Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.a (trivial) |
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: | yes |
Analytic conductor: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17009 | 1.53448 | 0.767241 | − | 0.641358i | \(-0.221629\pi\) | ||||
0.767241 | + | 0.641358i | \(0.221629\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.70928 | 1.35464 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.17009 | −0.885934 | ||||||||
\(7\) | 3.70928 | 1.40197 | 0.700987 | − | 0.713174i | \(-0.252743\pi\) | ||||
0.700987 | + | 0.713174i | \(0.252743\pi\) | |||||||
\(8\) | 1.53919 | 0.544185 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.70928 | −0.782100 | ||||||||
\(13\) | −1.70928 | −0.474068 | −0.237034 | − | 0.971501i | \(-0.576175\pi\) | ||||
−0.237034 | + | 0.971501i | \(0.576175\pi\) | |||||||
\(14\) | 8.04945 | 2.15131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | −6.04945 | −1.46721 | −0.733603 | − | 0.679578i | \(-0.762163\pi\) | ||||
−0.733603 | + | 0.679578i | \(0.762163\pi\) | |||||||
\(18\) | 2.17009 | 0.511494 | ||||||||
\(19\) | 3.07838 | 0.706228 | 0.353114 | − | 0.935580i | \(-0.385123\pi\) | ||||
0.353114 | + | 0.935580i | \(0.385123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.70928 | −0.809430 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −1.53919 | −0.314186 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.70928 | −0.727449 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 10.0494 | 1.89917 | ||||||||
\(29\) | −5.26180 | −0.977091 | −0.488545 | − | 0.872538i | \(-0.662472\pi\) | ||||
−0.488545 | + | 0.872538i | \(0.662472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.34017 | −1.13873 | −0.569364 | − | 0.822085i | \(-0.692811\pi\) | ||||
−0.569364 | + | 0.822085i | \(0.692811\pi\) | |||||||
\(32\) | −7.58864 | −1.34149 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.1278 | −2.25140 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.70928 | 0.451546 | ||||||||
\(37\) | 3.41855 | 0.562006 | 0.281003 | − | 0.959707i | \(-0.409333\pi\) | ||||
0.281003 | + | 0.959707i | \(0.409333\pi\) | |||||||
\(38\) | 6.68035 | 1.08370 | ||||||||
\(39\) | 1.70928 | 0.273703 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.57531 | −1.49541 | −0.747706 | − | 0.664030i | \(-0.768845\pi\) | ||||
−0.747706 | + | 0.664030i | \(0.768845\pi\) | |||||||
\(42\) | −8.04945 | −1.24206 | ||||||||
\(43\) | −3.12783 | −0.476989 | −0.238495 | − | 0.971144i | \(-0.576654\pi\) | ||||
−0.238495 | + | 0.971144i | \(0.576654\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.68035 | −1.27985 | ||||||||
\(47\) | −2.73820 | −0.399408 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(48\) | 2.07838 | 0.299988 | ||||||||
\(49\) | 6.75872 | 0.965532 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.04945 | 0.847092 | ||||||||
\(52\) | −4.63090 | −0.642190 | ||||||||
\(53\) | −13.7587 | −1.88991 | −0.944953 | − | 0.327206i | \(-0.893893\pi\) | ||||
−0.944953 | + | 0.327206i | \(0.893893\pi\) | |||||||
\(54\) | −2.17009 | −0.295311 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.70928 | 0.762934 | ||||||||
\(57\) | −3.07838 | −0.407741 | ||||||||
\(58\) | −11.4186 | −1.49933 | ||||||||
\(59\) | −3.60197 | −0.468936 | −0.234468 | − | 0.972124i | \(-0.575335\pi\) | ||||
−0.234468 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6803 | 1.87963 | 0.939813 | − | 0.341690i | \(-0.110999\pi\) | ||||
0.939813 | + | 0.341690i | \(0.110999\pi\) | |||||||
\(62\) | −13.7587 | −1.74736 | ||||||||
\(63\) | 3.70928 | 0.467325 | ||||||||
\(64\) | −12.3112 | −1.53891 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.84324 | −0.225188 | −0.112594 | − | 0.993641i | \(-0.535916\pi\) | ||||
−0.112594 | + | 0.993641i | \(0.535916\pi\) | |||||||
\(68\) | −16.3896 | −1.98753 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.23513 | −0.858652 | −0.429326 | − | 0.903150i | \(-0.641249\pi\) | ||||
−0.429326 | + | 0.903150i | \(0.641249\pi\) | |||||||
\(72\) | 1.53919 | 0.181395 | ||||||||
\(73\) | 6.38962 | 0.747849 | 0.373924 | − | 0.927459i | \(-0.378012\pi\) | ||||
0.373924 | + | 0.927459i | \(0.378012\pi\) | |||||||
\(74\) | 7.41855 | 0.862389 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.34017 | 0.956683 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.70928 | 0.419993 | ||||||||
\(79\) | 7.44521 | 0.837652 | 0.418826 | − | 0.908067i | \(-0.362442\pi\) | ||||
0.418826 | + | 0.908067i | \(0.362442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −20.7792 | −2.29468 | ||||||||
\(83\) | −7.86603 | −0.863409 | −0.431705 | − | 0.902015i | \(-0.642088\pi\) | ||||
−0.431705 | + | 0.902015i | \(0.642088\pi\) | |||||||
\(84\) | −10.0494 | −1.09648 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.78765 | −0.731931 | ||||||||
\(87\) | 5.26180 | 0.564124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.02052 | −0.532174 | −0.266087 | − | 0.963949i | \(-0.585731\pi\) | ||||
−0.266087 | + | 0.963949i | \(0.585731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.34017 | −0.664631 | ||||||||
\(92\) | −10.8371 | −1.12985 | ||||||||
\(93\) | 6.34017 | 0.657445 | ||||||||
\(94\) | −5.94214 | −0.612885 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.58864 | 0.774512 | ||||||||
\(97\) | −16.9939 | −1.72546 | −0.862732 | − | 0.505661i | \(-0.831249\pi\) | ||||
−0.862732 | + | 0.505661i | \(0.831249\pi\) | |||||||
\(98\) | 14.6670 | 1.48159 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.9360 | 1.88420 | 0.942101 | − | 0.335329i | \(-0.108847\pi\) | ||||
0.942101 | + | 0.335329i | \(0.108847\pi\) | |||||||
\(102\) | 13.1278 | 1.29985 | ||||||||
\(103\) | 11.7854 | 1.16125 | 0.580624 | − | 0.814172i | \(-0.302809\pi\) | ||||
0.580624 | + | 0.814172i | \(0.302809\pi\) | |||||||
\(104\) | −2.63090 | −0.257981 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.8576 | −2.90003 | ||||||||
\(107\) | 11.2846 | 1.09092 | 0.545461 | − | 0.838136i | \(-0.316355\pi\) | ||||
0.545461 | + | 0.838136i | \(0.316355\pi\) | |||||||
\(108\) | −2.70928 | −0.260700 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.41855 | −0.324474 | ||||||||
\(112\) | −7.70928 | −0.728458 | ||||||||
\(113\) | 0.496928 | 0.0467471 | 0.0233735 | − | 0.999727i | \(-0.492559\pi\) | ||||
0.0233735 | + | 0.999727i | \(0.492559\pi\) | |||||||
\(114\) | −6.68035 | −0.625672 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.2557 | −1.32360 | ||||||||
\(117\) | −1.70928 | −0.158023 | ||||||||
\(118\) | −7.81658 | −0.719575 | ||||||||
\(119\) | −22.4391 | −2.05699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 31.8576 | 2.88425 | ||||||||
