(0.0600899\pi\) | ||||
−0.982234 | + | 0.187659i | \(0.939910\pi\) | |||||||
\(600\) | −3140.30 | + | 14799.5i | −0.213670 | + | 1.00698i | ||||
\(601\) | − | 5814.58i | − | 0.394645i | −0.980339 | − | 0.197322i | \(-0.936775\pi\) | ||
0.980339 | − | 0.197322i | \(-0.0632246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7366.11 | + | 3273.41i | 0.497465 | + | 0.221067i | ||||
\(604\) | 6207.98 | 0.418210 | ||||||||
\(605\) | 405.074 | 0.0272208 | ||||||||
\(606\) | −495.777 | + | 2336.48i | −0.0332336 | + | 0.156622i | ||||
\(607\) | − | 13291.4i | − | 0.888765i | −0.895837 | − | 0.444382i | \(-0.853423\pi\) | ||
0.895837 | − | 0.444382i | \(-0.146577\pi\) | |||||||
\(608\) | 6847.90 | 0.456775 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1923.45 | −0.127669 | ||||||||
\(611\) | − | 7017.18i | − | 0.464623i | ||||||
\(612\) | 11255.8 | + | 5001.94i | 0.743447 | + | 0.330378i | ||||
\(613\) | 19594.3 | 1.29104 | 0.645520 | − | 0.763743i | \(-0.276641\pi\) | ||||
0.645520 | + | 0.763743i | \(0.276641\pi\) | |||||||
\(614\) | −20301.7 | −1.33438 | ||||||||
\(615\) | 1184.12 | + | 251.257i | 0.0776394 | + | 0.0164743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 348.388i | 0.0227319i | 0.999935 | + | 0.0113660i | \(0.00361797\pi\) | ||||
−0.999935 | + | 0.0113660i | \(0.996382\pi\) | |||||||
\(618\) | −10760.5 | − | 2283.26i | −0.700405 | − | 0.148619i | ||||
\(619\) | − | 6775.41i | − | 0.439946i | −0.975506 | − | 0.219973i | \(-0.929403\pi\) | ||
0.975506 | − | 0.219973i | \(-0.0705970\pi\) | |||||||
\(620\) | − | 543.553i | − | 0.0352091i | ||||||
\(621\) | −6620.86 | + | 9133.05i | −0.427836 | + | 0.590172i | ||||
\(622\) | − | 11016.2i | − | 0.710145i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 214.986 | − | 1013.18i | 0.0137922 | − | 0.0649994i | ||||
\(625\) | 15043.9 | 0.962810 | ||||||||
\(626\) | −4475.29 | −0.285733 | ||||||||
\(627\) | 8367.19 | + | 1775.43i | 0.532940 | + | 0.113084i | ||||
\(628\) | 1231.78i | 0.0782697i | ||||||||
\(629\) | −19893.9 | −1.26108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7326.82 | −0.462244 | −0.231122 | − | 0.972925i | \(-0.574240\pi\) | ||||
−0.231122 | + | 0.972925i | \(0.574240\pi\) | |||||||
\(632\) | 1460.28i | 0.0919092i | ||||||||
\(633\) | 20340.6 | + | 4316.07i | 1.27720 | + | 0.271009i | ||||
\(634\) | −15102.9 | −0.946078 | ||||||||
\(635\) | 1047.99 | 0.0654932 | ||||||||
\(636\) | −1988.21 | + | 9369.98i | −0.123959 | + | 0.584189i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16444.0i | 1.02042i | ||||||||
\(639\) | −4993.11 | + | 11235.9i | −0.309115 | + | 0.695598i | ||||
\(640\) | 726.120i | 0.0448475i | ||||||||
\(641\) | 2809.82i | 0.173138i | 0.996246 | + | 0.0865689i | \(0.0275903\pi\) | ||||
−0.996246 | + | 0.0865689i | \(0.972410\pi\) | |||||||
\(642\) | 10359.3 | + | 2198.13i | 0.636836 | + | 0.135130i | ||||
\(643\) | 27485.5i | 1.68573i | 0.538128 | + | 0.842863i | \(0.319132\pi\) | ||||
−0.538128 | + | 0.842863i | \(0.680868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1005.73 | − | 213.405i | −0.0613962 | − | 0.0130276i | ||||
\(646\) | 8086.43 | 0.492502 | ||||||||
\(647\) | −29319.8 | −1.78158 | −0.890790 | − | 0.454416i | \(-0.849848\pi\) | ||||
−0.890790 | + | 0.454416i | \(0.849848\pi\) | |||||||
\(648\) | 12761.7 | − | 11523.2i | 0.773654 | − | 0.698571i | ||||
