Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.62108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.88769 | −1.08986 | −0.544928 | − | 0.838483i | \(-0.683443\pi\) | ||||
−0.544928 | + | 0.838483i | \(0.683443\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.88769 | 0.770645 | ||||||||
\(7\) | 1.11871 | 0.422832 | 0.211416 | − | 0.977396i | \(-0.432193\pi\) | ||||
0.211416 | + | 0.977396i | \(0.432193\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.563364 | 0.187788 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.32315 | −1.90650 | −0.953250 | − | 0.302182i | \(-0.902285\pi\) | ||||
−0.953250 | + | 0.302182i | \(0.902285\pi\) | |||||||
\(12\) | −1.88769 | −0.544928 | ||||||||
\(13\) | −2.82666 | −0.783974 | −0.391987 | − | 0.919971i | \(-0.628212\pi\) | ||||
−0.391987 | + | 0.919971i | \(0.628212\pi\) | |||||||
\(14\) | −1.11871 | −0.298987 | ||||||||
\(15\) | 1.88769 | 0.487399 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.93054 | 0.953296 | 0.476648 | − | 0.879094i | \(-0.341852\pi\) | ||||
0.476648 | + | 0.879094i | \(0.341852\pi\) | |||||||
\(18\) | −0.563364 | −0.132786 | ||||||||
\(19\) | −1.08531 | −0.248988 | −0.124494 | − | 0.992220i | \(-0.539731\pi\) | ||||
−0.124494 | + | 0.992220i | \(0.539731\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.11177 | −0.460826 | ||||||||
\(22\) | 6.32315 | 1.34810 | ||||||||
\(23\) | 5.37635 | 1.12105 | 0.560523 | − | 0.828139i | \(-0.310600\pi\) | ||||
0.560523 | + | 0.828139i | \(0.310600\pi\) | |||||||
\(24\) | 1.88769 | 0.385323 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.82666 | 0.554353 | ||||||||
\(27\) | 4.59961 | 0.885195 | ||||||||
\(28\) | 1.11871 | 0.211416 | ||||||||
\(29\) | 3.07398 | 0.570823 | 0.285411 | − | 0.958405i | \(-0.407870\pi\) | ||||
0.285411 | + | 0.958405i | \(0.407870\pi\) | |||||||
\(30\) | −1.88769 | −0.344643 | ||||||||
\(31\) | 3.88716 | 0.698155 | 0.349078 | − | 0.937094i | \(-0.386495\pi\) | ||||
0.349078 | + | 0.937094i | \(0.386495\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 11.9361 | 2.07781 | ||||||||
\(34\) | −3.93054 | −0.674082 | ||||||||
\(35\) | −1.11871 | −0.189096 | ||||||||
\(36\) | 0.563364 | 0.0938939 | ||||||||
\(37\) | −0.283699 | −0.0466398 | −0.0233199 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233199 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(38\) | 1.08531 | 0.176061 | ||||||||
\(39\) | 5.33585 | 0.854419 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 11.9618 | 1.86812 | 0.934061 | − | 0.357113i | \(-0.116239\pi\) | ||||
0.934061 | + | 0.357113i | \(0.116239\pi\) | |||||||
\(42\) | 2.11177 | 0.325853 | ||||||||
\(43\) | −10.1723 | −1.55126 | −0.775632 | − | 0.631185i | \(-0.782569\pi\) | ||||
−0.775632 | + | 0.631185i | \(0.782569\pi\) | |||||||
\(44\) | −6.32315 | −0.953250 | ||||||||
\(45\) | −0.563364 | −0.0839813 | ||||||||
\(46\) | −5.37635 | −0.792699 | ||||||||
\(47\) | −6.23186 | −0.909010 | −0.454505 | − | 0.890744i | \(-0.650184\pi\) | ||||
−0.454505 | + | 0.890744i | \(0.650184\pi\) | |||||||
\(48\) | −1.88769 | −0.272464 | ||||||||
\(49\) | −5.74849 | −0.821214 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −7.41963 | −1.03896 | ||||||||
\(52\) | −2.82666 | −0.391987 | ||||||||
\(53\) | −0.293135 | −0.0402651 | −0.0201326 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201326 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(54\) | −4.59961 | −0.625927 | ||||||||
\(55\) | 6.32315 | 0.852613 | ||||||||
\(56\) | −1.11871 | −0.149494 | ||||||||
\(57\) | 2.04874 | 0.271362 | ||||||||
\(58\) | −3.07398 | −0.403633 | ||||||||
\(59\) | 6.60549 | 0.859962 | 0.429981 | − | 0.902838i | \(-0.358520\pi\) | ||||
0.429981 | + | 0.902838i | \(0.358520\pi\) | |||||||
\(60\) | 1.88769 | 0.243699 | ||||||||
\(61\) | 11.7860 | 1.50904 | 0.754520 | − | 0.656277i | \(-0.227870\pi\) | ||||
0.754520 | + | 0.656277i | \(0.227870\pi\) | |||||||
\(62\) | −3.88716 | −0.493670 | ||||||||
\(63\) | 0.630239 | 0.0794026 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.82666 | 0.350604 | ||||||||
\(66\) | −11.9361 | −1.46924 | ||||||||
\(67\) | 14.2743 | 1.74389 | 0.871944 | − | 0.489606i | \(-0.162860\pi\) | ||||
0.871944 | + | 0.489606i | \(0.162860\pi\) | |||||||
\(68\) | 3.93054 | 0.476648 | ||||||||
\(69\) | −10.1489 | −1.22178 | ||||||||
\(70\) | 1.11871 | 0.133711 | ||||||||
\(71\) | 4.56770 | 0.542086 | 0.271043 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271043 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(72\) | −0.563364 | −0.0663930 | ||||||||
\(73\) | −16.1342 | −1.88836 | −0.944181 | − | 0.329428i | \(-0.893144\pi\) | ||||
−0.944181 | + | 0.329428i | \(0.893144\pi\) | |||||||
\(74\) | 0.283699 | 0.0329793 | ||||||||
\(75\) | −1.88769 | −0.217971 | ||||||||
\(76\) | −1.08531 | −0.124494 | ||||||||
\(77\) | −7.07375 | −0.806128 | ||||||||
\(78\) | −5.33585 | −0.604166 | ||||||||
\(79\) | −11.2037 | −1.26051 | −0.630255 | − | 0.776388i | \(-0.717050\pi\) | ||||
−0.630255 | + | 0.776388i | \(0.717050\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.3727 | −1.15252 | ||||||||
\(82\) | −11.9618 | −1.32096 | ||||||||
\(83\) | −6.28436 | −0.689798 | −0.344899 | − | 0.938640i | \(-0.612087\pi\) | ||||
−0.344899 | + | 0.938640i | \(0.612087\pi\) | |||||||
\(84\) | −2.11177 | −0.230413 | ||||||||
\(85\) | −3.93054 | −0.426327 | ||||||||
\(86\) | 10.1723 | 1.09691 | ||||||||
\(87\) | −5.80270 | −0.622115 | ||||||||
\(88\) | 6.32315 | 0.674050 | ||||||||
\(89\) | 7.99086 | 0.847029 | 0.423515 | − | 0.905889i | \(-0.360796\pi\) | ||||
0.423515 | + | 0.905889i | \(0.360796\pi\) | |||||||
\(90\) | 0.563364 | 0.0593837 | ||||||||
\(91\) | −3.16220 | −0.331489 | ||||||||
\(92\) | 5.37635 | 0.560523 | ||||||||
\(93\) | −7.33775 | −0.760889 | ||||||||
\(94\) | 6.23186 | 0.642767 | ||||||||
\(95\) | 1.08531 | 0.111351 | ||||||||
\(96\) | 1.88769 | 0.192661 | ||||||||
\(97\) | −8.56664 | −0.869810 | −0.434905 | − | 0.900476i | \(-0.643218\pi\) | ||||
−0.434905 | + | 0.900476i | \(0.643218\pi\) | |||||||
\(98\) | 5.74849 | 0.580686 | ||||||||
\(99\) | −3.56223 | −0.358018 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.14404 | −0.113836 | −0.0569180 | − | 0.998379i | \(-0.518127\pi\) | ||||
−0.0569180 | + | 0.998379i | \(0.518127\pi\) | |||||||
\(102\) | 7.41963 | 0.734653 | ||||||||
\(103\) | −16.5367 | −1.62941 | −0.814704 | − | 0.579877i | \(-0.803101\pi\) | ||||
−0.814704 | + | 0.579877i | \(0.803101\pi\) | |||||||
\(104\) | 2.82666 | 0.277177 | ||||||||
\(105\) | 2.11177 | 0.206088 | ||||||||
\(106\) | 0.293135 | 0.0284717 | ||||||||
\(107\) | −0.551506 | −0.0533161 | −0.0266580 | − | 0.999645i | \(-0.508487\pi\) | ||||
−0.0266580 | + | 0.999645i | \(0.508487\pi\) | |||||||
\(108\) | 4.59961 | 0.442597 | ||||||||
\(109\) | 6.39040 | 0.612089 | 0.306045 | − | 0.952017i | \(-0.400994\pi\) | ||||
0.306045 | + | 0.952017i | \(0.400994\pi\) | |||||||
\(110\) | −6.32315 | −0.602888 | ||||||||
\(111\) | 0.535534 | 0.0508307 | ||||||||
\(112\) | 1.11871 | 0.105708 | ||||||||
\(113\) | 17.6089 | 1.65651 | 0.828254 | − | 0.560352i | \(-0.189334\pi\) | ||||
