Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, 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("725.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.240881.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 5x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.33090\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33090 | 1.64819 | 0.824097 | − | 0.566449i | \(-0.191683\pi\) | ||||
0.824097 | + | 0.566449i | \(0.191683\pi\) | |||||||
\(3\) | 0.318289 | 0.183764 | 0.0918821 | − | 0.995770i | \(-0.470712\pi\) | ||||
0.0918821 | + | 0.995770i | \(0.470712\pi\) | |||||||
\(4\) | 3.43308 | 1.71654 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.741899 | 0.302879 | ||||||||
\(7\) | 1.09271 | 0.413006 | 0.206503 | − | 0.978446i | \(-0.433792\pi\) | ||||
0.206503 | + | 0.978446i | \(0.433792\pi\) | |||||||
\(8\) | 3.34037 | 1.18100 | ||||||||
\(9\) | −2.89869 | −0.966231 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.26027 | 1.58603 | 0.793015 | − | 0.609202i | \(-0.208510\pi\) | ||||
0.793015 | + | 0.609202i | \(0.208510\pi\) | |||||||
\(12\) | 1.09271 | 0.315439 | ||||||||
\(13\) | 0.453000 | 0.125640 | 0.0628198 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628198 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(14\) | 2.54700 | 0.680714 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.919897 | 0.229974 | ||||||||
\(17\) | 4.82718 | 1.17076 | 0.585382 | − | 0.810758i | \(-0.300945\pi\) | ||||
0.585382 | + | 0.810758i | \(0.300945\pi\) | |||||||
\(18\) | −6.75655 | −1.59254 | ||||||||
\(19\) | −1.04329 | −0.239346 | −0.119673 | − | 0.992813i | \(-0.538185\pi\) | ||||
−0.119673 | + | 0.992813i | \(0.538185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.347798 | 0.0758958 | ||||||||
\(22\) | 12.2611 | 2.61409 | ||||||||
\(23\) | −2.49327 | −0.519883 | −0.259941 | − | 0.965624i | \(-0.583703\pi\) | ||||
−0.259941 | + | 0.965624i | \(0.583703\pi\) | |||||||
\(24\) | 1.06320 | 0.217025 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.05590 | 0.207078 | ||||||||
\(27\) | −1.87749 | −0.361323 | ||||||||
\(28\) | 3.75137 | 0.708943 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.45517 | −1.15938 | −0.579691 | − | 0.814836i | \(-0.696827\pi\) | ||||
−0.579691 | + | 0.814836i | \(0.696827\pi\) | |||||||
\(32\) | −4.53656 | −0.801958 | ||||||||
\(33\) | 1.67428 | 0.291456 | ||||||||
\(34\) | 11.2517 | 1.92965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.95145 | −1.65858 | ||||||||
\(37\) | −0.535270 | −0.0879978 | −0.0439989 | − | 0.999032i | \(-0.514010\pi\) | ||||
−0.0439989 | + | 0.999032i | \(0.514010\pi\) | |||||||
\(38\) | −2.43180 | −0.394489 | ||||||||
\(39\) | 0.144185 | 0.0230880 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.228712 | −0.0357187 | −0.0178594 | − | 0.999841i | \(-0.505685\pi\) | ||||
−0.0178594 | + | 0.999841i | \(0.505685\pi\) | |||||||
\(42\) | 0.810682 | 0.125091 | ||||||||
\(43\) | −5.21915 | −0.795913 | −0.397956 | − | 0.917404i | \(-0.630280\pi\) | ||||
−0.397956 | + | 0.917404i | \(0.630280\pi\) | |||||||
\(44\) | 18.0589 | 2.72249 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.81156 | −0.856868 | ||||||||
\(47\) | 3.52266 | 0.513833 | 0.256916 | − | 0.966434i | \(-0.417293\pi\) | ||||
0.256916 | + | 0.966434i | \(0.417293\pi\) | |||||||
\(48\) | 0.292793 | 0.0422610 | ||||||||
\(49\) | −5.80598 | −0.829426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.53644 | 0.215144 | ||||||||
\(52\) | 1.55519 | 0.215665 | ||||||||
\(53\) | −4.73447 | −0.650330 | −0.325165 | − | 0.945657i | \(-0.605420\pi\) | ||||
−0.325165 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(54\) | −4.37623 | −0.595530 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.65006 | 0.487760 | ||||||||
\(57\) | −0.332067 | −0.0439833 | ||||||||
\(58\) | 2.33090 | 0.306062 | ||||||||
\(59\) | −1.78076 | −0.231836 | −0.115918 | − | 0.993259i | \(-0.536981\pi\) | ||||
−0.115918 | + | 0.993259i | \(0.536981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.2394 | −1.82317 | −0.911583 | − | 0.411116i | \(-0.865139\pi\) | ||||
−0.911583 | + | 0.411116i | \(0.865139\pi\) | |||||||
\(62\) | −15.0463 | −1.91089 | ||||||||
\(63\) | −3.16744 | −0.399059 | ||||||||
\(64\) | −12.4140 | −1.55176 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.90259 | 0.480375 | ||||||||
\(67\) | 8.62927 | 1.05423 | 0.527117 | − | 0.849793i | \(-0.323273\pi\) | ||||
0.527117 | + | 0.849793i | \(0.323273\pi\) | |||||||
\(68\) | 16.5721 | 2.00967 | ||||||||
\(69\) | −0.793580 | −0.0955359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.08842 | −0.603884 | −0.301942 | − | 0.953326i | \(-0.597635\pi\) | ||||
−0.301942 | + | 0.953326i | \(0.597635\pi\) | |||||||
\(72\) | −9.68271 | −1.14112 | ||||||||
\(73\) | 11.9810 | 1.40227 | 0.701133 | − | 0.713031i | \(-0.252678\pi\) | ||||
0.701133 | + | 0.713031i | \(0.252678\pi\) | |||||||
\(74\) | −1.24766 | −0.145037 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.58169 | −0.410848 | ||||||||
\(77\) | 5.74796 | 0.655041 | ||||||||
\(78\) | 0.336080 | 0.0380536 | ||||||||
\(79\) | −12.6314 | −1.42115 | −0.710574 | − | 0.703623i | \(-0.751565\pi\) | ||||
−0.710574 | + | 0.703623i | \(0.751565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.09849 | 0.899833 | ||||||||
\(82\) | −0.533103 | −0.0588714 | ||||||||
\(83\) | 9.75840 | 1.07112 | 0.535562 | − | 0.844496i | \(-0.320100\pi\) | ||||
0.535562 | + | 0.844496i | \(0.320100\pi\) | |||||||
\(84\) | 1.19402 | 0.130278 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.1653 | −1.31182 | ||||||||
\(87\) | 0.318289 | 0.0341241 | ||||||||
\(88\) | 17.5712 | 1.87310 | ||||||||
\(89\) | −10.0347 | −1.06368 | −0.531838 | − | 0.846846i | \(-0.678498\pi\) | ||||
−0.531838 | + | 0.846846i | \(0.678498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.494998 | 0.0518899 | ||||||||
\(92\) | −8.55961 | −0.892401 | ||||||||
\(93\) | −2.05461 | −0.213053 | ||||||||
\(94\) | 8.21096 | 0.846896 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.44394 | −0.147371 | ||||||||
\(97\) | 15.4404 | 1.56774 | 0.783869 | − | 0.620927i | \(-0.213244\pi\) | ||||
0.783869 | + | 0.620927i | \(0.213244\pi\) | |||||||
\(98\) | −13.5331 | −1.36705 | ||||||||
\(99\) | −15.2479 | −1.53247 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5211 | 1.44490 | 0.722451 | − | 0.691422i | \(-0.243015\pi\) | ||||
0.722451 | + | 0.691422i | \(0.243015\pi\) | |||||||
\(102\) | 3.58128 | 0.354600 | ||||||||
\(103\) | 4.59534 | 0.452792 | 0.226396 | − | 0.974035i | \(-0.427306\pi\) | ||||
0.226396 | + | 0.974035i | \(0.427306\pi\) | |||||||
\(104\) | 1.51319 | 0.148380 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.0356 | −1.07187 | ||||||||
\(107\) | −20.1825 | −1.95111 | −0.975556 | − | 0.219753i | \(-0.929475\pi\) | ||||
−0.975556 | + | 0.219753i | \(0.929475\pi\) | |||||||
\(108\) | −6.44557 | −0.620226 | ||||||||
