Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(298,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("429.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.b (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: | \(3.42558224671\) |
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: | \( x^{10} + 13x^{8} + 54x^{6} + 74x^{4} + 21x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.10 | ||
Root | \(2.35969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.a.298.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35969i | 1.66855i | 0.551347 | + | 0.834276i | \(0.314114\pi\) | ||||
−0.551347 | + | 0.834276i | \(0.685886\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −3.56813 | −1.78407 | ||||||||
\(5\) | 1.80373i | 0.806655i | 0.915056 | + | 0.403327i | \(0.132146\pi\) | ||||
−0.915056 | + | 0.403327i | \(0.867854\pi\) | |||||||
\(6\) | − | 2.35969i | − | 0.963339i | ||||||
\(7\) | 4.78347i | 1.80798i | 0.427550 | + | 0.903991i | \(0.359377\pi\) | ||||
−0.427550 | + | 0.903991i | \(0.640623\pi\) | |||||||
\(8\) | − | 3.70030i | − | 1.30825i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.25625 | −1.34595 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 3.56813 | 1.03003 | ||||||||
\(13\) | 3.14435 | + | 1.76440i | 0.872085 | + | 0.489355i | ||||
\(14\) | −11.2875 | −3.01671 | ||||||||
\(15\) | − | 1.80373i | − | 0.465722i | ||||||
\(16\) | 1.59529 | 0.398823 | ||||||||
\(17\) | −2.63620 | −0.639373 | −0.319687 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319687 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(18\) | 2.35969i | 0.556184i | ||||||||
\(19\) | − | 6.47687i | − | 1.48590i | −0.669349 | − | 0.742948i | \(-0.733427\pi\) | ||
0.669349 | − | 0.742948i | \(-0.266573\pi\) | |||||||
\(20\) | − | 6.43596i | − | 1.43912i | ||||||
\(21\) | − | 4.78347i | − | 1.04384i | ||||||
\(22\) | 2.35969 | 0.503087 | ||||||||
\(23\) | −2.40352 | −0.501169 | −0.250585 | − | 0.968095i | \(-0.580623\pi\) | ||||
−0.250585 | + | 0.968095i | \(0.580623\pi\) | |||||||
\(24\) | 3.70030i | 0.755320i | ||||||||
\(25\) | 1.74654 | 0.349308 | ||||||||
\(26\) | −4.16342 | + | 7.41968i | −0.816515 | + | 1.45512i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − | 17.0681i | − | 3.22556i | ||||||
\(29\) | −1.40868 | −0.261586 | −0.130793 | − | 0.991410i | \(-0.541752\pi\) | ||||
−0.130793 | + | 0.991410i | \(0.541752\pi\) | |||||||
\(30\) | 4.25625 | 0.777082 | ||||||||
\(31\) | − | 6.06807i | − | 1.08986i | −0.838482 | − | 0.544929i | \(-0.816557\pi\) | ||
0.838482 | − | 0.544929i | \(-0.183443\pi\) | |||||||
\(32\) | − | 3.63620i | − | 0.642796i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | − | 6.22062i | − | 1.06683i | ||||||
\(35\) | −8.62812 | −1.45842 | ||||||||
\(36\) | −3.56813 | −0.594688 | ||||||||
\(37\) | 6.63223i | 1.09033i | 0.838328 | + | 0.545166i | \(0.183533\pi\) | ||||
−0.838328 | + | 0.545166i | \(0.816467\pi\) | |||||||
\(38\) | 15.2834 | 2.47929 | ||||||||
\(39\) | −3.14435 | − | 1.76440i | −0.503498 | − | 0.282529i | ||||
\(40\) | 6.67436 | 1.05531 | ||||||||
\(41\) | 7.21242i | 1.12639i | 0.826324 | + | 0.563195i | \(0.190428\pi\) | ||||
−0.826324 | + | 0.563195i | \(0.809572\pi\) | |||||||
\(42\) | 11.2875 | 1.74170 | ||||||||
\(43\) | 7.35558 | 1.12172 | 0.560858 | − | 0.827912i | \(-0.310471\pi\) | ||||
0.560858 | + | 0.827912i | \(0.310471\pi\) | |||||||
\(44\) | 3.56813i | 0.537916i | ||||||||
\(45\) | 1.80373i | 0.268885i | ||||||||
\(46\) | − | 5.67157i | − | 0.836227i | ||||||
\(47\) | 9.35160i | 1.36407i | 0.731319 | + | 0.682036i | \(0.238905\pi\) | ||||
−0.731319 | + | 0.682036i | \(0.761095\pi\) | |||||||
\(48\) | −1.59529 | −0.230261 | ||||||||
\(49\) | −15.8816 | −2.26880 | ||||||||
\(50\) | 4.12129i | 0.582839i | ||||||||
\(51\) | 2.63620 | 0.369142 | ||||||||
\(52\) | −11.2194 | − | 6.29559i | −1.55586 | − | 0.873042i | ||||
\(53\) | −4.20276 | −0.577294 | −0.288647 | − | 0.957436i | \(-0.593205\pi\) | ||||
−0.288647 | + | 0.957436i | \(0.593205\pi\) | |||||||
\(54\) | − | 2.35969i | − | 0.321113i | ||||||
\(55\) | 1.80373 | 0.243216 | ||||||||
\(56\) | 17.7003 | 2.36530 | ||||||||
\(57\) | 6.47687i | 0.857883i | ||||||||
\(58\) | − | 3.32405i | − | 0.436470i | ||||||
\(59\) | 0.288691i | 0.0375844i | 0.999823 | + | 0.0187922i | \(0.00598209\pi\) | ||||
−0.999823 | + | 0.0187922i | \(0.994018\pi\) | |||||||
\(60\) | 6.43596i | 0.830879i | ||||||||
\(61\) | 12.2851 | 1.57295 | 0.786473 | − | 0.617625i | \(-0.211905\pi\) | ||||
0.786473 | + | 0.617625i | \(0.211905\pi\) | |||||||
\(62\) | 14.3188 | 1.81848 | ||||||||
\(63\) | 4.78347i | 0.602661i | ||||||||
\(64\) | 11.7709 | 1.47136 | ||||||||
\(65\) | −3.18250 | + | 5.67157i | −0.394741 | + | 0.703471i | ||||
\(66\) | −2.35969 | −0.290458 | ||||||||
\(67\) | 13.1143i | 1.60217i | 0.598553 | + | 0.801083i | \(0.295743\pi\) | ||||
−0.598553 | + | 0.801083i | \(0.704257\pi\) | |||||||
\(68\) | 9.40632 | 1.14068 | ||||||||
\(69\) | 2.40352 | 0.289350 | ||||||||
\(70\) | − | 20.3597i | − | 2.43345i | ||||||
\(71\) | − | 8.88039i | − | 1.05391i | −0.849894 | − | 0.526954i | \(-0.823334\pi\) | ||
0.849894 | − | 0.526954i | \(-0.176666\pi\) | |||||||
\(72\) | − | 3.70030i | − | 0.436084i | ||||||
\(73\) | 2.61713i | 0.306311i | 0.988202 | + | 0.153156i | \(0.0489436\pi\) | ||||
−0.988202 | + | 0.153156i | \(0.951056\pi\) | |||||||
\(74\) | −15.6500 | −1.81927 | ||||||||
\(75\) | −1.74654 | −0.201673 | ||||||||
\(76\) | 23.1103i | 2.65094i | ||||||||
\(77\) | 4.78347 | 0.545127 | ||||||||
\(78\) | 4.16342 | − | 7.41968i | 0.471415 | − | 0.840113i | ||||
\(79\) | 3.32327 | 0.373897 | 0.186949 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186949 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(80\) | 2.87749i | 0.321713i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.0191 | −1.87944 | ||||||||
\(83\) | − | 9.78588i | − | 1.07414i | −0.843538 | − | 0.537070i | \(-0.819531\pi\) | ||
0.843538 | − | 0.537070i | \(-0.180469\pi\) | |||||||
\(84\) | 17.0681i | 1.86228i | ||||||||
\(85\) | − | 4.75501i | − | 0.515753i | ||||||
\(86\) | 17.3569i | 1.87164i | ||||||||
\(87\) | 1.40868 | 0.151027 | ||||||||
\(88\) | −3.70030 | −0.394453 | ||||||||
\(89\) | 14.0514i | 1.48944i | 0.667375 | + | 0.744722i | \(0.267418\pi\) | ||||
−0.667375 | + | 0.744722i | \(0.732582\pi\) | |||||||
\(90\) | −4.25625 | −0.448648 | ||||||||
\(91\) | −8.43994 | + | 15.0409i | −0.884746 | + | 1.57671i | ||||
\(92\) | 8.57608 | 0.894119 | ||||||||
\(93\) | 6.06807i | 0.629230i | ||||||||
\(94\) | −22.0669 | −2.27602 | ||||||||
\(95\) | 11.6826 | 1.19861 | ||||||||
\(96\) | 3.63620i | 0.371118i | ||||||||
\(97\) | − | 4.40604i | − | 0.447366i | −0.974662 | − | 0.223683i | \(-0.928192\pi\) | ||
0.974662 | − | 0.223683i | \(-0.0718080\pi\) | |||||||
\(98\) | − | 37.4757i | − | 3.78561i | ||||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | −6.23188 | −0.623188 | ||||||||
\(101\) | −6.42619 | −0.639430 | −0.319715 | − | 0.947514i | \(-0.603587\pi\) | ||||
−0.319715 | + | 0.947514i | \(0.603587\pi\) | |||||||
\(102\) | 6.22062i | 0.615933i | ||||||||
\(103\) | −6.42895 | −0.633463 | −0.316731 | − | 0.948515i | \(-0.602585\pi\) | ||||
−0.316731 | + | 0.948515i | \(0.602585\pi\) | |||||||
\(104\) | 6.52879 | − | 11.6350i | 0.640201 | − | 1.14091i | ||||
\(105\) | 8.62812 | 0.842018 | ||||||||
\(106\) | − | 9.91721i | − | 0.963245i | ||||||
\(107\) | −12.7575 | −1.23332 | −0.616659 | − | 0.787231i | \(-0.711514\pi\) | ||||
−0.616659 | + | 0.787231i | \(0.711514\pi\) | |||||||
\(108\) | 3.56813 | 0.343343 | ||||||||
\(109\) | − | 5.72108i | − | 0.547980i | −0.961733 | − | 0.273990i | \(-0.911656\pi\) | ||
