Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + \cdots + 33124 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.14 | ||
Root | \(1.20711 + 3.39361i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.e.601.10 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −1.57881 | + | 6.81963i | −0.225545 | + | 0.974233i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.15965 | −0.741786 | −0.370893 | − | 0.928676i | \(-0.620948\pi\) | ||||
−0.370893 | + | 0.928676i | \(0.620948\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 14.6064i | − | 1.12357i | −0.827284 | − | 0.561785i | \(-0.810115\pi\) | ||
0.827284 | − | 0.561785i | \(-0.189885\pi\) | |||||||
\(14\) | −2.23278 | + | 9.64441i | −0.159484 | + | 0.688887i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 5.81421i | 0.342012i | 0.985270 | + | 0.171006i | \(0.0547018\pi\) | ||||
−0.985270 | + | 0.171006i | \(0.945298\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 33.7736i | 1.77756i | 0.458337 | + | 0.888778i | \(0.348445\pi\) | ||||
−0.458337 | + | 0.888778i | \(0.651555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.8119 | − | 2.73459i | −0.562474 | − | 0.130218i | ||||
\(22\) | −11.5395 | −0.524522 | ||||||||
\(23\) | −37.2576 | −1.61989 | −0.809947 | − | 0.586503i | \(-0.800504\pi\) | ||||
−0.809947 | + | 0.586503i | \(0.800504\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 20.6566i | − | 0.794483i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −3.15763 | + | 13.6393i | −0.112772 | + | 0.487116i | ||||
\(29\) | 9.25305 | 0.319071 | 0.159535 | − | 0.987192i | \(-0.449000\pi\) | ||||
0.159535 | + | 0.987192i | \(0.449000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.2558i | 0.621154i | 0.950548 | + | 0.310577i | \(0.100522\pi\) | ||||
−0.950548 | + | 0.310577i | \(0.899478\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 14.1329i | − | 0.428270i | ||||||
\(34\) | 8.22253i | 0.241839i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −63.4350 | −1.71446 | −0.857230 | − | 0.514933i | \(-0.827817\pi\) | ||||
−0.857230 | + | 0.514933i | \(0.827817\pi\) | |||||||
\(38\) | 47.7631i | 1.25692i | ||||||||
\(39\) | 25.2990 | 0.648693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.25880i | − | 0.201434i | −0.994915 | − | 0.100717i | \(-0.967886\pi\) | ||
0.994915 | − | 0.100717i | \(-0.0321137\pi\) | |||||||
\(42\) | −16.7046 | − | 3.86729i | −0.397729 | − | 0.0920783i | ||||
\(43\) | 42.0893 | 0.978822 | 0.489411 | − | 0.872053i | \(-0.337212\pi\) | ||||
0.489411 | + | 0.872053i | \(0.337212\pi\) | |||||||
\(44\) | −16.3193 | −0.370893 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −52.6901 | −1.14544 | ||||||||
\(47\) | 23.3380i | 0.496552i | 0.968689 | + | 0.248276i | \(0.0798640\pi\) | ||||
−0.968689 | + | 0.248276i | \(0.920136\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −44.0147 | − | 21.5339i | −0.898259 | − | 0.439466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0705 | −0.197461 | ||||||||
\(52\) | − | 29.2128i | − | 0.561785i | ||||||
\(53\) | −71.3497 | −1.34622 | −0.673110 | − | 0.739542i | \(-0.735042\pi\) | ||||
−0.673110 | + | 0.739542i | \(0.735042\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.46556 | + | 19.2888i | −0.0797422 | + | 0.344443i | ||||
\(57\) | −58.4976 | −1.02627 | ||||||||
\(58\) | 13.0858 | 0.225617 | ||||||||
\(59\) | − | 42.9350i | − | 0.727712i | −0.931455 | − | 0.363856i | \(-0.881460\pi\) | ||
0.931455 | − | 0.363856i | \(-0.118540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.2864i | 0.562072i | 0.959697 | + | 0.281036i | \(0.0906781\pi\) | ||||
−0.959697 | + | 0.281036i | \(0.909322\pi\) | |||||||
\(62\) | 27.2318i | 0.439222i | ||||||||
\(63\) | 4.73644 | − | 20.4589i | 0.0751816 | − | 0.324744i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 19.9870i | − | 0.302833i | ||||||
\(67\) | −4.99889 | −0.0746102 | −0.0373051 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373051 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(68\) | 11.6284i | 0.171006i | ||||||||
\(69\) | − | 64.5320i | − | 0.935246i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38.8120 | −0.546648 | −0.273324 | − | 0.961922i | \(-0.588123\pi\) | ||||
−0.273324 | + | 0.961922i | \(0.588123\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | − | 124.629i | − | 1.70725i | −0.520886 | − | 0.853626i | \(-0.674398\pi\) | ||
0.520886 | − | 0.853626i | \(-0.325602\pi\) | |||||||
\(74\) | −89.7107 | −1.21231 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 67.5472i | 0.888778i | ||||||||
\(77\) | 12.8826 | − | 55.6458i | 0.167306 | − | 0.722672i | ||||
\(78\) | 35.7782 | 0.458695 | ||||||||
\(79\) | 56.1842 | 0.711192 | 0.355596 | − | 0.934640i | \(-0.384278\pi\) | ||||
0.355596 | + | 0.934640i | \(0.384278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 11.6797i | − | 0.142435i | ||||||
\(83\) | 90.3980i | 1.08913i | 0.838718 | + | 0.544566i | \(0.183306\pi\) | ||||
−0.838718 | + | 0.544566i | \(0.816694\pi\) | |||||||
\(84\) | −23.6239 | − | 5.46917i | −0.281237 | − | 0.0651092i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 59.5233 | 0.692131 | ||||||||
\(87\) | 16.0267i | 0.184215i | ||||||||
\(88\) | −23.0790 | −0.262261 | ||||||||
\(89\) | 16.2289i | 0.182347i | 0.995835 | + | 0.0911736i | \(0.0290618\pi\) | ||||
−0.995835 | + | 0.0911736i | \(0.970938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 99.6102 | + | 23.0608i | 1.09462 | + | 0.253415i | ||||
\(92\) | −74.5151 | −0.809947 | ||||||||
\(93\) | −33.3520 | −0.358624 | ||||||||
\(94\) | 33.0048i | 0.351115i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 82.7605i | 0.853201i | 0.904440 | + | 0.426601i | \(0.140289\pi\) | ||||
−0.904440 | + | 0.426601i | \(0.859711\pi\) | |||||||
\(98\) | −62.2462 | − | 30.4535i | −0.635165 | − | 0.310750i | ||||
\(99\) | 24.4789 | 0.247262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 87.2055i | 0.863420i | 0.902012 | + | 0.431710i | \(0.142090\pi\) | ||||
−0.902012 | + | 0.431710i | \(0.857910\pi\) | |||||||
\(102\) | −14.2418 | −0.139626 | ||||||||
\(103\) | 187.567i | 1.82104i | 0.413462 | + | 0.910521i | \(0.364319\pi\) | ||||
−0.413462 | + | 0.910521i | \(0.635681\pi\) | |||||||
\(104\) | − | 41.3131i | − | 0.397242i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.904 | −0.951922 | ||||||||
\(107\) | −157.858 | −1.47531 | −0.737653 | − | 0.675180i | \(-0.764066\pi\) | ||||
−0.737653 | + | 0.675180i | \(0.764066\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 112.073 | 1.02819 | 0.514097 | − | 0.857732i | \(-0.328127\pi\) | ||||
0.514097 | + | 0.857732i | \(0.328127\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 109.873i | − | 0.989844i | ||||||
\(112\) | −6.31526 | + | 27.2785i | −0.0563862 | + | 0.243558i | ||||
\(113\) | 141.987 | 1.25653 | 0.628263 | − | 0.778001i | \(-0.283766\pi\) | ||||
0.628263 | + | 0.778001i | \(0.283766\pi\) | |||||||
\(114\) | −82.7280 | −0.725684 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.5061 | 0.159535 | ||||||||
\(117\) | 43.8192i | 0.374523i | ||||||||
\(118\) | − | 60.7192i | − | 0.514570i | ||||||
\(119\) | −39.6507 | − | 9.17955i | −0.333199 | − | 0.0771391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.4202 | −0.449754 | ||||||||
\(122\) | 48.4883i | 0.397445i | ||||||||
\(123\) | 14.3047 | 0.116298 | ||||||||
\(124\) | 38.5116i | 0.310577i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.69834 | − | 28.9332i | 0.0531614 | − | 0.229629i | ||||
