Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.24698 | 1.87464 | 0.937322 | − | 0.348464i | \(-0.113297\pi\) | ||||
0.937322 | + | 0.348464i | \(0.113297\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.55496 | −0.695398 | −0.347699 | − | 0.937606i | \(-0.613037\pi\) | ||||
−0.347699 | + | 0.937606i | \(0.613037\pi\) | |||||||
\(6\) | −3.24698 | −1.32557 | ||||||||
\(7\) | 3.60388 | 1.36214 | 0.681068 | − | 0.732220i | \(-0.261516\pi\) | ||||
0.681068 | + | 0.732220i | \(0.261516\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.54288 | 2.51429 | ||||||||
\(10\) | 1.55496 | 0.491721 | ||||||||
\(11\) | 5.18598 | 1.56363 | 0.781816 | − | 0.623509i | \(-0.214294\pi\) | ||||
0.781816 | + | 0.623509i | \(0.214294\pi\) | |||||||
\(12\) | 3.24698 | 0.937322 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.60388 | −0.963176 | ||||||||
\(15\) | −5.04892 | −1.30362 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.96077 | −1.44570 | −0.722850 | − | 0.691005i | \(-0.757168\pi\) | ||||
−0.722850 | + | 0.691005i | \(0.757168\pi\) | |||||||
\(18\) | −7.54288 | −1.77787 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.55496 | −0.347699 | ||||||||
\(21\) | 11.7017 | 2.55352 | ||||||||
\(22\) | −5.18598 | −1.10565 | ||||||||
\(23\) | 4.29590 | 0.895756 | 0.447878 | − | 0.894095i | \(-0.352180\pi\) | ||||
0.447878 | + | 0.894095i | \(0.352180\pi\) | |||||||
\(24\) | −3.24698 | −0.662787 | ||||||||
\(25\) | −2.58211 | −0.516421 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.7506 | 2.83876 | ||||||||
\(28\) | 3.60388 | 0.681068 | ||||||||
\(29\) | 2.91185 | 0.540718 | 0.270359 | − | 0.962760i | \(-0.412858\pi\) | ||||
0.270359 | + | 0.962760i | \(0.412858\pi\) | |||||||
\(30\) | 5.04892 | 0.921802 | ||||||||
\(31\) | −6.04892 | −1.08642 | −0.543209 | − | 0.839598i | \(-0.682791\pi\) | ||||
−0.543209 | + | 0.839598i | \(0.682791\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 16.8388 | 2.93125 | ||||||||
\(34\) | 5.96077 | 1.02226 | ||||||||
\(35\) | −5.60388 | −0.947228 | ||||||||
\(36\) | 7.54288 | 1.25715 | ||||||||
\(37\) | 6.71379 | 1.10374 | 0.551870 | − | 0.833930i | \(-0.313914\pi\) | ||||
0.551870 | + | 0.833930i | \(0.313914\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.55496 | 0.245860 | ||||||||
\(41\) | 9.83877 | 1.53656 | 0.768279 | − | 0.640115i | \(-0.221113\pi\) | ||||
0.768279 | + | 0.640115i | \(0.221113\pi\) | |||||||
\(42\) | −11.7017 | −1.80561 | ||||||||
\(43\) | 5.16421 | 0.787535 | 0.393767 | − | 0.919210i | \(-0.371172\pi\) | ||||
0.393767 | + | 0.919210i | \(0.371172\pi\) | |||||||
\(44\) | 5.18598 | 0.781816 | ||||||||
\(45\) | −11.7289 | −1.74843 | ||||||||
\(46\) | −4.29590 | −0.633395 | ||||||||
\(47\) | −11.0315 | −1.60910 | −0.804552 | − | 0.593882i | \(-0.797594\pi\) | ||||
−0.804552 | + | 0.593882i | \(0.797594\pi\) | |||||||
\(48\) | 3.24698 | 0.468661 | ||||||||
\(49\) | 5.98792 | 0.855417 | ||||||||
\(50\) | 2.58211 | 0.365165 | ||||||||
\(51\) | −19.3545 | −2.71017 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.82908 | 0.525965 | 0.262983 | − | 0.964801i | \(-0.415294\pi\) | ||||
0.262983 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(54\) | −14.7506 | −2.00731 | ||||||||
\(55\) | −8.06398 | −1.08735 | ||||||||
\(56\) | −3.60388 | −0.481588 | ||||||||
\(57\) | 3.24698 | 0.430073 | ||||||||
\(58\) | −2.91185 | −0.382345 | ||||||||
\(59\) | −13.5254 | −1.76086 | −0.880430 | − | 0.474177i | \(-0.842746\pi\) | ||||
−0.880430 | + | 0.474177i | \(0.842746\pi\) | |||||||
\(60\) | −5.04892 | −0.651812 | ||||||||
\(61\) | −0.615957 | −0.0788652 | −0.0394326 | − | 0.999222i | \(-0.512555\pi\) | ||||
−0.0394326 | + | 0.999222i | \(0.512555\pi\) | |||||||
\(62\) | 6.04892 | 0.768213 | ||||||||
\(63\) | 27.1836 | 3.42481 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −16.8388 | −2.07271 | ||||||||
\(67\) | 0.987918 | 0.120693 | 0.0603467 | − | 0.998177i | \(-0.480779\pi\) | ||||
0.0603467 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(68\) | −5.96077 | −0.722850 | ||||||||
\(69\) | 13.9487 | 1.67922 | ||||||||
\(70\) | 5.60388 | 0.669791 | ||||||||
\(71\) | 4.71917 | 0.560062 | 0.280031 | − | 0.959991i | \(-0.409655\pi\) | ||||
0.280031 | + | 0.959991i | \(0.409655\pi\) | |||||||
\(72\) | −7.54288 | −0.888937 | ||||||||
\(73\) | −6.59179 | −0.771511 | −0.385756 | − | 0.922601i | \(-0.626059\pi\) | ||||
−0.385756 | + | 0.922601i | \(0.626059\pi\) | |||||||
\(74\) | −6.71379 | −0.780462 | ||||||||
\(75\) | −8.38404 | −0.968106 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 18.6896 | 2.12988 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7681 | 1.21150 | 0.605752 | − | 0.795653i | \(-0.292872\pi\) | ||||
0.605752 | + | 0.795653i | \(0.292872\pi\) | |||||||
\(80\) | −1.55496 | −0.173850 | ||||||||
\(81\) | 25.2664 | 2.80737 | ||||||||
\(82\) | −9.83877 | −1.08651 | ||||||||
\(83\) | −3.91723 | −0.429972 | −0.214986 | − | 0.976617i | \(-0.568971\pi\) | ||||
−0.214986 | + | 0.976617i | \(0.568971\pi\) | |||||||
\(84\) | 11.7017 | 1.27676 | ||||||||
\(85\) | 9.26875 | 1.00534 | ||||||||
\(86\) | −5.16421 | −0.556871 | ||||||||
\(87\) | 9.45473 | 1.01365 | ||||||||
\(88\) | −5.18598 | −0.552827 | ||||||||
\(89\) | −0.789856 | −0.0837246 | −0.0418623 | − | 0.999123i | \(-0.513329\pi\) | ||||
−0.0418623 | + | 0.999123i | \(0.513329\pi\) | |||||||
\(90\) | 11.7289 | 1.23633 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.29590 | 0.447878 | ||||||||
\(93\) | −19.6407 | −2.03665 | ||||||||
\(94\) | 11.0315 | 1.13781 | ||||||||
\(95\) | −1.55496 | −0.159535 | ||||||||
\(96\) | −3.24698 | −0.331393 | ||||||||
\(97\) | 15.9976 | 1.62431 | 0.812155 | − | 0.583441i | \(-0.198294\pi\) | ||||
0.812155 | + | 0.583441i | \(0.198294\pi\) | |||||||
\(98\) | −5.98792 | −0.604871 | ||||||||
\(99\) | 39.1172 | 3.93143 | ||||||||
\(100\) | −2.58211 | −0.258211 | ||||||||
\(101\) | 5.26205 | 0.523593 | 0.261797 | − | 0.965123i | \(-0.415685\pi\) | ||||
0.261797 | + | 0.965123i | \(0.415685\pi\) | |||||||
\(102\) | 19.3545 | 1.91638 | ||||||||
\(103\) | 0.396125 | 0.0390313 | 0.0195157 | − | 0.999810i | \(-0.493788\pi\) | ||||
0.0195157 | + | 0.999810i | \(0.493788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.1957 | −1.77572 | ||||||||
\(106\) | −3.82908 | −0.371914 | ||||||||
\(107\) | −0.488582 | −0.0472330 | −0.0236165 | − | 0.999721i | \(-0.507518\pi\) | ||||
−0.0236165 | + | 0.999721i | \(0.507518\pi\) | |||||||
\(108\) | 14.7506 | 1.41938 | ||||||||
\(109\) | −2.71379 | −0.259934 | −0.129967 | − | 0.991518i | \(-0.541487\pi\) | ||||
−0.129967 | + | 0.991518i | \(0.541487\pi\) | |||||||
\(110\) | 8.06398 | 0.768871 | ||||||||
\(111\) | 21.7995 | 2.06912 | ||||||||
\(112\) | 3.60388 | 0.340534 | ||||||||
\(113\) | −17.8780 | −1.68182 | −0.840910 | − | 0.541174i | \(-0.817980\pi\) | ||||
−0.840910 | + | 0.541174i | \(0.817980\pi\) | |||||||
\(114\) | −3.24698 | −0.304108 | ||||||||
\(115\) | −6.67994 | −0.622908 | ||||||||
\(116\) | 2.91185 | 0.270359 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.5254 | 1.24512 | ||||||||
