Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} - 6826 x^{11} + 7199 x^{10} + 9364 x^{9} - 14841 x^{8} - 5183 x^{7} + 14037 x^{6} + \cdots - 63 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64132\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64132 | −1.86770 | −0.933849 | − | 0.357667i | \(-0.883572\pi\) | ||||
−0.933849 | + | 0.357667i | \(0.883572\pi\) | |||||||
\(3\) | −0.762312 | −0.440121 | −0.220061 | − | 0.975486i | \(-0.570626\pi\) | ||||
−0.220061 | + | 0.975486i | \(0.570626\pi\) | |||||||
\(4\) | 4.97659 | 2.48830 | ||||||||
\(5\) | 1.72196 | 0.770084 | 0.385042 | − | 0.922899i | \(-0.374187\pi\) | ||||
0.385042 | + | 0.922899i | \(0.374187\pi\) | |||||||
\(6\) | 2.01351 | 0.822014 | ||||||||
\(7\) | 1.20730 | 0.456318 | 0.228159 | − | 0.973624i | \(-0.426729\pi\) | ||||
0.228159 | + | 0.973624i | \(0.426729\pi\) | |||||||
\(8\) | −7.86215 | −2.77969 | ||||||||
\(9\) | −2.41888 | −0.806293 | ||||||||
\(10\) | −4.54826 | −1.43829 | ||||||||
\(11\) | 3.89418 | 1.17414 | 0.587070 | − | 0.809536i | \(-0.300281\pi\) | ||||
0.587070 | + | 0.809536i | \(0.300281\pi\) | |||||||
\(12\) | −3.79372 | −1.09515 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −3.18888 | −0.852265 | ||||||||
\(15\) | −1.31267 | −0.338931 | ||||||||
\(16\) | 10.8133 | 2.70332 | ||||||||
\(17\) | −0.0584553 | −0.0141775 | −0.00708874 | − | 0.999975i | \(-0.502256\pi\) | ||||
−0.00708874 | + | 0.999975i | \(0.502256\pi\) | |||||||
\(18\) | 6.38905 | 1.50591 | ||||||||
\(19\) | −5.98373 | −1.37276 | −0.686380 | − | 0.727243i | \(-0.740801\pi\) | ||||
−0.686380 | + | 0.727243i | \(0.740801\pi\) | |||||||
\(20\) | 8.56950 | 1.91620 | ||||||||
\(21\) | −0.920343 | −0.200835 | ||||||||
\(22\) | −10.2858 | −2.19294 | ||||||||
\(23\) | −5.61188 | −1.17016 | −0.585079 | − | 0.810976i | \(-0.698937\pi\) | ||||
−0.585079 | + | 0.810976i | \(0.698937\pi\) | |||||||
\(24\) | 5.99341 | 1.22340 | ||||||||
\(25\) | −2.03485 | −0.406970 | ||||||||
\(26\) | −2.64132 | −0.518006 | ||||||||
\(27\) | 4.13088 | 0.794988 | ||||||||
\(28\) | 6.00826 | 1.13546 | ||||||||
\(29\) | −8.70027 | −1.61560 | −0.807800 | − | 0.589456i | \(-0.799342\pi\) | ||||
−0.807800 | + | 0.589456i | \(0.799342\pi\) | |||||||
\(30\) | 3.46719 | 0.633020 | ||||||||
\(31\) | −4.16435 | −0.747940 | −0.373970 | − | 0.927441i | \(-0.622004\pi\) | ||||
−0.373970 | + | 0.927441i | \(0.622004\pi\) | |||||||
\(32\) | −12.8371 | −2.26931 | ||||||||
\(33\) | −2.96858 | −0.516764 | ||||||||
\(34\) | 0.154399 | 0.0264793 | ||||||||
\(35\) | 2.07893 | 0.351403 | ||||||||
\(36\) | −12.0378 | −2.00630 | ||||||||
\(37\) | 7.87910 | 1.29532 | 0.647658 | − | 0.761931i | \(-0.275749\pi\) | ||||
0.647658 | + | 0.761931i | \(0.275749\pi\) | |||||||
\(38\) | 15.8050 | 2.56390 | ||||||||
\(39\) | −0.762312 | −0.122068 | ||||||||
\(40\) | −13.5383 | −2.14060 | ||||||||
\(41\) | −12.3647 | −1.93104 | −0.965518 | − | 0.260337i | \(-0.916166\pi\) | ||||
−0.965518 | + | 0.260337i | \(0.916166\pi\) | |||||||
\(42\) | 2.43092 | 0.375100 | ||||||||
\(43\) | 1.92562 | 0.293655 | 0.146827 | − | 0.989162i | \(-0.453094\pi\) | ||||
0.146827 | + | 0.989162i | \(0.453094\pi\) | |||||||
\(44\) | 19.3798 | 2.92161 | ||||||||
\(45\) | −4.16522 | −0.620914 | ||||||||
\(46\) | 14.8228 | 2.18550 | ||||||||
\(47\) | −8.52454 | −1.24343 | −0.621716 | − | 0.783243i | \(-0.713564\pi\) | ||||
−0.621716 | + | 0.783243i | \(0.713564\pi\) | |||||||
\(48\) | −8.24311 | −1.18979 | ||||||||
\(49\) | −5.54242 | −0.791774 | ||||||||
\(50\) | 5.37470 | 0.760097 | ||||||||
\(51\) | 0.0445612 | 0.00623981 | ||||||||
\(52\) | 4.97659 | 0.690129 | ||||||||
\(53\) | 4.15194 | 0.570313 | 0.285156 | − | 0.958481i | \(-0.407954\pi\) | ||||
0.285156 | + | 0.958481i | \(0.407954\pi\) | |||||||
\(54\) | −10.9110 | −1.48480 | ||||||||
\(55\) | 6.70563 | 0.904187 | ||||||||
\(56\) | −9.49201 | −1.26842 | ||||||||
\(57\) | 4.56147 | 0.604181 | ||||||||
\(58\) | 22.9802 | 3.01745 | ||||||||
\(59\) | −8.39711 | −1.09321 | −0.546605 | − | 0.837390i | \(-0.684080\pi\) | ||||
−0.546605 | + | 0.837390i | \(0.684080\pi\) | |||||||
\(60\) | −6.53264 | −0.843360 | ||||||||
\(61\) | 14.5547 | 1.86354 | 0.931772 | − | 0.363045i | \(-0.118263\pi\) | ||||
0.931772 | + | 0.363045i | \(0.118263\pi\) | |||||||
\(62\) | 10.9994 | 1.39693 | ||||||||
\(63\) | −2.92032 | −0.367926 | ||||||||
\(64\) | 12.2804 | 1.53505 | ||||||||
\(65\) | 1.72196 | 0.213583 | ||||||||
\(66\) | 7.84099 | 0.965159 | ||||||||
\(67\) | 2.97482 | 0.363432 | 0.181716 | − | 0.983351i | \(-0.441835\pi\) | ||||
0.181716 | + | 0.983351i | \(0.441835\pi\) | |||||||
\(68\) | −0.290908 | −0.0352778 | ||||||||
\(69\) | 4.27801 | 0.515012 | ||||||||
\(70\) | −5.49113 | −0.656316 | ||||||||
\(71\) | 0.367486 | 0.0436126 | 0.0218063 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218063 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(72\) | 19.0176 | 2.24125 | ||||||||
\(73\) | 11.0083 | 1.28842 | 0.644211 | − | 0.764848i | \(-0.277186\pi\) | ||||
0.644211 | + | 0.764848i | \(0.277186\pi\) | |||||||
\(74\) | −20.8113 | −2.41926 | ||||||||
\(75\) | 1.55119 | 0.179116 | ||||||||
\(76\) | −29.7786 | −3.41584 | ||||||||
\(77\) | 4.70146 | 0.535781 | ||||||||
\(78\) | 2.01351 | 0.227986 | ||||||||
\(79\) | 12.5782 | 1.41516 | 0.707580 | − | 0.706633i | \(-0.249787\pi\) | ||||
0.707580 | + | 0.706633i | \(0.249787\pi\) | |||||||
\(80\) | 18.6201 | 2.08179 | ||||||||
\(81\) | 4.10762 | 0.456402 | ||||||||
\(82\) | 32.6591 | 3.60659 | ||||||||
\(83\) | 7.81940 | 0.858291 | 0.429145 | − | 0.903235i | \(-0.358815\pi\) | ||||
0.429145 | + | 0.903235i | \(0.358815\pi\) | |||||||
\(84\) | −4.58017 | −0.499738 | ||||||||
\(85\) | −0.100658 | −0.0109179 | ||||||||
\(86\) | −5.08619 | −0.548458 | ||||||||
\(87\) | 6.63233 | 0.711060 | ||||||||
\(88\) | −30.6166 | −3.26374 | ||||||||
\(89\) | −18.0980 | −1.91838 | −0.959191 | − | 0.282758i | \(-0.908751\pi\) | ||||
−0.959191 | + | 0.282758i | \(0.908751\pi\) | |||||||
\(90\) | 11.0017 | 1.15968 | ||||||||
\(91\) | 1.20730 | 0.126560 | ||||||||
\(92\) | −27.9281 | −2.91170 | ||||||||
\(93\) | 3.17454 | 0.329184 | ||||||||
\(94\) | 22.5161 | 2.32236 | ||||||||
\(95\) | −10.3037 | −1.05714 | ||||||||
\(96\) | 9.78590 | 0.998769 | ||||||||
\(97\) | −16.9843 | −1.72450 | −0.862249 | − | 0.506485i | \(-0.830945\pi\) | ||||
−0.862249 | + | 0.506485i | \(0.830945\pi\) | |||||||
\(98\) | 14.6393 | 1.47879 | ||||||||
\(99\) | −9.41956 | −0.946701 | ||||||||
\(100\) | −10.1266 | −1.01266 | ||||||||
\(101\) | −11.6080 | −1.15504 | −0.577520 | − | 0.816377i | \(-0.695979\pi\) | ||||
−0.577520 | + | 0.816377i | \(0.695979\pi\) | |||||||
\(102\) | −0.117701 | −0.0116541 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −7.86215 | −0.770947 | ||||||||
\(105\) | −1.58479 | −0.154660 | ||||||||
\(106\) | −10.9666 | −1.06517 | ||||||||
\(107\) | −4.07642 | −0.394083 | −0.197041 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197041 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(108\) | 20.5577 | 1.97817 | ||||||||
\(109\) | −6.28688 | −0.602174 | −0.301087 | − | 0.953597i | \(-0.597349\pi\) | ||||
