Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (of order \(2\), degree \(1\), not 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: | \(20.9264843029\) |
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: | \( x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} + \cdots + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.11 | ||
Root | \(-2.18318 + 0.904303i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.g.641.12 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.32750 | − | 2.69031i | 0.442499 | − | 0.896769i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.640013 | −0.128003 | −0.0640013 | − | 0.997950i | \(-0.520386\pi\) | ||||
−0.0640013 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.72077 | −0.388681 | −0.194340 | − | 0.980934i | \(-0.562257\pi\) | ||||
−0.194340 | + | 0.980934i | \(0.562257\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.47550 | − | 7.14275i | −0.608389 | − | 0.793639i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.2836 | −1.02579 | −0.512893 | − | 0.858452i | \(-0.671426\pi\) | ||||
−0.512893 | + | 0.858452i | \(0.671426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.25176i | 0.403982i | 0.979387 | + | 0.201991i | \(0.0647411\pi\) | ||||
−0.979387 | + | 0.201991i | \(0.935259\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.849616 | + | 1.72183i | −0.0566411 | + | 0.114789i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.8718i | 0.874812i | 0.899264 | + | 0.437406i | \(0.144103\pi\) | ||||
−0.899264 | + | 0.437406i | \(0.855897\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 15.0798i | − | 0.793676i | −0.917889 | − | 0.396838i | \(-0.870107\pi\) | ||
0.917889 | − | 0.396838i | \(-0.129893\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.61181 | + | 7.31969i | −0.171991 | + | 0.348557i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 36.4411i | 1.58439i | 0.610266 | + | 0.792197i | \(0.291063\pi\) | ||||
−0.610266 | + | 0.792197i | \(0.708937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.5904 | −0.983615 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.4849 | + | 5.24877i | −0.980923 | + | 0.194399i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.7310 | 1.78383 | 0.891914 | − | 0.452205i | \(-0.149362\pi\) | ||||
0.891914 | + | 0.452205i | \(0.149362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.5009 | −1.17745 | −0.588724 | − | 0.808334i | \(-0.700370\pi\) | ||||
−0.588724 | + | 0.808334i | \(0.700370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.9790 | + | 30.3565i | −0.453910 | + | 0.919893i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.74133 | 0.0497522 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63.6951i | 1.72149i | 0.509036 | + | 0.860745i | \(0.330002\pi\) | ||||
−0.509036 | + | 0.860745i | \(0.669998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.1289 | + | 6.97170i | 0.362278 | + | 0.178762i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1500i | 0.296342i | 0.988962 | + | 0.148171i | \(0.0473386\pi\) | ||||
−0.988962 | + | 0.148171i | \(0.952661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.8032i | − | 0.274493i | −0.990537 | − | 0.137247i | \(-0.956175\pi\) | ||
0.990537 | − | 0.137247i | \(-0.0438253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.50439 | + | 4.57146i | 0.0778753 | + | 0.101588i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 61.1247i | − | 1.30053i | −0.759709 | − | 0.650263i | \(-0.774659\pi\) | ||
0.759709 | − | 0.650263i | \(-0.225341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.5974 | −0.848927 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.0097 | + | 19.7423i | 0.784504 | + | 0.387104i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −59.1695 | −1.11641 | −0.558203 | − | 0.829705i | \(-0.688509\pi\) | ||||
−0.558203 | + | 0.829705i | \(0.688509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.22168 | 0.131303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −40.5694 | − | 20.0185i | −0.711744 | − | 0.351201i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37.2898 | 0.632031 | 0.316016 | − | 0.948754i | \(-0.397655\pi\) | ||||
0.316016 | + | 0.948754i | \(0.397655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58.1987i | 0.954076i | 0.878883 | + | 0.477038i | \(0.158290\pi\) | ||||
−0.878883 | + | 0.477038i | \(0.841710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.8975 | + | 19.4338i | 0.236469 | + | 0.308472i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.36120i | − | 0.0517107i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 23.0991i | − | 0.344762i | −0.985030 | − | 0.172381i | \(-0.944854\pi\) | ||
0.985030 | − | 0.172381i | \(-0.0551461\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 98.0376 | + | 48.3754i | 1.42084 | + | 0.701093i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.29656i | 0.102768i | 0.998679 | + | 0.0513842i | \(0.0163633\pi\) | ||||
−0.998679 | + | 0.0513842i | \(0.983637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −73.4504 | −1.00617 | −0.503085 | − | 0.864237i | \(-0.667802\pi\) | ||||
−0.503085 | + | 0.864237i | \(0.667802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32.6437 | + | 66.1557i | −0.435249 | + | 0.882076i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30.7002 | 0.398703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.5098 | 0.740630 | 0.370315 | − | 0.928906i | \(-0.379250\pi\) | ||||
0.370315 | + | 0.928906i | \(0.379250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −21.0379 | + | 78.2203i | −0.259727 | + | 0.965682i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32.3939 | −0.390287 | −0.195144 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195144 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.51815i | − | 0.111978i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 68.6728 | − | 139.172i | 0.789343 | − | 1.59968i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 112.260i | 1.26135i | 0.776046 | + | 0.630677i | \(0.217223\pi\) | ||||
−0.776046 | + | 0.630677i | \(0.782777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.2888i | − | 0.157020i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −48.4549 | + | 98.1987i | −0.521020 | + | 1.05590i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.65130i | 0.101593i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −80.0338 | −0.825090 | −0.412545 | − | 0.910937i | \(-0.635360\pi\) | ||||
−0.412545 | + | 0.910937i | \(0.635360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 61.7836 | + | 80.5963i | 0.624077 | + | 0.814104i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 119.373 | 1.18191 | 0.590954 | − | 0.806705i | \(-0.298751\pi\) | ||||
0.590954 | + | 0.806705i | \(0.298751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −125.522 | −1.21866 | −0.609330 | − | 0.792917i | \(-0.708562\pi\) | ||||
−0.609330 | + | 0.792917i | \(0.708562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.31161 | − | 4.68470i | 0.0220153 | − | 0.0446162i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 148.669 | 1.38943 | 0.694716 | − | 0.719284i | \(-0.255530\pi\) | ||||
0.694716 | + | 0.719284i | \(0.255530\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.6664i | 0.648316i | 0.946003 | + | 0.324158i | \(0.105081\pi\) | ||||