0.961733 | − | 0.273990i | \(-0.0883435\pi\) | |||||||
\(110\) | 4.25625i | 0.405818i | ||||||||
\(111\) | − | 6.63223i | − | 0.629503i | ||||||
\(112\) | 7.63104i | 0.721066i | ||||||||
\(113\) | 2.12408 | 0.199817 | 0.0999085 | − | 0.994997i | \(-0.468145\pi\) | ||||
0.0999085 | + | 0.994997i | \(0.468145\pi\) | |||||||
\(114\) | −15.2834 | −1.43142 | ||||||||
\(115\) | − | 4.33532i | − | 0.404271i | ||||||
\(116\) | 5.02637 | 0.466686 | ||||||||
\(117\) | 3.14435 | + | 1.76440i | 0.290695 | + | 0.163118i | ||||
\(118\) | −0.681221 | −0.0627115 | ||||||||
\(119\) | − | 12.6102i | − | 1.15598i | ||||||
\(120\) | −6.67436 | −0.609283 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 28.9890i | 2.62454i | ||||||||
\(123\) | − | 7.21242i | − | 0.650322i | ||||||
\(124\) | 21.6517i | 1.94438i | ||||||||
\(125\) | 12.1690i | 1.08843i | ||||||||
\(126\) | −11.2875 | −1.00557 | ||||||||
\(127\) | −3.12818 | −0.277581 | −0.138790 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138790 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(128\) | 20.5032i | 1.81225i | ||||||||
\(129\) | −7.35558 | −0.647623 | ||||||||
\(130\) | −13.3831 | − | 7.50971i | −1.17378 | − | 0.658645i | ||||
\(131\) | 6.62690 | 0.578995 | 0.289497 | − | 0.957179i | \(-0.406512\pi\) | ||||
0.289497 | + | 0.957179i | \(0.406512\pi\) | |||||||
\(132\) | − | 3.56813i | − | 0.310566i | ||||||
\(133\) | 30.9819 | 2.68647 | ||||||||
\(134\) | −30.9457 | −2.67330 | ||||||||
\(135\) | − | 1.80373i | − | 0.155241i | ||||||
\(136\) | 9.75474i | 0.836462i | ||||||||
\(137\) | − | 4.79829i | − | 0.409945i | −0.978768 | − | 0.204973i | \(-0.934289\pi\) | ||
0.978768 | − | 0.204973i | \(-0.0657106\pi\) | |||||||
\(138\) | 5.67157i | 0.482796i | ||||||||
\(139\) | −16.9020 | −1.43361 | −0.716804 | − | 0.697275i | \(-0.754396\pi\) | ||||
−0.716804 | + | 0.697275i | \(0.754396\pi\) | |||||||
\(140\) | 30.7862 | 2.60191 | ||||||||
\(141\) | − | 9.35160i | − | 0.787547i | ||||||
\(142\) | 20.9550 | 1.75850 | ||||||||
\(143\) | 1.76440 | − | 3.14435i | 0.147546 | − | 0.262943i | ||||
\(144\) | 1.59529 | 0.132941 | ||||||||
\(145\) | − | 2.54089i | − | 0.211010i | ||||||
\(146\) | −6.17560 | −0.511096 | ||||||||
\(147\) | 15.8816 | 1.30989 | ||||||||
\(148\) | − | 23.6646i | − | 1.94522i | ||||||
\(149\) | 22.0259i | 1.80443i | 0.431284 | + | 0.902216i | \(0.358061\pi\) | ||||
−0.431284 | + | 0.902216i | \(0.641939\pi\) | |||||||
\(150\) | − | 4.12129i | − | 0.336502i | ||||||
\(151\) | − | 6.77937i | − | 0.551697i | −0.961201 | − | 0.275848i | \(-0.911041\pi\) | ||
0.961201 | − | 0.275848i | \(-0.0889588\pi\) | |||||||
\(152\) | −23.9664 | −1.94393 | ||||||||
\(153\) | −2.63620 | −0.213124 | ||||||||
\(154\) | 11.2875i | 0.909573i | ||||||||
\(155\) | 10.9452 | 0.879139 | ||||||||
\(156\) | 11.2194 | + | 6.29559i | 0.898274 | + | 0.504051i | ||||
\(157\) | 4.44168 | 0.354485 | 0.177242 | − | 0.984167i | \(-0.443282\pi\) | ||||
0.177242 | + | 0.984167i | \(0.443282\pi\) | |||||||
\(158\) | 7.84189i | 0.623867i | ||||||||
\(159\) | 4.20276 | 0.333301 | ||||||||
\(160\) | 6.55875 | 0.518514 | ||||||||
\(161\) | − | 11.4972i | − | 0.906105i | ||||||
\(162\) | 2.35969i | 0.185395i | ||||||||
\(163\) | 17.9152i | 1.40323i | 0.712556 | + | 0.701615i | \(0.247537\pi\) | ||||
−0.712556 | + | 0.701615i | \(0.752463\pi\) | |||||||
\(164\) | − | 25.7348i | − | 2.00955i | ||||||
\(165\) | −1.80373 | −0.140421 | ||||||||
\(166\) | 23.0916 | 1.79226 | ||||||||
\(167\) | − | 18.0543i | − | 1.39708i | −0.715569 | − | 0.698542i | \(-0.753833\pi\) | ||
0.715569 | − | 0.698542i | \(-0.246167\pi\) | |||||||
\(168\) | −17.7003 | −1.36561 | ||||||||
\(169\) | 6.77382 | + | 11.0957i | 0.521063 | + | 0.853518i | ||||
\(170\) | 11.2203 | 0.860561 | ||||||||
\(171\) | − | 6.47687i | − | 0.495299i | ||||||
\(172\) | −26.2457 | −2.00121 | ||||||||
\(173\) | 25.4260 | 1.93311 | 0.966553 | − | 0.256466i | \(-0.0825583\pi\) | ||||
0.966553 | + | 0.256466i | \(0.0825583\pi\) | |||||||
\(174\) | 3.32405i | 0.251996i | ||||||||
\(175\) | 8.35453i | 0.631543i | ||||||||
\(176\) | − | 1.59529i | − | 0.120250i | ||||||
\(177\) | − | 0.288691i | − | 0.0216994i | ||||||
\(178\) | −33.1569 | −2.48521 | ||||||||
\(179\) | 13.7969 | 1.03123 | 0.515613 | − | 0.856821i | \(-0.327564\pi\) | ||||
0.515613 | + | 0.856821i | \(0.327564\pi\) | |||||||
\(180\) | − | 6.43596i | − | 0.479708i | ||||||
\(181\) | 18.0141 | 1.33898 | 0.669490 | − | 0.742821i | \(-0.266513\pi\) | ||||
0.669490 | + | 0.742821i | \(0.266513\pi\) | |||||||
\(182\) | −35.4918 | − | 19.9156i | −2.63083 | − | 1.47624i | ||||
\(183\) | −12.2851 | −0.908141 | ||||||||
\(184\) | 8.89375i | 0.655656i | ||||||||
\(185\) | −11.9628 | −0.879521 | ||||||||
\(186\) | −14.3188 | −1.04990 | ||||||||
\(187\) | 2.63620i | 0.192778i | ||||||||
\(188\) | − | 33.3677i | − | 2.43359i | ||||||
\(189\) | − | 4.78347i | − | 0.347946i | ||||||
\(190\) | 27.5672i | 1.99994i | ||||||||
\(191\) | −8.72663 | −0.631436 | −0.315718 | − | 0.948853i | \(-0.602245\pi\) | ||||
−0.315718 | + | 0.948853i | \(0.602245\pi\) | |||||||
\(192\) | −11.7709 | −0.849491 | ||||||||
\(193\) | 4.46458i | 0.321367i | 0.987006 | + | 0.160684i | \(0.0513699\pi\) | ||||
−0.987006 | + | 0.160684i | \(0.948630\pi\) | |||||||
\(194\) | 10.3969 | 0.746453 | ||||||||
\(195\) | 3.18250 | − | 5.67157i | 0.227904 | − | 0.406149i | ||||
\(196\) | 56.6677 | 4.04769 | ||||||||
\(197\) | − | 5.53927i | − | 0.394656i | −0.980337 | − | 0.197328i | \(-0.936774\pi\) | ||
0.980337 | − | 0.197328i | \(-0.0632264\pi\) | |||||||
\(198\) | 2.35969 | 0.167696 | ||||||||
\(199\) | 22.7640 | 1.61370 | 0.806848 | − | 0.590759i | \(-0.201172\pi\) | ||||
0.806848 | + | 0.590759i | \(0.201172\pi\) | |||||||
\(200\) | − | 6.46272i | − | 0.456983i | ||||||
\(201\) | − | 13.1143i | − | 0.925011i | ||||||
\(202\) | − | 15.1638i | − | 1.06692i | ||||||
\(203\) | − | 6.73840i | − | 0.472943i | ||||||
\(204\) | −9.40632 | −0.658574 | ||||||||
\(205\) | −13.0093 | −0.908608 | ||||||||
\(206\) | − | 15.1703i | − | 1.05697i | ||||||
\(207\) | −2.40352 | −0.167056 | ||||||||
\(208\) | 5.01615 | + | 2.81473i | 0.347808 | + | 0.195166i | ||||
\(209\) | −6.47687 | −0.448015 | ||||||||
\(210\) | 20.3597i | 1.40495i | ||||||||
\(211\) | 5.58761 | 0.384667 | 0.192334 | − | 0.981330i | \(-0.438394\pi\) | ||||
0.192334 | + | 0.981330i | \(0.438394\pi\) | |||||||
\(212\) | 14.9960 | 1.02993 | ||||||||
\(213\) | 8.88039i | 0.608475i | ||||||||
\(214\) | − | 30.1038i | − | 2.05785i | ||||||
\(215\) | 13.2675i | 0.904837i | ||||||||
\(216\) | 3.70030i | 0.251773i | ||||||||
\(217\) | 29.0265 | 1.97044 | ||||||||
\(218\) | 13.5000 | 0.914333 | ||||||||
\(219\) | − | 2.61713i | − | 0.176849i | ||||||
\(220\) | −6.43596 | −0.433912 | ||||||||
\(221\) | −8.28913 | − | 4.65130i | −0.557587 | − | 0.312881i | ||||
\(222\) | 15.6500 | 1.05036 | ||||||||
\(223\) | 10.1832i | 0.681920i | 0.940078 | + | 0.340960i | \(0.110752\pi\) | ||||
−0.940078 | + | 0.340960i | \(0.889248\pi\) | |||||||
\(224\) | 17.3937 | 1.16216 | ||||||||
\(225\) | 1.74654 | 0.116436 | ||||||||
\(226\) | 5.01218i | 0.333405i | ||||||||
\(227\) | 0.783473i | 0.0520010i | 0.999662 | + | 0.0260005i | \(0.00827714\pi\) | ||||
−0.999662 | + | 0.0260005i | \(0.991723\pi\) | |||||||
\(228\) | − | 23.1103i | − | 1.53052i | ||||||
\(229\) | − | 20.8340i | − | 1.37675i | −0.725355 | − | 0.688375i | \(-0.758324\pi\) | ||
0.725355 | − | 0.688375i | \(-0.241676\pi\) | |||||||
\(230\) | 10.2300 | 0.674546 | ||||||||
\(231\) | −4.78347 | −0.314729 | ||||||||
\(232\) | 5.21255i | 0.342221i | ||||||||
\(233\) | −8.50679 | −0.557298 | −0.278649 | − | 0.960393i | \(-0.589887\pi\) | ||||
−0.278649 | + | 0.960393i | \(0.589887\pi\) | |||||||