\(127\) | −202.414 | −1.59381 | −0.796905 | − | 0.604104i | \(-0.793531\pi\) | ||||
−0.796905 | + | 0.604104i | \(0.793531\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 72.9008i | 0.565123i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 141.260i | − | 1.07832i | −0.842203 | − | 0.539160i | \(-0.818742\pi\) | ||
0.842203 | − | 0.539160i | \(-0.181258\pi\) | |||||||
\(132\) | − | 28.2658i | − | 0.214135i | ||||||
\(133\) | −230.323 | − | 53.3222i | −1.73175 | − | 0.400919i | ||||
\(134\) | −7.06949 | −0.0527574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.4451i | 0.120920i | ||||||||
\(137\) | 50.6430 | 0.369657 | 0.184829 | − | 0.982771i | \(-0.440827\pi\) | ||||
0.184829 | + | 0.982771i | \(0.440827\pi\) | |||||||
\(138\) | − | 91.2620i | − | 0.661319i | ||||||
\(139\) | 74.0256i | 0.532559i | 0.963896 | + | 0.266279i | \(0.0857943\pi\) | ||||
−0.963896 | + | 0.266279i | \(0.914206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −40.4225 | −0.286685 | ||||||||
\(142\) | −54.8885 | −0.386538 | ||||||||
\(143\) | 119.183i | 0.833448i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 176.253i | − | 1.20721i | ||||||
\(147\) | 37.2977 | − | 76.2357i | 0.253726 | − | 0.518610i | ||||
\(148\) | −126.870 | −0.857230 | ||||||||
\(149\) | 226.979 | 1.52335 | 0.761676 | − | 0.647958i | \(-0.224377\pi\) | ||||
0.761676 | + | 0.647958i | \(0.224377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 294.426 | 1.94984 | 0.974920 | − | 0.222558i | \(-0.0714406\pi\) | ||||
0.974920 | + | 0.222558i | \(0.0714406\pi\) | |||||||
\(152\) | 95.5261i | 0.628461i | ||||||||
\(153\) | − | 17.4426i | − | 0.114004i | ||||||
\(154\) | 18.2187 | − | 78.6950i | 0.118303 | − | 0.511006i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 50.5981 | 0.324346 | ||||||||
\(157\) | − | 65.8596i | − | 0.419488i | −0.977756 | − | 0.209744i | \(-0.932737\pi\) | ||
0.977756 | − | 0.209744i | \(-0.0672630\pi\) | |||||||
\(158\) | 79.4564 | 0.502889 | ||||||||
\(159\) | − | 123.581i | − | 0.777241i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 58.8227 | − | 254.083i | 0.365359 | − | 1.57815i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 28.2075 | 0.173052 | 0.0865260 | − | 0.996250i | \(-0.472423\pi\) | ||||
0.0865260 | + | 0.996250i | \(0.472423\pi\) | |||||||
\(164\) | − | 16.5176i | − | 0.100717i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 127.842i | 0.770133i | ||||||||
\(167\) | 128.461i | 0.769227i | 0.923078 | + | 0.384614i | \(0.125665\pi\) | ||||
−0.923078 | + | 0.384614i | \(0.874335\pi\) | |||||||
\(168\) | −33.4092 | − | 7.73458i | −0.198864 | − | 0.0460392i | ||||
\(169\) | −44.3469 | −0.262408 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 101.321i | − | 0.592519i | ||||||
\(172\) | 84.1786 | 0.489411 | ||||||||
\(173\) | − | 112.446i | − | 0.649976i | −0.945718 | − | 0.324988i | \(-0.894640\pi\) | ||
0.945718 | − | 0.324988i | \(-0.105360\pi\) | |||||||
\(174\) | 22.6652i | 0.130260i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −32.6386 | −0.185446 | ||||||||
\(177\) | 74.3656 | 0.420144 | ||||||||
\(178\) | 22.9511i | 0.128939i | ||||||||
\(179\) | 68.9019 | 0.384927 | 0.192464 | − | 0.981304i | \(-0.438352\pi\) | ||||
0.192464 | + | 0.981304i | \(0.438352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.537i | 0.920094i | 0.887895 | + | 0.460047i | \(0.152167\pi\) | ||||
−0.887895 | + | 0.460047i | \(0.847833\pi\) | |||||||
\(182\) | 140.870 | + | 32.6129i | 0.774012 | + | 0.179192i | ||||
\(183\) | −59.3858 | −0.324513 | ||||||||
\(184\) | −105.380 | −0.572719 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −47.1668 | −0.253585 | ||||||||
\(187\) | − | 47.4419i | − | 0.253700i | ||||||
\(188\) | 46.6759i | 0.248276i | ||||||||
\(189\) | 35.4358 | + | 8.20376i | 0.187491 | + | 0.0434061i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −148.289 | −0.776382 | −0.388191 | − | 0.921579i | \(-0.626900\pi\) | ||||
−0.388191 | + | 0.921579i | \(0.626900\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −35.1886 | −0.182324 | −0.0911622 | − | 0.995836i | \(-0.529058\pi\) | ||||
−0.0911622 | + | 0.995836i | \(0.529058\pi\) | |||||||
\(194\) | 117.041i | 0.603304i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −88.0294 | − | 43.0677i | −0.449130 | − | 0.219733i | ||||
\(197\) | −193.634 | −0.982915 | −0.491457 | − | 0.870902i | \(-0.663536\pi\) | ||||
−0.491457 | + | 0.870902i | \(0.663536\pi\) | |||||||
\(198\) | 34.6184 | 0.174841 | ||||||||
\(199\) | 181.838i | 0.913759i | 0.889529 | + | 0.456880i | \(0.151033\pi\) | ||||
−0.889529 | + | 0.456880i | \(0.848967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.65832i | − | 0.0430762i | ||||||
\(202\) | 123.327i | 0.610530i | ||||||||
\(203\) | −14.6088 | + | 63.1023i | −0.0719647 | + | 0.310849i | ||||
\(204\) | −20.1410 | −0.0987304 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 265.260i | 1.28767i | ||||||||
\(207\) | 111.773 | 0.539965 | ||||||||
\(208\) | − | 58.4256i | − | 0.280892i | ||||||
\(209\) | − | 275.580i | − | 1.31857i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 175.914 | 0.833717 | 0.416859 | − | 0.908971i | \(-0.363131\pi\) | ||||
0.416859 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(212\) | −142.699 | −0.673110 | ||||||||
\(213\) | − | 67.2244i | − | 0.315607i | ||||||
\(214\) | −223.244 | −1.04320 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −131.317 | − | 30.4013i | −0.605149 | − | 0.140098i | ||||
\(218\) | 158.495 | 0.727042 | ||||||||
\(219\) | 215.864 | 0.985683 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 84.9246 | 0.384274 | ||||||||
\(222\) | − | 155.384i | − | 0.699926i | ||||||
\(223\) | − | 20.5675i | − | 0.0922308i | −0.998936 | − | 0.0461154i | \(-0.985316\pi\) | ||
0.998936 | − | 0.0461154i | \(-0.0146842\pi\) | |||||||
\(224\) | −8.93112 | + | 38.5776i | −0.0398711 | + | 0.172222i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 200.801 | 0.888498 | ||||||||
\(227\) | − | 414.087i | − | 1.82417i | −0.410001 | − | 0.912085i | \(-0.634472\pi\) | ||
0.410001 | − | 0.912085i | \(-0.365528\pi\) | |||||||
\(228\) | −116.995 | −0.513136 | ||||||||
\(229\) | 195.520i | 0.853799i | 0.904299 | + | 0.426899i | \(0.140394\pi\) | ||||
−0.904299 | + | 0.426899i | \(0.859606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 96.3813 | + | 22.3133i | 0.417235 | + | 0.0965942i | ||||
\(232\) | 26.1716 | 0.112808 | ||||||||
\(233\) | −81.3006 | −0.348930 | −0.174465 | − | 0.984663i | \(-0.555820\pi\) | ||||
−0.174465 | + | 0.984663i | \(0.555820\pi\) | |||||||
\(234\) | 61.9697i | 0.264828i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 85.8700i | − | 0.363856i | ||||||
\(237\) | 97.3138i | 0.410607i | ||||||||
\(238\) | −56.0746 | − | 12.9818i | −0.235608 | − | 0.0545456i | ||||
\(239\) | 249.265 | 1.04295 | 0.521475 | − | 0.853267i | \(-0.325382\pi\) | ||||
0.521475 | + | 0.853267i | \(0.325382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 262.343i | 1.08856i | 0.838904 | + | 0.544280i | \(0.183197\pi\) | ||||
−0.838904 | + | 0.544280i | \(0.816803\pi\) | |||||||
\(242\) | −76.9618 | −0.318024 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 68.5728i | 0.281036i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 20.2298 | 0.0822351 | ||||||||
\(247\) | 493.310 | 1.99721 | ||||||||
\(248\) | 54.4636i | 0.219611i | ||||||||
\(249\) | −156.574 | −0.628811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 141.917i | 0.565406i | 0.959208 | + | 0.282703i | \(0.0912310\pi\) | ||||
