Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 42x^{6} + 771x^{4} - 7098x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-3.32308 + 1.39897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.f.151.7 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.79793i | − | 1.39897i | −0.714649 | − | 0.699483i | \(-0.753414\pi\) | ||
0.714649 | − | 0.699483i | \(-0.246586\pi\) | |||||||
\(3\) | 1.15894i | 0.386314i | 0.981168 | + | 0.193157i | \(0.0618727\pi\) | ||||
−0.981168 | + | 0.193157i | \(0.938127\pi\) | |||||||
\(4\) | −3.82843 | −0.957107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.24264 | 0.540440 | ||||||||
\(7\) | −6.64617 | −0.949453 | −0.474726 | − | 0.880133i | \(-0.657453\pi\) | ||||
−0.474726 | + | 0.880133i | \(0.657453\pi\) | |||||||
\(8\) | − | 0.480049i | − | 0.0600062i | ||||||
\(9\) | 7.65685 | 0.850762 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.24264 | −0.567513 | −0.283756 | − | 0.958896i | \(-0.591581\pi\) | ||||
−0.283756 | + | 0.958896i | \(0.591581\pi\) | |||||||
\(12\) | − | 4.43692i | − | 0.369744i | ||||||
\(13\) | 18.6254i | 1.43273i | 0.697728 | + | 0.716363i | \(0.254194\pi\) | ||||
−0.697728 | + | 0.716363i | \(0.745806\pi\) | |||||||
\(14\) | 18.5955i | 1.32825i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.6569 | −1.04105 | ||||||||
\(17\) | −29.3376 | −1.72574 | −0.862871 | − | 0.505424i | \(-0.831336\pi\) | ||||
−0.862871 | + | 0.505424i | \(0.831336\pi\) | |||||||
\(18\) | − | 21.4234i | − | 1.19019i | ||||||
\(19\) | 3.89949 | − | 18.5955i | 0.205237 | − | 0.978712i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.70252i | − | 0.366787i | ||||||
\(22\) | 17.4665i | 0.793931i | ||||||||
\(23\) | −19.9385 | −0.866892 | −0.433446 | − | 0.901180i | \(-0.642702\pi\) | ||||
−0.433446 | + | 0.901180i | \(0.642702\pi\) | |||||||
\(24\) | 0.556349 | 0.0231812 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 52.1127 | 2.00433 | ||||||||
\(27\) | 19.3043i | 0.714975i | ||||||||
\(28\) | 25.4444 | 0.908728 | ||||||||
\(29\) | 29.4885i | 1.01685i | 0.861107 | + | 0.508423i | \(0.169771\pi\) | ||||
−0.861107 | + | 0.508423i | \(0.830229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.2981i | 0.848324i | 0.905586 | + | 0.424162i | \(0.139431\pi\) | ||||
−0.905586 | + | 0.424162i | \(0.860569\pi\) | |||||||
\(32\) | 44.6846i | 1.39639i | ||||||||
\(33\) | − | 7.23486i | − | 0.219238i | ||||||
\(34\) | 82.0847i | 2.41425i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −29.3137 | −0.814270 | ||||||||
\(37\) | − | 47.4825i | − | 1.28331i | −0.766993 | − | 0.641655i | \(-0.778248\pi\) | ||
0.766993 | − | 0.641655i | \(-0.221752\pi\) | |||||||
\(38\) | −52.0291 | − | 10.9105i | −1.36919 | − | 0.287119i | ||||
\(39\) | −21.5858 | −0.553482 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.7031i | 1.01715i | 0.861018 | + | 0.508574i | \(0.169827\pi\) | ||||
−0.861018 | + | 0.508574i | \(0.830173\pi\) | |||||||
\(42\) | −21.5511 | −0.513122 | ||||||||
\(43\) | −14.9050 | −0.346627 | −0.173314 | − | 0.984867i | \(-0.555447\pi\) | ||||
−0.173314 | + | 0.984867i | \(0.555447\pi\) | |||||||
\(44\) | 23.8995 | 0.543170 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 55.7866i | 1.21275i | ||||||||
\(47\) | −5.50587 | −0.117146 | −0.0585731 | − | 0.998283i | \(-0.518655\pi\) | ||||
−0.0585731 | + | 0.998283i | \(0.518655\pi\) | |||||||
\(48\) | − | 19.3043i | − | 0.402173i | ||||||
\(49\) | −4.82843 | −0.0985393 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 34.0006i | − | 0.666678i | ||||||
\(52\) | − | 71.3061i | − | 1.37127i | ||||||
\(53\) | 55.4786i | 1.04677i | 0.852098 | + | 0.523383i | \(0.175330\pi\) | ||||
−0.852098 | + | 0.523383i | \(0.824670\pi\) | |||||||
\(54\) | 54.0122 | 1.00023 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.19049i | 0.0569730i | ||||||||
\(57\) | 21.5511 | + | 4.51929i | 0.378090 | + | 0.0792857i | ||||
\(58\) | 82.5070 | 1.42253 | ||||||||
\(59\) | 86.5967i | 1.46774i | 0.679290 | + | 0.733870i | \(0.262288\pi\) | ||||
−0.679290 | + | 0.733870i | \(0.737712\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 20.5858 | 0.337472 | 0.168736 | − | 0.985661i | \(-0.446031\pi\) | ||||
0.168736 | + | 0.985661i | \(0.446031\pi\) | |||||||
\(62\) | 73.5802 | 1.18678 | ||||||||
\(63\) | −50.8888 | −0.807758 | ||||||||
\(64\) | 58.3970 | 0.912453 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.2426 | −0.306707 | ||||||||
\(67\) | 0.363570i | 0.00542642i | 0.999996 | + | 0.00271321i | \(0.000863642\pi\) | ||||
−0.999996 | + | 0.00271321i | \(0.999136\pi\) | |||||||
\(68\) | 112.317 | 1.65172 | ||||||||
\(69\) | − | 23.1076i | − | 0.334892i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 100.680i | − | 1.41803i | −0.705193 | − | 0.709015i | \(-0.749140\pi\) | ||
0.705193 | − | 0.709015i | \(-0.250860\pi\) | |||||||
\(72\) | − | 3.67567i | − | 0.0510509i | ||||||
\(73\) | −0.472329 | −0.00647026 | −0.00323513 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323513 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(74\) | −132.853 | −1.79531 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9289 | + | 71.1917i | −0.196433 | + | 0.936732i | ||||
\(77\) | 41.4896 | 0.538827 | ||||||||
\(78\) | 60.3956i | 0.774302i | ||||||||
\(79\) | − | 120.597i | − | 1.52655i | −0.646075 | − | 0.763274i | \(-0.723591\pi\) | ||
0.646075 | − | 0.763274i | \(-0.276409\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 46.5391 | 0.574557 | ||||||||
\(82\) | 116.682 | 1.42296 | ||||||||
\(83\) | −42.1576 | −0.507923 | −0.253962 | − | 0.967214i | \(-0.581734\pi\) | ||||
−0.253962 | + | 0.967214i | \(0.581734\pi\) | |||||||
\(84\) | 29.4885i | 0.351054i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 41.7031i | 0.484920i | ||||||||
\(87\) | −34.1755 | −0.392822 | ||||||||
\(88\) | 2.99678i | 0.0340543i | ||||||||
\(89\) | 4.51203i | 0.0506970i | 0.999679 | + | 0.0253485i | \(0.00806954\pi\) | ||||
−0.999679 | + | 0.0253485i | \(0.991930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 123.788i | − | 1.36031i | ||||||
\(92\) | 76.3331 | 0.829708 | ||||||||
\(93\) | −30.4779 | −0.327720 | ||||||||
\(94\) | 15.4050i | 0.163883i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −51.7868 | −0.539446 | ||||||||
\(97\) | − | 11.5894i | − | 0.119479i | −0.998214 | − | 0.0597393i | \(-0.980973\pi\) | ||
0.998214 | − | 0.0597393i | \(-0.0190269\pi\) | |||||||
\(98\) | 13.5096i | 0.137853i | ||||||||
\(99\) | −47.7990 | −0.482818 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −96.4924 | −0.955371 | −0.477685 | − | 0.878531i | \(-0.658524\pi\) | ||||
−0.477685 | + | 0.878531i | \(0.658524\pi\) | |||||||
\(102\) | −95.1313 | −0.932660 | ||||||||
\(103\) | − | 131.702i | − | 1.27866i | −0.768934 | − | 0.639329i | \(-0.779212\pi\) | ||
0.768934 | − | 0.639329i | \(-0.220788\pi\) | |||||||
\(104\) | 8.94113 | 0.0859724 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 155.225 | 1.46439 | ||||||||
\(107\) | 43.2785i | 0.404472i | 0.979337 | + | 0.202236i | \(0.0648208\pi\) | ||||
−0.979337 | + | 0.202236i | \(0.935179\pi\) | |||||||
\(108\) | − | 73.9052i | − | 0.684307i | ||||||
\(109\) | − | 14.0835i | − | 0.129206i | −0.997911 | − | 0.0646032i | \(-0.979422\pi\) | ||
0.997911 | − | 0.0646032i | \(-0.0205782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 55.0294 | 0.495761 | ||||||||
