Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(7,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.j (of order \(4\), 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: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.6 | ||
Character | \(\chi\) | \(=\) | 60.7 |
Dual form | 60.4.j.b.43.6 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.949450 | + | 2.66431i | −0.335681 | + | 0.941976i | ||||
\(3\) | 2.12132 | + | 2.12132i | 0.408248 | + | 0.408248i | ||||
\(4\) | −6.19709 | − | 5.05926i | −0.774636 | − | 0.632407i | ||||
\(5\) | −10.6252 | − | 3.47923i | −0.950347 | − | 0.311191i | ||||
\(6\) | −7.66594 | + | 3.63776i | −0.521601 | + | 0.247519i | ||||
\(7\) | −24.7270 | + | 24.7270i | −1.33513 | + | 1.33513i | −0.434426 | + | 0.900708i | \(0.643049\pi\) |
−0.900708 | + | 0.434426i | \(0.856951\pi\) | |||||||
\(8\) | 19.3633 | − | 11.7074i | 0.855743 | − | 0.517401i | ||||
\(9\) | 9.00000i | 0.333333i | ||||||||
\(10\) | 19.3578 | − | 25.0055i | 0.612149 | − | 0.790743i | ||||
\(11\) | − | 35.1552i | − | 0.963609i | −0.876279 | − | 0.481805i | \(-0.839981\pi\) | ||
0.876279 | − | 0.481805i | \(-0.160019\pi\) | |||||||
\(12\) | −2.41370 | − | 23.8783i | −0.0580646 | − | 0.574423i | ||||
\(13\) | −28.9954 | + | 28.9954i | −0.618607 | + | 0.618607i | −0.945174 | − | 0.326567i | \(-0.894108\pi\) |
0.326567 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(14\) | −42.4033 | − | 89.3575i | −0.809484 | − | 1.70584i | ||||
\(15\) | −15.1589 | − | 29.9200i | −0.260934 | − | 0.515021i | ||||
\(16\) | 12.8078 | + | 62.7053i | 0.200122 | + | 0.979771i | ||||
\(17\) | 54.2483 | + | 54.2483i | 0.773950 | + | 0.773950i | 0.978795 | − | 0.204844i | \(-0.0656689\pi\) |
−0.204844 | + | 0.978795i | \(0.565669\pi\) | |||||||
\(18\) | −23.9788 | − | 8.54505i | −0.313992 | − | 0.111894i | ||||
\(19\) | −20.8686 | −0.251979 | −0.125989 | − | 0.992032i | \(-0.540211\pi\) | ||||
−0.125989 | + | 0.992032i | \(0.540211\pi\) | |||||||
\(20\) | 48.2430 | + | 75.3167i | 0.539373 | + | 0.842067i | ||||
\(21\) | −104.908 | −1.09013 | ||||||||
\(22\) | 93.6644 | + | 33.3782i | 0.907696 | + | 0.323466i | ||||
\(23\) | −14.3469 | − | 14.3469i | −0.130067 | − | 0.130067i | 0.639076 | − | 0.769143i | \(-0.279317\pi\) |
−0.769143 | + | 0.639076i | \(0.779317\pi\) | |||||||
\(24\) | 65.9109 | + | 16.2404i | 0.560584 | + | 0.138128i | ||||
\(25\) | 100.790 | + | 73.9350i | 0.806320 | + | 0.591480i | ||||
\(26\) | −49.7231 | − | 104.783i | −0.375058 | − | 0.790367i | ||||
\(27\) | −19.0919 | + | 19.0919i | −0.136083 | + | 0.136083i | ||||
\(28\) | 278.336 | − | 28.1351i | 1.87859 | − | 0.189894i | ||||
\(29\) | 120.702i | 0.772888i | 0.922313 | + | 0.386444i | \(0.126297\pi\) | ||||
−0.922313 | + | 0.386444i | \(0.873703\pi\) | |||||||
\(30\) | 94.1088 | − | 11.9805i | 0.572728 | − | 0.0729107i | ||||
\(31\) | 183.498i | 1.06314i | 0.847015 | + | 0.531569i | \(0.178398\pi\) | ||||
−0.847015 | + | 0.531569i | \(0.821602\pi\) | |||||||
\(32\) | −179.227 | − | 25.4117i | −0.990098 | − | 0.140381i | ||||
\(33\) | 74.5755 | − | 74.5755i | 0.393392 | − | 0.393392i | ||||
\(34\) | −196.040 | + | 93.0282i | −0.988843 | + | 0.469241i | ||||
\(35\) | 348.760 | − | 176.699i | 1.68432 | − | 0.853358i | ||||
\(36\) | 45.5333 | − | 55.7738i | 0.210802 | − | 0.258212i | ||||
\(37\) | 96.2550 | + | 96.2550i | 0.427682 | + | 0.427682i | 0.887838 | − | 0.460156i | \(-0.152207\pi\) |
−0.460156 | + | 0.887838i | \(0.652207\pi\) | |||||||
\(38\) | 19.8137 | − | 55.6005i | 0.0845846 | − | 0.237358i | ||||
\(39\) | −123.017 | −0.505090 | ||||||||
\(40\) | −246.471 | + | 57.0248i | −0.974264 | + | 0.225410i | ||||
\(41\) | −363.161 | −1.38332 | −0.691661 | − | 0.722222i | \(-0.743121\pi\) | ||||
−0.691661 | + | 0.722222i | \(0.743121\pi\) | |||||||
\(42\) | 99.6048 | − | 279.507i | 0.365937 | − | 1.02688i | ||||
\(43\) | −159.934 | − | 159.934i | −0.567202 | − | 0.567202i | 0.364142 | − | 0.931344i | \(-0.381362\pi\) |
−0.931344 | + | 0.364142i | \(0.881362\pi\) | |||||||
\(44\) | −177.859 | + | 217.860i | −0.609394 | + | 0.746446i | ||||
\(45\) | 31.3130 | − | 95.6268i | 0.103730 | − | 0.316782i | ||||
\(46\) | 51.8464 | − | 24.6030i | 0.166181 | − | 0.0788589i | ||||
\(47\) | 24.6756 | − | 24.6756i | 0.0765810 | − | 0.0765810i | −0.667779 | − | 0.744360i | \(-0.732755\pi\) |
0.744360 | + | 0.667779i | \(0.232755\pi\) | |||||||
\(48\) | −105.849 | + | 160.188i | −0.318290 | + | 0.481689i | ||||
\(49\) | − | 879.851i | − | 2.56516i | ||||||
\(50\) | −292.681 | + | 198.338i | −0.827826 | + | 0.560985i | ||||
\(51\) | 230.156i | 0.631928i | ||||||||
\(52\) | 326.383 | − | 32.9918i | 0.870406 | − | 0.0879835i | ||||
\(53\) | 270.152 | − | 270.152i | 0.700155 | − | 0.700155i | −0.264289 | − | 0.964444i | \(-0.585137\pi\) |
0.964444 | + | 0.264289i | \(0.0851372\pi\) | |||||||
\(54\) | −32.7399 | − | 68.9935i | −0.0825062 | − | 0.173867i | ||||
\(55\) | −122.313 | + | 373.532i | −0.299867 | + | 0.915763i | ||||
\(56\) | −189.305 | + | 768.286i | −0.451732 | + | 1.83333i | ||||
\(57\) | −44.2691 | − | 44.2691i | −0.102870 | − | 0.102870i | ||||
\(58\) | −321.587 | − | 114.600i | −0.728041 | − | 0.259444i | ||||
\(59\) | 417.707 | 0.921709 | 0.460854 | − | 0.887476i | \(-0.347543\pi\) | ||||
0.460854 | + | 0.887476i | \(0.347543\pi\) | |||||||
\(60\) | −57.4320 | + | 262.110i | −0.123574 | + | 0.563971i | ||||
\(61\) | −110.271 | −0.231455 | −0.115727 | − | 0.993281i | \(-0.536920\pi\) | ||||
−0.115727 | + | 0.993281i | \(0.536920\pi\) | |||||||
\(62\) | −488.897 | − | 174.223i | −1.00145 | − | 0.356876i | ||||
\(63\) | −222.543 | − | 222.543i | −0.445044 | − | 0.445044i | ||||
\(64\) | 237.872 | − | 453.388i | 0.464593 | − | 0.885524i | ||||
\(65\) | 408.964 | − | 207.201i | 0.780396 | − | 0.395386i | ||||
\(66\) | 127.886 | + | 269.498i | 0.238511 | + | 0.502620i | ||||
\(67\) | 51.4010 | − | 51.4010i | 0.0937259 | − | 0.0937259i | −0.658689 | − | 0.752415i | \(-0.728889\pi\) |
0.752415 | + | 0.658689i | \(0.228889\pi\) | |||||||
\(68\) | −61.7253 | − | 610.638i | −0.110078 | − | 1.08898i | ||||
\(69\) | − | 60.8689i | − | 0.106199i | ||||||
\(70\) | 139.649 | + | 1096.97i | 0.238447 | + | 1.87305i | ||||
\(71\) | − | 291.518i | − | 0.487279i | −0.969866 | − | 0.243640i | \(-0.921659\pi\) | ||
0.969866 | − | 0.243640i | \(-0.0783414\pi\) | |||||||
\(72\) | 105.367 | + | 174.269i | 0.172467 | + | 0.285248i | ||||
\(73\) | −752.831 | + | 752.831i | −1.20702 | + | 1.20702i | −0.235028 | + | 0.971988i | \(0.575518\pi\) |
−0.971988 | + | 0.235028i | \(0.924482\pi\) | |||||||
\(74\) | −347.843 | + | 165.064i | −0.546431 | + | 0.259301i | ||||
\(75\) | 56.9681 | + | 370.648i | 0.0877081 | + | 0.570649i | ||||
\(76\) | 129.325 | + | 105.580i | 0.195192 | + | 0.159353i | ||||
\(77\) | 869.284 | + | 869.284i | 1.28655 | + | 1.28655i | ||||
\(78\) | 116.799 | − | 327.756i | 0.169549 | − | 0.475783i | ||||
\(79\) | 127.922 | 0.182182 | 0.0910911 | − | 0.995843i | \(-0.470965\pi\) | ||||
0.0910911 | + | 0.995843i | \(0.470965\pi\) | |||||||
\(80\) | 82.0806 | − | 710.818i | 0.114711 | − | 0.993399i | ||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 344.804 | − | 967.574i | 0.464356 | − | 1.30306i | ||||
\(83\) | 187.015 | + | 187.015i | 0.247320 | + | 0.247320i | 0.819870 | − | 0.572550i | \(-0.194046\pi\) |
−0.572550 | + | 0.819870i | \(0.694046\pi\) | |||||||
\(84\) | 650.123 | + | 530.756i | 0.844455 | + | 0.689407i | ||||
\(85\) | −387.657 | − | 765.142i | −0.494675 | − | 0.976368i | ||||
\(86\) | 577.963 | − | 274.264i | 0.724690 | − | 0.343891i | ||||
\(87\) | −256.047 | + | 256.047i | −0.315530 | + | 0.315530i | ||||
\(88\) | −411.578 | − | 680.720i | −0.498572 | − | 0.824602i | ||||
\(89\) | 51.0463i | 0.0607966i | 0.999538 | + | 0.0303983i | \(0.00967757\pi\) | ||||
−0.999538 | + | 0.0303983i | \(0.990322\pi\) | |||||||
\(90\) | 225.049 | + | 174.221i | 0.263581 | + | 0.204050i | ||||
\(91\) | − | 1433.94i | − | 1.65184i | ||||||
\(92\) | 16.3244 | + | 161.494i | 0.0184993 | + | 0.183010i | ||||
\(93\) | −389.259 | + | 389.259i | −0.434025 | + | 0.434025i | ||||
\(94\) | 42.3152 | + | 89.1717i | 0.0464306 | + | 0.0978442i | ||||
\(95\) | 221.734 | + | 72.6067i | 0.239467 | + | 0.0784136i | ||||
\(96\) | −326.291 | − | 434.104i | −0.346895 | − | 0.461516i | ||||
\(97\) | 676.202 | + | 676.202i | 0.707813 | + | 0.707813i | 0.966075 | − | 0.258262i | \(-0.0831497\pi\) |
−0.258262 | + | 0.966075i | \(0.583150\pi\) | |||||||
\(98\) | 2344.19 | + | 835.375i | 2.41632 | + | 0.861077i | ||||
\(99\) | 316.397 | 0.321203 | ||||||||
\(100\) | −250.548 | − | 968.104i | −0.250548 | − | 0.968104i | ||||
\(101\) | −772.225 | −0.760785 | −0.380392 | − | 0.924825i | \(-0.624211\pi\) | ||||
−0.380392 | + | 0.924825i | \(0.624211\pi\) | |||||||
\(102\) | −613.207 | − | 218.522i | −0.595260 | − | 0.212126i | ||||
\(103\) | −68.3141 | − | 68.3141i | −0.0653514 | − | 0.0653514i | 0.673676 | − | 0.739027i | \(-0.264714\pi\) |
−0.739027 | + | 0.673676i | \(0.764714\pi\) | |||||||
\(104\) | −221.984 | + | 900.908i | −0.209301 | + | 0.849436i | ||||
\(105\) | 1114.67 | + | 364.998i | 1.03600 | + | 0.339240i | ||||
\(106\) | 463.272 | + | 976.264i | 0.424500 | + | 0.894558i | ||||
\(107\) | −213.988 | + | 213.988i | −0.193336 | + | 0.193336i | −0.797136 | − | 0.603800i | \(-0.793653\pi\) |
0.603800 | + | 0.797136i | \(0.293653\pi\) | |||||||
\(108\) | 214.905 | − | 21.7233i | 0.191474 | − | 0.0193549i | ||||
\(109\) | 1178.72i | 1.03579i | 0.855445 | + | 0.517893i | \(0.173284\pi\) | ||||
−0.855445 | + | 0.517893i | \(0.826716\pi\) | |||||||
\(110\) | −879.074 | − | 680.529i | −0.761967 | − | 0.589872i | ||||
\(111\) | 408.375i | 0.349201i | ||||||||
\(112\) | −1867.21 | − | 1233.82i | −1.57531 | − | 1.04094i | ||||
\(113\) | −888.386 | + | 888.386i | −0.739578 | + | 0.739578i | −0.972496 | − | 0.232918i | \(-0.925173\pi\) |
0.232918 | + | 0.972496i | \(0.425173\pi\) | |||||||
\(114\) | 159.978 | − | 75.9152i | 0.131432 | − | 0.0623694i | ||||
