Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [925,2,Mod(1,925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(925, 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("925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 925 = 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 925.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: | \(7.38616218697\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 6x^{7} + 30x^{6} + 15x^{5} - 70x^{4} - 22x^{3} + 44x^{2} + 4x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 185) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.58855\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 925.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58855 | −1.83038 | −0.915190 | − | 0.403023i | \(-0.867960\pi\) | ||||
−0.915190 | + | 0.403023i | \(0.867960\pi\) | |||||||
\(3\) | 1.45668 | 0.841012 | 0.420506 | − | 0.907290i | \(-0.361853\pi\) | ||||
0.420506 | + | 0.907290i | \(0.361853\pi\) | |||||||
\(4\) | 4.70058 | 2.35029 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.77067 | −1.53937 | ||||||||
\(7\) | 0.648627 | 0.245158 | 0.122579 | − | 0.992459i | \(-0.460883\pi\) | ||||
0.122579 | + | 0.992459i | \(0.460883\pi\) | |||||||
\(8\) | −6.99059 | −2.47155 | ||||||||
\(9\) | −0.878097 | −0.292699 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00426 | 0.604307 | 0.302154 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302154 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(12\) | 6.84722 | 1.97662 | ||||||||
\(13\) | −4.52102 | −1.25390 | −0.626952 | − | 0.779058i | \(-0.715698\pi\) | ||||
−0.626952 | + | 0.779058i | \(0.715698\pi\) | |||||||
\(14\) | −1.67900 | −0.448733 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.69431 | 2.17358 | ||||||||
\(17\) | −5.56202 | −1.34899 | −0.674494 | − | 0.738280i | \(-0.735638\pi\) | ||||
−0.674494 | + | 0.738280i | \(0.735638\pi\) | |||||||
\(18\) | 2.27300 | 0.535750 | ||||||||
\(19\) | 1.84662 | 0.423644 | 0.211822 | − | 0.977308i | \(-0.432060\pi\) | ||||
0.211822 | + | 0.977308i | \(0.432060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.944840 | 0.206181 | ||||||||
\(22\) | −5.18813 | −1.10611 | ||||||||
\(23\) | −6.29488 | −1.31257 | −0.656287 | − | 0.754511i | \(-0.727874\pi\) | ||||
−0.656287 | + | 0.754511i | \(0.727874\pi\) | |||||||
\(24\) | −10.1830 | −2.07860 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.7029 | 2.29512 | ||||||||
\(27\) | −5.64913 | −1.08718 | ||||||||
\(28\) | 3.04893 | 0.576193 | ||||||||
\(29\) | −7.93267 | −1.47306 | −0.736530 | − | 0.676405i | \(-0.763537\pi\) | ||||
−0.736530 | + | 0.676405i | \(0.763537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.87798 | −0.516900 | −0.258450 | − | 0.966025i | \(-0.583212\pi\) | ||||
−0.258450 | + | 0.966025i | \(0.583212\pi\) | |||||||
\(32\) | −8.52446 | −1.50693 | ||||||||
\(33\) | 2.91956 | 0.508230 | ||||||||
\(34\) | 14.3976 | 2.46916 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.12757 | −0.687928 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −4.78007 | −0.775430 | ||||||||
\(39\) | −6.58565 | −1.05455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.59442 | −1.49840 | −0.749199 | − | 0.662345i | \(-0.769561\pi\) | ||||
−0.749199 | + | 0.662345i | \(0.769561\pi\) | |||||||
\(42\) | −2.44576 | −0.377389 | ||||||||
\(43\) | 6.67357 | 1.01771 | 0.508855 | − | 0.860852i | \(-0.330069\pi\) | ||||
0.508855 | + | 0.860852i | \(0.330069\pi\) | |||||||
\(44\) | 9.42119 | 1.42030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.2946 | 2.40251 | ||||||||
\(47\) | 4.62245 | 0.674253 | 0.337127 | − | 0.941459i | \(-0.390545\pi\) | ||||
0.337127 | + | 0.941459i | \(0.390545\pi\) | |||||||
\(48\) | 12.6648 | 1.82800 | ||||||||
\(49\) | −6.57928 | −0.939897 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.10206 | −1.13451 | ||||||||
\(52\) | −21.2514 | −2.94704 | ||||||||
\(53\) | 6.63289 | 0.911097 | 0.455549 | − | 0.890211i | \(-0.349443\pi\) | ||||
0.455549 | + | 0.890211i | \(0.349443\pi\) | |||||||
\(54\) | 14.6230 | 1.98994 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.53429 | −0.605920 | ||||||||
\(57\) | 2.68993 | 0.356290 | ||||||||
\(58\) | 20.5341 | 2.69626 | ||||||||
\(59\) | 3.55444 | 0.462749 | 0.231374 | − | 0.972865i | \(-0.425678\pi\) | ||||
0.231374 | + | 0.972865i | \(0.425678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.98508 | 1.15042 | 0.575211 | − | 0.818005i | \(-0.304920\pi\) | ||||
0.575211 | + | 0.818005i | \(0.304920\pi\) | |||||||
\(62\) | 7.44979 | 0.946124 | ||||||||
\(63\) | −0.569558 | −0.0717575 | ||||||||
\(64\) | 4.67736 | 0.584670 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.55741 | −0.930253 | ||||||||
\(67\) | 11.7962 | 1.44113 | 0.720567 | − | 0.693385i | \(-0.243882\pi\) | ||||
0.720567 | + | 0.693385i | \(0.243882\pi\) | |||||||
\(68\) | −26.1447 | −3.17051 | ||||||||
\(69\) | −9.16960 | −1.10389 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.92865 | 0.940957 | 0.470479 | − | 0.882411i | \(-0.344081\pi\) | ||||
0.470479 | + | 0.882411i | \(0.344081\pi\) | |||||||
\(72\) | 6.13841 | 0.723419 | ||||||||
\(73\) | −8.94146 | −1.04652 | −0.523259 | − | 0.852174i | \(-0.675284\pi\) | ||||
−0.523259 | + | 0.852174i | \(0.675284\pi\) | |||||||
\(74\) | −2.58855 | −0.300913 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.68020 | 0.995687 | ||||||||
\(77\) | 1.30002 | 0.148151 | ||||||||
\(78\) | 17.0473 | 1.93022 | ||||||||
\(79\) | 5.85260 | 0.658469 | 0.329235 | − | 0.944248i | \(-0.393209\pi\) | ||||
0.329235 | + | 0.944248i | \(0.393209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.59466 | −0.621629 | ||||||||
\(82\) | 24.8356 | 2.74264 | ||||||||
\(83\) | −17.0540 | −1.87192 | −0.935961 | − | 0.352103i | \(-0.885467\pi\) | ||||
−0.935961 | + | 0.352103i | \(0.885467\pi\) | |||||||
\(84\) | 4.44130 | 0.484585 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.2748 | −1.86279 | ||||||||
\(87\) | −11.5553 | −1.23886 | ||||||||
\(88\) | −14.0110 | −1.49357 | ||||||||
\(89\) | −15.5198 | −1.64509 | −0.822546 | − | 0.568699i | \(-0.807447\pi\) | ||||
−0.822546 | + | 0.568699i | \(0.807447\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.93245 | −0.307405 | ||||||||
\(92\) | −29.5896 | −3.08493 | ||||||||
\(93\) | −4.19228 | −0.434719 | ||||||||
\(94\) | −11.9654 | −1.23414 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.4174 | −1.26734 | ||||||||
\(97\) | −7.82669 | −0.794680 | −0.397340 | − | 0.917672i | \(-0.630067\pi\) | ||||
−0.397340 | + | 0.917672i | \(0.630067\pi\) | |||||||
\(98\) | 17.0308 | 1.72037 | ||||||||
\(99\) | −1.75993 | −0.176880 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.64993 | −0.860701 | −0.430350 | − | 0.902662i | \(-0.641610\pi\) | ||||
−0.430350 | + | 0.902662i | \(0.641610\pi\) | |||||||
\(102\) | 20.9726 | 2.07659 | ||||||||
\(103\) | 4.85153 | 0.478036 | 0.239018 | − | 0.971015i | \(-0.423175\pi\) | ||||
0.239018 | + | 0.971015i | \(0.423175\pi\) | |||||||