\(112\) | 110.704 | 0.988431 | ||||||||
\(113\) | − | 78.2256i | − | 0.692262i | −0.938186 | − | 0.346131i | \(-0.887495\pi\) | ||
0.938186 | − | 0.346131i | \(-0.112505\pi\) | |||||||
\(114\) | 12.6447 | − | 60.2986i | 0.110918 | − | 0.528935i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 112.895i | − | 0.973231i | ||||||
\(117\) | 142.612i | 1.21891i | ||||||||
\(118\) | 242.292 | 2.05332 | ||||||||
\(119\) | 194.983 | 1.63851 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −82.0294 | −0.677929 | ||||||||
\(122\) | − | 57.5976i | − | 0.472112i | ||||||
\(123\) | −48.3315 | −0.392939 | ||||||||
\(124\) | − | 100.680i | − | 0.811937i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 142.383i | 1.13003i | ||||||||
\(127\) | − | 71.5532i | − | 0.563411i | −0.959501 | − | 0.281705i | \(-0.909100\pi\) | ||
0.959501 | − | 0.281705i | \(-0.0909001\pi\) | |||||||
\(128\) | 15.3474i | 0.119902i | ||||||||
\(129\) | − | 17.2740i | − | 0.133907i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −154.593 | −1.18010 | −0.590049 | − | 0.807367i | \(-0.700892\pi\) | ||||
−0.590049 | + | 0.807367i | \(0.700892\pi\) | |||||||
\(132\) | 27.6981i | 0.209834i | ||||||||
\(133\) | −25.9167 | + | 123.589i | −0.194862 | + | 0.929241i | ||||
\(134\) | 1.01724 | 0.00759137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.0835i | 0.103555i | ||||||||
\(137\) | −182.004 | −1.32850 | −0.664248 | − | 0.747513i | \(-0.731248\pi\) | ||||
−0.664248 | + | 0.747513i | \(0.731248\pi\) | |||||||
\(138\) | −64.6534 | −0.468503 | ||||||||
\(139\) | −180.191 | −1.29634 | −0.648169 | − | 0.761497i | \(-0.724465\pi\) | ||||
−0.648169 | + | 0.761497i | \(0.724465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.38098i | − | 0.0452552i | ||||||
\(142\) | −281.696 | −1.98378 | ||||||||
\(143\) | − | 116.272i | − | 0.813090i | ||||||
\(144\) | −127.539 | −0.885688 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.32154i | 0.00905167i | ||||||||
\(147\) | − | 5.59587i | − | 0.0380671i | ||||||
\(148\) | 181.783i | 1.22827i | ||||||||
\(149\) | 139.054 | 0.933247 | 0.466624 | − | 0.884456i | \(-0.345470\pi\) | ||||
0.466624 | + | 0.884456i | \(0.345470\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 49.9530i | − | 0.330815i | −0.986225 | − | 0.165407i | \(-0.947106\pi\) | ||
0.986225 | − | 0.165407i | \(-0.0528939\pi\) | |||||||
\(152\) | −8.92677 | − | 1.87195i | −0.0587288 | − | 0.0123155i | ||||
\(153\) | −224.634 | −1.46819 | ||||||||
\(154\) | − | 116.085i | − | 0.753800i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 82.6396 | 0.529741 | ||||||||
\(157\) | 19.7429 | 0.125751 | 0.0628754 | − | 0.998021i | \(-0.479973\pi\) | ||||
0.0628754 | + | 0.998021i | \(0.479973\pi\) | |||||||
\(158\) | −337.423 | −2.13559 | ||||||||
\(159\) | −64.2965 | −0.404380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 132.515 | 0.823073 | ||||||||
\(162\) | − | 130.213i | − | 0.803786i | ||||||
\(163\) | 266.123 | 1.63266 | 0.816330 | − | 0.577586i | \(-0.196005\pi\) | ||||
0.816330 | + | 0.577586i | \(0.196005\pi\) | |||||||
\(164\) | − | 159.657i | − | 0.973520i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 117.954i | 0.710567i | ||||||||
\(167\) | 91.4058i | 0.547340i | 0.961824 | + | 0.273670i | \(0.0882376\pi\) | ||||
−0.961824 | + | 0.273670i | \(0.911762\pi\) | |||||||
\(168\) | −3.69759 | −0.0220095 | ||||||||
\(169\) | −177.907 | −1.05270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 29.8579 | − | 142.383i | 0.174607 | − | 0.832651i | ||||
\(172\) | 57.0626 | 0.331759 | ||||||||
\(173\) | 136.221i | 0.787404i | 0.919238 | + | 0.393702i | \(0.128806\pi\) | ||||
−0.919238 | + | 0.393702i | \(0.871194\pi\) | |||||||
\(174\) | 95.6208i | 0.549545i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 103.983 | 0.590811 | ||||||||
\(177\) | −100.361 | −0.567009 | ||||||||
\(178\) | 12.6244 | 0.0709234 | ||||||||
\(179\) | − | 328.339i | − | 1.83429i | −0.398549 | − | 0.917147i | \(-0.630486\pi\) | ||
0.398549 | − | 0.917147i | \(-0.369514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 83.4062i | − | 0.460808i | −0.973095 | − | 0.230404i | \(-0.925995\pi\) | ||
0.973095 | − | 0.230404i | \(-0.0740047\pi\) | |||||||
\(182\) | −346.350 | −1.90302 | ||||||||
\(183\) | 23.8577i | 0.130370i | ||||||||
\(184\) | 9.57147i | 0.0520189i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 85.2752i | 0.458469i | ||||||||
\(187\) | 183.144 | 0.979381 | ||||||||
\(188\) | 21.0788 | 0.112121 | ||||||||
\(189\) | − | 128.300i | − | 0.678835i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −89.9878 | −0.471140 | −0.235570 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235570 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(192\) | 67.6787i | 0.352493i | ||||||||
\(193\) | 311.613i | 1.61458i | 0.590158 | + | 0.807288i | \(0.299065\pi\) | ||||
−0.590158 | + | 0.807288i | \(0.700935\pi\) | |||||||
\(194\) | −32.4264 | −0.167146 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.4853 | 0.0943127 | ||||||||
\(197\) | 14.9050 | 0.0756598 | 0.0378299 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378299 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(198\) | 133.738i | 0.675446i | ||||||||
\(199\) | 293.149 | 1.47311 | 0.736556 | − | 0.676377i | \(-0.236451\pi\) | ||||
0.736556 | + | 0.676377i | \(0.236451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.421356 | −0.00209630 | ||||||||
\(202\) | 269.979i | 1.33653i | ||||||||
\(203\) | − | 195.986i | − | 0.965448i | ||||||
\(204\) | 130.169i | 0.638082i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −368.492 | −1.78880 | ||||||||
\(207\) | −152.666 | −0.737518 | ||||||||
\(208\) | − | 310.241i | − | 1.49154i | ||||||
\(209\) | −24.3431 | + | 116.085i | −0.116474 | + | 0.555432i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 36.6437i | 0.173667i | 0.996223 | + | 0.0868333i | \(0.0276748\pi\) | ||||
−0.996223 | + | 0.0868333i | \(0.972325\pi\) | |||||||
\(212\) | − | 212.396i | − | 1.00187i | ||||||
\(213\) | 116.682 | 0.547805 | ||||||||
\(214\) | 121.090 | 0.565843 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.26703 | 0.0429029 | ||||||||
\(217\) | − | 174.781i | − | 0.805444i | ||||||
\(218\) | −39.4047 | −0.180755 | ||||||||
\(219\) | − | 0.547401i | − | 0.00249955i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 546.426i | − | 2.47251i | ||||||
\(222\) | − | 153.969i | − | 0.693553i | ||||||
\(223\) | − | 122.780i | − | 0.550581i | −0.961361 | − | 0.275291i | \(-0.911226\pi\) | ||
0.961361 | − | 0.275291i | \(-0.0887741\pi\) | |||||||
\(224\) | − | 296.981i | − | 1.32581i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −218.870 | −0.968452 | ||||||||
\(227\) | 108.742i | 0.479038i | 0.970892 | + | 0.239519i | \(0.0769898\pi\) | ||||
−0.970892 | + | 0.239519i | \(0.923010\pi\) | |||||||
\(228\) | −82.5070 | − | 17.3018i | −0.361873 | − | 0.0758849i | ||||
\(229\) | −266.627 | −1.16431 | −0.582156 | − | 0.813077i | \(-0.697791\pi\) | ||||
−0.582156 | + | 0.813077i | \(0.697791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 48.0841i | 0.208156i | ||||||||
\(232\) | 14.1560 | 0.0610171 | ||||||||
\(233\) | −164.623 | −0.706535 | −0.353267 | − | 0.935522i | \(-0.614929\pi\) | ||||
−0.353267 | + | 0.935522i | \(0.614929\pi\) | |||||||
\(234\) | 399.019 | 1.70521 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 331.529i | − | 1.40478i | ||||||
