Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.62 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09813 | 1.48360 | 0.741800 | − | 0.670621i | \(-0.233972\pi\) | ||||
0.741800 | + | 0.670621i | \(0.233972\pi\) | |||||||
\(3\) | 1.29704 | 0.748846 | 0.374423 | − | 0.927258i | \(-0.377841\pi\) | ||||
0.374423 | + | 0.927258i | \(0.377841\pi\) | |||||||
\(4\) | 2.40214 | 1.20107 | ||||||||
\(5\) | 1.04726 | 0.468351 | 0.234176 | − | 0.972194i | \(-0.424761\pi\) | ||||
0.234176 | + | 0.972194i | \(0.424761\pi\) | |||||||
\(6\) | 2.72135 | 1.11099 | ||||||||
\(7\) | −4.44368 | −1.67955 | −0.839776 | − | 0.542933i | \(-0.817314\pi\) | ||||
−0.839776 | + | 0.542933i | \(0.817314\pi\) | |||||||
\(8\) | 0.843733 | 0.298305 | ||||||||
\(9\) | −1.31769 | −0.439229 | ||||||||
\(10\) | 2.19729 | 0.694846 | ||||||||
\(11\) | 2.24351 | 0.676445 | 0.338223 | − | 0.941066i | \(-0.390174\pi\) | ||||
0.338223 | + | 0.941066i | \(0.390174\pi\) | |||||||
\(12\) | 3.11567 | 0.899415 | ||||||||
\(13\) | −6.49092 | −1.80026 | −0.900129 | − | 0.435623i | \(-0.856528\pi\) | ||||
−0.900129 | + | 0.435623i | \(0.856528\pi\) | |||||||
\(14\) | −9.32340 | −2.49178 | ||||||||
\(15\) | 1.35834 | 0.350723 | ||||||||
\(16\) | −3.03401 | −0.758503 | ||||||||
\(17\) | 0.862835 | 0.209268 | 0.104634 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104634 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(18\) | −2.76468 | −0.651641 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.51567 | 0.562522 | ||||||||
\(21\) | −5.76363 | −1.25773 | ||||||||
\(22\) | 4.70718 | 1.00357 | ||||||||
\(23\) | 0.555918 | 0.115917 | 0.0579585 | − | 0.998319i | \(-0.481541\pi\) | ||||
0.0579585 | + | 0.998319i | \(0.481541\pi\) | |||||||
\(24\) | 1.09436 | 0.223384 | ||||||||
\(25\) | −3.90324 | −0.780647 | ||||||||
\(26\) | −13.6188 | −2.67086 | ||||||||
\(27\) | −5.60021 | −1.07776 | ||||||||
\(28\) | −10.6743 | −2.01726 | ||||||||
\(29\) | −3.63048 | −0.674162 | −0.337081 | − | 0.941476i | \(-0.609440\pi\) | ||||
−0.337081 | + | 0.941476i | \(0.609440\pi\) | |||||||
\(30\) | 2.84998 | 0.520332 | ||||||||
\(31\) | 2.77163 | 0.497799 | 0.248899 | − | 0.968529i | \(-0.419931\pi\) | ||||
0.248899 | + | 0.968529i | \(0.419931\pi\) | |||||||
\(32\) | −8.05321 | −1.42362 | ||||||||
\(33\) | 2.90993 | 0.506553 | ||||||||
\(34\) | 1.81034 | 0.310470 | ||||||||
\(35\) | −4.65371 | −0.786620 | ||||||||
\(36\) | −3.16527 | −0.527545 | ||||||||
\(37\) | −2.37924 | −0.391144 | −0.195572 | − | 0.980689i | \(-0.562656\pi\) | ||||
−0.195572 | + | 0.980689i | \(0.562656\pi\) | |||||||
\(38\) | 2.09813 | 0.340361 | ||||||||
\(39\) | −8.41898 | −1.34812 | ||||||||
\(40\) | 0.883612 | 0.139711 | ||||||||
\(41\) | −6.25508 | −0.976879 | −0.488439 | − | 0.872598i | \(-0.662434\pi\) | ||||
−0.488439 | + | 0.872598i | \(0.662434\pi\) | |||||||
\(42\) | −12.0928 | −1.86596 | ||||||||
\(43\) | 4.44636 | 0.678063 | 0.339032 | − | 0.940775i | \(-0.389901\pi\) | ||||
0.339032 | + | 0.940775i | \(0.389901\pi\) | |||||||
\(44\) | 5.38923 | 0.812457 | ||||||||
\(45\) | −1.37997 | −0.205714 | ||||||||
\(46\) | 1.16639 | 0.171974 | ||||||||
\(47\) | 6.66058 | 0.971546 | 0.485773 | − | 0.874085i | \(-0.338538\pi\) | ||||
0.485773 | + | 0.874085i | \(0.338538\pi\) | |||||||
\(48\) | −3.93524 | −0.568002 | ||||||||
\(49\) | 12.7463 | 1.82090 | ||||||||
\(50\) | −8.18949 | −1.15817 | ||||||||
\(51\) | 1.11913 | 0.156710 | ||||||||
\(52\) | −15.5921 | −2.16223 | ||||||||
\(53\) | −8.77722 | −1.20564 | −0.602822 | − | 0.797876i | \(-0.705957\pi\) | ||||
−0.602822 | + | 0.797876i | \(0.705957\pi\) | |||||||
\(54\) | −11.7500 | −1.59897 | ||||||||
\(55\) | 2.34955 | 0.316814 | ||||||||
\(56\) | −3.74928 | −0.501018 | ||||||||
\(57\) | 1.29704 | 0.171797 | ||||||||
\(58\) | −7.61720 | −1.00019 | ||||||||
\(59\) | 1.01193 | 0.131742 | 0.0658711 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658711 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(60\) | 3.26293 | 0.421242 | ||||||||
\(61\) | −10.1469 | −1.29918 | −0.649588 | − | 0.760286i | \(-0.725059\pi\) | ||||
−0.649588 | + | 0.760286i | \(0.725059\pi\) | |||||||
\(62\) | 5.81523 | 0.738534 | ||||||||
\(63\) | 5.85538 | 0.737709 | ||||||||
\(64\) | −10.8286 | −1.35358 | ||||||||
\(65\) | −6.79771 | −0.843153 | ||||||||
\(66\) | 6.10540 | 0.751522 | ||||||||
\(67\) | 13.2545 | 1.61930 | 0.809650 | − | 0.586912i | \(-0.199657\pi\) | ||||
0.809650 | + | 0.586912i | \(0.199657\pi\) | |||||||
\(68\) | 2.07265 | 0.251345 | ||||||||
\(69\) | 0.721048 | 0.0868040 | ||||||||
\(70\) | −9.76407 | −1.16703 | ||||||||
\(71\) | 5.89404 | 0.699494 | 0.349747 | − | 0.936844i | \(-0.386268\pi\) | ||||
0.349747 | + | 0.936844i | \(0.386268\pi\) | |||||||
\(72\) | −1.11178 | −0.131024 | ||||||||
\(73\) | 4.79546 | 0.561266 | 0.280633 | − | 0.959815i | \(-0.409456\pi\) | ||||
0.280633 | + | 0.959815i | \(0.409456\pi\) | |||||||
\(74\) | −4.99194 | −0.580301 | ||||||||
\(75\) | −5.06265 | −0.584585 | ||||||||
\(76\) | 2.40214 | 0.275544 | ||||||||
\(77\) | −9.96945 | −1.13612 | ||||||||
\(78\) | −17.6641 | −2.00006 | ||||||||
\(79\) | 0.749154 | 0.0842865 | 0.0421432 | − | 0.999112i | \(-0.486581\pi\) | ||||
0.0421432 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(80\) | −3.17742 | −0.355246 | ||||||||
\(81\) | −3.31063 | −0.367848 | ||||||||
\(82\) | −13.1239 | −1.44930 | ||||||||
\(83\) | 8.32026 | 0.913267 | 0.456634 | − | 0.889655i | \(-0.349055\pi\) | ||||
0.456634 | + | 0.889655i | \(0.349055\pi\) | |||||||
\(84\) | −13.8450 | −1.51062 | ||||||||
\(85\) | 0.903617 | 0.0980110 | ||||||||
\(86\) | 9.32902 | 1.00597 | ||||||||
\(87\) | −4.70887 | −0.504844 | ||||||||
\(88\) | 1.89293 | 0.201787 | ||||||||
\(89\) | −3.92777 | −0.416343 | −0.208172 | − | 0.978092i | \(-0.566751\pi\) | ||||
−0.208172 | + | 0.978092i | \(0.566751\pi\) | |||||||
\(90\) | −2.89535 | −0.305197 | ||||||||
\(91\) | 28.8436 | 3.02363 | ||||||||
\(92\) | 1.33539 | 0.139224 | ||||||||
\(93\) | 3.59491 | 0.372775 | ||||||||
\(94\) | 13.9747 | 1.44138 | ||||||||
\(95\) | 1.04726 | 0.107447 | ||||||||
\(96\) | −10.4453 | −1.06607 | ||||||||
\(97\) | −9.57864 | −0.972564 | −0.486282 | − | 0.873802i | \(-0.661647\pi\) | ||||
−0.486282 | + | 0.873802i | \(0.661647\pi\) | |||||||
\(98\) | 26.7433 | 2.70148 | ||||||||
\(99\) | −2.95625 | −0.297115 | ||||||||
\(100\) | −9.37611 | −0.937611 | ||||||||
\(101\) | −5.98188 | −0.595219 | −0.297610 | − | 0.954688i | \(-0.596189\pi\) | ||||
−0.297610 | + | 0.954688i | \(0.596189\pi\) | |||||||
\(102\) | 2.34808 | 0.232495 | ||||||||
\(103\) | 1.75148 | 0.172579 | 0.0862893 | − | 0.996270i | \(-0.472499\pi\) | ||||
0.0862893 | + | 0.996270i | \(0.472499\pi\) | |||||||
\(104\) | −5.47661 | −0.537025 | ||||||||
\(105\) | −6.03604 | −0.589057 | ||||||||
\(106\) | −18.4157 | −1.78869 | ||||||||
\(107\) | −12.6277 | −1.22076 | −0.610381 | − | 0.792108i | \(-0.708984\pi\) | ||||
−0.610381 | + | 0.792108i | \(0.708984\pi\) | |||||||
\(108\) | −13.4525 | −1.29446 | ||||||||
\(109\) | −7.70014 | −0.737540 | −0.368770 | − | 0.929521i | \(-0.620221\pi\) | ||||
−0.368770 | + | 0.929521i | \(0.620221\pi\) | |||||||