−0.946003 | + | 0.324158i | \(0.894919\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 171.359 | + | 84.5552i | 1.54378 | + | 0.761758i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 130.968i | − | 1.15901i | −0.814969 | − | 0.579504i | \(-0.803246\pi\) | ||
0.814969 | − | 0.579504i | \(-0.196754\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 23.3228i | − | 0.202807i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37.5120 | − | 28.7560i | 0.320616 | − | 0.245778i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 40.4627i | − | 0.340023i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32073 | 0.0522374 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 32.6873 | + | 16.1291i | 0.265750 | + | 0.131131i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.7385 | 0.253908 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −209.206 | −1.64729 | −0.823647 | − | 0.567103i | \(-0.808064\pi\) | ||||
−0.823647 | + | 0.567103i | \(0.808064\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31.7543 | − | 15.6687i | −0.246157 | − | 0.121463i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −174.839 | −1.33465 | −0.667326 | − | 0.744766i | \(-0.732561\pi\) | ||||
−0.667326 | + | 0.744766i | \(0.732561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.0287i | 0.308487i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.9507 | − | 3.35929i | 0.125561 | − | 0.0248836i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 162.945i | 1.18938i | 0.803956 | + | 0.594689i | \(0.202725\pi\) | ||||
−0.803956 | + | 0.594689i | \(0.797275\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 194.227i | − | 1.39732i | −0.715454 | − | 0.698660i | \(-0.753780\pi\) | ||
0.715454 | − | 0.698660i | \(-0.246220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −164.444 | − | 81.1429i | −1.16627 | − | 0.575482i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 59.2590i | − | 0.414399i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.1085 | −0.228335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −55.2205 | + | 111.910i | −0.375650 | + | 0.761291i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −83.4695 | −0.560198 | −0.280099 | − | 0.959971i | \(-0.590367\pi\) | ||||
−0.280099 | + | 0.959971i | \(0.590367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −60.3488 | −0.399661 | −0.199830 | − | 0.979830i | \(-0.564039\pi\) | ||||
−0.199830 | + | 0.979830i | \(0.564039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 106.226 | − | 81.4306i | 0.694285 | − | 0.532226i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.3611 | 0.150717 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 100.762i | − | 0.641798i | −0.947113 | − | 0.320899i | \(-0.896015\pi\) | ||
0.947113 | − | 0.320899i | \(-0.103985\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −78.5474 | + | 159.184i | −0.494009 | + | 1.00116i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 99.1476i | − | 0.615824i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 69.7149i | − | 0.427699i | −0.976867 | − | 0.213849i | \(-0.931400\pi\) | ||
0.976867 | − | 0.213849i | \(-0.0686002\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.58677 | − | 19.4285i | 0.0581016 | − | 0.117749i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 120.823i | 0.723491i | 0.932277 | + | 0.361745i | \(0.117819\pi\) | ||||
−0.932277 | + | 0.361745i | \(0.882181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 141.419 | 0.836799 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −107.712 | + | 82.5697i | −0.629893 | + | 0.482863i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −30.0602 | −0.173758 | −0.0868791 | − | 0.996219i | \(-0.527689\pi\) | ||||
−0.0868791 | + | 0.996219i | \(0.527689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 66.9047 | 0.382312 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 49.5022 | − | 100.321i | 0.279673 | − | 0.566786i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −114.784 | −0.641250 | −0.320625 | − | 0.947206i | \(-0.603893\pi\) | ||||
−0.320625 | + | 0.947206i | \(0.603893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 181.627i | − | 1.00347i | −0.865022 | − | 0.501733i | \(-0.832696\pi\) | ||
0.865022 | − | 0.501733i | \(-0.167304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 156.572 | + | 77.2586i | 0.855586 | + | 0.422178i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 40.7657i | − | 0.220355i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 167.808i | − | 0.897370i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 72.0592 | − | 14.2807i | 0.381266 | − | 0.0755592i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 209.226i | 1.09543i | 0.836666 | + | 0.547713i | \(0.184502\pi\) | ||||
−0.836666 | + | 0.547713i | \(0.815498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 161.330 | 0.835907 | 0.417954 | − | 0.908468i | \(-0.362747\pi\) | ||||
0.417954 | + | 0.908468i | \(0.362747\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.04265 | − | 4.46198i | −0.0463726 | − | 0.0228820i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −144.953 | −0.735801 | −0.367901 | − | 0.929865i | \(-0.619923\pi\) | ||||
−0.367901 | + | 0.929865i | \(0.619923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −237.264 | −1.19228 | −0.596140 | − | 0.802880i | \(-0.703300\pi\) | ||||
−0.596140 | + | 0.802880i | \(0.703300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −62.1436 | − | 30.6640i | −0.309172 | − | 0.152557i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −140.748 | −0.693340 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 7.77617i | − | 0.0379325i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 260.289 | − | 199.533i | 1.25744 | − | 0.963927i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 170.156i | 0.814142i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 307.117i | − | 1.45553i | −0.685827 | − | 0.727765i | \(-0.740559\pi\) | ||
0.685827 | − | 0.727765i | \(-0.259441\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.6300 | + | 9.68617i | 0.0921595 | + | 0.0454750i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.55422i | 0.0351359i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 99.3105 | 0.457652 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −97.5053 | + | 197.604i | −0.445230 | + | 0.902302i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −78.1032 | −0.353408 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −438.001 | −1.96413 | −0.982065 | − | 0.188544i | \(-0.939623\pi\) | ||||
−0.982065 | + | 0.188544i | \(0.939623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 134.645 | + | 175.643i | 0.598420 | + | 0.780636i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 270.755 | 1.19275 | 0.596376 | − | 0.802705i | \(-0.296607\pi\) | ||||
0.596376 | + | 0.802705i | \(0.296607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 98.6778i | − | 0.430907i | −0.976514 | − | 0.215454i | \(-0.930877\pi\) | ||
0.976514 | − | 0.215454i | \(-0.0691230\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 40.7544 | − | 82.5929i | 0.176426 | − | 0.357545i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 432.405i | − | 1.85581i | −0.372812 | − | 0.927907i | \(-0.621606\pi\) | ||
0.372812 | − | 0.927907i | \(-0.378394\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.1206i | 0.166471i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 77.6717 | − | 157.409i | 0.327729 | − | 0.664174i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 275.799i | − | 1.15397i | −0.816754 | − | 0.576986i | \(-0.804229\pi\) | ||