\(109\) | 4.36762 | 0.418343 | 0.209171 | − | 0.977879i | \(-0.432923\pi\) | ||||
0.209171 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.170370 | −0.0161708 | ||||||||
\(112\) | 1.00518 | 0.0949808 | ||||||||
\(113\) | 13.0446 | 1.22713 | 0.613567 | − | 0.789643i | \(-0.289734\pi\) | ||||
0.613567 | + | 0.789643i | \(0.289734\pi\) | |||||||
\(114\) | −0.774013 | −0.0724930 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.43308 | 0.318754 | ||||||||
\(117\) | −1.31311 | −0.121397 | ||||||||
\(118\) | −4.15077 | −0.382110 | ||||||||
\(119\) | 5.27472 | 0.483533 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6704 | 1.51549 | ||||||||
\(122\) | −33.1905 | −3.00493 | ||||||||
\(123\) | −0.0727963 | −0.00656382 | ||||||||
\(124\) | −22.1611 | −1.99013 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.38297 | −0.657727 | ||||||||
\(127\) | 12.0378 | 1.06818 | 0.534092 | − | 0.845426i | \(-0.320654\pi\) | ||||
0.534092 | + | 0.845426i | \(0.320654\pi\) | |||||||
\(128\) | −19.8628 | −1.75564 | ||||||||
\(129\) | −1.66120 | −0.146260 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0578 | −1.57772 | −0.788860 | − | 0.614572i | \(-0.789329\pi\) | ||||
−0.788860 | + | 0.614572i | \(0.789329\pi\) | |||||||
\(132\) | 5.74796 | 0.500296 | ||||||||
\(133\) | −1.14001 | −0.0988516 | ||||||||
\(134\) | 20.1139 | 1.73758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.1246 | 1.38267 | ||||||||
\(137\) | −11.3447 | −0.969240 | −0.484620 | − | 0.874725i | \(-0.661042\pi\) | ||||
−0.484620 | + | 0.874725i | \(0.661042\pi\) | |||||||
\(138\) | −1.84975 | −0.157462 | ||||||||
\(139\) | 10.5504 | 0.894870 | 0.447435 | − | 0.894316i | \(-0.352338\pi\) | ||||
0.447435 | + | 0.894316i | \(0.352338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12122 | 0.0944241 | ||||||||
\(142\) | −11.8606 | −0.995318 | ||||||||
\(143\) | 2.38290 | 0.199268 | ||||||||
\(144\) | −2.66650 | −0.222208 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 27.9264 | 2.31121 | ||||||||
\(147\) | −1.84798 | −0.152419 | ||||||||
\(148\) | −1.83763 | −0.151052 | ||||||||
\(149\) | −5.56554 | −0.455947 | −0.227973 | − | 0.973667i | \(-0.573210\pi\) | ||||
−0.227973 | + | 0.973667i | \(0.573210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.4696 | 1.09614 | 0.548071 | − | 0.836432i | \(-0.315362\pi\) | ||||
0.548071 | + | 0.836432i | \(0.315362\pi\) | |||||||
\(152\) | −3.48497 | −0.282668 | ||||||||
\(153\) | −13.9925 | −1.13123 | ||||||||
\(154\) | 13.3979 | 1.07963 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.494998 | 0.0396316 | ||||||||
\(157\) | −18.7100 | −1.49322 | −0.746612 | − | 0.665260i | \(-0.768321\pi\) | ||||
−0.746612 | + | 0.665260i | \(0.768321\pi\) | |||||||
\(158\) | −29.4426 | −2.34233 | ||||||||
\(159\) | −1.50693 | −0.119507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.72443 | −0.214715 | ||||||||
\(162\) | 18.8768 | 1.48310 | ||||||||
\(163\) | 12.3812 | 0.969771 | 0.484886 | − | 0.874578i | \(-0.338861\pi\) | ||||
0.484886 | + | 0.874578i | \(0.338861\pi\) | |||||||
\(164\) | −0.785186 | −0.0613127 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.7458 | 1.76542 | ||||||||
\(167\) | 20.6501 | 1.59795 | 0.798976 | − | 0.601363i | \(-0.205375\pi\) | ||||
0.798976 | + | 0.601363i | \(0.205375\pi\) | |||||||
\(168\) | 1.16177 | 0.0896329 | ||||||||
\(169\) | −12.7948 | −0.984215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.02417 | 0.231264 | ||||||||
\(172\) | −17.9178 | −1.36622 | ||||||||
\(173\) | 4.75783 | 0.361731 | 0.180866 | − | 0.983508i | \(-0.442110\pi\) | ||||
0.180866 | + | 0.983508i | \(0.442110\pi\) | |||||||
\(174\) | 0.741899 | 0.0562432 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.83890 | 0.364746 | ||||||||
\(177\) | −0.566797 | −0.0426031 | ||||||||
\(178\) | −23.3898 | −1.75314 | ||||||||
\(179\) | 11.5557 | 0.863716 | 0.431858 | − | 0.901942i | \(-0.357858\pi\) | ||||
0.431858 | + | 0.901942i | \(0.357858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.55520 | 0.710232 | 0.355116 | − | 0.934822i | \(-0.384441\pi\) | ||||
0.355116 | + | 0.934822i | \(0.384441\pi\) | |||||||
\(182\) | 1.15379 | 0.0855246 | ||||||||
\(183\) | −4.53224 | −0.335033 | ||||||||
\(184\) | −8.32845 | −0.613982 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.78908 | −0.351152 | ||||||||
\(187\) | 25.3923 | 1.85687 | ||||||||
\(188\) | 12.0936 | 0.882016 | ||||||||
\(189\) | −2.05155 | −0.149229 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9747 | −1.51768 | −0.758839 | − | 0.651278i | \(-0.774233\pi\) | ||||
−0.758839 | + | 0.651278i | \(0.774233\pi\) | |||||||
\(192\) | −3.95125 | −0.285157 | ||||||||
\(193\) | −22.8064 | −1.64164 | −0.820821 | − | 0.571185i | \(-0.806484\pi\) | ||||
−0.820821 | + | 0.571185i | \(0.806484\pi\) | |||||||
\(194\) | 35.9900 | 2.58393 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.9324 | −1.42374 | ||||||||
\(197\) | −14.1188 | −1.00592 | −0.502962 | − | 0.864309i | \(-0.667756\pi\) | ||||
−0.502962 | + | 0.864309i | \(0.667756\pi\) | |||||||
\(198\) | −35.5413 | −2.52581 | ||||||||
\(199\) | −9.06536 | −0.642626 | −0.321313 | − | 0.946973i | \(-0.604124\pi\) | ||||
−0.321313 | + | 0.946973i | \(0.604124\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.74660 | 0.193730 | ||||||||
\(202\) | 33.8472 | 2.38148 | ||||||||
\(203\) | 1.09271 | 0.0766934 | ||||||||
\(204\) | 5.27472 | 0.369305 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.7113 | 0.746289 | ||||||||
\(207\) | 7.22723 | 0.502327 | ||||||||
\(208\) | 0.416713 | 0.0288938 | ||||||||
\(209\) | −5.48797 | −0.379611 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.15564 | 0.492614 | 0.246307 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246307 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(212\) | −16.2538 | −1.11632 | ||||||||
\(213\) | −1.61959 | −0.110972 | ||||||||
\(214\) | −47.0432 | −3.21581 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.27151 | −0.426722 | ||||||||
\(217\) | −7.05364 | −0.478832 | ||||||||
\(218\) | 10.1805 | 0.689509 | ||||||||
\(219\) | 3.81341 | 0.257686 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.18671 | 0.147094 | ||||||||
\(222\) | −0.397116 | −0.0266527 | ||||||||
\(223\) | 8.90055 | 0.596025 | 0.298012 | − | 0.954562i | \(-0.403676\pi\) | ||||
0.298012 | + | 0.954562i | \(0.403676\pi\) | |||||||
\(224\) | −4.95715 | −0.331214 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.4056 | 2.02255 | ||||||||
\(227\) | −2.85842 | −0.189720 | −0.0948600 | − | 0.995491i | \(-0.530240\pi\) | ||||
−0.0948600 | + | 0.995491i | \(0.530240\pi\) | |||||||
\(228\) | −1.14001 | −0.0754992 | ||||||||
\(229\) | 23.3358 | 1.54207 | 0.771037 | − | 0.636791i | \(-0.219739\pi\) | ||||
0.771037 | + | 0.636791i | \(0.219739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.82951 | 0.120373 | ||||||||
\(232\) | 3.34037 | 0.219306 | ||||||||
