Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04848 | −0.741387 | −0.370693 | − | 0.928755i | \(-0.620880\pi\) | ||||
−0.370693 | + | 0.928755i | \(0.620880\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.900691 | −0.450346 | ||||||||
\(5\) | −0.0290827 | −0.0130062 | −0.00650308 | − | 0.999979i | \(-0.502070\pi\) | ||||
−0.00650308 | + | 0.999979i | \(0.502070\pi\) | |||||||
\(6\) | 1.04848 | 0.428040 | ||||||||
\(7\) | 2.65326 | 1.00284 | 0.501419 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501419 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(8\) | 3.04131 | 1.07527 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0304926 | 0.00964260 | ||||||||
\(11\) | −4.86193 | −1.46593 | −0.732963 | − | 0.680268i | \(-0.761863\pi\) | ||||
−0.732963 | + | 0.680268i | \(0.761863\pi\) | |||||||
\(12\) | 0.900691 | 0.260007 | ||||||||
\(13\) | 5.69010 | 1.57815 | 0.789074 | − | 0.614298i | \(-0.210561\pi\) | ||||
0.789074 | + | 0.614298i | \(0.210561\pi\) | |||||||
\(14\) | −2.78189 | −0.743491 | ||||||||
\(15\) | 0.0290827 | 0.00750911 | ||||||||
\(16\) | −1.38737 | −0.346843 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.04848 | −0.247129 | ||||||||
\(19\) | −4.01215 | −0.920450 | −0.460225 | − | 0.887802i | \(-0.652231\pi\) | ||||
−0.460225 | + | 0.887802i | \(0.652231\pi\) | |||||||
\(20\) | 0.0261945 | 0.00585727 | ||||||||
\(21\) | −2.65326 | −0.578989 | ||||||||
\(22\) | 5.09763 | 1.08682 | ||||||||
\(23\) | 6.54961 | 1.36569 | 0.682844 | − | 0.730564i | \(-0.260743\pi\) | ||||
0.682844 | + | 0.730564i | \(0.260743\pi\) | |||||||
\(24\) | −3.04131 | −0.620806 | ||||||||
\(25\) | −4.99915 | −0.999831 | ||||||||
\(26\) | −5.96595 | −1.17002 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.38977 | −0.451624 | ||||||||
\(29\) | 2.20837 | 0.410085 | 0.205042 | − | 0.978753i | \(-0.434267\pi\) | ||||
0.205042 | + | 0.978753i | \(0.434267\pi\) | |||||||
\(30\) | −0.0304926 | −0.00556716 | ||||||||
\(31\) | −4.01939 | −0.721903 | −0.360952 | − | 0.932585i | \(-0.617548\pi\) | ||||
−0.360952 | + | 0.932585i | \(0.617548\pi\) | |||||||
\(32\) | −4.62800 | −0.818122 | ||||||||
\(33\) | 4.86193 | 0.846353 | ||||||||
\(34\) | 1.04848 | 0.179813 | ||||||||
\(35\) | −0.0771639 | −0.0130431 | ||||||||
\(36\) | −0.900691 | −0.150115 | ||||||||
\(37\) | −9.08854 | −1.49415 | −0.747073 | − | 0.664742i | \(-0.768541\pi\) | ||||
−0.747073 | + | 0.664742i | \(0.768541\pi\) | |||||||
\(38\) | 4.20666 | 0.682410 | ||||||||
\(39\) | −5.69010 | −0.911145 | ||||||||
\(40\) | −0.0884495 | −0.0139851 | ||||||||
\(41\) | 3.70009 | 0.577857 | 0.288928 | − | 0.957351i | \(-0.406701\pi\) | ||||
0.288928 | + | 0.957351i | \(0.406701\pi\) | |||||||
\(42\) | 2.78189 | 0.429255 | ||||||||
\(43\) | −11.0541 | −1.68573 | −0.842867 | − | 0.538122i | \(-0.819134\pi\) | ||||
−0.842867 | + | 0.538122i | \(0.819134\pi\) | |||||||
\(44\) | 4.37910 | 0.660174 | ||||||||
\(45\) | −0.0290827 | −0.00433539 | ||||||||
\(46\) | −6.86713 | −1.01250 | ||||||||
\(47\) | 10.4871 | 1.52970 | 0.764849 | − | 0.644209i | \(-0.222814\pi\) | ||||
0.764849 | + | 0.644209i | \(0.222814\pi\) | |||||||
\(48\) | 1.38737 | 0.200250 | ||||||||
\(49\) | 0.0397868 | 0.00568383 | ||||||||
\(50\) | 5.24151 | 0.741261 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −5.12502 | −0.710712 | ||||||||
\(53\) | 1.67145 | 0.229592 | 0.114796 | − | 0.993389i | \(-0.463379\pi\) | ||||
0.114796 | + | 0.993389i | \(0.463379\pi\) | |||||||
\(54\) | 1.04848 | 0.142680 | ||||||||
\(55\) | 0.141398 | 0.0190661 | ||||||||
\(56\) | 8.06940 | 1.07832 | ||||||||
\(57\) | 4.01215 | 0.531422 | ||||||||
\(58\) | −2.31543 | −0.304031 | ||||||||
\(59\) | −9.85933 | −1.28357 | −0.641787 | − | 0.766883i | \(-0.721807\pi\) | ||||
−0.641787 | + | 0.766883i | \(0.721807\pi\) | |||||||
\(60\) | −0.0261945 | −0.00338170 | ||||||||
\(61\) | 10.0521 | 1.28704 | 0.643519 | − | 0.765430i | \(-0.277474\pi\) | ||||
0.643519 | + | 0.765430i | \(0.277474\pi\) | |||||||
\(62\) | 4.21425 | 0.535210 | ||||||||
\(63\) | 2.65326 | 0.334279 | ||||||||
\(64\) | 7.62711 | 0.953388 | ||||||||
\(65\) | −0.165483 | −0.0205257 | ||||||||
\(66\) | −5.09763 | −0.627475 | ||||||||
\(67\) | −5.10986 | −0.624268 | −0.312134 | − | 0.950038i | \(-0.601044\pi\) | ||||
−0.312134 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(68\) | 0.900691 | 0.109225 | ||||||||
\(69\) | −6.54961 | −0.788480 | ||||||||
\(70\) | 0.0809047 | 0.00966996 | ||||||||
\(71\) | 6.23056 | 0.739431 | 0.369716 | − | 0.929145i | \(-0.379455\pi\) | ||||
0.369716 | + | 0.929145i | \(0.379455\pi\) | |||||||
\(72\) | 3.04131 | 0.358422 | ||||||||
\(73\) | −2.43967 | −0.285542 | −0.142771 | − | 0.989756i | \(-0.545601\pi\) | ||||
−0.142771 | + | 0.989756i | \(0.545601\pi\) | |||||||
\(74\) | 9.52914 | 1.10774 | ||||||||
\(75\) | 4.99915 | 0.577253 | ||||||||
\(76\) | 3.61371 | 0.414521 | ||||||||
\(77\) | −12.9000 | −1.47009 | ||||||||
\(78\) | 5.96595 | 0.675511 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0.0403485 | 0.00451110 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.87947 | −0.428415 | ||||||||
\(83\) | 9.03700 | 0.991940 | 0.495970 | − | 0.868340i | \(-0.334813\pi\) | ||||
0.495970 | + | 0.868340i | \(0.334813\pi\) | |||||||
\(84\) | 2.38977 | 0.260745 | ||||||||
\(85\) | 0.0290827 | 0.00315446 | ||||||||
\(86\) | 11.5900 | 1.24978 | ||||||||
\(87\) | −2.20837 | −0.236762 | ||||||||
\(88\) | −14.7867 | −1.57626 | ||||||||
\(89\) | −1.57190 | −0.166621 | −0.0833104 | − | 0.996524i | \(-0.526549\pi\) | ||||
−0.0833104 | + | 0.996524i | \(0.526549\pi\) | |||||||
\(90\) | 0.0304926 | 0.00321420 | ||||||||
\(91\) | 15.0973 | 1.58263 | ||||||||
\(92\) | −5.89917 | −0.615031 | ||||||||
\(93\) | 4.01939 | 0.416791 | ||||||||
\(94\) | −10.9955 | −1.13410 | ||||||||
\(95\) | 0.116684 | 0.0119715 | ||||||||
\(96\) | 4.62800 | 0.472343 | ||||||||
\(97\) | −4.85856 | −0.493312 | −0.246656 | − | 0.969103i | \(-0.579332\pi\) | ||||
−0.246656 | + | 0.969103i | \(0.579332\pi\) | |||||||
\(98\) | −0.0417156 | −0.00421391 | ||||||||
\(99\) | −4.86193 | −0.488642 | ||||||||
\(100\) | 4.50269 | 0.450269 | ||||||||
\(101\) | 9.77685 | 0.972833 | 0.486416 | − | 0.873727i | \(-0.338304\pi\) | ||||
0.486416 | + | 0.873727i | \(0.338304\pi\) | |||||||
\(102\) | −1.04848 | −0.103815 | ||||||||
\(103\) | 3.93988 | 0.388207 | 0.194104 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194104 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(104\) | 17.3054 | 1.69693 | ||||||||
\(105\) | 0.0771639 | 0.00753042 | ||||||||
\(106\) | −1.75248 | −0.170216 | ||||||||
\(107\) | −12.4093 | −1.19965 | −0.599825 | − | 0.800131i | \(-0.704763\pi\) | ||||
−0.599825 | + | 0.800131i | \(0.704763\pi\) | |||||||
\(108\) | 0.900691 | 0.0866690 | ||||||||
\(109\) | −6.91498 | −0.662335 | −0.331167 | − | 0.943572i | \(-0.607442\pi\) | ||||
−0.331167 | + | 0.943572i | \(0.607442\pi\) | |||||||
\(110\) | −0.148253 | −0.0141353 | ||||||||
\(111\) | 9.08854 | 0.862646 | ||||||||
\(112\) | −3.68106 | −0.347828 | ||||||||
\(113\) | −14.2593 | −1.34140 | −0.670702 | − | 0.741727i | \(-0.734007\pi\) | ||||
−0.670702 | + | 0.741727i | \(0.734007\pi\) | |||||||