−0.301087 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(110\) | −17.7117 | −1.68875 | ||||||||
\(111\) | −6.00634 | −0.570096 | ||||||||
\(112\) | 13.0549 | 1.23358 | ||||||||
\(113\) | 18.1047 | 1.70315 | 0.851573 | − | 0.524237i | \(-0.175649\pi\) | ||||
0.851573 | + | 0.524237i | \(0.175649\pi\) | |||||||
\(114\) | −12.0483 | −1.12843 | ||||||||
\(115\) | −9.66345 | −0.901121 | ||||||||
\(116\) | −43.2977 | −4.02009 | ||||||||
\(117\) | −2.41888 | −0.223626 | ||||||||
\(118\) | 22.1795 | 2.04179 | ||||||||
\(119\) | −0.0705733 | −0.00646944 | ||||||||
\(120\) | 10.3204 | 0.942122 | ||||||||
\(121\) | 4.16465 | 0.378605 | ||||||||
\(122\) | −38.4438 | −3.48054 | ||||||||
\(123\) | 9.42574 | 0.849890 | ||||||||
\(124\) | −20.7243 | −1.86110 | ||||||||
\(125\) | −12.1137 | −1.08349 | ||||||||
\(126\) | 7.71352 | 0.687175 | ||||||||
\(127\) | −14.7488 | −1.30874 | −0.654371 | − | 0.756174i | \(-0.727067\pi\) | ||||
−0.654371 | + | 0.756174i | \(0.727067\pi\) | |||||||
\(128\) | −6.76232 | −0.597710 | ||||||||
\(129\) | −1.46793 | −0.129244 | ||||||||
\(130\) | −4.54826 | −0.398909 | ||||||||
\(131\) | −6.88906 | −0.601900 | −0.300950 | − | 0.953640i | \(-0.597304\pi\) | ||||
−0.300950 | + | 0.953640i | \(0.597304\pi\) | |||||||
\(132\) | −14.7734 | −1.28586 | ||||||||
\(133\) | −7.22418 | −0.626416 | ||||||||
\(134\) | −7.85747 | −0.678782 | ||||||||
\(135\) | 7.11321 | 0.612208 | ||||||||
\(136\) | 0.459584 | 0.0394090 | ||||||||
\(137\) | −20.3110 | −1.73529 | −0.867644 | − | 0.497186i | \(-0.834367\pi\) | ||||
−0.867644 | + | 0.497186i | \(0.834367\pi\) | |||||||
\(138\) | −11.2996 | −0.961887 | ||||||||
\(139\) | 6.11416 | 0.518596 | 0.259298 | − | 0.965797i | \(-0.416509\pi\) | ||||
0.259298 | + | 0.965797i | \(0.416509\pi\) | |||||||
\(140\) | 10.3460 | 0.874396 | ||||||||
\(141\) | 6.49836 | 0.547261 | ||||||||
\(142\) | −0.970651 | −0.0814552 | ||||||||
\(143\) | 3.89418 | 0.325648 | ||||||||
\(144\) | −26.1561 | −2.17967 | ||||||||
\(145\) | −14.9815 | −1.24415 | ||||||||
\(146\) | −29.0764 | −2.40638 | ||||||||
\(147\) | 4.22505 | 0.348476 | ||||||||
\(148\) | 39.2111 | 3.22313 | ||||||||
\(149\) | 13.9439 | 1.14233 | 0.571164 | − | 0.820836i | \(-0.306492\pi\) | ||||
0.571164 | + | 0.820836i | \(0.306492\pi\) | |||||||
\(150\) | −4.09720 | −0.334535 | ||||||||
\(151\) | −8.10283 | −0.659399 | −0.329699 | − | 0.944086i | \(-0.606947\pi\) | ||||
−0.329699 | + | 0.944086i | \(0.606947\pi\) | |||||||
\(152\) | 47.0449 | 3.81585 | ||||||||
\(153\) | 0.141396 | 0.0114312 | ||||||||
\(154\) | −12.4181 | −1.00068 | ||||||||
\(155\) | −7.17085 | −0.575977 | ||||||||
\(156\) | −3.79372 | −0.303741 | ||||||||
\(157\) | −4.61492 | −0.368310 | −0.184155 | − | 0.982897i | \(-0.558955\pi\) | ||||
−0.184155 | + | 0.982897i | \(0.558955\pi\) | |||||||
\(158\) | −33.2232 | −2.64309 | ||||||||
\(159\) | −3.16508 | −0.251007 | ||||||||
\(160\) | −22.1050 | −1.74756 | ||||||||
\(161\) | −6.77525 | −0.533965 | ||||||||
\(162\) | −10.8496 | −0.852422 | ||||||||
\(163\) | 11.4170 | 0.894247 | 0.447124 | − | 0.894472i | \(-0.352448\pi\) | ||||
0.447124 | + | 0.894472i | \(0.352448\pi\) | |||||||
\(164\) | −61.5339 | −4.80499 | ||||||||
\(165\) | −5.11178 | −0.397952 | ||||||||
\(166\) | −20.6536 | −1.60303 | ||||||||
\(167\) | −8.40805 | −0.650635 | −0.325317 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325317 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(168\) | 7.23587 | 0.558260 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.265870 | 0.0203913 | ||||||||
\(171\) | 14.4739 | 1.10685 | ||||||||
\(172\) | 9.58304 | 0.730700 | ||||||||
\(173\) | −3.78023 | −0.287405 | −0.143703 | − | 0.989621i | \(-0.545901\pi\) | ||||
−0.143703 | + | 0.989621i | \(0.545901\pi\) | |||||||
\(174\) | −17.5181 | −1.32805 | ||||||||
\(175\) | −2.45668 | −0.185708 | ||||||||
\(176\) | 42.1090 | 3.17408 | ||||||||
\(177\) | 6.40122 | 0.481145 | ||||||||
\(178\) | 47.8026 | 3.58296 | ||||||||
\(179\) | 15.4398 | 1.15402 | 0.577011 | − | 0.816736i | \(-0.304219\pi\) | ||||
0.577011 | + | 0.816736i | \(0.304219\pi\) | |||||||
\(180\) | −20.7286 | −1.54502 | ||||||||
\(181\) | −1.64581 | −0.122332 | −0.0611659 | − | 0.998128i | \(-0.519482\pi\) | ||||
−0.0611659 | + | 0.998128i | \(0.519482\pi\) | |||||||
\(182\) | −3.18888 | −0.236376 | ||||||||
\(183\) | −11.0953 | −0.820185 | ||||||||
\(184\) | 44.1215 | 3.25268 | ||||||||
\(185\) | 13.5675 | 0.997503 | ||||||||
\(186\) | −8.38498 | −0.614817 | ||||||||
\(187\) | −0.227635 | −0.0166464 | ||||||||
\(188\) | −42.4232 | −3.09403 | ||||||||
\(189\) | 4.98723 | 0.362767 | ||||||||
\(190\) | 27.2155 | 1.97442 | ||||||||
\(191\) | 26.5533 | 1.92133 | 0.960665 | − | 0.277710i | \(-0.0895756\pi\) | ||||
0.960665 | + | 0.277710i | \(0.0895756\pi\) | |||||||
\(192\) | −9.36152 | −0.675609 | ||||||||
\(193\) | −15.8380 | −1.14004 | −0.570021 | − | 0.821630i | \(-0.693065\pi\) | ||||
−0.570021 | + | 0.821630i | \(0.693065\pi\) | |||||||
\(194\) | 44.8611 | 3.22084 | ||||||||
\(195\) | −1.31267 | −0.0940024 | ||||||||
\(196\) | −27.5824 | −1.97017 | ||||||||
\(197\) | −0.455598 | −0.0324600 | −0.0162300 | − | 0.999868i | \(-0.505166\pi\) | ||||
−0.0162300 | + | 0.999868i | \(0.505166\pi\) | |||||||
\(198\) | 24.8801 | 1.76815 | ||||||||
\(199\) | −16.2559 | −1.15235 | −0.576174 | − | 0.817327i | \(-0.695455\pi\) | ||||
−0.576174 | + | 0.817327i | \(0.695455\pi\) | |||||||
\(200\) | 15.9983 | 1.13125 | ||||||||
\(201\) | −2.26774 | −0.159954 | ||||||||
\(202\) | 30.6605 | 2.15727 | ||||||||
\(203\) | −10.5039 | −0.737228 | ||||||||
\(204\) | 0.221763 | 0.0155265 | ||||||||
\(205\) | −21.2915 | −1.48706 | ||||||||
\(206\) | −2.64132 | −0.184030 | ||||||||
\(207\) | 13.5745 | 0.943491 | ||||||||
\(208\) | 10.8133 | 0.749767 | ||||||||
\(209\) | −23.3017 | −1.61181 | ||||||||
\(210\) | 4.18596 | 0.288858 | ||||||||
\(211\) | −8.05535 | −0.554553 | −0.277277 | − | 0.960790i | \(-0.589432\pi\) | ||||
−0.277277 | + | 0.960790i | \(0.589432\pi\) | |||||||
\(212\) | 20.6625 | 1.41911 | ||||||||
\(213\) | −0.280139 | −0.0191948 | ||||||||
\(214\) | 10.7672 | 0.736027 | ||||||||
\(215\) | 3.31585 | 0.226139 | ||||||||
\(216\) | −32.4776 | −2.20982 | ||||||||
\(217\) | −5.02764 | −0.341299 | ||||||||
\(218\) | 16.6057 | 1.12468 | ||||||||
\(219\) | −8.39174 | −0.567061 | ||||||||
\(220\) | 33.3712 | 2.24989 | ||||||||
\(221\) | −0.0584553 | −0.00393213 | ||||||||
\(222\) | 15.8647 | 1.06477 | ||||||||
\(223\) | −24.3618 | −1.63139 | −0.815695 | − | 0.578482i | \(-0.803645\pi\) | ||||
−0.815695 | + | 0.578482i | \(0.803645\pi\) | |||||||
\(224\) | −15.4983 | −1.03553 | ||||||||
\(225\) | 4.92206 | 0.328137 | ||||||||
\(226\) | −47.8203 | −3.18096 | ||||||||
\(227\) | 20.6110 | 1.36800 | 0.684000 | − | 0.729482i | \(-0.260239\pi\) | ||||
0.684000 | + | 0.729482i | \(0.260239\pi\) | |||||||
\(228\) | 22.7006 | 1.50338 | ||||||||
\(229\) | 12.5177 | 0.827192 | 0.413596 | − | 0.910460i | \(-0.364273\pi\) | ||||
0.413596 | + | 0.910460i | \(0.364273\pi\) | |||||||
\(230\) | 25.5243 | 1.68302 | ||||||||
\(231\) | −3.58398 | −0.235809 | ||||||||
\(232\) | 68.4029 | 4.49087 | ||||||||
\(233\) | −20.3300 | −1.33186 | −0.665930 | − | 0.746014i | \(-0.731965\pi\) | ||||