\(115\) | 102.523 | + | 202.355i | 0.0831332 | + | 0.164085i | ||||
\(116\) | 610.661 | − | 747.999i | 0.488780 | − | 0.598707i | ||||
\(117\) | −260.959 | − | 260.959i | −0.206202 | − | 0.206202i | ||||
\(118\) | −396.592 | + | 1112.90i | −0.309401 | + | 0.868227i | ||||
\(119\) | −2682.80 | −2.06665 | ||||||||
\(120\) | −643.813 | − | 401.877i | −0.489765 | − | 0.305718i | ||||
\(121\) | 95.1094 | 0.0714571 | ||||||||
\(122\) | 104.697 | − | 293.796i | 0.0776951 | − | 0.218025i | ||||
\(123\) | −770.381 | − | 770.381i | −0.564739 | − | 0.564739i | ||||
\(124\) | 928.366 | − | 1137.16i | 0.672337 | − | 0.823546i | ||||
\(125\) | −813.678 | − | 1136.25i | −0.582220 | − | 0.813031i | ||||
\(126\) | 804.217 | − | 381.630i | 0.568614 | − | 0.269828i | ||||
\(127\) | −1452.14 | + | 1452.14i | −1.01462 | + | 1.01462i | −0.0147282 | + | 0.999892i | \(0.504688\pi\) |
−0.999892 | + | 0.0147282i | \(0.995312\pi\) | |||||||
\(128\) | 982.120 | + | 1064.23i | 0.678187 | + | 0.734889i | ||||
\(129\) | − | 678.542i | − | 0.463118i | ||||||
\(130\) | 163.756 | + | 1286.33i | 0.110479 | + | 0.867838i | ||||
\(131\) | 306.809i | 0.204626i | 0.994752 | + | 0.102313i | \(0.0326244\pi\) | ||||
−0.994752 | + | 0.102313i | \(0.967376\pi\) | |||||||
\(132\) | −839.448 | + | 84.8542i | −0.553519 | + | 0.0559516i | ||||
\(133\) | 516.019 | − | 516.019i | 0.336425 | − | 0.336425i | ||||
\(134\) | 88.1455 | + | 185.751i | 0.0568254 | + | 0.119749i | ||||
\(135\) | 269.280 | − | 136.430i | 0.171674 | − | 0.0869781i | ||||
\(136\) | 1685.53 | + | 415.315i | 1.06274 | + | 0.261860i | ||||
\(137\) | −212.111 | − | 212.111i | −0.132276 | − | 0.132276i | 0.637869 | − | 0.770145i | \(-0.279816\pi\) |
−0.770145 | + | 0.637869i | \(0.779816\pi\) | |||||||
\(138\) | 162.174 | + | 57.7920i | 0.100037 | + | 0.0356492i | ||||
\(139\) | 1953.77 | 1.19220 | 0.596102 | − | 0.802909i | \(-0.296715\pi\) | ||||
0.596102 | + | 0.802909i | \(0.296715\pi\) | |||||||
\(140\) | −3055.26 | − | 669.452i | −1.84441 | − | 0.404136i | ||||
\(141\) | 104.690 | 0.0625281 | ||||||||
\(142\) | 776.694 | + | 276.782i | 0.459005 | + | 0.163571i | ||||
\(143\) | 1019.34 | + | 1019.34i | 0.596095 | + | 0.596095i | ||||
\(144\) | −564.348 | + | 115.270i | −0.326590 | + | 0.0667073i | ||||
\(145\) | 419.948 | − | 1282.48i | 0.240516 | − | 0.734512i | ||||
\(146\) | −1291.00 | − | 2720.55i | −0.731807 | − | 1.54215i | ||||
\(147\) | 1866.45 | − | 1866.45i | 1.04722 | − | 1.04722i | ||||
\(148\) | −109.522 | − | 1083.48i | −0.0608286 | − | 0.601767i | ||||
\(149\) | − | 398.340i | − | 0.219015i | −0.993986 | − | 0.109508i | \(-0.965073\pi\) | ||
0.993986 | − | 0.109508i | \(-0.0349274\pi\) | |||||||
\(150\) | −1041.61 | − | 200.131i | −0.566980 | − | 0.108938i | ||||
\(151\) | − | 1429.31i | − | 0.770302i | −0.922854 | − | 0.385151i | \(-0.874149\pi\) | ||
0.922854 | − | 0.385151i | \(-0.125851\pi\) | |||||||
\(152\) | −404.085 | + | 244.319i | −0.215629 | + | 0.130374i | ||||
\(153\) | −488.235 | + | 488.235i | −0.257983 | + | 0.257983i | ||||
\(154\) | −3141.38 | + | 1490.70i | −1.64377 | + | 0.780026i | ||||
\(155\) | 638.433 | − | 1949.71i | 0.330840 | − | 1.01035i | ||||
\(156\) | 762.348 | + | 622.376i | 0.391261 | + | 0.319423i | ||||
\(157\) | −253.872 | − | 253.872i | −0.129052 | − | 0.129052i | 0.639630 | − | 0.768683i | \(-0.279087\pi\) |
−0.768683 | + | 0.639630i | \(0.779087\pi\) | |||||||
\(158\) | −121.456 | + | 340.825i | −0.0611552 | + | 0.171611i | ||||
\(159\) | 1146.16 | 0.571674 | ||||||||
\(160\) | 1815.91 | + | 893.575i | 0.897251 | + | 0.441521i | ||||
\(161\) | 709.514 | 0.347314 | ||||||||
\(162\) | 76.9055 | − | 215.809i | 0.0372979 | − | 0.104664i | ||||
\(163\) | 2598.96 | + | 2598.96i | 1.24887 | + | 1.24887i | 0.956218 | + | 0.292657i | \(0.0945394\pi\) |
0.292657 | + | 0.956218i | \(0.405461\pi\) | |||||||
\(164\) | 2250.54 | + | 1837.33i | 1.07157 | + | 0.874824i | ||||
\(165\) | −1051.85 | + | 532.915i | −0.496279 | + | 0.251439i | ||||
\(166\) | −675.828 | + | 320.705i | −0.315991 | + | 0.149949i | ||||
\(167\) | −2551.77 | + | 2551.77i | −1.18241 | + | 1.18241i | −0.203286 | + | 0.979119i | \(0.565162\pi\) |
−0.979119 | + | 0.203286i | \(0.934838\pi\) | |||||||
\(168\) | −2031.36 | + | 1228.20i | −0.932873 | + | 0.564035i | ||||
\(169\) | 515.530i | 0.234652i | ||||||||
\(170\) | 2406.64 | − | 306.375i | 1.08577 | − | 0.138223i | ||||
\(171\) | − | 187.818i | − | 0.0839929i | ||||||
\(172\) | 181.977 | + | 1800.27i | 0.0806723 | + | 0.798078i | ||||
\(173\) | 2002.13 | − | 2002.13i | 0.879878 | − | 0.879878i | −0.113644 | − | 0.993522i | \(-0.536252\pi\) |
0.993522 | + | 0.113644i | \(0.0362523\pi\) | |||||||
\(174\) | −439.084 | − | 925.292i | −0.191304 | − | 0.403139i | ||||
\(175\) | −4320.43 | + | 664.044i | −1.86625 | + | 0.286840i | ||||
\(176\) | 2204.42 | − | 450.261i | 0.944117 | − | 0.192839i | ||||
\(177\) | 886.091 | + | 886.091i | 0.376286 | + | 0.376286i | ||||
\(178\) | −136.003 | − | 48.4659i | −0.0572689 | − | 0.0204083i | ||||
\(179\) | 1233.94 | 0.515245 | 0.257622 | − | 0.966246i | \(-0.417061\pi\) | ||||
0.257622 | + | 0.966246i | \(0.417061\pi\) | |||||||
\(180\) | −677.851 | + | 434.187i | −0.280689 | + | 0.179791i | ||||
\(181\) | 3372.19 | 1.38482 | 0.692412 | − | 0.721502i | \(-0.256548\pi\) | ||||
0.692412 | + | 0.721502i | \(0.256548\pi\) | |||||||
\(182\) | 3820.46 | + | 1361.46i | 1.55600 | + | 0.554493i | ||||
\(183\) | −233.920 | − | 233.920i | −0.0944910 | − | 0.0944910i | ||||
\(184\) | −445.770 | − | 109.838i | −0.178601 | − | 0.0440072i | ||||
\(185\) | −687.836 | − | 1357.62i | −0.273355 | − | 0.539537i | ||||
\(186\) | −667.524 | − | 1406.69i | −0.263147 | − | 0.554535i | ||||
\(187\) | 1907.11 | − | 1907.11i | 0.745785 | − | 0.745785i | ||||
\(188\) | −277.757 | + | 28.0766i | −0.107753 | + | 0.0108920i | ||||
\(189\) | − | 944.171i | − | 0.363377i | ||||||
\(190\) | −403.972 | + | 521.831i | −0.154248 | + | 0.199250i | ||||
\(191\) | 238.122i | 0.0902091i | 0.998982 | + | 0.0451045i | \(0.0143621\pi\) | ||||
−0.998982 | + | 0.0451045i | \(0.985638\pi\) | |||||||
\(192\) | 1466.38 | − | 457.180i | 0.551183 | − | 0.171845i | ||||
\(193\) | −1990.01 | + | 1990.01i | −0.742196 | + | 0.742196i | −0.973000 | − | 0.230804i | \(-0.925864\pi\) |
0.230804 | + | 0.973000i | \(0.425864\pi\) | |||||||
\(194\) | −2443.63 | + | 1159.59i | −0.904343 | + | 0.429143i | ||||
\(195\) | 1307.08 | + | 428.005i | 0.480011 | + | 0.157180i | ||||
\(196\) | −4451.39 | + | 5452.51i | −1.62223 | + | 1.98707i | ||||
\(197\) | −1671.87 | − | 1671.87i | −0.604650 | − | 0.604650i | 0.336893 | − | 0.941543i | \(-0.390624\pi\) |
−0.941543 | + | 0.336893i | \(0.890624\pi\) | |||||||
\(198\) | −300.403 | + | 842.980i | −0.107822 | + | 0.302565i | ||||
\(199\) | 4536.41 | 1.61597 | 0.807984 | − | 0.589204i | \(-0.200559\pi\) | ||||
0.807984 | + | 0.589204i | \(0.200559\pi\) | |||||||
\(200\) | 2817.21 | + | 251.629i | 0.996035 | + | 0.0889643i | ||||
\(201\) | 218.076 | 0.0765268 | ||||||||
\(202\) | 733.189 | − | 2057.45i | 0.255381 | − | 0.716641i | ||||
\(203\) | −2984.59 | − | 2984.59i | −1.03191 | − | 1.03191i | ||||
\(204\) | 1164.42 | − | 1426.30i | 0.399636 | − | 0.489514i | ||||
\(205\) | 3858.66 | + | 1263.52i | 1.31464 | + | 0.430478i | ||||
\(206\) | 246.871 | − | 117.149i | 0.0834966 | − | 0.0396221i | ||||
\(207\) | 129.122 | − | 129.122i | 0.0433557 | − | 0.0433557i | ||||
\(208\) | −2189.54 | − | 1446.80i | −0.729889 | − | 0.482296i | ||||
\(209\) | 733.642i | 0.242809i | ||||||||
\(210\) | −2030.79 | + | 2623.27i | −0.667323 | + | 0.862014i | ||||
\(211\) | 61.2230i | 0.0199752i | 0.999950 | + | 0.00998760i | \(0.00317920\pi\) | ||||
−0.999950 | + | 0.00998760i | \(0.996821\pi\) | |||||||
\(212\) | −3040.92 | + | 307.386i | −0.985148 | + | 0.0995820i | ||||
\(213\) | 618.403 | − | 618.403i | 0.198931 | − | 0.198931i | ||||
\(214\) | −366.959 | − | 773.300i | −0.117219 | − | 0.247017i | ||||
\(215\) | 1142.88 | + | 2255.78i | 0.362530 | + | 0.715547i | ||||
\(216\) | −146.164 | + | 593.198i | −0.0460426 | + | 0.186861i | ||||
\(217\) | −4537.37 | − | 4537.37i | −1.41943 | − | 1.41943i | ||||
\(218\) | −3140.47 | − | 1119.13i | −0.975686 | − | 0.347694i | ||||
\(219\) | −3193.99 | −0.985525 | ||||||||
\(220\) | 2647.78 | − | 1695.99i | 0.811423 | − | 0.519745i | ||||
\(221\) | −3145.91 | −0.957541 | ||||||||
\(222\) | −1088.04 | − | 387.732i | −0.328939 | − | 0.117220i | ||||
\(223\) | −2752.79 | − | 2752.79i | −0.826639 | − | 0.826639i | 0.160411 | − | 0.987050i | \(-0.448718\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(224\) | 5060.10 | − | 3803.39i | 1.50934 | − | 1.13448i | ||||
\(225\) | −665.415 | + | 907.110i | −0.197160 | + | 0.268773i | ||||
\(226\) | −1523.46 | − | 3210.41i | −0.448402 | − | 0.944928i | ||||
\(227\) | 1077.03 | − | 1077.03i | 0.314912 | − | 0.314912i | −0.531897 | − | 0.846809i | \(-0.678521\pi\) |
0.846809 | + | 0.531897i | \(0.178521\pi\) | |||||||
\(228\) | 50.3706 | + | 498.308i | 0.0146310 | + | 0.144742i | ||||
\(229\) | 2189.64i | 0.631859i | 0.948783 | + | 0.315929i | \(0.102316\pi\) | ||||
−0.948783 | + | 0.315929i | \(0.897684\pi\) | |||||||
\(230\) | −636.478 | + | 81.0264i | −0.182470 | + | 0.0232292i | ||||
\(231\) | 3688.06i | 1.05046i | ||||||||
\(232\) | 1413.11 | + | 2337.18i | 0.399893 | + | 0.661393i | ||||
\(233\) | 3410.98 | − | 3410.98i | 0.959060 | − | 0.959060i | −0.0401343 | − | 0.999194i | \(-0.512779\pi\) |
0.999194 | + | 0.0401343i | \(0.0127786\pi\) | |||||||
\(234\) | 943.043 | − | 447.508i | 0.263456 | − | 0.125019i | ||||
\(235\) | −348.035 | + | 176.331i | −0.0966098 | + | 0.0489472i | ||||
\(236\) | −2588.57 | − | 2113.29i | −0.713989 | − | 0.582896i | ||||
\(237\) | 271.364 | + | 271.364i | 0.0743756 | + | 0.0743756i | ||||
\(238\) | 2547.18 | − | 7147.80i | 0.693737 | − | 1.94674i | ||||
\(239\) | −5713.06 | −1.54622 | −0.773111 | − | 0.634271i | \(-0.781300\pi\) | ||||
−0.773111 | + | 0.634271i | \(0.781300\pi\) | |||||||