\(123\) | 9.57531 | 0.863376 | ||||||||
\(124\) | −17.1773 | −1.54256 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.04945 | 0.717102 | ||||||||
\(127\) | 2.81432 | 0.249730 | 0.124865 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124865 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(128\) | −11.5392 | −1.01993 | ||||||||
\(129\) | 3.12783 | 0.275390 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.68035 | −0.758405 | −0.379203 | − | 0.925314i | \(-0.623802\pi\) | ||||
−0.379203 | + | 0.925314i | \(0.623802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4186 | 0.990114 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.31124 | −0.798433 | ||||||||
\(137\) | −1.07838 | −0.0921320 | −0.0460660 | − | 0.998938i | \(-0.514668\pi\) | ||||
−0.0460660 | + | 0.998938i | \(0.514668\pi\) | |||||||
\(138\) | 8.68035 | 0.738920 | ||||||||
\(139\) | −10.2823 | −0.872135 | −0.436067 | − | 0.899914i | \(-0.643629\pi\) | ||||
−0.436067 | + | 0.899914i | \(0.643629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.73820 | 0.230598 | ||||||||
\(142\) | −15.7009 | −1.31759 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.07838 | −0.173198 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.8660 | 1.14756 | ||||||||
\(147\) | −6.75872 | −0.557450 | ||||||||
\(148\) | 9.26180 | 0.761315 | ||||||||
\(149\) | −11.4186 | −0.935444 | −0.467722 | − | 0.883876i | \(-0.654925\pi\) | ||||
−0.467722 | + | 0.883876i | \(0.654925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.92162 | 0.400516 | 0.200258 | − | 0.979743i | \(-0.435822\pi\) | ||||
0.200258 | + | 0.979743i | \(0.435822\pi\) | |||||||
\(152\) | 4.73820 | 0.384319 | ||||||||
\(153\) | −6.04945 | −0.489069 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.63090 | 0.370769 | ||||||||
\(157\) | 3.41855 | 0.272830 | 0.136415 | − | 0.990652i | \(-0.456442\pi\) | ||||
0.136415 | + | 0.990652i | \(0.456442\pi\) | |||||||
\(158\) | 16.1568 | 1.28536 | ||||||||
\(159\) | 13.7587 | 1.09114 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.8371 | −1.16933 | ||||||||
\(162\) | 2.17009 | 0.170498 | ||||||||
\(163\) | −9.26180 | −0.725440 | −0.362720 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362720 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(164\) | −25.9421 | −2.02574 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.0700 | −1.32489 | ||||||||
\(167\) | 7.55252 | 0.584432 | 0.292216 | − | 0.956352i | \(-0.405607\pi\) | ||||
0.292216 | + | 0.956352i | \(0.405607\pi\) | |||||||
\(168\) | −5.70928 | −0.440480 | ||||||||
\(169\) | −10.0784 | −0.775260 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.07838 | 0.235409 | ||||||||
\(172\) | −8.47414 | −0.646147 | ||||||||
\(173\) | 6.14834 | 0.467450 | 0.233725 | − | 0.972303i | \(-0.424908\pi\) | ||||
0.233725 | + | 0.972303i | \(0.424908\pi\) | |||||||
\(174\) | 11.4186 | 0.865638 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.60197 | 0.270741 | ||||||||
\(178\) | −10.8950 | −0.816612 | ||||||||
\(179\) | −6.15676 | −0.460178 | −0.230089 | − | 0.973170i | \(-0.573902\pi\) | ||||
−0.230089 | + | 0.973170i | \(0.573902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5958 | 1.08490 | 0.542450 | − | 0.840088i | \(-0.317497\pi\) | ||||
0.542450 | + | 0.840088i | \(0.317497\pi\) | |||||||
\(182\) | −13.7587 | −1.01986 | ||||||||
\(183\) | −14.6803 | −1.08520 | ||||||||
\(184\) | −6.15676 | −0.453882 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.7587 | 1.00884 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.41855 | −0.541053 | ||||||||
\(189\) | −3.70928 | −0.269810 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.84324 | 0.422802 | 0.211401 | − | 0.977399i | \(-0.432197\pi\) | ||||
0.211401 | + | 0.977399i | \(0.432197\pi\) | |||||||
\(192\) | 12.3112 | 0.888487 | ||||||||
\(193\) | 2.02279 | 0.145603 | 0.0728017 | − | 0.997346i | \(-0.476806\pi\) | ||||
0.0728017 | + | 0.997346i | \(0.476806\pi\) | |||||||
\(194\) | −36.8781 | −2.64770 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.3112 | 1.30795 | ||||||||
\(197\) | 17.8348 | 1.27068 | 0.635340 | − | 0.772233i | \(-0.280860\pi\) | ||||
0.635340 | + | 0.772233i | \(0.280860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.6742 | 1.82000 | 0.909998 | − | 0.414613i | \(-0.136083\pi\) | ||||
0.909998 | + | 0.414613i | \(0.136083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.84324 | 0.130012 | ||||||||
\(202\) | 41.0928 | 2.89128 | ||||||||
\(203\) | −19.5174 | −1.36986 | ||||||||
\(204\) | 16.3896 | 1.14750 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 25.5753 | 1.78192 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 3.55252 | 0.246323 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.43907 | −0.580970 | −0.290485 | − | 0.956880i | \(-0.593817\pi\) | ||||
−0.290485 | + | 0.956880i | \(0.593817\pi\) | |||||||
\(212\) | −37.2762 | −2.56014 | ||||||||
\(213\) | 7.23513 | 0.495743 | ||||||||
\(214\) | 24.4885 | 1.67400 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.53919 | −0.104729 | ||||||||
\(217\) | −23.5174 | −1.59647 | ||||||||
\(218\) | 21.7009 | 1.46977 | ||||||||
\(219\) | −6.38962 | −0.431771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3402 | 0.695555 | ||||||||
\(222\) | −7.41855 | −0.497901 | ||||||||
\(223\) | −12.5814 | −0.842516 | −0.421258 | − | 0.906941i | \(-0.638411\pi\) | ||||
−0.421258 | + | 0.906941i | \(0.638411\pi\) | |||||||
\(224\) | −28.1483 | −1.88074 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.07838 | 0.0717326 | ||||||||
\(227\) | 4.23287 | 0.280945 | 0.140473 | − | 0.990085i | \(-0.455138\pi\) | ||||
0.140473 | + | 0.990085i | \(0.455138\pi\) | |||||||
\(228\) | −8.34017 | −0.552341 | ||||||||
\(229\) | −26.1978 | −1.73120 | −0.865599 | − | 0.500737i | \(-0.833062\pi\) | ||||
−0.865599 | + | 0.500737i | \(0.833062\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.09890 | −0.531719 | ||||||||
\(233\) | −18.6309 | −1.22055 | −0.610275 | − | 0.792189i | \(-0.708941\pi\) | ||||
−0.610275 | + | 0.792189i | \(0.708941\pi\) | |||||||
\(234\) | −3.70928 | −0.242483 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.75872 | −0.635239 | ||||||||
\(237\) | −7.44521 | −0.483619 | ||||||||
\(238\) | −48.6947 | −3.15641 | ||||||||
\(239\) | −22.3545 | −1.44600 | −0.722998 | − | 0.690850i | \(-0.757236\pi\) | ||||
−0.722998 | + | 0.690850i | \(0.757236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.20394 | −0.592878 | −0.296439 | − | 0.955052i | \(-0.595799\pi\) | ||||