\(233\) | 12.3160 | 0.806846 | 0.403423 | − | 0.915014i | \(-0.367820\pi\) | ||||
0.403423 | + | 0.915014i | \(0.367820\pi\) | |||||||
\(234\) | −3.06072 | −0.200085 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.11351 | −0.397955 | ||||||||
\(237\) | −4.02045 | −0.261156 | ||||||||
\(238\) | 12.2948 | 0.796956 | ||||||||
\(239\) | 29.7130 | 1.92198 | 0.960988 | − | 0.276591i | \(-0.0892047\pi\) | ||||
0.960988 | + | 0.276591i | \(0.0892047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1647 | 1.17009 | 0.585045 | − | 0.811001i | \(-0.301077\pi\) | ||||
0.585045 | + | 0.811001i | \(0.301077\pi\) | |||||||
\(242\) | 38.8570 | 2.49783 | ||||||||
\(243\) | 8.21012 | 0.526680 | ||||||||
\(244\) | −48.8850 | −3.12954 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.169681 | −0.0108185 | ||||||||
\(247\) | −0.472609 | −0.0300714 | ||||||||
\(248\) | −21.5627 | −1.36923 | ||||||||
\(249\) | 3.10599 | 0.196834 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.1232 | 0.954569 | 0.477284 | − | 0.878749i | \(-0.341621\pi\) | ||||
0.477284 | + | 0.878749i | \(0.341621\pi\) | |||||||
\(252\) | −10.8741 | −0.685002 | ||||||||
\(253\) | −13.1153 | −0.824550 | ||||||||
\(254\) | 28.0589 | 1.76057 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.4700 | −1.34187 | ||||||||
\(257\) | −21.5436 | −1.34385 | −0.671927 | − | 0.740617i | \(-0.734533\pi\) | ||||
−0.671927 | + | 0.740617i | \(0.734533\pi\) | |||||||
\(258\) | −3.87208 | −0.241065 | ||||||||
\(259\) | −0.584896 | −0.0363437 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.89869 | −0.179425 | ||||||||
\(262\) | −42.0910 | −2.60039 | ||||||||
\(263\) | 16.4285 | 1.01302 | 0.506512 | − | 0.862233i | \(-0.330934\pi\) | ||||
0.506512 | + | 0.862233i | \(0.330934\pi\) | |||||||
\(264\) | 5.59273 | 0.344209 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.65725 | −0.162927 | ||||||||
\(267\) | −3.19393 | −0.195465 | ||||||||
\(268\) | 29.6250 | 1.80964 | ||||||||
\(269\) | −9.71327 | −0.592228 | −0.296114 | − | 0.955153i | \(-0.595691\pi\) | ||||
−0.296114 | + | 0.955153i | \(0.595691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.02188 | −0.0620749 | −0.0310374 | − | 0.999518i | \(-0.509881\pi\) | ||||
−0.0310374 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(272\) | 4.44051 | 0.269245 | ||||||||
\(273\) | 0.157552 | 0.00953551 | ||||||||
\(274\) | −26.4432 | −1.59750 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.72443 | −0.163991 | ||||||||
\(277\) | −4.82608 | −0.289971 | −0.144986 | − | 0.989434i | \(-0.546314\pi\) | ||||
−0.144986 | + | 0.989434i | \(0.546314\pi\) | |||||||
\(278\) | 24.5918 | 1.47492 | ||||||||
\(279\) | 18.7115 | 1.12023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.09507 | 0.423256 | 0.211628 | − | 0.977350i | \(-0.432123\pi\) | ||||
0.211628 | + | 0.977350i | \(0.432123\pi\) | |||||||
\(282\) | 2.61346 | 0.155629 | ||||||||
\(283\) | 20.7674 | 1.23450 | 0.617248 | − | 0.786769i | \(-0.288248\pi\) | ||||
0.617248 | + | 0.786769i | \(0.288248\pi\) | |||||||
\(284\) | −17.4690 | −1.03659 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.55430 | 0.328432 | ||||||||
\(287\) | −0.249916 | −0.0147521 | ||||||||
\(288\) | 13.1501 | 0.774876 | ||||||||
\(289\) | 6.30171 | 0.370689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.91451 | 0.288094 | ||||||||
\(292\) | 41.1316 | 2.40705 | ||||||||
\(293\) | 12.4880 | 0.729557 | 0.364779 | − | 0.931094i | \(-0.381145\pi\) | ||||
0.364779 | + | 0.931094i | \(0.381145\pi\) | |||||||
\(294\) | −4.30745 | −0.251216 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.78800 | −0.103925 | ||||||||
\(297\) | −9.87609 | −0.573069 | ||||||||
\(298\) | −12.9727 | −0.751488 | ||||||||
\(299\) | −1.12945 | −0.0653178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.70303 | −0.328717 | ||||||||
\(302\) | 31.3963 | 1.80665 | ||||||||
\(303\) | 4.62190 | 0.265521 | ||||||||
\(304\) | −0.959716 | −0.0550435 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −32.6151 | −1.86448 | ||||||||
\(307\) | 18.1776 | 1.03745 | 0.518725 | − | 0.854941i | \(-0.326407\pi\) | ||||
0.518725 | + | 0.854941i | \(0.326407\pi\) | |||||||
\(308\) | 19.7332 | 1.12440 | ||||||||
\(309\) | 1.46264 | 0.0832070 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.6250 | −0.999421 | −0.499710 | − | 0.866193i | \(-0.666560\pi\) | ||||
−0.499710 | + | 0.866193i | \(0.666560\pi\) | |||||||
\(312\) | 0.481631 | 0.0272670 | ||||||||
\(313\) | 5.27338 | 0.298069 | 0.149034 | − | 0.988832i | \(-0.452383\pi\) | ||||
0.149034 | + | 0.988832i | \(0.452383\pi\) | |||||||
\(314\) | −43.6112 | −2.46112 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.3648 | −2.43946 | ||||||||
\(317\) | −19.6121 | −1.10152 | −0.550762 | − | 0.834662i | \(-0.685663\pi\) | ||||
−0.550762 | + | 0.834662i | \(0.685663\pi\) | |||||||
\(318\) | −3.51250 | −0.196971 | ||||||||
\(319\) | 5.26027 | 0.294518 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.42385 | −0.358544 | ||||||||
\(322\) | −6.35036 | −0.353892 | ||||||||
\(323\) | −5.03614 | −0.280218 | ||||||||
\(324\) | 27.8028 | 1.54460 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 28.8593 | 1.59837 | ||||||||
\(327\) | 1.39017 | 0.0768764 | ||||||||
\(328\) | −0.763981 | −0.0421838 | ||||||||
\(329\) | 3.84925 | 0.212216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.67888 | 0.257175 | 0.128587 | − | 0.991698i | \(-0.458956\pi\) | ||||
0.128587 | + | 0.991698i | \(0.458956\pi\) | |||||||
\(332\) | 33.5014 | 1.83863 | ||||||||
\(333\) | 1.55158 | 0.0850262 | ||||||||
\(334\) | 48.1333 | 2.63373 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.319938 | 0.0174541 | ||||||||
\(337\) | 8.06881 | 0.439536 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(338\) | −29.8233 | −1.62218 | ||||||||
\(339\) | 4.15195 | 0.225503 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.9559 | −1.83882 | ||||||||
\(342\) | 7.04903 | 0.381168 | ||||||||
\(343\) | −13.9933 | −0.755565 | ||||||||
\(344\) | −17.4339 | −0.939973 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0900 | 0.596203 | ||||||||
\(347\) | −7.31950 | −0.392931 | −0.196466 | − | 0.980511i | \(-0.562946\pi\) | ||||
−0.196466 | + | 0.980511i | \(0.562946\pi\) | |||||||
\(348\) | 1.09271 | 0.0585755 | ||||||||
\(349\) | 3.60205 | 0.192813 | 0.0964066 | − | 0.995342i | \(-0.469265\pi\) | ||||
0.0964066 | + | 0.995342i | \(0.469265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.850501 | −0.0453964 | ||||||||
\(352\) | −23.8635 | −1.27193 | ||||||||
\(353\) | 34.1603 | 1.81817 | 0.909085 | − | 0.416610i | \(-0.136782\pi\) | ||||
0.909085 | + | 0.416610i | \(0.136782\pi\) | |||||||
\(354\) | −1.32115 | −0.0702181 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −34.4499 | −1.82584 | ||||||||
\(357\) | 1.67889 | 0.0888560 | ||||||||
\(358\) | 26.9352 | 1.42357 | ||||||||
\(359\) | −2.30982 | −0.121908 | −0.0609539 | − | 0.998141i | \(-0.519414\pi\) | ||||