−0.959208 | + | 0.282703i | \(0.908769\pi\) | |||||||
\(252\) | 9.47288 | − | 40.9178i | 0.0375908 | − | 0.162372i | ||||
\(253\) | 304.008 | 1.20161 | ||||||||
\(254\) | −286.257 | −1.12699 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 170.843i | 0.664757i | 0.943146 | + | 0.332379i | \(0.107851\pi\) | ||||
−0.943146 | + | 0.332379i | \(0.892149\pi\) | |||||||
\(258\) | 103.097i | 0.399602i | ||||||||
\(259\) | 100.152 | − | 432.604i | 0.386688 | − | 1.67028i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.7591 | −0.106357 | ||||||||
\(262\) | − | 199.772i | − | 0.762488i | ||||||
\(263\) | 383.417 | 1.45786 | 0.728930 | − | 0.684588i | \(-0.240018\pi\) | ||||
0.728930 | + | 0.684588i | \(0.240018\pi\) | |||||||
\(264\) | − | 39.9739i | − | 0.151416i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −325.726 | − | 75.4090i | −1.22454 | − | 0.283492i | ||||
\(267\) | −28.1093 | −0.105278 | ||||||||
\(268\) | −9.99777 | −0.0373051 | ||||||||
\(269\) | − | 154.512i | − | 0.574393i | −0.957872 | − | 0.287196i | \(-0.907277\pi\) | ||
0.957872 | − | 0.287196i | \(-0.0927232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 320.328i | 1.18202i | 0.806664 | + | 0.591010i | \(0.201271\pi\) | ||||
−0.806664 | + | 0.591010i | \(0.798729\pi\) | |||||||
\(272\) | 23.2568i | 0.0855030i | ||||||||
\(273\) | −39.9425 | + | 172.530i | −0.146309 | + | 0.631978i | ||||
\(274\) | 71.6200 | 0.261387 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 129.064i | − | 0.467623i | ||||||
\(277\) | 222.854 | 0.804526 | 0.402263 | − | 0.915524i | \(-0.368224\pi\) | ||||
0.402263 | + | 0.915524i | \(0.368224\pi\) | |||||||
\(278\) | 104.688i | 0.376576i | ||||||||
\(279\) | − | 57.7673i | − | 0.207051i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 218.973 | 0.779263 | 0.389631 | − | 0.920971i | \(-0.372602\pi\) | ||||
0.389631 | + | 0.920971i | \(0.372602\pi\) | |||||||
\(282\) | −57.1661 | −0.202717 | ||||||||
\(283\) | − | 36.3957i | − | 0.128607i | −0.997930 | − | 0.0643034i | \(-0.979517\pi\) | ||
0.997930 | − | 0.0643034i | \(-0.0204825\pi\) | |||||||
\(284\) | −77.6240 | −0.273324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 168.550i | 0.589337i | ||||||||
\(287\) | 56.3219 | + | 13.0391i | 0.196244 | + | 0.0454324i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 255.195 | 0.883028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −143.345 | −0.492596 | ||||||||
\(292\) | − | 249.259i | − | 0.853626i | ||||||
\(293\) | 168.440i | 0.574882i | 0.957798 | + | 0.287441i | \(0.0928045\pi\) | ||||
−0.957798 | + | 0.287441i | \(0.907195\pi\) | |||||||
\(294\) | 52.7470 | − | 107.814i | 0.179411 | − | 0.366713i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −179.421 | −0.606153 | ||||||||
\(297\) | 42.3988i | 0.142757i | ||||||||
\(298\) | 320.997 | 1.07717 | ||||||||
\(299\) | 544.199i | 1.82006i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −66.4512 | + | 287.034i | −0.220768 | + | 0.953600i | ||||
\(302\) | 416.381 | 1.37874 | ||||||||
\(303\) | −151.044 | −0.498496 | ||||||||
\(304\) | 135.094i | 0.444389i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 24.6676i | − | 0.0806130i | ||||||
\(307\) | 223.400i | 0.727688i | 0.931460 | + | 0.363844i | \(0.118536\pi\) | ||||
−0.931460 | + | 0.363844i | \(0.881464\pi\) | |||||||
\(308\) | 25.7651 | − | 111.292i | 0.0836530 | − | 0.361336i | ||||
\(309\) | −324.876 | −1.05138 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 46.0396i | − | 0.148037i | −0.997257 | − | 0.0740186i | \(-0.976418\pi\) | ||
0.997257 | − | 0.0740186i | \(-0.0235824\pi\) | |||||||
\(312\) | 71.5565 | 0.229348 | ||||||||
\(313\) | 80.0375i | 0.255711i | 0.991793 | + | 0.127855i | \(0.0408094\pi\) | ||||
−0.991793 | + | 0.127855i | \(0.959191\pi\) | |||||||
\(314\) | − | 93.1395i | − | 0.296623i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 112.368 | 0.355596 | ||||||||
\(317\) | 185.237 | 0.584343 | 0.292171 | − | 0.956366i | \(-0.405622\pi\) | ||||
0.292171 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(318\) | − | 174.770i | − | 0.549592i | ||||||
\(319\) | −75.5016 | −0.236682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 273.418i | − | 0.851768i | ||||||
\(322\) | 83.1879 | − | 359.327i | 0.258348 | − | 1.11592i | ||||
\(323\) | −196.367 | −0.607946 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.8914 | 0.122366 | ||||||||
\(327\) | 194.116i | 0.593628i | ||||||||
\(328\) | − | 23.3594i | − | 0.0712177i | ||||||
\(329\) | −159.156 | − | 36.8463i | −0.483757 | − | 0.111995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 61.4686 | 0.185706 | 0.0928529 | − | 0.995680i | \(-0.470401\pi\) | ||||
0.0928529 | + | 0.995680i | \(0.470401\pi\) | |||||||
\(332\) | 180.796i | 0.544566i | ||||||||
\(333\) | 190.305 | 0.571487 | ||||||||
\(334\) | 181.671i | 0.543926i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −47.2478 | − | 10.9383i | −0.140618 | − | 0.0325546i | ||||
\(337\) | 656.501 | 1.94807 | 0.974037 | − | 0.226387i | \(-0.0726914\pi\) | ||||
0.974037 | + | 0.226387i | \(0.0726914\pi\) | |||||||
\(338\) | −62.7160 | −0.185550 | ||||||||
\(339\) | 245.929i | 0.725456i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 157.120i | − | 0.460764i | ||||||
\(342\) | − | 143.289i | − | 0.418974i | ||||||
\(343\) | 216.344 | − | 266.166i | 0.630740 | − | 0.775994i | ||||
\(344\) | 119.047 | 0.346066 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 159.022i | − | 0.459603i | ||||||
\(347\) | 321.323 | 0.926002 | 0.463001 | − | 0.886358i | \(-0.346773\pi\) | ||||
0.463001 | + | 0.886358i | \(0.346773\pi\) | |||||||
\(348\) | 32.0535i | 0.0921077i | ||||||||
\(349\) | − | 185.135i | − | 0.530474i | −0.964183 | − | 0.265237i | \(-0.914550\pi\) | ||
0.964183 | − | 0.265237i | \(-0.0854501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −75.8971 | −0.216231 | ||||||||
\(352\) | −46.1579 | −0.131130 | ||||||||
\(353\) | − | 597.338i | − | 1.69218i | −0.533043 | − | 0.846088i | \(-0.678952\pi\) | ||
0.533043 | − | 0.846088i | \(-0.321048\pi\) | |||||||
\(354\) | 105.169 | 0.297087 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 32.4578i | 0.0911736i | ||||||||
\(357\) | 15.8995 | − | 68.6771i | 0.0445363 | − | 0.192373i | ||||
\(358\) | 97.4421 | 0.272185 | ||||||||
\(359\) | −239.446 | −0.666982 | −0.333491 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333491 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −779.655 | −2.15971 | ||||||||
\(362\) | 235.519i | 0.650604i | ||||||||
\(363\) | − | 94.2585i | − | 0.259665i | ||||||
\(364\) | 199.220 | + | 46.1216i | 0.547309 | + | 0.126708i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −83.9842 | −0.229465 | ||||||||
\(367\) | 398.743i | 1.08649i | 0.839573 | + | 0.543246i | \(0.182805\pi\) | ||||
−0.839573 | + | 0.543246i | \(0.817195\pi\) | |||||||
\(368\) | −149.030 | −0.404973 | ||||||||
\(369\) | 24.7764i | 0.0671447i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 112.648 | − | 486.578i | 0.303633 | − | 1.31153i | ||||
\(372\) | −66.7040 | −0.179312 | ||||||||
\(373\) | −34.7064 | −0.0930466 | −0.0465233 | − | 0.998917i | \(-0.514814\pi\) | ||||
−0.0465233 | + | 0.998917i | \(0.514814\pi\) | |||||||
\(374\) | − | 67.0929i | − | 0.179393i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 66.0097i | 0.175558i | ||||||||
\(377\) | − | 135.154i | − | 0.358498i | ||||||
\(378\) | 50.1138 | + | 11.6019i | 0.132576 | + | 0.0306928i | ||||