\(649\) | 25454.5i | 1.53957i | ||||||||
\(650\) | −4617.78 | −0.278653 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10089.9 | 0.606061 | ||||||||
\(653\) | − | 16743.8i | − | 1.00343i | −0.865034 | − | 0.501713i | \(-0.832704\pi\) | ||
0.865034 | − | 0.501713i | \(-0.167296\pi\) | |||||||
\(654\) | 20.7680 | − | 97.8747i | 0.00124173 | − | 0.00585199i | ||||
\(655\) | −646.037 | −0.0385386 | ||||||||
\(656\) | 1899.49 | 0.113053 | ||||||||
\(657\) | −5500.69 | + | 12378.1i | −0.326640 | + | 0.735034i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9520.47i | 0.562769i | 0.959595 | + | 0.281385i | \(0.0907937\pi\) | ||||
−0.959595 | + | 0.281385i | \(0.909206\pi\) | |||||||
\(660\) | −238.491 | + | 1123.95i | −0.0140655 | + | 0.0662875i | ||||
\(661\) | 23345.1i | 1.37371i | 0.726797 | + | 0.686853i | \(0.241008\pi\) | ||||
−0.726797 | + | 0.686853i | \(0.758992\pi\) | |||||||
\(662\) | 9315.16i | 0.546894i | ||||||||
\(663\) | −2213.41 | + | 10431.3i | −0.129656 | + | 0.611037i | ||||
\(664\) | 1724.58i | 0.100793i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3976.08 | + | 8947.34i | −0.231337 | + | 0.520574i | ||||
\(667\) | 17022.6 | 0.988183 | ||||||||
\(668\) | −10214.4 | −0.591626 | ||||||||
\(669\) | −3279.39 | + | 15455.0i | −0.189519 | + | 0.893161i | ||||
\(670\) | 710.863i | 0.0409896i | ||||||||
\(671\) | 32869.9 | 1.89110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12283.5 | −0.703559 | −0.351780 | − | 0.936083i | \(-0.614423\pi\) | ||||
−0.351780 | + | 0.936083i | \(0.614423\pi\) | |||||||
\(674\) | 7895.67i | 0.451231i | ||||||||
\(675\) | −14021.8 | − | 10164.9i | −0.799557 | − | 0.579626i | ||||
\(676\) | 7897.85 | 0.449354 | ||||||||
\(677\) | 12991.8 | 0.737538 | 0.368769 | − | 0.929521i | \(-0.379779\pi\) | ||||
0.368769 | + | 0.929521i | \(0.379779\pi\) | |||||||
\(678\) | −8579.91 | − | 1820.57i | −0.486002 | − | 0.103125i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3081.00i | 0.173751i | ||||||||
\(681\) | −22347.2 | − | 4741.84i | −1.25748 | − | 0.266825i | ||||
\(682\) | − | 7769.11i | − | 0.436209i | ||||||
\(683\) | − | 8506.24i | − | 0.476548i | −0.971198 | − | 0.238274i | \(-0.923418\pi\) | ||
0.971198 | − | 0.238274i | \(-0.0765816\pi\) | |||||||
\(684\) | −1932.33 | + | 4348.30i | −0.108018 | + | 0.243072i | ||||
\(685\) | 1369.74i | 0.0764018i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2139.38 | − | 10082.4i | 0.118810 | − | 0.559923i | ||||
\(688\) | −1613.33 | −0.0894009 | ||||||||
\(689\) | −8292.63 | −0.458525 | ||||||||
\(690\) | −973.142 | − | 206.491i | −0.0536911 | − | 0.0113927i | ||||
\(691\) | − | 25832.9i | − | 1.42219i | −0.703097 | − | 0.711093i | \(-0.748200\pi\) | ||
0.703097 | − | 0.711093i | \(-0.251800\pi\) | |||||||
\(692\) | −4503.61 | −0.247401 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4429.93 | −0.242303 | ||||||||
\(695\) | − | 1033.19i | − | 0.0563902i | ||||||
\(696\) | −25381.8 | − | 5385.76i | −1.38232 | − | 0.293314i | ||||
\(697\) | −19556.4 | −1.06277 | ||||||||
\(698\) | −432.913 | −0.0234757 | ||||||||
\(699\) | 4717.33 | − | 22231.7i | 0.255259 | − | 1.20298i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22607.8i | 1.21810i | 0.793134 | + | 0.609048i | \(0.208448\pi\) | ||||
−0.793134 | + | 0.609048i | \(0.791552\pi\) | |||||||
\(702\) | 4249.12 | + | 3080.33i | 0.228451 | + | 0.165612i | ||||
