Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(107\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62131 | −1.85355 | −0.926774 | − | 0.375621i | \(-0.877430\pi\) | ||||
−0.926774 | + | 0.375621i | \(0.877430\pi\) | |||||||
\(3\) | 1.98857 | 1.14810 | 0.574051 | − | 0.818820i | \(-0.305371\pi\) | ||||
0.574051 | + | 0.818820i | \(0.305371\pi\) | |||||||
\(4\) | 4.87127 | 2.43564 | ||||||||
\(5\) | −3.39892 | −1.52004 | −0.760022 | − | 0.649897i | \(-0.774812\pi\) | ||||
−0.760022 | + | 0.649897i | \(0.774812\pi\) | |||||||
\(6\) | −5.21266 | −2.12806 | ||||||||
\(7\) | −2.62575 | −0.992440 | −0.496220 | − | 0.868197i | \(-0.665279\pi\) | ||||
−0.496220 | + | 0.868197i | \(0.665279\pi\) | |||||||
\(8\) | −7.52650 | −2.66102 | ||||||||
\(9\) | 0.954412 | 0.318137 | ||||||||
\(10\) | 8.90963 | 2.81747 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 9.68687 | 2.79636 | ||||||||
\(13\) | −4.77883 | −1.32541 | −0.662704 | − | 0.748881i | \(-0.730591\pi\) | ||||
−0.662704 | + | 0.748881i | \(0.730591\pi\) | |||||||
\(14\) | 6.88290 | 1.83953 | ||||||||
\(15\) | −6.75899 | −1.74516 | ||||||||
\(16\) | 9.98676 | 2.49669 | ||||||||
\(17\) | 6.37974 | 1.54731 | 0.773657 | − | 0.633605i | \(-0.218425\pi\) | ||||
0.773657 | + | 0.633605i | \(0.218425\pi\) | |||||||
\(18\) | −2.50181 | −0.589682 | ||||||||
\(19\) | 1.24752 | 0.286200 | 0.143100 | − | 0.989708i | \(-0.454293\pi\) | ||||
0.143100 | + | 0.989708i | \(0.454293\pi\) | |||||||
\(20\) | −16.5571 | −3.70227 | ||||||||
\(21\) | −5.22149 | −1.13942 | ||||||||
\(22\) | 2.62131 | 0.558865 | ||||||||
\(23\) | 0.341368 | 0.0711801 | 0.0355900 | − | 0.999366i | \(-0.488669\pi\) | ||||
0.0355900 | + | 0.999366i | \(0.488669\pi\) | |||||||
\(24\) | −14.9670 | −3.05512 | ||||||||
\(25\) | 6.55267 | 1.31053 | ||||||||
\(26\) | 12.5268 | 2.45671 | ||||||||
\(27\) | −4.06780 | −0.782848 | ||||||||
\(28\) | −12.7907 | −2.41722 | ||||||||
\(29\) | 7.39206 | 1.37267 | 0.686336 | − | 0.727285i | \(-0.259218\pi\) | ||||
0.686336 | + | 0.727285i | \(0.259218\pi\) | |||||||
\(30\) | 17.7174 | 3.23474 | ||||||||
\(31\) | 5.53910 | 0.994851 | 0.497426 | − | 0.867507i | \(-0.334279\pi\) | ||||
0.497426 | + | 0.867507i | \(0.334279\pi\) | |||||||
\(32\) | −11.1254 | −1.96671 | ||||||||
\(33\) | −1.98857 | −0.346166 | ||||||||
\(34\) | −16.7233 | −2.86802 | ||||||||
\(35\) | 8.92471 | 1.50855 | ||||||||
\(36\) | 4.64920 | 0.774867 | ||||||||
\(37\) | −7.86385 | −1.29281 | −0.646404 | − | 0.762995i | \(-0.723728\pi\) | ||||
−0.646404 | + | 0.762995i | \(0.723728\pi\) | |||||||
\(38\) | −3.27013 | −0.530486 | ||||||||
\(39\) | −9.50303 | −1.52170 | ||||||||
\(40\) | 25.5820 | 4.04487 | ||||||||
\(41\) | 3.54712 | 0.553968 | 0.276984 | − | 0.960875i | \(-0.410665\pi\) | ||||
0.276984 | + | 0.960875i | \(0.410665\pi\) | |||||||
\(42\) | 13.6871 | 2.11197 | ||||||||
\(43\) | 11.7515 | 1.79208 | 0.896042 | − | 0.443970i | \(-0.146430\pi\) | ||||
0.896042 | + | 0.443970i | \(0.146430\pi\) | |||||||
\(44\) | −4.87127 | −0.734372 | ||||||||
\(45\) | −3.24397 | −0.483583 | ||||||||
\(46\) | −0.894831 | −0.131936 | ||||||||
\(47\) | 2.90410 | 0.423606 | 0.211803 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211803 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(48\) | 19.8594 | 2.86645 | ||||||||
\(49\) | −0.105445 | −0.0150636 | ||||||||
\(50\) | −17.1766 | −2.42913 | ||||||||
\(51\) | 12.6866 | 1.77647 | ||||||||
\(52\) | −23.2790 | −3.22821 | ||||||||
\(53\) | −12.8682 | −1.76758 | −0.883789 | − | 0.467886i | \(-0.845016\pi\) | ||||
−0.883789 | + | 0.467886i | \(0.845016\pi\) | |||||||
\(54\) | 10.6630 | 1.45105 | ||||||||
\(55\) | 3.39892 | 0.458310 | ||||||||
\(56\) | 19.7627 | 2.64090 | ||||||||
\(57\) | 2.48078 | 0.328587 | ||||||||
\(58\) | −19.3769 | −2.54431 | ||||||||
\(59\) | 7.24949 | 0.943804 | 0.471902 | − | 0.881651i | \(-0.343568\pi\) | ||||
0.471902 | + | 0.881651i | \(0.343568\pi\) | |||||||
\(60\) | −32.9249 | −4.25059 | ||||||||
\(61\) | −3.35498 | −0.429561 | −0.214781 | − | 0.976662i | \(-0.568904\pi\) | ||||
−0.214781 | + | 0.976662i | \(0.568904\pi\) | |||||||
\(62\) | −14.5197 | −1.84400 | ||||||||
\(63\) | −2.50605 | −0.315732 | ||||||||
\(64\) | 9.18962 | 1.14870 | ||||||||
\(65\) | 16.2429 | 2.01468 | ||||||||
\(66\) | 5.21266 | 0.641634 | ||||||||
\(67\) | −6.74590 | −0.824143 | −0.412072 | − | 0.911152i | \(-0.635195\pi\) | ||||
−0.412072 | + | 0.911152i | \(0.635195\pi\) | |||||||
\(68\) | 31.0774 | 3.76869 | ||||||||
\(69\) | 0.678834 | 0.0817220 | ||||||||
\(70\) | −23.3944 | −2.79617 | ||||||||
\(71\) | −4.38121 | −0.519954 | −0.259977 | − | 0.965615i | \(-0.583715\pi\) | ||||
−0.259977 | + | 0.965615i | \(0.583715\pi\) | |||||||
\(72\) | −7.18338 | −0.846570 | ||||||||
\(73\) | −16.0706 | −1.88092 | −0.940460 | − | 0.339904i | \(-0.889605\pi\) | ||||
−0.940460 | + | 0.339904i | \(0.889605\pi\) | |||||||
\(74\) | 20.6136 | 2.39628 | ||||||||
\(75\) | 13.0304 | 1.50463 | ||||||||
\(76\) | 6.07700 | 0.697080 | ||||||||
\(77\) | 2.62575 | 0.299232 | ||||||||
\(78\) | 24.9104 | 2.82055 | ||||||||
\(79\) | 10.9589 | 1.23297 | 0.616485 | − | 0.787367i | \(-0.288556\pi\) | ||||
0.616485 | + | 0.787367i | \(0.288556\pi\) | |||||||
\(80\) | −33.9442 | −3.79508 | ||||||||
\(81\) | −10.9523 | −1.21693 | ||||||||
\(82\) | −9.29812 | −1.02681 | ||||||||
\(83\) | 17.2970 | 1.89859 | 0.949295 | − | 0.314388i | \(-0.101799\pi\) | ||||
0.949295 | + | 0.314388i | \(0.101799\pi\) | |||||||
\(84\) | −25.4353 | −2.77522 | ||||||||
\(85\) | −21.6842 | −2.35198 | ||||||||
\(86\) | −30.8043 | −3.32171 | ||||||||
\(87\) | 14.6996 | 1.57597 | ||||||||
\(88\) | 7.52650 | 0.802328 | ||||||||
\(89\) | 18.5041 | 1.96143 | 0.980716 | − | 0.195440i | \(-0.0626136\pi\) | ||||
0.980716 | + | 0.195440i | \(0.0626136\pi\) | |||||||
\(90\) | 8.50346 | 0.896343 | ||||||||
\(91\) | 12.5480 | 1.31539 | ||||||||
\(92\) | 1.66290 | 0.173369 | ||||||||
\(93\) | 11.0149 | 1.14219 | ||||||||
\(94\) | −7.61255 | −0.785175 | ||||||||
\(95\) | −4.24022 | −0.435037 | ||||||||
\(96\) | −22.1236 | −2.25798 | ||||||||
\(97\) | 1.40907 | 0.143070 | 0.0715349 | − | 0.997438i | \(-0.477210\pi\) | ||||
0.0715349 | + | 0.997438i | \(0.477210\pi\) | |||||||
\(98\) | 0.276405 | 0.0279211 | ||||||||
\(99\) | −0.954412 | −0.0959220 | ||||||||
\(100\) | 31.9198 | 3.19198 | ||||||||
\(101\) | 1.21753 | 0.121149 | 0.0605745 | − | 0.998164i | \(-0.480707\pi\) | ||||
0.0605745 | + | 0.998164i | \(0.480707\pi\) | |||||||
\(102\) | −33.2554 | −3.29278 | ||||||||
\(103\) | 0.446152 | 0.0439607 | 0.0219803 | − | 0.999758i | \(-0.493003\pi\) | ||||
0.0219803 | + | 0.999758i | \(0.493003\pi\) | |||||||
\(104\) | 35.9679 | 3.52694 | ||||||||
\(105\) | 17.7474 | 1.73197 | ||||||||
\(106\) | 33.7315 | 3.27629 | ||||||||
\(107\) | 4.34871 | 0.420406 | 0.210203 | − | 0.977658i | \(-0.432588\pi\) | ||||
0.210203 | + | 0.977658i | \(0.432588\pi\) | |||||||
\(108\) | −19.8153 | −1.90673 | ||||||||
\(109\) | −15.1620 | −1.45226 | −0.726129 | − | 0.687558i | \(-0.758683\pi\) | ||||
−0.726129 | + | 0.687558i | \(0.758683\pi\) | |||||||
\(110\) | −8.90963 | −0.849500 | ||||||||