0.816754 | − | 0.576986i | \(-0.195771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 416.770 | 1.72934 | 0.864669 | − | 0.502343i | \(-0.167528\pi\) | ||||
0.864669 | + | 0.502343i | \(0.167528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 182.509 | + | 160.436i | 0.751065 | + | 0.660228i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.6229 | 0.108665 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 79.1958 | 0.320631 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −43.0028 | + | 87.1494i | −0.172702 | + | 0.349998i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −165.903 | −0.660966 | −0.330483 | − | 0.943812i | \(-0.607212\pi\) | ||||
−0.330483 | + | 0.943812i | \(0.607212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 411.188i | − | 1.62525i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.6068 | − | 12.6353i | −0.100419 | − | 0.0495503i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 59.6381i | − | 0.232055i | −0.993246 | − | 0.116028i | \(-0.962984\pi\) | ||
0.993246 | − | 0.116028i | \(-0.0370161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 173.300i | − | 0.669110i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −283.253 | − | 369.502i | −1.08526 | − | 1.41572i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 67.2606i | 0.255744i | 0.991791 | + | 0.127872i | \(0.0408146\pi\) | ||||
−0.991791 | + | 0.127872i | \(0.959185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.8693 | 0.142903 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 302.015 | + | 149.026i | 1.13114 | + | 0.558148i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 36.1495 | 0.134385 | 0.0671923 | − | 0.997740i | \(-0.478596\pi\) | ||||
0.0671923 | + | 0.997740i | \(0.478596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 328.311 | 1.21148 | 0.605741 | − | 0.795662i | \(-0.292877\pi\) | ||||
0.605741 | + | 0.795662i | \(0.292877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.4413 | − | 18.9684i | −0.140811 | − | 0.0694812i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 277.469 | 1.00898 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 60.7455i | 0.219298i | 0.993970 | + | 0.109649i | \(0.0349727\pi\) | ||||
−0.993970 | + | 0.109649i | \(0.965027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 199.861 | + | 260.717i | 0.716347 | + | 0.934470i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 366.827i | − | 1.30543i | −0.757602 | − | 0.652717i | \(-0.773629\pi\) | ||
0.757602 | − | 0.652717i | \(-0.226371\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 104.032i | 0.367603i | 0.982963 | + | 0.183801i | \(0.0588404\pi\) | ||||
−0.982963 | + | 0.183801i | \(0.941160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.9650 | + | 12.8121i | 0.0911051 | + | 0.0449547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 33.0574i | − | 0.115182i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 67.8293 | 0.234703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −106.245 | + | 215.315i | −0.365102 | + | 0.739915i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −410.579 | −1.40129 | −0.700647 | − | 0.713508i | \(-0.747105\pi\) | ||||
−0.700647 | + | 0.713508i | \(0.747105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.8660 | −0.0809017 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 298.846 | − | 59.2253i | 1.00622 | − | 0.199412i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −191.380 | −0.640066 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.1138i | 0.106690i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 158.467 | − | 321.149i | 0.522994 | − | 1.05990i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 37.2479i | − | 0.122124i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 270.025i | 0.879561i | 0.898105 | + | 0.439781i | \(0.144944\pi\) | ||||
−0.898105 | + | 0.439781i | \(0.855056\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −166.630 | + | 337.693i | −0.539256 | + | 1.09286i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 251.555i | − | 0.808858i | −0.914569 | − | 0.404429i | \(-0.867470\pi\) | ||
0.914569 | − | 0.404429i | \(-0.132530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 83.9560 | 0.268230 | 0.134115 | − | 0.990966i | \(-0.457181\pi\) | ||||
0.134115 | + | 0.990966i | \(0.457181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.53463 | − | 12.4379i | −0.0302687 | − | 0.0394853i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −270.737 | −0.854060 | −0.427030 | − | 0.904238i | \(-0.640440\pi\) | ||||
−0.427030 | + | 0.904238i | \(0.640440\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −583.715 | −1.82983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 197.358 | − | 399.966i | 0.614823 | − | 1.24600i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 224.265 | 0.694318 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 129.143i | − | 0.397363i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 190.114 | + | 93.8095i | 0.581389 | + | 0.286879i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 166.306i | 0.505489i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.91562i | 0.0299566i | 0.999888 | + | 0.0149783i | \(0.00476791\pi\) | ||||
−0.999888 | + | 0.0149783i | \(0.995232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 454.959 | − | 348.763i | 1.36624 | − | 1.04733i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.7837i | 0.0441305i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −289.542 | −0.859174 | −0.429587 | − | 0.903025i | \(-0.641341\pi\) | ||||
−0.429587 | + | 0.903025i | \(0.641341\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −352.344 | − | 173.860i | −1.03936 | − | 0.512860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 411.864 | 1.20781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 246.494 | 0.718643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −62.7454 | − | 30.9609i | −0.181871 | − | 0.0897418i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 331.079 | 0.954119 | 0.477060 | − | 0.878871i | \(-0.341703\pi\) | ||||
0.477060 | + | 0.878871i | \(0.341703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 302.280i | − | 0.866133i | −0.901362 | − | 0.433067i | \(-0.857431\pi\) | ||
0.901362 | − | 0.433067i | \(-0.142569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.5653 | − | 139.092i | −0.0785337 | − | 0.396275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 528.345i | 1.49673i | 0.663289 | + | 0.748364i | \(0.269160\pi\) | ||||
−0.663289 | + | 0.748364i | \(0.730840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.66989i | − | 0.0131546i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −108.857 | − | 53.7142i | −0.304922 | − | 0.150460i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 59.5167i | 0.165785i | 0.996559 | + | 0.0828923i | \(0.0264158\pi\) | ||||
−0.996559 | + | 0.0828923i | \(0.973584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 133.598 | 0.370078 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.39076 | − | 17.0047i | 0.0231150 | − | 0.0468449i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.0092 | 0.128792 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 423.762 | 1.15466 | 0.577332 | − | 0.816509i | \(-0.304094\pi\) | ||||