−0.296439 | + | 0.955052i | \(0.595799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 39.7731 | 2.54621 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 20.7792 | 1.32484 | ||||||||
\(247\) | −5.26180 | −0.334800 | ||||||||
\(248\) | −9.75872 | −0.619680 | ||||||||
\(249\) | 7.86603 | 0.498489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1256 | −1.39655 | −0.698276 | − | 0.715828i | \(-0.746049\pi\) | ||||
−0.698276 | + | 0.715828i | \(0.746049\pi\) | |||||||
\(252\) | 10.0494 | 0.633056 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.10731 | 0.383207 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | −3.02052 | −0.188415 | −0.0942074 | − | 0.995553i | \(-0.530032\pi\) | ||||
−0.0942074 | + | 0.995553i | \(0.530032\pi\) | |||||||
\(258\) | 6.78765 | 0.422581 | ||||||||
\(259\) | 12.6803 | 0.787918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.26180 | −0.325697 | ||||||||
\(262\) | −18.8371 | −1.16376 | ||||||||
\(263\) | 18.2907 | 1.12785 | 0.563927 | − | 0.825825i | \(-0.309290\pi\) | ||||
0.563927 | + | 0.825825i | \(0.309290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 24.7792 | 1.51931 | ||||||||
\(267\) | 5.02052 | 0.307251 | ||||||||
\(268\) | −4.99386 | −0.305048 | ||||||||
\(269\) | 30.5646 | 1.86356 | 0.931779 | − | 0.363026i | \(-0.118256\pi\) | ||||
0.931779 | + | 0.363026i | \(0.118256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0722 | 1.21930 | 0.609651 | − | 0.792670i | \(-0.291310\pi\) | ||||
0.609651 | + | 0.792670i | \(0.291310\pi\) | |||||||
\(272\) | 12.5730 | 0.762352 | ||||||||
\(273\) | 6.34017 | 0.383725 | ||||||||
\(274\) | −2.34017 | −0.141375 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.8371 | 0.652317 | ||||||||
\(277\) | 0.760991 | 0.0457235 | 0.0228618 | − | 0.999739i | \(-0.492722\pi\) | ||||
0.0228618 | + | 0.999739i | \(0.492722\pi\) | |||||||
\(278\) | −22.3135 | −1.33828 | ||||||||
\(279\) | −6.34017 | −0.379576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.581449 | −0.0346864 | −0.0173432 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173432 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(282\) | 5.94214 | 0.353849 | ||||||||
\(283\) | −10.8143 | −0.642844 | −0.321422 | − | 0.946936i | \(-0.604161\pi\) | ||||
−0.321422 | + | 0.946936i | \(0.604161\pi\) | |||||||
\(284\) | −19.6020 | −1.16316 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −35.5174 | −2.09653 | ||||||||
\(288\) | −7.58864 | −0.447165 | ||||||||
\(289\) | 19.5958 | 1.15270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.9939 | 0.996198 | ||||||||
\(292\) | 17.3112 | 1.01306 | ||||||||
\(293\) | 7.04331 | 0.411474 | 0.205737 | − | 0.978607i | \(-0.434041\pi\) | ||||
0.205737 | + | 0.978607i | \(0.434041\pi\) | |||||||
\(294\) | −14.6670 | −0.855398 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.26180 | 0.305836 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.7792 | −1.43542 | ||||||||
\(299\) | 6.83710 | 0.395400 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.6020 | −0.668726 | ||||||||
\(302\) | 10.6803 | 0.614585 | ||||||||
\(303\) | −18.9360 | −1.08784 | ||||||||
\(304\) | −6.39803 | −0.366952 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.1278 | −0.750468 | ||||||||
\(307\) | −20.1750 | −1.15145 | −0.575724 | − | 0.817644i | \(-0.695280\pi\) | ||||
−0.575724 | + | 0.817644i | \(0.695280\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.7854 | −0.670447 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2762 | 1.20646 | 0.603230 | − | 0.797567i | \(-0.293880\pi\) | ||||
0.603230 | + | 0.797567i | \(0.293880\pi\) | |||||||
\(312\) | 2.63090 | 0.148945 | ||||||||
\(313\) | −16.4657 | −0.930698 | −0.465349 | − | 0.885127i | \(-0.654071\pi\) | ||||
−0.465349 | + | 0.885127i | \(0.654071\pi\) | |||||||
\(314\) | 7.41855 | 0.418653 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.1711 | 1.13471 | ||||||||
\(317\) | 22.1711 | 1.24525 | 0.622627 | − | 0.782518i | \(-0.286065\pi\) | ||||
0.622627 | + | 0.782518i | \(0.286065\pi\) | |||||||
\(318\) | 29.8576 | 1.67433 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.2846 | −0.629844 | ||||||||
\(322\) | −32.1978 | −1.79431 | ||||||||
\(323\) | −18.6225 | −1.03618 | ||||||||
\(324\) | 2.70928 | 0.150515 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.0989 | −1.11317 | ||||||||
\(327\) | −10.0000 | −0.553001 | ||||||||
\(328\) | −14.7382 | −0.813781 | ||||||||
\(329\) | −10.1568 | −0.559960 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.34017 | −0.348487 | −0.174244 | − | 0.984703i | \(-0.555748\pi\) | ||||
−0.174244 | + | 0.984703i | \(0.555748\pi\) | |||||||
\(332\) | −21.3112 | −1.16961 | ||||||||
\(333\) | 3.41855 | 0.187335 | ||||||||
\(334\) | 16.3896 | 0.896800 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.70928 | 0.420575 | ||||||||
\(337\) | 3.18568 | 0.173535 | 0.0867677 | − | 0.996229i | \(-0.472346\pi\) | ||||
0.0867677 | + | 0.996229i | \(0.472346\pi\) | |||||||
\(338\) | −21.8710 | −1.18962 | ||||||||
\(339\) | −0.496928 | −0.0269894 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.68035 | 0.361232 | ||||||||
\(343\) | −0.894960 | −0.0483233 | ||||||||
\(344\) | −4.81432 | −0.259570 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3424 | 0.717294 | ||||||||
\(347\) | −5.39576 | −0.289660 | −0.144830 | − | 0.989457i | \(-0.546263\pi\) | ||||
−0.144830 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(348\) | 14.2557 | 0.764183 | ||||||||
\(349\) | 15.6742 | 0.839021 | 0.419510 | − | 0.907751i | \(-0.362202\pi\) | ||||
0.419510 | + | 0.907751i | \(0.362202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.70928 | 0.0912344 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.75872 | 0.306506 | 0.153253 | − | 0.988187i | \(-0.451025\pi\) | ||||
0.153253 | + | 0.988187i | \(0.451025\pi\) | |||||||
\(354\) | 7.81658 | 0.415447 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.6020 | −0.720903 | ||||||||
\(357\) | 22.4391 | 1.18760 | ||||||||
\(358\) | −13.3607 | −0.706135 | ||||||||
\(359\) | 10.5236 | 0.555414 | 0.277707 | − | 0.960666i | \(-0.410426\pi\) | ||||
0.277707 | + | 0.960666i | \(0.410426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.52359 | −0.501242 | ||||||||
\(362\) | 31.6742 | 1.66476 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.1773 | −0.900334 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −31.8576 | −1.66522 | ||||||||
\(367\) | −8.89496 | −0.464313 | −0.232157 | − | 0.972678i | \(-0.574578\pi\) | ||||
−0.232157 | + | 0.972678i | \(0.574578\pi\) | |||||||
\(368\) | 8.31351 | 0.433372 | ||||||||
\(369\) | −9.57531 | −0.498471 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −51.0349 | −2.64960 | ||||||||