\(104\) | 31.6046 | 3.09908 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.1696 | −1.66765 | ||||||||
\(107\) | 10.4460 | 1.00985 | 0.504925 | − | 0.863163i | \(-0.331520\pi\) | ||||
0.504925 | + | 0.863163i | \(0.331520\pi\) | |||||||
\(108\) | −26.5542 | −2.55518 | ||||||||
\(109\) | −6.96214 | −0.666852 | −0.333426 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333426 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45668 | 0.138262 | ||||||||
\(112\) | 5.63937 | 0.532870 | ||||||||
\(113\) | 3.68347 | 0.346512 | 0.173256 | − | 0.984877i | \(-0.444571\pi\) | ||||
0.173256 | + | 0.984877i | \(0.444571\pi\) | |||||||
\(114\) | −6.96301 | −0.652146 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −37.2882 | −3.46212 | ||||||||
\(117\) | 3.96989 | 0.367016 | ||||||||
\(118\) | −9.20084 | −0.847006 | ||||||||
\(119\) | −3.60768 | −0.330715 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.98294 | −0.634813 | ||||||||
\(122\) | −23.2583 | −2.10571 | ||||||||
\(123\) | −13.9760 | −1.26017 | ||||||||
\(124\) | −13.5282 | −1.21487 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.47433 | 0.131344 | ||||||||
\(127\) | 0.651297 | 0.0577933 | 0.0288966 | − | 0.999582i | \(-0.490801\pi\) | ||||
0.0288966 | + | 0.999582i | \(0.490801\pi\) | |||||||
\(128\) | 4.94134 | 0.436757 | ||||||||
\(129\) | 9.72122 | 0.855906 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.04184 | −0.178396 | −0.0891982 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891982 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(132\) | 13.7236 | 1.19449 | ||||||||
\(133\) | 1.19777 | 0.103860 | ||||||||
\(134\) | −30.5350 | −2.63782 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.8818 | 3.33408 | ||||||||
\(137\) | −10.4388 | −0.891845 | −0.445923 | − | 0.895071i | \(-0.647124\pi\) | ||||
−0.445923 | + | 0.895071i | \(0.647124\pi\) | |||||||
\(138\) | 23.7360 | 2.02054 | ||||||||
\(139\) | 13.4010 | 1.13666 | 0.568329 | − | 0.822802i | \(-0.307590\pi\) | ||||
0.568329 | + | 0.822802i | \(0.307590\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.73341 | 0.567055 | ||||||||
\(142\) | −20.5237 | −1.72231 | ||||||||
\(143\) | −9.06129 | −0.757743 | ||||||||
\(144\) | −7.63444 | −0.636204 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.1454 | 1.91553 | ||||||||
\(147\) | −9.58388 | −0.790465 | ||||||||
\(148\) | 4.70058 | 0.386385 | ||||||||
\(149\) | −7.69388 | −0.630307 | −0.315154 | − | 0.949041i | \(-0.602056\pi\) | ||||
−0.315154 | + | 0.949041i | \(0.602056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8303 | −1.20687 | −0.603437 | − | 0.797410i | \(-0.706203\pi\) | ||||
−0.603437 | + | 0.797410i | \(0.706203\pi\) | |||||||
\(152\) | −12.9090 | −1.04706 | ||||||||
\(153\) | 4.88399 | 0.394847 | ||||||||
\(154\) | −3.36516 | −0.271172 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −30.9564 | −2.47850 | ||||||||
\(157\) | 6.58086 | 0.525210 | 0.262605 | − | 0.964903i | \(-0.415418\pi\) | ||||
0.262605 | + | 0.964903i | \(0.415418\pi\) | |||||||
\(158\) | −15.1497 | −1.20525 | ||||||||
\(159\) | 9.66197 | 0.766244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08303 | −0.321788 | ||||||||
\(162\) | 14.4820 | 1.13782 | ||||||||
\(163\) | −9.03162 | −0.707411 | −0.353705 | − | 0.935357i | \(-0.615078\pi\) | ||||
−0.353705 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(164\) | −45.0994 | −3.52167 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 44.1452 | 3.42633 | ||||||||
\(167\) | −13.6411 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(168\) | −6.60498 | −0.509586 | ||||||||
\(169\) | 7.43958 | 0.572275 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.62151 | −0.124000 | ||||||||
\(172\) | 31.3696 | 2.39191 | ||||||||
\(173\) | 2.31736 | 0.176186 | 0.0880928 | − | 0.996112i | \(-0.471923\pi\) | ||||
0.0880928 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(174\) | 29.9115 | 2.26759 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.4257 | 1.31351 | ||||||||
\(177\) | 5.17766 | 0.389177 | ||||||||
\(178\) | 40.1737 | 3.01114 | ||||||||
\(179\) | 15.2482 | 1.13970 | 0.569852 | − | 0.821747i | \(-0.307000\pi\) | ||||
0.569852 | + | 0.821747i | \(0.307000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.21203 | −0.0900896 | −0.0450448 | − | 0.998985i | \(-0.514343\pi\) | ||||
−0.0450448 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(182\) | 7.59080 | 0.562668 | ||||||||
\(183\) | 13.0883 | 0.967518 | ||||||||
\(184\) | 44.0049 | 3.24409 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.8519 | 0.795702 | ||||||||
\(187\) | −11.1477 | −0.815203 | ||||||||
\(188\) | 21.7282 | 1.58469 | ||||||||
\(189\) | −3.66418 | −0.266530 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5011 | 1.48341 | 0.741705 | − | 0.670726i | \(-0.234017\pi\) | ||||
0.741705 | + | 0.670726i | \(0.234017\pi\) | |||||||
\(192\) | 6.81340 | 0.491715 | ||||||||
\(193\) | 1.57831 | 0.113609 | 0.0568045 | − | 0.998385i | \(-0.481909\pi\) | ||||
0.0568045 | + | 0.998385i | \(0.481909\pi\) | |||||||
\(194\) | 20.2598 | 1.45457 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.9265 | −2.20903 | ||||||||
\(197\) | 15.9367 | 1.13544 | 0.567722 | − | 0.823221i | \(-0.307825\pi\) | ||||
0.567722 | + | 0.823221i | \(0.307825\pi\) | |||||||
\(198\) | 4.55567 | 0.323758 | ||||||||
\(199\) | 4.38722 | 0.311002 | 0.155501 | − | 0.987836i | \(-0.450301\pi\) | ||||
0.155501 | + | 0.987836i | \(0.450301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.1832 | 1.21201 | ||||||||
\(202\) | 22.3908 | 1.57541 | ||||||||
\(203\) | −5.14535 | −0.361132 | ||||||||
\(204\) | −38.0844 | −2.66644 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.5584 | −0.874987 | ||||||||
\(207\) | 5.52752 | 0.384189 | ||||||||
\(208\) | −39.3071 | −2.72546 | ||||||||
\(209\) | 3.70111 | 0.256011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.5270 | −1.13777 | −0.568883 | − | 0.822418i | \(-0.692624\pi\) | ||||
−0.568883 | + | 0.822418i | \(0.692624\pi\) | |||||||
\(212\) | 31.1784 | 2.14134 | ||||||||
\(213\) | 11.5495 | 0.791356 | ||||||||
\(214\) | −27.0399 | −1.84841 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 39.4907 | 2.68700 | ||||||||
\(217\) | −1.86674 | −0.126722 | ||||||||
\(218\) | 18.0218 | 1.22059 | ||||||||
\(219\) | −13.0248 | −0.880135 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.1460 | 1.69150 | ||||||||
\(222\) | −3.77067 | −0.253071 | ||||||||
\(223\) | 22.6093 | 1.51403 | 0.757014 | − | 0.653399i | \(-0.226657\pi\) | ||||
0.757014 | + | 0.653399i | \(0.226657\pi\) | |||||||
\(224\) | −5.52920 | −0.369435 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.53484 | −0.634248 | ||||||||
\(227\) | −2.56112 | −0.169987 | −0.0849937 | − | 0.996381i | \(-0.527087\pi\) | ||||
−0.0849937 | + | 0.996381i | \(0.527087\pi\) | |||||||
\(228\) | 12.6442 | 0.837385 | ||||||||
\(229\) | 1.73702 | 0.114786 | 0.0573929 | − | 0.998352i | \(-0.481721\pi\) | ||||