\(110\) | 4.92966 | 0.470025 | ||||||||
\(111\) | −3.08596 | −0.292907 | ||||||||
\(112\) | 13.4822 | 1.27395 | ||||||||
\(113\) | 15.5042 | 1.45851 | 0.729256 | − | 0.684241i | \(-0.239866\pi\) | ||||
0.729256 | + | 0.684241i | \(0.239866\pi\) | |||||||
\(114\) | 2.72135 | 0.254878 | ||||||||
\(115\) | 0.582194 | 0.0542898 | ||||||||
\(116\) | −8.72090 | −0.809715 | ||||||||
\(117\) | 8.55301 | 0.790726 | ||||||||
\(118\) | 2.12316 | 0.195453 | ||||||||
\(119\) | −3.83416 | −0.351477 | ||||||||
\(120\) | 1.14608 | 0.104622 | ||||||||
\(121\) | −5.96664 | −0.542422 | ||||||||
\(122\) | −21.2895 | −1.92746 | ||||||||
\(123\) | −8.11308 | −0.731532 | ||||||||
\(124\) | 6.65783 | 0.597890 | ||||||||
\(125\) | −9.32405 | −0.833968 | ||||||||
\(126\) | 12.2853 | 1.09446 | ||||||||
\(127\) | −22.1737 | −1.96759 | −0.983797 | − | 0.179287i | \(-0.942621\pi\) | ||||
−0.983797 | + | 0.179287i | \(0.942621\pi\) | |||||||
\(128\) | −6.61342 | −0.584549 | ||||||||
\(129\) | 5.76710 | 0.507765 | ||||||||
\(130\) | −14.2625 | −1.25090 | ||||||||
\(131\) | 5.35571 | 0.467931 | 0.233965 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233965 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(132\) | 6.99004 | 0.608405 | ||||||||
\(133\) | −4.44368 | −0.385316 | ||||||||
\(134\) | 27.8097 | 2.40239 | ||||||||
\(135\) | −5.86491 | −0.504771 | ||||||||
\(136\) | 0.728003 | 0.0624257 | ||||||||
\(137\) | 16.8479 | 1.43942 | 0.719709 | − | 0.694276i | \(-0.244275\pi\) | ||||
0.719709 | + | 0.694276i | \(0.244275\pi\) | |||||||
\(138\) | 1.51285 | 0.128782 | ||||||||
\(139\) | −1.71682 | −0.145618 | −0.0728092 | − | 0.997346i | \(-0.523196\pi\) | ||||
−0.0728092 | + | 0.997346i | \(0.523196\pi\) | |||||||
\(140\) | −11.1788 | −0.944784 | ||||||||
\(141\) | 8.63904 | 0.727538 | ||||||||
\(142\) | 12.3665 | 1.03777 | ||||||||
\(143\) | −14.5625 | −1.21778 | ||||||||
\(144\) | 3.99788 | 0.333157 | ||||||||
\(145\) | −3.80207 | −0.315745 | ||||||||
\(146\) | 10.0615 | 0.832695 | ||||||||
\(147\) | 16.5324 | 1.36357 | ||||||||
\(148\) | −5.71525 | −0.469790 | ||||||||
\(149\) | −9.81425 | −0.804015 | −0.402007 | − | 0.915636i | \(-0.631687\pi\) | ||||
−0.402007 | + | 0.915636i | \(0.631687\pi\) | |||||||
\(150\) | −10.6221 | −0.867290 | ||||||||
\(151\) | −1.90938 | −0.155383 | −0.0776915 | − | 0.996977i | \(-0.524755\pi\) | ||||
−0.0776915 | + | 0.996977i | \(0.524755\pi\) | |||||||
\(152\) | 0.843733 | 0.0684358 | ||||||||
\(153\) | −1.13695 | −0.0919168 | ||||||||
\(154\) | −20.9172 | −1.68555 | ||||||||
\(155\) | 2.90263 | 0.233145 | ||||||||
\(156\) | −20.2235 | −1.61918 | ||||||||
\(157\) | 15.4067 | 1.22959 | 0.614793 | − | 0.788689i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788689i | \(0.289240\pi\) | |||||||
\(158\) | 1.57182 | 0.125047 | ||||||||
\(159\) | −11.3844 | −0.902842 | ||||||||
\(160\) | −8.43385 | −0.666754 | ||||||||
\(161\) | −2.47032 | −0.194689 | ||||||||
\(162\) | −6.94613 | −0.545739 | ||||||||
\(163\) | −0.0626218 | −0.00490492 | −0.00245246 | − | 0.999997i | \(-0.500781\pi\) | ||||
−0.00245246 | + | 0.999997i | \(0.500781\pi\) | |||||||
\(164\) | −15.0255 | −1.17330 | ||||||||
\(165\) | 3.04746 | 0.237245 | ||||||||
\(166\) | 17.4570 | 1.35492 | ||||||||
\(167\) | 3.12383 | 0.241729 | 0.120864 | − | 0.992669i | \(-0.461433\pi\) | ||||
0.120864 | + | 0.992669i | \(0.461433\pi\) | |||||||
\(168\) | −4.86296 | −0.375186 | ||||||||
\(169\) | 29.1321 | 2.24093 | ||||||||
\(170\) | 1.89590 | 0.145409 | ||||||||
\(171\) | −1.31769 | −0.100766 | ||||||||
\(172\) | 10.6808 | 0.814400 | ||||||||
\(173\) | 5.99542 | 0.455824 | 0.227912 | − | 0.973682i | \(-0.426810\pi\) | ||||
0.227912 | + | 0.973682i | \(0.426810\pi\) | |||||||
\(174\) | −9.87981 | −0.748986 | ||||||||
\(175\) | 17.3447 | 1.31114 | ||||||||
\(176\) | −6.80685 | −0.513086 | ||||||||
\(177\) | 1.31252 | 0.0986547 | ||||||||
\(178\) | −8.24097 | −0.617687 | ||||||||
\(179\) | 14.1110 | 1.05471 | 0.527354 | − | 0.849646i | \(-0.323184\pi\) | ||||
0.527354 | + | 0.849646i | \(0.323184\pi\) | |||||||
\(180\) | −3.31487 | −0.247076 | ||||||||
\(181\) | −24.7124 | −1.83685 | −0.918427 | − | 0.395590i | \(-0.870540\pi\) | ||||
−0.918427 | + | 0.395590i | \(0.870540\pi\) | |||||||
\(182\) | 60.5175 | 4.48585 | ||||||||
\(183\) | −13.1609 | −0.972883 | ||||||||
\(184\) | 0.469047 | 0.0345786 | ||||||||
\(185\) | −2.49169 | −0.183193 | ||||||||
\(186\) | 7.54258 | 0.553049 | ||||||||
\(187\) | 1.93578 | 0.141558 | ||||||||
\(188\) | 15.9996 | 1.16689 | ||||||||
\(189\) | 24.8855 | 1.81016 | ||||||||
\(190\) | 2.19729 | 0.159408 | ||||||||
\(191\) | −0.0355414 | −0.00257168 | −0.00128584 | − | 0.999999i | \(-0.500409\pi\) | ||||
−0.00128584 | + | 0.999999i | \(0.500409\pi\) | |||||||
\(192\) | −14.0452 | −1.01362 | ||||||||
\(193\) | −22.6374 | −1.62948 | −0.814739 | − | 0.579828i | \(-0.803120\pi\) | ||||
−0.814739 | + | 0.579828i | \(0.803120\pi\) | |||||||
\(194\) | −20.0972 | −1.44289 | ||||||||
\(195\) | −8.81691 | −0.631392 | ||||||||
\(196\) | 30.6183 | 2.18702 | ||||||||
\(197\) | 15.6341 | 1.11388 | 0.556942 | − | 0.830551i | \(-0.311975\pi\) | ||||
0.556942 | + | 0.830551i | \(0.311975\pi\) | |||||||
\(198\) | −6.20259 | −0.440799 | ||||||||
\(199\) | −20.7116 | −1.46821 | −0.734104 | − | 0.679037i | \(-0.762398\pi\) | ||||
−0.734104 | + | 0.679037i | \(0.762398\pi\) | |||||||
\(200\) | −3.29329 | −0.232871 | ||||||||
\(201\) | 17.1917 | 1.21261 | ||||||||
\(202\) | −12.5507 | −0.883067 | ||||||||
\(203\) | 16.1327 | 1.13229 | ||||||||
\(204\) | 2.68831 | 0.188219 | ||||||||
\(205\) | −6.55072 | −0.457522 | ||||||||
\(206\) | 3.67483 | 0.256038 | ||||||||
\(207\) | −0.732527 | −0.0509141 | ||||||||
\(208\) | 19.6935 | 1.36550 | ||||||||
\(209\) | 2.24351 | 0.155187 | ||||||||
\(210\) | −12.6644 | −0.873926 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −21.0841 | −1.44806 | ||||||||
\(213\) | 7.64481 | 0.523814 | ||||||||
\(214\) | −26.4944 | −1.81112 | ||||||||
\(215\) | 4.65652 | 0.317572 | ||||||||
\(216\) | −4.72509 | −0.321501 | ||||||||
\(217\) | −12.3162 | −0.836079 | ||||||||
\(218\) | −16.1559 | −1.09421 | ||||||||
\(219\) | 6.21990 | 0.420302 | ||||||||
\(220\) | 5.64395 | 0.380515 | ||||||||
\(221\) | −5.60060 | −0.376737 | ||||||||
\(222\) | −6.47474 | −0.434556 | ||||||||
\(223\) | −14.6037 | −0.977939 | −0.488969 | − | 0.872301i | \(-0.662627\pi\) | ||||
−0.488969 | + | 0.872301i | \(0.662627\pi\) | |||||||
\(224\) | 35.7859 | 2.39104 | ||||||||
\(225\) | 5.14325 | 0.342883 | ||||||||
\(226\) | 32.5298 | 2.16385 | ||||||||
\(227\) | 9.00004 | 0.597354 | 0.298677 | − | 0.954354i | \(-0.403455\pi\) | ||||
0.298677 | + | 0.954354i | \(0.403455\pi\) | |||||||
\(228\) | 3.11567 | 0.206340 | ||||||||
\(229\) | 18.6656 | 1.23345 | 0.616727 | − | 0.787177i | \(-0.288458\pi\) | ||||
0.616727 | + | 0.787177i | \(0.288458\pi\) | |||||||
\(230\) | 1.22152 | 0.0805444 | ||||||||
\(231\) | −12.9308 | −0.850783 | ||||||||
\(232\) | −3.06315 | −0.201106 | ||||||||
\(233\) | 0.777953 | 0.0509654 | 0.0254827 | − | 0.999675i | \(-0.491888\pi\) | ||||
0.0254827 | + | 0.999675i | \(0.491888\pi\) | |||||||
\(234\) | 17.9453 | 1.17312 | ||||||||