\(237\) | 139.765 | 0.589727 | ||||||||
\(238\) | − | 545.549i | − | 2.29222i | ||||||
\(239\) | −277.825 | −1.16245 | −0.581225 | − | 0.813743i | \(-0.697426\pi\) | ||||
−0.581225 | + | 0.813743i | \(0.697426\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 102.549i | 0.425515i | 0.977105 | + | 0.212758i | \(0.0682445\pi\) | ||||
−0.977105 | + | 0.212758i | \(0.931756\pi\) | |||||||
\(242\) | 229.513i | 0.948400i | ||||||||
\(243\) | 227.675i | 0.936934i | ||||||||
\(244\) | −78.8112 | −0.322997 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 135.228i | 0.549708i | ||||||||
\(247\) | 346.350 | + | 72.6298i | 1.40223 | + | 0.294048i | ||||
\(248\) | 12.6244 | 0.0509047 | ||||||||
\(249\) | − | 48.8582i | − | 0.196218i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 260.184 | 1.03659 | 0.518294 | − | 0.855202i | \(-0.326567\pi\) | ||||
0.518294 | + | 0.855202i | \(0.326567\pi\) | |||||||
\(252\) | 194.824 | 0.773111 | ||||||||
\(253\) | 124.469 | 0.491972 | ||||||||
\(254\) | −200.201 | −0.788193 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 276.529 | 1.08019 | ||||||||
\(257\) | − | 373.585i | − | 1.45364i | −0.686829 | − | 0.726819i | \(-0.740998\pi\) | ||
0.686829 | − | 0.726819i | \(-0.259002\pi\) | |||||||
\(258\) | −48.3315 | −0.187331 | ||||||||
\(259\) | 315.577i | 1.21844i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 225.790i | 0.865094i | ||||||||
\(262\) | 432.541i | 1.65092i | ||||||||
\(263\) | 222.353 | 0.845450 | 0.422725 | − | 0.906258i | \(-0.361074\pi\) | ||||
0.422725 | + | 0.906258i | \(0.361074\pi\) | |||||||
\(264\) | −3.47309 | −0.0131556 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 345.794 | + | 72.5132i | 1.29998 | + | 0.272606i | ||||
\(267\) | −5.22918 | −0.0195850 | ||||||||
\(268\) | − | 1.39190i | − | 0.00519366i | ||||||
\(269\) | 216.765i | 0.805820i | 0.915240 | + | 0.402910i | \(0.132001\pi\) | ||||
−0.915240 | + | 0.402910i | \(0.867999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.01724 | 0.0258939 | 0.0129469 | − | 0.999916i | \(-0.495879\pi\) | ||||
0.0129469 | + | 0.999916i | \(0.495879\pi\) | |||||||
\(272\) | 488.672 | 1.79659 | ||||||||
\(273\) | 143.463 | 0.525505 | ||||||||
\(274\) | 509.235i | 1.85852i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 88.4656i | 0.320528i | ||||||||
\(277\) | 247.993 | 0.895282 | 0.447641 | − | 0.894213i | \(-0.352264\pi\) | ||||
0.447641 | + | 0.894213i | \(0.352264\pi\) | |||||||
\(278\) | 504.162i | 1.81353i | ||||||||
\(279\) | 201.360i | 0.721722i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 350.899i | 1.24875i | 0.781125 | + | 0.624375i | \(0.214646\pi\) | ||||
−0.781125 | + | 0.624375i | \(0.785354\pi\) | |||||||
\(282\) | −17.8535 | −0.0633105 | ||||||||
\(283\) | 222.353 | 0.785700 | 0.392850 | − | 0.919602i | \(-0.371489\pi\) | ||||
0.392850 | + | 0.919602i | \(0.371489\pi\) | |||||||
\(284\) | 385.447i | 1.35721i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −325.321 | −1.13749 | ||||||||
\(287\) | − | 277.166i | − | 0.965735i | ||||||
\(288\) | 342.143i | 1.18800i | ||||||||
\(289\) | 571.696 | 1.97819 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.4315 | 0.0461562 | ||||||||
\(292\) | 1.80828 | 0.00619273 | ||||||||
\(293\) | − | 432.788i | − | 1.47709i | −0.674204 | − | 0.738546i | \(-0.735513\pi\) | ||
0.674204 | − | 0.738546i | \(-0.264487\pi\) | |||||||
\(294\) | −15.6569 | −0.0532546 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.7939 | −0.0770066 | ||||||||
\(297\) | − | 120.510i | − | 0.405757i | ||||||
\(298\) | − | 389.063i | − | 1.30558i | ||||||
\(299\) | − | 371.363i | − | 1.24202i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 99.0610 | 0.329106 | ||||||||
\(302\) | −139.765 | −0.462799 | ||||||||
\(303\) | − | 111.829i | − | 0.369073i | ||||||
\(304\) | −64.9533 | + | 309.743i | −0.213662 | + | 1.01889i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 628.510i | 2.05396i | ||||||||
\(307\) | 185.788i | 0.605174i | 0.953122 | + | 0.302587i | \(0.0978503\pi\) | ||||
−0.953122 | + | 0.302587i | \(0.902150\pi\) | |||||||
\(308\) | −158.840 | −0.515715 | ||||||||
\(309\) | 152.635 | 0.493963 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −288.345 | −0.927155 | −0.463578 | − | 0.886056i | \(-0.653434\pi\) | ||||
−0.463578 | + | 0.886056i | \(0.653434\pi\) | |||||||
\(312\) | 10.3622i | 0.0332123i | ||||||||
\(313\) | 561.976 | 1.79545 | 0.897725 | − | 0.440556i | \(-0.145219\pi\) | ||||
0.897725 | + | 0.440556i | \(0.145219\pi\) | |||||||
\(314\) | − | 55.2392i | − | 0.175921i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 461.698i | 1.46107i | ||||||||
\(317\) | 18.3642i | 0.0579313i | 0.999580 | + | 0.0289656i | \(0.00922134\pi\) | ||||
−0.999580 | + | 0.0289656i | \(0.990779\pi\) | |||||||
\(318\) | 179.897i | 0.565714i | ||||||||
\(319\) | − | 184.086i | − | 0.577073i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −50.1573 | −0.156253 | ||||||||
\(322\) | − | 370.767i | − | 1.15145i | ||||||
\(323\) | −114.402 | + | 545.549i | −0.354185 | + | 1.68901i | ||||
\(324\) | −178.172 | −0.549912 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 744.596i | − | 2.28404i | ||||||
\(327\) | 16.3220 | 0.0499142 | ||||||||
\(328\) | 20.0195 | 0.0610352 | ||||||||
\(329\) | 36.5929 | 0.111225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 319.862i | 0.966350i | 0.875524 | + | 0.483175i | \(0.160517\pi\) | ||||
−0.875524 | + | 0.483175i | \(0.839483\pi\) | |||||||
\(332\) | 161.397 | 0.486137 | ||||||||
\(333\) | − | 363.567i | − | 1.09179i | ||||||
\(334\) | 255.747 | 0.765710 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 128.300i | 0.381845i | ||||||||
\(337\) | − | 72.9992i | − | 0.216615i | −0.994117 | − | 0.108307i | \(-0.965457\pi\) | ||
0.994117 | − | 0.108307i | \(-0.0345431\pi\) | |||||||
\(338\) | 497.771i | 1.47269i | ||||||||
\(339\) | 90.6589 | 0.267431 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 164.169i | − | 0.481435i | ||||||
\(342\) | −398.379 | − | 83.5403i | −1.16485 | − | 0.244270i | ||||
\(343\) | 357.753 | 1.04301 | ||||||||
\(344\) | 7.15512i | 0.0207998i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 381.137 | 1.10155 | ||||||||
\(347\) | 370.850 | 1.06873 | 0.534365 | − | 0.845254i | \(-0.320551\pi\) | ||||
0.534365 | + | 0.845254i | \(0.320551\pi\) | |||||||
\(348\) | 130.838 | 0.375973 | ||||||||
\(349\) | −41.5980 | −0.119192 | −0.0595960 | − | 0.998223i | \(-0.518981\pi\) | ||||
−0.0595960 | + | 0.998223i | \(0.518981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −359.551 | −1.02436 | ||||||||
\(352\) | − | 278.950i | − | 0.792471i | ||||||
\(353\) | −402.468 | −1.14014 | −0.570068 | − | 0.821598i | \(-0.693083\pi\) | ||||
−0.570068 | + | 0.821598i | \(0.693083\pi\) | |||||||
\(354\) | 280.802i | 0.793226i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 17.2740i | − | 0.0485224i | ||||||
\(357\) | 225.974i | 0.632979i | ||||||||
\(358\) | −918.669 | −2.56612 | ||||||||
\(359\) | −386.556 | −1.07676 | −0.538379 | − | 0.842703i | \(-0.680963\pi\) | ||||
−0.538379 | + | 0.842703i | \(0.680963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −330.588 | − | 145.026i | −0.915756 | − | 0.401735i | ||||
\(362\) | −233.365 | −0.644655 | ||||||||
\(363\) | − | 95.0673i | − | 0.261893i | ||||||
