Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(204,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.204");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 60x^{6} + 118x^{4} + 96x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 204.6 | ||
Root | \(1.45275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.204 |
Dual form | 287.2.c.a.204.5 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.889527 | 0.628991 | 0.314495 | − | 0.949259i | \(-0.398165\pi\) | ||||
0.314495 | + | 0.949259i | \(0.398165\pi\) | |||||||
\(3\) | 2.45275i | 1.41609i | 0.706165 | + | 0.708047i | \(0.250424\pi\) | ||||
−0.706165 | + | 0.708047i | \(0.749576\pi\) | |||||||
\(4\) | −1.20874 | −0.604371 | ||||||||
\(5\) | 0.645522 | 0.288686 | 0.144343 | − | 0.989528i | \(-0.453893\pi\) | ||||
0.144343 | + | 0.989528i | \(0.453893\pi\) | |||||||
\(6\) | 2.18179i | 0.890710i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.85426 | −1.00913 | ||||||||
\(9\) | −3.01597 | −1.00532 | ||||||||
\(10\) | 0.574209 | 0.181581 | ||||||||
\(11\) | 3.84327i | 1.15879i | 0.815047 | + | 0.579395i | \(0.196711\pi\) | ||||
−0.815047 | + | 0.579395i | \(0.803289\pi\) | |||||||
\(12\) | − | 2.96474i | − | 0.855845i | ||||||
\(13\) | 2.91648i | 0.808887i | 0.914563 | + | 0.404443i | \(0.132535\pi\) | ||||
−0.914563 | + | 0.404443i | \(0.867465\pi\) | |||||||
\(14\) | 0.889527i | 0.237736i | ||||||||
\(15\) | 1.58330i | 0.408807i | ||||||||
\(16\) | −0.121463 | −0.0303657 | ||||||||
\(17\) | − | 3.75599i | − | 0.910962i | −0.890245 | − | 0.455481i | \(-0.849467\pi\) | ||
0.890245 | − | 0.455481i | \(-0.150533\pi\) | |||||||
\(18\) | −2.68278 | −0.632338 | ||||||||
\(19\) | − | 3.44176i | − | 0.789593i | −0.918769 | − | 0.394797i | \(-0.870815\pi\) | ||
0.918769 | − | 0.394797i | \(-0.129185\pi\) | |||||||
\(20\) | −0.780269 | −0.174473 | ||||||||
\(21\) | −2.45275 | −0.535233 | ||||||||
\(22\) | 3.41870i | 0.728869i | ||||||||
\(23\) | 3.35824 | 0.700241 | 0.350121 | − | 0.936705i | \(-0.386141\pi\) | ||||
0.350121 | + | 0.936705i | \(0.386141\pi\) | |||||||
\(24\) | − | 7.00078i | − | 1.42903i | ||||||
\(25\) | −4.58330 | −0.916660 | ||||||||
\(26\) | 2.59429i | 0.508782i | ||||||||
\(27\) | − | 0.0391601i | − | 0.00753637i | ||||||
\(28\) | − | 1.20874i | − | 0.228431i | ||||||
\(29\) | 5.39429i | 1.00169i | 0.865536 | + | 0.500847i | \(0.166978\pi\) | ||||
−0.865536 | + | 0.500847i | \(0.833022\pi\) | |||||||
\(30\) | 1.40839i | 0.257136i | ||||||||
\(31\) | 6.35648 | 1.14166 | 0.570828 | − | 0.821069i | \(-0.306622\pi\) | ||||
0.570828 | + | 0.821069i | \(0.306622\pi\) | |||||||
\(32\) | 5.60048 | 0.990035 | ||||||||
\(33\) | −9.42657 | −1.64096 | ||||||||
\(34\) | − | 3.34106i | − | 0.572987i | ||||||
\(35\) | 0.645522i | 0.109113i | ||||||||
\(36\) | 3.64552 | 0.607587 | ||||||||
\(37\) | 5.14531 | 0.845883 | 0.422942 | − | 0.906157i | \(-0.360998\pi\) | ||||
0.422942 | + | 0.906157i | \(0.360998\pi\) | |||||||
\(38\) | − | 3.06154i | − | 0.496647i | ||||||
\(39\) | −7.15339 | −1.14546 | ||||||||
\(40\) | −1.84249 | −0.291323 | ||||||||
\(41\) | 5.62233 | − | 3.06422i | 0.878060 | − | 0.478550i | ||||
\(42\) | −2.18179 | −0.336657 | ||||||||
\(43\) | 10.5370 | 1.60688 | 0.803442 | − | 0.595383i | \(-0.203000\pi\) | ||||
0.803442 | + | 0.595383i | \(0.203000\pi\) | |||||||
\(44\) | − | 4.64552i | − | 0.700339i | ||||||
\(45\) | −1.94687 | −0.290223 | ||||||||
\(46\) | 2.98725 | 0.440445 | ||||||||
\(47\) | − | 6.65972i | − | 0.971421i | −0.874120 | − | 0.485710i | \(-0.838561\pi\) | ||
0.874120 | − | 0.485710i | \(-0.161439\pi\) | |||||||
\(48\) | − | 0.297917i | − | 0.0430007i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.07697 | −0.576571 | ||||||||
\(51\) | 9.21250 | 1.29001 | ||||||||
\(52\) | − | 3.52527i | − | 0.488867i | ||||||
\(53\) | − | 2.47849i | − | 0.340447i | −0.985406 | − | 0.170223i | \(-0.945551\pi\) | ||
0.985406 | − | 0.170223i | \(-0.0544489\pi\) | |||||||
\(54\) | − | 0.0348340i | − | 0.00474031i | ||||||
\(55\) | 2.48092i | 0.334527i | ||||||||
\(56\) | − | 2.85426i | − | 0.381417i | ||||||
\(57\) | 8.44176 | 1.11814 | ||||||||
\(58\) | 4.79837i | 0.630056i | ||||||||
\(59\) | 6.30256 | 0.820524 | 0.410262 | − | 0.911968i | \(-0.365437\pi\) | ||||
0.410262 | + | 0.911968i | \(0.365437\pi\) | |||||||
\(60\) | − | 1.91380i | − | 0.247071i | ||||||
\(61\) | −11.1343 | −1.42560 | −0.712802 | − | 0.701366i | \(-0.752574\pi\) | ||||
−0.712802 | + | 0.701366i | \(0.752574\pi\) | |||||||
\(62\) | 5.65426 | 0.718092 | ||||||||
\(63\) | − | 3.01597i | − | 0.379976i | ||||||
\(64\) | 5.22471 | 0.653088 | ||||||||
\(65\) | 1.88265i | 0.233514i | ||||||||
\(66\) | −8.38520 | −1.03215 | ||||||||
\(67\) | 3.57300i | 0.436511i | 0.975892 | + | 0.218255i | \(0.0700366\pi\) | ||||
−0.975892 | + | 0.218255i | \(0.929963\pi\) | |||||||
\(68\) | 4.54002i | 0.550559i | ||||||||
\(69\) | 8.23691i | 0.991608i | ||||||||
\(70\) | 0.574209i | 0.0686311i | ||||||||
\(71\) | 8.70265i | 1.03281i | 0.856343 | + | 0.516407i | \(0.172731\pi\) | ||||
−0.856343 | + | 0.516407i | \(0.827269\pi\) | |||||||
\(72\) | 8.60836 | 1.01450 | ||||||||
\(73\) | −6.04224 | −0.707190 | −0.353595 | − | 0.935399i | \(-0.615041\pi\) | ||||
−0.353595 | + | 0.935399i | \(0.615041\pi\) | |||||||
\(74\) | 4.57689 | 0.532053 | ||||||||
\(75\) | − | 11.2417i | − | 1.29808i | ||||||
\(76\) | 4.16019i | 0.477207i | ||||||||
\(77\) | −3.84327 | −0.437982 | ||||||||
\(78\) | −6.36314 | −0.720484 | ||||||||
\(79\) | − | 6.53949i | − | 0.735751i | −0.929875 | − | 0.367875i | \(-0.880085\pi\) | ||
0.929875 | − | 0.367875i | \(-0.119915\pi\) | |||||||
\(80\) | −0.0784069 | −0.00876615 | ||||||||
\(81\) | −8.95185 | −0.994650 | ||||||||
\(82\) | 5.00121 | − | 2.72571i | 0.552292 | − | 0.301004i | ||||
\(83\) | −13.3872 | −1.46944 | −0.734718 | − | 0.678373i | \(-0.762685\pi\) | ||||
−0.734718 | + | 0.678373i | \(0.762685\pi\) | |||||||
\(84\) | 2.96474 | 0.323479 | ||||||||
\(85\) | − | 2.42458i | − | 0.262982i | ||||||
\(86\) | 9.37299 | 1.01072 | ||||||||
\(87\) | −13.2308 | −1.41849 | ||||||||
\(88\) | − | 10.9697i | − | 1.16938i | ||||||
\(89\) | 1.08030i | 0.114512i | 0.998360 | + | 0.0572560i | \(0.0182351\pi\) | ||||
−0.998360 | + | 0.0572560i | \(0.981765\pi\) | |||||||
\(90\) | −1.73180 | −0.182547 | ||||||||
\(91\) | −2.91648 | −0.305731 | ||||||||
\(92\) | −4.05924 | −0.423205 | ||||||||
\(93\) | 15.5908i | 1.61669i | ||||||||
\(94\) | − | 5.92401i | − | 0.611015i | ||||||
\(95\) | − | 2.22173i | − | 0.227945i | ||||||
\(96\) | 13.7366i | 1.40198i | ||||||||
\(97\) | − | 13.8403i | − | 1.40527i | −0.711551 | − | 0.702635i | \(-0.752007\pi\) | ||
0.711551 | − | 0.702635i | \(-0.247993\pi\) | |||||||
\(98\) | −0.889527 | −0.0898558 | ||||||||
\(99\) | − | 11.5912i | − | 1.16496i | ||||||
\(100\) | 5.54002 | 0.554002 | ||||||||
\(101\) | 2.45596i | 0.244377i | 0.992507 | + | 0.122189i | \(0.0389912\pi\) | ||||
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(102\) | 8.19477 | 0.811403 | ||||||||
\(103\) | 2.14720 | 0.211570 | 0.105785 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(104\) | − | 8.32441i | − | 0.816276i | ||||||
\(105\) | −1.58330 | −0.154514 | ||||||||
\(106\) | − | 2.20468i | − | 0.214138i | ||||||
\(107\) | −7.70173 | −0.744554 | −0.372277 | − | 0.928122i | \(-0.621423\pi\) | ||||
−0.372277 | + | 0.928122i | \(0.621423\pi\) | |||||||
\(108\) | 0.0473345i | 0.00455476i | ||||||||
\(109\) | − | 8.54592i | − | 0.818551i | −0.912411 | − | 0.409275i | \(-0.865782\pi\) | ||
0.912411 | − | 0.409275i | \(-0.134218\pi\) | |||||||