\(235\) | 6.97539 | 0.455024 | ||||||||
\(236\) | 2.43080 | 0.158231 | ||||||||
\(237\) | 0.971683 | 0.0631176 | ||||||||
\(238\) | −8.04456 | −0.521451 | ||||||||
\(239\) | 22.8760 | 1.47972 | 0.739862 | − | 0.672758i | \(-0.234891\pi\) | ||||
0.739862 | + | 0.672758i | \(0.234891\pi\) | |||||||
\(240\) | −4.12123 | −0.266025 | ||||||||
\(241\) | −9.49697 | −0.611754 | −0.305877 | − | 0.952071i | \(-0.598950\pi\) | ||||
−0.305877 | + | 0.952071i | \(0.598950\pi\) | |||||||
\(242\) | −12.5188 | −0.804737 | ||||||||
\(243\) | 12.5066 | 0.802300 | ||||||||
\(244\) | −24.3742 | −1.56040 | ||||||||
\(245\) | 13.3487 | 0.852819 | ||||||||
\(246\) | −17.0223 | −1.08530 | ||||||||
\(247\) | −6.49092 | −0.413008 | ||||||||
\(248\) | 2.33851 | 0.148496 | ||||||||
\(249\) | 10.7917 | 0.683897 | ||||||||
\(250\) | −19.5630 | −1.23727 | ||||||||
\(251\) | −0.187156 | −0.0118132 | −0.00590658 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590658 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(252\) | 14.0654 | 0.886039 | ||||||||
\(253\) | 1.24721 | 0.0784115 | ||||||||
\(254\) | −46.5231 | −2.91912 | ||||||||
\(255\) | 1.17203 | 0.0733952 | ||||||||
\(256\) | 7.78147 | 0.486342 | ||||||||
\(257\) | 20.2010 | 1.26010 | 0.630051 | − | 0.776554i | \(-0.283034\pi\) | ||||
0.630051 | + | 0.776554i | \(0.283034\pi\) | |||||||
\(258\) | 12.1001 | 0.753320 | ||||||||
\(259\) | 10.5726 | 0.656947 | ||||||||
\(260\) | −16.3290 | −1.01268 | ||||||||
\(261\) | 4.78383 | 0.296112 | ||||||||
\(262\) | 11.2370 | 0.694222 | ||||||||
\(263\) | −5.53122 | −0.341070 | −0.170535 | − | 0.985352i | \(-0.554550\pi\) | ||||
−0.170535 | + | 0.985352i | \(0.554550\pi\) | |||||||
\(264\) | 2.45520 | 0.151107 | ||||||||
\(265\) | −9.19207 | −0.564665 | ||||||||
\(266\) | −9.32340 | −0.571654 | ||||||||
\(267\) | −5.09448 | −0.311777 | ||||||||
\(268\) | 31.8392 | 1.94489 | ||||||||
\(269\) | 7.80601 | 0.475941 | 0.237970 | − | 0.971272i | \(-0.423518\pi\) | ||||
0.237970 | + | 0.971272i | \(0.423518\pi\) | |||||||
\(270\) | −12.3053 | −0.748878 | ||||||||
\(271\) | −1.28339 | −0.0779601 | −0.0389801 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389801 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(272\) | −2.61785 | −0.158731 | ||||||||
\(273\) | 37.4112 | 2.26423 | ||||||||
\(274\) | 35.3491 | 2.13552 | ||||||||
\(275\) | −8.75697 | −0.528065 | ||||||||
\(276\) | 1.73206 | 0.104257 | ||||||||
\(277\) | −23.4206 | −1.40721 | −0.703603 | − | 0.710593i | \(-0.748427\pi\) | ||||
−0.703603 | + | 0.710593i | \(0.748427\pi\) | |||||||
\(278\) | −3.60210 | −0.216040 | ||||||||
\(279\) | −3.65214 | −0.218648 | ||||||||
\(280\) | −3.92649 | −0.234653 | ||||||||
\(281\) | 2.16613 | 0.129220 | 0.0646102 | − | 0.997911i | \(-0.479420\pi\) | ||||
0.0646102 | + | 0.997911i | \(0.479420\pi\) | |||||||
\(282\) | 18.1258 | 1.07938 | ||||||||
\(283\) | −13.4163 | −0.797515 | −0.398757 | − | 0.917057i | \(-0.630558\pi\) | ||||
−0.398757 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(284\) | 14.1583 | 0.840140 | ||||||||
\(285\) | 1.35834 | 0.0804614 | ||||||||
\(286\) | −30.5539 | −1.80669 | ||||||||
\(287\) | 27.7955 | 1.64072 | ||||||||
\(288\) | 10.6116 | 0.625296 | ||||||||
\(289\) | −16.2555 | −0.956207 | ||||||||
\(290\) | −7.97722 | −0.468439 | ||||||||
\(291\) | −12.4239 | −0.728300 | ||||||||
\(292\) | 11.5194 | 0.674119 | ||||||||
\(293\) | −20.9770 | −1.22549 | −0.612745 | − | 0.790281i | \(-0.709935\pi\) | ||||
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(294\) | 34.6871 | 2.02299 | ||||||||
\(295\) | 1.05976 | 0.0617016 | ||||||||
\(296\) | −2.00744 | −0.116680 | ||||||||
\(297\) | −12.5642 | −0.729046 | ||||||||
\(298\) | −20.5915 | −1.19284 | ||||||||
\(299\) | −3.60842 | −0.208680 | ||||||||
\(300\) | −12.1612 | −0.702126 | ||||||||
\(301\) | −19.7582 | −1.13884 | ||||||||
\(302\) | −4.00612 | −0.230526 | ||||||||
\(303\) | −7.75873 | −0.445728 | ||||||||
\(304\) | −3.03401 | −0.174013 | ||||||||
\(305\) | −10.6265 | −0.608470 | ||||||||
\(306\) | −2.38546 | −0.136368 | ||||||||
\(307\) | −25.0664 | −1.43062 | −0.715309 | − | 0.698809i | \(-0.753714\pi\) | ||||
−0.715309 | + | 0.698809i | \(0.753714\pi\) | |||||||
\(308\) | −23.9480 | −1.36456 | ||||||||
\(309\) | 2.27174 | 0.129235 | ||||||||
\(310\) | 6.09008 | 0.345893 | ||||||||
\(311\) | −20.4264 | −1.15827 | −0.579137 | − | 0.815230i | \(-0.696611\pi\) | ||||
−0.579137 | + | 0.815230i | \(0.696611\pi\) | |||||||
\(312\) | −7.10338 | −0.402149 | ||||||||
\(313\) | −13.0662 | −0.738547 | −0.369273 | − | 0.929321i | \(-0.620393\pi\) | ||||
−0.369273 | + | 0.929321i | \(0.620393\pi\) | |||||||
\(314\) | 32.3251 | 1.82421 | ||||||||
\(315\) | 6.13214 | 0.345507 | ||||||||
\(316\) | 1.79957 | 0.101234 | ||||||||
\(317\) | 5.77241 | 0.324211 | 0.162105 | − | 0.986773i | \(-0.448172\pi\) | ||||
0.162105 | + | 0.986773i | \(0.448172\pi\) | |||||||
\(318\) | −23.8859 | −1.33946 | ||||||||
\(319\) | −8.14502 | −0.456034 | ||||||||
\(320\) | −11.3404 | −0.633950 | ||||||||
\(321\) | −16.3786 | −0.914163 | ||||||||
\(322\) | −5.18305 | −0.288840 | ||||||||
\(323\) | 0.862835 | 0.0480094 | ||||||||
\(324\) | −7.95259 | −0.441811 | ||||||||
\(325\) | 25.3356 | 1.40537 | ||||||||
\(326\) | −0.131389 | −0.00727694 | ||||||||
\(327\) | −9.98739 | −0.552304 | ||||||||
\(328\) | −5.27761 | −0.291408 | ||||||||
\(329\) | −29.5975 | −1.63176 | ||||||||
\(330\) | 6.39397 | 0.351976 | ||||||||
\(331\) | −34.6799 | −1.90618 | −0.953090 | − | 0.302688i | \(-0.902116\pi\) | ||||
−0.953090 | + | 0.302688i | \(0.902116\pi\) | |||||||
\(332\) | 19.9864 | 1.09690 | ||||||||
\(333\) | 3.13509 | 0.171802 | ||||||||
\(334\) | 6.55418 | 0.358629 | ||||||||
\(335\) | 13.8810 | 0.758401 | ||||||||
\(336\) | 17.4869 | 0.953990 | ||||||||
\(337\) | −17.0961 | −0.931283 | −0.465641 | − | 0.884974i | \(-0.654176\pi\) | ||||
−0.465641 | + | 0.884974i | \(0.654176\pi\) | |||||||
\(338\) | 61.1228 | 3.32464 | ||||||||
\(339\) | 20.1095 | 1.09220 | ||||||||
\(340\) | 2.17061 | 0.117718 | ||||||||
\(341\) | 6.21819 | 0.336734 | ||||||||
\(342\) | −2.76468 | −0.149497 | ||||||||
\(343\) | −25.5346 | −1.37874 | ||||||||
\(344\) | 3.75154 | 0.202270 | ||||||||
\(345\) | 0.755128 | 0.0406547 | ||||||||
\(346\) | 12.5792 | 0.676260 | ||||||||
\(347\) | 19.2223 | 1.03191 | 0.515955 | − | 0.856616i | \(-0.327437\pi\) | ||||
0.515955 | + | 0.856616i | \(0.327437\pi\) | |||||||
\(348\) | −11.3113 | −0.606352 | ||||||||
\(349\) | 30.7423 | 1.64560 | 0.822800 | − | 0.568331i | \(-0.192411\pi\) | ||||
0.822800 | + | 0.568331i | \(0.192411\pi\) | |||||||
\(350\) | 36.3914 | 1.94520 | ||||||||
\(351\) | 36.3505 | 1.94025 | ||||||||
\(352\) | −18.0675 | −0.963001 | ||||||||
\(353\) | 30.4596 | 1.62120 | 0.810600 | − | 0.585600i | \(-0.199141\pi\) | ||||
0.810600 | + | 0.585600i | \(0.199141\pi\) | |||||||
\(354\) | 2.75382 | 0.146364 | ||||||||
\(355\) | 6.17262 | 0.327609 | ||||||||
\(356\) | −9.43505 | −0.500057 | ||||||||
\(357\) | −4.97306 | −0.263202 | ||||||||
\(358\) | 29.6067 | 1.56477 | ||||||||
\(359\) | 12.6836 | 0.669415 | 0.334708 | − | 0.942322i | \(-0.391362\pi\) | ||||