\(114\) | −4.20666 | −0.393989 | ||||||||
\(115\) | −0.190480 | −0.0177624 | ||||||||
\(116\) | −1.98906 | −0.184680 | ||||||||
\(117\) | 5.69010 | 0.526050 | ||||||||
\(118\) | 10.3373 | 0.951626 | ||||||||
\(119\) | −2.65326 | −0.243224 | ||||||||
\(120\) | 0.0884495 | 0.00807430 | ||||||||
\(121\) | 12.6384 | 1.14894 | ||||||||
\(122\) | −10.5394 | −0.954193 | ||||||||
\(123\) | −3.70009 | −0.333626 | ||||||||
\(124\) | 3.62023 | 0.325106 | ||||||||
\(125\) | 0.290802 | 0.0260101 | ||||||||
\(126\) | −2.78189 | −0.247830 | ||||||||
\(127\) | −0.354495 | −0.0314564 | −0.0157282 | − | 0.999876i | \(-0.505007\pi\) | ||||
−0.0157282 | + | 0.999876i | \(0.505007\pi\) | |||||||
\(128\) | 1.25913 | 0.111293 | ||||||||
\(129\) | 11.0541 | 0.973259 | ||||||||
\(130\) | 0.173506 | 0.0152175 | ||||||||
\(131\) | 6.11834 | 0.534562 | 0.267281 | − | 0.963619i | \(-0.413875\pi\) | ||||
0.267281 | + | 0.963619i | \(0.413875\pi\) | |||||||
\(132\) | −4.37910 | −0.381151 | ||||||||
\(133\) | −10.6453 | −0.923062 | ||||||||
\(134\) | 5.35758 | 0.462824 | ||||||||
\(135\) | 0.0290827 | 0.00250304 | ||||||||
\(136\) | −3.04131 | −0.260791 | ||||||||
\(137\) | 8.20828 | 0.701281 | 0.350640 | − | 0.936510i | \(-0.385964\pi\) | ||||
0.350640 | + | 0.936510i | \(0.385964\pi\) | |||||||
\(138\) | 6.86713 | 0.584569 | ||||||||
\(139\) | 2.79349 | 0.236941 | 0.118471 | − | 0.992958i | \(-0.462201\pi\) | ||||
0.118471 | + | 0.992958i | \(0.462201\pi\) | |||||||
\(140\) | 0.0695008 | 0.00587389 | ||||||||
\(141\) | −10.4871 | −0.883172 | ||||||||
\(142\) | −6.53261 | −0.548204 | ||||||||
\(143\) | −27.6648 | −2.31345 | ||||||||
\(144\) | −1.38737 | −0.115614 | ||||||||
\(145\) | −0.0642254 | −0.00533363 | ||||||||
\(146\) | 2.55795 | 0.211697 | ||||||||
\(147\) | −0.0397868 | −0.00328156 | ||||||||
\(148\) | 8.18596 | 0.672882 | ||||||||
\(149\) | 13.1191 | 1.07476 | 0.537378 | − | 0.843342i | \(-0.319415\pi\) | ||||
0.537378 | + | 0.843342i | \(0.319415\pi\) | |||||||
\(150\) | −5.24151 | −0.427967 | ||||||||
\(151\) | 1.38193 | 0.112460 | 0.0562299 | − | 0.998418i | \(-0.482092\pi\) | ||||
0.0562299 | + | 0.998418i | \(0.482092\pi\) | |||||||
\(152\) | −12.2022 | −0.989730 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 13.5253 | 1.08990 | ||||||||
\(155\) | 0.116895 | 0.00938919 | ||||||||
\(156\) | 5.12502 | 0.410330 | ||||||||
\(157\) | 6.17154 | 0.492543 | 0.246271 | − | 0.969201i | \(-0.420795\pi\) | ||||
0.246271 | + | 0.969201i | \(0.420795\pi\) | |||||||
\(158\) | 1.04848 | 0.0834125 | ||||||||
\(159\) | −1.67145 | −0.132555 | ||||||||
\(160\) | 0.134594 | 0.0106406 | ||||||||
\(161\) | 17.3778 | 1.36956 | ||||||||
\(162\) | −1.04848 | −0.0823763 | ||||||||
\(163\) | −7.23385 | −0.566599 | −0.283300 | − | 0.959031i | \(-0.591429\pi\) | ||||
−0.283300 | + | 0.959031i | \(0.591429\pi\) | |||||||
\(164\) | −3.33264 | −0.260235 | ||||||||
\(165\) | −0.141398 | −0.0110078 | ||||||||
\(166\) | −9.47511 | −0.735411 | ||||||||
\(167\) | −7.66967 | −0.593497 | −0.296749 | − | 0.954956i | \(-0.595902\pi\) | ||||
−0.296749 | + | 0.954956i | \(0.595902\pi\) | |||||||
\(168\) | −8.06940 | −0.622568 | ||||||||
\(169\) | 19.3772 | 1.49055 | ||||||||
\(170\) | −0.0304926 | −0.00233867 | ||||||||
\(171\) | −4.01215 | −0.306817 | ||||||||
\(172\) | 9.95633 | 0.759163 | ||||||||
\(173\) | 4.59359 | 0.349244 | 0.174622 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174622 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(174\) | 2.31543 | 0.175533 | ||||||||
\(175\) | −13.2641 | −1.00267 | ||||||||
\(176\) | 6.74531 | 0.508447 | ||||||||
\(177\) | 9.85933 | 0.741072 | ||||||||
\(178\) | 1.64810 | 0.123530 | ||||||||
\(179\) | −11.8850 | −0.888325 | −0.444162 | − | 0.895946i | \(-0.646499\pi\) | ||||
−0.444162 | + | 0.895946i | \(0.646499\pi\) | |||||||
\(180\) | 0.0261945 | 0.00195242 | ||||||||
\(181\) | 1.12907 | 0.0839232 | 0.0419616 | − | 0.999119i | \(-0.486639\pi\) | ||||
0.0419616 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(182\) | −15.8292 | −1.17334 | ||||||||
\(183\) | −10.0521 | −0.743072 | ||||||||
\(184\) | 19.9194 | 1.46848 | ||||||||
\(185\) | 0.264319 | 0.0194331 | ||||||||
\(186\) | −4.21425 | −0.309003 | ||||||||
\(187\) | 4.86193 | 0.355539 | ||||||||
\(188\) | −9.44562 | −0.688893 | ||||||||
\(189\) | −2.65326 | −0.192996 | ||||||||
\(190\) | −0.122341 | −0.00887553 | ||||||||
\(191\) | −21.6882 | −1.56931 | −0.784653 | − | 0.619935i | \(-0.787159\pi\) | ||||
−0.784653 | + | 0.619935i | \(0.787159\pi\) | |||||||
\(192\) | −7.62711 | −0.550439 | ||||||||
\(193\) | −21.2176 | −1.52727 | −0.763637 | − | 0.645646i | \(-0.776588\pi\) | ||||
−0.763637 | + | 0.645646i | \(0.776588\pi\) | |||||||
\(194\) | 5.09410 | 0.365735 | ||||||||
\(195\) | 0.165483 | 0.0118505 | ||||||||
\(196\) | −0.0358356 | −0.00255969 | ||||||||
\(197\) | 1.92916 | 0.137447 | 0.0687236 | − | 0.997636i | \(-0.478107\pi\) | ||||
0.0687236 | + | 0.997636i | \(0.478107\pi\) | |||||||
\(198\) | 5.09763 | 0.362273 | ||||||||
\(199\) | −11.8049 | −0.836824 | −0.418412 | − | 0.908257i | \(-0.637413\pi\) | ||||
−0.418412 | + | 0.908257i | \(0.637413\pi\) | |||||||
\(200\) | −15.2040 | −1.07509 | ||||||||
\(201\) | 5.10986 | 0.360421 | ||||||||
\(202\) | −10.2508 | −0.721245 | ||||||||
\(203\) | 5.85939 | 0.411248 | ||||||||
\(204\) | −0.900691 | −0.0630610 | ||||||||
\(205\) | −0.107608 | −0.00751570 | ||||||||
\(206\) | −4.13088 | −0.287812 | ||||||||
\(207\) | 6.54961 | 0.455229 | ||||||||
\(208\) | −7.89429 | −0.547370 | ||||||||
\(209\) | 19.5068 | 1.34931 | ||||||||
\(210\) | −0.0809047 | −0.00558296 | ||||||||
\(211\) | 6.25806 | 0.430823 | 0.215411 | − | 0.976523i | \(-0.430891\pi\) | ||||
0.215411 | + | 0.976523i | \(0.430891\pi\) | |||||||
\(212\) | −1.50546 | −0.103396 | ||||||||
\(213\) | −6.23056 | −0.426911 | ||||||||
\(214\) | 13.0109 | 0.889405 | ||||||||
\(215\) | 0.321483 | 0.0219249 | ||||||||
\(216\) | −3.04131 | −0.206935 | ||||||||
\(217\) | −10.6645 | −0.723952 | ||||||||
\(218\) | 7.25021 | 0.491046 | ||||||||
\(219\) | 2.43967 | 0.164858 | ||||||||
\(220\) | −0.127356 | −0.00858633 | ||||||||
\(221\) | −5.69010 | −0.382757 | ||||||||
\(222\) | −9.52914 | −0.639554 | ||||||||
\(223\) | −19.3188 | −1.29368 | −0.646840 | − | 0.762626i | \(-0.723910\pi\) | ||||
−0.646840 | + | 0.762626i | \(0.723910\pi\) | |||||||
\(224\) | −12.2793 | −0.820444 | ||||||||
\(225\) | −4.99915 | −0.333277 | ||||||||
\(226\) | 14.9506 | 0.994499 | ||||||||
\(227\) | 4.30211 | 0.285541 | 0.142771 | − | 0.989756i | \(-0.454399\pi\) | ||||
0.142771 | + | 0.989756i | \(0.454399\pi\) | |||||||
\(228\) | −3.61371 | −0.239324 | ||||||||
\(229\) | −22.8035 | −1.50690 | −0.753450 | − | 0.657505i | \(-0.771612\pi\) | ||||
−0.753450 | + | 0.657505i | \(0.771612\pi\) | |||||||
\(230\) | 0.199714 | 0.0131688 | ||||||||
\(231\) | 12.9000 | 0.848755 | ||||||||
\(232\) | 6.71636 | 0.440950 | ||||||||
\(233\) | 16.3679 | 1.07230 | 0.536148 | − | 0.844124i | \(-0.319879\pi\) | ||||
0.536148 | + | 0.844124i | \(0.319879\pi\) | |||||||
\(234\) | −5.96595 | −0.390006 | ||||||||
\(235\) | −0.304992 | −0.0198955 | ||||||||
\(236\) | 8.88021 | 0.578052 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 2.78189 | 0.180323 | ||||||||