\(703\) | − | 7685.33i | − | 0.412315i | ||||||
\(704\) | 16458.8i | 0.881129i | ||||||||
\(705\) | 2270.36 | + | 481.747i | 0.121286 | + | 0.0257356i | ||||
\(706\) | 2835.96i | 0.151180i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13852.0 | − | 2939.26i | −0.735298 | − | 0.156023i | ||||
\(709\) | −10944.8 | −0.579748 | −0.289874 | − | 0.957065i | \(-0.593613\pi\) | ||||
−0.289874 | + | 0.957065i | \(0.593613\pi\) | |||||||
\(710\) | −1084.32 | −0.0573152 | ||||||||
\(711\) | −1527.59 | − | 678.841i | −0.0805753 | − | 0.0358066i | ||||
\(712\) | 2706.39i | 0.142453i | ||||||||
\(713\) | −8042.46 | −0.422430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −994.720 | −0.0520285 | ||||||||
\(716\) | 631.160i | 0.0329435i | ||||||||
\(717\) | −4127.00 | + | 19449.6i | −0.214959 | + | 1.01305i | ||||
\(718\) | 20762.8 | 1.07919 | ||||||||
\(719\) | −25770.5 | −1.33669 | −0.668344 | − | 0.743852i | \(-0.732997\pi\) | ||||
−0.668344 | + | 0.743852i | \(0.732997\pi\) | |||||||
\(720\) | 313.048 | + | 139.114i | 0.0162036 | + | 0.00720068i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 9968.76i | − | 0.513849i | ||||||
\(723\) | 3710.11 | − | 17484.9i | 0.190844 | − | 0.899405i | ||||
\(724\) | − | 8961.78i | − | 0.460030i | ||||||
\(725\) | 26134.6i | 1.33878i | ||||||||
\(726\) | −668.552 | + | 3150.73i | −0.0341767 | + | 0.161067i | ||||
\(727\) | 15593.1i | 0.795485i | 0.917497 | + | 0.397742i | \(0.130206\pi\) | ||||
−0.917497 | + | 0.397742i | \(0.869794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6121.81 | + | 18706.8i | 0.311020 | + | 0.950403i | ||||
\(730\) | −1194.55 | −0.0605646 | ||||||||
\(731\) | 16610.3 | 0.840428 | ||||||||
\(732\) | −3795.51 | + | 17887.4i | −0.191648 | + | 0.903191i | ||||
\(733\) | 800.044i | 0.0403142i | 0.999797 | + | 0.0201571i | \(0.00641664\pi\) | ||||
−0.999797 | + | 0.0201571i | \(0.993583\pi\) | |||||||
\(734\) | 7272.94 | 0.365734 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13610.4 | 0.681641 | ||||||||
\(737\) | − | 12148.0i | − | 0.607159i | ||||||
\(738\) | −3908.64 | + | 8795.56i | −0.194958 | + | 0.438712i | ||||
\(739\) | −908.890 | −0.0452423 | −0.0226211 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226211 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(740\) | 1032.36 | 0.0512841 | ||||||||
\(741\) | −4029.77 | − | 855.076i | −0.199781 | − | 0.0423914i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8109.00i | 0.400391i | 0.979756 | + | 0.200195i | \(0.0641577\pi\) | ||||
−0.979756 | + | 0.200195i | \(0.935842\pi\) | |||||||
\(744\) | 11991.8 | + | 2544.54i | 0.590916 | + | 0.125386i | ||||
\(745\) | − | 1113.43i | − | 0.0547555i | ||||||
\(746\) | 18590.3i | 0.912384i | ||||||||
\(747\) | −1804.07 | − | 801.707i | −0.0883635 | − | 0.0392676i | ||||
\(748\) | − | 18562.8i | − | 0.907382i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 638.041 | − | 3006.94i | 0.0310639 | − | 0.146397i | ||||
\(751\) | −20764.4 | −1.00893 | −0.504463 | − | 0.863433i | \(-0.668310\pi\) | ||||
−0.504463 | + | 0.863433i | \(0.668310\pi\) | |||||||
\(752\) | 3641.98 | 0.176608 | ||||||||
\(753\) | −10402.9 | − | 2207.38i | −0.503455 | − | 0.106828i | ||||
\(754\) | − | 7919.71i | − | 0.382518i | ||||||