\(234\) | −4.16342 | + | 7.41968i | −0.272172 | + | 0.485039i | ||||
\(235\) | −16.8678 | −1.10033 | ||||||||
\(236\) | − | 1.03009i | − | 0.0670530i | ||||||
\(237\) | −3.32327 | −0.215870 | ||||||||
\(238\) | 29.7562 | 1.92881 | ||||||||
\(239\) | − | 2.74768i | − | 0.177733i | −0.996044 | − | 0.0888665i | \(-0.971676\pi\) | ||
0.996044 | − | 0.0888665i | \(-0.0283244\pi\) | |||||||
\(240\) | − | 2.87749i | − | 0.185741i | ||||||
\(241\) | 10.3746i | 0.668288i | 0.942522 | + | 0.334144i | \(0.108447\pi\) | ||||
−0.942522 | + | 0.334144i | \(0.891553\pi\) | |||||||
\(242\) | − | 2.35969i | − | 0.151687i | ||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −43.8348 | −2.80624 | ||||||||
\(245\) | − | 28.6462i | − | 1.83014i | ||||||
\(246\) | 17.0191 | 1.08510 | ||||||||
\(247\) | 11.4278 | − | 20.3655i | 0.727131 | − | 1.29583i | ||||
\(248\) | −22.4537 | −1.42581 | ||||||||
\(249\) | 9.78588i | 0.620155i | ||||||||
\(250\) | −28.7150 | −1.81609 | ||||||||
\(251\) | −24.1897 | −1.52684 | −0.763421 | − | 0.645901i | \(-0.776482\pi\) | ||||
−0.763421 | + | 0.645901i | \(0.776482\pi\) | |||||||
\(252\) | − | 17.0681i | − | 1.07519i | ||||||
\(253\) | 2.40352i | 0.151108i | ||||||||
\(254\) | − | 7.38152i | − | 0.463158i | ||||||
\(255\) | 4.75501i | 0.297770i | ||||||||
\(256\) | −24.8395 | −1.55247 | ||||||||
\(257\) | −4.06662 | −0.253669 | −0.126834 | − | 0.991924i | \(-0.540482\pi\) | ||||
−0.126834 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(258\) | − | 17.3569i | − | 1.08059i | ||||||
\(259\) | −31.7251 | −1.97130 | ||||||||
\(260\) | 11.3556 | − | 20.2369i | 0.704243 | − | 1.25504i | ||||
\(261\) | −1.40868 | −0.0871953 | ||||||||
\(262\) | 15.6374i | 0.966082i | ||||||||
\(263\) | −6.36570 | −0.392526 | −0.196263 | − | 0.980551i | \(-0.562881\pi\) | ||||
−0.196263 | + | 0.980551i | \(0.562881\pi\) | |||||||
\(264\) | 3.70030 | 0.227738 | ||||||||
\(265\) | − | 7.58067i | − | 0.465677i | ||||||
\(266\) | 73.1077i | 4.48252i | ||||||||
\(267\) | − | 14.0514i | − | 0.859931i | ||||||
\(268\) | − | 46.7935i | − | 2.85837i | ||||||
\(269\) | 28.4905 | 1.73710 | 0.868548 | − | 0.495605i | \(-0.165054\pi\) | ||||
0.868548 | + | 0.495605i | \(0.165054\pi\) | |||||||
\(270\) | 4.25625 | 0.259027 | ||||||||
\(271\) | − | 13.5110i | − | 0.820737i | −0.911920 | − | 0.410368i | \(-0.865400\pi\) | ||
0.911920 | − | 0.410368i | \(-0.134600\pi\) | |||||||
\(272\) | −4.20552 | −0.254997 | ||||||||
\(273\) | 8.43994 | − | 15.0409i | 0.510808 | − | 0.910316i | ||||
\(274\) | 11.3225 | 0.684015 | ||||||||
\(275\) | − | 1.74654i | − | 0.105320i | ||||||
\(276\) | −8.57608 | −0.516220 | ||||||||
\(277\) | −2.04052 | −0.122603 | −0.0613016 | − | 0.998119i | \(-0.519525\pi\) | ||||
−0.0613016 | + | 0.998119i | \(0.519525\pi\) | |||||||
\(278\) | − | 39.8834i | − | 2.39205i | ||||||
\(279\) | − | 6.06807i | − | 0.363286i | ||||||
\(280\) | 31.9266i | 1.90798i | ||||||||
\(281\) | 15.7569i | 0.939976i | 0.882673 | + | 0.469988i | \(0.155742\pi\) | ||||
−0.882673 | + | 0.469988i | \(0.844258\pi\) | |||||||
\(282\) | 22.0669 | 1.31406 | ||||||||
\(283\) | −21.8937 | −1.30144 | −0.650722 | − | 0.759316i | \(-0.725533\pi\) | ||||
−0.650722 | + | 0.759316i | \(0.725533\pi\) | |||||||
\(284\) | 31.6864i | 1.88024i | ||||||||
\(285\) | −11.6826 | −0.692015 | ||||||||
\(286\) | 7.41968 | + | 4.16342i | 0.438735 | + | 0.246188i | ||||
\(287\) | −34.5004 | −2.03649 | ||||||||
\(288\) | − | 3.63620i | − | 0.214265i | ||||||
\(289\) | −10.0504 | −0.591202 | ||||||||
\(290\) | 5.99571 | 0.352080 | ||||||||
\(291\) | 4.40604i | 0.258287i | ||||||||
\(292\) | − | 9.33824i | − | 0.546479i | ||||||
\(293\) | 15.0681i | 0.880285i | 0.897928 | + | 0.440143i | \(0.145072\pi\) | ||||
−0.897928 | + | 0.440143i | \(0.854928\pi\) | |||||||
\(294\) | 37.4757i | 2.18563i | ||||||||
\(295\) | −0.520722 | −0.0303176 | ||||||||
\(296\) | 24.5412 | 1.42643 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | −51.9743 | −3.01079 | ||||||||
\(299\) | −7.55751 | − | 4.24076i | −0.437062 | − | 0.245250i | ||||
\(300\) | 6.23188 | 0.359798 | ||||||||
\(301\) | 35.1852i | 2.02804i | ||||||||
\(302\) | 15.9972 | 0.920535 | ||||||||
\(303\) | 6.42619 | 0.369175 | ||||||||
\(304\) | − | 10.3325i | − | 0.592610i | ||||||
\(305\) | 22.1591i | 1.26882i | ||||||||
\(306\) | − | 6.22062i | − | 0.355609i | ||||||
\(307\) | − | 17.0334i | − | 0.972146i | −0.873918 | − | 0.486073i | \(-0.838429\pi\) | ||
0.873918 | − | 0.486073i | \(-0.161571\pi\) | |||||||
\(308\) | −17.0681 | −0.972543 | ||||||||
\(309\) | 6.42895 | 0.365730 | ||||||||
\(310\) | 25.8273i | 1.46689i | ||||||||
\(311\) | 15.3734 | 0.871748 | 0.435874 | − | 0.900008i | \(-0.356439\pi\) | ||||
0.435874 | + | 0.900008i | \(0.356439\pi\) | |||||||
\(312\) | −6.52879 | + | 11.6350i | −0.369620 | + | 0.658703i | ||||
\(313\) | 16.7286 | 0.945558 | 0.472779 | − | 0.881181i | \(-0.343251\pi\) | ||||
0.472779 | + | 0.881181i | \(0.343251\pi\) | |||||||
\(314\) | 10.4810i | 0.591476i | ||||||||
\(315\) | −8.62812 | −0.486139 | ||||||||
\(316\) | −11.8579 | −0.667057 | ||||||||
\(317\) | 5.33201i | 0.299475i | 0.988726 | + | 0.149738i | \(0.0478429\pi\) | ||||
−0.988726 | + | 0.149738i | \(0.952157\pi\) | |||||||
\(318\) | 9.91721i | 0.556130i | ||||||||
\(319\) | 1.40868i | 0.0788711i | ||||||||
\(320\) | 21.2316i | 1.18688i | ||||||||
\(321\) | 12.7575 | 0.712056 | ||||||||
\(322\) | 27.1298 | 1.51188 | ||||||||
\(323\) | 17.0743i | 0.950042i | ||||||||
\(324\) | −3.56813 | −0.198229 | ||||||||
\(325\) | 5.49173 | + | 3.08159i | 0.304626 | + | 0.170936i | ||||
\(326\) | −42.2744 | −2.34136 | ||||||||
\(327\) | 5.72108i | 0.316376i | ||||||||
\(328\) | 26.6881 | 1.47360 | ||||||||
\(329\) | −44.7331 | −2.46622 | ||||||||
\(330\) | − | 4.25625i | − | 0.234299i | ||||||
\(331\) | 22.1737i | 1.21878i | 0.792871 | + | 0.609389i | \(0.208585\pi\) | ||||
−0.792871 | + | 0.609389i | \(0.791415\pi\) | |||||||
\(332\) | 34.9173i | 1.91634i | ||||||||
\(333\) | 6.63223i | 0.363444i | ||||||||
\(334\) | 42.6025 | 2.33111 | ||||||||
\(335\) | −23.6547 | −1.29240 | ||||||||
\(336\) | − | 7.63104i | − | 0.416308i | ||||||
\(337\) | 12.9050 | 0.702982 | 0.351491 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351491 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(338\) | −26.1825 | + | 15.9841i | −1.42414 | + | 0.869421i | ||||
\(339\) | −2.12408 | −0.115364 | ||||||||
\(340\) | 16.9665i | 0.920138i | ||||||||
\(341\) | −6.06807 | −0.328605 | ||||||||
\(342\) | 15.2834 | 0.826432 | ||||||||
\(343\) | − | 42.4850i | − | 2.29397i | ||||||
\(344\) | − | 27.2178i | − | 1.46749i | ||||||
\(345\) | 4.33532i | 0.233406i | ||||||||
\(346\) | 59.9975i | 3.22549i | ||||||||
\(347\) | 30.7457 | 1.65052 | 0.825259 | − | 0.564755i | \(-0.191029\pi\) | ||||
0.825259 | + | 0.564755i | \(0.191029\pi\) | |||||||
\(348\) | −5.02637 | −0.269441 | ||||||||
\(349\) | − | 15.5239i | − | 0.830974i | −0.909599 | − | 0.415487i | \(-0.863611\pi\) | ||
0.909599 | − | 0.415487i | \(-0.136389\pi\) | |||||||
\(350\) | −19.7141 | −1.05376 | ||||||||
\(351\) | −3.14435 | − | 1.76440i | −0.167833 | − | 0.0941765i | ||||
\(352\) | −3.63620 | −0.193810 | ||||||||
\(353\) | − | 21.4800i | − | 1.14326i | −0.820510 | − | 0.571632i | \(-0.806310\pi\) | ||
0.820510 | − | 0.571632i | \(-0.193690\pi\) | |||||||
\(354\) | 0.681221 | 0.0362065 | ||||||||
\(355\) | 16.0179 | 0.850141 | ||||||||
\(356\) | − | 50.1372i | − | 2.65726i | ||||||
\(357\) | 12.6102i | 0.667403i | ||||||||
\(358\) | 32.5563i | 1.72066i | ||||||||
\(359\) | − | 19.1458i | − | 1.01047i | −0.862980 | − | 0.505237i | \(-0.831405\pi\) | ||
0.862980 | − | 0.505237i | \(-0.168595\pi\) | |||||||