0.577332 | + | 0.816509i | \(0.304094\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 86.7846 | − | 66.5274i | 0.235189 | − | 0.180291i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 160.986 | 0.433925 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.5076i | 0.0710660i | 0.999369 | + | 0.0355330i | \(0.0113129\pi\) | ||||
−0.999369 | + | 0.0355330i | \(0.988687\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 42.1328 | − | 85.3863i | 0.112354 | − | 0.227697i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 271.679i | 0.720634i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 383.169i | − | 1.01100i | −0.862827 | − | 0.505500i | \(-0.831308\pi\) | ||
0.862827 | − | 0.505500i | \(-0.168692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −277.721 | + | 562.829i | −0.728927 | + | 1.47724i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 299.496i | 0.781973i | 0.920396 | + | 0.390987i | \(0.127866\pi\) | ||||
−0.920396 | + | 0.390987i | \(0.872134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.6485 | −0.0510351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −84.3075 | + | 64.6285i | −0.217849 | + | 0.166999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 437.687 | 1.12516 | 0.562580 | − | 0.826743i | \(-0.309809\pi\) | ||||
0.562580 | + | 0.826743i | \(0.309809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −541.944 | −1.38605 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −232.099 | + | 470.372i | −0.590583 | + | 1.19687i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −37.4470 | −0.0948027 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 669.283i | 1.68585i | 0.538029 | + | 0.842926i | \(0.319169\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 110.380 | + | 54.4656i | 0.276641 | + | 0.136505i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 56.1062i | 0.139916i | 0.997550 | + | 0.0699578i | \(0.0222865\pi\) | ||||
−0.997550 | + | 0.0699578i | \(0.977714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 191.694i | − | 0.475668i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.4645 | − | 50.0620i | 0.0332457 | − | 0.123610i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 718.713i | − | 1.76588i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −248.582 | −0.607779 | −0.303889 | − | 0.952707i | \(-0.598285\pi\) | ||||
−0.303889 | + | 0.952707i | \(0.598285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 438.371 | + | 216.309i | 1.06660 | + | 0.526299i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −101.457 | −0.245658 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7325 | 0.0499578 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −522.531 | − | 257.836i | −1.25307 | − | 0.618313i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −459.935 | −1.09770 | −0.548849 | − | 0.835922i | \(-0.684934\pi\) | ||||
−0.548849 | + | 0.835922i | \(0.684934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 97.4789i | − | 0.231541i | −0.993276 | − | 0.115771i | \(-0.963066\pi\) | ||
0.993276 | − | 0.115771i | \(-0.0369338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −436.599 | + | 334.688i | −1.03215 | + | 0.791225i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 365.703i | − | 0.860479i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 158.345i | − | 0.370831i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −159.425 | − | 78.6663i | −0.371620 | − | 0.183371i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 545.207i | 1.26498i | 0.774568 | + | 0.632490i | \(0.217967\pi\) | ||||
−0.774568 | + | 0.632490i | \(0.782033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.5297 | −0.0566506 | −0.0283253 | − | 0.999599i | \(-0.509017\pi\) | ||||
−0.0283253 | + | 0.999599i | \(0.509017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −43.9515 | + | 89.0721i | −0.101038 | + | 0.204763i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 549.526 | 1.25750 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −81.8743 | −0.186502 | −0.0932509 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932509 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 227.767 | + | 297.120i | 0.516478 | + | 0.673742i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −831.356 | −1.87665 | −0.938325 | − | 0.345753i | \(-0.887623\pi\) | ||||
−0.938325 | + | 0.345753i | \(0.887623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 71.8482i | − | 0.161457i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −110.806 | + | 224.559i | −0.247887 | + | 0.502368i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 259.553i | − | 0.578070i | −0.957319 | − | 0.289035i | \(-0.906666\pi\) | ||
0.957319 | − | 0.289035i | \(-0.0933344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 137.097i | − | 0.303983i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −80.1129 | + | 162.357i | −0.176850 | + | 0.358403i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.14503i | 0.0200990i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −373.184 | −0.816596 | −0.408298 | − | 0.912849i | \(-0.633878\pi\) | ||||
−0.408298 | + | 0.912849i | \(0.633878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −78.0588 | − | 393.879i | −0.170063 | − | 0.858123i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −672.996 | −1.45986 | −0.729930 | − | 0.683522i | \(-0.760447\pi\) | ||||
−0.729930 | + | 0.683522i | \(0.760447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0435 | −0.0605690 | −0.0302845 | − | 0.999541i | \(-0.509641\pi\) | ||||
−0.0302845 | + | 0.999541i | \(0.509641\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.0118 | − | 62.8484i | 0.0666920 | − | 0.135158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −373.758 | −0.800339 | −0.400169 | − | 0.916441i | \(-0.631049\pi\) | ||||
−0.400169 | + | 0.916441i | \(0.631049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62.8472i | 0.134003i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −271.082 | − | 133.762i | −0.575545 | − | 0.283995i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 133.183i | 0.281572i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 370.819i | 0.780672i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 323.982 | + | 422.633i | 0.679208 | + | 0.886023i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 915.154i | 1.91055i | 0.295718 | + | 0.955275i | \(0.404441\pi\) | ||||
−0.295718 | + | 0.955275i | \(0.595559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −334.512 | −0.695451 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −266.737 | − | 131.618i | −0.552251 | − | 0.272502i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 51.2227 | 0.105614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 238.560 | 0.489856 | 0.244928 | − | 0.969541i | \(-0.421236\pi\) | ||||
0.244928 | + | 0.969541i | \(0.421236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −187.555 | − | 92.5464i | −0.383547 | − | 0.189257i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 435.657 | 0.887286 | 0.443643 | − | 0.896204i | \(-0.353686\pi\) | ||||
0.443643 | + | 0.896204i | \(0.353686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 769.334i | 1.56052i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −39.5423 | − | 51.5827i | −0.0798835 | − | 0.104207i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 19.8522i | − | 0.0399441i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 209.499i | 0.419838i | 0.977719 | + | 0.209919i | \(0.0673200\pi\) | ||||