−0.665930 | + | 0.746014i | \(0.731965\pi\) | |||||||
\(234\) | 6.38905 | 0.417665 | ||||||||
\(235\) | −14.6789 | −0.957548 | ||||||||
\(236\) | −41.7890 | −2.72023 | ||||||||
\(237\) | −9.58853 | −0.622842 | ||||||||
\(238\) | 0.186407 | 0.0120830 | ||||||||
\(239\) | −21.3704 | −1.38233 | −0.691167 | − | 0.722695i | \(-0.742903\pi\) | ||||
−0.691167 | + | 0.722695i | \(0.742903\pi\) | |||||||
\(240\) | −14.1943 | −0.916239 | ||||||||
\(241\) | 9.51199 | 0.612721 | 0.306361 | − | 0.951916i | \(-0.400889\pi\) | ||||
0.306361 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(242\) | −11.0002 | −0.707120 | ||||||||
\(243\) | −15.5239 | −0.995860 | ||||||||
\(244\) | 72.4330 | 4.63705 | ||||||||
\(245\) | −9.54382 | −0.609733 | ||||||||
\(246\) | −24.8964 | −1.58734 | ||||||||
\(247\) | −5.98373 | −0.380735 | ||||||||
\(248\) | 32.7408 | 2.07904 | ||||||||
\(249\) | −5.96082 | −0.377752 | ||||||||
\(250\) | 31.9963 | 2.02362 | ||||||||
\(251\) | −4.46858 | −0.282054 | −0.141027 | − | 0.990006i | \(-0.545041\pi\) | ||||
−0.141027 | + | 0.990006i | \(0.545041\pi\) | |||||||
\(252\) | −14.5333 | −0.915510 | ||||||||
\(253\) | −21.8537 | −1.37393 | ||||||||
\(254\) | 38.9563 | 2.44434 | ||||||||
\(255\) | 0.0767326 | 0.00480518 | ||||||||
\(256\) | −6.69936 | −0.418710 | ||||||||
\(257\) | 0.331613 | 0.0206854 | 0.0103427 | − | 0.999947i | \(-0.496708\pi\) | ||||
0.0103427 | + | 0.999947i | \(0.496708\pi\) | |||||||
\(258\) | 3.87727 | 0.241388 | ||||||||
\(259\) | 9.51247 | 0.591076 | ||||||||
\(260\) | 8.56950 | 0.531458 | ||||||||
\(261\) | 21.0449 | 1.30265 | ||||||||
\(262\) | 18.1962 | 1.12417 | ||||||||
\(263\) | 26.9020 | 1.65885 | 0.829424 | − | 0.558620i | \(-0.188669\pi\) | ||||
0.829424 | + | 0.558620i | \(0.188669\pi\) | |||||||
\(264\) | 23.3394 | 1.43644 | ||||||||
\(265\) | 7.14948 | 0.439189 | ||||||||
\(266\) | 19.0814 | 1.16996 | ||||||||
\(267\) | 13.7963 | 0.844321 | ||||||||
\(268\) | 14.8045 | 0.904327 | ||||||||
\(269\) | −10.4968 | −0.640004 | −0.320002 | − | 0.947417i | \(-0.603684\pi\) | ||||
−0.320002 | + | 0.947417i | \(0.603684\pi\) | |||||||
\(270\) | −18.7883 | −1.14342 | ||||||||
\(271\) | 7.87413 | 0.478319 | 0.239160 | − | 0.970980i | \(-0.423128\pi\) | ||||
0.239160 | + | 0.970980i | \(0.423128\pi\) | |||||||
\(272\) | −0.632094 | −0.0383263 | ||||||||
\(273\) | −0.920343 | −0.0557017 | ||||||||
\(274\) | 53.6480 | 3.24100 | ||||||||
\(275\) | −7.92408 | −0.477840 | ||||||||
\(276\) | 21.2899 | 1.28150 | ||||||||
\(277\) | −2.14339 | −0.128784 | −0.0643919 | − | 0.997925i | \(-0.520511\pi\) | ||||
−0.0643919 | + | 0.997925i | \(0.520511\pi\) | |||||||
\(278\) | −16.1495 | −0.968582 | ||||||||
\(279\) | 10.0731 | 0.603059 | ||||||||
\(280\) | −16.3449 | −0.976793 | ||||||||
\(281\) | −2.84828 | −0.169914 | −0.0849572 | − | 0.996385i | \(-0.527075\pi\) | ||||
−0.0849572 | + | 0.996385i | \(0.527075\pi\) | |||||||
\(282\) | −17.1643 | −1.02212 | ||||||||
\(283\) | 13.9600 | 0.829838 | 0.414919 | − | 0.909858i | \(-0.363810\pi\) | ||||
0.414919 | + | 0.909858i | \(0.363810\pi\) | |||||||
\(284\) | 1.82883 | 0.108521 | ||||||||
\(285\) | 7.85467 | 0.465270 | ||||||||
\(286\) | −10.2858 | −0.608212 | ||||||||
\(287\) | −14.9279 | −0.881167 | ||||||||
\(288\) | 31.0515 | 1.82973 | ||||||||
\(289\) | −16.9966 | −0.999799 | ||||||||
\(290\) | 39.5711 | 2.32369 | ||||||||
\(291\) | 12.9474 | 0.758988 | ||||||||
\(292\) | 54.7837 | 3.20597 | ||||||||
\(293\) | 19.2917 | 1.12703 | 0.563517 | − | 0.826104i | \(-0.309448\pi\) | ||||
0.563517 | + | 0.826104i | \(0.309448\pi\) | |||||||
\(294\) | −11.1597 | −0.650849 | ||||||||
\(295\) | −14.4595 | −0.841864 | ||||||||
\(296\) | −61.9467 | −3.60058 | ||||||||
\(297\) | 16.0864 | 0.933427 | ||||||||
\(298\) | −36.8303 | −2.13352 | ||||||||
\(299\) | −5.61188 | −0.324544 | ||||||||
\(300\) | 7.71965 | 0.445694 | ||||||||
\(301\) | 2.32481 | 0.134000 | ||||||||
\(302\) | 21.4022 | 1.23156 | ||||||||
\(303\) | 8.84892 | 0.508357 | ||||||||
\(304\) | −64.7038 | −3.71102 | ||||||||
\(305\) | 25.0627 | 1.43509 | ||||||||
\(306\) | −0.373473 | −0.0213501 | ||||||||
\(307\) | 13.2691 | 0.757308 | 0.378654 | − | 0.925538i | \(-0.376387\pi\) | ||||
0.378654 | + | 0.925538i | \(0.376387\pi\) | |||||||
\(308\) | 23.3973 | 1.33318 | ||||||||
\(309\) | −0.762312 | −0.0433664 | ||||||||
\(310\) | 18.9406 | 1.07575 | ||||||||
\(311\) | 6.23805 | 0.353728 | 0.176864 | − | 0.984235i | \(-0.443405\pi\) | ||||
0.176864 | + | 0.984235i | \(0.443405\pi\) | |||||||
\(312\) | 5.99341 | 0.339310 | ||||||||
\(313\) | 9.47102 | 0.535334 | 0.267667 | − | 0.963512i | \(-0.413747\pi\) | ||||
0.267667 | + | 0.963512i | \(0.413747\pi\) | |||||||
\(314\) | 12.1895 | 0.687893 | ||||||||
\(315\) | −5.02868 | −0.283334 | ||||||||
\(316\) | 62.5967 | 3.52134 | ||||||||
\(317\) | −11.5158 | −0.646790 | −0.323395 | − | 0.946264i | \(-0.604824\pi\) | ||||
−0.323395 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(318\) | 8.35999 | 0.468805 | ||||||||
\(319\) | −33.8804 | −1.89694 | ||||||||
\(320\) | 21.1464 | 1.18212 | ||||||||
\(321\) | 3.10751 | 0.173444 | ||||||||
\(322\) | 17.8956 | 0.997285 | ||||||||
\(323\) | 0.349780 | 0.0194623 | ||||||||
\(324\) | 20.4420 | 1.13566 | ||||||||
\(325\) | −2.03485 | −0.112873 | ||||||||
\(326\) | −30.1560 | −1.67018 | ||||||||
\(327\) | 4.79256 | 0.265029 | ||||||||
\(328\) | 97.2128 | 5.36768 | ||||||||
\(329\) | −10.2917 | −0.567401 | ||||||||
\(330\) | 13.5019 | 0.743254 | ||||||||
\(331\) | −9.87943 | −0.543023 | −0.271511 | − | 0.962435i | \(-0.587523\pi\) | ||||
−0.271511 | + | 0.962435i | \(0.587523\pi\) | |||||||
\(332\) | 38.9140 | 2.13568 | ||||||||
\(333\) | −19.0586 | −1.04440 | ||||||||
\(334\) | 22.2084 | 1.21519 | ||||||||
\(335\) | 5.12253 | 0.279873 | ||||||||
\(336\) | −9.95194 | −0.542923 | ||||||||
\(337\) | −13.1699 | −0.717408 | −0.358704 | − | 0.933451i | \(-0.616781\pi\) | ||||
−0.358704 | + | 0.933451i | \(0.616781\pi\) | |||||||
\(338\) | −2.64132 | −0.143669 | ||||||||
\(339\) | −13.8014 | −0.749590 | ||||||||
\(340\) | −0.500932 | −0.0271669 | ||||||||
\(341\) | −16.2168 | −0.878186 | ||||||||
\(342\) | −38.2303 | −2.06726 | ||||||||
\(343\) | −15.1425 | −0.817619 | ||||||||
\(344\) | −15.1395 | −0.816269 | ||||||||
\(345\) | 7.36656 | 0.396602 | ||||||||
\(346\) | 9.98480 | 0.536786 | ||||||||
\(347\) | 9.72141 | 0.521872 | 0.260936 | − | 0.965356i | \(-0.415969\pi\) | ||||
0.260936 | + | 0.965356i | \(0.415969\pi\) | |||||||
\(348\) | 33.0064 | 1.76933 | ||||||||
\(349\) | 2.97097 | 0.159032 | 0.0795162 | − | 0.996834i | \(-0.474662\pi\) | ||||
0.0795162 | + | 0.996834i | \(0.474662\pi\) | |||||||
\(350\) | 6.48890 | 0.346846 | ||||||||
\(351\) | 4.13088 | 0.220490 | ||||||||
\(352\) | −49.9901 | −2.66448 | ||||||||
\(353\) | −20.1012 | −1.06988 | −0.534941 | − | 0.844890i | \(-0.679666\pi\) | ||||
−0.534941 | + | 0.844890i | \(0.679666\pi\) | |||||||
\(354\) | −16.9077 | −0.898634 | ||||||||
\(355\) | 0.632797 | 0.0335854 | ||||||||
\(356\) | −90.0663 | −4.77350 | ||||||||
\(357\) | 0.0537989 | 0.00284734 | ||||||||
\(358\) | −40.7814 | −2.15536 | ||||||||