\(360\) | 6.67436 | 0.351770 | ||||||||
\(361\) | −22.9499 | −1.20789 | ||||||||
\(362\) | 42.5077i | 2.23416i | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 30.1148 | − | 53.6679i | 1.57844 | − | 2.81296i | ||||
\(365\) | −4.72060 | −0.247087 | ||||||||
\(366\) | − | 28.9890i | − | 1.51528i | ||||||
\(367\) | 16.7868 | 0.876262 | 0.438131 | − | 0.898911i | \(-0.355641\pi\) | ||||
0.438131 | + | 0.898911i | \(0.355641\pi\) | |||||||
\(368\) | −3.83432 | −0.199878 | ||||||||
\(369\) | 7.21242i | 0.375464i | ||||||||
\(370\) | − | 28.2284i | − | 1.46753i | ||||||
\(371\) | − | 20.1038i | − | 1.04374i | ||||||
\(372\) | − | 21.6517i | − | 1.12259i | ||||||
\(373\) | −10.3674 | −0.536802 | −0.268401 | − | 0.963307i | \(-0.586495\pi\) | ||||
−0.268401 | + | 0.963307i | \(0.586495\pi\) | |||||||
\(374\) | −6.22062 | −0.321661 | ||||||||
\(375\) | − | 12.1690i | − | 0.628403i | ||||||
\(376\) | 34.6037 | 1.78455 | ||||||||
\(377\) | −4.42939 | − | 2.48547i | −0.228125 | − | 0.128008i | ||||
\(378\) | 11.2875 | 0.580567 | ||||||||
\(379\) | 25.3516i | 1.30223i | 0.758981 | + | 0.651113i | \(0.225698\pi\) | ||||
−0.758981 | + | 0.651113i | \(0.774302\pi\) | |||||||
\(380\) | −41.6849 | −2.13839 | ||||||||
\(381\) | 3.12818 | 0.160261 | ||||||||
\(382\) | − | 20.5921i | − | 1.05358i | ||||||
\(383\) | − | 27.2749i | − | 1.39368i | −0.717227 | − | 0.696840i | \(-0.754589\pi\) | ||
0.717227 | − | 0.696840i | \(-0.245411\pi\) | |||||||
\(384\) | − | 20.5032i | − | 1.04630i | ||||||
\(385\) | 8.62812i | 0.439730i | ||||||||
\(386\) | −10.5350 | −0.536218 | ||||||||
\(387\) | 7.35558 | 0.373905 | ||||||||
\(388\) | 15.7213i | 0.798130i | ||||||||
\(389\) | 5.78177 | 0.293147 | 0.146574 | − | 0.989200i | \(-0.453175\pi\) | ||||
0.146574 | + | 0.989200i | \(0.453175\pi\) | |||||||
\(390\) | 13.3831 | + | 7.50971i | 0.677681 | + | 0.380269i | ||||
\(391\) | 6.33618 | 0.320434 | ||||||||
\(392\) | 58.7667i | 2.96817i | ||||||||
\(393\) | −6.62690 | −0.334283 | ||||||||
\(394\) | 13.0709 | 0.658505 | ||||||||
\(395\) | 5.99430i | 0.301606i | ||||||||
\(396\) | 3.56813i | 0.179305i | ||||||||
\(397\) | − | 14.2696i | − | 0.716172i | −0.933689 | − | 0.358086i | \(-0.883429\pi\) | ||
0.933689 | − | 0.358086i | \(-0.116571\pi\) | |||||||
\(398\) | 53.7159i | 2.69253i | ||||||||
\(399\) | −30.9819 | −1.55104 | ||||||||
\(400\) | 2.78624 | 0.139312 | ||||||||
\(401\) | − | 16.4746i | − | 0.822704i | −0.911477 | − | 0.411352i | \(-0.865057\pi\) | ||
0.911477 | − | 0.411352i | \(-0.134943\pi\) | |||||||
\(402\) | 30.9457 | 1.54343 | ||||||||
\(403\) | 10.7065 | − | 19.0801i | 0.533328 | − | 0.950448i | ||||
\(404\) | 22.9295 | 1.14078 | ||||||||
\(405\) | 1.80373i | 0.0896283i | ||||||||
\(406\) | 15.9005 | 0.789130 | ||||||||
\(407\) | 6.63223 | 0.328747 | ||||||||
\(408\) | − | 9.75474i | − | 0.482932i | ||||||
\(409\) | − | 4.40230i | − | 0.217680i | −0.994059 | − | 0.108840i | \(-0.965286\pi\) | ||
0.994059 | − | 0.108840i | \(-0.0347136\pi\) | |||||||
\(410\) | − | 30.6979i | − | 1.51606i | ||||||
\(411\) | 4.79829i | 0.236682i | ||||||||
\(412\) | 22.9393 | 1.13014 | ||||||||
\(413\) | −1.38095 | −0.0679519 | ||||||||
\(414\) | − | 5.67157i | − | 0.278742i | ||||||
\(415\) | 17.6511 | 0.866460 | ||||||||
\(416\) | 6.41570 | − | 11.4335i | 0.314556 | − | 0.560572i | ||||
\(417\) | 16.9020 | 0.827694 | ||||||||
\(418\) | − | 15.2834i | − | 0.747535i | ||||||
\(419\) | 37.6890 | 1.84123 | 0.920614 | − | 0.390474i | \(-0.127689\pi\) | ||||
0.920614 | + | 0.390474i | \(0.127689\pi\) | |||||||
\(420\) | −30.7862 | −1.50222 | ||||||||
\(421\) | 13.7632i | 0.670775i | 0.942080 | + | 0.335388i | \(0.108867\pi\) | ||||
−0.942080 | + | 0.335388i | \(0.891133\pi\) | |||||||
\(422\) | 13.1850i | 0.641837i | ||||||||
\(423\) | 9.35160i | 0.454691i | ||||||||
\(424\) | 15.5515i | 0.755247i | ||||||||
\(425\) | −4.60423 | −0.223338 | ||||||||
\(426\) | −20.9550 | −1.01527 | ||||||||
\(427\) | 58.7655i | 2.84386i | ||||||||
\(428\) | 45.5205 | 2.20032 | ||||||||
\(429\) | −1.76440 | + | 3.14435i | −0.0851858 | + | 0.151810i | ||||
\(430\) | −31.3072 | −1.50977 | ||||||||
\(431\) | − | 23.4202i | − | 1.12811i | −0.825736 | − | 0.564056i | \(-0.809240\pi\) | ||
0.825736 | − | 0.564056i | \(-0.190760\pi\) | |||||||
\(432\) | −1.59529 | −0.0767536 | ||||||||
\(433\) | −21.1826 | −1.01797 | −0.508985 | − | 0.860775i | \(-0.669979\pi\) | ||||
−0.508985 | + | 0.860775i | \(0.669979\pi\) | |||||||
\(434\) | 68.4934i | 3.28779i | ||||||||
\(435\) | 2.54089i | 0.121826i | ||||||||
\(436\) | 20.4136i | 0.977632i | ||||||||
\(437\) | 15.5673i | 0.744685i | ||||||||
\(438\) | 6.17560 | 0.295082 | ||||||||
\(439\) | 6.52337 | 0.311344 | 0.155672 | − | 0.987809i | \(-0.450246\pi\) | ||||
0.155672 | + | 0.987809i | \(0.450246\pi\) | |||||||
\(440\) | − | 6.67436i | − | 0.318188i | ||||||
\(441\) | −15.8816 | −0.756267 | ||||||||
\(442\) | 10.9756 | − | 19.5598i | 0.522057 | − | 0.930364i | ||||
\(443\) | −35.8996 | −1.70564 | −0.852821 | − | 0.522203i | \(-0.825110\pi\) | ||||
−0.852821 | + | 0.522203i | \(0.825110\pi\) | |||||||
\(444\) | 23.6646i | 1.12307i | ||||||||
\(445\) | −25.3450 | −1.20147 | ||||||||
\(446\) | −24.0293 | −1.13782 | ||||||||
\(447\) | − | 22.0259i | − | 1.04179i | ||||||
\(448\) | 56.3058i | 2.66020i | ||||||||
\(449\) | 6.86446i | 0.323954i | 0.986795 | + | 0.161977i | \(0.0517870\pi\) | ||||
−0.986795 | + | 0.161977i | \(0.948213\pi\) | |||||||
\(450\) | 4.12129i | 0.194280i | ||||||||
\(451\) | 7.21242 | 0.339620 | ||||||||
\(452\) | −7.57901 | −0.356487 | ||||||||
\(453\) | 6.77937i | 0.318522i | ||||||||
\(454\) | −1.84875 | −0.0867663 | ||||||||
\(455\) | −27.1298 | − | 15.2234i | −1.27186 | − | 0.713685i | ||||
\(456\) | 23.9664 | 1.12233 | ||||||||
\(457\) | − | 34.4445i | − | 1.61124i | −0.592430 | − | 0.805622i | \(-0.701831\pi\) | ||
0.592430 | − | 0.805622i | \(-0.298169\pi\) | |||||||
\(458\) | 49.1618 | 2.29718 | ||||||||
\(459\) | 2.63620 | 0.123047 | ||||||||
\(460\) | 15.4690i | 0.721245i | ||||||||
\(461\) | − | 10.0997i | − | 0.470390i | −0.971948 | − | 0.235195i | \(-0.924427\pi\) | ||
0.971948 | − | 0.235195i | \(-0.0755729\pi\) | |||||||
\(462\) | − | 11.2875i | − | 0.525142i | ||||||
\(463\) | − | 6.44706i | − | 0.299620i | −0.988715 | − | 0.149810i | \(-0.952134\pi\) | ||
0.988715 | − | 0.149810i | \(-0.0478662\pi\) | |||||||
\(464\) | −2.24726 | −0.104327 | ||||||||
\(465\) | −10.9452 | −0.507571 | ||||||||
\(466\) | − | 20.0734i | − | 0.929881i | ||||||
\(467\) | 17.9485 | 0.830555 | 0.415278 | − | 0.909695i | \(-0.363684\pi\) | ||||
0.415278 | + | 0.909695i | \(0.363684\pi\) | |||||||
\(468\) | −11.2194 | − | 6.29559i | −0.518619 | − | 0.291014i | ||||
\(469\) | −62.7319 | −2.89669 | ||||||||
\(470\) | − | 39.8028i | − | 1.83597i | ||||||
\(471\) | −4.44168 | −0.204662 | ||||||||
\(472\) | 1.06824 | 0.0491699 | ||||||||
\(473\) | − | 7.35558i | − | 0.338210i | ||||||
\(474\) | − | 7.84189i | − | 0.360190i | ||||||
\(475\) | − | 11.3121i | − | 0.519035i | ||||||
\(476\) | 44.9949i | 2.06234i | ||||||||
\(477\) | −4.20276 | −0.192431 | ||||||||
\(478\) | 6.48368 | 0.296557 | ||||||||
\(479\) | − | 4.09911i | − | 0.187293i | −0.995606 | − | 0.0936466i | \(-0.970148\pi\) | ||
0.995606 | − | 0.0936466i | \(-0.0298524\pi\) | |||||||
\(480\) | −6.55875 | −0.299364 | ||||||||
\(481\) | −11.7019 | + | 20.8540i | −0.533559 | + | 0.950861i | ||||
\(482\) | −24.4809 | −1.11507 | ||||||||
\(483\) | 11.4972i | 0.523140i | ||||||||
\(484\) | 3.56813 | 0.162188 | ||||||||
\(485\) | 7.94734 | 0.360870 | ||||||||
\(486\) | − | 2.35969i | − | 0.107038i | ||||||
\(487\) | 6.10989i | 0.276865i | 0.990372 | + | 0.138433i | \(0.0442065\pi\) | ||||