\(240\) | 1681.99 | − | 1333.75i | 0.452384 | − | 0.358723i | ||||
\(241\) | −2598.16 | −0.694448 | −0.347224 | − | 0.937782i | \(-0.612876\pi\) | ||||
−0.347224 | + | 0.937782i | \(0.612876\pi\) | |||||||
\(242\) | −90.3016 | + | 253.401i | −0.0239868 | + | 0.0673108i | ||||
\(243\) | −171.827 | − | 171.827i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 683.358 | + | 557.889i | 0.179293 | + | 0.146374i | ||||
\(245\) | −3061.20 | + | 9348.59i | −0.798256 | + | 2.43779i | ||||
\(246\) | 2783.97 | − | 1321.09i | 0.721543 | − | 0.342398i | ||||
\(247\) | 605.095 | − | 605.095i | 0.155876 | − | 0.155876i | ||||
\(248\) | 2148.30 | + | 3553.13i | 0.550069 | + | 0.909774i | ||||
\(249\) | 793.438i | 0.201936i | ||||||||
\(250\) | 3799.86 | − | 1089.08i | 0.961296 | − | 0.275518i | ||||
\(251\) | 6357.14i | 1.59864i | 0.600904 | + | 0.799321i | \(0.294807\pi\) | ||||
−0.600904 | + | 0.799321i | \(0.705193\pi\) | |||||||
\(252\) | 253.216 | + | 2505.02i | 0.0632980 | + | 0.626197i | ||||
\(253\) | −504.370 | + | 504.370i | −0.125334 | + | 0.125334i | ||||
\(254\) | −2490.22 | − | 5247.69i | −0.615158 | − | 1.29634i | ||||
\(255\) | 800.765 | − | 2445.46i | 0.196650 | − | 0.600551i | ||||
\(256\) | −3767.92 | + | 1606.23i | −0.919903 | + | 0.392147i | ||||
\(257\) | 5632.26 | + | 5632.26i | 1.36705 | + | 1.36705i | 0.864620 | + | 0.502426i | \(0.167559\pi\) |
0.502426 | + | 0.864620i | \(0.332441\pi\) | |||||||
\(258\) | 1807.85 | + | 644.242i | 0.436246 | + | 0.155460i | ||||
\(259\) | −4760.20 | −1.14202 | ||||||||
\(260\) | −3582.67 | − | 785.014i | −0.854568 | − | 0.187248i | ||||
\(261\) | −1086.32 | −0.257629 | ||||||||
\(262\) | −817.435 | − | 291.300i | −0.192753 | − | 0.0686893i | ||||
\(263\) | 2996.95 | + | 2996.95i | 0.702661 | + | 0.702661i | 0.964981 | − | 0.262320i | \(-0.0844875\pi\) |
−0.262320 | + | 0.964981i | \(0.584487\pi\) | |||||||
\(264\) | 570.936 | − | 2317.11i | 0.133101 | − | 0.540184i | ||||
\(265\) | −3810.34 | + | 1930.50i | −0.883272 | + | 0.447508i | ||||
\(266\) | 884.900 | + | 1864.77i | 0.203973 | + | 0.429836i | ||||
\(267\) | −108.286 | + | 108.286i | −0.0248201 | + | 0.0248201i | ||||
\(268\) | −578.588 | + | 58.4855i | −0.131876 | + | 0.0133305i | ||||
\(269\) | − | 1623.82i | − | 0.368051i | −0.982921 | − | 0.184026i | \(-0.941087\pi\) | ||
0.982921 | − | 0.184026i | \(-0.0589130\pi\) | |||||||
\(270\) | 107.824 | + | 846.979i | 0.0243036 | + | 0.190909i | ||||
\(271\) | − | 1754.44i | − | 0.393264i | −0.980477 | − | 0.196632i | \(-0.937000\pi\) | ||
0.980477 | − | 0.196632i | \(-0.0630004\pi\) | |||||||
\(272\) | −2706.86 | + | 4096.46i | −0.603410 | + | 0.913178i | ||||
\(273\) | 3041.85 | − | 3041.85i | 0.674363 | − | 0.674363i | ||||
\(274\) | 766.517 | − | 363.740i | 0.169004 | − | 0.0801983i | ||||
\(275\) | 2599.20 | − | 3543.30i | 0.569955 | − | 0.776977i | ||||
\(276\) | −307.952 | + | 377.210i | −0.0671613 | + | 0.0822659i | ||||
\(277\) | −1806.98 | − | 1806.98i | −0.391953 | − | 0.391953i | 0.483430 | − | 0.875383i | \(-0.339391\pi\) |
−0.875383 | + | 0.483430i | \(0.839391\pi\) | |||||||
\(278\) | −1855.00 | + | 5205.44i | −0.400201 | + | 1.12303i | ||||
\(279\) | −1651.49 | −0.354380 | ||||||||
\(280\) | 4684.45 | − | 7504.56i | 0.999819 | − | 1.60173i | ||||
\(281\) | 3208.09 | 0.681062 | 0.340531 | − | 0.940233i | \(-0.389393\pi\) | ||||
0.340531 | + | 0.940233i | \(0.389393\pi\) | |||||||
\(282\) | −99.3977 | + | 278.926i | −0.0209895 | + | 0.0588999i | ||||
\(283\) | 1659.92 | + | 1659.92i | 0.348664 | + | 0.348664i | 0.859612 | − | 0.510948i | \(-0.170705\pi\) |
−0.510948 | + | 0.859612i | \(0.670705\pi\) | |||||||
\(284\) | −1474.87 | + | 1806.56i | −0.308159 | + | 0.377464i | ||||
\(285\) | 316.346 | + | 624.390i | 0.0657499 | + | 0.129774i | ||||
\(286\) | −3683.65 | + | 1748.03i | −0.761605 | + | 0.361409i | ||||
\(287\) | 8979.89 | − | 8979.89i | 1.84692 | − | 1.84692i | ||||
\(288\) | 228.705 | − | 1613.04i | 0.0467937 | − | 0.330033i | ||||
\(289\) | 972.761i | 0.197997i | ||||||||
\(290\) | 3018.20 | + | 2336.52i | 0.611155 | + | 0.473122i | ||||
\(291\) | 2868.88i | 0.577927i | ||||||||
\(292\) | 8474.13 | − | 856.593i | 1.69833 | − | 0.171672i | ||||
\(293\) | −3662.88 | + | 3662.88i | −0.730334 | + | 0.730334i | −0.970686 | − | 0.240352i | \(-0.922737\pi\) |
0.240352 | + | 0.970686i | \(0.422737\pi\) | |||||||
\(294\) | 3200.69 | + | 6744.88i | 0.634925 | + | 1.33799i | ||||
\(295\) | −4438.22 | − | 1453.30i | −0.875944 | − | 0.286828i | ||||
\(296\) | 2990.71 | + | 736.911i | 0.587269 | + | 0.144703i | ||||
\(297\) | 671.180 | + | 671.180i | 0.131131 | + | 0.131131i | ||||
\(298\) | 1061.30 | + | 378.204i | 0.206307 | + | 0.0735194i | ||||
\(299\) | 831.991 | 0.160921 | ||||||||
\(300\) | 1522.17 | − | 2585.15i | 0.292941 | − | 0.497513i | ||||
\(301\) | 7909.37 | 1.51458 | ||||||||
\(302\) | 3808.12 | + | 1357.06i | 0.725605 | + | 0.258576i | ||||
\(303\) | −1638.14 | − | 1638.14i | −0.310589 | − | 0.310589i | ||||
\(304\) | −267.281 | − | 1308.58i | −0.0504264 | − | 0.246881i | ||||
\(305\) | 1171.65 | + | 383.657i | 0.219962 | + | 0.0720267i | ||||
\(306\) | −837.254 | − | 1764.36i | −0.156414 | − | 0.329614i | ||||
\(307\) | −4150.58 | + | 4150.58i | −0.771615 | + | 0.771615i | −0.978389 | − | 0.206774i | \(-0.933704\pi\) |
0.206774 | + | 0.978389i | \(0.433704\pi\) | |||||||
\(308\) | −989.096 | − | 9784.96i | −0.182984 | − | 1.81023i | ||||
\(309\) | − | 289.832i | − | 0.0533592i | ||||||
\(310\) | 4588.47 | + | 3552.13i | 0.840669 | + | 0.650799i | ||||
\(311\) | − | 4316.72i | − | 0.787070i | −0.919310 | − | 0.393535i | \(-0.871252\pi\) | ||
0.919310 | − | 0.393535i | \(-0.128748\pi\) | |||||||
\(312\) | −2382.01 | + | 1440.22i | −0.432227 | + | 0.261334i | ||||
\(313\) | 4399.27 | − | 4399.27i | 0.794445 | − | 0.794445i | −0.187768 | − | 0.982213i | \(-0.560125\pi\) |
0.982213 | + | 0.187768i | \(0.0601254\pi\) | |||||||
\(314\) | 917.433 | − | 435.355i | 0.164884 | − | 0.0782436i | ||||
\(315\) | 1590.29 | + | 3138.84i | 0.284453 | + | 0.561441i | ||||
\(316\) | −792.746 | − | 647.192i | −0.141125 | − | 0.115213i | ||||
\(317\) | −7436.77 | − | 7436.77i | −1.31764 | − | 1.31764i | −0.915643 | − | 0.401993i | \(-0.868318\pi\) |
−0.401993 | − | 0.915643i | \(-0.631682\pi\) | |||||||
\(318\) | −1088.22 | + | 3053.72i | −0.191900 | + | 0.538503i | ||||
\(319\) | 4243.30 | 0.744762 | ||||||||
\(320\) | −4104.88 | + | 3989.74i | −0.717092 | + | 0.696978i | ||||
\(321\) | −907.873 | −0.157858 | ||||||||
\(322\) | −673.649 | + | 1890.37i | −0.116587 | + | 0.327161i | ||||
\(323\) | −1132.09 | − | 1132.09i | −0.195019 | − | 0.195019i | ||||
\(324\) | 501.964 | + | 409.800i | 0.0860707 | + | 0.0702675i | ||||
\(325\) | −5066.22 | + | 778.672i | −0.864688 | + | 0.132901i | ||||
\(326\) | −9392.03 | + | 4456.86i | −1.59563 | + | 0.757185i | ||||
\(327\) | −2500.44 | + | 2500.44i | −0.422858 | + | 0.422858i | ||||
\(328\) | −7031.98 | + | 4251.69i | −1.18377 | + | 0.715732i | ||||
\(329\) | 1220.31i | 0.204492i | ||||||||
\(330\) | −421.176 | − | 3308.42i | −0.0702575 | − | 0.551886i | ||||
\(331\) | − | 9421.59i | − | 1.56452i | −0.622949 | − | 0.782262i | \(-0.714066\pi\) | ||
0.622949 | − | 0.782262i | \(-0.285934\pi\) | |||||||
\(332\) | −212.791 | − | 2105.11i | −0.0351760 | − | 0.347990i | ||||
\(333\) | −866.295 | + | 866.295i | −0.142561 | + | 0.142561i | ||||
\(334\) | −4375.92 | − | 9221.47i | −0.716885 | − | 1.51071i | ||||
\(335\) | −724.982 | + | 367.311i | −0.118239 | + | 0.0599054i | ||||
\(336\) | −1343.64 | − | 6578.28i | −0.218159 | − | 1.06808i | ||||
\(337\) | 310.592 | + | 310.592i | 0.0502048 | + | 0.0502048i | 0.731763 | − | 0.681559i | \(-0.238698\pi\) |
−0.681559 | + | 0.731763i | \(0.738698\pi\) | |||||||
\(338\) | −1373.53 | − | 489.471i | −0.221036 | − | 0.0787683i | ||||
\(339\) | −3769.10 | −0.603863 | ||||||||
\(340\) | −1468.70 | + | 6702.91i | −0.234269 | + | 1.06917i | ||||
\(341\) | 6450.93 | 1.02445 | ||||||||
\(342\) | 500.405 | + | 178.324i | 0.0791193 | + | 0.0281949i | ||||
\(343\) | 13274.7 | + | 13274.7i | 2.08970 | + | 2.08970i | ||||
\(344\) | −4969.26 | − | 1224.42i | −0.778850 | − | 0.191909i | ||||
\(345\) | −211.777 | + | 646.745i | −0.0330483 | + | 0.100926i | ||||
\(346\) | 3433.36 | + | 7235.20i | 0.533465 | + | 1.12418i | ||||
\(347\) | 831.727 | − | 831.727i | 0.128673 | − | 0.128673i | −0.639837 | − | 0.768510i | \(-0.720998\pi\) |
0.768510 | + | 0.639837i | \(0.220998\pi\) | |||||||
\(348\) | 2882.15 | − | 291.338i | 0.443965 | − | 0.0448774i | ||||
\(349\) | − | 1646.43i | − | 0.252525i | −0.991997 | − | 0.126263i | \(-0.959702\pi\) | ||
0.991997 | − | 0.126263i | \(-0.0402982\pi\) | |||||||
\(350\) | 2332.81 | − | 12141.4i | 0.356269 | − | 1.85425i | ||||
\(351\) | − | 1107.15i | − | 0.168363i | ||||||
\(352\) | −893.354 | + | 6300.76i | −0.135273 | + | 0.954067i | ||||
\(353\) | 3573.21 | − | 3573.21i | 0.538761 | − | 0.538761i | −0.384404 | − | 0.923165i | \(-0.625593\pi\) |
0.923165 | + | 0.384404i | \(0.125593\pi\) | |||||||
\(354\) | −3202.12 | + | 1519.52i | −0.480765 | + | 0.228140i | ||||
\(355\) | −1014.26 | + | 3097.44i | −0.151637 | + | 0.463085i | ||||
\(356\) | 258.256 | − | 316.338i | 0.0384482 | − | 0.0470952i | ||||
\(357\) | −5691.07 | − | 5691.07i | −0.843708 | − | 0.843708i | ||||
\(358\) | −1171.56 | + | 3287.59i | −0.172958 | + | 0.485348i | ||||
\(359\) | 8383.39 | 1.23247 | 0.616237 | − | 0.787561i | \(-0.288656\pi\) | ||||
0.616237 | + | 0.787561i | \(0.288656\pi\) | |||||||
\(360\) | −513.224 | − | 2218.24i | −0.0751368 | − | 0.324755i | ||||
\(361\) | −6423.50 | −0.936507 | ||||||||
\(362\) | −3201.73 | + | 8984.56i | −0.464860 | + | 1.30447i | ||||
\(363\) | 201.757 | + | 201.757i | 0.0291722 | + | 0.0291722i | ||||
\(364\) | −7254.68 | + | 8886.26i | −1.04464 | + | 1.27958i | ||||
\(365\) | 10618.3 | − | 5379.72i | 1.52270 | − | 0.771472i | ||||
\(366\) | 845.330 | − | 401.140i | 0.120727 | − | 0.0572894i | ||||
\(367\) | −6243.28 | + | 6243.28i | −0.888002 | + | 0.888002i | −0.994331 | − | 0.106329i | \(-0.966090\pi\) |