\(372\) | 17.1773 | 0.890600 | ||||||||
\(373\) | −23.1689 | −1.19964 | −0.599819 | − | 0.800136i | \(-0.704761\pi\) | ||||
−0.599819 | + | 0.800136i | \(0.704761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.21461 | −0.217352 | ||||||||
\(377\) | 8.99386 | 0.463207 | ||||||||
\(378\) | −8.04945 | −0.414019 | ||||||||
\(379\) | −11.8310 | −0.607716 | −0.303858 | − | 0.952717i | \(-0.598275\pi\) | ||||
−0.303858 | + | 0.952717i | \(0.598275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.81432 | −0.144182 | ||||||||
\(382\) | 12.6803 | 0.648783 | ||||||||
\(383\) | −25.9421 | −1.32558 | −0.662791 | − | 0.748805i | \(-0.730628\pi\) | ||||
−0.662791 | + | 0.748805i | \(0.730628\pi\) | |||||||
\(384\) | 11.5392 | 0.588857 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.38962 | 0.223426 | ||||||||
\(387\) | −3.12783 | −0.158996 | ||||||||
\(388\) | −46.0410 | −2.33738 | ||||||||
\(389\) | 1.00614 | 0.0510135 | 0.0255067 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255067 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.1978 | 1.22374 | ||||||||
\(392\) | 10.4030 | 0.525428 | ||||||||
\(393\) | 8.68035 | 0.437866 | ||||||||
\(394\) | 38.7031 | 1.94984 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.7214 | −1.74262 | −0.871308 | − | 0.490736i | \(-0.836728\pi\) | ||||
−0.871308 | + | 0.490736i | \(0.836728\pi\) | |||||||
\(398\) | 55.7152 | 2.79275 | ||||||||
\(399\) | −11.4186 | −0.571643 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.0205 | −0.650214 | −0.325107 | − | 0.945677i | \(-0.605400\pi\) | ||||
−0.325107 | + | 0.945677i | \(0.605400\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | 10.8371 | 0.539834 | ||||||||
\(404\) | 51.3028 | 2.55241 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −42.3545 | −2.10202 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.31124 | 0.460975 | ||||||||
\(409\) | 29.5174 | 1.45954 | 0.729772 | − | 0.683691i | \(-0.239626\pi\) | ||||
0.729772 | + | 0.683691i | \(0.239626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.07838 | 0.0531925 | ||||||||
\(412\) | 31.9299 | 1.57307 | ||||||||
\(413\) | −13.3607 | −0.657437 | ||||||||
\(414\) | −8.68035 | −0.426616 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.9711 | 0.635959 | ||||||||
\(417\) | 10.2823 | 0.503527 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.15676 | −0.300777 | −0.150389 | − | 0.988627i | \(-0.548052\pi\) | ||||
−0.150389 | + | 0.988627i | \(0.548052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.96880 | 0.485850 | 0.242925 | − | 0.970045i | \(-0.421893\pi\) | ||||
0.242925 | + | 0.970045i | \(0.421893\pi\) | |||||||
\(422\) | −18.3135 | −0.891488 | ||||||||
\(423\) | −2.73820 | −0.133136 | ||||||||
\(424\) | −21.1773 | −1.02846 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.7009 | 0.760709 | ||||||||
\(427\) | 54.4534 | 2.63519 | ||||||||
\(428\) | 30.5730 | 1.47780 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.68035 | −0.418118 | −0.209059 | − | 0.977903i | \(-0.567040\pi\) | ||||
−0.209059 | + | 0.977903i | \(0.567040\pi\) | |||||||
\(432\) | 2.07838 | 0.0999960 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | −51.0349 | −2.44975 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.0928 | 1.29751 | ||||||||
\(437\) | −12.3135 | −0.589035 | ||||||||
\(438\) | −13.8660 | −0.662545 | ||||||||
\(439\) | −3.07838 | −0.146923 | −0.0734615 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734615 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.75872 | 0.321844 | ||||||||
\(442\) | 22.4391 | 1.06732 | ||||||||
\(443\) | −29.2618 | −1.39027 | −0.695135 | − | 0.718879i | \(-0.744655\pi\) | ||||
−0.695135 | + | 0.718879i | \(0.744655\pi\) | |||||||
\(444\) | −9.26180 | −0.439545 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −27.3028 | −1.29283 | ||||||||
\(447\) | 11.4186 | 0.540079 | ||||||||
\(448\) | −45.6658 | −2.15751 | ||||||||
\(449\) | 10.6947 | 0.504715 | 0.252358 | − | 0.967634i | \(-0.418794\pi\) | ||||
0.252358 | + | 0.967634i | \(0.418794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.34632 | 0.0633254 | ||||||||
\(453\) | −4.92162 | −0.231238 | ||||||||
\(454\) | 9.18568 | 0.431106 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.73820 | −0.221887 | ||||||||
\(457\) | 22.8554 | 1.06913 | 0.534564 | − | 0.845128i | \(-0.320476\pi\) | ||||
0.534564 | + | 0.845128i | \(0.320476\pi\) | |||||||
\(458\) | −56.8515 | −2.65650 | ||||||||
\(459\) | 6.04945 | 0.282364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7731 | 1.01407 | 0.507037 | − | 0.861924i | \(-0.330741\pi\) | ||||
0.507037 | + | 0.861924i | \(0.330741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8950 | −1.15697 | −0.578483 | − | 0.815694i | \(-0.696355\pi\) | ||||
−0.578483 | + | 0.815694i | \(0.696355\pi\) | |||||||
\(464\) | 10.9360 | 0.507691 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.4307 | −1.87291 | ||||||||
\(467\) | 19.2039 | 0.888652 | 0.444326 | − | 0.895865i | \(-0.353443\pi\) | ||||
0.444326 | + | 0.895865i | \(0.353443\pi\) | |||||||
\(468\) | −4.63090 | −0.214063 | ||||||||
\(469\) | −6.83710 | −0.315708 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.41855 | −0.157519 | ||||||||
\(472\) | −5.54411 | −0.255188 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −16.1568 | −0.742104 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −60.7936 | −2.78647 | ||||||||
\(477\) | −13.7587 | −0.629969 | ||||||||
\(478\) | −48.5113 | −2.21886 | ||||||||
\(479\) | −9.47641 | −0.432988 | −0.216494 | − | 0.976284i | \(-0.569462\pi\) | ||||
−0.216494 | + | 0.976284i | \(0.569462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.84324 | −0.266429 | ||||||||
\(482\) | −19.9733 | −0.909761 | ||||||||
\(483\) | 14.8371 | 0.675111 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.17009 | −0.0984371 | ||||||||
\(487\) | −35.2039 | −1.59524 | −0.797621 | − | 0.603159i | \(-0.793909\pi\) | ||||
−0.797621 | + | 0.603159i | \(0.793909\pi\) | |||||||
\(488\) | 22.5958 | 1.02286 | ||||||||
\(489\) | 9.26180 | 0.418833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | 25.9421 | 1.16956 | ||||||||
\(493\) | 31.8310 | 1.43359 | ||||||||
\(494\) | −11.4186 | −0.513745 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.1773 | 0.591677 | ||||||||
\(497\) | −26.8371 | −1.20381 | ||||||||
\(498\) | 17.0700 | 0.764924 | ||||||||
\(499\) | 26.1568 | 1.17094 | 0.585469 | − | 0.810695i | \(-0.300911\pi\) | ||||
0.585469 | + | 0.810695i | \(0.300911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.55252 | −0.337422 | ||||||||