\(111\) | −15.6378 | −1.48428 | ||||||||
\(112\) | −26.2227 | −2.47781 | ||||||||
\(113\) | −5.47251 | −0.514810 | −0.257405 | − | 0.966304i | \(-0.582867\pi\) | ||||
−0.257405 | + | 0.966304i | \(0.582867\pi\) | |||||||
\(114\) | −6.50289 | −0.609052 | ||||||||
\(115\) | −1.16028 | −0.108197 | ||||||||
\(116\) | 36.0088 | 3.34333 | ||||||||
\(117\) | −4.56097 | −0.421662 | ||||||||
\(118\) | −19.0032 | −1.74938 | ||||||||
\(119\) | −16.7516 | −1.53562 | ||||||||
\(120\) | 50.8716 | 4.64392 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.79445 | 0.796212 | ||||||||
\(123\) | 7.05371 | 0.636011 | ||||||||
\(124\) | 26.9825 | 2.42310 | ||||||||
\(125\) | −5.27739 | −0.472024 | ||||||||
\(126\) | 6.56912 | 0.585224 | ||||||||
\(127\) | 14.5050 | 1.28711 | 0.643556 | − | 0.765399i | \(-0.277458\pi\) | ||||
0.643556 | + | 0.765399i | \(0.277458\pi\) | |||||||
\(128\) | −1.83806 | −0.162463 | ||||||||
\(129\) | 23.3686 | 2.05749 | ||||||||
\(130\) | −42.5776 | −3.73430 | ||||||||
\(131\) | 12.0882 | 1.05615 | 0.528077 | − | 0.849196i | \(-0.322913\pi\) | ||||
0.528077 | + | 0.849196i | \(0.322913\pi\) | |||||||
\(132\) | −9.68687 | −0.843134 | ||||||||
\(133\) | −3.27567 | −0.284037 | ||||||||
\(134\) | 17.6831 | 1.52759 | ||||||||
\(135\) | 13.8261 | 1.18996 | ||||||||
\(136\) | −48.0171 | −4.11743 | ||||||||
\(137\) | −17.9901 | −1.53700 | −0.768500 | − | 0.639850i | \(-0.778996\pi\) | ||||
−0.768500 | + | 0.639850i | \(0.778996\pi\) | |||||||
\(138\) | −1.77943 | −0.151475 | ||||||||
\(139\) | 11.4626 | 0.972245 | 0.486123 | − | 0.873891i | \(-0.338411\pi\) | ||||
0.486123 | + | 0.873891i | \(0.338411\pi\) | |||||||
\(140\) | 43.4747 | 3.67428 | ||||||||
\(141\) | 5.77501 | 0.486343 | ||||||||
\(142\) | 11.4845 | 0.963760 | ||||||||
\(143\) | 4.77883 | 0.399626 | ||||||||
\(144\) | 9.53148 | 0.794290 | ||||||||
\(145\) | −25.1250 | −2.08652 | ||||||||
\(146\) | 42.1260 | 3.48637 | ||||||||
\(147\) | −0.209685 | −0.0172946 | ||||||||
\(148\) | −38.3070 | −3.14881 | ||||||||
\(149\) | 6.78579 | 0.555913 | 0.277957 | − | 0.960594i | \(-0.410343\pi\) | ||||
0.277957 | + | 0.960594i | \(0.410343\pi\) | |||||||
\(150\) | −34.1568 | −2.78889 | ||||||||
\(151\) | −6.75010 | −0.549315 | −0.274658 | − | 0.961542i | \(-0.588565\pi\) | ||||
−0.274658 | + | 0.961542i | \(0.588565\pi\) | |||||||
\(152\) | −9.38945 | −0.761585 | ||||||||
\(153\) | 6.08890 | 0.492258 | ||||||||
\(154\) | −6.88290 | −0.554640 | ||||||||
\(155\) | −18.8270 | −1.51222 | ||||||||
\(156\) | −46.2919 | −3.70632 | ||||||||
\(157\) | 17.0875 | 1.36373 | 0.681866 | − | 0.731477i | \(-0.261169\pi\) | ||||
0.681866 | + | 0.731477i | \(0.261169\pi\) | |||||||
\(158\) | −28.7266 | −2.28537 | ||||||||
\(159\) | −25.5892 | −2.02936 | ||||||||
\(160\) | 37.8144 | 2.98949 | ||||||||
\(161\) | −0.896346 | −0.0706419 | ||||||||
\(162\) | 28.7095 | 2.25563 | ||||||||
\(163\) | −17.2817 | −1.35361 | −0.676803 | − | 0.736164i | \(-0.736635\pi\) | ||||
−0.676803 | + | 0.736164i | \(0.736635\pi\) | |||||||
\(164\) | 17.2790 | 1.34926 | ||||||||
\(165\) | 6.75899 | 0.526187 | ||||||||
\(166\) | −45.3407 | −3.51912 | ||||||||
\(167\) | −1.87154 | −0.144824 | −0.0724122 | − | 0.997375i | \(-0.523070\pi\) | ||||
−0.0724122 | + | 0.997375i | \(0.523070\pi\) | |||||||
\(168\) | 39.2995 | 3.03202 | ||||||||
\(169\) | 9.83719 | 0.756707 | ||||||||
\(170\) | 56.8411 | 4.35951 | ||||||||
\(171\) | 1.19065 | 0.0910510 | ||||||||
\(172\) | 57.2447 | 4.36486 | ||||||||
\(173\) | −6.51135 | −0.495049 | −0.247524 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247524 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(174\) | −38.5323 | −2.92113 | ||||||||
\(175\) | −17.2057 | −1.30062 | ||||||||
\(176\) | −9.98676 | −0.752780 | ||||||||
\(177\) | 14.4161 | 1.08358 | ||||||||
\(178\) | −48.5050 | −3.63560 | ||||||||
\(179\) | 8.03685 | 0.600702 | 0.300351 | − | 0.953829i | \(-0.402896\pi\) | ||||
0.300351 | + | 0.953829i | \(0.402896\pi\) | |||||||
\(180\) | −15.8023 | −1.17783 | ||||||||
\(181\) | −23.1805 | −1.72299 | −0.861495 | − | 0.507765i | \(-0.830472\pi\) | ||||
−0.861495 | + | 0.507765i | \(0.830472\pi\) | |||||||
\(182\) | −32.8922 | −2.43813 | ||||||||
\(183\) | −6.67162 | −0.493180 | ||||||||
\(184\) | −2.56930 | −0.189412 | ||||||||
\(185\) | 26.7286 | 1.96513 | ||||||||
\(186\) | −28.8734 | −2.11710 | ||||||||
\(187\) | −6.37974 | −0.466533 | ||||||||
\(188\) | 14.1467 | 1.03175 | ||||||||
\(189\) | 10.6810 | 0.776929 | ||||||||
\(190\) | 11.1149 | 0.806362 | ||||||||
\(191\) | −16.9709 | −1.22797 | −0.613985 | − | 0.789318i | \(-0.710435\pi\) | ||||
−0.613985 | + | 0.789318i | \(0.710435\pi\) | |||||||
\(192\) | 18.2742 | 1.31883 | ||||||||
\(193\) | −13.5002 | −0.971768 | −0.485884 | − | 0.874023i | \(-0.661502\pi\) | ||||
−0.485884 | + | 0.874023i | \(0.661502\pi\) | |||||||
\(194\) | −3.69362 | −0.265187 | ||||||||
\(195\) | 32.3001 | 2.31306 | ||||||||
\(196\) | −0.513653 | −0.0366895 | ||||||||
\(197\) | 18.4072 | 1.31146 | 0.655730 | − | 0.754996i | \(-0.272361\pi\) | ||||
0.655730 | + | 0.754996i | \(0.272361\pi\) | |||||||
\(198\) | 2.50181 | 0.177796 | ||||||||
\(199\) | 22.8795 | 1.62188 | 0.810942 | − | 0.585127i | \(-0.198955\pi\) | ||||
0.810942 | + | 0.585127i | \(0.198955\pi\) | |||||||
\(200\) | −49.3186 | −3.48736 | ||||||||
\(201\) | −13.4147 | −0.946200 | ||||||||
\(202\) | −3.19153 | −0.224555 | ||||||||
\(203\) | −19.4097 | −1.36229 | ||||||||
\(204\) | 61.7997 | 4.32684 | ||||||||
\(205\) | −12.0564 | −0.842055 | ||||||||
\(206\) | −1.16950 | −0.0814832 | ||||||||
\(207\) | 0.325805 | 0.0226450 | ||||||||
\(208\) | −47.7250 | −3.30913 | ||||||||
\(209\) | −1.24752 | −0.0862927 | ||||||||
\(210\) | −46.5215 | −3.21029 | ||||||||
\(211\) | −21.0055 | −1.44608 | −0.723040 | − | 0.690806i | \(-0.757256\pi\) | ||||
−0.723040 | + | 0.690806i | \(0.757256\pi\) | |||||||
\(212\) | −62.6843 | −4.30518 | ||||||||
\(213\) | −8.71235 | −0.596960 | ||||||||
\(214\) | −11.3993 | −0.779241 | ||||||||
\(215\) | −39.9423 | −2.72405 | ||||||||
\(216\) | 30.6163 | 2.08317 | ||||||||
\(217\) | −14.5443 | −0.987330 | ||||||||
\(218\) | 39.7444 | 2.69183 | ||||||||
\(219\) | −31.9575 | −2.15949 | ||||||||
\(220\) | 16.5571 | 1.11628 | ||||||||
\(221\) | −30.4877 | −2.05082 | ||||||||
\(222\) | 40.9916 | 2.75118 | ||||||||
\(223\) | −1.81138 | −0.121299 | −0.0606493 | − | 0.998159i | \(-0.519317\pi\) | ||||
−0.0606493 | + | 0.998159i | \(0.519317\pi\) | |||||||
\(224\) | 29.2125 | 1.95184 | ||||||||
\(225\) | 6.25394 | 0.416929 | ||||||||
\(226\) | 14.3451 | 0.954225 | ||||||||
\(227\) | −12.9529 | −0.859713 | −0.429856 | − | 0.902897i | \(-0.641436\pi\) | ||||
−0.429856 | + | 0.902897i | \(0.641436\pi\) | |||||||
\(228\) | 12.0845 | 0.800319 | ||||||||
\(229\) | −19.9258 | −1.31673 | −0.658366 | − | 0.752698i | \(-0.728752\pi\) | ||||
−0.658366 | + | 0.752698i | \(0.728752\pi\) | |||||||
\(230\) | 3.04146 | 0.200548 | ||||||||
\(231\) | 5.22149 | 0.343549 | ||||||||
\(232\) | −55.6364 | −3.65271 | ||||||||
\(233\) | −7.91408 | −0.518468 | −0.259234 | − | 0.965814i | \(-0.583470\pi\) | ||||