\(119\) | −21.4819 | −1.96924 | ||||||||
\(120\) | 5.04892 | 0.460901 | ||||||||
\(121\) | 15.8944 | 1.44495 | ||||||||
\(122\) | 0.615957 | 0.0557661 | ||||||||
\(123\) | 31.9463 | 2.88050 | ||||||||
\(124\) | −6.04892 | −0.543209 | ||||||||
\(125\) | 11.7899 | 1.05452 | ||||||||
\(126\) | −27.1836 | −2.42171 | ||||||||
\(127\) | −1.60388 | −0.142321 | −0.0711605 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711605 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 16.7681 | 1.47635 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3599 | −1.69148 | −0.845740 | − | 0.533595i | \(-0.820841\pi\) | ||||
−0.845740 | + | 0.533595i | \(0.820841\pi\) | |||||||
\(132\) | 16.8388 | 1.46563 | ||||||||
\(133\) | 3.60388 | 0.312496 | ||||||||
\(134\) | −0.987918 | −0.0853432 | ||||||||
\(135\) | −22.9366 | −1.97407 | ||||||||
\(136\) | 5.96077 | 0.511132 | ||||||||
\(137\) | 6.61596 | 0.565239 | 0.282620 | − | 0.959232i | \(-0.408797\pi\) | ||||
0.282620 | + | 0.959232i | \(0.408797\pi\) | |||||||
\(138\) | −13.9487 | −1.18739 | ||||||||
\(139\) | 0.933624 | 0.0791890 | 0.0395945 | − | 0.999216i | \(-0.487393\pi\) | ||||
0.0395945 | + | 0.999216i | \(0.487393\pi\) | |||||||
\(140\) | −5.60388 | −0.473614 | ||||||||
\(141\) | −35.8189 | −3.01650 | ||||||||
\(142\) | −4.71917 | −0.396024 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.54288 | 0.628573 | ||||||||
\(145\) | −4.52781 | −0.376014 | ||||||||
\(146\) | 6.59179 | 0.545541 | ||||||||
\(147\) | 19.4426 | 1.60360 | ||||||||
\(148\) | 6.71379 | 0.551870 | ||||||||
\(149\) | 6.13706 | 0.502768 | 0.251384 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251384 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(150\) | 8.38404 | 0.684554 | ||||||||
\(151\) | −11.2838 | −0.918264 | −0.459132 | − | 0.888368i | \(-0.651839\pi\) | ||||
−0.459132 | + | 0.888368i | \(0.651839\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −44.9614 | −3.63491 | ||||||||
\(154\) | −18.6896 | −1.50605 | ||||||||
\(155\) | 9.40581 | 0.755493 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.41550 | −0.192778 | −0.0963890 | − | 0.995344i | \(-0.530729\pi\) | ||||
−0.0963890 | + | 0.995344i | \(0.530729\pi\) | |||||||
\(158\) | −10.7681 | −0.856663 | ||||||||
\(159\) | 12.4330 | 0.985998 | ||||||||
\(160\) | 1.55496 | 0.122930 | ||||||||
\(161\) | 15.4819 | 1.22014 | ||||||||
\(162\) | −25.2664 | −1.98511 | ||||||||
\(163\) | 4.63102 | 0.362730 | 0.181365 | − | 0.983416i | \(-0.441949\pi\) | ||||
0.181365 | + | 0.983416i | \(0.441949\pi\) | |||||||
\(164\) | 9.83877 | 0.768279 | ||||||||
\(165\) | −26.1836 | −2.03839 | ||||||||
\(166\) | 3.91723 | 0.304036 | ||||||||
\(167\) | 18.0344 | 1.39555 | 0.697774 | − | 0.716318i | \(-0.254174\pi\) | ||||
0.697774 | + | 0.716318i | \(0.254174\pi\) | |||||||
\(168\) | −11.7017 | −0.902807 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.26875 | −0.710881 | ||||||||
\(171\) | 7.54288 | 0.576818 | ||||||||
\(172\) | 5.16421 | 0.393767 | ||||||||
\(173\) | −22.2107 | −1.68865 | −0.844325 | − | 0.535831i | \(-0.819999\pi\) | ||||
−0.844325 | + | 0.535831i | \(0.819999\pi\) | |||||||
\(174\) | −9.45473 | −0.716761 | ||||||||
\(175\) | −9.30559 | −0.703436 | ||||||||
\(176\) | 5.18598 | 0.390908 | ||||||||
\(177\) | −43.9168 | −3.30099 | ||||||||
\(178\) | 0.789856 | 0.0592022 | ||||||||
\(179\) | −22.0248 | −1.64621 | −0.823104 | − | 0.567891i | \(-0.807759\pi\) | ||||
−0.823104 | + | 0.567891i | \(0.807759\pi\) | |||||||
\(180\) | −11.7289 | −0.874217 | ||||||||
\(181\) | 12.3134 | 0.915244 | 0.457622 | − | 0.889147i | \(-0.348701\pi\) | ||||
0.457622 | + | 0.889147i | \(0.348701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −4.29590 | −0.316698 | ||||||||
\(185\) | −10.4397 | −0.767539 | ||||||||
\(186\) | 19.6407 | 1.44013 | ||||||||
\(187\) | −30.9124 | −2.26054 | ||||||||
\(188\) | −11.0315 | −0.804552 | ||||||||
\(189\) | 53.1594 | 3.86678 | ||||||||
\(190\) | 1.55496 | 0.112809 | ||||||||
\(191\) | 9.21313 | 0.666639 | 0.333319 | − | 0.942814i | \(-0.391831\pi\) | ||||
0.333319 | + | 0.942814i | \(0.391831\pi\) | |||||||
\(192\) | 3.24698 | 0.234331 | ||||||||
\(193\) | −14.2784 | −1.02778 | −0.513892 | − | 0.857855i | \(-0.671797\pi\) | ||||
−0.513892 | + | 0.857855i | \(0.671797\pi\) | |||||||
\(194\) | −15.9976 | −1.14856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.98792 | 0.427708 | ||||||||
\(197\) | −11.7802 | −0.839302 | −0.419651 | − | 0.907685i | \(-0.637848\pi\) | ||||
−0.419651 | + | 0.907685i | \(0.637848\pi\) | |||||||
\(198\) | −39.1172 | −2.77994 | ||||||||
\(199\) | 5.88040 | 0.416850 | 0.208425 | − | 0.978038i | \(-0.433166\pi\) | ||||
0.208425 | + | 0.978038i | \(0.433166\pi\) | |||||||
\(200\) | 2.58211 | 0.182582 | ||||||||
\(201\) | 3.20775 | 0.226257 | ||||||||
\(202\) | −5.26205 | −0.370236 | ||||||||
\(203\) | 10.4940 | 0.736532 | ||||||||
\(204\) | −19.3545 | −1.35509 | ||||||||
\(205\) | −15.2989 | −1.06852 | ||||||||
\(206\) | −0.396125 | −0.0275993 | ||||||||
\(207\) | 32.4034 | 2.25219 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.18598 | 0.358722 | ||||||||
\(210\) | 18.1957 | 1.25562 | ||||||||
\(211\) | −10.5894 | −0.729004 | −0.364502 | − | 0.931203i | \(-0.618761\pi\) | ||||
−0.364502 | + | 0.931203i | \(0.618761\pi\) | |||||||
\(212\) | 3.82908 | 0.262983 | ||||||||
\(213\) | 15.3230 | 1.04992 | ||||||||
\(214\) | 0.488582 | 0.0333988 | ||||||||
\(215\) | −8.03013 | −0.547650 | ||||||||
\(216\) | −14.7506 | −1.00365 | ||||||||
\(217\) | −21.7995 | −1.47985 | ||||||||
\(218\) | 2.71379 | 0.183801 | ||||||||
\(219\) | −21.4034 | −1.44631 | ||||||||
\(220\) | −8.06398 | −0.543674 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −21.7995 | −1.46309 | ||||||||
\(223\) | 1.04652 | 0.0700805 | 0.0350402 | − | 0.999386i | \(-0.488844\pi\) | ||||
0.0350402 | + | 0.999386i | \(0.488844\pi\) | |||||||
\(224\) | −3.60388 | −0.240794 | ||||||||
\(225\) | −19.4765 | −1.29843 | ||||||||
\(226\) | 17.8780 | 1.18923 | ||||||||
\(227\) | −7.10992 | −0.471902 | −0.235951 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235951 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(228\) | 3.24698 | 0.215036 | ||||||||
\(229\) | 16.6679 | 1.10144 | 0.550722 | − | 0.834689i | \(-0.314353\pi\) | ||||
0.550722 | + | 0.834689i | \(0.314353\pi\) | |||||||
\(230\) | 6.67994 | 0.440462 | ||||||||
\(231\) | 60.6848 | 3.99277 | ||||||||
\(232\) | −2.91185 | −0.191173 | ||||||||
\(233\) | −10.5187 | −0.689104 | −0.344552 | − | 0.938767i | \(-0.611969\pi\) | ||||
−0.344552 | + | 0.938767i | \(0.611969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.1535 | 1.11897 | ||||||||
\(236\) | −13.5254 | −0.880430 | ||||||||
\(237\) | 34.9638 | 2.27114 | ||||||||
\(238\) | 21.4819 | 1.39246 | ||||||||
\(239\) | −0.548253 | −0.0354636 | −0.0177318 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177318 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(240\) | −5.04892 | −0.325906 | ||||||||