\(110\) | 2.20684i | 0.210414i | ||||||||
\(111\) | 12.6201i | 1.19785i | ||||||||
\(112\) | − | 0.121463i | − | 0.0114772i | ||||||
\(113\) | −9.09439 | −0.855528 | −0.427764 | − | 0.903890i | \(-0.640699\pi\) | ||||
−0.427764 | + | 0.903890i | \(0.640699\pi\) | |||||||
\(114\) | 7.50917 | 0.703299 | ||||||||
\(115\) | 2.16782 | 0.202150 | ||||||||
\(116\) | − | 6.52030i | − | 0.605394i | ||||||
\(117\) | − | 8.79601i | − | 0.813192i | ||||||
\(118\) | 5.60630 | 0.516102 | ||||||||
\(119\) | 3.75599 | 0.344311 | ||||||||
\(120\) | − | 4.51916i | − | 0.412541i | ||||||
\(121\) | −3.77075 | −0.342795 | ||||||||
\(122\) | −9.90428 | −0.896691 | ||||||||
\(123\) | 7.51575 | + | 13.7901i | 0.677672 | + | 1.24342i | ||||
\(124\) | −7.68333 | −0.689984 | ||||||||
\(125\) | −6.18623 | −0.553313 | ||||||||
\(126\) | − | 2.68278i | − | 0.239001i | ||||||
\(127\) | 1.11545 | 0.0989800 | 0.0494900 | − | 0.998775i | \(-0.484240\pi\) | ||||
0.0494900 | + | 0.998775i | \(0.484240\pi\) | |||||||
\(128\) | −6.55344 | −0.579248 | ||||||||
\(129\) | 25.8447i | 2.27550i | ||||||||
\(130\) | 1.67467i | 0.146878i | ||||||||
\(131\) | 9.15951 | 0.800270 | 0.400135 | − | 0.916456i | \(-0.368963\pi\) | ||||
0.400135 | + | 0.916456i | \(0.368963\pi\) | |||||||
\(132\) | 11.3943 | 0.991745 | ||||||||
\(133\) | 3.44176 | 0.298438 | ||||||||
\(134\) | 3.17828i | 0.274561i | ||||||||
\(135\) | − | 0.0252787i | − | 0.00217565i | ||||||
\(136\) | 10.7206i | 0.919284i | ||||||||
\(137\) | 12.1087i | 1.03452i | 0.855830 | + | 0.517258i | \(0.173047\pi\) | ||||
−0.855830 | + | 0.517258i | \(0.826953\pi\) | |||||||
\(138\) | 7.32696i | 0.623712i | ||||||||
\(139\) | 23.1662 | 1.96494 | 0.982468 | − | 0.186433i | \(-0.0596926\pi\) | ||||
0.982468 | + | 0.186433i | \(0.0596926\pi\) | |||||||
\(140\) | − | 0.780269i | − | 0.0659447i | ||||||
\(141\) | 16.3346 | 1.37562 | ||||||||
\(142\) | 7.74124i | 0.649631i | ||||||||
\(143\) | −11.2088 | −0.937330 | ||||||||
\(144\) | 0.366328 | 0.0305273 | ||||||||
\(145\) | 3.48213i | 0.289175i | ||||||||
\(146\) | −5.37474 | −0.444816 | ||||||||
\(147\) | − | 2.45275i | − | 0.202299i | ||||||
\(148\) | −6.21934 | −0.511227 | ||||||||
\(149\) | 19.4195i | 1.59091i | 0.606015 | + | 0.795453i | \(0.292767\pi\) | ||||
−0.606015 | + | 0.795453i | \(0.707233\pi\) | |||||||
\(150\) | − | 9.99978i | − | 0.816479i | ||||||
\(151\) | − | 20.2144i | − | 1.64502i | −0.568749 | − | 0.822511i | \(-0.692573\pi\) | ||
0.568749 | − | 0.822511i | \(-0.307427\pi\) | |||||||
\(152\) | 9.82368i | 0.796806i | ||||||||
\(153\) | 11.3280i | 0.915811i | ||||||||
\(154\) | −3.41870 | −0.275486 | ||||||||
\(155\) | 4.10324 | 0.329581 | ||||||||
\(156\) | 8.64660 | 0.692282 | ||||||||
\(157\) | − | 9.86633i | − | 0.787419i | −0.919235 | − | 0.393710i | \(-0.871192\pi\) | ||
0.919235 | − | 0.393710i | \(-0.128808\pi\) | |||||||
\(158\) | − | 5.81706i | − | 0.462780i | ||||||
\(159\) | 6.07910 | 0.482104 | ||||||||
\(160\) | 3.61523 | 0.285809 | ||||||||
\(161\) | 3.35824i | 0.264666i | ||||||||
\(162\) | −7.96291 | −0.625626 | ||||||||
\(163\) | −3.17416 | −0.248619 | −0.124310 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124310 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(164\) | −6.79594 | + | 3.70385i | −0.530674 | + | 0.289222i | ||||
\(165\) | −6.08506 | −0.473721 | ||||||||
\(166\) | −11.9083 | −0.924261 | ||||||||
\(167\) | − | 15.2755i | − | 1.18205i | −0.806652 | − | 0.591027i | \(-0.798723\pi\) | ||
0.806652 | − | 0.591027i | \(-0.201277\pi\) | |||||||
\(168\) | 7.00078 | 0.540122 | ||||||||
\(169\) | 4.49413 | 0.345702 | ||||||||
\(170\) | − | 2.15673i | − | 0.165413i | ||||||
\(171\) | 10.3802i | 0.793795i | ||||||||
\(172\) | −12.7366 | −0.971154 | ||||||||
\(173\) | −12.0717 | −0.917798 | −0.458899 | − | 0.888489i | \(-0.651756\pi\) | ||||
−0.458899 | + | 0.888489i | \(0.651756\pi\) | |||||||
\(174\) | −11.7692 | −0.892219 | ||||||||
\(175\) | − | 4.58330i | − | 0.346465i | ||||||
\(176\) | − | 0.466815i | − | 0.0351875i | ||||||
\(177\) | 15.4586i | 1.16194i | ||||||||
\(178\) | 0.960961i | 0.0720270i | ||||||||
\(179\) | 22.8279i | 1.70624i | 0.521719 | + | 0.853118i | \(0.325291\pi\) | ||||
−0.521719 | + | 0.853118i | \(0.674709\pi\) | |||||||
\(180\) | 2.35326 | 0.175402 | ||||||||
\(181\) | − | 12.9774i | − | 0.964599i | −0.876006 | − | 0.482300i | \(-0.839802\pi\) | ||
0.876006 | − | 0.482300i | \(-0.160198\pi\) | |||||||
\(182\) | −2.59429 | −0.192302 | ||||||||
\(183\) | − | 27.3097i | − | 2.01879i | ||||||
\(184\) | −9.58530 | −0.706638 | ||||||||
\(185\) | 3.32141 | 0.244195 | ||||||||
\(186\) | 13.8685i | 1.01689i | ||||||||
\(187\) | 14.4353 | 1.05561 | ||||||||
\(188\) | 8.04988i | 0.587098i | ||||||||
\(189\) | 0.0391601 | 0.00284848 | ||||||||
\(190\) | − | 1.97629i | − | 0.143375i | ||||||
\(191\) | 4.12201i | 0.298258i | 0.988818 | + | 0.149129i | \(0.0476470\pi\) | ||||
−0.988818 | + | 0.149129i | \(0.952353\pi\) | |||||||
\(192\) | 12.8149i | 0.924834i | ||||||||
\(193\) | − | 12.5219i | − | 0.901344i | −0.892690 | − | 0.450672i | \(-0.851184\pi\) | ||
0.892690 | − | 0.450672i | \(-0.148816\pi\) | |||||||
\(194\) | − | 12.3113i | − | 0.883901i | ||||||
\(195\) | −4.61767 | −0.330678 | ||||||||
\(196\) | 1.20874 | 0.0863386 | ||||||||
\(197\) | −7.78119 | −0.554387 | −0.277193 | − | 0.960814i | \(-0.589404\pi\) | ||||
−0.277193 | + | 0.960814i | \(0.589404\pi\) | |||||||
\(198\) | − | 10.3107i | − | 0.732747i | ||||||
\(199\) | − | 6.42847i | − | 0.455702i | −0.973696 | − | 0.227851i | \(-0.926830\pi\) | ||
0.973696 | − | 0.227851i | \(-0.0731700\pi\) | |||||||
\(200\) | 13.0819 | 0.925033 | ||||||||
\(201\) | −8.76365 | −0.618140 | ||||||||
\(202\) | 2.18464i | 0.153711i | ||||||||
\(203\) | −5.39429 | −0.378605 | ||||||||
\(204\) | −11.1355 | −0.779643 | ||||||||
\(205\) | 3.62934 | − | 1.97802i | 0.253484 | − | 0.138151i | ||||
\(206\) | 1.91000 | 0.133076 | ||||||||
\(207\) | −10.1283 | −0.703968 | ||||||||
\(208\) | − | 0.354244i | − | 0.0245624i | ||||||
\(209\) | 13.2276 | 0.914973 | ||||||||
\(210\) | −1.40839 | −0.0971881 | ||||||||
\(211\) | 23.8093i | 1.63910i | 0.573006 | + | 0.819551i | \(0.305777\pi\) | ||||
−0.573006 | + | 0.819551i | \(0.694223\pi\) | |||||||
\(212\) | 2.99585i | 0.205756i | ||||||||
\(213\) | −21.3454 | −1.46256 | ||||||||
\(214\) | −6.85090 | −0.468318 | ||||||||
\(215\) | 6.80189 | 0.463885 | ||||||||
\(216\) | 0.111773i | 0.00760521i | ||||||||
\(217\) | 6.35648i | 0.431506i | ||||||||
\(218\) | − | 7.60183i | − | 0.514861i | ||||||
\(219\) | − | 14.8201i | − | 1.00145i | ||||||
\(220\) | − | 2.99879i | − | 0.202178i | ||||||
\(221\) | 10.9543 | 0.736866 | ||||||||
\(222\) | 11.2260i | 0.753437i | ||||||||
\(223\) | −0.0390260 | −0.00261338 | −0.00130669 | − | 0.999999i | \(-0.500416\pi\) | ||||
−0.00130669 | + | 0.999999i | \(0.500416\pi\) | |||||||
\(224\) | 5.60048i | 0.374198i | ||||||||
\(225\) | 13.8231 | 0.921539 | ||||||||
\(226\) | −8.08971 | −0.538119 | ||||||||
\(227\) | − | 0.138275i | − | 0.00917760i | −0.999989 | − | 0.00458880i | \(-0.998539\pi\) | ||
0.999989 | − | 0.00458880i | \(-0.00146067\pi\) | |||||||
\(228\) | −10.2039 | −0.675770 | ||||||||
\(229\) | − | 15.1728i | − | 1.00265i | −0.865260 | − | 0.501323i | \(-0.832847\pi\) | ||
0.865260 | − | 0.501323i | \(-0.167153\pi\) | |||||||
\(230\) | 1.92833 | 0.127150 | ||||||||
\(231\) | − | 9.42657i | − | 0.620223i | ||||||
\(232\) | − | 15.3967i | − | 1.01084i | ||||||
\(233\) | 13.9493i | 0.913849i | 0.889505 | + | 0.456925i | \(0.151049\pi\) | ||||