0.106329 | + | 0.994331i | \(0.466090\pi\) | |||||||
\(368\) | 715.877 | − | 1083.38i | 0.101407 | − | 0.153465i | ||||
\(369\) | − | 3268.45i | − | 0.461108i | ||||||
\(370\) | 4270.19 | − | 543.614i | 0.599991 | − | 0.0763815i | ||||
\(371\) | 13360.1i | 1.86960i | ||||||||
\(372\) | 4381.64 | − | 442.910i | 0.610691 | − | 0.0617307i | ||||
\(373\) | 5265.16 | − | 5265.16i | 0.730884 | − | 0.730884i | −0.239911 | − | 0.970795i | \(-0.577118\pi\) |
0.970795 | + | 0.239911i | \(0.0771183\pi\) | |||||||
\(374\) | 3270.43 | + | 6891.85i | 0.452165 | + | 0.952858i | ||||
\(375\) | 684.269 | − | 4136.41i | 0.0942280 | − | 0.569609i | ||||
\(376\) | 188.912 | − | 766.688i | 0.0259106 | − | 0.105157i | ||||
\(377\) | −3499.80 | − | 3499.80i | −0.478113 | − | 0.478113i | ||||
\(378\) | 2515.56 | + | 896.443i | 0.342293 | + | 0.121979i | ||||
\(379\) | −8343.55 | −1.13082 | −0.565408 | − | 0.824811i | \(-0.691281\pi\) | ||||
−0.565408 | + | 0.824811i | \(0.691281\pi\) | |||||||
\(380\) | −1006.77 | − | 1571.76i | −0.135911 | − | 0.212183i | ||||
\(381\) | −6160.91 | −0.828434 | ||||||||
\(382\) | −634.432 | − | 226.085i | −0.0849747 | − | 0.0302815i | ||||
\(383\) | −5925.06 | − | 5925.06i | −0.790486 | − | 0.790486i | 0.191087 | − | 0.981573i | \(-0.438799\pi\) |
−0.981573 | + | 0.191087i | \(0.938799\pi\) | |||||||
\(384\) | −174.189 | + | 4340.97i | −0.0231486 | + | 0.576886i | ||||
\(385\) | −6211.89 | − | 12260.8i | −0.822304 | − | 1.62303i | ||||
\(386\) | −3412.58 | − | 7191.41i | −0.449989 | − | 0.948272i | ||||
\(387\) | 1439.40 | − | 1439.40i | 0.189067 | − | 0.189067i | ||||
\(388\) | −769.402 | − | 7611.56i | −0.100671 | − | 0.995924i | ||||
\(389\) | − | 81.4316i | − | 0.0106137i | −0.999986 | − | 0.00530687i | \(-0.998311\pi\) | ||
0.999986 | − | 0.00530687i | \(-0.00168924\pi\) | |||||||
\(390\) | −2381.35 | + | 3076.10i | −0.309190 | + | 0.399396i | ||||
\(391\) | − | 1556.60i | − | 0.201331i | ||||||
\(392\) | −10300.8 | − | 17036.8i | −1.32722 | − | 2.19512i | ||||
\(393\) | −650.841 | + | 650.841i | −0.0835384 | + | 0.0835384i | ||||
\(394\) | 6041.75 | − | 2867.03i | 0.772536 | − | 0.366596i | ||||
\(395\) | −1359.20 | − | 445.071i | −0.173136 | − | 0.0566935i | ||||
\(396\) | −1960.74 | − | 1600.74i | −0.248815 | − | 0.203131i | ||||
\(397\) | 10554.8 | + | 10554.8i | 1.33433 | + | 1.33433i | 0.901454 | + | 0.432876i | \(0.142501\pi\) |
0.432876 | + | 0.901454i | \(0.357499\pi\) | |||||||
\(398\) | −4307.10 | + | 12086.4i | −0.542451 | + | 1.52220i | ||||
\(399\) | 2189.28 | 0.274690 | ||||||||
\(400\) | −3345.22 | + | 7267.01i | −0.418153 | + | 0.908377i | ||||
\(401\) | −6515.71 | −0.811419 | −0.405710 | − | 0.914002i | \(-0.632976\pi\) | ||||
−0.405710 | + | 0.914002i | \(0.632976\pi\) | |||||||
\(402\) | −207.052 | + | 581.022i | −0.0256886 | + | 0.0720864i | ||||
\(403\) | −5320.62 | − | 5320.62i | −0.657665 | − | 0.657665i | ||||
\(404\) | 4785.55 | + | 3906.89i | 0.589331 | + | 0.481126i | ||||
\(405\) | 860.642 | + | 281.817i | 0.105594 | + | 0.0345768i | ||||
\(406\) | 10785.6 | − | 5118.16i | 1.31842 | − | 0.625640i | ||||
\(407\) | 3383.87 | − | 3383.87i | 0.412118 | − | 0.412118i | ||||
\(408\) | 2694.54 | + | 4456.57i | 0.326960 | + | 0.540768i | ||||
\(409\) | 4656.50i | 0.562956i | 0.959568 | + | 0.281478i | \(0.0908247\pi\) | ||||
−0.959568 | + | 0.281478i | \(0.909175\pi\) | |||||||
\(410\) | −7030.01 | + | 9081.02i | −0.846799 | + | 1.09385i | ||||
\(411\) | − | 899.909i | − | 0.108003i | ||||||
\(412\) | 77.7298 | + | 768.967i | 0.00929483 | + | 0.0919522i | ||||
\(413\) | −10328.6 | + | 10328.6i | −1.23060 | + | 1.23060i | ||||
\(414\) | 221.427 | + | 466.618i | 0.0262863 | + | 0.0553937i | ||||
\(415\) | −1336.41 | − | 2637.74i | −0.158076 | − | 0.312004i | ||||
\(416\) | 5933.58 | − | 4459.93i | 0.699321 | − | 0.525640i | ||||
\(417\) | 4144.57 | + | 4144.57i | 0.486715 | + | 0.486715i | ||||
\(418\) | −1954.65 | − | 696.557i | −0.228720 | − | 0.0815065i | ||||
\(419\) | 8824.96 | 1.02894 | 0.514472 | − | 0.857507i | \(-0.327988\pi\) | ||||
0.514472 | + | 0.857507i | \(0.327988\pi\) | |||||||
\(420\) | −5061.07 | − | 7901.32i | −0.587988 | − | 0.917964i | ||||
\(421\) | 15889.0 | 1.83939 | 0.919696 | − | 0.392632i | \(-0.128435\pi\) | ||||
0.919696 | + | 0.392632i | \(0.128435\pi\) | |||||||
\(422\) | −163.117 | − | 58.1282i | −0.0188161 | − | 0.00670530i | ||||
\(423\) | 222.080 | + | 222.080i | 0.0255270 | + | 0.0255270i | ||||
\(424\) | 2068.23 | − | 8393.81i | 0.236892 | − | 0.961413i | ||||
\(425\) | 1456.84 | + | 9478.54i | 0.166275 | + | 1.08183i | ||||
\(426\) | 1060.47 | + | 2234.76i | 0.120611 | + | 0.254166i | ||||
\(427\) | 2726.67 | − | 2726.67i | 0.309023 | − | 0.309023i | ||||
\(428\) | 2408.72 | − | 243.481i | 0.272032 | − | 0.0274979i | ||||
\(429\) | 4324.70i | 0.486710i | ||||||||
\(430\) | −7095.20 | + | 903.249i | −0.795723 | + | 0.101299i | ||||
\(431\) | − | 12016.0i | − | 1.34290i | −0.741048 | − | 0.671452i | \(-0.765671\pi\) | ||
0.741048 | − | 0.671452i | \(-0.234329\pi\) | |||||||
\(432\) | −1441.69 | − | 952.638i | −0.160563 | − | 0.106097i | ||||
\(433\) | −11629.7 | + | 11629.7i | −1.29073 | + | 1.29073i | −0.356396 | + | 0.934335i | \(0.615995\pi\) |
−0.934335 | + | 0.356396i | \(0.884005\pi\) | |||||||
\(434\) | 16397.0 | − | 7780.95i | 1.81355 | − | 0.860593i | ||||
\(435\) | 3611.40 | − | 1829.71i | 0.398053 | − | 0.201673i | ||||
\(436\) | 5963.44 | − | 7304.62i | 0.655039 | − | 0.802358i | ||||
\(437\) | 299.401 | + | 299.401i | 0.0327742 | + | 0.0327742i | ||||
\(438\) | 3032.54 | − | 8509.78i | 0.330823 | − | 0.928341i | ||||
\(439\) | 9052.02 | 0.984121 | 0.492061 | − | 0.870561i | \(-0.336244\pi\) | ||||
0.492061 | + | 0.870561i | \(0.336244\pi\) | |||||||
\(440\) | 2004.72 | + | 8664.76i | 0.217208 | + | 0.938810i | ||||
\(441\) | 7918.66 | 0.855054 | ||||||||
\(442\) | 2986.88 | − | 8381.67i | 0.321429 | − | 0.901980i | ||||
\(443\) | −12202.6 | − | 12202.6i | −1.30873 | − | 1.30873i | −0.922336 | − | 0.386389i | \(-0.873722\pi\) |
−0.386389 | − | 0.922336i | \(-0.626278\pi\) | |||||||
\(444\) | 2066.08 | − | 2530.74i | 0.220837 | − | 0.270503i | ||||
\(445\) | 177.602 | − | 542.377i | 0.0189194 | − | 0.0577779i | ||||
\(446\) | 9947.93 | − | 4720.65i | 1.05616 | − | 0.501187i | ||||
\(447\) | 845.007 | − | 845.007i | 0.0894127 | − | 0.0894127i | ||||
\(448\) | 5329.09 | + | 17092.8i | 0.562000 | + | 1.80259i | ||||
\(449\) | − | 287.237i | − | 0.0301906i | −0.999886 | − | 0.0150953i | \(-0.995195\pi\) | ||
0.999886 | − | 0.0150953i | \(-0.00480516\pi\) | |||||||
\(450\) | −1785.04 | − | 2634.13i | −0.186995 | − | 0.275942i | ||||
\(451\) | 12767.0i | 1.33298i | ||||||||
\(452\) | 9999.99 | − | 1010.83i | 1.04062 | − | 0.105189i | ||||
\(453\) | 3032.02 | − | 3032.02i | 0.314474 | − | 0.314474i | ||||
\(454\) | 1846.96 | + | 3892.13i | 0.190929 | + | 0.402350i | ||||
\(455\) | −4989.00 | + | 15235.9i | −0.514040 | + | 1.56983i | ||||
\(456\) | −1375.47 | − | 338.916i | −0.141255 | − | 0.0348053i | ||||
\(457\) | −1239.27 | − | 1239.27i | −0.126851 | − | 0.126851i | 0.640831 | − | 0.767682i | \(-0.278590\pi\) |
−0.767682 | + | 0.640831i | \(0.778590\pi\) | |||||||
\(458\) | −5833.88 | − | 2078.96i | −0.595195 | − | 0.212103i | ||||
\(459\) | −2071.41 | −0.210643 | ||||||||
\(460\) | 388.425 | − | 1772.70i | 0.0393704 | − | 0.179680i | ||||
\(461\) | −6295.73 | −0.636055 | −0.318027 | − | 0.948082i | \(-0.603020\pi\) | ||||
−0.318027 | + | 0.948082i | \(0.603020\pi\) | |||||||
\(462\) | −9826.13 | − | 3501.63i | −0.989509 | − | 0.352620i | ||||
\(463\) | 2108.18 | + | 2108.18i | 0.211610 | + | 0.211610i | 0.804951 | − | 0.593341i | \(-0.202192\pi\) |
−0.593341 | + | 0.804951i | \(0.702192\pi\) | |||||||
\(464\) | −7568.64 | + | 1545.92i | −0.757253 | + | 0.154672i | ||||
\(465\) | 5490.28 | − | 2781.64i | 0.547539 | − | 0.277409i | ||||
\(466\) | 5849.36 | + | 12326.5i | 0.581472 | + | 1.22535i | ||||
\(467\) | −13383.7 | + | 13383.7i | −1.32617 | + | 1.32617i | −0.417491 | + | 0.908681i | \(0.637091\pi\) |
−0.908681 | + | 0.417491i | \(0.862909\pi\) | |||||||
\(468\) | 296.926 | + | 2937.44i | 0.0293278 | + | 0.290135i | ||||
\(469\) | 2541.99i | 0.250273i | ||||||||
\(470\) | −139.359 | − | 1094.69i | −0.0136769 | − | 0.107435i | ||||
\(471\) | − | 1077.09i | − | 0.105371i | ||||||
\(472\) | 8088.17 | − | 4890.28i | 0.788746 | − | 0.476893i | ||||
\(473\) | −5622.51 | + | 5622.51i | −0.546561 | + | 0.546561i | ||||
\(474\) | −980.645 | + | 465.352i | −0.0950265 | + | 0.0450935i | ||||
\(475\) | −2103.35 | − | 1542.92i | −0.203175 | − | 0.149040i | ||||
\(476\) | 16625.5 | + | 13573.0i | 1.60090 | + | 1.30697i | ||||
\(477\) | 2431.37 | + | 2431.37i | 0.233385 | + | 0.233385i | ||||
\(478\) | 5424.26 | − | 15221.4i | 0.519038 | − | 1.45650i | ||||
\(479\) | −966.896 | −0.0922309 | −0.0461154 | − | 0.998936i | \(-0.514684\pi\) | ||||
−0.0461154 | + | 0.998936i | \(0.514684\pi\) | |||||||
\(480\) | 1956.56 | + | 5747.68i | 0.186051 | + | 0.546551i | ||||
\(481\) | −5581.91 | −0.529134 | ||||||||
\(482\) | 2466.82 | − | 6922.29i | 0.233113 | − | 0.654153i | ||||
\(483\) | 1505.11 | + | 1505.11i | 0.141790 | + | 0.141790i | ||||
\(484\) | −589.401 | − | 481.183i | −0.0553532 | − | 0.0451900i | ||||
\(485\) | −4832.12 | − | 9537.44i | −0.452403 | − | 0.892934i | ||||
\(486\) | 620.941 | − | 294.659i | 0.0579557 | − | 0.0275021i | ||||
\(487\) | 2440.48 | − | 2440.48i | 0.227082 | − | 0.227082i | −0.584391 | − | 0.811472i | \(-0.698666\pi\) |
0.811472 | + | 0.584391i | \(0.198666\pi\) | |||||||
\(488\) | −2135.20 | + | 1290.99i | −0.198066 | + | 0.119755i | ||||
\(489\) | 11026.5i | 1.01970i | ||||||||
\(490\) | −22001.1 | − | 17032.0i | −2.02838 | − | 1.57026i | ||||
\(491\) | 4478.81i | 0.411661i | 0.978588 | + | 0.205831i | \(0.0659896\pi\) | ||||
−0.978588 | + | 0.205831i | \(0.934010\pi\) | |||||||
\(492\) | 876.562 | + | 8671.68i | 0.0803221 | + | 0.794613i | ||||