\(359\) | 5.94631 | 0.313834 | 0.156917 | − | 0.987612i | \(-0.449844\pi\) | ||||
0.156917 | + | 0.987612i | \(0.449844\pi\) | |||||||
\(360\) | 32.7476 | 1.72595 | ||||||||
\(361\) | 16.8050 | 0.884472 | ||||||||
\(362\) | 4.34711 | 0.228479 | ||||||||
\(363\) | −3.17477 | −0.166632 | ||||||||
\(364\) | 6.00826 | 0.314919 | ||||||||
\(365\) | 18.9558 | 0.992193 | ||||||||
\(366\) | 29.3062 | 1.53186 | ||||||||
\(367\) | 24.7077 | 1.28973 | 0.644867 | − | 0.764295i | \(-0.276913\pi\) | ||||
0.644867 | + | 0.764295i | \(0.276913\pi\) | |||||||
\(368\) | −60.6830 | −3.16332 | ||||||||
\(369\) | 29.9086 | 1.55698 | ||||||||
\(370\) | −35.8362 | −1.86303 | ||||||||
\(371\) | 5.01266 | 0.260244 | ||||||||
\(372\) | 15.7984 | 0.819108 | ||||||||
\(373\) | 4.30041 | 0.222667 | 0.111333 | − | 0.993783i | \(-0.464488\pi\) | ||||
0.111333 | + | 0.993783i | \(0.464488\pi\) | |||||||
\(374\) | 0.601259 | 0.0310904 | ||||||||
\(375\) | 9.23445 | 0.476865 | ||||||||
\(376\) | 67.0212 | 3.45636 | ||||||||
\(377\) | −8.70027 | −0.448087 | ||||||||
\(378\) | −13.1729 | −0.677540 | ||||||||
\(379\) | −36.5270 | −1.87627 | −0.938134 | − | 0.346273i | \(-0.887447\pi\) | ||||
−0.938134 | + | 0.346273i | \(0.887447\pi\) | |||||||
\(380\) | −51.2775 | −2.63048 | ||||||||
\(381\) | 11.2432 | 0.576005 | ||||||||
\(382\) | −70.1359 | −3.58846 | ||||||||
\(383\) | −23.8547 | −1.21892 | −0.609459 | − | 0.792818i | \(-0.708613\pi\) | ||||
−0.609459 | + | 0.792818i | \(0.708613\pi\) | |||||||
\(384\) | 5.15500 | 0.263065 | ||||||||
\(385\) | 8.09574 | 0.412597 | ||||||||
\(386\) | 41.8332 | 2.12926 | ||||||||
\(387\) | −4.65785 | −0.236772 | ||||||||
\(388\) | −84.5241 | −4.29106 | ||||||||
\(389\) | −22.1914 | −1.12515 | −0.562575 | − | 0.826746i | \(-0.690189\pi\) | ||||
−0.562575 | + | 0.826746i | \(0.690189\pi\) | |||||||
\(390\) | 3.46719 | 0.175568 | ||||||||
\(391\) | 0.328044 | 0.0165899 | ||||||||
\(392\) | 43.5753 | 2.20089 | ||||||||
\(393\) | 5.25162 | 0.264909 | ||||||||
\(394\) | 1.20338 | 0.0606255 | ||||||||
\(395\) | 21.6592 | 1.08979 | ||||||||
\(396\) | −46.8773 | −2.35567 | ||||||||
\(397\) | −30.2099 | −1.51619 | −0.758096 | − | 0.652143i | \(-0.773870\pi\) | ||||
−0.758096 | + | 0.652143i | \(0.773870\pi\) | |||||||
\(398\) | 42.9370 | 2.15224 | ||||||||
\(399\) | 5.50708 | 0.275699 | ||||||||
\(400\) | −22.0034 | −1.10017 | ||||||||
\(401\) | 11.0603 | 0.552327 | 0.276163 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276163 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(402\) | 5.98984 | 0.298746 | ||||||||
\(403\) | −4.16435 | −0.207441 | ||||||||
\(404\) | −57.7683 | −2.87408 | ||||||||
\(405\) | 7.07316 | 0.351468 | ||||||||
\(406\) | 27.7442 | 1.37692 | ||||||||
\(407\) | 30.6827 | 1.52088 | ||||||||
\(408\) | −0.350347 | −0.0173447 | ||||||||
\(409\) | −7.17152 | −0.354609 | −0.177304 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177304 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(410\) | 56.2377 | 2.77738 | ||||||||
\(411\) | 15.4834 | 0.763737 | ||||||||
\(412\) | 4.97659 | 0.245179 | ||||||||
\(413\) | −10.1379 | −0.498852 | ||||||||
\(414\) | −35.8546 | −1.76216 | ||||||||
\(415\) | 13.4647 | 0.660956 | ||||||||
\(416\) | −12.8371 | −0.629392 | ||||||||
\(417\) | −4.66090 | −0.228245 | ||||||||
\(418\) | 61.5474 | 3.01038 | ||||||||
\(419\) | −5.89661 | −0.288068 | −0.144034 | − | 0.989573i | \(-0.546008\pi\) | ||||
−0.144034 | + | 0.989573i | \(0.546008\pi\) | |||||||
\(420\) | −7.88688 | −0.384840 | ||||||||
\(421\) | 28.3580 | 1.38209 | 0.691043 | − | 0.722814i | \(-0.257152\pi\) | ||||
0.691043 | + | 0.722814i | \(0.257152\pi\) | |||||||
\(422\) | 21.2768 | 1.03574 | ||||||||
\(423\) | 20.6198 | 1.00257 | ||||||||
\(424\) | −32.6432 | −1.58529 | ||||||||
\(425\) | 0.118948 | 0.00576981 | ||||||||
\(426\) | 0.739939 | 0.0358502 | ||||||||
\(427\) | 17.5720 | 0.850369 | ||||||||
\(428\) | −20.2867 | −0.980595 | ||||||||
\(429\) | −2.96858 | −0.143325 | ||||||||
\(430\) | −8.75823 | −0.422359 | ||||||||
\(431\) | 22.8449 | 1.10040 | 0.550201 | − | 0.835032i | \(-0.314551\pi\) | ||||
0.550201 | + | 0.835032i | \(0.314551\pi\) | |||||||
\(432\) | 44.6684 | 2.14911 | ||||||||
\(433\) | −11.4452 | −0.550023 | −0.275011 | − | 0.961441i | \(-0.588682\pi\) | ||||
−0.275011 | + | 0.961441i | \(0.588682\pi\) | |||||||
\(434\) | 13.2796 | 0.637443 | ||||||||
\(435\) | 11.4206 | 0.547576 | ||||||||
\(436\) | −31.2872 | −1.49839 | ||||||||
\(437\) | 33.5800 | 1.60635 | ||||||||
\(438\) | 22.1653 | 1.05910 | ||||||||
\(439\) | 13.8740 | 0.662168 | 0.331084 | − | 0.943601i | \(-0.392586\pi\) | ||||
0.331084 | + | 0.943601i | \(0.392586\pi\) | |||||||
\(440\) | −52.7207 | −2.51336 | ||||||||
\(441\) | 13.4064 | 0.638402 | ||||||||
\(442\) | 0.154399 | 0.00734403 | ||||||||
\(443\) | 20.9100 | 0.993463 | 0.496732 | − | 0.867904i | \(-0.334533\pi\) | ||||
0.496732 | + | 0.867904i | \(0.334533\pi\) | |||||||
\(444\) | −29.8911 | −1.41857 | ||||||||
\(445\) | −31.1640 | −1.47732 | ||||||||
\(446\) | 64.3475 | 3.04694 | ||||||||
\(447\) | −10.6296 | −0.502763 | ||||||||
\(448\) | 14.8262 | 0.700472 | ||||||||
\(449\) | −8.64121 | −0.407804 | −0.203902 | − | 0.978991i | \(-0.565362\pi\) | ||||
−0.203902 | + | 0.978991i | \(0.565362\pi\) | |||||||
\(450\) | −13.0008 | −0.612861 | ||||||||
\(451\) | −48.1502 | −2.26731 | ||||||||
\(452\) | 90.0997 | 4.23793 | ||||||||
\(453\) | 6.17689 | 0.290215 | ||||||||
\(454\) | −54.4403 | −2.55501 | ||||||||
\(455\) | 2.07893 | 0.0974618 | ||||||||
\(456\) | −35.8629 | −1.67944 | ||||||||
\(457\) | −22.3853 | −1.04714 | −0.523569 | − | 0.851983i | \(-0.675400\pi\) | ||||
−0.523569 | + | 0.851983i | \(0.675400\pi\) | |||||||
\(458\) | −33.0633 | −1.54495 | ||||||||
\(459\) | −0.241472 | −0.0112709 | ||||||||
\(460\) | −48.0910 | −2.24226 | ||||||||
\(461\) | −10.3907 | −0.483942 | −0.241971 | − | 0.970284i | \(-0.577794\pi\) | ||||
−0.241971 | + | 0.970284i | \(0.577794\pi\) | |||||||
\(462\) | 9.46646 | 0.440420 | ||||||||
\(463\) | 18.6261 | 0.865627 | 0.432814 | − | 0.901483i | \(-0.357521\pi\) | ||||
0.432814 | + | 0.901483i | \(0.357521\pi\) | |||||||
\(464\) | −94.0787 | −4.36749 | ||||||||
\(465\) | 5.46643 | 0.253500 | ||||||||
\(466\) | 53.6980 | 2.48751 | ||||||||
\(467\) | 28.7158 | 1.32881 | 0.664405 | − | 0.747373i | \(-0.268685\pi\) | ||||
0.664405 | + | 0.747373i | \(0.268685\pi\) | |||||||
\(468\) | −12.0378 | −0.556447 | ||||||||
\(469\) | 3.59151 | 0.165841 | ||||||||
\(470\) | 38.7718 | 1.78841 | ||||||||
\(471\) | 3.51801 | 0.162101 | ||||||||
\(472\) | 66.0193 | 3.03879 | ||||||||
\(473\) | 7.49873 | 0.344792 | ||||||||
\(474\) | 25.3264 | 1.16328 | ||||||||
\(475\) | 12.1760 | 0.558672 | ||||||||
\(476\) | −0.351215 | −0.0160979 | ||||||||
\(477\) | −10.0430 | −0.459839 | ||||||||
\(478\) | 56.4461 | 2.58178 | ||||||||
\(479\) | 4.08885 | 0.186824 | 0.0934122 | − | 0.995628i | \(-0.470223\pi\) | ||||
0.0934122 | + | 0.995628i | \(0.470223\pi\) | |||||||
\(480\) | 16.8509 | 0.769137 | ||||||||
\(481\) | 7.87910 | 0.359256 | ||||||||
\(482\) | −25.1243 | −1.14438 | ||||||||
\(483\) | 5.16486 | 0.235009 | ||||||||
\(484\) | 20.7258 | 0.942081 | ||||||||