0.0573929 | + | 0.998352i | \(0.481721\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.89370 | 0.124597 | ||||||||
\(232\) | 55.4540 | 3.64073 | ||||||||
\(233\) | −9.32879 | −0.611149 | −0.305575 | − | 0.952168i | \(-0.598849\pi\) | ||||
−0.305575 | + | 0.952168i | \(0.598849\pi\) | |||||||
\(234\) | −10.2762 | −0.671779 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.7079 | 1.08759 | ||||||||
\(237\) | 8.52534 | 0.553780 | ||||||||
\(238\) | 9.33865 | 0.605335 | ||||||||
\(239\) | 0.602230 | 0.0389550 | 0.0194775 | − | 0.999810i | \(-0.493800\pi\) | ||||
0.0194775 | + | 0.999810i | \(0.493800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5974 | −0.940304 | −0.470152 | − | 0.882585i | \(-0.655801\pi\) | ||||
−0.470152 | + | 0.882585i | \(0.655801\pi\) | |||||||
\(242\) | 18.0757 | 1.16195 | ||||||||
\(243\) | 8.79779 | 0.564378 | ||||||||
\(244\) | 42.2351 | 2.70382 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 36.1775 | 2.30659 | ||||||||
\(247\) | −8.34861 | −0.531209 | ||||||||
\(248\) | 20.1188 | 1.27754 | ||||||||
\(249\) | −24.8422 | −1.57431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9341 | −1.13199 | −0.565996 | − | 0.824408i | \(-0.691508\pi\) | ||||
−0.565996 | + | 0.824408i | \(0.691508\pi\) | |||||||
\(252\) | −2.67725 | −0.168651 | ||||||||
\(253\) | −12.6166 | −0.793198 | ||||||||
\(254\) | −1.68591 | −0.105784 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.1456 | −1.38410 | ||||||||
\(257\) | −1.13398 | −0.0707356 | −0.0353678 | − | 0.999374i | \(-0.511260\pi\) | ||||
−0.0353678 | + | 0.999374i | \(0.511260\pi\) | |||||||
\(258\) | −25.1638 | −1.56663 | ||||||||
\(259\) | 0.648627 | 0.0403037 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.96565 | 0.431163 | ||||||||
\(262\) | 5.28540 | 0.326533 | ||||||||
\(263\) | 0.576045 | 0.0355204 | 0.0177602 | − | 0.999842i | \(-0.494346\pi\) | ||||
0.0177602 | + | 0.999842i | \(0.494346\pi\) | |||||||
\(264\) | −20.4094 | −1.25611 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.10048 | −0.190103 | ||||||||
\(267\) | −22.6073 | −1.38354 | ||||||||
\(268\) | 55.4490 | 3.38708 | ||||||||
\(269\) | 14.8308 | 0.904249 | 0.452124 | − | 0.891955i | \(-0.350666\pi\) | ||||
0.452124 | + | 0.891955i | \(0.350666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5579 | −1.43104 | −0.715520 | − | 0.698592i | \(-0.753810\pi\) | ||||
−0.715520 | + | 0.698592i | \(0.753810\pi\) | |||||||
\(272\) | −48.3579 | −2.93213 | ||||||||
\(273\) | −4.27163 | −0.258531 | ||||||||
\(274\) | 27.0213 | 1.63242 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −43.1025 | −2.59446 | ||||||||
\(277\) | −1.55020 | −0.0931422 | −0.0465711 | − | 0.998915i | \(-0.514829\pi\) | ||||
−0.0465711 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(278\) | −34.6891 | −2.08051 | ||||||||
\(279\) | 2.52714 | 0.151296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.3095 | 1.86777 | 0.933884 | − | 0.357575i | \(-0.116396\pi\) | ||||
0.933884 | + | 0.357575i | \(0.116396\pi\) | |||||||
\(282\) | −17.4297 | −1.03793 | ||||||||
\(283\) | −27.6189 | −1.64177 | −0.820886 | − | 0.571091i | \(-0.806520\pi\) | ||||
−0.820886 | + | 0.571091i | \(0.806520\pi\) | |||||||
\(284\) | 37.2693 | 2.21152 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.4556 | 1.38696 | ||||||||
\(287\) | −6.22321 | −0.367344 | ||||||||
\(288\) | 7.48530 | 0.441076 | ||||||||
\(289\) | 13.9361 | 0.819768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4009 | −0.668335 | ||||||||
\(292\) | −42.0301 | −2.45962 | ||||||||
\(293\) | −9.90491 | −0.578651 | −0.289326 | − | 0.957231i | \(-0.593431\pi\) | ||||
−0.289326 | + | 0.957231i | \(0.593431\pi\) | |||||||
\(294\) | 24.8083 | 1.44685 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.99059 | −0.406320 | ||||||||
\(297\) | −11.3223 | −0.656988 | ||||||||
\(298\) | 19.9160 | 1.15370 | ||||||||
\(299\) | 28.4593 | 1.64584 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.32866 | 0.249500 | ||||||||
\(302\) | 38.3890 | 2.20904 | ||||||||
\(303\) | −12.6001 | −0.723859 | ||||||||
\(304\) | 16.0551 | 0.920823 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.6424 | −0.722720 | ||||||||
\(307\) | 7.83799 | 0.447338 | 0.223669 | − | 0.974665i | \(-0.428197\pi\) | ||||
0.223669 | + | 0.974665i | \(0.428197\pi\) | |||||||
\(308\) | 6.11084 | 0.348198 | ||||||||
\(309\) | 7.06711 | 0.402034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.4352 | 1.38560 | 0.692798 | − | 0.721132i | \(-0.256378\pi\) | ||||
0.692798 | + | 0.721132i | \(0.256378\pi\) | |||||||
\(312\) | 46.0376 | 2.60636 | ||||||||
\(313\) | −18.0084 | −1.01789 | −0.508947 | − | 0.860798i | \(-0.669965\pi\) | ||||
−0.508947 | + | 0.860798i | \(0.669965\pi\) | |||||||
\(314\) | −17.0349 | −0.961334 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.5106 | 1.54759 | ||||||||
\(317\) | 14.3769 | 0.807486 | 0.403743 | − | 0.914872i | \(-0.367709\pi\) | ||||
0.403743 | + | 0.914872i | \(0.367709\pi\) | |||||||
\(318\) | −25.0105 | −1.40252 | ||||||||
\(319\) | −15.8991 | −0.890180 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2164 | 0.849296 | ||||||||
\(322\) | 10.5691 | 0.588995 | ||||||||
\(323\) | −10.2709 | −0.571491 | ||||||||
\(324\) | −26.2981 | −1.46101 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.3788 | 1.29483 | ||||||||
\(327\) | −10.1416 | −0.560831 | ||||||||
\(328\) | 67.0707 | 3.70336 | ||||||||
\(329\) | 2.99825 | 0.165299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5918 | 1.35169 | 0.675845 | − | 0.737044i | \(-0.263779\pi\) | ||||
0.675845 | + | 0.737044i | \(0.263779\pi\) | |||||||
\(332\) | −80.1639 | −4.39956 | ||||||||
\(333\) | −0.878097 | −0.0481194 | ||||||||
\(334\) | 35.3107 | 1.93212 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.21473 | 0.448150 | ||||||||
\(337\) | 23.0495 | 1.25559 | 0.627793 | − | 0.778381i | \(-0.283959\pi\) | ||||
0.627793 | + | 0.778381i | \(0.283959\pi\) | |||||||
\(338\) | −19.2577 | −1.04748 | ||||||||
\(339\) | 5.36562 | 0.291420 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.76822 | −0.312367 | ||||||||
\(342\) | 4.19736 | 0.226967 | ||||||||
\(343\) | −8.80790 | −0.475582 | ||||||||
\(344\) | −46.6521 | −2.51532 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.99860 | −0.322487 | ||||||||
\(347\) | 2.01655 | 0.108254 | 0.0541271 | − | 0.998534i | \(-0.482762\pi\) | ||||
0.0541271 | + | 0.998534i | \(0.482762\pi\) | |||||||
\(348\) | −54.3167 | −2.91168 | ||||||||
\(349\) | 5.86531 | 0.313963 | 0.156981 | − | 0.987602i | \(-0.449824\pi\) | ||||
0.156981 | + | 0.987602i | \(0.449824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.5398 | 1.36321 | ||||||||
\(352\) | −17.0852 | −0.910646 | ||||||||
\(353\) | 20.8137 | 1.10780 | 0.553900 | − | 0.832583i | \(-0.313139\pi\) | ||||
0.553900 | + | 0.832583i | \(0.313139\pi\) | |||||||
\(354\) | −13.4026 | −0.712342 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −72.9519 | −3.86644 | ||||||||
\(357\) | −5.25522 | −0.278136 | ||||||||