\(493\) | −6547.86 | + | 6547.86i | −0.598176 | + | 0.598176i | ||||
\(494\) | 1037.65 | + | 2186.67i | 0.0945065 | + | 0.199156i | ||||
\(495\) | −3361.78 | − | 1100.82i | −0.305254 | − | 0.0999556i | ||||
\(496\) | −11506.3 | + | 2350.21i | −1.04163 | + | 0.212757i | ||||
\(497\) | 7208.37 | + | 7208.37i | 0.650583 | + | 0.650583i | ||||
\(498\) | −2113.97 | − | 753.330i | −0.190219 | − | 0.0677862i | ||||
\(499\) | 3918.32 | 0.351519 | 0.175759 | − | 0.984433i | \(-0.443762\pi\) | ||||
0.175759 | + | 0.984433i | \(0.443762\pi\) | |||||||
\(500\) | −706.127 | + | 11158.0i | −0.0631579 | + | 0.998004i | ||||
\(501\) | −10826.2 | −0.965430 | ||||||||
\(502\) | −16937.4 | − | 6035.79i | −1.50588 | − | 0.536635i | ||||
\(503\) | 9403.59 | + | 9403.59i | 0.833569 | + | 0.833569i | 0.988003 | − | 0.154434i | \(-0.0493554\pi\) |
−0.154434 | + | 0.988003i | \(0.549355\pi\) | |||||||
\(504\) | −6914.57 | − | 1703.75i | −0.611110 | − | 0.150577i | ||||
\(505\) | 8205.05 | + | 2686.75i | 0.723010 | + | 0.236750i | ||||
\(506\) | −864.924 | − | 1822.67i | −0.0759892 | − | 0.160134i | ||||
\(507\) | −1093.61 | + | 1093.61i | −0.0957963 | + | 0.0957963i | ||||
\(508\) | 16345.8 | − | 1652.29i | 1.42761 | − | 0.144308i | ||||
\(509\) | − | 8533.02i | − | 0.743063i | −0.928420 | − | 0.371532i | \(-0.878833\pi\) | ||
0.928420 | − | 0.371532i | \(-0.121167\pi\) | |||||||
\(510\) | 5755.16 | + | 4455.33i | 0.499692 | + | 0.386834i | ||||
\(511\) | − | 37230.5i | − | 3.22306i | ||||||
\(512\) | −702.051 | − | 11563.9i | −0.0605987 | − | 0.998162i | ||||
\(513\) | 398.422 | − | 398.422i | 0.0342900 | − | 0.0342900i | ||||
\(514\) | −20353.6 | + | 9658.53i | −1.74662 | + | 0.828832i | ||||
\(515\) | 488.171 | + | 963.532i | 0.0417697 | + | 0.0824433i | ||||
\(516\) | −3432.92 | + | 4204.98i | −0.292880 | + | 0.358748i | ||||
\(517\) | −867.476 | − | 867.476i | −0.0737941 | − | 0.0737941i | ||||
\(518\) | 4519.57 | − | 12682.6i | 0.383356 | − | 1.07576i | ||||
\(519\) | 8494.30 | 0.718417 | ||||||||
\(520\) | 5493.09 | − | 8800.00i | 0.463246 | − | 0.742126i | ||||
\(521\) | 9514.75 | 0.800094 | 0.400047 | − | 0.916495i | \(-0.368994\pi\) | ||||
0.400047 | + | 0.916495i | \(0.368994\pi\) | |||||||
\(522\) | 1031.40 | − | 2894.28i | 0.0864813 | − | 0.242680i | ||||
\(523\) | −2837.39 | − | 2837.39i | −0.237228 | − | 0.237228i | 0.578473 | − | 0.815701i | \(-0.303649\pi\) |
−0.815701 | + | 0.578473i | \(0.803649\pi\) | |||||||
\(524\) | 1552.23 | − | 1901.32i | 0.129407 | − | 0.158511i | ||||
\(525\) | −10573.7 | − | 7756.36i | −0.878995 | − | 0.644791i | ||||
\(526\) | −10830.3 | + | 5139.35i | −0.897760 | + | 0.426019i | ||||
\(527\) | −9954.49 | + | 9954.49i | −0.822816 | + | 0.822816i | ||||
\(528\) | 5631.43 | + | 3721.14i | 0.464160 | + | 0.306708i | ||||
\(529\) | − | 11755.3i | − | 0.966165i | ||||||
\(530\) | −1525.72 | − | 11984.8i | −0.125044 | − | 0.982241i | ||||
\(531\) | 3759.36i | 0.307236i | ||||||||
\(532\) | −5808.49 | + | 587.142i | −0.473365 | + | 0.0478493i | ||||
\(533\) | 10530.0 | − | 10530.0i | 0.855733 | − | 0.855733i | ||||
\(534\) | −185.694 | − | 391.318i | −0.0150483 | − | 0.0317116i | ||||
\(535\) | 3018.17 | − | 1529.15i | 0.243901 | − | 0.123572i | ||||
\(536\) | 393.517 | − | 1597.07i | 0.0317114 | − | 0.128699i | ||||
\(537\) | 2617.58 | + | 2617.58i | 0.210348 | + | 0.210348i | ||||
\(538\) | 4326.35 | + | 1541.73i | 0.346696 | + | 0.123548i | ||||
\(539\) | −30931.4 | −2.47181 | ||||||||
\(540\) | −2358.99 | − | 516.888i | −0.187990 | − | 0.0411913i | ||||
\(541\) | −21064.4 | −1.67399 | −0.836996 | − | 0.547210i | \(-0.815690\pi\) | ||||
−0.836996 | + | 0.547210i | \(0.815690\pi\) | |||||||
\(542\) | 4674.36 | + | 1665.75i | 0.370445 | + | 0.132011i | ||||
\(543\) | 7153.50 | + | 7153.50i | 0.565352 | + | 0.565352i | ||||
\(544\) | −8344.21 | − | 11101.3i | −0.657638 | − | 0.874934i | ||||
\(545\) | 4101.03 | − | 12524.1i | 0.322328 | − | 0.984357i | ||||
\(546\) | 5216.34 | + | 10992.5i | 0.408862 | + | 0.861604i | ||||
\(547\) | 1757.20 | − | 1757.20i | 0.137354 | − | 0.137354i | −0.635087 | − | 0.772441i | \(-0.719036\pi\) |
0.772441 | + | 0.635087i | \(0.219036\pi\) | |||||||
\(548\) | 241.346 | + | 2387.59i | 0.0188134 | + | 0.186118i | ||||
\(549\) | − | 992.438i | − | 0.0771516i | ||||||
\(550\) | 6972.62 | + | 10289.3i | 0.540570 | + | 0.797701i | ||||
\(551\) | − | 2518.88i | − | 0.194751i | ||||||
\(552\) | −712.619 | − | 1178.62i | −0.0549476 | − | 0.0908794i | ||||
\(553\) | −3163.14 | + | 3163.14i | −0.243237 | + | 0.243237i | ||||
\(554\) | 6530.00 | − | 3098.72i | 0.500782 | − | 0.237639i | ||||
\(555\) | 1420.83 | − | 4339.07i | 0.108668 | − | 0.331862i | ||||
\(556\) | −12107.7 | − | 9884.61i | −0.923524 | − | 0.753959i | ||||
\(557\) | 4185.97 | + | 4185.97i | 0.318430 | + | 0.318430i | 0.848164 | − | 0.529734i | \(-0.177708\pi\) |
−0.529734 | + | 0.848164i | \(0.677708\pi\) | |||||||
\(558\) | 1568.00 | − | 4400.07i | 0.118959 | − | 0.333817i | ||||
\(559\) | 9274.70 | 0.701750 | ||||||||
\(560\) | 15546.8 | + | 19606.0i | 1.17317 | + | 1.47947i | ||||
\(561\) | 8091.19 | 0.608931 | ||||||||
\(562\) | −3045.92 | + | 8547.33i | −0.228620 | + | 0.641543i | ||||
\(563\) | 4751.36 | + | 4751.36i | 0.355677 | + | 0.355677i | 0.862216 | − | 0.506540i | \(-0.169076\pi\) |
−0.506540 | + | 0.862216i | \(0.669076\pi\) | |||||||
\(564\) | −648.771 | − | 529.652i | −0.0484365 | − | 0.0395432i | ||||
\(565\) | 12530.2 | − | 6348.39i | 0.933007 | − | 0.472706i | ||||
\(566\) | −5998.55 | + | 2846.53i | −0.445473 | + | 0.211393i | ||||
\(567\) | 2002.89 | − | 2002.89i | 0.148348 | − | 0.148348i | ||||
\(568\) | −3412.93 | − | 5644.74i | −0.252119 | − | 0.416986i | ||||
\(569\) | − | 15307.4i | − | 1.12781i | −0.825841 | − | 0.563903i | \(-0.809299\pi\) | ||
0.825841 | − | 0.563903i | \(-0.190701\pi\) | |||||||
\(570\) | −1963.92 | + | 250.016i | −0.144315 | + | 0.0183720i | ||||
\(571\) | 18367.1i | 1.34613i | 0.739585 | + | 0.673063i | \(0.235022\pi\) | ||||
−0.739585 | + | 0.673063i | \(0.764978\pi\) | |||||||
\(572\) | −1159.84 | − | 11474.1i | −0.0847817 | − | 0.838732i | ||||
\(573\) | −505.134 | + | 505.134i | −0.0368277 | + | 0.0368277i | ||||
\(574\) | 15399.2 | + | 32451.2i | 1.11978 | + | 2.35973i | ||||
\(575\) | −385.287 | − | 2506.77i | −0.0279436 | − | 0.181808i | ||||
\(576\) | 4080.50 | + | 2140.84i | 0.295175 | + | 0.154864i | ||||
\(577\) | −6309.83 | − | 6309.83i | −0.455254 | − | 0.455254i | 0.441840 | − | 0.897094i | \(-0.354326\pi\) |
−0.897094 | + | 0.441840i | \(0.854326\pi\) | |||||||
\(578\) | −2591.74 | − | 923.588i | −0.186509 | − | 0.0664640i | ||||
\(579\) | −8442.89 | −0.606001 | ||||||||
\(580\) | −9090.86 | + | 5823.02i | −0.650823 | + | 0.416875i | ||||
\(581\) | −9248.66 | −0.660411 | ||||||||
\(582\) | −7643.59 | − | 2723.86i | −0.544393 | − | 0.193999i | ||||
\(583\) | −9497.25 | − | 9497.25i | −0.674676 | − | 0.674676i | ||||
\(584\) | −5763.54 | + | 23391.0i | −0.408385 | + | 1.65741i | ||||
\(585\) | 1864.81 | + | 3680.68i | 0.131795 | + | 0.260132i | ||||
\(586\) | −6281.33 | − | 13236.8i | −0.442797 | − | 0.933116i | ||||
\(587\) | 6395.12 | − | 6395.12i | 0.449667 | − | 0.449667i | −0.445577 | − | 0.895244i | \(-0.647001\pi\) |
0.895244 | + | 0.445577i | \(0.147001\pi\) | |||||||
\(588\) | −21009.4 | + | 2123.69i | −1.47349 | + | 0.148945i | ||||
\(589\) | − | 3829.37i | − | 0.267888i | ||||||
\(590\) | 8085.91 | − | 10445.0i | 0.564223 | − | 0.728835i | ||||
\(591\) | − | 7093.16i | − | 0.493695i | ||||||
\(592\) | −4802.89 | + | 7268.52i | −0.333442 | + | 0.504619i | ||||
\(593\) | −924.317 | + | 924.317i | −0.0640087 | + | 0.0640087i | −0.738386 | − | 0.674378i | \(-0.764412\pi\) |
0.674378 | + | 0.738386i | \(0.264412\pi\) | |||||||
\(594\) | −2425.48 | + | 1150.98i | −0.167540 | + | 0.0795037i | ||||
\(595\) | 28505.3 | + | 9334.06i | 1.96404 | + | 0.643125i | ||||
\(596\) | −2015.31 | + | 2468.55i | −0.138507 | + | 0.169657i | ||||
\(597\) | 9623.18 | + | 9623.18i | 0.659716 | + | 0.659716i | ||||
\(598\) | −789.935 | + | 2216.68i | −0.0540181 | + | 0.151583i | ||||
\(599\) | 16688.6 | 1.13836 | 0.569181 | − | 0.822212i | \(-0.307260\pi\) | ||||
0.569181 | + | 0.822212i | \(0.307260\pi\) | |||||||
\(600\) | 5442.42 | + | 6509.99i | 0.370310 | + | 0.442949i | ||||
\(601\) | −224.497 | −0.0152370 | −0.00761848 | − | 0.999971i | \(-0.502425\pi\) | ||||
−0.00761848 | + | 0.999971i | \(0.502425\pi\) | |||||||
\(602\) | −7509.56 | + | 21073.0i | −0.508417 | + | 1.42670i | ||||
\(603\) | 462.609 | + | 462.609i | 0.0312420 | + | 0.0312420i | ||||
\(604\) | −7231.25 | + | 8857.56i | −0.487144 | + | 0.596703i | ||||
\(605\) | −1010.56 | − | 330.907i | −0.0679090 | − | 0.0222368i | ||||
\(606\) | 5919.83 | − | 2809.17i | 0.396826 | − | 0.188308i | ||||
\(607\) | 2845.34 | − | 2845.34i | 0.190262 | − | 0.190262i | −0.605547 | − | 0.795809i | \(-0.707046\pi\) |
0.795809 | + | 0.605547i | \(0.207046\pi\) | |||||||
\(608\) | 3740.22 | + | 530.308i | 0.249484 | + | 0.0353731i | ||||
\(609\) | − | 12662.6i | − | 0.842549i | ||||||
\(610\) | −2134.61 | + | 2757.38i | −0.141685 | + | 0.183021i | ||||
\(611\) | 1430.96i | 0.0947470i | ||||||||
\(612\) | 5495.74 | − | 555.528i | 0.362994 | − | 0.0366926i | ||||
\(613\) | 16137.6 | − | 16137.6i | 1.06328 | − | 1.06328i | 0.0654249 | − | 0.997857i | \(-0.479160\pi\) |
0.997857 | − | 0.0654249i | \(-0.0208403\pi\) | |||||||
\(614\) | −7117.65 | − | 14999.2i | −0.467826 | − | 0.985859i | ||||
\(615\) | 5505.13 | + | 10865.8i | 0.360956 | + | 0.712440i | ||||
\(616\) | 27009.3 | + | 6655.08i | 1.76661 | + | 0.435293i | ||||
\(617\) | −187.494 | − | 187.494i | −0.0122338 | − | 0.0122338i | 0.700963 | − | 0.713197i | \(-0.252754\pi\) |
−0.713197 | + | 0.700963i | \(0.752754\pi\) | |||||||
\(618\) | 772.203 | + | 275.181i | 0.0502630 | + | 0.0179117i | ||||
\(619\) | −14428.3 | −0.936867 | −0.468434 | − | 0.883499i | \(-0.655181\pi\) | ||||
−0.468434 | + | 0.883499i | \(0.655181\pi\) | |||||||