−0.990372 | + | 0.138433i | \(0.955794\pi\) | |||||||
\(488\) | − | 45.4585i | − | 2.05781i | ||||||
\(489\) | − | 17.9152i | − | 0.810155i | ||||||
\(490\) | 67.5962 | 3.05368 | ||||||||
\(491\) | 11.8025 | 0.532641 | 0.266320 | − | 0.963885i | \(-0.414192\pi\) | ||||
0.266320 | + | 0.963885i | \(0.414192\pi\) | |||||||
\(492\) | 25.7348i | 1.16022i | ||||||||
\(493\) | 3.71358 | 0.167251 | ||||||||
\(494\) | 48.0563 | + | 26.9660i | 2.16215 | + | 1.21326i | ||||
\(495\) | 1.80373 | 0.0810719 | ||||||||
\(496\) | − | 9.68036i | − | 0.434661i | ||||||
\(497\) | 42.4791 | 1.90545 | ||||||||
\(498\) | −23.0916 | −1.03476 | ||||||||
\(499\) | − | 2.07874i | − | 0.0930570i | −0.998917 | − | 0.0465285i | \(-0.985184\pi\) | ||
0.998917 | − | 0.0465285i | \(-0.0148158\pi\) | |||||||
\(500\) | − | 43.4205i | − | 1.94182i | ||||||
\(501\) | 18.0543i | 0.806606i | ||||||||
\(502\) | − | 57.0802i | − | 2.54762i | ||||||
\(503\) | 33.4841 | 1.49298 | 0.746490 | − | 0.665396i | \(-0.231737\pi\) | ||||
0.746490 | + | 0.665396i | \(0.231737\pi\) | |||||||
\(504\) | 17.7003 | 0.788433 | ||||||||
\(505\) | − | 11.5911i | − | 0.515799i | ||||||
\(506\) | −5.67157 | −0.252132 | ||||||||
\(507\) | −6.77382 | − | 11.0957i | −0.300836 | − | 0.492779i | ||||
\(508\) | 11.1617 | 0.495222 | ||||||||
\(509\) | 25.3434i | 1.12332i | 0.827366 | + | 0.561662i | \(0.189838\pi\) | ||||
−0.827366 | + | 0.561662i | \(0.810162\pi\) | |||||||
\(510\) | −11.2203 | −0.496845 | ||||||||
\(511\) | −12.5189 | −0.553806 | ||||||||
\(512\) | − | 17.6069i | − | 0.778124i | ||||||
\(513\) | 6.47687i | 0.285961i | ||||||||
\(514\) | − | 9.59595i | − | 0.423259i | ||||||
\(515\) | − | 11.5961i | − | 0.510986i | ||||||
\(516\) | 26.2457 | 1.15540 | ||||||||
\(517\) | 9.35160 | 0.411283 | ||||||||
\(518\) | − | 74.8613i | − | 3.28922i | ||||||
\(519\) | −25.4260 | −1.11608 | ||||||||
\(520\) | 20.9865 | + | 11.7762i | 0.920319 | + | 0.516421i | ||||
\(521\) | 28.6222 | 1.25396 | 0.626980 | − | 0.779036i | \(-0.284291\pi\) | ||||
0.626980 | + | 0.779036i | \(0.284291\pi\) | |||||||
\(522\) | − | 3.32405i | − | 0.145490i | ||||||
\(523\) | 31.8440 | 1.39244 | 0.696221 | − | 0.717827i | \(-0.254863\pi\) | ||||
0.696221 | + | 0.717827i | \(0.254863\pi\) | |||||||
\(524\) | −23.6456 | −1.03296 | ||||||||
\(525\) | − | 8.35453i | − | 0.364622i | ||||||
\(526\) | − | 15.0211i | − | 0.654950i | ||||||
\(527\) | 15.9967i | 0.696826i | ||||||||
\(528\) | 1.59529i | 0.0694262i | ||||||||
\(529\) | −17.2231 | −0.748829 | ||||||||
\(530\) | 17.8880 | 0.777006 | ||||||||
\(531\) | 0.288691i | 0.0125281i | ||||||||
\(532\) | −110.548 | −4.79285 | ||||||||
\(533\) | −12.7256 | + | 22.6783i | −0.551205 | + | 0.982308i | ||||
\(534\) | 33.1569 | 1.43484 | ||||||||
\(535\) | − | 23.0112i | − | 0.994861i | ||||||
\(536\) | 48.5268 | 2.09604 | ||||||||
\(537\) | −13.7969 | −0.595379 | ||||||||
\(538\) | 67.2287i | 2.89843i | ||||||||
\(539\) | 15.8816i | 0.684070i | ||||||||
\(540\) | 6.43596i | 0.276960i | ||||||||
\(541\) | 30.2013i | 1.29846i | 0.760594 | + | 0.649228i | \(0.224908\pi\) | ||||
−0.760594 | + | 0.649228i | \(0.775092\pi\) | |||||||
\(542\) | 31.8818 | 1.36944 | ||||||||
\(543\) | −18.0141 | −0.773060 | ||||||||
\(544\) | 9.58577i | 0.410986i | ||||||||
\(545\) | 10.3193 | 0.442031 | ||||||||
\(546\) | 35.4918 | + | 19.9156i | 1.51891 | + | 0.852310i | ||||
\(547\) | −9.53137 | −0.407532 | −0.203766 | − | 0.979020i | \(-0.565318\pi\) | ||||
−0.203766 | + | 0.979020i | \(0.565318\pi\) | |||||||
\(548\) | 17.1209i | 0.731369i | ||||||||
\(549\) | 12.2851 | 0.524315 | ||||||||
\(550\) | 4.12129 | 0.175732 | ||||||||
\(551\) | 9.12386i | 0.388690i | ||||||||
\(552\) | − | 8.89375i | − | 0.378543i | ||||||
\(553\) | 15.8968i | 0.676000i | ||||||||
\(554\) | − | 4.81500i | − | 0.204570i | ||||||
\(555\) | 11.9628 | 0.507792 | ||||||||
\(556\) | 60.3085 | 2.55765 | ||||||||
\(557\) | 15.8630i | 0.672135i | 0.941838 | + | 0.336068i | \(0.109097\pi\) | ||||
−0.941838 | + | 0.336068i | \(0.890903\pi\) | |||||||
\(558\) | 14.3188 | 0.606162 | ||||||||
\(559\) | 23.1285 | + | 12.9782i | 0.978231 | + | 0.548917i | ||||
\(560\) | −13.7644 | −0.581651 | ||||||||
\(561\) | − | 2.63620i | − | 0.111301i | ||||||
\(562\) | −37.1813 | −1.56840 | ||||||||
\(563\) | 5.85319 | 0.246683 | 0.123341 | − | 0.992364i | \(-0.460639\pi\) | ||||
0.123341 | + | 0.992364i | \(0.460639\pi\) | |||||||
\(564\) | 33.3677i | 1.40504i | ||||||||
\(565\) | 3.83128i | 0.161183i | ||||||||
\(566\) | − | 51.6622i | − | 2.17153i | ||||||
\(567\) | 4.78347i | 0.200887i | ||||||||
\(568\) | −32.8601 | −1.37878 | ||||||||
\(569\) | 16.3417 | 0.685078 | 0.342539 | − | 0.939504i | \(-0.388713\pi\) | ||||
0.342539 | + | 0.939504i | \(0.388713\pi\) | |||||||
\(570\) | − | 27.5672i | − | 1.15466i | ||||||
\(571\) | −27.6986 | −1.15915 | −0.579574 | − | 0.814919i | \(-0.696781\pi\) | ||||
−0.579574 | + | 0.814919i | \(0.696781\pi\) | |||||||
\(572\) | −6.29559 | + | 11.2194i | −0.263232 | + | 0.469108i | ||||
\(573\) | 8.72663 | 0.364560 | ||||||||
\(574\) | − | 81.4102i | − | 3.39800i | ||||||
\(575\) | −4.19785 | −0.175062 | ||||||||
\(576\) | 11.7709 | 0.490454 | ||||||||
\(577\) | 5.36008i | 0.223143i | 0.993756 | + | 0.111571i | \(0.0355884\pi\) | ||||
−0.993756 | + | 0.111571i | \(0.964412\pi\) | |||||||
\(578\) | − | 23.7159i | − | 0.986451i | ||||||
\(579\) | − | 4.46458i | − | 0.185542i | ||||||
\(580\) | 9.06623i | 0.376455i | ||||||||
\(581\) | 46.8105 | 1.94203 | ||||||||
\(582\) | −10.3969 | −0.430965 | ||||||||
\(583\) | 4.20276i | 0.174061i | ||||||||
\(584\) | 9.68415 | 0.400733 | ||||||||
\(585\) | −3.18250 | + | 5.67157i | −0.131580 | + | 0.234490i | ||||
\(586\) | −35.5559 | −1.46880 | ||||||||
\(587\) | 5.50925i | 0.227391i | 0.993516 | + | 0.113696i | \(0.0362688\pi\) | ||||
−0.993516 | + | 0.113696i | \(0.963731\pi\) | |||||||
\(588\) | −56.6677 | −2.33694 | ||||||||
\(589\) | −39.3021 | −1.61942 | ||||||||
\(590\) | − | 1.22874i | − | 0.0505865i | ||||||
\(591\) | 5.53927i | 0.227855i | ||||||||
\(592\) | 10.5803i | 0.434850i | ||||||||
\(593\) | − | 28.9757i | − | 1.18989i | −0.803767 | − | 0.594944i | \(-0.797174\pi\) | ||
0.803767 | − | 0.594944i | \(-0.202826\pi\) | |||||||
\(594\) | −2.35969 | −0.0968192 | ||||||||
\(595\) | 22.7455 | 0.932473 | ||||||||
\(596\) | − | 78.5913i | − | 3.21923i | ||||||
\(597\) | −22.7640 | −0.931667 | ||||||||
\(598\) | 10.0069 | − | 17.8334i | 0.409212 | − | 0.729260i | ||||
\(599\) | −9.17852 | −0.375024 | −0.187512 | − | 0.982262i | \(-0.560042\pi\) | ||||
−0.187512 | + | 0.982262i | \(0.560042\pi\) | |||||||
\(600\) | 6.46272i | 0.263839i | ||||||||
\(601\) | 41.2205 | 1.68142 | 0.840710 | − | 0.541485i | \(-0.182138\pi\) | ||||
0.840710 | + | 0.541485i | \(0.182138\pi\) | |||||||
\(602\) | −83.0262 | −3.38389 | ||||||||
\(603\) | 13.1143i | 0.534055i | ||||||||
\(604\) | 24.1897i | 0.984263i | ||||||||
\(605\) | − | 1.80373i | − | 0.0733323i | ||||||
\(606\) | 15.1638i | 0.615988i | ||||||||
\(607\) | −36.7876 | −1.49316 | −0.746581 | − | 0.665294i | \(-0.768306\pi\) | ||||
−0.746581 | + | 0.665294i | \(0.768306\pi\) | |||||||
\(608\) | −23.5512 | −0.955128 | ||||||||
\(609\) | 6.73840i | 0.273054i | ||||||||
\(610\) | −52.2885 | −2.11710 | ||||||||
\(611\) | −16.4999 | + | 29.4047i | −0.667516 | + | 1.18959i | ||||
\(612\) | 9.40632 | 0.380228 | ||||||||
\(613\) | − | 29.7486i | − | 1.20153i | −0.799424 | − | 0.600767i | \(-0.794862\pi\) | ||
0.799424 | − | 0.600767i | \(-0.205138\pi\) | |||||||
\(614\) | 40.1935 | 1.62208 | ||||||||
\(615\) | 13.0093 | 0.524585 | ||||||||
\(616\) | − | 17.7003i | − | 0.713165i | ||||||
\(617\) | − | 37.5288i | − | 1.51085i | −0.655233 | − | 0.755427i | \(-0.727430\pi\) | ||