\(755\) | −1777.61 | −0.0856870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23295.6 | 1.11848 | 0.559242 | − | 0.829005i | \(-0.311092\pi\) | ||||
0.559242 | + | 0.829005i | \(0.311092\pi\) | |||||||
\(758\) | − | 611.152i | − | 0.0292850i | ||||||
\(759\) | 16630.1 | + | 3528.73i | 0.795301 | + | 0.168755i | ||||
\(760\) | −1190.24 | −0.0568085 | ||||||||
\(761\) | −10028.8 | −0.477717 | −0.238858 | − | 0.971054i | \(-0.576773\pi\) | ||||
−0.238858 | + | 0.971054i | \(0.576773\pi\) | |||||||
\(762\) | −1729.65 | + | 8151.43i | −0.0822290 | + | 0.387526i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 12845.7i | − | 0.608299i | ||||||
\(765\) | −3223.02 | − | 1432.27i | −0.152325 | − | 0.0676912i | ||||
\(766\) | − | 8342.08i | − | 0.393488i | ||||||
\(767\) | − | 12259.3i | − | 0.577130i | ||||||
\(768\) | −22095.8 | − | 4688.51i | −1.03817 | − | 0.220289i | ||||
\(769\) | − | 13500.3i | − | 0.633074i | −0.948580 | − | 0.316537i | \(-0.897480\pi\) | ||
0.948580 | − | 0.316537i | \(-0.102520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30757.8 | + | 6526.49i | 1.43673 | + | 0.304858i | ||||
\(772\) | −9892.42 | −0.461187 | ||||||||
\(773\) | −23289.7 | −1.08367 | −0.541833 | − | 0.840486i | \(-0.682269\pi\) | ||||
−0.541833 | + | 0.840486i | \(0.682269\pi\) | |||||||
\(774\) | 3319.80 | − | 7470.51i | 0.154170 | − | 0.346928i | ||||
\(775\) | − | 12347.5i | − | 0.572303i | ||||||
\(776\) | −33410.2 | −1.54556 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26179.3 | 1.20639 | ||||||||
\(779\) | − | 7554.96i | − | 0.347477i | ||||||
\(780\) | 114.861 | − | 541.313i | 0.00527267 | − | 0.0248489i | ||||
\(781\) | 18530.0 | 0.848982 | ||||||||
\(782\) | 16072.0 | 0.734956 | ||||||||
\(783\) | 17433.3 | − | 24048.1i | 0.795677 | − | 1.09759i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 352.711i | − | 0.0160367i | ||||||
\(786\) | 1066.25 | − | 5024.98i | 0.0483865 | − | 0.228034i | ||||
\(787\) | 23827.7i | 1.07924i | 0.841907 | + | 0.539622i | \(0.181433\pi\) | ||||
−0.841907 | + | 0.539622i | \(0.818567\pi\) | |||||||
\(788\) | − | 2160.10i | − | 0.0976528i | ||||||
\(789\) | 6767.16 | − | 31892.1i | 0.305345 | − | 1.43902i | ||||
\(790\) | − | 147.419i | − | 0.00663916i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −23680.1 | − | 10523.1i | −1.06242 | − | 0.472125i | ||||
\(793\) | −15830.7 | −0.708908 | ||||||||
\(794\) | −4808.54 | −0.214923 | ||||||||
\(795\) | 569.309 | − | 2683.02i | 0.0253979 | − | 0.119694i | ||||
\(796\) | − | 3658.06i | − | 0.162885i | ||||||
\(797\) | −12609.3 | −0.560406 | −0.280203 | − | 0.959941i | \(-0.590402\pi\) | ||||
−0.280203 | + | 0.959941i | \(0.590402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37496.4 | −1.66023 | ||||||||
\(800\) | 20895.9i | 0.923478i | ||||||||
\(801\) | −2831.14 | − | 1258.12i | −0.124886 | − | 0.0554977i | ||||
\(802\) | −5001.08 | −0.220192 | ||||||||
\(803\) | 20413.7 | 0.897114 | ||||||||
\(804\) | 6610.76 | + | 1402.74i | 0.289980 | + | 0.0615307i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3741.73i | 0.163519i | ||||||||
\(807\) | 16958.6 | + | 3598.44i | 0.739742 | + | 0.156966i | ||||
\(808\) | 5679.82i | 0.247296i | ||||||||
\(809\) | − | 34966.0i | − | 1.51958i | −0.650169 | − | 0.759789i | \(-0.725302\pi\) | ||
0.650169 | − | 0.759789i | \(-0.274698\pi\) | |||||||
\(810\) | −1288.33 | + | 1163.30i | −0.0558857 | + | 0.0504620i | ||||