\(502\) | −48.0144 | −2.14299 | ||||||||
\(503\) | −28.2784 | −1.26087 | −0.630437 | − | 0.776241i | \(-0.717124\pi\) | ||||
−0.630437 | + | 0.776241i | \(0.717124\pi\) | |||||||
\(504\) | 5.70928 | 0.254311 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0784 | 0.447596 | ||||||||
\(508\) | 7.62475 | 0.338294 | ||||||||
\(509\) | 8.47027 | 0.375438 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7009 | 1.04846 | ||||||||
\(512\) | 22.1701 | 0.979789 | ||||||||
\(513\) | −3.07838 | −0.135914 | ||||||||
\(514\) | −6.55479 | −0.289119 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.47414 | 0.373053 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 27.5174 | 1.20905 | ||||||||
\(519\) | −6.14834 | −0.269882 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.7009 | 0.600246 | 0.300123 | − | 0.953901i | \(-0.402972\pi\) | ||||
0.300123 | + | 0.953901i | \(0.402972\pi\) | |||||||
\(522\) | −11.4186 | −0.499776 | ||||||||
\(523\) | 24.4885 | 1.07081 | 0.535404 | − | 0.844596i | \(-0.320159\pi\) | ||||
0.535404 | + | 0.844596i | \(0.320159\pi\) | |||||||
\(524\) | −23.5174 | −1.02736 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 39.6925 | 1.73067 | ||||||||
\(527\) | 38.3545 | 1.67075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.60197 | −0.156312 | ||||||||
\(532\) | 30.9360 | 1.34125 | ||||||||
\(533\) | 16.3668 | 0.708926 | ||||||||
\(534\) | 10.8950 | 0.471471 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.83710 | −0.122544 | ||||||||
\(537\) | 6.15676 | 0.265684 | ||||||||
\(538\) | 66.3279 | 2.85960 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.83710 | −0.207963 | −0.103982 | − | 0.994579i | \(-0.533158\pi\) | ||||
−0.103982 | + | 0.994579i | \(0.533158\pi\) | |||||||
\(542\) | 43.5585 | 1.87100 | ||||||||
\(543\) | −14.5958 | −0.626367 | ||||||||
\(544\) | 45.9071 | 1.96825 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.7587 | 0.588819 | ||||||||
\(547\) | −30.5464 | −1.30607 | −0.653034 | − | 0.757328i | \(-0.726504\pi\) | ||||
−0.653034 | + | 0.757328i | \(0.726504\pi\) | |||||||
\(548\) | −2.92162 | −0.124806 | ||||||||
\(549\) | 14.6803 | 0.626542 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1978 | −0.690049 | ||||||||
\(552\) | 6.15676 | 0.262049 | ||||||||
\(553\) | 27.6163 | 1.17437 | ||||||||
\(554\) | 1.65142 | 0.0701620 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.8576 | −1.18143 | ||||||||
\(557\) | −7.57918 | −0.321140 | −0.160570 | − | 0.987024i | \(-0.551333\pi\) | ||||
−0.160570 | + | 0.987024i | \(0.551333\pi\) | |||||||
\(558\) | −13.7587 | −0.582453 | ||||||||
\(559\) | 5.34632 | 0.226125 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.26180 | −0.0532256 | ||||||||
\(563\) | −14.1750 | −0.597405 | −0.298703 | − | 0.954346i | \(-0.596554\pi\) | ||||
−0.298703 | + | 0.954346i | \(0.596554\pi\) | |||||||
\(564\) | 7.41855 | 0.312377 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.4680 | −0.986434 | ||||||||
\(567\) | 3.70928 | 0.155775 | ||||||||
\(568\) | −11.1362 | −0.467266 | ||||||||
\(569\) | 14.7382 | 0.617858 | 0.308929 | − | 0.951085i | \(-0.400030\pi\) | ||||
0.308929 | + | 0.951085i | \(0.400030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23513 | −0.0516887 | −0.0258444 | − | 0.999666i | \(-0.508227\pi\) | ||||
−0.0258444 | + | 0.999666i | \(0.508227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.84324 | −0.244105 | ||||||||
\(574\) | −77.0759 | −3.21709 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.3112 | −0.512968 | ||||||||
\(577\) | −28.9770 | −1.20633 | −0.603165 | − | 0.797617i | \(-0.706094\pi\) | ||||
−0.603165 | + | 0.797617i | \(0.706094\pi\) | |||||||
\(578\) | 42.5246 | 1.76879 | ||||||||
\(579\) | −2.02279 | −0.0840641 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.1773 | −1.21048 | ||||||||
\(582\) | 36.8781 | 1.52865 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.83483 | 0.406968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.2846 | 0.631400 | ||||||||
\(587\) | 20.9939 | 0.866509 | 0.433255 | − | 0.901272i | \(-0.357365\pi\) | ||||
0.433255 | + | 0.901272i | \(0.357365\pi\) | |||||||
\(588\) | −18.3112 | −0.755143 | ||||||||
\(589\) | −19.5174 | −0.804202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.8348 | −0.733627 | ||||||||
\(592\) | −7.10504 | −0.292015 | ||||||||
\(593\) | −23.8927 | −0.981155 | −0.490578 | − | 0.871397i | \(-0.663214\pi\) | ||||
−0.490578 | + | 0.871397i | \(0.663214\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.9360 | −1.26719 | ||||||||
\(597\) | −25.6742 | −1.05078 | ||||||||
\(598\) | 14.8371 | 0.606734 | ||||||||
\(599\) | −45.6742 | −1.86620 | −0.933099 | − | 0.359620i | \(-0.882906\pi\) | ||||
−0.933099 | + | 0.359620i | \(0.882906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2101 | 0.661223 | 0.330611 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330611 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(602\) | −25.1773 | −1.02615 | ||||||||
\(603\) | −1.84324 | −0.0750627 | ||||||||
\(604\) | 13.3340 | 0.542554 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −41.0928 | −1.66928 | ||||||||
\(607\) | 20.8020 | 0.844328 | 0.422164 | − | 0.906519i | \(-0.361271\pi\) | ||||
0.422164 | + | 0.906519i | \(0.361271\pi\) | |||||||
\(608\) | −23.3607 | −0.947401 | ||||||||
\(609\) | 19.5174 | 0.790887 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.68035 | 0.189347 | ||||||||
\(612\) | −16.3896 | −0.662511 | ||||||||
\(613\) | 15.3835 | 0.621333 | 0.310666 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310666 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(614\) | −43.7815 | −1.76688 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.9733 | −0.884613 | −0.442307 | − | 0.896864i | \(-0.645840\pi\) | ||||
−0.442307 | + | 0.896864i | \(0.645840\pi\) | |||||||
\(618\) | −25.5753 | −1.02879 | ||||||||
\(619\) | 10.3935 | 0.417750 | 0.208875 | − | 0.977942i | \(-0.433020\pi\) | ||||
0.208875 | + | 0.977942i | \(0.433020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 46.1711 | 1.85129 | ||||||||
\(623\) | −18.6225 | −0.746094 | ||||||||
\(624\) | −3.55252 | −0.142215 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −35.7321 | −1.42814 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.26180 | 0.369586 | ||||||||
\(629\) | −20.6803 | −0.824579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.7214 | 1.54147 | 0.770737 | − | 0.637153i | \(-0.219888\pi\) | ||||
0.770737 | + | 0.637153i | \(0.219888\pi\) | |||||||
\(632\) | 11.4596 | 0.455838 | ||||||||
\(633\) | 8.43907 | 0.335423 | ||||||||