\(364\) | 473.912i | 1.30196i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 66.7523 | 0.182383 | ||||||||
\(367\) | −404.829 | −1.10308 | −0.551539 | − | 0.834149i | \(-0.685959\pi\) | ||||
−0.551539 | + | 0.834149i | \(0.685959\pi\) | |||||||
\(368\) | 332.113 | 0.902481 | ||||||||
\(369\) | 319.315i | 0.865351i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 368.720i | − | 0.993855i | ||||||
\(372\) | 116.682 | 0.313663 | ||||||||
\(373\) | − | 22.0399i | − | 0.0590881i | −0.999563 | − | 0.0295441i | \(-0.990594\pi\) | ||
0.999563 | − | 0.0295441i | \(-0.00940554\pi\) | |||||||
\(374\) | − | 512.425i | − | 1.37012i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.64309i | 0.00702949i | ||||||||
\(377\) | −549.237 | −1.45686 | ||||||||
\(378\) | −358.974 | −0.949667 | ||||||||
\(379\) | − | 296.981i | − | 0.783591i | −0.920052 | − | 0.391796i | \(-0.871854\pi\) | ||
0.920052 | − | 0.391796i | \(-0.128146\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 82.9260 | 0.217653 | ||||||||
\(382\) | 251.780i | 0.659109i | ||||||||
\(383\) | 291.198i | 0.760308i | 0.924923 | + | 0.380154i | \(0.124129\pi\) | ||||
−0.924923 | + | 0.380154i | \(0.875871\pi\) | |||||||
\(384\) | −17.7868 | −0.0463198 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 871.872 | 2.25874 | ||||||||
\(387\) | −114.125 | −0.294897 | ||||||||
\(388\) | 44.3692i | 0.114354i | ||||||||
\(389\) | −292.243 | −0.751266 | −0.375633 | − | 0.926768i | \(-0.622575\pi\) | ||||
−0.375633 | + | 0.926768i | \(0.622575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 584.948 | 1.49603 | ||||||||
\(392\) | 2.31788i | 0.00591297i | ||||||||
\(393\) | − | 179.164i | − | 0.455889i | ||||||
\(394\) | − | 41.7031i | − | 0.105845i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 182.995 | 0.462108 | ||||||||
\(397\) | 235.092 | 0.592172 | 0.296086 | − | 0.955161i | \(-0.404319\pi\) | ||||
0.296086 | + | 0.955161i | \(0.404319\pi\) | |||||||
\(398\) | − | 820.212i | − | 2.06083i | ||||||
\(399\) | −143.233 | − | 30.0359i | −0.358979 | − | 0.0752781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 254.731i | − | 0.635239i | −0.948218 | − | 0.317619i | \(-0.897117\pi\) | ||
0.948218 | − | 0.317619i | \(-0.102883\pi\) | |||||||
\(402\) | 1.17893i | 0.00293265i | ||||||||
\(403\) | −489.813 | −1.21542 | ||||||||
\(404\) | 369.414 | 0.914392 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −548.355 | −1.35063 | ||||||||
\(407\) | 296.416i | 0.728295i | ||||||||
\(408\) | −16.3220 | −0.0400048 | ||||||||
\(409\) | 671.308i | 1.64134i | 0.571402 | + | 0.820670i | \(0.306400\pi\) | ||||
−0.571402 | + | 0.820670i | \(0.693600\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 210.932i | − | 0.513216i | ||||||
\(412\) | 504.210i | 1.22381i | ||||||||
\(413\) | − | 575.536i | − | 1.39355i | ||||||
\(414\) | 427.150i | 1.03176i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −832.269 | −2.00065 | ||||||||
\(417\) | − | 208.831i | − | 0.500793i | ||||||
\(418\) | 324.799 | + | 68.1105i | 0.777030 | + | 0.162944i | ||||
\(419\) | 524.492 | 1.25177 | 0.625886 | − | 0.779915i | \(-0.284738\pi\) | ||||
0.625886 | + | 0.779915i | \(0.284738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 599.022i | 1.42285i | 0.702760 | + | 0.711427i | \(0.251951\pi\) | ||||
−0.702760 | + | 0.711427i | \(0.748049\pi\) | |||||||
\(422\) | 102.527 | 0.242954 | ||||||||
\(423\) | −42.1576 | −0.0996634 | ||||||||
\(424\) | 26.6325 | 0.0628124 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 326.470i | − | 0.766361i | ||||||
\(427\) | −136.817 | −0.320414 | ||||||||
\(428\) | − | 165.689i | − | 0.387123i | ||||||
\(429\) | 134.752 | 0.314108 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 50.7272i | 0.117696i | 0.998267 | + | 0.0588482i | \(0.0187428\pi\) | ||||
−0.998267 | + | 0.0588482i | \(0.981257\pi\) | |||||||
\(432\) | − | 321.549i | − | 0.744327i | ||||||
\(433\) | 651.322i | 1.50421i | 0.659045 | + | 0.752104i | \(0.270961\pi\) | ||||
−0.659045 | + | 0.752104i | \(0.729039\pi\) | |||||||
\(434\) | −489.026 | −1.12679 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 53.9177i | 0.123664i | ||||||||
\(437\) | −77.7501 | + | 370.767i | −0.177918 | + | 0.848438i | ||||
\(438\) | −1.53159 | −0.00349679 | ||||||||
\(439\) | − | 373.780i | − | 0.851434i | −0.904856 | − | 0.425717i | \(-0.860022\pi\) | ||
0.904856 | − | 0.425717i | \(-0.139978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.9706 | −0.0838335 | ||||||||
\(442\) | −1528.86 | −3.45896 | ||||||||
\(443\) | 457.331 | 1.03235 | 0.516175 | − | 0.856483i | \(-0.327356\pi\) | ||||
0.516175 | + | 0.856483i | \(0.327356\pi\) | |||||||
\(444\) | −210.676 | −0.474496 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −343.529 | −0.770244 | ||||||||
\(447\) | 161.155i | 0.360526i | ||||||||
\(448\) | −388.116 | −0.866331 | ||||||||
\(449\) | 309.196i | 0.688632i | 0.938854 | + | 0.344316i | \(0.111889\pi\) | ||||
−0.938854 | + | 0.344316i | \(0.888111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 260.337i | − | 0.577245i | ||||||
\(452\) | 299.481i | 0.662569i | ||||||||
\(453\) | 57.8926 | 0.127798 | ||||||||
\(454\) | 304.252 | 0.670158 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.16948 | − | 10.3456i | 0.00475763 | − | 0.0226877i | ||||
\(457\) | 64.6534 | 0.141474 | 0.0707368 | − | 0.997495i | \(-0.477465\pi\) | ||||
0.0707368 | + | 0.997495i | \(0.477465\pi\) | |||||||
\(458\) | 746.006i | 1.62883i | ||||||||
\(459\) | − | 566.343i | − | 1.23386i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −328.531 | −0.712649 | −0.356324 | − | 0.934362i | \(-0.615970\pi\) | ||||
−0.356324 | + | 0.934362i | \(0.615970\pi\) | |||||||
\(462\) | 134.536 | 0.291204 | ||||||||
\(463\) | −619.396 | −1.33779 | −0.668894 | − | 0.743357i | \(-0.733232\pi\) | ||||
−0.668894 | + | 0.743357i | \(0.733232\pi\) | |||||||
\(464\) | − | 491.186i | − | 1.05859i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 460.603i | 0.988419i | ||||||||
\(467\) | −303.167 | −0.649179 | −0.324589 | − | 0.945855i | \(-0.605226\pi\) | ||||
−0.324589 | + | 0.945855i | \(0.605226\pi\) | |||||||
\(468\) | − | 545.980i | − | 1.16662i | ||||||
\(469\) | − | 2.41635i | − | 0.00515213i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8808i | 0.0485793i | ||||||||
\(472\) | 41.5707 | 0.0880735 | ||||||||
\(473\) | 93.0464 | 0.196715 | ||||||||
\(474\) | − | 391.054i | − | 0.825008i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −746.477 | −1.56823 | ||||||||
\(477\) | 424.792i | 0.890548i | ||||||||
\(478\) | 777.337i | 1.62623i | ||||||||
\(479\) | 313.314 | 0.654100 | 0.327050 | − | 0.945007i | \(-0.393946\pi\) | ||||
0.327050 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 884.382 | 1.83863 | ||||||||
\(482\) | 286.926 | 0.595281 | ||||||||
\(483\) | 153.577i | 0.317964i | ||||||||
\(484\) | 314.044 | 0.648851 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 637.019 | 1.31074 | ||||||||
\(487\) | 19.7644i | 0.0405840i | 0.999794 | + | 0.0202920i | \(0.00645958\pi\) | ||||
−0.999794 | + | 0.0202920i | \(0.993540\pi\) | |||||||
\(488\) | − | 9.88219i | − | 0.0202504i | ||||||
\(489\) | 308.422i | 0.630719i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 232.222 | 0.472958 | 0.236479 | − | 0.971637i | \(-0.424007\pi\) | ||||
0.236479 | + | 0.971637i | \(0.424007\pi\) | |||||||