0.828254 | + | 0.560352i | \(0.189334\pi\) | |||||||
\(114\) | −2.04874 | −0.191882 | ||||||||
\(115\) | −5.37635 | −0.501347 | ||||||||
\(116\) | 3.07398 | 0.285411 | ||||||||
\(117\) | −1.59244 | −0.147221 | ||||||||
\(118\) | −6.60549 | −0.608085 | ||||||||
\(119\) | 4.39712 | 0.403083 | ||||||||
\(120\) | −1.88769 | −0.172321 | ||||||||
\(121\) | 28.9822 | 2.63474 | ||||||||
\(122\) | −11.7860 | −1.06705 | ||||||||
\(123\) | −22.5802 | −2.03599 | ||||||||
\(124\) | 3.88716 | 0.349078 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.630239 | −0.0561461 | ||||||||
\(127\) | 16.8182 | 1.49238 | 0.746188 | − | 0.665736i | \(-0.231882\pi\) | ||||
0.746188 | + | 0.665736i | \(0.231882\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 19.2022 | 1.69066 | ||||||||
\(130\) | −2.82666 | −0.247914 | ||||||||
\(131\) | 9.34216 | 0.816229 | 0.408114 | − | 0.912931i | \(-0.366186\pi\) | ||||
0.408114 | + | 0.912931i | \(0.366186\pi\) | |||||||
\(132\) | 11.9361 | 1.03891 | ||||||||
\(133\) | −1.21415 | −0.105280 | ||||||||
\(134\) | −14.2743 | −1.23311 | ||||||||
\(135\) | −4.59961 | −0.395871 | ||||||||
\(136\) | −3.93054 | −0.337041 | ||||||||
\(137\) | −10.1181 | −0.864444 | −0.432222 | − | 0.901767i | \(-0.642270\pi\) | ||||
−0.432222 | + | 0.901767i | \(0.642270\pi\) | |||||||
\(138\) | 10.1489 | 0.863929 | ||||||||
\(139\) | −18.4350 | −1.56364 | −0.781818 | − | 0.623507i | \(-0.785707\pi\) | ||||
−0.781818 | + | 0.623507i | \(0.785707\pi\) | |||||||
\(140\) | −1.11871 | −0.0945480 | ||||||||
\(141\) | 11.7638 | 0.990691 | ||||||||
\(142\) | −4.56770 | −0.383313 | ||||||||
\(143\) | 17.8734 | 1.49465 | ||||||||
\(144\) | 0.563364 | 0.0469470 | ||||||||
\(145\) | −3.07398 | −0.255280 | ||||||||
\(146\) | 16.1342 | 1.33527 | ||||||||
\(147\) | 10.8514 | 0.895005 | ||||||||
\(148\) | −0.283699 | −0.0233199 | ||||||||
\(149\) | 5.02014 | 0.411266 | 0.205633 | − | 0.978629i | \(-0.434075\pi\) | ||||
0.205633 | + | 0.978629i | \(0.434075\pi\) | |||||||
\(150\) | 1.88769 | 0.154129 | ||||||||
\(151\) | 10.6556 | 0.867144 | 0.433572 | − | 0.901119i | \(-0.357253\pi\) | ||||
0.433572 | + | 0.901119i | \(0.357253\pi\) | |||||||
\(152\) | 1.08531 | 0.0880307 | ||||||||
\(153\) | 2.21432 | 0.179017 | ||||||||
\(154\) | 7.07375 | 0.570019 | ||||||||
\(155\) | −3.88716 | −0.312225 | ||||||||
\(156\) | 5.33585 | 0.427210 | ||||||||
\(157\) | 11.3236 | 0.903724 | 0.451862 | − | 0.892088i | \(-0.350760\pi\) | ||||
0.451862 | + | 0.892088i | \(0.350760\pi\) | |||||||
\(158\) | 11.2037 | 0.891315 | ||||||||
\(159\) | 0.553346 | 0.0438832 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.01456 | 0.474014 | ||||||||
\(162\) | 10.3727 | 0.814957 | ||||||||
\(163\) | −20.0968 | −1.57411 | −0.787053 | − | 0.616886i | \(-0.788394\pi\) | ||||
−0.787053 | + | 0.616886i | \(0.788394\pi\) | |||||||
\(164\) | 11.9618 | 0.934061 | ||||||||
\(165\) | −11.9361 | −0.929226 | ||||||||
\(166\) | 6.28436 | 0.487761 | ||||||||
\(167\) | −4.63853 | −0.358940 | −0.179470 | − | 0.983763i | \(-0.557438\pi\) | ||||
−0.179470 | + | 0.983763i | \(0.557438\pi\) | |||||||
\(168\) | 2.11177 | 0.162927 | ||||||||
\(169\) | −5.01001 | −0.385385 | ||||||||
\(170\) | 3.93054 | 0.301459 | ||||||||
\(171\) | −0.611427 | −0.0467570 | ||||||||
\(172\) | −10.1723 | −0.775632 | ||||||||
\(173\) | −11.5342 | −0.876928 | −0.438464 | − | 0.898749i | \(-0.644477\pi\) | ||||
−0.438464 | + | 0.898749i | \(0.644477\pi\) | |||||||
\(174\) | 5.80270 | 0.439902 | ||||||||
\(175\) | 1.11871 | 0.0845663 | ||||||||
\(176\) | −6.32315 | −0.476625 | ||||||||
\(177\) | −12.4691 | −0.937235 | ||||||||
\(178\) | −7.99086 | −0.598940 | ||||||||
\(179\) | 15.8541 | 1.18499 | 0.592494 | − | 0.805575i | \(-0.298143\pi\) | ||||
0.592494 | + | 0.805575i | \(0.298143\pi\) | |||||||
\(180\) | −0.563364 | −0.0419906 | ||||||||
\(181\) | −23.0672 | −1.71457 | −0.857284 | − | 0.514844i | \(-0.827850\pi\) | ||||
−0.857284 | + | 0.514844i | \(0.827850\pi\) | |||||||
\(182\) | 3.16220 | 0.234398 | ||||||||
\(183\) | −22.2483 | −1.64464 | ||||||||
\(184\) | −5.37635 | −0.396350 | ||||||||
\(185\) | 0.283699 | 0.0208579 | ||||||||
\(186\) | 7.33775 | 0.538030 | ||||||||
\(187\) | −24.8534 | −1.81746 | ||||||||
\(188\) | −6.23186 | −0.454505 | ||||||||
\(189\) | 5.14561 | 0.374288 | ||||||||
\(190\) | −1.08531 | −0.0787370 | ||||||||
\(191\) | −0.0467554 | −0.00338310 | −0.00169155 | − | 0.999999i | \(-0.500538\pi\) | ||||
−0.00169155 | + | 0.999999i | \(0.500538\pi\) | |||||||
\(192\) | −1.88769 | −0.136232 | ||||||||
\(193\) | 6.39884 | 0.460599 | 0.230299 | − | 0.973120i | \(-0.426029\pi\) | ||||
0.230299 | + | 0.973120i | \(0.426029\pi\) | |||||||
\(194\) | 8.56664 | 0.615049 | ||||||||
\(195\) | −5.33585 | −0.382108 | ||||||||
\(196\) | −5.74849 | −0.410607 | ||||||||
\(197\) | −12.5182 | −0.891882 | −0.445941 | − | 0.895062i | \(-0.647131\pi\) | ||||
−0.445941 | + | 0.895062i | \(0.647131\pi\) | |||||||
\(198\) | 3.56223 | 0.253157 | ||||||||
\(199\) | −5.08884 | −0.360738 | −0.180369 | − | 0.983599i | \(-0.557729\pi\) | ||||
−0.180369 | + | 0.983599i | \(0.557729\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −26.9455 | −1.90059 | ||||||||
\(202\) | 1.14404 | 0.0804942 | ||||||||
\(203\) | 3.43888 | 0.241362 | ||||||||
\(204\) | −7.41963 | −0.519478 | ||||||||
\(205\) | −11.9618 | −0.835450 | ||||||||
\(206\) | 16.5367 | 1.15217 | ||||||||
\(207\) | 3.02884 | 0.210519 | ||||||||
\(208\) | −2.82666 | −0.195993 | ||||||||
\(209\) | 6.86261 | 0.474696 | ||||||||
\(210\) | −2.11177 | −0.145726 | ||||||||
\(211\) | −15.9524 | −1.09821 | −0.549103 | − | 0.835754i | \(-0.685031\pi\) | ||||
−0.549103 | + | 0.835754i | \(0.685031\pi\) | |||||||
\(212\) | −0.293135 | −0.0201326 | ||||||||
\(213\) | −8.62239 | −0.590796 | ||||||||
\(214\) | 0.551506 | 0.0377002 | ||||||||
\(215\) | 10.1723 | 0.693746 | ||||||||
\(216\) | −4.59961 | −0.312964 | ||||||||
\(217\) | 4.34860 | 0.295202 | ||||||||
\(218\) | −6.39040 | −0.432813 | ||||||||
\(219\) | 30.4563 | 2.05804 | ||||||||
\(220\) | 6.32315 | 0.426306 | ||||||||
\(221\) | −11.1103 | −0.747359 | ||||||||
\(222\) | −0.535534 | −0.0359427 | ||||||||
\(223\) | −5.88038 | −0.393780 | −0.196890 | − | 0.980426i | \(-0.563084\pi\) | ||||
−0.196890 | + | 0.980426i | \(0.563084\pi\) | |||||||
\(224\) | −1.11871 | −0.0747468 | ||||||||
\(225\) | 0.563364 | 0.0375576 | ||||||||
\(226\) | −17.6089 | −1.17133 | ||||||||
\(227\) | 2.83467 | 0.188143 | 0.0940717 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940717 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(228\) | 2.04874 | 0.135681 | ||||||||
\(229\) | 0.844296 | 0.0557926 | 0.0278963 | − | 0.999611i | \(-0.491119\pi\) | ||||
0.0278963 | + | 0.999611i | \(0.491119\pi\) | |||||||
\(230\) | 5.37635 | 0.354506 | ||||||||
\(231\) | 13.3530 | 0.878565 | ||||||||
\(232\) | −3.07398 | −0.201816 | ||||||||
\(233\) | −10.7431 | −0.703802 | −0.351901 | − | 0.936037i | \(-0.614465\pi\) | ||||
−0.351901 | + | 0.936037i | \(0.614465\pi\) | |||||||
\(234\) | 1.59244 | 0.104101 | ||||||||
\(235\) | 6.23186 | 0.406522 | ||||||||
\(236\) | 6.60549 | 0.429981 | ||||||||