\(634\) | 48.1133 | 1.91082 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 37.2762 | 1.47810 | ||||||||
\(637\) | −11.5525 | −0.457728 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.23513 | −0.286217 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.2245 | 0.956808 | 0.478404 | − | 0.878140i | \(-0.341215\pi\) | ||||
0.478404 | + | 0.878140i | \(0.341215\pi\) | |||||||
\(642\) | −24.4885 | −0.966485 | ||||||||
\(643\) | 25.8888 | 1.02096 | 0.510478 | − | 0.859891i | \(-0.329469\pi\) | ||||
0.510478 | + | 0.859891i | \(0.329469\pi\) | |||||||
\(644\) | −40.1978 | −1.58401 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −40.4124 | −1.59000 | ||||||||
\(647\) | 0.581449 | 0.0228591 | 0.0114296 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114296 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(648\) | 1.53919 | 0.0604650 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.5174 | 0.921721 | ||||||||
\(652\) | −25.0928 | −0.982708 | ||||||||
\(653\) | −37.0082 | −1.44824 | −0.724122 | − | 0.689672i | \(-0.757755\pi\) | ||||
−0.724122 | + | 0.689672i | \(0.757755\pi\) | |||||||
\(654\) | −21.7009 | −0.848571 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.9011 | 0.777008 | ||||||||
\(657\) | 6.38962 | 0.249283 | ||||||||
\(658\) | −22.0410 | −0.859249 | ||||||||
\(659\) | −30.5236 | −1.18903 | −0.594515 | − | 0.804084i | \(-0.702656\pi\) | ||||
−0.594515 | + | 0.804084i | \(0.702656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.88428 | 0.228872 | 0.114436 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114436 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(662\) | −13.7587 | −0.534748 | ||||||||
\(663\) | −10.3402 | −0.401579 | ||||||||
\(664\) | −12.1073 | −0.469855 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.41855 | 0.287463 | ||||||||
\(667\) | 21.0472 | 0.814950 | ||||||||
\(668\) | 20.4619 | 0.791693 | ||||||||
\(669\) | 12.5814 | 0.486427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 28.1483 | 1.08585 | ||||||||
\(673\) | −26.9711 | −1.03966 | −0.519829 | − | 0.854270i | \(-0.674004\pi\) | ||||
−0.519829 | + | 0.854270i | \(0.674004\pi\) | |||||||
\(674\) | 6.91321 | 0.266287 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.3051 | −1.05020 | ||||||||
\(677\) | −17.9506 | −0.689896 | −0.344948 | − | 0.938622i | \(-0.612103\pi\) | ||||
−0.344948 | + | 0.938622i | \(0.612103\pi\) | |||||||
\(678\) | −1.07838 | −0.0414148 | ||||||||
\(679\) | −63.0349 | −2.41906 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.23287 | −0.162204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.77924 | −0.335928 | −0.167964 | − | 0.985793i | \(-0.553719\pi\) | ||||
−0.167964 | + | 0.985793i | \(0.553719\pi\) | |||||||
\(684\) | 8.34017 | 0.318894 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.94214 | −0.0741513 | ||||||||
\(687\) | 26.1978 | 0.999508 | ||||||||
\(688\) | 6.50080 | 0.247841 | ||||||||
\(689\) | 23.5174 | 0.895943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7214 | −0.560028 | −0.280014 | − | 0.959996i | \(-0.590339\pi\) | ||||
−0.280014 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(692\) | 16.6576 | 0.633225 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.7093 | −0.444478 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.09890 | 0.306988 | ||||||||
\(697\) | 57.9253 | 2.19408 | ||||||||
\(698\) | 34.0144 | 1.28746 | ||||||||
\(699\) | 18.6309 | 0.704685 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.10504 | 0.268354 | 0.134177 | − | 0.990957i | \(-0.457161\pi\) | ||||
0.134177 | + | 0.990957i | \(0.457161\pi\) | |||||||
\(702\) | 3.70928 | 0.139998 | ||||||||
\(703\) | 10.5236 | 0.396905 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.4969 | 0.470328 | ||||||||
\(707\) | 70.2388 | 2.64160 | ||||||||
\(708\) | 9.75872 | 0.366755 | ||||||||
\(709\) | −34.1666 | −1.28315 | −0.641577 | − | 0.767059i | \(-0.721719\pi\) | ||||
−0.641577 | + | 0.767059i | \(0.721719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.44521 | 0.279217 | ||||||||
\(712\) | −7.72753 | −0.289601 | ||||||||
\(713\) | 25.3607 | 0.949765 | ||||||||
\(714\) | 48.6947 | 1.82235 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.6803 | −0.623374 | ||||||||
\(717\) | 22.3545 | 0.834846 | ||||||||
\(718\) | 22.8371 | 0.852273 | ||||||||
\(719\) | 31.8310 | 1.18709 | 0.593547 | − | 0.804799i | \(-0.297727\pi\) | ||||
0.593547 | + | 0.804799i | \(0.297727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.7152 | 1.62804 | ||||||||
\(722\) | −20.6670 | −0.769147 | ||||||||
\(723\) | 9.20394 | 0.342298 | ||||||||
\(724\) | 39.5441 | 1.46965 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.16290 | −0.191481 | −0.0957407 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957407 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(728\) | −9.75872 | −0.361682 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9216 | 0.699841 | ||||||||
\(732\) | −39.7731 | −1.47006 | ||||||||
\(733\) | −36.4475 | −1.34622 | −0.673109 | − | 0.739543i | \(-0.735042\pi\) | ||||
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(734\) | −19.3028 | −0.712481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.3545 | 1.11888 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −20.7792 | −0.764894 | ||||||||
\(739\) | −25.4329 | −0.935565 | −0.467783 | − | 0.883844i | \(-0.654947\pi\) | ||||
−0.467783 | + | 0.883844i | \(0.654947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.26180 | 0.193297 | ||||||||
\(742\) | −110.750 | −4.06577 | ||||||||
\(743\) | 10.1217 | 0.371329 | 0.185664 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185664 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(744\) | 9.75872 | 0.357772 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.2784 | −1.84082 | ||||||||
\(747\) | −7.86603 | −0.287803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.8576 | 1.52944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4703 | 0.382065 | 0.191033 | − | 0.981584i | \(-0.438816\pi\) | ||||
0.191033 | + | 0.981584i | \(0.438816\pi\) | |||||||
\(752\) | 5.69102 | 0.207530 | ||||||||
\(753\) | 22.1256 | 0.806300 | ||||||||
\(754\) | 19.5174 | 0.710784 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.0494 | −0.365495 | ||||||||
\(757\) | 6.73820 | 0.244904 | 0.122452 | − | 0.992474i | \(-0.460924\pi\) | ||||
0.122452 | + | 0.992474i | \(0.460924\pi\) | |||||||
\(758\) | −25.6742 | −0.932529 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.57531 | 0.202105 | 0.101052 | − | 0.994881i | \(-0.467779\pi\) | ||||
0.101052 | + | 0.994881i | \(0.467779\pi\) | |||||||