\(492\) | 185.033 | 0.376084 | ||||||||
\(493\) | − | 865.124i | − | 1.75481i | ||||||
\(494\) | 203.213 | − | 969.064i | 0.411363 | − | 1.96167i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 438.043i | − | 0.883151i | ||||||
\(497\) | 669.138i | 1.34635i | ||||||||
\(498\) | −136.702 | −0.274502 | ||||||||
\(499\) | −824.237 | −1.65178 | −0.825889 | − | 0.563833i | \(-0.809326\pi\) | ||||
−0.825889 | + | 0.563833i | \(0.809326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −105.934 | −0.211445 | ||||||||
\(502\) | − | 727.977i | − | 1.45015i | ||||||
\(503\) | −330.777 | −0.657608 | −0.328804 | − | 0.944398i | \(-0.606646\pi\) | ||||
−0.328804 | + | 0.944398i | \(0.606646\pi\) | |||||||
\(504\) | 24.4291i | 0.0484705i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 348.256i | − | 0.688252i | ||||||
\(507\) | − | 206.183i | − | 0.406673i | ||||||
\(508\) | 273.936i | 0.539244i | ||||||||
\(509\) | 375.649i | 0.738013i | 0.929427 | + | 0.369006i | \(0.120302\pi\) | ||||
−0.929427 | + | 0.369006i | \(0.879698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.13918 | 0.00614320 | ||||||||
\(512\) | − | 712.320i | − | 1.39125i | ||||||
\(513\) | 358.974 | + | 75.2771i | 0.699755 | + | 0.146739i | ||||
\(514\) | −1045.27 | −2.03359 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 66.1322i | 0.128163i | ||||||||
\(517\) | 34.3712 | 0.0664819 | ||||||||
\(518\) | 882.962 | 1.70456 | ||||||||
\(519\) | −157.872 | −0.304185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 769.799i | 1.47754i | 0.673957 | + | 0.738770i | \(0.264593\pi\) | ||||
−0.673957 | + | 0.738770i | \(0.735407\pi\) | |||||||
\(522\) | 631.744 | 1.21024 | ||||||||
\(523\) | − | 228.999i | − | 0.437856i | −0.975741 | − | 0.218928i | \(-0.929744\pi\) | ||
0.975741 | − | 0.218928i | \(-0.0702560\pi\) | |||||||
\(524\) | 591.848 | 1.12948 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 622.129i | − | 1.18276i | ||||||
\(527\) | − | 771.522i | − | 1.46399i | ||||||
\(528\) | 120.510i | 0.228239i | ||||||||
\(529\) | −131.456 | −0.248499 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 663.058i | 1.24870i | ||||||||
\(532\) | 99.2202 | − | 473.152i | 0.186504 | − | 0.889383i | ||||
\(533\) | −776.738 | −1.45730 | ||||||||
\(534\) | 14.6309i | 0.0273987i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.174531 | 0.000325618 | ||||||||
\(537\) | 380.525 | 0.708613 | ||||||||
\(538\) | 606.495 | 1.12731 | ||||||||
\(539\) | 30.1421 | 0.0559223 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −67.4487 | −0.124674 | −0.0623371 | − | 0.998055i | \(-0.519855\pi\) | ||||
−0.0623371 | + | 0.998055i | \(0.519855\pi\) | |||||||
\(542\) | − | 19.6338i | − | 0.0362247i | ||||||
\(543\) | 96.6629 | 0.178016 | ||||||||
\(544\) | − | 1310.94i | − | 2.40981i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 401.399i | − | 0.735163i | ||||||
\(547\) | − | 788.659i | − | 1.44179i | −0.693044 | − | 0.720895i | \(-0.743731\pi\) | ||
0.693044 | − | 0.720895i | \(-0.256269\pi\) | |||||||
\(548\) | 696.789 | 1.27151 | ||||||||
\(549\) | 157.622 | 0.287108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 548.355 | + | 114.990i | 0.995200 | + | 0.208694i | ||||
\(552\) | −11.0928 | −0.0200956 | ||||||||
\(553\) | 801.510i | 1.44939i | ||||||||
\(554\) | − | 693.868i | − | 1.25247i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 689.848 | 1.24073 | ||||||||
\(557\) | −676.735 | −1.21496 | −0.607482 | − | 0.794333i | \(-0.707820\pi\) | ||||
−0.607482 | + | 0.794333i | \(0.707820\pi\) | |||||||
\(558\) | 563.393 | 1.00966 | ||||||||
\(559\) | − | 277.611i | − | 0.496622i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 212.253i | 0.378348i | ||||||||
\(562\) | 981.791 | 1.74696 | ||||||||
\(563\) | 822.729i | 1.46133i | 0.682736 | + | 0.730665i | \(0.260790\pi\) | ||||
−0.682736 | + | 0.730665i | \(0.739210\pi\) | |||||||
\(564\) | 24.4291i | 0.0433140i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 622.129i | − | 1.09917i | ||||||
\(567\) | −309.307 | −0.545515 | ||||||||
\(568\) | −48.3315 | −0.0850906 | ||||||||
\(569\) | 414.388i | 0.728274i | 0.931345 | + | 0.364137i | \(0.118636\pi\) | ||||
−0.931345 | + | 0.364137i | \(0.881364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1105.17 | −1.93550 | −0.967748 | − | 0.251919i | \(-0.918938\pi\) | ||||
−0.967748 | + | 0.251919i | \(0.918938\pi\) | |||||||
\(572\) | 445.138i | 0.778214i | ||||||||
\(573\) | − | 104.291i | − | 0.182008i | ||||||
\(574\) | −775.492 | −1.35103 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 447.137 | 0.776280 | ||||||||
\(577\) | 768.918 | 1.33261 | 0.666307 | − | 0.745678i | \(-0.267874\pi\) | ||||
0.666307 | + | 0.745678i | \(0.267874\pi\) | |||||||
\(578\) | − | 1599.57i | − | 2.76741i | ||||||
\(579\) | −361.141 | −0.623733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 280.187 | 0.482249 | ||||||||
\(582\) | − | 37.5803i | − | 0.0645710i | ||||||
\(583\) | − | 346.333i | − | 0.594053i | ||||||
\(584\) | 0.226741i | 0.000388255i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1210.91 | −2.06640 | ||||||||
\(587\) | 285.313 | 0.486053 | 0.243026 | − | 0.970020i | \(-0.421860\pi\) | ||||
0.243026 | + | 0.970020i | \(0.421860\pi\) | |||||||
\(588\) | 21.4234i | 0.0364343i | ||||||||
\(589\) | 489.026 | + | 102.549i | 0.830266 | + | 0.174107i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.2740i | 0.0292284i | ||||||||
\(592\) | 790.909i | 1.33599i | ||||||||
\(593\) | 114.516 | 0.193114 | 0.0965569 | − | 0.995327i | \(-0.469217\pi\) | ||||
0.0965569 | + | 0.995327i | \(0.469217\pi\) | |||||||
\(594\) | −337.179 | −0.567641 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −532.357 | −0.893217 | ||||||||
\(597\) | 339.743i | 0.569084i | ||||||||
\(598\) | −1039.05 | −1.73754 | ||||||||
\(599\) | − | 841.859i | − | 1.40544i | −0.711467 | − | 0.702720i | \(-0.751969\pi\) | ||
0.711467 | − | 0.702720i | \(-0.248031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1048.51i | 1.74460i | 0.488970 | + | 0.872300i | \(0.337373\pi\) | ||||
−0.488970 | + | 0.872300i | \(0.662627\pi\) | |||||||
\(602\) | − | 277.166i | − | 0.460408i | ||||||
\(603\) | 2.78380i | 0.00461659i | ||||||||
\(604\) | 191.242i | 0.316625i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −312.890 | −0.516321 | ||||||||
\(607\) | 226.715i | 0.373501i | 0.982407 | + | 0.186750i | \(0.0597955\pi\) | ||||
−0.982407 | + | 0.186750i | \(0.940204\pi\) | |||||||
\(608\) | 830.933 | + | 174.247i | 1.36667 | + | 0.286591i | ||||
\(609\) | 227.136 | 0.372966 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 102.549i | − | 0.167838i | ||||||
\(612\) | 859.994 | 1.40522 | ||||||||
\(613\) | −406.833 | −0.663676 | −0.331838 | − | 0.943336i | \(-0.607669\pi\) | ||||
−0.331838 | + | 0.943336i | \(0.607669\pi\) | |||||||
\(614\) | 519.823 | 0.846618 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 19.9171i | − | 0.0323329i | ||||||
\(617\) | 215.903 | 0.349923 | 0.174962 | − | 0.984575i | \(-0.444020\pi\) | ||||
0.174962 | + | 0.984575i | \(0.444020\pi\) | |||||||
\(618\) | − | 427.061i | − | 0.691038i | ||||||
\(619\) | 838.586 | 1.35474 | 0.677371 | − | 0.735641i | \(-0.263119\pi\) | ||||
0.677371 | + | 0.735641i | \(0.263119\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 384.899i | − | 0.619806i | ||||||
\(622\) | 806.771i | 1.29706i | ||||||||