−0.977719 | + | 0.209919i | \(0.932680\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 325.051 | + | 160.392i | 0.648804 | + | 0.320144i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 558.314i | 1.10997i | 0.831861 | + | 0.554984i | \(0.187276\pi\) | ||||
−0.831861 | + | 0.554984i | \(0.812724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76.4002 | −0.151287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 187.733 | − | 380.460i | 0.370283 | − | 0.750415i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 319.621 | 0.627939 | 0.313969 | − | 0.949433i | \(-0.398341\pi\) | ||||
0.313969 | + | 0.949433i | \(0.398341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 199.841 | 0.391079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 79.1507 | + | 399.388i | 0.154290 | + | 0.778535i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 80.3357 | 0.155992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 689.710i | 1.33406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.9048 | + | 80.8710i | −0.0768879 | + | 0.155821i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 771.602i | 1.48100i | 0.672055 | + | 0.740501i | \(0.265412\pi\) | ||||
−0.672055 | + | 0.740501i | \(0.734588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 288.856i | 0.552306i | 0.961114 | + | 0.276153i | \(0.0890597\pi\) | ||||
−0.961114 | + | 0.276153i | \(0.910940\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 88.8158 | − | 179.994i | 0.169173 | − | 0.342846i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 542.835i | − | 1.03005i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −798.951 | −1.51030 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −204.180 | − | 266.352i | −0.384521 | − | 0.501605i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −63.8090 | −0.119717 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −95.1503 | −0.177851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −152.375 | + | 308.803i | −0.283753 | + | 0.575053i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 469.371 | 0.870818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 232.871i | − | 0.430446i | −0.976565 | − | 0.215223i | \(-0.930952\pi\) | ||
0.976565 | − | 0.215223i | \(-0.0690478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −488.633 | − | 241.110i | −0.899877 | − | 0.444033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 45.2274i | − | 0.0829861i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 910.003i | 1.66363i | 0.555056 | + | 0.831813i | \(0.312697\pi\) | ||||
−0.555056 | + | 0.831813i | \(0.687303\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 415.699 | − | 318.667i | 0.757192 | − | 0.580449i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 780.096i | − | 1.41578i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −159.191 | −0.287869 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −109.672 | − | 54.1164i | −0.197608 | − | 0.0975071i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 297.809 | 0.534666 | 0.267333 | − | 0.963604i | \(-0.413858\pi\) | ||||
0.267333 | + | 0.963604i | \(0.413858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 61.9877 | 0.110890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −451.456 | − | 222.765i | −0.804734 | − | 0.397086i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 184.465 | 0.327647 | 0.163824 | − | 0.986490i | \(-0.447617\pi\) | ||||
0.163824 | + | 0.986490i | \(0.447617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 83.8212i | 0.148356i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 57.2391 | − | 212.819i | 0.100951 | − | 0.375342i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 404.137i | − | 0.710258i | −0.934817 | − | 0.355129i | \(-0.884437\pi\) | ||
0.934817 | − | 0.355129i | \(-0.115563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 762.365i | − | 1.33514i | −0.744547 | − | 0.667570i | \(-0.767334\pi\) | ||
0.744547 | − | 0.667570i | \(-0.232666\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 562.883 | + | 277.748i | 0.982344 | + | 0.484726i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 896.100i | − | 1.55843i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −290.766 | −0.503927 | −0.251964 | − | 0.967737i | \(-0.581076\pi\) | ||||
−0.251964 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 214.165 | − | 434.027i | 0.369888 | − | 0.749616i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 88.1361 | 0.151697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 667.648 | 1.14519 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.0082 | + | 18.4042i | −0.0410397 | + | 0.0314602i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −224.506 | −0.382464 | −0.191232 | − | 0.981545i | \(-0.561248\pi\) | ||||
−0.191232 | + | 0.981545i | \(0.561248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 550.428i | 0.934513i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −192.425 | + | 389.968i | −0.325592 | + | 0.659844i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 482.620i | 0.813862i | 0.913459 | + | 0.406931i | \(0.133401\pi\) | ||||
−0.913459 | + | 0.406931i | \(0.866599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.8967i | 0.0435238i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −314.967 | + | 638.312i | −0.527583 | + | 1.06920i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 803.277i | 1.34103i | 0.741896 | + | 0.670515i | \(0.233927\pi\) | ||||
−0.741896 | + | 0.670515i | \(0.766073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 126.365 | 0.210258 | 0.105129 | − | 0.994459i | \(-0.466474\pi\) | ||||
0.105129 | + | 0.994459i | \(0.466474\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −164.991 | + | 126.479i | −0.273617 | + | 0.209750i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.04535 | −0.00668653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 397.356 | 0.654623 | 0.327312 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327312 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −186.843 | + | 378.655i | −0.306802 | + | 0.621766i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 321.012 | 0.525388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1056.55i | 1.72357i | 0.507275 | + | 0.861785i | \(0.330653\pi\) | ||||
−0.507275 | + | 0.861785i | \(0.669347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.9203 | − | 10.3229i | −0.0340167 | − | 0.0167851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 411.284i | 0.666586i | 0.942823 | + | 0.333293i | \(0.108160\pi\) | ||||
−0.942823 | + | 0.333293i | \(0.891840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 691.383i | 1.11693i | 0.829526 | + | 0.558467i | \(0.188610\pi\) | ||||
−0.829526 | + | 0.558467i | \(0.811390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −191.271 | − | 965.138i | −0.308005 | − | 1.55417i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 305.435i | − | 0.490264i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 594.447 | 0.951114 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 457.771 | + | 225.881i | 0.730097 | + | 0.360257i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −947.262 | −1.50598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 528.057 | 0.836858 | 0.418429 | − | 0.908250i | \(-0.362581\pi\) | ||||