\(620\) | −13820.5 | + | 8852.52i | −0.895234 | + | 0.573429i | ||||
\(621\) | 547.820 | 0.0353998 | ||||||||
\(622\) | 11501.1 | + | 4098.51i | 0.741401 | + | 0.264205i | ||||
\(623\) | −1262.22 | − | 1262.22i | −0.0811715 | − | 0.0811715i | ||||
\(624\) | −1575.58 | − | 7713.83i | −0.101080 | − | 0.494873i | ||||
\(625\) | 4692.24 | + | 14903.8i | 0.300303 | + | 0.953844i | ||||
\(626\) | 7544.12 | + | 15897.9i | 0.481667 | + | 1.01503i | ||||
\(627\) | −1556.29 | + | 1556.29i | −0.0991264 | + | 0.0991264i | ||||
\(628\) | 288.863 | + | 2857.67i | 0.0183549 | + | 0.181582i | ||||
\(629\) | 10443.3i | 0.662009i | ||||||||
\(630\) | −9872.75 | + | 1256.84i | −0.624349 | + | 0.0794823i | ||||
\(631\) | 23046.4i | 1.45398i | 0.686648 | + | 0.726990i | \(0.259081\pi\) | ||||
−0.686648 | + | 0.726990i | \(0.740919\pi\) | |||||||
\(632\) | 2476.99 | − | 1497.64i | 0.155901 | − | 0.0942612i | ||||
\(633\) | −129.874 | + | 129.874i | −0.00815484 | + | 0.00815484i | ||||
\(634\) | 26874.7 | − | 12753.0i | 1.68349 | − | 0.798875i | ||||
\(635\) | 20481.6 | − | 10377.0i | 1.27998 | − | 0.648500i | ||||
\(636\) | −7102.84 | − | 5798.71i | −0.442839 | − | 0.361531i | ||||
\(637\) | 25511.6 | + | 25511.6i | 1.58683 | + | 1.58683i | ||||
\(638\) | −4028.80 | + | 11305.5i | −0.250003 | + | 0.701547i | ||||
\(639\) | 2623.66 | 0.162426 | ||||||||
\(640\) | −6732.52 | − | 14724.7i | −0.415822 | − | 0.909446i | ||||
\(641\) | −19800.3 | −1.22007 | −0.610036 | − | 0.792374i | \(-0.708845\pi\) | ||||
−0.610036 | + | 0.792374i | \(0.708845\pi\) | |||||||
\(642\) | 861.980 | − | 2418.85i | 0.0529901 | − | 0.148699i | ||||
\(643\) | −2880.22 | − | 2880.22i | −0.176648 | − | 0.176648i | 0.613245 | − | 0.789893i | \(-0.289864\pi\) |
−0.789893 | + | 0.613245i | \(0.789864\pi\) | |||||||
\(644\) | −4396.92 | − | 3589.62i | −0.269042 | − | 0.219644i | ||||
\(645\) | −2360.80 | + | 7209.65i | −0.144118 | + | 0.440123i | ||||
\(646\) | 4091.10 | − | 1941.37i | 0.249167 | − | 0.118239i | ||||
\(647\) | −304.839 | + | 304.839i | −0.0185231 | + | 0.0185231i | −0.716308 | − | 0.697785i | \(-0.754169\pi\) |
0.697785 | + | 0.716308i | \(0.254169\pi\) | |||||||
\(648\) | −1568.42 | + | 948.303i | −0.0950826 | + | 0.0574890i | ||||
\(649\) | − | 14684.6i | − | 0.888167i | ||||||
\(650\) | 2735.51 | − | 14237.3i | 0.165070 | − | 0.859127i | ||||
\(651\) | − | 19250.4i | − | 1.15896i | ||||||
\(652\) | −2957.17 | − | 29254.8i | −0.177626 | − | 1.75722i | ||||
\(653\) | −2622.41 | + | 2622.41i | −0.157156 | + | 0.157156i | −0.781305 | − | 0.624149i | \(-0.785446\pi\) |
0.624149 | + | 0.781305i | \(0.285446\pi\) | |||||||
\(654\) | −4287.90 | − | 9035.99i | −0.256376 | − | 0.540268i | ||||
\(655\) | 1067.46 | − | 3259.91i | 0.0636780 | − | 0.194466i | ||||
\(656\) | −4651.29 | − | 22772.1i | −0.276833 | − | 1.35534i | ||||
\(657\) | −6775.48 | − | 6775.48i | −0.402339 | − | 0.402339i | ||||
\(658\) | −3251.28 | − | 1158.62i | −0.192626 | − | 0.0686440i | ||||
\(659\) | 4095.69 | 0.242102 | 0.121051 | − | 0.992646i | \(-0.461373\pi\) | ||||
0.121051 | + | 0.992646i | \(0.461373\pi\) | |||||||
\(660\) | 9214.53 | + | 2019.04i | 0.543447 | + | 0.119077i | ||||
\(661\) | −13157.5 | −0.774232 | −0.387116 | − | 0.922031i | \(-0.626529\pi\) | ||||
−0.387116 | + | 0.922031i | \(0.626529\pi\) | |||||||
\(662\) | 25102.0 | + | 8945.33i | 1.47374 | + | 0.525182i | ||||
\(663\) | −6673.48 | − | 6673.48i | −0.390915 | − | 0.390915i | ||||
\(664\) | 5810.69 | + | 1431.75i | 0.339606 | + | 0.0836790i | ||||
\(665\) | −7278.16 | + | 3687.46i | −0.424413 | + | 0.215028i | ||||
\(666\) | −1485.57 | − | 3130.58i | −0.0864337 | − | 0.182144i | ||||
\(667\) | 1731.70 | − | 1731.70i | 0.100527 | − | 0.100527i | ||||
\(668\) | 28723.6 | − | 2903.47i | 1.66370 | − | 0.168172i | ||||
\(669\) | − | 11679.1i | − | 0.674948i | ||||||
\(670\) | −290.294 | − | 2280.32i | −0.0167389 | − | 0.131487i | ||||
\(671\) | 3876.60i | 0.223032i | ||||||||
\(672\) | 18802.3 | + | 2665.89i | 1.07934 | + | 0.153034i | ||||
\(673\) | −1199.59 | + | 1199.59i | −0.0687087 | + | 0.0687087i | −0.740626 | − | 0.671917i | \(-0.765471\pi\) |
0.671917 | + | 0.740626i | \(0.265471\pi\) | |||||||
\(674\) | −1122.40 | + | 532.621i | −0.0641445 | + | 0.0304389i | ||||
\(675\) | −3335.83 | + | 512.713i | −0.190216 | + | 0.0292360i | ||||
\(676\) | 2608.20 | − | 3194.79i | 0.148396 | − | 0.181770i | ||||
\(677\) | 9185.47 | + | 9185.47i | 0.521457 | + | 0.521457i | 0.918011 | − | 0.396554i | \(-0.129794\pi\) |
−0.396554 | + | 0.918011i | \(0.629794\pi\) | |||||||
\(678\) | 3578.58 | − | 10042.1i | 0.202706 | − | 0.568824i | ||||
\(679\) | −33440.9 | −1.89005 | ||||||||
\(680\) | −16464.2 | − | 10277.2i | −0.928488 | − | 0.579575i | ||||
\(681\) | 4569.46 | 0.257125 | ||||||||
\(682\) | −6124.84 | + | 17187.3i | −0.343889 | + | 0.965007i | ||||
\(683\) | −7460.74 | − | 7460.74i | −0.417975 | − | 0.417975i | 0.466530 | − | 0.884505i | \(-0.345504\pi\) |
−0.884505 | + | 0.466530i | \(0.845504\pi\) | |||||||
\(684\) | −950.219 | + | 1163.92i | −0.0531177 | + | 0.0650639i | ||||
\(685\) | 1515.74 | + | 2991.70i | 0.0845451 | + | 0.166871i | ||||
\(686\) | −47971.6 | + | 22764.3i | −2.66992 | + | 1.26697i | ||||
\(687\) | −4644.93 | + | 4644.93i | −0.257955 | + | 0.257955i | ||||
\(688\) | 7980.31 | − | 12077.1i | 0.442219 | − | 0.669238i | ||||
\(689\) | 15666.3i | 0.866241i | ||||||||
\(690\) | −1522.06 | − | 1178.29i | −0.0839764 | − | 0.0650098i | ||||
\(691\) | 24513.0i | 1.34952i | 0.738036 | + | 0.674761i | \(0.235753\pi\) | ||||
−0.738036 | + | 0.674761i | \(0.764247\pi\) | |||||||
\(692\) | −22536.6 | + | 2278.08i | −1.23803 | + | 0.125144i | ||||
\(693\) | −7823.56 | + | 7823.56i | −0.428849 | + | 0.428849i | ||||
\(694\) | 1426.29 | + | 3005.66i | 0.0780136 | + | 0.164400i | ||||
\(695\) | −20759.2 | − | 6797.60i | −1.13301 | − | 0.371004i | ||||
\(696\) | −1960.25 | + | 7955.56i | −0.106757 | + | 0.433268i | ||||
\(697\) | −19700.9 | − | 19700.9i | −1.07062 | − | 1.07062i | ||||
\(698\) | 4386.59 | + | 1563.20i | 0.237873 | + | 0.0847680i | ||||
\(699\) | 14471.6 | 0.783069 | ||||||||
\(700\) | 30133.6 | + | 17743.0i | 1.62706 | + | 0.958033i | ||||
\(701\) | 11328.2 | 0.610355 | 0.305178 | − | 0.952295i | \(-0.401284\pi\) | ||||
0.305178 | + | 0.952295i | \(0.401284\pi\) | |||||||
\(702\) | 2949.80 | + | 1051.19i | 0.158594 | + | 0.0565165i | ||||
\(703\) | −2008.71 | − | 2008.71i | −0.107767 | − | 0.107767i | ||||
\(704\) | −15939.0 | − | 8362.43i | −0.853300 | − | 0.447686i | ||||
\(705\) | −1112.35 | − | 364.239i | −0.0594234 | − | 0.0194582i | ||||
\(706\) | 6127.55 | + | 12912.7i | 0.326648 | + | 0.688352i | ||||
\(707\) | 19094.8 | − | 19094.8i | 1.01575 | − | 1.01575i | ||||
\(708\) | −1008.22 | − | 9974.14i | −0.0535186 | − | 0.529451i | ||||
\(709\) | 21881.0i | 1.15904i | 0.814958 | + | 0.579520i | \(0.196760\pi\) | ||||
−0.814958 | + | 0.579520i | \(0.803240\pi\) | |||||||
\(710\) | −7289.55 | − | 5643.16i | −0.385313 | − | 0.298287i | ||||
\(711\) | 1151.30i | 0.0607274i | ||||||||
\(712\) | 597.621 | + | 988.422i | 0.0314562 | + | 0.0520263i | ||||
\(713\) | 2632.64 | − | 2632.64i | 0.138279 | − | 0.138279i | ||||
\(714\) | 20566.2 | − | 9759.39i | 1.07797 | − | 0.511535i | ||||
\(715\) | −7284.19 | − | 14377.2i | −0.380998 | − | 0.751997i | ||||
\(716\) | −7646.82 | − | 6242.81i | −0.399127 | − | 0.325844i | ||||
\(717\) | −12119.2 | − | 12119.2i | −0.631242 | − | 0.631242i | ||||
\(718\) | −7959.61 | + | 22335.9i | −0.413719 | + | 1.16096i | ||||
\(719\) | 1377.95 | 0.0714728 | 0.0357364 | − | 0.999361i | \(-0.488622\pi\) | ||||
0.0357364 | + | 0.999361i | \(0.488622\pi\) | |||||||
\(720\) | 6397.37 | + | 738.726i | 0.331133 | + | 0.0382370i | ||||
\(721\) | 3378.41 | 0.174506 | ||||||||
\(722\) | 6098.79 | − | 17114.2i | 0.314368 | − | 0.882166i | ||||
\(723\) | −5511.52 | − | 5511.52i | −0.283507 | − | 0.283507i | ||||
\(724\) | −20897.8 | − | 17060.8i | −1.07273 | − | 0.875773i | ||||
\(725\) | −8924.08 | + | 12165.5i | −0.457147 | + | 0.623195i | ||||
\(726\) | −729.103 | + | 345.986i | −0.0372721 | + | 0.0176870i | ||||
\(727\) | −14563.5 | + | 14563.5i | −0.742957 | + | 0.742957i | −0.973146 | − | 0.230189i | \(-0.926066\pi\) |
0.230189 | + | 0.973146i | \(0.426066\pi\) | |||||||
\(728\) | −16787.8 | − | 27765.8i | −0.854666 | − | 1.41355i | ||||
\(729\) | − | 729.000i | − | 0.0370370i | ||||||
\(730\) | 4251.72 | + | 33398.1i | 0.215566 | + | 1.69331i | ||||
\(731\) | − | 17352.3i | − | 0.877972i | ||||||
\(732\) | 266.161 | + | 2633.08i | 0.0134393 | + | 0.132953i | ||||
\(733\) | 14095.0 | − | 14095.0i | 0.710247 | − | 0.710247i | −0.256340 | − | 0.966587i | \(-0.582517\pi\) |
0.966587 | + | 0.256340i | \(0.0825167\pi\) | |||||||
\(734\) | −10706.3 | − | 22561.7i | −0.538390 | − | 1.13456i | ||||
\(735\) | −26325.1 | + | 13337.6i | −1.32111 | + | 0.669339i | ||||
\(736\) | 2206.78 | + | 2935.94i | 0.110520 | + | 0.147038i | ||||
\(737\) | −1807.01 | − | 1807.01i | −0.0903151 | − | 0.0903151i | ||||
\(738\) | 8708.16 | + | 3103.23i | 0.434352 | + | 0.154785i | ||||
\(739\) | 21280.1 | 1.05927 | 0.529635 | − | 0.848225i | \(-0.322329\pi\) | ||||
0.529635 | + | 0.848225i | \(0.322329\pi\) | |||||||
\(740\) | −2605.98 | + | 11893.2i | −0.129456 | + | 0.590817i | ||||
\(741\) | 2567.20 | 0.127272 | ||||||||
\(742\) | −35595.4 | − | 12684.8i | −1.76112 | − | 0.627590i | ||||
\(743\) | 21284.9 | + | 21284.9i | 1.05096 | + | 1.05096i | 0.998630 | + | 0.0523340i | \(0.0166661\pi\) |
0.0523340 | + | 0.998630i | \(0.483334\pi\) | |||||||
\(744\) | −2980.10 | + | 12094.6i | −0.146849 | + | 0.595978i | ||||
\(745\) | −1385.92 | + | 4232.45i | −0.0681557 | + | 0.208141i | ||||
\(746\) | 9029.01 | + | 19027.0i | 0.443131 | + | 0.933819i | ||||
\(747\) | −1683.14 | + | 1683.14i | −0.0824401 | + | 0.0824401i | ||||
\(748\) | −21467.1 | + | 2169.97i | −1.04935 | + | 0.106072i | ||||
\(749\) | − | 10582.6i | − | 0.516259i | ||||||
\(750\) | 10371.0 | + | 5750.42i | 0.504927 | + | 0.279968i | ||||