\(485\) | −29.2464 | −1.32801 | ||||||||
\(486\) | 41.0037 | 1.85997 | ||||||||
\(487\) | 10.1198 | 0.458573 | 0.229287 | − | 0.973359i | \(-0.426361\pi\) | ||||
0.229287 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(488\) | −114.432 | −5.18007 | ||||||||
\(489\) | −8.70331 | −0.393577 | ||||||||
\(490\) | 25.2083 | 1.13880 | ||||||||
\(491\) | −1.20805 | −0.0545186 | −0.0272593 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272593 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(492\) | 46.9081 | 2.11478 | ||||||||
\(493\) | 0.508577 | 0.0229051 | ||||||||
\(494\) | 15.8050 | 0.711099 | ||||||||
\(495\) | −16.2201 | −0.729040 | ||||||||
\(496\) | −45.0304 | −2.02192 | ||||||||
\(497\) | 0.443668 | 0.0199012 | ||||||||
\(498\) | 15.7445 | 0.705527 | ||||||||
\(499\) | 18.7895 | 0.841134 | 0.420567 | − | 0.907262i | \(-0.361831\pi\) | ||||
0.420567 | + | 0.907262i | \(0.361831\pi\) | |||||||
\(500\) | −60.2852 | −2.69603 | ||||||||
\(501\) | 6.40956 | 0.286358 | ||||||||
\(502\) | 11.8030 | 0.526793 | ||||||||
\(503\) | 34.1846 | 1.52422 | 0.762108 | − | 0.647450i | \(-0.224164\pi\) | ||||
0.762108 | + | 0.647450i | \(0.224164\pi\) | |||||||
\(504\) | 22.9600 | 1.02272 | ||||||||
\(505\) | −19.9885 | −0.889478 | ||||||||
\(506\) | 57.7227 | 2.56609 | ||||||||
\(507\) | −0.762312 | −0.0338555 | ||||||||
\(508\) | −73.3986 | −3.25654 | ||||||||
\(509\) | −5.78374 | −0.256360 | −0.128180 | − | 0.991751i | \(-0.540914\pi\) | ||||
−0.128180 | + | 0.991751i | \(0.540914\pi\) | |||||||
\(510\) | −0.202676 | −0.00897463 | ||||||||
\(511\) | 13.2903 | 0.587930 | ||||||||
\(512\) | 31.2198 | 1.37973 | ||||||||
\(513\) | −24.7180 | −1.09133 | ||||||||
\(514\) | −0.875897 | −0.0386342 | ||||||||
\(515\) | 1.72196 | 0.0758787 | ||||||||
\(516\) | −7.30527 | −0.321597 | ||||||||
\(517\) | −33.1961 | −1.45996 | ||||||||
\(518\) | −25.1255 | −1.10395 | ||||||||
\(519\) | 2.88171 | 0.126493 | ||||||||
\(520\) | −13.5383 | −0.593694 | ||||||||
\(521\) | −32.1466 | −1.40837 | −0.704184 | − | 0.710017i | \(-0.748687\pi\) | ||||
−0.704184 | + | 0.710017i | \(0.748687\pi\) | |||||||
\(522\) | −55.5865 | −2.43295 | ||||||||
\(523\) | 29.9727 | 1.31061 | 0.655306 | − | 0.755363i | \(-0.272540\pi\) | ||||
0.655306 | + | 0.755363i | \(0.272540\pi\) | |||||||
\(524\) | −34.2840 | −1.49771 | ||||||||
\(525\) | 1.87276 | 0.0817340 | ||||||||
\(526\) | −71.0569 | −3.09823 | ||||||||
\(527\) | 0.243428 | 0.0106039 | ||||||||
\(528\) | −32.1002 | −1.39698 | ||||||||
\(529\) | 8.49324 | 0.369271 | ||||||||
\(530\) | −18.8841 | −0.820273 | ||||||||
\(531\) | 20.3116 | 0.881448 | ||||||||
\(532\) | −35.9518 | −1.55871 | ||||||||
\(533\) | −12.3647 | −0.535573 | ||||||||
\(534\) | −36.4405 | −1.57694 | ||||||||
\(535\) | −7.01944 | −0.303477 | ||||||||
\(536\) | −23.3885 | −1.01023 | ||||||||
\(537\) | −11.7699 | −0.507910 | ||||||||
\(538\) | 27.7256 | 1.19533 | ||||||||
\(539\) | −21.5832 | −0.929653 | ||||||||
\(540\) | 35.3996 | 1.52336 | ||||||||
\(541\) | 17.9152 | 0.770233 | 0.385116 | − | 0.922868i | \(-0.374161\pi\) | ||||
0.385116 | + | 0.922868i | \(0.374161\pi\) | |||||||
\(542\) | −20.7981 | −0.893356 | ||||||||
\(543\) | 1.25462 | 0.0538408 | ||||||||
\(544\) | 0.750398 | 0.0321730 | ||||||||
\(545\) | −10.8258 | −0.463724 | ||||||||
\(546\) | 2.43092 | 0.104034 | ||||||||
\(547\) | −17.4198 | −0.744816 | −0.372408 | − | 0.928069i | \(-0.621468\pi\) | ||||
−0.372408 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(548\) | −101.080 | −4.31791 | ||||||||
\(549\) | −35.2062 | −1.50256 | ||||||||
\(550\) | 20.9301 | 0.892461 | ||||||||
\(551\) | 52.0600 | 2.21783 | ||||||||
\(552\) | −33.6343 | −1.43157 | ||||||||
\(553\) | 15.1857 | 0.645764 | ||||||||
\(554\) | 5.66138 | 0.240529 | ||||||||
\(555\) | −10.3427 | −0.439022 | ||||||||
\(556\) | 30.4277 | 1.29042 | ||||||||
\(557\) | −6.33083 | −0.268246 | −0.134123 | − | 0.990965i | \(-0.542822\pi\) | ||||
−0.134123 | + | 0.990965i | \(0.542822\pi\) | |||||||
\(558\) | −26.6062 | −1.12633 | ||||||||
\(559\) | 1.92562 | 0.0814452 | ||||||||
\(560\) | 22.4801 | 0.949958 | ||||||||
\(561\) | 0.173529 | 0.00732641 | ||||||||
\(562\) | 7.52324 | 0.317349 | ||||||||
\(563\) | 15.9403 | 0.671803 | 0.335902 | − | 0.941897i | \(-0.390959\pi\) | ||||
0.335902 | + | 0.941897i | \(0.390959\pi\) | |||||||
\(564\) | 32.3397 | 1.36175 | ||||||||
\(565\) | 31.1756 | 1.31157 | ||||||||
\(566\) | −36.8730 | −1.54989 | ||||||||
\(567\) | 4.95915 | 0.208265 | ||||||||
\(568\) | −2.88923 | −0.121230 | ||||||||
\(569\) | 11.2380 | 0.471123 | 0.235561 | − | 0.971859i | \(-0.424307\pi\) | ||||
0.235561 | + | 0.971859i | \(0.424307\pi\) | |||||||
\(570\) | −20.7467 | −0.868985 | ||||||||
\(571\) | 23.4027 | 0.979372 | 0.489686 | − | 0.871899i | \(-0.337111\pi\) | ||||
0.489686 | + | 0.871899i | \(0.337111\pi\) | |||||||
\(572\) | 19.3798 | 0.810309 | ||||||||
\(573\) | −20.2419 | −0.845618 | ||||||||
\(574\) | 39.4295 | 1.64575 | ||||||||
\(575\) | 11.4193 | 0.476220 | ||||||||
\(576\) | −29.7049 | −1.23770 | ||||||||
\(577\) | −6.07093 | −0.252736 | −0.126368 | − | 0.991983i | \(-0.540332\pi\) | ||||
−0.126368 | + | 0.991983i | \(0.540332\pi\) | |||||||
\(578\) | 44.8935 | 1.86732 | ||||||||
\(579\) | 12.0735 | 0.501757 | ||||||||
\(580\) | −74.5570 | −3.09581 | ||||||||
\(581\) | 9.44040 | 0.391654 | ||||||||
\(582\) | −34.1982 | −1.41756 | ||||||||
\(583\) | 16.1684 | 0.669627 | ||||||||
\(584\) | −86.5487 | −3.58141 | ||||||||
\(585\) | −4.16522 | −0.172211 | ||||||||
\(586\) | −50.9557 | −2.10496 | ||||||||
\(587\) | −35.8925 | −1.48144 | −0.740720 | − | 0.671814i | \(-0.765515\pi\) | ||||
−0.740720 | + | 0.671814i | \(0.765515\pi\) | |||||||
\(588\) | 21.0264 | 0.867113 | ||||||||
\(589\) | 24.9183 | 1.02674 | ||||||||
\(590\) | 38.1922 | 1.57235 | ||||||||
\(591\) | 0.347308 | 0.0142863 | ||||||||
\(592\) | 85.1991 | 3.50166 | ||||||||
\(593\) | −40.8481 | −1.67743 | −0.838715 | − | 0.544571i | \(-0.816692\pi\) | ||||
−0.838715 | + | 0.544571i | \(0.816692\pi\) | |||||||
\(594\) | −42.4894 | −1.74336 | ||||||||
\(595\) | −0.121524 | −0.00498202 | ||||||||
\(596\) | 69.3931 | 2.84245 | ||||||||
\(597\) | 12.3920 | 0.507173 | ||||||||
\(598\) | 14.8228 | 0.606150 | ||||||||
\(599\) | 25.7487 | 1.05206 | 0.526031 | − | 0.850465i | \(-0.323679\pi\) | ||||
0.526031 | + | 0.850465i | \(0.323679\pi\) | |||||||
\(600\) | −12.1957 | −0.497887 | ||||||||
\(601\) | 12.9563 | 0.528500 | 0.264250 | − | 0.964454i | \(-0.414876\pi\) | ||||
0.264250 | + | 0.964454i | \(0.414876\pi\) | |||||||
\(602\) | −6.14058 | −0.250272 | ||||||||
\(603\) | −7.19573 | −0.293033 | ||||||||
\(604\) | −40.3245 | −1.64078 | ||||||||
\(605\) | 7.17137 | 0.291558 | ||||||||
\(606\) | −23.3729 | −0.949458 | ||||||||
\(607\) | 20.1175 | 0.816543 | 0.408271 | − | 0.912861i | \(-0.366132\pi\) | ||||
0.408271 | + | 0.912861i | \(0.366132\pi\) | |||||||
\(608\) | 76.8139 | 3.11521 | ||||||||
\(609\) | 8.00724 | 0.324470 | ||||||||
\(610\) | −66.1987 | −2.68031 | ||||||||
\(611\) | −8.52454 | −0.344866 | ||||||||
\(612\) | 0.703672 | 0.0284442 | ||||||||
\(613\) | −4.19807 | −0.169558 | −0.0847792 | − | 0.996400i | \(-0.527018\pi\) | ||||