\(358\) | −39.4707 | −2.08609 | ||||||||
\(359\) | −32.6574 | −1.72359 | −0.861796 | − | 0.507256i | \(-0.830660\pi\) | ||||
−0.861796 | + | 0.507256i | \(0.830660\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5900 | −0.820526 | ||||||||
\(362\) | 3.13740 | 0.164898 | ||||||||
\(363\) | −10.1719 | −0.533885 | ||||||||
\(364\) | −13.7842 | −0.722491 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −33.8798 | −1.77093 | ||||||||
\(367\) | −19.8239 | −1.03480 | −0.517400 | − | 0.855743i | \(-0.673100\pi\) | ||||
−0.517400 | + | 0.855743i | \(0.673100\pi\) | |||||||
\(368\) | −54.7297 | −2.85298 | ||||||||
\(369\) | 8.42483 | 0.438579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.30227 | 0.223363 | ||||||||
\(372\) | −19.7062 | −1.02172 | ||||||||
\(373\) | −7.05575 | −0.365333 | −0.182666 | − | 0.983175i | \(-0.558473\pi\) | ||||
−0.182666 | + | 0.983175i | \(0.558473\pi\) | |||||||
\(374\) | 28.8565 | 1.49213 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.3136 | −1.66645 | ||||||||
\(377\) | 35.8637 | 1.84707 | ||||||||
\(378\) | 9.48491 | 0.487851 | ||||||||
\(379\) | 14.3983 | 0.739593 | 0.369797 | − | 0.929113i | \(-0.379427\pi\) | ||||
0.369797 | + | 0.929113i | \(0.379427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.948729 | 0.0486048 | ||||||||
\(382\) | −53.0682 | −2.71521 | ||||||||
\(383\) | −4.98755 | −0.254852 | −0.127426 | − | 0.991848i | \(-0.540671\pi\) | ||||
−0.127426 | + | 0.991848i | \(0.540671\pi\) | |||||||
\(384\) | 7.19793 | 0.367318 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.08552 | −0.207948 | ||||||||
\(387\) | −5.86004 | −0.297882 | ||||||||
\(388\) | −36.7900 | −1.86773 | ||||||||
\(389\) | 22.0079 | 1.11585 | 0.557923 | − | 0.829893i | \(-0.311598\pi\) | ||||
0.557923 | + | 0.829893i | \(0.311598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.0123 | 1.77065 | ||||||||
\(392\) | 45.9930 | 2.32300 | ||||||||
\(393\) | −2.97430 | −0.150034 | ||||||||
\(394\) | −41.2529 | −2.07829 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.27272 | −0.415720 | ||||||||
\(397\) | −8.24549 | −0.413829 | −0.206915 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206915 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(398\) | −11.3565 | −0.569251 | ||||||||
\(399\) | 1.74476 | 0.0873473 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1806 | −0.708144 | −0.354072 | − | 0.935218i | \(-0.615203\pi\) | ||||
−0.354072 | + | 0.935218i | \(0.615203\pi\) | |||||||
\(402\) | −44.4796 | −2.21844 | ||||||||
\(403\) | 13.0114 | 0.648143 | ||||||||
\(404\) | −40.6597 | −2.02290 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.3190 | 0.661010 | ||||||||
\(407\) | 2.00426 | 0.0993475 | ||||||||
\(408\) | 56.6381 | 2.80401 | ||||||||
\(409\) | −5.60504 | −0.277152 | −0.138576 | − | 0.990352i | \(-0.544252\pi\) | ||||
−0.138576 | + | 0.990352i | \(0.544252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.2059 | −0.750053 | ||||||||
\(412\) | 22.8050 | 1.12352 | ||||||||
\(413\) | 2.30551 | 0.113447 | ||||||||
\(414\) | −14.3082 | −0.703212 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 38.5392 | 1.88954 | ||||||||
\(417\) | 19.5209 | 0.955942 | ||||||||
\(418\) | −9.58051 | −0.468598 | ||||||||
\(419\) | −15.2102 | −0.743067 | −0.371533 | − | 0.928420i | \(-0.621168\pi\) | ||||
−0.371533 | + | 0.928420i | \(0.621168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3853 | −1.23720 | −0.618602 | − | 0.785705i | \(-0.712301\pi\) | ||||
−0.618602 | + | 0.785705i | \(0.712301\pi\) | |||||||
\(422\) | 42.7810 | 2.08255 | ||||||||
\(423\) | −4.05896 | −0.197353 | ||||||||
\(424\) | −46.3678 | −2.25182 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −29.8963 | −1.44848 | ||||||||
\(427\) | 5.82797 | 0.282035 | ||||||||
\(428\) | 49.1021 | 2.37344 | ||||||||
\(429\) | −13.1994 | −0.637271 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.47455 | 0.360036 | 0.180018 | − | 0.983663i | \(-0.442384\pi\) | ||||
0.180018 | + | 0.983663i | \(0.442384\pi\) | |||||||
\(432\) | −49.1153 | −2.36306 | ||||||||
\(433\) | 27.2983 | 1.31187 | 0.655937 | − | 0.754816i | \(-0.272274\pi\) | ||||
0.655937 | + | 0.754816i | \(0.272274\pi\) | |||||||
\(434\) | 4.83214 | 0.231950 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.7261 | −1.56730 | ||||||||
\(437\) | −11.6243 | −0.556064 | ||||||||
\(438\) | 33.7153 | 1.61098 | ||||||||
\(439\) | 6.63267 | 0.316560 | 0.158280 | − | 0.987394i | \(-0.449405\pi\) | ||||
0.158280 | + | 0.987394i | \(0.449405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.77725 | 0.275107 | ||||||||
\(442\) | −65.0916 | −3.09609 | ||||||||
\(443\) | 14.3893 | 0.683655 | 0.341828 | − | 0.939763i | \(-0.388954\pi\) | ||||
0.341828 | + | 0.939763i | \(0.388954\pi\) | |||||||
\(444\) | 6.84722 | 0.324955 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −58.5252 | −2.77125 | ||||||||
\(447\) | −11.2075 | −0.530096 | ||||||||
\(448\) | 3.03387 | 0.143337 | ||||||||
\(449\) | −15.9023 | −0.750475 | −0.375238 | − | 0.926929i | \(-0.622439\pi\) | ||||
−0.375238 | + | 0.926929i | \(0.622439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.2297 | −0.905492 | ||||||||
\(452\) | 17.3144 | 0.814403 | ||||||||
\(453\) | −21.6030 | −1.01500 | ||||||||
\(454\) | 6.62957 | 0.311141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.8042 | −0.880587 | ||||||||
\(457\) | 2.27388 | 0.106368 | 0.0531839 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531839 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(458\) | −4.49637 | −0.210102 | ||||||||
\(459\) | 31.4206 | 1.46659 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.8481 | 1.25044 | 0.625220 | − | 0.780448i | \(-0.285009\pi\) | ||||
0.625220 | + | 0.780448i | \(0.285009\pi\) | |||||||
\(462\) | −4.90195 | −0.228059 | ||||||||
\(463\) | −5.51116 | −0.256125 | −0.128063 | − | 0.991766i | \(-0.540876\pi\) | ||||
−0.128063 | + | 0.991766i | \(0.540876\pi\) | |||||||
\(464\) | −68.9690 | −3.20181 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.1480 | 1.11864 | ||||||||
\(467\) | −18.8103 | −0.870436 | −0.435218 | − | 0.900325i | \(-0.643329\pi\) | ||||
−0.435218 | + | 0.900325i | \(0.643329\pi\) | |||||||
\(468\) | 18.6608 | 0.862595 | ||||||||
\(469\) | 7.65133 | 0.353306 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.58618 | 0.441708 | ||||||||
\(472\) | −24.8476 | −1.14370 | ||||||||
\(473\) | 13.3756 | 0.615009 | ||||||||
\(474\) | −22.0683 | −1.01363 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.9582 | −0.777277 | ||||||||
\(477\) | −5.82432 | −0.266677 | ||||||||
\(478\) | −1.55890 | −0.0713025 | ||||||||
\(479\) | 8.00482 | 0.365750 | 0.182875 | − | 0.983136i | \(-0.441460\pi\) | ||||
0.182875 | + | 0.983136i | \(0.441460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.52102 | −0.206141 | ||||||||
\(482\) | 37.7862 | 1.72111 | ||||||||
\(483\) | −5.94766 | −0.270628 | ||||||||
\(484\) | −32.8239 | −1.49199 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.7735 | −1.03303 | ||||||||
