Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.6 | ||
Root | \(-1.86235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.15 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.86235i | − | 0.931176i | −0.885001 | − | 0.465588i | \(-0.845843\pi\) | ||
0.885001 | − | 0.465588i | \(-0.154157\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0.531642 | 0.132910 | ||||||||
\(5\) | −9.04540 | −1.80908 | −0.904540 | − | 0.426388i | \(-0.859786\pi\) | ||||
−0.904540 | + | 0.426388i | \(0.859786\pi\) | |||||||
\(6\) | 3.22569i | 0.537615i | ||||||||
\(7\) | 1.29987 | 0.185696 | 0.0928478 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928478 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(8\) | − | 8.43952i | − | 1.05494i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 16.8457i | 1.68457i | ||||||||
\(11\) | 12.8790i | 1.17082i | 0.810736 | + | 0.585411i | \(0.199067\pi\) | ||||
−0.810736 | + | 0.585411i | \(0.800933\pi\) | |||||||
\(12\) | −0.920831 | −0.0767359 | ||||||||
\(13\) | 23.5709i | 1.81315i | 0.422050 | + | 0.906573i | \(0.361311\pi\) | ||||
−0.422050 | + | 0.906573i | \(0.638689\pi\) | |||||||
\(14\) | − | 2.42081i | − | 0.172915i | ||||||
\(15\) | 15.6671 | 1.04447 | ||||||||
\(16\) | −13.5908 | −0.849424 | ||||||||
\(17\) | −10.1284 | −0.595790 | −0.297895 | − | 0.954599i | \(-0.596285\pi\) | ||||
−0.297895 | + | 0.954599i | \(0.596285\pi\) | |||||||
\(18\) | − | 5.58706i | − | 0.310392i | ||||||
\(19\) | −23.3600 | −1.22948 | −0.614738 | − | 0.788731i | \(-0.710738\pi\) | ||||
−0.614738 | + | 0.788731i | \(0.710738\pi\) | |||||||
\(20\) | −4.80892 | −0.240446 | ||||||||
\(21\) | −2.25144 | −0.107211 | ||||||||
\(22\) | 23.9853 | 1.09024 | ||||||||
\(23\) | 9.25801i | 0.402522i | 0.979538 | + | 0.201261i | \(0.0645039\pi\) | ||||
−0.979538 | + | 0.201261i | \(0.935496\pi\) | |||||||
\(24\) | 14.6177i | 0.609070i | ||||||||
\(25\) | 56.8193 | 2.27277 | ||||||||
\(26\) | 43.8973 | 1.68836 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0.691065 | 0.0246809 | ||||||||
\(29\) | −25.9681 | −0.895452 | −0.447726 | − | 0.894171i | \(-0.647766\pi\) | ||||
−0.447726 | + | 0.894171i | \(0.647766\pi\) | |||||||
\(30\) | − | 29.1777i | − | 0.972589i | ||||||
\(31\) | − | 28.4380i | − | 0.917355i | −0.888603 | − | 0.458678i | \(-0.848323\pi\) | ||
0.888603 | − | 0.458678i | \(-0.151677\pi\) | |||||||
\(32\) | − | 8.44722i | − | 0.263976i | ||||||
\(33\) | − | 22.3072i | − | 0.675975i | ||||||
\(34\) | 18.8627i | 0.554786i | ||||||||
\(35\) | −11.7578 | −0.335938 | ||||||||
\(36\) | 1.59493 | 0.0443035 | ||||||||
\(37\) | 22.3933i | 0.605225i | 0.953114 | + | 0.302613i | \(0.0978588\pi\) | ||||
−0.953114 | + | 0.302613i | \(0.902141\pi\) | |||||||
\(38\) | 43.5046i | 1.14486i | ||||||||
\(39\) | − | 40.8260i | − | 1.04682i | ||||||
\(40\) | 76.3388i | 1.90847i | ||||||||
\(41\) | −44.4678 | −1.08458 | −0.542290 | − | 0.840191i | \(-0.682443\pi\) | ||||
−0.542290 | + | 0.840191i | \(0.682443\pi\) | |||||||
\(42\) | 4.19297i | 0.0998327i | ||||||||
\(43\) | − | 42.8166i | − | 0.995736i | −0.867253 | − | 0.497868i | \(-0.834116\pi\) | ||
0.867253 | − | 0.497868i | \(-0.165884\pi\) | |||||||
\(44\) | 6.84704i | 0.155615i | ||||||||
\(45\) | −27.1362 | −0.603027 | ||||||||
\(46\) | 17.2417 | 0.374819 | ||||||||
\(47\) | − | 30.6792i | − | 0.652749i | −0.945241 | − | 0.326374i | \(-0.894173\pi\) | ||
0.945241 | − | 0.326374i | \(-0.105827\pi\) | |||||||
\(48\) | 23.5399 | 0.490415 | ||||||||
\(49\) | −47.3103 | −0.965517 | ||||||||
\(50\) | − | 105.818i | − | 2.11635i | ||||||
\(51\) | 17.5430 | 0.343980 | ||||||||
\(52\) | 12.5313i | 0.240986i | ||||||||
\(53\) | 41.9742 | 0.791967 | 0.395983 | − | 0.918258i | \(-0.370404\pi\) | ||||
0.395983 | + | 0.918258i | \(0.370404\pi\) | |||||||
\(54\) | 9.67707i | 0.179205i | ||||||||
\(55\) | − | 116.496i | − | 2.11811i | ||||||
\(56\) | − | 10.9703i | − | 0.195898i | ||||||
\(57\) | 40.4608 | 0.709838 | ||||||||
\(58\) | 48.3618i | 0.833824i | ||||||||
\(59\) | −2.69759 | + | 58.9383i | −0.0457219 | + | 0.998954i | ||||
\(60\) | 8.32929 | 0.138821 | ||||||||
\(61\) | − | 31.9823i | − | 0.524300i | −0.965027 | − | 0.262150i | \(-0.915569\pi\) | ||
0.965027 | − | 0.262150i | \(-0.0844315\pi\) | |||||||
\(62\) | −52.9616 | −0.854219 | ||||||||
\(63\) | 3.89961 | 0.0618985 | ||||||||
\(64\) | −70.0949 | −1.09523 | ||||||||
\(65\) | − | 213.208i | − | 3.28013i | ||||||
\(66\) | −41.5438 | −0.629452 | ||||||||
\(67\) | 94.0998i | 1.40447i | 0.711943 | + | 0.702237i | \(0.247815\pi\) | ||||
−0.711943 | + | 0.702237i | \(0.752185\pi\) | |||||||
\(68\) | −5.38470 | −0.0791868 | ||||||||
\(69\) | − | 16.0353i | − | 0.232396i | ||||||
\(70\) | 21.8972i | 0.312818i | ||||||||
\(71\) | 5.78244 | 0.0814428 | 0.0407214 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407214 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(72\) | − | 25.3185i | − | 0.351647i | ||||||
\(73\) | 41.5942i | 0.569783i | 0.958560 | + | 0.284892i | \(0.0919577\pi\) | ||||
−0.958560 | + | 0.284892i | \(0.908042\pi\) | |||||||
\(74\) | 41.7043 | 0.563571 | ||||||||
\(75\) | −98.4139 | −1.31219 | ||||||||
\(76\) | −12.4192 | −0.163410 | ||||||||
\(77\) | 16.7411i | 0.217417i | ||||||||
\(78\) | −76.0324 | −0.974774 | ||||||||
\(79\) | −105.782 | −1.33901 | −0.669503 | − | 0.742809i | \(-0.733493\pi\) | ||||
−0.669503 | + | 0.742809i | \(0.733493\pi\) | |||||||
\(80\) | 122.934 | 1.53668 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 82.8148i | 1.00994i | ||||||||
\(83\) | − | 3.14451i | − | 0.0378857i | −0.999821 | − | 0.0189428i | \(-0.993970\pi\) | ||
0.999821 | − | 0.0189428i | \(-0.00603006\pi\) | |||||||
\(84\) | −1.19696 | −0.0142495 | ||||||||
\(85\) | 91.6157 | 1.07783 | ||||||||
\(86\) | −79.7397 | −0.927206 | ||||||||
\(87\) | 44.9781 | 0.516990 | ||||||||
\(88\) | 108.693 | 1.23515 | ||||||||
\(89\) | − | 21.8316i | − | 0.245299i | −0.992450 | − | 0.122649i | \(-0.960861\pi\) | ||
0.992450 | − | 0.122649i | \(-0.0391391\pi\) | |||||||
\(90\) | 50.5372i | 0.561524i | ||||||||
\(91\) | 30.6391i | 0.336693i | ||||||||
\(92\) | 4.92194i | 0.0534994i | ||||||||
\(93\) | 49.2561i | 0.529635i | ||||||||
\(94\) | −57.1355 | −0.607824 | ||||||||
\(95\) | 211.301 | 2.22422 | ||||||||
\(96\) | 14.6310i | 0.152406i | ||||||||
\(97\) | − | 126.206i | − | 1.30109i | −0.759468 | − | 0.650544i | \(-0.774541\pi\) | ||
0.759468 | − | 0.650544i | \(-0.225459\pi\) | |||||||
\(98\) | 88.1085i | 0.899067i | ||||||||
\(99\) | 38.6371i | 0.390274i | ||||||||
\(100\) | 30.2075 | 0.302075 | ||||||||
\(101\) | 71.4450i | 0.707376i | 0.935363 | + | 0.353688i | \(0.115073\pi\) | ||||
−0.935363 | + | 0.353688i | \(0.884927\pi\) | |||||||
\(102\) | − | 32.6712i | − | 0.320306i | ||||||
\(103\) | 166.064i | 1.61228i | 0.591728 | + | 0.806138i | \(0.298446\pi\) | ||||
−0.591728 | + | 0.806138i | \(0.701554\pi\) | |||||||
\(104\) | 198.927 | 1.91276 | ||||||||
\(105\) | 20.3652 | 0.193954 | ||||||||
\(106\) | − | 78.1708i | − | 0.737461i | ||||||
\(107\) | 27.6484 | 0.258396 | 0.129198 | − | 0.991619i | \(-0.458760\pi\) | ||||
0.129198 | + | 0.991619i | \(0.458760\pi\) | |||||||
\(108\) | −2.76249 | −0.0255786 | ||||||||
\(109\) | − | 110.232i | − | 1.01130i | −0.862738 | − | 0.505651i | \(-0.831252\pi\) | ||
0.862738 | − | 0.505651i | \(-0.168748\pi\) | |||||||
\(110\) | −216.957 | −1.97234 | ||||||||
\(111\) | − | 38.7864i | − | 0.349427i | ||||||
\(112\) | −17.6662 | −0.157734 | ||||||||