0.334708 | + | 0.942322i | \(0.391362\pi\) | |||||||
\(360\) | −1.16433 | −0.0613653 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −51.8496 | −2.72516 | ||||||||
\(363\) | −7.73897 | −0.406191 | ||||||||
\(364\) | 69.2862 | 3.63158 | ||||||||
\(365\) | 5.02212 | 0.262870 | ||||||||
\(366\) | −27.6133 | −1.44337 | ||||||||
\(367\) | 13.2861 | 0.693531 | 0.346766 | − | 0.937952i | \(-0.387280\pi\) | ||||
0.346766 | + | 0.937952i | \(0.387280\pi\) | |||||||
\(368\) | −1.68666 | −0.0879234 | ||||||||
\(369\) | 8.24224 | 0.429074 | ||||||||
\(370\) | −5.22788 | −0.271785 | ||||||||
\(371\) | 39.0031 | 2.02494 | ||||||||
\(372\) | 8.63546 | 0.447728 | ||||||||
\(373\) | 10.7372 | 0.555952 | 0.277976 | − | 0.960588i | \(-0.410337\pi\) | ||||
0.277976 | + | 0.960588i | \(0.410337\pi\) | |||||||
\(374\) | 4.06152 | 0.210016 | ||||||||
\(375\) | −12.0937 | −0.624514 | ||||||||
\(376\) | 5.61975 | 0.289817 | ||||||||
\(377\) | 23.5651 | 1.21367 | ||||||||
\(378\) | 52.2130 | 2.68555 | ||||||||
\(379\) | 2.77982 | 0.142790 | 0.0713950 | − | 0.997448i | \(-0.477255\pi\) | ||||
0.0713950 | + | 0.997448i | \(0.477255\pi\) | |||||||
\(380\) | 2.51567 | 0.129051 | ||||||||
\(381\) | −28.7601 | −1.47342 | ||||||||
\(382\) | −0.0745703 | −0.00381535 | ||||||||
\(383\) | −0.345409 | −0.0176496 | −0.00882478 | − | 0.999961i | \(-0.502809\pi\) | ||||
−0.00882478 | + | 0.999961i | \(0.502809\pi\) | |||||||
\(384\) | −8.57787 | −0.437738 | ||||||||
\(385\) | −10.4407 | −0.532105 | ||||||||
\(386\) | −47.4962 | −2.41749 | ||||||||
\(387\) | −5.85891 | −0.297825 | ||||||||
\(388\) | −23.0092 | −1.16812 | ||||||||
\(389\) | −3.14417 | −0.159416 | −0.0797079 | − | 0.996818i | \(-0.525399\pi\) | ||||
−0.0797079 | + | 0.996818i | \(0.525399\pi\) | |||||||
\(390\) | −18.4990 | −0.936733 | ||||||||
\(391\) | 0.479666 | 0.0242577 | ||||||||
\(392\) | 10.7545 | 0.543182 | ||||||||
\(393\) | 6.94657 | 0.350408 | ||||||||
\(394\) | 32.8023 | 1.65256 | ||||||||
\(395\) | 0.784563 | 0.0394756 | ||||||||
\(396\) | −7.10132 | −0.356855 | ||||||||
\(397\) | 17.0151 | 0.853963 | 0.426982 | − | 0.904260i | \(-0.359577\pi\) | ||||
0.426982 | + | 0.904260i | \(0.359577\pi\) | |||||||
\(398\) | −43.4556 | −2.17823 | ||||||||
\(399\) | −5.76363 | −0.288542 | ||||||||
\(400\) | 11.8425 | 0.592124 | ||||||||
\(401\) | 1.84999 | 0.0923841 | 0.0461921 | − | 0.998933i | \(-0.485291\pi\) | ||||
0.0461921 | + | 0.998933i | \(0.485291\pi\) | |||||||
\(402\) | 36.0703 | 1.79902 | ||||||||
\(403\) | −17.9904 | −0.896167 | ||||||||
\(404\) | −14.3693 | −0.714899 | ||||||||
\(405\) | −3.46711 | −0.172282 | ||||||||
\(406\) | 33.8484 | 1.67987 | ||||||||
\(407\) | −5.33785 | −0.264587 | ||||||||
\(408\) | 0.944248 | 0.0467473 | ||||||||
\(409\) | −0.703759 | −0.0347986 | −0.0173993 | − | 0.999849i | \(-0.505539\pi\) | ||||
−0.0173993 | + | 0.999849i | \(0.505539\pi\) | |||||||
\(410\) | −13.7442 | −0.678780 | ||||||||
\(411\) | 21.8525 | 1.07790 | ||||||||
\(412\) | 4.20730 | 0.207279 | ||||||||
\(413\) | −4.49670 | −0.221268 | ||||||||
\(414\) | −1.53693 | −0.0755362 | ||||||||
\(415\) | 8.71352 | 0.427730 | ||||||||
\(416\) | 52.2728 | 2.56288 | ||||||||
\(417\) | −2.22678 | −0.109046 | ||||||||
\(418\) | 4.70718 | 0.230236 | ||||||||
\(419\) | 30.9871 | 1.51382 | 0.756909 | − | 0.653520i | \(-0.226708\pi\) | ||||
0.756909 | + | 0.653520i | \(0.226708\pi\) | |||||||
\(420\) | −14.4994 | −0.707498 | ||||||||
\(421\) | −6.04667 | −0.294696 | −0.147348 | − | 0.989085i | \(-0.547074\pi\) | ||||
−0.147348 | + | 0.989085i | \(0.547074\pi\) | |||||||
\(422\) | 2.09813 | 0.102135 | ||||||||
\(423\) | −8.77657 | −0.426731 | ||||||||
\(424\) | −7.40563 | −0.359649 | ||||||||
\(425\) | −3.36785 | −0.163365 | ||||||||
\(426\) | 16.0398 | 0.777130 | ||||||||
\(427\) | 45.0895 | 2.18203 | ||||||||
\(428\) | −30.3334 | −1.46622 | ||||||||
\(429\) | −18.8881 | −0.911927 | ||||||||
\(430\) | 9.76996 | 0.471149 | ||||||||
\(431\) | 7.43875 | 0.358312 | 0.179156 | − | 0.983821i | \(-0.442663\pi\) | ||||
0.179156 | + | 0.983821i | \(0.442663\pi\) | |||||||
\(432\) | 16.9911 | 0.817486 | ||||||||
\(433\) | −7.50896 | −0.360858 | −0.180429 | − | 0.983588i | \(-0.557749\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557749\pi\) | |||||||
\(434\) | −25.8410 | −1.24041 | ||||||||
\(435\) | −4.93143 | −0.236444 | ||||||||
\(436\) | −18.4968 | −0.885835 | ||||||||
\(437\) | 0.555918 | 0.0265932 | ||||||||
\(438\) | 13.0501 | 0.623560 | ||||||||
\(439\) | −6.96888 | −0.332607 | −0.166303 | − | 0.986075i | \(-0.553183\pi\) | ||||
−0.166303 | + | 0.986075i | \(0.553183\pi\) | |||||||
\(440\) | 1.98240 | 0.0945070 | ||||||||
\(441\) | −16.7956 | −0.799791 | ||||||||
\(442\) | −11.7508 | −0.558927 | ||||||||
\(443\) | −2.64701 | −0.125763 | −0.0628816 | − | 0.998021i | \(-0.520029\pi\) | ||||
−0.0628816 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(444\) | −7.41290 | −0.351801 | ||||||||
\(445\) | −4.11342 | −0.194995 | ||||||||
\(446\) | −30.6405 | −1.45087 | ||||||||
\(447\) | −12.7295 | −0.602083 | ||||||||
\(448\) | 48.1190 | 2.27341 | ||||||||
\(449\) | −32.3865 | −1.52841 | −0.764206 | − | 0.644972i | \(-0.776869\pi\) | ||||
−0.764206 | + | 0.644972i | \(0.776869\pi\) | |||||||
\(450\) | 10.7912 | 0.508702 | ||||||||
\(451\) | −14.0334 | −0.660805 | ||||||||
\(452\) | 37.2432 | 1.75177 | ||||||||
\(453\) | −2.47654 | −0.116358 | ||||||||
\(454\) | 18.8832 | 0.886234 | ||||||||
\(455\) | 30.2069 | 1.41612 | ||||||||
\(456\) | 1.09436 | 0.0512479 | ||||||||
\(457\) | −32.3720 | −1.51430 | −0.757148 | − | 0.653243i | \(-0.773408\pi\) | ||||
−0.757148 | + | 0.653243i | \(0.773408\pi\) | |||||||
\(458\) | 39.1627 | 1.82995 | ||||||||
\(459\) | −4.83206 | −0.225541 | ||||||||
\(460\) | 1.39851 | 0.0652058 | ||||||||
\(461\) | 4.80178 | 0.223641 | 0.111821 | − | 0.993728i | \(-0.464332\pi\) | ||||
0.111821 | + | 0.993728i | \(0.464332\pi\) | |||||||
\(462\) | −27.1304 | −1.26222 | ||||||||
\(463\) | −23.2991 | −1.08280 | −0.541399 | − | 0.840766i | \(-0.682105\pi\) | ||||
−0.541399 | + | 0.840766i | \(0.682105\pi\) | |||||||
\(464\) | 11.0149 | 0.511354 | ||||||||
\(465\) | 3.76482 | 0.174589 | ||||||||
\(466\) | 1.63224 | 0.0756123 | ||||||||
\(467\) | −23.6997 | −1.09669 | −0.548345 | − | 0.836252i | \(-0.684742\pi\) | ||||
−0.548345 | + | 0.836252i | \(0.684742\pi\) | |||||||
\(468\) | 20.5455 | 0.949716 | ||||||||
\(469\) | −58.8989 | −2.71970 | ||||||||
\(470\) | 14.6353 | 0.675074 | ||||||||
\(471\) | 19.9830 | 0.920770 | ||||||||
\(472\) | 0.853800 | 0.0392993 | ||||||||
\(473\) | 9.97547 | 0.458673 | ||||||||
\(474\) | 2.03871 | 0.0936412 | ||||||||
\(475\) | −3.90324 | −0.179093 | ||||||||
\(476\) | −9.21018 | −0.422148 | ||||||||
\(477\) | 11.5656 | 0.529554 | ||||||||
\(478\) | 47.9967 | 2.19532 | ||||||||
\(479\) | −21.3331 | −0.974735 | −0.487367 | − | 0.873197i | \(-0.662043\pi\) | ||||
−0.487367 | + | 0.873197i | \(0.662043\pi\) | |||||||
\(480\) | −10.9390 | −0.499296 | ||||||||
\(481\) | 15.4434 | 0.704160 | ||||||||
\(482\) | −19.9259 | −0.907598 | ||||||||
\(483\) | −3.20410 | −0.145792 | ||||||||
\(484\) | −14.3327 | −0.651486 | ||||||||