−0.0609539 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9116 | −0.942713 | ||||||||
\(362\) | 22.2722 | 1.17060 | ||||||||
\(363\) | 5.30601 | 0.278493 | ||||||||
\(364\) | 1.69937 | 0.0890712 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5642 | −0.552199 | ||||||||
\(367\) | 11.6033 | 0.605688 | 0.302844 | − | 0.953040i | \(-0.402064\pi\) | ||||
0.302844 | + | 0.953040i | \(0.402064\pi\) | |||||||
\(368\) | −2.29355 | −0.119560 | ||||||||
\(369\) | 0.662964 | 0.0345125 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.17342 | −0.268590 | ||||||||
\(372\) | −7.05364 | −0.365714 | ||||||||
\(373\) | −21.1965 | −1.09752 | −0.548758 | − | 0.835982i | \(-0.684899\pi\) | ||||
−0.548758 | + | 0.835982i | \(0.684899\pi\) | |||||||
\(374\) | 59.1868 | 3.06048 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7670 | 0.606837 | ||||||||
\(377\) | 0.453000 | 0.0233307 | ||||||||
\(378\) | −4.78196 | −0.245958 | ||||||||
\(379\) | −26.3613 | −1.35409 | −0.677046 | − | 0.735941i | \(-0.736740\pi\) | ||||
−0.677046 | + | 0.735941i | \(0.736740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.83151 | 0.196294 | ||||||||
\(382\) | −48.8900 | −2.50143 | ||||||||
\(383\) | −12.5563 | −0.641595 | −0.320797 | − | 0.947148i | \(-0.603951\pi\) | ||||
−0.320797 | + | 0.947148i | \(0.603951\pi\) | |||||||
\(384\) | −6.32209 | −0.322623 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −53.1595 | −2.70575 | ||||||||
\(387\) | 15.1287 | 0.769035 | ||||||||
\(388\) | 53.0083 | 2.69109 | ||||||||
\(389\) | −34.1976 | −1.73389 | −0.866945 | − | 0.498405i | \(-0.833919\pi\) | ||||
−0.866945 | + | 0.498405i | \(0.833919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0355 | −0.608660 | ||||||||
\(392\) | −19.3941 | −0.979552 | ||||||||
\(393\) | −5.74761 | −0.289929 | ||||||||
\(394\) | −32.9095 | −1.65796 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −52.3473 | −2.63055 | ||||||||
\(397\) | −33.8726 | −1.70002 | −0.850008 | − | 0.526769i | \(-0.823403\pi\) | ||||
−0.850008 | + | 0.526769i | \(0.823403\pi\) | |||||||
\(398\) | −21.1304 | −1.05917 | ||||||||
\(399\) | −0.362853 | −0.0181654 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.985155 | −0.0491963 | −0.0245982 | − | 0.999697i | \(-0.507831\pi\) | ||||
−0.0245982 | + | 0.999697i | \(0.507831\pi\) | |||||||
\(402\) | 6.40204 | 0.319305 | ||||||||
\(403\) | −2.92419 | −0.145664 | ||||||||
\(404\) | 49.8521 | 2.48024 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.54700 | 0.126406 | ||||||||
\(407\) | −2.81566 | −0.139567 | ||||||||
\(408\) | 5.13228 | 0.254086 | ||||||||
\(409\) | 22.7925 | 1.12701 | 0.563507 | − | 0.826111i | \(-0.309452\pi\) | ||||
0.563507 | + | 0.826111i | \(0.309452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.61088 | −0.178112 | ||||||||
\(412\) | 15.7762 | 0.777237 | ||||||||
\(413\) | −1.94586 | −0.0957496 | ||||||||
\(414\) | 16.8459 | 0.827932 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.05506 | −0.100758 | ||||||||
\(417\) | 3.35806 | 0.164445 | ||||||||
\(418\) | −12.7919 | −0.625672 | ||||||||
\(419\) | 12.5213 | 0.611705 | 0.305852 | − | 0.952079i | \(-0.401059\pi\) | ||||
0.305852 | + | 0.952079i | \(0.401059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8030 | 1.01388 | 0.506939 | − | 0.861982i | \(-0.330777\pi\) | ||||
0.506939 | + | 0.861982i | \(0.330777\pi\) | |||||||
\(422\) | 16.6791 | 0.811924 | ||||||||
\(423\) | −10.2111 | −0.496481 | ||||||||
\(424\) | −15.8149 | −0.768039 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.77509 | −0.182904 | ||||||||
\(427\) | −15.5595 | −0.752979 | ||||||||
\(428\) | −69.2880 | −3.34916 | ||||||||
\(429\) | 0.758450 | 0.0366183 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.48833 | 0.360700 | 0.180350 | − | 0.983602i | \(-0.442277\pi\) | ||||
0.180350 | + | 0.983602i | \(0.442277\pi\) | |||||||
\(432\) | −1.72709 | −0.0830949 | ||||||||
\(433\) | −15.4670 | −0.743296 | −0.371648 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371648 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(434\) | −16.4413 | −0.789208 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.9944 | 0.718102 | ||||||||
\(437\) | 2.60120 | 0.124432 | ||||||||
\(438\) | 8.88866 | 0.424717 | ||||||||
\(439\) | 35.3418 | 1.68677 | 0.843387 | − | 0.537306i | \(-0.180558\pi\) | ||||
0.843387 | + | 0.537306i | \(0.180558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.8297 | 0.801417 | ||||||||
\(442\) | 5.09700 | 0.242440 | ||||||||
\(443\) | 16.1085 | 0.765340 | 0.382670 | − | 0.923885i | \(-0.375005\pi\) | ||||
0.382670 | + | 0.923885i | \(0.375005\pi\) | |||||||
\(444\) | −0.584896 | −0.0277579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.7463 | 0.982364 | ||||||||
\(447\) | −1.77145 | −0.0837866 | ||||||||
\(448\) | −13.5650 | −0.640885 | ||||||||
\(449\) | −7.08842 | −0.334523 | −0.167262 | − | 0.985913i | \(-0.553492\pi\) | ||||
−0.167262 | + | 0.985913i | \(0.553492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.20308 | −0.0566510 | ||||||||
\(452\) | 44.7832 | 2.10643 | ||||||||
\(453\) | 4.28723 | 0.201432 | ||||||||
\(454\) | −6.66269 | −0.312695 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.10923 | −0.0519443 | ||||||||
\(457\) | −18.5143 | −0.866065 | −0.433032 | − | 0.901378i | \(-0.642556\pi\) | ||||
−0.433032 | + | 0.901378i | \(0.642556\pi\) | |||||||
\(458\) | 54.3934 | 2.54163 | ||||||||
\(459\) | −9.06298 | −0.423024 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2153 | 0.988093 | 0.494047 | − | 0.869435i | \(-0.335517\pi\) | ||||
0.494047 | + | 0.869435i | \(0.335517\pi\) | |||||||
\(462\) | 4.26440 | 0.198398 | ||||||||
\(463\) | 6.41188 | 0.297985 | 0.148993 | − | 0.988838i | \(-0.452397\pi\) | ||||
0.148993 | + | 0.988838i | \(0.452397\pi\) | |||||||
\(464\) | 0.919897 | 0.0427051 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.7072 | 1.32984 | ||||||||
\(467\) | 28.2463 | 1.30708 | 0.653540 | − | 0.756892i | \(-0.273283\pi\) | ||||
0.653540 | + | 0.756892i | \(0.273283\pi\) | |||||||
\(468\) | −4.50800 | −0.208383 | ||||||||
\(469\) | 9.42931 | 0.435405 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.95520 | −0.274401 | ||||||||
\(472\) | −5.94841 | −0.273798 | ||||||||
\(473\) | −27.4541 | −1.26234 | ||||||||
\(474\) | −9.37125 | −0.430436 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.1086 | 0.830005 | ||||||||
\(477\) | 13.7238 | 0.628369 | ||||||||
\(478\) | 69.2580 | 3.16779 | ||||||||
\(479\) | 42.0968 | 1.92345 | 0.961725 | − | 0.274015i | \(-0.0883517\pi\) | ||||
0.961725 | + | 0.274015i | \(0.0883517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.242477 | −0.0110560 | ||||||||
\(482\) | 42.3400 | 1.92853 | ||||||||
\(483\) | −0.867155 | −0.0394569 | ||||||||
\(484\) | 57.2309 | 2.60141 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.1370 | 0.868070 | ||||||||
\(487\) | −12.9359 | −0.586180 | −0.293090 | − | 0.956085i | \(-0.594684\pi\) | ||||