\(113\) | 69.5553i | 0.615534i | 0.951462 | + | 0.307767i | \(0.0995817\pi\) | ||||
−0.951462 | + | 0.307767i | \(0.900418\pi\) | |||||||
\(114\) | − | 75.3522i | − | 0.660985i | ||||||
\(115\) | − | 83.7424i | − | 0.728195i | ||||||
\(116\) | −13.8057 | −0.119015 | ||||||||
\(117\) | 70.7127i | 0.604382i | ||||||||
\(118\) | 109.764 | + | 5.02387i | 0.930203 | + | 0.0425752i | ||||
\(119\) | −13.1656 | −0.110636 | ||||||||
\(120\) | − | 132.223i | − | 1.10186i | ||||||
\(121\) | −44.8699 | −0.370826 | ||||||||
\(122\) | −59.5623 | −0.488215 | ||||||||
\(123\) | 77.0205 | 0.626183 | ||||||||
\(124\) | − | 15.1188i | − | 0.121926i | ||||||
\(125\) | −287.818 | −2.30255 | ||||||||
\(126\) | − | 7.26244i | − | 0.0576384i | ||||||
\(127\) | 218.788 | 1.72274 | 0.861370 | − | 0.507977i | \(-0.169607\pi\) | ||||
0.861370 | + | 0.507977i | \(0.169607\pi\) | |||||||
\(128\) | 96.7525i | 0.755879i | ||||||||
\(129\) | 74.1606i | 0.574888i | ||||||||
\(130\) | −397.069 | −3.05438 | ||||||||
\(131\) | 245.998i | 1.87785i | 0.344127 | + | 0.938923i | \(0.388175\pi\) | ||||
−0.344127 | + | 0.938923i | \(0.611825\pi\) | |||||||
\(132\) | − | 11.8594i | − | 0.0898441i | ||||||
\(133\) | −30.3650 | −0.228308 | ||||||||
\(134\) | 175.247 | 1.30781 | ||||||||
\(135\) | 47.0013 | 0.348158 | ||||||||
\(136\) | 85.4791i | 0.628522i | ||||||||
\(137\) | 250.848 | 1.83101 | 0.915504 | − | 0.402308i | \(-0.131792\pi\) | ||||
0.915504 | + | 0.402308i | \(0.131792\pi\) | |||||||
\(138\) | −29.8635 | −0.216402 | ||||||||
\(139\) | −14.5923 | −0.104981 | −0.0524903 | − | 0.998621i | \(-0.516716\pi\) | ||||
−0.0524903 | + | 0.998621i | \(0.516716\pi\) | |||||||
\(140\) | −6.25096 | −0.0446497 | ||||||||
\(141\) | 53.1379i | 0.376865i | ||||||||
\(142\) | − | 10.7689i | − | 0.0758376i | ||||||
\(143\) | −303.571 | −2.12287 | ||||||||
\(144\) | −40.7724 | −0.283141 | ||||||||
\(145\) | 234.892 | 1.61995 | ||||||||
\(146\) | 77.4631 | 0.530569 | ||||||||
\(147\) | 81.9439 | 0.557442 | ||||||||
\(148\) | 11.9052i | 0.0804408i | ||||||||
\(149\) | − | 182.069i | − | 1.22194i | −0.791653 | − | 0.610971i | \(-0.790779\pi\) | ||
0.791653 | − | 0.610971i | \(-0.209221\pi\) | |||||||
\(150\) | 183.281i | 1.22188i | ||||||||
\(151\) | − | 31.7495i | − | 0.210262i | −0.994458 | − | 0.105131i | \(-0.966474\pi\) | ||
0.994458 | − | 0.105131i | \(-0.0335262\pi\) | |||||||
\(152\) | 197.147i | 1.29702i | ||||||||
\(153\) | −30.3853 | −0.198597 | ||||||||
\(154\) | 31.1778 | 0.202453 | ||||||||
\(155\) | 257.233i | 1.65957i | ||||||||
\(156\) | − | 21.7048i | − | 0.139133i | ||||||
\(157\) | − | 243.661i | − | 1.55198i | −0.630744 | − | 0.775991i | \(-0.717250\pi\) | ||
0.630744 | − | 0.775991i | \(-0.282750\pi\) | |||||||
\(158\) | 197.002i | 1.24685i | ||||||||
\(159\) | −72.7015 | −0.457242 | ||||||||
\(160\) | 76.4085i | 0.477553i | ||||||||
\(161\) | 12.0342i | 0.0747465i | ||||||||
\(162\) | − | 16.7612i | − | 0.103464i | ||||||
\(163\) | −9.01747 | −0.0553219 | −0.0276610 | − | 0.999617i | \(-0.508806\pi\) | ||||
−0.0276610 | + | 0.999617i | \(0.508806\pi\) | |||||||
\(164\) | −23.6410 | −0.144152 | ||||||||
\(165\) | 201.777i | 1.22289i | ||||||||
\(166\) | −5.85619 | −0.0352783 | ||||||||
\(167\) | −134.849 | −0.807482 | −0.403741 | − | 0.914873i | \(-0.632290\pi\) | ||||
−0.403741 | + | 0.914873i | \(0.632290\pi\) | |||||||
\(168\) | 19.0011i | 0.113102i | ||||||||
\(169\) | −386.587 | −2.28750 | ||||||||
\(170\) | − | 170.621i | − | 1.00365i | ||||||
\(171\) | −70.0801 | −0.409825 | ||||||||
\(172\) | − | 22.7631i | − | 0.132344i | ||||||
\(173\) | − | 273.027i | − | 1.57819i | −0.614271 | − | 0.789095i | \(-0.710550\pi\) | ||
0.614271 | − | 0.789095i | \(-0.289450\pi\) | |||||||
\(174\) | − | 83.7651i | − | 0.481409i | ||||||
\(175\) | 73.8576 | 0.422044 | ||||||||
\(176\) | − | 175.036i | − | 0.994525i | ||||||
\(177\) | 4.67237 | − | 102.084i | 0.0263976 | − | 0.576746i | ||||
\(178\) | −40.6581 | −0.228417 | ||||||||
\(179\) | 110.268i | 0.616025i | 0.951382 | + | 0.308012i | \(0.0996638\pi\) | ||||
−0.951382 | + | 0.308012i | \(0.900336\pi\) | |||||||
\(180\) | −14.4267 | −0.0801486 | ||||||||
\(181\) | 21.7461 | 0.120144 | 0.0600721 | − | 0.998194i | \(-0.480867\pi\) | ||||
0.0600721 | + | 0.998194i | \(0.480867\pi\) | |||||||
\(182\) | 57.0607 | 0.313521 | ||||||||
\(183\) | 55.3949i | 0.302705i | ||||||||
\(184\) | 78.1331 | 0.424636 | ||||||||
\(185\) | − | 202.557i | − | 1.09490i | ||||||
\(186\) | 91.7322 | 0.493184 | ||||||||
\(187\) | − | 130.445i | − | 0.697564i | ||||||
\(188\) | − | 16.3104i | − | 0.0867572i | ||||||
\(189\) | −6.75432 | −0.0357371 | ||||||||
\(190\) | − | 393.517i | − | 2.07114i | ||||||
\(191\) | − | 25.4664i | − | 0.133332i | −0.997775 | − | 0.0666660i | \(-0.978764\pi\) | ||
0.997775 | − | 0.0666660i | \(-0.0212362\pi\) | |||||||
\(192\) | 121.408 | 0.632333 | ||||||||
\(193\) | −140.722 | −0.729130 | −0.364565 | − | 0.931178i | \(-0.618782\pi\) | ||||
−0.364565 | + | 0.931178i | \(0.618782\pi\) | |||||||
\(194\) | −235.039 | −1.21154 | ||||||||
\(195\) | 369.287i | 1.89378i | ||||||||
\(196\) | −25.1522 | −0.128327 | ||||||||
\(197\) | −221.365 | −1.12368 | −0.561841 | − | 0.827245i | \(-0.689907\pi\) | ||||
−0.561841 | + | 0.827245i | \(0.689907\pi\) | |||||||
\(198\) | 71.9560 | 0.363414 | ||||||||
\(199\) | 282.321 | 1.41870 | 0.709348 | − | 0.704858i | \(-0.248989\pi\) | ||||
0.709348 | + | 0.704858i | \(0.248989\pi\) | |||||||
\(200\) | − | 479.527i | − | 2.39764i | ||||||
\(201\) | − | 162.986i | − | 0.810873i | ||||||
\(202\) | 133.056 | 0.658692 | ||||||||
\(203\) | −33.7551 | −0.166282 | ||||||||
\(204\) | 9.32657 | 0.0457185 | ||||||||
\(205\) | 402.229 | 1.96209 | ||||||||
\(206\) | 309.270 | 1.50131 | ||||||||
\(207\) | 27.7740i | 0.134174i | ||||||||
\(208\) | − | 320.347i | − | 1.54013i | ||||||
\(209\) | − | 300.855i | − | 1.43950i | ||||||
\(210\) | − | 37.9271i | − | 0.180605i | ||||||
\(211\) | − | 2.24194i | − | 0.0106253i | −0.999986 | − | 0.00531265i | \(-0.998309\pi\) | ||
0.999986 | − | 0.00531265i | \(-0.00169108\pi\) | |||||||
\(212\) | 22.3153 | 0.105261 | ||||||||
\(213\) | −10.0155 | −0.0470210 | ||||||||
\(214\) | − | 51.4910i | − | 0.240612i | ||||||
\(215\) | 387.294i | 1.80137i | ||||||||
\(216\) | 43.8530i | 0.203023i | ||||||||
\(217\) | − | 36.9657i | − | 0.170349i | ||||||
\(218\) | −205.291 | −0.941701 | ||||||||
\(219\) | − | 72.0433i | − | 0.328965i | ||||||
\(220\) | − | 61.9343i | − | 0.281519i | ||||||
\(221\) | − | 238.736i | − | 1.08025i | ||||||
\(222\) | −72.2339 | −0.325378 | ||||||||
\(223\) | −313.196 | −1.40447 | −0.702234 | − | 0.711946i | \(-0.747814\pi\) | ||||
−0.702234 | + | 0.711946i | \(0.747814\pi\) | |||||||
\(224\) | − | 10.9803i | − | 0.0490191i | ||||||
\(225\) | 170.458 | 0.757591 | ||||||||
\(226\) | 129.537 | 0.573170 | ||||||||
\(227\) | 398.887i | 1.75721i | 0.477548 | + | 0.878605i | \(0.341526\pi\) | ||||
−0.477548 | + | 0.878605i | \(0.658474\pi\) | |||||||
\(228\) | 21.5106 | 0.0943449 | ||||||||
\(229\) | − | 52.2219i | − | 0.228043i | −0.993478 | − | 0.114022i | \(-0.963627\pi\) | ||
0.993478 | − | 0.114022i | \(-0.0363733\pi\) | |||||||
\(230\) | −155.958 | −0.678078 | ||||||||
\(231\) | − | 28.9964i | − | 0.125525i | ||||||
\(232\) | 219.158i | 0.944648i | ||||||||
\(233\) | 420.216i | 1.80350i | 0.432255 | + | 0.901751i | \(0.357718\pi\) | ||||
−0.432255 | + | 0.901751i | \(0.642282\pi\) | |||||||
\(234\) | 131.692 | 0.562786 | ||||||||
\(235\) | 277.506i | 1.18088i | ||||||||