−0.889505 | + | 0.456925i | \(0.848951\pi\) | |||||||
\(234\) | − | 7.82429i | − | 0.511490i | ||||||
\(235\) | − | 4.29900i | − | 0.280436i | ||||||
\(236\) | −7.61817 | −0.495901 | ||||||||
\(237\) | 16.0397 | 1.04189 | ||||||||
\(238\) | 3.34106 | 0.216569 | ||||||||
\(239\) | − | 10.1689i | − | 0.657773i | −0.944370 | − | 0.328886i | \(-0.893327\pi\) | ||
0.944370 | − | 0.328886i | \(-0.106673\pi\) | |||||||
\(240\) | − | 0.192312i | − | 0.0124137i | ||||||
\(241\) | 18.8926 | 1.21698 | 0.608490 | − | 0.793562i | \(-0.291776\pi\) | ||||
0.608490 | + | 0.793562i | \(0.291776\pi\) | |||||||
\(242\) | −3.35418 | −0.215615 | ||||||||
\(243\) | − | 22.0741i | − | 1.41605i | ||||||
\(244\) | 13.4585 | 0.861593 | ||||||||
\(245\) | −0.645522 | −0.0412409 | ||||||||
\(246\) | 6.68547 | + | 12.2667i | 0.426250 | + | 0.782097i | ||||
\(247\) | 10.0378 | 0.638692 | ||||||||
\(248\) | −18.1431 | −1.15209 | ||||||||
\(249\) | − | 32.8354i | − | 2.08086i | ||||||
\(250\) | −5.50282 | −0.348029 | ||||||||
\(251\) | −0.256759 | −0.0162065 | −0.00810325 | − | 0.999967i | \(-0.502579\pi\) | ||||
−0.00810325 | + | 0.999967i | \(0.502579\pi\) | |||||||
\(252\) | 3.64552i | 0.229646i | ||||||||
\(253\) | 12.9066i | 0.811433i | ||||||||
\(254\) | 0.992222 | 0.0622575 | ||||||||
\(255\) | 5.94687 | 0.372408 | ||||||||
\(256\) | −16.2789 | −1.01743 | ||||||||
\(257\) | 3.75296i | 0.234103i | 0.993126 | + | 0.117052i | \(0.0373443\pi\) | ||||
−0.993126 | + | 0.117052i | \(0.962656\pi\) | |||||||
\(258\) | 22.9896i | 1.43127i | ||||||||
\(259\) | 5.14531i | 0.319714i | ||||||||
\(260\) | − | 2.27564i | − | 0.141129i | ||||||
\(261\) | − | 16.2690i | − | 1.00703i | ||||||
\(262\) | 8.14763 | 0.503362 | ||||||||
\(263\) | 12.4356i | 0.766811i | 0.923580 | + | 0.383405i | \(0.125249\pi\) | ||||
−0.923580 | + | 0.383405i | \(0.874751\pi\) | |||||||
\(264\) | 26.9059 | 1.65595 | ||||||||
\(265\) | − | 1.59992i | − | 0.0982822i | ||||||
\(266\) | 3.06154 | 0.187715 | ||||||||
\(267\) | −2.64971 | −0.162160 | ||||||||
\(268\) | − | 4.31883i | − | 0.263814i | ||||||
\(269\) | 18.8382 | 1.14858 | 0.574292 | − | 0.818651i | \(-0.305277\pi\) | ||||
0.574292 | + | 0.818651i | \(0.305277\pi\) | |||||||
\(270\) | − | 0.0224861i | − | 0.00136846i | ||||||
\(271\) | −28.1232 | −1.70836 | −0.854182 | − | 0.519974i | \(-0.825942\pi\) | ||||
−0.854182 | + | 0.519974i | \(0.825942\pi\) | |||||||
\(272\) | 0.456213i | 0.0276620i | ||||||||
\(273\) | − | 7.15339i | − | 0.432943i | ||||||
\(274\) | 10.7710i | 0.650701i | ||||||||
\(275\) | − | 17.6149i | − | 1.06222i | ||||||
\(276\) | − | 9.95629i | − | 0.599298i | ||||||
\(277\) | 10.7064 | 0.643286 | 0.321643 | − | 0.946861i | \(-0.395765\pi\) | ||||
0.321643 | + | 0.946861i | \(0.395765\pi\) | |||||||
\(278\) | 20.6070 | 1.23593 | ||||||||
\(279\) | −19.1709 | −1.14773 | ||||||||
\(280\) | − | 1.84249i | − | 0.110110i | ||||||
\(281\) | 2.23098i | 0.133089i | 0.997783 | + | 0.0665447i | \(0.0211975\pi\) | ||||
−0.997783 | + | 0.0665447i | \(0.978803\pi\) | |||||||
\(282\) | 14.5301 | 0.865254 | ||||||||
\(283\) | 19.7225 | 1.17238 | 0.586190 | − | 0.810174i | \(-0.300627\pi\) | ||||
0.586190 | + | 0.810174i | \(0.300627\pi\) | |||||||
\(284\) | − | 10.5192i | − | 0.624202i | ||||||
\(285\) | 5.44934 | 0.322791 | ||||||||
\(286\) | −9.97057 | −0.589572 | ||||||||
\(287\) | 3.06422 | + | 5.62233i | 0.180875 | + | 0.331876i | ||||
\(288\) | −16.8909 | −0.995304 | ||||||||
\(289\) | 2.89251 | 0.170147 | ||||||||
\(290\) | 3.09745i | 0.181889i | ||||||||
\(291\) | 33.9467 | 1.98999 | ||||||||
\(292\) | 7.30350 | 0.427405 | ||||||||
\(293\) | 5.28426i | 0.308710i | 0.988015 | + | 0.154355i | \(0.0493300\pi\) | ||||
−0.988015 | + | 0.154355i | \(0.950670\pi\) | |||||||
\(294\) | − | 2.18179i | − | 0.127244i | ||||||
\(295\) | 4.06844 | 0.236874 | ||||||||
\(296\) | −14.6861 | −0.853610 | ||||||||
\(297\) | 0.150503 | 0.00873308 | ||||||||
\(298\) | 17.2742i | 1.00067i | ||||||||
\(299\) | 9.79425i | 0.566416i | ||||||||
\(300\) | 13.5883i | 0.784520i | ||||||||
\(301\) | 10.5370i | 0.607345i | ||||||||
\(302\) | − | 17.9812i | − | 1.03470i | ||||||
\(303\) | −6.02384 | −0.346061 | ||||||||
\(304\) | 0.418045i | 0.0239765i | ||||||||
\(305\) | −7.18744 | −0.411552 | ||||||||
\(306\) | 10.0765i | 0.576036i | ||||||||
\(307\) | −14.7602 | −0.842407 | −0.421204 | − | 0.906966i | \(-0.638392\pi\) | ||||
−0.421204 | + | 0.906966i | \(0.638392\pi\) | |||||||
\(308\) | 4.64552 | 0.264703 | ||||||||
\(309\) | 5.26655i | 0.299603i | ||||||||
\(310\) | 3.64995 | 0.207303 | ||||||||
\(311\) | − | 25.7770i | − | 1.46168i | −0.682548 | − | 0.730841i | \(-0.739128\pi\) | ||
0.682548 | − | 0.730841i | \(-0.260872\pi\) | |||||||
\(312\) | 20.4177 | 1.15592 | ||||||||
\(313\) | 4.07102i | 0.230107i | 0.993359 | + | 0.115054i | \(0.0367040\pi\) | ||||
−0.993359 | + | 0.115054i | \(0.963296\pi\) | |||||||
\(314\) | − | 8.77637i | − | 0.495279i | ||||||
\(315\) | − | 1.94687i | − | 0.109694i | ||||||
\(316\) | 7.90456i | 0.444666i | ||||||||
\(317\) | − | 26.3149i | − | 1.47799i | −0.673711 | − | 0.738995i | \(-0.735301\pi\) | ||
0.673711 | − | 0.738995i | \(-0.264699\pi\) | |||||||
\(318\) | 5.40753 | 0.303239 | ||||||||
\(319\) | −20.7317 | −1.16075 | ||||||||
\(320\) | 3.37266 | 0.188538 | ||||||||
\(321\) | − | 18.8904i | − | 1.05436i | ||||||
\(322\) | 2.98725i | 0.166473i | ||||||||
\(323\) | −12.9272 | −0.719290 | ||||||||
\(324\) | 10.8205 | 0.601137 | ||||||||
\(325\) | − | 13.3671i | − | 0.741475i | ||||||
\(326\) | −2.82350 | −0.156379 | ||||||||
\(327\) | 20.9610 | 1.15914 | ||||||||
\(328\) | −16.0476 | + | 8.74608i | −0.886081 | + | 0.482922i | ||||
\(329\) | 6.65972 | 0.367162 | ||||||||
\(330\) | −5.41283 | −0.297966 | ||||||||
\(331\) | − | 33.3838i | − | 1.83494i | −0.397808 | − | 0.917468i | \(-0.630229\pi\) | ||
0.397808 | − | 0.917468i | \(-0.369771\pi\) | |||||||
\(332\) | 16.1817 | 0.888083 | ||||||||
\(333\) | −15.5181 | −0.850385 | ||||||||
\(334\) | − | 13.5880i | − | 0.743501i | ||||||
\(335\) | 2.30645i | 0.126015i | ||||||||
\(336\) | 0.297917 | 0.0162527 | ||||||||
\(337\) | −23.0974 | −1.25820 | −0.629098 | − | 0.777326i | \(-0.716576\pi\) | ||||
−0.629098 | + | 0.777326i | \(0.716576\pi\) | |||||||
\(338\) | 3.99765 | 0.217443 | ||||||||
\(339\) | − | 22.3062i | − | 1.21151i | ||||||
\(340\) | 2.93069i | 0.158939i | ||||||||
\(341\) | 24.4297i | 1.32294i | ||||||||
\(342\) | 9.23349i | 0.499290i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −30.0755 | −1.62156 | ||||||||
\(345\) | 5.31711i | 0.286263i | ||||||||
\(346\) | −10.7381 | −0.577286 | ||||||||
\(347\) | − | 17.2216i | − | 0.924505i | −0.886748 | − | 0.462252i | \(-0.847041\pi\) | ||
0.886748 | − | 0.462252i | \(-0.152959\pi\) | |||||||
\(348\) | 15.9926 | 0.857295 | ||||||||
\(349\) | 24.2807 | 1.29971 | 0.649857 | − | 0.760057i | \(-0.274829\pi\) | ||||
0.649857 | + | 0.760057i | \(0.274829\pi\) | |||||||
\(350\) | − | 4.07697i | − | 0.217923i | ||||||
\(351\) | 0.114210 | 0.00609607 | ||||||||
\(352\) | 21.5242i | 1.14724i | ||||||||
\(353\) | 27.7546 | 1.47723 | 0.738615 | − | 0.674127i | \(-0.235480\pi\) | ||||
0.738615 | + | 0.674127i | \(0.235480\pi\) | |||||||
\(354\) | 13.7508i | 0.730849i | ||||||||
\(355\) | 5.61775i | 0.298159i | ||||||||
\(356\) | − | 1.30581i | − | 0.0692077i | ||||||
\(357\) | 9.21250i | 0.487577i | ||||||||
\(358\) | 20.3060i | 1.07321i | ||||||||
\(359\) | −19.6216 | −1.03559 | −0.517793 | − | 0.855506i | \(-0.673246\pi\) | ||||
−0.517793 | + | 0.855506i | \(0.673246\pi\) | |||||||