−0.293090 | + | 0.956085i | \(0.594684\pi\) | |||||||
\(488\) | −47.5648 | −2.15316 | ||||||||
\(489\) | 3.94080 | 0.178209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9885 | 0.495903 | 0.247951 | − | 0.968772i | \(-0.420243\pi\) | ||||
0.247951 | + | 0.968772i | \(0.420243\pi\) | |||||||
\(492\) | −0.249916 | −0.0112671 | ||||||||
\(493\) | 4.82718 | 0.217405 | ||||||||
\(494\) | −1.10160 | −0.0495634 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.93809 | −0.266628 | ||||||||
\(497\) | −5.56018 | −0.249408 | ||||||||
\(498\) | 7.23975 | 0.324421 | ||||||||
\(499\) | 15.4837 | 0.693143 | 0.346572 | − | 0.938023i | \(-0.387346\pi\) | ||||
0.346572 | + | 0.938023i | \(0.387346\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.57269 | 0.293646 | ||||||||
\(502\) | 35.2507 | 1.57331 | ||||||||
\(503\) | −11.6465 | −0.519293 | −0.259646 | − | 0.965704i | \(-0.583606\pi\) | ||||
−0.259646 | + | 0.965704i | \(0.583606\pi\) | |||||||
\(504\) | −10.5804 | −0.471289 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −30.5704 | −1.35902 | ||||||||
\(507\) | −4.07244 | −0.180863 | ||||||||
\(508\) | 41.3269 | 1.83358 | ||||||||
\(509\) | −14.2587 | −0.632004 | −0.316002 | − | 0.948759i | \(-0.602341\pi\) | ||||
−0.316002 | + | 0.948759i | \(0.602341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.0917 | 0.579145 | ||||||||
\(512\) | −10.3188 | −0.456029 | ||||||||
\(513\) | 1.95876 | 0.0864813 | ||||||||
\(514\) | −50.2160 | −2.21493 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.70303 | −0.251062 | ||||||||
\(517\) | 18.5301 | 0.814955 | ||||||||
\(518\) | −1.36333 | −0.0599014 | ||||||||
\(519\) | 1.51436 | 0.0664732 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.9107 | −0.959923 | −0.479962 | − | 0.877290i | \(-0.659349\pi\) | ||||
−0.479962 | + | 0.877290i | \(0.659349\pi\) | |||||||
\(522\) | −6.75655 | −0.295726 | ||||||||
\(523\) | 21.1579 | 0.925170 | 0.462585 | − | 0.886575i | \(-0.346922\pi\) | ||||
0.462585 | + | 0.886575i | \(0.346922\pi\) | |||||||
\(524\) | −61.9941 | −2.70822 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.2932 | 1.66966 | ||||||||
\(527\) | −31.1603 | −1.35736 | ||||||||
\(528\) | 1.54017 | 0.0670272 | ||||||||
\(529\) | −16.7836 | −0.729722 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.16188 | 0.224007 | ||||||||
\(532\) | −3.91376 | −0.169683 | ||||||||
\(533\) | −0.103606 | −0.00448768 | ||||||||
\(534\) | −7.44472 | −0.322165 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 28.8250 | 1.24505 | ||||||||
\(537\) | 3.67806 | 0.158720 | ||||||||
\(538\) | −22.6406 | −0.976107 | ||||||||
\(539\) | −30.5410 | −1.31549 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.75379 | 0.290368 | 0.145184 | − | 0.989405i | \(-0.453623\pi\) | ||||
0.145184 | + | 0.989405i | \(0.453623\pi\) | |||||||
\(542\) | −2.38190 | −0.102311 | ||||||||
\(543\) | 3.04131 | 0.130515 | ||||||||
\(544\) | −21.8988 | −0.938903 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.367239 | 0.0157164 | ||||||||
\(547\) | 37.8019 | 1.61629 | 0.808147 | − | 0.588981i | \(-0.200471\pi\) | ||||
0.808147 | + | 0.588981i | \(0.200471\pi\) | |||||||
\(548\) | −38.9472 | −1.66374 | ||||||||
\(549\) | 41.2756 | 1.76160 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.04329 | −0.0444455 | ||||||||
\(552\) | −2.65085 | −0.112828 | ||||||||
\(553\) | −13.8025 | −0.586943 | ||||||||
\(554\) | −11.2491 | −0.477929 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.2203 | 1.53608 | ||||||||
\(557\) | 10.1691 | 0.430878 | 0.215439 | − | 0.976517i | \(-0.430882\pi\) | ||||
0.215439 | + | 0.976517i | \(0.430882\pi\) | |||||||
\(558\) | 43.6147 | 1.84636 | ||||||||
\(559\) | −2.36427 | −0.0999981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.08208 | 0.341226 | ||||||||
\(562\) | 16.5379 | 0.697608 | ||||||||
\(563\) | −41.8569 | −1.76406 | −0.882029 | − | 0.471196i | \(-0.843822\pi\) | ||||
−0.882029 | + | 0.471196i | \(0.843822\pi\) | |||||||
\(564\) | 3.84925 | 0.162083 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 48.4068 | 2.03469 | ||||||||
\(567\) | 8.84932 | 0.371637 | ||||||||
\(568\) | −16.9972 | −0.713187 | ||||||||
\(569\) | −25.4072 | −1.06512 | −0.532562 | − | 0.846391i | \(-0.678771\pi\) | ||||
−0.532562 | + | 0.846391i | \(0.678771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.07657 | −0.0869018 | −0.0434509 | − | 0.999056i | \(-0.513835\pi\) | ||||
−0.0434509 | + | 0.999056i | \(0.513835\pi\) | |||||||
\(572\) | 8.18069 | 0.342052 | ||||||||
\(573\) | −6.67602 | −0.278895 | ||||||||
\(574\) | −0.582528 | −0.0243143 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 35.9845 | 1.49935 | ||||||||
\(577\) | −4.05652 | −0.168875 | −0.0844375 | − | 0.996429i | \(-0.526909\pi\) | ||||
−0.0844375 | + | 0.996429i | \(0.526909\pi\) | |||||||
\(578\) | 14.6886 | 0.610967 | ||||||||
\(579\) | −7.25903 | −0.301675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.6631 | 0.442381 | ||||||||
\(582\) | 11.4552 | 0.474834 | ||||||||
\(583\) | −24.9046 | −1.03144 | ||||||||
\(584\) | 40.0209 | 1.65608 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.1083 | 1.20245 | ||||||||
\(587\) | −20.3218 | −0.838770 | −0.419385 | − | 0.907809i | \(-0.637754\pi\) | ||||
−0.419385 | + | 0.907809i | \(0.637754\pi\) | |||||||
\(588\) | −6.34427 | −0.261633 | ||||||||
\(589\) | 6.73459 | 0.277494 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.49386 | −0.184853 | ||||||||
\(592\) | −0.492393 | −0.0202372 | ||||||||
\(593\) | −23.5594 | −0.967469 | −0.483734 | − | 0.875215i | \(-0.660720\pi\) | ||||
−0.483734 | + | 0.875215i | \(0.660720\pi\) | |||||||
\(594\) | −23.0202 | −0.944528 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.1070 | −0.782652 | ||||||||
\(597\) | −2.88540 | −0.118092 | ||||||||
\(598\) | −2.63263 | −0.107656 | ||||||||
\(599\) | −29.8661 | −1.22029 | −0.610147 | − | 0.792288i | \(-0.708890\pi\) | ||||
−0.610147 | + | 0.792288i | \(0.708890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.3886 | −1.81065 | −0.905325 | − | 0.424720i | \(-0.860373\pi\) | ||||
−0.905325 | + | 0.424720i | \(0.860373\pi\) | |||||||
\(602\) | −13.2932 | −0.541789 | ||||||||
\(603\) | −25.0136 | −1.01863 | ||||||||
\(604\) | 46.2423 | 1.88157 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.7732 | 0.437631 | ||||||||
\(607\) | 28.0273 | 1.13759 | 0.568796 | − | 0.822479i | \(-0.307409\pi\) | ||||
0.568796 | + | 0.822479i | \(0.307409\pi\) | |||||||
\(608\) | 4.73293 | 0.191946 | ||||||||
\(609\) | 0.347798 | 0.0140935 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.59576 | 0.0645577 | ||||||||
\(612\) | −48.0375 | −1.94180 | ||||||||
\(613\) | 43.2256 | 1.74587 | 0.872933 | − | 0.487841i | \(-0.162215\pi\) | ||||
0.872933 | + | 0.487841i | \(0.162215\pi\) | |||||||
\(614\) | 42.3701 | 1.70992 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.2003 | 0.773603 | ||||||||