\(236\) | −1.43415 | + | 31.3341i | −0.00607692 | + | 0.132771i | ||||
\(237\) | 183.219 | 0.773076 | ||||||||
\(238\) | 24.5191i | 0.103021i | ||||||||
\(239\) | −157.064 | −0.657171 | −0.328585 | − | 0.944474i | \(-0.606572\pi\) | ||||
−0.328585 | + | 0.944474i | \(0.606572\pi\) | |||||||
\(240\) | −212.928 | −0.887201 | ||||||||
\(241\) | 97.2511 | 0.403531 | 0.201766 | − | 0.979434i | \(-0.435332\pi\) | ||||
0.201766 | + | 0.979434i | \(0.435332\pi\) | |||||||
\(242\) | 83.5636i | 0.345304i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 17.0031i | − | 0.0696849i | ||||||
\(245\) | 427.941 | 1.74670 | ||||||||
\(246\) | − | 143.439i | − | 0.583087i | ||||||
\(247\) | − | 550.617i | − | 2.22922i | ||||||
\(248\) | −240.003 | −0.967754 | ||||||||
\(249\) | 5.44645i | 0.0218733i | ||||||||
\(250\) | 536.019i | 2.14408i | ||||||||
\(251\) | 298.241 | 1.18821 | 0.594105 | − | 0.804387i | \(-0.297506\pi\) | ||||
0.594105 | + | 0.804387i | \(0.297506\pi\) | |||||||
\(252\) | 2.07319 | 0.00822696 | ||||||||
\(253\) | −119.234 | −0.471282 | ||||||||
\(254\) | − | 407.461i | − | 1.60418i | ||||||
\(255\) | −158.683 | −0.622287 | ||||||||
\(256\) | −100.192 | −0.391376 | ||||||||
\(257\) | 398.043 | 1.54881 | 0.774403 | − | 0.632692i | \(-0.218050\pi\) | ||||
0.774403 | + | 0.632692i | \(0.218050\pi\) | |||||||
\(258\) | 138.113 | 0.535322 | ||||||||
\(259\) | 29.1084i | 0.112388i | ||||||||
\(260\) | − | 113.350i | − | 0.435963i | ||||||
\(261\) | −77.9044 | −0.298484 | ||||||||
\(262\) | 458.135 | 1.74861 | ||||||||
\(263\) | 205.829 | 0.782620 | 0.391310 | − | 0.920259i | \(-0.372022\pi\) | ||||
0.391310 | + | 0.920259i | \(0.372022\pi\) | |||||||
\(264\) | −188.262 | −0.713112 | ||||||||
\(265\) | −379.674 | −1.43273 | ||||||||
\(266\) | 56.5503i | 0.212595i | ||||||||
\(267\) | 37.8134i | 0.141623i | ||||||||
\(268\) | 50.0274i | 0.186669i | ||||||||
\(269\) | 161.097i | 0.598874i | 0.954116 | + | 0.299437i | \(0.0967989\pi\) | ||||
−0.954116 | + | 0.299437i | \(0.903201\pi\) | |||||||
\(270\) | − | 87.5330i | − | 0.324196i | ||||||
\(271\) | −222.809 | −0.822173 | −0.411086 | − | 0.911596i | \(-0.634851\pi\) | ||||
−0.411086 | + | 0.911596i | \(0.634851\pi\) | |||||||
\(272\) | 137.653 | 0.506079 | ||||||||
\(273\) | − | 53.0684i | − | 0.194390i | ||||||
\(274\) | − | 467.168i | − | 1.70499i | ||||||
\(275\) | 731.779i | 2.66101i | ||||||||
\(276\) | − | 8.52506i | − | 0.0308879i | ||||||
\(277\) | −407.546 | −1.47128 | −0.735642 | − | 0.677371i | \(-0.763119\pi\) | ||||
−0.735642 | + | 0.677371i | \(0.763119\pi\) | |||||||
\(278\) | 27.1760i | 0.0977555i | ||||||||
\(279\) | − | 85.3140i | − | 0.305785i | ||||||
\(280\) | 99.2304i | 0.354394i | ||||||||
\(281\) | −374.820 | −1.33388 | −0.666940 | − | 0.745112i | \(-0.732396\pi\) | ||||
−0.666940 | + | 0.745112i | \(0.732396\pi\) | |||||||
\(282\) | 98.9616 | 0.350928 | ||||||||
\(283\) | 361.855i | 1.27864i | 0.768941 | + | 0.639320i | \(0.220784\pi\) | ||||
−0.768941 | + | 0.639320i | \(0.779216\pi\) | |||||||
\(284\) | 3.07419 | 0.0108246 | ||||||||
\(285\) | −365.984 | −1.28415 | ||||||||
\(286\) | 565.356i | 1.97677i | ||||||||
\(287\) | −57.8023 | −0.201402 | ||||||||
\(288\) | − | 25.3417i | − | 0.0879919i | ||||||
\(289\) | −186.415 | −0.645034 | ||||||||
\(290\) | − | 437.452i | − | 1.50845i | ||||||
\(291\) | 218.595i | 0.751184i | ||||||||
\(292\) | 22.1132i | 0.0757302i | ||||||||
\(293\) | 299.087 | 1.02078 | 0.510388 | − | 0.859944i | \(-0.329502\pi\) | ||||
0.510388 | + | 0.859944i | \(0.329502\pi\) | |||||||
\(294\) | − | 152.608i | − | 0.519076i | ||||||
\(295\) | 24.4008 | − | 533.121i | 0.0827146 | − | 1.80719i | ||||
\(296\) | 188.989 | 0.638476 | ||||||||
\(297\) | − | 66.9215i | − | 0.225325i | ||||||
\(298\) | −339.078 | −1.13784 | ||||||||
\(299\) | −218.219 | −0.729831 | ||||||||
\(300\) | −52.3210 | −0.174403 | ||||||||
\(301\) | − | 55.6560i | − | 0.184904i | ||||||
\(302\) | −59.1288 | −0.195791 | ||||||||
\(303\) | − | 123.746i | − | 0.408404i | ||||||
\(304\) | 317.481 | 1.04435 | ||||||||
\(305\) | 289.293i | 0.948500i | ||||||||
\(306\) | 56.5881i | 0.184929i | ||||||||
\(307\) | 183.459 | 0.597585 | 0.298793 | − | 0.954318i | \(-0.403416\pi\) | ||||
0.298793 | + | 0.954318i | \(0.403416\pi\) | |||||||
\(308\) | 8.90026i | 0.0288969i | ||||||||
\(309\) | − | 287.632i | − | 0.930848i | ||||||
\(310\) | 479.059 | 1.54535 | ||||||||
\(311\) | −198.361 | −0.637816 | −0.318908 | − | 0.947786i | \(-0.603316\pi\) | ||||
−0.318908 | + | 0.947786i | \(0.603316\pi\) | |||||||
\(312\) | −344.551 | −1.10433 | ||||||||
\(313\) | − | 81.4573i | − | 0.260247i | −0.991498 | − | 0.130124i | \(-0.958463\pi\) | ||
0.991498 | − | 0.130124i | \(-0.0415374\pi\) | |||||||
\(314\) | −453.783 | −1.44517 | ||||||||
\(315\) | −35.2735 | −0.111979 | ||||||||
\(316\) | −56.2379 | −0.177968 | ||||||||
\(317\) | −272.467 | −0.859516 | −0.429758 | − | 0.902944i | \(-0.641401\pi\) | ||||
−0.429758 | + | 0.902944i | \(0.641401\pi\) | |||||||
\(318\) | 135.396i | 0.425773i | ||||||||
\(319\) | − | 334.445i | − | 1.04842i | ||||||
\(320\) | 634.036 | 1.98136 | ||||||||
\(321\) | −47.8884 | −0.149185 | ||||||||
\(322\) | 22.4119 | 0.0696022 | ||||||||
\(323\) | 236.601 | 0.732509 | ||||||||
\(324\) | 4.78478 | 0.0147678 | ||||||||
\(325\) | 1339.28i | 4.12087i | ||||||||
\(326\) | 16.7937i | 0.0515145i | ||||||||
\(327\) | 190.927i | 0.583876i | ||||||||
\(328\) | 375.287i | 1.14417i | ||||||||
\(329\) | − | 39.8789i | − | 0.121213i | ||||||
\(330\) | 375.781 | 1.13873 | ||||||||
\(331\) | −145.462 | −0.439463 | −0.219732 | − | 0.975560i | \(-0.570518\pi\) | ||||
−0.219732 | + | 0.975560i | \(0.570518\pi\) | |||||||
\(332\) | − | 1.67175i | − | 0.00503541i | ||||||
\(333\) | 67.1800i | 0.201742i | ||||||||
\(334\) | 251.137i | 0.751908i | ||||||||
\(335\) | − | 851.170i | − | 2.54081i | ||||||
\(336\) | 30.5988 | 0.0910679 | ||||||||
\(337\) | 174.373i | 0.517427i | 0.965954 | + | 0.258714i | \(0.0832986\pi\) | ||||
−0.965954 | + | 0.258714i | \(0.916701\pi\) | |||||||
\(338\) | 719.961i | 2.13006i | ||||||||
\(339\) | − | 120.473i | − | 0.355379i | ||||||
\(340\) | 48.7068 | 0.143255 | ||||||||
\(341\) | 366.255 | 1.07406 | ||||||||
\(342\) | 130.514i | 0.381620i | ||||||||
\(343\) | −125.191 | −0.364988 | ||||||||
\(344\) | −361.352 | −1.05044 | ||||||||
\(345\) | 145.046i | 0.420423i | ||||||||
\(346\) | −508.472 | −1.46957 | ||||||||
\(347\) | − | 366.795i | − | 1.05705i | −0.848919 | − | 0.528524i | \(-0.822746\pi\) | ||
0.848919 | − | 0.528524i | \(-0.177254\pi\) | |||||||
\(348\) | 23.9122 | 0.0687134 | ||||||||
\(349\) | 208.270i | 0.596763i | 0.954447 | + | 0.298382i | \(0.0964468\pi\) | ||||
−0.954447 | + | 0.298382i | \(0.903553\pi\) | |||||||
\(350\) | − | 137.549i | − | 0.392997i | ||||||
\(351\) | − | 122.478i | − | 0.348940i | ||||||
\(352\) | 108.792 | 0.309069 | ||||||||
\(353\) | 174.980i | 0.495695i | 0.968799 | + | 0.247847i | \(0.0797231\pi\) | ||||
−0.968799 | + | 0.247847i | \(0.920277\pi\) | |||||||
\(354\) | −190.117 | − | 8.70160i | −0.537053 | − | 0.0245808i | ||||
\(355\) | −52.3045 | −0.147337 | ||||||||
\(356\) | − | 11.6066i | − | 0.0326028i | ||||||
\(357\) | 22.8035 | 0.0638755 | ||||||||
\(358\) | 205.359 | 0.573628 | ||||||||
\(359\) | 203.293 | 0.566275 | 0.283137 | − | 0.959079i | \(-0.408625\pi\) | ||||
0.283137 | + | 0.959079i | \(0.408625\pi\) | |||||||
\(360\) | 229.016i | 0.636157i | ||||||||
\(361\) | 184.691 | 0.511610 | ||||||||