\(751\) | 15103.2i | 0.733855i | 0.930250 | + | 0.366927i | \(0.119590\pi\) | ||||
−0.930250 | + | 0.366927i | \(0.880410\pi\) | |||||||
\(752\) | 1863.33 | + | 1231.25i | 0.0903573 | + | 0.0597063i | ||||
\(753\) | −13485.5 | + | 13485.5i | −0.652643 | + | 0.652643i | ||||
\(754\) | 12647.4 | − | 6001.66i | 0.610865 | − | 0.289877i | ||||
\(755\) | −4972.89 | + | 15186.7i | −0.239711 | + | 0.732054i | ||||
\(756\) | −4776.80 | + | 5851.11i | −0.229802 | + | 0.281485i | ||||
\(757\) | −3670.42 | − | 3670.42i | −0.176227 | − | 0.176227i | 0.613482 | − | 0.789709i | \(-0.289768\pi\) |
−0.789709 | + | 0.613482i | \(0.789768\pi\) | |||||||
\(758\) | 7921.78 | − | 22229.8i | 0.379594 | − | 1.06520i | ||||
\(759\) | −2139.86 | −0.102335 | ||||||||
\(760\) | 5143.53 | − | 1190.03i | 0.245494 | − | 0.0567986i | ||||
\(761\) | 37834.8 | 1.80225 | 0.901123 | − | 0.433564i | \(-0.142744\pi\) | ||||
0.901123 | + | 0.433564i | \(0.142744\pi\) | |||||||
\(762\) | 5849.48 | − | 16414.6i | 0.278090 | − | 0.780364i | ||||
\(763\) | −29146.2 | − | 29146.2i | −1.38291 | − | 1.38291i | ||||
\(764\) | 1204.72 | − | 1475.67i | 0.0570489 | − | 0.0698792i | ||||
\(765\) | 6886.28 | − | 3488.92i | 0.325456 | − | 0.164892i | ||||
\(766\) | 21411.7 | − | 10160.6i | 1.00997 | − | 0.479267i | ||||
\(767\) | −12111.6 | + | 12111.6i | −0.570175 | + | 0.570175i | ||||
\(768\) | −11400.3 | − | 4585.63i | −0.535642 | − | 0.215455i | ||||
\(769\) | 30282.3i | 1.42004i | 0.704183 | + | 0.710019i | \(0.251314\pi\) | ||||
−0.704183 | + | 0.710019i | \(0.748686\pi\) | |||||||
\(770\) | 38564.3 | − | 4909.41i | 1.80489 | − | 0.229770i | ||||
\(771\) | 23895.7i | 1.11619i | ||||||||
\(772\) | 22400.2 | − | 2264.29i | 1.04430 | − | 0.105562i | ||||
\(773\) | −23218.3 | + | 23218.3i | −1.08034 | + | 1.08034i | −0.0838641 | + | 0.996477i | \(0.526726\pi\) |
−0.996477 | + | 0.0838641i | \(0.973274\pi\) | |||||||
\(774\) | 2468.38 | + | 5201.66i | 0.114630 | + | 0.241563i | ||||
\(775\) | −13567.0 | + | 18494.8i | −0.628825 | + | 0.857230i | ||||
\(776\) | 21010.1 | + | 5176.88i | 0.971929 | + | 0.239483i | ||||
\(777\) | −10097.9 | − | 10097.9i | −0.466230 | − | 0.466230i | ||||
\(778\) | 216.959 | + | 77.3152i | 0.00999788 | + | 0.00356284i | ||||
\(779\) | 7578.68 | 0.348568 | ||||||||
\(780\) | −5934.72 | − | 9265.25i | −0.272432 | − | 0.425320i | ||||
\(781\) | −10248.4 | −0.469547 | ||||||||
\(782\) | 4147.25 | + | 1477.91i | 0.189649 | + | 0.0675831i | ||||
\(783\) | −2304.42 | − | 2304.42i | −0.105177 | − | 0.105177i | ||||
\(784\) | 55171.3 | − | 11268.9i | 2.51327 | − | 0.513345i | ||||
\(785\) | 1814.16 | + | 3580.72i | 0.0824845 | + | 0.162804i | ||||
\(786\) | −1116.10 | − | 2351.98i | −0.0506488 | − | 0.106733i | ||||
\(787\) | 19881.2 | − | 19881.2i | 0.900492 | − | 0.900492i | −0.0949865 | − | 0.995479i | \(-0.530281\pi\) |
0.995479 | + | 0.0949865i | \(0.0302808\pi\) | |||||||
\(788\) | 1902.31 | + | 18819.2i | 0.0859985 | + | 0.850769i | ||||
\(789\) | 12715.0i | 0.573721i | ||||||||
\(790\) | 2476.30 | − | 3198.76i | 0.111523 | − | 0.144059i | ||||
\(791\) | − | 43934.3i | − | 1.97487i | ||||||
\(792\) | 6126.48 | − | 3704.20i | 0.274867 | − | 0.166191i | ||||
\(793\) | 3197.35 | − | 3197.35i | 0.143179 | − | 0.143179i | ||||
\(794\) | −38142.4 | + | 18099.9i | −1.70482 | + | 0.808996i | ||||
\(795\) | −12178.2 | − | 3987.74i | −0.543289 | − | 0.177900i | ||||
\(796\) | −28112.5 | − | 22950.9i | −1.25179 | − | 1.02195i | ||||
\(797\) | −17974.6 | − | 17974.6i | −0.798862 | − | 0.798862i | 0.184054 | − | 0.982916i | \(-0.441078\pi\) |
−0.982916 | + | 0.184054i | \(0.941078\pi\) | |||||||
\(798\) | −2078.62 | + | 5832.93i | −0.0922083 | + | 0.258751i | ||||
\(799\) | 2677.22 | 0.118540 | ||||||||
\(800\) | −16185.5 | − | 15812.4i | −0.715303 | − | 0.698815i | ||||
\(801\) | −459.417 | −0.0202655 | ||||||||
\(802\) | 6186.35 | − | 17359.9i | 0.272378 | − | 0.764337i | ||||
\(803\) | 26466.0 | + | 26466.0i | 1.16309 | + | 1.16309i | ||||
\(804\) | −1351.44 | − | 1103.30i | −0.0592804 | − | 0.0483961i | ||||
\(805\) | −7538.73 | − | 2468.56i | −0.330069 | − | 0.108081i | ||||
\(806\) | 19227.4 | − | 9124.11i | 0.840270 | − | 0.398738i | ||||
\(807\) | 3444.64 | − | 3444.64i | 0.150256 | − | 0.150256i | ||||
\(808\) | −14952.8 | + | 9040.78i | −0.651036 | + | 0.393631i | ||||
\(809\) | 33951.7i | 1.47550i | 0.675075 | + | 0.737749i | \(0.264111\pi\) | ||||
−0.675075 | + | 0.737749i | \(0.735889\pi\) | |||||||
\(810\) | −1567.98 | + | 2025.44i | −0.0680165 | + | 0.0878603i | ||||
\(811\) | 5751.71i | 0.249038i | 0.992217 | + | 0.124519i | \(0.0397388\pi\) | ||||
−0.992217 | + | 0.124519i | \(0.960261\pi\) | |||||||
\(812\) | 3395.95 | + | 33595.6i | 0.146767 | + | 1.45194i | ||||
\(813\) | 3721.72 | − | 3721.72i | 0.160549 | − | 0.160549i | ||||
\(814\) | 5802.86 | + | 12228.5i | 0.249865 | + | 0.526546i | ||||
\(815\) | −18572.1 | − | 36656.9i | −0.798225 | − | 1.57550i | ||||
\(816\) | −14432.0 | + | 2947.79i | −0.619144 | + | 0.126462i | ||||
\(817\) | 3337.60 | + | 3337.60i | 0.142923 | + | 0.142923i | ||||
\(818\) | −12406.4 | − | 4421.12i | −0.530291 | − | 0.188974i | ||||
\(819\) | 12905.5 | 0.550615 | ||||||||
\(820\) | −17520.0 | − | 27352.1i | −0.746128 | − | 1.16485i | ||||
\(821\) | −4301.92 | −0.182872 | −0.0914361 | − | 0.995811i | \(-0.529146\pi\) | ||||
−0.0914361 | + | 0.995811i | \(0.529146\pi\) | |||||||
\(822\) | 2397.64 | + | 854.419i | 0.101736 | + | 0.0362546i | ||||
\(823\) | 25444.1 | + | 25444.1i | 1.07767 | + | 1.07767i | 0.996718 | + | 0.0809559i | \(0.0257973\pi\) |
0.0809559 | + | 0.996718i | \(0.474203\pi\) | |||||||
\(824\) | −2122.57 | − | 523.000i | −0.0897368 | − | 0.0221111i | ||||
\(825\) | 13030.2 | − | 2002.73i | 0.549883 | − | 0.0845163i | ||||
\(826\) | −17712.2 | − | 37325.3i | −0.746108 | − | 1.57229i | ||||
\(827\) | 14358.8 | − | 14358.8i | 0.603756 | − | 0.603756i | −0.337551 | − | 0.941307i | \(-0.609599\pi\) |
0.941307 | + | 0.337551i | \(0.109599\pi\) | |||||||
\(828\) | −1453.45 | + | 146.919i | −0.0610034 | + | 0.00616642i | ||||
\(829\) | 1655.91i | 0.0693753i | 0.999398 | + | 0.0346877i | \(0.0110436\pi\) | ||||
−0.999398 | + | 0.0346877i | \(0.988956\pi\) | |||||||
\(830\) | 8296.62 | − | 1056.19i | 0.346964 | − | 0.0441700i | ||||
\(831\) | − | 7666.37i | − | 0.320028i | ||||||
\(832\) | 6249.00 | + | 20043.4i | 0.260391 | + | 0.835191i | ||||
\(833\) | 47730.4 | − | 47730.4i | 1.98531 | − | 1.98531i | ||||
\(834\) | −14977.5 | + | 7107.34i | −0.621855 | + | 0.295093i | ||||
\(835\) | 35991.2 | − | 18234.9i | 1.49165 | − | 0.755741i | ||||
\(836\) | 3711.69 | − | 4546.45i | 0.153554 | − | 0.188089i | ||||
\(837\) | −3503.33 | − | 3503.33i | −0.144675 | − | 0.144675i | ||||
\(838\) | −8378.86 | + | 23512.4i | −0.345397 | + | 0.969240i | ||||
\(839\) | 21952.9 | 0.903337 | 0.451669 | − | 0.892186i | \(-0.350829\pi\) | ||||
0.451669 | + | 0.892186i | \(0.350829\pi\) | |||||||
\(840\) | 25856.8 | − | 5982.35i | 1.06208 | − | 0.245727i | ||||
\(841\) | 9820.10 | 0.402645 | ||||||||
\(842\) | −15085.8 | + | 42333.3i | −0.617450 | + | 1.73266i | ||||
\(843\) | 6805.38 | + | 6805.38i | 0.278042 | + | 0.278042i | ||||
\(844\) | 309.743 | − | 379.404i | 0.0126325 | − | 0.0154735i | ||||
\(845\) | 1793.65 | − | 5477.62i | 0.0730217 | − | 0.223001i | ||||
\(846\) | −802.545 | + | 380.836i | −0.0326147 | + | 0.0154769i | ||||
\(847\) | −2351.77 | + | 2351.77i | −0.0954047 | + | 0.0954047i | ||||
\(848\) | 20400.0 | + | 13479.9i | 0.826108 | + | 0.545875i | ||||
\(849\) | 7042.44i | 0.284683i | ||||||||
\(850\) | −26636.9 | − | 5117.93i | −1.07487 | − | 0.206522i | ||||
\(851\) | − | 2761.93i | − | 0.111255i | ||||||
\(852\) | −6960.96 | + | 703.637i | −0.279905 | + | 0.0282937i | ||||
\(853\) | 2701.54 | − | 2701.54i | 0.108440 | − | 0.108440i | −0.650805 | − | 0.759245i | \(-0.725569\pi\) |
0.759245 | + | 0.650805i | \(0.225569\pi\) | |||||||
\(854\) | 4675.86 | + | 9853.53i | 0.187359 | + | 0.394825i | ||||
\(855\) | −653.461 | + | 1995.60i | −0.0261379 | + | 0.0798224i | ||||
\(856\) | −1638.25 | + | 6648.75i | −0.0654138 | + | 0.265478i | ||||
\(857\) | 9284.02 | + | 9284.02i | 0.370054 | + | 0.370054i | 0.867497 | − | 0.497443i | \(-0.165728\pi\) |
−0.497443 | + | 0.867497i | \(0.665728\pi\) | |||||||
\(858\) | −11522.3 | − | 4106.09i | −0.458468 | − | 0.163379i | ||||
\(859\) | −27094.0 | −1.07618 | −0.538089 | − | 0.842888i | \(-0.680854\pi\) | ||||
−0.538089 | + | 0.842888i | \(0.680854\pi\) | |||||||
\(860\) | 4330.00 | − | 19761.4i | 0.171688 | − | 0.783556i | ||||
\(861\) | 38098.5 | 1.50800 | ||||||||
\(862\) | 32014.4 | + | 11408.6i | 1.26498 | + | 0.450788i | ||||
\(863\) | −500.709 | − | 500.709i | −0.0197501 | − | 0.0197501i | 0.697163 | − | 0.716913i | \(-0.254445\pi\) |
−0.716913 | + | 0.697163i | \(0.754445\pi\) | |||||||
\(864\) | 3906.93 | − | 2936.62i | 0.153839 | − | 0.115632i | ||||
\(865\) | −28238.8 | + | 14307.2i | −1.11000 | + | 0.562379i | ||||
\(866\) | −19943.3 | − | 42026.9i | −0.782563 | − | 1.64911i | ||||
\(867\) | −2063.54 | + | 2063.54i | −0.0808321 | + | 0.0808321i | ||||
\(868\) | 5162.75 | + | 51074.2i | 0.201884 | + | 1.99720i | ||||
\(869\) | − | 4497.14i | − | 0.175552i | ||||||
\(870\) | 1446.06 | + | 11359.1i | 0.0563518 | + | 0.442654i | ||||
\(871\) | 2980.79i | 0.115959i | ||||||||
\(872\) | 13799.8 | + | 22823.8i | 0.535917 | + | 0.886368i | ||||
\(873\) | −6085.82 | + | 6085.82i | −0.235938 | + | 0.235938i | ||||
\(874\) | −1081.96 | + | 513.431i | −0.0418741 | + | 0.0198708i | ||||
\(875\) | 48215.8 | + | 7976.13i | 1.86285 | + | 0.308163i | ||||
\(876\) | 19793.5 | + | 16159.2i | 0.763423 | + | 0.623253i | ||||
\(877\) | −35402.9 | − | 35402.9i | −1.36314 | − | 1.36314i | −0.869887 | − | 0.493252i | \(-0.835808\pi\) |
−0.493252 | − | 0.869887i | \(-0.664192\pi\) | |||||||
\(878\) | −8594.44 | + | 24117.4i | −0.330351 | + | 0.927018i | ||||
\(879\) | −15540.3 | −0.596315 | ||||||||
\(880\) | −24989.0 | − | 2885.56i | −0.957248 | − | 0.110537i | ||||