\(617\) | 11.6093 | 0.467372 | 0.233686 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233686 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(618\) | 3.40928 | 0.137141 | ||||||||
\(619\) | 7.25400 | 0.291563 | 0.145781 | − | 0.989317i | \(-0.453430\pi\) | ||||
0.145781 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.68109 | 0.187846 | ||||||||
\(622\) | −41.0820 | −1.64724 | ||||||||
\(623\) | −10.9650 | −0.439305 | ||||||||
\(624\) | 0.132635 | 0.00530965 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2917 | 0.491275 | ||||||||
\(627\) | −1.74676 | −0.0697589 | ||||||||
\(628\) | −64.2331 | −2.56318 | ||||||||
\(629\) | −2.58385 | −0.103025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.0705 | −1.63499 | −0.817496 | − | 0.575935i | \(-0.804638\pi\) | ||||
−0.817496 | + | 0.575935i | \(0.804638\pi\) | |||||||
\(632\) | −42.1937 | −1.67838 | ||||||||
\(633\) | 2.27756 | 0.0905249 | ||||||||
\(634\) | −45.7138 | −1.81553 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.17342 | −0.205139 | ||||||||
\(637\) | −2.63011 | −0.104209 | ||||||||
\(638\) | 12.2611 | 0.485423 | ||||||||
\(639\) | 14.7498 | 0.583492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.6090 | 1.40647 | 0.703235 | − | 0.710958i | \(-0.251738\pi\) | ||||
0.703235 | + | 0.710958i | \(0.251738\pi\) | |||||||
\(642\) | −14.9733 | −0.590950 | ||||||||
\(643\) | 14.3315 | 0.565179 | 0.282590 | − | 0.959241i | \(-0.408807\pi\) | ||||
0.282590 | + | 0.959241i | \(0.408807\pi\) | |||||||
\(644\) | −9.35319 | −0.368567 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.7387 | −0.461854 | ||||||||
\(647\) | −36.2899 | −1.42670 | −0.713352 | − | 0.700806i | \(-0.752824\pi\) | ||||
−0.713352 | + | 0.700806i | \(0.752824\pi\) | |||||||
\(648\) | 27.0520 | 1.06270 | ||||||||
\(649\) | −9.36729 | −0.367698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.24509 | −0.0879922 | ||||||||
\(652\) | 42.5057 | 1.66465 | ||||||||
\(653\) | −32.6269 | −1.27679 | −0.638395 | − | 0.769709i | \(-0.720401\pi\) | ||||
−0.638395 | + | 0.769709i | \(0.720401\pi\) | |||||||
\(654\) | 3.24033 | 0.126707 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.210391 | −0.00821439 | ||||||||
\(657\) | −34.7291 | −1.35491 | ||||||||
\(658\) | 8.97222 | 0.349774 | ||||||||
\(659\) | 2.94107 | 0.114568 | 0.0572839 | − | 0.998358i | \(-0.481756\pi\) | ||||
0.0572839 | + | 0.998358i | \(0.481756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1618 | 1.32874 | 0.664370 | − | 0.747404i | \(-0.268700\pi\) | ||||
0.664370 | + | 0.747404i | \(0.268700\pi\) | |||||||
\(662\) | 10.9060 | 0.423874 | ||||||||
\(663\) | 0.696006 | 0.0270306 | ||||||||
\(664\) | 32.5967 | 1.26500 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.61658 | 0.140140 | ||||||||
\(667\) | −2.49327 | −0.0965398 | ||||||||
\(668\) | 70.8935 | 2.74295 | ||||||||
\(669\) | 2.83295 | 0.109528 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −74.9030 | −2.89160 | ||||||||
\(672\) | −1.57781 | −0.0608652 | ||||||||
\(673\) | −23.9800 | −0.924360 | −0.462180 | − | 0.886786i | \(-0.652933\pi\) | ||||
−0.462180 | + | 0.886786i | \(0.652933\pi\) | |||||||
\(674\) | 18.8076 | 0.724441 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.9256 | −1.68945 | ||||||||
\(677\) | −9.44718 | −0.363085 | −0.181542 | − | 0.983383i | \(-0.558109\pi\) | ||||
−0.181542 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(678\) | 9.67778 | 0.371673 | ||||||||
\(679\) | 16.8719 | 0.647485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.909803 | −0.0348637 | ||||||||
\(682\) | −79.1477 | −3.03072 | ||||||||
\(683\) | −30.0862 | −1.15122 | −0.575608 | − | 0.817726i | \(-0.695235\pi\) | ||||
−0.575608 | + | 0.817726i | \(0.695235\pi\) | |||||||
\(684\) | 10.3822 | 0.396974 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −32.6168 | −1.24532 | ||||||||
\(687\) | 7.42753 | 0.283378 | ||||||||
\(688\) | −4.80108 | −0.183039 | ||||||||
\(689\) | −2.14471 | −0.0817071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.0873 | −1.60108 | −0.800538 | − | 0.599282i | \(-0.795453\pi\) | ||||
−0.800538 | + | 0.599282i | \(0.795453\pi\) | |||||||
\(692\) | 16.3340 | 0.620927 | ||||||||
\(693\) | −16.6616 | −0.632921 | ||||||||
\(694\) | −17.0610 | −0.647627 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.06320 | 0.0403006 | ||||||||
\(697\) | −1.10403 | −0.0418182 | ||||||||
\(698\) | 8.39600 | 0.317793 | ||||||||
\(699\) | 3.92003 | 0.148269 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.4785 | −1.79324 | −0.896620 | − | 0.442801i | \(-0.853985\pi\) | ||||
−0.896620 | + | 0.442801i | \(0.853985\pi\) | |||||||
\(702\) | −1.98243 | −0.0748221 | ||||||||
\(703\) | 0.558440 | 0.0210620 | ||||||||
\(704\) | −65.3012 | −2.46113 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 79.6242 | 2.99670 | ||||||||
\(707\) | 15.8674 | 0.596754 | ||||||||
\(708\) | −1.94586 | −0.0731299 | ||||||||
\(709\) | −25.0996 | −0.942634 | −0.471317 | − | 0.881964i | \(-0.656221\pi\) | ||||
−0.471317 | + | 0.881964i | \(0.656221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.6146 | 1.37316 | ||||||||
\(712\) | −33.5196 | −1.25620 | ||||||||
\(713\) | 16.0945 | 0.602743 | ||||||||
\(714\) | 3.91331 | 0.146452 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 39.6718 | 1.48260 | ||||||||
\(717\) | 9.45732 | 0.353190 | ||||||||
\(718\) | −5.38397 | −0.200928 | ||||||||
\(719\) | −9.06763 | −0.338165 | −0.169083 | − | 0.985602i | \(-0.554080\pi\) | ||||
−0.169083 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.02138 | 0.187006 | ||||||||
\(722\) | −41.7500 | −1.55377 | ||||||||
\(723\) | 5.78161 | 0.215020 | ||||||||
\(724\) | 32.8038 | 1.21914 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.3678 | 0.459011 | ||||||||
\(727\) | 28.5399 | 1.05849 | 0.529243 | − | 0.848470i | \(-0.322476\pi\) | ||||
0.529243 | + | 0.848470i | \(0.322476\pi\) | |||||||
\(728\) | 1.65348 | 0.0612820 | ||||||||
\(729\) | −21.6823 | −0.803048 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.1938 | −0.931826 | ||||||||
\(732\) | −15.5595 | −0.575097 | ||||||||
\(733\) | −29.3871 | −1.08544 | −0.542718 | − | 0.839915i | \(-0.682605\pi\) | ||||
−0.542718 | + | 0.839915i | \(0.682605\pi\) | |||||||
\(734\) | 27.0461 | 0.998290 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.3109 | 0.416924 | ||||||||
\(737\) | 45.3923 | 1.67205 | ||||||||
\(738\) | 1.54530 | 0.0568833 | ||||||||
\(739\) | 11.0473 | 0.406381 | 0.203190 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203190 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.150426 | −0.00552604 | ||||||||
\(742\) | −12.0587 | −0.442689 | ||||||||
\(743\) | −16.7348 | −0.613941 | −0.306971 | − | 0.951719i | \(-0.599315\pi\) | ||||
−0.306971 | + | 0.951719i | \(0.599315\pi\) | |||||||
\(744\) | −6.86315 | −0.251615 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −49.4070 | −1.80892 | ||||||||