\(485\) | −10.0314 | −0.455501 | ||||||||
\(486\) | 26.2405 | 1.19029 | ||||||||
\(487\) | 4.37734 | 0.198356 | 0.0991781 | − | 0.995070i | \(-0.468379\pi\) | ||||
0.0991781 | + | 0.995070i | \(0.468379\pi\) | |||||||
\(488\) | −8.56127 | −0.387550 | ||||||||
\(489\) | −0.0812230 | −0.00367303 | ||||||||
\(490\) | 28.0073 | 1.26524 | ||||||||
\(491\) | −2.63593 | −0.118958 | −0.0594788 | − | 0.998230i | \(-0.518944\pi\) | ||||
−0.0594788 | + | 0.998230i | \(0.518944\pi\) | |||||||
\(492\) | −19.4887 | −0.878620 | ||||||||
\(493\) | −3.13250 | −0.141081 | ||||||||
\(494\) | −13.6188 | −0.612738 | ||||||||
\(495\) | −3.09598 | −0.139154 | ||||||||
\(496\) | −8.40915 | −0.377582 | ||||||||
\(497\) | −26.1912 | −1.17484 | ||||||||
\(498\) | 22.6424 | 1.01463 | ||||||||
\(499\) | 18.8424 | 0.843500 | 0.421750 | − | 0.906712i | \(-0.361416\pi\) | ||||
0.421750 | + | 0.906712i | \(0.361416\pi\) | |||||||
\(500\) | −22.3976 | −1.00165 | ||||||||
\(501\) | 4.05173 | 0.181018 | ||||||||
\(502\) | −0.392676 | −0.0175260 | ||||||||
\(503\) | −21.7574 | −0.970113 | −0.485056 | − | 0.874483i | \(-0.661201\pi\) | ||||
−0.485056 | + | 0.874483i | \(0.661201\pi\) | |||||||
\(504\) | 4.94038 | 0.220062 | ||||||||
\(505\) | −6.26461 | −0.278772 | ||||||||
\(506\) | 2.61681 | 0.116331 | ||||||||
\(507\) | 37.7855 | 1.67811 | ||||||||
\(508\) | −53.2641 | −2.36321 | ||||||||
\(509\) | −19.8113 | −0.878121 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(510\) | 2.45906 | 0.108889 | ||||||||
\(511\) | −21.3095 | −0.942676 | ||||||||
\(512\) | 29.5533 | 1.30609 | ||||||||
\(513\) | −5.60021 | −0.247255 | ||||||||
\(514\) | 42.3842 | 1.86949 | ||||||||
\(515\) | 1.83427 | 0.0808274 | ||||||||
\(516\) | 13.8534 | 0.609861 | ||||||||
\(517\) | 14.9431 | 0.657197 | ||||||||
\(518\) | 22.1826 | 0.974646 | ||||||||
\(519\) | 7.77630 | 0.341342 | ||||||||
\(520\) | −5.73546 | −0.251516 | ||||||||
\(521\) | 11.3441 | 0.496994 | 0.248497 | − | 0.968633i | \(-0.420063\pi\) | ||||
0.248497 | + | 0.968633i | \(0.420063\pi\) | |||||||
\(522\) | 10.0371 | 0.439312 | ||||||||
\(523\) | −10.3078 | −0.450728 | −0.225364 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225364 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(524\) | 12.8652 | 0.562017 | ||||||||
\(525\) | 22.4968 | 0.981841 | ||||||||
\(526\) | −11.6052 | −0.506011 | ||||||||
\(527\) | 2.39146 | 0.104174 | ||||||||
\(528\) | −8.82876 | −0.384222 | ||||||||
\(529\) | −22.6910 | −0.986563 | ||||||||
\(530\) | −19.2861 | −0.837736 | ||||||||
\(531\) | −1.33341 | −0.0578651 | ||||||||
\(532\) | −10.6743 | −0.462790 | ||||||||
\(533\) | 40.6012 | 1.75863 | ||||||||
\(534\) | −10.6889 | −0.462552 | ||||||||
\(535\) | −13.2245 | −0.571745 | ||||||||
\(536\) | 11.1833 | 0.483045 | ||||||||
\(537\) | 18.3026 | 0.789814 | ||||||||
\(538\) | 16.3780 | 0.706106 | ||||||||
\(539\) | 28.5964 | 1.23174 | ||||||||
\(540\) | −14.0883 | −0.606264 | ||||||||
\(541\) | 24.8746 | 1.06944 | 0.534721 | − | 0.845029i | \(-0.320417\pi\) | ||||
0.534721 | + | 0.845029i | \(0.320417\pi\) | |||||||
\(542\) | −2.69271 | −0.115662 | ||||||||
\(543\) | −32.0529 | −1.37552 | ||||||||
\(544\) | −6.94859 | −0.297918 | ||||||||
\(545\) | −8.06409 | −0.345427 | ||||||||
\(546\) | 78.4935 | 3.35921 | ||||||||
\(547\) | −19.2194 | −0.821761 | −0.410881 | − | 0.911689i | \(-0.634779\pi\) | ||||
−0.410881 | + | 0.911689i | \(0.634779\pi\) | |||||||
\(548\) | 40.4711 | 1.72884 | ||||||||
\(549\) | 13.3704 | 0.570636 | ||||||||
\(550\) | −18.3732 | −0.783437 | ||||||||
\(551\) | −3.63048 | −0.154663 | ||||||||
\(552\) | 0.608372 | 0.0258940 | ||||||||
\(553\) | −3.32900 | −0.141564 | ||||||||
\(554\) | −49.1393 | −2.08773 | ||||||||
\(555\) | −3.23182 | −0.137183 | ||||||||
\(556\) | −4.12403 | −0.174898 | ||||||||
\(557\) | −8.97320 | −0.380207 | −0.190103 | − | 0.981764i | \(-0.560882\pi\) | ||||
−0.190103 | + | 0.981764i | \(0.560882\pi\) | |||||||
\(558\) | −7.66265 | −0.324386 | ||||||||
\(559\) | −28.8610 | −1.22069 | ||||||||
\(560\) | 14.1194 | 0.596654 | ||||||||
\(561\) | 2.51079 | 0.106006 | ||||||||
\(562\) | 4.54481 | 0.191711 | ||||||||
\(563\) | −27.4628 | −1.15742 | −0.578710 | − | 0.815534i | \(-0.696443\pi\) | ||||
−0.578710 | + | 0.815534i | \(0.696443\pi\) | |||||||
\(564\) | 20.7521 | 0.873823 | ||||||||
\(565\) | 16.2370 | 0.683095 | ||||||||
\(566\) | −28.1490 | −1.18319 | ||||||||
\(567\) | 14.7114 | 0.617820 | ||||||||
\(568\) | 4.97300 | 0.208662 | ||||||||
\(569\) | −29.6879 | −1.24458 | −0.622291 | − | 0.782786i | \(-0.713798\pi\) | ||||
−0.622291 | + | 0.782786i | \(0.713798\pi\) | |||||||
\(570\) | 2.84998 | 0.119372 | ||||||||
\(571\) | −35.5672 | −1.48844 | −0.744220 | − | 0.667935i | \(-0.767179\pi\) | ||||
−0.744220 | + | 0.667935i | \(0.767179\pi\) | |||||||
\(572\) | −34.9811 | −1.46263 | ||||||||
\(573\) | −0.0460986 | −0.00192580 | ||||||||
\(574\) | 58.3186 | 2.43417 | ||||||||
\(575\) | −2.16988 | −0.0904903 | ||||||||
\(576\) | 14.2688 | 0.594532 | ||||||||
\(577\) | −32.0389 | −1.33380 | −0.666898 | − | 0.745149i | \(-0.732378\pi\) | ||||
−0.666898 | + | 0.745149i | \(0.732378\pi\) | |||||||
\(578\) | −34.1061 | −1.41863 | ||||||||
\(579\) | −29.3616 | −1.22023 | ||||||||
\(580\) | −9.13309 | −0.379231 | ||||||||
\(581\) | −36.9726 | −1.53388 | ||||||||
\(582\) | −26.0669 | −1.08051 | ||||||||
\(583\) | −19.6918 | −0.815552 | ||||||||
\(584\) | 4.04609 | 0.167428 | ||||||||
\(585\) | 8.95727 | 0.370338 | ||||||||
\(586\) | −44.0124 | −1.81814 | ||||||||
\(587\) | −2.08587 | −0.0860929 | −0.0430465 | − | 0.999073i | \(-0.513706\pi\) | ||||
−0.0430465 | + | 0.999073i | \(0.513706\pi\) | |||||||
\(588\) | 39.7131 | 1.63774 | ||||||||
\(589\) | 2.77163 | 0.114203 | ||||||||
\(590\) | 2.22351 | 0.0915405 | ||||||||
\(591\) | 20.2781 | 0.834128 | ||||||||
\(592\) | 7.21863 | 0.296684 | ||||||||
\(593\) | 39.3869 | 1.61743 | 0.808713 | − | 0.588203i | \(-0.200165\pi\) | ||||
0.808713 | + | 0.588203i | \(0.200165\pi\) | |||||||
\(594\) | −26.3612 | −1.08161 | ||||||||
\(595\) | −4.01538 | −0.164615 | ||||||||
\(596\) | −23.5752 | −0.965677 | ||||||||
\(597\) | −26.8638 | −1.09946 | ||||||||
\(598\) | −7.57093 | −0.309598 | ||||||||
\(599\) | 10.2820 | 0.420109 | 0.210055 | − | 0.977690i | \(-0.432636\pi\) | ||||
0.210055 | + | 0.977690i | \(0.432636\pi\) | |||||||
\(600\) | −4.27153 | −0.174384 | ||||||||
\(601\) | 1.57055 | 0.0640639 | 0.0320320 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320320 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(602\) | −41.4552 | −1.68959 | ||||||||
\(603\) | −17.4654 | −0.711245 | ||||||||
\(604\) | −4.58659 | −0.186626 | ||||||||
\(605\) | −6.24866 | −0.254044 | ||||||||
\(606\) | −16.2788 | −0.661281 | ||||||||
\(607\) | 9.66958 | 0.392476 | 0.196238 | − | 0.980556i | \(-0.437127\pi\) | ||||
0.196238 | + | 0.980556i | \(0.437127\pi\) | |||||||
\(608\) | −8.05321 | −0.326601 | ||||||||
\(609\) | 20.9247 | 0.847912 | ||||||||
\(610\) | −22.2957 | −0.902727 | ||||||||
\(611\) | −43.2333 | −1.74903 | ||||||||
\(612\) | −2.73110 | −0.110398 | ||||||||
\(613\) | 22.0410 | 0.890229 | 0.445114 | − | 0.895474i | \(-0.353163\pi\) | ||||
