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: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
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 | 58.15 | ||
Root | \(1.86235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.6 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(0.154157\pi\) | ||||
−0.885001 | + | 0.465588i | \(0.845843\pi\) | |||||||
\(3\) | −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 | \(-0.800933\pi\) | ||
0.810736 | − | 0.585411i | \(-0.199067\pi\) | |||||||
\(12\) | −0.920831 | −0.0767359 | ||||||||
\(13\) | − | 23.5709i | − | 1.81315i | −0.422050 | − | 0.906573i | \(-0.638689\pi\) | ||
0.422050 | − | 0.906573i | \(-0.361311\pi\) | |||||||
\(14\) | 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 | \(-0.935496\pi\) | ||
0.979538 | − | 0.201261i | \(-0.0645039\pi\) | |||||||
\(24\) | − | 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 | \(0.151677\pi\) | ||||
−0.888603 | + | 0.458678i | \(0.848323\pi\) | |||||||
\(32\) | 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 | \(-0.902141\pi\) | ||
0.953114 | − | 0.302613i | \(-0.0978588\pi\) | |||||||
\(38\) | − | 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 | \(0.165884\pi\) | ||||
−0.867253 | + | 0.497868i | \(0.834116\pi\) | |||||||
\(44\) | − | 6.84704i | − | 0.155615i | ||||||
\(45\) | −27.1362 | −0.603027 | ||||||||
\(46\) | 17.2417 | 0.374819 | ||||||||
\(47\) | 30.6792i | 0.652749i | 0.945241 | + | 0.326374i | \(0.105827\pi\) | ||||
−0.945241 | + | 0.326374i | \(0.894173\pi\) | |||||||
\(48\) | 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 | \(0.0844315\pi\) | ||||
−0.965027 | + | 0.262150i | \(0.915569\pi\) | |||||||
\(62\) | −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 | \(-0.752185\pi\) | ||
0.711943 | − | 0.702237i | \(-0.247815\pi\) | |||||||
\(68\) | −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 | \(-0.908042\pi\) | ||
0.958560 | − | 0.284892i | \(-0.0919577\pi\) | |||||||
\(74\) | 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 | \(0.00603006\pi\) | ||||
−0.999821 | + | 0.0189428i | \(0.993970\pi\) | |||||||
\(84\) | −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 | \(0.0391391\pi\) | ||||
−0.992450 | + | 0.122649i | \(0.960861\pi\) | |||||||
\(90\) | − | 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 | \(0.225459\pi\) | ||||
−0.759468 | + | 0.650544i | \(0.774541\pi\) | |||||||
\(98\) | − | 88.1085i | − | 0.899067i | ||||||
\(99\) | − | 38.6371i | − | 0.390274i | ||||||
\(100\) | 30.2075 | 0.302075 | ||||||||
\(101\) | − | 71.4450i | − | 0.707376i | −0.935363 | − | 0.353688i | \(-0.884927\pi\) | ||
0.935363 | − | 0.353688i | \(-0.115073\pi\) | |||||||
\(102\) | 32.6712i | 0.320306i | ||||||||
\(103\) | − | 166.064i | − | 1.61228i | −0.591728 | − | 0.806138i | \(-0.701554\pi\) | ||
0.591728 | − | 0.806138i | \(-0.298446\pi\) | |||||||
\(104\) | 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 | \(0.168748\pi\) | ||||
−0.862738 | + | 0.505651i | \(0.831252\pi\) | |||||||
\(110\) | −216.957 | −1.97234 | ||||||||
\(111\) | 38.7864i | 0.349427i | ||||||||
\(112\) | −17.6662 | −0.157734 | ||||||||
\(113\) | − | 69.5553i | − | 0.615534i | −0.951462 | − | 0.307767i | \(-0.900418\pi\) | ||
0.951462 | − | 0.307767i | \(-0.0995817\pi\) | |||||||
\(114\) | 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 | \(-0.611825\pi\) | ||
0.344127 | − | 0.938923i | \(-0.388175\pi\) | |||||||
\(132\) | 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 | \(0.209221\pi\) | ||||
−0.791653 | + | 0.610971i | \(0.790779\pi\) | |||||||
\(150\) | − | 183.281i | − | 1.22188i | ||||||
\(151\) | 31.7495i | 0.210262i | 0.994458 | + | 0.105131i | \(0.0335262\pi\) | ||||