\(747\) | −28.2866 | −1.03495 | ||||||||
\(748\) | 87.1738 | 3.18739 | ||||||||
\(749\) | −22.0536 | −0.805821 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5839 | 0.386212 | 0.193106 | − | 0.981178i | \(-0.438144\pi\) | ||||
0.193106 | + | 0.981178i | \(0.438144\pi\) | |||||||
\(752\) | 3.24048 | 0.118168 | ||||||||
\(753\) | 4.81355 | 0.175415 | ||||||||
\(754\) | 1.05590 | 0.0384535 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.04316 | −0.256157 | ||||||||
\(757\) | 9.19821 | 0.334315 | 0.167157 | − | 0.985930i | \(-0.446541\pi\) | ||||
0.167157 | + | 0.985930i | \(0.446541\pi\) | |||||||
\(758\) | −61.4456 | −2.23180 | ||||||||
\(759\) | −4.17445 | −0.151523 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1554 | −0.658134 | −0.329067 | − | 0.944307i | \(-0.606734\pi\) | ||||
−0.329067 | + | 0.944307i | \(0.606734\pi\) | |||||||
\(762\) | 8.93085 | 0.323530 | ||||||||
\(763\) | 4.77256 | 0.172778 | ||||||||
\(764\) | −72.0080 | −2.60516 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.2673 | −1.05747 | ||||||||
\(767\) | −0.806685 | −0.0291277 | ||||||||
\(768\) | −6.83365 | −0.246588 | ||||||||
\(769\) | 13.9125 | 0.501697 | 0.250848 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250848 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.85709 | −0.246952 | ||||||||
\(772\) | −78.2964 | −2.81795 | ||||||||
\(773\) | 7.95625 | 0.286167 | 0.143083 | − | 0.989711i | \(-0.454298\pi\) | ||||
0.143083 | + | 0.989711i | \(0.454298\pi\) | |||||||
\(774\) | 35.2635 | 1.26752 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 51.5767 | 1.85150 | ||||||||
\(777\) | −0.186166 | −0.00667866 | ||||||||
\(778\) | −79.7112 | −2.85778 | ||||||||
\(779\) | 0.238612 | 0.00854915 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.7665 | −0.957779 | ||||||||
\(782\) | −28.0535 | −1.00319 | ||||||||
\(783\) | −1.87749 | −0.0670959 | ||||||||
\(784\) | −5.34090 | −0.190746 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.3971 | −0.477858 | ||||||||
\(787\) | 10.4325 | 0.371877 | 0.185939 | − | 0.982561i | \(-0.440467\pi\) | ||||
0.185939 | + | 0.982561i | \(0.440467\pi\) | |||||||
\(788\) | −48.4711 | −1.72671 | ||||||||
\(789\) | 5.22901 | 0.186158 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2540 | 0.506814 | ||||||||
\(792\) | −50.9336 | −1.80985 | ||||||||
\(793\) | −6.45044 | −0.229062 | ||||||||
\(794\) | −78.9536 | −2.80196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.1221 | −1.10309 | ||||||||
\(797\) | −43.1743 | −1.52931 | −0.764656 | − | 0.644438i | \(-0.777091\pi\) | ||||
−0.764656 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(798\) | −0.845774 | −0.0299401 | ||||||||
\(799\) | 17.0045 | 0.601577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.0875 | 1.02776 | ||||||||
\(802\) | −2.29630 | −0.0810850 | ||||||||
\(803\) | 63.0231 | 2.22404 | ||||||||
\(804\) | 9.42931 | 0.332546 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.81598 | −0.240083 | ||||||||
\(807\) | −3.09162 | −0.108830 | ||||||||
\(808\) | 48.5058 | 1.70643 | ||||||||
\(809\) | −9.00706 | −0.316671 | −0.158336 | − | 0.987385i | \(-0.550613\pi\) | ||||
−0.158336 | + | 0.987385i | \(0.550613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.6431 | −0.795108 | −0.397554 | − | 0.917579i | \(-0.630141\pi\) | ||||
−0.397554 | + | 0.917579i | \(0.630141\pi\) | |||||||
\(812\) | 3.75137 | 0.131647 | ||||||||
\(813\) | −0.325254 | −0.0114071 | ||||||||
\(814\) | −6.56302 | −0.230034 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.41336 | 0.0494777 | ||||||||
\(817\) | 5.44507 | 0.190499 | ||||||||
\(818\) | 53.1269 | 1.85754 | ||||||||
\(819\) | −1.43485 | −0.0501376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.7306 | 0.793302 | 0.396651 | − | 0.917969i | \(-0.370172\pi\) | ||||
0.396651 | + | 0.917969i | \(0.370172\pi\) | |||||||
\(822\) | −8.41659 | −0.293562 | ||||||||
\(823\) | −12.2503 | −0.427018 | −0.213509 | − | 0.976941i | \(-0.568489\pi\) | ||||
−0.213509 | + | 0.976941i | \(0.568489\pi\) | |||||||
\(824\) | 15.3501 | 0.534747 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.53560 | −0.157814 | ||||||||
\(827\) | 12.6356 | 0.439382 | 0.219691 | − | 0.975569i | \(-0.429495\pi\) | ||||
0.219691 | + | 0.975569i | \(0.429495\pi\) | |||||||
\(828\) | 24.8117 | 0.862265 | ||||||||
\(829\) | −6.63044 | −0.230285 | −0.115142 | − | 0.993349i | \(-0.536732\pi\) | ||||
−0.115142 | + | 0.993349i | \(0.536732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53609 | −0.0532863 | ||||||||
\(832\) | −5.62356 | −0.194962 | ||||||||
\(833\) | −28.0265 | −0.971062 | ||||||||
\(834\) | 7.82730 | 0.271037 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.8407 | −0.651618 | ||||||||
\(837\) | 12.1195 | 0.418911 | ||||||||
\(838\) | 29.1858 | 1.00821 | ||||||||
\(839\) | −19.4935 | −0.672989 | −0.336495 | − | 0.941685i | \(-0.609241\pi\) | ||||
−0.336495 | + | 0.941685i | \(0.609241\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 48.4897 | 1.67107 | ||||||||
\(843\) | 2.25828 | 0.0777793 | ||||||||
\(844\) | 24.5659 | 0.845593 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.8011 | −0.818297 | ||||||||
\(847\) | 18.2160 | 0.625908 | ||||||||
\(848\) | −4.35522 | −0.149559 | ||||||||
\(849\) | 6.61004 | 0.226856 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.33457 | 0.0457486 | ||||||||
\(852\) | −5.56018 | −0.190489 | ||||||||
\(853\) | 40.5640 | 1.38888 | 0.694442 | − | 0.719549i | \(-0.255651\pi\) | ||||
0.694442 | + | 0.719549i | \(0.255651\pi\) | |||||||
\(854\) | −36.2677 | −1.24106 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −67.4169 | −2.30426 | ||||||||
\(857\) | −18.3430 | −0.626584 | −0.313292 | − | 0.949657i | \(-0.601432\pi\) | ||||
−0.313292 | + | 0.949657i | \(0.601432\pi\) | |||||||
\(858\) | 1.76787 | 0.0603541 | ||||||||
\(859\) | 7.13688 | 0.243507 | 0.121754 | − | 0.992560i | \(-0.461148\pi\) | ||||
0.121754 | + | 0.992560i | \(0.461148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0795454 | −0.00271090 | ||||||||
\(862\) | 17.4545 | 0.594504 | ||||||||
\(863\) | 21.8379 | 0.743372 | 0.371686 | − | 0.928359i | \(-0.378780\pi\) | ||||
0.371686 | + | 0.928359i | \(0.378780\pi\) | |||||||
\(864\) | 8.51733 | 0.289766 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36.0520 | −1.22510 | ||||||||
\(867\) | 2.00576 | 0.0681193 | ||||||||
\(868\) | −24.2157 | −0.821936 | ||||||||
\(869\) | −66.4447 | −2.25398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.90906 | 0.132453 | ||||||||
\(872\) | 14.5895 | 0.494062 | ||||||||
\(873\) | −44.7570 | −1.51480 | ||||||||
\(874\) | 6.06313 | 0.205088 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.0917 | 0.442329 | ||||||||
\(877\) | −4.35988 | −0.147223 | −0.0736113 | − | 0.997287i | \(-0.523452\pi\) | ||||
−0.0736113 | + | 0.997287i | \(0.523452\pi\) | |||||||
\(878\) | 82.3782 | 2.78013 | ||||||||