\(362\) | − | 40.4989i | − | 0.111876i | ||||||
\(363\) | 77.7169 | 0.214096 | ||||||||
\(364\) | 16.2890i | 0.0447500i | ||||||||
\(365\) | − | 376.236i | − | 1.03078i | ||||||
\(366\) | 103.165 | 0.281871 | ||||||||
\(367\) | 514.435i | 1.40173i | 0.713293 | + | 0.700866i | \(0.247203\pi\) | ||||
−0.713293 | + | 0.700866i | \(0.752797\pi\) | |||||||
\(368\) | − | 125.824i | − | 0.341912i | ||||||
\(369\) | −133.403 | −0.361527 | ||||||||
\(370\) | −377.232 | −1.01955 | ||||||||
\(371\) | 54.5610 | 0.147065 | ||||||||
\(372\) | 26.1866i | 0.0703941i | ||||||||
\(373\) | 631.405 | 1.69278 | 0.846388 | − | 0.532567i | \(-0.178773\pi\) | ||||
0.846388 | + | 0.532567i | \(0.178773\pi\) | |||||||
\(374\) | −242.934 | −0.649556 | ||||||||
\(375\) | 498.516 | 1.32938 | ||||||||
\(376\) | −258.918 | −0.688611 | ||||||||
\(377\) | − | 612.092i | − | 1.62359i | ||||||
\(378\) | 12.5789i | 0.0332776i | ||||||||
\(379\) | 196.674 | 0.518930 | 0.259465 | − | 0.965753i | \(-0.416454\pi\) | ||||
0.259465 | + | 0.965753i | \(0.416454\pi\) | |||||||
\(380\) | 112.336 | 0.295622 | ||||||||
\(381\) | −378.952 | −0.994625 | ||||||||
\(382\) | −47.4275 | −0.124156 | ||||||||
\(383\) | −127.877 | −0.333883 | −0.166941 | − | 0.985967i | \(-0.553389\pi\) | ||||
−0.166941 | + | 0.985967i | \(0.553389\pi\) | |||||||
\(384\) | − | 167.580i | − | 0.436407i | ||||||
\(385\) | − | 151.430i | − | 0.393324i | ||||||
\(386\) | 262.074i | 0.678949i | ||||||||
\(387\) | − | 128.450i | − | 0.331912i | ||||||
\(388\) | − | 67.0962i | − | 0.172928i | ||||||
\(389\) | 188.964 | 0.485770 | 0.242885 | − | 0.970055i | \(-0.421906\pi\) | ||||
0.242885 | + | 0.970055i | \(0.421906\pi\) | |||||||
\(390\) | 687.743 | 1.76344 | ||||||||
\(391\) | − | 93.7691i | − | 0.239819i | ||||||
\(392\) | 399.276i | 1.01856i | ||||||||
\(393\) | − | 426.081i | − | 1.08417i | ||||||
\(394\) | 412.261i | 1.04635i | ||||||||
\(395\) | 956.836 | 2.42237 | ||||||||
\(396\) | 20.5411i | 0.0518715i | ||||||||
\(397\) | − | 507.775i | − | 1.27903i | −0.768779 | − | 0.639515i | \(-0.779135\pi\) | ||
0.768779 | − | 0.639515i | \(-0.220865\pi\) | |||||||
\(398\) | − | 525.780i | − | 1.32106i | ||||||
\(399\) | 52.5937 | 0.131814 | ||||||||
\(400\) | −772.219 | −1.93055 | ||||||||
\(401\) | 427.106i | 1.06510i | 0.846398 | + | 0.532551i | \(0.178767\pi\) | ||||
−0.846398 | + | 0.532551i | \(0.821233\pi\) | |||||||
\(402\) | −303.537 | −0.755066 | ||||||||
\(403\) | 670.309 | 1.66330 | ||||||||
\(404\) | 37.9832i | 0.0940177i | ||||||||
\(405\) | −81.4086 | −0.201009 | ||||||||
\(406\) | 62.8640i | 0.154837i | ||||||||
\(407\) | −288.405 | −0.708611 | ||||||||
\(408\) | − | 148.054i | − | 0.362878i | ||||||
\(409\) | − | 154.410i | − | 0.377530i | −0.982022 | − | 0.188765i | \(-0.939551\pi\) | ||
0.982022 | − | 0.188765i | \(-0.0604485\pi\) | |||||||
\(410\) | − | 749.093i | − | 1.82706i | ||||||
\(411\) | −434.482 | −1.05713 | ||||||||
\(412\) | 88.2868i | 0.214288i | ||||||||
\(413\) | −3.50652 | + | 76.6121i | −0.00849035 | + | 0.185501i | ||||
\(414\) | 51.7250 | 0.124940 | ||||||||
\(415\) | 28.4434i | 0.0685383i | ||||||||
\(416\) | 199.108 | 0.478626 | ||||||||
\(417\) | 25.2746 | 0.0606106 | ||||||||
\(418\) | −560.298 | −1.34043 | ||||||||
\(419\) | − | 381.674i | − | 0.910917i | −0.890257 | − | 0.455458i | \(-0.849475\pi\) | ||
0.890257 | − | 0.455458i | \(-0.150525\pi\) | |||||||
\(420\) | 10.8270 | 0.0257785 | ||||||||
\(421\) | 223.524i | 0.530935i | 0.964120 | + | 0.265468i | \(0.0855263\pi\) | ||||
−0.964120 | + | 0.265468i | \(0.914474\pi\) | |||||||
\(422\) | −4.17528 | −0.00989403 | ||||||||
\(423\) | − | 92.0376i | − | 0.217583i | ||||||
\(424\) | − | 354.242i | − | 0.835477i | ||||||
\(425\) | −575.490 | −1.35410 | ||||||||
\(426\) | 18.6524i | 0.0437849i | ||||||||
\(427\) | − | 41.5728i | − | 0.0973601i | ||||||
\(428\) | 14.6990 | 0.0343435 | ||||||||
\(429\) | 525.800 | 1.22564 | ||||||||
\(430\) | 721.278 | 1.67739 | ||||||||
\(431\) | − | 59.8456i | − | 0.138853i | −0.997587 | − | 0.0694264i | \(-0.977883\pi\) | ||
0.997587 | − | 0.0694264i | \(-0.0221169\pi\) | |||||||
\(432\) | 70.6198 | 0.163472 | ||||||||
\(433\) | 654.088 | 1.51060 | 0.755298 | − | 0.655381i | \(-0.227492\pi\) | ||||
0.755298 | + | 0.655381i | \(0.227492\pi\) | |||||||
\(434\) | −68.8431 | −0.158625 | ||||||||
\(435\) | −406.845 | −0.935276 | ||||||||
\(436\) | − | 58.6039i | − | 0.134413i | ||||||
\(437\) | − | 216.267i | − | 0.494891i | ||||||
\(438\) | −134.170 | −0.306324 | ||||||||
\(439\) | 308.578 | 0.702910 | 0.351455 | − | 0.936205i | \(-0.385687\pi\) | ||||
0.351455 | + | 0.936205i | \(0.385687\pi\) | |||||||
\(440\) | −983.171 | −2.23448 | ||||||||
\(441\) | −141.931 | −0.321839 | ||||||||
\(442\) | −444.611 | −1.00591 | ||||||||
\(443\) | 94.0704i | 0.212348i | 0.994348 | + | 0.106174i | \(0.0338601\pi\) | ||||
−0.994348 | + | 0.106174i | \(0.966140\pi\) | |||||||
\(444\) | − | 20.6205i | − | 0.0464425i | ||||||
\(445\) | 197.476i | 0.443765i | ||||||||
\(446\) | 583.282i | 1.30781i | ||||||||
\(447\) | 315.354i | 0.705489i | ||||||||
\(448\) | −91.1141 | −0.203380 | ||||||||
\(449\) | −447.832 | −0.997399 | −0.498699 | − | 0.866775i | \(-0.666189\pi\) | ||||
−0.498699 | + | 0.866775i | \(0.666189\pi\) | |||||||
\(450\) | − | 317.453i | − | 0.705451i | ||||||
\(451\) | − | 572.703i | − | 1.26985i | ||||||
\(452\) | 36.9785i | 0.0818109i | ||||||||
\(453\) | 54.9918i | 0.121395i | ||||||||
\(454\) | 742.868 | 1.63627 | ||||||||
\(455\) | − | 277.143i | − | 0.609105i | ||||||
\(456\) | − | 341.469i | − | 0.748836i | ||||||
\(457\) | − | 351.865i | − | 0.769946i | −0.922928 | − | 0.384973i | \(-0.874211\pi\) | ||
0.922928 | − | 0.384973i | \(-0.125789\pi\) | |||||||
\(458\) | −97.2555 | −0.212348 | ||||||||
\(459\) | 52.6289 | 0.114660 | ||||||||
\(460\) | − | 44.5210i | − | 0.0967847i | ||||||
\(461\) | −350.814 | −0.760984 | −0.380492 | − | 0.924784i | \(-0.624245\pi\) | ||||
−0.380492 | + | 0.924784i | \(0.624245\pi\) | |||||||
\(462\) | −54.0015 | −0.116886 | ||||||||
\(463\) | 321.469i | 0.694318i | 0.937806 | + | 0.347159i | \(0.112854\pi\) | ||||
−0.937806 | + | 0.347159i | \(0.887146\pi\) | |||||||
\(464\) | 352.927 | 0.760619 | ||||||||
\(465\) | − | 445.541i | − | 0.958153i | ||||||
\(466\) | 782.591 | 1.67938 | ||||||||
\(467\) | 631.306i | 1.35183i | 0.736978 | + | 0.675916i | \(0.236252\pi\) | ||||
−0.736978 | + | 0.675916i | \(0.763748\pi\) | |||||||
\(468\) | 37.5938i | 0.0803287i | ||||||||
\(469\) | 122.317i | 0.260805i | ||||||||
\(470\) | 516.814 | 1.09960 | ||||||||
\(471\) | 422.033i | 0.896037i | ||||||||
\(472\) | 497.411 | + | 22.7664i | 1.05384 | + | 0.0482338i | ||||
\(473\) | 551.438 | 1.16583 | ||||||||
\(474\) | − | 341.218i | − | 0.719870i | ||||||
\(475\) | −1327.30 | −2.79432 | ||||||||
\(476\) | −6.99940 | −0.0147046 | ||||||||
\(477\) | 125.923 | 0.263989 | ||||||||
\(478\) | 292.508i | 0.611942i | ||||||||
\(479\) | −134.615 | −0.281032 | −0.140516 | − | 0.990078i | \(-0.544876\pi\) | ||||
−0.140516 | + | 0.990078i | \(0.544876\pi\) | |||||||
\(480\) | − | 132.343i | − | 0.275715i | ||||||
\(481\) | −527.831 | −1.09736 | ||||||||
\(482\) | − | 181.116i | − | 0.375759i | ||||||
\(483\) | − | 20.8438i | − | 0.0431549i | ||||||
\(484\) | −23.8547 | −0.0492866 | ||||||||
\(485\) | 1141.58i | 2.35377i | ||||||||
\(486\) | 29.0312i | 0.0597350i | ||||||||
\(487\) | −739.718 | −1.51893 | −0.759464 | − | 0.650549i | \(-0.774539\pi\) | ||||
−0.759464 | + | 0.650549i | \(0.774539\pi\) | |||||||