\(239\) | −12.4023 | −0.802238 | −0.401119 | − | 0.916026i | \(-0.631379\pi\) | ||||
−0.401119 | + | 0.916026i | \(0.631379\pi\) | |||||||
\(240\) | −0.0403485 | −0.00260449 | ||||||||
\(241\) | 7.49506 | 0.482800 | 0.241400 | − | 0.970426i | \(-0.422393\pi\) | ||||
0.241400 | + | 0.970426i | \(0.422393\pi\) | |||||||
\(242\) | −13.2511 | −0.851810 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.05382 | −0.579612 | ||||||||
\(245\) | −0.00115711 | −7.39248e−5 0 | ||||||||
\(246\) | 3.87947 | 0.247346 | ||||||||
\(247\) | −22.8295 | −1.45261 | ||||||||
\(248\) | −12.2242 | −0.776239 | ||||||||
\(249\) | −9.03700 | −0.572697 | ||||||||
\(250\) | −0.304900 | −0.0192836 | ||||||||
\(251\) | −27.1669 | −1.71476 | −0.857380 | − | 0.514684i | \(-0.827909\pi\) | ||||
−0.857380 | + | 0.514684i | \(0.827909\pi\) | |||||||
\(252\) | −2.38977 | −0.150541 | ||||||||
\(253\) | −31.8437 | −2.00200 | ||||||||
\(254\) | 0.371681 | 0.0233213 | ||||||||
\(255\) | −0.0290827 | −0.00182123 | ||||||||
\(256\) | −16.5744 | −1.03590 | ||||||||
\(257\) | 17.1018 | 1.06678 | 0.533390 | − | 0.845870i | \(-0.320918\pi\) | ||||
0.533390 | + | 0.845870i | \(0.320918\pi\) | |||||||
\(258\) | −11.5900 | −0.721561 | ||||||||
\(259\) | −24.1142 | −1.49839 | ||||||||
\(260\) | 0.149049 | 0.00924364 | ||||||||
\(261\) | 2.20837 | 0.136695 | ||||||||
\(262\) | −6.41495 | −0.396317 | ||||||||
\(263\) | −24.1366 | −1.48832 | −0.744162 | − | 0.667999i | \(-0.767151\pi\) | ||||
−0.744162 | + | 0.667999i | \(0.767151\pi\) | |||||||
\(264\) | 14.7867 | 0.910056 | ||||||||
\(265\) | −0.0486103 | −0.00298611 | ||||||||
\(266\) | 11.1613 | 0.684346 | ||||||||
\(267\) | 1.57190 | 0.0961986 | ||||||||
\(268\) | 4.60240 | 0.281136 | ||||||||
\(269\) | −4.48564 | −0.273494 | −0.136747 | − | 0.990606i | \(-0.543665\pi\) | ||||
−0.136747 | + | 0.990606i | \(0.543665\pi\) | |||||||
\(270\) | −0.0304926 | −0.00185572 | ||||||||
\(271\) | 26.4955 | 1.60949 | 0.804743 | − | 0.593624i | \(-0.202303\pi\) | ||||
0.804743 | + | 0.593624i | \(0.202303\pi\) | |||||||
\(272\) | 1.38737 | 0.0841219 | ||||||||
\(273\) | −15.0973 | −0.913730 | ||||||||
\(274\) | −8.60621 | −0.519920 | ||||||||
\(275\) | 24.3055 | 1.46568 | ||||||||
\(276\) | 5.89917 | 0.355089 | ||||||||
\(277\) | −1.86292 | −0.111932 | −0.0559661 | − | 0.998433i | \(-0.517824\pi\) | ||||
−0.0559661 | + | 0.998433i | \(0.517824\pi\) | |||||||
\(278\) | −2.92892 | −0.175665 | ||||||||
\(279\) | −4.01939 | −0.240634 | ||||||||
\(280\) | −0.234680 | −0.0140248 | ||||||||
\(281\) | −6.81221 | −0.406382 | −0.203191 | − | 0.979139i | \(-0.565131\pi\) | ||||
−0.203191 | + | 0.979139i | \(0.565131\pi\) | |||||||
\(282\) | 10.9955 | 0.654772 | ||||||||
\(283\) | −14.4451 | −0.858673 | −0.429337 | − | 0.903145i | \(-0.641253\pi\) | ||||
−0.429337 | + | 0.903145i | \(0.641253\pi\) | |||||||
\(284\) | −5.61181 | −0.332999 | ||||||||
\(285\) | −0.116684 | −0.00691176 | ||||||||
\(286\) | 29.0060 | 1.71516 | ||||||||
\(287\) | 9.81729 | 0.579497 | ||||||||
\(288\) | −4.62800 | −0.272707 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.0673390 | 0.00395428 | ||||||||
\(291\) | 4.85856 | 0.284814 | ||||||||
\(292\) | 2.19739 | 0.128593 | ||||||||
\(293\) | −12.8907 | −0.753084 | −0.376542 | − | 0.926400i | \(-0.622887\pi\) | ||||
−0.376542 | + | 0.926400i | \(0.622887\pi\) | |||||||
\(294\) | 0.0417156 | 0.00243290 | ||||||||
\(295\) | 0.286735 | 0.0166944 | ||||||||
\(296\) | −27.6411 | −1.60661 | ||||||||
\(297\) | 4.86193 | 0.282118 | ||||||||
\(298\) | −13.7551 | −0.796809 | ||||||||
\(299\) | 37.2679 | 2.15526 | ||||||||
\(300\) | −4.50269 | −0.259963 | ||||||||
\(301\) | −29.3294 | −1.69052 | ||||||||
\(302\) | −1.44892 | −0.0833761 | ||||||||
\(303\) | −9.77685 | −0.561665 | ||||||||
\(304\) | 5.56635 | 0.319252 | ||||||||
\(305\) | −0.292341 | −0.0167394 | ||||||||
\(306\) | 1.04848 | 0.0599376 | ||||||||
\(307\) | −32.5298 | −1.85658 | −0.928288 | − | 0.371862i | \(-0.878719\pi\) | ||||
−0.928288 | + | 0.371862i | \(0.878719\pi\) | |||||||
\(308\) | 11.6189 | 0.662047 | ||||||||
\(309\) | −3.93988 | −0.224132 | ||||||||
\(310\) | −0.122561 | −0.00696102 | ||||||||
\(311\) | 28.1002 | 1.59342 | 0.796709 | − | 0.604363i | \(-0.206572\pi\) | ||||
0.796709 | + | 0.604363i | \(0.206572\pi\) | |||||||
\(312\) | −17.3054 | −0.979724 | ||||||||
\(313\) | 4.42249 | 0.249974 | 0.124987 | − | 0.992158i | \(-0.460111\pi\) | ||||
0.124987 | + | 0.992158i | \(0.460111\pi\) | |||||||
\(314\) | −6.47074 | −0.365165 | ||||||||
\(315\) | −0.0771639 | −0.00434769 | ||||||||
\(316\) | 0.900691 | 0.0506678 | ||||||||
\(317\) | −26.9923 | −1.51604 | −0.758019 | − | 0.652233i | \(-0.773832\pi\) | ||||
−0.758019 | + | 0.652233i | \(0.773832\pi\) | |||||||
\(318\) | 1.75248 | 0.0982744 | ||||||||
\(319\) | −10.7370 | −0.601154 | ||||||||
\(320\) | −0.221817 | −0.0123999 | ||||||||
\(321\) | 12.4093 | 0.692619 | ||||||||
\(322\) | −18.2203 | −1.01538 | ||||||||
\(323\) | 4.01215 | 0.223242 | ||||||||
\(324\) | −0.900691 | −0.0500384 | ||||||||
\(325\) | −28.4457 | −1.57788 | ||||||||
\(326\) | 7.58455 | 0.420069 | ||||||||
\(327\) | 6.91498 | 0.382399 | ||||||||
\(328\) | 11.2531 | 0.621350 | ||||||||
\(329\) | 27.8250 | 1.53404 | ||||||||
\(330\) | 0.148253 | 0.00816104 | ||||||||
\(331\) | −23.4339 | −1.28804 | −0.644021 | − | 0.765008i | \(-0.722735\pi\) | ||||
−0.644021 | + | 0.765008i | \(0.722735\pi\) | |||||||
\(332\) | −8.13955 | −0.446716 | ||||||||
\(333\) | −9.08854 | −0.498049 | ||||||||
\(334\) | 8.04150 | 0.440011 | ||||||||
\(335\) | 0.148608 | 0.00811934 | ||||||||
\(336\) | 3.68106 | 0.200818 | ||||||||
\(337\) | −6.05229 | −0.329689 | −0.164845 | − | 0.986320i | \(-0.552712\pi\) | ||||
−0.164845 | + | 0.986320i | \(0.552712\pi\) | |||||||
\(338\) | −20.3166 | −1.10508 | ||||||||
\(339\) | 14.2593 | 0.774460 | ||||||||
\(340\) | −0.0261945 | −0.00142060 | ||||||||
\(341\) | 19.5420 | 1.05826 | ||||||||
\(342\) | 4.20666 | 0.227470 | ||||||||
\(343\) | −18.4673 | −0.997138 | ||||||||
\(344\) | −33.6190 | −1.81261 | ||||||||
\(345\) | 0.190480 | 0.0102551 | ||||||||
\(346\) | −4.81628 | −0.258925 | ||||||||
\(347\) | −22.5338 | −1.20968 | −0.604839 | − | 0.796347i | \(-0.706763\pi\) | ||||
−0.604839 | + | 0.796347i | \(0.706763\pi\) | |||||||
\(348\) | 1.98906 | 0.106625 | ||||||||
\(349\) | −2.38801 | −0.127827 | −0.0639137 | − | 0.997955i | \(-0.520358\pi\) | ||||
−0.0639137 | + | 0.997955i | \(0.520358\pi\) | |||||||
\(350\) | 13.9071 | 0.743365 | ||||||||
\(351\) | −5.69010 | −0.303715 | ||||||||
\(352\) | 22.5010 | 1.19931 | ||||||||
\(353\) | 20.0148 | 1.06528 | 0.532640 | − | 0.846342i | \(-0.321200\pi\) | ||||
0.532640 | + | 0.846342i | \(0.321200\pi\) | |||||||
\(354\) | −10.3373 | −0.549421 | ||||||||
\(355\) | −0.181201 | −0.00961716 | ||||||||
\(356\) | 1.41579 | 0.0750369 | ||||||||
\(357\) | 2.65326 | 0.140425 | ||||||||
\(358\) | 12.4611 | 0.658592 | ||||||||
\(359\) | −23.8118 | −1.25674 | −0.628368 | − | 0.777916i | \(-0.716277\pi\) | ||||
−0.628368 | + | 0.777916i | \(0.716277\pi\) | |||||||
\(360\) | −0.0884495 | −0.00466170 | ||||||||
\(361\) | −2.90266 | −0.152771 | ||||||||
\(362\) | −1.18381 | −0.0622195 | ||||||||