\(237\) | 21.1490 | 1.37378 | ||||||||
\(238\) | −4.39712 | −0.285023 | ||||||||
\(239\) | 19.0311 | 1.23102 | 0.615509 | − | 0.788130i | \(-0.288951\pi\) | ||||
0.615509 | + | 0.788130i | \(0.288951\pi\) | |||||||
\(240\) | 1.88769 | 0.121850 | ||||||||
\(241\) | 11.7762 | 0.758569 | 0.379285 | − | 0.925280i | \(-0.376170\pi\) | ||||
0.379285 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(242\) | −28.9822 | −1.86305 | ||||||||
\(243\) | 5.78161 | 0.370891 | ||||||||
\(244\) | 11.7860 | 0.754520 | ||||||||
\(245\) | 5.74849 | 0.367258 | ||||||||
\(246\) | 22.5802 | 1.43966 | ||||||||
\(247\) | 3.06781 | 0.195200 | ||||||||
\(248\) | −3.88716 | −0.246835 | ||||||||
\(249\) | 11.8629 | 0.751781 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −19.1035 | −1.20580 | −0.602900 | − | 0.797817i | \(-0.705988\pi\) | ||||
−0.602900 | + | 0.797817i | \(0.705988\pi\) | |||||||
\(252\) | 0.630239 | 0.0397013 | ||||||||
\(253\) | −33.9954 | −2.13727 | ||||||||
\(254\) | −16.8182 | −1.05527 | ||||||||
\(255\) | 7.41963 | 0.464635 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.77930 | 0.422881 | 0.211441 | − | 0.977391i | \(-0.432185\pi\) | ||||
0.211441 | + | 0.977391i | \(0.432185\pi\) | |||||||
\(258\) | −19.2022 | −1.19547 | ||||||||
\(259\) | −0.317376 | −0.0197208 | ||||||||
\(260\) | 2.82666 | 0.175302 | ||||||||
\(261\) | 1.73177 | 0.107194 | ||||||||
\(262\) | −9.34216 | −0.577161 | ||||||||
\(263\) | −23.3670 | −1.44087 | −0.720437 | − | 0.693521i | \(-0.756059\pi\) | ||||
−0.720437 | + | 0.693521i | \(0.756059\pi\) | |||||||
\(264\) | −11.9361 | −0.734618 | ||||||||
\(265\) | 0.293135 | 0.0180071 | ||||||||
\(266\) | 1.21415 | 0.0744443 | ||||||||
\(267\) | −15.0842 | −0.923141 | ||||||||
\(268\) | 14.2743 | 0.871944 | ||||||||
\(269\) | 6.81642 | 0.415604 | 0.207802 | − | 0.978171i | \(-0.433369\pi\) | ||||
0.207802 | + | 0.978171i | \(0.433369\pi\) | |||||||
\(270\) | 4.59961 | 0.279923 | ||||||||
\(271\) | 2.58394 | 0.156963 | 0.0784815 | − | 0.996916i | \(-0.474993\pi\) | ||||
0.0784815 | + | 0.996916i | \(0.474993\pi\) | |||||||
\(272\) | 3.93054 | 0.238324 | ||||||||
\(273\) | 5.96925 | 0.361275 | ||||||||
\(274\) | 10.1181 | 0.611254 | ||||||||
\(275\) | −6.32315 | −0.381300 | ||||||||
\(276\) | −10.1489 | −0.610890 | ||||||||
\(277\) | −26.6772 | −1.60288 | −0.801439 | − | 0.598076i | \(-0.795932\pi\) | ||||
−0.801439 | + | 0.598076i | \(0.795932\pi\) | |||||||
\(278\) | 18.4350 | 1.10566 | ||||||||
\(279\) | 2.18989 | 0.131105 | ||||||||
\(280\) | 1.11871 | 0.0668555 | ||||||||
\(281\) | 14.4915 | 0.864492 | 0.432246 | − | 0.901756i | \(-0.357721\pi\) | ||||
0.432246 | + | 0.901756i | \(0.357721\pi\) | |||||||
\(282\) | −11.7638 | −0.700524 | ||||||||
\(283\) | 1.14439 | 0.0680271 | 0.0340136 | − | 0.999421i | \(-0.489171\pi\) | ||||
0.0340136 | + | 0.999421i | \(0.489171\pi\) | |||||||
\(284\) | 4.56770 | 0.271043 | ||||||||
\(285\) | −2.04874 | −0.121357 | ||||||||
\(286\) | −17.8734 | −1.05687 | ||||||||
\(287\) | 13.3818 | 0.789901 | ||||||||
\(288\) | −0.563364 | −0.0331965 | ||||||||
\(289\) | −1.55086 | −0.0912272 | ||||||||
\(290\) | 3.07398 | 0.180510 | ||||||||
\(291\) | 16.1711 | 0.947969 | ||||||||
\(292\) | −16.1342 | −0.944181 | ||||||||
\(293\) | −27.9405 | −1.63230 | −0.816151 | − | 0.577838i | \(-0.803896\pi\) | ||||
−0.816151 | + | 0.577838i | \(0.803896\pi\) | |||||||
\(294\) | −10.8514 | −0.632864 | ||||||||
\(295\) | −6.60549 | −0.384587 | ||||||||
\(296\) | 0.283699 | 0.0164896 | ||||||||
\(297\) | −29.0840 | −1.68762 | ||||||||
\(298\) | −5.02014 | −0.290809 | ||||||||
\(299\) | −15.1971 | −0.878871 | ||||||||
\(300\) | −1.88769 | −0.108986 | ||||||||
\(301\) | −11.3798 | −0.655923 | ||||||||
\(302\) | −10.6556 | −0.613163 | ||||||||
\(303\) | 2.15959 | 0.124065 | ||||||||
\(304\) | −1.08531 | −0.0622471 | ||||||||
\(305\) | −11.7860 | −0.674864 | ||||||||
\(306\) | −2.21432 | −0.126584 | ||||||||
\(307\) | −16.9869 | −0.969492 | −0.484746 | − | 0.874655i | \(-0.661088\pi\) | ||||
−0.484746 | + | 0.874655i | \(0.661088\pi\) | |||||||
\(308\) | −7.07375 | −0.403064 | ||||||||
\(309\) | 31.2161 | 1.77582 | ||||||||
\(310\) | 3.88716 | 0.220776 | ||||||||
\(311\) | −31.2663 | −1.77295 | −0.886476 | − | 0.462775i | \(-0.846854\pi\) | ||||
−0.886476 | + | 0.462775i | \(0.846854\pi\) | |||||||
\(312\) | −5.33585 | −0.302083 | ||||||||
\(313\) | 24.6006 | 1.39051 | 0.695254 | − | 0.718764i | \(-0.255292\pi\) | ||||
0.695254 | + | 0.718764i | \(0.255292\pi\) | |||||||
\(314\) | −11.3236 | −0.639029 | ||||||||
\(315\) | −0.630239 | −0.0355099 | ||||||||
\(316\) | −11.2037 | −0.630255 | ||||||||
\(317\) | −12.4915 | −0.701592 | −0.350796 | − | 0.936452i | \(-0.614089\pi\) | ||||
−0.350796 | + | 0.936452i | \(0.614089\pi\) | |||||||
\(318\) | −0.553346 | −0.0310301 | ||||||||
\(319\) | −19.4372 | −1.08827 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 1.04107 | 0.0581069 | ||||||||
\(322\) | −6.01456 | −0.335178 | ||||||||
\(323\) | −4.26587 | −0.237360 | ||||||||
\(324\) | −10.3727 | −0.576262 | ||||||||
\(325\) | −2.82666 | −0.156795 | ||||||||
\(326\) | 20.0968 | 1.11306 | ||||||||
\(327\) | −12.0631 | −0.667090 | ||||||||
\(328\) | −11.9618 | −0.660481 | ||||||||
\(329\) | −6.97163 | −0.384358 | ||||||||
\(330\) | 11.9361 | 0.657062 | ||||||||
\(331\) | −33.8103 | −1.85838 | −0.929191 | − | 0.369600i | \(-0.879495\pi\) | ||||
−0.929191 | + | 0.369600i | \(0.879495\pi\) | |||||||
\(332\) | −6.28436 | −0.344899 | ||||||||
\(333\) | −0.159825 | −0.00875838 | ||||||||
\(334\) | 4.63853 | 0.253809 | ||||||||
\(335\) | −14.2743 | −0.779890 | ||||||||
\(336\) | −2.11177 | −0.115206 | ||||||||
\(337\) | 5.49671 | 0.299425 | 0.149712 | − | 0.988730i | \(-0.452165\pi\) | ||||
0.149712 | + | 0.988730i | \(0.452165\pi\) | |||||||
\(338\) | 5.01001 | 0.272508 | ||||||||
\(339\) | −33.2402 | −1.80536 | ||||||||
\(340\) | −3.93054 | −0.213163 | ||||||||
\(341\) | −24.5791 | −1.33103 | ||||||||
\(342\) | 0.611427 | 0.0330622 | ||||||||
\(343\) | −14.2618 | −0.770066 | ||||||||
\(344\) | 10.1723 | 0.548455 | ||||||||
\(345\) | 10.1489 | 0.546396 | ||||||||
\(346\) | 11.5342 | 0.620082 | ||||||||
\(347\) | −4.26340 | −0.228871 | −0.114436 | − | 0.993431i | \(-0.536506\pi\) | ||||
−0.114436 | + | 0.993431i | \(0.536506\pi\) | |||||||
\(348\) | −5.80270 | −0.311058 | ||||||||
\(349\) | 20.0459 | 1.07303 | 0.536515 | − | 0.843891i | \(-0.319740\pi\) | ||||
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(350\) | −1.11871 | −0.0597974 | ||||||||
\(351\) | −13.0015 | −0.693970 | ||||||||
\(352\) | 6.32315 | 0.337025 | ||||||||
\(353\) | 16.6467 | 0.886013 | 0.443007 | − | 0.896518i | \(-0.353912\pi\) | ||||
0.443007 | + | 0.896518i | \(0.353912\pi\) | |||||||
\(354\) | 12.4691 | 0.662725 | ||||||||
\(355\) | −4.56770 | −0.242428 | ||||||||
\(356\) | 7.99086 | 0.423515 | ||||||||
\(357\) | −8.30039 | −0.439303 | ||||||||
\(358\) | −15.8541 | −0.837913 | ||||||||
\(359\) | 21.7678 | 1.14886 | 0.574430 | − | 0.818554i | \(-0.305224\pi\) | ||||
0.574430 | + | 0.818554i | \(0.305224\pi\) | |||||||
\(360\) | 0.563364 | 0.0296919 | ||||||||