\(487\) | 7.39645 | 0.335165 | 0.167582 | − | 0.985858i | \(-0.446404\pi\) | ||||
0.167582 | + | 0.985858i | \(0.446404\pi\) | |||||||
\(488\) | −62.8110 | −2.84332 | ||||||||
\(489\) | −13.1561 | −0.594941 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.8861 | 1.84517 | 0.922583 | − | 0.385799i | \(-0.126074\pi\) | ||||
0.922583 | + | 0.385799i | \(0.126074\pi\) | |||||||
\(492\) | −65.6952 | −2.96177 | ||||||||
\(493\) | 44.1216 | 1.98714 | ||||||||
\(494\) | 21.6108 | 0.972315 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.0220 | −1.12352 | ||||||||
\(497\) | 5.14274 | 0.230683 | ||||||||
\(498\) | 64.3052 | 2.88158 | ||||||||
\(499\) | 4.30244 | 0.192604 | 0.0963019 | − | 0.995352i | \(-0.469299\pi\) | ||||
0.0963019 | + | 0.995352i | \(0.469299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.8707 | −0.887757 | ||||||||
\(502\) | 46.4234 | 2.07198 | ||||||||
\(503\) | 21.1220 | 0.941786 | 0.470893 | − | 0.882190i | \(-0.343932\pi\) | ||||
0.470893 | + | 0.882190i | \(0.343932\pi\) | |||||||
\(504\) | 3.98154 | 0.177352 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 32.6586 | 1.45185 | ||||||||
\(507\) | 10.8371 | 0.481290 | ||||||||
\(508\) | 3.06148 | 0.135831 | ||||||||
\(509\) | 12.1512 | 0.538594 | 0.269297 | − | 0.963057i | \(-0.413209\pi\) | ||||
0.269297 | + | 0.963057i | \(0.413209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.79968 | −0.256563 | ||||||||
\(512\) | 47.4423 | 2.09668 | ||||||||
\(513\) | −10.4318 | −0.460575 | ||||||||
\(514\) | 2.93536 | 0.129473 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 45.6954 | 2.01163 | ||||||||
\(517\) | 9.26459 | 0.407456 | ||||||||
\(518\) | −1.67900 | −0.0737712 | ||||||||
\(519\) | 3.37564 | 0.148174 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.8351 | −1.70140 | −0.850699 | − | 0.525653i | \(-0.823821\pi\) | ||||
−0.850699 | + | 0.525653i | \(0.823821\pi\) | |||||||
\(522\) | −18.0309 | −0.789192 | ||||||||
\(523\) | −8.84445 | −0.386741 | −0.193371 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193371 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(524\) | −9.59784 | −0.419283 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.49112 | −0.0650159 | ||||||||
\(527\) | 16.0074 | 0.697292 | ||||||||
\(528\) | 25.3835 | 1.10468 | ||||||||
\(529\) | 16.6256 | 0.722850 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.12114 | −0.135446 | ||||||||
\(532\) | 5.63022 | 0.244101 | ||||||||
\(533\) | 43.3765 | 1.87885 | ||||||||
\(534\) | 58.5200 | 2.53241 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −82.4623 | −3.56183 | ||||||||
\(537\) | 22.2117 | 0.958505 | ||||||||
\(538\) | −38.3902 | −1.65512 | ||||||||
\(539\) | −13.1866 | −0.567987 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2938 | −0.700527 | −0.350263 | − | 0.936651i | \(-0.613908\pi\) | ||||
−0.350263 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(542\) | 60.9808 | 2.61935 | ||||||||
\(543\) | −1.76554 | −0.0757664 | ||||||||
\(544\) | 47.4132 | 2.03282 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.0573 | 0.473210 | ||||||||
\(547\) | −12.1716 | −0.520419 | −0.260210 | − | 0.965552i | \(-0.583792\pi\) | ||||
−0.260210 | + | 0.965552i | \(0.583792\pi\) | |||||||
\(548\) | −49.0684 | −2.09610 | ||||||||
\(549\) | −7.88977 | −0.336727 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.6486 | −0.624053 | ||||||||
\(552\) | 64.1009 | 2.72832 | ||||||||
\(553\) | 3.79616 | 0.161429 | ||||||||
\(554\) | 4.01276 | 0.170486 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.9925 | 2.67148 | ||||||||
\(557\) | −17.7309 | −0.751282 | −0.375641 | − | 0.926765i | \(-0.622577\pi\) | ||||
−0.375641 | + | 0.926765i | \(0.622577\pi\) | |||||||
\(558\) | −6.54163 | −0.276929 | ||||||||
\(559\) | −30.1713 | −1.27611 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.2386 | −0.685596 | ||||||||
\(562\) | −81.0462 | −3.41873 | ||||||||
\(563\) | 31.2138 | 1.31550 | 0.657752 | − | 0.753234i | \(-0.271507\pi\) | ||||
0.657752 | + | 0.753234i | \(0.271507\pi\) | |||||||
\(564\) | 31.6509 | 1.33274 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 71.4928 | 3.00507 | ||||||||
\(567\) | −3.62885 | −0.152397 | ||||||||
\(568\) | −55.4259 | −2.32562 | ||||||||
\(569\) | 30.2875 | 1.26972 | 0.634860 | − | 0.772628i | \(-0.281058\pi\) | ||||
0.634860 | + | 0.772628i | \(0.281058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.958299 | 0.0401035 | 0.0200518 | − | 0.999799i | \(-0.493617\pi\) | ||||
0.0200518 | + | 0.999799i | \(0.493617\pi\) | |||||||
\(572\) | −42.5933 | −1.78092 | ||||||||
\(573\) | 29.8635 | 1.24757 | ||||||||
\(574\) | 16.1091 | 0.672380 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.10718 | −0.171132 | ||||||||
\(577\) | −24.2765 | −1.01064 | −0.505321 | − | 0.862931i | \(-0.668626\pi\) | ||||
−0.505321 | + | 0.862931i | \(0.668626\pi\) | |||||||
\(578\) | −36.0742 | −1.50049 | ||||||||
\(579\) | 2.29908 | 0.0955465 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0617 | −0.458917 | ||||||||
\(582\) | 29.5119 | 1.22331 | ||||||||
\(583\) | 13.2940 | 0.550583 | ||||||||
\(584\) | 62.5060 | 2.58652 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.6393 | 1.05915 | ||||||||
\(587\) | −17.3137 | −0.714611 | −0.357305 | − | 0.933988i | \(-0.616304\pi\) | ||||
−0.357305 | + | 0.933988i | \(0.616304\pi\) | |||||||
\(588\) | −45.0498 | −1.85782 | ||||||||
\(589\) | −5.31454 | −0.218982 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2146 | 0.954922 | ||||||||
\(592\) | 8.69431 | 0.357334 | ||||||||
\(593\) | 6.71905 | 0.275918 | 0.137959 | − | 0.990438i | \(-0.455946\pi\) | ||||
0.137959 | + | 0.990438i | \(0.455946\pi\) | |||||||
\(594\) | 29.3084 | 1.20254 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.1657 | −1.48141 | ||||||||
\(597\) | 6.39075 | 0.261556 | ||||||||
\(598\) | −73.6682 | −3.01252 | ||||||||
\(599\) | 29.5517 | 1.20745 | 0.603725 | − | 0.797193i | \(-0.293683\pi\) | ||||
0.603725 | + | 0.797193i | \(0.293683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.9680 | −0.977674 | −0.488837 | − | 0.872375i | \(-0.662579\pi\) | ||||
−0.488837 | + | 0.872375i | \(0.662579\pi\) | |||||||
\(602\) | −11.2049 | −0.456679 | ||||||||
\(603\) | −10.3582 | −0.421818 | ||||||||
\(604\) | −69.7112 | −2.83651 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 32.6161 | 1.32494 | ||||||||
\(607\) | 12.1272 | 0.492228 | 0.246114 | − | 0.969241i | \(-0.420846\pi\) | ||||
0.246114 | + | 0.969241i | \(0.420846\pi\) | |||||||
\(608\) | −15.7415 | −0.638400 | ||||||||
\(609\) | −7.49510 | −0.303717 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8982 | −0.845449 | ||||||||
\(612\) | 22.9576 | 0.928006 | ||||||||
\(613\) | −19.9682 | −0.806508 | −0.403254 | − | 0.915088i | \(-0.632121\pi\) | ||||
−0.403254 | + | 0.915088i | \(0.632121\pi\) | |||||||
\(614\) | −20.2890 | −0.818798 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.08789 | −0.366162 | ||||||||