0.445114 | + | 0.895474i | \(0.353163\pi\) | |||||||
\(614\) | −52.5926 | −2.12246 | ||||||||
\(615\) | −8.49654 | −0.342614 | ||||||||
\(616\) | −8.41156 | −0.338911 | ||||||||
\(617\) | −20.8105 | −0.837797 | −0.418899 | − | 0.908033i | \(-0.637584\pi\) | ||||
−0.418899 | + | 0.908033i | \(0.637584\pi\) | |||||||
\(618\) | 4.76640 | 0.191733 | ||||||||
\(619\) | 2.59263 | 0.104206 | 0.0521032 | − | 0.998642i | \(-0.483408\pi\) | ||||
0.0521032 | + | 0.998642i | \(0.483408\pi\) | |||||||
\(620\) | 6.97251 | 0.280023 | ||||||||
\(621\) | −3.11326 | −0.124931 | ||||||||
\(622\) | −42.8572 | −1.71842 | ||||||||
\(623\) | 17.4538 | 0.699270 | ||||||||
\(624\) | 25.5433 | 1.02255 | ||||||||
\(625\) | 9.75144 | 0.390057 | ||||||||
\(626\) | −27.4146 | −1.09571 | ||||||||
\(627\) | 2.90993 | 0.116211 | ||||||||
\(628\) | 37.0089 | 1.47682 | ||||||||
\(629\) | −2.05289 | −0.0818540 | ||||||||
\(630\) | 12.8660 | 0.512594 | ||||||||
\(631\) | −32.4017 | −1.28989 | −0.644946 | − | 0.764228i | \(-0.723120\pi\) | ||||
−0.644946 | + | 0.764228i | \(0.723120\pi\) | |||||||
\(632\) | 0.632086 | 0.0251430 | ||||||||
\(633\) | 1.29704 | 0.0515527 | ||||||||
\(634\) | 12.1112 | 0.480999 | ||||||||
\(635\) | −23.2217 | −0.921525 | ||||||||
\(636\) | −27.3469 | −1.08437 | ||||||||
\(637\) | −82.7351 | −3.27808 | ||||||||
\(638\) | −17.0893 | −0.676572 | ||||||||
\(639\) | −7.76651 | −0.307238 | ||||||||
\(640\) | −6.92600 | −0.273774 | ||||||||
\(641\) | 37.7273 | 1.49014 | 0.745069 | − | 0.666987i | \(-0.232416\pi\) | ||||
0.745069 | + | 0.666987i | \(0.232416\pi\) | |||||||
\(642\) | −34.3643 | −1.35625 | ||||||||
\(643\) | 27.3168 | 1.07727 | 0.538635 | − | 0.842539i | \(-0.318940\pi\) | ||||
0.538635 | + | 0.842539i | \(0.318940\pi\) | |||||||
\(644\) | −5.93405 | −0.233834 | ||||||||
\(645\) | 6.03968 | 0.237812 | ||||||||
\(646\) | 1.81034 | 0.0712268 | ||||||||
\(647\) | −26.5713 | −1.04462 | −0.522312 | − | 0.852754i | \(-0.674930\pi\) | ||||
−0.522312 | + | 0.852754i | \(0.674930\pi\) | |||||||
\(648\) | −2.79329 | −0.109731 | ||||||||
\(649\) | 2.27028 | 0.0891164 | ||||||||
\(650\) | 53.1573 | 2.08500 | ||||||||
\(651\) | −15.9746 | −0.626095 | ||||||||
\(652\) | −0.150426 | −0.00589114 | ||||||||
\(653\) | 39.0140 | 1.52674 | 0.763368 | − | 0.645964i | \(-0.223545\pi\) | ||||
0.763368 | + | 0.645964i | \(0.223545\pi\) | |||||||
\(654\) | −20.9548 | −0.819398 | ||||||||
\(655\) | 5.60885 | 0.219156 | ||||||||
\(656\) | 18.9780 | 0.740966 | ||||||||
\(657\) | −6.31892 | −0.246525 | ||||||||
\(658\) | −62.0993 | −2.42088 | ||||||||
\(659\) | −2.95550 | −0.115130 | −0.0575649 | − | 0.998342i | \(-0.518334\pi\) | ||||
−0.0575649 | + | 0.998342i | \(0.518334\pi\) | |||||||
\(660\) | 7.32042 | 0.284947 | ||||||||
\(661\) | −27.9159 | −1.08580 | −0.542902 | − | 0.839796i | \(-0.682674\pi\) | ||||
−0.542902 | + | 0.839796i | \(0.682674\pi\) | |||||||
\(662\) | −72.7628 | −2.82801 | ||||||||
\(663\) | −7.26419 | −0.282118 | ||||||||
\(664\) | 7.02008 | 0.272432 | ||||||||
\(665\) | −4.65371 | −0.180463 | ||||||||
\(666\) | 6.57782 | 0.254885 | ||||||||
\(667\) | −2.01825 | −0.0781469 | ||||||||
\(668\) | 7.50386 | 0.290333 | ||||||||
\(669\) | −18.9416 | −0.732326 | ||||||||
\(670\) | 29.1241 | 1.12516 | ||||||||
\(671\) | −22.7647 | −0.878821 | ||||||||
\(672\) | 46.4157 | 1.79052 | ||||||||
\(673\) | 38.2268 | 1.47353 | 0.736767 | − | 0.676146i | \(-0.236351\pi\) | ||||
0.736767 | + | 0.676146i | \(0.236351\pi\) | |||||||
\(674\) | −35.8697 | −1.38165 | ||||||||
\(675\) | 21.8590 | 0.841352 | ||||||||
\(676\) | 69.9792 | 2.69151 | ||||||||
\(677\) | −46.1987 | −1.77556 | −0.887780 | − | 0.460268i | \(-0.847753\pi\) | ||||
−0.887780 | + | 0.460268i | \(0.847753\pi\) | |||||||
\(678\) | 42.1924 | 1.62039 | ||||||||
\(679\) | 42.5644 | 1.63347 | ||||||||
\(680\) | 0.762412 | 0.0292371 | ||||||||
\(681\) | 11.6734 | 0.447326 | ||||||||
\(682\) | 13.0465 | 0.499578 | ||||||||
\(683\) | −33.2989 | −1.27415 | −0.637074 | − | 0.770803i | \(-0.719855\pi\) | ||||
−0.637074 | + | 0.770803i | \(0.719855\pi\) | |||||||
\(684\) | −3.16527 | −0.121027 | ||||||||
\(685\) | 17.6443 | 0.674153 | ||||||||
\(686\) | −53.5748 | −2.04549 | ||||||||
\(687\) | 24.2100 | 0.923668 | ||||||||
\(688\) | −13.4903 | −0.514313 | ||||||||
\(689\) | 56.9723 | 2.17047 | ||||||||
\(690\) | 1.58435 | 0.0603154 | ||||||||
\(691\) | 10.6975 | 0.406952 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(692\) | 14.4018 | 0.547475 | ||||||||
\(693\) | 13.1366 | 0.499019 | ||||||||
\(694\) | 40.3309 | 1.53094 | ||||||||
\(695\) | −1.79796 | −0.0682006 | ||||||||
\(696\) | −3.97303 | −0.150597 | ||||||||
\(697\) | −5.39710 | −0.204430 | ||||||||
\(698\) | 64.5013 | 2.44141 | ||||||||
\(699\) | 1.00904 | 0.0381653 | ||||||||
\(700\) | 41.6644 | 1.57477 | ||||||||
\(701\) | 13.4978 | 0.509804 | 0.254902 | − | 0.966967i | \(-0.417957\pi\) | ||||
0.254902 | + | 0.966967i | \(0.417957\pi\) | |||||||
\(702\) | 76.2681 | 2.87855 | ||||||||
\(703\) | −2.37924 | −0.0897346 | ||||||||
\(704\) | −24.2942 | −0.915622 | ||||||||
\(705\) | 9.04736 | 0.340743 | ||||||||
\(706\) | 63.9081 | 2.40521 | ||||||||
\(707\) | 26.5815 | 0.999702 | ||||||||
\(708\) | 3.15284 | 0.118491 | ||||||||
\(709\) | 29.4137 | 1.10466 | 0.552328 | − | 0.833627i | \(-0.313740\pi\) | ||||
0.552328 | + | 0.833627i | \(0.313740\pi\) | |||||||
\(710\) | 12.9509 | 0.486040 | ||||||||
\(711\) | −0.987152 | −0.0370211 | ||||||||
\(712\) | −3.31399 | −0.124197 | ||||||||
\(713\) | 1.54080 | 0.0577033 | ||||||||
\(714\) | −10.4341 | −0.390487 | ||||||||
\(715\) | −15.2508 | −0.570346 | ||||||||
\(716\) | 33.8966 | 1.26678 | ||||||||
\(717\) | 29.6711 | 1.10809 | ||||||||
\(718\) | 26.6118 | 0.993144 | ||||||||
\(719\) | −19.7348 | −0.735985 | −0.367993 | − | 0.929829i | \(-0.619955\pi\) | ||||
−0.367993 | + | 0.929829i | \(0.619955\pi\) | |||||||
\(720\) | 4.18684 | 0.156034 | ||||||||
\(721\) | −7.78302 | −0.289855 | ||||||||
\(722\) | 2.09813 | 0.0780842 | ||||||||
\(723\) | −12.3179 | −0.458109 | ||||||||
\(724\) | −59.3624 | −2.20619 | ||||||||
\(725\) | 14.1706 | 0.526283 | ||||||||
\(726\) | −16.2373 | −0.602624 | ||||||||
\(727\) | 33.3056 | 1.23523 | 0.617617 | − | 0.786479i | \(-0.288098\pi\) | ||||
0.617617 | + | 0.786479i | \(0.288098\pi\) | |||||||
\(728\) | 24.3363 | 0.901962 | ||||||||
\(729\) | 26.1535 | 0.968647 | ||||||||
\(730\) | 10.5370 | 0.389993 | ||||||||
\(731\) | 3.83647 | 0.141897 | ||||||||
\(732\) | −31.6143 | −1.16850 | ||||||||
\(733\) | −1.18908 | −0.0439196 | −0.0219598 | − | 0.999759i | \(-0.506991\pi\) | ||||
−0.0219598 | + | 0.999759i | \(0.506991\pi\) | |||||||
\(734\) | 27.8760 | 1.02892 | ||||||||
\(735\) | 17.3138 | 0.638630 | ||||||||
\(736\) | −4.47693 | −0.165022 | ||||||||
\(737\) | 29.7368 | 1.09537 | ||||||||
\(738\) | 17.2933 | 0.636574 | ||||||||
\(739\) | 19.1641 | 0.704962 | 0.352481 | − | 0.935819i | \(-0.385338\pi\) | ||||
0.352481 | + | 0.935819i | \(0.385338\pi\) | |||||||
\(740\) | −5.98538 | −0.220027 | ||||||||
\(741\) | −8.41898 | −0.309279 | ||||||||
\(742\) | 81.8335 | 3.00420 | ||||||||