−0.259234 | + | 0.965814i | \(0.583470\pi\) | |||||||
\(234\) | 11.9557 | 0.781570 | ||||||||
\(235\) | −9.87081 | −0.643900 | ||||||||
\(236\) | 35.3143 | 2.29876 | ||||||||
\(237\) | 21.7925 | 1.41557 | ||||||||
\(238\) | 43.9111 | 2.84634 | ||||||||
\(239\) | −6.61194 | −0.427691 | −0.213846 | − | 0.976867i | \(-0.568599\pi\) | ||||
−0.213846 | + | 0.976867i | \(0.568599\pi\) | |||||||
\(240\) | −67.5004 | −4.35713 | ||||||||
\(241\) | −20.4680 | −1.31846 | −0.659231 | − | 0.751940i | \(-0.729118\pi\) | ||||
−0.659231 | + | 0.751940i | \(0.729118\pi\) | |||||||
\(242\) | −2.62131 | −0.168504 | ||||||||
\(243\) | −9.57610 | −0.614307 | ||||||||
\(244\) | −16.3430 | −1.04626 | ||||||||
\(245\) | 0.358400 | 0.0228974 | ||||||||
\(246\) | −18.4900 | −1.17888 | ||||||||
\(247\) | −5.96168 | −0.379332 | ||||||||
\(248\) | −41.6900 | −2.64732 | ||||||||
\(249\) | 34.3962 | 2.17977 | ||||||||
\(250\) | 13.8337 | 0.874918 | ||||||||
\(251\) | −11.4223 | −0.720968 | −0.360484 | − | 0.932765i | \(-0.617389\pi\) | ||||
−0.360484 | + | 0.932765i | \(0.617389\pi\) | |||||||
\(252\) | −12.2076 | −0.769009 | ||||||||
\(253\) | −0.341368 | −0.0214616 | ||||||||
\(254\) | −38.0222 | −2.38572 | ||||||||
\(255\) | −43.1206 | −2.70032 | ||||||||
\(256\) | −13.5611 | −0.847570 | ||||||||
\(257\) | −9.98222 | −0.622673 | −0.311337 | − | 0.950300i | \(-0.600777\pi\) | ||||
−0.311337 | + | 0.950300i | \(0.600777\pi\) | |||||||
\(258\) | −61.2565 | −3.81366 | ||||||||
\(259\) | 20.6485 | 1.28303 | ||||||||
\(260\) | 79.1234 | 4.90703 | ||||||||
\(261\) | 7.05507 | 0.436698 | ||||||||
\(262\) | −31.6870 | −1.95763 | ||||||||
\(263\) | −31.6669 | −1.95267 | −0.976333 | − | 0.216275i | \(-0.930609\pi\) | ||||
−0.976333 | + | 0.216275i | \(0.930609\pi\) | |||||||
\(264\) | 14.9670 | 0.921154 | ||||||||
\(265\) | 43.7379 | 2.68680 | ||||||||
\(266\) | 8.58655 | 0.526475 | ||||||||
\(267\) | 36.7967 | 2.25192 | ||||||||
\(268\) | −32.8611 | −2.00731 | ||||||||
\(269\) | 5.99065 | 0.365257 | 0.182628 | − | 0.983182i | \(-0.441540\pi\) | ||||
0.182628 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(270\) | −36.2426 | −2.20565 | ||||||||
\(271\) | −8.45587 | −0.513658 | −0.256829 | − | 0.966457i | \(-0.582678\pi\) | ||||
−0.256829 | + | 0.966457i | \(0.582678\pi\) | |||||||
\(272\) | 63.7129 | 3.86316 | ||||||||
\(273\) | 24.9526 | 1.51020 | ||||||||
\(274\) | 47.1577 | 2.84890 | ||||||||
\(275\) | −6.55267 | −0.395141 | ||||||||
\(276\) | 3.30678 | 0.199045 | ||||||||
\(277\) | −2.10986 | −0.126769 | −0.0633847 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633847 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(278\) | −30.0470 | −1.80210 | ||||||||
\(279\) | 5.28658 | 0.316499 | ||||||||
\(280\) | −67.1719 | −4.01429 | ||||||||
\(281\) | −19.1822 | −1.14432 | −0.572158 | − | 0.820144i | \(-0.693894\pi\) | ||||
−0.572158 | + | 0.820144i | \(0.693894\pi\) | |||||||
\(282\) | −15.1381 | −0.901460 | ||||||||
\(283\) | 3.99261 | 0.237336 | 0.118668 | − | 0.992934i | \(-0.462138\pi\) | ||||
0.118668 | + | 0.992934i | \(0.462138\pi\) | |||||||
\(284\) | −21.3421 | −1.26642 | ||||||||
\(285\) | −8.43197 | −0.499467 | ||||||||
\(286\) | −12.5268 | −0.740725 | ||||||||
\(287\) | −9.31386 | −0.549780 | ||||||||
\(288\) | −10.6182 | −0.625684 | ||||||||
\(289\) | 23.7011 | 1.39418 | ||||||||
\(290\) | 65.8606 | 3.86747 | ||||||||
\(291\) | 2.80204 | 0.164259 | ||||||||
\(292\) | −78.2842 | −4.58124 | ||||||||
\(293\) | 4.68195 | 0.273523 | 0.136761 | − | 0.990604i | \(-0.456331\pi\) | ||||
0.136761 | + | 0.990604i | \(0.456331\pi\) | |||||||
\(294\) | 0.549651 | 0.0320563 | ||||||||
\(295\) | −24.6405 | −1.43462 | ||||||||
\(296\) | 59.1873 | 3.44019 | ||||||||
\(297\) | 4.06780 | 0.236037 | ||||||||
\(298\) | −17.7877 | −1.03041 | ||||||||
\(299\) | −1.63134 | −0.0943427 | ||||||||
\(300\) | 63.4748 | 3.66472 | ||||||||
\(301\) | −30.8564 | −1.77853 | ||||||||
\(302\) | 17.6941 | 1.01818 | ||||||||
\(303\) | 2.42115 | 0.139091 | ||||||||
\(304\) | 12.4587 | 0.714554 | ||||||||
\(305\) | 11.4033 | 0.652952 | ||||||||
\(306\) | −15.9609 | −0.912424 | ||||||||
\(307\) | 11.5554 | 0.659501 | 0.329750 | − | 0.944068i | \(-0.393035\pi\) | ||||
0.329750 | + | 0.944068i | \(0.393035\pi\) | |||||||
\(308\) | 12.7907 | 0.728820 | ||||||||
\(309\) | 0.887205 | 0.0504713 | ||||||||
\(310\) | 49.3513 | 2.80297 | ||||||||
\(311\) | −0.388501 | −0.0220299 | −0.0110149 | − | 0.999939i | \(-0.503506\pi\) | ||||
−0.0110149 | + | 0.999939i | \(0.503506\pi\) | |||||||
\(312\) | 71.5246 | 4.04928 | ||||||||
\(313\) | 16.0482 | 0.907096 | 0.453548 | − | 0.891232i | \(-0.350158\pi\) | ||||
0.453548 | + | 0.891232i | \(0.350158\pi\) | |||||||
\(314\) | −44.7917 | −2.52774 | ||||||||
\(315\) | 8.51785 | 0.479926 | ||||||||
\(316\) | 53.3837 | 3.00307 | ||||||||
\(317\) | 0.917078 | 0.0515082 | 0.0257541 | − | 0.999668i | \(-0.491801\pi\) | ||||
0.0257541 | + | 0.999668i | \(0.491801\pi\) | |||||||
\(318\) | 67.0774 | 3.76151 | ||||||||
\(319\) | −7.39206 | −0.413876 | ||||||||
\(320\) | −31.2348 | −1.74608 | ||||||||
\(321\) | 8.64771 | 0.482668 | ||||||||
\(322\) | 2.34960 | 0.130938 | ||||||||
\(323\) | 7.95884 | 0.442842 | ||||||||
\(324\) | −53.3518 | −2.96399 | ||||||||
\(325\) | −31.3141 | −1.73699 | ||||||||
\(326\) | 45.3007 | 2.50897 | ||||||||
\(327\) | −30.1507 | −1.66734 | ||||||||
\(328\) | −26.6974 | −1.47412 | ||||||||
\(329\) | −7.62543 | −0.420404 | ||||||||
\(330\) | −17.7174 | −0.975312 | ||||||||
\(331\) | 20.0616 | 1.10268 | 0.551342 | − | 0.834280i | \(-0.314116\pi\) | ||||
0.551342 | + | 0.834280i | \(0.314116\pi\) | |||||||
\(332\) | 84.2583 | 4.62427 | ||||||||
\(333\) | −7.50535 | −0.411291 | ||||||||
\(334\) | 4.90590 | 0.268439 | ||||||||
\(335\) | 22.9288 | 1.25273 | ||||||||
\(336\) | −52.1457 | −2.84478 | ||||||||
\(337\) | −2.64737 | −0.144211 | −0.0721056 | − | 0.997397i | \(-0.522972\pi\) | ||||
−0.0721056 | + | 0.997397i | \(0.522972\pi\) | |||||||
\(338\) | −25.7863 | −1.40259 | ||||||||
\(339\) | −10.8825 | −0.591054 | ||||||||
\(340\) | −105.630 | −5.72858 | ||||||||
\(341\) | −5.53910 | −0.299959 | ||||||||
\(342\) | −3.12106 | −0.168767 | ||||||||
\(343\) | 18.6571 | 1.00739 | ||||||||
\(344\) | −88.4475 | −4.76877 | ||||||||
\(345\) | −2.30730 | −0.124221 | ||||||||
\(346\) | 17.0683 | 0.917596 | ||||||||
\(347\) | −32.0944 | −1.72292 | −0.861458 | − | 0.507828i | \(-0.830448\pi\) | ||||
−0.861458 | + | 0.507828i | \(0.830448\pi\) | |||||||
\(348\) | 71.6060 | 3.83848 | ||||||||
\(349\) | −12.3599 | −0.661612 | −0.330806 | − | 0.943699i | \(-0.607321\pi\) | ||||
−0.330806 | + | 0.943699i | \(0.607321\pi\) | |||||||
\(350\) | 45.1014 | 2.41077 | ||||||||
\(351\) | 19.4393 | 1.03759 | ||||||||
\(352\) | 11.1254 | 0.592986 | ||||||||
\(353\) | 19.7893 | 1.05328 | 0.526639 | − | 0.850089i | \(-0.323452\pi\) | ||||
0.526639 | + | 0.850089i | \(0.323452\pi\) | |||||||
\(354\) | −37.7892 | −2.00847 | ||||||||
\(355\) | 14.8914 | 0.790353 | ||||||||
\(356\) | 90.1386 | 4.77733 | ||||||||
\(357\) | −33.3117 | −1.76304 | ||||||||
\(358\) | −21.0671 | −1.11343 | ||||||||