0.655233 | − | 0.755427i | \(-0.272570\pi\) | |||||||
\(618\) | 15.1703i | 0.610239i | ||||||||
\(619\) | 14.1147i | 0.567316i | 0.958925 | + | 0.283658i | \(0.0915481\pi\) | ||||
−0.958925 | + | 0.283658i | \(0.908452\pi\) | |||||||
\(620\) | −39.0539 | −1.56844 | ||||||||
\(621\) | 2.40352 | 0.0964501 | ||||||||
\(622\) | 36.2765i | 1.45456i | ||||||||
\(623\) | −67.2144 | −2.69289 | ||||||||
\(624\) | −5.01615 | − | 2.81473i | −0.200807 | − | 0.112679i | ||||
\(625\) | −13.2169 | −0.528676 | ||||||||
\(626\) | 39.4744i | 1.57771i | ||||||||
\(627\) | 6.47687 | 0.258661 | ||||||||
\(628\) | −15.8485 | −0.632424 | ||||||||
\(629\) | − | 17.4839i | − | 0.697129i | ||||||
\(630\) | − | 20.3597i | − | 0.811149i | ||||||
\(631\) | 20.2949i | 0.807925i | 0.914775 | + | 0.403963i | \(0.132367\pi\) | ||||
−0.914775 | + | 0.403963i | \(0.867633\pi\) | |||||||
\(632\) | − | 12.2971i | − | 0.489153i | ||||||
\(633\) | −5.58761 | −0.222088 | ||||||||
\(634\) | −12.5819 | −0.499690 | ||||||||
\(635\) | − | 5.64240i | − | 0.223912i | ||||||
\(636\) | −14.9960 | −0.594630 | ||||||||
\(637\) | −49.9373 | − | 28.0215i | −1.97859 | − | 1.11025i | ||||
\(638\) | −3.32405 | −0.131601 | ||||||||
\(639\) | − | 8.88039i | − | 0.351303i | ||||||
\(640\) | −36.9824 | −1.46186 | ||||||||
\(641\) | −8.88022 | −0.350748 | −0.175374 | − | 0.984502i | \(-0.556113\pi\) | ||||
−0.175374 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(642\) | 30.1038i | 1.18810i | ||||||||
\(643\) | 9.48507i | 0.374055i | 0.982355 | + | 0.187027i | \(0.0598853\pi\) | ||||
−0.982355 | + | 0.187027i | \(0.940115\pi\) | |||||||
\(644\) | 41.0235i | 1.61655i | ||||||||
\(645\) | − | 13.2675i | − | 0.522408i | ||||||
\(646\) | −40.2901 | −1.58519 | ||||||||
\(647\) | 5.92069 | 0.232767 | 0.116383 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116383 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(648\) | − | 3.70030i | − | 0.145361i | ||||||
\(649\) | 0.288691 | 0.0113321 | ||||||||
\(650\) | −7.27159 | + | 12.9588i | −0.285215 | + | 0.508284i | ||||
\(651\) | −29.0265 | −1.13764 | ||||||||
\(652\) | − | 63.9239i | − | 2.50345i | ||||||
\(653\) | −12.6446 | −0.494821 | −0.247410 | − | 0.968911i | \(-0.579580\pi\) | ||||
−0.247410 | + | 0.968911i | \(0.579580\pi\) | |||||||
\(654\) | −13.5000 | −0.527890 | ||||||||
\(655\) | 11.9532i | 0.467049i | ||||||||
\(656\) | 11.5059i | 0.449231i | ||||||||
\(657\) | 2.61713i | 0.102104i | ||||||||
\(658\) | − | 105.556i | − | 4.11501i | ||||||
\(659\) | 28.4668 | 1.10891 | 0.554454 | − | 0.832214i | \(-0.312927\pi\) | ||||
0.554454 | + | 0.832214i | \(0.312927\pi\) | |||||||
\(660\) | 6.43596 | 0.250519 | ||||||||
\(661\) | 40.5531i | 1.57733i | 0.614822 | + | 0.788666i | \(0.289228\pi\) | ||||
−0.614822 | + | 0.788666i | \(0.710772\pi\) | |||||||
\(662\) | −52.3231 | −2.03359 | ||||||||
\(663\) | 8.28913 | + | 4.65130i | 0.321923 | + | 0.180642i | ||||
\(664\) | −36.2107 | −1.40525 | ||||||||
\(665\) | 55.8832i | 2.16706i | ||||||||
\(666\) | −15.6500 | −0.606425 | ||||||||
\(667\) | 3.38580 | 0.131099 | ||||||||
\(668\) | 64.4201i | 2.49249i | ||||||||
\(669\) | − | 10.1832i | − | 0.393707i | ||||||
\(670\) | − | 55.8178i | − | 2.15643i | ||||||
\(671\) | − | 12.2851i | − | 0.474261i | ||||||
\(672\) | −17.3937 | −0.670976 | ||||||||
\(673\) | −10.3646 | −0.399525 | −0.199763 | − | 0.979844i | \(-0.564017\pi\) | ||||
−0.199763 | + | 0.979844i | \(0.564017\pi\) | |||||||
\(674\) | 30.4519i | 1.17296i | ||||||||
\(675\) | −1.74654 | −0.0672244 | ||||||||
\(676\) | −24.1699 | − | 39.5910i | −0.929610 | − | 1.52273i | ||||
\(677\) | 47.8616 | 1.83947 | 0.919734 | − | 0.392541i | \(-0.128404\pi\) | ||||
0.919734 | + | 0.392541i | \(0.128404\pi\) | |||||||
\(678\) | − | 5.01218i | − | 0.192491i | ||||||
\(679\) | 21.0762 | 0.808830 | ||||||||
\(680\) | −17.5950 | −0.674736 | ||||||||
\(681\) | − | 0.783473i | − | 0.0300228i | ||||||
\(682\) | − | 14.3188i | − | 0.548294i | ||||||
\(683\) | 20.7800i | 0.795123i | 0.917576 | + | 0.397562i | \(0.130143\pi\) | ||||
−0.917576 | + | 0.397562i | \(0.869857\pi\) | |||||||
\(684\) | 23.1103i | 0.883645i | ||||||||
\(685\) | 8.65484 | 0.330684 | ||||||||
\(686\) | 100.251 | 3.82761 | ||||||||
\(687\) | 20.8340i | 0.794868i | ||||||||
\(688\) | 11.7343 | 0.447366 | ||||||||
\(689\) | −13.2149 | − | 7.41534i | −0.503449 | − | 0.282502i | ||||
\(690\) | −10.2300 | −0.389450 | ||||||||
\(691\) | − | 27.6573i | − | 1.05213i | −0.850443 | − | 0.526067i | \(-0.823666\pi\) | ||
0.850443 | − | 0.526067i | \(-0.176334\pi\) | |||||||
\(692\) | −90.7234 | −3.44879 | ||||||||
\(693\) | 4.78347 | 0.181709 | ||||||||
\(694\) | 72.5503i | 2.75397i | ||||||||
\(695\) | − | 30.4867i | − | 1.15643i | ||||||
\(696\) | − | 5.21255i | − | 0.197581i | ||||||
\(697\) | − | 19.0134i | − | 0.720184i | ||||||
\(698\) | 36.6315 | 1.38652 | ||||||||
\(699\) | 8.50679 | 0.321756 | ||||||||
\(700\) | − | 29.8100i | − | 1.12671i | ||||||
\(701\) | 34.9434 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(702\) | 4.16342 | − | 7.41968i | 0.157138 | − | 0.280038i | ||||
\(703\) | 42.9561 | 1.62012 | ||||||||
\(704\) | − | 11.7709i | − | 0.443632i | ||||||
\(705\) | 16.8678 | 0.635279 | ||||||||
\(706\) | 50.6861 | 1.90760 | ||||||||
\(707\) | − | 30.7395i | − | 1.15608i | ||||||
\(708\) | 1.03009i | 0.0387131i | ||||||||
\(709\) | − | 2.08738i | − | 0.0783932i | −0.999232 | − | 0.0391966i | \(-0.987520\pi\) | ||
0.999232 | − | 0.0391966i | \(-0.0124799\pi\) | |||||||
\(710\) | 37.7972i | 1.41850i | ||||||||
\(711\) | 3.32327 | 0.124632 | ||||||||
\(712\) | 51.9943 | 1.94857 | ||||||||
\(713\) | 14.5848i | 0.546203i | ||||||||
\(714\) | −29.7562 | −1.11360 | ||||||||
\(715\) | 5.67157 | + | 3.18250i | 0.212105 | + | 0.119019i | ||||
\(716\) | −49.2290 | −1.83978 | ||||||||
\(717\) | 2.74768i | 0.102614i | ||||||||
\(718\) | 45.1780 | 1.68603 | ||||||||
\(719\) | 38.9755 | 1.45354 | 0.726770 | − | 0.686880i | \(-0.241020\pi\) | ||||
0.726770 | + | 0.686880i | \(0.241020\pi\) | |||||||
\(720\) | 2.87749i | 0.107238i | ||||||||
\(721\) | − | 30.7527i | − | 1.14529i | ||||||
\(722\) | − | 54.1545i | − | 2.01542i | ||||||
\(723\) | − | 10.3746i | − | 0.385836i | ||||||
\(724\) | −64.2768 | −2.38883 | ||||||||
\(725\) | −2.46032 | −0.0913741 | ||||||||
\(726\) | 2.35969i | 0.0875763i | ||||||||
\(727\) | −29.4308 | −1.09153 | −0.545764 | − | 0.837939i | \(-0.683760\pi\) | ||||
−0.545764 | + | 0.837939i | \(0.683760\pi\) | |||||||
\(728\) | 55.6558 | + | 31.2303i | 2.06274 | + | 1.15747i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 11.1391i | − | 0.412278i | ||||||
\(731\) | −19.3908 | −0.717195 | ||||||||
\(732\) | 43.8348 | 1.62018 | ||||||||
\(733\) | − | 17.2457i | − | 0.636984i | −0.947926 | − | 0.318492i | \(-0.896824\pi\) | ||
0.947926 | − | 0.318492i | \(-0.103176\pi\) | |||||||
\(734\) | 39.6115i | 1.46209i | ||||||||
\(735\) | 28.6462i | 1.05663i | ||||||||
\(736\) | 8.73970i | 0.322150i | ||||||||
\(737\) | 13.1143 | 0.483071 | ||||||||
\(738\) | −17.0191 | −0.626480 | ||||||||
\(739\) | 3.42420i | 0.125961i | 0.998015 | + | 0.0629807i | \(0.0200607\pi\) | ||||
−0.998015 | + | 0.0629807i | \(0.979939\pi\) | |||||||
\(740\) | 42.6848 | 1.56912 | ||||||||
\(741\) | −11.4278 | + | 20.3655i | −0.419809 | + | 0.748146i | ||||
\(742\) | 47.4387 | 1.74153 | ||||||||
\(743\) | 22.5661i | 0.827870i | 0.910307 | + | 0.413935i | \(0.135846\pi\) | ||||
−0.910307 | + | 0.413935i | \(0.864154\pi\) | |||||||
\(744\) | 22.4537 | 0.823192 | ||||||||
\(745\) | −39.7289 | −1.45555 | ||||||||
\(746\) | − | 24.4638i | − | 0.895682i | ||||||
\(747\) | − | 9.78588i | − | 0.358047i | ||||||