\(360\) | 5.55688 | 0.292874 | ||||||||
\(361\) | 7.15431 | 0.376543 | ||||||||
\(362\) | − | 11.5437i | − | 0.606724i | ||||||
\(363\) | − | 9.24868i | − | 0.485430i | ||||||
\(364\) | 3.52527 | 0.184775 | ||||||||
\(365\) | −3.90040 | −0.204156 | ||||||||
\(366\) | − | 24.2927i | − | 1.26980i | ||||||
\(367\) | −3.61014 | −0.188448 | −0.0942238 | − | 0.995551i | \(-0.530037\pi\) | ||||
−0.0942238 | + | 0.995551i | \(0.530037\pi\) | |||||||
\(368\) | −0.407901 | −0.0212633 | ||||||||
\(369\) | −16.9567 | + | 9.24158i | −0.882733 | + | 0.481097i | ||||
\(370\) | 2.95448 | 0.153596 | ||||||||
\(371\) | 2.47849 | 0.128677 | ||||||||
\(372\) | − | 18.8453i | − | 0.977082i | ||||||
\(373\) | −12.0593 | −0.624407 | −0.312204 | − | 0.950015i | \(-0.601067\pi\) | ||||
−0.312204 | + | 0.950015i | \(0.601067\pi\) | |||||||
\(374\) | 12.8406 | 0.663972 | ||||||||
\(375\) | − | 15.1733i | − | 0.783544i | ||||||
\(376\) | 19.0086i | 0.980294i | ||||||||
\(377\) | −15.7324 | −0.810257 | ||||||||
\(378\) | 0.0348340 | 0.00179167 | ||||||||
\(379\) | 34.5175 | 1.77304 | 0.886522 | − | 0.462687i | \(-0.153114\pi\) | ||||
0.886522 | + | 0.462687i | \(0.153114\pi\) | |||||||
\(380\) | 2.68550i | 0.137763i | ||||||||
\(381\) | 2.73591i | 0.140165i | ||||||||
\(382\) | 3.66664i | 0.187602i | ||||||||
\(383\) | 21.2590i | 1.08628i | 0.839641 | + | 0.543142i | \(0.182765\pi\) | ||||
−0.839641 | + | 0.543142i | \(0.817235\pi\) | |||||||
\(384\) | − | 16.0739i | − | 0.820270i | ||||||
\(385\) | −2.48092 | −0.126439 | ||||||||
\(386\) | − | 11.1385i | − | 0.566937i | ||||||
\(387\) | −31.7794 | −1.61544 | ||||||||
\(388\) | 16.7293i | 0.849303i | ||||||||
\(389\) | −14.8091 | −0.750851 | −0.375425 | − | 0.926853i | \(-0.622503\pi\) | ||||
−0.375425 | + | 0.926853i | \(0.622503\pi\) | |||||||
\(390\) | −4.10755 | −0.207994 | ||||||||
\(391\) | − | 12.6135i | − | 0.637894i | ||||||
\(392\) | 2.85426 | 0.144162 | ||||||||
\(393\) | 22.4660i | 1.13326i | ||||||||
\(394\) | −6.92158 | −0.348704 | ||||||||
\(395\) | − | 4.22139i | − | 0.212401i | ||||||
\(396\) | 14.0107i | 0.704066i | ||||||||
\(397\) | − | 19.0348i | − | 0.955329i | −0.878542 | − | 0.477665i | \(-0.841483\pi\) | ||
0.878542 | − | 0.477665i | \(-0.158517\pi\) | |||||||
\(398\) | − | 5.71830i | − | 0.286633i | ||||||
\(399\) | 8.44176i | 0.422616i | ||||||||
\(400\) | 0.556700 | 0.0278350 | ||||||||
\(401\) | −37.6448 | −1.87989 | −0.939947 | − | 0.341321i | \(-0.889126\pi\) | ||||
−0.939947 | + | 0.341321i | \(0.889126\pi\) | |||||||
\(402\) | −7.79551 | −0.388805 | ||||||||
\(403\) | 18.5386i | 0.923471i | ||||||||
\(404\) | − | 2.96862i | − | 0.147694i | ||||||
\(405\) | −5.77861 | −0.287142 | ||||||||
\(406\) | −4.79837 | −0.238139 | ||||||||
\(407\) | 19.7748i | 0.980201i | ||||||||
\(408\) | −26.2949 | −1.30179 | ||||||||
\(409\) | 5.97595 | 0.295492 | 0.147746 | − | 0.989025i | \(-0.452798\pi\) | ||||
0.147746 | + | 0.989025i | \(0.452798\pi\) | |||||||
\(410\) | 3.22839 | − | 1.75950i | 0.159439 | − | 0.0868956i | ||||
\(411\) | −29.6996 | −1.46497 | ||||||||
\(412\) | −2.59541 | −0.127867 | ||||||||
\(413\) | 6.30256i | 0.310129i | ||||||||
\(414\) | −9.00943 | −0.442789 | ||||||||
\(415\) | −8.64173 | −0.424206 | ||||||||
\(416\) | 16.3337i | 0.800826i | ||||||||
\(417\) | 56.8209i | 2.78253i | ||||||||
\(418\) | 11.7663 | 0.575510 | ||||||||
\(419\) | −7.95709 | −0.388729 | −0.194365 | − | 0.980929i | \(-0.562265\pi\) | ||||
−0.194365 | + | 0.980929i | \(0.562265\pi\) | |||||||
\(420\) | 1.91380 | 0.0933840 | ||||||||
\(421\) | 12.4641i | 0.607462i | 0.952758 | + | 0.303731i | \(0.0982324\pi\) | ||||
−0.952758 | + | 0.303731i | \(0.901768\pi\) | |||||||
\(422\) | 21.1791i | 1.03098i | ||||||||
\(423\) | 20.0855i | 0.976590i | ||||||||
\(424\) | 7.07426i | 0.343556i | ||||||||
\(425\) | 17.2149i | 0.835043i | ||||||||
\(426\) | −18.9873 | −0.919938 | ||||||||
\(427\) | − | 11.1343i | − | 0.538827i | ||||||
\(428\) | 9.30939 | 0.449987 | ||||||||
\(429\) | − | 27.4924i | − | 1.32735i | ||||||
\(430\) | 6.05047 | 0.291780 | ||||||||
\(431\) | 34.7284 | 1.67281 | 0.836403 | − | 0.548115i | \(-0.184654\pi\) | ||||
0.836403 | + | 0.548115i | \(0.184654\pi\) | |||||||
\(432\) | 0.00475650i | 0.000228847i | ||||||||
\(433\) | 0.996713 | 0.0478989 | 0.0239495 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239495 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(434\) | 5.65426i | 0.271413i | ||||||||
\(435\) | −8.54078 | −0.409499 | ||||||||
\(436\) | 10.3298i | 0.494708i | ||||||||
\(437\) | − | 11.5582i | − | 0.552906i | ||||||
\(438\) | − | 13.1829i | − | 0.629902i | ||||||
\(439\) | − | 16.1744i | − | 0.771964i | −0.922506 | − | 0.385982i | \(-0.873863\pi\) | ||
0.922506 | − | 0.385982i | \(-0.126137\pi\) | |||||||
\(440\) | − | 7.08119i | − | 0.337582i | ||||||
\(441\) | 3.01597 | 0.143617 | ||||||||
\(442\) | 9.74415 | 0.463482 | ||||||||
\(443\) | 11.6540 | 0.553699 | 0.276849 | − | 0.960913i | \(-0.410710\pi\) | ||||
0.276849 | + | 0.960913i | \(0.410710\pi\) | |||||||
\(444\) | − | 15.2545i | − | 0.723945i | ||||||
\(445\) | 0.697360i | 0.0330581i | ||||||||
\(446\) | −0.0347147 | −0.00164379 | ||||||||
\(447\) | −47.6311 | −2.25287 | ||||||||
\(448\) | 5.22471i | 0.246844i | ||||||||
\(449\) | 22.6529 | 1.06905 | 0.534527 | − | 0.845151i | \(-0.320490\pi\) | ||||
0.534527 | + | 0.845151i | \(0.320490\pi\) | |||||||
\(450\) | 12.2960 | 0.579639 | ||||||||
\(451\) | 11.7766 | + | 21.6081i | 0.554540 | + | 1.01749i | ||||
\(452\) | 10.9928 | 0.517056 | ||||||||
\(453\) | 49.5807 | 2.32951 | ||||||||
\(454\) | − | 0.122999i | − | 0.00577263i | ||||||
\(455\) | −1.88265 | −0.0882602 | ||||||||
\(456\) | −24.0950 | −1.12835 | ||||||||
\(457\) | 18.9997i | 0.888766i | 0.895837 | + | 0.444383i | \(0.146577\pi\) | ||||
−0.895837 | + | 0.444383i | \(0.853423\pi\) | |||||||
\(458\) | − | 13.4966i | − | 0.630655i | ||||||
\(459\) | −0.147085 | −0.00686535 | ||||||||
\(460\) | −2.62033 | −0.122174 | ||||||||
\(461\) | −33.6054 | −1.56516 | −0.782581 | − | 0.622549i | \(-0.786097\pi\) | ||||
−0.782581 | + | 0.622549i | \(0.786097\pi\) | |||||||
\(462\) | − | 8.38520i | − | 0.390115i | ||||||
\(463\) | 7.83834i | 0.364278i | 0.983273 | + | 0.182139i | \(0.0583022\pi\) | ||||
−0.983273 | + | 0.182139i | \(0.941698\pi\) | |||||||
\(464\) | − | 0.655205i | − | 0.0304171i | ||||||
\(465\) | 10.0642i | 0.466717i | ||||||||
\(466\) | 12.4083i | 0.574803i | ||||||||
\(467\) | −13.5150 | −0.625400 | −0.312700 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312700 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(468\) | 10.6321i | 0.491469i | ||||||||
\(469\) | −3.57300 | −0.164986 | ||||||||
\(470\) | − | 3.82408i | − | 0.176391i | ||||||
\(471\) | 24.1996 | 1.11506 | ||||||||
\(472\) | −17.9892 | −0.828019 | ||||||||
\(473\) | 40.4967i | 1.86204i | ||||||||
\(474\) | 14.2678 | 0.655340 | ||||||||
\(475\) | 15.7746i | 0.723789i | ||||||||
\(476\) | −4.54002 | −0.208092 | ||||||||
\(477\) | 7.47504i | 0.342258i | ||||||||
\(478\) | − | 9.04553i | − | 0.413733i | ||||||
\(479\) | 38.0621i | 1.73910i | 0.493843 | + | 0.869551i | \(0.335592\pi\) | ||||
−0.493843 | + | 0.869551i | \(0.664408\pi\) | |||||||
\(480\) | 8.86725i | 0.404733i | ||||||||
\(481\) | 15.0062i | 0.684224i | ||||||||
\(482\) | 16.8055 | 0.765469 | ||||||||
\(483\) | −8.23691 | −0.374792 | ||||||||
\(484\) | 4.55786 | 0.207175 | ||||||||
\(485\) | − | 8.93421i | − | 0.405682i | ||||||
\(486\) | − | 19.6355i | − | 0.890685i | ||||||