\(379\) | 109.217 | 0.288172 | 0.144086 | − | 0.989565i | \(-0.453976\pi\) | ||||
0.144086 | + | 0.989565i | \(0.453976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 350.591i | − | 0.920187i | ||||||
\(382\) | −209.712 | −0.548985 | ||||||||
\(383\) | − | 336.420i | − | 0.878381i | −0.898394 | − | 0.439191i | \(-0.855265\pi\) | ||
0.898394 | − | 0.439191i | \(-0.144735\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −49.7642 | −0.128923 | ||||||||
\(387\) | −126.268 | −0.326274 | ||||||||
\(388\) | 165.521i | 0.426601i | ||||||||
\(389\) | 311.173 | 0.799930 | 0.399965 | − | 0.916530i | \(-0.369022\pi\) | ||||
0.399965 | + | 0.916530i | \(0.369022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 216.623i | − | 0.554023i | ||||||
\(392\) | −124.492 | − | 60.9069i | −0.317583 | − | 0.155375i | ||||
\(393\) | 244.669 | 0.622568 | ||||||||
\(394\) | −273.840 | −0.695026 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 48.9579 | 0.123631 | ||||||||
\(397\) | − | 41.2679i | − | 0.103949i | −0.998648 | − | 0.0519747i | \(-0.983448\pi\) | ||
0.998648 | − | 0.0519747i | \(-0.0165515\pi\) | |||||||
\(398\) | 257.158i | 0.646125i | ||||||||
\(399\) | 92.3568 | − | 398.932i | 0.231471 | − | 0.999829i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −495.642 | −1.23601 | −0.618007 | − | 0.786173i | \(-0.712060\pi\) | ||||
−0.618007 | + | 0.786173i | \(0.712060\pi\) | |||||||
\(402\) | − | 12.2447i | − | 0.0304595i | ||||||
\(403\) | 281.258 | 0.697910 | ||||||||
\(404\) | 174.411i | 0.431710i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.6600 | + | 89.2402i | −0.0508867 | + | 0.219803i | ||||
\(407\) | 517.608 | 1.27176 | ||||||||
\(408\) | −28.4837 | −0.0698129 | ||||||||
\(409\) | 359.920i | 0.880001i | 0.897998 | + | 0.440000i | \(0.145022\pi\) | ||||
−0.897998 | + | 0.440000i | \(0.854978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 87.7163i | 0.213422i | ||||||||
\(412\) | 375.135i | 0.910521i | ||||||||
\(413\) | 292.801 | + | 67.7863i | 0.708960 | + | 0.164132i | ||||
\(414\) | 158.070 | 0.381813 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 82.6263i | − | 0.198621i | ||||||
\(417\) | −128.216 | −0.307473 | ||||||||
\(418\) | − | 389.730i | − | 0.932367i | ||||||
\(419\) | − | 482.910i | − | 1.15253i | −0.817263 | − | 0.576265i | \(-0.804510\pi\) | ||
0.817263 | − | 0.576265i | \(-0.195490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −523.520 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(422\) | 248.780 | 0.589527 | ||||||||
\(423\) | − | 70.0139i | − | 0.165517i | ||||||
\(424\) | −201.807 | −0.475961 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 95.0696i | − | 0.223168i | ||||||
\(427\) | −233.821 | − | 54.1319i | −0.547589 | − | 0.126773i | ||||
\(428\) | −315.715 | −0.737653 | ||||||||
\(429\) | −206.431 | −0.481191 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 517.027 | 1.19960 | 0.599799 | − | 0.800150i | \(-0.295247\pi\) | ||||
0.599799 | + | 0.800150i | \(0.295247\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | 567.712i | 1.31111i | 0.755146 | + | 0.655557i | \(0.227566\pi\) | ||||
−0.755146 | + | 0.655557i | \(0.772434\pi\) | |||||||
\(434\) | −185.711 | − | 42.9939i | −0.427905 | − | 0.0990644i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 224.146 | 0.514097 | ||||||||
\(437\) | − | 1258.32i | − | 2.87945i | ||||||
\(438\) | 305.279 | 0.696983 | ||||||||
\(439\) | 622.875i | 1.41885i | 0.704781 | + | 0.709425i | \(0.251045\pi\) | ||||
−0.704781 | + | 0.709425i | \(0.748955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 132.044 | + | 64.6016i | 0.299420 | + | 0.146489i | ||||
\(442\) | 120.102 | 0.271723 | ||||||||
\(443\) | −476.699 | −1.07607 | −0.538035 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538035 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(444\) | − | 219.745i | − | 0.494922i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 29.0868i | − | 0.0652170i | ||||||
\(447\) | 393.140i | 0.879507i | ||||||||
\(448\) | −12.6305 | + | 54.5570i | −0.0281931 | + | 0.121779i | ||||
\(449\) | −861.931 | −1.91967 | −0.959834 | − | 0.280570i | \(-0.909477\pi\) | ||||
−0.959834 | + | 0.280570i | \(0.909477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.3889i | 0.149421i | ||||||||
\(452\) | 283.975 | 0.628263 | ||||||||
\(453\) | 509.960i | 1.12574i | ||||||||
\(454\) | − | 585.607i | − | 1.28988i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −165.456 | −0.362842 | ||||||||
\(457\) | −27.5401 | −0.0602629 | −0.0301314 | − | 0.999546i | \(-0.509593\pi\) | ||||
−0.0301314 | + | 0.999546i | \(0.509593\pi\) | |||||||
\(458\) | 276.507i | 0.603727i | ||||||||
\(459\) | 30.2115 | 0.0658203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 378.183i | − | 0.820353i | −0.912006 | − | 0.410176i | \(-0.865467\pi\) | ||
0.912006 | − | 0.410176i | \(-0.134533\pi\) | |||||||
\(462\) | 136.304 | + | 31.5557i | 0.295030 | + | 0.0683024i | ||||
\(463\) | −724.994 | −1.56586 | −0.782931 | − | 0.622108i | \(-0.786276\pi\) | ||||
−0.782931 | + | 0.622108i | \(0.786276\pi\) | |||||||
\(464\) | 37.0122 | 0.0797676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −114.976 | −0.246731 | ||||||||
\(467\) | − | 371.451i | − | 0.795398i | −0.917516 | − | 0.397699i | \(-0.869809\pi\) | ||
0.917516 | − | 0.397699i | \(-0.130191\pi\) | |||||||
\(468\) | 87.6384i | 0.187262i | ||||||||
\(469\) | 7.89231 | − | 34.0905i | 0.0168280 | − | 0.0726877i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 114.072 | 0.242191 | ||||||||
\(472\) | − | 121.438i | − | 0.257285i | ||||||
\(473\) | −343.434 | −0.726076 | ||||||||
\(474\) | 137.623i | 0.290343i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −79.3015 | − | 18.3591i | −0.166600 | − | 0.0385695i | ||||
\(477\) | 214.049 | 0.448740 | ||||||||
\(478\) | 352.514 | 0.737477 | ||||||||
\(479\) | − | 860.650i | − | 1.79677i | −0.439214 | − | 0.898383i | \(-0.644743\pi\) | ||
0.439214 | − | 0.898383i | \(-0.355257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 926.558i | 1.92632i | ||||||||
\(482\) | 371.009i | 0.769728i | ||||||||
\(483\) | 440.084 | + | 101.884i | 0.911147 | + | 0.210940i | ||||
\(484\) | −108.840 | −0.224877 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −887.173 | −1.82171 | −0.910855 | − | 0.412726i | \(-0.864577\pi\) | ||||
−0.910855 | + | 0.412726i | \(0.864577\pi\) | |||||||
\(488\) | 96.9766i | 0.198723i | ||||||||
\(489\) | 48.8568i | 0.0999116i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −50.1823 | −0.102204 | −0.0511021 | − | 0.998693i | \(-0.516273\pi\) | ||||
−0.0511021 | + | 0.998693i | \(0.516273\pi\) | |||||||
\(492\) | 28.6093 | 0.0581490 | ||||||||
\(493\) | 53.7991i | 0.109126i | ||||||||
\(494\) | 697.646 | 1.41224 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 77.0231i | 0.155289i | ||||||||
\(497\) | 61.2769 | − | 264.683i | 0.123294 | − | 0.532562i | ||||
\(498\) | −221.429 | −0.444636 | ||||||||
\(499\) | −160.443 | −0.321529 | −0.160765 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160765 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −222.501 | −0.444113 | ||||||||
\(502\) | 200.701i | 0.399802i | ||||||||
\(503\) | − | 742.042i | − | 1.47523i | −0.675220 | − | 0.737616i | \(-0.735951\pi\) | ||
0.675220 | − | 0.737616i | \(-0.264049\pi\) | |||||||
\(504\) | 13.3967 | − | 57.8665i | 0.0265807 | − | 0.114814i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 429.933 | 0.849670 | ||||||||