\(361\) | −17.8221 | −0.938005 | ||||||||
\(362\) | 23.0672 | 1.21238 | ||||||||
\(363\) | −54.7093 | −2.87149 | ||||||||
\(364\) | −3.16220 | −0.165744 | ||||||||
\(365\) | 16.1342 | 0.844501 | ||||||||
\(366\) | 22.2483 | 1.16294 | ||||||||
\(367\) | −25.6853 | −1.34076 | −0.670382 | − | 0.742017i | \(-0.733870\pi\) | ||||
−0.670382 | + | 0.742017i | \(0.733870\pi\) | |||||||
\(368\) | 5.37635 | 0.280261 | ||||||||
\(369\) | 6.73885 | 0.350811 | ||||||||
\(370\) | −0.283699 | −0.0147488 | ||||||||
\(371\) | −0.327932 | −0.0170254 | ||||||||
\(372\) | −7.33775 | −0.380445 | ||||||||
\(373\) | 0.356374 | 0.0184524 | 0.00922618 | − | 0.999957i | \(-0.497063\pi\) | ||||
0.00922618 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(374\) | 24.8534 | 1.28514 | ||||||||
\(375\) | 1.88769 | 0.0974798 | ||||||||
\(376\) | 6.23186 | 0.321384 | ||||||||
\(377\) | −8.68908 | −0.447510 | ||||||||
\(378\) | −5.14561 | −0.264662 | ||||||||
\(379\) | −21.9006 | −1.12496 | −0.562480 | − | 0.826811i | \(-0.690153\pi\) | ||||
−0.562480 | + | 0.826811i | \(0.690153\pi\) | |||||||
\(380\) | 1.08531 | 0.0556755 | ||||||||
\(381\) | −31.7475 | −1.62648 | ||||||||
\(382\) | 0.0467554 | 0.00239222 | ||||||||
\(383\) | 21.5332 | 1.10029 | 0.550146 | − | 0.835068i | \(-0.314572\pi\) | ||||
0.550146 | + | 0.835068i | \(0.314572\pi\) | |||||||
\(384\) | 1.88769 | 0.0963306 | ||||||||
\(385\) | 7.07375 | 0.360512 | ||||||||
\(386\) | −6.39884 | −0.325692 | ||||||||
\(387\) | −5.73071 | −0.291309 | ||||||||
\(388\) | −8.56664 | −0.434905 | ||||||||
\(389\) | 32.5057 | 1.64810 | 0.824052 | − | 0.566514i | \(-0.191708\pi\) | ||||
0.824052 | + | 0.566514i | \(0.191708\pi\) | |||||||
\(390\) | 5.33585 | 0.270191 | ||||||||
\(391\) | 21.1319 | 1.06869 | ||||||||
\(392\) | 5.74849 | 0.290343 | ||||||||
\(393\) | −17.6351 | −0.889572 | ||||||||
\(394\) | 12.5182 | 0.630656 | ||||||||
\(395\) | 11.2037 | 0.563717 | ||||||||
\(396\) | −3.56223 | −0.179009 | ||||||||
\(397\) | 2.06463 | 0.103621 | 0.0518104 | − | 0.998657i | \(-0.483501\pi\) | ||||
0.0518104 | + | 0.998657i | \(0.483501\pi\) | |||||||
\(398\) | 5.08884 | 0.255080 | ||||||||
\(399\) | 2.29193 | 0.114740 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 26.9455 | 1.34392 | ||||||||
\(403\) | −10.9877 | −0.547335 | ||||||||
\(404\) | −1.14404 | −0.0569180 | ||||||||
\(405\) | 10.3727 | 0.515424 | ||||||||
\(406\) | −3.43888 | −0.170669 | ||||||||
\(407\) | 1.79387 | 0.0889187 | ||||||||
\(408\) | 7.41963 | 0.367326 | ||||||||
\(409\) | 19.7765 | 0.977883 | 0.488942 | − | 0.872317i | \(-0.337383\pi\) | ||||
0.488942 | + | 0.872317i | \(0.337383\pi\) | |||||||
\(410\) | 11.9618 | 0.590752 | ||||||||
\(411\) | 19.0997 | 0.942120 | ||||||||
\(412\) | −16.5367 | −0.814704 | ||||||||
\(413\) | 7.38961 | 0.363619 | ||||||||
\(414\) | −3.02884 | −0.148859 | ||||||||
\(415\) | 6.28436 | 0.308487 | ||||||||
\(416\) | 2.82666 | 0.138588 | ||||||||
\(417\) | 34.7995 | 1.70414 | ||||||||
\(418\) | −6.86261 | −0.335661 | ||||||||
\(419\) | −12.3716 | −0.604390 | −0.302195 | − | 0.953246i | \(-0.597719\pi\) | ||||
−0.302195 | + | 0.953246i | \(0.597719\pi\) | |||||||
\(420\) | 2.11177 | 0.103044 | ||||||||
\(421\) | −12.3321 | −0.601031 | −0.300515 | − | 0.953777i | \(-0.597159\pi\) | ||||
−0.300515 | + | 0.953777i | \(0.597159\pi\) | |||||||
\(422\) | 15.9524 | 0.776549 | ||||||||
\(423\) | −3.51080 | −0.170701 | ||||||||
\(424\) | 0.293135 | 0.0142359 | ||||||||
\(425\) | 3.93054 | 0.190659 | ||||||||
\(426\) | 8.62239 | 0.417756 | ||||||||
\(427\) | 13.1851 | 0.638070 | ||||||||
\(428\) | −0.551506 | −0.0266580 | ||||||||
\(429\) | −33.7393 | −1.62895 | ||||||||
\(430\) | −10.1723 | −0.490553 | ||||||||
\(431\) | 8.60836 | 0.414650 | 0.207325 | − | 0.978272i | \(-0.433524\pi\) | ||||
0.207325 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(432\) | 4.59961 | 0.221299 | ||||||||
\(433\) | 38.3308 | 1.84206 | 0.921029 | − | 0.389493i | \(-0.127350\pi\) | ||||
0.921029 | + | 0.389493i | \(0.127350\pi\) | |||||||
\(434\) | −4.34860 | −0.208739 | ||||||||
\(435\) | 5.80270 | 0.278218 | ||||||||
\(436\) | 6.39040 | 0.306045 | ||||||||
\(437\) | −5.83503 | −0.279127 | ||||||||
\(438\) | −30.4563 | −1.45526 | ||||||||
\(439\) | −11.4306 | −0.545553 | −0.272777 | − | 0.962077i | \(-0.587942\pi\) | ||||
−0.272777 | + | 0.962077i | \(0.587942\pi\) | |||||||
\(440\) | −6.32315 | −0.301444 | ||||||||
\(441\) | −3.23849 | −0.154214 | ||||||||
\(442\) | 11.1103 | 0.528463 | ||||||||
\(443\) | −10.0730 | −0.478581 | −0.239290 | − | 0.970948i | \(-0.576915\pi\) | ||||
−0.239290 | + | 0.970948i | \(0.576915\pi\) | |||||||
\(444\) | 0.535534 | 0.0254153 | ||||||||
\(445\) | −7.99086 | −0.378803 | ||||||||
\(446\) | 5.88038 | 0.278444 | ||||||||
\(447\) | −9.47646 | −0.448221 | ||||||||
\(448\) | 1.11871 | 0.0528539 | ||||||||
\(449\) | −2.76964 | −0.130707 | −0.0653537 | − | 0.997862i | \(-0.520818\pi\) | ||||
−0.0653537 | + | 0.997862i | \(0.520818\pi\) | |||||||
\(450\) | −0.563364 | −0.0265572 | ||||||||
\(451\) | −75.6363 | −3.56158 | ||||||||
\(452\) | 17.6089 | 0.828254 | ||||||||
\(453\) | −20.1145 | −0.945063 | ||||||||
\(454\) | −2.83467 | −0.133037 | ||||||||
\(455\) | 3.16220 | 0.148246 | ||||||||
\(456\) | −2.04874 | −0.0959408 | ||||||||
\(457\) | 11.5039 | 0.538131 | 0.269066 | − | 0.963122i | \(-0.413285\pi\) | ||||
0.269066 | + | 0.963122i | \(0.413285\pi\) | |||||||
\(458\) | −0.844296 | −0.0394513 | ||||||||
\(459\) | 18.0789 | 0.843853 | ||||||||
\(460\) | −5.37635 | −0.250673 | ||||||||
\(461\) | −27.0428 | −1.25951 | −0.629753 | − | 0.776795i | \(-0.716844\pi\) | ||||
−0.629753 | + | 0.776795i | \(0.716844\pi\) | |||||||
\(462\) | −13.3530 | −0.621239 | ||||||||
\(463\) | −6.63967 | −0.308571 | −0.154286 | − | 0.988026i | \(-0.549308\pi\) | ||||
−0.154286 | + | 0.988026i | \(0.549308\pi\) | |||||||
\(464\) | 3.07398 | 0.142706 | ||||||||
\(465\) | 7.33775 | 0.340280 | ||||||||
\(466\) | 10.7431 | 0.497663 | ||||||||
\(467\) | −29.1236 | −1.34768 | −0.673840 | − | 0.738878i | \(-0.735356\pi\) | ||||
−0.673840 | + | 0.738878i | \(0.735356\pi\) | |||||||
\(468\) | −1.59244 | −0.0736104 | ||||||||
\(469\) | 15.9688 | 0.737370 | ||||||||
\(470\) | −6.23186 | −0.287454 | ||||||||
\(471\) | −21.3755 | −0.984930 | ||||||||
\(472\) | −6.60549 | −0.304042 | ||||||||
\(473\) | 64.3211 | 2.95749 | ||||||||
\(474\) | −21.1490 | −0.971406 | ||||||||
\(475\) | −1.08531 | −0.0497977 | ||||||||
\(476\) | 4.39712 | 0.201542 | ||||||||
\(477\) | −0.165141 | −0.00756130 | ||||||||
\(478\) | −19.0311 | −0.870460 | ||||||||
\(479\) | −24.4284 | −1.11616 | −0.558082 | − | 0.829786i | \(-0.688463\pi\) | ||||
−0.558082 | + | 0.829786i | \(0.688463\pi\) | |||||||
\(480\) | −1.88769 | −0.0861607 | ||||||||
\(481\) | 0.801919 | 0.0365644 | ||||||||
\(482\) | −11.7762 | −0.536389 | ||||||||
\(483\) | −11.3536 | −0.516607 | ||||||||
\(484\) | 28.9822 | 1.31737 | ||||||||
\(485\) | 8.56664 | 0.388991 | ||||||||
\(486\) | −5.78161 | −0.262259 | ||||||||
\(487\) | 13.9875 | 0.633832 | 0.316916 | − | 0.948454i | \(-0.397353\pi\) | ||||
0.316916 | + | 0.948454i | \(0.397353\pi\) | |||||||