\(359\) | −12.0187 | −0.634323 | −0.317161 | − | 0.948372i | \(-0.602730\pi\) | ||||
−0.317161 | + | 0.948372i | \(0.602730\pi\) | |||||||
\(360\) | 24.4157 | 1.28682 | ||||||||
\(361\) | −17.4437 | −0.918089 | ||||||||
\(362\) | 60.7632 | 3.19364 | ||||||||
\(363\) | 1.98857 | 0.104373 | ||||||||
\(364\) | 61.1247 | 3.20381 | ||||||||
\(365\) | 54.6227 | 2.85908 | ||||||||
\(366\) | 17.4884 | 0.914132 | ||||||||
\(367\) | −36.9937 | −1.93106 | −0.965528 | − | 0.260299i | \(-0.916179\pi\) | ||||
−0.965528 | + | 0.260299i | \(0.916179\pi\) | |||||||
\(368\) | 3.40916 | 0.177715 | ||||||||
\(369\) | 3.38542 | 0.176238 | ||||||||
\(370\) | −70.0640 | −3.64245 | ||||||||
\(371\) | 33.7886 | 1.75421 | ||||||||
\(372\) | 53.6565 | 2.78196 | ||||||||
\(373\) | −9.41821 | −0.487656 | −0.243828 | − | 0.969818i | \(-0.578403\pi\) | ||||
−0.243828 | + | 0.969818i | \(0.578403\pi\) | |||||||
\(374\) | 16.7233 | 0.864740 | ||||||||
\(375\) | −10.4945 | −0.541931 | ||||||||
\(376\) | −21.8577 | −1.12723 | ||||||||
\(377\) | −35.3254 | −1.81935 | ||||||||
\(378\) | −27.9982 | −1.44007 | ||||||||
\(379\) | 26.4154 | 1.35687 | 0.678433 | − | 0.734662i | \(-0.262659\pi\) | ||||
0.678433 | + | 0.734662i | \(0.262659\pi\) | |||||||
\(380\) | −20.6553 | −1.05959 | ||||||||
\(381\) | 28.8442 | 1.47774 | ||||||||
\(382\) | 44.4860 | 2.27610 | ||||||||
\(383\) | 25.8275 | 1.31972 | 0.659862 | − | 0.751387i | \(-0.270615\pi\) | ||||
0.659862 | + | 0.751387i | \(0.270615\pi\) | |||||||
\(384\) | −3.65511 | −0.186524 | ||||||||
\(385\) | −8.92471 | −0.454845 | ||||||||
\(386\) | 35.3883 | 1.80122 | ||||||||
\(387\) | 11.2157 | 0.570129 | ||||||||
\(388\) | 6.86399 | 0.348466 | ||||||||
\(389\) | −11.2536 | −0.570581 | −0.285291 | − | 0.958441i | \(-0.592090\pi\) | ||||
−0.285291 | + | 0.958441i | \(0.592090\pi\) | |||||||
\(390\) | −84.6685 | −4.28736 | ||||||||
\(391\) | 2.17784 | 0.110138 | ||||||||
\(392\) | 0.793635 | 0.0400846 | ||||||||
\(393\) | 24.0383 | 1.21257 | ||||||||
\(394\) | −48.2510 | −2.43085 | ||||||||
\(395\) | −37.2483 | −1.87417 | ||||||||
\(396\) | −4.64920 | −0.233631 | ||||||||
\(397\) | −2.18903 | −0.109864 | −0.0549320 | − | 0.998490i | \(-0.517494\pi\) | ||||
−0.0549320 | + | 0.998490i | \(0.517494\pi\) | |||||||
\(398\) | −59.9743 | −3.00624 | ||||||||
\(399\) | −6.51390 | −0.326103 | ||||||||
\(400\) | 65.4399 | 3.27199 | ||||||||
\(401\) | 4.99967 | 0.249672 | 0.124836 | − | 0.992177i | \(-0.460160\pi\) | ||||
0.124836 | + | 0.992177i | \(0.460160\pi\) | |||||||
\(402\) | 35.1641 | 1.75383 | ||||||||
\(403\) | −26.4704 | −1.31858 | ||||||||
\(404\) | 5.93093 | 0.295075 | ||||||||
\(405\) | 37.2261 | 1.84978 | ||||||||
\(406\) | 50.8789 | 2.52508 | ||||||||
\(407\) | 7.86385 | 0.389797 | ||||||||
\(408\) | −95.4854 | −4.72723 | ||||||||
\(409\) | 22.0928 | 1.09242 | 0.546209 | − | 0.837649i | \(-0.316070\pi\) | ||||
0.546209 | + | 0.837649i | \(0.316070\pi\) | |||||||
\(410\) | 31.6036 | 1.56079 | ||||||||
\(411\) | −35.7746 | −1.76463 | ||||||||
\(412\) | 2.17333 | 0.107072 | ||||||||
\(413\) | −19.0353 | −0.936668 | ||||||||
\(414\) | −0.854037 | −0.0419736 | ||||||||
\(415\) | −58.7910 | −2.88594 | ||||||||
\(416\) | 53.1664 | 2.60670 | ||||||||
\(417\) | 22.7942 | 1.11624 | ||||||||
\(418\) | 3.27013 | 0.159948 | ||||||||
\(419\) | 11.0473 | 0.539697 | 0.269849 | − | 0.962903i | \(-0.413026\pi\) | ||||
0.269849 | + | 0.962903i | \(0.413026\pi\) | |||||||
\(420\) | 86.4525 | 4.21845 | ||||||||
\(421\) | −4.06262 | −0.198000 | −0.0990000 | − | 0.995087i | \(-0.531564\pi\) | ||||
−0.0990000 | + | 0.995087i | \(0.531564\pi\) | |||||||
\(422\) | 55.0620 | 2.68038 | ||||||||
\(423\) | 2.77171 | 0.134765 | ||||||||
\(424\) | 96.8522 | 4.70356 | ||||||||
\(425\) | 41.8043 | 2.02781 | ||||||||
\(426\) | 22.8378 | 1.10649 | ||||||||
\(427\) | 8.80934 | 0.426314 | ||||||||
\(428\) | 21.1837 | 1.02396 | ||||||||
\(429\) | 9.50303 | 0.458811 | ||||||||
\(430\) | 104.701 | 5.04915 | ||||||||
\(431\) | 4.48615 | 0.216090 | 0.108045 | − | 0.994146i | \(-0.465541\pi\) | ||||
0.108045 | + | 0.994146i | \(0.465541\pi\) | |||||||
\(432\) | −40.6241 | −1.95453 | ||||||||
\(433\) | −21.5501 | −1.03563 | −0.517817 | − | 0.855492i | \(-0.673255\pi\) | ||||
−0.517817 | + | 0.855492i | \(0.673255\pi\) | |||||||
\(434\) | 38.1251 | 1.83006 | ||||||||
\(435\) | −49.9629 | −2.39554 | ||||||||
\(436\) | −73.8584 | −3.53717 | ||||||||
\(437\) | 0.425862 | 0.0203718 | ||||||||
\(438\) | 83.7706 | 4.00271 | ||||||||
\(439\) | −24.3851 | −1.16384 | −0.581919 | − | 0.813247i | \(-0.697698\pi\) | ||||
−0.581919 | + | 0.813247i | \(0.697698\pi\) | |||||||
\(440\) | −25.5820 | −1.21957 | ||||||||
\(441\) | −0.100638 | −0.00479230 | ||||||||
\(442\) | 79.9177 | 3.80130 | ||||||||
\(443\) | −10.5395 | −0.500745 | −0.250372 | − | 0.968150i | \(-0.580553\pi\) | ||||
−0.250372 | + | 0.968150i | \(0.580553\pi\) | |||||||
\(444\) | −76.1761 | −3.61516 | ||||||||
\(445\) | −62.8940 | −2.98146 | ||||||||
\(446\) | 4.74818 | 0.224833 | ||||||||
\(447\) | 13.4940 | 0.638245 | ||||||||
\(448\) | −24.1296 | −1.14002 | ||||||||
\(449\) | −29.3277 | −1.38406 | −0.692030 | − | 0.721869i | \(-0.743283\pi\) | ||||
−0.692030 | + | 0.721869i | \(0.743283\pi\) | |||||||
\(450\) | −16.3935 | −0.772798 | ||||||||
\(451\) | −3.54712 | −0.167028 | ||||||||
\(452\) | −26.6581 | −1.25389 | ||||||||
\(453\) | −13.4230 | −0.630670 | ||||||||
\(454\) | 33.9535 | 1.59352 | ||||||||
\(455\) | −42.6497 | −1.99945 | ||||||||
\(456\) | −18.6716 | −0.874377 | ||||||||
\(457\) | −38.3699 | −1.79487 | −0.897433 | − | 0.441150i | \(-0.854571\pi\) | ||||
−0.897433 | + | 0.441150i | \(0.854571\pi\) | |||||||
\(458\) | 52.2317 | 2.44063 | ||||||||
\(459\) | −25.9515 | −1.21131 | ||||||||
\(460\) | −5.65205 | −0.263528 | ||||||||
\(461\) | 14.4851 | 0.674638 | 0.337319 | − | 0.941390i | \(-0.390480\pi\) | ||||
0.337319 | + | 0.941390i | \(0.390480\pi\) | |||||||
\(462\) | −13.6871 | −0.636783 | ||||||||
\(463\) | −10.3397 | −0.480525 | −0.240263 | − | 0.970708i | \(-0.577234\pi\) | ||||
−0.240263 | + | 0.970708i | \(0.577234\pi\) | |||||||
\(464\) | 73.8228 | 3.42714 | ||||||||
\(465\) | −37.4387 | −1.73618 | ||||||||
\(466\) | 20.7453 | 0.961006 | ||||||||
\(467\) | 10.2825 | 0.475817 | 0.237908 | − | 0.971288i | \(-0.423538\pi\) | ||||
0.237908 | + | 0.971288i | \(0.423538\pi\) | |||||||
\(468\) | −22.2177 | −1.02701 | ||||||||
\(469\) | 17.7130 | 0.817912 | ||||||||
\(470\) | 25.8745 | 1.19350 | ||||||||
\(471\) | 33.9797 | 1.56570 | ||||||||
\(472\) | −54.5633 | −2.51148 | ||||||||
\(473\) | −11.7515 | −0.540334 | ||||||||
\(474\) | −57.1249 | −2.62383 | ||||||||
\(475\) | 8.17457 | 0.375075 | ||||||||
\(476\) | −81.6016 | −3.74020 | ||||||||
\(477\) | −12.2815 | −0.562332 | ||||||||
\(478\) | 17.3320 | 0.792745 | ||||||||
\(479\) | −13.4202 | −0.613186 | −0.306593 | − | 0.951841i | \(-0.599189\pi\) | ||||
−0.306593 | + | 0.951841i | \(0.599189\pi\) | |||||||
\(480\) | 75.1965 | 3.43224 | ||||||||
\(481\) | 37.5800 | 1.71350 | ||||||||
\(482\) | 53.6531 | 2.44383 | ||||||||
\(483\) | −1.78245 | −0.0811041 | ||||||||
\(484\) | 4.87127 | 0.221422 | ||||||||