\(241\) | −17.5743 | −1.13206 | −0.566031 | − | 0.824384i | \(-0.691522\pi\) | ||||
−0.566031 | + | 0.824384i | \(0.691522\pi\) | |||||||
\(242\) | −15.8944 | −1.02173 | ||||||||
\(243\) | 37.7875 | 2.42407 | ||||||||
\(244\) | −0.615957 | −0.0394326 | ||||||||
\(245\) | −9.31096 | −0.594856 | ||||||||
\(246\) | −31.9463 | −2.03682 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.04892 | 0.384107 | ||||||||
\(249\) | −12.7192 | −0.806045 | ||||||||
\(250\) | −11.7899 | −0.745656 | ||||||||
\(251\) | 4.09783 | 0.258653 | 0.129327 | − | 0.991602i | \(-0.458718\pi\) | ||||
0.129327 | + | 0.991602i | \(0.458718\pi\) | |||||||
\(252\) | 27.1836 | 1.71241 | ||||||||
\(253\) | 22.2784 | 1.40063 | ||||||||
\(254\) | 1.60388 | 0.100636 | ||||||||
\(255\) | 30.0954 | 1.88465 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.65950 | −0.415408 | −0.207704 | − | 0.978192i | \(-0.566599\pi\) | ||||
−0.207704 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(258\) | −16.7681 | −1.04394 | ||||||||
\(259\) | 24.1957 | 1.50345 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.9638 | 1.35952 | ||||||||
\(262\) | 19.3599 | 1.19606 | ||||||||
\(263\) | 20.3763 | 1.25645 | 0.628227 | − | 0.778030i | \(-0.283781\pi\) | ||||
0.628227 | + | 0.778030i | \(0.283781\pi\) | |||||||
\(264\) | −16.8388 | −1.03635 | ||||||||
\(265\) | −5.95407 | −0.365755 | ||||||||
\(266\) | −3.60388 | −0.220968 | ||||||||
\(267\) | −2.56465 | −0.156954 | ||||||||
\(268\) | 0.987918 | 0.0603467 | ||||||||
\(269\) | −20.9638 | −1.27818 | −0.639091 | − | 0.769131i | \(-0.720689\pi\) | ||||
−0.639091 | + | 0.769131i | \(0.720689\pi\) | |||||||
\(270\) | 22.9366 | 1.39588 | ||||||||
\(271\) | −9.40821 | −0.571508 | −0.285754 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285754 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(272\) | −5.96077 | −0.361425 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.61596 | −0.399685 | ||||||||
\(275\) | −13.3907 | −0.807492 | ||||||||
\(276\) | 13.9487 | 0.839612 | ||||||||
\(277\) | 22.0194 | 1.32302 | 0.661508 | − | 0.749938i | \(-0.269917\pi\) | ||||
0.661508 | + | 0.749938i | \(0.269917\pi\) | |||||||
\(278\) | −0.933624 | −0.0559951 | ||||||||
\(279\) | −45.6262 | −2.73157 | ||||||||
\(280\) | 5.60388 | 0.334896 | ||||||||
\(281\) | −24.4373 | −1.45781 | −0.728903 | − | 0.684617i | \(-0.759969\pi\) | ||||
−0.728903 | + | 0.684617i | \(0.759969\pi\) | |||||||
\(282\) | 35.8189 | 2.13299 | ||||||||
\(283\) | 15.9323 | 0.947077 | 0.473538 | − | 0.880773i | \(-0.342977\pi\) | ||||
0.473538 | + | 0.880773i | \(0.342977\pi\) | |||||||
\(284\) | 4.71917 | 0.280031 | ||||||||
\(285\) | −5.04892 | −0.299072 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.4577 | 2.09300 | ||||||||
\(288\) | −7.54288 | −0.444468 | ||||||||
\(289\) | 18.5308 | 1.09005 | ||||||||
\(290\) | 4.52781 | 0.265882 | ||||||||
\(291\) | 51.9439 | 3.04501 | ||||||||
\(292\) | −6.59179 | −0.385756 | ||||||||
\(293\) | −15.5013 | −0.905593 | −0.452796 | − | 0.891614i | \(-0.649574\pi\) | ||||
−0.452796 | + | 0.891614i | \(0.649574\pi\) | |||||||
\(294\) | −19.4426 | −1.13392 | ||||||||
\(295\) | 21.0315 | 1.22450 | ||||||||
\(296\) | −6.71379 | −0.390231 | ||||||||
\(297\) | 76.4965 | 4.43878 | ||||||||
\(298\) | −6.13706 | −0.355511 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −8.38404 | −0.484053 | ||||||||
\(301\) | 18.6112 | 1.07273 | ||||||||
\(302\) | 11.2838 | 0.649311 | ||||||||
\(303\) | 17.0858 | 0.981551 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0.957787 | 0.0548427 | ||||||||
\(306\) | 44.9614 | 2.57027 | ||||||||
\(307\) | 10.0871 | 0.575700 | 0.287850 | − | 0.957675i | \(-0.407060\pi\) | ||||
0.287850 | + | 0.957675i | \(0.407060\pi\) | |||||||
\(308\) | 18.6896 | 1.06494 | ||||||||
\(309\) | 1.28621 | 0.0731698 | ||||||||
\(310\) | −9.40581 | −0.534214 | ||||||||
\(311\) | −6.15644 | −0.349100 | −0.174550 | − | 0.984648i | \(-0.555847\pi\) | ||||
−0.174550 | + | 0.984648i | \(0.555847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4101 | 0.814508 | 0.407254 | − | 0.913315i | \(-0.366486\pi\) | ||||
0.407254 | + | 0.913315i | \(0.366486\pi\) | |||||||
\(314\) | 2.41550 | 0.136315 | ||||||||
\(315\) | −42.2693 | −2.38161 | ||||||||
\(316\) | 10.7681 | 0.605752 | ||||||||
\(317\) | 20.5241 | 1.15275 | 0.576374 | − | 0.817186i | \(-0.304467\pi\) | ||||
0.576374 | + | 0.817186i | \(0.304467\pi\) | |||||||
\(318\) | −12.4330 | −0.697206 | ||||||||
\(319\) | 15.1008 | 0.845484 | ||||||||
\(320\) | −1.55496 | −0.0869248 | ||||||||
\(321\) | −1.58642 | −0.0885452 | ||||||||
\(322\) | −15.4819 | −0.862771 | ||||||||
\(323\) | −5.96077 | −0.331666 | ||||||||
\(324\) | 25.2664 | 1.40369 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.63102 | −0.256489 | ||||||||
\(327\) | −8.81163 | −0.487284 | ||||||||
\(328\) | −9.83877 | −0.543255 | ||||||||
\(329\) | −39.7560 | −2.19182 | ||||||||
\(330\) | 26.1836 | 1.44136 | ||||||||
\(331\) | 22.4155 | 1.23207 | 0.616034 | − | 0.787720i | \(-0.288739\pi\) | ||||
0.616034 | + | 0.787720i | \(0.288739\pi\) | |||||||
\(332\) | −3.91723 | −0.214986 | ||||||||
\(333\) | 50.6413 | 2.77513 | ||||||||
\(334\) | −18.0344 | −0.986801 | ||||||||
\(335\) | −1.53617 | −0.0839300 | ||||||||
\(336\) | 11.7017 | 0.638381 | ||||||||
\(337\) | 25.1293 | 1.36888 | 0.684440 | − | 0.729069i | \(-0.260047\pi\) | ||||
0.684440 | + | 0.729069i | \(0.260047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −58.0495 | −3.15282 | ||||||||
\(340\) | 9.26875 | 0.502669 | ||||||||
\(341\) | −31.3696 | −1.69876 | ||||||||
\(342\) | −7.54288 | −0.407872 | ||||||||
\(343\) | −3.64742 | −0.196942 | ||||||||
\(344\) | −5.16421 | −0.278436 | ||||||||
\(345\) | −21.6896 | −1.16773 | ||||||||
\(346\) | 22.2107 | 1.19406 | ||||||||
\(347\) | −20.3370 | −1.09175 | −0.545875 | − | 0.837867i | \(-0.683803\pi\) | ||||
−0.545875 | + | 0.837867i | \(0.683803\pi\) | |||||||
\(348\) | 9.45473 | 0.506827 | ||||||||
\(349\) | −7.12498 | −0.381392 | −0.190696 | − | 0.981649i | \(-0.561074\pi\) | ||||
−0.190696 | + | 0.981649i | \(0.561074\pi\) | |||||||
\(350\) | 9.30559 | 0.497404 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.18598 | −0.276414 | ||||||||
\(353\) | −22.4155 | −1.19306 | −0.596528 | − | 0.802592i | \(-0.703454\pi\) | ||||
−0.596528 | + | 0.802592i | \(0.703454\pi\) | |||||||
\(354\) | 43.9168 | 2.33415 | ||||||||
\(355\) | −7.33811 | −0.389466 | ||||||||
\(356\) | −0.789856 | −0.0418623 | ||||||||
\(357\) | −69.7512 | −3.69163 | ||||||||
\(358\) | 22.0248 | 1.16404 | ||||||||
\(359\) | 6.29829 | 0.332411 | 0.166206 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166206 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(360\) | 11.7289 | 0.618165 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.3134 | −0.647176 | ||||||||
\(363\) | 51.6088 | 2.70876 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2500 | 0.536508 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 1.90754 | 0.0995729 | 0.0497864 | − | 0.998760i | \(-0.484146\pi\) | ||||