\(488\) | −11.7860 | −0.533527 | ||||||||
\(489\) | 37.9365 | 1.71555 | ||||||||
\(490\) | −5.74849 | −0.259691 | ||||||||
\(491\) | 14.0743 | 0.635164 | 0.317582 | − | 0.948231i | \(-0.397129\pi\) | ||||
0.317582 | + | 0.948231i | \(0.397129\pi\) | |||||||
\(492\) | −22.5802 | −1.01799 | ||||||||
\(493\) | 12.0824 | 0.544163 | ||||||||
\(494\) | −3.06781 | −0.138027 | ||||||||
\(495\) | 3.56223 | 0.160110 | ||||||||
\(496\) | 3.88716 | 0.174539 | ||||||||
\(497\) | 5.10992 | 0.229211 | ||||||||
\(498\) | −11.8629 | −0.531589 | ||||||||
\(499\) | −31.8753 | −1.42693 | −0.713466 | − | 0.700690i | \(-0.752876\pi\) | ||||
−0.713466 | + | 0.700690i | \(0.752876\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 8.75609 | 0.391193 | ||||||||
\(502\) | 19.1035 | 0.852629 | ||||||||
\(503\) | −20.0354 | −0.893336 | −0.446668 | − | 0.894700i | \(-0.647389\pi\) | ||||
−0.446668 | + | 0.894700i | \(0.647389\pi\) | |||||||
\(504\) | −0.630239 | −0.0280731 | ||||||||
\(505\) | 1.14404 | 0.0509090 | ||||||||
\(506\) | 33.9954 | 1.51128 | ||||||||
\(507\) | 9.45733 | 0.420015 | ||||||||
\(508\) | 16.8182 | 0.746188 | ||||||||
\(509\) | −43.8582 | −1.94398 | −0.971990 | − | 0.235020i | \(-0.924484\pi\) | ||||
−0.971990 | + | 0.235020i | \(0.924484\pi\) | |||||||
\(510\) | −7.41963 | −0.328547 | ||||||||
\(511\) | −18.0494 | −0.798459 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.99202 | −0.220403 | ||||||||
\(514\) | −6.77930 | −0.299022 | ||||||||
\(515\) | 16.5367 | 0.728693 | ||||||||
\(516\) | 19.2022 | 0.845328 | ||||||||
\(517\) | 39.4050 | 1.73303 | ||||||||
\(518\) | 0.317376 | 0.0139447 | ||||||||
\(519\) | 21.7729 | 0.955726 | ||||||||
\(520\) | −2.82666 | −0.123957 | ||||||||
\(521\) | 13.3044 | 0.582878 | 0.291439 | − | 0.956589i | \(-0.405866\pi\) | ||||
0.291439 | + | 0.956589i | \(0.405866\pi\) | |||||||
\(522\) | −1.73177 | −0.0757973 | ||||||||
\(523\) | 42.5883 | 1.86226 | 0.931128 | − | 0.364693i | \(-0.118826\pi\) | ||||
0.931128 | + | 0.364693i | \(0.118826\pi\) | |||||||
\(524\) | 9.34216 | 0.408114 | ||||||||
\(525\) | −2.11177 | −0.0921652 | ||||||||
\(526\) | 23.3670 | 1.01885 | ||||||||
\(527\) | 15.2787 | 0.665549 | ||||||||
\(528\) | 11.9361 | 0.519453 | ||||||||
\(529\) | 5.90511 | 0.256744 | ||||||||
\(530\) | −0.293135 | −0.0127330 | ||||||||
\(531\) | 3.72129 | 0.161490 | ||||||||
\(532\) | −1.21415 | −0.0526401 | ||||||||
\(533\) | −33.8120 | −1.46456 | ||||||||
\(534\) | 15.0842 | 0.652759 | ||||||||
\(535\) | 0.551506 | 0.0238437 | ||||||||
\(536\) | −14.2743 | −0.616557 | ||||||||
\(537\) | −29.9275 | −1.29147 | ||||||||
\(538\) | −6.81642 | −0.293877 | ||||||||
\(539\) | 36.3486 | 1.56564 | ||||||||
\(540\) | −4.59961 | −0.197936 | ||||||||
\(541\) | 17.1178 | 0.735954 | 0.367977 | − | 0.929835i | \(-0.380051\pi\) | ||||
0.367977 | + | 0.929835i | \(0.380051\pi\) | |||||||
\(542\) | −2.58394 | −0.110990 | ||||||||
\(543\) | 43.5436 | 1.86863 | ||||||||
\(544\) | −3.93054 | −0.168520 | ||||||||
\(545\) | −6.39040 | −0.273735 | ||||||||
\(546\) | −5.96925 | −0.255460 | ||||||||
\(547\) | −21.8392 | −0.933776 | −0.466888 | − | 0.884316i | \(-0.654625\pi\) | ||||
−0.466888 | + | 0.884316i | \(0.654625\pi\) | |||||||
\(548\) | −10.1181 | −0.432222 | ||||||||
\(549\) | 6.63979 | 0.283380 | ||||||||
\(550\) | 6.32315 | 0.269620 | ||||||||
\(551\) | −3.33623 | −0.142128 | ||||||||
\(552\) | 10.1489 | 0.431964 | ||||||||
\(553\) | −12.5336 | −0.532984 | ||||||||
\(554\) | 26.6772 | 1.13341 | ||||||||
\(555\) | −0.535534 | −0.0227322 | ||||||||
\(556\) | −18.4350 | −0.781818 | ||||||||
\(557\) | 22.3679 | 0.947760 | 0.473880 | − | 0.880589i | \(-0.342853\pi\) | ||||
0.473880 | + | 0.880589i | \(0.342853\pi\) | |||||||
\(558\) | −2.18989 | −0.0927053 | ||||||||
\(559\) | 28.7537 | 1.21615 | ||||||||
\(560\) | −1.11871 | −0.0472740 | ||||||||
\(561\) | 46.9154 | 1.98077 | ||||||||
\(562\) | −14.4915 | −0.611288 | ||||||||
\(563\) | 3.39487 | 0.143077 | 0.0715383 | − | 0.997438i | \(-0.477209\pi\) | ||||
0.0715383 | + | 0.997438i | \(0.477209\pi\) | |||||||
\(564\) | 11.7638 | 0.495346 | ||||||||
\(565\) | −17.6089 | −0.740813 | ||||||||
\(566\) | −1.14439 | −0.0481025 | ||||||||
\(567\) | −11.6040 | −0.487323 | ||||||||
\(568\) | −4.56770 | −0.191656 | ||||||||
\(569\) | −40.4114 | −1.69414 | −0.847068 | − | 0.531484i | \(-0.821634\pi\) | ||||
−0.847068 | + | 0.531484i | \(0.821634\pi\) | |||||||
\(570\) | 2.04874 | 0.0858121 | ||||||||
\(571\) | 5.23106 | 0.218913 | 0.109457 | − | 0.993992i | \(-0.465089\pi\) | ||||
0.109457 | + | 0.993992i | \(0.465089\pi\) | |||||||
\(572\) | 17.8734 | 0.747323 | ||||||||
\(573\) | 0.0882596 | 0.00368710 | ||||||||
\(574\) | −13.3818 | −0.558544 | ||||||||
\(575\) | 5.37635 | 0.224209 | ||||||||
\(576\) | 0.563364 | 0.0234735 | ||||||||
\(577\) | 6.48134 | 0.269822 | 0.134911 | − | 0.990858i | \(-0.456925\pi\) | ||||
0.134911 | + | 0.990858i | \(0.456925\pi\) | |||||||
\(578\) | 1.55086 | 0.0645074 | ||||||||
\(579\) | −12.0790 | −0.501987 | ||||||||
\(580\) | −3.07398 | −0.127640 | ||||||||
\(581\) | −7.03035 | −0.291668 | ||||||||
\(582\) | −16.1711 | −0.670315 | ||||||||
\(583\) | 1.85353 | 0.0767655 | ||||||||
\(584\) | 16.1342 | 0.667637 | ||||||||
\(585\) | 1.59244 | 0.0658391 | ||||||||
\(586\) | 27.9405 | 1.15421 | ||||||||
\(587\) | 9.53819 | 0.393683 | 0.196842 | − | 0.980435i | \(-0.436931\pi\) | ||||
0.196842 | + | 0.980435i | \(0.436931\pi\) | |||||||
\(588\) | 10.8514 | 0.447503 | ||||||||
\(589\) | −4.21880 | −0.173833 | ||||||||
\(590\) | 6.60549 | 0.271944 | ||||||||
\(591\) | 23.6304 | 0.972023 | ||||||||
\(592\) | −0.283699 | −0.0116599 | ||||||||
\(593\) | −36.0759 | −1.48146 | −0.740730 | − | 0.671803i | \(-0.765520\pi\) | ||||
−0.740730 | + | 0.671803i | \(0.765520\pi\) | |||||||
\(594\) | 29.0840 | 1.19333 | ||||||||
\(595\) | −4.39712 | −0.180264 | ||||||||
\(596\) | 5.02014 | 0.205633 | ||||||||
\(597\) | 9.60614 | 0.393153 | ||||||||
\(598\) | 15.1971 | 0.621455 | ||||||||
\(599\) | −7.81205 | −0.319192 | −0.159596 | − | 0.987182i | \(-0.551019\pi\) | ||||
−0.159596 | + | 0.987182i | \(0.551019\pi\) | |||||||
\(600\) | 1.88769 | 0.0770645 | ||||||||
\(601\) | 26.5910 | 1.08467 | 0.542335 | − | 0.840162i | \(-0.317540\pi\) | ||||
0.542335 | + | 0.840162i | \(0.317540\pi\) | |||||||
\(602\) | 11.3798 | 0.463808 | ||||||||
\(603\) | 8.04164 | 0.327481 | ||||||||
\(604\) | 10.6556 | 0.433572 | ||||||||
\(605\) | −28.9822 | −1.17829 | ||||||||
\(606\) | −2.15959 | −0.0877272 | ||||||||
\(607\) | 28.9721 | 1.17594 | 0.587971 | − | 0.808882i | \(-0.299927\pi\) | ||||
0.587971 | + | 0.808882i | \(0.299927\pi\) | |||||||
\(608\) | 1.08531 | 0.0440153 | ||||||||
\(609\) | −6.49153 | −0.263050 | ||||||||
\(610\) | 11.7860 | 0.477201 | ||||||||
\(611\) | 17.6153 | 0.712640 | ||||||||
\(612\) | 2.21432 | 0.0895087 | ||||||||
\(613\) | −41.4118 | −1.67261 | −0.836304 | − | 0.548266i | \(-0.815288\pi\) | ||||
−0.836304 | + | 0.548266i | \(0.815288\pi\) | |||||||
\(614\) | 16.9869 | 0.685535 | ||||||||
\(615\) | 22.5802 | 0.910521 | ||||||||
\(616\) | 7.07375 | 0.285009 | ||||||||