\(507\) | − | 76.8111i | − | 0.151501i | ||||||
\(508\) | −404.828 | −0.796905 | ||||||||
\(509\) | 978.447i | 1.92229i | 0.276038 | + | 0.961147i | \(0.410979\pi\) | ||||
−0.276038 | + | 0.961147i | \(0.589021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 849.927 | + | 196.767i | 1.66326 | + | 0.385062i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 175.493 | 0.342091 | ||||||||
\(514\) | 241.608i | 0.470054i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 145.802i | 0.282561i | ||||||||
\(517\) | − | 190.429i | − | 0.368335i | ||||||
\(518\) | 141.637 | − | 611.794i | 0.273430 | − | 1.18107i | ||||
\(519\) | 194.762 | 0.375264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 575.650i | 1.10489i | 0.833548 | + | 0.552447i | \(0.186306\pi\) | ||||
−0.833548 | + | 0.552447i | \(0.813694\pi\) | |||||||
\(522\) | −39.2573 | −0.0752056 | ||||||||
\(523\) | 339.090i | 0.648355i | 0.945996 | + | 0.324178i | \(0.105088\pi\) | ||||
−0.945996 | + | 0.324178i | \(0.894912\pi\) | |||||||
\(524\) | − | 282.520i | − | 0.539160i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 542.234 | 1.03086 | ||||||||
\(527\) | −111.957 | −0.212442 | ||||||||
\(528\) | − | 56.5317i | − | 0.107068i | ||||||
\(529\) | 859.125 | 1.62406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 128.805i | 0.242571i | ||||||||
\(532\) | −460.647 | − | 106.644i | −0.865877 | − | 0.200459i | ||||
\(533\) | −120.631 | −0.226325 | ||||||||
\(534\) | −39.7525 | −0.0744429 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.1390 | −0.0263787 | ||||||||
\(537\) | 119.342i | 0.222238i | ||||||||
\(538\) | − | 218.512i | − | 0.406157i | ||||||
\(539\) | 359.144 | + | 175.709i | 0.666316 | + | 0.325990i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8638 | 0.0662916 | 0.0331458 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331458 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(542\) | 453.012i | 0.835815i | ||||||||
\(543\) | −288.450 | −0.531216 | ||||||||
\(544\) | 32.8901i | 0.0604598i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −56.4872 | + | 243.994i | −0.103456 | + | 0.446876i | ||||
\(547\) | 700.845 | 1.28125 | 0.640626 | − | 0.767853i | \(-0.278675\pi\) | ||||
0.640626 | + | 0.767853i | \(0.278675\pi\) | |||||||
\(548\) | 101.286 | 0.184829 | ||||||||
\(549\) | − | 102.859i | − | 0.187357i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 312.508i | 0.567166i | ||||||||
\(552\) | − | 182.524i | − | 0.330659i | ||||||
\(553\) | −88.7044 | + | 383.155i | −0.160406 | + | 0.692867i | ||||
\(554\) | 315.163 | 0.568886 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 148.051i | 0.266279i | ||||||||
\(557\) | −639.349 | −1.14784 | −0.573922 | − | 0.818910i | \(-0.694579\pi\) | ||||
−0.573922 | + | 0.818910i | \(0.694579\pi\) | |||||||
\(558\) | − | 81.6954i | − | 0.146407i | ||||||
\(559\) | − | 614.773i | − | 1.09977i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 82.1717 | 0.146474 | ||||||||
\(562\) | 309.674 | 0.551022 | ||||||||
\(563\) | 227.519i | 0.404120i | 0.979373 | + | 0.202060i | \(0.0647636\pi\) | ||||
−0.979373 | + | 0.202060i | \(0.935236\pi\) | |||||||
\(564\) | −80.8450 | −0.143342 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 51.4713i | − | 0.0909387i | ||||||
\(567\) | −14.2093 | + | 61.3767i | −0.0250605 | + | 0.108248i | ||||
\(568\) | −109.777 | −0.193269 | ||||||||
\(569\) | −613.901 | −1.07891 | −0.539456 | − | 0.842014i | \(-0.681370\pi\) | ||||
−0.539456 | + | 0.842014i | \(0.681370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 366.674 | 0.642161 | 0.321081 | − | 0.947052i | \(-0.395954\pi\) | ||||
0.321081 | + | 0.947052i | \(0.395954\pi\) | |||||||
\(572\) | 238.366i | 0.416724i | ||||||||
\(573\) | − | 256.844i | − | 0.448244i | ||||||
\(574\) | 79.6513 | + | 18.4401i | 0.138765 | + | 0.0321256i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − | 62.1951i | − | 0.107790i | −0.998547 | − | 0.0538952i | \(-0.982836\pi\) | ||
0.998547 | − | 0.0538952i | \(-0.0171637\pi\) | |||||||
\(578\) | 360.900 | 0.624395 | ||||||||
\(579\) | − | 60.9485i | − | 0.105265i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −616.481 | − | 142.722i | −1.06107 | − | 0.245648i | ||||
\(582\) | −202.721 | −0.348318 | ||||||||
\(583\) | 582.188 | 0.998607 | ||||||||
\(584\) | − | 352.505i | − | 0.603605i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 238.211i | 0.406503i | ||||||||
\(587\) | − | 176.872i | − | 0.301315i | −0.988586 | − | 0.150658i | \(-0.951861\pi\) | ||
0.988586 | − | 0.150658i | \(-0.0481391\pi\) | |||||||
\(588\) | 74.5955 | − | 152.471i | 0.126863 | − | 0.259305i | ||||
\(589\) | −650.337 | −1.10414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 335.384i | − | 0.567486i | ||||||
\(592\) | −253.740 | −0.428615 | ||||||||
\(593\) | − | 154.878i | − | 0.261176i | −0.991437 | − | 0.130588i | \(-0.958313\pi\) | ||
0.991437 | − | 0.130588i | \(-0.0416866\pi\) | |||||||
\(594\) | 59.9609i | 0.100944i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 453.959 | 0.761676 | ||||||||
\(597\) | −314.953 | −0.527559 | ||||||||
\(598\) | 769.613i | 1.28698i | ||||||||
\(599\) | −900.825 | −1.50388 | −0.751940 | − | 0.659231i | \(-0.770882\pi\) | ||||
−0.751940 | + | 0.659231i | \(0.770882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 682.387i | − | 1.13542i | −0.823229 | − | 0.567710i | \(-0.807830\pi\) | ||
0.823229 | − | 0.567710i | \(-0.192170\pi\) | |||||||
\(602\) | −93.9762 | + | 405.927i | −0.156107 | + | 0.674297i | ||||
\(603\) | 14.9967 | 0.0248701 | ||||||||
\(604\) | 588.851 | 0.974920 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −213.609 | −0.352490 | ||||||||
\(607\) | 367.814i | 0.605954i | 0.952998 | + | 0.302977i | \(0.0979806\pi\) | ||||
−0.952998 | + | 0.302977i | \(0.902019\pi\) | |||||||
\(608\) | 191.052i | 0.314231i | ||||||||
\(609\) | −109.296 | − | 25.3032i | −0.179469 | − | 0.0415488i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 340.883 | 0.557911 | ||||||||
\(612\) | − | 34.8852i | − | 0.0570020i | ||||||
\(613\) | 117.271 | 0.191306 | 0.0956532 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956532 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(614\) | 315.936i | 0.514553i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.4374 | − | 157.390i | 0.0591516 | − | 0.255503i | ||||
\(617\) | −1070.18 | −1.73449 | −0.867245 | − | 0.497881i | \(-0.834112\pi\) | ||||
−0.867245 | + | 0.497881i | \(0.834112\pi\) | |||||||
\(618\) | −459.444 | −0.743438 | ||||||||
\(619\) | 532.192i | 0.859761i | 0.902886 | + | 0.429880i | \(0.141444\pi\) | ||||
−0.902886 | + | 0.429880i | \(0.858556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 193.596i | 0.311749i | ||||||||
\(622\) | − | 65.1098i | − | 0.104678i | ||||||
\(623\) | −110.675 | − | 25.6224i | −0.177649 | − | 0.0411275i | ||||
\(624\) | 101.196 | 0.162173 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 113.190i | 0.180815i | ||||||||
\(627\) | 477.319 | 0.761275 | ||||||||
\(628\) | − | 131.719i | − | 0.209744i | ||||||
\(629\) | − | 368.825i | − | 0.586366i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 472.933 | 0.749498 | 0.374749 | − | 0.927126i | \(-0.377729\pi\) | ||||
0.374749 | + | 0.927126i | \(0.377729\pi\) | |||||||
\(632\) | 158.913 | 0.251444 | ||||||||
\(633\) | 304.693i | 0.481347i | ||||||||
\(634\) | 261.964 | 0.413193 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 247.163i | − | 0.388620i | ||||||