\(617\) | −42.9149 | −1.72769 | −0.863844 | − | 0.503759i | \(-0.831950\pi\) | ||||
−0.863844 | + | 0.503759i | \(0.831950\pi\) | |||||||
\(618\) | −18.2936 | −0.735875 | ||||||||
\(619\) | 33.0261 | 1.32743 | 0.663715 | − | 0.747986i | \(-0.268979\pi\) | ||||
0.663715 | + | 0.747986i | \(0.268979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.5606 | 1.42700 | ||||||||
\(622\) | −63.2518 | −2.53617 | ||||||||
\(623\) | −10.0665 | −0.403308 | ||||||||
\(624\) | −57.2577 | −2.29214 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 46.6156 | 1.86313 | ||||||||
\(627\) | 5.39132 | 0.215309 | ||||||||
\(628\) | 30.9339 | 1.23440 | ||||||||
\(629\) | −5.56202 | −0.221772 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4741 | 0.775254 | 0.387627 | − | 0.921816i | \(-0.373295\pi\) | ||||
0.387627 | + | 0.921816i | \(0.373295\pi\) | |||||||
\(632\) | −40.9131 | −1.62744 | ||||||||
\(633\) | −24.0745 | −0.956875 | ||||||||
\(634\) | −37.2153 | −1.47801 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 45.4169 | 1.80090 | ||||||||
\(637\) | 29.7450 | 1.17854 | ||||||||
\(638\) | 41.1557 | 1.62937 | ||||||||
\(639\) | −6.96212 | −0.275417 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.19723 | −0.363269 | −0.181634 | − | 0.983366i | \(-0.558139\pi\) | ||||
−0.181634 | + | 0.983366i | \(0.558139\pi\) | |||||||
\(642\) | −39.3883 | −1.55453 | ||||||||
\(643\) | −11.4689 | −0.452287 | −0.226144 | − | 0.974094i | \(-0.572612\pi\) | ||||
−0.226144 | + | 0.974094i | \(0.572612\pi\) | |||||||
\(644\) | −19.1926 | −0.756296 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.5868 | 1.04605 | ||||||||
\(647\) | −28.9348 | −1.13754 | −0.568771 | − | 0.822496i | \(-0.692581\pi\) | ||||
−0.568771 | + | 0.822496i | \(0.692581\pi\) | |||||||
\(648\) | 39.1099 | 1.53638 | ||||||||
\(649\) | 7.12402 | 0.279642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.71923 | −0.106575 | ||||||||
\(652\) | −42.4539 | −1.66262 | ||||||||
\(653\) | −6.72542 | −0.263186 | −0.131593 | − | 0.991304i | \(-0.542009\pi\) | ||||
−0.131593 | + | 0.991304i | \(0.542009\pi\) | |||||||
\(654\) | 26.2520 | 1.02653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −83.4169 | −3.25688 | ||||||||
\(657\) | 7.85146 | 0.306315 | ||||||||
\(658\) | −7.76111 | −0.302559 | ||||||||
\(659\) | 8.46642 | 0.329805 | 0.164902 | − | 0.986310i | \(-0.447269\pi\) | ||||
0.164902 | + | 0.986310i | \(0.447269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.25862 | −0.321223 | −0.160611 | − | 0.987018i | \(-0.551347\pi\) | ||||
−0.160611 | + | 0.987018i | \(0.551347\pi\) | |||||||
\(662\) | −63.6572 | −2.47411 | ||||||||
\(663\) | 36.6295 | 1.42257 | ||||||||
\(664\) | 119.218 | 4.62654 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.27300 | 0.0880768 | ||||||||
\(667\) | 49.9352 | 1.93350 | ||||||||
\(668\) | −64.1212 | −2.48092 | ||||||||
\(669\) | 32.9343 | 1.27332 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0084 | 0.695208 | ||||||||
\(672\) | −8.05425 | −0.310699 | ||||||||
\(673\) | 35.7431 | 1.37779 | 0.688897 | − | 0.724859i | \(-0.258095\pi\) | ||||
0.688897 | + | 0.724859i | \(0.258095\pi\) | |||||||
\(674\) | −59.6647 | −2.29820 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.9703 | 1.34501 | ||||||||
\(677\) | 2.70690 | 0.104035 | 0.0520174 | − | 0.998646i | \(-0.483435\pi\) | ||||
0.0520174 | + | 0.998646i | \(0.483435\pi\) | |||||||
\(678\) | −13.8892 | −0.533410 | ||||||||
\(679\) | −5.07660 | −0.194822 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.73072 | −0.142961 | ||||||||
\(682\) | 14.9313 | 0.571750 | ||||||||
\(683\) | 0.816828 | 0.0312551 | 0.0156275 | − | 0.999878i | \(-0.495025\pi\) | ||||
0.0156275 | + | 0.999878i | \(0.495025\pi\) | |||||||
\(684\) | −7.62205 | −0.291436 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 22.7997 | 0.870495 | ||||||||
\(687\) | 2.53028 | 0.0965363 | ||||||||
\(688\) | 58.0220 | 2.21207 | ||||||||
\(689\) | −29.9874 | −1.14243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.6228 | 0.518237 | 0.259118 | − | 0.965846i | \(-0.416568\pi\) | ||||
0.259118 | + | 0.965846i | \(0.416568\pi\) | |||||||
\(692\) | 10.8929 | 0.414087 | ||||||||
\(693\) | −1.14154 | −0.0433636 | ||||||||
\(694\) | −5.21994 | −0.198146 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 80.7785 | 3.06190 | ||||||||
\(697\) | 53.3644 | 2.02132 | ||||||||
\(698\) | −15.1826 | −0.574671 | ||||||||
\(699\) | −13.5890 | −0.513984 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6077 | −0.476185 | −0.238092 | − | 0.971243i | \(-0.576522\pi\) | ||||
−0.238092 | + | 0.971243i | \(0.576522\pi\) | |||||||
\(702\) | −66.1110 | −2.49520 | ||||||||
\(703\) | 1.84662 | 0.0696467 | ||||||||
\(704\) | 9.37466 | 0.353321 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −53.8772 | −2.02770 | ||||||||
\(707\) | −5.61058 | −0.211008 | ||||||||
\(708\) | 24.3380 | 0.914679 | ||||||||
\(709\) | −23.1737 | −0.870305 | −0.435153 | − | 0.900357i | \(-0.643306\pi\) | ||||
−0.435153 | + | 0.900357i | \(0.643306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.13915 | −0.192733 | ||||||||
\(712\) | 108.492 | 4.06592 | ||||||||
\(713\) | 18.1165 | 0.678470 | ||||||||
\(714\) | 13.6034 | 0.509094 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 71.6755 | 2.67864 | ||||||||
\(717\) | 0.877254 | 0.0327616 | ||||||||
\(718\) | 84.5352 | 3.15483 | ||||||||
\(719\) | −14.1759 | −0.528671 | −0.264335 | − | 0.964431i | \(-0.585153\pi\) | ||||
−0.264335 | + | 0.964431i | \(0.585153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.14684 | 0.117194 | ||||||||
\(722\) | 40.3554 | 1.50187 | ||||||||
\(723\) | −21.2637 | −0.790807 | ||||||||
\(724\) | −5.69725 | −0.211737 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.3304 | 0.977213 | ||||||||
\(727\) | −26.9601 | −0.999893 | −0.499947 | − | 0.866056i | \(-0.666647\pi\) | ||||
−0.499947 | + | 0.866056i | \(0.666647\pi\) | |||||||
\(728\) | 20.4996 | 0.759765 | ||||||||
\(729\) | 29.5995 | 1.09628 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.1185 | −1.37288 | ||||||||
\(732\) | 61.5228 | 2.27395 | ||||||||
\(733\) | 19.5075 | 0.720528 | 0.360264 | − | 0.932850i | \(-0.382687\pi\) | ||||
0.360264 | + | 0.932850i | \(0.382687\pi\) | |||||||
\(734\) | 51.3152 | 1.89408 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 53.6605 | 1.97795 | ||||||||
\(737\) | 23.6426 | 0.870888 | ||||||||
\(738\) | −21.8081 | −0.802767 | ||||||||
\(739\) | −54.0231 | −1.98727 | −0.993636 | − | 0.112640i | \(-0.964069\pi\) | ||||
−0.993636 | + | 0.112640i | \(0.964069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1612 | −0.446753 | ||||||||
\(742\) | −11.1366 | −0.408839 | ||||||||
\(743\) | −50.0450 | −1.83597 | −0.917986 | − | 0.396612i | \(-0.870186\pi\) | ||||
−0.917986 | + | 0.396612i | \(0.870186\pi\) | |||||||
\(744\) | 29.3065 | 1.07443 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.2641 | 0.668698 | ||||||||
\(747\) | 14.9751 | 0.547910 | ||||||||