\(623\) | − | 29.9877i | − | 0.0481344i | ||||||
\(624\) | 359.551 | 0.576204 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1572.37i | − | 2.51177i | ||||||
\(627\) | −134.536 | − | 28.2123i | −0.214571 | − | 0.0449957i | ||||
\(628\) | −75.5841 | −0.120357 | ||||||||
\(629\) | 1393.02i | 2.21466i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −267.661 | −0.424185 | −0.212093 | − | 0.977250i | \(-0.568028\pi\) | ||||
−0.212093 | + | 0.977250i | \(0.568028\pi\) | |||||||
\(632\) | −57.8926 | −0.0916023 | ||||||||
\(633\) | −42.4679 | −0.0670898 | ||||||||
\(634\) | 51.3818 | 0.0810439 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 246.154 | 0.387035 | ||||||||
\(637\) | − | 89.9315i | − | 0.141180i | ||||||
\(638\) | −515.061 | −0.807306 | ||||||||
\(639\) | − | 770.894i | − | 1.20641i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 449.257i | 0.700868i | 0.936587 | + | 0.350434i | \(0.113966\pi\) | ||||
−0.936587 | + | 0.350434i | \(0.886034\pi\) | |||||||
\(642\) | 140.337i | 0.218593i | ||||||||
\(643\) | 368.569 | 0.573202 | 0.286601 | − | 0.958050i | \(-0.407475\pi\) | ||||
0.286601 | + | 0.958050i | \(0.407475\pi\) | |||||||
\(644\) | −507.323 | −0.787769 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1526.41 | + | 320.089i | 2.36286 | + | 0.495493i | ||||
\(647\) | 371.599 | 0.574341 | 0.287170 | − | 0.957879i | \(-0.407285\pi\) | ||||
0.287170 | + | 0.957879i | \(0.407285\pi\) | |||||||
\(648\) | − | 22.3411i | − | 0.0344770i | ||||||
\(649\) | − | 540.592i | − | 0.832962i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 202.561 | 0.311154 | ||||||||
\(652\) | −1018.83 | −1.56263 | ||||||||
\(653\) | −257.669 | −0.394593 | −0.197296 | − | 0.980344i | \(-0.563216\pi\) | ||||
−0.197296 | + | 0.980344i | \(0.563216\pi\) | |||||||
\(654\) | − | 45.6677i | − | 0.0698283i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 694.643i | − | 1.05891i | ||||||
\(657\) | −3.61655 | −0.00550465 | ||||||||
\(658\) | − | 102.385i | − | 0.155600i | ||||||
\(659\) | 32.4523i | 0.0492448i | 0.999697 | + | 0.0246224i | \(0.00783834\pi\) | ||||
−0.999697 | + | 0.0246224i | \(0.992162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 992.719i | − | 1.50184i | −0.660391 | − | 0.750922i | \(-0.729610\pi\) | ||
0.660391 | − | 0.750922i | \(-0.270390\pi\) | |||||||
\(662\) | 894.952 | 1.35189 | ||||||||
\(663\) | 633.275 | 0.955167 | ||||||||
\(664\) | 20.2377i | 0.0304785i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1017.23 | −1.52738 | ||||||||
\(667\) | − | 587.958i | − | 0.881496i | ||||||
\(668\) | − | 349.940i | − | 0.523863i | ||||||
\(669\) | 142.294 | 0.212697 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −128.510 | −0.191520 | ||||||||
\(672\) | 344.184 | 0.512178 | ||||||||
\(673\) | 649.462i | 0.965025i | 0.875889 | + | 0.482512i | \(0.160276\pi\) | ||||
−0.875889 | + | 0.482512i | \(0.839724\pi\) | |||||||
\(674\) | −204.247 | −0.303037 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 681.103 | 1.00755 | ||||||||
\(677\) | 1219.86i | 1.80186i | 0.433969 | + | 0.900928i | \(0.357113\pi\) | ||||
−0.433969 | + | 0.900928i | \(0.642887\pi\) | |||||||
\(678\) | − | 253.658i | − | 0.374126i | ||||||
\(679\) | 77.0252i | 0.113439i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −126.025 | −0.185059 | ||||||||
\(682\) | −459.335 | −0.673511 | ||||||||
\(683\) | − | 97.8453i | − | 0.143258i | −0.997431 | − | 0.0716290i | \(-0.977180\pi\) | ||
0.997431 | − | 0.0716290i | \(-0.0228198\pi\) | |||||||
\(684\) | −114.309 | + | 545.104i | −0.167118 | + | 0.796936i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1000.97i | − | 1.45914i | ||||||
\(687\) | − | 309.006i | − | 0.449790i | ||||||
\(688\) | 248.270 | 0.360857 | ||||||||
\(689\) | −1033.31 | −1.49973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −255.951 | −0.370407 | −0.185203 | − | 0.982700i | \(-0.559294\pi\) | ||||
−0.185203 | + | 0.982700i | \(0.559294\pi\) | |||||||
\(692\) | − | 521.512i | − | 0.753630i | ||||||
\(693\) | 317.680 | 0.458413 | ||||||||
\(694\) | − | 1037.61i | − | 1.49512i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.4059i | 0.0235717i | ||||||||
\(697\) | − | 1223.47i | − | 1.75534i | ||||||
\(698\) | 116.388i | 0.166745i | ||||||||
\(699\) | − | 190.788i | − | 0.272944i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −290.329 | −0.414164 | −0.207082 | − | 0.978324i | \(-0.566397\pi\) | ||||
−0.207082 | + | 0.978324i | \(0.566397\pi\) | |||||||
\(702\) | 1006.00i | 1.43305i | ||||||||
\(703\) | −882.962 | − | 185.158i | −1.25599 | − | 0.263382i | ||||
\(704\) | −364.551 | −0.517829 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1126.08i | 1.59501i | ||||||||
\(707\) | 641.305 | 0.907079 | ||||||||
\(708\) | 384.223 | 0.542688 | ||||||||
\(709\) | 248.916 | 0.351080 | 0.175540 | − | 0.984472i | \(-0.443833\pi\) | ||||
0.175540 | + | 0.984472i | \(0.443833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 923.396i | − | 1.29873i | ||||||
\(712\) | 2.16600 | 0.00304213 | ||||||||
\(713\) | − | 524.344i | − | 0.735405i | ||||||
\(714\) | 632.259 | 0.885517 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1257.02i | 1.75562i | ||||||||
\(717\) | − | 321.984i | − | 0.449070i | ||||||
\(718\) | 1081.56i | 1.50635i | ||||||||
\(719\) | −1233.16 | −1.71511 | −0.857555 | − | 0.514393i | \(-0.828017\pi\) | ||||
−0.857555 | + | 0.514393i | \(0.828017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 875.312i | 1.21402i | ||||||||
\(722\) | −405.774 | + | 924.963i | −0.562014 | + | 1.28111i | ||||
\(723\) | −118.848 | −0.164382 | ||||||||
\(724\) | 319.315i | 0.441042i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −265.992 | −0.366380 | ||||||||
\(727\) | 176.613 | 0.242933 | 0.121467 | − | 0.992596i | \(-0.461240\pi\) | ||||
0.121467 | + | 0.992596i | \(0.461240\pi\) | |||||||
\(728\) | −59.4242 | −0.0816267 | ||||||||
\(729\) | 154.990 | 0.212606 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 437.276 | 0.598189 | ||||||||
\(732\) | − | 91.3376i | − | 0.124778i | ||||||
\(733\) | −1135.13 | −1.54860 | −0.774301 | − | 0.632817i | \(-0.781898\pi\) | ||||
−0.774301 | + | 0.632817i | \(0.781898\pi\) | |||||||
\(734\) | 1132.69i | 1.54317i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 890.943i | − | 1.21052i | ||||||
\(737\) | − | 2.26964i | − | 0.00307956i | ||||||
\(738\) | 893.421 | 1.21060 | ||||||||
\(739\) | 556.673 | 0.753279 | 0.376640 | − | 0.926360i | \(-0.377080\pi\) | ||||
0.376640 | + | 0.926360i | \(0.377080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −84.1737 | + | 401.399i | −0.113595 | + | 0.541699i | ||||
\(742\) | −1031.65 | −1.39037 | ||||||||
\(743\) | 126.242i | 0.169909i | 0.996385 | + | 0.0849544i | \(0.0270745\pi\) | ||||
−0.996385 | + | 0.0849544i | \(0.972926\pi\) | |||||||
\(744\) | 14.6309i | 0.0196652i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −61.6661 | −0.0826623 | ||||||||
\(747\) | −322.795 | −0.432122 | ||||||||
\(748\) | −701.154 | −0.937372 | ||||||||
\(749\) | − | 287.636i | − | 0.384027i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 550.711i | 0.733304i | 0.930358 | + | 0.366652i | \(0.119496\pi\) | ||||
−0.930358 | + | 0.366652i | \(0.880504\pi\) | |||||||
\(752\) | 91.7104 | 0.121955 | ||||||||
\(753\) | 301.538i | 0.400449i | ||||||||