0.418429 | + | 0.908250i | \(0.362581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −826.238 | − | 407.697i | −1.30527 | − | 0.644071i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 133.895 | 0.210858 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 218.460i | − | 0.342951i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 52.1175 | − | 39.9523i | 0.0815611 | − | 0.0625232i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 134.165i | 0.209306i | 0.994509 | + | 0.104653i | \(0.0333731\pi\) | ||||
−0.994509 | + | 0.104653i | \(0.966627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 633.985i | − | 0.985979i | −0.870035 | − | 0.492990i | \(-0.835904\pi\) | ||
0.870035 | − | 0.492990i | \(-0.164096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.3232 | + | 10.0282i | 0.0315088 | + | 0.0155476i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 227.758i | − | 0.352021i | −0.984388 | − | 0.176011i | \(-0.943681\pi\) | ||
0.984388 | − | 0.176011i | \(-0.0563193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −420.766 | −0.648329 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 131.834 | − | 267.176i | 0.202511 | − | 0.410408i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1190.65 | 1.82336 | 0.911678 | − | 0.410906i | \(-0.134788\pi\) | ||||
0.911678 | + | 0.410906i | \(0.134788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 111.900 | 0.170839 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 402.178 | + | 524.638i | 0.612142 | + | 0.798536i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 266.873 | 0.404967 | 0.202484 | − | 0.979286i | \(-0.435099\pi\) | ||||
0.202484 | + | 0.979286i | \(0.435099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1045.10i | − | 1.58109i | −0.612405 | − | 0.790544i | \(-0.709798\pi\) | ||
0.612405 | − | 0.790544i | \(-0.290202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −103.682 | + | 210.122i | −0.156383 | + | 0.316925i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 26.2589i | − | 0.0394871i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1885.13i | 2.82629i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −581.445 | + | 1178.36i | −0.869126 | + | 1.76137i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 656.693i | − | 0.978678i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 408.300 | 0.606687 | 0.303343 | − | 0.952881i | \(-0.401897\pi\) | ||||
0.303343 | + | 0.952881i | \(0.401897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 651.274 | − | 129.069i | 0.964850 | − | 0.191214i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 749.557 | 1.10717 | 0.553587 | − | 0.832791i | \(-0.313259\pi\) | ||||
0.553587 | + | 0.832791i | \(0.313259\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 217.753 | 0.320697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 359.426 | − | 728.413i | 0.527792 | − | 1.06962i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −258.242 | −0.378099 | −0.189050 | − | 0.981968i | \(-0.560541\pi\) | ||||
−0.189050 | + | 0.981968i | \(0.560541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 104.287i | − | 0.152244i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −265.474 | − | 130.995i | −0.386424 | − | 0.190676i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 310.744i | − | 0.451007i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 929.714i | 1.34546i | 0.739887 | + | 0.672731i | \(0.234879\pi\) | ||||
−0.739887 | + | 0.672731i | \(0.765121\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −168.099 | − | 219.284i | −0.242567 | − | 0.316427i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 124.308i | 0.178861i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −180.693 | −0.259244 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1163.30 | − | 574.016i | −1.66424 | − | 0.821197i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 335.731 | 0.478932 | 0.239466 | − | 0.970905i | \(-0.423028\pi\) | ||||
0.239466 | + | 0.970905i | \(0.423028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 960.513 | 1.36631 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 105.246 | + | 51.9325i | 0.149286 | + | 0.0736632i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −324.785 | −0.459385 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 356.121i | 0.502287i | 0.967950 | + | 0.251143i | \(0.0808065\pi\) | ||||
−0.967950 | + | 0.251143i | \(0.919193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −320.370 | − | 417.921i | −0.450591 | − | 0.587793i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1330.13i | − | 1.86554i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.9266i | 0.0530442i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −741.985 | − | 366.123i | −1.03485 | − | 0.510632i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.7234i | − | 0.0441216i | −0.999757 | − | 0.0220608i | \(-0.992977\pi\) | ||
0.999757 | − | 0.0220608i | \(-0.00702274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 341.516 | 0.473670 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 553.262 | − | 1121.24i | 0.765231 | − | 1.55082i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1272.09 | −1.75460 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 234.202 | 0.322148 | 0.161074 | − | 0.986942i | \(-0.448504\pi\) | ||||
0.161074 | + | 0.986942i | \(0.448504\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 673.901 | − | 278.027i | 0.924418 | − | 0.381381i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 175.535 | 0.240130 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 616.813i | − | 0.841491i | −0.907179 | − | 0.420745i | \(-0.861769\pi\) | ||
0.907179 | − | 0.420745i | \(-0.138231\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.3419 | − | 71.6238i | 0.0480842 | − | 0.0974473i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 260.642i | 0.353653i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 605.806i | 0.819764i | 0.912138 | + | 0.409882i | \(0.134430\pi\) | ||||
−0.912138 | + | 0.409882i | \(0.865570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 105.132 | − | 213.061i | 0.141879 | − | 0.287532i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1033.33i | 1.39076i | 0.718642 | + | 0.695380i | \(0.244764\pi\) | ||||
−0.718642 | + | 0.695380i | \(0.755236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.4216 | 0.0717068 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 177.372 | + | 231.381i | 0.237446 | + | 0.309747i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −404.494 | −0.540046 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −969.301 | −1.29068 | −0.645340 | − | 0.763896i | \(-0.723284\pi\) | ||||
−0.645340 | + | 0.763896i | \(0.723284\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −220.235 | + | 446.329i | −0.292477 | + | 0.592734i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.6240 | 0.0511577 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 533.594i | − | 0.704880i | −0.935835 | − | 0.352440i | \(-0.885352\pi\) | ||
0.935835 | − | 0.352440i | \(-0.114648\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1106.22 | − | 545.851i | −1.45747 | − | 0.719172i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 867.717i | 1.14023i | 0.821564 | + | 0.570116i | \(0.193102\pi\) | ||||