\(762\) | −6.10731 | −0.221244 | ||||||||
\(763\) | 37.0928 | 1.34285 | ||||||||
\(764\) | 15.8310 | 0.572744 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.2967 | −2.03408 | ||||||||
\(767\) | 6.15676 | 0.222308 | ||||||||
\(768\) | 0.418551 | 0.0151031 | ||||||||
\(769\) | 11.5297 | 0.415773 | 0.207886 | − | 0.978153i | \(-0.433342\pi\) | ||||
0.207886 | + | 0.978153i | \(0.433342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.02052 | 0.108781 | ||||||||
\(772\) | 5.48029 | 0.197240 | ||||||||
\(773\) | 28.7480 | 1.03400 | 0.516998 | − | 0.855987i | \(-0.327050\pi\) | ||||
0.516998 | + | 0.855987i | \(0.327050\pi\) | |||||||
\(774\) | −6.78765 | −0.243977 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.1568 | −0.938973 | ||||||||
\(777\) | −12.6803 | −0.454905 | ||||||||
\(778\) | 2.18342 | 0.0782793 | ||||||||
\(779\) | −29.4764 | −1.05610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 52.5113 | 1.87780 | ||||||||
\(783\) | 5.26180 | 0.188041 | ||||||||
\(784\) | −14.0472 | −0.501685 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.8371 | 0.671897 | ||||||||
\(787\) | −13.4536 | −0.479570 | −0.239785 | − | 0.970826i | \(-0.577077\pi\) | ||||
−0.239785 | + | 0.970826i | \(0.577077\pi\) | |||||||
\(788\) | 48.3195 | 1.72131 | ||||||||
\(789\) | −18.2907 | −0.651167 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.84324 | 0.0655382 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0928 | −0.891070 | ||||||||
\(794\) | −75.3484 | −2.67401 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 69.5585 | 2.46544 | ||||||||
\(797\) | 48.3279 | 1.71186 | 0.855931 | − | 0.517090i | \(-0.172985\pi\) | ||||
0.855931 | + | 0.517090i | \(0.172985\pi\) | |||||||
\(798\) | −24.7792 | −0.877176 | ||||||||
\(799\) | 16.5646 | 0.586014 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.02052 | −0.177391 | ||||||||
\(802\) | −28.2557 | −0.997742 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.99386 | 0.176120 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.5174 | 0.828367 | ||||||||
\(807\) | −30.5646 | −1.07593 | ||||||||
\(808\) | 29.1461 | 1.02536 | ||||||||
\(809\) | 43.8141 | 1.54042 | 0.770212 | − | 0.637789i | \(-0.220151\pi\) | ||||
0.770212 | + | 0.637789i | \(0.220151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.2762 | 1.66009 | 0.830045 | − | 0.557696i | \(-0.188314\pi\) | ||||
0.830045 | + | 0.557696i | \(0.188314\pi\) | |||||||
\(812\) | −52.8781 | −1.85566 | ||||||||
\(813\) | −20.0722 | −0.703964 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.5730 | −0.440144 | ||||||||
\(817\) | −9.62863 | −0.336863 | ||||||||
\(818\) | 64.0554 | 2.23965 | ||||||||
\(819\) | −6.34017 | −0.221544 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.30283 | 0.115270 | 0.0576348 | − | 0.998338i | \(-0.481644\pi\) | ||||
0.0576348 | + | 0.998338i | \(0.481644\pi\) | |||||||
\(822\) | 2.34017 | 0.0816229 | ||||||||
\(823\) | −11.0517 | −0.385239 | −0.192619 | − | 0.981274i | \(-0.561698\pi\) | ||||
−0.192619 | + | 0.981274i | \(0.561698\pi\) | |||||||
\(824\) | 18.1399 | 0.631935 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.9939 | −1.00883 | ||||||||
\(827\) | 5.12783 | 0.178312 | 0.0891560 | − | 0.996018i | \(-0.471583\pi\) | ||||
0.0891560 | + | 0.996018i | \(0.471583\pi\) | |||||||
\(828\) | −10.8371 | −0.376615 | ||||||||
\(829\) | −6.39803 | −0.222213 | −0.111106 | − | 0.993809i | \(-0.535439\pi\) | ||||
−0.111106 | + | 0.993809i | \(0.535439\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.760991 | −0.0263985 | ||||||||
\(832\) | 21.0433 | 0.729545 | ||||||||
\(833\) | −40.8865 | −1.41663 | ||||||||
\(834\) | 22.3135 | 0.772654 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.34017 | 0.219148 | ||||||||
\(838\) | −13.3607 | −0.461537 | ||||||||
\(839\) | −22.0722 | −0.762018 | −0.381009 | − | 0.924571i | \(-0.624423\pi\) | ||||
−0.381009 | + | 0.924571i | \(0.624423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.31351 | −0.0452935 | ||||||||
\(842\) | 21.6332 | 0.745528 | ||||||||
\(843\) | 0.581449 | 0.0200262 | ||||||||
\(844\) | −22.8638 | −0.787003 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.94214 | −0.204295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 28.5958 | 0.981985 | ||||||||
\(849\) | 10.8143 | 0.371146 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6742 | −0.468746 | ||||||||
\(852\) | 19.6020 | 0.671552 | ||||||||
\(853\) | −8.76099 | −0.299971 | −0.149985 | − | 0.988688i | \(-0.547923\pi\) | ||||
−0.149985 | + | 0.988688i | \(0.547923\pi\) | |||||||
\(854\) | 118.169 | 4.04365 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3691 | 0.593664 | ||||||||
\(857\) | −36.5730 | −1.24931 | −0.624656 | − | 0.780900i | \(-0.714761\pi\) | ||||
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.6886 | −1.69535 | −0.847676 | − | 0.530514i | \(-0.821999\pi\) | ||||
−0.847676 | + | 0.530514i | \(0.821999\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.5174 | 1.21043 | ||||||||
\(862\) | −18.8371 | −0.641594 | ||||||||
\(863\) | 34.1399 | 1.16214 | 0.581068 | − | 0.813855i | \(-0.302635\pi\) | ||||
0.581068 | + | 0.813855i | \(0.302635\pi\) | |||||||
\(864\) | 7.58864 | 0.258171 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.7214 | 1.17988 | ||||||||
\(867\) | −19.5958 | −0.665509 | ||||||||
\(868\) | −63.7152 | −2.16264 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.15061 | 0.106754 | ||||||||
\(872\) | 15.3919 | 0.521235 | ||||||||
\(873\) | −16.9939 | −0.575155 | ||||||||
\(874\) | −26.7214 | −0.903864 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.3112 | −0.584893 | ||||||||
\(877\) | −43.5357 | −1.47010 | −0.735048 | − | 0.678015i | \(-0.762840\pi\) | ||||
−0.735048 | + | 0.678015i | \(0.762840\pi\) | |||||||
\(878\) | −6.68035 | −0.225451 | ||||||||
\(879\) | −7.04331 | −0.237565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.52359 | −0.287167 | −0.143584 | − | 0.989638i | \(-0.545863\pi\) | ||||
−0.143584 | + | 0.989638i | \(0.545863\pi\) | |||||||
\(882\) | 14.6670 | 0.493864 | ||||||||
\(883\) | −43.0349 | −1.44824 | −0.724120 | − | 0.689674i | \(-0.757754\pi\) | ||||
−0.724120 | + | 0.689674i | \(0.757754\pi\) | |||||||
\(884\) | 28.0144 | 0.942225 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −63.5006 | −2.13335 | ||||||||
\(887\) | 17.0289 | 0.571775 | 0.285888 | − | 0.958263i | \(-0.407712\pi\) | ||||
0.285888 | + | 0.958263i | \(0.407712\pi\) | |||||||
\(888\) | −5.26180 | −0.176574 | ||||||||
\(889\) | 10.4391 | 0.350115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.0866 | −1.14130 | ||||||||