\(754\) | 1536.73i | 2.03810i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 491.186i | 0.649718i | ||||||||
\(757\) | −965.388 | −1.27528 | −0.637641 | − | 0.770334i | \(-0.720090\pi\) | ||||
−0.637641 | + | 0.770334i | \(0.720090\pi\) | |||||||
\(758\) | −830.933 | −1.09622 | ||||||||
\(759\) | 144.252i | 0.190056i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 682.013 | 0.896207 | 0.448103 | − | 0.893982i | \(-0.352100\pi\) | ||||
0.448103 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(762\) | − | 232.021i | − | 0.304490i | ||||||
\(763\) | 93.6013i | 0.122675i | ||||||||
\(764\) | 344.512 | 0.450932 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 814.752 | 1.06365 | ||||||||
\(767\) | −1612.90 | −2.10287 | ||||||||
\(768\) | 320.481i | 0.417293i | ||||||||
\(769\) | −279.579 | −0.363561 | −0.181781 | − | 0.983339i | \(-0.558186\pi\) | ||||
−0.181781 | + | 0.983339i | \(0.558186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 432.963 | 0.561561 | ||||||||
\(772\) | − | 1192.99i | − | 1.54532i | ||||||
\(773\) | − | 527.781i | − | 0.682770i | −0.939924 | − | 0.341385i | \(-0.889104\pi\) | ||
0.939924 | − | 0.341385i | \(-0.110896\pi\) | |||||||
\(774\) | 319.315i | 0.412551i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.56349 | −0.00716945 | ||||||||
\(777\) | −365.735 | −0.470701 | ||||||||
\(778\) | 817.675i | 1.05100i | ||||||||
\(779\) | 775.492 | + | 162.621i | 0.995496 | + | 0.208756i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 628.510i | 0.804751i | ||||||||
\(782\) | − | 1636.65i | − | 2.09290i | ||||||
\(783\) | −569.256 | −0.727020 | ||||||||
\(784\) | 80.4264 | 0.102585 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −501.289 | −0.637773 | ||||||||
\(787\) | 761.947i | 0.968167i | 0.875022 | + | 0.484083i | \(0.160847\pi\) | ||||
−0.875022 | + | 0.484083i | \(0.839153\pi\) | |||||||
\(788\) | −57.0626 | −0.0724145 | ||||||||
\(789\) | 257.694i | 0.326609i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 519.901i | 0.657270i | ||||||||
\(792\) | 22.9459i | 0.0289721i | ||||||||
\(793\) | 383.419i | 0.483505i | ||||||||
\(794\) | − | 657.772i | − | 0.828428i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1122.30 | −1.40993 | ||||||||
\(797\) | − | 989.767i | − | 1.24187i | −0.783864 | − | 0.620933i | \(-0.786754\pi\) | ||
0.783864 | − | 0.620933i | \(-0.213246\pi\) | |||||||
\(798\) | −84.0386 | + | 400.755i | −0.105311 | + | 0.502199i | ||||
\(799\) | 161.529 | 0.202164 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.5480i | 0.0431311i | ||||||||
\(802\) | −712.719 | −0.888677 | ||||||||
\(803\) | 2.94858 | 0.00367195 | ||||||||
\(804\) | 1.61313 | 0.00200638 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1370.46i | 1.70033i | ||||||||
\(807\) | −251.219 | −0.311299 | ||||||||
\(808\) | 46.3211i | 0.0573281i | ||||||||
\(809\) | 1148.89 | 1.42013 | 0.710066 | − | 0.704135i | \(-0.248665\pi\) | ||||
0.710066 | + | 0.704135i | \(0.248665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 660.963i | − | 0.814997i | −0.913206 | − | 0.407499i | \(-0.866401\pi\) | ||
0.913206 | − | 0.407499i | \(-0.133599\pi\) | |||||||
\(812\) | 750.318i | 0.924037i | ||||||||
\(813\) | 8.13258i | 0.0100032i | ||||||||
\(814\) | 829.352 | 1.01886 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 566.343i | 0.694047i | ||||||||
\(817\) | −58.1219 | + | 277.166i | −0.0711406 | + | 0.339248i | ||||
\(818\) | 1878.28 | 2.29618 | ||||||||
\(819\) | − | 947.825i | − | 1.15730i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1048.30 | 1.27686 | 0.638430 | − | 0.769680i | \(-0.279584\pi\) | ||||
0.638430 | + | 0.769680i | \(0.279584\pi\) | |||||||
\(822\) | −590.173 | −0.717972 | ||||||||
\(823\) | −140.352 | −0.170537 | −0.0852686 | − | 0.996358i | \(-0.527175\pi\) | ||||
−0.0852686 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(824\) | −63.2233 | −0.0767273 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1610.31 | −1.94953 | ||||||||
\(827\) | 41.2618i | 0.0498934i | 0.999689 | + | 0.0249467i | \(0.00794160\pi\) | ||||
−0.999689 | + | 0.0249467i | \(0.992058\pi\) | |||||||
\(828\) | 584.472 | 0.705884 | ||||||||
\(829\) | 315.350i | 0.380398i | 0.981746 | + | 0.190199i | \(0.0609133\pi\) | ||||
−0.981746 | + | 0.190199i | \(0.939087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 287.410i | 0.345860i | ||||||||
\(832\) | 1087.67i | 1.30729i | ||||||||
\(833\) | 141.655 | 0.170053 | ||||||||
\(834\) | −584.294 | −0.700593 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 93.1960 | − | 444.424i | 0.111478 | − | 0.531608i | ||||
\(837\) | −507.666 | −0.606531 | ||||||||
\(838\) | − | 1467.49i | − | 1.75119i | ||||||
\(839\) | 1541.79i | 1.83765i | 0.394667 | + | 0.918824i | \(0.370860\pi\) | ||||
−0.394667 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5745 | −0.0339768 | ||||||||
\(842\) | 1676.02 | 1.99053 | ||||||||
\(843\) | −406.671 | −0.482410 | ||||||||
\(844\) | − | 140.288i | − | 0.166218i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 117.954i | 0.139426i | ||||||||
\(847\) | 545.182 | 0.643662 | ||||||||
\(848\) | − | 924.099i | − | 1.08974i | ||||||
\(849\) | 257.694i | 0.303527i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 946.730i | 1.11249i | ||||||||
\(852\) | −446.710 | −0.524308 | ||||||||
\(853\) | 633.242 | 0.742370 | 0.371185 | − | 0.928559i | \(-0.378952\pi\) | ||||
0.371185 | + | 0.928559i | \(0.378952\pi\) | |||||||
\(854\) | 382.804i | 0.448248i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.7758 | 0.0242708 | ||||||||
\(857\) | − | 365.640i | − | 0.426651i | −0.976981 | − | 0.213325i | \(-0.931571\pi\) | ||
0.976981 | − | 0.213325i | \(-0.0684294\pi\) | |||||||
\(858\) | − | 377.028i | − | 0.439426i | ||||||
\(859\) | −1141.98 | −1.32943 | −0.664713 | − | 0.747099i | \(-0.731446\pi\) | ||||
−0.664713 | + | 0.747099i | \(0.731446\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 321.219 | 0.373077 | ||||||||
\(862\) | 141.931 | 0.164653 | ||||||||
\(863\) | 805.728i | 0.933636i | 0.884353 | + | 0.466818i | \(0.154600\pi\) | ||||
−0.884353 | + | 0.466818i | \(0.845400\pi\) | |||||||
\(864\) | −862.605 | −0.998386 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1822.35 | 2.10434 | ||||||||
\(867\) | 662.562i | 0.764200i | ||||||||
\(868\) | 669.138i | 0.770896i | ||||||||
\(869\) | 752.845i | 0.866335i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.77164 | −0.00777456 | ||||||||
\(872\) | −6.76078 | −0.00775318 | ||||||||
\(873\) | − | 88.7385i | − | 0.101648i | ||||||
\(874\) | 1037.38 | + | 217.540i | 1.18694 | + | 0.248901i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.09569i | 0.00239234i | ||||||||
\(877\) | 884.064i | 1.00806i | 0.863688 | + | 0.504028i | \(0.168149\pi\) | ||||
−0.863688 | + | 0.504028i | \(0.831851\pi\) | |||||||
\(878\) | −1045.81 | −1.19113 | ||||||||
\(879\) | 501.576 | 0.570621 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1348.89 | −1.53109 | −0.765543 | − | 0.643384i | \(-0.777530\pi\) | ||||
−0.765543 | + | 0.643384i | \(0.777530\pi\) | |||||||
\(882\) | 103.441i | 0.117280i | ||||||||
\(883\) | −990.084 | −1.12127 | −0.560636 | − | 0.828062i | \(-0.689443\pi\) | ||||
−0.560636 | + | 0.828062i | \(0.689443\pi\) | |||||||
\(884\) | 2091.95i | 2.36646i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1279.58i | − | 1.44422i | ||||||