\(743\) | −24.4294 | −0.896229 | −0.448114 | − | 0.893976i | \(-0.647904\pi\) | ||||
−0.448114 | + | 0.893976i | \(0.647904\pi\) | |||||||
\(744\) | 3.03315 | 0.111200 | ||||||||
\(745\) | −10.2781 | −0.376561 | ||||||||
\(746\) | 22.5280 | 0.824810 | ||||||||
\(747\) | −10.9635 | −0.401134 | ||||||||
\(748\) | 4.65001 | 0.170021 | ||||||||
\(749\) | 56.1133 | 2.05033 | ||||||||
\(750\) | −25.3740 | −0.926528 | ||||||||
\(751\) | −31.7586 | −1.15889 | −0.579444 | − | 0.815012i | \(-0.696730\pi\) | ||||
−0.579444 | + | 0.815012i | \(0.696730\pi\) | |||||||
\(752\) | −20.2083 | −0.736921 | ||||||||
\(753\) | −0.242748 | −0.00884624 | ||||||||
\(754\) | 49.4426 | 1.80059 | ||||||||
\(755\) | −1.99963 | −0.0727738 | ||||||||
\(756\) | 59.7785 | 2.17412 | ||||||||
\(757\) | −2.39216 | −0.0869445 | −0.0434722 | − | 0.999055i | \(-0.513842\pi\) | ||||
−0.0434722 | + | 0.999055i | \(0.513842\pi\) | |||||||
\(758\) | 5.83243 | 0.211843 | ||||||||
\(759\) | 1.61768 | 0.0587181 | ||||||||
\(760\) | 0.883612 | 0.0320520 | ||||||||
\(761\) | 14.9245 | 0.541013 | 0.270506 | − | 0.962718i | \(-0.412809\pi\) | ||||
0.270506 | + | 0.962718i | \(0.412809\pi\) | |||||||
\(762\) | −60.3424 | −2.18597 | ||||||||
\(763\) | 34.2169 | 1.23874 | ||||||||
\(764\) | −0.0853752 | −0.00308877 | ||||||||
\(765\) | −1.19069 | −0.0430493 | ||||||||
\(766\) | −0.724711 | −0.0261849 | ||||||||
\(767\) | −6.56837 | −0.237170 | ||||||||
\(768\) | 10.0929 | 0.364195 | ||||||||
\(769\) | −26.9105 | −0.970419 | −0.485210 | − | 0.874398i | \(-0.661257\pi\) | ||||
−0.485210 | + | 0.874398i | \(0.661257\pi\) | |||||||
\(770\) | −21.9058 | −0.789431 | ||||||||
\(771\) | 26.2015 | 0.943623 | ||||||||
\(772\) | −54.3782 | −1.95711 | ||||||||
\(773\) | 48.3216 | 1.73801 | 0.869004 | − | 0.494805i | \(-0.164761\pi\) | ||||
0.869004 | + | 0.494805i | \(0.164761\pi\) | |||||||
\(774\) | −12.2927 | −0.441854 | ||||||||
\(775\) | −10.8183 | −0.388605 | ||||||||
\(776\) | −8.08182 | −0.290120 | ||||||||
\(777\) | 13.7130 | 0.491952 | ||||||||
\(778\) | −6.59687 | −0.236509 | ||||||||
\(779\) | −6.25508 | −0.224111 | ||||||||
\(780\) | −21.1794 | −0.758345 | ||||||||
\(781\) | 13.2234 | 0.473169 | ||||||||
\(782\) | 1.00640 | 0.0359888 | ||||||||
\(783\) | 20.3314 | 0.726586 | ||||||||
\(784\) | −38.6724 | −1.38116 | ||||||||
\(785\) | 16.1349 | 0.575878 | ||||||||
\(786\) | 14.5748 | 0.519865 | ||||||||
\(787\) | −25.6110 | −0.912932 | −0.456466 | − | 0.889741i | \(-0.650885\pi\) | ||||
−0.456466 | + | 0.889741i | \(0.650885\pi\) | |||||||
\(788\) | 37.5553 | 1.33785 | ||||||||
\(789\) | −7.17421 | −0.255409 | ||||||||
\(790\) | 1.64611 | 0.0585661 | ||||||||
\(791\) | −68.8956 | −2.44965 | ||||||||
\(792\) | −2.49429 | −0.0886307 | ||||||||
\(793\) | 65.8627 | 2.33885 | ||||||||
\(794\) | 35.6998 | 1.26694 | ||||||||
\(795\) | −11.9225 | −0.422847 | ||||||||
\(796\) | −49.7522 | −1.76342 | ||||||||
\(797\) | −37.6890 | −1.33501 | −0.667506 | − | 0.744605i | \(-0.732638\pi\) | ||||
−0.667506 | + | 0.744605i | \(0.732638\pi\) | |||||||
\(798\) | −12.0928 | −0.428081 | ||||||||
\(799\) | 5.74698 | 0.203314 | ||||||||
\(800\) | 31.4336 | 1.11135 | ||||||||
\(801\) | 5.17558 | 0.182870 | ||||||||
\(802\) | 3.88151 | 0.137061 | ||||||||
\(803\) | 10.7587 | 0.379666 | ||||||||
\(804\) | 41.2967 | 1.45642 | ||||||||
\(805\) | −2.58708 | −0.0911826 | ||||||||
\(806\) | −37.7462 | −1.32955 | ||||||||
\(807\) | 10.1247 | 0.356407 | ||||||||
\(808\) | −5.04711 | −0.177557 | ||||||||
\(809\) | 3.80843 | 0.133897 | 0.0669486 | − | 0.997756i | \(-0.478674\pi\) | ||||
0.0669486 | + | 0.997756i | \(0.478674\pi\) | |||||||
\(810\) | −7.27444 | −0.255598 | ||||||||
\(811\) | 48.4893 | 1.70269 | 0.851344 | − | 0.524607i | \(-0.175788\pi\) | ||||
0.851344 | + | 0.524607i | \(0.175788\pi\) | |||||||
\(812\) | 38.7529 | 1.35996 | ||||||||
\(813\) | −1.66460 | −0.0583801 | ||||||||
\(814\) | −11.1995 | −0.392542 | ||||||||
\(815\) | −0.0655816 | −0.00229722 | ||||||||
\(816\) | −3.39546 | −0.118865 | ||||||||
\(817\) | 4.44636 | 0.155558 | ||||||||
\(818\) | −1.47658 | −0.0516273 | ||||||||
\(819\) | −38.0068 | −1.32807 | ||||||||
\(820\) | −15.7357 | −0.549515 | ||||||||
\(821\) | −23.5608 | −0.822277 | −0.411138 | − | 0.911573i | \(-0.634869\pi\) | ||||
−0.411138 | + | 0.911573i | \(0.634869\pi\) | |||||||
\(822\) | 45.8492 | 1.59918 | ||||||||
\(823\) | −14.8910 | −0.519069 | −0.259535 | − | 0.965734i | \(-0.583569\pi\) | ||||
−0.259535 | + | 0.965734i | \(0.583569\pi\) | |||||||
\(824\) | 1.47778 | 0.0514810 | ||||||||
\(825\) | −11.3581 | −0.395439 | ||||||||
\(826\) | −9.43464 | −0.328273 | ||||||||
\(827\) | 33.9453 | 1.18039 | 0.590197 | − | 0.807259i | \(-0.299050\pi\) | ||||
0.590197 | + | 0.807259i | \(0.299050\pi\) | |||||||
\(828\) | −1.75963 | −0.0611514 | ||||||||
\(829\) | 0.768540 | 0.0266925 | 0.0133462 | − | 0.999911i | \(-0.495752\pi\) | ||||
0.0133462 | + | 0.999911i | \(0.495752\pi\) | |||||||
\(830\) | 18.2821 | 0.634580 | ||||||||
\(831\) | −30.3774 | −1.05378 | ||||||||
\(832\) | 70.2878 | 2.43679 | ||||||||
\(833\) | 10.9979 | 0.381056 | ||||||||
\(834\) | −4.67207 | −0.161780 | ||||||||
\(835\) | 3.27147 | 0.113214 | ||||||||
\(836\) | 5.38923 | 0.186390 | ||||||||
\(837\) | −15.5217 | −0.536509 | ||||||||
\(838\) | 65.0149 | 2.24590 | ||||||||
\(839\) | 14.6577 | 0.506041 | 0.253020 | − | 0.967461i | \(-0.418576\pi\) | ||||
0.253020 | + | 0.967461i | \(0.418576\pi\) | |||||||
\(840\) | −5.09281 | −0.175719 | ||||||||
\(841\) | −15.8196 | −0.545505 | ||||||||
\(842\) | −12.6867 | −0.437212 | ||||||||
\(843\) | 2.80955 | 0.0967662 | ||||||||
\(844\) | 2.40214 | 0.0826849 | ||||||||
\(845\) | 30.5090 | 1.04954 | ||||||||
\(846\) | −18.4144 | −0.633099 | ||||||||
\(847\) | 26.5138 | 0.911026 | ||||||||
\(848\) | 26.6302 | 0.914485 | ||||||||
\(849\) | −17.4014 | −0.597216 | ||||||||
\(850\) | −7.06618 | −0.242368 | ||||||||
\(851\) | −1.32266 | −0.0453402 | ||||||||
\(852\) | 18.3639 | 0.629136 | ||||||||
\(853\) | −0.189713 | −0.00649564 | −0.00324782 | − | 0.999995i | \(-0.501034\pi\) | ||||
−0.00324782 | + | 0.999995i | \(0.501034\pi\) | |||||||
\(854\) | 94.6035 | 3.23726 | ||||||||
\(855\) | −1.37997 | −0.0471939 | ||||||||
\(856\) | −10.6544 | −0.364159 | ||||||||
\(857\) | 36.6495 | 1.25192 | 0.625961 | − | 0.779854i | \(-0.284707\pi\) | ||||
0.625961 | + | 0.779854i | \(0.284707\pi\) | |||||||
\(858\) | −39.6297 | −1.35293 | ||||||||
\(859\) | −33.4942 | −1.14281 | −0.571403 | − | 0.820670i | \(-0.693601\pi\) | ||||
−0.571403 | + | 0.820670i | \(0.693601\pi\) | |||||||
\(860\) | 11.1856 | 0.381425 | ||||||||
\(861\) | 36.0519 | 1.22865 | ||||||||
\(862\) | 15.6074 | 0.531592 | ||||||||
\(863\) | 43.4514 | 1.47910 | 0.739551 | − | 0.673101i | \(-0.235038\pi\) | ||||
0.739551 | + | 0.673101i | \(0.235038\pi\) | |||||||
\(864\) | 45.0997 | 1.53432 | ||||||||
\(865\) | 6.27880 | 0.213486 | ||||||||
\(866\) | −15.7547 | −0.535368 | ||||||||
\(867\) | −21.0840 | −0.716052 | ||||||||
\(868\) | −29.5852 | −1.00419 | ||||||||
\(869\) | 1.68074 | 0.0570151 | ||||||||
\(870\) | −10.3468 | −0.350789 | ||||||||
\(871\) | −86.0343 | −2.91516 | ||||||||
\(872\) | −6.49686 | −0.220012 | ||||||||