0.0497864 | + | 0.998760i | \(0.484146\pi\) | |||||||
\(368\) | 4.29590 | 0.223939 | ||||||||
\(369\) | 74.2127 | 3.86336 | ||||||||
\(370\) | 10.4397 | 0.542732 | ||||||||
\(371\) | 13.7995 | 0.716437 | ||||||||
\(372\) | −19.6407 | −1.01832 | ||||||||
\(373\) | 9.57540 | 0.495795 | 0.247898 | − | 0.968786i | \(-0.420260\pi\) | ||||
0.247898 | + | 0.968786i | \(0.420260\pi\) | |||||||
\(374\) | 30.9124 | 1.59844 | ||||||||
\(375\) | 38.2814 | 1.97684 | ||||||||
\(376\) | 11.0315 | 0.568904 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −53.1594 | −2.73423 | ||||||||
\(379\) | −11.1400 | −0.572226 | −0.286113 | − | 0.958196i | \(-0.592363\pi\) | ||||
−0.286113 | + | 0.958196i | \(0.592363\pi\) | |||||||
\(380\) | −1.55496 | −0.0797677 | ||||||||
\(381\) | −5.20775 | −0.266801 | ||||||||
\(382\) | −9.21313 | −0.471385 | ||||||||
\(383\) | 14.0489 | 0.717866 | 0.358933 | − | 0.933363i | \(-0.383141\pi\) | ||||
0.358933 | + | 0.933363i | \(0.383141\pi\) | |||||||
\(384\) | −3.24698 | −0.165697 | ||||||||
\(385\) | −29.0616 | −1.48112 | ||||||||
\(386\) | 14.2784 | 0.726753 | ||||||||
\(387\) | 38.9530 | 1.98009 | ||||||||
\(388\) | 15.9976 | 0.812155 | ||||||||
\(389\) | 9.95646 | 0.504813 | 0.252406 | − | 0.967621i | \(-0.418778\pi\) | ||||
0.252406 | + | 0.967621i | \(0.418778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.6069 | −1.29499 | ||||||||
\(392\) | −5.98792 | −0.302436 | ||||||||
\(393\) | −62.8611 | −3.17092 | ||||||||
\(394\) | 11.7802 | 0.593476 | ||||||||
\(395\) | −16.7439 | −0.842478 | ||||||||
\(396\) | 39.1172 | 1.96571 | ||||||||
\(397\) | −16.0683 | −0.806445 | −0.403222 | − | 0.915102i | \(-0.632110\pi\) | ||||
−0.403222 | + | 0.915102i | \(0.632110\pi\) | |||||||
\(398\) | −5.88040 | −0.294758 | ||||||||
\(399\) | 11.7017 | 0.585818 | ||||||||
\(400\) | −2.58211 | −0.129105 | ||||||||
\(401\) | −4.59717 | −0.229572 | −0.114786 | − | 0.993390i | \(-0.536618\pi\) | ||||
−0.114786 | + | 0.993390i | \(0.536618\pi\) | |||||||
\(402\) | −3.20775 | −0.159988 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.26205 | 0.261797 | ||||||||
\(405\) | −39.2881 | −1.95224 | ||||||||
\(406\) | −10.4940 | −0.520806 | ||||||||
\(407\) | 34.8176 | 1.72584 | ||||||||
\(408\) | 19.3545 | 0.958191 | ||||||||
\(409\) | 1.56033 | 0.0771536 | 0.0385768 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385768 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(410\) | 15.2989 | 0.755558 | ||||||||
\(411\) | 21.4819 | 1.05962 | ||||||||
\(412\) | 0.396125 | 0.0195157 | ||||||||
\(413\) | −48.7439 | −2.39853 | ||||||||
\(414\) | −32.4034 | −1.59254 | ||||||||
\(415\) | 6.09113 | 0.299002 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.03146 | 0.148451 | ||||||||
\(418\) | −5.18598 | −0.253655 | ||||||||
\(419\) | 12.4590 | 0.608664 | 0.304332 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304332 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(420\) | −18.1957 | −0.887858 | ||||||||
\(421\) | −4.71379 | −0.229736 | −0.114868 | − | 0.993381i | \(-0.536645\pi\) | ||||
−0.114868 | + | 0.993381i | \(0.536645\pi\) | |||||||
\(422\) | 10.5894 | 0.515484 | ||||||||
\(423\) | −83.2089 | −4.04576 | ||||||||
\(424\) | −3.82908 | −0.185957 | ||||||||
\(425\) | 15.3913 | 0.746590 | ||||||||
\(426\) | −15.3230 | −0.742404 | ||||||||
\(427\) | −2.21983 | −0.107425 | ||||||||
\(428\) | −0.488582 | −0.0236165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.03013 | 0.387247 | ||||||||
\(431\) | −15.0707 | −0.725929 | −0.362965 | − | 0.931803i | \(-0.618235\pi\) | ||||
−0.362965 | + | 0.931803i | \(0.618235\pi\) | |||||||
\(432\) | 14.7506 | 0.709690 | ||||||||
\(433\) | 18.4263 | 0.885509 | 0.442755 | − | 0.896643i | \(-0.354001\pi\) | ||||
0.442755 | + | 0.896643i | \(0.354001\pi\) | |||||||
\(434\) | 21.7995 | 1.04641 | ||||||||
\(435\) | −14.7017 | −0.704893 | ||||||||
\(436\) | −2.71379 | −0.129967 | ||||||||
\(437\) | 4.29590 | 0.205501 | ||||||||
\(438\) | 21.4034 | 1.02269 | ||||||||
\(439\) | −38.1909 | −1.82275 | −0.911376 | − | 0.411575i | \(-0.864979\pi\) | ||||
−0.911376 | + | 0.411575i | \(0.864979\pi\) | |||||||
\(440\) | 8.06398 | 0.384435 | ||||||||
\(441\) | 45.1661 | 2.15077 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.3599 | −1.48995 | −0.744976 | − | 0.667091i | \(-0.767539\pi\) | ||||
−0.744976 | + | 0.667091i | \(0.767539\pi\) | |||||||
\(444\) | 21.7995 | 1.03456 | ||||||||
\(445\) | 1.22819 | 0.0582219 | ||||||||
\(446\) | −1.04652 | −0.0495544 | ||||||||
\(447\) | 19.9269 | 0.942511 | ||||||||
\(448\) | 3.60388 | 0.170267 | ||||||||
\(449\) | 15.5104 | 0.731979 | 0.365989 | − | 0.930619i | \(-0.380731\pi\) | ||||
0.365989 | + | 0.930619i | \(0.380731\pi\) | |||||||
\(450\) | 19.4765 | 0.918131 | ||||||||
\(451\) | 51.0237 | 2.40261 | ||||||||
\(452\) | −17.8780 | −0.840910 | ||||||||
\(453\) | −36.6383 | −1.72142 | ||||||||
\(454\) | 7.10992 | 0.333685 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.24698 | −0.152054 | ||||||||
\(457\) | 33.8538 | 1.58362 | 0.791808 | − | 0.610770i | \(-0.209140\pi\) | ||||
0.791808 | + | 0.610770i | \(0.209140\pi\) | |||||||
\(458\) | −16.6679 | −0.778838 | ||||||||
\(459\) | −87.9251 | −4.10399 | ||||||||
\(460\) | −6.67994 | −0.311454 | ||||||||
\(461\) | −16.9989 | −0.791719 | −0.395860 | − | 0.918311i | \(-0.629553\pi\) | ||||
−0.395860 | + | 0.918311i | \(0.629553\pi\) | |||||||
\(462\) | −60.6848 | −2.82331 | ||||||||
\(463\) | 33.5254 | 1.55806 | 0.779029 | − | 0.626988i | \(-0.215712\pi\) | ||||
0.779029 | + | 0.626988i | \(0.215712\pi\) | |||||||
\(464\) | 2.91185 | 0.135179 | ||||||||
\(465\) | 30.5405 | 1.41628 | ||||||||
\(466\) | 10.5187 | 0.487270 | ||||||||
\(467\) | −24.8659 | −1.15066 | −0.575329 | − | 0.817922i | \(-0.695126\pi\) | ||||
−0.575329 | + | 0.817922i | \(0.695126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.56033 | 0.164401 | ||||||||
\(470\) | −17.1535 | −0.791230 | ||||||||
\(471\) | −7.84309 | −0.361390 | ||||||||
\(472\) | 13.5254 | 0.622558 | ||||||||
\(473\) | 26.7815 | 1.23141 | ||||||||
\(474\) | −34.9638 | −1.60594 | ||||||||
\(475\) | −2.58211 | −0.118475 | ||||||||
\(476\) | −21.4819 | −0.984620 | ||||||||
\(477\) | 28.8823 | 1.32243 | ||||||||
\(478\) | 0.548253 | 0.0250765 | ||||||||
\(479\) | 43.5120 | 1.98811 | 0.994057 | − | 0.108859i | \(-0.0347197\pi\) | ||||
0.994057 | + | 0.108859i | \(0.0347197\pi\) | |||||||
\(480\) | 5.04892 | 0.230450 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 17.5743 | 0.800489 | ||||||||
\(483\) | 50.2693 | 2.28733 | ||||||||
\(484\) | 15.8944 | 0.722473 | ||||||||
\(485\) | −24.8756 | −1.12954 | ||||||||
\(486\) | −37.7875 | −1.71407 | ||||||||
\(487\) | 9.41657 | 0.426705 | 0.213353 | − | 0.976975i | \(-0.431562\pi\) | ||||
0.213353 | + | 0.976975i | \(0.431562\pi\) | |||||||
\(488\) | 0.615957 | 0.0278831 | ||||||||
\(489\) | 15.0368 | 0.679989 | ||||||||
\(490\) | 9.31096 | 0.420626 | ||||||||
\(491\) | 1.67755 | 0.0757066 | 0.0378533 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378533 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(492\) | 31.9463 | 1.44025 | ||||||||