\(748\) | −52.4008 | −1.91596 | ||||||||
\(749\) | 6.77554 | 0.247573 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.6999 | −1.15675 | −0.578373 | − | 0.815773i | \(-0.696312\pi\) | ||||
−0.578373 | + | 0.815773i | \(0.696312\pi\) | |||||||
\(752\) | 40.1890 | 1.46554 | ||||||||
\(753\) | −26.1242 | −0.952019 | ||||||||
\(754\) | −92.8349 | −3.38085 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −17.2238 | −0.626423 | ||||||||
\(757\) | 46.2679 | 1.68164 | 0.840818 | − | 0.541318i | \(-0.182075\pi\) | ||||
0.840818 | + | 0.541318i | \(0.182075\pi\) | |||||||
\(758\) | −37.2708 | −1.35374 | ||||||||
\(759\) | −18.3783 | −0.667089 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1741 | −0.876312 | −0.438156 | − | 0.898899i | \(-0.644368\pi\) | ||||
−0.438156 | + | 0.898899i | \(0.644368\pi\) | |||||||
\(762\) | −2.45583 | −0.0889653 | ||||||||
\(763\) | −4.51584 | −0.163484 | ||||||||
\(764\) | 96.3673 | 3.48645 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.9105 | 0.466475 | ||||||||
\(767\) | −16.0697 | −0.580242 | ||||||||
\(768\) | −32.2590 | −1.16405 | ||||||||
\(769\) | 28.2406 | 1.01838 | 0.509191 | − | 0.860654i | \(-0.329945\pi\) | ||||
0.509191 | + | 0.860654i | \(0.329945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.65184 | −0.0594895 | ||||||||
\(772\) | 7.41896 | 0.267014 | ||||||||
\(773\) | −34.8025 | −1.25176 | −0.625880 | − | 0.779919i | \(-0.715260\pi\) | ||||
−0.625880 | + | 0.779919i | \(0.715260\pi\) | |||||||
\(774\) | 15.1690 | 0.545238 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 54.7131 | 1.96409 | ||||||||
\(777\) | 0.944840 | 0.0338959 | ||||||||
\(778\) | −56.9686 | −2.04242 | ||||||||
\(779\) | −17.7173 | −0.634787 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8911 | 0.568627 | ||||||||
\(782\) | −90.6309 | −3.24096 | ||||||||
\(783\) | 44.8127 | 1.60147 | ||||||||
\(784\) | −57.2023 | −2.04294 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.69912 | 0.274618 | ||||||||
\(787\) | −30.9025 | −1.10155 | −0.550777 | − | 0.834653i | \(-0.685668\pi\) | ||||
−0.550777 | + | 0.834653i | \(0.685668\pi\) | |||||||
\(788\) | 74.9118 | 2.66862 | ||||||||
\(789\) | 0.839110 | 0.0298731 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.38920 | 0.0849501 | ||||||||
\(792\) | 12.3030 | 0.437167 | ||||||||
\(793\) | −40.6217 | −1.44252 | ||||||||
\(794\) | 21.3439 | 0.757465 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.6225 | 0.730944 | ||||||||
\(797\) | 5.94861 | 0.210711 | 0.105355 | − | 0.994435i | \(-0.466402\pi\) | ||||
0.105355 | + | 0.994435i | \(0.466402\pi\) | |||||||
\(798\) | −4.51640 | −0.159879 | ||||||||
\(799\) | −25.7101 | −0.909559 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6279 | 0.481516 | ||||||||
\(802\) | 36.7071 | 1.29617 | ||||||||
\(803\) | −17.9210 | −0.632419 | ||||||||
\(804\) | 80.7711 | 2.84858 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.6806 | −1.18635 | ||||||||
\(807\) | 21.6036 | 0.760484 | ||||||||
\(808\) | 60.4681 | 2.12726 | ||||||||
\(809\) | 1.88364 | 0.0662253 | 0.0331126 | − | 0.999452i | \(-0.489458\pi\) | ||||
0.0331126 | + | 0.999452i | \(0.489458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.16615 | 0.286752 | 0.143376 | − | 0.989668i | \(-0.454204\pi\) | ||||
0.143376 | + | 0.989668i | \(0.454204\pi\) | |||||||
\(812\) | −24.1861 | −0.848766 | ||||||||
\(813\) | −34.3162 | −1.20352 | ||||||||
\(814\) | −5.18813 | −0.181844 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −70.4418 | −2.46596 | ||||||||
\(817\) | 12.3236 | 0.431147 | ||||||||
\(818\) | 14.5089 | 0.507293 | ||||||||
\(819\) | 2.57498 | 0.0899770 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.6381 | 1.97668 | 0.988341 | − | 0.152255i | \(-0.0486535\pi\) | ||||
0.988341 | + | 0.152255i | \(0.0486535\pi\) | |||||||
\(822\) | 39.3613 | 1.37288 | ||||||||
\(823\) | 44.6548 | 1.55657 | 0.778284 | − | 0.627913i | \(-0.216091\pi\) | ||||
0.778284 | + | 0.627913i | \(0.216091\pi\) | |||||||
\(824\) | −33.9151 | −1.18149 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.96792 | −0.207650 | ||||||||
\(827\) | −33.2193 | −1.15515 | −0.577574 | − | 0.816339i | \(-0.696000\pi\) | ||||
−0.577574 | + | 0.816339i | \(0.696000\pi\) | |||||||
\(828\) | 25.9825 | 0.902956 | ||||||||
\(829\) | 11.4093 | 0.396260 | 0.198130 | − | 0.980176i | \(-0.436513\pi\) | ||||
0.198130 | + | 0.980176i | \(0.436513\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.25813 | −0.0783337 | ||||||||
\(832\) | −21.1464 | −0.733121 | ||||||||
\(833\) | 36.5941 | 1.26791 | ||||||||
\(834\) | −50.5308 | −1.74974 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.3974 | 0.601701 | ||||||||
\(837\) | 16.2581 | 0.561961 | ||||||||
\(838\) | 39.3723 | 1.36009 | ||||||||
\(839\) | 4.83863 | 0.167048 | 0.0835240 | − | 0.996506i | \(-0.473382\pi\) | ||||
0.0835240 | + | 0.996506i | \(0.473382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.9272 | 1.16990 | ||||||||
\(842\) | 65.7110 | 2.26455 | ||||||||
\(843\) | 45.6078 | 1.57082 | ||||||||
\(844\) | −77.6866 | −2.67408 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.5068 | 0.361231 | ||||||||
\(847\) | −4.52933 | −0.155630 | ||||||||
\(848\) | 57.6684 | 1.98034 | ||||||||
\(849\) | −40.2318 | −1.38075 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.29488 | −0.215786 | ||||||||
\(852\) | 54.2892 | 1.85992 | ||||||||
\(853\) | −36.7663 | −1.25885 | −0.629427 | − | 0.777060i | \(-0.716710\pi\) | ||||
−0.629427 | + | 0.777060i | \(0.716710\pi\) | |||||||
\(854\) | −15.0860 | −0.516231 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −73.0234 | −2.49589 | ||||||||
\(857\) | −46.3913 | −1.58470 | −0.792349 | − | 0.610068i | \(-0.791142\pi\) | ||||
−0.792349 | + | 0.610068i | \(0.791142\pi\) | |||||||
\(858\) | 34.1672 | 1.16645 | ||||||||
\(859\) | −48.0751 | −1.64030 | −0.820151 | − | 0.572147i | \(-0.806111\pi\) | ||||
−0.820151 | + | 0.572147i | \(0.806111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.06519 | −0.308941 | ||||||||
\(862\) | −19.3482 | −0.659004 | ||||||||
\(863\) | 6.00436 | 0.204391 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(864\) | 48.1558 | 1.63829 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −70.6631 | −2.40123 | ||||||||
\(867\) | 20.3003 | 0.689435 | ||||||||
\(868\) | −8.77475 | −0.297834 | ||||||||
\(869\) | 11.7301 | 0.397918 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.3307 | −1.80704 | ||||||||
\(872\) | 48.6695 | 1.64816 | ||||||||
\(873\) | 6.87259 | 0.232602 | ||||||||
\(874\) | 30.0900 | 1.01781 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −61.2242 | −2.06857 | ||||||||
\(877\) | 22.5527 | 0.761550 | 0.380775 | − | 0.924668i | \(-0.375657\pi\) | ||||
0.380775 | + | 0.924668i | \(0.375657\pi\) | |||||||
\(878\) | −17.1690 | −0.579425 | ||||||||
\(879\) | −14.4282 | −0.486653 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.0374 | 1.48366 | 0.741829 | − | 0.670589i | \(-0.233959\pi\) | ||||