\(811\) | 5691.42i | 0.246428i | 0.992380 | + | 0.123214i | \(0.0393201\pi\) | ||||
−0.992380 | + | 0.123214i | \(0.960680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3066.52 | + | 14451.8i | −0.132285 | + | 0.623428i | ||||
\(814\) | 14755.7 | 0.635364 | ||||||||
\(815\) | −2889.17 | −0.124176 | ||||||||
\(816\) | −5413.94 | − | 1148.78i | −0.232262 | − | 0.0492836i | ||||
\(817\) | 6416.81i | 0.274781i | ||||||||
\(818\) | 26578.9 | 1.13607 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1014.85 | 0.0432195 | ||||||||
\(821\) | 12109.4i | 0.514764i | 0.966310 | + | 0.257382i | \(0.0828598\pi\) | ||||
−0.966310 | + | 0.257382i | \(0.917140\pi\) | |||||||
\(822\) | −10654.1 | − | 2260.69i | −0.452073 | − | 0.0959252i | ||||
\(823\) | −31721.9 | −1.34357 | −0.671784 | − | 0.740747i | \(-0.734472\pi\) | ||||
−0.671784 | + | 0.740747i | \(0.734472\pi\) | |||||||
\(824\) | −26158.0 | −1.10589 | ||||||||
\(825\) | −5417.61 | + | 25531.9i | −0.228627 | + | 1.07746i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36401.9i | − | 1.53061i | −0.643666 | − | 0.765307i | \(-0.722587\pi\) | ||
0.643666 | − | 0.765307i | \(-0.277413\pi\) | |||||||
\(828\) | −3840.57 | + | 8642.40i | −0.161195 | + | 0.362734i | ||||
\(829\) | − | 31509.2i | − | 1.32010i | −0.751223 | − | 0.660049i | \(-0.770536\pi\) | ||
0.751223 | − | 0.660049i | \(-0.229464\pi\) | |||||||
\(830\) | − | 174.101i | − | 0.00728088i | ||||||
\(831\) | 32268.5 | + | 6847.04i | 1.34703 | + | 0.285826i | ||||
\(832\) | − | 7926.83i | − | 0.330305i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8036.32 | + | 1705.22i | 0.333663 | + | 0.0707998i | ||||
\(835\) | 2924.81 | 0.121218 | ||||||||
\(836\) | 7171.09 | 0.296671 | ||||||||
\(837\) | −8236.50 | + | 11361.7i | −0.340137 | + | 0.469197i | ||||
\(838\) | 28959.0i | 1.19376i | ||||||||
\(839\) | −13781.4 | −0.567090 | −0.283545 | − | 0.958959i | \(-0.591510\pi\) | ||||
−0.283545 | + | 0.958959i | \(0.591510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20433.0 | −0.837796 | ||||||||
\(842\) | 2009.10i | 0.0822304i | ||||||||
\(843\) | 4029.35 | − | 18989.4i | 0.164624 | − | 0.775836i | ||||
\(844\) | 17432.9 | 0.710979 | ||||||||
\(845\) | −2261.49 | −0.0920682 | ||||||||
\(846\) | −7494.20 | + | 16864.1i | −0.304558 | + | 0.685343i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4303.95i | − | 0.174290i | ||||||
\(849\) | −5950.52 | + | 28043.4i | −0.240543 | + | 1.13362i | ||||
\(850\) | 24675.2i | 0.995709i | ||||||||
\(851\) | − | 15274.9i | − | 0.615294i | ||||||
\(852\) | −2139.67 | + | 10083.8i | −0.0860374 | + | 0.405474i | ||||
\(853\) | − | 11376.3i | − | 0.456645i | −0.973586 | − | 0.228322i | \(-0.926676\pi\) | ||
0.973586 | − | 0.228322i | \(-0.0733240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 553.308 | − | 1245.10i | 0.0221318 | − | 0.0498030i | ||||
\(856\) | 25182.7 | 1.00552 | ||||||||
\(857\) | 43119.2 | 1.71870 | 0.859349 | − | 0.511390i | \(-0.170869\pi\) | ||||
0.859349 | + | 0.511390i | \(0.170869\pi\) | |||||||
\(858\) | 1641.73 | − | 7737.08i | 0.0653236 | − | 0.307855i | ||||
\(859\) | 37326.7i | 1.48262i | 0.671162 | + | 0.741311i | \(0.265796\pi\) | ||||
−0.671162 | + | 0.741311i | \(0.734204\pi\) | |||||||
\(860\) | −861.960 | −0.0341774 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15260.5 | 0.602986 | ||||||||