−0.0847792 | + | 0.996400i | \(0.527018\pi\) | |||||||
\(614\) | −35.0480 | −1.41442 | ||||||||
\(615\) | 16.2307 | 0.654487 | ||||||||
\(616\) | −36.9636 | −1.48931 | ||||||||
\(617\) | 43.3447 | 1.74499 | 0.872496 | − | 0.488620i | \(-0.162500\pi\) | ||||
0.872496 | + | 0.488620i | \(0.162500\pi\) | |||||||
\(618\) | 2.01351 | 0.0809954 | ||||||||
\(619\) | 0.314554 | 0.0126430 | 0.00632149 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632149 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(620\) | −35.6864 | −1.43320 | ||||||||
\(621\) | −23.1820 | −0.930262 | ||||||||
\(622\) | −16.4767 | −0.660656 | ||||||||
\(623\) | −21.8498 | −0.875393 | ||||||||
\(624\) | −8.24311 | −0.329989 | ||||||||
\(625\) | −10.6851 | −0.427405 | ||||||||
\(626\) | −25.0160 | −0.999842 | ||||||||
\(627\) | 17.7632 | 0.709393 | ||||||||
\(628\) | −22.9666 | −0.916466 | ||||||||
\(629\) | −0.460575 | −0.0183643 | ||||||||
\(630\) | 13.2824 | 0.529183 | ||||||||
\(631\) | 14.6013 | 0.581269 | 0.290634 | − | 0.956834i | \(-0.406134\pi\) | ||||
0.290634 | + | 0.956834i | \(0.406134\pi\) | |||||||
\(632\) | −98.8919 | −3.93371 | ||||||||
\(633\) | 6.14070 | 0.244071 | ||||||||
\(634\) | 30.4169 | 1.20801 | ||||||||
\(635\) | −25.3968 | −1.00784 | ||||||||
\(636\) | −15.7513 | −0.624579 | ||||||||
\(637\) | −5.54242 | −0.219599 | ||||||||
\(638\) | 89.4893 | 3.54291 | ||||||||
\(639\) | −0.888906 | −0.0351646 | ||||||||
\(640\) | −11.6445 | −0.460287 | ||||||||
\(641\) | −38.5844 | −1.52399 | −0.761997 | − | 0.647581i | \(-0.775781\pi\) | ||||
−0.761997 | + | 0.647581i | \(0.775781\pi\) | |||||||
\(642\) | −8.20793 | −0.323941 | ||||||||
\(643\) | −13.4610 | −0.530851 | −0.265426 | − | 0.964131i | \(-0.585512\pi\) | ||||
−0.265426 | + | 0.964131i | \(0.585512\pi\) | |||||||
\(644\) | −33.7177 | −1.32866 | ||||||||
\(645\) | −2.52771 | −0.0995285 | ||||||||
\(646\) | −0.923883 | −0.0363497 | ||||||||
\(647\) | 5.20195 | 0.204510 | 0.102255 | − | 0.994758i | \(-0.467394\pi\) | ||||
0.102255 | + | 0.994758i | \(0.467394\pi\) | |||||||
\(648\) | −32.2947 | −1.26866 | ||||||||
\(649\) | −32.6999 | −1.28358 | ||||||||
\(650\) | 5.37470 | 0.210813 | ||||||||
\(651\) | 3.83263 | 0.150213 | ||||||||
\(652\) | 56.8177 | 2.22515 | ||||||||
\(653\) | −29.3086 | −1.14693 | −0.573466 | − | 0.819229i | \(-0.694402\pi\) | ||||
−0.573466 | + | 0.819229i | \(0.694402\pi\) | |||||||
\(654\) | −12.6587 | −0.494995 | ||||||||
\(655\) | −11.8627 | −0.463514 | ||||||||
\(656\) | −133.703 | −5.22022 | ||||||||
\(657\) | −26.6277 | −1.03885 | ||||||||
\(658\) | 27.1838 | 1.05973 | ||||||||
\(659\) | −30.4381 | −1.18570 | −0.592851 | − | 0.805312i | \(-0.701998\pi\) | ||||
−0.592851 | + | 0.805312i | \(0.701998\pi\) | |||||||
\(660\) | −25.4393 | −0.990222 | ||||||||
\(661\) | −9.51139 | −0.369950 | −0.184975 | − | 0.982743i | \(-0.559220\pi\) | ||||
−0.184975 | + | 0.982743i | \(0.559220\pi\) | |||||||
\(662\) | 26.0948 | 1.01420 | ||||||||
\(663\) | 0.0445612 | 0.00173061 | ||||||||
\(664\) | −61.4773 | −2.38578 | ||||||||
\(665\) | −12.4398 | −0.482393 | ||||||||
\(666\) | 50.3399 | 1.95063 | ||||||||
\(667\) | 48.8249 | 1.89051 | ||||||||
\(668\) | −41.8435 | −1.61897 | ||||||||
\(669\) | 18.5713 | 0.718009 | ||||||||
\(670\) | −13.5303 | −0.522719 | ||||||||
\(671\) | 56.6788 | 2.18806 | ||||||||
\(672\) | 11.8146 | 0.455757 | ||||||||
\(673\) | −15.0736 | −0.581043 | −0.290521 | − | 0.956868i | \(-0.593829\pi\) | ||||
−0.290521 | + | 0.956868i | \(0.593829\pi\) | |||||||
\(674\) | 34.7859 | 1.33990 | ||||||||
\(675\) | −8.40572 | −0.323536 | ||||||||
\(676\) | 4.97659 | 0.191407 | ||||||||
\(677\) | 24.9232 | 0.957875 | 0.478938 | − | 0.877849i | \(-0.341022\pi\) | ||||
0.478938 | + | 0.877849i | \(0.341022\pi\) | |||||||
\(678\) | 36.4540 | 1.40001 | ||||||||
\(679\) | −20.5053 | −0.786920 | ||||||||
\(680\) | 0.791386 | 0.0303483 | ||||||||
\(681\) | −15.7120 | −0.602086 | ||||||||
\(682\) | 42.8337 | 1.64019 | ||||||||
\(683\) | −24.6663 | −0.943831 | −0.471916 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471916 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(684\) | 72.0308 | 2.75417 | ||||||||
\(685\) | −34.9748 | −1.33632 | ||||||||
\(686\) | 39.9963 | 1.52707 | ||||||||
\(687\) | −9.54239 | −0.364065 | ||||||||
\(688\) | 20.8223 | 0.793844 | ||||||||
\(689\) | 4.15194 | 0.158176 | ||||||||
\(690\) | −19.4575 | −0.740734 | ||||||||
\(691\) | −13.5160 | −0.514172 | −0.257086 | − | 0.966389i | \(-0.582762\pi\) | ||||
−0.257086 | + | 0.966389i | \(0.582762\pi\) | |||||||
\(692\) | −18.8126 | −0.715150 | ||||||||
\(693\) | −11.3723 | −0.431997 | ||||||||
\(694\) | −25.6774 | −0.974700 | ||||||||
\(695\) | 10.5283 | 0.399363 | ||||||||
\(696\) | −52.1443 | −1.97653 | ||||||||
\(697\) | 0.722780 | 0.0273772 | ||||||||
\(698\) | −7.84729 | −0.297024 | ||||||||
\(699\) | 15.4978 | 0.586180 | ||||||||
\(700\) | −12.2259 | −0.462096 | ||||||||
\(701\) | 30.4944 | 1.15176 | 0.575879 | − | 0.817535i | \(-0.304660\pi\) | ||||
0.575879 | + | 0.817535i | \(0.304660\pi\) | |||||||
\(702\) | −10.9110 | −0.411809 | ||||||||
\(703\) | −47.1464 | −1.77816 | ||||||||
\(704\) | 47.8222 | 1.80237 | ||||||||
\(705\) | 11.1899 | 0.421437 | ||||||||
\(706\) | 53.0939 | 1.99822 | ||||||||
\(707\) | −14.0144 | −0.527066 | ||||||||
\(708\) | 31.8563 | 1.19723 | ||||||||
\(709\) | 17.0796 | 0.641438 | 0.320719 | − | 0.947174i | \(-0.396075\pi\) | ||||
0.320719 | + | 0.947174i | \(0.396075\pi\) | |||||||
\(710\) | −1.67142 | −0.0627274 | ||||||||
\(711\) | −30.4252 | −1.14103 | ||||||||
\(712\) | 142.289 | 5.33251 | ||||||||
\(713\) | 23.3699 | 0.875209 | ||||||||
\(714\) | −0.142100 | −0.00531797 | ||||||||
\(715\) | 6.70563 | 0.250776 | ||||||||
\(716\) | 76.8374 | 2.87155 | ||||||||
\(717\) | 16.2909 | 0.608395 | ||||||||
\(718\) | −15.7061 | −0.586148 | ||||||||
\(719\) | 25.1709 | 0.938715 | 0.469358 | − | 0.883008i | \(-0.344486\pi\) | ||||
0.469358 | + | 0.883008i | \(0.344486\pi\) | |||||||
\(720\) | −45.0397 | −1.67853 | ||||||||
\(721\) | 1.20730 | 0.0449624 | ||||||||
\(722\) | −44.3874 | −1.65193 | ||||||||
\(723\) | −7.25111 | −0.269672 | ||||||||
\(724\) | −8.19051 | −0.304398 | ||||||||
\(725\) | 17.7038 | 0.657501 | ||||||||
\(726\) | 8.38559 | 0.311218 | ||||||||
\(727\) | 17.4201 | 0.646075 | 0.323038 | − | 0.946386i | \(-0.395296\pi\) | ||||
0.323038 | + | 0.946386i | \(0.395296\pi\) | |||||||
\(728\) | −9.49201 | −0.351797 | ||||||||
\(729\) | −0.488777 | −0.0181028 | ||||||||
\(730\) | −50.0685 | −1.85312 | ||||||||
\(731\) | −0.112563 | −0.00416329 | ||||||||
\(732\) | −55.2166 | −2.04086 | ||||||||
\(733\) | 15.0667 | 0.556502 | 0.278251 | − | 0.960508i | \(-0.410245\pi\) | ||||
0.278251 | + | 0.960508i | \(0.410245\pi\) | |||||||
\(734\) | −65.2612 | −2.40883 | ||||||||
\(735\) | 7.27538 | 0.268356 | ||||||||
\(736\) | 72.0405 | 2.65545 | ||||||||
\(737\) | 11.5845 | 0.426720 | ||||||||
\(738\) | −78.9984 | −2.90797 | ||||||||
\(739\) | −23.3677 | −0.859593 | −0.429797 | − | 0.902926i | \(-0.641415\pi\) | ||||
−0.429797 | + | 0.902926i | \(0.641415\pi\) | |||||||
\(740\) | 67.5200 | 2.48208 | ||||||||
\(741\) | 4.56147 | 0.167570 | ||||||||