\(617\) | −17.3638 | −0.699040 | −0.349520 | − | 0.936929i | \(-0.613655\pi\) | ||||
−0.349520 | + | 0.936929i | \(0.613655\pi\) | |||||||
\(618\) | −31.2161 | −1.25570 | ||||||||
\(619\) | 24.6645 | 0.991351 | 0.495676 | − | 0.868508i | \(-0.334921\pi\) | ||||
0.495676 | + | 0.868508i | \(0.334921\pi\) | |||||||
\(620\) | −3.88716 | −0.156112 | ||||||||
\(621\) | 24.7291 | 0.992344 | ||||||||
\(622\) | 31.2663 | 1.25367 | ||||||||
\(623\) | 8.93943 | 0.358151 | ||||||||
\(624\) | 5.33585 | 0.213605 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.6006 | −0.983238 | ||||||||
\(627\) | −12.9545 | −0.517351 | ||||||||
\(628\) | 11.3236 | 0.451862 | ||||||||
\(629\) | −1.11509 | −0.0444615 | ||||||||
\(630\) | 0.630239 | 0.0251093 | ||||||||
\(631\) | −4.10085 | −0.163252 | −0.0816261 | − | 0.996663i | \(-0.526011\pi\) | ||||
−0.0816261 | + | 0.996663i | \(0.526011\pi\) | |||||||
\(632\) | 11.2037 | 0.445658 | ||||||||
\(633\) | 30.1131 | 1.19689 | ||||||||
\(634\) | 12.4915 | 0.496100 | ||||||||
\(635\) | −16.8182 | −0.667410 | ||||||||
\(636\) | 0.553346 | 0.0219416 | ||||||||
\(637\) | 16.2490 | 0.643810 | ||||||||
\(638\) | 19.4372 | 0.769526 | ||||||||
\(639\) | 2.57328 | 0.101797 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 3.53153 | 0.139487 | 0.0697434 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697434 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(642\) | −1.04107 | −0.0410878 | ||||||||
\(643\) | −1.61958 | −0.0638698 | −0.0319349 | − | 0.999490i | \(-0.510167\pi\) | ||||
−0.0319349 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(644\) | 6.01456 | 0.237007 | ||||||||
\(645\) | −19.2022 | −0.756084 | ||||||||
\(646\) | 4.26587 | 0.167839 | ||||||||
\(647\) | −19.8361 | −0.779838 | −0.389919 | − | 0.920849i | \(-0.627497\pi\) | ||||
−0.389919 | + | 0.920849i | \(0.627497\pi\) | |||||||
\(648\) | 10.3727 | 0.407479 | ||||||||
\(649\) | −41.7675 | −1.63952 | ||||||||
\(650\) | 2.82666 | 0.110871 | ||||||||
\(651\) | −8.20879 | −0.321728 | ||||||||
\(652\) | −20.0968 | −0.787053 | ||||||||
\(653\) | 5.88330 | 0.230231 | 0.115116 | − | 0.993352i | \(-0.463276\pi\) | ||||
0.115116 | + | 0.993352i | \(0.463276\pi\) | |||||||
\(654\) | 12.0631 | 0.471704 | ||||||||
\(655\) | −9.34216 | −0.365029 | ||||||||
\(656\) | 11.9618 | 0.467031 | ||||||||
\(657\) | −9.08940 | −0.354611 | ||||||||
\(658\) | 6.97163 | 0.271782 | ||||||||
\(659\) | 13.9830 | 0.544700 | 0.272350 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272350 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(660\) | −11.9361 | −0.464613 | ||||||||
\(661\) | −26.3791 | −1.02603 | −0.513015 | − | 0.858380i | \(-0.671471\pi\) | ||||
−0.513015 | + | 0.858380i | \(0.671471\pi\) | |||||||
\(662\) | 33.8103 | 1.31407 | ||||||||
\(663\) | 20.9728 | 0.814514 | ||||||||
\(664\) | 6.28436 | 0.243880 | ||||||||
\(665\) | 1.21415 | 0.0470827 | ||||||||
\(666\) | 0.159825 | 0.00619311 | ||||||||
\(667\) | 16.5268 | 0.639919 | ||||||||
\(668\) | −4.63853 | −0.179470 | ||||||||
\(669\) | 11.1003 | 0.429163 | ||||||||
\(670\) | 14.2743 | 0.551466 | ||||||||
\(671\) | −74.5245 | −2.87699 | ||||||||
\(672\) | 2.11177 | 0.0814633 | ||||||||
\(673\) | −15.1399 | −0.583600 | −0.291800 | − | 0.956479i | \(-0.594254\pi\) | ||||
−0.291800 | + | 0.956479i | \(0.594254\pi\) | |||||||
\(674\) | −5.49671 | −0.211725 | ||||||||
\(675\) | 4.59961 | 0.177039 | ||||||||
\(676\) | −5.01001 | −0.192693 | ||||||||
\(677\) | −30.4463 | −1.17015 | −0.585073 | − | 0.810981i | \(-0.698934\pi\) | ||||
−0.585073 | + | 0.810981i | \(0.698934\pi\) | |||||||
\(678\) | 33.2402 | 1.27658 | ||||||||
\(679\) | −9.58356 | −0.367783 | ||||||||
\(680\) | 3.93054 | 0.150729 | ||||||||
\(681\) | −5.35096 | −0.205049 | ||||||||
\(682\) | 24.5791 | 0.941183 | ||||||||
\(683\) | 28.6511 | 1.09630 | 0.548151 | − | 0.836379i | \(-0.315332\pi\) | ||||
0.548151 | + | 0.836379i | \(0.315332\pi\) | |||||||
\(684\) | −0.611427 | −0.0233785 | ||||||||
\(685\) | 10.1181 | 0.386591 | ||||||||
\(686\) | 14.2618 | 0.544519 | ||||||||
\(687\) | −1.59377 | −0.0608060 | ||||||||
\(688\) | −10.1723 | −0.387816 | ||||||||
\(689\) | 0.828591 | 0.0315668 | ||||||||
\(690\) | −10.1489 | −0.386361 | ||||||||
\(691\) | −19.6343 | −0.746922 | −0.373461 | − | 0.927646i | \(-0.621829\pi\) | ||||
−0.373461 | + | 0.927646i | \(0.621829\pi\) | |||||||
\(692\) | −11.5342 | −0.438464 | ||||||||
\(693\) | −3.98509 | −0.151381 | ||||||||
\(694\) | 4.26340 | 0.161836 | ||||||||
\(695\) | 18.4350 | 0.699279 | ||||||||
\(696\) | 5.80270 | 0.219951 | ||||||||
\(697\) | 47.0164 | 1.78087 | ||||||||
\(698\) | −20.0459 | −0.758747 | ||||||||
\(699\) | 20.2796 | 0.767043 | ||||||||
\(700\) | 1.11871 | 0.0422832 | ||||||||
\(701\) | 26.9110 | 1.01641 | 0.508207 | − | 0.861235i | \(-0.330309\pi\) | ||||
0.508207 | + | 0.861235i | \(0.330309\pi\) | |||||||
\(702\) | 13.0015 | 0.490711 | ||||||||
\(703\) | 0.307902 | 0.0116128 | ||||||||
\(704\) | −6.32315 | −0.238313 | ||||||||
\(705\) | −11.7638 | −0.443051 | ||||||||
\(706\) | −16.6467 | −0.626506 | ||||||||
\(707\) | −1.27984 | −0.0481335 | ||||||||
\(708\) | −12.4691 | −0.468618 | ||||||||
\(709\) | 43.8293 | 1.64604 | 0.823022 | − | 0.568009i | \(-0.192286\pi\) | ||||
0.823022 | + | 0.568009i | \(0.192286\pi\) | |||||||
\(710\) | 4.56770 | 0.171423 | ||||||||
\(711\) | −6.31173 | −0.236709 | ||||||||
\(712\) | −7.99086 | −0.299470 | ||||||||
\(713\) | 20.8987 | 0.782664 | ||||||||
\(714\) | 8.30039 | 0.310634 | ||||||||
\(715\) | −17.8734 | −0.668426 | ||||||||
\(716\) | 15.8541 | 0.592494 | ||||||||
\(717\) | −35.9247 | −1.34163 | ||||||||
\(718\) | −21.7678 | −0.812367 | ||||||||
\(719\) | 12.7580 | 0.475792 | 0.237896 | − | 0.971291i | \(-0.423542\pi\) | ||||
0.237896 | + | 0.971291i | \(0.423542\pi\) | |||||||
\(720\) | −0.563364 | −0.0209953 | ||||||||
\(721\) | −18.4997 | −0.688965 | ||||||||
\(722\) | 17.8221 | 0.663270 | ||||||||
\(723\) | −22.2297 | −0.826732 | ||||||||
\(724\) | −23.0672 | −0.857284 | ||||||||
\(725\) | 3.07398 | 0.114165 | ||||||||
\(726\) | 54.7093 | 2.03045 | ||||||||
\(727\) | 17.8320 | 0.661352 | 0.330676 | − | 0.943744i | \(-0.392723\pi\) | ||||
0.330676 | + | 0.943744i | \(0.392723\pi\) | |||||||
\(728\) | 3.16220 | 0.117199 | ||||||||
\(729\) | 20.2043 | 0.748306 | ||||||||
\(730\) | −16.1342 | −0.597152 | ||||||||
\(731\) | −39.9827 | −1.47881 | ||||||||
\(732\) | −22.2483 | −0.822319 | ||||||||
\(733\) | 19.6882 | 0.727201 | 0.363601 | − | 0.931555i | \(-0.381547\pi\) | ||||
0.363601 | + | 0.931555i | \(0.381547\pi\) | |||||||
\(734\) | 25.6853 | 0.948063 | ||||||||
\(735\) | −10.8514 | −0.400258 | ||||||||
\(736\) | −5.37635 | −0.198175 | ||||||||
\(737\) | −90.2587 | −3.32472 | ||||||||
\(738\) | −6.73885 | −0.248061 | ||||||||
\(739\) | −28.9558 | −1.06516 | −0.532579 | − | 0.846380i | \(-0.678777\pi\) | ||||
−0.532579 | + | 0.846380i | \(0.678777\pi\) | |||||||
\(740\) | 0.283699 | 0.0104290 | ||||||||
\(741\) | −5.79107 | −0.212740 | ||||||||
\(742\) | 0.327932 | 0.0120388 | ||||||||
\(743\) | −17.2562 | −0.633070 | −0.316535 | − | 0.948581i | \(-0.602519\pi\) | ||||