\(363\) | −12.6384 | −0.663341 | ||||||||
\(364\) | −13.5980 | −0.712729 | ||||||||
\(365\) | 0.0709522 | 0.00371381 | ||||||||
\(366\) | 10.5394 | 0.550903 | ||||||||
\(367\) | 21.0106 | 1.09674 | 0.548372 | − | 0.836234i | \(-0.315248\pi\) | ||||
0.548372 | + | 0.836234i | \(0.315248\pi\) | |||||||
\(368\) | −9.08675 | −0.473680 | ||||||||
\(369\) | 3.70009 | 0.192619 | ||||||||
\(370\) | −0.277133 | −0.0144074 | ||||||||
\(371\) | 4.43480 | 0.230243 | ||||||||
\(372\) | −3.62023 | −0.187700 | ||||||||
\(373\) | −36.7765 | −1.90422 | −0.952108 | − | 0.305761i | \(-0.901089\pi\) | ||||
−0.952108 | + | 0.305761i | \(0.901089\pi\) | |||||||
\(374\) | −5.09763 | −0.263592 | ||||||||
\(375\) | −0.290802 | −0.0150170 | ||||||||
\(376\) | 31.8945 | 1.64483 | ||||||||
\(377\) | 12.5659 | 0.647175 | ||||||||
\(378\) | 2.78189 | 0.143085 | ||||||||
\(379\) | 28.9867 | 1.48894 | 0.744472 | − | 0.667653i | \(-0.232701\pi\) | ||||
0.744472 | + | 0.667653i | \(0.232701\pi\) | |||||||
\(380\) | −0.105096 | −0.00539132 | ||||||||
\(381\) | 0.354495 | 0.0181613 | ||||||||
\(382\) | 22.7397 | 1.16346 | ||||||||
\(383\) | −10.3087 | −0.526752 | −0.263376 | − | 0.964693i | \(-0.584836\pi\) | ||||
−0.263376 | + | 0.964693i | \(0.584836\pi\) | |||||||
\(384\) | −1.25913 | −0.0642548 | ||||||||
\(385\) | 0.375165 | 0.0191202 | ||||||||
\(386\) | 22.2462 | 1.13230 | ||||||||
\(387\) | −11.0541 | −0.561911 | ||||||||
\(388\) | 4.37607 | 0.222161 | ||||||||
\(389\) | −12.0478 | −0.610847 | −0.305423 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305423 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(390\) | −0.173506 | −0.00878580 | ||||||||
\(391\) | −6.54961 | −0.331228 | ||||||||
\(392\) | 0.121004 | 0.00611163 | ||||||||
\(393\) | −6.11834 | −0.308629 | ||||||||
\(394\) | −2.02269 | −0.101902 | ||||||||
\(395\) | 0.0290827 | 0.00146331 | ||||||||
\(396\) | 4.37910 | 0.220058 | ||||||||
\(397\) | −14.4500 | −0.725227 | −0.362614 | − | 0.931940i | \(-0.618115\pi\) | ||||
−0.362614 | + | 0.931940i | \(0.618115\pi\) | |||||||
\(398\) | 12.3771 | 0.620410 | ||||||||
\(399\) | 10.6453 | 0.532930 | ||||||||
\(400\) | 6.93569 | 0.346785 | ||||||||
\(401\) | −28.3766 | −1.41706 | −0.708531 | − | 0.705680i | \(-0.750642\pi\) | ||||
−0.708531 | + | 0.705680i | \(0.750642\pi\) | |||||||
\(402\) | −5.35758 | −0.267212 | ||||||||
\(403\) | −22.8707 | −1.13927 | ||||||||
\(404\) | −8.80592 | −0.438111 | ||||||||
\(405\) | −0.0290827 | −0.00144513 | ||||||||
\(406\) | −6.14345 | −0.304894 | ||||||||
\(407\) | 44.1878 | 2.19031 | ||||||||
\(408\) | 3.04131 | 0.150568 | ||||||||
\(409\) | −3.27719 | −0.162046 | −0.0810232 | − | 0.996712i | \(-0.525819\pi\) | ||||
−0.0810232 | + | 0.996712i | \(0.525819\pi\) | |||||||
\(410\) | 0.112825 | 0.00557204 | ||||||||
\(411\) | −8.20828 | −0.404885 | ||||||||
\(412\) | −3.54861 | −0.174827 | ||||||||
\(413\) | −26.1594 | −1.28722 | ||||||||
\(414\) | −6.86713 | −0.337501 | ||||||||
\(415\) | −0.262820 | −0.0129013 | ||||||||
\(416\) | −26.3338 | −1.29112 | ||||||||
\(417\) | −2.79349 | −0.136798 | ||||||||
\(418\) | −20.4525 | −1.00036 | ||||||||
\(419\) | −18.3150 | −0.894747 | −0.447373 | − | 0.894347i | \(-0.647640\pi\) | ||||
−0.447373 | + | 0.894347i | \(0.647640\pi\) | |||||||
\(420\) | −0.0695008 | −0.00339129 | ||||||||
\(421\) | −3.92987 | −0.191530 | −0.0957651 | − | 0.995404i | \(-0.530530\pi\) | ||||
−0.0957651 | + | 0.995404i | \(0.530530\pi\) | |||||||
\(422\) | −6.56145 | −0.319406 | ||||||||
\(423\) | 10.4871 | 0.509899 | ||||||||
\(424\) | 5.08342 | 0.246872 | ||||||||
\(425\) | 4.99915 | 0.242495 | ||||||||
\(426\) | 6.53261 | 0.316506 | ||||||||
\(427\) | 26.6708 | 1.29069 | ||||||||
\(428\) | 11.1769 | 0.540257 | ||||||||
\(429\) | 27.6648 | 1.33567 | ||||||||
\(430\) | −0.337068 | −0.0162549 | ||||||||
\(431\) | 17.8750 | 0.861007 | 0.430503 | − | 0.902589i | \(-0.358336\pi\) | ||||
0.430503 | + | 0.902589i | \(0.358336\pi\) | |||||||
\(432\) | 1.38737 | 0.0667500 | ||||||||
\(433\) | 31.2642 | 1.50246 | 0.751231 | − | 0.660040i | \(-0.229461\pi\) | ||||
0.751231 | + | 0.660040i | \(0.229461\pi\) | |||||||
\(434\) | 11.1815 | 0.536729 | ||||||||
\(435\) | 0.0642254 | 0.00307937 | ||||||||
\(436\) | 6.22826 | 0.298280 | ||||||||
\(437\) | −26.2780 | −1.25705 | ||||||||
\(438\) | −2.55795 | −0.122223 | ||||||||
\(439\) | −7.50935 | −0.358402 | −0.179201 | − | 0.983813i | \(-0.557351\pi\) | ||||
−0.179201 | + | 0.983813i | \(0.557351\pi\) | |||||||
\(440\) | 0.430035 | 0.0205011 | ||||||||
\(441\) | 0.0397868 | 0.00189461 | ||||||||
\(442\) | 5.96595 | 0.283771 | ||||||||
\(443\) | 13.1677 | 0.625617 | 0.312809 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312809 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(444\) | −8.18596 | −0.388489 | ||||||||
\(445\) | 0.0457150 | 0.00216710 | ||||||||
\(446\) | 20.2553 | 0.959117 | ||||||||
\(447\) | −13.1191 | −0.620510 | ||||||||
\(448\) | 20.2367 | 0.956094 | ||||||||
\(449\) | 13.3870 | 0.631771 | 0.315885 | − | 0.948797i | \(-0.397698\pi\) | ||||
0.315885 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(450\) | 5.24151 | 0.247087 | ||||||||
\(451\) | −17.9896 | −0.847096 | ||||||||
\(452\) | 12.8432 | 0.604095 | ||||||||
\(453\) | −1.38193 | −0.0649286 | ||||||||
\(454\) | −4.51068 | −0.211697 | ||||||||
\(455\) | −0.439070 | −0.0205839 | ||||||||
\(456\) | 12.2022 | 0.571421 | ||||||||
\(457\) | 0.813175 | 0.0380387 | 0.0190194 | − | 0.999819i | \(-0.493946\pi\) | ||||
0.0190194 | + | 0.999819i | \(0.493946\pi\) | |||||||
\(458\) | 23.9090 | 1.11720 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.171564 | 0.00799920 | ||||||||
\(461\) | −21.8646 | −1.01834 | −0.509169 | − | 0.860667i | \(-0.670047\pi\) | ||||
−0.509169 | + | 0.860667i | \(0.670047\pi\) | |||||||
\(462\) | −13.5253 | −0.629256 | ||||||||
\(463\) | 13.5844 | 0.631322 | 0.315661 | − | 0.948872i | \(-0.397774\pi\) | ||||
0.315661 | + | 0.948872i | \(0.397774\pi\) | |||||||
\(464\) | −3.06384 | −0.142235 | ||||||||
\(465\) | −0.116895 | −0.00542085 | ||||||||
\(466\) | −17.1614 | −0.794986 | ||||||||
\(467\) | −9.89268 | −0.457779 | −0.228889 | − | 0.973452i | \(-0.573509\pi\) | ||||
−0.228889 | + | 0.973452i | \(0.573509\pi\) | |||||||
\(468\) | −5.12502 | −0.236904 | ||||||||
\(469\) | −13.5578 | −0.626040 | ||||||||
\(470\) | 0.319778 | 0.0147503 | ||||||||
\(471\) | −6.17154 | −0.284370 | ||||||||
\(472\) | −29.9853 | −1.38019 | ||||||||
\(473\) | 53.7442 | 2.47116 | ||||||||
\(474\) | −1.04848 | −0.0481582 | ||||||||
\(475\) | 20.0574 | 0.920294 | ||||||||
\(476\) | 2.38977 | 0.109535 | ||||||||
\(477\) | 1.67145 | 0.0765306 | ||||||||
\(478\) | 13.0036 | 0.594769 | ||||||||
\(479\) | 8.67265 | 0.396263 | 0.198132 | − | 0.980175i | \(-0.436513\pi\) | ||||
0.198132 | + | 0.980175i | \(0.436513\pi\) | |||||||
\(480\) | −0.134594 | −0.00614337 | ||||||||
\(481\) | −51.7147 | −2.35799 | ||||||||
\(482\) | −7.85842 | −0.357941 | ||||||||
\(483\) | −17.3778 | −0.790718 | ||||||||
\(484\) | −11.3833 | −0.517421 | ||||||||
\(485\) | 0.141300 | 0.00641610 | ||||||||
\(486\) | 1.04848 | 0.0475600 | ||||||||
\(487\) | 7.14346 | 0.323701 | 0.161850 | − | 0.986815i | \(-0.448254\pi\) | ||||