\(742\) | −13.2400 | −0.486057 | ||||||||
\(743\) | −14.8019 | −0.543029 | −0.271515 | − | 0.962434i | \(-0.587524\pi\) | ||||
−0.271515 | + | 0.962434i | \(0.587524\pi\) | |||||||
\(744\) | −24.9587 | −0.915030 | ||||||||
\(745\) | 24.0108 | 0.879689 | ||||||||
\(746\) | −11.3588 | −0.415874 | ||||||||
\(747\) | −18.9142 | −0.692034 | ||||||||
\(748\) | −1.13285 | −0.0414211 | ||||||||
\(749\) | −4.92148 | −0.179827 | ||||||||
\(750\) | −24.3912 | −0.890640 | ||||||||
\(751\) | −31.8584 | −1.16253 | −0.581265 | − | 0.813715i | \(-0.697442\pi\) | ||||
−0.581265 | + | 0.813715i | \(0.697442\pi\) | |||||||
\(752\) | −92.1784 | −3.36140 | ||||||||
\(753\) | 3.40646 | 0.124138 | ||||||||
\(754\) | 22.9802 | 0.836891 | ||||||||
\(755\) | −13.9528 | −0.507793 | ||||||||
\(756\) | 24.8194 | 0.902673 | ||||||||
\(757\) | 17.6112 | 0.640088 | 0.320044 | − | 0.947403i | \(-0.396302\pi\) | ||||
0.320044 | + | 0.947403i | \(0.396302\pi\) | |||||||
\(758\) | 96.4797 | 3.50430 | ||||||||
\(759\) | 16.6593 | 0.604696 | ||||||||
\(760\) | 81.0096 | 2.93853 | ||||||||
\(761\) | −15.3209 | −0.555384 | −0.277692 | − | 0.960670i | \(-0.589569\pi\) | ||||
−0.277692 | + | 0.960670i | \(0.589569\pi\) | |||||||
\(762\) | −29.6969 | −1.07580 | ||||||||
\(763\) | −7.59017 | −0.274783 | ||||||||
\(764\) | 132.145 | 4.78084 | ||||||||
\(765\) | 0.243479 | 0.00880300 | ||||||||
\(766\) | 63.0080 | 2.27657 | ||||||||
\(767\) | −8.39711 | −0.303202 | ||||||||
\(768\) | 5.10701 | 0.184283 | ||||||||
\(769\) | 4.30357 | 0.155191 | 0.0775954 | − | 0.996985i | \(-0.475276\pi\) | ||||
0.0775954 | + | 0.996985i | \(0.475276\pi\) | |||||||
\(770\) | −21.3835 | −0.770607 | ||||||||
\(771\) | −0.252793 | −0.00910411 | ||||||||
\(772\) | −78.8192 | −2.83677 | ||||||||
\(773\) | 1.54770 | 0.0556670 | 0.0278335 | − | 0.999613i | \(-0.491139\pi\) | ||||
0.0278335 | + | 0.999613i | \(0.491139\pi\) | |||||||
\(774\) | 12.3029 | 0.442218 | ||||||||
\(775\) | 8.47384 | 0.304389 | ||||||||
\(776\) | 133.533 | 4.79357 | ||||||||
\(777\) | −7.25148 | −0.260145 | ||||||||
\(778\) | 58.6148 | 2.10144 | ||||||||
\(779\) | 73.9867 | 2.65085 | ||||||||
\(780\) | −6.53264 | −0.233906 | ||||||||
\(781\) | 1.43106 | 0.0512073 | ||||||||
\(782\) | −0.866471 | −0.0309849 | ||||||||
\(783\) | −35.9398 | −1.28438 | ||||||||
\(784\) | −59.9318 | −2.14042 | ||||||||
\(785\) | −7.94671 | −0.283630 | ||||||||
\(786\) | −13.8712 | −0.494770 | ||||||||
\(787\) | −8.25042 | −0.294096 | −0.147048 | − | 0.989129i | \(-0.546977\pi\) | ||||
−0.147048 | + | 0.989129i | \(0.546977\pi\) | |||||||
\(788\) | −2.26733 | −0.0807702 | ||||||||
\(789\) | −20.5077 | −0.730094 | ||||||||
\(790\) | −57.2090 | −2.03540 | ||||||||
\(791\) | 21.8579 | 0.777176 | ||||||||
\(792\) | 74.0580 | 2.63154 | ||||||||
\(793\) | 14.5547 | 0.516854 | ||||||||
\(794\) | 79.7942 | 2.83179 | ||||||||
\(795\) | −5.45014 | −0.193296 | ||||||||
\(796\) | −80.8988 | −2.86738 | ||||||||
\(797\) | 36.4560 | 1.29134 | 0.645669 | − | 0.763617i | \(-0.276579\pi\) | ||||
0.645669 | + | 0.763617i | \(0.276579\pi\) | |||||||
\(798\) | −14.5460 | −0.514922 | ||||||||
\(799\) | 0.498304 | 0.0176287 | ||||||||
\(800\) | 26.1216 | 0.923539 | ||||||||
\(801\) | 43.7768 | 1.54678 | ||||||||
\(802\) | −29.2139 | −1.03158 | ||||||||
\(803\) | 42.8682 | 1.51279 | ||||||||
\(804\) | −11.2856 | −0.398014 | ||||||||
\(805\) | −11.6667 | −0.411198 | ||||||||
\(806\) | 10.9994 | 0.387438 | ||||||||
\(807\) | 8.00188 | 0.281679 | ||||||||
\(808\) | 91.2639 | 3.21065 | ||||||||
\(809\) | −34.9356 | −1.22827 | −0.614135 | − | 0.789201i | \(-0.710495\pi\) | ||||
−0.614135 | + | 0.789201i | \(0.710495\pi\) | |||||||
\(810\) | −18.6825 | −0.656436 | ||||||||
\(811\) | 42.5876 | 1.49545 | 0.747727 | − | 0.664006i | \(-0.231145\pi\) | ||||
0.747727 | + | 0.664006i | \(0.231145\pi\) | |||||||
\(812\) | −52.2735 | −1.83444 | ||||||||
\(813\) | −6.00255 | −0.210518 | ||||||||
\(814\) | −81.0428 | −2.84055 | ||||||||
\(815\) | 19.6596 | 0.688646 | ||||||||
\(816\) | 0.481853 | 0.0168682 | ||||||||
\(817\) | −11.5224 | −0.403118 | ||||||||
\(818\) | 18.9423 | 0.662302 | ||||||||
\(819\) | −2.92032 | −0.102044 | ||||||||
\(820\) | −105.959 | −3.70025 | ||||||||
\(821\) | 48.0950 | 1.67853 | 0.839264 | − | 0.543724i | \(-0.182986\pi\) | ||||
0.839264 | + | 0.543724i | \(0.182986\pi\) | |||||||
\(822\) | −40.8965 | −1.42643 | ||||||||
\(823\) | −40.1416 | −1.39925 | −0.699623 | − | 0.714512i | \(-0.746649\pi\) | ||||
−0.699623 | + | 0.714512i | \(0.746649\pi\) | |||||||
\(824\) | −7.86215 | −0.273891 | ||||||||
\(825\) | 6.04062 | 0.210307 | ||||||||
\(826\) | 26.7774 | 0.931705 | ||||||||
\(827\) | −27.6109 | −0.960125 | −0.480062 | − | 0.877234i | \(-0.659386\pi\) | ||||
−0.480062 | + | 0.877234i | \(0.659386\pi\) | |||||||
\(828\) | 67.5546 | 2.34769 | ||||||||
\(829\) | −26.7196 | −0.928011 | −0.464005 | − | 0.885832i | \(-0.653588\pi\) | ||||
−0.464005 | + | 0.885832i | \(0.653588\pi\) | |||||||
\(830\) | −35.5646 | −1.23447 | ||||||||
\(831\) | 1.63393 | 0.0566804 | ||||||||
\(832\) | 12.2804 | 0.425747 | ||||||||
\(833\) | 0.323983 | 0.0112254 | ||||||||
\(834\) | 12.3110 | 0.426293 | ||||||||
\(835\) | −14.4783 | −0.501044 | ||||||||
\(836\) | −115.963 | −4.01067 | ||||||||
\(837\) | −17.2024 | −0.594603 | ||||||||
\(838\) | 15.5749 | 0.538025 | ||||||||
\(839\) | 32.7767 | 1.13158 | 0.565789 | − | 0.824550i | \(-0.308572\pi\) | ||||
0.565789 | + | 0.824550i | \(0.308572\pi\) | |||||||
\(840\) | 12.4599 | 0.429907 | ||||||||
\(841\) | 46.6948 | 1.61016 | ||||||||
\(842\) | −74.9028 | −2.58132 | ||||||||
\(843\) | 2.17128 | 0.0747830 | ||||||||
\(844\) | −40.0882 | −1.37989 | ||||||||
\(845\) | 1.72196 | 0.0592373 | ||||||||
\(846\) | −54.4637 | −1.87250 | ||||||||
\(847\) | 5.02800 | 0.172764 | ||||||||
\(848\) | 44.8962 | 1.54174 | ||||||||
\(849\) | −10.6419 | −0.365230 | ||||||||
\(850\) | −0.314179 | −0.0107763 | ||||||||
\(851\) | −44.2166 | −1.51573 | ||||||||
\(852\) | −1.39414 | −0.0477625 | ||||||||
\(853\) | −27.3084 | −0.935020 | −0.467510 | − | 0.883988i | \(-0.654849\pi\) | ||||
−0.467510 | + | 0.883988i | \(0.654849\pi\) | |||||||
\(854\) | −46.4134 | −1.58823 | ||||||||
\(855\) | 24.9235 | 0.852366 | ||||||||
\(856\) | 32.0494 | 1.09543 | ||||||||
\(857\) | 30.5265 | 1.04277 | 0.521383 | − | 0.853323i | \(-0.325416\pi\) | ||||
0.521383 | + | 0.853323i | \(0.325416\pi\) | |||||||
\(858\) | 7.84099 | 0.267687 | ||||||||
\(859\) | 15.1596 | 0.517240 | 0.258620 | − | 0.965979i | \(-0.416732\pi\) | ||||
0.258620 | + | 0.965979i | \(0.416732\pi\) | |||||||
\(860\) | 16.5016 | 0.562701 | ||||||||
\(861\) | 11.3797 | 0.387820 | ||||||||
\(862\) | −60.3409 | −2.05522 | ||||||||
\(863\) | 9.53717 | 0.324649 | 0.162324 | − | 0.986737i | \(-0.448101\pi\) | ||||
0.162324 | + | 0.986737i | \(0.448101\pi\) | |||||||
\(864\) | −53.0286 | −1.80407 | ||||||||
\(865\) | −6.50940 | −0.221326 | ||||||||
\(866\) | 30.2306 | 1.02728 | ||||||||
\(867\) | 12.9567 | 0.440033 | ||||||||
\(868\) | −25.0205 | −0.849252 | ||||||||
\(869\) | 48.9819 | 1.66160 | ||||||||
\(870\) | −30.1655 | −1.02271 | ||||||||
\(871\) | 2.97482 | 0.100798 | ||||||||