\(748\) | − | 9.40632i | − | 0.343929i | ||||||
\(749\) | − | 61.0253i | − | 2.22982i | ||||||
\(750\) | 28.7150 | 1.04852 | ||||||||
\(751\) | −32.4314 | −1.18344 | −0.591719 | − | 0.806145i | \(-0.701550\pi\) | ||||
−0.591719 | + | 0.806145i | \(0.701550\pi\) | |||||||
\(752\) | 14.9186i | 0.544024i | ||||||||
\(753\) | 24.1897 | 0.881523 | ||||||||
\(754\) | 5.86495 | − | 10.4520i | 0.213589 | − | 0.380638i | ||||
\(755\) | 12.2282 | 0.445029 | ||||||||
\(756\) | 17.0681i | 0.620759i | ||||||||
\(757\) | −15.2431 | −0.554021 | −0.277011 | − | 0.960867i | \(-0.589344\pi\) | ||||
−0.277011 | + | 0.960867i | \(0.589344\pi\) | |||||||
\(758\) | −59.8219 | −2.17283 | ||||||||
\(759\) | − | 2.40352i | − | 0.0872424i | ||||||
\(760\) | − | 43.2290i | − | 1.56808i | ||||||
\(761\) | − | 21.2733i | − | 0.771155i | −0.922675 | − | 0.385577i | \(-0.874002\pi\) | ||
0.922675 | − | 0.385577i | \(-0.125998\pi\) | |||||||
\(762\) | 7.38152i | 0.267404i | ||||||||
\(763\) | 27.3666 | 0.990738 | ||||||||
\(764\) | 31.1377 | 1.12652 | ||||||||
\(765\) | − | 4.75501i | − | 0.171918i | ||||||
\(766\) | 64.3602 | 2.32543 | ||||||||
\(767\) | −0.509365 | + | 0.907745i | −0.0183921 | + | 0.0327768i | ||||
\(768\) | 24.8395 | 0.896317 | ||||||||
\(769\) | − | 4.87325i | − | 0.175734i | −0.996132 | − | 0.0878670i | \(-0.971995\pi\) | ||
0.996132 | − | 0.0878670i | \(-0.0280051\pi\) | |||||||
\(770\) | −20.3597 | −0.733712 | ||||||||
\(771\) | 4.06662 | 0.146456 | ||||||||
\(772\) | − | 15.9302i | − | 0.573340i | ||||||
\(773\) | − | 49.7555i | − | 1.78958i | −0.446487 | − | 0.894790i | \(-0.647325\pi\) | ||
0.446487 | − | 0.894790i | \(-0.352675\pi\) | |||||||
\(774\) | 17.3569i | 0.623880i | ||||||||
\(775\) | − | 10.5981i | − | 0.380696i | ||||||
\(776\) | −16.3037 | −0.585268 | ||||||||
\(777\) | 31.7251 | 1.13813 | ||||||||
\(778\) | 13.6432i | 0.489132i | ||||||||
\(779\) | 46.7139 | 1.67370 | ||||||||
\(780\) | −11.3556 | + | 20.2369i | −0.406595 | + | 0.724597i | ||||
\(781\) | −8.88039 | −0.317765 | ||||||||
\(782\) | 14.9514i | 0.534661i | ||||||||
\(783\) | 1.40868 | 0.0503422 | ||||||||
\(784\) | −25.3358 | −0.904851 | ||||||||
\(785\) | 8.01161i | 0.285947i | ||||||||
\(786\) | − | 15.6374i | − | 0.557768i | ||||||
\(787\) | 15.0422i | 0.536197i | 0.963391 | + | 0.268099i | \(0.0863953\pi\) | ||||
−0.963391 | + | 0.268099i | \(0.913605\pi\) | |||||||
\(788\) | 19.7648i | 0.704093i | ||||||||
\(789\) | 6.36570 | 0.226625 | ||||||||
\(790\) | −14.1447 | −0.503246 | ||||||||
\(791\) | 10.1605i | 0.361266i | ||||||||
\(792\) | −3.70030 | −0.131484 | ||||||||
\(793\) | 38.6286 | + | 21.6758i | 1.37174 | + | 0.769729i | ||||
\(794\) | 33.6719 | 1.19497 | ||||||||
\(795\) | 7.58067i | 0.268859i | ||||||||
\(796\) | −81.2248 | −2.87894 | ||||||||
\(797\) | −2.71446 | −0.0961512 | −0.0480756 | − | 0.998844i | \(-0.515309\pi\) | ||||
−0.0480756 | + | 0.998844i | \(0.515309\pi\) | |||||||
\(798\) | − | 73.1077i | − | 2.58799i | ||||||
\(799\) | − | 24.6527i | − | 0.872151i | ||||||
\(800\) | − | 6.35077i | − | 0.224534i | ||||||
\(801\) | 14.0514i | 0.496481i | ||||||||
\(802\) | 38.8750 | 1.37272 | ||||||||
\(803\) | 2.61713 | 0.0923563 | ||||||||
\(804\) | 46.7935i | 1.65028i | ||||||||
\(805\) | 20.7379 | 0.730914 | ||||||||
\(806\) | 45.0231 | + | 25.2640i | 1.58587 | + | 0.889885i | ||||
\(807\) | −28.4905 | −1.00291 | ||||||||
\(808\) | 23.7788i | 0.836536i | ||||||||
\(809\) | 16.8023 | 0.590737 | 0.295368 | − | 0.955383i | \(-0.404558\pi\) | ||||
0.295368 | + | 0.955383i | \(0.404558\pi\) | |||||||
\(810\) | −4.25625 | −0.149549 | ||||||||
\(811\) | − | 16.0876i | − | 0.564912i | −0.959280 | − | 0.282456i | \(-0.908851\pi\) | ||
0.959280 | − | 0.282456i | \(-0.0911491\pi\) | |||||||
\(812\) | 24.0435i | 0.843761i | ||||||||
\(813\) | 13.5110i | 0.473853i | ||||||||
\(814\) | 15.6500i | 0.548532i | ||||||||
\(815\) | −32.3143 | −1.13192 | ||||||||
\(816\) | 4.20552 | 0.147223 | ||||||||
\(817\) | − | 47.6411i | − | 1.66675i | ||||||
\(818\) | 10.3881 | 0.363210 | ||||||||
\(819\) | −8.43994 | + | 15.0409i | −0.294915 | + | 0.525571i | ||||
\(820\) | 46.4188 | 1.62102 | ||||||||
\(821\) | 41.9751i | 1.46494i | 0.680799 | + | 0.732470i | \(0.261633\pi\) | ||||
−0.680799 | + | 0.732470i | \(0.738367\pi\) | |||||||
\(822\) | −11.3225 | −0.394916 | ||||||||
\(823\) | 23.6512 | 0.824428 | 0.412214 | − | 0.911087i | \(-0.364756\pi\) | ||||
0.412214 | + | 0.911087i | \(0.364756\pi\) | |||||||
\(824\) | 23.7890i | 0.828730i | ||||||||
\(825\) | 1.74654i | 0.0608067i | ||||||||
\(826\) | − | 3.25860i | − | 0.113381i | ||||||
\(827\) | 7.51585i | 0.261352i | 0.991425 | + | 0.130676i | \(0.0417147\pi\) | ||||
−0.991425 | + | 0.130676i | \(0.958285\pi\) | |||||||
\(828\) | 8.57608 | 0.298040 | ||||||||
\(829\) | 36.7820 | 1.27749 | 0.638745 | − | 0.769418i | \(-0.279454\pi\) | ||||
0.638745 | + | 0.769418i | \(0.279454\pi\) | |||||||
\(830\) | 41.6512i | 1.44573i | ||||||||
\(831\) | 2.04052 | 0.0707850 | ||||||||
\(832\) | 37.0118 | + | 20.7685i | 1.28315 | + | 0.720019i | ||||
\(833\) | 41.8672 | 1.45061 | ||||||||
\(834\) | 39.8834i | 1.38105i | ||||||||
\(835\) | 32.5652 | 1.12696 | ||||||||
\(836\) | 23.1103 | 0.799287 | ||||||||
\(837\) | 6.06807i | 0.209743i | ||||||||
\(838\) | 88.9343i | 3.07218i | ||||||||
\(839\) | − | 13.8418i | − | 0.477873i | −0.971035 | − | 0.238937i | \(-0.923201\pi\) | ||
0.971035 | − | 0.238937i | \(-0.0767988\pi\) | |||||||
\(840\) | − | 31.9266i | − | 1.10157i | ||||||
\(841\) | −27.0156 | −0.931573 | ||||||||
\(842\) | −32.4768 | −1.11922 | ||||||||
\(843\) | − | 15.7569i | − | 0.542695i | ||||||
\(844\) | −19.9373 | −0.686271 | ||||||||
\(845\) | −20.0138 | + | 12.2182i | −0.688495 | + | 0.420318i | ||||
\(846\) | −22.0669 | −0.758675 | ||||||||
\(847\) | − | 4.78347i | − | 0.164362i | ||||||
\(848\) | −6.70464 | −0.230238 | ||||||||
\(849\) | 21.8937 | 0.751389 | ||||||||
\(850\) | − | 10.8646i | − | 0.372651i | ||||||
\(851\) | − | 15.9407i | − | 0.546440i | ||||||
\(852\) | − | 31.6864i | − | 1.08556i | ||||||
\(853\) | 19.6602i | 0.673152i | 0.941656 | + | 0.336576i | \(0.109269\pi\) | ||||
−0.941656 | + | 0.336576i | \(0.890731\pi\) | |||||||
\(854\) | −138.668 | −4.74513 | ||||||||
\(855\) | 11.6826 | 0.399535 | ||||||||
\(856\) | 47.2067i | 1.61349i | ||||||||
\(857\) | 7.52889 | 0.257182 | 0.128591 | − | 0.991698i | \(-0.458955\pi\) | ||||
0.128591 | + | 0.991698i | \(0.458955\pi\) | |||||||
\(858\) | −7.41968 | − | 4.16342i | −0.253304 | − | 0.142137i | ||||
\(859\) | −12.2190 | −0.416907 | −0.208453 | − | 0.978032i | \(-0.566843\pi\) | ||||
−0.208453 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(860\) | − | 47.3402i | − | 1.61429i | ||||||
\(861\) | 34.5004 | 1.17577 | ||||||||
\(862\) | 55.2644 | 1.88231 | ||||||||
\(863\) | − | 2.88331i | − | 0.0981491i | −0.998795 | − | 0.0490746i | \(-0.984373\pi\) | ||
0.998795 | − | 0.0490746i | \(-0.0156272\pi\) | |||||||
\(864\) | 3.63620i | 0.123706i | ||||||||
\(865\) | 45.8618i | 1.55935i | ||||||||
\(866\) | − | 49.9843i | − | 1.69854i | ||||||
\(867\) | 10.0504 | 0.341331 | ||||||||
\(868\) | −103.570 | −3.51540 | ||||||||
\(869\) | − | 3.32327i | − | 0.112734i | ||||||
\(870\) | −5.99571 | −0.203274 | ||||||||
\(871\) | −23.1388 | + | 41.2359i | −0.784028 | + | 1.39722i | ||||
\(872\) | −21.1697 | −0.716897 | ||||||||
\(873\) | − | 4.40604i | − | 0.149122i | ||||||
\(874\) | −36.7340 | −1.24255 | ||||||||
\(875\) | −58.2099 | −1.96786 | ||||||||
\(876\) | 9.33824i | 0.315510i | ||||||||
\(877\) | 17.6010i | 0.594343i | 0.954824 | + | 0.297172i | \(0.0960434\pi\) | ||||
−0.954824 | + | 0.297172i | \(0.903957\pi\) | |||||||
\(878\) | 15.3931i | 0.519493i | ||||||||