\(493\) | −17.3569 | −0.781715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60.8256 | −2.73391 | ||||||||
\(496\) | −6.04892 | −0.271604 | ||||||||
\(497\) | 17.0073 | 0.762881 | ||||||||
\(498\) | 12.7192 | 0.569960 | ||||||||
\(499\) | −39.4077 | −1.76413 | −0.882066 | − | 0.471126i | \(-0.843848\pi\) | ||||
−0.882066 | + | 0.471126i | \(0.843848\pi\) | |||||||
\(500\) | 11.7899 | 0.527258 | ||||||||
\(501\) | 58.5575 | 2.61615 | ||||||||
\(502\) | −4.09783 | −0.182895 | ||||||||
\(503\) | −1.86725 | −0.0832565 | −0.0416282 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416282 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(504\) | −27.1836 | −1.21085 | ||||||||
\(505\) | −8.18226 | −0.364106 | ||||||||
\(506\) | −22.2784 | −0.990397 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.60388 | −0.0711605 | ||||||||
\(509\) | 20.8853 | 0.925725 | 0.462862 | − | 0.886430i | \(-0.346822\pi\) | ||||
0.462862 | + | 0.886430i | \(0.346822\pi\) | |||||||
\(510\) | −30.0954 | −1.33265 | ||||||||
\(511\) | −23.7560 | −1.05090 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.7506 | 0.651256 | ||||||||
\(514\) | 6.65950 | 0.293738 | ||||||||
\(515\) | −0.615957 | −0.0271423 | ||||||||
\(516\) | 16.7681 | 0.738174 | ||||||||
\(517\) | −57.2089 | −2.51605 | ||||||||
\(518\) | −24.1957 | −1.06310 | ||||||||
\(519\) | −72.1178 | −3.16562 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.01075 | −0.263336 | −0.131668 | − | 0.991294i | \(-0.542033\pi\) | ||||
−0.131668 | + | 0.991294i | \(0.542033\pi\) | |||||||
\(522\) | −21.9638 | −0.961327 | ||||||||
\(523\) | 25.2325 | 1.10334 | 0.551670 | − | 0.834062i | \(-0.313991\pi\) | ||||
0.551670 | + | 0.834062i | \(0.313991\pi\) | |||||||
\(524\) | −19.3599 | −0.845740 | ||||||||
\(525\) | −30.2150 | −1.31869 | ||||||||
\(526\) | −20.3763 | −0.888448 | ||||||||
\(527\) | 36.0562 | 1.57063 | ||||||||
\(528\) | 16.8388 | 0.732814 | ||||||||
\(529\) | −4.54527 | −0.197620 | ||||||||
\(530\) | 5.95407 | 0.258628 | ||||||||
\(531\) | −102.021 | −4.42732 | ||||||||
\(532\) | 3.60388 | 0.156248 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.56465 | 0.110983 | ||||||||
\(535\) | 0.759725 | 0.0328458 | ||||||||
\(536\) | −0.987918 | −0.0426716 | ||||||||
\(537\) | −71.5139 | −3.08605 | ||||||||
\(538\) | 20.9638 | 0.903812 | ||||||||
\(539\) | 31.0532 | 1.33756 | ||||||||
\(540\) | −22.9366 | −0.987034 | ||||||||
\(541\) | −15.3459 | −0.659771 | −0.329885 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329885 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(542\) | 9.40821 | 0.404117 | ||||||||
\(543\) | 39.9812 | 1.71576 | ||||||||
\(544\) | 5.96077 | 0.255566 | ||||||||
\(545\) | 4.21983 | 0.180758 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.97525 | −0.0844554 | −0.0422277 | − | 0.999108i | \(-0.513445\pi\) | ||||
−0.0422277 | + | 0.999108i | \(0.513445\pi\) | |||||||
\(548\) | 6.61596 | 0.282620 | ||||||||
\(549\) | −4.64609 | −0.198290 | ||||||||
\(550\) | 13.3907 | 0.570983 | ||||||||
\(551\) | 2.91185 | 0.124049 | ||||||||
\(552\) | −13.9487 | −0.593696 | ||||||||
\(553\) | 38.8068 | 1.65023 | ||||||||
\(554\) | −22.0194 | −0.935514 | ||||||||
\(555\) | −33.8974 | −1.43886 | ||||||||
\(556\) | 0.933624 | 0.0395945 | ||||||||
\(557\) | 22.6920 | 0.961492 | 0.480746 | − | 0.876860i | \(-0.340366\pi\) | ||||
0.480746 | + | 0.876860i | \(0.340366\pi\) | |||||||
\(558\) | 45.6262 | 1.93151 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.60388 | −0.236807 | ||||||||
\(561\) | −100.372 | −4.23771 | ||||||||
\(562\) | 24.4373 | 1.03082 | ||||||||
\(563\) | 22.4373 | 0.945618 | 0.472809 | − | 0.881165i | \(-0.343240\pi\) | ||||
0.472809 | + | 0.881165i | \(0.343240\pi\) | |||||||
\(564\) | −35.8189 | −1.50825 | ||||||||
\(565\) | 27.7995 | 1.16954 | ||||||||
\(566\) | −15.9323 | −0.669684 | ||||||||
\(567\) | 91.0568 | 3.82403 | ||||||||
\(568\) | −4.71917 | −0.198012 | ||||||||
\(569\) | 23.9711 | 1.00492 | 0.502459 | − | 0.864601i | \(-0.332429\pi\) | ||||
0.502459 | + | 0.864601i | \(0.332429\pi\) | |||||||
\(570\) | 5.04892 | 0.211476 | ||||||||
\(571\) | −9.84787 | −0.412121 | −0.206060 | − | 0.978539i | \(-0.566064\pi\) | ||||
−0.206060 | + | 0.978539i | \(0.566064\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.9148 | 1.24971 | ||||||||
\(574\) | −35.4577 | −1.47998 | ||||||||
\(575\) | −11.0925 | −0.462587 | ||||||||
\(576\) | 7.54288 | 0.314287 | ||||||||
\(577\) | 25.2922 | 1.05293 | 0.526464 | − | 0.850198i | \(-0.323518\pi\) | ||||
0.526464 | + | 0.850198i | \(0.323518\pi\) | |||||||
\(578\) | −18.5308 | −0.770779 | ||||||||
\(579\) | −46.3618 | −1.92673 | ||||||||
\(580\) | −4.52781 | −0.188007 | ||||||||
\(581\) | −14.1172 | −0.585681 | ||||||||
\(582\) | −51.9439 | −2.15314 | ||||||||
\(583\) | 19.8576 | 0.822416 | ||||||||
\(584\) | 6.59179 | 0.272770 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.5013 | 0.640351 | ||||||||
\(587\) | −41.2922 | −1.70431 | −0.852155 | − | 0.523289i | \(-0.824705\pi\) | ||||
−0.852155 | + | 0.523289i | \(0.824705\pi\) | |||||||
\(588\) | 19.4426 | 0.801801 | ||||||||
\(589\) | −6.04892 | −0.249241 | ||||||||
\(590\) | −21.0315 | −0.865851 | ||||||||
\(591\) | −38.2500 | −1.57339 | ||||||||
\(592\) | 6.71379 | 0.275935 | ||||||||
\(593\) | 13.8043 | 0.566876 | 0.283438 | − | 0.958991i | \(-0.408525\pi\) | ||||
0.283438 | + | 0.958991i | \(0.408525\pi\) | |||||||
\(594\) | −76.4965 | −3.13869 | ||||||||
\(595\) | 33.4034 | 1.36941 | ||||||||
\(596\) | 6.13706 | 0.251384 | ||||||||
\(597\) | 19.0935 | 0.781446 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.84309 | 0.402178 | 0.201089 | − | 0.979573i | \(-0.435552\pi\) | ||||
0.201089 | + | 0.979573i | \(0.435552\pi\) | |||||||
\(600\) | 8.38404 | 0.342277 | ||||||||
\(601\) | 14.2198 | 0.580039 | 0.290020 | − | 0.957021i | \(-0.406338\pi\) | ||||
0.290020 | + | 0.957021i | \(0.406338\pi\) | |||||||
\(602\) | −18.6112 | −0.758535 | ||||||||
\(603\) | 7.45175 | 0.303459 | ||||||||
\(604\) | −11.2838 | −0.459132 | ||||||||
\(605\) | −24.7151 | −1.00481 | ||||||||
\(606\) | −17.0858 | −0.694061 | ||||||||
\(607\) | 19.3056 | 0.783590 | 0.391795 | − | 0.920053i | \(-0.371854\pi\) | ||||
0.391795 | + | 0.920053i | \(0.371854\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 34.0737 | 1.38073 | ||||||||
\(610\) | −0.957787 | −0.0387797 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −44.9614 | −1.81746 | ||||||||
\(613\) | −36.6058 | −1.47849 | −0.739247 | − | 0.673434i | \(-0.764818\pi\) | ||||
−0.739247 | + | 0.673434i | \(0.764818\pi\) | |||||||
\(614\) | −10.0871 | −0.407081 | ||||||||
\(615\) | −49.6752 | −2.00310 | ||||||||
\(616\) | −18.6896 | −0.753027 | ||||||||
\(617\) | −6.14138 | −0.247242 | −0.123621 | − | 0.992329i | \(-0.539451\pi\) | ||||
−0.123621 | + | 0.992329i | \(0.539451\pi\) | |||||||
\(618\) | −1.28621 | −0.0517389 | ||||||||