−0.821564 | + | 0.570116i | \(0.806898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 192.267i | − | 0.251988i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −67.9858 | + | 52.1166i | −0.0888704 | + | 0.0681263i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 195.837i | 0.255329i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 194.555 | 0.252997 | 0.126498 | − | 0.991967i | \(-0.459626\pi\) | ||||
0.126498 | + | 0.991967i | \(0.459626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −160.445 | − | 79.1695i | −0.208100 | − | 0.102684i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −420.140 | −0.543519 | −0.271760 | − | 0.962365i | \(-0.587606\pi\) | ||||
−0.271760 | + | 0.962365i | \(0.587606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 897.572 | 1.15816 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −466.229 | − | 230.055i | −0.600037 | − | 0.296081i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 183.220 | 0.235199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 82.3318i | − | 0.105418i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1370.09 | + | 271.524i | −1.74980 | + | 0.346775i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 64.4892i | 0.0821519i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 849.081i | − | 1.07888i | −0.842023 | − | 0.539441i | \(-0.818635\pi\) | ||
0.842023 | − | 0.539441i | \(-0.181365\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 180.952 | + | 89.2883i | 0.229343 | + | 0.113166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 356.333i | 0.450484i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −305.646 | −0.385429 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 50.2714 | − | 101.880i | 0.0632344 | − | 0.128151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 779.186 | 0.977648 | 0.488824 | − | 0.872382i | \(-0.337426\pi\) | ||||
0.488824 | + | 0.872382i | \(0.337426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 909.035 | 1.13772 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 801.849 | − | 614.682i | 1.00106 | − | 0.767393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 828.789 | 1.03212 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 63.4558i | 0.0788270i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 47.9884 | − | 97.2532i | 0.0594651 | − | 0.120512i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 865.140i | 1.06939i | 0.845044 | + | 0.534697i | \(0.179574\pi\) | ||||
−0.845044 | + | 0.534697i | \(0.820426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 251.360i | − | 0.309938i | −0.987919 | − | 0.154969i | \(-0.950472\pi\) | ||
0.987919 | − | 0.154969i | \(-0.0495278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 435.833 | − | 883.258i | 0.536080 | − | 1.08642i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.6185i | 0.0547466i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −177.991 | −0.217859 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −102.061 | + | 78.2384i | −0.124617 | + | 0.0955292i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −103.359 | −0.125894 | −0.0629470 | − | 0.998017i | \(-0.520050\pi\) | ||||
−0.0629470 | + | 0.998017i | \(0.520050\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −474.728 | −0.576826 | −0.288413 | − | 0.957506i | \(-0.593128\pi\) | ||||
−0.288413 | + | 0.957506i | \(0.593128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 368.340 | − | 746.477i | 0.446473 | − | 0.904821i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 471.776 | 0.570467 | 0.285234 | − | 0.958458i | \(-0.407929\pi\) | ||||
0.285234 | + | 0.958458i | \(0.407929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 771.883i | − | 0.931102i | −0.885021 | − | 0.465551i | \(-0.845856\pi\) | ||
0.885021 | − | 0.465551i | \(-0.154144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 163.424 | + | 80.6396i | 0.196660 | + | 0.0970392i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 618.629i | − | 0.742652i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 77.3283i | − | 0.0926087i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 966.723 | − | 191.585i | 1.15499 | − | 0.228895i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 510.944i | 0.608992i | 0.952514 | + | 0.304496i | \(0.0984881\pi\) | ||||
−0.952514 | + | 0.304496i | \(0.901512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1835.10 | 2.18204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −986.877 | − | 486.962i | −1.17067 | − | 0.577654i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −90.5100 | −0.107112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.1972 | −0.0203037 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 279.877 | + | 138.102i | 0.329655 | + | 0.162664i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2321.12 | −2.72752 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 581.090i | − | 0.681231i | −0.940203 | − | 0.340616i | \(-0.889365\pi\) | ||
0.940203 | − | 0.340616i | \(-0.110635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 68.9369 | − | 52.8457i | 0.0806279 | − | 0.0618078i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.21760i | 0.00842193i | 0.999991 | + | 0.00421097i | \(0.00134040\pi\) | ||||
−0.999991 | + | 0.00421097i | \(0.998660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 104.856i | − | 0.122068i | −0.998136 | − | 0.0610339i | \(-0.980560\pi\) | ||
0.998136 | − | 0.0610339i | \(-0.0194398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −88.9344 | − | 43.8836i | −0.103292 | − | 0.0509681i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1213.72i | − | 1.40640i | −0.710992 | − | 0.703200i | \(-0.751754\pi\) | ||
0.710992 | − | 0.703200i | \(-0.248246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.2389 | 0.0222415 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 90.0432 | − | 182.482i | 0.103856 | − | 0.210475i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −660.204 | −0.759729 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 121.311 | 0.139278 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 438.225 | + | 571.661i | 0.501975 | + | 0.654824i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −86.3530 | −0.0986892 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 706.591i | 0.805691i | 0.915268 | + | 0.402846i | \(0.131979\pi\) | ||||
−0.915268 | + | 0.402846i | \(0.868021\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −545.043 | + | 1104.58i | −0.620072 | + | 1.25664i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1715.95i | − | 1.94773i | −0.227134 | − | 0.973864i | \(-0.572935\pi\) | ||
0.227134 | − | 0.973864i | \(-0.427065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1472.11i | 1.66717i | 0.552390 | + | 0.833586i | \(0.313716\pi\) | ||||
−0.552390 | + | 0.833586i | \(0.686284\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.6821 | + | 64.2068i | −0.0357989 | + | 0.0725501i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 277.658i | − | 0.313030i | −0.987676 | − | 0.156515i | \(-0.949974\pi\) | ||