0.161850 | + | 0.986815i | \(0.448254\pi\) | |||||||
\(488\) | 30.5716 | 1.38391 | ||||||||
\(489\) | 7.23385 | 0.327126 | ||||||||
\(490\) | 0.00121320 | 5.48069e−5 0 | ||||||||
\(491\) | −13.8187 | −0.623628 | −0.311814 | − | 0.950143i | \(-0.600937\pi\) | ||||
−0.311814 | + | 0.950143i | \(0.600937\pi\) | |||||||
\(492\) | 3.33264 | 0.150247 | ||||||||
\(493\) | −2.20837 | −0.0994601 | ||||||||
\(494\) | 23.9363 | 1.07694 | ||||||||
\(495\) | 0.141398 | 0.00635536 | ||||||||
\(496\) | 5.57639 | 0.250387 | ||||||||
\(497\) | 16.5313 | 0.741529 | ||||||||
\(498\) | 9.47511 | 0.424590 | ||||||||
\(499\) | −9.30638 | −0.416611 | −0.208305 | − | 0.978064i | \(-0.566795\pi\) | ||||
−0.208305 | + | 0.978064i | \(0.566795\pi\) | |||||||
\(500\) | −0.261923 | −0.0117135 | ||||||||
\(501\) | 7.66967 | 0.342656 | ||||||||
\(502\) | 28.4839 | 1.27130 | ||||||||
\(503\) | 30.5367 | 1.36157 | 0.680783 | − | 0.732486i | \(-0.261640\pi\) | ||||
0.680783 | + | 0.732486i | \(0.261640\pi\) | |||||||
\(504\) | 8.06940 | 0.359440 | ||||||||
\(505\) | −0.284337 | −0.0126528 | ||||||||
\(506\) | 33.3875 | 1.48426 | ||||||||
\(507\) | −19.3772 | −0.860572 | ||||||||
\(508\) | 0.319291 | 0.0141662 | ||||||||
\(509\) | 22.1835 | 0.983267 | 0.491634 | − | 0.870802i | \(-0.336400\pi\) | ||||
0.491634 | + | 0.870802i | \(0.336400\pi\) | |||||||
\(510\) | 0.0304926 | 0.00135023 | ||||||||
\(511\) | −6.47309 | −0.286352 | ||||||||
\(512\) | 14.8596 | 0.656709 | ||||||||
\(513\) | 4.01215 | 0.177141 | ||||||||
\(514\) | −17.9309 | −0.790896 | ||||||||
\(515\) | −0.114582 | −0.00504909 | ||||||||
\(516\) | −9.95633 | −0.438303 | ||||||||
\(517\) | −50.9874 | −2.24243 | ||||||||
\(518\) | 25.2833 | 1.11088 | ||||||||
\(519\) | −4.59359 | −0.201636 | ||||||||
\(520\) | −0.503286 | −0.0220706 | ||||||||
\(521\) | −1.90747 | −0.0835679 | −0.0417840 | − | 0.999127i | \(-0.513304\pi\) | ||||
−0.0417840 | + | 0.999127i | \(0.513304\pi\) | |||||||
\(522\) | −2.31543 | −0.101344 | ||||||||
\(523\) | −20.9029 | −0.914020 | −0.457010 | − | 0.889462i | \(-0.651080\pi\) | ||||
−0.457010 | + | 0.889462i | \(0.651080\pi\) | |||||||
\(524\) | −5.51073 | −0.240738 | ||||||||
\(525\) | 13.2641 | 0.578891 | ||||||||
\(526\) | 25.3067 | 1.10342 | ||||||||
\(527\) | 4.01939 | 0.175087 | ||||||||
\(528\) | −6.74531 | −0.293552 | ||||||||
\(529\) | 19.8974 | 0.865103 | ||||||||
\(530\) | 0.0509669 | 0.00221386 | ||||||||
\(531\) | −9.85933 | −0.427858 | ||||||||
\(532\) | 9.58810 | 0.415697 | ||||||||
\(533\) | 21.0539 | 0.911944 | ||||||||
\(534\) | −1.64810 | −0.0713203 | ||||||||
\(535\) | 0.360895 | 0.0156029 | ||||||||
\(536\) | −15.5407 | −0.671255 | ||||||||
\(537\) | 11.8850 | 0.512874 | ||||||||
\(538\) | 4.70310 | 0.202765 | ||||||||
\(539\) | −0.193441 | −0.00833207 | ||||||||
\(540\) | −0.0261945 | −0.00112723 | ||||||||
\(541\) | 39.8925 | 1.71511 | 0.857556 | − | 0.514391i | \(-0.171982\pi\) | ||||
0.857556 | + | 0.514391i | \(0.171982\pi\) | |||||||
\(542\) | −27.7799 | −1.19325 | ||||||||
\(543\) | −1.12907 | −0.0484531 | ||||||||
\(544\) | 4.62800 | 0.198424 | ||||||||
\(545\) | 0.201106 | 0.00861443 | ||||||||
\(546\) | 15.8292 | 0.677428 | ||||||||
\(547\) | −26.5623 | −1.13572 | −0.567860 | − | 0.823125i | \(-0.692229\pi\) | ||||
−0.567860 | + | 0.823125i | \(0.692229\pi\) | |||||||
\(548\) | −7.39313 | −0.315819 | ||||||||
\(549\) | 10.0521 | 0.429013 | ||||||||
\(550\) | −25.4838 | −1.08663 | ||||||||
\(551\) | −8.86032 | −0.377462 | ||||||||
\(552\) | −19.9194 | −0.847827 | ||||||||
\(553\) | −2.65326 | −0.112828 | ||||||||
\(554\) | 1.95324 | 0.0829850 | ||||||||
\(555\) | −0.264319 | −0.0112197 | ||||||||
\(556\) | −2.51607 | −0.106705 | ||||||||
\(557\) | 7.69438 | 0.326021 | 0.163011 | − | 0.986624i | \(-0.447879\pi\) | ||||
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(558\) | 4.21425 | 0.178403 | ||||||||
\(559\) | −62.8989 | −2.66034 | ||||||||
\(560\) | 0.107055 | 0.00452390 | ||||||||
\(561\) | −4.86193 | −0.205271 | ||||||||
\(562\) | 7.14246 | 0.301286 | ||||||||
\(563\) | 11.7260 | 0.494191 | 0.247095 | − | 0.968991i | \(-0.420524\pi\) | ||||
0.247095 | + | 0.968991i | \(0.420524\pi\) | |||||||
\(564\) | 9.44562 | 0.397732 | ||||||||
\(565\) | 0.414699 | 0.0174465 | ||||||||
\(566\) | 15.1454 | 0.636609 | ||||||||
\(567\) | 2.65326 | 0.111426 | ||||||||
\(568\) | 18.9491 | 0.795086 | ||||||||
\(569\) | −22.9170 | −0.960732 | −0.480366 | − | 0.877068i | \(-0.659496\pi\) | ||||
−0.480366 | + | 0.877068i | \(0.659496\pi\) | |||||||
\(570\) | 0.122341 | 0.00512429 | ||||||||
\(571\) | −34.9908 | −1.46432 | −0.732160 | − | 0.681133i | \(-0.761488\pi\) | ||||
−0.732160 | + | 0.681133i | \(0.761488\pi\) | |||||||
\(572\) | 24.9175 | 1.04185 | ||||||||
\(573\) | 21.6882 | 0.906039 | ||||||||
\(574\) | −10.2932 | −0.429631 | ||||||||
\(575\) | −32.7425 | −1.36546 | ||||||||
\(576\) | 7.62711 | 0.317796 | ||||||||
\(577\) | −28.8737 | −1.20203 | −0.601014 | − | 0.799239i | \(-0.705236\pi\) | ||||
−0.601014 | + | 0.799239i | \(0.705236\pi\) | |||||||
\(578\) | −1.04848 | −0.0436110 | ||||||||
\(579\) | 21.2176 | 0.881772 | ||||||||
\(580\) | 0.0578472 | 0.00240198 | ||||||||
\(581\) | 23.9775 | 0.994755 | ||||||||
\(582\) | −5.09410 | −0.211157 | ||||||||
\(583\) | −8.12649 | −0.336565 | ||||||||
\(584\) | −7.41981 | −0.307034 | ||||||||
\(585\) | −0.165483 | −0.00684189 | ||||||||
\(586\) | 13.5157 | 0.558327 | ||||||||
\(587\) | 27.8908 | 1.15118 | 0.575588 | − | 0.817740i | \(-0.304773\pi\) | ||||
0.575588 | + | 0.817740i | \(0.304773\pi\) | |||||||
\(588\) | 0.0358356 | 0.00147784 | ||||||||
\(589\) | 16.1264 | 0.664476 | ||||||||
\(590\) | −0.300636 | −0.0123770 | ||||||||
\(591\) | −1.92916 | −0.0793552 | ||||||||
\(592\) | 12.6092 | 0.518235 | ||||||||
\(593\) | 43.4134 | 1.78277 | 0.891387 | − | 0.453242i | \(-0.149733\pi\) | ||||
0.891387 | + | 0.453242i | \(0.149733\pi\) | |||||||
\(594\) | −5.09763 | −0.209158 | ||||||||
\(595\) | 0.0771639 | 0.00316341 | ||||||||
\(596\) | −11.8162 | −0.484011 | ||||||||
\(597\) | 11.8049 | 0.483140 | ||||||||
\(598\) | −39.0746 | −1.59788 | ||||||||
\(599\) | 15.2412 | 0.622739 | 0.311370 | − | 0.950289i | \(-0.399212\pi\) | ||||
0.311370 | + | 0.950289i | \(0.399212\pi\) | |||||||
\(600\) | 15.2040 | 0.620701 | ||||||||
\(601\) | 28.8790 | 1.17800 | 0.589000 | − | 0.808133i | \(-0.299522\pi\) | ||||
0.589000 | + | 0.808133i | \(0.299522\pi\) | |||||||
\(602\) | 30.7513 | 1.25333 | ||||||||
\(603\) | −5.10986 | −0.208089 | ||||||||
\(604\) | −1.24469 | −0.0506457 | ||||||||
\(605\) | −0.367557 | −0.0149433 | ||||||||
\(606\) | 10.2508 | 0.416411 | ||||||||
\(607\) | −20.3652 | −0.826599 | −0.413300 | − | 0.910595i | \(-0.635624\pi\) | ||||
−0.413300 | + | 0.910595i | \(0.635624\pi\) | |||||||
\(608\) | 18.5682 | 0.753041 | ||||||||
\(609\) | −5.85939 | −0.237434 | ||||||||
\(610\) | 0.306514 | 0.0124104 | ||||||||
\(611\) | 59.6725 | 2.41409 | ||||||||
\(612\) | 0.900691 | 0.0364083 | ||||||||
\(613\) | 41.0433 | 1.65772 | 0.828862 | − | 0.559454i | \(-0.188989\pi\) | ||||
0.828862 | + | 0.559454i | \(0.188989\pi\) | |||||||
\(614\) | 34.1069 | 1.37644 | ||||||||
\(615\) | 0.107608 | 0.00433919 | ||||||||