\(872\) | 49.4284 | 1.67386 | ||||||||
\(873\) | 41.0831 | 1.39045 | ||||||||
\(874\) | −88.6956 | −3.00017 | ||||||||
\(875\) | −14.6250 | −0.494414 | ||||||||
\(876\) | −41.7623 | −1.41102 | ||||||||
\(877\) | 26.9268 | 0.909255 | 0.454627 | − | 0.890682i | \(-0.349772\pi\) | ||||
0.454627 | + | 0.890682i | \(0.349772\pi\) | |||||||
\(878\) | −36.6456 | −1.23673 | ||||||||
\(879\) | −14.7063 | −0.496032 | ||||||||
\(880\) | 72.5100 | 2.44431 | ||||||||
\(881\) | 7.53629 | 0.253904 | 0.126952 | − | 0.991909i | \(-0.459481\pi\) | ||||
0.126952 | + | 0.991909i | \(0.459481\pi\) | |||||||
\(882\) | −35.4108 | −1.19234 | ||||||||
\(883\) | 31.2649 | 1.05215 | 0.526074 | − | 0.850439i | \(-0.323664\pi\) | ||||
0.526074 | + | 0.850439i | \(0.323664\pi\) | |||||||
\(884\) | −0.290908 | −0.00978430 | ||||||||
\(885\) | 11.0226 | 0.370522 | ||||||||
\(886\) | −55.2301 | −1.85549 | ||||||||
\(887\) | −3.40037 | −0.114173 | −0.0570866 | − | 0.998369i | \(-0.518181\pi\) | ||||
−0.0570866 | + | 0.998369i | \(0.518181\pi\) | |||||||
\(888\) | 47.2227 | 1.58469 | ||||||||
\(889\) | −17.8063 | −0.597203 | ||||||||
\(890\) | 82.3143 | 2.75918 | ||||||||
\(891\) | 15.9958 | 0.535880 | ||||||||
\(892\) | −121.239 | −4.05938 | ||||||||
\(893\) | 51.0085 | 1.70694 | ||||||||
\(894\) | 28.0762 | 0.939009 | ||||||||
\(895\) | 26.5867 | 0.888694 | ||||||||
\(896\) | −8.16418 | −0.272746 | ||||||||
\(897\) | 4.27801 | 0.142839 | ||||||||
\(898\) | 22.8242 | 0.761654 | ||||||||
\(899\) | 36.2310 | 1.20837 | ||||||||
\(900\) | 24.4951 | 0.816503 | ||||||||
\(901\) | −0.242703 | −0.00808560 | ||||||||
\(902\) | 127.180 | 4.23464 | ||||||||
\(903\) | −1.77223 | −0.0589762 | ||||||||
\(904\) | −142.342 | −4.73422 | ||||||||
\(905\) | −2.83401 | −0.0942058 | ||||||||
\(906\) | −16.3152 | −0.542035 | ||||||||
\(907\) | 35.2903 | 1.17179 | 0.585897 | − | 0.810385i | \(-0.300742\pi\) | ||||
0.585897 | + | 0.810385i | \(0.300742\pi\) | |||||||
\(908\) | 102.573 | 3.40399 | ||||||||
\(909\) | 28.0784 | 0.931301 | ||||||||
\(910\) | −5.49113 | −0.182029 | ||||||||
\(911\) | −36.7498 | −1.21758 | −0.608788 | − | 0.793333i | \(-0.708344\pi\) | ||||
−0.608788 | + | 0.793333i | \(0.708344\pi\) | |||||||
\(912\) | 49.3245 | 1.63330 | ||||||||
\(913\) | 30.4502 | 1.00775 | ||||||||
\(914\) | 59.1268 | 1.95574 | ||||||||
\(915\) | −19.1056 | −0.631612 | ||||||||
\(916\) | 62.2955 | 2.05830 | ||||||||
\(917\) | −8.31719 | −0.274658 | ||||||||
\(918\) | 0.637805 | 0.0210507 | ||||||||
\(919\) | −35.9149 | −1.18472 | −0.592362 | − | 0.805672i | \(-0.701804\pi\) | ||||
−0.592362 | + | 0.805672i | \(0.701804\pi\) | |||||||
\(920\) | 75.9755 | 2.50484 | ||||||||
\(921\) | −10.1152 | −0.333307 | ||||||||
\(922\) | 27.4451 | 0.903857 | ||||||||
\(923\) | 0.367486 | 0.0120960 | ||||||||
\(924\) | −17.8360 | −0.586762 | ||||||||
\(925\) | −16.0328 | −0.527155 | ||||||||
\(926\) | −49.1975 | −1.61673 | ||||||||
\(927\) | −2.41888 | −0.0794464 | ||||||||
\(928\) | 111.687 | 3.66629 | ||||||||
\(929\) | −43.1704 | −1.41637 | −0.708187 | − | 0.706025i | \(-0.750486\pi\) | ||||
−0.708187 | + | 0.706025i | \(0.750486\pi\) | |||||||
\(930\) | −14.4386 | −0.473461 | ||||||||
\(931\) | 33.1643 | 1.08692 | ||||||||
\(932\) | −101.174 | −3.31406 | ||||||||
\(933\) | −4.75535 | −0.155683 | ||||||||
\(934\) | −75.8478 | −2.48181 | ||||||||
\(935\) | −0.391979 | −0.0128191 | ||||||||
\(936\) | 19.0176 | 0.621610 | ||||||||
\(937\) | −38.6169 | −1.26156 | −0.630779 | − | 0.775962i | \(-0.717265\pi\) | ||||
−0.630779 | + | 0.775962i | \(0.717265\pi\) | |||||||
\(938\) | −9.48635 | −0.309740 | ||||||||
\(939\) | −7.21987 | −0.235612 | ||||||||
\(940\) | −73.0511 | −2.38266 | ||||||||
\(941\) | −23.1432 | −0.754446 | −0.377223 | − | 0.926122i | \(-0.623121\pi\) | ||||
−0.377223 | + | 0.926122i | \(0.623121\pi\) | |||||||
\(942\) | −9.29220 | −0.302756 | ||||||||
\(943\) | 69.3891 | 2.25962 | ||||||||
\(944\) | −90.8004 | −2.95530 | ||||||||
\(945\) | 8.58781 | 0.279362 | ||||||||
\(946\) | −19.8066 | −0.643967 | ||||||||
\(947\) | 56.3926 | 1.83251 | 0.916256 | − | 0.400594i | \(-0.131196\pi\) | ||||
0.916256 | + | 0.400594i | \(0.131196\pi\) | |||||||
\(948\) | −47.7182 | −1.54982 | ||||||||
\(949\) | 11.0083 | 0.357344 | ||||||||
\(950\) | −32.1607 | −1.04343 | ||||||||
\(951\) | 8.77861 | 0.284666 | ||||||||
\(952\) | 0.554858 | 0.0179830 | ||||||||
\(953\) | −5.81186 | −0.188265 | −0.0941323 | − | 0.995560i | \(-0.530008\pi\) | ||||
−0.0941323 | + | 0.995560i | \(0.530008\pi\) | |||||||
\(954\) | 26.5269 | 0.858841 | ||||||||
\(955\) | 45.7238 | 1.47959 | ||||||||
\(956\) | −106.352 | −3.43966 | ||||||||
\(957\) | 25.8275 | 0.834884 | ||||||||
\(958\) | −10.8000 | −0.348932 | ||||||||
\(959\) | −24.5216 | −0.791844 | ||||||||
\(960\) | −16.1202 | −0.520276 | ||||||||
\(961\) | −13.6582 | −0.440586 | ||||||||
\(962\) | −20.8113 | −0.670982 | ||||||||
\(963\) | 9.86038 | 0.317746 | ||||||||
\(964\) | 47.3373 | 1.52463 | ||||||||
\(965\) | −27.2724 | −0.877929 | ||||||||
\(966\) | −13.6421 | −0.438926 | ||||||||
\(967\) | 38.5738 | 1.24045 | 0.620224 | − | 0.784425i | \(-0.287042\pi\) | ||||
0.620224 | + | 0.784425i | \(0.287042\pi\) | |||||||
\(968\) | −32.7431 | −1.05240 | ||||||||
\(969\) | −0.266642 | −0.00856577 | ||||||||
\(970\) | 77.2491 | 2.48032 | ||||||||
\(971\) | −30.3351 | −0.973501 | −0.486750 | − | 0.873541i | \(-0.661818\pi\) | ||||
−0.486750 | + | 0.873541i | \(0.661818\pi\) | |||||||
\(972\) | −77.2563 | −2.47800 | ||||||||
\(973\) | 7.38165 | 0.236645 | ||||||||
\(974\) | −26.7298 | −0.856477 | ||||||||
\(975\) | 1.55119 | 0.0496779 | ||||||||
\(976\) | 157.385 | 5.03776 | ||||||||
\(977\) | −50.9220 | −1.62914 | −0.814569 | − | 0.580067i | \(-0.803027\pi\) | ||||
−0.814569 | + | 0.580067i | \(0.803027\pi\) | |||||||
\(978\) | 22.9883 | 0.735083 | ||||||||
\(979\) | −70.4768 | −2.25245 | ||||||||
\(980\) | −47.4957 | −1.51720 | ||||||||
\(981\) | 15.2072 | 0.485529 | ||||||||
\(982\) | 3.19086 | 0.101824 | ||||||||
\(983\) | 40.5055 | 1.29193 | 0.645963 | − | 0.763369i | \(-0.276456\pi\) | ||||
0.645963 | + | 0.763369i | \(0.276456\pi\) | |||||||
\(984\) | −74.1065 | −2.36243 | ||||||||
\(985\) | −0.784522 | −0.0249970 | ||||||||
\(986\) | −1.34332 | −0.0427799 | ||||||||
\(987\) | 7.84550 | 0.249725 | ||||||||
\(988\) | −29.7786 | −0.947383 | ||||||||
\(989\) | −10.8064 | −0.343623 | ||||||||
\(990\) | 42.8426 | 1.36163 | ||||||||
\(991\) | −24.7278 | −0.785504 | −0.392752 | − | 0.919644i | \(-0.628477\pi\) | ||||
−0.392752 | + | 0.919644i | \(0.628477\pi\) | |||||||
\(992\) | 53.4583 | 1.69730 | ||||||||
\(993\) | 7.53121 | 0.238996 | ||||||||
\(994\) | −1.17187 | −0.0371695 | ||||||||
\(995\) | −27.9920 | −0.887405 | ||||||||
\(996\) | −29.6646 | −0.939959 | ||||||||
\(997\) | −10.1884 | −0.322671 | −0.161335 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161335 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(998\) | −49.6292 | −1.57098 | ||||||||
\(999\) | 32.5476 | 1.02976 |
(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 | 1339.2.a.d.1.2 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.d.1.2 | ✓ | 19 | 1.1 | even | 1 | trivial |