\(863\) | − | 34944.3i | − | 1.37835i | −0.724594 | − | 0.689176i | \(-0.757973\pi\) | ||
0.724594 | − | 0.689176i | \(-0.242027\pi\) | |||||||
\(864\) | 13938.8 | − | 19227.7i | 0.548852 | − | 0.757106i | ||||
\(865\) | 1289.58 | 0.0506900 | ||||||||
\(866\) | −24603.7 | −0.965437 | ||||||||
\(867\) | 30767.1 | + | 6528.45i | 1.20520 | + | 0.255730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2519.25i | 0.0983426i | ||||||||
\(870\) | 2562.37 | + | 543.708i | 0.0998533 | + | 0.0211878i | ||||
\(871\) | 5850.66i | 0.227603i | ||||||||
\(872\) | − | 237.926i | − | 0.00923991i | ||||||
\(873\) | 15531.4 | − | 34950.2i | 0.602130 | − | 1.35497i | ||||
\(874\) | 6208.89i | 0.240296i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2357.18 | + | 11108.8i | −0.0909152 | + | 0.428462i | ||||
\(877\) | 4109.19 | 0.158218 | 0.0791092 | − | 0.996866i | \(-0.474792\pi\) | ||||
0.0791092 | + | 0.996866i | \(0.474792\pi\) | |||||||
\(878\) | 27456.2 | 1.05536 | ||||||||
\(879\) | 38501.0 | + | 8169.52i | 1.47737 | + | 0.313482i | ||||
\(880\) | − | 516.269i | − | 0.0197766i | ||||||
\(881\) | 15697.6 | 0.600301 | 0.300151 | − | 0.953892i | \(-0.402963\pi\) | ||||
0.300151 | + | 0.953892i | \(0.402963\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44102.6 | −1.68083 | −0.840413 | − | 0.541946i | \(-0.817688\pi\) | ||||
−0.840413 | + | 0.541946i | \(0.817688\pi\) | |||||||
\(884\) | 8940.12i | 0.340146i | ||||||||
\(885\) | 3966.42 | + | 841.633i | 0.150655 | + | 0.0319674i | ||||
\(886\) | −7564.93 | −0.286850 | ||||||||
\(887\) | 28328.9 | 1.07237 | 0.536185 | − | 0.844101i | \(-0.319865\pi\) | ||||
0.536185 | + | 0.844101i | \(0.319865\pi\) | |||||||
\(888\) | −4832.79 | + | 22775.8i | −0.182633 | + | 0.860704i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 273.218i | − | 0.0102902i | ||||||
\(891\) | 22016.4 | − | 19879.7i | 0.827808 | − | 0.747469i | ||||
\(892\) | 13245.7i | 0.497195i | ||||||||
\(893\) | − | 14485.5i | − | 0.542819i | ||||||
\(894\) | 8660.42 | + | 1837.65i | 0.323991 | + | 0.0687475i | ||||
\(895\) | − | 180.728i | − | 0.00674979i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8009.31 | − | 1699.49i | −0.298131 | − | 0.0632602i | ||||
\(898\) | −25729.4 | −0.956125 | ||||||||
\(899\) | 21176.5 | 0.785624 | ||||||||
\(900\) | −13268.6 | − | 5896.38i | −0.491428 | − | 0.218384i | ||||
\(901\) | 44311.8i | 1.63845i | ||||||||
\(902\) | 14505.4 | 0.535450 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20857.1 | −0.767365 | ||||||||
\(905\) | 2566.14i | 0.0942555i | ||||||||
\(906\) | 2933.84 | − | 13826.5i | 0.107583 | − | 0.507014i | ||||
\(907\) | 14205.6 | 0.520054 | 0.260027 | − | 0.965601i | \(-0.416269\pi\) | ||||
0.260027 | + | 0.965601i | \(0.416269\pi\) | |||||||
\(908\) | −19152.6 | −0.700003 | ||||||||
\(909\) | −5941.64 | − | 2640.39i | −0.216800 | − | 0.0963434i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 17955.9i | − | 0.653025i | −0.945193 | − | 0.326512i | \(-0.894127\pi\) | ||
0.945193 | − | 0.326512i | \(-0.105873\pi\) | |||||||
\(912\) | 443.792 | − | 2091.49i | 0.0161134 | − | 0.0759388i | ||||
\(913\) | 2975.22i | 0.107848i | ||||||||
\(914\) | − | 7596.35i | − | 0.274907i | ||||||
\(915\) | 1086.82 | − | 5121.91i | 0.0392667 | − | 0.185055i | ||||
\(916\) | − | 8641.09i | − | 0.311692i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 16459.8 | − | 22705.2i | 0.591781 | − | 0.816323i | ||||