\(879\) | − | 15.0681i | − | 0.508233i | ||||||
\(880\) | 2.87749 | 0.0970000 | ||||||||
\(881\) | 14.9734 | 0.504466 | 0.252233 | − | 0.967666i | \(-0.418835\pi\) | ||||
0.252233 | + | 0.967666i | \(0.418835\pi\) | |||||||
\(882\) | − | 37.4757i | − | 1.26187i | ||||||
\(883\) | −38.1672 | −1.28443 | −0.642215 | − | 0.766524i | \(-0.721984\pi\) | ||||
−0.642215 | + | 0.766524i | \(0.721984\pi\) | |||||||
\(884\) | 29.5767 | + | 16.5965i | 0.994772 | + | 0.558199i | ||||
\(885\) | 0.520722 | 0.0175039 | ||||||||
\(886\) | − | 84.7119i | − | 2.84595i | ||||||
\(887\) | 8.74591 | 0.293659 | 0.146829 | − | 0.989162i | \(-0.453093\pi\) | ||||
0.146829 | + | 0.989162i | \(0.453093\pi\) | |||||||
\(888\) | −24.5412 | −0.823549 | ||||||||
\(889\) | − | 14.9635i | − | 0.501861i | ||||||
\(890\) | − | 59.8062i | − | 2.00471i | ||||||
\(891\) | − | 1.00000i | − | 0.0335013i | ||||||
\(892\) | − | 36.3351i | − | 1.21659i | ||||||
\(893\) | 60.5691 | 2.02687 | ||||||||
\(894\) | 51.9743 | 1.73828 | ||||||||
\(895\) | 24.8859i | 0.831844i | ||||||||
\(896\) | −98.0767 | −3.27651 | ||||||||
\(897\) | 7.55751 | + | 4.24076i | 0.252338 | + | 0.141595i | ||||
\(898\) | −16.1980 | −0.540534 | ||||||||
\(899\) | 8.54799i | 0.285092i | ||||||||
\(900\) | −6.23188 | −0.207729 | ||||||||
\(901\) | 11.0793 | 0.369106 | ||||||||
\(902\) | 17.0191i | 0.566673i | ||||||||
\(903\) | − | 35.1852i | − | 1.17089i | ||||||
\(904\) | − | 7.85975i | − | 0.261411i | ||||||
\(905\) | 32.4927i | 1.08009i | ||||||||
\(906\) | −15.9972 | −0.531471 | ||||||||
\(907\) | 35.8443 | 1.19019 | 0.595096 | − | 0.803655i | \(-0.297114\pi\) | ||||
0.595096 | + | 0.803655i | \(0.297114\pi\) | |||||||
\(908\) | − | 2.79553i | − | 0.0927731i | ||||||
\(909\) | −6.42619 | −0.213143 | ||||||||
\(910\) | 35.9225 | − | 64.0178i | 1.19082 | − | 2.12217i | ||||
\(911\) | −52.9308 | −1.75367 | −0.876837 | − | 0.480788i | \(-0.840351\pi\) | ||||
−0.876837 | + | 0.480788i | \(0.840351\pi\) | |||||||
\(912\) | 10.3325i | 0.342144i | ||||||||
\(913\) | −9.78588 | −0.323865 | ||||||||
\(914\) | 81.2782 | 2.68844 | ||||||||
\(915\) | − | 22.1591i | − | 0.732556i | ||||||
\(916\) | 74.3385i | 2.45621i | ||||||||
\(917\) | 31.6996i | 1.04681i | ||||||||
\(918\) | 6.22062i | 0.205311i | ||||||||
\(919\) | 23.1774 | 0.764553 | 0.382276 | − | 0.924048i | \(-0.375140\pi\) | ||||
0.382276 | + | 0.924048i | \(0.375140\pi\) | |||||||
\(920\) | −16.0420 | −0.528888 | ||||||||
\(921\) | 17.0334i | 0.561269i | ||||||||
\(922\) | 23.8322 | 0.784870 | ||||||||
\(923\) | 15.6685 | − | 27.9230i | 0.515736 | − | 0.919098i | ||||
\(924\) | 17.0681 | 0.561498 | ||||||||
\(925\) | 11.5834i | 0.380861i | ||||||||
\(926\) | 15.2130 | 0.499932 | ||||||||
\(927\) | −6.42895 | −0.211154 | ||||||||
\(928\) | 5.12226i | 0.168146i | ||||||||
\(929\) | − | 6.97790i | − | 0.228937i | −0.993427 | − | 0.114469i | \(-0.963483\pi\) | ||
0.993427 | − | 0.114469i | \(-0.0365166\pi\) | |||||||
\(930\) | − | 25.8273i | − | 0.846909i | ||||||
\(931\) | 102.863i | 3.37120i | ||||||||
\(932\) | 30.3533 | 0.994256 | ||||||||
\(933\) | −15.3734 | −0.503304 | ||||||||
\(934\) | 42.3528i | 1.38582i | ||||||||
\(935\) | −4.75501 | −0.155506 | ||||||||
\(936\) | 6.52879 | − | 11.6350i | 0.213400 | − | 0.380303i | ||||
\(937\) | 33.9630 | 1.10952 | 0.554762 | − | 0.832009i | \(-0.312809\pi\) | ||||
0.554762 | + | 0.832009i | \(0.312809\pi\) | |||||||
\(938\) | − | 148.028i | − | 4.83328i | ||||||
\(939\) | −16.7286 | −0.545918 | ||||||||
\(940\) | 60.1866 | 1.96307 | ||||||||
\(941\) | − | 25.8486i | − | 0.842641i | −0.906912 | − | 0.421320i | \(-0.861567\pi\) | ||
0.906912 | − | 0.421320i | \(-0.138433\pi\) | |||||||
\(942\) | − | 10.4810i | − | 0.341489i | ||||||
\(943\) | − | 17.3352i | − | 0.564512i | ||||||
\(944\) | 0.460547i | 0.0149895i | ||||||||
\(945\) | 8.62812 | 0.280673 | ||||||||
\(946\) | 17.3569 | 0.564321 | ||||||||
\(947\) | 38.2502i | 1.24296i | 0.783428 | + | 0.621482i | \(0.213469\pi\) | ||||
−0.783428 | + | 0.621482i | \(0.786531\pi\) | |||||||
\(948\) | 11.8579 | 0.385126 | ||||||||
\(949\) | −4.61764 | + | 8.22915i | −0.149895 | + | 0.267129i | ||||
\(950\) | 26.6931 | 0.866038 | ||||||||
\(951\) | − | 5.33201i | − | 0.172902i | ||||||
\(952\) | −46.6615 | −1.51231 | ||||||||
\(953\) | −50.6456 | −1.64057 | −0.820286 | − | 0.571953i | \(-0.806186\pi\) | ||||
−0.820286 | + | 0.571953i | \(0.806186\pi\) | |||||||
\(954\) | − | 9.91721i | − | 0.321082i | ||||||
\(955\) | − | 15.7405i | − | 0.509351i | ||||||
\(956\) | 9.80410i | 0.317087i | ||||||||
\(957\) | − | 1.40868i | − | 0.0455363i | ||||||
\(958\) | 9.67263 | 0.312508 | ||||||||
\(959\) | 22.9525 | 0.741174 | ||||||||
\(960\) | − | 21.2316i | − | 0.685246i | ||||||
\(961\) | −5.82151 | −0.187791 | ||||||||
\(962\) | −49.2090 | − | 27.6128i | −1.58656 | − | 0.890271i | ||||
\(963\) | −12.7575 | −0.411106 | ||||||||
\(964\) | − | 37.0180i | − | 1.19227i | ||||||
\(965\) | −8.05292 | −0.259233 | ||||||||
\(966\) | −27.1298 | −0.872887 | ||||||||
\(967\) | − | 24.8458i | − | 0.798988i | −0.916736 | − | 0.399494i | \(-0.869186\pi\) | ||
0.916736 | − | 0.399494i | \(-0.130814\pi\) | |||||||
\(968\) | 3.70030i | 0.118932i | ||||||||
\(969\) | − | 17.0743i | − | 0.548507i | ||||||
\(970\) | 18.7532i | 0.602130i | ||||||||
\(971\) | 4.13593 | 0.132728 | 0.0663642 | − | 0.997795i | \(-0.478860\pi\) | ||||
0.0663642 | + | 0.997795i | \(0.478860\pi\) | |||||||
\(972\) | 3.56813 | 0.114448 | ||||||||
\(973\) | − | 80.8502i | − | 2.59194i | ||||||
\(974\) | −14.4174 | −0.461964 | ||||||||
\(975\) | −5.49173 | − | 3.08159i | −0.175876 | − | 0.0986898i | ||||
\(976\) | 19.5983 | 0.627328 | ||||||||
\(977\) | 45.4528i | 1.45416i | 0.686551 | + | 0.727081i | \(0.259124\pi\) | ||||
−0.686551 | + | 0.727081i | \(0.740876\pi\) | |||||||
\(978\) | 42.2744 | 1.35179 | ||||||||
\(979\) | 14.0514 | 0.449084 | ||||||||
\(980\) | 102.213i | 3.26509i | ||||||||
\(981\) | − | 5.72108i | − | 0.182660i | ||||||
\(982\) | 27.8503i | 0.888739i | ||||||||
\(983\) | 35.2215i | 1.12339i | 0.827344 | + | 0.561696i | \(0.189851\pi\) | ||||
−0.827344 | + | 0.561696i | \(0.810149\pi\) | |||||||
\(984\) | −26.6881 | −0.850786 | ||||||||
\(985\) | 9.99137 | 0.318351 | ||||||||
\(986\) | 8.76288i | 0.279067i | ||||||||
\(987\) | 44.7331 | 1.42387 | ||||||||
\(988\) | −40.7757 | + | 72.6668i | −1.29725 | + | 2.31184i | ||||
\(989\) | −17.6793 | −0.562169 | ||||||||
\(990\) | 4.25625i | 0.135273i | ||||||||
\(991\) | 27.4173 | 0.870939 | 0.435470 | − | 0.900203i | \(-0.356582\pi\) | ||||
0.435470 | + | 0.900203i | \(0.356582\pi\) | |||||||
\(992\) | −22.0647 | −0.700556 | ||||||||
\(993\) | − | 22.1737i | − | 0.703662i | ||||||
\(994\) | 100.238i | 3.17934i | ||||||||
\(995\) | 41.0602i | 1.30170i | ||||||||
\(996\) | − | 34.9173i | − | 1.10640i | ||||||
\(997\) | 34.0683 | 1.07895 | 0.539477 | − | 0.842000i | \(-0.318622\pi\) | ||||
0.539477 | + | 0.842000i | \(0.318622\pi\) | |||||||
\(998\) | 4.90517 | 0.155270 | ||||||||
\(999\) | − | 6.63223i | − | 0.209834i |
(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 | 429.2.b.a.298.10 | yes | 10 | |
3.2 | odd | 2 | 1287.2.b.a.298.1 | 10 | |||
13.5 | odd | 4 | 5577.2.a.q.1.5 | 5 | |||
13.8 | odd | 4 | 5577.2.a.t.1.1 | 5 | |||
13.12 | even | 2 | inner | 429.2.b.a.298.1 | ✓ | 10 | |
39.38 | odd | 2 | 1287.2.b.a.298.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.a.298.1 | ✓ | 10 | 13.12 | even | 2 | inner | |
429.2.b.a.298.10 | yes | 10 | 1.1 | even | 1 | trivial | |
1287.2.b.a.298.1 | 10 | 3.2 | odd | 2 | |||
1287.2.b.a.298.10 | 10 | 39.38 | odd | 2 | |||
5577.2.a.q.1.5 | 5 | 13.5 | odd | 4 | |||
5577.2.a.t.1.1 | 5 | 13.8 | odd | 4 |