\(485\) | −4.78933 | −0.217472 | ||||||||
\(486\) | 25.1019 | 1.13865 | ||||||||
\(487\) | 30.6858 | 1.39051 | 0.695253 | − | 0.718765i | \(-0.255292\pi\) | ||||
0.695253 | + | 0.718765i | \(0.255292\pi\) | |||||||
\(488\) | 25.2513 | 1.14307 | ||||||||
\(489\) | −34.3659 | −1.55408 | ||||||||
\(490\) | −0.939479 | −0.0424413 | ||||||||
\(491\) | 27.7664 | 1.25308 | 0.626541 | − | 0.779389i | \(-0.284470\pi\) | ||||
0.626541 | + | 0.779389i | \(0.284470\pi\) | |||||||
\(492\) | 34.3605 | 1.54909 | ||||||||
\(493\) | 47.1594 | 2.12395 | ||||||||
\(494\) | 15.6274 | 0.703110 | ||||||||
\(495\) | 3.24397 | 0.145806 | ||||||||
\(496\) | 55.3176 | 2.48383 | ||||||||
\(497\) | 11.5040 | 0.516023 | ||||||||
\(498\) | −90.1633 | −4.04031 | ||||||||
\(499\) | 10.7926 | 0.483145 | 0.241573 | − | 0.970383i | \(-0.422337\pi\) | ||||
0.241573 | + | 0.970383i | \(0.422337\pi\) | |||||||
\(500\) | −25.7076 | −1.14968 | ||||||||
\(501\) | −3.72170 | −0.166273 | ||||||||
\(502\) | 29.9414 | 1.33635 | ||||||||
\(503\) | 7.82077 | 0.348711 | 0.174355 | − | 0.984683i | \(-0.444216\pi\) | ||||
0.174355 | + | 0.984683i | \(0.444216\pi\) | |||||||
\(504\) | 18.8618 | 0.840169 | ||||||||
\(505\) | −4.13830 | −0.184152 | ||||||||
\(506\) | 0.894831 | 0.0397801 | ||||||||
\(507\) | 19.5619 | 0.868777 | ||||||||
\(508\) | 70.6579 | 3.13494 | ||||||||
\(509\) | −16.7584 | −0.742804 | −0.371402 | − | 0.928472i | \(-0.621123\pi\) | ||||
−0.371402 | + | 0.928472i | \(0.621123\pi\) | |||||||
\(510\) | 113.033 | 5.00517 | ||||||||
\(511\) | 42.1973 | 1.86670 | ||||||||
\(512\) | 39.2240 | 1.73347 | ||||||||
\(513\) | −5.07465 | −0.224051 | ||||||||
\(514\) | 26.1665 | 1.15415 | ||||||||
\(515\) | −1.51644 | −0.0668222 | ||||||||
\(516\) | 113.835 | 5.01131 | ||||||||
\(517\) | −2.90410 | −0.127722 | ||||||||
\(518\) | −54.1261 | −2.37817 | ||||||||
\(519\) | −12.9483 | −0.568366 | ||||||||
\(520\) | −122.252 | −5.36110 | ||||||||
\(521\) | 16.7968 | 0.735881 | 0.367940 | − | 0.929849i | \(-0.380063\pi\) | ||||
0.367940 | + | 0.929849i | \(0.380063\pi\) | |||||||
\(522\) | −18.4935 | −0.809440 | ||||||||
\(523\) | 32.6983 | 1.42980 | 0.714898 | − | 0.699228i | \(-0.246473\pi\) | ||||
0.714898 | + | 0.699228i | \(0.246473\pi\) | |||||||
\(524\) | 58.8851 | 2.57241 | ||||||||
\(525\) | −34.2146 | −1.49325 | ||||||||
\(526\) | 83.0088 | 3.61936 | ||||||||
\(527\) | 35.3380 | 1.53935 | ||||||||
\(528\) | −19.8594 | −0.864268 | ||||||||
\(529\) | −22.8835 | −0.994933 | ||||||||
\(530\) | −114.651 | −4.98010 | ||||||||
\(531\) | 6.91900 | 0.300259 | ||||||||
\(532\) | −15.9567 | −0.691810 | ||||||||
\(533\) | −16.9511 | −0.734233 | ||||||||
\(534\) | −96.4556 | −4.17404 | ||||||||
\(535\) | −14.7809 | −0.639035 | ||||||||
\(536\) | 50.7730 | 2.19306 | ||||||||
\(537\) | 15.9818 | 0.689667 | ||||||||
\(538\) | −15.7034 | −0.677020 | ||||||||
\(539\) | 0.105445 | 0.00454185 | ||||||||
\(540\) | 67.3508 | 2.89832 | ||||||||
\(541\) | −6.07192 | −0.261052 | −0.130526 | − | 0.991445i | \(-0.541667\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(542\) | 22.1655 | 0.952089 | ||||||||
\(543\) | −46.0960 | −1.97817 | ||||||||
\(544\) | −70.9771 | −3.04312 | ||||||||
\(545\) | 51.5345 | 2.20750 | ||||||||
\(546\) | −65.4085 | −2.79922 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −87.6348 | −3.74357 | ||||||||
\(549\) | −3.20203 | −0.136659 | ||||||||
\(550\) | 17.1766 | 0.732412 | ||||||||
\(551\) | 9.22174 | 0.392859 | ||||||||
\(552\) | −5.10924 | −0.217464 | ||||||||
\(553\) | −28.7752 | −1.22365 | ||||||||
\(554\) | 5.53061 | 0.234973 | ||||||||
\(555\) | 53.1517 | 2.25616 | ||||||||
\(556\) | 55.8375 | 2.36804 | ||||||||
\(557\) | 22.9557 | 0.972665 | 0.486333 | − | 0.873774i | \(-0.338334\pi\) | ||||
0.486333 | + | 0.873774i | \(0.338334\pi\) | |||||||
\(558\) | −13.8578 | −0.586646 | ||||||||
\(559\) | −56.1583 | −2.37524 | ||||||||
\(560\) | 89.1289 | 3.76639 | ||||||||
\(561\) | −12.6866 | −0.535627 | ||||||||
\(562\) | 50.2826 | 2.12104 | ||||||||
\(563\) | 29.3636 | 1.23753 | 0.618764 | − | 0.785577i | \(-0.287634\pi\) | ||||
0.618764 | + | 0.785577i | \(0.287634\pi\) | |||||||
\(564\) | 28.1316 | 1.18456 | ||||||||
\(565\) | 18.6006 | 0.782534 | ||||||||
\(566\) | −10.4659 | −0.439913 | ||||||||
\(567\) | 28.7581 | 1.20773 | ||||||||
\(568\) | 32.9752 | 1.38361 | ||||||||
\(569\) | −27.1032 | −1.13623 | −0.568113 | − | 0.822951i | \(-0.692326\pi\) | ||||
−0.568113 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(570\) | 22.1028 | 0.925785 | ||||||||
\(571\) | 35.4328 | 1.48282 | 0.741408 | − | 0.671055i | \(-0.234159\pi\) | ||||
0.741408 | + | 0.671055i | \(0.234159\pi\) | |||||||
\(572\) | 23.2790 | 0.973343 | ||||||||
\(573\) | −33.7478 | −1.40983 | ||||||||
\(574\) | 24.4145 | 1.01904 | ||||||||
\(575\) | 2.23687 | 0.0932838 | ||||||||
\(576\) | 8.77068 | 0.365445 | ||||||||
\(577\) | −23.5697 | −0.981219 | −0.490610 | − | 0.871380i | \(-0.663226\pi\) | ||||
−0.490610 | + | 0.871380i | \(0.663226\pi\) | |||||||
\(578\) | −62.1278 | −2.58418 | ||||||||
\(579\) | −26.8462 | −1.11569 | ||||||||
\(580\) | −122.391 | −5.08201 | ||||||||
\(581\) | −45.4175 | −1.88423 | ||||||||
\(582\) | −7.34503 | −0.304461 | ||||||||
\(583\) | 12.8682 | 0.532945 | ||||||||
\(584\) | 120.955 | 5.00517 | ||||||||
\(585\) | 15.5024 | 0.640944 | ||||||||
\(586\) | −12.2729 | −0.506987 | ||||||||
\(587\) | −26.0626 | −1.07572 | −0.537859 | − | 0.843035i | \(-0.680767\pi\) | ||||
−0.537859 | + | 0.843035i | \(0.680767\pi\) | |||||||
\(588\) | −1.02144 | −0.0421233 | ||||||||
\(589\) | 6.91013 | 0.284727 | ||||||||
\(590\) | 64.5903 | 2.65914 | ||||||||
\(591\) | 36.6040 | 1.50569 | ||||||||
\(592\) | −78.5344 | −3.22774 | ||||||||
\(593\) | 28.2838 | 1.16148 | 0.580739 | − | 0.814090i | \(-0.302764\pi\) | ||||
0.580739 | + | 0.814090i | \(0.302764\pi\) | |||||||
\(594\) | −10.6630 | −0.437507 | ||||||||
\(595\) | 56.9373 | 2.33420 | ||||||||
\(596\) | 33.0554 | 1.35400 | ||||||||
\(597\) | 45.4975 | 1.86209 | ||||||||
\(598\) | 4.27624 | 0.174869 | ||||||||
\(599\) | −12.7547 | −0.521142 | −0.260571 | − | 0.965455i | \(-0.583911\pi\) | ||||
−0.260571 | + | 0.965455i | \(0.583911\pi\) | |||||||
\(600\) | −98.0736 | −4.00384 | ||||||||
\(601\) | 48.1728 | 1.96501 | 0.982505 | − | 0.186237i | \(-0.0596293\pi\) | ||||
0.982505 | + | 0.186237i | \(0.0596293\pi\) | |||||||
\(602\) | 80.8843 | 3.29660 | ||||||||
\(603\) | −6.43837 | −0.262191 | ||||||||
\(604\) | −32.8816 | −1.33793 | ||||||||
\(605\) | −3.39892 | −0.138186 | ||||||||
\(606\) | −6.34659 | −0.257812 | ||||||||
\(607\) | −46.6140 | −1.89200 | −0.946002 | − | 0.324160i | \(-0.894918\pi\) | ||||
−0.946002 | + | 0.324160i | \(0.894918\pi\) | |||||||
\(608\) | −13.8791 | −0.562874 | ||||||||
\(609\) | −38.5976 | −1.56405 | ||||||||
\(610\) | −29.8916 | −1.21028 | ||||||||
\(611\) | −13.8782 | −0.561452 | ||||||||
\(612\) | 29.6607 | 1.19896 | ||||||||
\(613\) | −28.1114 | −1.13541 | −0.567704 | − | 0.823233i | \(-0.692168\pi\) | ||||
−0.567704 | + | 0.823233i | \(0.692168\pi\) | |||||||
\(614\) | −30.2903 | −1.22242 | ||||||||