0.741829 | + | 0.670589i | \(0.233959\pi\) | |||||||
\(882\) | −14.9547 | −0.503550 | ||||||||
\(883\) | −20.8462 | −0.701529 | −0.350764 | − | 0.936464i | \(-0.614078\pi\) | ||||
−0.350764 | + | 0.936464i | \(0.614078\pi\) | |||||||
\(884\) | 118.201 | 3.97552 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.2473 | −1.25135 | ||||||||
\(887\) | −26.8194 | −0.900509 | −0.450254 | − | 0.892900i | \(-0.648667\pi\) | ||||
−0.450254 | + | 0.892900i | \(0.648667\pi\) | |||||||
\(888\) | −10.1830 | −0.341720 | ||||||||
\(889\) | 0.422449 | 0.0141685 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2131 | −0.375655 | ||||||||
\(892\) | 106.277 | 3.55841 | ||||||||
\(893\) | 8.53591 | 0.285643 | ||||||||
\(894\) | 29.0111 | 0.970277 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.20509 | 0.107075 | ||||||||
\(897\) | 41.4559 | 1.38417 | ||||||||
\(898\) | 41.1638 | 1.37366 | ||||||||
\(899\) | 22.8301 | 0.761425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.8922 | −1.22906 | ||||||||
\(902\) | 49.7771 | 1.65740 | ||||||||
\(903\) | 6.30545 | 0.209832 | ||||||||
\(904\) | −25.7496 | −0.856419 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 55.9203 | 1.85783 | ||||||||
\(907\) | −37.2904 | −1.23821 | −0.619103 | − | 0.785310i | \(-0.712504\pi\) | ||||
−0.619103 | + | 0.785310i | \(0.712504\pi\) | |||||||
\(908\) | −12.0387 | −0.399520 | ||||||||
\(909\) | 7.59548 | 0.251926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.67857 | −0.0556136 | −0.0278068 | − | 0.999613i | \(-0.508852\pi\) | ||||
−0.0278068 | + | 0.999613i | \(0.508852\pi\) | |||||||
\(912\) | 23.3871 | 0.774423 | ||||||||
\(913\) | −34.1807 | −1.13122 | ||||||||
\(914\) | −5.88606 | −0.194694 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.16503 | 0.269780 | ||||||||
\(917\) | −1.32439 | −0.0437353 | ||||||||
\(918\) | −81.3336 | −2.68441 | ||||||||
\(919\) | −28.9936 | −0.956411 | −0.478206 | − | 0.878248i | \(-0.658713\pi\) | ||||
−0.478206 | + | 0.878248i | \(0.658713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.4174 | 0.376216 | ||||||||
\(922\) | −69.4976 | −2.28878 | ||||||||
\(923\) | −35.8455 | −1.17987 | ||||||||
\(924\) | 8.90152 | 0.292838 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.2659 | 0.468807 | ||||||||
\(927\) | −4.26012 | −0.139921 | ||||||||
\(928\) | 67.6217 | 2.21979 | ||||||||
\(929\) | 21.1104 | 0.692611 | 0.346305 | − | 0.938122i | \(-0.387436\pi\) | ||||
0.346305 | + | 0.938122i | \(0.387436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.1494 | −0.398182 | ||||||||
\(932\) | −43.8507 | −1.43638 | ||||||||
\(933\) | 35.5942 | 1.16530 | ||||||||
\(934\) | 48.6913 | 1.59323 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −27.7518 | −0.907098 | ||||||||
\(937\) | 36.3577 | 1.18775 | 0.593877 | − | 0.804556i | \(-0.297597\pi\) | ||||
0.593877 | + | 0.804556i | \(0.297597\pi\) | |||||||
\(938\) | −19.8058 | −0.646684 | ||||||||
\(939\) | −26.2324 | −0.856061 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.15990 | 0.298604 | 0.149302 | − | 0.988792i | \(-0.452297\pi\) | ||||
0.149302 | + | 0.988792i | \(0.452297\pi\) | |||||||
\(942\) | −24.8143 | −0.808493 | ||||||||
\(943\) | 60.3958 | 1.96676 | ||||||||
\(944\) | 30.9034 | 1.00582 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.6233 | −1.12570 | ||||||||
\(947\) | −25.6230 | −0.832637 | −0.416319 | − | 0.909219i | \(-0.636680\pi\) | ||||
−0.416319 | + | 0.909219i | \(0.636680\pi\) | |||||||
\(948\) | 40.0741 | 1.30155 | ||||||||
\(949\) | 40.4245 | 1.31223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.9425 | 0.679105 | ||||||||
\(952\) | 25.2198 | 0.817378 | ||||||||
\(953\) | −34.2849 | −1.11060 | −0.555299 | − | 0.831651i | \(-0.687396\pi\) | ||||
−0.555299 | + | 0.831651i | \(0.687396\pi\) | |||||||
\(954\) | 15.0765 | 0.488120 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.83083 | 0.0915557 | ||||||||
\(957\) | −23.1599 | −0.748652 | ||||||||
\(958\) | −20.7209 | −0.669461 | ||||||||
\(959\) | −6.77088 | −0.218643 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7172 | −0.732814 | ||||||||
\(962\) | 11.7029 | 0.377316 | ||||||||
\(963\) | −9.17257 | −0.295582 | ||||||||
\(964\) | −68.6165 | −2.20999 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.3958 | 0.495352 | ||||||||
\(967\) | −10.6663 | −0.343004 | −0.171502 | − | 0.985184i | \(-0.554862\pi\) | ||||
−0.171502 | + | 0.985184i | \(0.554862\pi\) | |||||||
\(968\) | 48.8148 | 1.56897 | ||||||||
\(969\) | −14.9614 | −0.480631 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.6665 | −1.62596 | −0.812982 | − | 0.582289i | \(-0.802157\pi\) | ||||
−0.812982 | + | 0.582289i | \(0.802157\pi\) | |||||||
\(972\) | 41.3547 | 1.32645 | ||||||||
\(973\) | 8.69225 | 0.278661 | ||||||||
\(974\) | −19.1461 | −0.613479 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 78.1190 | 2.50053 | ||||||||
\(977\) | −5.91123 | −0.189117 | −0.0945584 | − | 0.995519i | \(-0.530144\pi\) | ||||
−0.0945584 | + | 0.995519i | \(0.530144\pi\) | |||||||
\(978\) | 34.0553 | 1.08897 | ||||||||
\(979\) | −31.1056 | −0.994141 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.11343 | 0.195187 | ||||||||
\(982\) | −105.836 | −3.37735 | ||||||||
\(983\) | 51.4039 | 1.63953 | 0.819765 | − | 0.572701i | \(-0.194104\pi\) | ||||
0.819765 | + | 0.572701i | \(0.194104\pi\) | |||||||
\(984\) | 97.7002 | 3.11457 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −114.211 | −3.63722 | ||||||||
\(987\) | 4.36747 | 0.139018 | ||||||||
\(988\) | −39.2433 | −1.24850 | ||||||||
\(989\) | −42.0093 | −1.33582 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.90736 | 0.187653 | 0.0938267 | − | 0.995589i | \(-0.470090\pi\) | ||||
0.0938267 | + | 0.995589i | \(0.470090\pi\) | |||||||
\(992\) | 24.5332 | 0.778931 | ||||||||
\(993\) | 35.8223 | 1.13679 | ||||||||
\(994\) | −13.3122 | −0.422238 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −116.773 | −3.70009 | ||||||||
\(997\) | −12.5708 | −0.398122 | −0.199061 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199061 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(998\) | −11.1371 | −0.352538 | ||||||||
\(999\) | −5.64913 | −0.178731 |
(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 | 925.2.a.l.1.2 | 9 | ||
3.2 | odd | 2 | 8325.2.a.cr.1.8 | 9 | |||
5.2 | odd | 4 | 185.2.b.a.149.2 | ✓ | 18 | ||
5.3 | odd | 4 | 185.2.b.a.149.17 | yes | 18 | ||
5.4 | even | 2 | 925.2.a.m.1.8 | 9 | |||
15.2 | even | 4 | 1665.2.c.e.334.17 | 18 | |||
15.8 | even | 4 | 1665.2.c.e.334.2 | 18 | |||
15.14 | odd | 2 | 8325.2.a.cq.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
185.2.b.a.149.2 | ✓ | 18 | 5.2 | odd | 4 | ||
185.2.b.a.149.17 | yes | 18 | 5.3 | odd | 4 | ||
925.2.a.l.1.2 | 9 | 1.1 | even | 1 | trivial | ||
925.2.a.m.1.8 | 9 | 5.4 | even | 2 | |||
1665.2.c.e.334.2 | 18 | 15.8 | even | 4 | |||
1665.2.c.e.334.17 | 18 | 15.2 | even | 4 | |||
8325.2.a.cq.1.2 | 9 | 15.14 | odd | 2 | |||
8325.2.a.cr.1.8 | 9 | 3.2 | odd | 2 |