\(637\) | −314.532 | + | 642.896i | −0.493771 | + | 1.00926i | ||||
\(638\) | −106.775 | −0.167359 | ||||||||
\(639\) | 116.436 | 0.182216 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −486.990 | −0.759734 | −0.379867 | − | 0.925041i | \(-0.624030\pi\) | ||||
−0.379867 | + | 0.925041i | \(0.624030\pi\) | |||||||
\(642\) | − | 386.671i | − | 0.602291i | ||||||
\(643\) | 111.425i | 0.173289i | 0.996239 | + | 0.0866447i | \(0.0276145\pi\) | ||||
−0.996239 | + | 0.0866447i | \(0.972386\pi\) | |||||||
\(644\) | 117.645 | − | 508.165i | 0.182679 | − | 0.789077i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −277.704 | −0.429883 | ||||||||
\(647\) | 737.696i | 1.14018i | 0.821583 | + | 0.570090i | \(0.193092\pi\) | ||||
−0.821583 | + | 0.570090i | \(0.806908\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 350.334i | 0.539806i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 52.6566 | − | 227.448i | 0.0808857 | − | 0.349383i | ||||
\(652\) | 56.4149 | 0.0865260 | ||||||||
\(653\) | 193.734 | 0.296682 | 0.148341 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148341 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(654\) | 274.522i | 0.419758i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 33.0352i | − | 0.0503585i | ||||||
\(657\) | 373.888i | 0.569084i | ||||||||
\(658\) | −225.081 | − | 52.1085i | −0.342068 | − | 0.0791923i | ||||
\(659\) | 823.339 | 1.24938 | 0.624688 | − | 0.780874i | \(-0.285226\pi\) | ||||
0.624688 | + | 0.780874i | \(0.285226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 657.833i | − | 0.995208i | −0.867404 | − | 0.497604i | \(-0.834213\pi\) | ||
0.867404 | − | 0.497604i | \(-0.165787\pi\) | |||||||
\(662\) | 86.9298 | 0.131314 | ||||||||
\(663\) | 147.094i | 0.221861i | ||||||||
\(664\) | 255.684i | 0.385066i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 269.132 | 0.404102 | ||||||||
\(667\) | −344.746 | −0.516860 | ||||||||
\(668\) | 256.922i | 0.384614i | ||||||||
\(669\) | 35.6239 | 0.0532495 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 279.765i | − | 0.416937i | ||||||
\(672\) | −66.8184 | − | 15.4692i | −0.0994322 | − | 0.0230196i | ||||
\(673\) | −727.300 | −1.08068 | −0.540342 | − | 0.841446i | \(-0.681705\pi\) | ||||
−0.540342 | + | 0.841446i | \(0.681705\pi\) | |||||||
\(674\) | 928.433 | 1.37750 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −88.6938 | −0.131204 | ||||||||
\(677\) | − | 385.964i | − | 0.570110i | −0.958511 | − | 0.285055i | \(-0.907988\pi\) | ||
0.958511 | − | 0.285055i | \(-0.0920118\pi\) | |||||||
\(678\) | 347.797i | 0.512975i | ||||||||
\(679\) | −564.396 | − | 130.663i | −0.831217 | − | 0.192435i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 717.219 | 1.05319 | ||||||||
\(682\) | − | 222.202i | − | 0.325809i | ||||||
\(683\) | 236.488 | 0.346249 | 0.173124 | − | 0.984900i | \(-0.444614\pi\) | ||||
0.173124 | + | 0.984900i | \(0.444614\pi\) | |||||||
\(684\) | − | 202.641i | − | 0.296259i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 305.957 | − | 376.415i | 0.446001 | − | 0.548711i | ||||
\(687\) | −338.650 | −0.492941 | ||||||||
\(688\) | 168.357 | 0.244705 | ||||||||
\(689\) | 1042.16i | 1.51257i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 337.426i | − | 0.488316i | −0.969735 | − | 0.244158i | \(-0.921488\pi\) | ||
0.969735 | − | 0.244158i | \(-0.0785116\pi\) | |||||||
\(692\) | − | 224.892i | − | 0.324988i | ||||||
\(693\) | −38.6477 | + | 166.937i | −0.0557687 | + | 0.240891i | ||||
\(694\) | 454.419 | 0.654782 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 45.3305i | 0.0651300i | ||||||||
\(697\) | 48.0184 | 0.0688929 | ||||||||
\(698\) | − | 261.821i | − | 0.375101i | ||||||
\(699\) | − | 140.817i | − | 0.201455i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 89.2192 | 0.127274 | 0.0636371 | − | 0.997973i | \(-0.479730\pi\) | ||||
0.0636371 | + | 0.997973i | \(0.479730\pi\) | |||||||
\(702\) | −107.335 | −0.152898 | ||||||||
\(703\) | − | 2142.43i | − | 3.04755i | ||||||
\(704\) | −65.2772 | −0.0927232 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 844.764i | − | 1.19655i | ||||||
\(707\) | −594.709 | − | 137.681i | −0.841172 | − | 0.194740i | ||||
\(708\) | 148.731 | 0.210072 | ||||||||
\(709\) | −569.646 | −0.803450 | −0.401725 | − | 0.915760i | \(-0.631589\pi\) | ||||
−0.401725 | + | 0.915760i | \(0.631589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −168.552 | −0.237064 | ||||||||
\(712\) | 45.9023i | 0.0644695i | ||||||||
\(713\) | − | 717.423i | − | 1.00620i | ||||||
\(714\) | 22.4852 | − | 97.1241i | 0.0314919 | − | 0.136028i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 137.804 | 0.192464 | ||||||||
\(717\) | 431.740i | 0.602147i | ||||||||
\(718\) | −338.628 | −0.471627 | ||||||||
\(719\) | 1261.33i | 1.75428i | 0.480233 | + | 0.877141i | \(0.340552\pi\) | ||||
−0.480233 | + | 0.877141i | \(0.659448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1279.14 | − | 296.134i | −1.77412 | − | 0.410727i | ||||
\(722\) | −1102.60 | −1.52714 | ||||||||
\(723\) | −454.391 | −0.628481 | ||||||||
\(724\) | 333.074i | 0.460047i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 133.302i | − | 0.183611i | ||||||
\(727\) | − | 307.746i | − | 0.423310i | −0.977344 | − | 0.211655i | \(-0.932115\pi\) | ||
0.977344 | − | 0.211655i | \(-0.0678852\pi\) | |||||||
\(728\) | 281.740 | + | 65.2258i | 0.387006 | + | 0.0895958i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 244.716i | 0.334769i | ||||||||
\(732\) | −118.772 | −0.162256 | ||||||||
\(733\) | 633.490i | 0.864243i | 0.901815 | + | 0.432121i | \(0.142235\pi\) | ||||
−0.901815 | + | 0.432121i | \(0.857765\pi\) | |||||||
\(734\) | 563.908i | 0.768266i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −210.761 | −0.286359 | ||||||||
\(737\) | 40.7891 | 0.0553448 | ||||||||
\(738\) | 35.0391i | 0.0474785i | ||||||||
\(739\) | −749.557 | −1.01428 | −0.507142 | − | 0.861862i | \(-0.669298\pi\) | ||||
−0.507142 | + | 0.861862i | \(0.669298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 854.439i | 1.15309i | ||||||||
\(742\) | 159.308 | − | 688.126i | 0.214701 | − | 0.927393i | ||||
\(743\) | −145.699 | −0.196095 | −0.0980476 | − | 0.995182i | \(-0.531260\pi\) | ||||
−0.0980476 | + | 0.995182i | \(0.531260\pi\) | |||||||
\(744\) | −94.3337 | −0.126793 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −49.0822 | −0.0657939 | ||||||||
\(747\) | − | 271.194i | − | 0.363044i | ||||||
\(748\) | − | 94.8837i | − | 0.126850i | ||||||
\(749\) | 249.228 | − | 1076.53i | 0.332748 | − | 1.43729i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 156.811 | 0.208803 | 0.104402 | − | 0.994535i | \(-0.466707\pi\) | ||||
0.104402 | + | 0.994535i | \(0.466707\pi\) | |||||||
\(752\) | 93.3518i | 0.124138i | ||||||||
\(753\) | −245.807 | −0.326437 | ||||||||
\(754\) | − | 191.136i | − | 0.253496i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 70.8717 | + | 16.4075i | 0.0937456 | + | 0.0217031i | ||||
\(757\) | −296.377 | −0.391515 | −0.195758 | − | 0.980652i | \(-0.562717\pi\) | ||||
−0.195758 | + | 0.980652i | \(0.562717\pi\) | |||||||
\(758\) | 154.457 | 0.203769 | ||||||||
\(759\) | 526.558i | 0.693752i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 312.747i | 0.410968i | 0.978660 | + | 0.205484i | \(0.0658769\pi\) | ||||
−0.978660 | + | 0.205484i | \(0.934123\pi\) | |||||||
\(762\) | − | 495.811i | − | 0.650670i | ||||||
\(763\) | −176.942 | + | 764.297i | −0.231904 | + | 1.00170i | ||||