−0.316535 | + | 0.948581i | \(0.602519\pi\) | |||||||
\(744\) | 7.33775 | 0.269015 | ||||||||
\(745\) | −5.02014 | −0.183924 | ||||||||
\(746\) | −0.356374 | −0.0130478 | ||||||||
\(747\) | −3.54038 | −0.129536 | ||||||||
\(748\) | −24.8534 | −0.908729 | ||||||||
\(749\) | −0.616974 | −0.0225437 | ||||||||
\(750\) | −1.88769 | −0.0689286 | ||||||||
\(751\) | 9.47577 | 0.345776 | 0.172888 | − | 0.984942i | \(-0.444690\pi\) | ||||
0.172888 | + | 0.984942i | \(0.444690\pi\) | |||||||
\(752\) | −6.23186 | −0.227253 | ||||||||
\(753\) | 36.0614 | 1.31415 | ||||||||
\(754\) | 8.68908 | 0.316437 | ||||||||
\(755\) | −10.6556 | −0.387799 | ||||||||
\(756\) | 5.14561 | 0.187144 | ||||||||
\(757\) | −33.2134 | −1.20716 | −0.603581 | − | 0.797302i | \(-0.706260\pi\) | ||||
−0.603581 | + | 0.797302i | \(0.706260\pi\) | |||||||
\(758\) | 21.9006 | 0.795467 | ||||||||
\(759\) | 64.1727 | 2.32932 | ||||||||
\(760\) | −1.08531 | −0.0393685 | ||||||||
\(761\) | 25.4815 | 0.923703 | 0.461852 | − | 0.886957i | \(-0.347185\pi\) | ||||
0.461852 | + | 0.886957i | \(0.347185\pi\) | |||||||
\(762\) | 31.7475 | 1.15009 | ||||||||
\(763\) | 7.14899 | 0.258811 | ||||||||
\(764\) | −0.0467554 | −0.00169155 | ||||||||
\(765\) | −2.21432 | −0.0800590 | ||||||||
\(766\) | −21.5332 | −0.778025 | ||||||||
\(767\) | −18.6715 | −0.674187 | ||||||||
\(768\) | −1.88769 | −0.0681161 | ||||||||
\(769\) | −38.3795 | −1.38400 | −0.691999 | − | 0.721898i | \(-0.743270\pi\) | ||||
−0.691999 | + | 0.721898i | \(0.743270\pi\) | |||||||
\(770\) | −7.07375 | −0.254920 | ||||||||
\(771\) | −12.7972 | −0.460880 | ||||||||
\(772\) | 6.39884 | 0.230299 | ||||||||
\(773\) | −47.4193 | −1.70555 | −0.852777 | − | 0.522275i | \(-0.825083\pi\) | ||||
−0.852777 | + | 0.522275i | \(0.825083\pi\) | |||||||
\(774\) | 5.73071 | 0.205986 | ||||||||
\(775\) | 3.88716 | 0.139631 | ||||||||
\(776\) | 8.56664 | 0.307524 | ||||||||
\(777\) | 0.599106 | 0.0214928 | ||||||||
\(778\) | −32.5057 | −1.16539 | ||||||||
\(779\) | −12.9823 | −0.465141 | ||||||||
\(780\) | −5.33585 | −0.191054 | ||||||||
\(781\) | −28.8822 | −1.03349 | ||||||||
\(782\) | −21.1319 | −0.755677 | ||||||||
\(783\) | 14.1391 | 0.505289 | ||||||||
\(784\) | −5.74849 | −0.205303 | ||||||||
\(785\) | −11.3236 | −0.404158 | ||||||||
\(786\) | 17.6351 | 0.629023 | ||||||||
\(787\) | 29.2019 | 1.04093 | 0.520467 | − | 0.853882i | \(-0.325758\pi\) | ||||
0.520467 | + | 0.853882i | \(0.325758\pi\) | |||||||
\(788\) | −12.5182 | −0.445941 | ||||||||
\(789\) | 44.1097 | 1.57035 | ||||||||
\(790\) | −11.2037 | −0.398608 | ||||||||
\(791\) | 19.6992 | 0.700424 | ||||||||
\(792\) | 3.56223 | 0.126578 | ||||||||
\(793\) | −33.3149 | −1.18305 | ||||||||
\(794\) | −2.06463 | −0.0732709 | ||||||||
\(795\) | −0.553346 | −0.0196252 | ||||||||
\(796\) | −5.08884 | −0.180369 | ||||||||
\(797\) | 30.7905 | 1.09065 | 0.545327 | − | 0.838223i | \(-0.316405\pi\) | ||||
0.545327 | + | 0.838223i | \(0.316405\pi\) | |||||||
\(798\) | −2.29193 | −0.0811336 | ||||||||
\(799\) | −24.4946 | −0.866556 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 4.50176 | 0.159062 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 102.019 | 3.60016 | ||||||||
\(804\) | −26.9455 | −0.950294 | ||||||||
\(805\) | −6.01456 | −0.211985 | ||||||||
\(806\) | 10.9877 | 0.387025 | ||||||||
\(807\) | −12.8673 | −0.452949 | ||||||||
\(808\) | 1.14404 | 0.0402471 | ||||||||
\(809\) | 40.3267 | 1.41781 | 0.708906 | − | 0.705303i | \(-0.249189\pi\) | ||||
0.708906 | + | 0.705303i | \(0.249189\pi\) | |||||||
\(810\) | −10.3727 | −0.364460 | ||||||||
\(811\) | −47.0840 | −1.65334 | −0.826672 | − | 0.562684i | \(-0.809769\pi\) | ||||
−0.826672 | + | 0.562684i | \(0.809769\pi\) | |||||||
\(812\) | 3.43888 | 0.120681 | ||||||||
\(813\) | −4.87766 | −0.171067 | ||||||||
\(814\) | −1.79387 | −0.0628750 | ||||||||
\(815\) | 20.0968 | 0.703961 | ||||||||
\(816\) | −7.41963 | −0.259739 | ||||||||
\(817\) | 11.0402 | 0.386247 | ||||||||
\(818\) | −19.7765 | −0.691468 | ||||||||
\(819\) | −1.78147 | −0.0622496 | ||||||||
\(820\) | −11.9618 | −0.417725 | ||||||||
\(821\) | 47.0778 | 1.64303 | 0.821514 | − | 0.570188i | \(-0.193130\pi\) | ||||
0.821514 | + | 0.570188i | \(0.193130\pi\) | |||||||
\(822\) | −19.0997 | −0.666179 | ||||||||
\(823\) | −0.172122 | −0.00599978 | −0.00299989 | − | 0.999996i | \(-0.500955\pi\) | ||||
−0.00299989 | + | 0.999996i | \(0.500955\pi\) | |||||||
\(824\) | 16.5367 | 0.576083 | ||||||||
\(825\) | 11.9361 | 0.415563 | ||||||||
\(826\) | −7.38961 | −0.257117 | ||||||||
\(827\) | 17.9045 | 0.622602 | 0.311301 | − | 0.950311i | \(-0.399235\pi\) | ||||
0.311301 | + | 0.950311i | \(0.399235\pi\) | |||||||
\(828\) | 3.02884 | 0.105259 | ||||||||
\(829\) | 56.5520 | 1.96413 | 0.982066 | − | 0.188535i | \(-0.0603739\pi\) | ||||
0.982066 | + | 0.188535i | \(0.0603739\pi\) | |||||||
\(830\) | −6.28436 | −0.218133 | ||||||||
\(831\) | 50.3582 | 1.74691 | ||||||||
\(832\) | −2.82666 | −0.0979967 | ||||||||
\(833\) | −22.5947 | −0.782859 | ||||||||
\(834\) | −34.7995 | −1.20501 | ||||||||
\(835\) | 4.63853 | 0.160523 | ||||||||
\(836\) | 6.86261 | 0.237348 | ||||||||
\(837\) | 17.8794 | 0.618004 | ||||||||
\(838\) | 12.3716 | 0.427368 | ||||||||
\(839\) | −33.5857 | −1.15951 | −0.579753 | − | 0.814792i | \(-0.696851\pi\) | ||||
−0.579753 | + | 0.814792i | \(0.696851\pi\) | |||||||
\(840\) | −2.11177 | −0.0728630 | ||||||||
\(841\) | −19.5507 | −0.674161 | ||||||||
\(842\) | 12.3321 | 0.424993 | ||||||||
\(843\) | −27.3555 | −0.942173 | ||||||||
\(844\) | −15.9524 | −0.549103 | ||||||||
\(845\) | 5.01001 | 0.172349 | ||||||||
\(846\) | 3.51080 | 0.120704 | ||||||||
\(847\) | 32.4226 | 1.11405 | ||||||||
\(848\) | −0.293135 | −0.0100663 | ||||||||
\(849\) | −2.16026 | −0.0741398 | ||||||||
\(850\) | −3.93054 | −0.134816 | ||||||||
\(851\) | −1.52526 | −0.0522853 | ||||||||
\(852\) | −8.62239 | −0.295398 | ||||||||
\(853\) | 12.4194 | 0.425234 | 0.212617 | − | 0.977136i | \(-0.431801\pi\) | ||||
0.212617 | + | 0.977136i | \(0.431801\pi\) | |||||||
\(854\) | −13.1851 | −0.451184 | ||||||||
\(855\) | 0.611427 | 0.0209104 | ||||||||
\(856\) | 0.551506 | 0.0188501 | ||||||||
\(857\) | −19.8772 | −0.678993 | −0.339496 | − | 0.940607i | \(-0.610257\pi\) | ||||
−0.339496 | + | 0.940607i | \(0.610257\pi\) | |||||||
\(858\) | 33.7393 | 1.15184 | ||||||||
\(859\) | 7.25545 | 0.247553 | 0.123776 | − | 0.992310i | \(-0.460499\pi\) | ||||
0.123776 | + | 0.992310i | \(0.460499\pi\) | |||||||
\(860\) | 10.1723 | 0.346873 | ||||||||
\(861\) | −25.2606 | −0.860879 | ||||||||
\(862\) | −8.60836 | −0.293202 | ||||||||
\(863\) | −54.1785 | −1.84426 | −0.922129 | − | 0.386883i | \(-0.873552\pi\) | ||||
−0.922129 | + | 0.386883i | \(0.873552\pi\) | |||||||
\(864\) | −4.59961 | −0.156482 | ||||||||
\(865\) | 11.5342 | 0.392174 | ||||||||
\(866\) | −38.3308 | −1.30253 | ||||||||
\(867\) | 2.92754 | 0.0994246 | ||||||||
\(868\) | 4.34860 | 0.147601 | ||||||||
\(869\) | 70.8424 | 2.40316 | ||||||||
\(870\) | −5.80270 | −0.196730 | ||||||||
\(871\) | −40.3486 | −1.36716 | ||||||||
\(872\) | −6.39040 | −0.216406 | ||||||||
\(873\) | −4.82613 | −0.163340 | ||||||||