−0.994458 | + | 0.105131i | \(0.966474\pi\) | |||||||
\(152\) | − | 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 | \(0.282750\pi\) | ||||
−0.630744 | + | 0.775991i | \(0.717250\pi\) | |||||||
\(158\) | − | 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 | \(0.289450\pi\) | ||||
−0.614271 | + | 0.789095i | \(0.710550\pi\) | |||||||
\(174\) | 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 | \(-0.900336\pi\) | ||
0.951382 | − | 0.308012i | \(-0.0996638\pi\) | |||||||
\(180\) | −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 | \(0.0212362\pi\) | ||||
−0.997775 | + | 0.0666660i | \(0.978764\pi\) | |||||||
\(192\) | 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 | \(0.00169108\pi\) | ||||
−0.999986 | + | 0.00531265i | \(0.998309\pi\) | |||||||
\(212\) | 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 | \(-0.658474\pi\) | ||
0.477548 | − | 0.878605i | \(-0.341526\pi\) | |||||||
\(228\) | 21.5106 | 0.0943449 | ||||||||
\(229\) | 52.2219i | 0.228043i | 0.993478 | + | 0.114022i | \(0.0363733\pi\) | ||||
−0.993478 | + | 0.114022i | \(0.963627\pi\) | |||||||
\(230\) | −155.958 | −0.678078 | ||||||||
\(231\) | 28.9964i | 0.125525i | ||||||||
\(232\) | − | 219.158i | − | 0.944648i | ||||||
\(233\) | − | 420.216i | − | 1.80350i | −0.432255 | − | 0.901751i | \(-0.642282\pi\) | ||
0.432255 | − | 0.901751i | \(-0.357718\pi\) | |||||||
\(234\) | 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 | \(-0.903201\pi\) | ||
0.954116 | − | 0.299437i | \(-0.0967989\pi\) | |||||||
\(270\) | 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 | \(-0.779216\pi\) | ||
0.768941 | − | 0.639320i | \(-0.220784\pi\) | |||||||
\(284\) | 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 | \(0.0415374\pi\) | ||||
−0.991498 | + | 0.130124i | \(0.958463\pi\) | |||||||
\(314\) | −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 | \(-0.916701\pi\) | ||
0.965954 | − | 0.258714i | \(-0.0832986\pi\) | |||||||
\(338\) | − | 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 | \(0.177254\pi\) | ||||
−0.848919 | + | 0.528524i | \(0.822746\pi\) | |||||||
\(348\) | 23.9122 | 0.0687134 | ||||||||
\(349\) | − | 208.270i | − | 0.596763i | −0.954447 | − | 0.298382i | \(-0.903553\pi\) | ||
0.954447 | − | 0.298382i | \(-0.0964468\pi\) | |||||||
\(350\) | 137.549i | 0.392997i | ||||||||
\(351\) | 122.478i | 0.348940i | ||||||||
\(352\) | 108.792 | 0.309069 | ||||||||
\(353\) | − | 174.980i | − | 0.495695i | −0.968799 | − | 0.247847i | \(-0.920277\pi\) | ||
0.968799 | − | 0.247847i | \(-0.0797231\pi\) | |||||||
\(354\) | −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 | \(-0.752797\pi\) | ||
0.713293 | − | 0.700866i | \(-0.247203\pi\) | |||||||
\(368\) | 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 | \(0.220865\pi\) | ||||
−0.768779 | + | 0.639515i | \(0.779135\pi\) | |||||||
\(398\) | 525.780i | 1.32106i | ||||||||
\(399\) | 52.5937 | 0.131814 | ||||||||
\(400\) | −772.219 | −1.93055 | ||||||||
\(401\) | − | 427.106i | − | 1.06510i | −0.846398 | − | 0.532551i | \(-0.821233\pi\) | ||
0.846398 | − | 0.532551i | \(-0.178767\pi\) | |||||||
\(402\) | −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 | \(0.0604485\pi\) | ||||
−0.982022 | + | 0.188765i | \(0.939551\pi\) | |||||||
\(410\) | 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 | \(0.150525\pi\) | ||||
−0.890257 | + | 0.455458i | \(0.849475\pi\) | |||||||
\(420\) | 10.8270 | 0.0257785 | ||||||||
\(421\) | − | 223.524i | − | 0.530935i | −0.964120 | − | 0.265468i | \(-0.914474\pi\) | ||
0.964120 | − | 0.265468i | \(-0.0855263\pi\) | |||||||
\(422\) | −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 | \(0.0221169\pi\) | ||||