\(616\) | −39.2328 | −1.58074 | ||||||||
\(617\) | −42.7053 | −1.71925 | −0.859626 | − | 0.510923i | \(-0.829304\pi\) | ||||
−0.859626 | + | 0.510923i | \(0.829304\pi\) | |||||||
\(618\) | 4.13088 | 0.166168 | ||||||||
\(619\) | −9.35159 | −0.375872 | −0.187936 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187936 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(620\) | −0.105286 | −0.00422838 | ||||||||
\(621\) | −6.54961 | −0.262827 | ||||||||
\(622\) | −29.4625 | −1.18134 | ||||||||
\(623\) | −4.17065 | −0.167094 | ||||||||
\(624\) | 7.89429 | 0.316024 | ||||||||
\(625\) | 24.9873 | 0.999493 | ||||||||
\(626\) | −4.63689 | −0.185327 | ||||||||
\(627\) | −19.5068 | −0.779026 | ||||||||
\(628\) | −5.55866 | −0.221815 | ||||||||
\(629\) | 9.08854 | 0.362384 | ||||||||
\(630\) | 0.0809047 | 0.00322332 | ||||||||
\(631\) | 7.16286 | 0.285149 | 0.142575 | − | 0.989784i | \(-0.454462\pi\) | ||||
0.142575 | + | 0.989784i | \(0.454462\pi\) | |||||||
\(632\) | −3.04131 | −0.120977 | ||||||||
\(633\) | −6.25806 | −0.248736 | ||||||||
\(634\) | 28.3008 | 1.12397 | ||||||||
\(635\) | 0.0103097 | 0.000409127 0 | ||||||||
\(636\) | 1.50546 | 0.0596955 | ||||||||
\(637\) | 0.226391 | 0.00896993 | ||||||||
\(638\) | 11.2575 | 0.445688 | ||||||||
\(639\) | 6.23056 | 0.246477 | ||||||||
\(640\) | −0.0366189 | −0.00144749 | ||||||||
\(641\) | −31.4710 | −1.24303 | −0.621515 | − | 0.783402i | \(-0.713483\pi\) | ||||
−0.621515 | + | 0.783402i | \(0.713483\pi\) | |||||||
\(642\) | −13.0109 | −0.513498 | ||||||||
\(643\) | 7.95454 | 0.313696 | 0.156848 | − | 0.987623i | \(-0.449867\pi\) | ||||
0.156848 | + | 0.987623i | \(0.449867\pi\) | |||||||
\(644\) | −15.6520 | −0.616777 | ||||||||
\(645\) | −0.321483 | −0.0126584 | ||||||||
\(646\) | −4.20666 | −0.165509 | ||||||||
\(647\) | −25.2224 | −0.991594 | −0.495797 | − | 0.868438i | \(-0.665124\pi\) | ||||
−0.495797 | + | 0.868438i | \(0.665124\pi\) | |||||||
\(648\) | 3.04131 | 0.119474 | ||||||||
\(649\) | 47.9353 | 1.88163 | ||||||||
\(650\) | 29.8247 | 1.16982 | ||||||||
\(651\) | 10.6645 | 0.417974 | ||||||||
\(652\) | 6.51547 | 0.255165 | ||||||||
\(653\) | 30.1848 | 1.18122 | 0.590612 | − | 0.806956i | \(-0.298886\pi\) | ||||
0.590612 | + | 0.806956i | \(0.298886\pi\) | |||||||
\(654\) | −7.25021 | −0.283506 | ||||||||
\(655\) | −0.177938 | −0.00695260 | ||||||||
\(656\) | −5.13340 | −0.200426 | ||||||||
\(657\) | −2.43967 | −0.0951807 | ||||||||
\(658\) | −29.1739 | −1.13732 | ||||||||
\(659\) | −15.2520 | −0.594133 | −0.297067 | − | 0.954857i | \(-0.596008\pi\) | ||||
−0.297067 | + | 0.954857i | \(0.596008\pi\) | |||||||
\(660\) | 0.127356 | 0.00495732 | ||||||||
\(661\) | 43.6528 | 1.69790 | 0.848948 | − | 0.528477i | \(-0.177237\pi\) | ||||
0.848948 | + | 0.528477i | \(0.177237\pi\) | |||||||
\(662\) | 24.5699 | 0.954937 | ||||||||
\(663\) | 5.69010 | 0.220985 | ||||||||
\(664\) | 27.4844 | 1.06660 | ||||||||
\(665\) | 0.309593 | 0.0120055 | ||||||||
\(666\) | 9.52914 | 0.369247 | ||||||||
\(667\) | 14.4640 | 0.560047 | ||||||||
\(668\) | 6.90801 | 0.267279 | ||||||||
\(669\) | 19.3188 | 0.746906 | ||||||||
\(670\) | −0.155813 | −0.00601957 | ||||||||
\(671\) | −48.8725 | −1.88670 | ||||||||
\(672\) | 12.2793 | 0.473683 | ||||||||
\(673\) | −17.1600 | −0.661470 | −0.330735 | − | 0.943724i | \(-0.607297\pi\) | ||||
−0.330735 | + | 0.943724i | \(0.607297\pi\) | |||||||
\(674\) | 6.34570 | 0.244427 | ||||||||
\(675\) | 4.99915 | 0.192418 | ||||||||
\(676\) | −17.4529 | −0.671264 | ||||||||
\(677\) | −14.7120 | −0.565429 | −0.282714 | − | 0.959204i | \(-0.591235\pi\) | ||||
−0.282714 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(678\) | −14.9506 | −0.574174 | ||||||||
\(679\) | −12.8910 | −0.494712 | ||||||||
\(680\) | 0.0884495 | 0.00339188 | ||||||||
\(681\) | −4.30211 | −0.164857 | ||||||||
\(682\) | −20.4894 | −0.784578 | ||||||||
\(683\) | 23.3629 | 0.893958 | 0.446979 | − | 0.894544i | \(-0.352500\pi\) | ||||
0.446979 | + | 0.894544i | \(0.352500\pi\) | |||||||
\(684\) | 3.61371 | 0.138174 | ||||||||
\(685\) | −0.238719 | −0.00912097 | ||||||||
\(686\) | 19.3625 | 0.739265 | ||||||||
\(687\) | 22.8035 | 0.870009 | ||||||||
\(688\) | 15.3362 | 0.584685 | ||||||||
\(689\) | 9.51073 | 0.362330 | ||||||||
\(690\) | −0.199714 | −0.00760300 | ||||||||
\(691\) | 10.7717 | 0.409775 | 0.204888 | − | 0.978786i | \(-0.434317\pi\) | ||||
0.204888 | + | 0.978786i | \(0.434317\pi\) | |||||||
\(692\) | −4.13740 | −0.157280 | ||||||||
\(693\) | −12.9000 | −0.490029 | ||||||||
\(694\) | 23.6262 | 0.896840 | ||||||||
\(695\) | −0.0812422 | −0.00308169 | ||||||||
\(696\) | −6.71636 | −0.254583 | ||||||||
\(697\) | −3.70009 | −0.140151 | ||||||||
\(698\) | 2.50378 | 0.0947696 | ||||||||
\(699\) | −16.3679 | −0.619091 | ||||||||
\(700\) | 11.9468 | 0.451547 | ||||||||
\(701\) | −30.9481 | −1.16889 | −0.584446 | − | 0.811433i | \(-0.698688\pi\) | ||||
−0.584446 | + | 0.811433i | \(0.698688\pi\) | |||||||
\(702\) | 5.96595 | 0.225170 | ||||||||
\(703\) | 36.4646 | 1.37529 | ||||||||
\(704\) | −37.0824 | −1.39760 | ||||||||
\(705\) | 0.304992 | 0.0114867 | ||||||||
\(706\) | −20.9851 | −0.789785 | ||||||||
\(707\) | 25.9405 | 0.975593 | ||||||||
\(708\) | −8.88021 | −0.333739 | ||||||||
\(709\) | −8.41122 | −0.315890 | −0.157945 | − | 0.987448i | \(-0.550487\pi\) | ||||
−0.157945 | + | 0.987448i | \(0.550487\pi\) | |||||||
\(710\) | 0.189986 | 0.00713004 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | −4.78063 | −0.179162 | ||||||||
\(713\) | −26.3254 | −0.985895 | ||||||||
\(714\) | −2.78189 | −0.104110 | ||||||||
\(715\) | 0.804567 | 0.0300891 | ||||||||
\(716\) | 10.7047 | 0.400053 | ||||||||
\(717\) | 12.4023 | 0.463172 | ||||||||
\(718\) | 24.9661 | 0.931728 | ||||||||
\(719\) | 16.5780 | 0.618256 | 0.309128 | − | 0.951021i | \(-0.399963\pi\) | ||||
0.309128 | + | 0.951021i | \(0.399963\pi\) | |||||||
\(720\) | 0.0403485 | 0.00150370 | ||||||||
\(721\) | 10.4535 | 0.389309 | ||||||||
\(722\) | 3.04338 | 0.113263 | ||||||||
\(723\) | −7.49506 | −0.278744 | ||||||||
\(724\) | −1.01694 | −0.0377944 | ||||||||
\(725\) | −11.0400 | −0.410015 | ||||||||
\(726\) | 13.2511 | 0.491793 | ||||||||
\(727\) | −8.39259 | −0.311264 | −0.155632 | − | 0.987815i | \(-0.549741\pi\) | ||||
−0.155632 | + | 0.987815i | \(0.549741\pi\) | |||||||
\(728\) | 45.9157 | 1.70175 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0743919 | −0.00275337 | ||||||||
\(731\) | 11.0541 | 0.408850 | ||||||||
\(732\) | 9.05382 | 0.334639 | ||||||||
\(733\) | −33.9614 | −1.25439 | −0.627196 | − | 0.778862i | \(-0.715797\pi\) | ||||
−0.627196 | + | 0.778862i | \(0.715797\pi\) | |||||||
\(734\) | −22.0292 | −0.813112 | ||||||||
\(735\) | 0.00115711 | 4.26805e−5 0 | ||||||||
\(736\) | −30.3116 | −1.11730 | ||||||||
\(737\) | 24.8438 | 0.915132 | ||||||||
\(738\) | −3.87947 | −0.142805 | ||||||||
\(739\) | 44.9041 | 1.65183 | 0.825913 | − | 0.563798i | \(-0.190660\pi\) | ||||
0.825913 | + | 0.563798i | \(0.190660\pi\) | |||||||
\(740\) | −0.238070 | −0.00875161 | ||||||||
\(741\) | 22.8295 | 0.838663 | ||||||||
\(742\) | −4.64980 | −0.170699 | ||||||||
\(743\) | 16.9651 | 0.622389 | 0.311194 | − | 0.950346i | \(-0.399271\pi\) | ||||