\(488\) | −269.915 | −0.553104 | ||||||||
\(489\) | 15.6187 | 0.0319401 | ||||||||
\(490\) | − | 796.977i | − | 1.62648i | ||||||
\(491\) | −424.454 | −0.864469 | −0.432234 | − | 0.901761i | \(-0.642275\pi\) | ||||
−0.432234 | + | 0.901761i | \(0.642275\pi\) | |||||||
\(492\) | 40.9473 | 0.0832263 | ||||||||
\(493\) | 263.016 | 0.533502 | ||||||||
\(494\) | −1025.44 | −2.07580 | ||||||||
\(495\) | − | 349.489i | − | 0.706037i | ||||||
\(496\) | 386.495i | 0.779224i | ||||||||
\(497\) | 7.51641 | 0.0151236 | ||||||||
\(498\) | 10.1432 | 0.0203679 | ||||||||
\(499\) | 10.2031 | 0.0204471 | 0.0102236 | − | 0.999948i | \(-0.496746\pi\) | ||||
0.0102236 | + | 0.999948i | \(0.496746\pi\) | |||||||
\(500\) | −153.016 | −0.306033 | ||||||||
\(501\) | 233.566 | 0.466200 | ||||||||
\(502\) | − | 555.429i | − | 1.10643i | ||||||
\(503\) | − | 188.722i | − | 0.375193i | −0.982246 | − | 0.187596i | \(-0.939930\pi\) | ||
0.982246 | − | 0.187596i | \(-0.0600697\pi\) | |||||||
\(504\) | − | 32.9108i | − | 0.0652992i | ||||||
\(505\) | − | 646.249i | − | 1.27970i | ||||||
\(506\) | 222.056i | 0.438847i | ||||||||
\(507\) | 669.588 | 1.32069 | ||||||||
\(508\) | 116.317 | 0.228970 | ||||||||
\(509\) | − | 939.054i | − | 1.84490i | −0.386116 | − | 0.922450i | \(-0.626184\pi\) | ||
0.386116 | − | 0.922450i | \(-0.373816\pi\) | |||||||
\(510\) | 295.524i | 0.579459i | ||||||||
\(511\) | 54.0670i | 0.105806i | ||||||||
\(512\) | 573.603i | 1.12032i | ||||||||
\(513\) | 121.382 | 0.236613 | ||||||||
\(514\) | − | 741.297i | − | 1.44221i | ||||||
\(515\) | − | 1502.12i | − | 2.91674i | ||||||
\(516\) | 39.4269i | 0.0764087i | ||||||||
\(517\) | 395.119 | 0.764253 | ||||||||
\(518\) | 54.2101 | 0.104653 | ||||||||
\(519\) | 472.896i | 0.911168i | ||||||||
\(520\) | −1799.37 | −3.46033 | ||||||||
\(521\) | −7.53069 | −0.0144543 | −0.00722715 | − | 0.999974i | \(-0.502300\pi\) | ||||
−0.00722715 | + | 0.999974i | \(0.502300\pi\) | |||||||
\(522\) | 145.085i | 0.277941i | ||||||||
\(523\) | −843.214 | −1.61226 | −0.806132 | − | 0.591736i | \(-0.798443\pi\) | ||||
−0.806132 | + | 0.591736i | \(0.798443\pi\) | |||||||
\(524\) | 130.783i | 0.249585i | ||||||||
\(525\) | −127.925 | −0.243667 | ||||||||
\(526\) | − | 383.326i | − | 0.728757i | ||||||
\(527\) | 288.032i | 0.546551i | ||||||||
\(528\) | 303.172i | 0.574189i | ||||||||
\(529\) | 443.289 | 0.837976 | ||||||||
\(530\) | 707.087i | 1.33413i | ||||||||
\(531\) | −8.09278 | + | 176.815i | −0.0152406 | + | 0.332985i | ||||
\(532\) | −16.1433 | −0.0303445 | ||||||||
\(533\) | − | 1048.15i | − | 1.96650i | ||||||
\(534\) | 70.4220 | 0.131876 | ||||||||
\(535\) | −250.091 | −0.467459 | ||||||||
\(536\) | 794.156 | 1.48164 | ||||||||
\(537\) | − | 190.991i | − | 0.355662i | ||||||
\(538\) | 300.020 | 0.557658 | ||||||||
\(539\) | − | 609.312i | − | 1.13045i | ||||||
\(540\) | 24.9879 | 0.0462738 | ||||||||
\(541\) | 895.843i | 1.65590i | 0.560800 | + | 0.827951i | \(0.310494\pi\) | ||||
−0.560800 | + | 0.827951i | \(0.689506\pi\) | |||||||
\(542\) | 414.949i | 0.765588i | ||||||||
\(543\) | −37.6654 | −0.0693653 | ||||||||
\(544\) | 85.5571i | 0.157274i | ||||||||
\(545\) | 997.092i | 1.82953i | ||||||||
\(546\) | −98.8321 | −0.181011 | ||||||||
\(547\) | 217.435 | 0.397504 | 0.198752 | − | 0.980050i | \(-0.436311\pi\) | ||||
0.198752 | + | 0.980050i | \(0.436311\pi\) | |||||||
\(548\) | 133.361 | 0.243360 | ||||||||
\(549\) | − | 95.9468i | − | 0.174767i | ||||||
\(550\) | 1362.83 | 2.47787 | ||||||||
\(551\) | 606.616 | 1.10094 | ||||||||
\(552\) | −135.330 | −0.245164 | ||||||||
\(553\) | −137.502 | −0.248648 | ||||||||
\(554\) | 758.994i | 1.37002i | ||||||||
\(555\) | 350.838i | 0.632141i | ||||||||
\(556\) | −7.75788 | −0.0139530 | ||||||||
\(557\) | −946.289 | −1.69890 | −0.849451 | − | 0.527667i | \(-0.823067\pi\) | ||||
−0.849451 | + | 0.527667i | \(0.823067\pi\) | |||||||
\(558\) | −158.885 | −0.284740 | ||||||||
\(559\) | 1009.23 | 1.80541 | ||||||||
\(560\) | 159.798 | 0.285354 | ||||||||
\(561\) | 225.937i | 0.402739i | ||||||||
\(562\) | 698.047i | 1.24208i | ||||||||
\(563\) | 273.838i | 0.486391i | 0.969977 | + | 0.243195i | \(0.0781956\pi\) | ||||
−0.969977 | + | 0.243195i | \(0.921804\pi\) | |||||||
\(564\) | 28.2504i | 0.0500893i | ||||||||
\(565\) | − | 629.156i | − | 1.11355i | ||||||
\(566\) | 673.902 | 1.19064 | ||||||||
\(567\) | 11.6988 | 0.0206328 | ||||||||
\(568\) | − | 48.8010i | − | 0.0859173i | ||||||
\(569\) | − | 652.571i | − | 1.14687i | −0.819250 | − | 0.573437i | \(-0.805610\pi\) | ||
0.819250 | − | 0.573437i | \(-0.194390\pi\) | |||||||
\(570\) | 681.591i | 1.19577i | ||||||||
\(571\) | 373.051i | 0.653329i | 0.945140 | + | 0.326664i | \(0.105925\pi\) | ||||
−0.945140 | + | 0.326664i | \(0.894075\pi\) | |||||||
\(572\) | −161.391 | −0.282152 | ||||||||
\(573\) | 44.1091i | 0.0769793i | ||||||||
\(574\) | 107.648i | 0.187541i | ||||||||
\(575\) | 526.033i | 0.914841i | ||||||||
\(576\) | −210.285 | −0.365077 | ||||||||
\(577\) | −565.048 | −0.979286 | −0.489643 | − | 0.871923i | \(-0.662873\pi\) | ||||
−0.489643 | + | 0.871923i | \(0.662873\pi\) | |||||||
\(578\) | 347.170i | 0.600641i | ||||||||
\(579\) | 243.738 | 0.420963 | ||||||||
\(580\) | 124.878 | 0.215308 | ||||||||
\(581\) | − | 4.08745i | − | 0.00703520i | ||||||
\(582\) | 407.100 | 0.699485 | ||||||||
\(583\) | 540.588i | 0.927253i | ||||||||
\(584\) | 351.035 | 0.601087 | ||||||||
\(585\) | − | 639.624i | − | 1.09338i | ||||||
\(586\) | − | 557.006i | − | 0.950523i | ||||||
\(587\) | 34.5560i | 0.0588688i | 0.999567 | + | 0.0294344i | \(0.00937062\pi\) | ||||
−0.999567 | + | 0.0294344i | \(0.990629\pi\) | |||||||
\(588\) | 43.5648 | 0.0740898 | ||||||||
\(589\) | 664.313i | 1.12787i | ||||||||
\(590\) | −992.859 | − | 45.4429i | −1.68281 | − | 0.0770219i | ||||
\(591\) | 383.416 | 0.648758 | ||||||||
\(592\) | − | 304.343i | − | 0.514093i | ||||||
\(593\) | 179.049 | 0.301937 | 0.150968 | − | 0.988539i | \(-0.451761\pi\) | ||||
0.150968 | + | 0.988539i | \(0.451761\pi\) | |||||||
\(594\) | −124.631 | −0.209817 | ||||||||
\(595\) | 119.088 | 0.200149 | ||||||||
\(596\) | − | 96.7958i | − | 0.162409i | ||||||
\(597\) | −488.993 | −0.819085 | ||||||||
\(598\) | 406.402i | 0.679601i | ||||||||
\(599\) | 41.4253 | 0.0691575 | 0.0345787 | − | 0.999402i | \(-0.488991\pi\) | ||||
0.0345787 | + | 0.999402i | \(0.488991\pi\) | |||||||
\(600\) | 830.566i | 1.38428i | ||||||||
\(601\) | 107.487i | 0.178847i | 0.995994 | + | 0.0894236i | \(0.0285025\pi\) | ||||
−0.995994 | + | 0.0894236i | \(0.971498\pi\) | |||||||
\(602\) | −103.651 | −0.172178 | ||||||||
\(603\) | 282.299i | 0.468158i | ||||||||
\(604\) | − | 16.8794i | − | 0.0279460i | ||||||
\(605\) | 405.866 | 0.670853 | ||||||||
\(606\) | −230.459 | −0.380296 | ||||||||
\(607\) | 594.804 | 0.979908 | 0.489954 | − | 0.871748i | \(-0.337014\pi\) | ||||
0.489954 | + | 0.871748i | \(0.337014\pi\) | |||||||
\(608\) | 197.327i | 0.324552i | ||||||||
\(609\) | 58.4656 | 0.0960027 | ||||||||
\(610\) | 538.765 | 0.883221 | ||||||||
\(611\) | 723.136 | 1.18353 | ||||||||
\(612\) | −16.1541 | −0.0263956 | ||||||||
\(613\) | 898.671i | 1.46602i | 0.680217 | + | 0.733011i | \(0.261885\pi\) | ||||
−0.680217 | + | 0.733011i | \(0.738115\pi\) | |||||||
\(614\) | − | 341.665i | − | 0.556457i | ||||||
\(615\) | −696.682 | −1.13282 | ||||||||
\(616\) | 141.287 | 0.229361 | ||||||||
\(617\) | 479.889 | 0.777778 | 0.388889 | − | 0.921285i | \(-0.372859\pi\) | ||||