\(487\) | −24.5908 | −1.11432 | −0.557158 | − | 0.830407i | \(-0.688108\pi\) | ||||
−0.557158 | + | 0.830407i | \(0.688108\pi\) | |||||||
\(488\) | 31.7803 | 1.43863 | ||||||||
\(489\) | − | 7.78541i | − | 0.352068i | ||||||
\(490\) | −0.574209 | −0.0259401 | ||||||||
\(491\) | 39.9182 | 1.80148 | 0.900741 | − | 0.434356i | \(-0.143024\pi\) | ||||
0.900741 | + | 0.434356i | \(0.143024\pi\) | |||||||
\(492\) | −9.08460 | − | 16.6687i | −0.409565 | − | 0.751484i | ||||
\(493\) | 20.2609 | 0.912506 | ||||||||
\(494\) | 8.92892 | 0.401731 | ||||||||
\(495\) | − | 7.48236i | − | 0.336307i | ||||||
\(496\) | −0.772075 | −0.0346672 | ||||||||
\(497\) | −8.70265 | −0.390367 | ||||||||
\(498\) | − | 29.2080i | − | 1.30884i | ||||||
\(499\) | 16.6258i | 0.744272i | 0.928178 | + | 0.372136i | \(0.121375\pi\) | ||||
−0.928178 | + | 0.372136i | \(0.878625\pi\) | |||||||
\(500\) | 7.47755 | 0.334406 | ||||||||
\(501\) | 37.4669 | 1.67390 | ||||||||
\(502\) | −0.228394 | −0.0101937 | ||||||||
\(503\) | − | 0.346135i | − | 0.0154334i | −0.999970 | − | 0.00771671i | \(-0.997544\pi\) | ||
0.999970 | − | 0.00771671i | \(-0.00245633\pi\) | |||||||
\(504\) | 8.60836i | 0.383447i | ||||||||
\(505\) | 1.58537i | 0.0705483i | ||||||||
\(506\) | 11.4808i | 0.510384i | ||||||||
\(507\) | 11.0230i | 0.489546i | ||||||||
\(508\) | −1.34829 | −0.0598206 | ||||||||
\(509\) | − | 27.3746i | − | 1.21336i | −0.794948 | − | 0.606678i | \(-0.792502\pi\) | ||
0.794948 | − | 0.606678i | \(-0.207498\pi\) | |||||||
\(510\) | 5.28991 | 0.234241 | ||||||||
\(511\) | − | 6.04224i | − | 0.267293i | ||||||
\(512\) | −1.37362 | −0.0607061 | ||||||||
\(513\) | −0.134780 | −0.00595067 | ||||||||
\(514\) | 3.33836i | 0.147249i | ||||||||
\(515\) | 1.38607 | 0.0610774 | ||||||||
\(516\) | − | 31.2396i | − | 1.37524i | ||||||
\(517\) | 25.5951 | 1.12567 | ||||||||
\(518\) | 4.57689i | 0.201097i | ||||||||
\(519\) | − | 29.6089i | − | 1.29969i | ||||||
\(520\) | − | 5.37359i | − | 0.235647i | ||||||
\(521\) | 5.42942i | 0.237867i | 0.992902 | + | 0.118934i | \(0.0379476\pi\) | ||||
−0.992902 | + | 0.118934i | \(0.962052\pi\) | |||||||
\(522\) | − | 14.4717i | − | 0.633410i | ||||||
\(523\) | −10.7992 | −0.472214 | −0.236107 | − | 0.971727i | \(-0.575872\pi\) | ||||
−0.236107 | + | 0.971727i | \(0.575872\pi\) | |||||||
\(524\) | −11.0715 | −0.483660 | ||||||||
\(525\) | 11.2417 | 0.490627 | ||||||||
\(526\) | 11.0618i | 0.482317i | ||||||||
\(527\) | − | 23.8749i | − | 1.04001i | ||||||
\(528\) | 1.14498 | 0.0498288 | ||||||||
\(529\) | −11.7222 | −0.509662 | ||||||||
\(530\) | − | 1.42317i | − | 0.0618186i | ||||||
\(531\) | −19.0083 | −0.824891 | ||||||||
\(532\) | −4.16019 | −0.180367 | ||||||||
\(533\) | 8.93674 | + | 16.3974i | 0.387093 | + | 0.710251i | ||||
\(534\) | −2.35699 | −0.101997 | ||||||||
\(535\) | −4.97163 | −0.214942 | ||||||||
\(536\) | − | 10.1983i | − | 0.440498i | ||||||
\(537\) | −55.9910 | −2.41619 | ||||||||
\(538\) | 16.7571 | 0.722449 | ||||||||
\(539\) | − | 3.84327i | − | 0.165541i | ||||||
\(540\) | 0.0305554i | 0.00131490i | ||||||||
\(541\) | −42.5735 | −1.83038 | −0.915189 | − | 0.403026i | \(-0.867959\pi\) | ||||
−0.915189 | + | 0.403026i | \(0.867959\pi\) | |||||||
\(542\) | −25.0164 | −1.07455 | ||||||||
\(543\) | 31.8302 | 1.36596 | ||||||||
\(544\) | − | 21.0354i | − | 0.901884i | ||||||
\(545\) | − | 5.51658i | − | 0.236304i | ||||||
\(546\) | − | 6.36314i | − | 0.272317i | ||||||
\(547\) | − | 21.2514i | − | 0.908646i | −0.890837 | − | 0.454323i | \(-0.849881\pi\) | ||
0.890837 | − | 0.454323i | \(-0.150119\pi\) | |||||||
\(548\) | − | 14.6363i | − | 0.625231i | ||||||
\(549\) | 33.5807 | 1.43319 | ||||||||
\(550\) | − | 15.6689i | − | 0.668125i | ||||||
\(551\) | 18.5658 | 0.790931 | ||||||||
\(552\) | − | 23.5103i | − | 1.00067i | ||||||
\(553\) | 6.53949 | 0.278088 | ||||||||
\(554\) | 9.52364 | 0.404621 | ||||||||
\(555\) | 8.14657i | 0.345803i | ||||||||
\(556\) | −28.0020 | −1.18755 | ||||||||
\(557\) | − | 45.6364i | − | 1.93367i | −0.255394 | − | 0.966837i | \(-0.582205\pi\) | ||
0.255394 | − | 0.966837i | \(-0.417795\pi\) | |||||||
\(558\) | −17.0531 | −0.721913 | ||||||||
\(559\) | 30.7311i | 1.29979i | ||||||||
\(560\) | − | 0.0784069i | − | 0.00331329i | ||||||
\(561\) | 35.4062i | 1.49485i | ||||||||
\(562\) | 1.98452i | 0.0837120i | ||||||||
\(563\) | 18.5553i | 0.782014i | 0.920388 | + | 0.391007i | \(0.127873\pi\) | ||||
−0.920388 | + | 0.391007i | \(0.872127\pi\) | |||||||
\(564\) | −19.7443 | −0.831386 | ||||||||
\(565\) | −5.87062 | −0.246979 | ||||||||
\(566\) | 17.5437 | 0.737416 | ||||||||
\(567\) | − | 8.95185i | − | 0.375942i | ||||||
\(568\) | − | 24.8396i | − | 1.04225i | ||||||
\(569\) | −41.2306 | −1.72848 | −0.864239 | − | 0.503082i | \(-0.832199\pi\) | ||||
−0.864239 | + | 0.503082i | \(0.832199\pi\) | |||||||
\(570\) | 4.84734 | 0.203033 | ||||||||
\(571\) | − | 39.2844i | − | 1.64400i | −0.569487 | − | 0.822000i | \(-0.692858\pi\) | ||
0.569487 | − | 0.822000i | \(-0.307142\pi\) | |||||||
\(572\) | 13.5486 | 0.566495 | ||||||||
\(573\) | −10.1103 | −0.422362 | ||||||||
\(574\) | 2.72571 | + | 5.00121i | 0.113769 | + | 0.208747i | ||||
\(575\) | −15.3918 | −0.641883 | ||||||||
\(576\) | −15.7575 | −0.656564 | ||||||||
\(577\) | 45.4309i | 1.89131i | 0.325168 | + | 0.945656i | \(0.394579\pi\) | ||||
−0.325168 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(578\) | 2.57296 | 0.107021 | ||||||||
\(579\) | 30.7130 | 1.27639 | ||||||||
\(580\) | − | 4.20899i | − | 0.174769i | ||||||
\(581\) | − | 13.3872i | − | 0.555394i | ||||||
\(582\) | 30.1966 | 1.25169 | ||||||||
\(583\) | 9.52551 | 0.394506 | ||||||||
\(584\) | 17.2461 | 0.713650 | ||||||||
\(585\) | − | 5.67802i | − | 0.234757i | ||||||
\(586\) | 4.70050i | 0.194176i | ||||||||
\(587\) | 2.87888i | 0.118824i | 0.998234 | + | 0.0594120i | \(0.0189226\pi\) | ||||
−0.998234 | + | 0.0594120i | \(0.981077\pi\) | |||||||
\(588\) | 2.96474i | 0.122264i | ||||||||
\(589\) | − | 21.8774i | − | 0.901444i | ||||||
\(590\) | 3.61899 | 0.148992 | ||||||||
\(591\) | − | 19.0853i | − | 0.785063i | ||||||
\(592\) | −0.624963 | −0.0256858 | ||||||||
\(593\) | − | 7.89822i | − | 0.324341i | −0.986763 | − | 0.162171i | \(-0.948151\pi\) | ||
0.986763 | − | 0.162171i | \(-0.0518495\pi\) | |||||||
\(594\) | 0.133877 | 0.00549302 | ||||||||
\(595\) | 2.42458 | 0.0993979 | ||||||||
\(596\) | − | 23.4731i | − | 0.961497i | ||||||
\(597\) | 15.7674 | 0.645317 | ||||||||
\(598\) | 8.71225i | 0.356271i | ||||||||
\(599\) | 31.3373 | 1.28041 | 0.640204 | − | 0.768205i | \(-0.278850\pi\) | ||||
0.640204 | + | 0.768205i | \(0.278850\pi\) | |||||||
\(600\) | 32.0867i | 1.30993i | ||||||||
\(601\) | − | 36.4610i | − | 1.48727i | −0.668583 | − | 0.743637i | \(-0.733099\pi\) | ||
0.668583 | − | 0.743637i | \(-0.266901\pi\) | |||||||
\(602\) | 9.37299i | 0.382015i | ||||||||
\(603\) | − | 10.7760i | − | 0.438834i | ||||||
\(604\) | 24.4339i | 0.994203i | ||||||||
\(605\) | −2.43410 | −0.0989602 | ||||||||
\(606\) | −5.35837 | −0.217669 | ||||||||
\(607\) | −29.0596 | −1.17949 | −0.589745 | − | 0.807589i | \(-0.700772\pi\) | ||||
−0.589745 | + | 0.807589i | \(0.700772\pi\) | |||||||
\(608\) | − | 19.2755i | − | 0.781724i | ||||||
\(609\) | − | 13.2308i | − | 0.536140i | ||||||
\(610\) | −6.39343 | −0.258862 | ||||||||
\(611\) | 19.4230 | 0.785769 | ||||||||
\(612\) | − | 13.6926i | − | 0.553489i | ||||||
\(613\) | −5.82721 | −0.235359 | −0.117679 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117679 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(614\) | −13.1296 | −0.529867 | ||||||||