\(619\) | −10.5080 | −0.422351 | −0.211175 | − | 0.977448i | \(-0.567729\pi\) | ||||
−0.211175 | + | 0.977448i | \(0.567729\pi\) | |||||||
\(620\) | 9.40581 | 0.377747 | ||||||||
\(621\) | 63.3672 | 2.54284 | ||||||||
\(622\) | 6.15644 | 0.246851 | ||||||||
\(623\) | −2.84654 | −0.114044 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.42221 | −0.216888 | ||||||||
\(626\) | −14.4101 | −0.575944 | ||||||||
\(627\) | 16.8388 | 0.672476 | ||||||||
\(628\) | −2.41550 | −0.0963890 | ||||||||
\(629\) | −40.0194 | −1.59568 | ||||||||
\(630\) | 42.2693 | 1.68405 | ||||||||
\(631\) | −38.7090 | −1.54098 | −0.770491 | − | 0.637451i | \(-0.779989\pi\) | ||||
−0.770491 | + | 0.637451i | \(0.779989\pi\) | |||||||
\(632\) | −10.7681 | −0.428331 | ||||||||
\(633\) | −34.3836 | −1.36662 | ||||||||
\(634\) | −20.5241 | −0.815116 | ||||||||
\(635\) | 2.49396 | 0.0989698 | ||||||||
\(636\) | 12.4330 | 0.492999 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.1008 | −0.597847 | ||||||||
\(639\) | 35.5961 | 1.40816 | ||||||||
\(640\) | 1.55496 | 0.0614651 | ||||||||
\(641\) | −46.7767 | −1.84757 | −0.923784 | − | 0.382913i | \(-0.874921\pi\) | ||||
−0.923784 | + | 0.382913i | \(0.874921\pi\) | |||||||
\(642\) | 1.58642 | 0.0626109 | ||||||||
\(643\) | 30.6853 | 1.21011 | 0.605055 | − | 0.796183i | \(-0.293151\pi\) | ||||
0.605055 | + | 0.796183i | \(0.293151\pi\) | |||||||
\(644\) | 15.4819 | 0.610071 | ||||||||
\(645\) | −26.0737 | −1.02665 | ||||||||
\(646\) | 5.96077 | 0.234523 | ||||||||
\(647\) | −43.3846 | −1.70563 | −0.852813 | − | 0.522216i | \(-0.825105\pi\) | ||||
−0.852813 | + | 0.522216i | \(0.825105\pi\) | |||||||
\(648\) | −25.2664 | −0.992556 | ||||||||
\(649\) | −70.1426 | −2.75334 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −70.7827 | −2.77419 | ||||||||
\(652\) | 4.63102 | 0.181365 | ||||||||
\(653\) | −24.6025 | −0.962772 | −0.481386 | − | 0.876509i | \(-0.659866\pi\) | ||||
−0.481386 | + | 0.876509i | \(0.659866\pi\) | |||||||
\(654\) | 8.81163 | 0.344562 | ||||||||
\(655\) | 30.1038 | 1.17625 | ||||||||
\(656\) | 9.83877 | 0.384140 | ||||||||
\(657\) | −49.7211 | −1.93980 | ||||||||
\(658\) | 39.7560 | 1.54985 | ||||||||
\(659\) | 25.3013 | 0.985598 | 0.492799 | − | 0.870143i | \(-0.335974\pi\) | ||||
0.492799 | + | 0.870143i | \(0.335974\pi\) | |||||||
\(660\) | −26.1836 | −1.01919 | ||||||||
\(661\) | −20.2983 | −0.789512 | −0.394756 | − | 0.918786i | \(-0.629171\pi\) | ||||
−0.394756 | + | 0.918786i | \(0.629171\pi\) | |||||||
\(662\) | −22.4155 | −0.871203 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.91723 | 0.152018 | ||||||||
\(665\) | −5.60388 | −0.217309 | ||||||||
\(666\) | −50.6413 | −1.96231 | ||||||||
\(667\) | 12.5090 | 0.484351 | ||||||||
\(668\) | 18.0344 | 0.697774 | ||||||||
\(669\) | 3.39804 | 0.131376 | ||||||||
\(670\) | 1.53617 | 0.0593475 | ||||||||
\(671\) | −3.19434 | −0.123316 | ||||||||
\(672\) | −11.7017 | −0.451403 | ||||||||
\(673\) | 10.8552 | 0.418436 | 0.209218 | − | 0.977869i | \(-0.432908\pi\) | ||||
0.209218 | + | 0.977869i | \(0.432908\pi\) | |||||||
\(674\) | −25.1293 | −0.967944 | ||||||||
\(675\) | −38.0877 | −1.46600 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0204 | 1.03848 | 0.519240 | − | 0.854628i | \(-0.326215\pi\) | ||||
0.519240 | + | 0.854628i | \(0.326215\pi\) | |||||||
\(678\) | 58.0495 | 2.22938 | ||||||||
\(679\) | 57.6534 | 2.21253 | ||||||||
\(680\) | −9.26875 | −0.355440 | ||||||||
\(681\) | −23.0858 | −0.884648 | ||||||||
\(682\) | 31.3696 | 1.20120 | ||||||||
\(683\) | −26.8659 | −1.02800 | −0.513998 | − | 0.857791i | \(-0.671836\pi\) | ||||
−0.513998 | + | 0.857791i | \(0.671836\pi\) | |||||||
\(684\) | 7.54288 | 0.288409 | ||||||||
\(685\) | −10.2875 | −0.393067 | ||||||||
\(686\) | 3.64742 | 0.139259 | ||||||||
\(687\) | 54.1202 | 2.06481 | ||||||||
\(688\) | 5.16421 | 0.196884 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 21.6896 | 0.825710 | ||||||||
\(691\) | −20.9855 | −0.798327 | −0.399164 | − | 0.916880i | \(-0.630699\pi\) | ||||
−0.399164 | + | 0.916880i | \(0.630699\pi\) | |||||||
\(692\) | −22.2107 | −0.844325 | ||||||||
\(693\) | 140.974 | 5.35514 | ||||||||
\(694\) | 20.3370 | 0.771984 | ||||||||
\(695\) | −1.45175 | −0.0550679 | ||||||||
\(696\) | −9.45473 | −0.358381 | ||||||||
\(697\) | −58.6467 | −2.22140 | ||||||||
\(698\) | 7.12498 | 0.269685 | ||||||||
\(699\) | −34.1540 | −1.29182 | ||||||||
\(700\) | −9.30559 | −0.351718 | ||||||||
\(701\) | −29.2922 | −1.10635 | −0.553175 | − | 0.833065i | \(-0.686584\pi\) | ||||
−0.553175 | + | 0.833065i | \(0.686584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.71379 | 0.253215 | ||||||||
\(704\) | 5.18598 | 0.195454 | ||||||||
\(705\) | 55.6969 | 2.09767 | ||||||||
\(706\) | 22.4155 | 0.843619 | ||||||||
\(707\) | 18.9638 | 0.713205 | ||||||||
\(708\) | −43.9168 | −1.65049 | ||||||||
\(709\) | 11.9758 | 0.449762 | 0.224881 | − | 0.974386i | \(-0.427801\pi\) | ||||
0.224881 | + | 0.974386i | \(0.427801\pi\) | |||||||
\(710\) | 7.33811 | 0.275394 | ||||||||
\(711\) | 81.2223 | 3.04608 | ||||||||
\(712\) | 0.789856 | 0.0296011 | ||||||||
\(713\) | −25.9855 | −0.973166 | ||||||||
\(714\) | 69.7512 | 2.61037 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.0248 | −0.823104 | ||||||||
\(717\) | −1.78017 | −0.0664816 | ||||||||
\(718\) | −6.29829 | −0.235050 | ||||||||
\(719\) | 47.0025 | 1.75290 | 0.876449 | − | 0.481495i | \(-0.159906\pi\) | ||||
0.876449 | + | 0.481495i | \(0.159906\pi\) | |||||||
\(720\) | −11.7289 | −0.437109 | ||||||||
\(721\) | 1.42758 | 0.0531660 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −57.0635 | −2.12221 | ||||||||
\(724\) | 12.3134 | 0.457622 | ||||||||
\(725\) | −7.51871 | −0.279238 | ||||||||
\(726\) | −51.6088 | −1.91538 | ||||||||
\(727\) | −10.7832 | −0.399925 | −0.199962 | − | 0.979804i | \(-0.564082\pi\) | ||||
−0.199962 | + | 0.979804i | \(0.564082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 46.8961 | 1.73689 | ||||||||
\(730\) | −10.2500 | −0.379368 | ||||||||
\(731\) | −30.7827 | −1.13854 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | 16.9554 | 0.626262 | 0.313131 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313131 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(734\) | −1.90754 | −0.0704087 | ||||||||
\(735\) | −30.2325 | −1.11514 | ||||||||
\(736\) | −4.29590 | −0.158349 | ||||||||
\(737\) | 5.12333 | 0.188720 | ||||||||
\(738\) | −74.2127 | −2.73181 | ||||||||
\(739\) | 25.3817 | 0.933679 | 0.466840 | − | 0.884342i | \(-0.345393\pi\) | ||||
0.466840 | + | 0.884342i | \(0.345393\pi\) | |||||||
\(740\) | −10.4397 | −0.383770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.7995 | −0.506597 | ||||||||
\(743\) | 8.47517 | 0.310924 | 0.155462 | − | 0.987842i | \(-0.450313\pi\) | ||||
0.155462 | + | 0.987842i | \(0.450313\pi\) | |||||||
\(744\) | 19.6407 | 0.720063 | ||||||||
\(745\) | −9.54288 | −0.349624 | ||||||||
\(746\) | −9.57540 | −0.350580 | ||||||||
\(747\) | −29.5472 | −1.08108 | ||||||||
\(748\) | −30.9124 | −1.13027 | ||||||||
\(749\) | −1.76079 | −0.0643379 | ||||||||