0.388889 | + | 0.921285i | \(0.372859\pi\) | |||||||
\(618\) | −535.672 | −0.866783 | ||||||||
\(619\) | −622.793 | −1.00613 | −0.503064 | − | 0.864249i | \(-0.667794\pi\) | ||||
−0.503064 | + | 0.864249i | \(0.667794\pi\) | |||||||
\(620\) | 136.756i | 0.220574i | ||||||||
\(621\) | − | 48.1060i | − | 0.0774654i | ||||||
\(622\) | 369.418i | 0.593920i | ||||||||
\(623\) | − | 28.3782i | − | 0.0455509i | ||||||
\(624\) | 554.857i | 0.889194i | ||||||||
\(625\) | 1182.95 | 1.89272 | ||||||||
\(626\) | −151.702 | −0.242336 | ||||||||
\(627\) | 521.096i | 0.831095i | ||||||||
\(628\) | − | 129.540i | − | 0.206275i | ||||||
\(629\) | − | 226.809i | − | 0.360587i | ||||||
\(630\) | 65.6917i | 0.104273i | ||||||||
\(631\) | 739.694 | 1.17226 | 0.586128 | − | 0.810218i | \(-0.300652\pi\) | ||||
0.586128 | + | 0.810218i | \(0.300652\pi\) | |||||||
\(632\) | 892.745i | 1.41257i | ||||||||
\(633\) | 3.88315i | 0.00613452i | ||||||||
\(634\) | 507.429i | 0.800361i | ||||||||
\(635\) | −1979.03 | −3.11658 | ||||||||
\(636\) | −38.6512 | −0.0607723 | ||||||||
\(637\) | − | 1115.15i | − | 1.75062i | ||||||
\(638\) | −622.854 | −0.976260 | ||||||||
\(639\) | 17.3473 | 0.0271476 | ||||||||
\(640\) | − | 875.165i | − | 1.36745i | ||||||
\(641\) | 509.503 | 0.794857 | 0.397428 | − | 0.917633i | \(-0.369903\pi\) | ||||
0.397428 | + | 0.917633i | \(0.369903\pi\) | |||||||
\(642\) | 89.1851i | 0.138918i | ||||||||
\(643\) | −1038.83 | −1.61560 | −0.807802 | − | 0.589454i | \(-0.799343\pi\) | ||||
−0.807802 | + | 0.589454i | \(0.799343\pi\) | |||||||
\(644\) | 6.39788i | 0.00993460i | ||||||||
\(645\) | − | 670.812i | − | 1.04002i | ||||||
\(646\) | − | 440.634i | − | 0.682095i | ||||||
\(647\) | 113.373 | 0.175228 | 0.0876142 | − | 0.996154i | \(-0.472076\pi\) | ||||
0.0876142 | + | 0.996154i | \(0.472076\pi\) | |||||||
\(648\) | − | 75.9556i | − | 0.117216i | ||||||
\(649\) | −759.069 | − | 34.7424i | −1.16960 | − | 0.0535322i | ||||
\(650\) | 2494.21 | 3.83725 | ||||||||
\(651\) | 64.0264i | 0.0983509i | ||||||||
\(652\) | −4.79407 | −0.00735286 | ||||||||
\(653\) | −196.978 | −0.301652 | −0.150826 | − | 0.988560i | \(-0.548193\pi\) | ||||
−0.150826 | + | 0.988560i | \(0.548193\pi\) | |||||||
\(654\) | 355.574 | 0.543691 | ||||||||
\(655\) | − | 2225.15i | − | 3.39717i | ||||||
\(656\) | 604.353 | 0.921269 | ||||||||
\(657\) | 124.783i | 0.189928i | ||||||||
\(658\) | −74.2686 | −0.112870 | ||||||||
\(659\) | 12.7484i | 0.0193451i | 0.999953 | + | 0.00967254i | \(0.00307891\pi\) | ||||
−0.999953 | + | 0.00967254i | \(0.996921\pi\) | |||||||
\(660\) | 107.273i | 0.162535i | ||||||||
\(661\) | −617.452 | −0.934118 | −0.467059 | − | 0.884226i | \(-0.654686\pi\) | ||||
−0.467059 | + | 0.884226i | \(0.654686\pi\) | |||||||
\(662\) | 270.902i | 0.409218i | ||||||||
\(663\) | 413.503i | 0.623685i | ||||||||
\(664\) | −26.5382 | −0.0399671 | ||||||||
\(665\) | 274.663 | 0.413028 | ||||||||
\(666\) | 125.113 | 0.187857 | ||||||||
\(667\) | − | 240.413i | − | 0.360439i | ||||||
\(668\) | −71.6917 | −0.107323 | ||||||||
\(669\) | 542.472 | 0.810870 | ||||||||
\(670\) | −1585.18 | −2.36594 | ||||||||
\(671\) | 411.901 | 0.613862 | ||||||||
\(672\) | 19.0184i | 0.0283012i | ||||||||
\(673\) | − | 525.509i | − | 0.780845i | −0.920636 | − | 0.390423i | \(-0.872329\pi\) | ||
0.920636 | − | 0.390423i | \(-0.127671\pi\) | |||||||
\(674\) | 324.744 | 0.481816 | ||||||||
\(675\) | −295.242 | −0.437395 | ||||||||
\(676\) | −205.526 | −0.304032 | ||||||||
\(677\) | −373.054 | −0.551040 | −0.275520 | − | 0.961295i | \(-0.588850\pi\) | ||||
−0.275520 | + | 0.961295i | \(0.588850\pi\) | |||||||
\(678\) | −224.364 | −0.330920 | ||||||||
\(679\) | − | 164.051i | − | 0.241606i | ||||||
\(680\) | − | 773.192i | − | 1.13705i | ||||||
\(681\) | − | 690.892i | − | 1.01453i | ||||||
\(682\) | − | 682.095i | − | 1.00014i | ||||||
\(683\) | 602.186i | 0.881679i | 0.897586 | + | 0.440839i | \(0.145319\pi\) | ||||
−0.897586 | + | 0.440839i | \(0.854681\pi\) | |||||||
\(684\) | −37.2575 | −0.0544701 | ||||||||
\(685\) | −2269.02 | −3.31244 | ||||||||
\(686\) | 233.149i | 0.339868i | ||||||||
\(687\) | 90.4509i | 0.131661i | ||||||||
\(688\) | 581.912i | 0.845802i | ||||||||
\(689\) | 989.370i | 1.43595i | ||||||||
\(690\) | 270.127 | 0.391488 | ||||||||
\(691\) | 1077.20i | 1.55889i | 0.626469 | + | 0.779447i | \(0.284500\pi\) | ||||
−0.626469 | + | 0.779447i | \(0.715500\pi\) | |||||||
\(692\) | − | 145.153i | − | 0.209758i | ||||||
\(693\) | 50.2232i | 0.0724722i | ||||||||
\(694\) | −683.103 | −0.984298 | ||||||||
\(695\) | 131.993 | 0.189918 | ||||||||
\(696\) | − | 379.593i | − | 0.545393i | ||||||
\(697\) | 450.389 | 0.646182 | ||||||||
\(698\) | 387.873 | 0.555692 | ||||||||
\(699\) | − | 727.836i | − | 1.04125i | ||||||
\(700\) | 39.2658 | 0.0560940 | ||||||||
\(701\) | 228.502i | 0.325965i | 0.986629 | + | 0.162983i | \(0.0521115\pi\) | ||||
−0.986629 | + | 0.162983i | \(0.947889\pi\) | |||||||
\(702\) | −228.097 | −0.324925 | ||||||||
\(703\) | − | 523.109i | − | 0.744109i | ||||||
\(704\) | − | 902.755i | − | 1.28232i | ||||||
\(705\) | − | 480.654i | − | 0.681779i | ||||||
\(706\) | 325.875 | 0.461579 | ||||||||
\(707\) | 92.8691i | 0.131357i | ||||||||
\(708\) | 2.48403 | − | 54.2722i | 0.00350851 | − | 0.0766557i | ||||
\(709\) | −162.647 | −0.229403 | −0.114701 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114701 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(710\) | 97.4094i | 0.137196i | ||||||||
\(711\) | −317.345 | −0.446335 | ||||||||
\(712\) | −184.248 | −0.258775 | ||||||||
\(713\) | 263.279 | 0.369256 | ||||||||
\(714\) | − | 42.4682i | − | 0.0594793i | ||||||
\(715\) | 2745.92 | 3.84045 | ||||||||
\(716\) | 58.6233i | 0.0818762i | ||||||||
\(717\) | 272.042 | 0.379418 | ||||||||
\(718\) | − | 378.603i | − | 0.527302i | ||||||
\(719\) | 719.737i | 1.00102i | 0.865729 | + | 0.500512i | \(0.166855\pi\) | ||||
−0.865729 | + | 0.500512i | \(0.833145\pi\) | |||||||
\(720\) | 368.802 | 0.512226 | ||||||||
\(721\) | 215.862i | 0.299392i | ||||||||
\(722\) | − | 343.961i | − | 0.476400i | ||||||
\(723\) | −168.444 | −0.232979 | ||||||||
\(724\) | 11.5611 | 0.0159684 | ||||||||
\(725\) | −1475.49 | −2.03516 | ||||||||
\(726\) | − | 144.736i | − | 0.199361i | ||||||
\(727\) | −484.589 | −0.666559 | −0.333280 | − | 0.942828i | \(-0.608155\pi\) | ||||
−0.333280 | + | 0.942828i | \(0.608155\pi\) | |||||||
\(728\) | 258.579 | 0.355191 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −700.685 | −0.959842 | ||||||||
\(731\) | 433.665i | 0.593250i | ||||||||
\(732\) | 29.4503i | 0.0402326i | ||||||||
\(733\) | 1164.71 | 1.58896 | 0.794480 | − | 0.607290i | \(-0.207743\pi\) | ||||
0.794480 | + | 0.607290i | \(0.207743\pi\) | |||||||
\(734\) | 958.060 | 1.30526 | ||||||||
\(735\) | −741.216 | −1.00846 | ||||||||
\(736\) | 78.2044 | 0.106256 | ||||||||
\(737\) | −1211.92 | −1.64439 | ||||||||
\(738\) | 248.444i | 0.336645i | ||||||||
\(739\) | − | 157.927i | − | 0.213703i | −0.994275 | − | 0.106852i | \(-0.965923\pi\) | ||
0.994275 | − | 0.106852i | \(-0.0340770\pi\) | |||||||
\(740\) | − | 107.688i | − | 0.145524i | ||||||
\(741\) | 953.696i | 1.28704i | ||||||||
\(742\) | − | 101.612i | − | 0.136943i | ||||||
\(743\) | 700.568 | 0.942891 | 0.471445 | − | 0.881895i | \(-0.343732\pi\) | ||||
0.471445 | + | 0.881895i | \(0.343732\pi\) | |||||||
\(744\) | 415.697 | 0.558733 | ||||||||
\(745\) | 1646.89i | 2.21059i | ||||||||
\(746\) | − | 1175.90i | − | 1.57627i | ||||||