−0.997587 | + | 0.0694264i | \(0.977883\pi\) | |||||||
\(432\) | 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 | \(-0.966140\pi\) | ||
0.994348 | − | 0.106174i | \(-0.0338601\pi\) | |||||||
\(444\) | 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 | \(0.125789\pi\) | ||||
−0.922928 | + | 0.384973i | \(0.874211\pi\) | |||||||
\(458\) | −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 | \(-0.887146\pi\) | ||
0.937806 | − | 0.347159i | \(-0.112854\pi\) | |||||||
\(464\) | 352.927 | 0.760619 | ||||||||
\(465\) | 445.541i | 0.958153i | ||||||||
\(466\) | 782.591 | 1.67938 | ||||||||
\(467\) | − | 631.306i | − | 1.35183i | −0.736978 | − | 0.675916i | \(-0.763748\pi\) | ||
0.736978 | − | 0.675916i | \(-0.236252\pi\) | |||||||
\(468\) | − | 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 | \(0.0600697\pi\) | ||||
−0.982246 | + | 0.187596i | \(0.939930\pi\) | |||||||
\(504\) | 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 | \(0.373816\pi\) | ||||
−0.386116 | + | 0.922450i | \(0.626184\pi\) | |||||||
\(510\) | − | 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 | \(-0.689506\pi\) | ||
0.560800 | − | 0.827951i | \(-0.310494\pi\) | |||||||
\(542\) | − | 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 | \(-0.921804\pi\) | ||
0.969977 | − | 0.243195i | \(-0.0781956\pi\) | |||||||
\(564\) | − | 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 | \(0.194390\pi\) | ||||
−0.819250 | + | 0.573437i | \(0.805610\pi\) | |||||||
\(570\) | − | 681.591i | − | 1.19577i | ||||||
\(571\) | − | 373.051i | − | 0.653329i | −0.945140 | − | 0.326664i | \(-0.894075\pi\) | ||
0.945140 | − | 0.326664i | \(-0.105925\pi\) | |||||||
\(572\) | −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 | \(-0.990629\pi\) | ||
0.999567 | − | 0.0294344i | \(-0.00937062\pi\) | |||||||
\(588\) | 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 | \(-0.971498\pi\) | ||
0.995994 | − | 0.0894236i | \(-0.0285025\pi\) | |||||||
\(602\) | −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 | \(-0.738115\pi\) | ||
0.680217 | − | 0.733011i | \(-0.261885\pi\) | |||||||
\(614\) | 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 | \(-0.996921\pi\) | ||
0.999953 | − | 0.00967254i | \(-0.00307891\pi\) | |||||||
\(660\) | − | 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 | \(0.127671\pi\) | ||||
−0.920636 | + | 0.390423i | \(0.872329\pi\) | |||||||
\(674\) | 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 | \(-0.854681\pi\) | ||
0.897586 | − | 0.440839i | \(-0.145319\pi\) | |||||||
\(684\) | −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 | \(-0.715500\pi\) | ||
0.626469 | − | 0.779447i | \(-0.284500\pi\) | |||||||
\(692\) | 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 | \(-0.947889\pi\) | ||
0.986629 | − | 0.162983i | \(-0.0521115\pi\) | |||||||
\(702\) | −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 | \(-0.833145\pi\) | ||
0.865729 | − | 0.500512i | \(-0.166855\pi\) | |||||||
\(720\) | 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 | \(0.0340770\pi\) | ||||
−0.994275 | + | 0.106852i | \(0.965923\pi\) | |||||||
\(740\) | 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 | \(-0.772395\pi\) | ||
0.755065 | − | 0.655650i | \(-0.227605\pi\) | |||||||
\(752\) | − | 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 | \(-0.879207\pi\) | ||
0.928856 | − | 0.370441i | \(-0.120793\pi\) | |||||||
\(770\) | −282.016 | −0.366254 | ||||||||
\(771\) | −689.431 | −0.894204 | ||||||||
\(772\) | −74.8138 | −0.0969090 | ||||||||
\(773\) | − | 401.753i | − | 0.519732i | −0.965645 | − | 0.259866i | \(-0.916322\pi\) | ||