\(764\) | −296.578 | −0.388191 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 475.770i | − | 0.621109i | ||||||
\(767\) | −627.125 | −0.817634 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 91.1460i | − | 0.118525i | −0.998242 | − | 0.0592627i | \(-0.981125\pi\) | ||
0.998242 | − | 0.0592627i | \(-0.0188750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −295.908 | −0.383798 | ||||||||
\(772\) | −70.3772 | −0.0911622 | ||||||||
\(773\) | − | 417.539i | − | 0.540154i | −0.962839 | − | 0.270077i | \(-0.912951\pi\) | ||
0.962839 | − | 0.270077i | \(-0.0870492\pi\) | |||||||
\(774\) | −178.570 | −0.230710 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 234.082i | 0.301652i | ||||||||
\(777\) | 749.291 | + | 173.469i | 0.964339 | + | 0.223254i | ||||
\(778\) | 440.065 | 0.565636 | ||||||||
\(779\) | 278.929 | 0.358061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 316.692 | 0.405496 | ||||||||
\(782\) | − | 306.351i | − | 0.391754i | ||||||
\(783\) | − | 48.0802i | − | 0.0614052i | ||||||
\(784\) | −176.059 | − | 86.1354i | −0.224565 | − | 0.109867i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 346.015 | 0.440222 | ||||||||
\(787\) | 318.111i | 0.404207i | 0.979364 | + | 0.202104i | \(0.0647778\pi\) | ||||
−0.979364 | + | 0.202104i | \(0.935222\pi\) | |||||||
\(788\) | −387.268 | −0.491457 | ||||||||
\(789\) | 664.098i | 0.841696i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −224.172 | + | 968.302i | −0.283403 | + | 1.22415i | ||||
\(792\) | 69.2369 | 0.0874203 | ||||||||
\(793\) | 500.801 | 0.631527 | ||||||||
\(794\) | − | 58.3616i | − | 0.0735033i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 363.676i | 0.456880i | ||||||||
\(797\) | 1188.06i | 1.49067i | 0.666690 | + | 0.745335i | \(0.267711\pi\) | ||||
−0.666690 | + | 0.745335i | \(0.732289\pi\) | |||||||
\(798\) | 130.612 | − | 564.175i | 0.163674 | − | 0.706986i | ||||
\(799\) | −135.692 | −0.169827 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 48.6867i | − | 0.0607824i | ||||||
\(802\) | −700.943 | −0.873994 | ||||||||
\(803\) | 1016.93i | 1.26642i | ||||||||
\(804\) | − | 17.3166i | − | 0.0215381i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 397.758 | 0.493497 | ||||||||
\(807\) | 267.622 | 0.331626 | ||||||||
\(808\) | 246.654i | 0.305265i | ||||||||
\(809\) | 223.374 | 0.276111 | 0.138055 | − | 0.990425i | \(-0.455915\pi\) | ||||
0.138055 | + | 0.990425i | \(0.455915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 366.185i | − | 0.451523i | −0.974183 | − | 0.225761i | \(-0.927513\pi\) | ||
0.974183 | − | 0.225761i | \(-0.0724870\pi\) | |||||||
\(812\) | −29.2177 | + | 126.205i | −0.0359824 | + | 0.155424i | ||||
\(813\) | −554.824 | −0.682440 | ||||||||
\(814\) | 732.008 | 0.899272 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −40.2820 | −0.0493652 | ||||||||
\(817\) | 1421.51i | 1.73991i | ||||||||
\(818\) | 509.004i | 0.622255i | ||||||||
\(819\) | −298.831 | − | 69.1824i | −0.364873 | − | 0.0844718i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1547.39 | −1.88476 | −0.942381 | − | 0.334543i | \(-0.891418\pi\) | ||||
−0.942381 | + | 0.334543i | \(0.891418\pi\) | |||||||
\(822\) | 124.050i | 0.150912i | ||||||||
\(823\) | −1284.25 | −1.56045 | −0.780225 | − | 0.625499i | \(-0.784895\pi\) | ||||
−0.780225 | + | 0.625499i | \(0.784895\pi\) | |||||||
\(824\) | 530.521i | 0.643836i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 414.083 | + | 95.8644i | 0.501311 | + | 0.116059i | ||||
\(827\) | −807.319 | −0.976202 | −0.488101 | − | 0.872787i | \(-0.662310\pi\) | ||||
−0.488101 | + | 0.872787i | \(0.662310\pi\) | |||||||
\(828\) | 223.545 | 0.269982 | ||||||||
\(829\) | − | 623.615i | − | 0.752250i | −0.926569 | − | 0.376125i | \(-0.877256\pi\) | ||
0.926569 | − | 0.376125i | \(-0.122744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 385.994i | 0.464493i | ||||||||
\(832\) | − | 116.851i | − | 0.140446i | ||||||
\(833\) | 125.202 | − | 255.911i | 0.150303 | − | 0.307216i | ||||
\(834\) | −181.325 | −0.217416 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 551.161i | − | 0.659283i | ||||||
\(837\) | 100.056 | 0.119541 | ||||||||
\(838\) | − | 682.938i | − | 0.814962i | ||||||
\(839\) | − | 1146.31i | − | 1.36628i | −0.730286 | − | 0.683142i | \(-0.760613\pi\) | ||
0.730286 | − | 0.683142i | \(-0.239387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −755.381 | −0.898194 | ||||||||
\(842\) | −740.368 | −0.879297 | ||||||||
\(843\) | 379.272i | 0.449908i | ||||||||
\(844\) | 351.829 | 0.416859 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 99.0145i | − | 0.117038i | ||||||
\(847\) | 85.9194 | − | 371.126i | 0.101440 | − | 0.438165i | ||||
\(848\) | −285.399 | −0.336555 | ||||||||
\(849\) | 63.0392 | 0.0742511 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2363.43 | 2.77724 | ||||||||
\(852\) | − | 134.449i | − | 0.157804i | ||||||
\(853\) | 948.920i | 1.11245i | 0.831032 | + | 0.556225i | \(0.187751\pi\) | ||||
−0.831032 | + | 0.556225i | \(0.812249\pi\) | |||||||
\(854\) | −330.672 | − | 76.5540i | −0.387204 | − | 0.0896417i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −446.489 | −0.521599 | ||||||||
\(857\) | − | 868.842i | − | 1.01382i | −0.862000 | − | 0.506909i | \(-0.830788\pi\) | ||
0.862000 | − | 0.506909i | \(-0.169212\pi\) | |||||||
\(858\) | −291.938 | −0.340254 | ||||||||
\(859\) | − | 119.981i | − | 0.139675i | −0.997558 | − | 0.0698377i | \(-0.977752\pi\) | ||
0.997558 | − | 0.0698377i | \(-0.0222482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5844 | + | 97.5525i | −0.0262304 | + | 0.113301i | ||||
\(862\) | 731.187 | 0.848245 | ||||||||
\(863\) | 788.430 | 0.913592 | 0.456796 | − | 0.889571i | \(-0.348997\pi\) | ||||
0.456796 | + | 0.889571i | \(0.348997\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 802.866i | 0.927097i | ||||||||
\(867\) | 442.011i | 0.509816i | ||||||||
\(868\) | −262.635 | − | 60.8026i | −0.302574 | − | 0.0700491i | ||||
\(869\) | −458.443 | −0.527552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.0157i | 0.0838298i | ||||||||
\(872\) | 316.990 | 0.363521 | ||||||||
\(873\) | − | 248.282i | − | 0.284400i | ||||||
\(874\) | − | 1779.53i | − | 2.03608i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 431.729 | 0.492841 | ||||||||
\(877\) | −234.663 | −0.267574 | −0.133787 | − | 0.991010i | \(-0.542714\pi\) | ||||
−0.133787 | + | 0.991010i | \(0.542714\pi\) | |||||||
\(878\) | 880.879i | 1.00328i | ||||||||
\(879\) | −291.747 | −0.331908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 750.816i | 0.852232i | 0.904669 | + | 0.426116i | \(0.140118\pi\) | ||||
−0.904669 | + | 0.426116i | \(0.859882\pi\) | |||||||
\(882\) | 186.739 | + | 91.3604i | 0.211722 | + | 0.103583i | ||||
\(883\) | 1293.79 | 1.46522 | 0.732610 | − | 0.680649i | \(-0.238302\pi\) | ||||
0.732610 | + | 0.680649i | \(0.238302\pi\) | |||||||
\(884\) | 169.849 | 0.192137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −674.154 | −0.760896 | ||||||||
\(887\) | 728.248i | 0.821024i | 0.911855 | + | 0.410512i | \(0.134650\pi\) | ||||
−0.911855 | + | 0.410512i | \(0.865350\pi\) | |||||||
\(888\) | − | 310.767i | − | 0.349963i | ||||||
\(889\) | 319.574 | − | 1380.39i | 0.359476 | − | 1.55274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −73.4368 | −0.0824207 | ||||||||
\(892\) | − | 41.1349i | − | 0.0461154i | ||||||
\(893\) | −788.206 | −0.882650 | ||||||||
\(894\) | 555.984i | 0.621906i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17.8622 | + | 77.1553i | −0.0199355 | + | 0.0861108i | ||||