\(615\) | 4.85158 | + | 8.90184i | 0.195635 | + | 0.358957i | ||||
\(616\) | 10.9697 | 0.441982 | ||||||||
\(617\) | 13.6244 | 0.548499 | 0.274249 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274249 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(618\) | 4.68474i | 0.188448i | ||||||||
\(619\) | −23.7891 | −0.956164 | −0.478082 | − | 0.878315i | \(-0.658668\pi\) | ||||
−0.478082 | + | 0.878315i | \(0.658668\pi\) | |||||||
\(620\) | −4.95976 | −0.199189 | ||||||||
\(621\) | − | 0.131509i | − | 0.00527728i | ||||||
\(622\) | − | 22.9294i | − | 0.919384i | ||||||
\(623\) | −1.08030 | −0.0432815 | ||||||||
\(624\) | 0.868871 | 0.0347827 | ||||||||
\(625\) | 18.9232 | 0.756926 | ||||||||
\(626\) | 3.62128i | 0.144735i | ||||||||
\(627\) | 32.4440i | 1.29569i | ||||||||
\(628\) | 11.9258i | 0.475893i | ||||||||
\(629\) | − | 19.3257i | − | 0.770568i | ||||||
\(630\) | − | 1.73180i | − | 0.0689964i | ||||||
\(631\) | −16.0309 | −0.638180 | −0.319090 | − | 0.947724i | \(-0.603377\pi\) | ||||
−0.319090 | + | 0.947724i | \(0.603377\pi\) | |||||||
\(632\) | 18.6654i | 0.742471i | ||||||||
\(633\) | −58.3983 | −2.32112 | ||||||||
\(634\) | − | 23.4078i | − | 0.929642i | ||||||
\(635\) | 0.720046 | 0.0285742 | ||||||||
\(636\) | −7.34806 | −0.291370 | ||||||||
\(637\) | − | 2.91648i | − | 0.115555i | ||||||
\(638\) | −18.4414 | −0.730103 | ||||||||
\(639\) | − | 26.2469i | − | 1.03831i | ||||||
\(640\) | −4.23039 | −0.167221 | ||||||||
\(641\) | − | 42.7206i | − | 1.68736i | −0.536846 | − | 0.843680i | \(-0.680384\pi\) | ||
0.536846 | − | 0.843680i | \(-0.319616\pi\) | |||||||
\(642\) | − | 16.8035i | − | 0.663182i | ||||||
\(643\) | 44.1165i | 1.73979i | 0.493241 | + | 0.869893i | \(0.335812\pi\) | ||||
−0.493241 | + | 0.869893i | \(0.664188\pi\) | |||||||
\(644\) | − | 4.05924i | − | 0.159957i | ||||||
\(645\) | 16.6833i | 0.656905i | ||||||||
\(646\) | −11.4991 | −0.452427 | ||||||||
\(647\) | −15.4908 | −0.609004 | −0.304502 | − | 0.952512i | \(-0.598490\pi\) | ||||
−0.304502 | + | 0.952512i | \(0.598490\pi\) | |||||||
\(648\) | 25.5509 | 1.00374 | ||||||||
\(649\) | 24.2225i | 0.950815i | ||||||||
\(650\) | − | 11.8904i | − | 0.466381i | ||||||
\(651\) | −15.5908 | −0.611053 | ||||||||
\(652\) | 3.83674 | 0.150258 | ||||||||
\(653\) | 8.30014i | 0.324809i | 0.986724 | + | 0.162405i | \(0.0519250\pi\) | ||||
−0.986724 | + | 0.162405i | \(0.948075\pi\) | |||||||
\(654\) | 18.6454 | 0.729091 | ||||||||
\(655\) | 5.91266 | 0.231027 | ||||||||
\(656\) | −0.682903 | + | 0.372188i | −0.0266629 | + | 0.0145315i | ||||
\(657\) | 18.2232 | 0.710954 | ||||||||
\(658\) | 5.92401 | 0.230942 | ||||||||
\(659\) | − | 2.29426i | − | 0.0893716i | −0.999001 | − | 0.0446858i | \(-0.985771\pi\) | ||
0.999001 | − | 0.0446858i | \(-0.0142287\pi\) | |||||||
\(660\) | 7.35526 | 0.286303 | ||||||||
\(661\) | 34.6650 | 1.34831 | 0.674156 | − | 0.738589i | \(-0.264508\pi\) | ||||
0.674156 | + | 0.738589i | \(0.264508\pi\) | |||||||
\(662\) | − | 29.6958i | − | 1.15416i | ||||||
\(663\) | 26.8681i | 1.04347i | ||||||||
\(664\) | 38.2106 | 1.48286 | ||||||||
\(665\) | 2.22173 | 0.0861550 | ||||||||
\(666\) | −13.8037 | −0.534884 | ||||||||
\(667\) | 18.1153i | 0.701428i | ||||||||
\(668\) | 18.4641i | 0.714399i | ||||||||
\(669\) | − | 0.0957209i | − | 0.00370078i | ||||||
\(670\) | 2.05165i | 0.0792620i | ||||||||
\(671\) | − | 42.7922i | − | 1.65198i | ||||||
\(672\) | −13.7366 | −0.529899 | ||||||||
\(673\) | − | 1.90177i | − | 0.0733080i | −0.999328 | − | 0.0366540i | \(-0.988330\pi\) | ||
0.999328 | − | 0.0366540i | \(-0.0116699\pi\) | |||||||
\(674\) | −20.5458 | −0.791394 | ||||||||
\(675\) | 0.179483i | 0.00690829i | ||||||||
\(676\) | −5.43223 | −0.208932 | ||||||||
\(677\) | −6.53953 | −0.251335 | −0.125667 | − | 0.992072i | \(-0.540107\pi\) | ||||
−0.125667 | + | 0.992072i | \(0.540107\pi\) | |||||||
\(678\) | − | 19.8420i | − | 0.762027i | ||||||
\(679\) | 13.8403 | 0.531142 | ||||||||
\(680\) | 6.92038i | 0.265384i | ||||||||
\(681\) | 0.339152 | 0.0129963 | ||||||||
\(682\) | 21.7309i | 0.832118i | ||||||||
\(683\) | 47.0502i | 1.80033i | 0.435554 | + | 0.900163i | \(0.356553\pi\) | ||||
−0.435554 | + | 0.900163i | \(0.643447\pi\) | |||||||
\(684\) | − | 12.5470i | − | 0.479746i | ||||||
\(685\) | 7.81643i | 0.298650i | ||||||||
\(686\) | − | 0.889527i | − | 0.0339623i | ||||||
\(687\) | 37.2150 | 1.41984 | ||||||||
\(688\) | −1.27986 | −0.0487942 | ||||||||
\(689\) | 7.22847 | 0.275383 | ||||||||
\(690\) | 4.72971i | 0.180057i | ||||||||
\(691\) | 44.3053i | 1.68545i | 0.538341 | + | 0.842727i | \(0.319051\pi\) | ||||
−0.538341 | + | 0.842727i | \(0.680949\pi\) | |||||||
\(692\) | 14.5916 | 0.554690 | ||||||||
\(693\) | 11.5912 | 0.440313 | ||||||||
\(694\) | − | 15.3191i | − | 0.581505i | ||||||
\(695\) | 14.9543 | 0.567250 | ||||||||
\(696\) | 37.7642 | 1.43145 | ||||||||
\(697\) | −11.5092 | − | 21.1174i | −0.435942 | − | 0.799880i | ||||
\(698\) | 21.5983 | 0.817508 | ||||||||
\(699\) | −34.2141 | −1.29410 | ||||||||
\(700\) | 5.54002i | 0.209393i | ||||||||
\(701\) | −35.7420 | −1.34996 | −0.674979 | − | 0.737837i | \(-0.735847\pi\) | ||||
−0.674979 | + | 0.737837i | \(0.735847\pi\) | |||||||
\(702\) | 0.101593 | 0.00383437 | ||||||||
\(703\) | − | 17.7089i | − | 0.667904i | ||||||
\(704\) | 20.0800i | 0.756793i | ||||||||
\(705\) | 10.5444 | 0.397123 | ||||||||
\(706\) | 24.6885 | 0.929165 | ||||||||
\(707\) | −2.45596 | −0.0923658 | ||||||||
\(708\) | − | 18.6854i | − | 0.702242i | ||||||
\(709\) | − | 42.0002i | − | 1.57735i | −0.614810 | − | 0.788675i | \(-0.710767\pi\) | ||
0.614810 | − | 0.788675i | \(-0.289233\pi\) | |||||||
\(710\) | 4.99714i | 0.187539i | ||||||||
\(711\) | 19.7229i | 0.739666i | ||||||||
\(712\) | − | 3.08347i | − | 0.115558i | ||||||
\(713\) | 21.3466 | 0.799435 | ||||||||
\(714\) | 8.19477i | 0.306682i | ||||||||
\(715\) | −7.23555 | −0.270594 | ||||||||
\(716\) | − | 27.5930i | − | 1.03120i | ||||||
\(717\) | 24.9418 | 0.931468 | ||||||||
\(718\) | −17.4539 | −0.651374 | ||||||||
\(719\) | 36.2543i | 1.35206i | 0.736876 | + | 0.676028i | \(0.236300\pi\) | ||||
−0.736876 | + | 0.676028i | \(0.763700\pi\) | |||||||
\(720\) | 0.236472 | 0.00881281 | ||||||||
\(721\) | 2.14720i | 0.0799661i | ||||||||
\(722\) | 6.36396 | 0.236842 | ||||||||
\(723\) | 46.3388i | 1.72336i | ||||||||
\(724\) | 15.6863i | 0.582975i | ||||||||
\(725\) | − | 24.7236i | − | 0.918213i | ||||||
\(726\) | − | 8.22696i | − | 0.305331i | ||||||
\(727\) | 42.9640i | 1.59345i | 0.604344 | + | 0.796724i | \(0.293435\pi\) | ||||
−0.604344 | + | 0.796724i | \(0.706565\pi\) | |||||||
\(728\) | 8.32441 | 0.308523 | ||||||||
\(729\) | 27.2866 | 1.01062 | ||||||||
\(730\) | −3.46951 | −0.128412 | ||||||||
\(731\) | − | 39.5771i | − | 1.46381i | ||||||
\(732\) | 33.0103i | 1.22010i | ||||||||
\(733\) | 2.87990 | 0.106371 | 0.0531857 | − | 0.998585i | \(-0.483062\pi\) | ||||
0.0531857 | + | 0.998585i | \(0.483062\pi\) | |||||||
\(734\) | −3.21132 | −0.118532 | ||||||||
\(735\) | − | 1.58330i | − | 0.0584010i | ||||||
\(736\) | 18.8078 | 0.693263 | ||||||||
\(737\) | −13.7320 | −0.505825 | ||||||||
\(738\) | −15.0835 | + | 8.22064i | −0.555231 | + | 0.302606i | ||||
\(739\) | 28.6479 | 1.05383 | 0.526914 | − | 0.849918i | \(-0.323349\pi\) | ||||
0.526914 | + | 0.849918i | \(0.323349\pi\) | |||||||
\(740\) | −4.01472 | −0.147584 | ||||||||
\(741\) | 24.6202i | 0.904447i | ||||||||
\(742\) | 2.20468 | 0.0809365 | ||||||||