\(873\) | 12.6217 | 0.427179 | ||||||||
\(874\) | 1.16639 | 0.0394536 | ||||||||
\(875\) | 41.4331 | 1.40069 | ||||||||
\(876\) | 14.9411 | 0.504812 | ||||||||
\(877\) | 21.5313 | 0.727060 | 0.363530 | − | 0.931582i | \(-0.381571\pi\) | ||||
0.363530 | + | 0.931582i | \(0.381571\pi\) | |||||||
\(878\) | −14.6216 | −0.493455 | ||||||||
\(879\) | −27.2080 | −0.917703 | ||||||||
\(880\) | −7.12858 | −0.240304 | ||||||||
\(881\) | 33.6439 | 1.13349 | 0.566746 | − | 0.823892i | \(-0.308202\pi\) | ||||
0.566746 | + | 0.823892i | \(0.308202\pi\) | |||||||
\(882\) | −35.2393 | −1.18657 | ||||||||
\(883\) | −40.5906 | −1.36598 | −0.682991 | − | 0.730427i | \(-0.739321\pi\) | ||||
−0.682991 | + | 0.730427i | \(0.739321\pi\) | |||||||
\(884\) | −13.4534 | −0.452487 | ||||||||
\(885\) | 1.37455 | 0.0462050 | ||||||||
\(886\) | −5.55376 | −0.186582 | ||||||||
\(887\) | 34.2297 | 1.14932 | 0.574660 | − | 0.818392i | \(-0.305134\pi\) | ||||
0.574660 | + | 0.818392i | \(0.305134\pi\) | |||||||
\(888\) | −2.60373 | −0.0873754 | ||||||||
\(889\) | 98.5326 | 3.30468 | ||||||||
\(890\) | −8.63048 | −0.289294 | ||||||||
\(891\) | −7.42745 | −0.248829 | ||||||||
\(892\) | −35.0802 | −1.17457 | ||||||||
\(893\) | 6.66058 | 0.222888 | ||||||||
\(894\) | −26.7081 | −0.893251 | ||||||||
\(895\) | 14.7780 | 0.493974 | ||||||||
\(896\) | 29.3879 | 0.981781 | ||||||||
\(897\) | −4.68027 | −0.156270 | ||||||||
\(898\) | −67.9509 | −2.26755 | ||||||||
\(899\) | −10.0623 | −0.335597 | ||||||||
\(900\) | 12.3548 | 0.411826 | ||||||||
\(901\) | −7.57329 | −0.252303 | ||||||||
\(902\) | −29.4437 | −0.980370 | ||||||||
\(903\) | −25.6271 | −0.852818 | ||||||||
\(904\) | 13.0814 | 0.435081 | ||||||||
\(905\) | −25.8804 | −0.860293 | ||||||||
\(906\) | −5.19610 | −0.172629 | ||||||||
\(907\) | −43.2753 | −1.43693 | −0.718466 | − | 0.695562i | \(-0.755155\pi\) | ||||
−0.718466 | + | 0.695562i | \(0.755155\pi\) | |||||||
\(908\) | 21.6193 | 0.717463 | ||||||||
\(909\) | 7.88225 | 0.261438 | ||||||||
\(910\) | 63.3778 | 2.10095 | ||||||||
\(911\) | −55.7370 | −1.84665 | −0.923324 | − | 0.384021i | \(-0.874539\pi\) | ||||
−0.923324 | + | 0.384021i | \(0.874539\pi\) | |||||||
\(912\) | −3.93524 | −0.130309 | ||||||||
\(913\) | 18.6666 | 0.617775 | ||||||||
\(914\) | −67.9205 | −2.24661 | ||||||||
\(915\) | −13.7830 | −0.455651 | ||||||||
\(916\) | 44.8372 | 1.48146 | ||||||||
\(917\) | −23.7991 | −0.785914 | ||||||||
\(918\) | −10.1383 | −0.334613 | ||||||||
\(919\) | 47.1638 | 1.55579 | 0.777895 | − | 0.628394i | \(-0.216287\pi\) | ||||
0.777895 | + | 0.628394i | \(0.216287\pi\) | |||||||
\(920\) | 0.491216 | 0.0161949 | ||||||||
\(921\) | −32.5122 | −1.07131 | ||||||||
\(922\) | 10.0747 | 0.331794 | ||||||||
\(923\) | −38.2578 | −1.25927 | ||||||||
\(924\) | −31.0615 | −1.02185 | ||||||||
\(925\) | 9.28672 | 0.305345 | ||||||||
\(926\) | −48.8844 | −1.60644 | ||||||||
\(927\) | −2.30791 | −0.0758016 | ||||||||
\(928\) | 29.2370 | 0.959751 | ||||||||
\(929\) | 5.13009 | 0.168313 | 0.0841565 | − | 0.996453i | \(-0.473180\pi\) | ||||
0.0841565 | + | 0.996453i | \(0.473180\pi\) | |||||||
\(930\) | 7.89908 | 0.259021 | ||||||||
\(931\) | 12.7463 | 0.417742 | ||||||||
\(932\) | 1.86875 | 0.0612129 | ||||||||
\(933\) | −26.4939 | −0.867370 | ||||||||
\(934\) | −49.7249 | −1.62705 | ||||||||
\(935\) | 2.02728 | 0.0662991 | ||||||||
\(936\) | 7.21646 | 0.235877 | ||||||||
\(937\) | −14.1273 | −0.461518 | −0.230759 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230759 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(938\) | −123.577 | −4.03495 | ||||||||
\(939\) | −16.9474 | −0.553058 | ||||||||
\(940\) | 16.7558 | 0.546515 | ||||||||
\(941\) | −56.0024 | −1.82563 | −0.912814 | − | 0.408376i | \(-0.866095\pi\) | ||||
−0.912814 | + | 0.408376i | \(0.866095\pi\) | |||||||
\(942\) | 41.9270 | 1.36605 | ||||||||
\(943\) | −3.47731 | −0.113237 | ||||||||
\(944\) | −3.07021 | −0.0999270 | ||||||||
\(945\) | 26.0618 | 0.847789 | ||||||||
\(946\) | 20.9298 | 0.680487 | ||||||||
\(947\) | 19.0292 | 0.618365 | 0.309182 | − | 0.951003i | \(-0.399945\pi\) | ||||
0.309182 | + | 0.951003i | \(0.399945\pi\) | |||||||
\(948\) | 2.33411 | 0.0758085 | ||||||||
\(949\) | −31.1270 | −1.01042 | ||||||||
\(950\) | −8.18949 | −0.265702 | ||||||||
\(951\) | 7.48704 | 0.242784 | ||||||||
\(952\) | −3.23501 | −0.104847 | ||||||||
\(953\) | 34.7501 | 1.12567 | 0.562833 | − | 0.826570i | \(-0.309711\pi\) | ||||
0.562833 | + | 0.826570i | \(0.309711\pi\) | |||||||
\(954\) | 24.2662 | 0.785647 | ||||||||
\(955\) | −0.0372212 | −0.00120445 | ||||||||
\(956\) | 54.9512 | 1.77725 | ||||||||
\(957\) | −10.5644 | −0.341499 | ||||||||
\(958\) | −44.7596 | −1.44612 | ||||||||
\(959\) | −74.8668 | −2.41758 | ||||||||
\(960\) | −14.7090 | −0.474731 | ||||||||
\(961\) | −23.3181 | −0.752196 | ||||||||
\(962\) | 32.4023 | 1.04469 | ||||||||
\(963\) | 16.6393 | 0.536195 | ||||||||
\(964\) | −22.8130 | −0.734758 | ||||||||
\(965\) | −23.7074 | −0.763168 | ||||||||
\(966\) | −6.72262 | −0.216297 | ||||||||
\(967\) | 8.59986 | 0.276553 | 0.138276 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138276 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(968\) | −5.03426 | −0.161807 | ||||||||
\(969\) | 1.11913 | 0.0359517 | ||||||||
\(970\) | −21.0471 | −0.675781 | ||||||||
\(971\) | 47.3606 | 1.51987 | 0.759937 | − | 0.649996i | \(-0.225230\pi\) | ||||
0.759937 | + | 0.649996i | \(0.225230\pi\) | |||||||
\(972\) | 30.0426 | 0.963617 | ||||||||
\(973\) | 7.62898 | 0.244574 | ||||||||
\(974\) | 9.18422 | 0.294281 | ||||||||
\(975\) | 32.8613 | 1.05240 | ||||||||
\(976\) | 30.7858 | 0.985429 | ||||||||
\(977\) | −15.9673 | −0.510840 | −0.255420 | − | 0.966830i | \(-0.582214\pi\) | ||||
−0.255420 | + | 0.966830i | \(0.582214\pi\) | |||||||
\(978\) | −0.170416 | −0.00544931 | ||||||||
\(979\) | −8.81202 | −0.281633 | ||||||||
\(980\) | 32.0655 | 1.02429 | ||||||||
\(981\) | 10.1464 | 0.323949 | ||||||||
\(982\) | −5.53051 | −0.176486 | ||||||||
\(983\) | 56.6749 | 1.80765 | 0.903825 | − | 0.427903i | \(-0.140748\pi\) | ||||
0.903825 | + | 0.427903i | \(0.140748\pi\) | |||||||
\(984\) | −6.84528 | −0.218219 | ||||||||
\(985\) | 16.3731 | 0.521689 | ||||||||
\(986\) | −6.57239 | −0.209307 | ||||||||
\(987\) | −38.3891 | −1.22194 | ||||||||
\(988\) | −15.5921 | −0.496050 | ||||||||
\(989\) | 2.47181 | 0.0785990 | ||||||||
\(990\) | −6.49576 | −0.206449 | ||||||||
\(991\) | −26.8142 | −0.851782 | −0.425891 | − | 0.904775i | \(-0.640039\pi\) | ||||
−0.425891 | + | 0.904775i | \(0.640039\pi\) | |||||||
\(992\) | −22.3205 | −0.708677 | ||||||||
\(993\) | −44.9812 | −1.42744 | ||||||||
\(994\) | −54.9525 | −1.74299 | ||||||||
\(995\) | −21.6906 | −0.687637 | ||||||||
\(996\) | 25.9232 | 0.821407 | ||||||||
\(997\) | −12.1263 | −0.384043 | −0.192021 | − | 0.981391i | \(-0.561504\pi\) | ||||
−0.192021 | + | 0.981391i | \(0.561504\pi\) | |||||||
\(998\) | 39.5336 | 1.25142 | ||||||||
\(999\) | 13.3242 | 0.421560 |
(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 | 4009.2.a.c.1.62 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.62 | ✓ | 71 | 1.1 | even | 1 | trivial |