\(887\) | 864.925i | 0.975112i | 0.873092 | + | 0.487556i | \(0.162112\pi\) | ||||
−0.873092 | + | 0.487556i | \(0.837888\pi\) | |||||||
\(888\) | − | 26.4168i | − | 0.0297487i | ||||||
\(889\) | 475.555i | 0.534932i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −290.527 | −0.326068 | ||||||||
\(892\) | 470.053i | 0.526965i | ||||||||
\(893\) | −21.4701 | + | 102.385i | −0.0240427 | + | 0.114652i | ||||
\(894\) | 450.902 | 0.504364 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 102.002i | − | 0.113841i | ||||||
\(897\) | 430.388 | 0.479809 | ||||||||
\(898\) | 865.109 | 0.963373 | ||||||||
\(899\) | −775.492 | −0.862616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1627.61i | − | 1.80645i | ||||||
\(902\) | −728.407 | −0.807546 | ||||||||
\(903\) | 114.806i | 0.127138i | ||||||||
\(904\) | −37.5522 | −0.0415400 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 161.980i | − | 0.178786i | ||||||
\(907\) | 1019.55i | 1.12409i | 0.827107 | + | 0.562045i | \(0.189985\pi\) | ||||
−0.827107 | + | 0.562045i | \(0.810015\pi\) | |||||||
\(908\) | − | 416.310i | − | 0.458491i | ||||||
\(909\) | −738.828 | −0.812793 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1069.97i | − | 1.17450i | −0.809405 | − | 0.587251i | \(-0.800210\pi\) | ||
0.809405 | − | 0.587251i | \(-0.199790\pi\) | |||||||
\(912\) | −358.974 | − | 75.2771i | −0.393612 | − | 0.0825407i | ||||
\(913\) | 263.175 | 0.288253 | ||||||||
\(914\) | − | 180.896i | − | 0.197917i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1020.76 | 1.11437 | ||||||||
\(917\) | 1027.45 | 1.12045 | ||||||||
\(918\) | −1584.59 | −1.72613 | ||||||||
\(919\) | −1166.06 | −1.26883 | −0.634415 | − | 0.772993i | \(-0.718759\pi\) | ||||
−0.634415 | + | 0.772993i | \(0.718759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −215.318 | −0.233787 | ||||||||
\(922\) | 919.208i | 0.996972i | ||||||||
\(923\) | 1875.21 | 2.03165 | ||||||||
\(924\) | − | 184.086i | − | 0.199228i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1733.03i | 1.87152i | ||||||||
\(927\) | − | 1008.42i | − | 1.08783i | ||||||
\(928\) | −1317.68 | −1.41992 | ||||||||
\(929\) | 183.514 | 0.197539 | 0.0987696 | − | 0.995110i | \(-0.468509\pi\) | ||||
0.0987696 | + | 0.995110i | \(0.468509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8284 | + | 89.7872i | −0.0202239 | + | 0.0964417i | ||||
\(932\) | 630.246 | 0.676229 | ||||||||
\(933\) | − | 334.175i | − | 0.358173i | ||||||
\(934\) | 848.240i | 0.908179i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 68.4609 | 0.0731420 | ||||||||
\(937\) | 273.714 | 0.292118 | 0.146059 | − | 0.989276i | \(-0.453341\pi\) | ||||
0.146059 | + | 0.989276i | \(0.453341\pi\) | |||||||
\(938\) | −6.76078 | −0.00720765 | ||||||||
\(939\) | 651.297i | 0.693607i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 313.160i | 0.332795i | 0.986059 | + | 0.166398i | \(0.0532135\pi\) | ||||
−0.986059 | + | 0.166398i | \(0.946786\pi\) | |||||||
\(942\) | 64.0190 | 0.0679607 | ||||||||
\(943\) | − | 831.498i | − | 0.881758i | ||||||
\(944\) | − | 1442.43i | − | 1.52800i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 260.337i | − | 0.275198i | ||||||
\(947\) | 129.698 | 0.136957 | 0.0684784 | − | 0.997653i | \(-0.478186\pi\) | ||||
0.0684784 | + | 0.997653i | \(0.478186\pi\) | |||||||
\(948\) | −535.081 | −0.564431 | ||||||||
\(949\) | − | 8.79733i | − | 0.00927010i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2830 | −0.0223796 | ||||||||
\(952\) | − | 93.6013i | − | 0.0983207i | ||||||
\(953\) | 353.917i | 0.371372i | 0.982609 | + | 0.185686i | \(0.0594507\pi\) | ||||
−0.982609 | + | 0.185686i | \(0.940549\pi\) | |||||||
\(954\) | 1188.54 | 1.24585 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1063.63 | 1.11259 | ||||||||
\(957\) | 213.345 | 0.222931 | ||||||||
\(958\) | − | 876.631i | − | 0.915063i | ||||||
\(959\) | 1209.63 | 1.26134 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 269.412 | 0.280346 | ||||||||
\(962\) | − | 2474.44i | − | 2.57218i | ||||||
\(963\) | 331.377i | 0.344109i | ||||||||
\(964\) | − | 392.602i | − | 0.407263i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 429.698 | 0.444822 | ||||||||
\(967\) | −383.913 | −0.397014 | −0.198507 | − | 0.980099i | \(-0.563609\pi\) | ||||
−0.198507 | + | 0.980099i | \(0.563609\pi\) | |||||||
\(968\) | 39.3782i | 0.0406799i | ||||||||
\(969\) | −632.259 | − | 132.585i | −0.652486 | − | 0.136827i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 307.647i | 0.316836i | 0.987372 | + | 0.158418i | \(0.0506393\pi\) | ||||
−0.987372 | + | 0.158418i | \(0.949361\pi\) | |||||||
\(972\) | − | 871.637i | − | 0.896746i | ||||||
\(973\) | 1197.58 | 1.23081 | ||||||||
\(974\) | 55.2994 | 0.0567756 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −342.894 | −0.351326 | ||||||||
\(977\) | 264.741i | 0.270974i | 0.990779 | + | 0.135487i | \(0.0432598\pi\) | ||||
−0.990779 | + | 0.135487i | \(0.956740\pi\) | |||||||
\(978\) | 862.943 | 0.882355 | ||||||||
\(979\) | − | 28.1670i | − | 0.0287712i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 107.835i | − | 0.109924i | ||||||
\(982\) | − | 649.743i | − | 0.661652i | ||||||
\(983\) | − | 383.178i | − | 0.389805i | −0.980823 | − | 0.194902i | \(-0.937561\pi\) | ||
0.980823 | − | 0.194902i | \(-0.0624390\pi\) | |||||||
\(984\) | 23.2015i | 0.0235787i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2420.56 | −2.45493 | ||||||||
\(987\) | 42.4091i | 0.0429676i | ||||||||
\(988\) | −1325.98 | − | 278.058i | −1.34208 | − | 0.281435i | ||||
\(989\) | 297.183 | 0.300488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1692.42i | − | 1.70779i | −0.520445 | − | 0.853895i | \(-0.674234\pi\) | ||
0.520445 | − | 0.853895i | \(-0.325766\pi\) | |||||||
\(992\) | −1175.12 | −1.18459 | ||||||||
\(993\) | −370.701 | −0.373315 | ||||||||
\(994\) | 1872.20 | 1.88350 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 187.050i | 0.187801i | ||||||||
\(997\) | 968.728 | 0.971643 | 0.485822 | − | 0.874058i | \(-0.338520\pi\) | ||||
0.485822 | + | 0.874058i | \(0.338520\pi\) | |||||||
\(998\) | 2306.16i | 2.31078i | ||||||||
\(999\) | 916.617 | 0.917535 |
(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 | 475.3.c.f.151.1 | 8 | ||
5.2 | odd | 4 | 95.3.d.d.94.8 | yes | 8 | ||
5.3 | odd | 4 | 95.3.d.d.94.1 | ✓ | 8 | ||
5.4 | even | 2 | inner | 475.3.c.f.151.8 | 8 | ||
15.2 | even | 4 | 855.3.g.g.379.1 | 8 | |||
15.8 | even | 4 | 855.3.g.g.379.8 | 8 | |||
19.18 | odd | 2 | inner | 475.3.c.f.151.7 | 8 | ||
95.18 | even | 4 | 95.3.d.d.94.7 | yes | 8 | ||
95.37 | even | 4 | 95.3.d.d.94.2 | yes | 8 | ||
95.94 | odd | 2 | inner | 475.3.c.f.151.2 | 8 | ||
285.113 | odd | 4 | 855.3.g.g.379.2 | 8 | |||
285.227 | odd | 4 | 855.3.g.g.379.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.3.d.d.94.1 | ✓ | 8 | 5.3 | odd | 4 | ||
95.3.d.d.94.2 | yes | 8 | 95.37 | even | 4 | ||
95.3.d.d.94.7 | yes | 8 | 95.18 | even | 4 | ||
95.3.d.d.94.8 | yes | 8 | 5.2 | odd | 4 | ||
475.3.c.f.151.1 | 8 | 1.1 | even | 1 | trivial | ||
475.3.c.f.151.2 | 8 | 95.94 | odd | 2 | inner | ||
475.3.c.f.151.7 | 8 | 19.18 | odd | 2 | inner | ||
475.3.c.f.151.8 | 8 | 5.4 | even | 2 | inner | ||
855.3.g.g.379.1 | 8 | 15.2 | even | 4 | |||
855.3.g.g.379.2 | 8 | 285.113 | odd | 4 | |||
855.3.g.g.379.7 | 8 | 285.227 | odd | 4 | |||
855.3.g.g.379.8 | 8 | 15.8 | even | 4 |