\(615\) | −23.9750 | −0.966765 | ||||||||
\(616\) | −19.7627 | −0.796262 | ||||||||
\(617\) | 10.9689 | 0.441590 | 0.220795 | − | 0.975320i | \(-0.429135\pi\) | ||||
0.220795 | + | 0.975320i | \(0.429135\pi\) | |||||||
\(618\) | −2.32564 | −0.0935510 | ||||||||
\(619\) | −19.8238 | −0.796785 | −0.398392 | − | 0.917215i | \(-0.630432\pi\) | ||||
−0.398392 | + | 0.917215i | \(0.630432\pi\) | |||||||
\(620\) | −91.7113 | −3.68321 | ||||||||
\(621\) | −1.38861 | −0.0557232 | ||||||||
\(622\) | 1.01838 | 0.0408334 | ||||||||
\(623\) | −48.5871 | −1.94660 | ||||||||
\(624\) | −94.9045 | −3.79922 | ||||||||
\(625\) | −14.8259 | −0.593036 | ||||||||
\(626\) | −42.0673 | −1.68135 | ||||||||
\(627\) | −2.48078 | −0.0990727 | ||||||||
\(628\) | 83.2380 | 3.32156 | ||||||||
\(629\) | −50.1693 | −2.00038 | ||||||||
\(630\) | −22.3279 | −0.889566 | ||||||||
\(631\) | −38.6081 | −1.53696 | −0.768481 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768481 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(632\) | −82.4820 | −3.28096 | ||||||||
\(633\) | −41.7710 | −1.66025 | ||||||||
\(634\) | −2.40395 | −0.0954729 | ||||||||
\(635\) | −49.3014 | −1.95647 | ||||||||
\(636\) | −124.652 | −4.94278 | ||||||||
\(637\) | 0.503905 | 0.0199654 | ||||||||
\(638\) | 19.3769 | 0.767139 | ||||||||
\(639\) | −4.18148 | −0.165417 | ||||||||
\(640\) | 6.24742 | 0.246951 | ||||||||
\(641\) | −44.1434 | −1.74356 | −0.871779 | − | 0.489899i | \(-0.837034\pi\) | ||||
−0.871779 | + | 0.489899i | \(0.837034\pi\) | |||||||
\(642\) | −22.6683 | −0.894648 | ||||||||
\(643\) | 47.5060 | 1.87345 | 0.936727 | − | 0.350059i | \(-0.113839\pi\) | ||||
0.936727 | + | 0.350059i | \(0.113839\pi\) | |||||||
\(644\) | −4.36634 | −0.172058 | ||||||||
\(645\) | −79.4282 | −3.12748 | ||||||||
\(646\) | −20.8626 | −0.820828 | ||||||||
\(647\) | −42.0758 | −1.65417 | −0.827085 | − | 0.562077i | \(-0.810003\pi\) | ||||
−0.827085 | + | 0.562077i | \(0.810003\pi\) | |||||||
\(648\) | 82.4328 | 3.23826 | ||||||||
\(649\) | −7.24949 | −0.284568 | ||||||||
\(650\) | 82.0839 | 3.21960 | ||||||||
\(651\) | −28.9223 | −1.13355 | ||||||||
\(652\) | −84.1838 | −3.29689 | ||||||||
\(653\) | −7.61860 | −0.298139 | −0.149069 | − | 0.988827i | \(-0.547628\pi\) | ||||
−0.149069 | + | 0.988827i | \(0.547628\pi\) | |||||||
\(654\) | 79.0345 | 3.09049 | ||||||||
\(655\) | −41.0870 | −1.60540 | ||||||||
\(656\) | 35.4243 | 1.38309 | ||||||||
\(657\) | −15.3380 | −0.598391 | ||||||||
\(658\) | 19.9886 | 0.779238 | ||||||||
\(659\) | 17.9862 | 0.700641 | 0.350321 | − | 0.936630i | \(-0.386073\pi\) | ||||
0.350321 | + | 0.936630i | \(0.386073\pi\) | |||||||
\(660\) | 32.9249 | 1.28160 | ||||||||
\(661\) | −21.9803 | −0.854934 | −0.427467 | − | 0.904031i | \(-0.640594\pi\) | ||||
−0.427467 | + | 0.904031i | \(0.640594\pi\) | |||||||
\(662\) | −52.5876 | −2.04388 | ||||||||
\(663\) | −60.6269 | −2.35455 | ||||||||
\(664\) | −130.186 | −5.05218 | ||||||||
\(665\) | 11.1337 | 0.431748 | ||||||||
\(666\) | 19.6739 | 0.762347 | ||||||||
\(667\) | 2.52341 | 0.0977069 | ||||||||
\(668\) | −9.11680 | −0.352740 | ||||||||
\(669\) | −3.60205 | −0.139263 | ||||||||
\(670\) | −60.1035 | −2.32200 | ||||||||
\(671\) | 3.35498 | 0.129518 | ||||||||
\(672\) | 58.0911 | 2.24091 | ||||||||
\(673\) | −32.2772 | −1.24419 | −0.622097 | − | 0.782940i | \(-0.713719\pi\) | ||||
−0.622097 | + | 0.782940i | \(0.713719\pi\) | |||||||
\(674\) | 6.93957 | 0.267302 | ||||||||
\(675\) | −26.6549 | −1.02595 | ||||||||
\(676\) | 47.9197 | 1.84306 | ||||||||
\(677\) | −15.9664 | −0.613637 | −0.306819 | − | 0.951768i | \(-0.599265\pi\) | ||||
−0.306819 | + | 0.951768i | \(0.599265\pi\) | |||||||
\(678\) | 28.5263 | 1.09555 | ||||||||
\(679\) | −3.69988 | −0.141988 | ||||||||
\(680\) | 163.206 | 6.25868 | ||||||||
\(681\) | −25.7577 | −0.987038 | ||||||||
\(682\) | 14.5197 | 0.555988 | ||||||||
\(683\) | −34.0716 | −1.30371 | −0.651856 | − | 0.758343i | \(-0.726009\pi\) | ||||
−0.651856 | + | 0.758343i | \(0.726009\pi\) | |||||||
\(684\) | 5.79996 | 0.221767 | ||||||||
\(685\) | 61.1470 | 2.33631 | ||||||||
\(686\) | −48.9061 | −1.86724 | ||||||||
\(687\) | −39.6238 | −1.51174 | ||||||||
\(688\) | 117.359 | 4.47428 | ||||||||
\(689\) | 61.4947 | 2.34276 | ||||||||
\(690\) | 6.04816 | 0.230249 | ||||||||
\(691\) | 15.1627 | 0.576815 | 0.288407 | − | 0.957508i | \(-0.406874\pi\) | ||||
0.288407 | + | 0.957508i | \(0.406874\pi\) | |||||||
\(692\) | −31.7186 | −1.20576 | ||||||||
\(693\) | 2.50605 | 0.0951968 | ||||||||
\(694\) | 84.1294 | 3.19351 | ||||||||
\(695\) | −38.9605 | −1.47786 | ||||||||
\(696\) | −110.637 | −4.19368 | ||||||||
\(697\) | 22.6297 | 0.857162 | ||||||||
\(698\) | 32.3992 | 1.22633 | ||||||||
\(699\) | −15.7377 | −0.595254 | ||||||||
\(700\) | −83.8134 | −3.16785 | ||||||||
\(701\) | −24.3826 | −0.920918 | −0.460459 | − | 0.887681i | \(-0.652315\pi\) | ||||
−0.460459 | + | 0.887681i | \(0.652315\pi\) | |||||||
\(702\) | −50.9564 | −1.92323 | ||||||||
\(703\) | −9.81030 | −0.370002 | ||||||||
\(704\) | −9.18962 | −0.346347 | ||||||||
\(705\) | −19.6288 | −0.739263 | ||||||||
\(706\) | −51.8739 | −1.95230 | ||||||||
\(707\) | −3.19693 | −0.120233 | ||||||||
\(708\) | 70.2249 | 2.63921 | ||||||||
\(709\) | 22.9588 | 0.862234 | 0.431117 | − | 0.902296i | \(-0.358120\pi\) | ||||
0.431117 | + | 0.902296i | \(0.358120\pi\) | |||||||
\(710\) | −39.0350 | −1.46496 | ||||||||
\(711\) | 10.4593 | 0.392254 | ||||||||
\(712\) | −139.271 | −5.21941 | ||||||||
\(713\) | 1.89087 | 0.0708136 | ||||||||
\(714\) | 87.3204 | 3.26788 | ||||||||
\(715\) | −16.2429 | −0.607448 | ||||||||
\(716\) | 39.1497 | 1.46309 | ||||||||
\(717\) | −13.1483 | −0.491033 | ||||||||
\(718\) | 31.5048 | 1.17575 | ||||||||
\(719\) | 12.5563 | 0.468269 | 0.234135 | − | 0.972204i | \(-0.424774\pi\) | ||||
0.234135 | + | 0.972204i | \(0.424774\pi\) | |||||||
\(720\) | −32.3967 | −1.20736 | ||||||||
\(721\) | −1.17148 | −0.0436283 | ||||||||
\(722\) | 45.7254 | 1.70172 | ||||||||
\(723\) | −40.7021 | −1.51373 | ||||||||
\(724\) | −112.918 | −4.19658 | ||||||||
\(725\) | 48.4377 | 1.79893 | ||||||||
\(726\) | −5.21266 | −0.193460 | ||||||||
\(727\) | −12.7478 | −0.472788 | −0.236394 | − | 0.971657i | \(-0.575966\pi\) | ||||
−0.236394 | + | 0.971657i | \(0.575966\pi\) | |||||||
\(728\) | −94.4425 | −3.50027 | ||||||||
\(729\) | 13.8143 | 0.511639 | ||||||||
\(730\) | −143.183 | −5.29944 | ||||||||
\(731\) | 74.9713 | 2.77292 | ||||||||
\(732\) | −32.4993 | −1.20121 | ||||||||
\(733\) | −8.10796 | −0.299475 | −0.149737 | − | 0.988726i | \(-0.547843\pi\) | ||||
−0.149737 | + | 0.988726i | \(0.547843\pi\) | |||||||
\(734\) | 96.9720 | 3.57930 | ||||||||
\(735\) | 0.712704 | 0.0262885 | ||||||||
\(736\) | −3.79785 | −0.139991 | ||||||||
\(737\) | 6.74590 | 0.248488 | ||||||||
\(738\) | −8.87423 | −0.326665 | ||||||||
\(739\) | −9.52182 | −0.350266 | −0.175133 | − | 0.984545i | \(-0.556036\pi\) | ||||
−0.175133 | + | 0.984545i | \(0.556036\pi\) | |||||||
\(740\) | 130.202 | 4.78633 | ||||||||
\(741\) | −11.8552 | −0.435512 | ||||||||
\(742\) | −88.5703 | −3.25152 | ||||||||