\(897\) | −942.580 | −1.05081 | ||||||||
\(898\) | −1218.95 | −1.35741 | ||||||||
\(899\) | 178.175i | 0.198192i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 414.842i | − | 0.460424i | ||||||
\(902\) | 95.3022i | 0.105657i | ||||||||
\(903\) | −497.157 | − | 115.097i | −0.550561 | − | 0.127461i | ||||
\(904\) | 401.601 | 0.444249 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 721.193i | 0.796018i | ||||||||
\(907\) | −913.713 | −1.00740 | −0.503700 | − | 0.863878i | \(-0.668028\pi\) | ||||
−0.503700 | + | 0.863878i | \(0.668028\pi\) | |||||||
\(908\) | − | 828.173i | − | 0.912085i | ||||||
\(909\) | − | 261.616i | − | 0.287807i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1331.32 | −1.46138 | −0.730690 | − | 0.682709i | \(-0.760802\pi\) | ||||
−0.730690 | + | 0.682709i | \(0.760802\pi\) | |||||||
\(912\) | −233.990 | −0.256568 | ||||||||
\(913\) | − | 737.615i | − | 0.807903i | ||||||
\(914\) | −38.9476 | −0.0426123 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 391.040i | 0.426899i | ||||||||
\(917\) | 963.341 | + | 223.023i | 1.05053 | + | 0.243210i | ||||
\(918\) | 42.7255 | 0.0465420 | ||||||||
\(919\) | 111.140 | 0.120936 | 0.0604678 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604678 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −386.941 | −0.420131 | ||||||||
\(922\) | − | 534.831i | − | 0.580077i | ||||||
\(923\) | 566.904i | 0.614197i | ||||||||
\(924\) | 192.763 | + | 44.6265i | 0.208617 | + | 0.0482971i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1025.30 | −1.10723 | ||||||||
\(927\) | − | 562.702i | − | 0.607014i | ||||||
\(928\) | 52.3431 | 0.0564042 | ||||||||
\(929\) | − | 571.383i | − | 0.615051i | −0.951540 | − | 0.307526i | \(-0.900499\pi\) | ||
0.951540 | − | 0.307526i | \(-0.0995010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 727.275 | − | 1486.53i | 0.781176 | − | 1.59671i | ||||
\(932\) | −162.601 | −0.174465 | ||||||||
\(933\) | 79.7428 | 0.0854693 | ||||||||
\(934\) | − | 525.311i | − | 0.562431i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 123.939i | 0.132414i | ||||||||
\(937\) | − | 1657.10i | − | 1.76852i | −0.466997 | − | 0.884259i | \(-0.654664\pi\) | ||
0.466997 | − | 0.884259i | \(-0.345336\pi\) | |||||||
\(938\) | 11.1614 | − | 48.2113i | 0.0118992 | − | 0.0513980i | ||||
\(939\) | −138.629 | −0.147635 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 519.083i | 0.551629i | 0.961211 | + | 0.275815i | \(0.0889476\pi\) | ||||
−0.961211 | + | 0.275815i | \(0.911052\pi\) | |||||||
\(942\) | 161.322 | 0.171255 | ||||||||
\(943\) | 307.703i | 0.326302i | ||||||||
\(944\) | − | 171.740i | − | 0.181928i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −485.689 | −0.513413 | ||||||||
\(947\) | −558.258 | −0.589502 | −0.294751 | − | 0.955574i | \(-0.595237\pi\) | ||||
−0.294751 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(948\) | 194.628i | 0.205303i | ||||||||
\(949\) | −1820.39 | −1.91822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 320.839i | 0.337370i | ||||||||
\(952\) | −112.149 | − | 25.9637i | −0.117804 | − | 0.0272728i | ||||
\(953\) | 291.413 | 0.305784 | 0.152892 | − | 0.988243i | \(-0.451141\pi\) | ||||
0.152892 | + | 0.988243i | \(0.451141\pi\) | |||||||
\(954\) | 302.711 | 0.317307 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 498.530 | 0.521475 | ||||||||
\(957\) | − | 130.773i | − | 0.136648i | ||||||
\(958\) | − | 1217.14i | − | 1.27050i | ||||||
\(959\) | −79.9559 | + | 345.367i | −0.0833742 | + | 0.360132i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 590.215 | 0.614167 | ||||||||
\(962\) | 1310.35i | 1.36211i | ||||||||
\(963\) | 473.573 | 0.491768 | ||||||||
\(964\) | 524.686i | 0.544280i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 622.373 | + | 144.086i | 0.644278 | + | 0.149157i | ||||
\(967\) | 323.558 | 0.334600 | 0.167300 | − | 0.985906i | \(-0.446495\pi\) | ||||
0.167300 | + | 0.985906i | \(0.446495\pi\) | |||||||
\(968\) | −153.924 | −0.159012 | ||||||||
\(969\) | − | 340.117i | − | 0.350998i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 219.659i | − | 0.226219i | −0.993583 | − | 0.113110i | \(-0.963919\pi\) | ||
0.993583 | − | 0.113110i | \(-0.0360812\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −504.827 | − | 116.873i | −0.518836 | − | 0.120116i | ||||
\(974\) | −1254.65 | −1.28814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 137.146i | 0.140518i | ||||||||
\(977\) | 1302.29 | 1.33295 | 0.666475 | − | 0.745527i | \(-0.267802\pi\) | ||||
0.666475 | + | 0.745527i | \(0.267802\pi\) | |||||||
\(978\) | 69.0939i | 0.0706482i | ||||||||
\(979\) | − | 132.422i | − | 0.135263i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −336.219 | −0.342731 | ||||||||
\(982\) | −70.9685 | −0.0722693 | ||||||||
\(983\) | 649.905i | 0.661144i | 0.943781 | + | 0.330572i | \(0.107242\pi\) | ||||
−0.943781 | + | 0.330572i | \(0.892758\pi\) | |||||||
\(984\) | 40.4597 | 0.0411176 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 76.0834i | 0.0771637i | ||||||||
\(987\) | 63.8196 | − | 275.667i | 0.0646602 | − | 0.279297i | ||||
\(988\) | 986.621 | 0.998604 | ||||||||
\(989\) | −1568.15 | −1.58559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −575.568 | −0.580795 | −0.290397 | − | 0.956906i | \(-0.593788\pi\) | ||||
−0.290397 | + | 0.956906i | \(0.593788\pi\) | |||||||
\(992\) | 108.927i | 0.109806i | ||||||||
\(993\) | 106.467i | 0.107217i | ||||||||
\(994\) | 86.6587 | − | 374.319i | 0.0871818 | − | 0.376578i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −313.148 | −0.314405 | ||||||||
\(997\) | 705.512i | 0.707635i | 0.935315 | + | 0.353817i | \(0.115117\pi\) | ||||
−0.935315 | + | 0.353817i | \(0.884883\pi\) | |||||||
\(998\) | −226.901 | −0.227355 | ||||||||
\(999\) | 329.618i | 0.329948i |
(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 | 1050.3.f.e.601.14 | 16 | ||
5.2 | odd | 4 | 210.3.h.a.139.13 | yes | 16 | ||
5.3 | odd | 4 | 210.3.h.a.139.4 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1050.3.f.e.601.3 | 16 | ||
7.6 | odd | 2 | inner | 1050.3.f.e.601.10 | 16 | ||
15.2 | even | 4 | 630.3.h.e.559.7 | 16 | |||
15.8 | even | 4 | 630.3.h.e.559.10 | 16 | |||
20.3 | even | 4 | 1680.3.bd.a.769.15 | 16 | |||
20.7 | even | 4 | 1680.3.bd.a.769.1 | 16 | |||
35.13 | even | 4 | 210.3.h.a.139.5 | yes | 16 | ||
35.27 | even | 4 | 210.3.h.a.139.12 | yes | 16 | ||
35.34 | odd | 2 | inner | 1050.3.f.e.601.7 | 16 | ||
105.62 | odd | 4 | 630.3.h.e.559.2 | 16 | |||
105.83 | odd | 4 | 630.3.h.e.559.15 | 16 | |||
140.27 | odd | 4 | 1680.3.bd.a.769.16 | 16 | |||
140.83 | odd | 4 | 1680.3.bd.a.769.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.4 | ✓ | 16 | 5.3 | odd | 4 | ||
210.3.h.a.139.5 | yes | 16 | 35.13 | even | 4 | ||
210.3.h.a.139.12 | yes | 16 | 35.27 | even | 4 | ||
210.3.h.a.139.13 | yes | 16 | 5.2 | odd | 4 | ||
630.3.h.e.559.2 | 16 | 105.62 | odd | 4 | |||
630.3.h.e.559.7 | 16 | 15.2 | even | 4 | |||
630.3.h.e.559.10 | 16 | 15.8 | even | 4 | |||
630.3.h.e.559.15 | 16 | 105.83 | odd | 4 | |||
1050.3.f.e.601.3 | 16 | 5.4 | even | 2 | inner | ||
1050.3.f.e.601.7 | 16 | 35.34 | odd | 2 | inner | ||
1050.3.f.e.601.10 | 16 | 7.6 | odd | 2 | inner | ||
1050.3.f.e.601.14 | 16 | 1.1 | even | 1 | trivial | ||
1680.3.bd.a.769.1 | 16 | 20.7 | even | 4 | |||
1680.3.bd.a.769.2 | 16 | 140.83 | odd | 4 | |||
1680.3.bd.a.769.15 | 16 | 20.3 | even | 4 | |||
1680.3.bd.a.769.16 | 16 | 140.27 | odd | 4 |