\(747\) | − | 9.43354i | − | 0.0126286i | ||||||
\(748\) | − | 69.3498i | − | 0.0927136i | ||||||
\(749\) | 35.9393 | 0.0479830 | ||||||||
\(750\) | − | 928.413i | − | 1.23788i | ||||||
\(751\) | 984.786i | 1.31130i | 0.755065 | + | 0.655650i | \(0.227605\pi\) | ||||
−0.755065 | + | 0.655650i | \(0.772395\pi\) | |||||||
\(752\) | 416.955i | 0.554461i | ||||||||
\(753\) | −516.568 | −0.686013 | ||||||||
\(754\) | −1139.93 | −1.51184 | ||||||||
\(755\) | 287.187i | 0.380381i | ||||||||
\(756\) | −3.59088 | −0.00474984 | ||||||||
\(757\) | −288.319 | −0.380870 | −0.190435 | − | 0.981700i | \(-0.560990\pi\) | ||||
−0.190435 | + | 0.981700i | \(0.560990\pi\) | |||||||
\(758\) | − | 366.277i | − | 0.483215i | ||||||
\(759\) | 206.520 | 0.272095 | ||||||||
\(760\) | − | 1783.28i | − | 2.34642i | ||||||
\(761\) | −462.140 | −0.607280 | −0.303640 | − | 0.952787i | \(-0.598202\pi\) | ||||
−0.303640 | + | 0.952787i | \(0.598202\pi\) | |||||||
\(762\) | 705.743i | 0.926171i | ||||||||
\(763\) | − | 143.287i | − | 0.187794i | ||||||
\(764\) | − | 13.5390i | − | 0.0177212i | ||||||
\(765\) | 274.847 | 0.359277 | ||||||||
\(766\) | 238.152i | 0.310904i | ||||||||
\(767\) | −1389.23 | − | 63.5846i | −1.81125 | − | 0.0829005i | ||||
\(768\) | 173.538 | 0.225961 | ||||||||
\(769\) | 569.738i | 0.740881i | 0.928856 | + | 0.370441i | \(0.120793\pi\) | ||||
−0.928856 | + | 0.370441i | \(0.879207\pi\) | |||||||
\(770\) | −282.016 | −0.366254 | ||||||||
\(771\) | −689.431 | −0.894204 | ||||||||
\(772\) | −74.8138 | −0.0969090 | ||||||||
\(773\) | 401.753i | 0.519732i | 0.965645 | + | 0.259866i | \(0.0836784\pi\) | ||||
−0.965645 | + | 0.259866i | \(0.916322\pi\) | |||||||
\(774\) | −239.219 | −0.309069 | ||||||||
\(775\) | − | 1615.83i | − | 2.08494i | ||||||
\(776\) | −1065.11 | −1.37257 | ||||||||
\(777\) | − | 50.4172i | − | 0.0648870i | ||||||
\(778\) | − | 351.918i | − | 0.452337i | ||||||
\(779\) | 1038.77 | 1.33347 | ||||||||
\(780\) | 196.329i | 0.251703i | ||||||||
\(781\) | 74.4723i | 0.0953551i | ||||||||
\(782\) | −174.631 | −0.223313 | ||||||||
\(783\) | 134.934 | 0.172330 | ||||||||
\(784\) | 642.985 | 0.820134 | ||||||||
\(785\) | 2204.01i | 2.80766i | ||||||||
\(786\) | −793.513 | −1.00956 | ||||||||
\(787\) | 454.102 | 0.577004 | 0.288502 | − | 0.957479i | \(-0.406843\pi\) | ||||
0.288502 | + | 0.957479i | \(0.406843\pi\) | |||||||
\(788\) | −117.687 | −0.149349 | ||||||||
\(789\) | −356.506 | −0.451846 | ||||||||
\(790\) | − | 1781.97i | − | 2.25565i | ||||||
\(791\) | 90.4128i | 0.114302i | ||||||||
\(792\) | 326.079 | 0.411716 | ||||||||
\(793\) | 753.851 | 0.950631 | ||||||||
\(794\) | −945.656 | −1.19100 | ||||||||
\(795\) | 657.614 | 0.827188 | ||||||||
\(796\) | 150.093 | 0.188560 | ||||||||
\(797\) | − | 1446.19i | − | 1.81454i | −0.420545 | − | 0.907272i | \(-0.638161\pi\) | ||
0.420545 | − | 0.907272i | \(-0.361839\pi\) | |||||||
\(798\) | − | 97.9480i | − | 0.122742i | ||||||
\(799\) | 310.732i | 0.388901i | ||||||||
\(800\) | − | 479.965i | − | 0.599957i | ||||||
\(801\) | − | 65.4948i | − | 0.0817663i | ||||||
\(802\) | 795.423 | 0.991799 | ||||||||
\(803\) | −535.694 | −0.667115 | ||||||||
\(804\) | − | 86.6500i | − | 0.107774i | ||||||
\(805\) | − | 108.854i | − | 0.135222i | ||||||
\(806\) | − | 1248.35i | − | 1.54882i | ||||||
\(807\) | − | 279.029i | − | 0.345760i | ||||||
\(808\) | 602.961 | 0.746239 | ||||||||
\(809\) | − | 763.887i | − | 0.944236i | −0.881535 | − | 0.472118i | \(-0.843490\pi\) | ||
0.881535 | − | 0.472118i | \(-0.156510\pi\) | |||||||
\(810\) | 151.612i | 0.187175i | ||||||||
\(811\) | 109.080i | 0.134500i | 0.997736 | + | 0.0672500i | \(0.0214225\pi\) | ||||
−0.997736 | + | 0.0672500i | \(0.978577\pi\) | |||||||
\(812\) | −17.9457 | −0.0221006 | ||||||||
\(813\) | 385.916 | 0.474682 | ||||||||
\(814\) | 537.111i | 0.659842i | ||||||||
\(815\) | 81.5667 | 0.100082 | ||||||||
\(816\) | −238.423 | −0.292185 | ||||||||
\(817\) | 1000.20i | 1.22423i | ||||||||
\(818\) | −287.566 | −0.351547 | ||||||||
\(819\) | 91.9172i | 0.112231i | ||||||||
\(820\) | 213.842 | 0.260783 | ||||||||
\(821\) | − | 561.607i | − | 0.684052i | −0.939690 | − | 0.342026i | \(-0.888887\pi\) | ||
0.939690 | − | 0.342026i | \(-0.111113\pi\) | |||||||
\(822\) | 809.158i | 0.984378i | ||||||||
\(823\) | 817.432i | 0.993235i | 0.867970 | + | 0.496617i | \(0.165425\pi\) | ||||
−0.867970 | + | 0.496617i | \(0.834575\pi\) | |||||||
\(824\) | 1401.50 | 1.70085 | ||||||||
\(825\) | − | 1267.48i | − | 1.53634i | ||||||
\(826\) | 142.679 | + | 6.53037i | 0.172734 | + | 0.00790602i | ||||
\(827\) | −430.868 | −0.521001 | −0.260501 | − | 0.965474i | \(-0.583888\pi\) | ||||
−0.260501 | + | 0.965474i | \(0.583888\pi\) | |||||||
\(828\) | 14.7658i | 0.0178331i | ||||||||
\(829\) | −144.179 | −0.173919 | −0.0869594 | − | 0.996212i | \(-0.527715\pi\) | ||||
−0.0869594 | + | 0.996212i | \(0.527715\pi\) | |||||||
\(830\) | 52.9716 | 0.0638212 | ||||||||
\(831\) | 705.890 | 0.849446 | ||||||||
\(832\) | − | 1652.20i | − | 1.98581i | ||||||
\(833\) | 479.180 | 0.575246 | ||||||||
\(834\) | − | 47.0703i | − | 0.0564392i | ||||||
\(835\) | 1219.77 | 1.46080 | ||||||||
\(836\) | − | 159.947i | − | 0.191324i | ||||||
\(837\) | 147.768i | 0.176545i | ||||||||
\(838\) | −710.812 | −0.848224 | ||||||||
\(839\) | − | 1284.54i | − | 1.53104i | −0.643415 | − | 0.765518i | \(-0.722483\pi\) | ||
0.643415 | − | 0.765518i | \(-0.277517\pi\) | |||||||
\(840\) | − | 171.872i | − | 0.204610i | ||||||
\(841\) | −166.657 | −0.198165 | ||||||||
\(842\) | 416.280 | 0.494394 | ||||||||
\(843\) | 649.208 | 0.770116 | ||||||||
\(844\) | − | 1.19191i | − | 0.00141221i | ||||||
\(845\) | 3496.83 | 4.13826 | ||||||||
\(846\) | −171.406 | −0.202608 | ||||||||
\(847\) | −58.3250 | −0.0688607 | ||||||||
\(848\) | −570.463 | −0.672716 | ||||||||
\(849\) | − | 626.751i | − | 0.738223i | ||||||
\(850\) | 1071.77i | 1.26090i | ||||||||
\(851\) | −207.318 | −0.243616 | ||||||||
\(852\) | −5.32465 | −0.00624959 | ||||||||
\(853\) | 1449.21 | 1.69896 | 0.849480 | − | 0.527620i | \(-0.176916\pi\) | ||||
0.849480 | + | 0.527620i | \(0.176916\pi\) | |||||||
\(854\) | −77.4231 | −0.0906594 | ||||||||
\(855\) | 633.903 | 0.741407 | ||||||||
\(856\) | − | 233.339i | − | 0.272592i | ||||||
\(857\) | 468.180i | 0.546301i | 0.961971 | + | 0.273150i | \(0.0880656\pi\) | ||||
−0.961971 | + | 0.273150i | \(0.911934\pi\) | |||||||
\(858\) | − | 979.225i | − | 1.14129i | ||||||
\(859\) | 387.001i | 0.450525i | 0.974298 | + | 0.225262i | \(0.0723239\pi\) | ||||
−0.974298 | + | 0.225262i | \(0.927676\pi\) | |||||||
\(860\) | 205.902i | 0.239420i | ||||||||
\(861\) | 100.117 | 0.116279 | ||||||||
\(862\) | −111.454 | −0.129296 | ||||||||
\(863\) | − | 1197.58i | − | 1.38769i | −0.720123 | − | 0.693846i | \(-0.755915\pi\) | ||
0.720123 | − | 0.693846i | \(-0.244085\pi\) | |||||||
\(864\) | 43.8930i | 0.0508021i | ||||||||
\(865\) | 2469.64i | 2.85507i | ||||||||
\(866\) | − | 1218.14i | − | 1.40663i | ||||||
\(867\) | 322.880 | 0.372411 | ||||||||
\(868\) | − | 19.6525i | − | 0.0226411i | ||||||
\(869\) | − | 1362.37i | − | 1.56774i | ||||||
\(870\) | 757.689i | 0.870907i | ||||||||
\(871\) | −2218.01 | −2.54652 | ||||||||
\(872\) | −930.304 | −1.06686 | ||||||||
\(873\) | − | 378.617i | − | 0.433696i | ||||||
\(874\) | −402.766 | −0.460831 | ||||||||
\(875\) | −374.126 | −0.427573 | ||||||||
\(876\) | − | 38.3012i | − | 0.0437229i | ||||||
\(877\) | −1017.97 | −1.16074 | −0.580371 | − | 0.814352i | \(-0.697092\pi\) | ||||