0.987676 | − | 0.156515i | \(-0.0500259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 569.202 | 0.640272 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 237.384 | − | 882.610i | 0.266424 | − | 0.990584i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −921.751 | −1.03220 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.4631 | 0.0820817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −254.056 | + | 514.870i | −0.283229 | + | 0.573991i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1888.23 | −2.10037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 879.957i | − | 0.976645i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 86.3959 | + | 42.6310i | 0.0956766 | + | 0.0472104i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 116.244i | 0.128446i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 365.591i | − | 0.403078i | −0.979481 | − | 0.201539i | \(-0.935406\pi\) | ||
0.979481 | − | 0.201539i | \(-0.0645942\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −653.625 | − | 852.650i | −0.719060 | − | 0.938009i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1664.90i | 1.82755i | 0.406223 | + | 0.913774i | \(0.366846\pi\) | ||||
−0.406223 | + | 0.913774i | \(0.633154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 365.521 | 0.400351 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −100.208 | − | 49.4465i | −0.109517 | − | 0.0540399i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 475.697 | 0.518754 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −195.745 | −0.212998 | −0.106499 | − | 0.994313i | \(-0.533964\pi\) | ||||
−0.106499 | + | 0.994313i | \(0.533964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 726.451 | + | 358.458i | 0.788763 | + | 0.389205i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.3198 | −0.0415166 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1566.29i | − | 1.69328i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 687.295 | + | 896.573i | 0.741419 | + | 0.967177i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 769.046i | − | 0.827822i | −0.910317 | − | 0.413911i | \(-0.864163\pi\) | ||
0.910317 | − | 0.413911i | \(-0.135837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 627.283i | 0.673773i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −676.760 | − | 333.939i | −0.725359 | − | 0.357919i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 107.400i | 0.114866i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0296961 | 3.16928e−5 | 1.58464e−5 | − | 1.00000i | \(-0.499995\pi\) | ||||
1.58464e−5 | 1.00000i | \(0.499995\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 111.451 | − | 225.867i | 0.118692 | − | 0.240540i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1283.68 | −1.36416 | −0.682081 | − | 0.731277i | \(-0.738925\pi\) | ||||
−0.682081 | + | 0.731277i | \(0.738925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −442.760 | −0.469522 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46.1189 | + | 9.13983i | −0.0488030 | + | 0.00967178i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1514.62 | 1.59938 | 0.799692 | − | 0.600410i | \(-0.204996\pi\) | ||||
0.799692 | + | 0.600410i | \(0.204996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 385.744i | − | 0.406474i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −359.403 | + | 728.365i | −0.377921 | + | 0.765894i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 937.870i | − | 0.984124i | −0.870560 | − | 0.492062i | \(-0.836243\pi\) | ||
0.870560 | − | 0.492062i | \(-0.163757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 133.908i | − | 0.140218i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −774.880 | + | 1570.37i | −0.809697 | + | 1.64093i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 443.335i | − | 0.462288i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 371.317 | 0.386386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −814.038 | − | 1061.91i | −0.845315 | − | 1.10271i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −103.253 | −0.106998 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −461.673 | −0.477428 | −0.238714 | − | 0.971090i | \(-0.576726\pi\) | ||||
−0.238714 | + | 0.971090i | \(0.576726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 297.711 | − | 603.340i | 0.307235 | − | 0.622642i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1360.95 | 1.40160 | 0.700798 | − | 0.713360i | \(-0.252827\pi\) | ||||
0.700798 | + | 0.713360i | \(0.252827\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 528.447i | 0.543111i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −347.434 | − | 171.437i | −0.356342 | − | 0.175833i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1162.17i | − | 1.18953i | −0.803901 | − | 0.594763i | \(-0.797246\pi\) | ||
0.803901 | − | 0.594763i | \(-0.202754\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1266.71i | − | 1.29388i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 504.753 | − | 386.934i | 0.514529 | − | 0.394428i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 969.961i | − | 0.986735i | −0.869821 | − | 0.493368i | \(-0.835766\pi\) | ||
0.869821 | − | 0.493368i | \(-0.164234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 92.7717 | 0.0941845 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 447.414 | + | 220.771i | 0.453307 | + | 0.223679i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 430.122 | 0.434906 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1602.81 | 1.61737 | 0.808684 | − | 0.588243i | \(-0.200180\pi\) | ||||
0.808684 | + | 0.588243i | \(0.200180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.6761 | + | 13.1630i | 0.0268641 | + | 0.0132558i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 151.852 | 0.152615 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 742.855i | − | 0.745090i | −0.928014 | − | 0.372545i | \(-0.878485\pi\) | ||
0.928014 | − | 0.372545i | \(-0.121515\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −334.321 | − | 1686.96i | −0.334656 | − | 1.68865i |
(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 | 768.3.h.g.641.11 | 16 | ||
3.2 | odd | 2 | inner | 768.3.h.g.641.5 | 16 | ||
4.3 | odd | 2 | 768.3.h.h.641.6 | 16 | |||
8.3 | odd | 2 | 768.3.h.h.641.11 | 16 | |||
8.5 | even | 2 | inner | 768.3.h.g.641.6 | 16 | ||
12.11 | even | 2 | 768.3.h.h.641.12 | 16 | |||
16.3 | odd | 4 | 384.3.e.c.257.1 | yes | 8 | ||
16.5 | even | 4 | 384.3.e.d.257.1 | yes | 8 | ||
16.11 | odd | 4 | 384.3.e.a.257.8 | yes | 8 | ||
16.13 | even | 4 | 384.3.e.b.257.8 | yes | 8 | ||
24.5 | odd | 2 | inner | 768.3.h.g.641.12 | 16 | ||
24.11 | even | 2 | 768.3.h.h.641.5 | 16 | |||
48.5 | odd | 4 | 384.3.e.d.257.2 | yes | 8 | ||
48.11 | even | 4 | 384.3.e.a.257.7 | ✓ | 8 | ||
48.29 | odd | 4 | 384.3.e.b.257.7 | yes | 8 | ||
48.35 | even | 4 | 384.3.e.c.257.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.7 | ✓ | 8 | 48.11 | even | 4 | ||
384.3.e.a.257.8 | yes | 8 | 16.11 | odd | 4 | ||
384.3.e.b.257.7 | yes | 8 | 48.29 | odd | 4 | ||
384.3.e.b.257.8 | yes | 8 | 16.13 | even | 4 | ||
384.3.e.c.257.1 | yes | 8 | 16.3 | odd | 4 | ||
384.3.e.c.257.2 | yes | 8 | 48.35 | even | 4 | ||
384.3.e.d.257.1 | yes | 8 | 16.5 | even | 4 | ||
384.3.e.d.257.2 | yes | 8 | 48.5 | odd | 4 | ||
768.3.h.g.641.5 | 16 | 3.2 | odd | 2 | inner | ||
768.3.h.g.641.6 | 16 | 8.5 | even | 2 | inner | ||
768.3.h.g.641.11 | 16 | 1.1 | even | 1 | trivial | ||
768.3.h.g.641.12 | 16 | 24.5 | odd | 2 | inner | ||
768.3.h.h.641.5 | 16 | 24.11 | even | 2 | |||
768.3.h.h.641.6 | 16 | 4.3 | odd | 2 | |||
768.3.h.h.641.11 | 16 | 8.3 | odd | 2 | |||
768.3.h.h.641.12 | 16 | 12.11 | even | 2 |