0.311194 | + | 0.950346i | \(0.399271\pi\) | |||||||
\(744\) | 12.2242 | 0.448162 | ||||||||
\(745\) | −0.381537 | −0.0139784 | ||||||||
\(746\) | 38.5594 | 1.41176 | ||||||||
\(747\) | 9.03700 | 0.330647 | ||||||||
\(748\) | −4.37910 | −0.160116 | ||||||||
\(749\) | −32.9250 | −1.20305 | ||||||||
\(750\) | 0.304900 | 0.0111334 | ||||||||
\(751\) | −53.5372 | −1.95360 | −0.976800 | − | 0.214152i | \(-0.931301\pi\) | ||||
−0.976800 | + | 0.214152i | \(0.931301\pi\) | |||||||
\(752\) | −14.5495 | −0.530566 | ||||||||
\(753\) | 27.1669 | 0.990017 | ||||||||
\(754\) | −13.1750 | −0.479807 | ||||||||
\(755\) | −0.0401901 | −0.00146267 | ||||||||
\(756\) | 2.38977 | 0.0869150 | ||||||||
\(757\) | 10.9325 | 0.397348 | 0.198674 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198674 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(758\) | −30.3919 | −1.10388 | ||||||||
\(759\) | 31.8437 | 1.15585 | ||||||||
\(760\) | 0.354873 | 0.0128726 | ||||||||
\(761\) | 0.300100 | 0.0108786 | 0.00543932 | − | 0.999985i | \(-0.498269\pi\) | ||||
0.00543932 | + | 0.999985i | \(0.498269\pi\) | |||||||
\(762\) | −0.371681 | −0.0134646 | ||||||||
\(763\) | −18.3472 | −0.664214 | ||||||||
\(764\) | 19.5344 | 0.706730 | ||||||||
\(765\) | 0.0290827 | 0.00105149 | ||||||||
\(766\) | 10.8085 | 0.390527 | ||||||||
\(767\) | −56.1005 | −2.02567 | ||||||||
\(768\) | 16.5744 | 0.598077 | ||||||||
\(769\) | 18.8122 | 0.678385 | 0.339192 | − | 0.940717i | \(-0.389846\pi\) | ||||
0.339192 | + | 0.940717i | \(0.389846\pi\) | |||||||
\(770\) | −0.393353 | −0.0141755 | ||||||||
\(771\) | −17.1018 | −0.615905 | ||||||||
\(772\) | 19.1105 | 0.687801 | ||||||||
\(773\) | −12.1872 | −0.438343 | −0.219172 | − | 0.975686i | \(-0.570335\pi\) | ||||
−0.219172 | + | 0.975686i | \(0.570335\pi\) | |||||||
\(774\) | 11.5900 | 0.416594 | ||||||||
\(775\) | 20.0935 | 0.721781 | ||||||||
\(776\) | −14.7764 | −0.530443 | ||||||||
\(777\) | 24.1142 | 0.865094 | ||||||||
\(778\) | 12.6318 | 0.452874 | ||||||||
\(779\) | −14.8453 | −0.531888 | ||||||||
\(780\) | −0.149049 | −0.00533682 | ||||||||
\(781\) | −30.2925 | −1.08395 | ||||||||
\(782\) | 6.86713 | 0.245568 | ||||||||
\(783\) | −2.20837 | −0.0789208 | ||||||||
\(784\) | −0.0551991 | −0.00197140 | ||||||||
\(785\) | −0.179485 | −0.00640609 | ||||||||
\(786\) | 6.41495 | 0.228814 | ||||||||
\(787\) | −19.1493 | −0.682598 | −0.341299 | − | 0.939955i | \(-0.610867\pi\) | ||||
−0.341299 | + | 0.939955i | \(0.610867\pi\) | |||||||
\(788\) | −1.73758 | −0.0618988 | ||||||||
\(789\) | 24.1366 | 0.859284 | ||||||||
\(790\) | −0.0304926 | −0.00108488 | ||||||||
\(791\) | −37.8337 | −1.34521 | ||||||||
\(792\) | −14.7867 | −0.525421 | ||||||||
\(793\) | 57.1973 | 2.03114 | ||||||||
\(794\) | 15.1506 | 0.537674 | ||||||||
\(795\) | 0.0486103 | 0.00172403 | ||||||||
\(796\) | 10.6325 | 0.376860 | ||||||||
\(797\) | −52.5098 | −1.85999 | −0.929996 | − | 0.367570i | \(-0.880190\pi\) | ||||
−0.929996 | + | 0.367570i | \(0.880190\pi\) | |||||||
\(798\) | −11.1613 | −0.395107 | ||||||||
\(799\) | −10.4871 | −0.371006 | ||||||||
\(800\) | 23.1361 | 0.817984 | ||||||||
\(801\) | −1.57190 | −0.0555403 | ||||||||
\(802\) | 29.7523 | 1.05059 | ||||||||
\(803\) | 11.8615 | 0.418584 | ||||||||
\(804\) | −4.60240 | −0.162314 | ||||||||
\(805\) | −0.505393 | −0.0178128 | ||||||||
\(806\) | 23.9795 | 0.844641 | ||||||||
\(807\) | 4.48564 | 0.157902 | ||||||||
\(808\) | 29.7345 | 1.04605 | ||||||||
\(809\) | −3.93181 | −0.138235 | −0.0691176 | − | 0.997609i | \(-0.522018\pi\) | ||||
−0.0691176 | + | 0.997609i | \(0.522018\pi\) | |||||||
\(810\) | 0.0304926 | 0.00107140 | ||||||||
\(811\) | 22.5161 | 0.790646 | 0.395323 | − | 0.918542i | \(-0.370633\pi\) | ||||
0.395323 | + | 0.918542i | \(0.370633\pi\) | |||||||
\(812\) | −5.27750 | −0.185204 | ||||||||
\(813\) | −26.4955 | −0.929237 | ||||||||
\(814\) | −46.3300 | −1.62387 | ||||||||
\(815\) | 0.210380 | 0.00736928 | ||||||||
\(816\) | −1.38737 | −0.0485678 | ||||||||
\(817\) | 44.3507 | 1.55163 | ||||||||
\(818\) | 3.43606 | 0.120139 | ||||||||
\(819\) | 15.0973 | 0.527543 | ||||||||
\(820\) | 0.0969219 | 0.00338466 | ||||||||
\(821\) | 34.2935 | 1.19685 | 0.598426 | − | 0.801178i | \(-0.295793\pi\) | ||||
0.598426 | + | 0.801178i | \(0.295793\pi\) | |||||||
\(822\) | 8.60621 | 0.300176 | ||||||||
\(823\) | 7.00859 | 0.244304 | 0.122152 | − | 0.992511i | \(-0.461020\pi\) | ||||
0.122152 | + | 0.992511i | \(0.461020\pi\) | |||||||
\(824\) | 11.9824 | 0.417427 | ||||||||
\(825\) | −24.3055 | −0.846210 | ||||||||
\(826\) | 27.4275 | 0.954326 | ||||||||
\(827\) | 4.13520 | 0.143795 | 0.0718976 | − | 0.997412i | \(-0.477095\pi\) | ||||
0.0718976 | + | 0.997412i | \(0.477095\pi\) | |||||||
\(828\) | −5.89917 | −0.205010 | ||||||||
\(829\) | −40.4100 | −1.40350 | −0.701749 | − | 0.712424i | \(-0.747597\pi\) | ||||
−0.701749 | + | 0.712424i | \(0.747597\pi\) | |||||||
\(830\) | 0.275561 | 0.00956488 | ||||||||
\(831\) | 1.86292 | 0.0646241 | ||||||||
\(832\) | 43.3990 | 1.50459 | ||||||||
\(833\) | −0.0397868 | −0.00137853 | ||||||||
\(834\) | 2.92892 | 0.101420 | ||||||||
\(835\) | 0.223055 | 0.00771912 | ||||||||
\(836\) | −17.5696 | −0.607657 | ||||||||
\(837\) | 4.01939 | 0.138930 | ||||||||
\(838\) | 19.2029 | 0.663354 | ||||||||
\(839\) | −50.9701 | −1.75968 | −0.879841 | − | 0.475267i | \(-0.842351\pi\) | ||||
−0.879841 | + | 0.475267i | \(0.842351\pi\) | |||||||
\(840\) | 0.234680 | 0.00809721 | ||||||||
\(841\) | −24.1231 | −0.831831 | ||||||||
\(842\) | 4.12039 | 0.141998 | ||||||||
\(843\) | 6.81221 | 0.234625 | ||||||||
\(844\) | −5.63658 | −0.194019 | ||||||||
\(845\) | −0.563541 | −0.0193864 | ||||||||
\(846\) | −10.9955 | −0.378033 | ||||||||
\(847\) | 33.5328 | 1.15220 | ||||||||
\(848\) | −2.31893 | −0.0796324 | ||||||||
\(849\) | 14.4451 | 0.495755 | ||||||||
\(850\) | −5.24151 | −0.179782 | ||||||||
\(851\) | −59.5264 | −2.04054 | ||||||||
\(852\) | 5.61181 | 0.192257 | ||||||||
\(853\) | −26.7903 | −0.917282 | −0.458641 | − | 0.888622i | \(-0.651664\pi\) | ||||
−0.458641 | + | 0.888622i | \(0.651664\pi\) | |||||||
\(854\) | −27.9638 | −0.956901 | ||||||||
\(855\) | 0.116684 | 0.00399051 | ||||||||
\(856\) | −37.7405 | −1.28994 | ||||||||
\(857\) | 2.44333 | 0.0834625 | 0.0417313 | − | 0.999129i | \(-0.486713\pi\) | ||||
0.0417313 | + | 0.999129i | \(0.486713\pi\) | |||||||
\(858\) | −29.0060 | −0.990249 | ||||||||
\(859\) | 2.59589 | 0.0885705 | 0.0442852 | − | 0.999019i | \(-0.485899\pi\) | ||||
0.0442852 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(860\) | −0.289556 | −0.00987379 | ||||||||
\(861\) | −9.81729 | −0.334572 | ||||||||
\(862\) | −18.7415 | −0.638339 | ||||||||
\(863\) | −29.6027 | −1.00769 | −0.503844 | − | 0.863795i | \(-0.668081\pi\) | ||||
−0.503844 | + | 0.863795i | \(0.668081\pi\) | |||||||
\(864\) | 4.62800 | 0.157448 | ||||||||
\(865\) | −0.133594 | −0.00454232 | ||||||||
\(866\) | −32.7799 | −1.11391 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 9.60540 | 0.326029 | ||||||||
\(869\) | 4.86193 | 0.164930 | ||||||||
\(870\) | −0.0673390 | −0.00228300 | ||||||||
\(871\) | −29.0756 | −0.985188 | ||||||||
\(872\) | −21.0306 | −0.712187 | ||||||||