\(919\) | −42242.5 | −1.51627 | −0.758135 | − | 0.652097i | \(-0.773889\pi\) | ||||
−0.758135 | + | 0.652097i | \(0.773889\pi\) | |||||||
\(920\) | −2365.64 | −0.0847748 | ||||||||
\(921\) | 11471.1 | − | 54060.8i | 0.410409 | − | 1.93416i | ||||
\(922\) | − | 17282.0i | − | 0.617303i | ||||||
\(923\) | −8924.34 | −0.318254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23451.3 | 0.833593 | ||||||||
\(926\) | 10949.2i | 0.388568i | ||||||||
\(927\) | 12160.1 | − | 27363.7i | 0.430841 | − | 0.969517i | ||||
\(928\) | −35837.5 | −1.26770 | ||||||||
\(929\) | 44676.1 | 1.57780 | 0.788900 | − | 0.614522i | \(-0.210651\pi\) | ||||
0.788900 | + | 0.614522i | \(0.210651\pi\) | |||||||
\(930\) | −1210.61 | − | 256.879i | −0.0426854 | − | 0.00905741i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 19053.6i | − | 0.669660i | ||||||
\(933\) | 29334.8 | + | 6224.55i | 1.02935 | + | 0.218416i | ||||
\(934\) | 23655.4i | 0.828724i | ||||||||
\(935\) | 5315.30i | 0.185913i | ||||||||
\(936\) | 11404.7 | + | 5068.11i | 0.398263 | + | 0.176983i | ||||
\(937\) | − | 15309.3i | − | 0.533761i | −0.963730 | − | 0.266880i | \(-0.914007\pi\) | ||
0.963730 | − | 0.266880i | \(-0.0859929\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2528.70 | − | 11917.2i | 0.0878817 | − | 0.414166i | ||||
\(940\) | 1945.81 | 0.0675163 | ||||||||
\(941\) | −42384.4 | −1.46832 | −0.734162 | − | 0.678974i | \(-0.762425\pi\) | ||||
−0.734162 | + | 0.678974i | \(0.762425\pi\) | |||||||
\(942\) | 2743.44 | + | 582.129i | 0.0948897 | + | 0.0201346i | ||||
\(943\) | − | 15015.7i | − | 0.518537i | ||||||
\(944\) | 6362.70 | 0.219373 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12320.1 | −0.423427 | ||||||||
\(947\) | 12295.4i | 0.421908i | 0.977496 | + | 0.210954i | \(0.0676570\pi\) | ||||
−0.977496 | + | 0.210954i | \(0.932343\pi\) | |||||||
\(948\) | −1370.94 | − | 290.900i | −0.0469685 | − | 0.00996623i | ||||
\(949\) | −9831.55 | −0.336297 | ||||||||
\(950\) | −9532.42 | −0.325550 | ||||||||
\(951\) | 8533.67 | − | 40217.2i | 0.290981 | − | 1.37133i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1322.78i | 0.0449621i | 0.999747 | + | 0.0224811i | \(0.00715655\pi\) | ||||
−0.999747 | + | 0.0224811i | \(0.992843\pi\) | |||||||
\(954\) | 19929.3 | + | 8856.35i | 0.676349 | + | 0.300561i | ||||
\(955\) | 3678.26i | 0.124634i | ||||||||
\(956\) | 16669.2i | 0.563935i | ||||||||
\(957\) | −43788.4 | − | 9291.45i | −1.47908 | − | 0.313845i | ||||
\(958\) | 15781.7i | 0.532238i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2564.67 | + | 544.197i | 0.0862234 | + | 0.0182957i | ||||
\(961\) | 19786.0 | 0.664160 | ||||||||
\(962\) | −7106.57 | −0.238176 | ||||||||
\(963\) | −11706.7 | + | 26343.5i | −0.391738 | + | 0.881524i | ||||
\(964\) | − | 14985.4i | − | 0.500672i | ||||||
\(965\) | 2832.62 | 0.0944925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36887.2 | 1.22669 | 0.613346 | − | 0.789814i | \(-0.289823\pi\) | ||||
0.613346 | + | 0.789814i | \(0.289823\pi\) | |||||||
\(968\) | 7659.19i | 0.254314i | ||||||||
\(969\) | −4569.11 | + | 21533.2i | −0.151477 | + | 0.713875i | ||||
\(970\) | 3372.85 | 0.111645 | ||||||||
\(971\) | −6819.58 | −0.225387 | −0.112693 | − | 0.993630i | \(-0.535948\pi\) | ||||
−0.112693 | + | 0.993630i | \(0.535948\pi\) | |||||||