\(743\) | −8.37331 | −0.307187 | −0.153594 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153594 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(744\) | − | 44.5003i | − | 1.63146i | ||||||
\(745\) | 12.5357i | 0.459272i | ||||||||
\(746\) | −10.7271 | −0.392746 | ||||||||
\(747\) | 40.3753 | 1.47726 | ||||||||
\(748\) | −17.4486 | −0.637982 | ||||||||
\(749\) | − | 7.70173i | − | 0.281415i | ||||||
\(750\) | − | 13.4970i | − | 0.492842i | ||||||
\(751\) | 18.7984i | 0.685965i | 0.939342 | + | 0.342982i | \(0.111437\pi\) | ||||
−0.939342 | + | 0.342982i | \(0.888563\pi\) | |||||||
\(752\) | 0.808908i | 0.0294979i | ||||||||
\(753\) | − | 0.629766i | − | 0.0229499i | ||||||
\(754\) | −13.9944 | −0.509644 | ||||||||
\(755\) | − | 13.0488i | − | 0.474895i | ||||||
\(756\) | −0.0473345 | −0.00172154 | ||||||||
\(757\) | 35.4181i | 1.28729i | 0.765323 | + | 0.643647i | \(0.222579\pi\) | ||||
−0.765323 | + | 0.643647i | \(0.777421\pi\) | |||||||
\(758\) | 30.7042 | 1.11523 | ||||||||
\(759\) | −31.6567 | −1.14907 | ||||||||
\(760\) | 6.34140i | 0.230027i | ||||||||
\(761\) | −29.9316 | −1.08502 | −0.542510 | − | 0.840049i | \(-0.682526\pi\) | ||||
−0.542510 | + | 0.840049i | \(0.682526\pi\) | |||||||
\(762\) | 2.43367i | 0.0881625i | ||||||||
\(763\) | 8.54592 | 0.309383 | ||||||||
\(764\) | − | 4.98245i | − | 0.180259i | ||||||
\(765\) | 7.31244i | 0.264382i | ||||||||
\(766\) | 18.9105i | 0.683262i | ||||||||
\(767\) | 18.3813i | 0.663711i | ||||||||
\(768\) | − | 39.9280i | − | 1.44078i | ||||||
\(769\) | −12.3539 | −0.445491 | −0.222746 | − | 0.974877i | \(-0.571502\pi\) | ||||
−0.222746 | + | 0.974877i | \(0.571502\pi\) | |||||||
\(770\) | −2.20684 | −0.0795291 | ||||||||
\(771\) | −9.20506 | −0.331512 | ||||||||
\(772\) | 15.1357i | 0.544746i | ||||||||
\(773\) | − | 34.0743i | − | 1.22557i | −0.790251 | − | 0.612784i | \(-0.790050\pi\) | ||
0.790251 | − | 0.612784i | \(-0.209950\pi\) | |||||||
\(774\) | −28.2686 | −1.01609 | ||||||||
\(775\) | −29.1336 | −1.04651 | ||||||||
\(776\) | 39.5038i | 1.41811i | ||||||||
\(777\) | −12.6201 | −0.452745 | ||||||||
\(778\) | −13.1731 | −0.472278 | ||||||||
\(779\) | −10.5463 | − | 19.3507i | −0.377860 | − | 0.693310i | ||||
\(780\) | 5.58157 | 0.199852 | ||||||||
\(781\) | −33.4466 | −1.19681 | ||||||||
\(782\) | − | 11.2201i | − | 0.401229i | ||||||
\(783\) | 0.211241 | 0.00754914 | ||||||||
\(784\) | 0.121463 | 0.00433796 | ||||||||
\(785\) | − | 6.36893i | − | 0.227317i | ||||||
\(786\) | 19.9841i | 0.712809i | ||||||||
\(787\) | −3.86537 | −0.137785 | −0.0688927 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688927 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(788\) | 9.40544 | 0.335055 | ||||||||
\(789\) | −30.5013 | −1.08588 | ||||||||
\(790\) | − | 3.75504i | − | 0.133598i | ||||||
\(791\) | − | 9.09439i | − | 0.323359i | ||||||
\(792\) | 33.0843i | 1.17560i | ||||||||
\(793\) | − | 32.4730i | − | 1.15315i | ||||||
\(794\) | − | 16.9320i | − | 0.600893i | ||||||
\(795\) | 3.92419 | 0.139177 | ||||||||
\(796\) | 7.77036i | 0.275413i | ||||||||
\(797\) | 6.47548 | 0.229373 | 0.114687 | − | 0.993402i | \(-0.463414\pi\) | ||||
0.114687 | + | 0.993402i | \(0.463414\pi\) | |||||||
\(798\) | 7.50917i | 0.265822i | ||||||||
\(799\) | −25.0139 | −0.884928 | ||||||||
\(800\) | −25.6687 | −0.907525 | ||||||||
\(801\) | − | 3.25816i | − | 0.115122i | ||||||
\(802\) | −33.4861 | −1.18244 | ||||||||
\(803\) | − | 23.2220i | − | 0.819485i | ||||||
\(804\) | 10.5930 | 0.373586 | ||||||||
\(805\) | 2.16782i | 0.0764055i | ||||||||
\(806\) | 16.4906i | 0.580855i | ||||||||
\(807\) | 46.2053i | 1.62650i | ||||||||
\(808\) | − | 7.00995i | − | 0.246609i | ||||||
\(809\) | − | 9.84578i | − | 0.346159i | −0.984908 | − | 0.173080i | \(-0.944628\pi\) | ||
0.984908 | − | 0.173080i | \(-0.0553718\pi\) | |||||||
\(810\) | −5.14023 | −0.180609 | ||||||||
\(811\) | −26.5573 | −0.932554 | −0.466277 | − | 0.884639i | \(-0.654405\pi\) | ||||
−0.466277 | + | 0.884639i | \(0.654405\pi\) | |||||||
\(812\) | 6.52030 | 0.228818 | ||||||||
\(813\) | − | 68.9791i | − | 2.41920i | ||||||
\(814\) | 17.5902i | 0.616538i | ||||||||
\(815\) | −2.04899 | −0.0717730 | ||||||||
\(816\) | −1.11898 | −0.0391720 | ||||||||
\(817\) | − | 36.2660i | − | 1.26878i | ||||||
\(818\) | 5.31577 | 0.185861 | ||||||||
\(819\) | 8.79601 | 0.307358 | ||||||||
\(820\) | −4.38693 | + | 2.39091i | −0.153198 | + | 0.0834943i | ||||
\(821\) | 26.3942 | 0.921163 | 0.460582 | − | 0.887617i | \(-0.347641\pi\) | ||||
0.460582 | + | 0.887617i | \(0.347641\pi\) | |||||||
\(822\) | −26.4186 | −0.921453 | ||||||||
\(823\) | − | 31.8394i | − | 1.10985i | −0.831899 | − | 0.554927i | \(-0.812746\pi\) | ||
0.831899 | − | 0.554927i | \(-0.187254\pi\) | |||||||
\(824\) | −6.12869 | −0.213503 | ||||||||
\(825\) | 43.2048 | 1.50420 | ||||||||
\(826\) | 5.60630i | 0.195068i | ||||||||
\(827\) | 14.8956i | 0.517972i | 0.965881 | + | 0.258986i | \(0.0833883\pi\) | ||||
−0.965881 | + | 0.258986i | \(0.916612\pi\) | |||||||
\(828\) | 12.2425 | 0.425458 | ||||||||
\(829\) | 18.3559 | 0.637528 | 0.318764 | − | 0.947834i | \(-0.396732\pi\) | ||||
0.318764 | + | 0.947834i | \(0.396732\pi\) | |||||||
\(830\) | −7.68705 | −0.266821 | ||||||||
\(831\) | 26.2601i | 0.910953i | ||||||||
\(832\) | 15.2378i | 0.528275i | ||||||||
\(833\) | 3.75599i | 0.130137i | ||||||||
\(834\) | 50.5438i | 1.75019i | ||||||||
\(835\) | − | 9.86067i | − | 0.341243i | ||||||
\(836\) | −15.9888 | −0.552983 | ||||||||
\(837\) | − | 0.248920i | − | 0.00860395i | ||||||
\(838\) | −7.07805 | −0.244507 | ||||||||
\(839\) | 23.0672i | 0.796368i | 0.917306 | + | 0.398184i | \(0.130359\pi\) | ||||
−0.917306 | + | 0.398184i | \(0.869641\pi\) | |||||||
\(840\) | 4.51916 | 0.155926 | ||||||||
\(841\) | −0.0983418 | −0.00339110 | ||||||||
\(842\) | 11.0871i | 0.382088i | ||||||||
\(843\) | −5.47204 | −0.188467 | ||||||||
\(844\) | − | 28.7793i | − | 0.990625i | ||||||
\(845\) | 2.90106 | 0.0997994 | ||||||||
\(846\) | 17.8666i | 0.614266i | ||||||||
\(847\) | − | 3.77075i | − | 0.129564i | ||||||
\(848\) | 0.301044i | 0.0103379i | ||||||||
\(849\) | 48.3742i | 1.66020i | ||||||||
\(850\) | 15.3131i | 0.525234i | ||||||||
\(851\) | 17.2792 | 0.592322 | ||||||||
\(852\) | 25.8010 | 0.883929 | ||||||||
\(853\) | −15.3915 | −0.526996 | −0.263498 | − | 0.964660i | \(-0.584876\pi\) | ||||
−0.263498 | + | 0.964660i | \(0.584876\pi\) | |||||||
\(854\) | − | 9.90428i | − | 0.338917i | ||||||
\(855\) | 6.70066i | 0.229158i | ||||||||
\(856\) | 21.9828 | 0.751355 | ||||||||
\(857\) | −41.0695 | −1.40291 | −0.701454 | − | 0.712715i | \(-0.747465\pi\) | ||||
−0.701454 | + | 0.712715i | \(0.747465\pi\) | |||||||
\(858\) | − | 24.4553i | − | 0.834890i | ||||||
\(859\) | 43.0405 | 1.46852 | 0.734262 | − | 0.678867i | \(-0.237529\pi\) | ||||
0.734262 | + | 0.678867i | \(0.237529\pi\) | |||||||
\(860\) | −8.22173 | −0.280359 | ||||||||
\(861\) | −13.7901 | + | 7.51575i | −0.469967 | + | 0.256136i | ||||
\(862\) | 30.8918 | 1.05218 | ||||||||
\(863\) | 55.2711 | 1.88145 | 0.940725 | − | 0.339170i | \(-0.110146\pi\) | ||||
0.940725 | + | 0.339170i | \(0.110146\pi\) | |||||||
\(864\) | − | 0.219316i | − | 0.00746127i | ||||||
\(865\) | −7.79257 | −0.264955 | ||||||||
\(866\) | 0.886603 | 0.0301280 | ||||||||
\(867\) | 7.09458i | 0.240945i | ||||||||
\(868\) | − | 7.68333i | − | 0.260789i | ||||||
\(869\) | 25.1331 | 0.852581 | ||||||||
\(870\) | −7.59726 | −0.257571 | ||||||||
\(871\) | −10.4206 | −0.353088 | ||||||||
\(872\) | 24.3923i | 0.826027i | ||||||||
\(873\) | 41.7419i | 1.41275i | ||||||||