−0.580371 | + | 0.814352i | \(0.697092\pi\) | |||||||
\(878\) | − | 574.680i | − | 0.654533i | ||||||
\(879\) | −518.035 | −0.589345 | ||||||||
\(880\) | 1583.27i | 1.79918i | ||||||||
\(881\) | − | 4.59455i | − | 0.00521515i | −0.999997 | − | 0.00260758i | \(-0.999170\pi\) | ||
0.999997 | − | 0.00260758i | \(-0.000830018\pi\) | |||||||
\(882\) | 264.326i | 0.299689i | ||||||||
\(883\) | −423.083 | −0.479143 | −0.239571 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239571 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(884\) | − | 126.922i | − | 0.143577i | ||||||
\(885\) | −42.2634 | + | 923.392i | −0.0477553 | + | 1.04338i | ||||
\(886\) | 175.192 | 0.197734 | ||||||||
\(887\) | − | 698.508i | − | 0.787495i | −0.919219 | − | 0.393747i | \(-0.871178\pi\) | ||
0.919219 | − | 0.393747i | \(-0.128822\pi\) | |||||||
\(888\) | −327.338 | −0.368624 | ||||||||
\(889\) | 284.396 | 0.319905 | ||||||||
\(890\) | 367.769 | 0.413224 | ||||||||
\(891\) | 115.911i | 0.130091i | ||||||||
\(892\) | −166.508 | −0.186668 | ||||||||
\(893\) | 716.667i | 0.802539i | ||||||||
\(894\) | 587.300 | 0.656935 | ||||||||
\(895\) | − | 997.422i | − | 1.11444i | ||||||
\(896\) | 125.766i | 0.140363i | ||||||||
\(897\) | 377.967 | 0.421368 | ||||||||
\(898\) | 834.021i | 0.928754i | ||||||||
\(899\) | 738.482i | 0.821448i | ||||||||
\(900\) | 90.6226 | 0.100692 | ||||||||
\(901\) | −425.133 | −0.471846 | ||||||||
\(902\) | −1066.58 | −1.18246 | ||||||||
\(903\) | 96.3990i | 0.106754i | ||||||||
\(904\) | 587.013 | 0.649351 | ||||||||
\(905\) | −196.702 | −0.217351 | ||||||||
\(906\) | 102.414 | 0.113040 | ||||||||
\(907\) | −564.844 | −0.622761 | −0.311381 | − | 0.950285i | \(-0.600791\pi\) | ||||
−0.311381 | + | 0.950285i | \(0.600791\pi\) | |||||||
\(908\) | 212.065i | 0.233552i | ||||||||
\(909\) | 214.335i | 0.235792i | ||||||||
\(910\) | −516.137 | −0.567184 | ||||||||
\(911\) | −70.7219 | −0.0776311 | −0.0388156 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388156 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(912\) | −549.894 | −0.602954 | ||||||||
\(913\) | 40.4983 | 0.0443574 | ||||||||
\(914\) | −655.297 | −0.716955 | ||||||||
\(915\) | − | 501.069i | − | 0.547617i | ||||||
\(916\) | − | 27.7633i | − | 0.0303093i | ||||||
\(917\) | 319.765i | 0.348708i | ||||||||
\(918\) | − | 98.0135i | − | 0.106769i | ||||||
\(919\) | 1102.02i | 1.19915i | 0.800318 | + | 0.599576i | \(0.204664\pi\) | ||||
−0.800318 | + | 0.599576i | \(0.795336\pi\) | |||||||
\(920\) | −706.745 | −0.768201 | ||||||||
\(921\) | −317.760 | −0.345016 | ||||||||
\(922\) | 653.339i | 0.708610i | ||||||||
\(923\) | 136.297i | 0.147668i | ||||||||
\(924\) | − | 15.4157i | − | 0.0166837i | ||||||
\(925\) | 1272.37i | 1.37554i | ||||||||
\(926\) | 598.689 | 0.646533 | ||||||||
\(927\) | 498.193i | 0.537425i | ||||||||
\(928\) | 219.358i | 0.236378i | ||||||||
\(929\) | 1042.64i | 1.12233i | 0.827705 | + | 0.561164i | \(0.189646\pi\) | ||||
−0.827705 | + | 0.561164i | \(0.810354\pi\) | |||||||
\(930\) | −829.755 | −0.892209 | ||||||||
\(931\) | 1105.17 | 1.18708 | ||||||||
\(932\) | 223.405i | 0.239704i | ||||||||
\(933\) | 343.571 | 0.368244 | ||||||||
\(934\) | 1175.71 | 1.25879 | ||||||||
\(935\) | 1179.92i | 1.26195i | ||||||||
\(936\) | 596.781 | 0.637586 | ||||||||
\(937\) | − | 567.136i | − | 0.605268i | −0.953107 | − | 0.302634i | \(-0.902134\pi\) | ||
0.953107 | − | 0.302634i | \(-0.0978660\pi\) | |||||||
\(938\) | 227.798 | 0.242855 | ||||||||
\(939\) | 141.088i | 0.150254i | ||||||||
\(940\) | 147.534i | 0.156951i | ||||||||
\(941\) | 105.988i | 0.112633i | 0.998413 | + | 0.0563167i | \(0.0179356\pi\) | ||||
−0.998413 | + | 0.0563167i | \(0.982064\pi\) | |||||||
\(942\) | 785.975 | 0.834368 | ||||||||
\(943\) | − | 411.683i | − | 0.436568i | ||||||
\(944\) | 36.6624 | − | 801.018i | 0.0388373 | − | 0.848536i | ||||
\(945\) | 61.0955 | 0.0646513 | ||||||||
\(946\) | − | 1026.97i | − | 1.08559i | ||||||
\(947\) | −600.889 | −0.634518 | −0.317259 | − | 0.948339i | \(-0.602763\pi\) | ||||
−0.317259 | + | 0.948339i | \(0.602763\pi\) | |||||||
\(948\) | 97.4069 | 0.102750 | ||||||||
\(949\) | −980.412 | −1.03310 | ||||||||
\(950\) | 2471.90i | 2.60200i | ||||||||
\(951\) | 471.926 | 0.496242 | ||||||||
\(952\) | 111.112i | 0.116714i | ||||||||
\(953\) | −265.279 | −0.278362 | −0.139181 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139181 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(954\) | − | 234.513i | − | 0.245820i | ||||||
\(955\) | 230.354i | 0.241208i | ||||||||
\(956\) | −83.5017 | −0.0873449 | ||||||||
\(957\) | 579.275i | 0.605303i | ||||||||
\(958\) | 250.700i | 0.261691i | ||||||||
\(959\) | 326.070 | 0.340010 | ||||||||
\(960\) | −1098.18 | −1.14394 | ||||||||
\(961\) | 152.280 | 0.158460 | ||||||||
\(962\) | 983.007i | 1.02184i | ||||||||
\(963\) | 82.9451 | 0.0861320 | ||||||||
\(964\) | 51.7027 | 0.0536336 | ||||||||
\(965\) | 1272.89 | 1.31905 | ||||||||
\(966\) | −38.8186 | −0.0401849 | ||||||||
\(967\) | − | 268.791i | − | 0.277964i | −0.990295 | − | 0.138982i | \(-0.955617\pi\) | ||
0.990295 | − | 0.138982i | \(-0.0443830\pi\) | |||||||
\(968\) | 378.680i | 0.391199i | ||||||||
\(969\) | −409.804 | −0.422915 | ||||||||
\(970\) | 2126.03 | 2.19178 | ||||||||
\(971\) | −1302.30 | −1.34120 | −0.670598 | − | 0.741821i | \(-0.733962\pi\) | ||||
−0.670598 | + | 0.741821i | \(0.733962\pi\) | |||||||
\(972\) | −8.28748 | −0.00852621 | ||||||||
\(973\) | −18.9681 | −0.0194944 | ||||||||
\(974\) | 1377.62i | 1.41439i | ||||||||
\(975\) | − | 2319.70i | − | 2.37918i | ||||||
\(976\) | 434.664i | 0.445353i | ||||||||
\(977\) | − | 657.742i | − | 0.673226i | −0.941643 | − | 0.336613i | \(-0.890719\pi\) | ||
0.941643 | − | 0.336613i | \(-0.109281\pi\) | |||||||
\(978\) | − | 29.0876i | − | 0.0297419i | ||||||
\(979\) | 281.170 | 0.287201 | ||||||||
\(980\) | 227.511 | 0.232155 | ||||||||
\(981\) | − | 330.696i | − | 0.337101i | ||||||
\(982\) | 790.483i | 0.804973i | ||||||||
\(983\) | − | 1066.97i | − | 1.08542i | −0.839920 | − | 0.542710i | \(-0.817398\pi\) | ||
0.839920 | − | 0.542710i | \(-0.182602\pi\) | |||||||
\(984\) | − | 650.016i | − | 0.660585i | ||||||
\(985\) | 2002.34 | 2.03283 | ||||||||
\(986\) | − | 489.829i | − | 0.496784i | ||||||
\(987\) | 69.0723i | 0.0699821i | ||||||||
\(988\) | − | 292.731i | − | 0.296286i | ||||||
\(989\) | 396.397 | 0.400806 | ||||||||
\(990\) | −650.871 | −0.657445 | ||||||||
\(991\) | − | 823.329i | − | 0.830806i | −0.909637 | − | 0.415403i | \(-0.863640\pi\) | ||
0.909637 | − | 0.415403i | \(-0.136360\pi\) | |||||||
\(992\) | −240.222 | −0.242159 | ||||||||
\(993\) | 251.948 | 0.253724 | ||||||||
\(994\) | − | 13.9982i | − | 0.0140827i | ||||||
\(995\) | −2553.70 | −2.56654 | ||||||||
\(996\) | 2.89556i | 0.00290719i | ||||||||
\(997\) | −135.805 | −0.136214 | −0.0681068 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681068 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(998\) | − | 19.0018i | − | 0.0190399i | ||||||
\(999\) | − | 116.359i | − | 0.116476i |
(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 | 177.3.c.a.58.6 | ✓ | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.15 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.15 | yes | 20 | |
177.176 | even | 2 | 531.3.c.c.235.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
177.3.c.a.58.15 | yes | 20 | 59.58 | odd | 2 | inner | |
531.3.c.c.235.6 | 20 | 177.176 | even | 2 | |||
531.3.c.c.235.15 | 20 | 3.2 | odd | 2 |