\(972\) | 8276.02 | + | 14276.5i | 0.273100 | + | 0.471111i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 1794.59i | − | 0.0590373i | ||||||
\(975\) | 2609.21 | − | 12296.6i | 0.0857041 | − | 0.403904i | ||||
\(976\) | − | 8216.27i | − | 0.269464i | ||||||
\(977\) | − | 49306.7i | − | 1.61460i | −0.590144 | − | 0.807298i | \(-0.700929\pi\) | ||
0.590144 | − | 0.807298i | \(-0.299071\pi\) | |||||||
\(978\) | 4768.41 | − | 22472.4i | 0.155907 | − | 0.734754i | ||||
\(979\) | 4669.03i | 0.152424i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 248.894 | + | 110.605i | 0.00810047 | + | 0.00359975i | ||||
\(982\) | 2018.21 | 0.0655843 | ||||||||
\(983\) | 19531.1 | 0.633718 | 0.316859 | − | 0.948473i | \(-0.397372\pi\) | ||||
0.316859 | + | 0.948473i | \(0.397372\pi\) | |||||||
\(984\) | −4750.81 | + | 22389.4i | −0.153913 | + | 0.725355i | ||||
\(985\) | 618.528i | 0.0200081i | ||||||||
\(986\) | −42319.1 | −1.36685 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3453.71 | −0.111212 | ||||||||
\(989\) | 12753.6i | 0.410052i | ||||||||
\(990\) | 2390.57 | + | 1062.34i | 0.0767448 | + | 0.0341044i | ||||
\(991\) | 18570.8 | 0.595278 | 0.297639 | − | 0.954678i | \(-0.403801\pi\) | ||||
0.297639 | + | 0.954678i | \(0.403801\pi\) | |||||||
\(992\) | 16931.7 | 0.541917 | ||||||||
\(993\) | −24805.1 | − | 5263.39i | −0.792716 | − | 0.168206i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1047.46i | 0.0333735i | ||||||||
\(996\) | −1619.07 | − | 343.551i | −0.0515084 | − | 0.0109295i | ||||
\(997\) | − | 22388.8i | − | 0.711195i | −0.934639 | − | 0.355598i | \(-0.884277\pi\) | ||
0.934639 | − | 0.355598i | \(-0.115723\pi\) | |||||||
\(998\) | 11783.8i | 0.373757i | ||||||||
\(999\) | −21579.0 | − | 15643.4i | −0.683414 | − | 0.495430i |
(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 | 147.4.c.a.146.6 | 12 | ||
3.2 | odd | 2 | inner | 147.4.c.a.146.7 | 12 | ||
7.2 | even | 3 | 21.4.g.a.17.3 | yes | 12 | ||
7.3 | odd | 6 | 21.4.g.a.5.4 | yes | 12 | ||
7.4 | even | 3 | 147.4.g.d.68.4 | 12 | |||
7.5 | odd | 6 | 147.4.g.d.80.3 | 12 | |||
7.6 | odd | 2 | inner | 147.4.c.a.146.5 | 12 | ||
21.2 | odd | 6 | 21.4.g.a.17.4 | yes | 12 | ||
21.5 | even | 6 | 147.4.g.d.80.4 | 12 | |||
21.11 | odd | 6 | 147.4.g.d.68.3 | 12 | |||
21.17 | even | 6 | 21.4.g.a.5.3 | ✓ | 12 | ||
21.20 | even | 2 | inner | 147.4.c.a.146.8 | 12 | ||
28.3 | even | 6 | 336.4.bc.d.257.3 | 12 | |||
28.23 | odd | 6 | 336.4.bc.d.17.5 | 12 | |||
84.23 | even | 6 | 336.4.bc.d.17.3 | 12 | |||
84.59 | odd | 6 | 336.4.bc.d.257.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.3 | ✓ | 12 | 21.17 | even | 6 | ||
21.4.g.a.5.4 | yes | 12 | 7.3 | odd | 6 | ||
21.4.g.a.17.3 | yes | 12 | 7.2 | even | 3 | ||
21.4.g.a.17.4 | yes | 12 | 21.2 | odd | 6 | ||
147.4.c.a.146.5 | 12 | 7.6 | odd | 2 | inner | ||
147.4.c.a.146.6 | 12 | 1.1 | even | 1 | trivial | ||
147.4.c.a.146.7 | 12 | 3.2 | odd | 2 | inner | ||
147.4.c.a.146.8 | 12 | 21.20 | even | 2 | inner | ||
147.4.g.d.68.3 | 12 | 21.11 | odd | 6 | |||
147.4.g.d.68.4 | 12 | 7.4 | even | 3 | |||
147.4.g.d.80.3 | 12 | 7.5 | odd | 6 | |||
147.4.g.d.80.4 | 12 | 21.5 | even | 6 | |||
336.4.bc.d.17.3 | 12 | 84.23 | even | 6 | |||
336.4.bc.d.17.5 | 12 | 28.23 | odd | 6 | |||
336.4.bc.d.257.3 | 12 | 28.3 | even | 6 | |||
336.4.bc.d.257.5 | 12 | 84.59 | odd | 6 |