\(750\) | −38.2814 | −1.39784 | ||||||||
\(751\) | 35.0315 | 1.27832 | 0.639158 | − | 0.769075i | \(-0.279283\pi\) | ||||
0.639158 | + | 0.769075i | \(0.279283\pi\) | |||||||
\(752\) | −11.0315 | −0.402276 | ||||||||
\(753\) | 13.3056 | 0.484882 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.5459 | 0.638559 | ||||||||
\(756\) | 53.1594 | 1.93339 | ||||||||
\(757\) | −37.0374 | −1.34615 | −0.673074 | − | 0.739575i | \(-0.735026\pi\) | ||||
−0.673074 | + | 0.739575i | \(0.735026\pi\) | |||||||
\(758\) | 11.1400 | 0.404625 | ||||||||
\(759\) | 72.3376 | 2.62569 | ||||||||
\(760\) | 1.55496 | 0.0564043 | ||||||||
\(761\) | 12.4155 | 0.450062 | 0.225031 | − | 0.974352i | \(-0.427752\pi\) | ||||
0.225031 | + | 0.974352i | \(0.427752\pi\) | |||||||
\(762\) | 5.20775 | 0.188657 | ||||||||
\(763\) | −9.78017 | −0.354066 | ||||||||
\(764\) | 9.21313 | 0.333319 | ||||||||
\(765\) | 69.9130 | 2.52771 | ||||||||
\(766\) | −14.0489 | −0.507608 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.24698 | 0.117165 | ||||||||
\(769\) | −31.8103 | −1.14711 | −0.573554 | − | 0.819168i | \(-0.694436\pi\) | ||||
−0.573554 | + | 0.819168i | \(0.694436\pi\) | |||||||
\(770\) | 29.0616 | 1.04731 | ||||||||
\(771\) | −21.6233 | −0.778742 | ||||||||
\(772\) | −14.2784 | −0.513892 | ||||||||
\(773\) | 9.54480 | 0.343302 | 0.171651 | − | 0.985158i | \(-0.445090\pi\) | ||||
0.171651 | + | 0.985158i | \(0.445090\pi\) | |||||||
\(774\) | −38.9530 | −1.40014 | ||||||||
\(775\) | 15.6189 | 0.561049 | ||||||||
\(776\) | −15.9976 | −0.574281 | ||||||||
\(777\) | 78.5628 | 2.81843 | ||||||||
\(778\) | −9.95646 | −0.356956 | ||||||||
\(779\) | 9.83877 | 0.352511 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.4735 | 0.875731 | ||||||||
\(782\) | 25.6069 | 0.915699 | ||||||||
\(783\) | 42.9517 | 1.53497 | ||||||||
\(784\) | 5.98792 | 0.213854 | ||||||||
\(785\) | 3.75600 | 0.134058 | ||||||||
\(786\) | 62.8611 | 2.24218 | ||||||||
\(787\) | 38.5763 | 1.37509 | 0.687547 | − | 0.726139i | \(-0.258687\pi\) | ||||
0.687547 | + | 0.726139i | \(0.258687\pi\) | |||||||
\(788\) | −11.7802 | −0.419651 | ||||||||
\(789\) | 66.1613 | 2.35541 | ||||||||
\(790\) | 16.7439 | 0.595722 | ||||||||
\(791\) | −64.4301 | −2.29087 | ||||||||
\(792\) | −39.1172 | −1.38997 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 16.0683 | 0.570242 | ||||||||
\(795\) | −19.3327 | −0.685661 | ||||||||
\(796\) | 5.88040 | 0.208425 | ||||||||
\(797\) | 42.2717 | 1.49734 | 0.748671 | − | 0.662942i | \(-0.230692\pi\) | ||||
0.748671 | + | 0.662942i | \(0.230692\pi\) | |||||||
\(798\) | −11.7017 | −0.414236 | ||||||||
\(799\) | 65.7560 | 2.32628 | ||||||||
\(800\) | 2.58211 | 0.0912912 | ||||||||
\(801\) | −5.95779 | −0.210508 | ||||||||
\(802\) | 4.59717 | 0.162332 | ||||||||
\(803\) | −34.1849 | −1.20636 | ||||||||
\(804\) | 3.20775 | 0.113129 | ||||||||
\(805\) | −24.0737 | −0.848485 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −68.0689 | −2.39614 | ||||||||
\(808\) | −5.26205 | −0.185118 | ||||||||
\(809\) | −13.2537 | −0.465975 | −0.232987 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232987 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(810\) | 39.2881 | 1.38044 | ||||||||
\(811\) | 8.98313 | 0.315440 | 0.157720 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157720 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(812\) | 10.4940 | 0.368266 | ||||||||
\(813\) | −30.5483 | −1.07137 | ||||||||
\(814\) | −34.8176 | −1.22036 | ||||||||
\(815\) | −7.20105 | −0.252242 | ||||||||
\(816\) | −19.3545 | −0.677543 | ||||||||
\(817\) | 5.16421 | 0.180673 | ||||||||
\(818\) | −1.56033 | −0.0545558 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.2989 | −0.534260 | ||||||||
\(821\) | 21.9302 | 0.765368 | 0.382684 | − | 0.923879i | \(-0.375000\pi\) | ||||
0.382684 | + | 0.923879i | \(0.375000\pi\) | |||||||
\(822\) | −21.4819 | −0.749267 | ||||||||
\(823\) | −12.0567 | −0.420270 | −0.210135 | − | 0.977672i | \(-0.567390\pi\) | ||||
−0.210135 | + | 0.977672i | \(0.567390\pi\) | |||||||
\(824\) | −0.396125 | −0.0137997 | ||||||||
\(825\) | −43.4795 | −1.51376 | ||||||||
\(826\) | 48.7439 | 1.69602 | ||||||||
\(827\) | 3.49529 | 0.121543 | 0.0607715 | − | 0.998152i | \(-0.480644\pi\) | ||||
0.0607715 | + | 0.998152i | \(0.480644\pi\) | |||||||
\(828\) | 32.4034 | 1.12610 | ||||||||
\(829\) | 33.8532 | 1.17577 | 0.587886 | − | 0.808944i | \(-0.299960\pi\) | ||||
0.587886 | + | 0.808944i | \(0.299960\pi\) | |||||||
\(830\) | −6.09113 | −0.211426 | ||||||||
\(831\) | 71.4965 | 2.48019 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.6926 | −1.23668 | ||||||||
\(834\) | −3.03146 | −0.104971 | ||||||||
\(835\) | −28.0428 | −0.970461 | ||||||||
\(836\) | 5.18598 | 0.179361 | ||||||||
\(837\) | −89.2253 | −3.08408 | ||||||||
\(838\) | −12.4590 | −0.430390 | ||||||||
\(839\) | −38.2959 | −1.32212 | −0.661061 | − | 0.750333i | \(-0.729893\pi\) | ||||
−0.661061 | + | 0.750333i | \(0.729893\pi\) | |||||||
\(840\) | 18.1957 | 0.627810 | ||||||||
\(841\) | −20.5211 | −0.707624 | ||||||||
\(842\) | 4.71379 | 0.162448 | ||||||||
\(843\) | −79.3473 | −2.73287 | ||||||||
\(844\) | −10.5894 | −0.364502 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 83.2089 | 2.86078 | ||||||||
\(847\) | 57.2814 | 1.96821 | ||||||||
\(848\) | 3.82908 | 0.131491 | ||||||||
\(849\) | 51.7318 | 1.77543 | ||||||||
\(850\) | −15.3913 | −0.527919 | ||||||||
\(851\) | 28.8418 | 0.988683 | ||||||||
\(852\) | 15.3230 | 0.524959 | ||||||||
\(853\) | 9.33619 | 0.319665 | 0.159833 | − | 0.987144i | \(-0.448905\pi\) | ||||
0.159833 | + | 0.987144i | \(0.448905\pi\) | |||||||
\(854\) | 2.21983 | 0.0759611 | ||||||||
\(855\) | −11.7289 | −0.401118 | ||||||||
\(856\) | 0.488582 | 0.0166994 | ||||||||
\(857\) | −47.7405 | −1.63078 | −0.815392 | − | 0.578910i | \(-0.803478\pi\) | ||||
−0.815392 | + | 0.578910i | \(0.803478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3913 | 0.354548 | 0.177274 | − | 0.984162i | \(-0.443272\pi\) | ||||
0.177274 | + | 0.984162i | \(0.443272\pi\) | |||||||
\(860\) | −8.03013 | −0.273825 | ||||||||
\(861\) | 115.130 | 3.92364 | ||||||||
\(862\) | 15.0707 | 0.513310 | ||||||||
\(863\) | 19.0398 | 0.648123 | 0.324061 | − | 0.946036i | \(-0.394952\pi\) | ||||
0.324061 | + | 0.946036i | \(0.394952\pi\) | |||||||
\(864\) | −14.7506 | −0.501827 | ||||||||
\(865\) | 34.5368 | 1.17429 | ||||||||
\(866\) | −18.4263 | −0.626150 | ||||||||
\(867\) | 60.1691 | 2.04345 | ||||||||
\(868\) | −21.7995 | −0.739925 | ||||||||
\(869\) | 55.8431 | 1.89435 | ||||||||
\(870\) | 14.7017 | 0.498435 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.71379 | 0.0919006 | ||||||||
\(873\) | 120.668 | 4.08399 | ||||||||
\(874\) | −4.29590 | −0.145311 | ||||||||
\(875\) | 42.4892 | 1.43640 | ||||||||
\(876\) | −21.4034 | −0.723155 | ||||||||
\(877\) | −35.8684 | −1.21119 | −0.605595 | − | 0.795773i | \(-0.707065\pi\) | ||||
−0.605595 | + | 0.795773i | \(0.707065\pi\) | |||||||
\(878\) | 38.1909 | 1.28888 | ||||||||