\(893\) | −8.42923 | −0.282073 | ||||||||
\(894\) | 24.7792 | 0.828742 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −42.8020 | −1.42992 | ||||||||
\(897\) | −6.83710 | −0.228284 | ||||||||
\(898\) | 23.2085 | 0.774477 | ||||||||
\(899\) | 33.3607 | 1.11264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.2327 | 2.77288 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.6020 | 0.386089 | ||||||||
\(904\) | 0.764867 | 0.0254391 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.6803 | −0.354831 | ||||||||
\(907\) | −6.13993 | −0.203873 | −0.101937 | − | 0.994791i | \(-0.532504\pi\) | ||||
−0.101937 | + | 0.994791i | \(0.532504\pi\) | |||||||
\(908\) | 11.4680 | 0.380579 | ||||||||
\(909\) | 18.9360 | 0.628067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.8720 | 1.78486 | 0.892429 | − | 0.451187i | \(-0.148999\pi\) | ||||
0.892429 | + | 0.451187i | \(0.148999\pi\) | |||||||
\(912\) | 6.39803 | 0.211860 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 49.5981 | 1.64056 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −70.9770 | −2.34515 | ||||||||
\(917\) | −32.1978 | −1.06326 | ||||||||
\(918\) | 13.1278 | 0.433283 | ||||||||
\(919\) | 48.2700 | 1.59228 | 0.796141 | − | 0.605112i | \(-0.206872\pi\) | ||||
0.796141 | + | 0.605112i | \(0.206872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.1750 | 0.664789 | ||||||||
\(922\) | 47.2495 | 1.55608 | ||||||||
\(923\) | 12.3668 | 0.407059 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −54.0242 | −1.77535 | ||||||||
\(927\) | 11.7854 | 0.387083 | ||||||||
\(928\) | 39.9299 | 1.31076 | ||||||||
\(929\) | 4.10343 | 0.134629 | 0.0673146 | − | 0.997732i | \(-0.478557\pi\) | ||||
0.0673146 | + | 0.997732i | \(0.478557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.8059 | 0.681886 | ||||||||
\(932\) | −50.4762 | −1.65340 | ||||||||
\(933\) | −21.2762 | −0.696551 | ||||||||
\(934\) | 41.6742 | 1.36362 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.63090 | −0.0859936 | ||||||||
\(937\) | −38.5341 | −1.25885 | −0.629427 | − | 0.777060i | \(-0.716710\pi\) | ||||
−0.629427 | + | 0.777060i | \(0.716710\pi\) | |||||||
\(938\) | −14.8371 | −0.484449 | ||||||||
\(939\) | 16.4657 | 0.537339 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.6849 | −0.478713 | −0.239357 | − | 0.970932i | \(-0.576937\pi\) | ||||
−0.239357 | + | 0.970932i | \(0.576937\pi\) | |||||||
\(942\) | −7.41855 | −0.241709 | ||||||||
\(943\) | 38.3012 | 1.24726 | ||||||||
\(944\) | 7.48625 | 0.243657 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.05786 | −0.196854 | −0.0984270 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984270 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(948\) | −20.1711 | −0.655128 | ||||||||
\(949\) | −10.9216 | −0.354531 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.1711 | −0.718948 | ||||||||
\(952\) | −34.5380 | −1.11938 | ||||||||
\(953\) | 40.1438 | 1.30039 | 0.650193 | − | 0.759769i | \(-0.274688\pi\) | ||||
0.650193 | + | 0.759769i | \(0.274688\pi\) | |||||||
\(954\) | −29.8576 | −0.966676 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −60.5646 | −1.95880 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.5646 | −0.664413 | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.19779 | 0.296703 | ||||||||
\(962\) | −12.6803 | −0.408831 | ||||||||
\(963\) | 11.2846 | 0.363641 | ||||||||
\(964\) | −24.9360 | −0.803134 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 32.1978 | 1.03595 | ||||||||
\(967\) | −50.6285 | −1.62810 | −0.814051 | − | 0.580794i | \(-0.802742\pi\) | ||||
−0.814051 | + | 0.580794i | \(0.802742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.6225 | 0.598240 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.69263 | −0.214777 | −0.107388 | − | 0.994217i | \(-0.534249\pi\) | ||||
−0.107388 | + | 0.994217i | \(0.534249\pi\) | |||||||
\(972\) | −2.70928 | −0.0869000 | ||||||||
\(973\) | −38.1399 | −1.22271 | ||||||||
\(974\) | −76.3956 | −2.44787 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.5113 | −0.976643 | ||||||||
\(977\) | −38.5835 | −1.23440 | −0.617198 | − | 0.786808i | \(-0.711732\pi\) | ||||
−0.617198 | + | 0.786808i | \(0.711732\pi\) | |||||||
\(978\) | 20.0989 | 0.642692 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 17.3607 | 0.554002 | ||||||||
\(983\) | 28.4657 | 0.907916 | 0.453958 | − | 0.891023i | \(-0.350012\pi\) | ||||
0.453958 | + | 0.891023i | \(0.350012\pi\) | |||||||
\(984\) | 14.7382 | 0.469837 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 69.0759 | 2.19983 | ||||||||
\(987\) | 10.1568 | 0.323293 | ||||||||
\(988\) | −14.2557 | −0.453533 | ||||||||
\(989\) | 12.5113 | 0.397836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.65368 | 0.0842970 | 0.0421485 | − | 0.999111i | \(-0.486580\pi\) | ||||
0.0421485 | + | 0.999111i | \(0.486580\pi\) | |||||||
\(992\) | 48.1133 | 1.52760 | ||||||||
\(993\) | 6.34017 | 0.201199 | ||||||||
\(994\) | −58.2388 | −1.84722 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.3112 | 0.675273 | ||||||||
\(997\) | −8.08065 | −0.255917 | −0.127958 | − | 0.991780i | \(-0.540842\pi\) | ||||
−0.127958 | + | 0.991780i | \(0.540842\pi\) | |||||||
\(998\) | 56.7624 | 1.79678 | ||||||||
\(999\) | −3.41855 | −0.108158 |
(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 | 9075.2.a.ch.1.3 | 3 | ||
5.2 | odd | 4 | 1815.2.c.e.364.6 | 6 | |||
5.3 | odd | 4 | 1815.2.c.e.364.1 | 6 | |||
5.4 | even | 2 | 9075.2.a.cg.1.1 | 3 | |||
11.10 | odd | 2 | 825.2.a.j.1.1 | 3 | |||
33.32 | even | 2 | 2475.2.a.bc.1.3 | 3 | |||
55.32 | even | 4 | 165.2.c.b.34.1 | ✓ | 6 | ||
55.43 | even | 4 | 165.2.c.b.34.6 | yes | 6 | ||
55.54 | odd | 2 | 825.2.a.l.1.3 | 3 | |||
165.32 | odd | 4 | 495.2.c.e.199.6 | 6 | |||
165.98 | odd | 4 | 495.2.c.e.199.1 | 6 | |||
165.164 | even | 2 | 2475.2.a.ba.1.1 | 3 | |||
220.43 | odd | 4 | 2640.2.d.h.529.6 | 6 | |||
220.87 | odd | 4 | 2640.2.d.h.529.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.b.34.1 | ✓ | 6 | 55.32 | even | 4 | ||
165.2.c.b.34.6 | yes | 6 | 55.43 | even | 4 | ||
495.2.c.e.199.1 | 6 | 165.98 | odd | 4 | |||
495.2.c.e.199.6 | 6 | 165.32 | odd | 4 | |||
825.2.a.j.1.1 | 3 | 11.10 | odd | 2 | |||
825.2.a.l.1.3 | 3 | 55.54 | odd | 2 | |||
1815.2.c.e.364.1 | 6 | 5.3 | odd | 4 | |||
1815.2.c.e.364.6 | 6 | 5.2 | odd | 4 | |||
2475.2.a.ba.1.1 | 3 | 165.164 | even | 2 | |||
2475.2.a.bc.1.3 | 3 | 33.32 | even | 2 | |||
2640.2.d.h.529.3 | 6 | 220.87 | odd | 4 | |||
2640.2.d.h.529.6 | 6 | 220.43 | odd | 4 | |||
9075.2.a.cg.1.1 | 3 | 5.4 | even | 2 | |||
9075.2.a.ch.1.3 | 3 | 1.1 | even | 1 | trivial |