\(881\) | 12786.2 | 0.488966 | 0.244483 | − | 0.969654i | \(-0.421382\pi\) | ||||
0.244483 | + | 0.969654i | \(0.421382\pi\) | |||||||
\(882\) | −7518.37 | + | 21097.7i | −0.287026 | + | 0.805440i | ||||
\(883\) | −24669.9 | − | 24669.9i | −0.940212 | − | 0.940212i | 0.0580988 | − | 0.998311i | \(-0.481496\pi\) |
−0.998311 | + | 0.0580988i | \(0.981496\pi\) | |||||||
\(884\) | 19495.5 | + | 15916.0i | 0.741746 | + | 0.605556i | ||||
\(885\) | −6331.98 | − | 12497.8i | −0.240505 | − | 0.474699i | ||||
\(886\) | 44097.4 | − | 20925.8i | 1.67210 | − | 0.793472i | ||||
\(887\) | −36047.5 | + | 36047.5i | −1.36455 | + | 1.36455i | −0.496535 | + | 0.868017i | \(0.665395\pi\) |
−0.868017 | + | 0.496535i | \(0.834605\pi\) | |||||||
\(888\) | 4781.03 | + | 7907.48i | 0.180677 | + | 0.298826i | ||||
\(889\) | − | 71814.2i | − | 2.70931i | ||||||
\(890\) | 1276.44 | + | 988.146i | 0.0480745 | + | 0.0372165i | ||||
\(891\) | 2847.57i | 0.107068i | ||||||||
\(892\) | 3132.21 | + | 30986.4i | 0.117572 | + | 1.16312i | ||||
\(893\) | −514.946 | + | 514.946i | −0.0192968 | + | 0.0192968i | ||||
\(894\) | 1449.07 | + | 3053.65i | 0.0542104 | + | 0.114239i | ||||
\(895\) | −13110.8 | − | 4293.15i | −0.489661 | − | 0.160340i | ||||
\(896\) | −50600.2 | − | 2030.42i | −1.88665 | − | 0.0757049i | ||||
\(897\) | 1764.92 | + | 1764.92i | 0.0656956 | + | 0.0656956i | ||||
\(898\) | 765.289 | + | 272.718i | 0.0284388 | + | 0.0101344i | ||||
\(899\) | −22148.6 | −0.821687 | ||||||||
\(900\) | 8712.94 | − | 2254.93i | 0.322701 | − | 0.0835160i | ||||
\(901\) | 29310.6 | 1.08377 | ||||||||
\(902\) | −34015.3 | − | 12121.6i | −1.25564 | − | 0.447458i | ||||
\(903\) | 16778.3 | + | 16778.3i | 0.618325 | + | 0.618325i | ||||
\(904\) | −6801.32 | + | 27602.8i | −0.250231 | + | 1.01555i | ||||
\(905\) | −35830.2 | − | 11732.6i | −1.31606 | − | 0.430945i | ||||
\(906\) | 5199.49 | + | 10957.0i | 0.190664 | + | 0.401790i | ||||
\(907\) | 21947.1 | − | 21947.1i | 0.803465 | − | 0.803465i | −0.180170 | − | 0.983635i | \(-0.557665\pi\) |
0.983635 | + | 0.180170i | \(0.0576649\pi\) | |||||||
\(908\) | −12123.4 | + | 1225.48i | −0.443095 | + | 0.0447895i | ||||
\(909\) | − | 6950.03i | − | 0.253595i | ||||||
\(910\) | −35856.4 | − | 27758.0i | −1.30618 | − | 1.01117i | ||||
\(911\) | 23974.7i | 0.871919i | 0.899966 | + | 0.435960i | \(0.143591\pi\) | ||||
−0.899966 | + | 0.435960i | \(0.856409\pi\) | |||||||
\(912\) | 2208.92 | − | 3342.90i | 0.0802024 | − | 0.121375i | ||||
\(913\) | 6574.56 | − | 6574.56i | 0.238320 | − | 0.238320i | ||||
\(914\) | 4478.44 | − | 2125.18i | 0.162072 | − | 0.0769088i | ||||
\(915\) | 1671.59 | + | 3299.31i | 0.0603945 | + | 0.119204i | ||||
\(916\) | 11078.0 | − | 13569.4i | 0.399592 | − | 0.489460i | ||||
\(917\) | −7586.48 | − | 7586.48i | −0.273204 | − | 0.273204i | ||||
\(918\) | 1966.70 | − | 5518.86i | 0.0707088 | − | 0.198420i | ||||
\(919\) | −12744.3 | −0.457448 | −0.228724 | − | 0.973491i | \(-0.573455\pi\) | ||||
−0.228724 | + | 0.973491i | \(0.573455\pi\) | |||||||
\(920\) | 4354.24 | + | 2717.98i | 0.156038 | + | 0.0974012i | ||||
\(921\) | −17609.4 | −0.630021 | ||||||||
\(922\) | 5977.48 | − | 16773.8i | 0.213512 | − | 0.599148i | ||||
\(923\) | 8452.69 | + | 8452.69i | 0.301434 | + | 0.301434i | ||||
\(924\) | 18658.9 | − | 22855.2i | 0.664319 | − | 0.813725i | ||||
\(925\) | 2584.93 | + | 16818.2i | 0.0918832 | + | 0.597814i | ||||
\(926\) | −7618.44 | + | 3615.23i | −0.270365 | + | 0.128298i | ||||
\(927\) | 614.827 | − | 614.827i | 0.0217838 | − | 0.0217838i | ||||
\(928\) | 3067.23 | − | 21633.0i | 0.108499 | − | 0.765234i | ||||
\(929\) | 39451.0i | 1.39327i | 0.717427 | + | 0.696634i | \(0.245320\pi\) | ||||
−0.717427 | + | 0.696634i | \(0.754680\pi\) | |||||||
\(930\) | 2198.40 | + | 17268.8i | 0.0775142 | + | 0.608889i | ||||
\(931\) | 18361.3i | 0.646366i | ||||||||
\(932\) | −38395.2 | + | 3881.11i | −1.34944 | + | 0.136406i | ||||
\(933\) | 9157.15 | − | 9157.15i | 0.321320 | − | 0.321320i | ||||
\(934\) | −22951.1 | − | 48365.4i | −0.804051 | − | 1.69439i | ||||
\(935\) | −26898.7 | + | 13628.2i | −0.940837 | + | 0.476673i | ||||
\(936\) | −8108.17 | − | 1997.85i | −0.283145 | − | 0.0697670i | ||||
\(937\) | 13496.0 | + | 13496.0i | 0.470539 | + | 0.470539i | 0.902089 | − | 0.431550i | \(-0.142033\pi\) |
−0.431550 | + | 0.902089i | \(0.642033\pi\) | |||||||
\(938\) | −6772.64 | − | 2413.49i | −0.235751 | − | 0.0840120i | ||||
\(939\) | 18664.5 | 0.648662 | ||||||||
\(940\) | 3048.91 | + | 668.060i | 0.105792 | + | 0.0231805i | ||||
\(941\) | 19991.7 | 0.692574 | 0.346287 | − | 0.938129i | \(-0.387442\pi\) | ||||
0.346287 | + | 0.938129i | \(0.387442\pi\) | |||||||
\(942\) | 2869.70 | + | 1022.64i | 0.0992566 | + | 0.0353710i | ||||
\(943\) | 5210.25 | + | 5210.25i | 0.179925 | + | 0.179925i | ||||
\(944\) | 5349.91 | + | 26192.5i | 0.184454 | + | 0.903064i | ||||
\(945\) | −3284.98 | + | 10032.0i | −0.113080 | + | 0.345335i | ||||
\(946\) | −9641.82 | − | 20318.4i | −0.331377 | − | 0.698318i | ||||
\(947\) | −11191.3 | + | 11191.3i | −0.384023 | + | 0.384023i | −0.872549 | − | 0.488526i | \(-0.837535\pi\) |
0.488526 | + | 0.872549i | \(0.337535\pi\) | |||||||
\(948\) | −308.766 | − | 3054.57i | −0.0105783 | − | 0.104650i | ||||
\(949\) | − | 43657.3i | − | 1.49334i | ||||||
\(950\) | 6107.85 | − | 4139.05i | 0.208595 | − | 0.141356i | ||||
\(951\) | − | 31551.5i | − | 1.07585i | ||||||
\(952\) | −51947.7 | + | 31408.7i | −1.76852 | + | 1.06929i | ||||
\(953\) | 2419.80 | − | 2419.80i | 0.0822506 | − | 0.0822506i | −0.664785 | − | 0.747035i | \(-0.731477\pi\) |
0.747035 | + | 0.664785i | \(0.231477\pi\) | |||||||
\(954\) | −8786.37 | + | 4169.45i | −0.298186 | + | 0.141500i | ||||
\(955\) | 828.482 | − | 2530.10i | 0.0280723 | − | 0.0857299i | ||||
\(956\) | 35404.3 | + | 28903.8i | 1.19776 | + | 0.977842i | ||||
\(957\) | 9001.39 | + | 9001.39i | 0.304048 | + | 0.304048i | ||||
\(958\) | 918.020 | − | 2576.11i | 0.0309602 | − | 0.0868792i | ||||
\(959\) | 10489.7 | 0.353213 | ||||||||
\(960\) | −17171.3 | − | 244.246i | −0.577292 | − | 0.00821145i | ||||
\(961\) | −3880.70 | −0.130264 | ||||||||
\(962\) | 5299.75 | − | 14871.9i | 0.177620 | − | 0.498431i | ||||
\(963\) | −1925.89 | − | 1925.89i | −0.0644454 | − | 0.0644454i | ||||
\(964\) | 16101.0 | + | 13144.8i | 0.537945 | + | 0.439174i | ||||
\(965\) | 28067.9 | − | 14220.6i | 0.936309 | − | 0.474379i | ||||
\(966\) | −5439.09 | + | 2581.05i | −0.181159 | + | 0.0859666i | ||||
\(967\) | 34223.1 | − | 34223.1i | 1.13810 | − | 1.13810i | 0.149308 | − | 0.988791i | \(-0.452295\pi\) |
0.988791 | − | 0.149308i | \(-0.0477046\pi\) | |||||||
\(968\) | 1841.63 | − | 1113.49i | 0.0611489 | − | 0.0369719i | ||||
\(969\) | − | 4803.05i | − | 0.159232i | ||||||
\(970\) | 29998.6 | − | 3818.95i | 0.992985 | − | 0.126411i | ||||
\(971\) | − | 6050.87i | − | 0.199981i | −0.994988 | − | 0.0999906i | \(-0.968119\pi\) | ||
0.994988 | − | 0.0999906i | \(-0.0318813\pi\) | |||||||
\(972\) | 195.510 | + | 1934.14i | 0.00645162 | + | 0.0638248i | ||||
\(973\) | −48310.8 | + | 48310.8i | −1.59175 | + | 1.59175i | ||||
\(974\) | 4185.08 | + | 8819.31i | 0.137678 | + | 0.290132i | ||||
\(975\) | −12398.9 | − | 9095.27i | −0.407264 | − | 0.298751i | ||||
\(976\) | −1412.33 | − | 6914.58i | −0.0463191 | − | 0.226773i | ||||
\(977\) | −37140.0 | − | 37140.0i | −1.21619 | − | 1.21619i | −0.968957 | − | 0.247230i | \(-0.920480\pi\) |
−0.247230 | − | 0.968957i | \(-0.579520\pi\) | |||||||
\(978\) | −29377.9 | − | 10469.1i | −0.960534 | − | 0.342295i | ||||
\(979\) | 1794.54 | 0.0585842 | ||||||||
\(980\) | 66267.5 | − | 42446.7i | 2.16004 | − | 1.38358i | ||||
\(981\) | −10608.5 | −0.345262 | ||||||||
\(982\) | −11932.9 | − | 4252.41i | −0.387775 | − | 0.138187i | ||||
\(983\) | 1908.75 | + | 1908.75i | 0.0619325 | + | 0.0619325i | 0.737395 | − | 0.675462i | \(-0.236056\pi\) |
−0.675462 | + | 0.737395i | \(0.736056\pi\) | |||||||
\(984\) | −23936.3 | − | 5897.90i | −0.775468 | − | 0.191075i | ||||
\(985\) | 11947.2 | + | 23580.8i | 0.386466 | + | 0.762790i | ||||
\(986\) | −11228.7 | − | 23662.4i | −0.362671 | − | 0.764264i | ||||
\(987\) | −2588.66 | + | 2588.66i | −0.0834833 | + | 0.0834833i | ||||
\(988\) | −6811.16 | + | 688.495i | −0.219324 | + | 0.0221700i | ||||
\(989\) | 4589.12i | 0.147549i | ||||||||
\(990\) | 6124.76 | − | 7911.66i | 0.196624 | − | 0.253989i | ||||
\(991\) | − | 33844.2i | − | 1.08486i | −0.840101 | − | 0.542430i | \(-0.817505\pi\) | ||
0.840101 | − | 0.542430i | \(-0.182495\pi\) | |||||||
\(992\) | 4663.01 | − | 32887.8i | 0.149245 | − | 1.05261i | ||||
\(993\) | 19986.2 | − | 19986.2i | 0.638714 | − | 0.638714i | ||||
\(994\) | −26049.3 | + | 12361.3i | −0.831222 | + | 0.394445i | ||||
\(995\) | −48200.3 | − | 15783.2i | −1.53573 | − | 0.502876i | ||||
\(996\) | 4014.21 | − | 4917.01i | 0.127706 | − | 0.156427i | ||||
\(997\) | 1241.05 | + | 1241.05i | 0.0394227 | + | 0.0394227i | 0.726543 | − | 0.687121i | \(-0.241126\pi\) |
−0.687121 | + | 0.726543i | \(0.741126\pi\) | |||||||
\(998\) | −3720.25 | + | 10439.6i | −0.117998 | + | 0.331122i | ||||
\(999\) | −3675.38 | −0.116400 |
(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 | 60.4.j.b.7.6 | ✓ | 28 | |
3.2 | odd | 2 | 180.4.k.f.127.9 | 28 | |||
4.3 | odd | 2 | inner | 60.4.j.b.7.13 | yes | 28 | |
5.3 | odd | 4 | inner | 60.4.j.b.43.13 | yes | 28 | |
12.11 | even | 2 | 180.4.k.f.127.2 | 28 | |||
15.8 | even | 4 | 180.4.k.f.163.2 | 28 | |||
20.3 | even | 4 | inner | 60.4.j.b.43.6 | yes | 28 | |
60.23 | odd | 4 | 180.4.k.f.163.9 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.j.b.7.6 | ✓ | 28 | 1.1 | even | 1 | trivial | |
60.4.j.b.7.13 | yes | 28 | 4.3 | odd | 2 | inner | |
60.4.j.b.43.6 | yes | 28 | 20.3 | even | 4 | inner | |
60.4.j.b.43.13 | yes | 28 | 5.3 | odd | 4 | inner | |
180.4.k.f.127.2 | 28 | 12.11 | even | 2 | |||
180.4.k.f.127.9 | 28 | 3.2 | odd | 2 | |||
180.4.k.f.163.2 | 28 | 15.8 | even | 4 | |||
180.4.k.f.163.9 | 28 | 60.23 | odd | 4 |