\(879\) | 3.97479 | 0.134066 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.41952 | −0.283661 | −0.141830 | − | 0.989891i | \(-0.545299\pi\) | ||||
−0.141830 | + | 0.989891i | \(0.545299\pi\) | |||||||
\(882\) | 39.2284 | 1.32089 | ||||||||
\(883\) | −7.23456 | −0.243462 | −0.121731 | − | 0.992563i | \(-0.538845\pi\) | ||||
−0.121731 | + | 0.992563i | \(0.538845\pi\) | |||||||
\(884\) | 7.50717 | 0.252493 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37.5474 | 1.26143 | ||||||||
\(887\) | −55.0112 | −1.84710 | −0.923548 | − | 0.383484i | \(-0.874724\pi\) | ||||
−0.923548 | + | 0.383484i | \(0.874724\pi\) | |||||||
\(888\) | −0.569101 | −0.0190978 | ||||||||
\(889\) | 13.1539 | 0.441167 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.6002 | 1.42716 | ||||||||
\(892\) | 30.5563 | 1.02310 | ||||||||
\(893\) | −3.67515 | −0.122984 | ||||||||
\(894\) | −4.12907 | −0.138097 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.7043 | −0.725089 | ||||||||
\(897\) | −0.359492 | −0.0120031 | ||||||||
\(898\) | −16.5224 | −0.551359 | ||||||||
\(899\) | −6.45517 | −0.215292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.8542 | −0.761383 | ||||||||
\(902\) | −2.80427 | −0.0933718 | ||||||||
\(903\) | −1.81521 | −0.0604064 | ||||||||
\(904\) | 43.5738 | 1.44924 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.99309 | 0.331998 | ||||||||
\(907\) | 53.4584 | 1.77506 | 0.887528 | − | 0.460754i | \(-0.152421\pi\) | ||||
0.887528 | + | 0.460754i | \(0.152421\pi\) | |||||||
\(908\) | −9.81320 | −0.325662 | ||||||||
\(909\) | −42.0922 | −1.39611 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.4019 | −1.23918 | −0.619590 | − | 0.784926i | \(-0.712701\pi\) | ||||
−0.619590 | + | 0.784926i | \(0.712701\pi\) | |||||||
\(912\) | −0.305467 | −0.0101150 | ||||||||
\(913\) | 51.3318 | 1.69883 | ||||||||
\(914\) | −43.1550 | −1.42744 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 80.1138 | 2.64703 | ||||||||
\(917\) | −19.7320 | −0.651609 | ||||||||
\(918\) | −21.1249 | −0.697225 | ||||||||
\(919\) | 17.9780 | 0.593039 | 0.296520 | − | 0.955027i | \(-0.404174\pi\) | ||||
0.296520 | + | 0.955027i | \(0.404174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.78572 | 0.190646 | ||||||||
\(922\) | 49.4506 | 1.62857 | ||||||||
\(923\) | −2.30505 | −0.0758717 | ||||||||
\(924\) | 6.28087 | 0.206625 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.9454 | 0.491137 | ||||||||
\(927\) | −13.3205 | −0.437502 | ||||||||
\(928\) | −4.53656 | −0.148920 | ||||||||
\(929\) | 3.80429 | 0.124815 | 0.0624074 | − | 0.998051i | \(-0.480122\pi\) | ||||
0.0624074 | + | 0.998051i | \(0.480122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.05730 | 0.198520 | ||||||||
\(932\) | 42.2817 | 1.38498 | ||||||||
\(933\) | −5.60983 | −0.183658 | ||||||||
\(934\) | 65.8391 | 2.15432 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.38626 | −0.143370 | ||||||||
\(937\) | 15.9334 | 0.520523 | 0.260261 | − | 0.965538i | \(-0.416191\pi\) | ||||
0.260261 | + | 0.965538i | \(0.416191\pi\) | |||||||
\(938\) | 21.9788 | 0.717632 | ||||||||
\(939\) | 1.67846 | 0.0547744 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.9708 | 1.33561 | 0.667805 | − | 0.744337i | \(-0.267234\pi\) | ||||
0.667805 | + | 0.744337i | \(0.267234\pi\) | |||||||
\(942\) | −13.8810 | −0.452266 | ||||||||
\(943\) | 0.570240 | 0.0185696 | ||||||||
\(944\) | −1.63812 | −0.0533162 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.9927 | −2.08058 | ||||||||
\(947\) | 49.3534 | 1.60377 | 0.801885 | − | 0.597478i | \(-0.203830\pi\) | ||||
0.801885 | + | 0.597478i | \(0.203830\pi\) | |||||||
\(948\) | −13.8025 | −0.448285 | ||||||||
\(949\) | 5.42737 | 0.176180 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.24231 | −0.202421 | ||||||||
\(952\) | 17.6195 | 0.571052 | ||||||||
\(953\) | −25.0523 | −0.811523 | −0.405762 | − | 0.913979i | \(-0.632994\pi\) | ||||
−0.405762 | + | 0.913979i | \(0.632994\pi\) | |||||||
\(954\) | 31.9887 | 1.03567 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 102.007 | 3.29915 | ||||||||
\(957\) | 1.67428 | 0.0541219 | ||||||||
\(958\) | 98.1233 | 3.17022 | ||||||||
\(959\) | −12.3965 | −0.400302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6692 | 0.344167 | ||||||||
\(962\) | −0.565189 | −0.0182224 | ||||||||
\(963\) | 58.5027 | 1.88522 | ||||||||
\(964\) | 62.3608 | 2.00851 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.02125 | −0.0650326 | ||||||||
\(967\) | −28.2473 | −0.908371 | −0.454185 | − | 0.890907i | \(-0.650070\pi\) | ||||
−0.454185 | + | 0.890907i | \(0.650070\pi\) | |||||||
\(968\) | 55.6854 | 1.78980 | ||||||||
\(969\) | −1.60295 | −0.0514941 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7212 | −0.600791 | −0.300396 | − | 0.953815i | \(-0.597119\pi\) | ||||
−0.300396 | + | 0.953815i | \(0.597119\pi\) | |||||||
\(972\) | 28.1860 | 0.904068 | ||||||||
\(973\) | 11.5285 | 0.369587 | ||||||||
\(974\) | −30.1522 | −0.966138 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.0988 | −0.419281 | ||||||||
\(977\) | −23.5777 | −0.754317 | −0.377158 | − | 0.926149i | \(-0.623099\pi\) | ||||
−0.377158 | + | 0.926149i | \(0.623099\pi\) | |||||||
\(978\) | 9.18561 | 0.293723 | ||||||||
\(979\) | −52.7852 | −1.68702 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6604 | −0.404215 | ||||||||
\(982\) | 25.6130 | 0.817344 | ||||||||
\(983\) | −48.0017 | −1.53102 | −0.765509 | − | 0.643426i | \(-0.777513\pi\) | ||||
−0.765509 | + | 0.643426i | \(0.777513\pi\) | |||||||
\(984\) | −0.243167 | −0.00775187 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.2517 | 0.358326 | ||||||||
\(987\) | 1.22517 | 0.0389977 | ||||||||
\(988\) | −1.62251 | −0.0516188 | ||||||||
\(989\) | 13.0128 | 0.413781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.4273 | −0.744192 | −0.372096 | − | 0.928194i | \(-0.621361\pi\) | ||||
−0.372096 | + | 0.928194i | \(0.621361\pi\) | |||||||
\(992\) | 29.2842 | 0.929776 | ||||||||
\(993\) | 1.48924 | 0.0472595 | ||||||||
\(994\) | −12.9602 | −0.411073 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.6631 | 0.337874 | ||||||||
\(997\) | 40.8481 | 1.29367 | 0.646836 | − | 0.762629i | \(-0.276092\pi\) | ||||
0.646836 | + | 0.762629i | \(0.276092\pi\) | |||||||
\(998\) | 36.0908 | 1.14243 | ||||||||
\(999\) | 1.00496 | 0.0317956 |
(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 | 725.2.a.k.1.5 | yes | 5 | |
3.2 | odd | 2 | 6525.2.a.bm.1.1 | 5 | |||
5.2 | odd | 4 | 725.2.b.f.349.10 | 10 | |||
5.3 | odd | 4 | 725.2.b.f.349.1 | 10 | |||
5.4 | even | 2 | 725.2.a.h.1.1 | ✓ | 5 | ||
15.14 | odd | 2 | 6525.2.a.bq.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
725.2.a.h.1.1 | ✓ | 5 | 5.4 | even | 2 | ||
725.2.a.k.1.5 | yes | 5 | 1.1 | even | 1 | trivial | |
725.2.b.f.349.1 | 10 | 5.3 | odd | 4 | |||
725.2.b.f.349.10 | 10 | 5.2 | odd | 4 | |||
6525.2.a.bm.1.1 | 5 | 3.2 | odd | 2 | |||
6525.2.a.bq.1.5 | 5 | 15.14 | odd | 2 |