\(874\) | − | 10.2814i | − | 0.347773i | ||||||
\(875\) | − | 6.18623i | − | 0.209133i | ||||||
\(876\) | 17.9136i | 0.605246i | ||||||||
\(877\) | −36.5325 | −1.23361 | −0.616807 | − | 0.787115i | \(-0.711574\pi\) | ||||
−0.616807 | + | 0.787115i | \(0.711574\pi\) | |||||||
\(878\) | − | 14.3876i | − | 0.485558i | ||||||
\(879\) | −12.9610 | −0.437162 | ||||||||
\(880\) | − | 0.301339i | − | 0.0101581i | ||||||
\(881\) | −52.3225 | −1.76279 | −0.881396 | − | 0.472379i | \(-0.843395\pi\) | ||||
−0.881396 | + | 0.472379i | \(0.843395\pi\) | |||||||
\(882\) | 2.68278 | 0.0903340 | ||||||||
\(883\) | − | 5.10109i | − | 0.171665i | −0.996310 | − | 0.0858327i | \(-0.972645\pi\) | ||
0.996310 | − | 0.0858327i | \(-0.0273551\pi\) | |||||||
\(884\) | −13.2409 | −0.445340 | ||||||||
\(885\) | 9.97886i | 0.335436i | ||||||||
\(886\) | 10.3666 | 0.348271 | ||||||||
\(887\) | − | 33.2560i | − | 1.11663i | −0.829630 | − | 0.558314i | \(-0.811449\pi\) | ||
0.829630 | − | 0.558314i | \(-0.188551\pi\) | |||||||
\(888\) | − | 36.0212i | − | 1.20879i | ||||||
\(889\) | 1.11545i | 0.0374109i | ||||||||
\(890\) | 0.620321i | 0.0207932i | ||||||||
\(891\) | − | 34.4044i | − | 1.15259i | ||||||
\(892\) | 0.0471723 | 0.00157945 | ||||||||
\(893\) | −22.9211 | −0.767027 | ||||||||
\(894\) | −42.3691 | −1.41704 | ||||||||
\(895\) | 14.7359i | 0.492566i | ||||||||
\(896\) | − | 6.55344i | − | 0.218935i | ||||||
\(897\) | −24.0228 | −0.802098 | ||||||||
\(898\) | 20.1503 | 0.672425 | ||||||||
\(899\) | 34.2887i | 1.14359i | ||||||||
\(900\) | −16.7085 | −0.556951 | ||||||||
\(901\) | −9.30919 | −0.310134 | ||||||||
\(902\) | 10.4756 | + | 19.2210i | 0.348800 | + | 0.639990i | ||||
\(903\) | −25.8447 | −0.860058 | ||||||||
\(904\) | 25.9578 | 0.863343 | ||||||||
\(905\) | − | 8.37717i | − | 0.278466i | ||||||
\(906\) | 44.1034 | 1.46524 | ||||||||
\(907\) | −26.9243 | −0.894006 | −0.447003 | − | 0.894532i | \(-0.647509\pi\) | ||||
−0.447003 | + | 0.894532i | \(0.647509\pi\) | |||||||
\(908\) | 0.167138i | 0.00554667i | ||||||||
\(909\) | − | 7.40709i | − | 0.245678i | ||||||
\(910\) | −1.67467 | −0.0555148 | ||||||||
\(911\) | 14.9485 | 0.495265 | 0.247633 | − | 0.968854i | \(-0.420347\pi\) | ||||
0.247633 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(912\) | −1.02536 | −0.0339530 | ||||||||
\(913\) | − | 51.4506i | − | 1.70277i | ||||||
\(914\) | 16.9007i | 0.559026i | ||||||||
\(915\) | − | 17.6290i | − | 0.582796i | ||||||
\(916\) | 18.3400i | 0.605970i | ||||||||
\(917\) | 9.15951i | 0.302474i | ||||||||
\(918\) | −0.130836 | −0.00431824 | ||||||||
\(919\) | 4.48515i | 0.147951i | 0.997260 | + | 0.0739757i | \(0.0235687\pi\) | ||||
−0.997260 | + | 0.0739757i | \(0.976431\pi\) | |||||||
\(920\) | −6.18752 | −0.203997 | ||||||||
\(921\) | − | 36.2030i | − | 1.19293i | ||||||
\(922\) | −29.8930 | −0.984472 | ||||||||
\(923\) | −25.3811 | −0.835430 | ||||||||
\(924\) | 11.3943i | 0.374845i | ||||||||
\(925\) | −23.5825 | −0.775388 | ||||||||
\(926\) | 6.97242i | 0.229128i | ||||||||
\(927\) | −6.47590 | −0.212696 | ||||||||
\(928\) | 30.2106i | 0.991712i | ||||||||
\(929\) | 4.23482i | 0.138940i | 0.997584 | + | 0.0694700i | \(0.0221308\pi\) | ||||
−0.997584 | + | 0.0694700i | \(0.977869\pi\) | |||||||
\(930\) | 8.95240i | 0.293561i | ||||||||
\(931\) | 3.44176i | 0.112799i | ||||||||
\(932\) | − | 16.8611i | − | 0.552303i | ||||||
\(933\) | 63.2245 | 2.06988 | ||||||||
\(934\) | −12.0220 | −0.393371 | ||||||||
\(935\) | 9.31831 | 0.304741 | ||||||||
\(936\) | 25.1061i | 0.820620i | ||||||||
\(937\) | − | 43.1984i | − | 1.41123i | −0.708595 | − | 0.705616i | \(-0.750670\pi\) | ||
0.708595 | − | 0.705616i | \(-0.249330\pi\) | |||||||
\(938\) | −3.17828 | −0.103774 | ||||||||
\(939\) | −9.98517 | −0.325854 | ||||||||
\(940\) | 5.19637i | 0.169487i | ||||||||
\(941\) | 26.6450 | 0.868603 | 0.434301 | − | 0.900768i | \(-0.356995\pi\) | ||||
0.434301 | + | 0.900768i | \(0.356995\pi\) | |||||||
\(942\) | 21.5262 | 0.701362 | ||||||||
\(943\) | 18.8811 | − | 10.2904i | 0.614854 | − | 0.335101i | ||||
\(944\) | −0.765527 | −0.0249158 | ||||||||
\(945\) | 0.0252787 | 0.000822317 | ||||||||
\(946\) | 36.0230i | 1.17121i | ||||||||
\(947\) | −0.964984 | −0.0313578 | −0.0156789 | − | 0.999877i | \(-0.504991\pi\) | ||||
−0.0156789 | + | 0.999877i | \(0.504991\pi\) | |||||||
\(948\) | −19.3879 | −0.629689 | ||||||||
\(949\) | − | 17.6221i | − | 0.572037i | ||||||
\(950\) | 14.0319i | 0.455256i | ||||||||
\(951\) | 64.5437 | 2.09297 | ||||||||
\(952\) | −10.7206 | −0.347457 | ||||||||
\(953\) | −42.0964 | −1.36363 | −0.681817 | − | 0.731522i | \(-0.738810\pi\) | ||||
−0.681817 | + | 0.731522i | \(0.738810\pi\) | |||||||
\(954\) | 6.64925i | 0.215277i | ||||||||
\(955\) | 2.66085i | 0.0861031i | ||||||||
\(956\) | 12.2916i | 0.397538i | ||||||||
\(957\) | − | 50.8497i | − | 1.64374i | ||||||
\(958\) | 33.8573i | 1.09388i | ||||||||
\(959\) | −12.1087 | −0.391010 | ||||||||
\(960\) | 8.27229i | 0.266987i | ||||||||
\(961\) | 9.40479 | 0.303380 | ||||||||
\(962\) | 13.3484i | 0.430371i | ||||||||
\(963\) | 23.2281 | 0.748517 | ||||||||
\(964\) | −22.8363 | −0.735507 | ||||||||
\(965\) | − | 8.08314i | − | 0.260205i | ||||||
\(966\) | −7.32696 | −0.235741 | ||||||||
\(967\) | − | 44.7535i | − | 1.43918i | −0.694401 | − | 0.719588i | \(-0.744331\pi\) | ||
0.694401 | − | 0.719588i | \(-0.255669\pi\) | |||||||
\(968\) | 10.7627 | 0.345926 | ||||||||
\(969\) | − | 31.7072i | − | 1.01858i | ||||||
\(970\) | − | 7.94723i | − | 0.255170i | ||||||
\(971\) | − | 13.4547i | − | 0.431780i | −0.976418 | − | 0.215890i | \(-0.930735\pi\) | ||
0.976418 | − | 0.215890i | \(-0.0692653\pi\) | |||||||
\(972\) | 26.6819i | 0.855821i | ||||||||
\(973\) | 23.1662i | 0.742676i | ||||||||
\(974\) | −21.8742 | −0.700894 | ||||||||
\(975\) | 32.7862 | 1.05000 | ||||||||
\(976\) | 1.35240 | 0.0432894 | ||||||||
\(977\) | 31.1565i | 0.996783i | 0.866952 | + | 0.498392i | \(0.166076\pi\) | ||||
−0.866952 | + | 0.498392i | \(0.833924\pi\) | |||||||
\(978\) | − | 6.92534i | − | 0.221448i | ||||||
\(979\) | −4.15191 | −0.132695 | ||||||||
\(980\) | 0.780269 | 0.0249248 | ||||||||
\(981\) | 25.7742i | 0.822907i | ||||||||
\(982\) | 35.5083 | 1.13312 | ||||||||
\(983\) | −48.0127 | −1.53137 | −0.765684 | − | 0.643217i | \(-0.777599\pi\) | ||||
−0.765684 | + | 0.643217i | \(0.777599\pi\) | |||||||
\(984\) | −21.4519 | − | 39.3607i | −0.683863 | − | 1.25477i | ||||
\(985\) | −5.02293 | −0.160044 | ||||||||
\(986\) | 18.0226 | 0.573958 | ||||||||
\(987\) | 16.3346i | 0.519937i | ||||||||
\(988\) | −12.1331 | −0.386006 | ||||||||
\(989\) | 35.3859 | 1.12521 | ||||||||
\(990\) | − | 6.65576i | − | 0.211534i | ||||||
\(991\) | 52.9823i | 1.68304i | 0.540227 | + | 0.841520i | \(0.318339\pi\) | ||||
−0.540227 | + | 0.841520i | \(0.681661\pi\) | |||||||
\(992\) | 35.5993 | 1.13028 | ||||||||
\(993\) | 81.8819 | 2.59844 | ||||||||
\(994\) | −7.74124 | −0.245537 | ||||||||
\(995\) | − | 4.14972i | − | 0.131555i | ||||||
\(996\) | 39.6895i | 1.25761i | ||||||||
\(997\) | − | 43.5980i | − | 1.38076i | −0.723445 | − | 0.690382i | \(-0.757442\pi\) | ||
0.723445 | − | 0.690382i | \(-0.242558\pi\) | |||||||
\(998\) | 14.7891i | 0.468140i | ||||||||
\(999\) | − | 0.201491i | − | 0.00637489i |
(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 | 287.2.c.a.204.6 | yes | 10 | |
41.40 | even | 2 | inner | 287.2.c.a.204.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.c.a.204.5 | ✓ | 10 | 41.40 | even | 2 | inner | |
287.2.c.a.204.6 | yes | 10 | 1.1 | even | 1 | trivial |