\(874\) | 5.83503 | 0.197373 | ||||||||
\(875\) | −1.11871 | −0.0378192 | ||||||||
\(876\) | 30.4563 | 1.02902 | ||||||||
\(877\) | −48.4468 | −1.63593 | −0.817967 | − | 0.575265i | \(-0.804899\pi\) | ||||
−0.817967 | + | 0.575265i | \(0.804899\pi\) | |||||||
\(878\) | 11.4306 | 0.385764 | ||||||||
\(879\) | 52.7430 | 1.77898 | ||||||||
\(880\) | 6.32315 | 0.213153 | ||||||||
\(881\) | 21.8562 | 0.736354 | 0.368177 | − | 0.929756i | \(-0.379982\pi\) | ||||
0.368177 | + | 0.929756i | \(0.379982\pi\) | |||||||
\(882\) | 3.23849 | 0.109046 | ||||||||
\(883\) | −1.11929 | −0.0376670 | −0.0188335 | − | 0.999823i | \(-0.505995\pi\) | ||||
−0.0188335 | + | 0.999823i | \(0.505995\pi\) | |||||||
\(884\) | −11.1103 | −0.373679 | ||||||||
\(885\) | 12.4691 | 0.419144 | ||||||||
\(886\) | 10.0730 | 0.338408 | ||||||||
\(887\) | −20.8129 | −0.698827 | −0.349414 | − | 0.936969i | \(-0.613619\pi\) | ||||
−0.349414 | + | 0.936969i | \(0.613619\pi\) | |||||||
\(888\) | −0.535534 | −0.0179714 | ||||||||
\(889\) | 18.8147 | 0.631023 | ||||||||
\(890\) | 7.99086 | 0.267854 | ||||||||
\(891\) | 65.5882 | 2.19729 | ||||||||
\(892\) | −5.88038 | −0.196890 | ||||||||
\(893\) | 6.76353 | 0.226333 | ||||||||
\(894\) | 9.47646 | 0.316940 | ||||||||
\(895\) | −15.8541 | −0.529943 | ||||||||
\(896\) | −1.11871 | −0.0373734 | ||||||||
\(897\) | 28.6874 | 0.957843 | ||||||||
\(898\) | 2.76964 | 0.0924241 | ||||||||
\(899\) | 11.9490 | 0.398523 | ||||||||
\(900\) | 0.563364 | 0.0187788 | ||||||||
\(901\) | −1.15218 | −0.0383846 | ||||||||
\(902\) | 75.6363 | 2.51841 | ||||||||
\(903\) | 21.4816 | 0.714862 | ||||||||
\(904\) | −17.6089 | −0.585664 | ||||||||
\(905\) | 23.0672 | 0.766778 | ||||||||
\(906\) | 20.1145 | 0.668260 | ||||||||
\(907\) | 11.6928 | 0.388252 | 0.194126 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194126 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(908\) | 2.83467 | 0.0940717 | ||||||||
\(909\) | −0.644509 | −0.0213770 | ||||||||
\(910\) | −3.16220 | −0.104826 | ||||||||
\(911\) | −20.6054 | −0.682686 | −0.341343 | − | 0.939939i | \(-0.610882\pi\) | ||||
−0.341343 | + | 0.939939i | \(0.610882\pi\) | |||||||
\(912\) | 2.04874 | 0.0678404 | ||||||||
\(913\) | 39.7369 | 1.31510 | ||||||||
\(914\) | −11.5039 | −0.380516 | ||||||||
\(915\) | 22.2483 | 0.735505 | ||||||||
\(916\) | 0.844296 | 0.0278963 | ||||||||
\(917\) | 10.4511 | 0.345127 | ||||||||
\(918\) | −18.0789 | −0.596694 | ||||||||
\(919\) | −33.4146 | −1.10224 | −0.551122 | − | 0.834424i | \(-0.685800\pi\) | ||||
−0.551122 | + | 0.834424i | \(0.685800\pi\) | |||||||
\(920\) | 5.37635 | 0.177253 | ||||||||
\(921\) | 32.0659 | 1.05661 | ||||||||
\(922\) | 27.0428 | 0.890606 | ||||||||
\(923\) | −12.9113 | −0.424981 | ||||||||
\(924\) | 13.3530 | 0.439282 | ||||||||
\(925\) | −0.283699 | −0.00932795 | ||||||||
\(926\) | 6.63967 | 0.218193 | ||||||||
\(927\) | −9.31616 | −0.305983 | ||||||||
\(928\) | −3.07398 | −0.100908 | ||||||||
\(929\) | 22.2841 | 0.731118 | 0.365559 | − | 0.930788i | \(-0.380878\pi\) | ||||
0.365559 | + | 0.930788i | \(0.380878\pi\) | |||||||
\(930\) | −7.33775 | −0.240614 | ||||||||
\(931\) | 6.23893 | 0.204473 | ||||||||
\(932\) | −10.7431 | −0.351901 | ||||||||
\(933\) | 59.0211 | 1.93226 | ||||||||
\(934\) | 29.1236 | 0.952953 | ||||||||
\(935\) | 24.8534 | 0.812792 | ||||||||
\(936\) | 1.59244 | 0.0520504 | ||||||||
\(937\) | −36.2633 | −1.18467 | −0.592335 | − | 0.805691i | \(-0.701794\pi\) | ||||
−0.592335 | + | 0.805691i | \(0.701794\pi\) | |||||||
\(938\) | −15.9688 | −0.521400 | ||||||||
\(939\) | −46.4382 | −1.51545 | ||||||||
\(940\) | 6.23186 | 0.203261 | ||||||||
\(941\) | 20.1434 | 0.656655 | 0.328328 | − | 0.944564i | \(-0.393515\pi\) | ||||
0.328328 | + | 0.944564i | \(0.393515\pi\) | |||||||
\(942\) | 21.3755 | 0.696450 | ||||||||
\(943\) | 64.3109 | 2.09425 | ||||||||
\(944\) | 6.60549 | 0.214990 | ||||||||
\(945\) | −5.14561 | −0.167387 | ||||||||
\(946\) | −64.3211 | −2.09126 | ||||||||
\(947\) | −35.3544 | −1.14886 | −0.574432 | − | 0.818552i | \(-0.694777\pi\) | ||||
−0.574432 | + | 0.818552i | \(0.694777\pi\) | |||||||
\(948\) | 21.1490 | 0.686888 | ||||||||
\(949\) | 45.6058 | 1.48043 | ||||||||
\(950\) | 1.08531 | 0.0352123 | ||||||||
\(951\) | 23.5800 | 0.764634 | ||||||||
\(952\) | −4.39712 | −0.142512 | ||||||||
\(953\) | 32.9513 | 1.06740 | 0.533699 | − | 0.845675i | \(-0.320802\pi\) | ||||
0.533699 | + | 0.845675i | \(0.320802\pi\) | |||||||
\(954\) | 0.165141 | 0.00534665 | ||||||||
\(955\) | 0.0467554 | 0.00151297 | ||||||||
\(956\) | 19.0311 | 0.615509 | ||||||||
\(957\) | 36.6913 | 1.18606 | ||||||||
\(958\) | 24.4284 | 0.789247 | ||||||||
\(959\) | −11.3191 | −0.365514 | ||||||||
\(960\) | 1.88769 | 0.0609248 | ||||||||
\(961\) | −15.8900 | −0.512579 | ||||||||
\(962\) | −0.801919 | −0.0258549 | ||||||||
\(963\) | −0.310698 | −0.0100121 | ||||||||
\(964\) | 11.7762 | 0.379285 | ||||||||
\(965\) | −6.39884 | −0.205986 | ||||||||
\(966\) | 11.3536 | 0.365296 | ||||||||
\(967\) | −57.1028 | −1.83630 | −0.918152 | − | 0.396229i | \(-0.870319\pi\) | ||||
−0.918152 | + | 0.396229i | \(0.870319\pi\) | |||||||
\(968\) | −28.9822 | −0.931523 | ||||||||
\(969\) | 8.05263 | 0.258688 | ||||||||
\(970\) | −8.56664 | −0.275058 | ||||||||
\(971\) | −24.8459 | −0.797344 | −0.398672 | − | 0.917094i | \(-0.630529\pi\) | ||||
−0.398672 | + | 0.917094i | \(0.630529\pi\) | |||||||
\(972\) | 5.78161 | 0.185445 | ||||||||
\(973\) | −20.6234 | −0.661154 | ||||||||
\(974\) | −13.9875 | −0.448187 | ||||||||
\(975\) | 5.33585 | 0.170884 | ||||||||
\(976\) | 11.7860 | 0.377260 | ||||||||
\(977\) | −19.4149 | −0.621139 | −0.310570 | − | 0.950551i | \(-0.600520\pi\) | ||||
−0.310570 | + | 0.950551i | \(0.600520\pi\) | |||||||
\(978\) | −37.9365 | −1.21308 | ||||||||
\(979\) | −50.5274 | −1.61486 | ||||||||
\(980\) | 5.74849 | 0.183629 | ||||||||
\(981\) | 3.60012 | 0.114943 | ||||||||
\(982\) | −14.0743 | −0.449128 | ||||||||
\(983\) | −25.1465 | −0.802050 | −0.401025 | − | 0.916067i | \(-0.631346\pi\) | ||||
−0.401025 | + | 0.916067i | \(0.631346\pi\) | |||||||
\(984\) | 22.5802 | 0.719830 | ||||||||
\(985\) | 12.5182 | 0.398862 | ||||||||
\(986\) | −12.0824 | −0.384781 | ||||||||
\(987\) | 13.1603 | 0.418895 | ||||||||
\(988\) | 3.06781 | 0.0976002 | ||||||||
\(989\) | −54.6899 | −1.73904 | ||||||||
\(990\) | −3.56223 | −0.113215 | ||||||||
\(991\) | −54.4483 | −1.72961 | −0.864804 | − | 0.502109i | \(-0.832558\pi\) | ||||
−0.864804 | + | 0.502109i | \(0.832558\pi\) | |||||||
\(992\) | −3.88716 | −0.123418 | ||||||||
\(993\) | 63.8233 | 2.02537 | ||||||||
\(994\) | −5.10992 | −0.162077 | ||||||||
\(995\) | 5.08884 | 0.161327 | ||||||||
\(996\) | 11.8629 | 0.375890 | ||||||||
\(997\) | 15.8069 | 0.500608 | 0.250304 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250304 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(998\) | 31.8753 | 1.00899 | ||||||||
\(999\) | −1.30490 | −0.0412853 |
(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 | 4010.2.a.k.1.5 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.5 | ✓ | 15 | 1.1 | even | 1 | trivial |