\(743\) | 12.3149 | 0.451789 | 0.225895 | − | 0.974152i | \(-0.427469\pi\) | ||||
0.225895 | + | 0.974152i | \(0.427469\pi\) | |||||||
\(744\) | −82.9036 | −3.03939 | ||||||||
\(745\) | −23.0644 | −0.845013 | ||||||||
\(746\) | 24.6881 | 0.903894 | ||||||||
\(747\) | 16.5084 | 0.604012 | ||||||||
\(748\) | −31.0774 | −1.13630 | ||||||||
\(749\) | −11.4186 | −0.417227 | ||||||||
\(750\) | 27.5092 | 1.00450 | ||||||||
\(751\) | 23.7336 | 0.866053 | 0.433026 | − | 0.901381i | \(-0.357446\pi\) | ||||
0.433026 | + | 0.901381i | \(0.357446\pi\) | |||||||
\(752\) | 29.0025 | 1.05761 | ||||||||
\(753\) | −22.7140 | −0.827745 | ||||||||
\(754\) | 92.5989 | 3.37225 | ||||||||
\(755\) | 22.9431 | 0.834983 | ||||||||
\(756\) | 52.0301 | 1.89232 | ||||||||
\(757\) | 29.1425 | 1.05920 | 0.529602 | − | 0.848246i | \(-0.322341\pi\) | ||||
0.529602 | + | 0.848246i | \(0.322341\pi\) | |||||||
\(758\) | −69.2429 | −2.51502 | ||||||||
\(759\) | −0.678834 | −0.0246401 | ||||||||
\(760\) | 31.9140 | 1.15764 | ||||||||
\(761\) | 20.5084 | 0.743430 | 0.371715 | − | 0.928347i | \(-0.378770\pi\) | ||||
0.371715 | + | 0.928347i | \(0.378770\pi\) | |||||||
\(762\) | −75.6097 | −2.73905 | ||||||||
\(763\) | 39.8117 | 1.44128 | ||||||||
\(764\) | −82.6698 | −2.99089 | ||||||||
\(765\) | −20.6957 | −0.748254 | ||||||||
\(766\) | −67.7019 | −2.44617 | ||||||||
\(767\) | −34.6441 | −1.25093 | ||||||||
\(768\) | −26.9672 | −0.973096 | ||||||||
\(769\) | −30.9971 | −1.11778 | −0.558892 | − | 0.829240i | \(-0.688773\pi\) | ||||
−0.558892 | + | 0.829240i | \(0.688773\pi\) | |||||||
\(770\) | 23.3944 | 0.843077 | ||||||||
\(771\) | −19.8503 | −0.714892 | ||||||||
\(772\) | −65.7633 | −2.36687 | ||||||||
\(773\) | −19.9782 | −0.718566 | −0.359283 | − | 0.933229i | \(-0.616979\pi\) | ||||
−0.359283 | + | 0.933229i | \(0.616979\pi\) | |||||||
\(774\) | −29.4000 | −1.05676 | ||||||||
\(775\) | 36.2959 | 1.30379 | ||||||||
\(776\) | −10.6054 | −0.380712 | ||||||||
\(777\) | 41.0610 | 1.47305 | ||||||||
\(778\) | 29.4992 | 1.05760 | ||||||||
\(779\) | 4.42510 | 0.158546 | ||||||||
\(780\) | 157.342 | 5.63376 | ||||||||
\(781\) | 4.38121 | 0.156772 | ||||||||
\(782\) | −5.70879 | −0.204146 | ||||||||
\(783\) | −30.0694 | −1.07459 | ||||||||
\(784\) | −1.05306 | −0.0376092 | ||||||||
\(785\) | −58.0791 | −2.07293 | ||||||||
\(786\) | −63.0119 | −2.24756 | ||||||||
\(787\) | −5.62379 | −0.200466 | −0.100233 | − | 0.994964i | \(-0.531959\pi\) | ||||
−0.100233 | + | 0.994964i | \(0.531959\pi\) | |||||||
\(788\) | 89.6665 | 3.19424 | ||||||||
\(789\) | −62.9719 | −2.24186 | ||||||||
\(790\) | 97.6395 | 3.47386 | ||||||||
\(791\) | 14.3694 | 0.510918 | ||||||||
\(792\) | 7.18338 | 0.255250 | ||||||||
\(793\) | 16.0329 | 0.569344 | ||||||||
\(794\) | 5.73812 | 0.203638 | ||||||||
\(795\) | 86.9758 | 3.08471 | ||||||||
\(796\) | 111.452 | 3.95032 | ||||||||
\(797\) | 46.0882 | 1.63253 | 0.816264 | − | 0.577679i | \(-0.196041\pi\) | ||||
0.816264 | + | 0.577679i | \(0.196041\pi\) | |||||||
\(798\) | 17.0750 | 0.604447 | ||||||||
\(799\) | 18.5274 | 0.655452 | ||||||||
\(800\) | −72.9010 | −2.57744 | ||||||||
\(801\) | 17.6605 | 0.624004 | ||||||||
\(802\) | −13.1057 | −0.462778 | ||||||||
\(803\) | 16.0706 | 0.567119 | ||||||||
\(804\) | −65.3467 | −2.30460 | ||||||||
\(805\) | 3.04661 | 0.107379 | ||||||||
\(806\) | 69.3871 | 2.44406 | ||||||||
\(807\) | 11.9128 | 0.419352 | ||||||||
\(808\) | −9.16376 | −0.322380 | ||||||||
\(809\) | 43.4188 | 1.52652 | 0.763262 | − | 0.646089i | \(-0.223597\pi\) | ||||
0.763262 | + | 0.646089i | \(0.223597\pi\) | |||||||
\(810\) | −97.5812 | −3.42866 | ||||||||
\(811\) | 7.13376 | 0.250500 | 0.125250 | − | 0.992125i | \(-0.460027\pi\) | ||||
0.125250 | + | 0.992125i | \(0.460027\pi\) | |||||||
\(812\) | −94.5500 | −3.31805 | ||||||||
\(813\) | −16.8151 | −0.589731 | ||||||||
\(814\) | −20.6136 | −0.722506 | ||||||||
\(815\) | 58.7391 | 2.05754 | ||||||||
\(816\) | 126.698 | 4.43530 | ||||||||
\(817\) | 14.6602 | 0.512895 | ||||||||
\(818\) | −57.9121 | −2.02485 | ||||||||
\(819\) | 11.9760 | 0.418474 | ||||||||
\(820\) | −58.7300 | −2.05094 | ||||||||
\(821\) | −26.5981 | −0.928280 | −0.464140 | − | 0.885762i | \(-0.653637\pi\) | ||||
−0.464140 | + | 0.885762i | \(0.653637\pi\) | |||||||
\(822\) | 93.7764 | 3.27083 | ||||||||
\(823\) | −0.831920 | −0.0289989 | −0.0144995 | − | 0.999895i | \(-0.504615\pi\) | ||||
−0.0144995 | + | 0.999895i | \(0.504615\pi\) | |||||||
\(824\) | −3.35797 | −0.116980 | ||||||||
\(825\) | −13.0304 | −0.453662 | ||||||||
\(826\) | 49.8976 | 1.73616 | ||||||||
\(827\) | 22.1773 | 0.771179 | 0.385589 | − | 0.922670i | \(-0.373998\pi\) | ||||
0.385589 | + | 0.922670i | \(0.373998\pi\) | |||||||
\(828\) | 1.58709 | 0.0551551 | ||||||||
\(829\) | −31.5224 | −1.09482 | −0.547408 | − | 0.836866i | \(-0.684386\pi\) | ||||
−0.547408 | + | 0.836866i | \(0.684386\pi\) | |||||||
\(830\) | 154.110 | 5.34922 | ||||||||
\(831\) | −4.19561 | −0.145544 | ||||||||
\(832\) | −43.9156 | −1.52250 | ||||||||
\(833\) | −0.672714 | −0.0233081 | ||||||||
\(834\) | −59.7507 | −2.06900 | ||||||||
\(835\) | 6.36123 | 0.220139 | ||||||||
\(836\) | −6.07700 | −0.210178 | ||||||||
\(837\) | −22.5319 | −0.778817 | ||||||||
\(838\) | −28.9585 | −1.00035 | ||||||||
\(839\) | 16.1003 | 0.555844 | 0.277922 | − | 0.960604i | \(-0.410354\pi\) | ||||
0.277922 | + | 0.960604i | \(0.410354\pi\) | |||||||
\(840\) | −133.576 | −4.60881 | ||||||||
\(841\) | 25.6426 | 0.884228 | ||||||||
\(842\) | 10.6494 | 0.367002 | ||||||||
\(843\) | −38.1452 | −1.31379 | ||||||||
\(844\) | −102.324 | −3.52213 | ||||||||
\(845\) | −33.4358 | −1.15023 | ||||||||
\(846\) | −7.26551 | −0.249793 | ||||||||
\(847\) | −2.62575 | −0.0902218 | ||||||||
\(848\) | −128.511 | −4.41309 | ||||||||
\(849\) | 7.93958 | 0.272486 | ||||||||
\(850\) | −109.582 | −3.75863 | ||||||||
\(851\) | −2.68446 | −0.0920222 | ||||||||
\(852\) | −42.4402 | −1.45398 | ||||||||
\(853\) | −9.49455 | −0.325087 | −0.162544 | − | 0.986701i | \(-0.551970\pi\) | ||||
−0.162544 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(854\) | −23.0920 | −0.790192 | ||||||||
\(855\) | −4.04691 | −0.138402 | ||||||||
\(856\) | −32.7306 | −1.11871 | ||||||||
\(857\) | −53.4992 | −1.82750 | −0.913750 | − | 0.406278i | \(-0.866826\pi\) | ||||
−0.913750 | + | 0.406278i | \(0.866826\pi\) | |||||||
\(858\) | −24.9104 | −0.850427 | ||||||||
\(859\) | −11.2340 | −0.383298 | −0.191649 | − | 0.981464i | \(-0.561383\pi\) | ||||
−0.191649 | + | 0.981464i | \(0.561383\pi\) | |||||||
\(860\) | −194.570 | −6.63479 | ||||||||
\(861\) | −18.5213 | −0.631203 | ||||||||
\(862\) | −11.7596 | −0.400533 | ||||||||
\(863\) | 3.73858 | 0.127263 | 0.0636314 | − | 0.997973i | \(-0.479732\pi\) | ||||
0.0636314 | + | 0.997973i | \(0.479732\pi\) | |||||||
\(864\) | 45.2559 | 1.53964 | ||||||||
\(865\) | 22.1316 | 0.752496 | ||||||||
\(866\) | 56.4896 | 1.91960 | ||||||||
\(867\) | 47.1312 | 1.60066 | ||||||||
\(868\) | −70.8492 | −2.40478 | ||||||||
\(869\) | −10.9589 | −0.371754 | ||||||||
\(870\) | 130.968 | 4.44024 | ||||||||
\(871\) | 32.2375 | 1.09233 | ||||||||
\(872\) | 114.117 | 3.86449 | ||||||||