\(873\) | −4.85856 | −0.164437 | ||||||||
\(874\) | 27.5519 | 0.931959 | ||||||||
\(875\) | 0.771573 | 0.0260839 | ||||||||
\(876\) | −2.19739 | −0.0742430 | ||||||||
\(877\) | −0.898159 | −0.0303287 | −0.0151643 | − | 0.999885i | \(-0.504827\pi\) | ||||
−0.0151643 | + | 0.999885i | \(0.504827\pi\) | |||||||
\(878\) | 7.87340 | 0.265714 | ||||||||
\(879\) | 12.8907 | 0.434793 | ||||||||
\(880\) | −0.196172 | −0.00661294 | ||||||||
\(881\) | −5.79109 | −0.195107 | −0.0975534 | − | 0.995230i | \(-0.531102\pi\) | ||||
−0.0975534 | + | 0.995230i | \(0.531102\pi\) | |||||||
\(882\) | −0.0417156 | −0.00140464 | ||||||||
\(883\) | −40.9805 | −1.37910 | −0.689551 | − | 0.724237i | \(-0.742192\pi\) | ||||
−0.689551 | + | 0.724237i | \(0.742192\pi\) | |||||||
\(884\) | 5.12502 | 0.172373 | ||||||||
\(885\) | −0.286735 | −0.00963851 | ||||||||
\(886\) | −13.8061 | −0.463824 | ||||||||
\(887\) | −22.2927 | −0.748516 | −0.374258 | − | 0.927325i | \(-0.622103\pi\) | ||||
−0.374258 | + | 0.927325i | \(0.622103\pi\) | |||||||
\(888\) | 27.6411 | 0.927574 | ||||||||
\(889\) | −0.940568 | −0.0315457 | ||||||||
\(890\) | −0.0479312 | −0.00160666 | ||||||||
\(891\) | −4.86193 | −0.162881 | ||||||||
\(892\) | 17.4002 | 0.582603 | ||||||||
\(893\) | −42.0757 | −1.40801 | ||||||||
\(894\) | 13.7551 | 0.460038 | ||||||||
\(895\) | 0.345647 | 0.0115537 | ||||||||
\(896\) | 3.34080 | 0.111608 | ||||||||
\(897\) | −37.2679 | −1.24434 | ||||||||
\(898\) | −14.0360 | −0.468387 | ||||||||
\(899\) | −8.87631 | −0.296041 | ||||||||
\(900\) | 4.50269 | 0.150090 | ||||||||
\(901\) | −1.67145 | −0.0556842 | ||||||||
\(902\) | 18.8617 | 0.628025 | ||||||||
\(903\) | 29.3294 | 0.976021 | ||||||||
\(904\) | −43.3671 | −1.44237 | ||||||||
\(905\) | −0.0328364 | −0.00109152 | ||||||||
\(906\) | 1.44892 | 0.0481372 | ||||||||
\(907\) | −54.4677 | −1.80857 | −0.904285 | − | 0.426929i | \(-0.859595\pi\) | ||||
−0.904285 | + | 0.426929i | \(0.859595\pi\) | |||||||
\(908\) | −3.87488 | −0.128592 | ||||||||
\(909\) | 9.77685 | 0.324278 | ||||||||
\(910\) | 0.460356 | 0.0152606 | ||||||||
\(911\) | −31.1586 | −1.03233 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516165 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(912\) | −5.56635 | −0.184320 | ||||||||
\(913\) | −43.9373 | −1.45411 | ||||||||
\(914\) | −0.852597 | −0.0282014 | ||||||||
\(915\) | 0.292341 | 0.00966451 | ||||||||
\(916\) | 20.5389 | 0.678626 | ||||||||
\(917\) | 16.2335 | 0.536079 | ||||||||
\(918\) | −1.04848 | −0.0346050 | ||||||||
\(919\) | 35.6814 | 1.17702 | 0.588510 | − | 0.808490i | \(-0.299715\pi\) | ||||
0.588510 | + | 0.808490i | \(0.299715\pi\) | |||||||
\(920\) | −0.579310 | −0.0190993 | ||||||||
\(921\) | 32.5298 | 1.07189 | ||||||||
\(922\) | 22.9246 | 0.754982 | ||||||||
\(923\) | 35.4525 | 1.16693 | ||||||||
\(924\) | −11.6189 | −0.382233 | ||||||||
\(925\) | 45.4350 | 1.49389 | ||||||||
\(926\) | −14.2430 | −0.468054 | ||||||||
\(927\) | 3.93988 | 0.129402 | ||||||||
\(928\) | −10.2203 | −0.335499 | ||||||||
\(929\) | −42.4484 | −1.39269 | −0.696344 | − | 0.717708i | \(-0.745191\pi\) | ||||
−0.696344 | + | 0.717708i | \(0.745191\pi\) | |||||||
\(930\) | 0.122561 | 0.00401895 | ||||||||
\(931\) | −0.159631 | −0.00523168 | ||||||||
\(932\) | −14.7424 | −0.482904 | ||||||||
\(933\) | −28.1002 | −0.919960 | ||||||||
\(934\) | 10.3723 | 0.339391 | ||||||||
\(935\) | −0.141398 | −0.00462420 | ||||||||
\(936\) | 17.3054 | 0.565644 | ||||||||
\(937\) | 36.4609 | 1.19112 | 0.595562 | − | 0.803309i | \(-0.296929\pi\) | ||||
0.595562 | + | 0.803309i | \(0.296929\pi\) | |||||||
\(938\) | 14.2150 | 0.464138 | ||||||||
\(939\) | −4.42249 | −0.144323 | ||||||||
\(940\) | 0.274704 | 0.00895985 | ||||||||
\(941\) | 28.0671 | 0.914961 | 0.457480 | − | 0.889220i | \(-0.348752\pi\) | ||||
0.457480 | + | 0.889220i | \(0.348752\pi\) | |||||||
\(942\) | 6.47074 | 0.210828 | ||||||||
\(943\) | 24.2341 | 0.789172 | ||||||||
\(944\) | 13.6786 | 0.445199 | ||||||||
\(945\) | 0.0771639 | 0.00251014 | ||||||||
\(946\) | −56.3497 | −1.83209 | ||||||||
\(947\) | −11.1419 | −0.362063 | −0.181031 | − | 0.983477i | \(-0.557944\pi\) | ||||
−0.181031 | + | 0.983477i | \(0.557944\pi\) | |||||||
\(948\) | −0.900691 | −0.0292531 | ||||||||
\(949\) | −13.8820 | −0.450628 | ||||||||
\(950\) | −21.0297 | −0.682294 | ||||||||
\(951\) | 26.9923 | 0.875285 | ||||||||
\(952\) | −8.06940 | −0.261531 | ||||||||
\(953\) | 36.5558 | 1.18416 | 0.592080 | − | 0.805880i | \(-0.298307\pi\) | ||||
0.592080 | + | 0.805880i | \(0.298307\pi\) | |||||||
\(954\) | −1.75248 | −0.0567388 | ||||||||
\(955\) | 0.630752 | 0.0204107 | ||||||||
\(956\) | 11.1706 | 0.361284 | ||||||||
\(957\) | 10.7370 | 0.347076 | ||||||||
\(958\) | −9.09309 | −0.293784 | ||||||||
\(959\) | 21.7787 | 0.703271 | ||||||||
\(960\) | 0.221817 | 0.00715910 | ||||||||
\(961\) | −14.8445 | −0.478855 | ||||||||
\(962\) | 54.2217 | 1.74818 | ||||||||
\(963\) | −12.4093 | −0.399884 | ||||||||
\(964\) | −6.75074 | −0.217427 | ||||||||
\(965\) | 0.617063 | 0.0198640 | ||||||||
\(966\) | 18.2203 | 0.586228 | ||||||||
\(967\) | 52.0779 | 1.67471 | 0.837357 | − | 0.546657i | \(-0.184100\pi\) | ||||
0.837357 | + | 0.546657i | \(0.184100\pi\) | |||||||
\(968\) | 38.4372 | 1.23542 | ||||||||
\(969\) | −4.01215 | −0.128889 | ||||||||
\(970\) | −0.148150 | −0.00475681 | ||||||||
\(971\) | −38.2043 | −1.22604 | −0.613018 | − | 0.790069i | \(-0.710045\pi\) | ||||
−0.613018 | + | 0.790069i | \(0.710045\pi\) | |||||||
\(972\) | 0.900691 | 0.0288897 | ||||||||
\(973\) | 7.41186 | 0.237613 | ||||||||
\(974\) | −7.48977 | −0.239988 | ||||||||
\(975\) | 28.4457 | 0.910991 | ||||||||
\(976\) | −13.9460 | −0.446400 | ||||||||
\(977\) | −25.0880 | −0.802636 | −0.401318 | − | 0.915939i | \(-0.631448\pi\) | ||||
−0.401318 | + | 0.915939i | \(0.631448\pi\) | |||||||
\(978\) | −7.58455 | −0.242527 | ||||||||
\(979\) | 7.64245 | 0.244254 | ||||||||
\(980\) | 0.00104219 | 3.32917e−5 0 | ||||||||
\(981\) | −6.91498 | −0.220778 | ||||||||
\(982\) | 14.4886 | 0.462350 | ||||||||
\(983\) | 23.8926 | 0.762054 | 0.381027 | − | 0.924564i | \(-0.375570\pi\) | ||||
0.381027 | + | 0.924564i | \(0.375570\pi\) | |||||||
\(984\) | −11.2531 | −0.358737 | ||||||||
\(985\) | −0.0561052 | −0.00178766 | ||||||||
\(986\) | 2.31543 | 0.0737384 | ||||||||
\(987\) | −27.8250 | −0.885678 | ||||||||
\(988\) | 20.5623 | 0.654175 | ||||||||
\(989\) | −72.4000 | −2.30219 | ||||||||
\(990\) | −0.148253 | −0.00471178 | ||||||||
\(991\) | 25.3724 | 0.805981 | 0.402991 | − | 0.915204i | \(-0.367971\pi\) | ||||
0.402991 | + | 0.915204i | \(0.367971\pi\) | |||||||
\(992\) | 18.6017 | 0.590605 | ||||||||
\(993\) | 23.4339 | 0.743651 | ||||||||
\(994\) | −17.3327 | −0.549760 | ||||||||
\(995\) | 0.343317 | 0.0108839 | ||||||||
\(996\) | 8.13955 | 0.257911 | ||||||||
\(997\) | −10.2375 | −0.324226 | −0.162113 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162113 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(998\) | 9.75754 | 0.308870 | ||||||||
\(999\) | 9.08854 | 0.287549 |
(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 | 4029.2.a.g.1.8 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.g.1.8 | ✓ | 22 | 1.1 | even | 1 | trivial |