0.965645 | − | 0.259866i | \(-0.0836784\pi\) | |||||||
\(774\) | −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 | \(0.361839\pi\) | ||||
−0.420545 | + | 0.907272i | \(0.638161\pi\) | |||||||
\(798\) | 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 | \(0.156510\pi\) | ||||
−0.881535 | + | 0.472118i | \(0.843490\pi\) | |||||||
\(810\) | − | 151.612i | − | 0.187175i | ||||||
\(811\) | − | 109.080i | − | 0.134500i | −0.997736 | − | 0.0672500i | \(-0.978577\pi\) | ||
0.997736 | − | 0.0672500i | \(-0.0214225\pi\) | |||||||
\(812\) | −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 | \(0.111113\pi\) | ||||
−0.939690 | + | 0.342026i | \(0.888887\pi\) | |||||||
\(822\) | − | 809.158i | − | 0.984378i | ||||||
\(823\) | − | 817.432i | − | 0.993235i | −0.867970 | − | 0.496617i | \(-0.834575\pi\) | ||
0.867970 | − | 0.496617i | \(-0.165425\pi\) | |||||||
\(824\) | 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 | \(0.277517\pi\) | ||||
−0.643415 | + | 0.765518i | \(0.722483\pi\) | |||||||
\(840\) | 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 | \(-0.911934\pi\) | ||
0.961971 | − | 0.273150i | \(-0.0880656\pi\) | |||||||
\(858\) | 979.225i | 1.14129i | ||||||||
\(859\) | − | 387.001i | − | 0.450525i | −0.974298 | − | 0.225262i | \(-0.927676\pi\) | ||
0.974298 | − | 0.225262i | \(-0.0723239\pi\) | |||||||
\(860\) | − | 205.902i | − | 0.239420i | ||||||
\(861\) | 100.117 | 0.116279 | ||||||||
\(862\) | −111.454 | −0.129296 | ||||||||
\(863\) | 1197.58i | 1.38769i | 0.720123 | + | 0.693846i | \(0.244085\pi\) | ||||
−0.720123 | + | 0.693846i | \(0.755915\pi\) | |||||||
\(864\) | − | 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 | \(0.000830018\pi\) | ||||
−0.999997 | + | 0.00260758i | \(0.999170\pi\) | |||||||
\(882\) | − | 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 | \(0.128822\pi\) | ||||
−0.919219 | + | 0.393747i | \(0.871178\pi\) | |||||||
\(888\) | −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 | \(-0.795336\pi\) | ||
0.800318 | − | 0.599576i | \(-0.204664\pi\) | |||||||
\(920\) | −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 | \(-0.810354\pi\) | ||
0.827705 | − | 0.561164i | \(-0.189646\pi\) | |||||||
\(930\) | −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 | \(0.0978660\pi\) | ||||
−0.953107 | + | 0.302634i | \(0.902134\pi\) | |||||||
\(938\) | 227.798 | 0.242855 | ||||||||
\(939\) | − | 141.088i | − | 0.150254i | ||||||
\(940\) | − | 147.534i | − | 0.156951i | ||||||
\(941\) | − | 105.988i | − | 0.112633i | −0.998413 | − | 0.0563167i | \(-0.982064\pi\) | ||
0.998413 | − | 0.0563167i | \(-0.0179356\pi\) | |||||||
\(942\) | 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 | \(0.0443830\pi\) | ||||
−0.990295 | + | 0.138982i | \(0.955617\pi\) | |||||||
\(968\) | − | 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 | \(0.109281\pi\) | ||||
−0.941643 | + | 0.336613i | \(0.890719\pi\) | |||||||
\(978\) | 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 | \(0.182602\pi\) | ||||
−0.839920 | + | 0.542710i | \(0.817398\pi\) | |||||||
\(984\) | 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 | \(0.136360\pi\) | ||||
−0.909637 | + | 0.415403i | \(0.863640\pi\) | |||||||
\(992\) | −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.58.15 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.6 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.6 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.15 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.6 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.15 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.6 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.15 | 20 | 177.176 | even | 2 |