\(879\) | −50.3323 | −1.69766 | ||||||||
\(880\) | −8.06398 | −0.271837 | ||||||||
\(881\) | −37.3631 | −1.25880 | −0.629398 | − | 0.777083i | \(-0.716698\pi\) | ||||
−0.629398 | + | 0.777083i | \(0.716698\pi\) | |||||||
\(882\) | −45.1661 | −1.52082 | ||||||||
\(883\) | −19.6823 | −0.662363 | −0.331182 | − | 0.943567i | \(-0.607447\pi\) | ||||
−0.331182 | + | 0.943567i | \(0.607447\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 68.2887 | 2.29550 | ||||||||
\(886\) | 31.3599 | 1.05356 | ||||||||
\(887\) | 35.6534 | 1.19712 | 0.598562 | − | 0.801077i | \(-0.295739\pi\) | ||||
0.598562 | + | 0.801077i | \(0.295739\pi\) | |||||||
\(888\) | −21.7995 | −0.731545 | ||||||||
\(889\) | −5.78017 | −0.193861 | ||||||||
\(890\) | −1.22819 | −0.0411691 | ||||||||
\(891\) | 131.031 | 4.38970 | ||||||||
\(892\) | 1.04652 | 0.0350402 | ||||||||
\(893\) | −11.0315 | −0.369154 | ||||||||
\(894\) | −19.9269 | −0.666456 | ||||||||
\(895\) | 34.2476 | 1.14477 | ||||||||
\(896\) | −3.60388 | −0.120397 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.5104 | −0.517587 | ||||||||
\(899\) | −17.6136 | −0.587445 | ||||||||
\(900\) | −19.4765 | −0.649217 | ||||||||
\(901\) | −22.8243 | −0.760388 | ||||||||
\(902\) | −51.0237 | −1.69890 | ||||||||
\(903\) | 60.4301 | 2.01099 | ||||||||
\(904\) | 17.8780 | 0.594614 | ||||||||
\(905\) | −19.1468 | −0.636460 | ||||||||
\(906\) | 36.6383 | 1.21723 | ||||||||
\(907\) | −16.5757 | −0.550386 | −0.275193 | − | 0.961389i | \(-0.588742\pi\) | ||||
−0.275193 | + | 0.961389i | \(0.588742\pi\) | |||||||
\(908\) | −7.10992 | −0.235951 | ||||||||
\(909\) | 39.6910 | 1.31647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4999 | −0.944245 | −0.472122 | − | 0.881533i | \(-0.656512\pi\) | ||||
−0.472122 | + | 0.881533i | \(0.656512\pi\) | |||||||
\(912\) | 3.24698 | 0.107518 | ||||||||
\(913\) | −20.3147 | −0.672318 | ||||||||
\(914\) | −33.8538 | −1.11979 | ||||||||
\(915\) | 3.10992 | 0.102811 | ||||||||
\(916\) | 16.6679 | 0.550722 | ||||||||
\(917\) | −69.7706 | −2.30403 | ||||||||
\(918\) | 87.9251 | 2.90196 | ||||||||
\(919\) | −53.5297 | −1.76578 | −0.882891 | − | 0.469577i | \(-0.844406\pi\) | ||||
−0.882891 | + | 0.469577i | \(0.844406\pi\) | |||||||
\(920\) | 6.67994 | 0.220231 | ||||||||
\(921\) | 32.7525 | 1.07923 | ||||||||
\(922\) | 16.9989 | 0.559830 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 60.6848 | 1.99638 | ||||||||
\(925\) | −17.3357 | −0.569995 | ||||||||
\(926\) | −33.5254 | −1.10171 | ||||||||
\(927\) | 2.98792 | 0.0981361 | ||||||||
\(928\) | −2.91185 | −0.0955863 | ||||||||
\(929\) | −12.5133 | −0.410549 | −0.205275 | − | 0.978704i | \(-0.565809\pi\) | ||||
−0.205275 | + | 0.978704i | \(0.565809\pi\) | |||||||
\(930\) | −30.5405 | −1.00146 | ||||||||
\(931\) | 5.98792 | 0.196246 | ||||||||
\(932\) | −10.5187 | −0.344552 | ||||||||
\(933\) | −19.9898 | −0.654438 | ||||||||
\(934\) | 24.8659 | 0.813638 | ||||||||
\(935\) | 48.0676 | 1.57198 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.3096 | 1.44753 | 0.723766 | − | 0.690045i | \(-0.242409\pi\) | ||||
0.723766 | + | 0.690045i | \(0.242409\pi\) | |||||||
\(938\) | −3.56033 | −0.116249 | ||||||||
\(939\) | 46.7894 | 1.52691 | ||||||||
\(940\) | 17.1535 | 0.559484 | ||||||||
\(941\) | −43.4094 | −1.41511 | −0.707553 | − | 0.706660i | \(-0.750201\pi\) | ||||
−0.707553 | + | 0.706660i | \(0.750201\pi\) | |||||||
\(942\) | 7.84309 | 0.255542 | ||||||||
\(943\) | 42.2664 | 1.37638 | ||||||||
\(944\) | −13.5254 | −0.440215 | ||||||||
\(945\) | −82.6607 | −2.68895 | ||||||||
\(946\) | −26.7815 | −0.870742 | ||||||||
\(947\) | −18.3338 | −0.595768 | −0.297884 | − | 0.954602i | \(-0.596281\pi\) | ||||
−0.297884 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(948\) | 34.9638 | 1.13557 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.58211 | 0.0837746 | ||||||||
\(951\) | 66.6413 | 2.16099 | ||||||||
\(952\) | 21.4819 | 0.696232 | ||||||||
\(953\) | −1.43237 | −0.0463990 | −0.0231995 | − | 0.999731i | \(-0.507385\pi\) | ||||
−0.0231995 | + | 0.999731i | \(0.507385\pi\) | |||||||
\(954\) | −28.8823 | −0.935099 | ||||||||
\(955\) | −14.3260 | −0.463579 | ||||||||
\(956\) | −0.548253 | −0.0177318 | ||||||||
\(957\) | 49.0320 | 1.58498 | ||||||||
\(958\) | −43.5120 | −1.40581 | ||||||||
\(959\) | 23.8431 | 0.769933 | ||||||||
\(960\) | −5.04892 | −0.162953 | ||||||||
\(961\) | 5.58940 | 0.180303 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.68532 | −0.118758 | ||||||||
\(964\) | −17.5743 | −0.566031 | ||||||||
\(965\) | 22.2024 | 0.714720 | ||||||||
\(966\) | −50.2693 | −1.61739 | ||||||||
\(967\) | 43.6233 | 1.40283 | 0.701415 | − | 0.712753i | \(-0.252552\pi\) | ||||
0.701415 | + | 0.712753i | \(0.252552\pi\) | |||||||
\(968\) | −15.8944 | −0.510865 | ||||||||
\(969\) | −19.3545 | −0.621756 | ||||||||
\(970\) | 24.8756 | 0.798708 | ||||||||
\(971\) | 33.2325 | 1.06648 | 0.533241 | − | 0.845963i | \(-0.320974\pi\) | ||||
0.533241 | + | 0.845963i | \(0.320974\pi\) | |||||||
\(972\) | 37.7875 | 1.21203 | ||||||||
\(973\) | 3.36467 | 0.107866 | ||||||||
\(974\) | −9.41657 | −0.301726 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.615957 | −0.0197163 | ||||||||
\(977\) | 39.5579 | 1.26557 | 0.632785 | − | 0.774327i | \(-0.281912\pi\) | ||||
0.632785 | + | 0.774327i | \(0.281912\pi\) | |||||||
\(978\) | −15.0368 | −0.480825 | ||||||||
\(979\) | −4.09618 | −0.130914 | ||||||||
\(980\) | −9.31096 | −0.297428 | ||||||||
\(981\) | −20.4698 | −0.653550 | ||||||||
\(982\) | −1.67755 | −0.0535327 | ||||||||
\(983\) | 6.38703 | 0.203715 | 0.101857 | − | 0.994799i | \(-0.467522\pi\) | ||||
0.101857 | + | 0.994799i | \(0.467522\pi\) | |||||||
\(984\) | −31.9463 | −1.01841 | ||||||||
\(985\) | 18.3177 | 0.583649 | ||||||||
\(986\) | 17.3569 | 0.552756 | ||||||||
\(987\) | −129.087 | −4.10888 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.1849 | 0.705439 | ||||||||
\(990\) | 60.8256 | 1.93317 | ||||||||
\(991\) | 1.76079 | 0.0559333 | 0.0279667 | − | 0.999609i | \(-0.491097\pi\) | ||||
0.0279667 | + | 0.999609i | \(0.491097\pi\) | |||||||
\(992\) | 6.04892 | 0.192053 | ||||||||
\(993\) | 72.7827 | 2.30969 | ||||||||
\(994\) | −17.0073 | −0.539439 | ||||||||
\(995\) | −9.14377 | −0.289877 | ||||||||
\(996\) | −12.7192 | −0.403022 | ||||||||
\(997\) | −39.5362 | −1.25212 | −0.626062 | − | 0.779774i | \(-0.715334\pi\) | ||||
−0.626062 | + | 0.779774i | \(0.715334\pi\) | |||||||
\(998\) | 39.4077 | 1.24743 | ||||||||
\(999\) | 99.0326 | 3.13325 |
(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 | 6422.2.a.q.1.3 | 3 | ||
13.12 | even | 2 | 494.2.a.g.1.3 | ✓ | 3 | ||
39.38 | odd | 2 | 4446.2.a.bd.1.2 | 3 | |||
52.51 | odd | 2 | 3952.2.a.m.1.1 | 3 | |||
247.246 | odd | 2 | 9386.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.a.g.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
3952.2.a.m.1.1 | 3 | 52.51 | odd | 2 | |||
4446.2.a.bd.1.2 | 3 | 39.38 | odd | 2 | |||
6422.2.a.q.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9386.2.a.u.1.1 | 3 | 247.246 | odd | 2 |