\(873\) | 1.34484 | 0.0455159 | ||||||||
\(874\) | −1.11632 | −0.0377600 | ||||||||
\(875\) | 13.8571 | 0.468455 | ||||||||
\(876\) | −155.674 | −5.25973 | ||||||||
\(877\) | −0.884778 | −0.0298768 | −0.0149384 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149384 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(878\) | 63.9210 | 2.15723 | ||||||||
\(879\) | 9.31040 | 0.314032 | ||||||||
\(880\) | 33.9442 | 1.14426 | ||||||||
\(881\) | 12.5963 | 0.424382 | 0.212191 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212191 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(882\) | 0.263804 | 0.00888275 | ||||||||
\(883\) | −46.5541 | −1.56667 | −0.783335 | − | 0.621600i | \(-0.786483\pi\) | ||||
−0.783335 | + | 0.621600i | \(0.786483\pi\) | |||||||
\(884\) | −148.514 | −4.99506 | ||||||||
\(885\) | −48.9993 | −1.64709 | ||||||||
\(886\) | 27.6272 | 0.928154 | ||||||||
\(887\) | −27.0479 | −0.908180 | −0.454090 | − | 0.890956i | \(-0.650036\pi\) | ||||
−0.454090 | + | 0.890956i | \(0.650036\pi\) | |||||||
\(888\) | 117.698 | 3.94969 | ||||||||
\(889\) | −38.0865 | −1.27738 | ||||||||
\(890\) | 164.865 | 5.52628 | ||||||||
\(891\) | 10.9523 | 0.366917 | ||||||||
\(892\) | −8.82371 | −0.295440 | ||||||||
\(893\) | 3.62292 | 0.121236 | ||||||||
\(894\) | −35.3720 | −1.18302 | ||||||||
\(895\) | −27.3166 | −0.913094 | ||||||||
\(896\) | 4.82628 | 0.161235 | ||||||||
\(897\) | −3.24403 | −0.108315 | ||||||||
\(898\) | 76.8771 | 2.56542 | ||||||||
\(899\) | 40.9454 | 1.36560 | ||||||||
\(900\) | 30.4647 | 1.01549 | ||||||||
\(901\) | −82.0955 | −2.73500 | ||||||||
\(902\) | 9.29812 | 0.309593 | ||||||||
\(903\) | −61.3602 | −2.04194 | ||||||||
\(904\) | 41.1888 | 1.36992 | ||||||||
\(905\) | 78.7886 | 2.61902 | ||||||||
\(906\) | 35.1860 | 1.16898 | ||||||||
\(907\) | −35.7723 | −1.18780 | −0.593899 | − | 0.804539i | \(-0.702412\pi\) | ||||
−0.593899 | + | 0.804539i | \(0.702412\pi\) | |||||||
\(908\) | −63.0970 | −2.09395 | ||||||||
\(909\) | 1.16203 | 0.0385420 | ||||||||
\(910\) | 111.798 | 3.70607 | ||||||||
\(911\) | 14.9009 | 0.493688 | 0.246844 | − | 0.969055i | \(-0.420606\pi\) | ||||
0.246844 | + | 0.969055i | \(0.420606\pi\) | |||||||
\(912\) | 24.7749 | 0.820380 | ||||||||
\(913\) | −17.2970 | −0.572446 | ||||||||
\(914\) | 100.579 | 3.32687 | ||||||||
\(915\) | 22.6763 | 0.749655 | ||||||||
\(916\) | −97.0639 | −3.20708 | ||||||||
\(917\) | −31.7407 | −1.04817 | ||||||||
\(918\) | 68.0269 | 2.24522 | ||||||||
\(919\) | −23.0874 | −0.761585 | −0.380792 | − | 0.924661i | \(-0.624349\pi\) | ||||
−0.380792 | + | 0.924661i | \(0.624349\pi\) | |||||||
\(920\) | 8.73286 | 0.287914 | ||||||||
\(921\) | 22.9787 | 0.757174 | ||||||||
\(922\) | −37.9700 | −1.25047 | ||||||||
\(923\) | 20.9371 | 0.689152 | ||||||||
\(924\) | 25.4353 | 0.836759 | ||||||||
\(925\) | −51.5292 | −1.69427 | ||||||||
\(926\) | 27.1035 | 0.890676 | ||||||||
\(927\) | 0.425813 | 0.0139855 | ||||||||
\(928\) | −82.2397 | −2.69965 | ||||||||
\(929\) | −15.4011 | −0.505294 | −0.252647 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252647 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(930\) | 98.1386 | 3.21809 | ||||||||
\(931\) | −0.131545 | −0.00431121 | ||||||||
\(932\) | −38.5516 | −1.26280 | ||||||||
\(933\) | −0.772562 | −0.0252925 | ||||||||
\(934\) | −26.9536 | −0.881949 | ||||||||
\(935\) | 21.6842 | 0.709150 | ||||||||
\(936\) | 34.3281 | 1.12205 | ||||||||
\(937\) | −21.4605 | −0.701083 | −0.350542 | − | 0.936547i | \(-0.614003\pi\) | ||||
−0.350542 | + | 0.936547i | \(0.614003\pi\) | |||||||
\(938\) | −46.4314 | −1.51604 | ||||||||
\(939\) | 31.9129 | 1.04144 | ||||||||
\(940\) | −48.0834 | −1.56831 | ||||||||
\(941\) | 42.4259 | 1.38304 | 0.691522 | − | 0.722355i | \(-0.256940\pi\) | ||||
0.691522 | + | 0.722355i | \(0.256940\pi\) | |||||||
\(942\) | −89.0715 | −2.90211 | ||||||||
\(943\) | 1.21087 | 0.0394315 | ||||||||
\(944\) | 72.3990 | 2.35639 | ||||||||
\(945\) | −36.3039 | −1.18097 | ||||||||
\(946\) | 30.8043 | 1.00153 | ||||||||
\(947\) | −11.2762 | −0.366427 | −0.183214 | − | 0.983073i | \(-0.558650\pi\) | ||||
−0.183214 | + | 0.983073i | \(0.558650\pi\) | |||||||
\(948\) | 106.157 | 3.44782 | ||||||||
\(949\) | 76.7986 | 2.49299 | ||||||||
\(950\) | −21.4281 | −0.695219 | ||||||||
\(951\) | 1.82367 | 0.0591367 | ||||||||
\(952\) | 126.081 | 4.08630 | ||||||||
\(953\) | 14.0789 | 0.456061 | 0.228030 | − | 0.973654i | \(-0.426771\pi\) | ||||
0.228030 | + | 0.973654i | \(0.426771\pi\) | |||||||
\(954\) | 32.1937 | 1.04231 | ||||||||
\(955\) | 57.6827 | 1.86657 | ||||||||
\(956\) | −32.2086 | −1.04170 | ||||||||
\(957\) | −14.6996 | −0.475172 | ||||||||
\(958\) | 35.1786 | 1.13657 | ||||||||
\(959\) | 47.2375 | 1.52538 | ||||||||
\(960\) | −62.1126 | −2.00468 | ||||||||
\(961\) | −0.318396 | −0.0102708 | ||||||||
\(962\) | −98.5088 | −3.17605 | ||||||||
\(963\) | 4.15046 | 0.133747 | ||||||||
\(964\) | −99.7054 | −3.21129 | ||||||||
\(965\) | 45.8862 | 1.47713 | ||||||||
\(966\) | 4.67235 | 0.150330 | ||||||||
\(967\) | 17.5871 | 0.565564 | 0.282782 | − | 0.959184i | \(-0.408743\pi\) | ||||
0.282782 | + | 0.959184i | \(0.408743\pi\) | |||||||
\(968\) | −7.52650 | −0.241911 | ||||||||
\(969\) | 15.8267 | 0.508427 | ||||||||
\(970\) | 12.5543 | 0.403095 | ||||||||
\(971\) | 22.9942 | 0.737918 | 0.368959 | − | 0.929446i | \(-0.379714\pi\) | ||||
0.368959 | + | 0.929446i | \(0.379714\pi\) | |||||||
\(972\) | −46.6478 | −1.49623 | ||||||||
\(973\) | −30.0979 | −0.964895 | ||||||||
\(974\) | −80.4370 | −2.57737 | ||||||||
\(975\) | −62.2702 | −1.99424 | ||||||||
\(976\) | −33.5054 | −1.07248 | ||||||||
\(977\) | −9.49749 | −0.303852 | −0.151926 | − | 0.988392i | \(-0.548547\pi\) | ||||
−0.151926 | + | 0.988392i | \(0.548547\pi\) | |||||||
\(978\) | 90.0836 | 2.88056 | ||||||||
\(979\) | −18.5041 | −0.591394 | ||||||||
\(980\) | 1.74587 | 0.0557697 | ||||||||
\(981\) | −14.4708 | −0.462018 | ||||||||
\(982\) | −72.7844 | −2.32265 | ||||||||
\(983\) | −8.67688 | −0.276750 | −0.138375 | − | 0.990380i | \(-0.544188\pi\) | ||||
−0.138375 | + | 0.990380i | \(0.544188\pi\) | |||||||
\(984\) | −53.0897 | −1.69244 | ||||||||
\(985\) | −62.5646 | −1.99348 | ||||||||
\(986\) | −123.620 | −3.93685 | ||||||||
\(987\) | −15.1637 | −0.482666 | ||||||||
\(988\) | −29.0410 | −0.923916 | ||||||||
\(989\) | 4.01157 | 0.127561 | ||||||||
\(990\) | −8.50346 | −0.270258 | ||||||||
\(991\) | 44.4643 | 1.41246 | 0.706228 | − | 0.707985i | \(-0.250395\pi\) | ||||
0.706228 | + | 0.707985i | \(0.250395\pi\) | |||||||
\(992\) | −61.6247 | −1.95659 | ||||||||
\(993\) | 39.8938 | 1.26599 | ||||||||
\(994\) | −30.1555 | −0.956473 | ||||||||
\(995\) | −77.7656 | −2.46533 | ||||||||
\(996\) | 167.553 | 5.30914 | ||||||||
\(997\) | −7.80694 | −0.247248 | −0.123624 | − | 0.992329i | \(-0.539452\pi\) | ||||
−0.123624 | + | 0.992329i | \(0.539452\pi\) | |||||||
\(998\) | −28.2909 | −0.895532 | ||||||||
\(999\) | 31.9885 | 1.01207 |
(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 | 6017.2.a.d.1.3 | ✓ | 107 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.d.1.3 | ✓ | 107 | 1.1 | even | 1 | trivial |